{"id":1,"expression_no_base_symbol":"($2015$∙∹∝$4315$)⊹∫⫚($2945$⫦⪉$8011$)","expression":"(⪩⨒∯133133∙∹∝⪩⨒∯1003123)⊹∫⫚(⪩⨒∯232001⫦⪉⪩⨒∯1331023)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":48,"operation_count":3,"complexity_ratio":16.0,"tree":{"type":"binary","operator":"⊹∫⫚","left_expr":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"numeric_atoms","value":2015,"base":4},"right_expr":{"type":"numeric_atoms","value":4315,"base":4}},"right_expr":{"type":"binary","operator":"⫦⪉","left_expr":{"type":"numeric_atoms","value":2945,"base":4},"right_expr":{"type":"numeric_atoms","value":8011,"base":4}}},"used_operators":["uWAJUKEvyW","HmxsFra2vL","wscyQdcy20"],"dependent_operators":["BiWNJpBvwn","w2P8NbNXyL","vg4gO5BX6G","k8jYdgA6NY","g55IO6H4Gj","2td37pGCOC","jLgFTUHLKL","BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","W4YGzv6Whe","B3sABdIn96","9HNa5Wba9A","g7Hmc5v1ko","nREPSIbpBE","D3AQDKkPcf"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2015","layer":2},{"info":"number node, value=4315","layer":2},{"info":"compute binary expreesion, left_input=2015, right_input=4315, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":1},{"info":"number node, value=2945","layer":2},{"info":"number node, value=8011","layer":2},{"info":"compute binary expreesion, left_input=2945, right_input=8011, op_id = wscyQdcy20 binary_op_definition= 'a⫦⪉b = { ((a⩌⋺206)⪹) , if (a∷677)>=23 ; ((b+a)*(b⨚b)) , else }', output=-990","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-990, op_id = uWAJUKEvyW binary_op_definition= 'a⊹∫⫚b = { (↩(a⊨b)) , if (⩦⩻⨪a)==479 or (b⊉↱≁467)==779 ; ((b⨸⪁b)%(b⩍⋽⫝̸187)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯133133∙∹∝⪩⨒∯1003123)⊹∫⫚(⪩⨒∯232001⫦⪉⪩⨒∯1331023)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯133133∙∹∝⪩⨒∯1003123)⊹∫⫚(⪩⨒∯232001⫦⪉⪩⨒∯1331023)","cot":[{"info":"⪩⨒∯133133∙∹∝⪩⨒∯1003123=⪩⨒∯0","layer":1},{"info":"⪩⨒∯232001⫦⪉⪩⨒∯1331023=⪩⨒∯-33132","layer":1},{"info":"⪩⨒∯0⊹∫⫚⪩⨒∯-33132=⪩⨒∯0","layer":0}]}
{"id":2,"expression_no_base_symbol":"$3692$⪔$1032$⊓⋫","expression":"⪩⨒∯321230⪔⪩⨒∯100020⊓⋫","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1152,"operation_count":2,"complexity_ratio":576.0,"tree":{"type":"unary","operator":"⊓⋫","unary_expr":{"type":"binary","operator":"⪔","left_expr":{"type":"numeric_atoms","value":3692,"base":4},"right_expr":{"type":"numeric_atoms","value":1032,"base":4}}},"used_operators":["IqGBaFP0uj","GjBEYRfMaF"],"dependent_operators":["2td37pGCOC","sdazOOVcIp","2DDjHMKMc0","f6k1SAg4EE","nCS4ZIUYfx","QMFrweE19q","YjI8oCXuph","8INZBEW696","dWAJyo7jo9","nREPSIbpBE","2DDjHMKMc0","IWmyXbctLI","PoHhknlbAi"],"result":"⪩⨒∯-21002","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3692","layer":2},{"info":"number node, value=1032","layer":2},{"info":"compute binary expreesion, left_input=3692, right_input=1032, op_id = GjBEYRfMaF binary_op_definition= 'a⪔b = { (((⫇a)∓⋝(61⪢b))⪮%⊝((b⋝⋈⪟b)⨚(a≀⩗∶a))) }', output=450","layer":1},{"info":"compute unary expreesion, input=450, op_id = IqGBaFP0uj, unary_op_definition = 'a⊓⋫ = { (((a⪨≂a)⨳⩥⨓(⩦⩻⨪230))⪒(a⋝⋈⪟(542⫡⨏384))) }', output=-578","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯321230⪔⪩⨒∯100020⊓⋫=⪩⨒∯-21002","reverse_text":"⪩⨒∯-21002=⪩⨒∯321230⪔⪩⨒∯100020⊓⋫","cot":[{"info":"⪩⨒∯321230⪔⪩⨒∯100020=⪩⨒∯13002","layer":1},{"info":"⪩⨒∯13002⊓⋫=⪩⨒∯-21002","layer":0}]}
{"id":3,"expression_no_base_symbol":"⨂⪏⇭(⇋↷$8660$)","expression":"⨂⪏⇭(⇋↷⪩⨒∯2013110)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":24,"operation_count":2,"complexity_ratio":12.0,"tree":{"type":"unary","operator":"⨂⪏⇭","unary_expr":{"type":"unary","operator":"⇋↷","unary_expr":{"type":"numeric_atoms","value":8660,"base":4}}},"used_operators":["AYdpE9sXAk","SWo3A1KBJH"],"dependent_operators":["eewbuw0ToL","NTOWxs364D","EBcxylXtPf","XPYlsWDdGa","23Mk6UjR3U","2DQ55sFlQl","u6S6b8DprG"],"result":"⪩⨒∯302200031","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8660","layer":2},{"info":"compute unary expreesion, input=8660, op_id = SWo3A1KBJH, unary_op_definition = '⇋↷a = { (⪲⇎((↽≂a)⋷(a⨵⪆a))) }', output=69280","layer":1},{"info":"compute unary expreesion, input=69280, op_id = AYdpE9sXAk, unary_op_definition = '⨂⪏⇭a = { (a⨰((85⩚⊴⇥a)⫌⩹⨱)) }', output=206861","layer":0}],"base":4,"result_base":4,"text":"⨂⪏⇭(⇋↷⪩⨒∯2013110)=⪩⨒∯302200031","reverse_text":"⪩⨒∯302200031=⨂⪏⇭(⇋↷⪩⨒∯2013110)","cot":[{"info":"⇋↷⪩⨒∯2013110=⪩⨒∯100322200","layer":1},{"info":"⨂⪏⇭⪩⨒∯100322200=⪩⨒∯302200031","layer":0}]}
{"id":4,"expression_no_base_symbol":"(↞≼$2160$)⫁($3816$∓⋝$2962$)","expression":"(↞≼⪩⨒∯201300)⫁(⪩⨒∯323220∓⋝⪩⨒∯232102)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":147,"operation_count":3,"complexity_ratio":49.0,"tree":{"type":"binary","operator":"⫁","left_expr":{"type":"unary","operator":"↞≼","unary_expr":{"type":"numeric_atoms","value":2160,"base":4}},"right_expr":{"type":"binary","operator":"∓⋝","left_expr":{"type":"numeric_atoms","value":3816,"base":4},"right_expr":{"type":"numeric_atoms","value":2962,"base":4}}},"used_operators":["0ajvFaJAv0","DE7zCoGJt9","PoHhknlbAi"],"dependent_operators":["cHh1gJQ2o6","AHs5Up7iyr","W4YGzv6Whe","D4vGDi5EA2","23Mk6UjR3U","BjRHVeLaeN","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","u6S6b8DprG","DZ8iAZOCBD","DbCuESL50I","mqXw5SEYmG","2MzE1hQ0cz"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2160","layer":2},{"info":"compute unary expreesion, input=2160, op_id = DE7zCoGJt9, unary_op_definition = '↞≼a = { (↽≂(197⨰(a⨸⪁a))) , if (a⨸⪁373)!=224 ; (((591⋷a)≧⫂∧(a+a))⨸⪁((a⫩⊇)≦≮≮)) , else }', output=16866","layer":1},{"info":"number node, value=3816","layer":2},{"info":"number node, value=2962","layer":2},{"info":"compute binary expreesion, left_input=3816, right_input=2962, op_id = PoHhknlbAi binary_op_definition= 'a∓⋝b = { (((a⊉≛↸a)⫸⊐(⋼∭⪍b))∩⋅) }', output=67","layer":1},{"info":"compute binary expreesion, left_input=16866, right_input=67, op_id = 0ajvFaJAv0 binary_op_definition= 'a⫁b = { (a≹⇙⪍6) , if a==154 ; (b⩘b) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(↞≼⪩⨒∯201300)⫁(⪩⨒∯323220∓⋝⪩⨒∯232102)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(↞≼⪩⨒∯201300)⫁(⪩⨒∯323220∓⋝⪩⨒∯232102)","cot":[{"info":"↞≼⪩⨒∯201300=⪩⨒∯10013202","layer":1},{"info":"⪩⨒∯323220∓⋝⪩⨒∯232102=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯10013202⫁⪩⨒∯1003=⪩⨒∯2200","layer":0}]}
{"id":5,"expression_no_base_symbol":"$1464$⪟⇏$1894$⨻⩈⩔($1016$⇉⇱⇎)","expression":"⪩⨒∯112320⪟⇏⪩⨒∯131212⨻⩈⩔(⪩⨒∯33320⇉⇱⇎)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":135,"operation_count":3,"complexity_ratio":45.0,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"binary","operator":"⪟⇏","left_expr":{"type":"numeric_atoms","value":1464,"base":4},"right_expr":{"type":"numeric_atoms","value":1894,"base":4}},"right_expr":{"type":"unary","operator":"⇉⇱⇎","unary_expr":{"type":"numeric_atoms","value":1016,"base":4}}},"used_operators":["nEsXyWgiOK","GODebY97qR","MRPaB8lBjK"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","gx7XJ7hdpj","XnXgA4xnOs","wEfv7U73WA","2DQ55sFlQl","f6k1SAg4EE","oacrs7FA3X","XhwjNDsVaA","QiR2Oyf5Xj","uFcxV4UQCh","EWw2JM7wp4","t8gj7n24qd","keWfFq85dY"],"result":"⪩⨒∯-2232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1464","layer":2},{"info":"number node, value=1894","layer":2},{"info":"compute binary expreesion, left_input=1464, right_input=1894, op_id = GODebY97qR binary_op_definition= 'a⪟⇏b = { ((b⨑≵⋬b)⫸⇳(440⪒a)) , if (b⇐≅)<189 ; ((219⨑≵⋬a)⪘⫢(b⨵⪆b)) , else }', output=-1","layer":1},{"info":"number node, value=1016","layer":2},{"info":"compute unary expreesion, input=1016, op_id = MRPaB8lBjK, unary_op_definition = 'a⇉⇱⇎ = { (((a/a)⪉⨛(≯757))⪛(∷≠(-a))) }', output=-798","layer":1},{"info":"compute binary expreesion, left_input=-1, right_input=-798, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=-174","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯112320⪟⇏⪩⨒∯131212⨻⩈⩔(⪩⨒∯33320⇉⇱⇎)=⪩⨒∯-2232","reverse_text":"⪩⨒∯-2232=⪩⨒∯112320⪟⇏⪩⨒∯131212⨻⩈⩔(⪩⨒∯33320⇉⇱⇎)","cot":[{"info":"⪩⨒∯112320⪟⇏⪩⨒∯131212=⪩⨒∯-1","layer":1},{"info":"⪩⨒∯33320⇉⇱⇎=⪩⨒∯-30132","layer":1},{"info":"⪩⨒∯-1⨻⩈⩔⪩⨒∯-30132=⪩⨒∯-2232","layer":0}]}
{"id":6,"expression_no_base_symbol":"($1087$⨽$1094$)⪟⇏($1458$⨒$1804$)","expression":"(⪩⨒∯100333⨽⪩⨒∯101012)⪟⇏(⪩⨒∯112302⨒⪩⨒∯130030)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1146,"operation_count":3,"complexity_ratio":382.0,"tree":{"type":"binary","operator":"⪟⇏","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1087,"base":4},"right_expr":{"type":"numeric_atoms","value":1094,"base":4}},"right_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":1458,"base":4},"right_expr":{"type":"numeric_atoms","value":1804,"base":4}}},"used_operators":["GODebY97qR","8HhzD0ZcuI","y75s1iXyHd"],"dependent_operators":["gx7XJ7hdpj","XnXgA4xnOs","wEfv7U73WA","2DQ55sFlQl","f6k1SAg4EE","oacrs7FA3X","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","srAu1WTS94","oacrs7FA3X","7qqUquhhSb"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1087","layer":2},{"info":"number node, value=1094","layer":2},{"info":"compute binary expreesion, left_input=1087, right_input=1094, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-3546675","layer":1},{"info":"number node, value=1458","layer":2},{"info":"number node, value=1804","layer":2},{"info":"compute binary expreesion, left_input=1458, right_input=1804, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-8376","layer":1},{"info":"compute binary expreesion, left_input=-3546675, right_input=-8376, op_id = GODebY97qR binary_op_definition= 'a⪟⇏b = { ((b⨑≵⋬b)⫸⇳(440⪒a)) , if (b⇐≅)<189 ; ((219⨑≵⋬a)⪘⫢(b⨵⪆b)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100333⨽⪩⨒∯101012)⪟⇏(⪩⨒∯112302⨒⪩⨒∯130030)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯100333⨽⪩⨒∯101012)⪟⇏(⪩⨒∯112302⨒⪩⨒∯130030)","cot":[{"info":"⪩⨒∯100333⨽⪩⨒∯101012=⪩⨒∯-31201320303","layer":1},{"info":"⪩⨒∯112302⨒⪩⨒∯130030=⪩⨒∯-2002320","layer":1},{"info":"⪩⨒∯-31201320303⪟⇏⪩⨒∯-2002320=⪩⨒∯0","layer":0}]}
{"id":7,"expression_no_base_symbol":"($1016$≭$1008$)⩷∴($3515$⫥∨⫟$2463$)","expression":"(⪩⨒∯33320≭⪩⨒∯33300)⩷∴(⪩⨒∯312323⫥∨⫟⪩⨒∯212133)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":161,"operation_count":3,"complexity_ratio":53.666666666666664,"tree":{"type":"binary","operator":"⩷∴","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":1016,"base":4},"right_expr":{"type":"numeric_atoms","value":1008,"base":4}},"right_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":3515,"base":4},"right_expr":{"type":"numeric_atoms","value":2463,"base":4}}},"used_operators":["9FxExcQeMw","rxpJgHHUmx","KYD54nUTWz"],"dependent_operators":["rysDP5nf3Z","AHs5Up7iyr","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1016","layer":2},{"info":"number node, value=1008","layer":2},{"info":"compute binary expreesion, left_input=1016, right_input=1008, op_id = rxpJgHHUmx binary_op_definition= 'a≭b = {-22, if b == 0; (a)≹⇙⪍(a≭(b-1)), if b > 0 and abs(b) < 100; -(a)≹⇙⪍(a≭(b+1)), if b < 0 and abs(b) < 100; NaN, else}', output=nan","layer":1},{"info":"number node, value=3515","layer":2},{"info":"number node, value=2463","layer":2},{"info":"compute binary expreesion, left_input=3515, right_input=2463, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯33320≭⪩⨒∯33300)⩷∴(⪩⨒∯312323⫥∨⫟⪩⨒∯212133)=NaN","reverse_text":"NaN=(⪩⨒∯33320≭⪩⨒∯33300)⩷∴(⪩⨒∯312323⫥∨⫟⪩⨒∯212133)","cot":[{"info":"⪩⨒∯33320≭⪩⨒∯33300=NaN","layer":1},{"info":"⪩⨒∯312323⫥∨⫟⪩⨒∯212133=NaN","layer":1},{"info":"NaN⩷∴NaN=NaN","layer":0}]}
{"id":8,"expression_no_base_symbol":"$2435$⫁⪎$6365$≠≀$2414$∳⫺$1581$","expression":"⪩⨒∯212003⫁⪎⪩⨒∯1203131≠≀⪩⨒∯211232∳⫺⪩⨒∯120231","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":73,"operation_count":3,"complexity_ratio":24.333333333333332,"tree":{"type":"binary","operator":"≠≀","left_expr":{"type":"binary","operator":"⫁⪎","left_expr":{"type":"numeric_atoms","value":2435,"base":4},"right_expr":{"type":"numeric_atoms","value":6365,"base":4}},"right_expr":{"type":"binary","operator":"∳⫺","left_expr":{"type":"numeric_atoms","value":2414,"base":4},"right_expr":{"type":"numeric_atoms","value":1581,"base":4}}},"used_operators":["IwW236VD4Y","xRrnTEsQ6j","AzXXKTstlj"],"dependent_operators":["eLAdDNolq6","NTOWxs364D","sdazOOVcIp","2DDjHMKMc0","2td37pGCOC","P8v4zCKN1o","Qy55tPpLXF","tifHPKVTfV","sdazOOVcIp","2DDjHMKMc0","i8ToyICDmI","F4yD0voBRQ","Tcnh7f0tEr","ZvLB05nZmT"],"result":"⪩⨒∯333211","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2435","layer":2},{"info":"number node, value=6365","layer":2},{"info":"compute binary expreesion, left_input=2435, right_input=6365, op_id = xRrnTEsQ6j binary_op_definition= 'a⫁⪎b = { ((b⋝⋈⪟a)⇼⇔∾a) , if (∥⊫b)!=57 ; ((191∲⫓a)⋥≓≎(a⪨≂368)) , else }', output=-3930","layer":1},{"info":"number node, value=2414","layer":2},{"info":"number node, value=1581","layer":2},{"info":"compute binary expreesion, left_input=2414, right_input=1581, op_id = AzXXKTstlj binary_op_definition= 'a∳⫺b = { (a≣⋋) , if (b⫳≱↱947)==166 ; (a⇣⩺⋵b) , else }', output=-260","layer":1},{"info":"compute binary expreesion, left_input=-3930, right_input=-260, op_id = IwW236VD4Y binary_op_definition= 'a≠≀b = { (⩦⩻⨪(a⩚⊴⇥b)) , if (≤/b)>10 ; ((a⪨≂a)⪨≂(a⋝⋈⪟356)) , else }', output=4069","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯212003⫁⪎⪩⨒∯1203131≠≀⪩⨒∯211232∳⫺⪩⨒∯120231=⪩⨒∯333211","reverse_text":"⪩⨒∯333211=⪩⨒∯212003⫁⪎⪩⨒∯1203131≠≀⪩⨒∯211232∳⫺⪩⨒∯120231","cot":[{"info":"⪩⨒∯212003⫁⪎⪩⨒∯1203131=⪩⨒∯-331122","layer":1},{"info":"⪩⨒∯211232∳⫺⪩⨒∯120231=⪩⨒∯-10010","layer":1},{"info":"⪩⨒∯-331122≠≀⪩⨒∯-10010=⪩⨒∯333211","layer":0}]}
{"id":9,"expression_no_base_symbol":"($1930$⪕$5294$)⋣⋖($1628$⊊)","expression":"(⪩⨒∯132022⪕⪩⨒∯1102232)⋣⋖(⪩⨒∯121130⊊)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":245,"operation_count":3,"complexity_ratio":81.66666666666667,"tree":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"binary","operator":"⪕","left_expr":{"type":"numeric_atoms","value":1930,"base":4},"right_expr":{"type":"numeric_atoms","value":5294,"base":4}},"right_expr":{"type":"unary","operator":"⊊","unary_expr":{"type":"numeric_atoms","value":1628,"base":4}}},"used_operators":["J0M6qkBnIM","umQnsF7QlU","W9R8I5fN5A"],"dependent_operators":["VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2","P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF","DlLNRPXxWL","aBQ6xLxuTc","8n5YIzOsVS","oZj3VtZNQx","MahUMFw56D","hyuBjUqXlG","aA7tF3KVD3","2DDjHMKMc0","QMFrweE19q","SxTAKzQCrw","8cLx32lpNA"],"result":"⪩⨒∯-313","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1930","layer":2},{"info":"number node, value=5294","layer":2},{"info":"compute binary expreesion, left_input=1930, right_input=5294, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=-55","layer":1},{"info":"number node, value=1628","layer":2},{"info":"compute unary expreesion, input=1628, op_id = W9R8I5fN5A, unary_op_definition = 'a⊊ = { (((⫛⫱⨽a)∙⊟a)∌((a⇂≾⫗536)⋝⋈⪟(a⫡⨏a))) , if ((a≚⋢)==7 or (a⪘⨀)==15) ; ((a≀⫉(6⪛⫼a))⫠↝⫳) , else }', output=90927","layer":1},{"info":"compute binary expreesion, left_input=-55, right_input=90927, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=-55","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯132022⪕⪩⨒∯1102232)⋣⋖(⪩⨒∯121130⊊)=⪩⨒∯-313","reverse_text":"⪩⨒∯-313=(⪩⨒∯132022⪕⪩⨒∯1102232)⋣⋖(⪩⨒∯121130⊊)","cot":[{"info":"⪩⨒∯132022⪕⪩⨒∯1102232=⪩⨒∯-313","layer":1},{"info":"⪩⨒∯121130⊊=⪩⨒∯112030233","layer":1},{"info":"⪩⨒∯-313⋣⋖⪩⨒∯112030233=⪩⨒∯-313","layer":0}]}
{"id":10,"expression_no_base_symbol":"⊀($1428$⋝⋈⪟$7067$)","expression":"⊀(⪩⨒∯112110⋝⋈⪟⪩⨒∯1232123)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":20,"operation_count":2,"complexity_ratio":10.0,"tree":{"type":"unary","operator":"⊀","unary_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":1428,"base":4},"right_expr":{"type":"numeric_atoms","value":7067,"base":4}}},"used_operators":["oPMjh9089D","2DDjHMKMc0"],"dependent_operators":["Qy55tPpLXF","XIabStNQrY","tifHPKVTfV","glklzrTFfD","sdazOOVcIp","8w2t5hMYqp","Ph9nP6C5qx","g55IO6H4Gj","2td37pGCOC","QMFrweE19q","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯1111022","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1428","layer":2},{"info":"number node, value=7067","layer":2},{"info":"compute binary expreesion, left_input=1428, right_input=7067, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=1428","layer":1},{"info":"compute unary expreesion, input=1428, op_id = oPMjh9089D, unary_op_definition = '⊀a = { (((⩦⩻⨪67)⪨≂(a⋥≓≎63))⇋≉) , if (a⇼⇔∾9)<290 ; (((⊄⩳↩a)⨁⊸⫻)⫡⨏((a≧⫂∧a)⨸⪁(a≧⫂∧a))) , else }', output=5450","layer":0}],"base":4,"result_base":4,"text":"⊀(⪩⨒∯112110⋝⋈⪟⪩⨒∯1232123)=⪩⨒∯1111022","reverse_text":"⪩⨒∯1111022=⊀(⪩⨒∯112110⋝⋈⪟⪩⨒∯1232123)","cot":[{"info":"⪩⨒∯112110⋝⋈⪟⪩⨒∯1232123=⪩⨒∯112110","layer":1},{"info":"⊀⪩⨒∯112110=⪩⨒∯1111022","layer":0}]}
{"id":11,"expression_no_base_symbol":"$2204$∑⇟⊟$5479$⇩","expression":"⪩⨒∯202130∑⇟⊟⪩⨒∯1111213⇩","highest_n_order":4,"priority_hierarchical_complexity":1,"normalized_expansion_degree":2,"operation_count":2,"complexity_ratio":1.0,"tree":{"type":"unary","operator":"⇩","unary_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":2204,"base":4},"right_expr":{"type":"numeric_atoms","value":5479,"base":4}}},"used_operators":["vRio1gEz1j","U7g4x0WXJJ"],"dependent_operators":["W4YGzv6Whe","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2204","layer":2},{"info":"number node, value=5479","layer":2},{"info":"compute binary expreesion, left_input=2204, right_input=5479, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = vRio1gEz1j, unary_op_definition = 'a⇩ = { (a+93) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯202130∑⇟⊟⪩⨒∯1111213⇩=NaN","reverse_text":"NaN=⪩⨒∯202130∑⇟⊟⪩⨒∯1111213⇩","cot":[{"info":"⪩⨒∯202130∑⇟⊟⪩⨒∯1111213=NaN","layer":1},{"info":"NaN⇩=NaN","layer":0}]}
{"id":12,"expression_no_base_symbol":"($1084$⨱∎)⨿(⋃$1006$)","expression":"(⪩⨒∯100330⨱∎)⨿(⋃⪩⨒∯33232)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":243,"operation_count":3,"complexity_ratio":81.0,"tree":{"type":"binary","operator":"⨿","left_expr":{"type":"unary","operator":"⨱∎","unary_expr":{"type":"numeric_atoms","value":1084,"base":4}},"right_expr":{"type":"unary","operator":"⋃","unary_expr":{"type":"numeric_atoms","value":1006,"base":4}}},"used_operators":["abYXlopdE0","MmTdOpaElr","3mBM5G4a3l"],"dependent_operators":["gJLn6v0xnP","KFSx94NKJn","jWTQ2TZYIH","yXekIHxTD4","KYD54nUTWz","i8ToyICDmI","PoHhknlbAi","tifHPKVTfV","g55IO6H4Gj"],"result":"⪩⨒∯1321","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1084","layer":2},{"info":"compute unary expreesion, input=1084, op_id = MmTdOpaElr, unary_op_definition = 'a⨱∎ = { (a⇼⇔∾a) }', output=0","layer":1},{"info":"number node, value=1006","layer":2},{"info":"compute unary expreesion, input=1006, op_id = 3mBM5G4a3l, unary_op_definition = '⋃a = { (51⨸⪁a) }', output=2114","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=2114, op_id = abYXlopdE0 binary_op_definition= 'a⨿b = { (((a∲⫓409)≬⇓(a⩒⫫a))∓⋝((146⫥∨⫟b)≥⨤⩑(219⨥⫆b))) }', output=121","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100330⨱∎)⨿(⋃⪩⨒∯33232)=⪩⨒∯1321","reverse_text":"⪩⨒∯1321=(⪩⨒∯100330⨱∎)⨿(⋃⪩⨒∯33232)","cot":[{"info":"⪩⨒∯100330⨱∎=⪩⨒∯0","layer":1},{"info":"⋃⪩⨒∯33232=⪩⨒∯201002","layer":1},{"info":"⪩⨒∯0⨿⪩⨒∯201002=⪩⨒∯1321","layer":0}]}
{"id":13,"expression_no_base_symbol":"⨝⨆$4085$∳⫺$1759$","expression":"⨝⨆⪩⨒∯333311∳⫺⪩⨒∯123133","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":59,"operation_count":2,"complexity_ratio":29.5,"tree":{"type":"unary","operator":"⨝⨆","unary_expr":{"type":"binary","operator":"∳⫺","left_expr":{"type":"numeric_atoms","value":4085,"base":4},"right_expr":{"type":"numeric_atoms","value":1759,"base":4}}},"used_operators":["bQ67fsrMVf","AzXXKTstlj"],"dependent_operators":["tifHPKVTfV","F4yD0voBRQ","Tcnh7f0tEr","ZvLB05nZmT"],"result":"⪩⨒∯-13111","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4085","layer":2},{"info":"number node, value=1759","layer":2},{"info":"compute binary expreesion, left_input=4085, right_input=1759, op_id = AzXXKTstlj binary_op_definition= 'a∳⫺b = { (a≣⋋) , if (b⫳≱↱947)==166 ; (a⇣⩺⋵b) , else }', output=-260","layer":1},{"info":"compute unary expreesion, input=-260, op_id = bQ67fsrMVf, unary_op_definition = '⨝⨆a = { (209⇼⇔∾a) }', output=-469","layer":0}],"base":4,"result_base":4,"text":"⨝⨆⪩⨒∯333311∳⫺⪩⨒∯123133=⪩⨒∯-13111","reverse_text":"⪩⨒∯-13111=⨝⨆⪩⨒∯333311∳⫺⪩⨒∯123133","cot":[{"info":"⪩⨒∯333311∳⫺⪩⨒∯123133=⪩⨒∯-10010","layer":1},{"info":"⨝⨆⪩⨒∯-10010=⪩⨒∯-13111","layer":0}]}
{"id":14,"expression_no_base_symbol":"$1012$∛$1456$*($5809$⪃↞⩐)","expression":"⪩⨒∯33310∛⪩⨒∯112300*(⪩⨒∯1122301⪃↞⩐)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":852,"operation_count":3,"complexity_ratio":284.0,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"∛","left_expr":{"type":"numeric_atoms","value":1012,"base":4},"right_expr":{"type":"numeric_atoms","value":1456,"base":4}},"right_expr":{"type":"unary","operator":"⪃↞⩐","unary_expr":{"type":"numeric_atoms","value":5809,"base":4}}},"used_operators":["9HNa5Wba9A","w2537kitQq","grXIztHqDa"],"dependent_operators":["W4YGzv6Whe","DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc","IwW236VD4Y","bF6eod5Gvf","l07mrZUIn9"],"result":"⪩⨒∯20333020020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1012","layer":2},{"info":"number node, value=1456","layer":2},{"info":"compute binary expreesion, left_input=1012, right_input=1456, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=67","layer":1},{"info":"number node, value=5809","layer":2},{"info":"compute unary expreesion, input=5809, op_id = grXIztHqDa, unary_op_definition = 'a⪃↞⩐ = { ((a→⨶⪴a)≠≀(a↪⪝)) }', output=35160","layer":1},{"info":"compute binary expreesion, left_input=67, right_input=35160, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=2355720","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯33310∛⪩⨒∯112300*(⪩⨒∯1122301⪃↞⩐)=⪩⨒∯20333020020","reverse_text":"⪩⨒∯20333020020=⪩⨒∯33310∛⪩⨒∯112300*(⪩⨒∯1122301⪃↞⩐)","cot":[{"info":"⪩⨒∯33310∛⪩⨒∯112300=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯1122301⪃↞⩐=⪩⨒∯20211120","layer":1},{"info":"⪩⨒∯1003*⪩⨒∯20211120=⪩⨒∯20333020020","layer":0}]}
{"id":15,"expression_no_base_symbol":"($1190$≣⋋)≁($7837$⨘⋶⪀)","expression":"(⪩⨒∯102212≣⋋)≁(⪩⨒∯1322131⨘⋶⪀)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":624,"operation_count":3,"complexity_ratio":208.0,"tree":{"type":"binary","operator":"≁","left_expr":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"numeric_atoms","value":1190,"base":4}},"right_expr":{"type":"unary","operator":"⨘⋶⪀","unary_expr":{"type":"numeric_atoms","value":7837,"base":4}}},"used_operators":["8N2wDY1A35","Tcnh7f0tEr","XVKwrhznBb"],"dependent_operators":["B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v","dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A","TpPTUOHfaN","FyVja0WsTP","UqFzSgLMvQ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1190","layer":2},{"info":"compute unary expreesion, input=1190, op_id = Tcnh7f0tEr, unary_op_definition = 'a≣⋋ = { ((a/a)⋥≓≎(a⨪↰⇹248)) , if (a⪢148)<38 ; ((511*a)⊠≄⫣) , else }', output=0","layer":1},{"info":"number node, value=7837","layer":2},{"info":"compute unary expreesion, input=7837, op_id = XVKwrhznBb, unary_op_definition = 'a⨘⋶⪀ = { ((326+⇶⊼a)⊱⇼⊻(a⇡)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯102212≣⋋)≁(⪩⨒∯1322131⨘⋶⪀)=NaN","reverse_text":"NaN=(⪩⨒∯102212≣⋋)≁(⪩⨒∯1322131⨘⋶⪀)","cot":[{"info":"⪩⨒∯102212≣⋋=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1322131⨘⋶⪀=NaN","layer":1},{"info":"⪩⨒∯0≁NaN=NaN","layer":0}]}
{"id":16,"expression_no_base_symbol":"⩎⋉($8397$⩵∡$4560$)","expression":"⩎⋉(⪩⨒∯2003031⩵∡⪩⨒∯1013100)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":87,"operation_count":2,"complexity_ratio":43.5,"tree":{"type":"unary","operator":"⩎⋉","unary_expr":{"type":"binary","operator":"⩵∡","left_expr":{"type":"numeric_atoms","value":8397,"base":4},"right_expr":{"type":"numeric_atoms","value":4560,"base":4}}},"used_operators":["FlXk3pOYe8","Y7wcNGrDQJ"],"dependent_operators":["KbjG8mgYpV","wztAlM01eG","JclMnS0uGI","XhwjNDsVaA","W7eaUhjymW","9ICcGScMcE","fG6uBQFnGz","8w2t5hMYqp","Bmrmz2XGnR","Noe24qw2ks","1aApVXNlOP","i8ToyICDmI","nCS4ZIUYfx","2DlMacCsIx","hrf7POJlIJ","NTOWxs364D","glklzrTFfD","tifHPKVTfV"],"result":"⪩⨒∯121302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8397","layer":2},{"info":"number node, value=4560","layer":2},{"info":"compute binary expreesion, left_input=8397, right_input=4560, op_id = Y7wcNGrDQJ binary_op_definition= 'a⩵∡b = { ((b⇼⇔∾a)⩚⊴⇥(a⨁⊸⫻)) }', output=-12355","layer":1},{"info":"compute unary expreesion, input=-12355, op_id = FlXk3pOYe8, unary_op_definition = '⩎⋉a = { (((a/a)∲⫓(≛a))∴((a⩨a)⨳⩥⨓(⊄⩳↩a))) , if (a⩇∃⫛268)<=24 or a==244 or (↩⪖a)>=4 ; (((a⨔⇊a)∠↢(↸⊣a))≚⊃≕((≦∁a)⨐461)) , else }', output=1650","layer":0}],"base":4,"result_base":4,"text":"⩎⋉(⪩⨒∯2003031⩵∡⪩⨒∯1013100)=⪩⨒∯121302","reverse_text":"⪩⨒∯121302=⩎⋉(⪩⨒∯2003031⩵∡⪩⨒∯1013100)","cot":[{"info":"⪩⨒∯2003031⩵∡⪩⨒∯1013100=⪩⨒∯-3001003","layer":1},{"info":"⩎⋉⪩⨒∯-3001003=⪩⨒∯121302","layer":0}]}
{"id":17,"expression_no_base_symbol":"(⨞⊢$4166$)∼($1186$⨐⩸⫘$2196$)","expression":"(⨞⊢⪩⨒∯1001012)∼(⪩⨒∯102202⨐⩸⫘⪩⨒∯202110)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":90,"operation_count":3,"complexity_ratio":30.0,"tree":{"type":"binary","operator":"∼","left_expr":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":4166,"base":4}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":1186,"base":4},"right_expr":{"type":"numeric_atoms","value":2196,"base":4}}},"used_operators":["DyGG3AbaNP","xUOZtlo3hN","fu6greOZ01"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4166","layer":2},{"info":"compute unary expreesion, input=4166, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-4340","layer":1},{"info":"number node, value=1186","layer":2},{"info":"number node, value=2196","layer":2},{"info":"compute binary expreesion, left_input=1186, right_input=2196, op_id = fu6greOZ01 binary_op_definition= 'a⨐⩸⫘b = {a, if b == 0; (a⨐⩸⫘(b-1))⨓(b), if b > 0 and abs(b) < 1000; -(a⨐⩸⫘(b+1))⨓(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-4340, right_input=nan, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⨞⊢⪩⨒∯1001012)∼(⪩⨒∯102202⨐⩸⫘⪩⨒∯202110)=NaN","reverse_text":"NaN=(⨞⊢⪩⨒∯1001012)∼(⪩⨒∯102202⨐⩸⫘⪩⨒∯202110)","cot":[{"info":"⨞⊢⪩⨒∯1001012=⪩⨒∯-1003310","layer":1},{"info":"⪩⨒∯102202⨐⩸⫘⪩⨒∯202110=NaN","layer":1},{"info":"⪩⨒∯-1003310∼NaN=NaN","layer":0}]}
{"id":18,"expression_no_base_symbol":"($1010$⨸⪁$3376$)⇯⋐","expression":"(⪩⨒∯33302⨸⪁⪩⨒∯310300)⇯⋐","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":26,"operation_count":2,"complexity_ratio":13.0,"tree":{"type":"unary","operator":"⇯⋐","unary_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":1010,"base":4},"right_expr":{"type":"numeric_atoms","value":3376,"base":4}}},"used_operators":["LkLIoiE525","g55IO6H4Gj"],"dependent_operators":["P8v4zCKN1o","DZ8iAZOCBD","7j4O788W3g","tifHPKVTfV","eewbuw0ToL","QMFrweE19q","W4YGzv6Whe"],"result":"⪩⨒∯12220322","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1010","layer":2},{"info":"number node, value=3376","layer":2},{"info":"compute binary expreesion, left_input=1010, right_input=3376, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=8772","layer":1},{"info":"compute unary expreesion, input=8772, op_id = LkLIoiE525, unary_op_definition = 'a⇯⋐ = { (((a↺a)⊉≛↸(∥⊫a))⨰((17⫡⨏a)⇼⇔∾a)) }', output=27194","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯33302⨸⪁⪩⨒∯310300)⇯⋐=⪩⨒∯12220322","reverse_text":"⪩⨒∯12220322=(⪩⨒∯33302⨸⪁⪩⨒∯310300)⇯⋐","cot":[{"info":"⪩⨒∯33302⨸⪁⪩⨒∯310300=⪩⨒∯2021010","layer":1},{"info":"⪩⨒∯2021010⇯⋐=⪩⨒∯12220322","layer":0}]}
{"id":19,"expression_no_base_symbol":"$1179$⊬⨰$3093$⨒(⫓⪴$2537$)","expression":"⪩⨒∯102123⊬⨰⪩⨒∯300111⨒(⫓⪴⪩⨒∯213221)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2566,"operation_count":3,"complexity_ratio":855.3333333333334,"tree":{"type":"binary","operator":"⨒","left_expr":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"numeric_atoms","value":1179,"base":4},"right_expr":{"type":"numeric_atoms","value":3093,"base":4}},"right_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":2537,"base":4}}},"used_operators":["y75s1iXyHd","s3Fd5m9Dh2","eLxqMNBOBk"],"dependent_operators":["srAu1WTS94","oacrs7FA3X","7qqUquhhSb","23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","9HNa5Wba9A"],"result":"⪩⨒∯-102031212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1179","layer":2},{"info":"number node, value=3093","layer":2},{"info":"compute binary expreesion, left_input=1179, right_input=3093, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=12495","layer":1},{"info":"number node, value=2537","layer":2},{"info":"compute unary expreesion, input=2537, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=6436369","layer":1},{"info":"compute binary expreesion, left_input=12495, right_input=6436369, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-74598","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102123⊬⨰⪩⨒∯300111⨒(⫓⪴⪩⨒∯213221)=⪩⨒∯-102031212","reverse_text":"⪩⨒∯-102031212=⪩⨒∯102123⊬⨰⪩⨒∯300111⨒(⫓⪴⪩⨒∯213221)","cot":[{"info":"⪩⨒∯102123⊬⨰⪩⨒∯300111=⪩⨒∯3003033","layer":1},{"info":"⫓⪴⪩⨒∯213221=⪩⨒∯120203120101","layer":1},{"info":"⪩⨒∯3003033⨒⪩⨒∯120203120101=⪩⨒∯-102031212","layer":0}]}
{"id":20,"expression_no_base_symbol":"(≸$3795$)⪚⩙≫","expression":"(≸⪩⨒∯323103)⪚⩙≫","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":74,"operation_count":2,"complexity_ratio":37.0,"tree":{"type":"unary","operator":"⪚⩙≫","unary_expr":{"type":"unary","operator":"≸","unary_expr":{"type":"numeric_atoms","value":3795,"base":4}}},"used_operators":["4n53wtyJvv","eOf03JbCpp"],"dependent_operators":["Uaa54Peajs","nCS4ZIUYfx","WR6HLWljOP","WmT3o8z6ya","l07mrZUIn9","NTOWxs364D","RygbFNSyEJ","tifHPKVTfV","oRDoc9rAEX","IwW236VD4Y","1aApVXNlOP","Z5m6OM72h2","mqXw5SEYmG","IWmyXbctLI"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3795","layer":2},{"info":"compute unary expreesion, input=3795, op_id = eOf03JbCpp, unary_op_definition = '≸a = { (29∘((630⊋≦⊧a)⩚⊴⇥(a≦↸a))) , if (a⋘⨑⨽)>2 ; (((a⪮%⊝a)⇼⇔∾(a↪⪝))⫸⊐((a⪮%⊝a)≠≀(3⩇∃⫛a))) , else }', output=58","layer":1},{"info":"compute unary expreesion, input=58, op_id = 4n53wtyJvv, unary_op_definition = 'a⪚⩙≫ = { ((316↢a)⨳⩥⨓(∂255)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(≸⪩⨒∯323103)⪚⩙≫=NaN","reverse_text":"NaN=(≸⪩⨒∯323103)⪚⩙≫","cot":[{"info":"≸⪩⨒∯323103=⪩⨒∯322","layer":1},{"info":"⪩⨒∯322⪚⩙≫=NaN","layer":0}]}
{"id":21,"expression_no_base_symbol":"≀↧⇸(⪸$2133$)","expression":"≀↧⇸(⪸⪩⨒∯201111)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":32,"operation_count":2,"complexity_ratio":16.0,"tree":{"type":"unary","operator":"≀↧⇸","unary_expr":{"type":"unary","operator":"⪸","unary_expr":{"type":"numeric_atoms","value":2133,"base":4}}},"used_operators":["ljTHtUsqzn","86A5ENbKR9"],"dependent_operators":["XPYlsWDdGa","23Mk6UjR3U","Qy55tPpLXF","23Mk6UjR3U","tifHPKVTfV","sdazOOVcIp","g55IO6H4Gj","AF7qkfDlqP","QMFrweE19q"],"result":"⪩⨒∯203031100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2133","layer":2},{"info":"compute unary expreesion, input=2133, op_id = 86A5ENbKR9, unary_op_definition = '⪸a = { (((220⪨≂51)⇼⇔∾(a⫡⨏303))⋷((a⨸⪁a)⋥≓≎(⨑⩽⪐a))) }', output=-36052","layer":1},{"info":"compute unary expreesion, input=-36052, op_id = ljTHtUsqzn, unary_op_definition = '≀↧⇸a = { (⪲⇎(a⋷a)) }', output=144208","layer":0}],"base":4,"result_base":4,"text":"≀↧⇸(⪸⪩⨒∯201111)=⪩⨒∯203031100","reverse_text":"⪩⨒∯203031100=≀↧⇸(⪸⪩⨒∯201111)","cot":[{"info":"⪸⪩⨒∯201111=⪩⨒∯-20303110","layer":1},{"info":"≀↧⇸⪩⨒∯-20303110=⪩⨒∯203031100","layer":0}]}
{"id":22,"expression_no_base_symbol":"↑($2747$⨎$4020$)","expression":"↑(⪩⨒∯222323⨎⪩⨒∯332310)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":45,"operation_count":2,"complexity_ratio":22.5,"tree":{"type":"unary","operator":"↑","unary_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":2747,"base":4},"right_expr":{"type":"numeric_atoms","value":4020,"base":4}}},"used_operators":["tR7O2zTn5j","rJVOvQCfKK"],"dependent_operators":["oRDoc9rAEX","RygbFNSyEJ","2DlMacCsIx","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"⪩⨒∯3000","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2747","layer":2},{"info":"number node, value=4020","layer":2},{"info":"compute binary expreesion, left_input=2747, right_input=4020, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=4020","layer":1},{"info":"compute unary expreesion, input=4020, op_id = tR7O2zTn5j, unary_op_definition = '↑a = { ((a⩨a)⊋≦⊧(a≦↸a)) }', output=192","layer":0}],"base":4,"result_base":4,"text":"↑(⪩⨒∯222323⨎⪩⨒∯332310)=⪩⨒∯3000","reverse_text":"⪩⨒∯3000=↑(⪩⨒∯222323⨎⪩⨒∯332310)","cot":[{"info":"⪩⨒∯222323⨎⪩⨒∯332310=⪩⨒∯332310","layer":1},{"info":"↑⪩⨒∯332310=⪩⨒∯3000","layer":0}]}
{"id":23,"expression_no_base_symbol":"($2712$⪄$3053$)⨻⩈⩔(⨂⪏⇭$1927$)","expression":"(⪩⨒∯222120⪄⪩⨒∯233231)⨻⩈⩔(⨂⪏⇭⪩⨒∯132013)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":202,"operation_count":3,"complexity_ratio":67.33333333333333,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2712,"base":4},"right_expr":{"type":"numeric_atoms","value":3053,"base":4}},"right_expr":{"type":"unary","operator":"⨂⪏⇭","unary_expr":{"type":"numeric_atoms","value":1927,"base":4}}},"used_operators":["nEsXyWgiOK","SUmda5xLS4","AYdpE9sXAk"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","eewbuw0ToL","NTOWxs364D","EBcxylXtPf"],"result":"⪩⨒∯-2232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2712","layer":2},{"info":"number node, value=3053","layer":2},{"info":"compute binary expreesion, left_input=2712, right_input=3053, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-409677","layer":1},{"info":"number node, value=1927","layer":2},{"info":"compute unary expreesion, input=1927, op_id = AYdpE9sXAk, unary_op_definition = '⨂⪏⇭a = { (a⨰((85⩚⊴⇥a)⫌⩹⨱)) }', output=4802","layer":1},{"info":"compute binary expreesion, left_input=-409677, right_input=4802, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=-174","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯222120⪄⪩⨒∯233231)⨻⩈⩔(⨂⪏⇭⪩⨒∯132013)=⪩⨒∯-2232","reverse_text":"⪩⨒∯-2232=(⪩⨒∯222120⪄⪩⨒∯233231)⨻⩈⩔(⨂⪏⇭⪩⨒∯132013)","cot":[{"info":"⪩⨒∯222120⪄⪩⨒∯233231=⪩⨒∯-1210001031","layer":1},{"info":"⨂⪏⇭⪩⨒∯132013=⪩⨒∯1023002","layer":1},{"info":"⪩⨒∯-1210001031⨻⩈⩔⪩⨒∯1023002=⪩⨒∯-2232","layer":0}]}
{"id":24,"expression_no_base_symbol":"(⇾⩊⇾$3094$)⨸⪁(∥⊫$4446$)","expression":"(⇾⩊⇾⪩⨒∯300112)⨸⪁(∥⊫⪩⨒∯1011132)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":20,"operation_count":3,"complexity_ratio":6.666666666666667,"tree":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"unary","operator":"⇾⩊⇾","unary_expr":{"type":"numeric_atoms","value":3094,"base":4}},"right_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":4446,"base":4}}},"used_operators":["g55IO6H4Gj","bx9Z9DAK5y","P8v4zCKN1o"],"dependent_operators":["W4YGzv6Whe","W4YGzv6Whe","BjRHVeLaeN","8w2t5hMYqp","QMFrweE19q","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-32022310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3094","layer":2},{"info":"compute unary expreesion, input=3094, op_id = bx9Z9DAK5y, unary_op_definition = '⇾⩊⇾a = { (⊄⩳↩((a+259)⫡⨏(a⫩⊇))) }', output=-34332","layer":1},{"info":"number node, value=4446","layer":2},{"info":"compute unary expreesion, input=4446, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=5314","layer":1},{"info":"compute binary expreesion, left_input=-34332, right_input=5314, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=-58036","layer":0}],"base":4,"result_base":4,"text":"(⇾⩊⇾⪩⨒∯300112)⨸⪁(∥⊫⪩⨒∯1011132)=⪩⨒∯-32022310","reverse_text":"⪩⨒∯-32022310=(⇾⩊⇾⪩⨒∯300112)⨸⪁(∥⊫⪩⨒∯1011132)","cot":[{"info":"⇾⩊⇾⪩⨒∯300112=⪩⨒∯-20120130","layer":1},{"info":"∥⊫⪩⨒∯1011132=⪩⨒∯1103002","layer":1},{"info":"⪩⨒∯-20120130⨸⪁⪩⨒∯1103002=⪩⨒∯-32022310","layer":0}]}
{"id":25,"expression_no_base_symbol":"⊄⩳↩(⊖∈$5682$)","expression":"⊄⩳↩(⊖∈⪩⨒∯1120302)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":59,"operation_count":2,"complexity_ratio":29.5,"tree":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"unary","operator":"⊖∈","unary_expr":{"type":"numeric_atoms","value":5682,"base":4}}},"used_operators":["8w2t5hMYqp","YFxL8Sc2Zy"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","zVYPLywUTj","sdazOOVcIp","ancx8kZcWl","YSKBFp38Pu"],"result":"⪩⨒∯-1033020222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5682","layer":2},{"info":"compute unary expreesion, input=5682, op_id = YFxL8Sc2Zy, unary_op_definition = '⊖∈a = { a , if (a⨝⩣∺)>=369 ; ((a⊪)⪨≂(a⇤a)) , else }', output=108046","layer":1},{"info":"compute unary expreesion, input=108046, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-324138","layer":0}],"base":4,"result_base":4,"text":"⊄⩳↩(⊖∈⪩⨒∯1120302)=⪩⨒∯-1033020222","reverse_text":"⪩⨒∯-1033020222=⊄⩳↩(⊖∈⪩⨒∯1120302)","cot":[{"info":"⊖∈⪩⨒∯1120302=⪩⨒∯122120032","layer":1},{"info":"⊄⩳↩⪩⨒∯122120032=⪩⨒∯-1033020222","layer":0}]}
{"id":26,"expression_no_base_symbol":"(⨵≀≌$1407$)∌($1519$⋖∅⋲)","expression":"(⨵≀≌⪩⨒∯111333)∌(⪩⨒∯113233⋖∅⋲)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":176,"operation_count":3,"complexity_ratio":58.666666666666664,"tree":{"type":"binary","operator":"∌","left_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":1407,"base":4}},"right_expr":{"type":"unary","operator":"⋖∅⋲","unary_expr":{"type":"numeric_atoms","value":1519,"base":4}}},"used_operators":["8cLx32lpNA","srAu1WTS94","L95AwlJzhO"],"dependent_operators":["N41Kp7NANJ","7j4O788W3g","t8gj7n24qd","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","gx7XJ7hdpj","3nqY3DE9mg","XTarYq4gQB","y4ImoPnbV5","i8ToyICDmI","xNBdhnnwKq"],"result":"⪩⨒∯-1001331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1407","layer":2},{"info":"compute unary expreesion, input=1407, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-4221","layer":1},{"info":"number node, value=1519","layer":2},{"info":"compute unary expreesion, input=1519, op_id = L95AwlJzhO, unary_op_definition = 'a⋖∅⋲ = { ((⪝⪂⫅431)⊍) , if (a∲⫓500)>7 ; ((a∽304)⫸⇳(a⊭∹↮)) , else }', output=-384231","layer":1},{"info":"compute binary expreesion, left_input=-4221, right_input=-384231, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-4221","layer":0}],"base":4,"result_base":4,"text":"(⨵≀≌⪩⨒∯111333)∌(⪩⨒∯113233⋖∅⋲)=⪩⨒∯-1001331","reverse_text":"⪩⨒∯-1001331=(⨵≀≌⪩⨒∯111333)∌(⪩⨒∯113233⋖∅⋲)","cot":[{"info":"⨵≀≌⪩⨒∯111333=⪩⨒∯-1001331","layer":1},{"info":"⪩⨒∯113233⋖∅⋲=⪩⨒∯-1131303213","layer":1},{"info":"⪩⨒∯-1001331∌⪩⨒∯-1131303213=⪩⨒∯-1001331","layer":0}]}
{"id":27,"expression_no_base_symbol":"↥($2095$↪⪝)","expression":"↥(⪩⨒∯200233↪⪝)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2513960,"operation_count":2,"complexity_ratio":1256980.0,"tree":{"type":"unary","operator":"↥","unary_expr":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"numeric_atoms","value":2095,"base":4}}},"used_operators":["A8NUZmVepG","l07mrZUIn9"],"dependent_operators":["k8jYdgA6NY","9HNa5Wba9A","2DDjHMKMc0"],"result":"⪩⨒∯132","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2095","layer":2},{"info":"compute unary expreesion, input=2095, op_id = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=128176290","layer":1},{"info":"compute unary expreesion, input=128176290, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=30","layer":0}],"base":4,"result_base":4,"text":"↥(⪩⨒∯200233↪⪝)=⪩⨒∯132","reverse_text":"⪩⨒∯132=↥(⪩⨒∯200233↪⪝)","cot":[{"info":"⪩⨒∯200233↪⪝=⪩⨒∯13220331002202","layer":1},{"info":"↥⪩⨒∯13220331002202=⪩⨒∯132","layer":0}]}
{"id":28,"expression_no_base_symbol":"($5263$∘$1328$)⇻⋧≁($1773$⊴$3602$)","expression":"(⪩⨒∯1102033∘⪩⨒∯110300)⇻⋧≁(⪩⨒∯123231⊴⪩⨒∯320102)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":14163,"operation_count":3,"complexity_ratio":4721.0,"tree":{"type":"binary","operator":"⇻⋧≁","left_expr":{"type":"binary","operator":"∘","left_expr":{"type":"numeric_atoms","value":5263,"base":4},"right_expr":{"type":"numeric_atoms","value":1328,"base":4}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1773,"base":4},"right_expr":{"type":"numeric_atoms","value":3602,"base":4}}},"used_operators":["jCPkEVoL5K","Z5m6OM72h2","Nsiff2A1zJ"],"dependent_operators":["eLxqMNBOBk","XnXgA4xnOs","3EYGwJThht","XTarYq4gQB","59igzFyhWz","dfKe02y8D2","X99M06cbEe","eH2TOUuTDT","rysDP5nf3Z","dWAJyo7jo9","14qkJME0vr"],"result":"⪩⨒∯-12333","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5263","layer":2},{"info":"number node, value=1328","layer":2},{"info":"compute binary expreesion, left_input=5263, right_input=1328, op_id = Z5m6OM72h2 binary_op_definition= 'a∘b = { (380-a) , if b<=483 ; (a⪐) , else }', output=10526","layer":1},{"info":"number node, value=1773","layer":2},{"info":"number node, value=3602","layer":2},{"info":"compute binary expreesion, left_input=1773, right_input=3602, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=10526, right_input=nan, op_id = jCPkEVoL5K binary_op_definition= 'a⇻⋧≁b = { ((⫓⪴a)⫚↹⊑(54≫≃)) , if (a∵≐)<=35 or a>411 ; ((⪝⪂⫅b)⇄(290⨑≵⋬a)) , else }', output=-447","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1102033∘⪩⨒∯110300)⇻⋧≁(⪩⨒∯123231⊴⪩⨒∯320102)=⪩⨒∯-12333","reverse_text":"⪩⨒∯-12333=(⪩⨒∯1102033∘⪩⨒∯110300)⇻⋧≁(⪩⨒∯123231⊴⪩⨒∯320102)","cot":[{"info":"⪩⨒∯1102033∘⪩⨒∯110300=⪩⨒∯2210132","layer":1},{"info":"⪩⨒∯123231⊴⪩⨒∯320102=NaN","layer":1},{"info":"⪩⨒∯2210132⇻⋧≁NaN=⪩⨒∯-12333","layer":0}]}
{"id":29,"expression_no_base_symbol":"$5807$⋝⋈⪟$5443$≀⩗∶$3706$≦↸$1072$","expression":"⪩⨒∯1122233⋝⋈⪟⪩⨒∯1111003≀⩗∶⪩⨒∯321322≦↸⪩⨒∯100300","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":37,"operation_count":3,"complexity_ratio":12.333333333333334,"tree":{"type":"binary","operator":"≀⩗∶","left_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":5807,"base":4},"right_expr":{"type":"numeric_atoms","value":5443,"base":4}},"right_expr":{"type":"binary","operator":"≦↸","left_expr":{"type":"numeric_atoms","value":3706,"base":4},"right_expr":{"type":"numeric_atoms","value":1072,"base":4}}},"used_operators":["8INZBEW696","2DDjHMKMc0","RygbFNSyEJ"],"dependent_operators":["KPf6cnQVty","2DlMacCsIx","l07mrZUIn9","W4YGzv6Whe","t8gj7n24qd","eLAdDNolq6","e1ybzncUwg","DZ8iAZOCBD","XIabStNQrY","12rbrZMWeM","2DDjHMKMc0","g55IO6H4Gj"],"result":"⪩⨒∯12","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5807","layer":2},{"info":"number node, value=5443","layer":2},{"info":"compute binary expreesion, left_input=5807, right_input=5443, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=5807","layer":1},{"info":"number node, value=3706","layer":2},{"info":"number node, value=1072","layer":2},{"info":"compute binary expreesion, left_input=3706, right_input=1072, op_id = RygbFNSyEJ binary_op_definition= 'a≦↸b = { (((≤/a)⋳⪒(b⊉≛↸a))⋝⋈⪟((a⇋≉)⨸⪁(≉a))) }', output=-8875","layer":1},{"info":"compute binary expreesion, left_input=5807, right_input=-8875, op_id = 8INZBEW696 binary_op_definition= 'a≀⩗∶b = { (a⩨b) , if (a∺≝⩲555)<251 ; (306↪⪝) , else }', output=6","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1122233⋝⋈⪟⪩⨒∯1111003≀⩗∶⪩⨒∯321322≦↸⪩⨒∯100300=⪩⨒∯12","reverse_text":"⪩⨒∯12=⪩⨒∯1122233⋝⋈⪟⪩⨒∯1111003≀⩗∶⪩⨒∯321322≦↸⪩⨒∯100300","cot":[{"info":"⪩⨒∯1122233⋝⋈⪟⪩⨒∯1111003=⪩⨒∯1122233","layer":1},{"info":"⪩⨒∯321322≦↸⪩⨒∯100300=⪩⨒∯-2022223","layer":1},{"info":"⪩⨒∯1122233≀⩗∶⪩⨒∯-2022223=⪩⨒∯12","layer":0}]}
{"id":30,"expression_no_base_symbol":"$1318$↬$3743$⇴($1023$⋷$2332$)","expression":"⪩⨒∯110212↬⪩⨒∯322133⇴(⪩⨒∯33333⋷⪩⨒∯210130)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":18,"operation_count":3,"complexity_ratio":6.0,"tree":{"type":"binary","operator":"⇴","left_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":1318,"base":4},"right_expr":{"type":"numeric_atoms","value":3743,"base":4}},"right_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":1023,"base":4},"right_expr":{"type":"numeric_atoms","value":2332,"base":4}}},"used_operators":["4JB6nKBMSY","B5M0gjZbta","23Mk6UjR3U"],"dependent_operators":["sdazOOVcIp","NTOWxs364D","COABgblf1C","rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1318","layer":2},{"info":"number node, value=3743","layer":2},{"info":"compute binary expreesion, left_input=1318, right_input=3743, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":1},{"info":"number node, value=1023","layer":2},{"info":"number node, value=2332","layer":2},{"info":"compute binary expreesion, left_input=1023, right_input=2332, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=3641","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=3641, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯110212↬⪩⨒∯322133⇴(⪩⨒∯33333⋷⪩⨒∯210130)=NaN","reverse_text":"NaN=⪩⨒∯110212↬⪩⨒∯322133⇴(⪩⨒∯33333⋷⪩⨒∯210130)","cot":[{"info":"⪩⨒∯110212↬⪩⨒∯322133=NaN","layer":1},{"info":"⪩⨒∯33333⋷⪩⨒∯210130=⪩⨒∯320321","layer":1},{"info":"NaN⇴⪩⨒∯320321=NaN","layer":0}]}
{"id":31,"expression_no_base_symbol":"$2488$↳≱$6282$↙(∂$4396$)","expression":"⪩⨒∯212320↳≱⪩⨒∯1202022↙(∂⪩⨒∯1010230)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":87,"operation_count":3,"complexity_ratio":29.0,"tree":{"type":"binary","operator":"↙","left_expr":{"type":"binary","operator":"↳≱","left_expr":{"type":"numeric_atoms","value":2488,"base":4},"right_expr":{"type":"numeric_atoms","value":6282,"base":4}},"right_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":4396,"base":4}}},"used_operators":["yyfyN0ffXY","JwTKLfZU96","Uaa54Peajs"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","DhbWaqg5eL","WR6HLWljOP","XhwjNDsVaA","T2fj7uvVaJ","7YooWSwCyH","B3sABdIn96","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2488","layer":2},{"info":"number node, value=6282","layer":2},{"info":"compute binary expreesion, left_input=2488, right_input=6282, op_id = JwTKLfZU96 binary_op_definition= 'a↳≱b = { (((a∪⫐104)↢(147/b))⋓((+⊝⨔b)⪹)) }', output=0","layer":1},{"info":"number node, value=4396","layer":2},{"info":"compute unary expreesion, input=4396, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯212320↳≱⪩⨒∯1202022↙(∂⪩⨒∯1010230)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯212320↳≱⪩⨒∯1202022↙(∂⪩⨒∯1010230)","cot":[{"info":"⪩⨒∯212320↳≱⪩⨒∯1202022=⪩⨒∯0","layer":1},{"info":"∂⪩⨒∯1010230=NaN","layer":1},{"info":"⪩⨒∯0↙NaN=⪩⨒∯0","layer":0}]}
{"id":32,"expression_no_base_symbol":"($3932$∙∹∝$6692$)⇉⇱⇎","expression":"(⪩⨒∯331130∙∹∝⪩⨒∯1220210)⇉⇱⇎","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":47,"operation_count":2,"complexity_ratio":23.5,"tree":{"type":"unary","operator":"⇉⇱⇎","unary_expr":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"numeric_atoms","value":3932,"base":4},"right_expr":{"type":"numeric_atoms","value":6692,"base":4}}},"used_operators":["MRPaB8lBjK","HmxsFra2vL"],"dependent_operators":["XhwjNDsVaA","QiR2Oyf5Xj","uFcxV4UQCh","EWw2JM7wp4","t8gj7n24qd","keWfFq85dY","BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3932","layer":2},{"info":"number node, value=6692","layer":2},{"info":"compute binary expreesion, left_input=3932, right_input=6692, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = MRPaB8lBjK, unary_op_definition = 'a⇉⇱⇎ = { (((a/a)⪉⨛(≯757))⪛(∷≠(-a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯331130∙∹∝⪩⨒∯1220210)⇉⇱⇎=NaN","reverse_text":"NaN=(⪩⨒∯331130∙∹∝⪩⨒∯1220210)⇉⇱⇎","cot":[{"info":"⪩⨒∯331130∙∹∝⪩⨒∯1220210=⪩⨒∯0","layer":1},{"info":"⪩⨒∯0⇉⇱⇎=NaN","layer":0}]}
{"id":33,"expression_no_base_symbol":"$1165$⨽∌$7786$⪥$7482$↳∿⪆$5208$","expression":"⪩⨒∯102031⨽∌⪩⨒∯1321222⪥⪩⨒∯1310322↳∿⪆⪩⨒∯1101120","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2547,"operation_count":3,"complexity_ratio":849.0,"tree":{"type":"binary","operator":"⪥","left_expr":{"type":"binary","operator":"⨽∌","left_expr":{"type":"numeric_atoms","value":1165,"base":4},"right_expr":{"type":"numeric_atoms","value":7786,"base":4}},"right_expr":{"type":"binary","operator":"↳∿⪆","left_expr":{"type":"numeric_atoms","value":7482,"base":4},"right_expr":{"type":"numeric_atoms","value":5208,"base":4}}},"used_operators":["QbnwKVWMIQ","9samAPKr6k","Cw4SuJJGHO"],"dependent_operators":["WR6HLWljOP","nhYeJWJD5X","f6k1SAg4EE","jLgFTUHLKL","PPChnnnBFF","YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu","hyuBjUqXlG","bF6eod5Gvf","nEsXyWgiOK","ruOEQAzv1W","Tw270M8GLb","QMFrweE19q"],"result":"⪩⨒∯1020230","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1165","layer":2},{"info":"number node, value=7786","layer":2},{"info":"compute binary expreesion, left_input=1165, right_input=7786, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":1},{"info":"number node, value=7482","layer":2},{"info":"number node, value=5208","layer":2},{"info":"compute binary expreesion, left_input=7482, right_input=5208, op_id = Cw4SuJJGHO binary_op_definition= 'a↳∿⪆b = { ((⨰⫟⨤(↔15))⨻⩈⩔((b⪛⫼133)⫡⨏(b→⨶⪴a))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = QbnwKVWMIQ binary_op_definition= 'a⪥b = { (b∇⊂⋱(58∣a)) , if (b↢721)<125 ; (↩(508⪒a)) , else }', output=4652","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102031⨽∌⪩⨒∯1321222⪥⪩⨒∯1310322↳∿⪆⪩⨒∯1101120=⪩⨒∯1020230","reverse_text":"⪩⨒∯1020230=⪩⨒∯102031⨽∌⪩⨒∯1321222⪥⪩⨒∯1310322↳∿⪆⪩⨒∯1101120","cot":[{"info":"⪩⨒∯102031⨽∌⪩⨒∯1321222=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1310322↳∿⪆⪩⨒∯1101120=NaN","layer":1},{"info":"⪩⨒∯0⪥NaN=⪩⨒∯1020230","layer":0}]}
{"id":34,"expression_no_base_symbol":"(⊑$1909$)⪚⩙≫","expression":"(⊑⪩⨒∯131311)⪚⩙≫","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":424,"operation_count":2,"complexity_ratio":212.0,"tree":{"type":"unary","operator":"⪚⩙≫","unary_expr":{"type":"unary","operator":"⊑","unary_expr":{"type":"numeric_atoms","value":1909,"base":4}}},"used_operators":["4n53wtyJvv","IkUmn0D7oy"],"dependent_operators":["Uaa54Peajs","nCS4ZIUYfx","WR6HLWljOP","oRDoc9rAEX","AdZkA7nFnk","megm06wKyl"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1909","layer":2},{"info":"compute unary expreesion, input=1909, op_id = IkUmn0D7oy, unary_op_definition = '⊑a = { ((a⋅⇍254)⊋≦⊧(⨈⫕a)) }', output=192","layer":1},{"info":"compute unary expreesion, input=192, op_id = 4n53wtyJvv, unary_op_definition = 'a⪚⩙≫ = { ((316↢a)⨳⩥⨓(∂255)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⊑⪩⨒∯131311)⪚⩙≫=NaN","reverse_text":"NaN=(⊑⪩⨒∯131311)⪚⩙≫","cot":[{"info":"⊑⪩⨒∯131311=⪩⨒∯3000","layer":1},{"info":"⪩⨒∯3000⪚⩙≫=NaN","layer":0}]}
{"id":35,"expression_no_base_symbol":"⋂($2527$⫥∨⫟$1092$)","expression":"⋂(⪩⨒∯213133⫥∨⫟⪩⨒∯101010)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":170,"operation_count":2,"complexity_ratio":85.0,"tree":{"type":"unary","operator":"⋂","unary_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":2527,"base":4},"right_expr":{"type":"numeric_atoms","value":1092,"base":4}}},"used_operators":["BUOGQAYlQx","KYD54nUTWz"],"dependent_operators":["NTOWxs364D","XPYlsWDdGa","QMFrweE19q","COABgblf1C","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2527","layer":2},{"info":"number node, value=1092","layer":2},{"info":"compute binary expreesion, left_input=2527, right_input=1092, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = BUOGQAYlQx, unary_op_definition = '⋂a = { a , if (⪲⇎a)==26 ; ((a⩚⊴⇥a)⫡⨏(a⊭↱102)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⋂(⪩⨒∯213133⫥∨⫟⪩⨒∯101010)=NaN","reverse_text":"NaN=⋂(⪩⨒∯213133⫥∨⫟⪩⨒∯101010)","cot":[{"info":"⪩⨒∯213133⫥∨⫟⪩⨒∯101010=NaN","layer":1},{"info":"⋂NaN=NaN","layer":0}]}
{"id":36,"expression_no_base_symbol":"($2129$⫡⨏$2337$)⊜","expression":"(⪩⨒∯201101⫡⨏⪩⨒∯210201)⊜","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":17,"operation_count":2,"complexity_ratio":8.5,"tree":{"type":"unary","operator":"⊜","unary_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":2129,"base":4},"right_expr":{"type":"numeric_atoms","value":2337,"base":4}}},"used_operators":["Eev2Q7dYIw","QMFrweE19q"],"dependent_operators":["g55IO6H4Gj","D4vGDi5EA2","P8v4zCKN1o","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-33103100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2129","layer":2},{"info":"number node, value=2337","layer":2},{"info":"compute binary expreesion, left_input=2129, right_input=2337, op_id = QMFrweE19q binary_op_definition= 'a⫡⨏b = { 497 , if (-b)==408 and (-a)>=56 ; (((a+783)+(a+a))+((b+a)+(a+b))) , else }', output=16102","layer":1},{"info":"compute unary expreesion, input=16102, op_id = Eev2Q7dYIw, unary_op_definition = 'a⊜ = { ((a≦≮≮)⨸⪁(∥⊫a)) }', output=-62672","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯201101⫡⨏⪩⨒∯210201)⊜=⪩⨒∯-33103100","reverse_text":"⪩⨒∯-33103100=(⪩⨒∯201101⫡⨏⪩⨒∯210201)⊜","cot":[{"info":"⪩⨒∯201101⫡⨏⪩⨒∯210201=⪩⨒∯3323212","layer":1},{"info":"⪩⨒∯3323212⊜=⪩⨒∯-33103100","layer":0}]}
{"id":37,"expression_no_base_symbol":"$3979$⫥∨⫟$1659$⪄($6727$∛≔)","expression":"⪩⨒∯332023⫥∨⫟⪩⨒∯121323⪄(⪩⨒∯1221013∛≔)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":52539,"operation_count":3,"complexity_ratio":17513.0,"tree":{"type":"binary","operator":"⪄","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":3979,"base":4},"right_expr":{"type":"numeric_atoms","value":1659,"base":4}},"right_expr":{"type":"unary","operator":"∛≔","unary_expr":{"type":"numeric_atoms","value":6727,"base":4}}},"used_operators":["SUmda5xLS4","KYD54nUTWz","mGnSCrte3L"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","8HhzD0ZcuI","rGHVDoGpnC","d7ASUq0ydm","OKKcZfAt5B","212REbPD9h","gx7XJ7hdpj","nEsXyWgiOK","oWn0xqSxBt"],"result":"⪩⨒∯332023","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3979","layer":2},{"info":"number node, value=1659","layer":2},{"info":"compute binary expreesion, left_input=3979, right_input=1659, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=6727","layer":2},{"info":"compute unary expreesion, input=6727, op_id = mGnSCrte3L, unary_op_definition = 'a∛≔ = { (((⊙↵-a)⋾⨃∁(a⨻⩈⩔a))≝⊿(a⫸⇳(a⫯⪬∳a))) }', output=-inf","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-inf, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=3979","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯332023⫥∨⫟⪩⨒∯121323⪄(⪩⨒∯1221013∛≔)=⪩⨒∯332023","reverse_text":"⪩⨒∯332023=⪩⨒∯332023⫥∨⫟⪩⨒∯121323⪄(⪩⨒∯1221013∛≔)","cot":[{"info":"⪩⨒∯332023⫥∨⫟⪩⨒∯121323=NaN","layer":1},{"info":"⪩⨒∯1221013∛≔=-Inf","layer":1},{"info":"NaN⪄-Inf=⪩⨒∯332023","layer":0}]}
{"id":38,"expression_no_base_symbol":"($5473$∇⊂⋱$3258$)⪃⊛⇣($1006$∣$1171$)","expression":"(⪩⨒∯1111201∇⊂⋱⪩⨒∯302322)⪃⊛⇣(⪩⨒∯33232∣⪩⨒∯102103)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":586,"operation_count":3,"complexity_ratio":195.33333333333334,"tree":{"type":"binary","operator":"⪃⊛⇣","left_expr":{"type":"binary","operator":"∇⊂⋱","left_expr":{"type":"numeric_atoms","value":5473,"base":4},"right_expr":{"type":"numeric_atoms","value":3258,"base":4}},"right_expr":{"type":"binary","operator":"∣","left_expr":{"type":"numeric_atoms","value":1006,"base":4},"right_expr":{"type":"numeric_atoms","value":1171,"base":4}}},"used_operators":["rrgAzCduG9","nhYeJWJD5X","PPChnnnBFF"],"dependent_operators":["Ez1Nq5fNfI","AHs5Up7iyr","2DDjHMKMc0","7IPrd9c3lf","8cLx32lpNA","P8v4zCKN1o","23Mk6UjR3U","f6k1SAg4EE","AF7qkfDlqP","nCS4ZIUYfx","eLAdDNolq6","eH2TOUuTDT","Ph9nP6C5qx","i8ToyICDmI"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5473","layer":2},{"info":"number node, value=3258","layer":2},{"info":"compute binary expreesion, left_input=5473, right_input=3258, op_id = nhYeJWJD5X binary_op_definition= 'a∇⊂⋱b = { (b⪒b) , if a<143 ; ((⨑⩽⪐a)⋷(∥⊫(a⨳⩥⨓a))) , else }', output=10400","layer":1},{"info":"number node, value=1006","layer":2},{"info":"number node, value=1171","layer":2},{"info":"compute binary expreesion, left_input=1006, right_input=1171, op_id = PPChnnnBFF binary_op_definition= 'a∣b = { (≤/((a⪐)≧⫂∧(a∲⫓b))) , if (b⪐)<590 ; a , else }', output=1006","layer":1},{"info":"compute binary expreesion, left_input=10400, right_input=1006, op_id = rrgAzCduG9 binary_op_definition= 'a⪃⊛⇣b = { ((b∌b)⊵↤) , if b==348 ; ((a≹⇙⪍a)⪬(a⋝⋈⪟a)) , else }', output=1234","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1111201∇⊂⋱⪩⨒∯302322)⪃⊛⇣(⪩⨒∯33232∣⪩⨒∯102103)=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=(⪩⨒∯1111201∇⊂⋱⪩⨒∯302322)⪃⊛⇣(⪩⨒∯33232∣⪩⨒∯102103)","cot":[{"info":"⪩⨒∯1111201∇⊂⋱⪩⨒∯302322=⪩⨒∯2202200","layer":1},{"info":"⪩⨒∯33232∣⪩⨒∯102103=⪩⨒∯33232","layer":1},{"info":"⪩⨒∯2202200⪃⊛⇣⪩⨒∯33232=⪩⨒∯103102","layer":0}]}
{"id":39,"expression_no_base_symbol":"⊑($7424$⇞)","expression":"⊑(⪩⨒∯1310000⇞)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":424,"operation_count":2,"complexity_ratio":212.0,"tree":{"type":"unary","operator":"⊑","unary_expr":{"type":"unary","operator":"⇞","unary_expr":{"type":"numeric_atoms","value":7424,"base":4}}},"used_operators":["IkUmn0D7oy","5JYyxRJd4f"],"dependent_operators":["oRDoc9rAEX","AdZkA7nFnk","megm06wKyl","9FxExcQeMw","rysDP5nf3Z","DZ8iAZOCBD","tifHPKVTfV","Ph9nP6C5qx","xUOZtlo3hN","g55IO6H4Gj","i8ToyICDmI","QMFrweE19q"],"result":"⪩⨒∯3000","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7424","layer":2},{"info":"compute unary expreesion, input=7424, op_id = 5JYyxRJd4f, unary_op_definition = 'a⇞ = { (a≧⫂∧((a⩷∴a)⨸⪁(a-a))) , if a<7 ; ((⨞⊢(a∲⫓a))⫡⨏(a⊉≛↸(a⇼⇔∾a))) , else }', output=29609","layer":1},{"info":"compute unary expreesion, input=29609, op_id = IkUmn0D7oy, unary_op_definition = '⊑a = { ((a⋅⇍254)⊋≦⊧(⨈⫕a)) }', output=192","layer":0}],"base":4,"result_base":4,"text":"⊑(⪩⨒∯1310000⇞)=⪩⨒∯3000","reverse_text":"⪩⨒∯3000=⊑(⪩⨒∯1310000⇞)","cot":[{"info":"⪩⨒∯1310000⇞=⪩⨒∯13032221","layer":1},{"info":"⊑⪩⨒∯13032221=⪩⨒∯3000","layer":0}]}
{"id":40,"expression_no_base_symbol":"↸⊣($3951$≃$4128$)","expression":"↸⊣(⪩⨒∯331233≃⪩⨒∯1000200)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":29,"operation_count":2,"complexity_ratio":14.5,"tree":{"type":"unary","operator":"↸⊣","unary_expr":{"type":"binary","operator":"≃","left_expr":{"type":"numeric_atoms","value":3951,"base":4},"right_expr":{"type":"numeric_atoms","value":4128,"base":4}}},"used_operators":["wztAlM01eG","YbVcJGFEVW"],"dependent_operators":["N41Kp7NANJ","XPYlsWDdGa","7j4O788W3g","DZ8iAZOCBD","8w2t5hMYqp","12rbrZMWeM","f6k1SAg4EE","9FxExcQeMw","Qy55tPpLXF","23Mk6UjR3U","JLbD19bQDL","7j4O788W3g","glklzrTFfD","tifHPKVTfV","t8gj7n24qd","i8ToyICDmI","COABgblf1C"],"result":"⪩⨒∯13233020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3951","layer":2},{"info":"number node, value=4128","layer":2},{"info":"compute binary expreesion, left_input=3951, right_input=4128, op_id = YbVcJGFEVW binary_op_definition= 'a≃b = { (((13⋥≓≎b)⋷(a⇼⇔∾b))⨁⊸⫻) , if ((b⨁⊸⫻)>=162 or (b⪠⩆⊳)<=569) ; ((-(17⋷a))↺((a⩷∴a)⊭↱(b∲⫓a))) , else }', output=-15844","layer":1},{"info":"compute unary expreesion, input=-15844, op_id = wztAlM01eG, unary_op_definition = '↸⊣a = { ((⊄⩳↩a)↺(a≋⫹)) , if (⪲⇎a)<33 ; ((a⪒a)⊉≛↸(a⋳⪒a)) , else }', output=31688","layer":0}],"base":4,"result_base":4,"text":"↸⊣(⪩⨒∯331233≃⪩⨒∯1000200)=⪩⨒∯13233020","reverse_text":"⪩⨒∯13233020=↸⊣(⪩⨒∯331233≃⪩⨒∯1000200)","cot":[{"info":"⪩⨒∯331233≃⪩⨒∯1000200=⪩⨒∯-3313210","layer":1},{"info":"↸⊣⪩⨒∯-3313210=⪩⨒∯13233020","layer":0}]}
{"id":41,"expression_no_base_symbol":"⨭⩧⫛(↩⪖$5959$)","expression":"⨭⩧⫛(↩⪖⪩⨒∯1131013)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":783,"operation_count":2,"complexity_ratio":391.5,"tree":{"type":"unary","operator":"⨭⩧⫛","unary_expr":{"type":"unary","operator":"↩⪖","unary_expr":{"type":"numeric_atoms","value":5959,"base":4}}},"used_operators":["g21JL6JxX7","fG6uBQFnGz"],"dependent_operators":["Ikt5ks8PT7","Asc51vEJeQ","A8NUZmVepG","rysDP5nf3Z","DpFCA1CohY","e1ybzncUwg","XIabStNQrY","eH2TOUuTDT","2DQ55sFlQl","Ph9nP6C5qx","Z2TMIBDE3Q","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5959","layer":2},{"info":"compute unary expreesion, input=5959, op_id = fG6uBQFnGz, unary_op_definition = '↩⪖a = { (((a-a)⨵⪆(a⪐))⫡⨏(a⩤)) , if (a⇋≉)==322 ; (((≉487)⨳⩥⨓(⋗⩬⋾a))⨸⪁((a⊦⊿)≧⫂∧(a∲⫓a))) , else }', output=-38736","layer":1},{"info":"compute unary expreesion, input=-38736, op_id = g21JL6JxX7, unary_op_definition = '⨭⩧⫛a = { ((↥a)⩧⪆(↣≠⋷a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⨭⩧⫛(↩⪖⪩⨒∯1131013)=NaN","reverse_text":"NaN=⨭⩧⫛(↩⪖⪩⨒∯1131013)","cot":[{"info":"↩⪖⪩⨒∯1131013=⪩⨒∯-21131100","layer":1},{"info":"⨭⩧⫛⪩⨒∯-21131100=NaN","layer":0}]}
{"id":42,"expression_no_base_symbol":"$6066$⩖⊿$5280$↬⩅∪","expression":"⪩⨒∯1132302⩖⊿⪩⨒∯1102200↬⩅∪","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":35,"operation_count":2,"complexity_ratio":17.5,"tree":{"type":"unary","operator":"↬⩅∪","unary_expr":{"type":"binary","operator":"⩖⊿","left_expr":{"type":"numeric_atoms","value":6066,"base":4},"right_expr":{"type":"numeric_atoms","value":5280,"base":4}}},"used_operators":["VJ330n2nnx","RZ5CV9rWsJ"],"dependent_operators":["D4vGDi5EA2","23Mk6UjR3U","u6S6b8DprG","HJ9erzHUuu","IWmyXbctLI","8cLx32lpNA"],"result":"⪩⨒∯-31012302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6066","layer":2},{"info":"number node, value=5280","layer":2},{"info":"compute binary expreesion, left_input=6066, right_input=5280, op_id = RZ5CV9rWsJ binary_op_definition= 'a⩖⊿b = { ((b⪔⊥a)⪮%⊝(a∌125)) }', output=17894","layer":1},{"info":"compute unary expreesion, input=17894, op_id = VJ330n2nnx, unary_op_definition = 'a↬⩅∪ = { (a≦≮≮) , if (↽≂a)!=185 or a>=376 or a<=585 ; (a⋷a) , else }', output=-53682","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1132302⩖⊿⪩⨒∯1102200↬⩅∪=⪩⨒∯-31012302","reverse_text":"⪩⨒∯-31012302=⪩⨒∯1132302⩖⊿⪩⨒∯1102200↬⩅∪","cot":[{"info":"⪩⨒∯1132302⩖⊿⪩⨒∯1102200=⪩⨒∯10113212","layer":1},{"info":"⪩⨒∯10113212↬⩅∪=⪩⨒∯-31012302","layer":0}]}
{"id":43,"expression_no_base_symbol":"($6700$⋓$1812$)⨔⇊($2319$⨎$2634$)","expression":"(⪩⨒∯1220230⋓⪩⨒∯130110)⨔⇊(⪩⨒∯210033⨎⪩⨒∯221022)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15,"operation_count":3,"complexity_ratio":5.0,"tree":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":6700,"base":4},"right_expr":{"type":"numeric_atoms","value":1812,"base":4}},"right_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":2319,"base":4},"right_expr":{"type":"numeric_atoms","value":2634,"base":4}}},"used_operators":["JclMnS0uGI","T2fj7uvVaJ","rJVOvQCfKK"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"⪩⨒∯221022","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6700","layer":2},{"info":"number node, value=1812","layer":2},{"info":"compute binary expreesion, left_input=6700, right_input=1812, op_id = T2fj7uvVaJ binary_op_definition= 'a⋓b = { (((60⪒b)⊭∹↮)%((a⪘⫢68)⪘⫢(⨵≀≌a))) , if (b>=803 and b<=372 and b<242) ; (16⪢((b⊠≄⫣)⋷(a⫌⩹⨱))) , else }', output=0","layer":1},{"info":"number node, value=2319","layer":2},{"info":"number node, value=2634","layer":2},{"info":"compute binary expreesion, left_input=2319, right_input=2634, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=2634","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=2634, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=2634","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1220230⋓⪩⨒∯130110)⨔⇊(⪩⨒∯210033⨎⪩⨒∯221022)=⪩⨒∯221022","reverse_text":"⪩⨒∯221022=(⪩⨒∯1220230⋓⪩⨒∯130110)⨔⇊(⪩⨒∯210033⨎⪩⨒∯221022)","cot":[{"info":"⪩⨒∯1220230⋓⪩⨒∯130110=⪩⨒∯0","layer":1},{"info":"⪩⨒∯210033⨎⪩⨒∯221022=⪩⨒∯221022","layer":1},{"info":"⪩⨒∯0⨔⇊⪩⨒∯221022=⪩⨒∯221022","layer":0}]}
{"id":44,"expression_no_base_symbol":"(↓⇌$2378$)⨽$1931$∴$1567$","expression":"(↓⇌⪩⨒∯211022)⨽⪩⨒∯132023∴⪩⨒∯120133","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2397,"operation_count":3,"complexity_ratio":799.0,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"unary","operator":"↓⇌","unary_expr":{"type":"numeric_atoms","value":2378,"base":4}},"right_expr":{"type":"binary","operator":"∴","left_expr":{"type":"numeric_atoms","value":1931,"base":4},"right_expr":{"type":"numeric_atoms","value":1567,"base":4}}},"used_operators":["8HhzD0ZcuI","PxpmPgHHJV","hrf7POJlIJ"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","23Mk6UjR3U","glklzrTFfD","Z2TMIBDE3Q","g55IO6H4Gj","P8v4zCKN1o","23Mk6UjR3U"],"result":"⪩⨒∯-1000301132130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2378","layer":2},{"info":"compute unary expreesion, input=2378, op_id = PxpmPgHHJV, unary_op_definition = '↓⇌a = { (a⋷507) , if a>=68 and (a⩤)>=87 ; (a⨁⊸⫻) , else }', output=2378","layer":1},{"info":"number node, value=1931","layer":2},{"info":"number node, value=1567","layer":2},{"info":"compute binary expreesion, left_input=1931, right_input=1567, op_id = hrf7POJlIJ binary_op_definition= 'a∴b = { ((∥⊫(22⋷b))⨸⪁a) }', output=5510","layer":1},{"info":"compute binary expreesion, left_input=2378, right_input=5510, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-16979868","layer":0}],"base":4,"result_base":4,"text":"(↓⇌⪩⨒∯211022)⨽⪩⨒∯132023∴⪩⨒∯120133=⪩⨒∯-1000301132130","reverse_text":"⪩⨒∯-1000301132130=(↓⇌⪩⨒∯211022)⨽⪩⨒∯132023∴⪩⨒∯120133","cot":[{"info":"↓⇌⪩⨒∯211022=⪩⨒∯211022","layer":1},{"info":"⪩⨒∯132023∴⪩⨒∯120133=⪩⨒∯1112012","layer":1},{"info":"⪩⨒∯211022⨽⪩⨒∯1112012=⪩⨒∯-1000301132130","layer":0}]}
{"id":45,"expression_no_base_symbol":"($2615$≨$1443$)⨜⨶($1261$⊋$1462$)","expression":"(⪩⨒∯220313≨⪩⨒∯112203)⨜⨶(⪩⨒∯103231⊋⪩⨒∯112312)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":442,"operation_count":3,"complexity_ratio":147.33333333333334,"tree":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"binary","operator":"≨","left_expr":{"type":"numeric_atoms","value":2615,"base":4},"right_expr":{"type":"numeric_atoms","value":1443,"base":4}},"right_expr":{"type":"binary","operator":"⊋","left_expr":{"type":"numeric_atoms","value":1261,"base":4},"right_expr":{"type":"numeric_atoms","value":1462,"base":4}}},"used_operators":["HiPekx5b7W","0KMCeP1Jsh","W4tP9CfskL"],"dependent_operators":["N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC","2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu"],"result":"⪩⨒∯-221320103011","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2615","layer":2},{"info":"number node, value=1443","layer":2},{"info":"compute binary expreesion, left_input=2615, right_input=1443, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-23674","layer":1},{"info":"number node, value=1261","layer":2},{"info":"number node, value=1462","layer":2},{"info":"compute binary expreesion, left_input=1261, right_input=1462, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=-1790424","layer":1},{"info":"compute binary expreesion, left_input=-23674, right_input=-1790424, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-10978501","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯220313≨⪩⨒∯112203)⨜⨶(⪩⨒∯103231⊋⪩⨒∯112312)=⪩⨒∯-221320103011","reverse_text":"⪩⨒∯-221320103011=(⪩⨒∯220313≨⪩⨒∯112203)⨜⨶(⪩⨒∯103231⊋⪩⨒∯112312)","cot":[{"info":"⪩⨒∯220313≨⪩⨒∯112203=⪩⨒∯-11301322","layer":1},{"info":"⪩⨒∯103231⊋⪩⨒∯112312=⪩⨒∯-12311013120","layer":1},{"info":"⪩⨒∯-11301322⨜⨶⪩⨒∯-12311013120=⪩⨒∯-221320103011","layer":0}]}
{"id":46,"expression_no_base_symbol":"($6266$⇻⋧≁$1707$)⋩≍≻","expression":"(⪩⨒∯1201322⇻⋧≁⪩⨒∯122223)⋩≍≻","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6328,"operation_count":2,"complexity_ratio":3164.0,"tree":{"type":"unary","operator":"⋩≍≻","unary_expr":{"type":"binary","operator":"⇻⋧≁","left_expr":{"type":"numeric_atoms","value":6266,"base":4},"right_expr":{"type":"numeric_atoms","value":1707,"base":4}}},"used_operators":["WYd1w68Nbz","jCPkEVoL5K"],"dependent_operators":["P8v4zCKN1o","Noe24qw2ks","mqXw5SEYmG","IWmyXbctLI","COABgblf1C","eLxqMNBOBk","XnXgA4xnOs","3EYGwJThht","XTarYq4gQB","59igzFyhWz","dfKe02y8D2","X99M06cbEe"],"result":"⪩⨒∯-110011","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6266","layer":2},{"info":"number node, value=1707","layer":2},{"info":"compute binary expreesion, left_input=6266, right_input=1707, op_id = jCPkEVoL5K binary_op_definition= 'a⇻⋧≁b = { ((⫓⪴a)⫚↹⊑(54≫≃)) , if (a∵≐)<=35 or a>411 ; ((⪝⪂⫅b)⇄(290⨑≵⋬a)) , else }', output=-447","layer":1},{"info":"compute unary expreesion, input=-447, op_id = WYd1w68Nbz, unary_op_definition = 'a⋩≍≻ = { (∥⊫(a⊭↱21)) , if a>=390 ; ((a⨐a)⫸⊐(a⪮%⊝a)) , else }', output=-1285","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1201322⇻⋧≁⪩⨒∯122223)⋩≍≻=⪩⨒∯-110011","reverse_text":"⪩⨒∯-110011=(⪩⨒∯1201322⇻⋧≁⪩⨒∯122223)⋩≍≻","cot":[{"info":"⪩⨒∯1201322⇻⋧≁⪩⨒∯122223=⪩⨒∯-12333","layer":1},{"info":"⪩⨒∯-12333⋩≍≻=⪩⨒∯-110011","layer":0}]}
{"id":47,"expression_no_base_symbol":"($7781$⨓$1007$)⨻⩈⩔($1333$≭$1840$)","expression":"(⪩⨒∯1321211⨓⪩⨒∯33233)⨻⩈⩔(⪩⨒∯110311≭⪩⨒∯130300)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1085,"operation_count":3,"complexity_ratio":361.6666666666667,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":7781,"base":4},"right_expr":{"type":"numeric_atoms","value":1007,"base":4}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":1333,"base":4},"right_expr":{"type":"numeric_atoms","value":1840,"base":4}}},"used_operators":["nEsXyWgiOK","3ViojmjbAp","rxpJgHHUmx"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7781","layer":2},{"info":"number node, value=1007","layer":2},{"info":"compute binary expreesion, left_input=7781, right_input=1007, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1010","layer":1},{"info":"number node, value=1333","layer":2},{"info":"number node, value=1840","layer":2},{"info":"compute binary expreesion, left_input=1333, right_input=1840, op_id = rxpJgHHUmx binary_op_definition= 'a≭b = {-22, if b == 0; (a)≹⇙⪍(a≭(b-1)), if b > 0 and abs(b) < 100; -(a)≹⇙⪍(a≭(b+1)), if b < 0 and abs(b) < 100; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-1010, right_input=nan, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1321211⨓⪩⨒∯33233)⨻⩈⩔(⪩⨒∯110311≭⪩⨒∯130300)=NaN","reverse_text":"NaN=(⪩⨒∯1321211⨓⪩⨒∯33233)⨻⩈⩔(⪩⨒∯110311≭⪩⨒∯130300)","cot":[{"info":"⪩⨒∯1321211⨓⪩⨒∯33233=⪩⨒∯-33302","layer":1},{"info":"⪩⨒∯110311≭⪩⨒∯130300=NaN","layer":1},{"info":"⪩⨒∯-33302⨻⩈⩔NaN=NaN","layer":0}]}
{"id":48,"expression_no_base_symbol":"($1213$⪡$1511$)⋾⨃∁$1675$↬$4169$","expression":"(⪩⨒∯102331⪡⪩⨒∯113213)⋾⨃∁⪩⨒∯122023↬⪩⨒∯1001021","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":44,"operation_count":3,"complexity_ratio":14.666666666666666,"tree":{"type":"binary","operator":"⋾⨃∁","left_expr":{"type":"binary","operator":"⪡","left_expr":{"type":"numeric_atoms","value":1213,"base":4},"right_expr":{"type":"numeric_atoms","value":1511,"base":4}},"right_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":1675,"base":4},"right_expr":{"type":"numeric_atoms","value":4169,"base":4}}},"used_operators":["212REbPD9h","oraRL2iQuh","B5M0gjZbta"],"dependent_operators":["eLxqMNBOBk","Qy55tPpLXF","w2P8NbNXyL","2DQ55sFlQl","f6k1SAg4EE","2Wsdkap16l","ljTHtUsqzn","k8jYdgA6NY","8WDwsbhb0R","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1213","layer":2},{"info":"number node, value=1511","layer":2},{"info":"compute binary expreesion, left_input=1213, right_input=1511, op_id = oraRL2iQuh binary_op_definition= 'a⪡b = { (107%(a⩹b)) , if a>=49 ; (≀↧⇸(∂⩏⊆a)) , else }', output=107","layer":1},{"info":"number node, value=1675","layer":2},{"info":"number node, value=4169","layer":2},{"info":"compute binary expreesion, left_input=1675, right_input=4169, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=107, right_input=nan, op_id = 212REbPD9h binary_op_definition= 'a⋾⨃∁b = { ((430⊉↱≁b)⨵⪆b) , if (a⪒898)>=359 ; ((⫓⪴b)⊉↱≁(26⋥≓≎b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯102331⪡⪩⨒∯113213)⋾⨃∁⪩⨒∯122023↬⪩⨒∯1001021=NaN","reverse_text":"NaN=(⪩⨒∯102331⪡⪩⨒∯113213)⋾⨃∁⪩⨒∯122023↬⪩⨒∯1001021","cot":[{"info":"⪩⨒∯102331⪡⪩⨒∯113213=⪩⨒∯1223","layer":1},{"info":"⪩⨒∯122023↬⪩⨒∯1001021=NaN","layer":1},{"info":"⪩⨒∯1223⋾⨃∁NaN=NaN","layer":0}]}
{"id":49,"expression_no_base_symbol":"($9091$⇣⩺⋵$2160$)⋣⋖(⪓⩚$1967$)","expression":"(⪩⨒∯2032003⇣⩺⋵⪩⨒∯201300)⋣⋖(⪓⩚⪩⨒∯132233)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3424,"operation_count":3,"complexity_ratio":1141.3333333333333,"tree":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"binary","operator":"⇣⩺⋵","left_expr":{"type":"numeric_atoms","value":9091,"base":4},"right_expr":{"type":"numeric_atoms","value":2160,"base":4}},"right_expr":{"type":"unary","operator":"⪓⩚","unary_expr":{"type":"numeric_atoms","value":1967,"base":4}}},"used_operators":["J0M6qkBnIM","F4yD0voBRQ","u0R0Locfp2"],"dependent_operators":["VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2","NTOWxs364D","KPf6cnQVty","8jW3W4yZS5","12rbrZMWeM","g55IO6H4Gj","2DlMacCsIx","6o9Blt3TJ6","mp7IySMOzn","Nsiff2A1zJ"],"result":"⪩⨒∯-10010","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=9091","layer":2},{"info":"number node, value=2160","layer":2},{"info":"compute binary expreesion, left_input=9091, right_input=2160, op_id = F4yD0voBRQ binary_op_definition= 'a⇣⩺⋵b = { (((a⩨565)∺≝⩲(5⨸⪁a))⩚⊴⇥(↯⪼(a⋳⪒b))) }', output=-260","layer":1},{"info":"number node, value=1967","layer":2},{"info":"compute unary expreesion, input=1967, op_id = u0R0Locfp2, unary_op_definition = '⪓⩚a = { (a⫰⋱a) , if (a⊴910)>461 ; (240⇷213) , else }', output=426","layer":1},{"info":"compute binary expreesion, left_input=-260, right_input=426, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=-260","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2032003⇣⩺⋵⪩⨒∯201300)⋣⋖(⪓⩚⪩⨒∯132233)=⪩⨒∯-10010","reverse_text":"⪩⨒∯-10010=(⪩⨒∯2032003⇣⩺⋵⪩⨒∯201300)⋣⋖(⪓⩚⪩⨒∯132233)","cot":[{"info":"⪩⨒∯2032003⇣⩺⋵⪩⨒∯201300=⪩⨒∯-10010","layer":1},{"info":"⪓⩚⪩⨒∯132233=⪩⨒∯12222","layer":1},{"info":"⪩⨒∯-10010⋣⋖⪩⨒∯12222=⪩⨒∯-10010","layer":0}]}
{"id":50,"expression_no_base_symbol":"⫖→$4770$⫁$3625$","expression":"⫖→⪩⨒∯1022202⫁⪩⨒∯320221","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":447,"operation_count":2,"complexity_ratio":223.5,"tree":{"type":"unary","operator":"⫖→","unary_expr":{"type":"binary","operator":"⫁","left_expr":{"type":"numeric_atoms","value":4770,"base":4},"right_expr":{"type":"numeric_atoms","value":3625,"base":4}}},"used_operators":["U4ylXWHChL","0ajvFaJAv0"],"dependent_operators":["tmPS8pqC7x","Ikt5ks8PT7","AFVx7xoS7T","o20kRiQErp","cHh1gJQ2o6","AHs5Up7iyr"],"result":"⪩⨒∯2301","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4770","layer":2},{"info":"number node, value=3625","layer":2},{"info":"compute binary expreesion, left_input=4770, right_input=3625, op_id = 0ajvFaJAv0 binary_op_definition= 'a⫁b = { (a≹⇙⪍6) , if a==154 ; (b⩘b) , else }', output=160","layer":1},{"info":"compute unary expreesion, input=160, op_id = U4ylXWHChL, unary_op_definition = '⫖→a = { (((a⨪↰⇹a)⇌⫙⪟(a⩧⪆a))∸) }', output=177","layer":0}],"base":4,"result_base":4,"text":"⫖→⪩⨒∯1022202⫁⪩⨒∯320221=⪩⨒∯2301","reverse_text":"⪩⨒∯2301=⫖→⪩⨒∯1022202⫁⪩⨒∯320221","cot":[{"info":"⪩⨒∯1022202⫁⪩⨒∯320221=⪩⨒∯2200","layer":1},{"info":"⫖→⪩⨒∯2200=⪩⨒∯2301","layer":0}]}
{"id":51,"expression_no_base_symbol":"(⪓⩚$2793$)⫸⇳$1142$⨐⩸⫘$1022$","expression":"(⪓⩚⪩⨒∯223221)⫸⇳⪩⨒∯101312⨐⩸⫘⪩⨒∯33332","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3377,"operation_count":3,"complexity_ratio":1125.6666666666667,"tree":{"type":"binary","operator":"⫸⇳","left_expr":{"type":"unary","operator":"⪓⩚","unary_expr":{"type":"numeric_atoms","value":2793,"base":4}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":1142,"base":4},"right_expr":{"type":"numeric_atoms","value":1022,"base":4}}},"used_operators":["gx7XJ7hdpj","u0R0Locfp2","fu6greOZ01"],"dependent_operators":["DpFCA1CohY","7j4O788W3g","tifHPKVTfV","2DQ55sFlQl","DIvbN7qnHd","12rbrZMWeM","t8gj7n24qd","14qkJME0vr","g55IO6H4Gj","eewbuw0ToL","6o9Blt3TJ6","mp7IySMOzn","Nsiff2A1zJ","3ViojmjbAp"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2793","layer":2},{"info":"compute unary expreesion, input=2793, op_id = u0R0Locfp2, unary_op_definition = '⪓⩚a = { (a⫰⋱a) , if (a⊴910)>461 ; (240⇷213) , else }', output=426","layer":1},{"info":"number node, value=1142","layer":2},{"info":"number node, value=1022","layer":2},{"info":"compute binary expreesion, left_input=1142, right_input=1022, op_id = fu6greOZ01 binary_op_definition= 'a⨐⩸⫘b = {a, if b == 0; (a⨐⩸⫘(b-1))⨓(b), if b > 0 and abs(b) < 1000; -(a⨐⩸⫘(b+1))⨓(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=426, right_input=nan, op_id = gx7XJ7hdpj binary_op_definition= 'a⫸⇳b = { (((494⋳⪒b)⇼⇔∾(⋗⩬⋾a))↺((b⊦⊿)⨸⪁(b⨵⪆b))) , if a==116 ; (-((a⨰a)⊠≄⫣)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪓⩚⪩⨒∯223221)⫸⇳⪩⨒∯101312⨐⩸⫘⪩⨒∯33332=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪓⩚⪩⨒∯223221)⫸⇳⪩⨒∯101312⨐⩸⫘⪩⨒∯33332","cot":[{"info":"⪓⩚⪩⨒∯223221=⪩⨒∯12222","layer":1},{"info":"⪩⨒∯101312⨐⩸⫘⪩⨒∯33332=NaN","layer":1},{"info":"⪩⨒∯12222⫸⇳NaN=⪩⨒∯0","layer":0}]}
{"id":52,"expression_no_base_symbol":"⫵↿($7628$⩺⋐⫨)","expression":"⫵↿(⪩⨒∯1313030⩺⋐⫨)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":592,"operation_count":2,"complexity_ratio":296.0,"tree":{"type":"unary","operator":"⫵↿","unary_expr":{"type":"unary","operator":"⩺⋐⫨","unary_expr":{"type":"numeric_atoms","value":7628,"base":4}}},"used_operators":["ivGwdmUAux","yS9ePUuUdn"],"dependent_operators":["LXhwmt4mBO","09Ly4LVMIf","LRNGc0VcxI","y4ImoPnbV5","8jW3W4yZS5","G9tJMlZ94a","9samAPKr6k","j9kHMeSvPp","Tcnh7f0tEr"],"result":"⪩⨒∯2021","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7628","layer":2},{"info":"compute unary expreesion, input=7628, op_id = yS9ePUuUdn, unary_op_definition = 'a⩺⋐⫨ = { ((a≣⋋)⨽∌(a⪭a)) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = ivGwdmUAux, unary_op_definition = '⫵↿a = { ((a⫃⨇256)∽(a∀⇚≩66)) , if (⇨a)>=1 ; (↯⪼(a⨫⇇↔a)) , else }', output=137","layer":0}],"base":4,"result_base":4,"text":"⫵↿(⪩⨒∯1313030⩺⋐⫨)=⪩⨒∯2021","reverse_text":"⪩⨒∯2021=⫵↿(⪩⨒∯1313030⩺⋐⫨)","cot":[{"info":"⪩⨒∯1313030⩺⋐⫨=⪩⨒∯0","layer":1},{"info":"⫵↿⪩⨒∯0=⪩⨒∯2021","layer":0}]}
{"id":53,"expression_no_base_symbol":"($1070$⫔⩽⩺$8119$)∓⋝(⫶⊄≣$8366$)","expression":"(⪩⨒∯100232⫔⩽⩺⪩⨒∯1332313)∓⋝(⫶⊄≣⪩⨒∯2002232)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8442,"operation_count":3,"complexity_ratio":2814.0,"tree":{"type":"binary","operator":"∓⋝","left_expr":{"type":"binary","operator":"⫔⩽⩺","left_expr":{"type":"numeric_atoms","value":1070,"base":4},"right_expr":{"type":"numeric_atoms","value":8119,"base":4}},"right_expr":{"type":"unary","operator":"⫶⊄≣","unary_expr":{"type":"numeric_atoms","value":8366,"base":4}}},"used_operators":["PoHhknlbAi","i9eR4S00cU","wxb3vTeyAj"],"dependent_operators":["DZ8iAZOCBD","DbCuESL50I","mqXw5SEYmG","2MzE1hQ0cz","Tw270M8GLb","fu6greOZ01","eLAdDNolq6","3nqY3DE9mg","8HhzD0ZcuI"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1070","layer":2},{"info":"number node, value=8119","layer":2},{"info":"compute binary expreesion, left_input=1070, right_input=8119, op_id = i9eR4S00cU binary_op_definition= 'a⫔⩽⩺b = { (⨰⫟⨤(a⨐⩸⫘b)) }', output=nan","layer":1},{"info":"number node, value=8366","layer":2},{"info":"compute unary expreesion, input=8366, op_id = wxb3vTeyAj, unary_op_definition = '⫶⊄≣a = { (≤/((a⨽a)⊍)) }', output=1259966485","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1259966485, op_id = PoHhknlbAi binary_op_definition= 'a∓⋝b = { (((a⊉≛↸a)⫸⊐(⋼∭⪍b))∩⋅) }', output=67","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100232⫔⩽⩺⪩⨒∯1332313)∓⋝(⫶⊄≣⪩⨒∯2002232)=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=(⪩⨒∯100232⫔⩽⩺⪩⨒∯1332313)∓⋝(⫶⊄≣⪩⨒∯2002232)","cot":[{"info":"⪩⨒∯100232⫔⩽⩺⪩⨒∯1332313=NaN","layer":1},{"info":"⫶⊄≣⪩⨒∯2002232=⪩⨒∯1023012121000111","layer":1},{"info":"NaN∓⋝⪩⨒∯1023012121000111=⪩⨒∯1003","layer":0}]}
{"id":54,"expression_no_base_symbol":"$2485$↬$4084$⫃⨇$1220$⨼⩣$1993$","expression":"⪩⨒∯212311↬⪩⨒∯333310⫃⨇⪩⨒∯103010⨼⩣⪩⨒∯133021","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":380,"operation_count":3,"complexity_ratio":126.66666666666667,"tree":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":2485,"base":4},"right_expr":{"type":"numeric_atoms","value":4084,"base":4}},"right_expr":{"type":"binary","operator":"⨼⩣","left_expr":{"type":"numeric_atoms","value":1220,"base":4},"right_expr":{"type":"numeric_atoms","value":1993,"base":4}}},"used_operators":["09Ly4LVMIf","B5M0gjZbta","JxwMv5le6e"],"dependent_operators":["9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG","rGHVDoGpnC","uFcxV4UQCh","cHh1gJQ2o6","SL6IHkK8vl","KYD54nUTWz","pRsWfj4Fpp","CArV6hThFE"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2485","layer":2},{"info":"number node, value=4084","layer":2},{"info":"compute binary expreesion, left_input=2485, right_input=4084, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":1},{"info":"number node, value=1220","layer":2},{"info":"number node, value=1993","layer":2},{"info":"compute binary expreesion, left_input=1220, right_input=1993, op_id = JxwMv5le6e binary_op_definition= 'a⨼⩣b = { ((∐⩳⋚(b⩘a))⪛((∡129)⫥∨⫟(a⫲⨊))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯212311↬⪩⨒∯333310⫃⨇⪩⨒∯103010⨼⩣⪩⨒∯133021=NaN","reverse_text":"NaN=⪩⨒∯212311↬⪩⨒∯333310⫃⨇⪩⨒∯103010⨼⩣⪩⨒∯133021","cot":[{"info":"⪩⨒∯212311↬⪩⨒∯333310=NaN","layer":1},{"info":"⪩⨒∯103010⨼⩣⪩⨒∯133021=NaN","layer":1},{"info":"NaN⫃⨇NaN=NaN","layer":0}]}
{"id":55,"expression_no_base_symbol":"$4008$⇡⇂$2864$*$3271$⊴$5291$","expression":"⪩⨒∯332220⇡⇂⪩⨒∯230300*⪩⨒∯303013⊴⪩⨒∯1102223","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":20468,"operation_count":3,"complexity_ratio":6822.666666666667,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"⇡⇂","left_expr":{"type":"numeric_atoms","value":4008,"base":4},"right_expr":{"type":"numeric_atoms","value":2864,"base":4}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":3271,"base":4},"right_expr":{"type":"numeric_atoms","value":5291,"base":4}}},"used_operators":["9HNa5Wba9A","UMwdvZNt44","Nsiff2A1zJ"],"dependent_operators":["W4YGzv6Whe","9FxExcQeMw","23Mk6UjR3U","z4E1FaHLuy","3tj9sqzovi","fu6greOZ01","AHs5Up7iyr","lvlrscuwVU","KPf6cnQVty","uBihLCJcMX","12rbrZMWeM","WPoGxAaPR1","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4008","layer":2},{"info":"number node, value=2864","layer":2},{"info":"compute binary expreesion, left_input=4008, right_input=2864, op_id = UMwdvZNt44 binary_op_definition= 'a⇡⇂b = { (((b≹⇙⪍b)⋳⪒(b⋷a))∺≝⩲(⫟(a⩷∴43))) , if (⊬↢a)==727 or (a⇔⨋)<18 ; ((604≴⪞⇿(≻⋜b))⨐⩸⫘a) , else }', output=nan","layer":1},{"info":"number node, value=3271","layer":2},{"info":"number node, value=5291","layer":2},{"info":"compute binary expreesion, left_input=3271, right_input=5291, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯332220⇡⇂⪩⨒∯230300*⪩⨒∯303013⊴⪩⨒∯1102223=NaN","reverse_text":"NaN=⪩⨒∯332220⇡⇂⪩⨒∯230300*⪩⨒∯303013⊴⪩⨒∯1102223","cot":[{"info":"⪩⨒∯332220⇡⇂⪩⨒∯230300=NaN","layer":1},{"info":"⪩⨒∯303013⊴⪩⨒∯1102223=NaN","layer":1},{"info":"NaN*NaN=NaN","layer":0}]}
{"id":56,"expression_no_base_symbol":"⇺⋃($3775$⨚$3631$)","expression":"⇺⋃(⪩⨒∯322333⨚⪩⨒∯320233)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":71,"operation_count":2,"complexity_ratio":35.5,"tree":{"type":"unary","operator":"⇺⋃","unary_expr":{"type":"binary","operator":"⨚","left_expr":{"type":"numeric_atoms","value":3775,"base":4},"right_expr":{"type":"numeric_atoms","value":3631,"base":4}}},"used_operators":["E5v5B3UAjG","nREPSIbpBE"],"dependent_operators":["bl5wxAcryP","Q3PJZHRvZv","gub5Cegaqo","8INZBEW696","kuIXHzHcAH","7YooWSwCyH","BjRHVeLaeN","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3775","layer":2},{"info":"number node, value=3631","layer":2},{"info":"compute binary expreesion, left_input=3775, right_input=3631, op_id = nREPSIbpBE binary_op_definition= 'a⨚b = { (((b⋳⪒a)⋳⪒31)⫩⊇) }', output=-6040","layer":1},{"info":"compute unary expreesion, input=-6040, op_id = E5v5B3UAjG, unary_op_definition = '⇺⋃a = { (((a≀⩗∶a)∪⫐(a⩁⩘229))⪨⊡(⊥(a↰))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇺⋃(⪩⨒∯322333⨚⪩⨒∯320233)=NaN","reverse_text":"NaN=⇺⋃(⪩⨒∯322333⨚⪩⨒∯320233)","cot":[{"info":"⪩⨒∯322333⨚⪩⨒∯320233=⪩⨒∯-1132120","layer":1},{"info":"⇺⋃⪩⨒∯-1132120=NaN","layer":0}]}
{"id":57,"expression_no_base_symbol":"($6197$⋘⨑⨽)⩌⋺(⪁⇼$4781$)","expression":"(⪩⨒∯1200311⋘⨑⨽)⩌⋺(⪁⇼⪩⨒∯1022231)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":29,"operation_count":3,"complexity_ratio":9.666666666666666,"tree":{"type":"binary","operator":"⩌⋺","left_expr":{"type":"unary","operator":"⋘⨑⨽","unary_expr":{"type":"numeric_atoms","value":6197,"base":4}},"right_expr":{"type":"unary","operator":"⪁⇼","unary_expr":{"type":"numeric_atoms","value":4781,"base":4}}},"used_operators":["g7Hmc5v1ko","WmT3o8z6ya","ZNVVrZ94lY"],"dependent_operators":["9FxExcQeMw","W4YGzv6Whe","NTOWxs364D","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","i8ToyICDmI","QMFrweE19q","W4YGzv6Whe","DpFCA1CohY","N41Kp7NANJ","8w2t5hMYqp","QMFrweE19q","sdazOOVcIp","2DQ55sFlQl","tifHPKVTfV"],"result":"⪩⨒∯-13320313","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6197","layer":2},{"info":"compute unary expreesion, input=6197, op_id = WmT3o8z6ya, unary_op_definition = 'a⋘⨑⨽ = { ((a⫡⨏a)+(a≋⫹)) , if (⊄⩳↩a)!=44 ; (⋗⩬⋾(394+a)) , else }', output=31768","layer":1},{"info":"number node, value=4781","layer":2},{"info":"compute unary expreesion, input=4781, op_id = ZNVVrZ94lY, unary_op_definition = '⪁⇼a = { ((a⨵⪆a)⪨≂(a⇼⇔∾a)) }', output=422","layer":1},{"info":"compute binary expreesion, left_input=31768, right_input=422, op_id = g7Hmc5v1ko binary_op_definition= 'a⩌⋺b = { ((⨞⊢(b⨵⪆b))∲⫓((a⪨≂b)⪨≂(b⩷∴919))) , if (b⫡⨏102)>364 and (-b)==524 ; (b⇼⇔∾((a+a)⩚⊴⇥(-a))) , else }', output=-32311","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1200311⋘⨑⨽)⩌⋺(⪁⇼⪩⨒∯1022231)=⪩⨒∯-13320313","reverse_text":"⪩⨒∯-13320313=(⪩⨒∯1200311⋘⨑⨽)⩌⋺(⪁⇼⪩⨒∯1022231)","cot":[{"info":"⪩⨒∯1200311⋘⨑⨽=⪩⨒∯13300120","layer":1},{"info":"⪁⇼⪩⨒∯1022231=⪩⨒∯12212","layer":1},{"info":"⪩⨒∯13300120⩌⋺⪩⨒∯12212=⪩⨒∯-13320313","layer":0}]}
{"id":58,"expression_no_base_symbol":"$2102$⨟⋌⩍$2277$⊾⪯⋞($4471$⩤)","expression":"⪩⨒∯200312⨟⋌⩍⪩⨒∯203211⊾⪯⋞(⪩⨒∯1011313⩤)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":56,"operation_count":3,"complexity_ratio":18.666666666666668,"tree":{"type":"binary","operator":"⊾⪯⋞","left_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":2102,"base":4},"right_expr":{"type":"numeric_atoms","value":2277,"base":4}},"right_expr":{"type":"unary","operator":"⩤","unary_expr":{"type":"numeric_atoms","value":4471,"base":4}}},"used_operators":["HK0tfVPux8","rGHVDoGpnC","Z2TMIBDE3Q"],"dependent_operators":["s3Fd5m9Dh2","KFSx94NKJn","MmTdOpaElr","XnXgA4xnOs","fOIeswaMU4","YSKBFp38Pu","oacrs7FA3X","xNBdhnnwKq","Tcnh7f0tEr","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2102","layer":2},{"info":"number node, value=2277","layer":2},{"info":"compute binary expreesion, left_input=2102, right_input=2277, op_id = rGHVDoGpnC binary_op_definition= 'a⨟⋌⩍b = {a, if b == 0; (a⨟⋌⩍(b-1))≣⋋, if b > 0 and abs(b) < 1000; -(a⨟⋌⩍(b+1))≣⋋, if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"number node, value=4471","layer":2},{"info":"compute unary expreesion, input=4471, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-4471","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-4471, op_id = HK0tfVPux8 binary_op_definition= 'a⊾⪯⋞b = { ((121⊭∹↮)⊬⨰(a⨑≵⋬b)) , if (a⩟)==395 or (a⨱∎)>94 ; ((b⪘⫢b)⩒⫫(a⇤b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯200312⨟⋌⩍⪩⨒∯203211⊾⪯⋞(⪩⨒∯1011313⩤)=NaN","reverse_text":"NaN=⪩⨒∯200312⨟⋌⩍⪩⨒∯203211⊾⪯⋞(⪩⨒∯1011313⩤)","cot":[{"info":"⪩⨒∯200312⨟⋌⩍⪩⨒∯203211=NaN","layer":1},{"info":"⪩⨒∯1011313⩤=⪩⨒∯-1011313","layer":1},{"info":"NaN⊾⪯⋞⪩⨒∯-1011313=NaN","layer":0}]}
{"id":59,"expression_no_base_symbol":"(⋗⩬⋾$2180$)⋓$6532$⊴$1360$","expression":"(⋗⩬⋾⪩⨒∯202010)⋓⪩⨒∯1212010⊴⪩⨒∯111100","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3293,"operation_count":3,"complexity_ratio":1097.6666666666667,"tree":{"type":"binary","operator":"⋓","left_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":2180,"base":4}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":6532,"base":4},"right_expr":{"type":"numeric_atoms","value":1360,"base":4}}},"used_operators":["T2fj7uvVaJ","DpFCA1CohY","Nsiff2A1zJ"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2180","layer":2},{"info":"compute unary expreesion, input=2180, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-6540","layer":1},{"info":"number node, value=6532","layer":2},{"info":"number node, value=1360","layer":2},{"info":"compute binary expreesion, left_input=6532, right_input=1360, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-6540, right_input=nan, op_id = T2fj7uvVaJ binary_op_definition= 'a⋓b = { (((60⪒b)⊭∹↮)%((a⪘⫢68)⪘⫢(⨵≀≌a))) , if (b>=803 and b<=372 and b<242) ; (16⪢((b⊠≄⫣)⋷(a⫌⩹⨱))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⋗⩬⋾⪩⨒∯202010)⋓⪩⨒∯1212010⊴⪩⨒∯111100=NaN","reverse_text":"NaN=(⋗⩬⋾⪩⨒∯202010)⋓⪩⨒∯1212010⊴⪩⨒∯111100","cot":[{"info":"⋗⩬⋾⪩⨒∯202010=⪩⨒∯-1212030","layer":1},{"info":"⪩⨒∯1212010⊴⪩⨒∯111100=NaN","layer":1},{"info":"⪩⨒∯-1212030⋓NaN=NaN","layer":0}]}
{"id":60,"expression_no_base_symbol":"($6223$≝⊿$1780$)⨽∌($3160$≑≱⪘)","expression":"(⪩⨒∯1201033≝⊿⪩⨒∯123310)⨽∌(⪩⨒∯301120≑≱⪘)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":166,"operation_count":3,"complexity_ratio":55.333333333333336,"tree":{"type":"binary","operator":"⨽∌","left_expr":{"type":"binary","operator":"≝⊿","left_expr":{"type":"numeric_atoms","value":6223,"base":4},"right_expr":{"type":"numeric_atoms","value":1780,"base":4}},"right_expr":{"type":"unary","operator":"≑≱⪘","unary_expr":{"type":"numeric_atoms","value":3160,"base":4}}},"used_operators":["9samAPKr6k","OKKcZfAt5B","tGSeddj7UK"],"dependent_operators":["YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu","12rbrZMWeM","9FxExcQeMw","9bazX3JMtO","RygbFNSyEJ","VwlE7vj6HS","v0DYgG9ikt","eRqsBgTDFp","6MpZysEj17","8w2t5hMYqp","Ph9nP6C5qx","DmTXOeWf9t","8HhzD0ZcuI","BiWNJpBvwn"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6223","layer":2},{"info":"number node, value=1780","layer":2},{"info":"compute binary expreesion, left_input=6223, right_input=1780, op_id = OKKcZfAt5B binary_op_definition= 'a≝⊿b = { ((82⋳⪒b)⋳⪒a) }', output=-10316","layer":1},{"info":"number node, value=3160","layer":2},{"info":"compute unary expreesion, input=3160, op_id = tGSeddj7UK, unary_op_definition = 'a≑≱⪘ = { ((⊄⩳↩(6≧⫂∧a))⩍⋽⫝̸((a⊲⩕⊾a)≦↸(a⋆⋳))) , if (a↹⊜255)>=30 or (a↯⫤)>122 ; ((a⩷∴(a⪒⊣⊆a))⨽(a⊬⫿⊭)) , else }', output=78525","layer":1},{"info":"compute binary expreesion, left_input=-10316, right_input=78525, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1201033≝⊿⪩⨒∯123310)⨽∌(⪩⨒∯301120≑≱⪘)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯1201033≝⊿⪩⨒∯123310)⨽∌(⪩⨒∯301120≑≱⪘)","cot":[{"info":"⪩⨒∯1201033≝⊿⪩⨒∯123310=⪩⨒∯-2201030","layer":1},{"info":"⪩⨒∯301120≑≱⪘=⪩⨒∯103022331","layer":1},{"info":"⪩⨒∯-2201030⨽∌⪩⨒∯103022331=⪩⨒∯0","layer":0}]}
{"id":61,"expression_no_base_symbol":"($4073$⇍⊗$2519$)↞⋁($1389$⪚$8195$)","expression":"(⪩⨒∯333221⇍⊗⪩⨒∯213113)↞⋁(⪩⨒∯111231⪚⪩⨒∯2000003)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":62,"operation_count":3,"complexity_ratio":20.666666666666668,"tree":{"type":"binary","operator":"↞⋁","left_expr":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"numeric_atoms","value":4073,"base":4},"right_expr":{"type":"numeric_atoms","value":2519,"base":4}},"right_expr":{"type":"binary","operator":"⪚","left_expr":{"type":"numeric_atoms","value":1389,"base":4},"right_expr":{"type":"numeric_atoms","value":8195,"base":4}}},"used_operators":["RqrPlJkxDo","5uvYHDjeKN","HrjLwUk87U"],"dependent_operators":["Uaa54Peajs","CArV6hThFE","13rbtpv6ld","Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o","9FxExcQeMw","rysDP5nf3Z","NTOWxs364D","DZ8iAZOCBD","tifHPKVTfV","eH2TOUuTDT","2DDjHMKMc0"],"result":"⪩⨒∯-3310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4073","layer":2},{"info":"number node, value=2519","layer":2},{"info":"compute binary expreesion, left_input=4073, right_input=2519, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=-244","layer":1},{"info":"number node, value=1389","layer":2},{"info":"number node, value=8195","layer":2},{"info":"compute binary expreesion, left_input=1389, right_input=8195, op_id = HrjLwUk87U binary_op_definition= 'a⪚b = { (((317⩚⊴⇥a)⋝⋈⪟(518-95))⊉≛↸((97⪐)⩷∴(b⇼⇔∾a))) }', output=-13968","layer":1},{"info":"compute binary expreesion, left_input=-244, right_input=-13968, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=-244","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯333221⇍⊗⪩⨒∯213113)↞⋁(⪩⨒∯111231⪚⪩⨒∯2000003)=⪩⨒∯-3310","reverse_text":"⪩⨒∯-3310=(⪩⨒∯333221⇍⊗⪩⨒∯213113)↞⋁(⪩⨒∯111231⪚⪩⨒∯2000003)","cot":[{"info":"⪩⨒∯333221⇍⊗⪩⨒∯213113=⪩⨒∯-3310","layer":1},{"info":"⪩⨒∯111231⪚⪩⨒∯2000003=⪩⨒∯-3122100","layer":1},{"info":"⪩⨒∯-3310↞⋁⪩⨒∯-3122100=⪩⨒∯-3310","layer":0}]}
{"id":62,"expression_no_base_symbol":"($1416$⨚⇆$2890$)≁↽≥(⨴⫝$1493$)","expression":"(⪩⨒∯112020⨚⇆⪩⨒∯231022)≁↽≥(⨴⫝⪩⨒∯113111)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11784,"operation_count":3,"complexity_ratio":3928.0,"tree":{"type":"binary","operator":"≁↽≥","left_expr":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"numeric_atoms","value":1416,"base":4},"right_expr":{"type":"numeric_atoms","value":2890,"base":4}},"right_expr":{"type":"unary","operator":"⨴⫝","unary_expr":{"type":"numeric_atoms","value":1493,"base":4}}},"used_operators":["ncHt1X6cMc","lwHaAYXP2r","SVb2v531z1"],"dependent_operators":["oWn0xqSxBt","3Oe9XWJUTD","gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi","oDCm7WA9JY","XnXgA4xnOs","ocnLzx9CaJ","3sJ7IOPOlU","9cloC0Ngie","SWo3A1KBJH","jWTQ2TZYIH","pRsWfj4Fpp","DyGG3AbaNP","5obUd6DV38","8HhzD0ZcuI","YbUVn0Rbpy","AdZkA7nFnk","SIgE0bArFf"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1416","layer":2},{"info":"number node, value=2890","layer":2},{"info":"compute binary expreesion, left_input=1416, right_input=2890, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":1},{"info":"number node, value=1493","layer":2},{"info":"compute unary expreesion, input=1493, op_id = SVb2v531z1, unary_op_definition = '⨴⫝a = { ((⪨⨬(⇋↷a))≬⇓((a⋅⇍a)⨑≵⋬(∡178))) , if (a⪇≇⋚963)!=62 ; (((541⋛107)⩼⇪↪(⪭⩑⪱a))⋻⩜⩜((a⊕∕a)∼(459⨽6))) , else }', output=2828198","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2828198, op_id = ncHt1X6cMc binary_op_definition= 'a≁↽≥b = { (a⊝⪿⪼b) , if b>=116 ; (⊙↵-b) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯112020⨚⇆⪩⨒∯231022)≁↽≥(⨴⫝⪩⨒∯113111)=NaN","reverse_text":"NaN=(⪩⨒∯112020⨚⇆⪩⨒∯231022)≁↽≥(⨴⫝⪩⨒∯113111)","cot":[{"info":"⪩⨒∯112020⨚⇆⪩⨒∯231022=NaN","layer":1},{"info":"⨴⫝⪩⨒∯113111=⪩⨒∯22302132212","layer":1},{"info":"NaN≁↽≥⪩⨒∯22302132212=NaN","layer":0}]}
{"id":63,"expression_no_base_symbol":"($3234$+$2251$)⊹∫⫚$5316$⊱⇼⊻$2650$","expression":"(⪩⨒∯302202+⪩⨒∯203023)⊹∫⫚⪩⨒∯1103010⊱⇼⊻⪩⨒∯221122","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":21,"operation_count":3,"complexity_ratio":7.0,"tree":{"type":"binary","operator":"⊹∫⫚","left_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":3234,"base":4},"right_expr":{"type":"numeric_atoms","value":2251,"base":4}},"right_expr":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"numeric_atoms","value":5316,"base":4},"right_expr":{"type":"numeric_atoms","value":2650,"base":4}}},"used_operators":["uWAJUKEvyW","W4YGzv6Whe","FyVja0WsTP"],"dependent_operators":["BiWNJpBvwn","w2P8NbNXyL","vg4gO5BX6G","k8jYdgA6NY","g55IO6H4Gj","2td37pGCOC","jLgFTUHLKL","W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf"],"result":"⪩⨒∯-3310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3234","layer":2},{"info":"number node, value=2251","layer":2},{"info":"compute binary expreesion, left_input=3234, right_input=2251, op_id = W4YGzv6Whe binary_op_definition= 'None', output=5485","layer":1},{"info":"number node, value=5316","layer":2},{"info":"number node, value=2650","layer":2},{"info":"compute binary expreesion, left_input=5316, right_input=2650, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":1},{"info":"compute binary expreesion, left_input=5485, right_input=434, op_id = uWAJUKEvyW binary_op_definition= 'a⊹∫⫚b = { (↩(a⊨b)) , if (⩦⩻⨪a)==479 or (b⊉↱≁467)==779 ; ((b⨸⪁b)%(b⩍⋽⫝̸187)) , else }', output=-244","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯302202+⪩⨒∯203023)⊹∫⫚⪩⨒∯1103010⊱⇼⊻⪩⨒∯221122=⪩⨒∯-3310","reverse_text":"⪩⨒∯-3310=(⪩⨒∯302202+⪩⨒∯203023)⊹∫⫚⪩⨒∯1103010⊱⇼⊻⪩⨒∯221122","cot":[{"info":"⪩⨒∯302202+⪩⨒∯203023=⪩⨒∯1111231","layer":1},{"info":"⪩⨒∯1103010⊱⇼⊻⪩⨒∯221122=⪩⨒∯12302","layer":1},{"info":"⪩⨒∯1111231⊹∫⫚⪩⨒∯12302=⪩⨒∯-3310","layer":0}]}
{"id":64,"expression_no_base_symbol":"$2325$⊬⨰$1880$⊭↱$3247$⇴∐$4274$","expression":"⪩⨒∯210111⊬⨰⪩⨒∯131120⊭↱⪩⨒∯302233⇴∐⪩⨒∯1002302","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":41,"operation_count":3,"complexity_ratio":13.666666666666666,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"numeric_atoms","value":2325,"base":4},"right_expr":{"type":"numeric_atoms","value":1880,"base":4}},"right_expr":{"type":"binary","operator":"⇴∐","left_expr":{"type":"numeric_atoms","value":3247,"base":4},"right_expr":{"type":"numeric_atoms","value":4274,"base":4}}},"used_operators":["COABgblf1C","s3Fd5m9Dh2","HnzytWxmAO"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2325","layer":2},{"info":"number node, value=1880","layer":2},{"info":"compute binary expreesion, left_input=2325, right_input=1880, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=8789","layer":1},{"info":"number node, value=3247","layer":2},{"info":"number node, value=4274","layer":2},{"info":"compute binary expreesion, left_input=3247, right_input=4274, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=8789, right_input=nan, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯210111⊬⨰⪩⨒∯131120⊭↱⪩⨒∯302233⇴∐⪩⨒∯1002302=NaN","reverse_text":"NaN=⪩⨒∯210111⊬⨰⪩⨒∯131120⊭↱⪩⨒∯302233⇴∐⪩⨒∯1002302","cot":[{"info":"⪩⨒∯210111⊬⨰⪩⨒∯131120=⪩⨒∯2021111","layer":1},{"info":"⪩⨒∯302233⇴∐⪩⨒∯1002302=NaN","layer":1},{"info":"⪩⨒∯2021111⊭↱NaN=NaN","layer":0}]}
{"id":65,"expression_no_base_symbol":"($2127$⪥⨬⪅)≧⫂∧$3941$⊮⊟↴$1517$","expression":"(⪩⨒∯201033⪥⨬⪅)≧⫂∧⪩⨒∯331211⊮⊟↴⪩⨒∯113231","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":145,"operation_count":3,"complexity_ratio":48.333333333333336,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"unary","operator":"⪥⨬⪅","unary_expr":{"type":"numeric_atoms","value":2127,"base":4}},"right_expr":{"type":"binary","operator":"⊮⊟↴","left_expr":{"type":"numeric_atoms","value":3941,"base":4},"right_expr":{"type":"numeric_atoms","value":1517,"base":4}}},"used_operators":["Ph9nP6C5qx","zNRQejTB5A","QDVgd2eftb"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","d7ASUq0ydm","Uaa54Peajs","3EYGwJThht","y4ImoPnbV5","JwTKLfZU96","rJVOvQCfKK","uWAJUKEvyW","XhwjNDsVaA","C6VvDP6HwP","WkeUrDK8WX","kuIXHzHcAH","3Oe9XWJUTD","rJVOvQCfKK"],"result":"⪩⨒∯-13121","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2127","layer":2},{"info":"compute unary expreesion, input=2127, op_id = zNRQejTB5A, unary_op_definition = 'a⪥⨬⪅ = { (((a⨎1)⊹∫⫚(a⇄a))⫯⪬∳((a∽a)↳≱(∂a))) }', output=-473","layer":1},{"info":"number node, value=3941","layer":2},{"info":"number node, value=1517","layer":2},{"info":"compute binary expreesion, left_input=3941, right_input=1517, op_id = QDVgd2eftb binary_op_definition= 'a⊮⊟↴b = { ((⩰267)⪨⊡(b⊝⪿⪼a)) , if a!=19 ; ((b⨎372)/(b⪑⩈)) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-473, right_input=0, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=-473","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯201033⪥⨬⪅)≧⫂∧⪩⨒∯331211⊮⊟↴⪩⨒∯113231=⪩⨒∯-13121","reverse_text":"⪩⨒∯-13121=(⪩⨒∯201033⪥⨬⪅)≧⫂∧⪩⨒∯331211⊮⊟↴⪩⨒∯113231","cot":[{"info":"⪩⨒∯201033⪥⨬⪅=⪩⨒∯-13121","layer":1},{"info":"⪩⨒∯331211⊮⊟↴⪩⨒∯113231=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-13121≧⫂∧⪩⨒∯0=⪩⨒∯-13121","layer":0}]}
{"id":66,"expression_no_base_symbol":"($2442$⪎⩰)⨽∌($2273$⩹$1524$)","expression":"(⪩⨒∯212022⪎⩰)⨽∌(⪩⨒∯203201⩹⪩⨒∯113310)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":61,"operation_count":3,"complexity_ratio":20.333333333333332,"tree":{"type":"binary","operator":"⨽∌","left_expr":{"type":"unary","operator":"⪎⩰","unary_expr":{"type":"numeric_atoms","value":2442,"base":4}},"right_expr":{"type":"binary","operator":"⩹","left_expr":{"type":"numeric_atoms","value":2273,"base":4},"right_expr":{"type":"numeric_atoms","value":1524,"base":4}}},"used_operators":["9samAPKr6k","2ufhKmSs5H","2Wsdkap16l"],"dependent_operators":["YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu","DpFCA1CohY","N41Kp7NANJ","sdazOOVcIp","EBcxylXtPf","f6k1SAg4EE","COABgblf1C","rysDP5nf3Z","NTOWxs364D","23Mk6UjR3U","XIabStNQrY","2DDjHMKMc0","12rbrZMWeM","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2442","layer":2},{"info":"compute unary expreesion, input=2442, op_id = 2ufhKmSs5H, unary_op_definition = 'a⪎⩰ = { (17≋⫹) , if a>=326 and a!=597 ; (((a⪒a)⫌⩹⨱)⊭↱(⋗⩬⋾(756⪨≂a))) , else }', output=-34","layer":1},{"info":"number node, value=2273","layer":2},{"info":"number node, value=1524","layer":2},{"info":"compute binary expreesion, left_input=2273, right_input=1524, op_id = 2Wsdkap16l binary_op_definition= 'a⩹b = { (b-((b⨳⩥⨓b)⨸⪁(1⋝⋈⪟b))) , if (b⇋≉)!=246 ; (((a⇋≉)⨰(a⋷a))⋳⪒((a⩚⊴⇥a)⨳⩥⨓(a≧⫂∧a))) , else }', output=1522","layer":1},{"info":"compute binary expreesion, left_input=-34, right_input=1522, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯212022⪎⩰)⨽∌(⪩⨒∯203201⩹⪩⨒∯113310)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯212022⪎⩰)⨽∌(⪩⨒∯203201⩹⪩⨒∯113310)","cot":[{"info":"⪩⨒∯212022⪎⩰=⪩⨒∯-202","layer":1},{"info":"⪩⨒∯203201⩹⪩⨒∯113310=⪩⨒∯113302","layer":1},{"info":"⪩⨒∯-202⨽∌⪩⨒∯113302=⪩⨒∯0","layer":0}]}
{"id":67,"expression_no_base_symbol":"($4661$∖$2397$)∠↢(⇾⩊⇾$2325$)","expression":"(⪩⨒∯1020311∖⪩⨒∯211131)∠↢(⇾⩊⇾⪩⨒∯210111)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":400,"operation_count":3,"complexity_ratio":133.33333333333334,"tree":{"type":"binary","operator":"∠↢","left_expr":{"type":"binary","operator":"∖","left_expr":{"type":"numeric_atoms","value":4661,"base":4},"right_expr":{"type":"numeric_atoms","value":2397,"base":4}},"right_expr":{"type":"unary","operator":"⇾⩊⇾","unary_expr":{"type":"numeric_atoms","value":2325,"base":4}}},"used_operators":["KbjG8mgYpV","tXD093vOjl","bx9Z9DAK5y"],"dependent_operators":["rysDP5nf3Z","NTOWxs364D","XPYlsWDdGa","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","nCS4ZIUYfx","COABgblf1C","rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC","W4YGzv6Whe","BjRHVeLaeN","8w2t5hMYqp","QMFrweE19q"],"result":"⪩⨒∯1131331010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4661","layer":2},{"info":"number node, value=2397","layer":2},{"info":"compute binary expreesion, left_input=4661, right_input=2397, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":1},{"info":"number node, value=2325","layer":2},{"info":"compute unary expreesion, input=2325, op_id = bx9Z9DAK5y, unary_op_definition = '⇾⩊⇾a = { (⊄⩳↩((a+259)⫡⨏(a⫩⊇))) }', output=-27411","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-27411, op_id = KbjG8mgYpV binary_op_definition= 'a∠↢b = { (a⊭↱((159⨳⩥⨓16)-(b⨸⪁a))) , if (b==488 or (⨞⊢a)==254) ; (⪲⇎((-b)⫡⨏(b⩚⊴⇥a))) , else }', output=384836","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1020311∖⪩⨒∯211131)∠↢(⇾⩊⇾⪩⨒∯210111)=⪩⨒∯1131331010","reverse_text":"⪩⨒∯1131331010=(⪩⨒∯1020311∖⪩⨒∯211131)∠↢(⇾⩊⇾⪩⨒∯210111)","cot":[{"info":"⪩⨒∯1020311∖⪩⨒∯211131=⪩⨒∯0","layer":1},{"info":"⇾⩊⇾⪩⨒∯210111=⪩⨒∯-12230103","layer":1},{"info":"⪩⨒∯0∠↢⪩⨒∯-12230103=⪩⨒∯1131331010","layer":0}]}
{"id":68,"expression_no_base_symbol":"$2010$⨿$3291$≎⊠⪸($1248$⪨⊡$1525$)","expression":"⪩⨒∯133122⨿⪩⨒∯303123≎⊠⪸(⪩⨒∯103200⪨⊡⪩⨒∯113311)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":505,"operation_count":3,"complexity_ratio":168.33333333333334,"tree":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"binary","operator":"⨿","left_expr":{"type":"numeric_atoms","value":2010,"base":4},"right_expr":{"type":"numeric_atoms","value":3291,"base":4}},"right_expr":{"type":"binary","operator":"⪨⊡","left_expr":{"type":"numeric_atoms","value":1248,"base":4},"right_expr":{"type":"numeric_atoms","value":1525,"base":4}}},"used_operators":["bJkvcejdHO","abYXlopdE0","kuIXHzHcAH"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","gJLn6v0xnP","KFSx94NKJn","jWTQ2TZYIH","yXekIHxTD4","KYD54nUTWz","i8ToyICDmI","PoHhknlbAi","JLbD19bQDL","glklzrTFfD","eewbuw0ToL","AF7qkfDlqP"],"result":"⪩⨒∯110022331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2010","layer":2},{"info":"number node, value=3291","layer":2},{"info":"compute binary expreesion, left_input=2010, right_input=3291, op_id = abYXlopdE0 binary_op_definition= 'a⨿b = { (((a∲⫓409)≬⇓(a⩒⫫a))∓⋝((146⫥∨⫟b)≥⨤⩑(219⨥⫆b))) }', output=-319","layer":1},{"info":"number node, value=1248","layer":2},{"info":"number node, value=1525","layer":2},{"info":"compute binary expreesion, left_input=1248, right_input=1525, op_id = kuIXHzHcAH binary_op_definition= 'a⪨⊡b = { (⨑⩽⪐(b⨁⊸⫻)) , if (⨑⩽⪐b)>42 ; ((a⨰b)⪠⩆⊳) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-319, right_input=0, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=82621","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯133122⨿⪩⨒∯303123≎⊠⪸(⪩⨒∯103200⪨⊡⪩⨒∯113311)=⪩⨒∯110022331","reverse_text":"⪩⨒∯110022331=⪩⨒∯133122⨿⪩⨒∯303123≎⊠⪸(⪩⨒∯103200⪨⊡⪩⨒∯113311)","cot":[{"info":"⪩⨒∯133122⨿⪩⨒∯303123=⪩⨒∯-10333","layer":1},{"info":"⪩⨒∯103200⪨⊡⪩⨒∯113311=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-10333≎⊠⪸⪩⨒∯0=⪩⨒∯110022331","layer":0}]}
{"id":69,"expression_no_base_symbol":"$1669$⫒⫫$1138$⊾⪯⋞(⇁⨣⪵$4208$)","expression":"⪩⨒∯122011⫒⫫⪩⨒∯101302⊾⪯⋞(⇁⨣⪵⪩⨒∯1001300)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":59,"operation_count":3,"complexity_ratio":19.666666666666668,"tree":{"type":"binary","operator":"⊾⪯⋞","left_expr":{"type":"binary","operator":"⫒⫫","left_expr":{"type":"numeric_atoms","value":1669,"base":4},"right_expr":{"type":"numeric_atoms","value":1138,"base":4}},"right_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":4208,"base":4}}},"used_operators":["HK0tfVPux8","6Ko8hGgeMq","inkyxCbjAn"],"dependent_operators":["s3Fd5m9Dh2","KFSx94NKJn","MmTdOpaElr","XnXgA4xnOs","fOIeswaMU4","YSKBFp38Pu","oacrs7FA3X","xNBdhnnwKq","jdwGQqwJi5","AHs5Up7iyr","AFVx7xoS7T","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1669","layer":2},{"info":"number node, value=1138","layer":2},{"info":"compute binary expreesion, left_input=1669, right_input=1138, op_id = 6Ko8hGgeMq binary_op_definition= 'a⫒⫫b = { (b≹⇙⪍a) , if (a∁)>135 ; (b⇌⫙⪟a) , else }', output=nan","layer":1},{"info":"number node, value=4208","layer":2},{"info":"compute unary expreesion, input=4208, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = HK0tfVPux8 binary_op_definition= 'a⊾⪯⋞b = { ((121⊭∹↮)⊬⨰(a⨑≵⋬b)) , if (a⩟)==395 or (a⨱∎)>94 ; ((b⪘⫢b)⩒⫫(a⇤b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯122011⫒⫫⪩⨒∯101302⊾⪯⋞(⇁⨣⪵⪩⨒∯1001300)=NaN","reverse_text":"NaN=⪩⨒∯122011⫒⫫⪩⨒∯101302⊾⪯⋞(⇁⨣⪵⪩⨒∯1001300)","cot":[{"info":"⪩⨒∯122011⫒⫫⪩⨒∯101302=NaN","layer":1},{"info":"⇁⨣⪵⪩⨒∯1001300=NaN","layer":1},{"info":"NaN⊾⪯⋞NaN=NaN","layer":0}]}
{"id":70,"expression_no_base_symbol":"$1702$⪥$6057$⊘","expression":"⪩⨒∯122212⪥⪩⨒∯1132221⊘","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":42,"operation_count":2,"complexity_ratio":21.0,"tree":{"type":"unary","operator":"⊘","unary_expr":{"type":"binary","operator":"⪥","left_expr":{"type":"numeric_atoms","value":1702,"base":4},"right_expr":{"type":"numeric_atoms","value":6057,"base":4}}},"used_operators":["gu96TGCTMs","QbnwKVWMIQ"],"dependent_operators":["XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","WR6HLWljOP","nhYeJWJD5X","f6k1SAg4EE","jLgFTUHLKL","PPChnnnBFF"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1702","layer":2},{"info":"number node, value=6057","layer":2},{"info":"compute binary expreesion, left_input=1702, right_input=6057, op_id = QbnwKVWMIQ binary_op_definition= 'a⪥b = { (b∇⊂⋱(58∣a)) , if (b↢721)<125 ; (↩(508⪒a)) , else }', output=11460","layer":1},{"info":"compute unary expreesion, input=11460, op_id = gu96TGCTMs, unary_op_definition = 'a⊘ = { ((a⨰a)/(∥⊫a)) , if (⨑⩽⪐a)!=520 or (a≧⫂∧486)>62 or (⊄⩳↩a)>=602 ; ((-240)⩚⊴⇥a) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯122212⪥⪩⨒∯1132221⊘=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯122212⪥⪩⨒∯1132221⊘","cot":[{"info":"⪩⨒∯122212⪥⪩⨒∯1132221=⪩⨒∯2303010","layer":1},{"info":"⪩⨒∯2303010⊘=⪩⨒∯0","layer":0}]}
{"id":71,"expression_no_base_symbol":"↡$4961$↳≱$2799$","expression":"↡⪩⨒∯1031201↳≱⪩⨒∯223233","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":103,"operation_count":2,"complexity_ratio":51.5,"tree":{"type":"unary","operator":"↡","unary_expr":{"type":"binary","operator":"↳≱","left_expr":{"type":"numeric_atoms","value":4961,"base":4},"right_expr":{"type":"numeric_atoms","value":2799,"base":4}}},"used_operators":["MXaNJeIAZ3","JwTKLfZU96"],"dependent_operators":["DpFCA1CohY","23Mk6UjR3U","7j4O788W3g","8w2t5hMYqp","sdazOOVcIp","nCS4ZIUYfx","DhbWaqg5eL","WR6HLWljOP","XhwjNDsVaA","T2fj7uvVaJ","7YooWSwCyH","B3sABdIn96"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4961","layer":2},{"info":"number node, value=2799","layer":2},{"info":"compute binary expreesion, left_input=4961, right_input=2799, op_id = JwTKLfZU96 binary_op_definition= 'a↳≱b = { (((a∪⫐104)↢(147/b))⋓((+⊝⨔b)⪹)) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = MXaNJeIAZ3, unary_op_definition = '↡a = { (((772⨳⩥⨓159)⪨≂(a⋷a))↺(⊄⩳↩(⋗⩬⋾a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"↡⪩⨒∯1031201↳≱⪩⨒∯223233=⪩⨒∯0","reverse_text":"⪩⨒∯0=↡⪩⨒∯1031201↳≱⪩⨒∯223233","cot":[{"info":"⪩⨒∯1031201↳≱⪩⨒∯223233=⪩⨒∯0","layer":1},{"info":"↡⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":72,"expression_no_base_symbol":"(⇖$3794$)⊊","expression":"(⇖⪩⨒∯323102)⊊","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":234,"operation_count":2,"complexity_ratio":117.0,"tree":{"type":"unary","operator":"⊊","unary_expr":{"type":"unary","operator":"⇖","unary_expr":{"type":"numeric_atoms","value":3794,"base":4}}},"used_operators":["W9R8I5fN5A","tfWHHpNKUN"],"dependent_operators":["DlLNRPXxWL","aBQ6xLxuTc","8n5YIzOsVS","oZj3VtZNQx","MahUMFw56D","hyuBjUqXlG","aA7tF3KVD3","2DDjHMKMc0","QMFrweE19q","SxTAKzQCrw","8cLx32lpNA","2DQ55sFlQl"],"result":"⪩⨒∯112030233","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3794","layer":2},{"info":"compute unary expreesion, input=3794, op_id = tfWHHpNKUN, unary_op_definition = '⇖a = { (221⨵⪆a) }', output=160","layer":1},{"info":"compute unary expreesion, input=160, op_id = W9R8I5fN5A, unary_op_definition = 'a⊊ = { (((⫛⫱⨽a)∙⊟a)∌((a⇂≾⫗536)⋝⋈⪟(a⫡⨏a))) , if ((a≚⋢)==7 or (a⪘⨀)==15) ; ((a≀⫉(6⪛⫼a))⫠↝⫳) , else }', output=90927","layer":0}],"base":4,"result_base":4,"text":"(⇖⪩⨒∯323102)⊊=⪩⨒∯112030233","reverse_text":"⪩⨒∯112030233=(⇖⪩⨒∯323102)⊊","cot":[{"info":"⇖⪩⨒∯323102=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯2200⊊=⪩⨒∯112030233","layer":0}]}
{"id":73,"expression_no_base_symbol":"($8854$≓∲$1233$)+⇶⊼$6059$⇣⩺⋵$3139$","expression":"(⪩⨒∯2022112≓∲⪩⨒∯103101)+⇶⊼⪩⨒∯1132223⇣⩺⋵⪩⨒∯301003","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":108,"operation_count":3,"complexity_ratio":36.0,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"binary","operator":"≓∲","left_expr":{"type":"numeric_atoms","value":8854,"base":4},"right_expr":{"type":"numeric_atoms","value":1233,"base":4}},"right_expr":{"type":"binary","operator":"⇣⩺⋵","left_expr":{"type":"numeric_atoms","value":6059,"base":4},"right_expr":{"type":"numeric_atoms","value":3139,"base":4}}},"used_operators":["TpPTUOHfaN","s1XTVnmDOJ","F4yD0voBRQ"],"dependent_operators":["AHs5Up7iyr","HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu","NTOWxs364D","KPf6cnQVty","8jW3W4yZS5","12rbrZMWeM","g55IO6H4Gj","2DlMacCsIx"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8854","layer":2},{"info":"number node, value=1233","layer":2},{"info":"compute binary expreesion, left_input=8854, right_input=1233, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=89323","layer":1},{"info":"number node, value=6059","layer":2},{"info":"number node, value=3139","layer":2},{"info":"compute binary expreesion, left_input=6059, right_input=3139, op_id = F4yD0voBRQ binary_op_definition= 'a⇣⩺⋵b = { (((a⩨565)∺≝⩲(5⨸⪁a))⩚⊴⇥(↯⪼(a⋳⪒b))) }', output=-260","layer":1},{"info":"compute binary expreesion, left_input=89323, right_input=-260, op_id = TpPTUOHfaN binary_op_definition= 'a+⇶⊼b = {b, if b == 0; (a)≹⇙⪍(a+⇶⊼(b-1)), if b > 0 and abs(b) < 100; -(a)≹⇙⪍(a+⇶⊼(b+1)), if b < 0 and abs(b) < 100; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2022112≓∲⪩⨒∯103101)+⇶⊼⪩⨒∯1132223⇣⩺⋵⪩⨒∯301003=NaN","reverse_text":"NaN=(⪩⨒∯2022112≓∲⪩⨒∯103101)+⇶⊼⪩⨒∯1132223⇣⩺⋵⪩⨒∯301003","cot":[{"info":"⪩⨒∯2022112≓∲⪩⨒∯103101=⪩⨒∯111303223","layer":1},{"info":"⪩⨒∯1132223⇣⩺⋵⪩⨒∯301003=⪩⨒∯-10010","layer":1},{"info":"⪩⨒∯111303223+⇶⊼⪩⨒∯-10010=NaN","layer":0}]}
{"id":74,"expression_no_base_symbol":"(≱⇩⩕$1265$)⊢($6575$∖$4237$)","expression":"(≱⇩⩕⪩⨒∯103301)⊢(⪩⨒∯1212233∖⪩⨒∯1002031)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":568,"operation_count":3,"complexity_ratio":189.33333333333334,"tree":{"type":"binary","operator":"⊢","left_expr":{"type":"unary","operator":"≱⇩⩕","unary_expr":{"type":"numeric_atoms","value":1265,"base":4}},"right_expr":{"type":"binary","operator":"∖","left_expr":{"type":"numeric_atoms","value":6575,"base":4},"right_expr":{"type":"numeric_atoms","value":4237,"base":4}}},"used_operators":["5twsqlHp2o","3DZMoQKiUl","tXD093vOjl"],"dependent_operators":["P8v4zCKN1o","Qy55tPpLXF","BjRHVeLaeN","DZ8iAZOCBD","7j4O788W3g","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","14qkJME0vr","D4vGDi5EA2","2td37pGCOC","AFVx7xoS7T","12rbrZMWeM","xNBdhnnwKq","rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC"],"result":"⪩⨒∯-13112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1265","layer":2},{"info":"compute unary expreesion, input=1265, op_id = 3DZMoQKiUl, unary_op_definition = '≱⇩⩕a = { (((a⋳⪒a)⊭∹↮)⇌⫙⪟a) }', output=113","layer":1},{"info":"number node, value=6575","layer":2},{"info":"number node, value=4237","layer":2},{"info":"compute binary expreesion, left_input=6575, right_input=4237, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=113, right_input=0, op_id = 5twsqlHp2o binary_op_definition= 'a⊢b = { (((225⫩⊇)⊉≛↸(∥⊫a))⨵⪆(25⊉≛↸(b⋥≓≎47))) , if (a≦≮≮)==364 ; (((b⊦⊿)⪨≂(⩦⩻⨪b))↺((⨞⊢a)⪨≂(-1))) , else }', output=-470","layer":0}],"base":4,"result_base":4,"text":"(≱⇩⩕⪩⨒∯103301)⊢(⪩⨒∯1212233∖⪩⨒∯1002031)=⪩⨒∯-13112","reverse_text":"⪩⨒∯-13112=(≱⇩⩕⪩⨒∯103301)⊢(⪩⨒∯1212233∖⪩⨒∯1002031)","cot":[{"info":"≱⇩⩕⪩⨒∯103301=⪩⨒∯1301","layer":1},{"info":"⪩⨒∯1212233∖⪩⨒∯1002031=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1301⊢⪩⨒∯0=⪩⨒∯-13112","layer":0}]}
{"id":75,"expression_no_base_symbol":"$2344$⫥∨⫟$1567$↺($3487$⊀⩕)","expression":"⪩⨒∯210220⫥∨⫟⪩⨒∯120133↺(⪩⨒∯312133⊀⩕)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1415,"operation_count":3,"complexity_ratio":471.6666666666667,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":2344,"base":4},"right_expr":{"type":"numeric_atoms","value":1567,"base":4}},"right_expr":{"type":"unary","operator":"⊀⩕","unary_expr":{"type":"numeric_atoms","value":3487,"base":4}}},"used_operators":["7j4O788W3g","KYD54nUTWz","r0FS3hW4cC"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","8HhzD0ZcuI","rGHVDoGpnC","rGHVDoGpnC","nhYeJWJD5X"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2344","layer":2},{"info":"number node, value=1567","layer":2},{"info":"compute binary expreesion, left_input=2344, right_input=1567, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=3487","layer":2},{"info":"compute unary expreesion, input=3487, op_id = r0FS3hW4cC, unary_op_definition = 'a⊀⩕ = { (a⨟⋌⩍(181∇⊂⋱a)) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=0, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯210220⫥∨⫟⪩⨒∯120133↺(⪩⨒∯312133⊀⩕)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯210220⫥∨⫟⪩⨒∯120133↺(⪩⨒∯312133⊀⩕)","cot":[{"info":"⪩⨒∯210220⫥∨⫟⪩⨒∯120133=NaN","layer":1},{"info":"⪩⨒∯312133⊀⩕=⪩⨒∯0","layer":1},{"info":"NaN↺⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":76,"expression_no_base_symbol":"($8774$⩱)⨚⇆($2804$≳⇉$6924$)","expression":"(⪩⨒∯2021012⩱)⨚⇆(⪩⨒∯223310≳⇉⪩⨒∯1230030)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":14121,"operation_count":3,"complexity_ratio":4707.0,"tree":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"unary","operator":"⩱","unary_expr":{"type":"numeric_atoms","value":8774,"base":4}},"right_expr":{"type":"binary","operator":"≳⇉","left_expr":{"type":"numeric_atoms","value":2804,"base":4},"right_expr":{"type":"numeric_atoms","value":6924,"base":4}}},"used_operators":["lwHaAYXP2r","uyq1hVkAcj","V0kx6qeWkN"],"dependent_operators":["gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi","DpFCA1CohY","7j4O788W3g","f6k1SAg4EE","g55IO6H4Gj","COABgblf1C","KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls"],"result":"-Inf","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8774","layer":2},{"info":"compute unary expreesion, input=8774, op_id = uyq1hVkAcj, unary_op_definition = 'a⩱ = { ((⋗⩬⋾(a⊭↱a))↺((a⨸⪁a)⪒(a⨸⪁125))) }', output=-52894","layer":1},{"info":"number node, value=2804","layer":2},{"info":"number node, value=6924","layer":2},{"info":"compute binary expreesion, left_input=2804, right_input=6924, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-52894, right_input=nan, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=-inf","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2021012⩱)⨚⇆(⪩⨒∯223310≳⇉⪩⨒∯1230030)=-Inf","reverse_text":"-Inf=(⪩⨒∯2021012⩱)⨚⇆(⪩⨒∯223310≳⇉⪩⨒∯1230030)","cot":[{"info":"⪩⨒∯2021012⩱=⪩⨒∯-30322132","layer":1},{"info":"⪩⨒∯223310≳⇉⪩⨒∯1230030=NaN","layer":1},{"info":"⪩⨒∯-30322132⨚⇆NaN=-Inf","layer":0}]}
{"id":77,"expression_no_base_symbol":"($6691$⪔⊥$3552$)⇻⋧≁($7690$⩹$1915$)","expression":"(⪩⨒∯1220203⪔⊥⪩⨒∯313200)⇻⋧≁(⪩⨒∯1320022⩹⪩⨒∯131323)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19520,"operation_count":3,"complexity_ratio":6506.666666666667,"tree":{"type":"binary","operator":"⇻⋧≁","left_expr":{"type":"binary","operator":"⪔⊥","left_expr":{"type":"numeric_atoms","value":6691,"base":4},"right_expr":{"type":"numeric_atoms","value":3552,"base":4}},"right_expr":{"type":"binary","operator":"⩹","left_expr":{"type":"numeric_atoms","value":7690,"base":4},"right_expr":{"type":"numeric_atoms","value":1915,"base":4}}},"used_operators":["jCPkEVoL5K","HJ9erzHUuu","2Wsdkap16l"],"dependent_operators":["eLxqMNBOBk","XnXgA4xnOs","3EYGwJThht","XTarYq4gQB","59igzFyhWz","dfKe02y8D2","X99M06cbEe","eLAdDNolq6","rysDP5nf3Z","7j4O788W3g","tifHPKVTfV","8w2t5hMYqp","sdazOOVcIp","2td37pGCOC","COABgblf1C","rysDP5nf3Z","NTOWxs364D","23Mk6UjR3U","XIabStNQrY","2DDjHMKMc0","12rbrZMWeM","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx"],"result":"⪩⨒∯-12333","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6691","layer":2},{"info":"number node, value=3552","layer":2},{"info":"compute binary expreesion, left_input=6691, right_input=3552, op_id = HJ9erzHUuu binary_op_definition= 'a⪔⊥b = { (⩦⩻⨪(≤/(315⇼⇔∾a))) , if b<175 ; ((⊄⩳↩(b-b))⇼⇔∾((b⪨≂a)⊭↱(a↺b))) , else }', output=19461","layer":1},{"info":"number node, value=7690","layer":2},{"info":"number node, value=1915","layer":2},{"info":"compute binary expreesion, left_input=7690, right_input=1915, op_id = 2Wsdkap16l binary_op_definition= 'a⩹b = { (b-((b⨳⩥⨓b)⨸⪁(1⋝⋈⪟b))) , if (b⇋≉)!=246 ; (((a⇋≉)⨰(a⋷a))⋳⪒((a⩚⊴⇥a)⨳⩥⨓(a≧⫂∧a))) , else }', output=1913","layer":1},{"info":"compute binary expreesion, left_input=19461, right_input=1913, op_id = jCPkEVoL5K binary_op_definition= 'a⇻⋧≁b = { ((⫓⪴a)⫚↹⊑(54≫≃)) , if (a∵≐)<=35 or a>411 ; ((⪝⪂⫅b)⇄(290⨑≵⋬a)) , else }', output=-447","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1220203⪔⊥⪩⨒∯313200)⇻⋧≁(⪩⨒∯1320022⩹⪩⨒∯131323)=⪩⨒∯-12333","reverse_text":"⪩⨒∯-12333=(⪩⨒∯1220203⪔⊥⪩⨒∯313200)⇻⋧≁(⪩⨒∯1320022⩹⪩⨒∯131323)","cot":[{"info":"⪩⨒∯1220203⪔⊥⪩⨒∯313200=⪩⨒∯10300011","layer":1},{"info":"⪩⨒∯1320022⩹⪩⨒∯131323=⪩⨒∯131321","layer":1},{"info":"⪩⨒∯10300011⇻⋧≁⪩⨒∯131321=⪩⨒∯-12333","layer":0}]}
{"id":78,"expression_no_base_symbol":"⇖⫷⫕$3302$∌$3431$","expression":"⇖⫷⫕⪩⨒∯303212∌⪩⨒∯311213","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":759,"operation_count":2,"complexity_ratio":379.5,"tree":{"type":"unary","operator":"⇖⫷⫕","unary_expr":{"type":"binary","operator":"∌","left_expr":{"type":"numeric_atoms","value":3302,"base":4},"right_expr":{"type":"numeric_atoms","value":3431,"base":4}}},"used_operators":["UHmRx3INFg","8cLx32lpNA"],"dependent_operators":["DE7zCoGJt9","FyVja0WsTP","oZj3VtZNQx","DyGG3AbaNP","N41Kp7NANJ","7j4O788W3g","t8gj7n24qd"],"result":"⪩⨒∯230012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3302","layer":2},{"info":"number node, value=3431","layer":2},{"info":"compute binary expreesion, left_input=3302, right_input=3431, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-3431","layer":1},{"info":"compute unary expreesion, input=-3431, op_id = UHmRx3INFg, unary_op_definition = '⇖⫷⫕a = { ((a∼125)≀⫉(↞≼(a⊱⇼⊻51))) }', output=2822","layer":0}],"base":4,"result_base":4,"text":"⇖⫷⫕⪩⨒∯303212∌⪩⨒∯311213=⪩⨒∯230012","reverse_text":"⪩⨒∯230012=⇖⫷⫕⪩⨒∯303212∌⪩⨒∯311213","cot":[{"info":"⪩⨒∯303212∌⪩⨒∯311213=⪩⨒∯-311213","layer":1},{"info":"⇖⫷⫕⪩⨒∯-311213=⪩⨒∯230012","layer":0}]}
{"id":79,"expression_no_base_symbol":"(⇖$3246$)⨚⇆$2242$+⪬∐$4250$","expression":"(⇖⪩⨒∯302232)⨚⇆⪩⨒∯203002+⪬∐⪩⨒∯1002122","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1155,"operation_count":3,"complexity_ratio":385.0,"tree":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"unary","operator":"⇖","unary_expr":{"type":"numeric_atoms","value":3246,"base":4}},"right_expr":{"type":"binary","operator":"+⪬∐","left_expr":{"type":"numeric_atoms","value":2242,"base":4},"right_expr":{"type":"numeric_atoms","value":4250,"base":4}}},"used_operators":["lwHaAYXP2r","tfWHHpNKUN","2GS7woTJqF"],"dependent_operators":["gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi","2DQ55sFlQl","g55IO6H4Gj","D4vGDi5EA2"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3246","layer":2},{"info":"compute unary expreesion, input=3246, op_id = tfWHHpNKUN, unary_op_definition = '⇖a = { (221⨵⪆a) }', output=160","layer":1},{"info":"number node, value=2242","layer":2},{"info":"number node, value=4250","layer":2},{"info":"compute binary expreesion, left_input=2242, right_input=4250, op_id = 2GS7woTJqF binary_op_definition= 'a+⪬∐b = { (a≦≮≮) , if b!=63 ; (b⨸⪁575) , else }', output=-6726","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=-6726, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⇖⪩⨒∯302232)⨚⇆⪩⨒∯203002+⪬∐⪩⨒∯1002122=NaN","reverse_text":"NaN=(⇖⪩⨒∯302232)⨚⇆⪩⨒∯203002+⪬∐⪩⨒∯1002122","cot":[{"info":"⇖⪩⨒∯302232=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯203002+⪬∐⪩⨒∯1002122=⪩⨒∯-1221012","layer":1},{"info":"⪩⨒∯2200⨚⇆⪩⨒∯-1221012=NaN","layer":0}]}
{"id":80,"expression_no_base_symbol":"$1159$⇷$4067$∖($6447$⋹)","expression":"⪩⨒∯102013⇷⪩⨒∯333203∖(⪩⨒∯1210233⋹)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16478,"operation_count":3,"complexity_ratio":5492.666666666667,"tree":{"type":"binary","operator":"∖","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":1159,"base":4},"right_expr":{"type":"numeric_atoms","value":4067,"base":4}},"right_expr":{"type":"unary","operator":"⋹","unary_expr":{"type":"numeric_atoms","value":6447,"base":4}}},"used_operators":["tXD093vOjl","mp7IySMOzn","opAxDRczMr"],"dependent_operators":["rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","13rbtpv6ld","mp7IySMOzn","z63VuFQld9","aN9a90urxU","27wFxooxGf","SVb2v531z1","eewbuw0ToL"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1159","layer":2},{"info":"number node, value=4067","layer":2},{"info":"compute binary expreesion, left_input=1159, right_input=4067, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=8134","layer":1},{"info":"number node, value=6447","layer":2},{"info":"compute unary expreesion, input=6447, op_id = opAxDRczMr, unary_op_definition = 'a⋹ = { ((⨴⫝a)⇷(a↤⩊a)) , if (a≃⋄)<20 or (⊢≑≆a)<=20 ; ((a⨰a)∧) , else }', output=-20","layer":1},{"info":"compute binary expreesion, left_input=8134, right_input=-20, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102013⇷⪩⨒∯333203∖(⪩⨒∯1210233⋹)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯102013⇷⪩⨒∯333203∖(⪩⨒∯1210233⋹)","cot":[{"info":"⪩⨒∯102013⇷⪩⨒∯333203=⪩⨒∯1333012","layer":1},{"info":"⪩⨒∯1210233⋹=⪩⨒∯-110","layer":1},{"info":"⪩⨒∯1333012∖⪩⨒∯-110=⪩⨒∯0","layer":0}]}
{"id":81,"expression_no_base_symbol":"(≤/$4363$)⨽∌($1527$≨$5488$)","expression":"(≤/⪩⨒∯1010023)⨽∌(⪩⨒∯113313≨⪩⨒∯1111300)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":225,"operation_count":3,"complexity_ratio":75.0,"tree":{"type":"binary","operator":"⨽∌","left_expr":{"type":"unary","operator":"≤/","unary_expr":{"type":"numeric_atoms","value":4363,"base":4}},"right_expr":{"type":"binary","operator":"≨","left_expr":{"type":"numeric_atoms","value":1527,"base":4},"right_expr":{"type":"numeric_atoms","value":5488,"base":4}}},"used_operators":["9samAPKr6k","eLAdDNolq6","0KMCeP1Jsh"],"dependent_operators":["YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu","rysDP5nf3Z","jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4363","layer":2},{"info":"compute unary expreesion, input=4363, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-3879","layer":1},{"info":"number node, value=1527","layer":2},{"info":"number node, value=5488","layer":2},{"info":"compute binary expreesion, left_input=1527, right_input=5488, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-12794","layer":1},{"info":"compute binary expreesion, left_input=-3879, right_input=-12794, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(≤/⪩⨒∯1010023)⨽∌(⪩⨒∯113313≨⪩⨒∯1111300)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(≤/⪩⨒∯1010023)⨽∌(⪩⨒∯113313≨⪩⨒∯1111300)","cot":[{"info":"≤/⪩⨒∯1010023=⪩⨒∯-330213","layer":1},{"info":"⪩⨒∯113313≨⪩⨒∯1111300=⪩⨒∯-3013322","layer":1},{"info":"⪩⨒∯-330213⨽∌⪩⨒∯-3013322=⪩⨒∯0","layer":0}]}
{"id":82,"expression_no_base_symbol":"⇐($1610$∖$3102$)","expression":"⇐(⪩⨒∯121022∖⪩⨒∯300132)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":471,"operation_count":2,"complexity_ratio":235.5,"tree":{"type":"unary","operator":"⇐","unary_expr":{"type":"binary","operator":"∖","left_expr":{"type":"numeric_atoms","value":1610,"base":4},"right_expr":{"type":"numeric_atoms","value":3102,"base":4}}},"used_operators":["nmZMaaE0Q9","tXD093vOjl"],"dependent_operators":["23Mk6UjR3U","ocnLzx9CaJ","SWo3A1KBJH","nREPSIbpBE","k8jYdgA6NY","u6S6b8DprG","rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1610","layer":2},{"info":"number node, value=3102","layer":2},{"info":"compute binary expreesion, left_input=1610, right_input=3102, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = nmZMaaE0Q9, unary_op_definition = '⇐a = { (((⇋↷a)⋷(a⩼⇪↪a))%(↽≂(a⨚a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⇐(⪩⨒∯121022∖⪩⨒∯300132)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⇐(⪩⨒∯121022∖⪩⨒∯300132)","cot":[{"info":"⪩⨒∯121022∖⪩⨒∯300132=⪩⨒∯0","layer":1},{"info":"⇐⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":83,"expression_no_base_symbol":"($2569$⪔$5034$)≴⪞⇿(⨈⫕$2284$)","expression":"(⪩⨒∯220021⪔⪩⨒∯1032222)≴⪞⇿(⨈⫕⪩⨒∯203230)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5730,"operation_count":3,"complexity_ratio":1910.0,"tree":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"binary","operator":"⪔","left_expr":{"type":"numeric_atoms","value":2569,"base":4},"right_expr":{"type":"numeric_atoms","value":5034,"base":4}},"right_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":2284,"base":4}}},"used_operators":["lvlrscuwVU","GjBEYRfMaF","megm06wKyl"],"dependent_operators":["DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP","YjI8oCXuph","8INZBEW696","dWAJyo7jo9","nREPSIbpBE","2DDjHMKMc0","IWmyXbctLI","PoHhknlbAi","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q"],"result":"⪩⨒∯30112113","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2569","layer":2},{"info":"number node, value=5034","layer":2},{"info":"compute binary expreesion, left_input=2569, right_input=5034, op_id = GjBEYRfMaF binary_op_definition= 'a⪔b = { (((⫇a)∓⋝(61⪢b))⪮%⊝((b⋝⋈⪟b)⨚(a≀⩗∶a))) }', output=450","layer":1},{"info":"number node, value=2284","layer":2},{"info":"compute unary expreesion, input=2284, op_id = megm06wKyl, unary_op_definition = '⨈⫕a = { (((a+a)⊦⊿)+⇶⊼123) , if (a⩤)!=46 and a==442 and (+⊝⨔a)!=531 ; (↯⪼(⊥(8⨁⊸⫻))) , else }', output=-21","layer":1},{"info":"compute binary expreesion, left_input=450, right_input=-21, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=50583","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯220021⪔⪩⨒∯1032222)≴⪞⇿(⨈⫕⪩⨒∯203230)=⪩⨒∯30112113","reverse_text":"⪩⨒∯30112113=(⪩⨒∯220021⪔⪩⨒∯1032222)≴⪞⇿(⨈⫕⪩⨒∯203230)","cot":[{"info":"⪩⨒∯220021⪔⪩⨒∯1032222=⪩⨒∯13002","layer":1},{"info":"⨈⫕⪩⨒∯203230=⪩⨒∯-111","layer":1},{"info":"⪩⨒∯13002≴⪞⇿⪩⨒∯-111=⪩⨒∯30112113","layer":0}]}
{"id":84,"expression_no_base_symbol":"⊬↢$1303$⇂≾⫗$3479$","expression":"⊬↢⪩⨒∯110113⇂≾⫗⪩⨒∯312113","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2737,"operation_count":2,"complexity_ratio":1368.5,"tree":{"type":"unary","operator":"⊬↢","unary_expr":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"numeric_atoms","value":1303,"base":4},"right_expr":{"type":"numeric_atoms","value":3479,"base":4}}},"used_operators":["WPoGxAaPR1","aBQ6xLxuTc"],"dependent_operators":["XGcMNugi78","d7ASUq0ydm","OwUj7dcsQK","FyVja0WsTP","1eCjFl0mb9","j6NVkjMzuk","SL6IHkK8vl","MRPaB8lBjK","yyfyN0ffXY","3Oe9XWJUTD","3tVxb0NHM4","8cLx32lpNA","g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U"],"result":"⪩⨒∯22110","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1303","layer":2},{"info":"number node, value=3479","layer":2},{"info":"compute binary expreesion, left_input=1303, right_input=3479, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-676","layer":1},{"info":"compute unary expreesion, input=-676, op_id = WPoGxAaPR1, unary_op_definition = '⊬↢a = { (((a⫞⩸⩒a)⊝⪿⪼(a⫯⪬∳a))⪎↠((a⨀⨒)↸(∐⩳⋚a))) , if (∓a)>278 ; (((a↙a)⊱⇼⊻(a∌480))⇉⇱⇎) , else }', output=660","layer":0}],"base":4,"result_base":4,"text":"⊬↢⪩⨒∯110113⇂≾⫗⪩⨒∯312113=⪩⨒∯22110","reverse_text":"⪩⨒∯22110=⊬↢⪩⨒∯110113⇂≾⫗⪩⨒∯312113","cot":[{"info":"⪩⨒∯110113⇂≾⫗⪩⨒∯312113=⪩⨒∯-22210","layer":1},{"info":"⊬↢⪩⨒∯-22210=⪩⨒∯22110","layer":0}]}
{"id":85,"expression_no_base_symbol":"($2975$↹⊜$1628$)↳≱($1430$⪉⨛$1902$)","expression":"(⪩⨒∯232133↹⊜⪩⨒∯121130)↳≱(⪩⨒∯112112⪉⨛⪩⨒∯131232)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":131,"operation_count":3,"complexity_ratio":43.666666666666664,"tree":{"type":"binary","operator":"↳≱","left_expr":{"type":"binary","operator":"↹⊜","left_expr":{"type":"numeric_atoms","value":2975,"base":4},"right_expr":{"type":"numeric_atoms","value":1628,"base":4}},"right_expr":{"type":"binary","operator":"⪉⨛","left_expr":{"type":"numeric_atoms","value":1430,"base":4},"right_expr":{"type":"numeric_atoms","value":1902,"base":4}}},"used_operators":["JwTKLfZU96","9bazX3JMtO","EWw2JM7wp4"],"dependent_operators":["DhbWaqg5eL","WR6HLWljOP","XhwjNDsVaA","T2fj7uvVaJ","7YooWSwCyH","B3sABdIn96","9FxExcQeMw","rysDP5nf3Z","23Mk6UjR3U","tifHPKVTfV","eH2TOUuTDT","DIvbN7qnHd","NTOWxs364D","tifHPKVTfV","12rbrZMWeM","i8ToyICDmI","eewbuw0ToL"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2975","layer":2},{"info":"number node, value=1628","layer":2},{"info":"compute binary expreesion, left_input=2975, right_input=1628, op_id = 9bazX3JMtO binary_op_definition= 'a↹⊜b = { (((a⊠≄⫣)⩷∴(b-a))⩷∴((a⋷b)⇼⇔∾(b⪐))) }', output=-658","layer":1},{"info":"number node, value=1430","layer":2},{"info":"number node, value=1902","layer":2},{"info":"compute binary expreesion, left_input=1430, right_input=1902, op_id = EWw2JM7wp4 binary_op_definition= 'a⪉⨛b = { (((82⇼⇔∾a)⩚⊴⇥a)⩚⊴⇥((b∲⫓a)⋳⪒(a⨰b))) }', output=2603","layer":1},{"info":"compute binary expreesion, left_input=-658, right_input=2603, op_id = JwTKLfZU96 binary_op_definition= 'a↳≱b = { (((a∪⫐104)↢(147/b))⋓((+⊝⨔b)⪹)) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯232133↹⊜⪩⨒∯121130)↳≱(⪩⨒∯112112⪉⨛⪩⨒∯131232)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯232133↹⊜⪩⨒∯121130)↳≱(⪩⨒∯112112⪉⨛⪩⨒∯131232)","cot":[{"info":"⪩⨒∯232133↹⊜⪩⨒∯121130=⪩⨒∯-22102","layer":1},{"info":"⪩⨒∯112112⪉⨛⪩⨒∯131232=⪩⨒∯220223","layer":1},{"info":"⪩⨒∯-22102↳≱⪩⨒∯220223=⪩⨒∯0","layer":0}]}
{"id":86,"expression_no_base_symbol":"(⫛⫱⨽$2429$)≓∲$2971$∑⇟⊟$4543$","expression":"(⫛⫱⨽⪩⨒∯211331)≓∲⪩⨒∯232123∑⇟⊟⪩⨒∯1012333","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1463,"operation_count":3,"complexity_ratio":487.6666666666667,"tree":{"type":"binary","operator":"≓∲","left_expr":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"numeric_atoms","value":2429,"base":4}},"right_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":2971,"base":4},"right_expr":{"type":"numeric_atoms","value":4543,"base":4}}},"used_operators":["s1XTVnmDOJ","DlLNRPXxWL","U7g4x0WXJJ"],"dependent_operators":["HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu","rGHVDoGpnC","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2429","layer":2},{"info":"compute unary expreesion, input=2429, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"number node, value=2971","layer":2},{"info":"number node, value=4543","layer":2},{"info":"compute binary expreesion, left_input=2971, right_input=4543, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⫛⫱⨽⪩⨒∯211331)≓∲⪩⨒∯232123∑⇟⊟⪩⨒∯1012333=NaN","reverse_text":"NaN=(⫛⫱⨽⪩⨒∯211331)≓∲⪩⨒∯232123∑⇟⊟⪩⨒∯1012333","cot":[{"info":"⫛⫱⨽⪩⨒∯211331=⪩⨒∯0","layer":1},{"info":"⪩⨒∯232123∑⇟⊟⪩⨒∯1012333=NaN","layer":1},{"info":"⪩⨒∯0≓∲NaN=NaN","layer":0}]}
{"id":87,"expression_no_base_symbol":"(↽≂$1399$)∙∹∝$3482$⨑⩅≇$2969$","expression":"(↽≂⪩⨒∯111313)∙∹∝⪩⨒∯312122⨑⩅≇⪩⨒∯232121","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3031,"operation_count":3,"complexity_ratio":1010.3333333333334,"tree":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"unary","operator":"↽≂","unary_expr":{"type":"numeric_atoms","value":1399,"base":4}},"right_expr":{"type":"binary","operator":"⨑⩅≇","left_expr":{"type":"numeric_atoms","value":3482,"base":4},"right_expr":{"type":"numeric_atoms","value":2969,"base":4}}},"used_operators":["HmxsFra2vL","u6S6b8DprG","h92wMvzauj"],"dependent_operators":["BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","s3Fd5m9Dh2","3sJ7IOPOlU","nREPSIbpBE","9Isq31Ruls","umQnsF7QlU","8HhzD0ZcuI","u6S6b8DprG","DmTXOeWf9t","AFVx7xoS7T","jLgFTUHLKL","oacrs7FA3X","xNBdhnnwKq"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1399","layer":2},{"info":"compute unary expreesion, input=1399, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-2798","layer":1},{"info":"number node, value=3482","layer":2},{"info":"number node, value=2969","layer":2},{"info":"compute binary expreesion, left_input=3482, right_input=2969, op_id = h92wMvzauj binary_op_definition= 'a⨑⩅≇b = { (((a⪇≇⋚b)⊬⨰(b⨽582))∌↝a) , if (↽≂a)<10 or (b⊭∹↮)==22 ; ((a⊲⩕⊾(↩a))⪕((a⨚243)⇌⫙⪟(b⪘⫢b))) , else }', output=-10446","layer":1},{"info":"compute binary expreesion, left_input=-2798, right_input=-10446, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(↽≂⪩⨒∯111313)∙∹∝⪩⨒∯312122⨑⩅≇⪩⨒∯232121=⪩⨒∯0","reverse_text":"⪩⨒∯0=(↽≂⪩⨒∯111313)∙∹∝⪩⨒∯312122⨑⩅≇⪩⨒∯232121","cot":[{"info":"↽≂⪩⨒∯111313=⪩⨒∯-223232","layer":1},{"info":"⪩⨒∯312122⨑⩅≇⪩⨒∯232121=⪩⨒∯-2203032","layer":1},{"info":"⪩⨒∯-223232∙∹∝⪩⨒∯-2203032=⪩⨒∯0","layer":0}]}
{"id":88,"expression_no_base_symbol":"$1052$⊱⇼⊻$1293$⋥≓≎$5438$≄⊠$5140$","expression":"⪩⨒∯100130⊱⇼⊻⪩⨒∯110031⋥≓≎⪩⨒∯1110332≄⊠⪩⨒∯1100110","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":70,"operation_count":3,"complexity_ratio":23.333333333333332,"tree":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"numeric_atoms","value":1052,"base":4},"right_expr":{"type":"numeric_atoms","value":1293,"base":4}},"right_expr":{"type":"binary","operator":"≄⊠","left_expr":{"type":"numeric_atoms","value":5438,"base":4},"right_expr":{"type":"numeric_atoms","value":5140,"base":4}}},"used_operators":["Qy55tPpLXF","FyVja0WsTP","vXNesLlMH1"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI"],"result":"⪩⨒∯222111213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1052","layer":2},{"info":"number node, value=1293","layer":2},{"info":"compute binary expreesion, left_input=1052, right_input=1293, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":1},{"info":"number node, value=5438","layer":2},{"info":"number node, value=5140","layer":2},{"info":"compute binary expreesion, left_input=5438, right_input=5140, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=86908","layer":1},{"info":"compute binary expreesion, left_input=434, right_input=86908, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=173415","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯100130⊱⇼⊻⪩⨒∯110031⋥≓≎⪩⨒∯1110332≄⊠⪩⨒∯1100110=⪩⨒∯222111213","reverse_text":"⪩⨒∯222111213=⪩⨒∯100130⊱⇼⊻⪩⨒∯110031⋥≓≎⪩⨒∯1110332≄⊠⪩⨒∯1100110","cot":[{"info":"⪩⨒∯100130⊱⇼⊻⪩⨒∯110031=⪩⨒∯12302","layer":1},{"info":"⪩⨒∯1110332≄⊠⪩⨒∯1100110=⪩⨒∯111031330","layer":1},{"info":"⪩⨒∯12302⋥≓≎⪩⨒∯111031330=⪩⨒∯222111213","layer":0}]}
{"id":89,"expression_no_base_symbol":"($6015$⪁$3304$)∲⫓$6451$⫲≸⪮$1179$","expression":"(⪩⨒∯1131333⪁⪩⨒∯303220)∲⫓⪩⨒∯1210303⫲≸⪮⪩⨒∯102123","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6473980,"operation_count":3,"complexity_ratio":2157993.3333333335,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"⪁","left_expr":{"type":"numeric_atoms","value":6015,"base":4},"right_expr":{"type":"numeric_atoms","value":3304,"base":4}},"right_expr":{"type":"binary","operator":"⫲≸⪮","left_expr":{"type":"numeric_atoms","value":6451,"base":4},"right_expr":{"type":"numeric_atoms","value":1179,"base":4}}},"used_operators":["i8ToyICDmI","I7sXao9hZE","P3lXMJvFrc"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","wxb3vTeyAj","nlCqmYiOvY","tmPS8pqC7x","oWn0xqSxBt","DbCuESL50I"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6015","layer":2},{"info":"number node, value=3304","layer":2},{"info":"compute binary expreesion, left_input=6015, right_input=3304, op_id = I7sXao9hZE binary_op_definition= 'a⪁b = { (((⫶⊄≣b)⨽⪊≇)⪢a) }', output=nan","layer":1},{"info":"number node, value=6451","layer":2},{"info":"number node, value=1179","layer":2},{"info":"compute binary expreesion, left_input=6451, right_input=1179, op_id = P3lXMJvFrc binary_op_definition= 'a⫲≸⪮b = { (⋼∭⪍a) , if (⊙↵-b)>333 ; (a⨪↰⇹b) , else }', output=6451","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=6451, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1131333⪁⪩⨒∯303220)∲⫓⪩⨒∯1210303⫲≸⪮⪩⨒∯102123=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯1131333⪁⪩⨒∯303220)∲⫓⪩⨒∯1210303⫲≸⪮⪩⨒∯102123","cot":[{"info":"⪩⨒∯1131333⪁⪩⨒∯303220=NaN","layer":1},{"info":"⪩⨒∯1210303⫲≸⪮⪩⨒∯102123=⪩⨒∯1210303","layer":1},{"info":"NaN∲⫓⪩⨒∯1210303=⪩⨒∯0","layer":0}]}
{"id":90,"expression_no_base_symbol":"(≸≮$1120$)⫚↹⊑(∟⋨$4529$)","expression":"(≸≮⪩⨒∯101200)⫚↹⊑(∟⋨⪩⨒∯1012301)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":14462,"operation_count":3,"complexity_ratio":4820.666666666667,"tree":{"type":"binary","operator":"⫚↹⊑","left_expr":{"type":"unary","operator":"≸≮","unary_expr":{"type":"numeric_atoms","value":1120,"base":4}},"right_expr":{"type":"unary","operator":"∟⋨","unary_expr":{"type":"numeric_atoms","value":4529,"base":4}}},"used_operators":["dfKe02y8D2","AljMvE3RRm","ctOc4cKSDt"],"dependent_operators":["2DQ55sFlQl","DIvbN7qnHd","t8gj7n24qd","12rbrZMWeM","g55IO6H4Gj","3UMq87Qwqg","QiR2Oyf5Xj","Z57zeUYC9z","6o9Blt3TJ6","kbkesczE7y","oPMjh9089D","Nsiff2A1zJ","7qqUquhhSb","eLAdDNolq6","tmPS8pqC7x"],"result":"⪩⨒∯-12333","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1120","layer":2},{"info":"compute unary expreesion, input=1120, op_id = AljMvE3RRm, unary_op_definition = '≸≮a = { (a⊴((a⨔≚≋a)⫰⋱(∤↝a))) , if (a>367 and (a≬⋮702)!=1) ; (⊀((∷≠a)⩉⊫⨁)) , else }', output=nan","layer":1},{"info":"number node, value=4529","layer":2},{"info":"compute unary expreesion, input=4529, op_id = ctOc4cKSDt, unary_op_definition = '∟⋨a = { (≤/(a⨪↰⇹a)) }', output=-4045","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-4045, op_id = dfKe02y8D2 binary_op_definition= 'a⫚↹⊑b = { ((126⊠≄⫣)⋳⪒((-b)⨵⪆(a⨸⪁b))) }', output=-447","layer":0}],"base":4,"result_base":4,"text":"(≸≮⪩⨒∯101200)⫚↹⊑(∟⋨⪩⨒∯1012301)=⪩⨒∯-12333","reverse_text":"⪩⨒∯-12333=(≸≮⪩⨒∯101200)⫚↹⊑(∟⋨⪩⨒∯1012301)","cot":[{"info":"≸≮⪩⨒∯101200=NaN","layer":1},{"info":"∟⋨⪩⨒∯1012301=⪩⨒∯-333031","layer":1},{"info":"NaN⫚↹⊑⪩⨒∯-333031=⪩⨒∯-12333","layer":0}]}
{"id":91,"expression_no_base_symbol":"($2859$∪⫐$3651$)≄⊠$3315$≨$1093$","expression":"(⪩⨒∯230223∪⫐⪩⨒∯321003)≄⊠⪩⨒∯303303≨⪩⨒∯101011","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":153,"operation_count":3,"complexity_ratio":51.0,"tree":{"type":"binary","operator":"≄⊠","left_expr":{"type":"binary","operator":"∪⫐","left_expr":{"type":"numeric_atoms","value":2859,"base":4},"right_expr":{"type":"numeric_atoms","value":3651,"base":4}},"right_expr":{"type":"binary","operator":"≨","left_expr":{"type":"numeric_atoms","value":3315,"base":4},"right_expr":{"type":"numeric_atoms","value":1093,"base":4}}},"used_operators":["vXNesLlMH1","7YooWSwCyH","0KMCeP1Jsh"],"dependent_operators":["d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI","rJVOvQCfKK","2DDjHMKMc0","jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC"],"result":"⪩⨒∯113130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2859","layer":2},{"info":"number node, value=3651","layer":2},{"info":"compute binary expreesion, left_input=2859, right_input=3651, op_id = 7YooWSwCyH binary_op_definition= 'a∪⫐b = { ((a⋝⋈⪟b)⨎a) }', output=2859","layer":1},{"info":"number node, value=3315","layer":2},{"info":"number node, value=1093","layer":2},{"info":"compute binary expreesion, left_input=3315, right_input=1093, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-30674","layer":1},{"info":"compute binary expreesion, left_input=2859, right_input=-30674, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=1500","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯230223∪⫐⪩⨒∯321003)≄⊠⪩⨒∯303303≨⪩⨒∯101011=⪩⨒∯113130","reverse_text":"⪩⨒∯113130=(⪩⨒∯230223∪⫐⪩⨒∯321003)≄⊠⪩⨒∯303303≨⪩⨒∯101011","cot":[{"info":"⪩⨒∯230223∪⫐⪩⨒∯321003=⪩⨒∯230223","layer":1},{"info":"⪩⨒∯303303≨⪩⨒∯101011=⪩⨒∯-13133102","layer":1},{"info":"⪩⨒∯230223≄⊠⪩⨒∯-13133102=⪩⨒∯113130","layer":0}]}
{"id":92,"expression_no_base_symbol":"(⪲⇎$2825$)%($3742$⇽⩪)","expression":"(⪲⇎⪩⨒∯230021)%(⪩⨒∯322132⇽⩪)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":24,"operation_count":3,"complexity_ratio":8.0,"tree":{"type":"binary","operator":"%","left_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":2825,"base":4}},"right_expr":{"type":"unary","operator":"⇽⩪","unary_expr":{"type":"numeric_atoms","value":3742,"base":4}}},"used_operators":["k8jYdgA6NY","XPYlsWDdGa","FonBHBYJbU"],"dependent_operators":["rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","e1ybzncUwg","23Mk6UjR3U","tifHPKVTfV","g55IO6H4Gj","eewbuw0ToL","AF7qkfDlqP"],"result":"⪩⨒∯1120102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2825","layer":2},{"info":"compute unary expreesion, input=2825, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=5650","layer":1},{"info":"number node, value=3742","layer":2},{"info":"compute unary expreesion, input=3742, op_id = FonBHBYJbU, unary_op_definition = 'a⇽⩪ = { (((≉88)⨰(⨑⩽⪐a))⨸⪁((a+95)⇼⇔∾(a⋷a))) }', output=8006","layer":1},{"info":"compute binary expreesion, left_input=5650, right_input=8006, op_id = k8jYdgA6NY binary_op_definition= 'None', output=5650","layer":0}],"base":4,"result_base":4,"text":"(⪲⇎⪩⨒∯230021)%(⪩⨒∯322132⇽⩪)=⪩⨒∯1120102","reverse_text":"⪩⨒∯1120102=(⪲⇎⪩⨒∯230021)%(⪩⨒∯322132⇽⩪)","cot":[{"info":"⪲⇎⪩⨒∯230021=⪩⨒∯1120102","layer":1},{"info":"⪩⨒∯322132⇽⩪=⪩⨒∯1331012","layer":1},{"info":"⪩⨒∯1120102%⪩⨒∯1331012=⪩⨒∯1120102","layer":0}]}
{"id":93,"expression_no_base_symbol":"($2719$⋻⩜⩜$2714$)⊋≦⊧$2352$⇴∐$1593$","expression":"(⪩⨒∯222133⋻⩜⩜⪩⨒∯222122)⊋≦⊧⪩⨒∯210300⇴∐⪩⨒∯120321","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":38047,"operation_count":3,"complexity_ratio":12682.333333333334,"tree":{"type":"binary","operator":"⊋≦⊧","left_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":2719,"base":4},"right_expr":{"type":"numeric_atoms","value":2714,"base":4}},"right_expr":{"type":"binary","operator":"⇴∐","left_expr":{"type":"numeric_atoms","value":2352,"base":4},"right_expr":{"type":"numeric_atoms","value":1593,"base":4}}},"used_operators":["oRDoc9rAEX","oDCm7WA9JY","HnzytWxmAO"],"dependent_operators":["DZ8iAZOCBD","tifHPKVTfV","sdazOOVcIp","glklzrTFfD","DIvbN7qnHd","12rbrZMWeM","Ph9nP6C5qx","eewbuw0ToL","2td37pGCOC","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2719","layer":2},{"info":"number node, value=2714","layer":2},{"info":"compute binary expreesion, left_input=2719, right_input=2714, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=5438","layer":1},{"info":"number node, value=2352","layer":2},{"info":"number node, value=1593","layer":2},{"info":"compute binary expreesion, left_input=2352, right_input=1593, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=5438, right_input=nan, op_id = oRDoc9rAEX binary_op_definition= 'a⊋≦⊧b = { (((24⊉≛↸a)⊉≛↸(⩦⩻⨪b))⊉≛↸((a⊠≄⫣)⪨≂(b⇼⇔∾a))) , if a<=128 ; (((a⇼⇔∾b)⨁⊸⫻)⇼⇔∾((22⋳⪒a)⨰(a≧⫂∧a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯222133⋻⩜⩜⪩⨒∯222122)⊋≦⊧⪩⨒∯210300⇴∐⪩⨒∯120321=NaN","reverse_text":"NaN=(⪩⨒∯222133⋻⩜⩜⪩⨒∯222122)⊋≦⊧⪩⨒∯210300⇴∐⪩⨒∯120321","cot":[{"info":"⪩⨒∯222133⋻⩜⩜⪩⨒∯222122=⪩⨒∯1110332","layer":1},{"info":"⪩⨒∯210300⇴∐⪩⨒∯120321=NaN","layer":1},{"info":"⪩⨒∯1110332⊋≦⊧NaN=NaN","layer":0}]}
{"id":94,"expression_no_base_symbol":"($2980$⪕$1334$)↞⋁$1950$⊕∕$1287$","expression":"(⪩⨒∯232210⪕⪩⨒∯110312)↞⋁⪩⨒∯132132⊕∕⪩⨒∯110013","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":186,"operation_count":3,"complexity_ratio":62.0,"tree":{"type":"binary","operator":"↞⋁","left_expr":{"type":"binary","operator":"⪕","left_expr":{"type":"numeric_atoms","value":2980,"base":4},"right_expr":{"type":"numeric_atoms","value":1334,"base":4}},"right_expr":{"type":"binary","operator":"⊕∕","left_expr":{"type":"numeric_atoms","value":1950,"base":4},"right_expr":{"type":"numeric_atoms","value":1287,"base":4}}},"used_operators":["RqrPlJkxDo","umQnsF7QlU","9cloC0Ngie"],"dependent_operators":["Uaa54Peajs","CArV6hThFE","13rbtpv6ld","P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF","Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2980","layer":2},{"info":"number node, value=1334","layer":2},{"info":"compute binary expreesion, left_input=2980, right_input=1334, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=5527","layer":1},{"info":"number node, value=1950","layer":2},{"info":"number node, value=1287","layer":2},{"info":"compute binary expreesion, left_input=1950, right_input=1287, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=1950","layer":1},{"info":"compute binary expreesion, left_input=5527, right_input=1950, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯232210⪕⪩⨒∯110312)↞⋁⪩⨒∯132132⊕∕⪩⨒∯110013=NaN","reverse_text":"NaN=(⪩⨒∯232210⪕⪩⨒∯110312)↞⋁⪩⨒∯132132⊕∕⪩⨒∯110013","cot":[{"info":"⪩⨒∯232210⪕⪩⨒∯110312=⪩⨒∯1112113","layer":1},{"info":"⪩⨒∯132132⊕∕⪩⨒∯110013=⪩⨒∯132132","layer":1},{"info":"⪩⨒∯1112113↞⋁⪩⨒∯132132=NaN","layer":0}]}
{"id":95,"expression_no_base_symbol":"($2086$⫠)∙∹∝$1526$⨚⇆$4181$","expression":"(⪩⨒∯200212⫠)∙∹∝⪩⨒∯113312⨚⇆⪩⨒∯1001111","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":39950,"operation_count":3,"complexity_ratio":13316.666666666666,"tree":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"unary","operator":"⫠","unary_expr":{"type":"numeric_atoms","value":2086,"base":4}},"right_expr":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"numeric_atoms","value":1526,"base":4},"right_expr":{"type":"numeric_atoms","value":4181,"base":4}}},"used_operators":["HmxsFra2vL","6SnOT2rOjz","lwHaAYXP2r"],"dependent_operators":["BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","Bmrmz2XGnR","tmPS8pqC7x","mp7IySMOzn","gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2086","layer":2},{"info":"compute unary expreesion, input=2086, op_id = 6SnOT2rOjz, unary_op_definition = 'a⫠ = { ((a⇷0)⨪↰⇹(a≚⊃≕a)) }', output=0","layer":1},{"info":"number node, value=1526","layer":2},{"info":"number node, value=4181","layer":2},{"info":"compute binary expreesion, left_input=1526, right_input=4181, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯200212⫠)∙∹∝⪩⨒∯113312⨚⇆⪩⨒∯1001111=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯200212⫠)∙∹∝⪩⨒∯113312⨚⇆⪩⨒∯1001111","cot":[{"info":"⪩⨒∯200212⫠=⪩⨒∯0","layer":1},{"info":"⪩⨒∯113312⨚⇆⪩⨒∯1001111=NaN","layer":1},{"info":"⪩⨒∯0∙∹∝NaN=⪩⨒∯0","layer":0}]}
{"id":96,"expression_no_base_symbol":"$4381$↳∿⪆$1345$⨭⪣$5121$⇍⊗$3557$","expression":"⪩⨒∯1010131↳∿⪆⪩⨒∯111001⨭⪣⪩⨒∯1100001⇍⊗⪩⨒∯313211","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2466,"operation_count":3,"complexity_ratio":822.0,"tree":{"type":"binary","operator":"⨭⪣","left_expr":{"type":"binary","operator":"↳∿⪆","left_expr":{"type":"numeric_atoms","value":4381,"base":4},"right_expr":{"type":"numeric_atoms","value":1345,"base":4}},"right_expr":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"numeric_atoms","value":5121,"base":4},"right_expr":{"type":"numeric_atoms","value":3557,"base":4}}},"used_operators":["kn8WO9XteQ","Cw4SuJJGHO","5uvYHDjeKN"],"dependent_operators":["vRio1gEz1j","61wBmkZwlr","SWo3A1KBJH","8jW3W4yZS5","LkLIoiE525","Y7wcNGrDQJ","PPChnnnBFF","hyuBjUqXlG","bF6eod5Gvf","nEsXyWgiOK","ruOEQAzv1W","Tw270M8GLb","QMFrweE19q","Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4381","layer":2},{"info":"number node, value=1345","layer":2},{"info":"compute binary expreesion, left_input=4381, right_input=1345, op_id = Cw4SuJJGHO binary_op_definition= 'a↳∿⪆b = { ((⨰⫟⨤(↔15))⨻⩈⩔((b⪛⫼133)⫡⨏(b→⨶⪴a))) }', output=nan","layer":1},{"info":"number node, value=5121","layer":2},{"info":"number node, value=3557","layer":2},{"info":"compute binary expreesion, left_input=5121, right_input=3557, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=-244","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-244, op_id = kn8WO9XteQ binary_op_definition= 'a⨭⪣b = { ((486⇩)⩵∡(a∣a)) , if (b⇯⋐)>445 or (≋b)>319 or b<=69 ; (↯⪼(⇋↷b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1010131↳∿⪆⪩⨒∯111001⨭⪣⪩⨒∯1100001⇍⊗⪩⨒∯313211=NaN","reverse_text":"NaN=⪩⨒∯1010131↳∿⪆⪩⨒∯111001⨭⪣⪩⨒∯1100001⇍⊗⪩⨒∯313211","cot":[{"info":"⪩⨒∯1010131↳∿⪆⪩⨒∯111001=NaN","layer":1},{"info":"⪩⨒∯1100001⇍⊗⪩⨒∯313211=⪩⨒∯-3310","layer":1},{"info":"NaN⨭⪣⪩⨒∯-3310=NaN","layer":0}]}
{"id":97,"expression_no_base_symbol":"($7074$≭$4315$)⊕∕($4971$↞⋁$2855$)","expression":"(⪩⨒∯1232202≭⪩⨒∯1003123)⊕∕(⪩⨒∯1031223↞⋁⪩⨒∯230213)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":176,"operation_count":3,"complexity_ratio":58.666666666666664,"tree":{"type":"binary","operator":"⊕∕","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":7074,"base":4},"right_expr":{"type":"numeric_atoms","value":4315,"base":4}},"right_expr":{"type":"binary","operator":"↞⋁","left_expr":{"type":"numeric_atoms","value":4971,"base":4},"right_expr":{"type":"numeric_atoms","value":2855,"base":4}}},"used_operators":["9cloC0Ngie","rxpJgHHUmx","RqrPlJkxDo"],"dependent_operators":["Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf","AHs5Up7iyr","Uaa54Peajs","CArV6hThFE","13rbtpv6ld"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7074","layer":2},{"info":"number node, value=4315","layer":2},{"info":"compute binary expreesion, left_input=7074, right_input=4315, op_id = rxpJgHHUmx binary_op_definition= 'a≭b = {-22, if b == 0; (a)≹⇙⪍(a≭(b-1)), if b > 0 and abs(b) < 100; -(a)≹⇙⪍(a≭(b+1)), if b < 0 and abs(b) < 100; NaN, else}', output=nan","layer":1},{"info":"number node, value=4971","layer":2},{"info":"number node, value=2855","layer":2},{"info":"compute binary expreesion, left_input=4971, right_input=2855, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1232202≭⪩⨒∯1003123)⊕∕(⪩⨒∯1031223↞⋁⪩⨒∯230213)=NaN","reverse_text":"NaN=(⪩⨒∯1232202≭⪩⨒∯1003123)⊕∕(⪩⨒∯1031223↞⋁⪩⨒∯230213)","cot":[{"info":"⪩⨒∯1232202≭⪩⨒∯1003123=NaN","layer":1},{"info":"⪩⨒∯1031223↞⋁⪩⨒∯230213=NaN","layer":1},{"info":"NaN⊕∕NaN=NaN","layer":0}]}
{"id":98,"expression_no_base_symbol":"$5122$⩦$1658$⨒$7396$⪛$3235$","expression":"⪩⨒∯1100002⩦⪩⨒∯121322⨒⪩⨒∯1303210⪛⪩⨒∯302203","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":40,"operation_count":3,"complexity_ratio":13.333333333333334,"tree":{"type":"binary","operator":"⨒","left_expr":{"type":"binary","operator":"⩦","left_expr":{"type":"numeric_atoms","value":5122,"base":4},"right_expr":{"type":"numeric_atoms","value":1658,"base":4}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":7396,"base":4},"right_expr":{"type":"numeric_atoms","value":3235,"base":4}}},"used_operators":["y75s1iXyHd","0kmYd0q39Y","uFcxV4UQCh"],"dependent_operators":["srAu1WTS94","oacrs7FA3X","7qqUquhhSb","N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⪩⨒∯-32322210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5122","layer":2},{"info":"number node, value=1658","layer":2},{"info":"compute binary expreesion, left_input=5122, right_input=1658, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=10244","layer":1},{"info":"number node, value=7396","layer":2},{"info":"number node, value=3235","layer":2},{"info":"compute binary expreesion, left_input=7396, right_input=3235, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=926","layer":1},{"info":"compute binary expreesion, left_input=10244, right_input=926, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-61092","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1100002⩦⪩⨒∯121322⨒⪩⨒∯1303210⪛⪩⨒∯302203=⪩⨒∯-32322210","reverse_text":"⪩⨒∯-32322210=⪩⨒∯1100002⩦⪩⨒∯121322⨒⪩⨒∯1303210⪛⪩⨒∯302203","cot":[{"info":"⪩⨒∯1100002⩦⪩⨒∯121322=⪩⨒∯2200010","layer":1},{"info":"⪩⨒∯1303210⪛⪩⨒∯302203=⪩⨒∯32132","layer":1},{"info":"⪩⨒∯2200010⨒⪩⨒∯32132=⪩⨒∯-32322210","layer":0}]}
{"id":99,"expression_no_base_symbol":"⨆≐≲($6023$⫩)","expression":"⨆≐≲(⪩⨒∯1132013⫩)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6066,"operation_count":2,"complexity_ratio":3033.0,"tree":{"type":"unary","operator":"⨆≐≲","unary_expr":{"type":"unary","operator":"⫩","unary_expr":{"type":"numeric_atoms","value":6023,"base":4}}},"used_operators":["Bi9z9uYZqW","6aG7x05OhS"],"dependent_operators":["SWo3A1KBJH","SUmda5xLS4","bx9Z9DAK5y","dWAJyo7jo9"],"result":"⪩⨒∯-221021210","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6023","layer":2},{"info":"compute unary expreesion, input=6023, op_id = 6aG7x05OhS, unary_op_definition = 'a⫩ = { (a⪢a) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = Bi9z9uYZqW, unary_op_definition = '⨆≐≲a = { (⇋↷(⇾⩊⇾(a⪄a))) }', output=-168548","layer":0}],"base":4,"result_base":4,"text":"⨆≐≲(⪩⨒∯1132013⫩)=⪩⨒∯-221021210","reverse_text":"⪩⨒∯-221021210=⨆≐≲(⪩⨒∯1132013⫩)","cot":[{"info":"⪩⨒∯1132013⫩=NaN","layer":1},{"info":"⨆≐≲NaN=⪩⨒∯-221021210","layer":0}]}
{"id":100,"expression_no_base_symbol":"⇖($1978$⫃⨇$4085$)","expression":"⇖(⪩⨒∯132322⫃⨇⪩⨒∯333311)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":13,"operation_count":2,"complexity_ratio":6.5,"tree":{"type":"unary","operator":"⇖","unary_expr":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"numeric_atoms","value":1978,"base":4},"right_expr":{"type":"numeric_atoms","value":4085,"base":4}}},"used_operators":["tfWHHpNKUN","09Ly4LVMIf"],"dependent_operators":["2DQ55sFlQl","9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1978","layer":2},{"info":"number node, value=4085","layer":2},{"info":"compute binary expreesion, left_input=1978, right_input=4085, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=-16372","layer":1},{"info":"compute unary expreesion, input=-16372, op_id = tfWHHpNKUN, unary_op_definition = '⇖a = { (221⨵⪆a) }', output=160","layer":0}],"base":4,"result_base":4,"text":"⇖(⪩⨒∯132322⫃⨇⪩⨒∯333311)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⇖(⪩⨒∯132322⫃⨇⪩⨒∯333311)","cot":[{"info":"⪩⨒∯132322⫃⨇⪩⨒∯333311=⪩⨒∯-3333310","layer":1},{"info":"⇖⪩⨒∯-3333310=⪩⨒∯2200","layer":0}]}
{"id":101,"expression_no_base_symbol":"(-$3945$)⩧⪆($6739$⩉⊫⨁)","expression":"(-⪩⨒∯331221)⩧⪆(⪩⨒∯1221103⩉⊫⨁)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4,"operation_count":3,"complexity_ratio":1.3333333333333333,"tree":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":3945,"base":4}},"right_expr":{"type":"unary","operator":"⩉⊫⨁","unary_expr":{"type":"numeric_atoms","value":6739,"base":4}}},"used_operators":["Ikt5ks8PT7","t8gj7n24qd","7qqUquhhSb"],"dependent_operators":["eewbuw0ToL","t8gj7n24qd","7j4O788W3g"],"result":"⪩⨒∯-1221103","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3945","layer":2},{"info":"compute unary expreesion, input=3945, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-3945","layer":1},{"info":"number node, value=6739","layer":2},{"info":"compute unary expreesion, input=6739, op_id = 7qqUquhhSb, unary_op_definition = 'a⩉⊫⨁ = { (331↺a) }', output=6739","layer":1},{"info":"compute binary expreesion, left_input=-3945, right_input=6739, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-6739","layer":0}],"base":4,"result_base":4,"text":"(-⪩⨒∯331221)⩧⪆(⪩⨒∯1221103⩉⊫⨁)=⪩⨒∯-1221103","reverse_text":"⪩⨒∯-1221103=(-⪩⨒∯331221)⩧⪆(⪩⨒∯1221103⩉⊫⨁)","cot":[{"info":"-⪩⨒∯331221=⪩⨒∯-331221","layer":1},{"info":"⪩⨒∯1221103⩉⊫⨁=⪩⨒∯1221103","layer":1},{"info":"⪩⨒∯-331221⩧⪆⪩⨒∯1221103=⪩⨒∯-1221103","layer":0}]}
{"id":102,"expression_no_base_symbol":"($1360$⫌⩉⩟$7611$)⊴$2959$⨔⇊$2140$","expression":"(⪩⨒∯111100⫌⩉⩟⪩⨒∯1312323)⊴⪩⨒∯232033⨔⇊⪩⨒∯201130","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":43451,"operation_count":3,"complexity_ratio":14483.666666666666,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"⫌⩉⩟","left_expr":{"type":"numeric_atoms","value":1360,"base":4},"right_expr":{"type":"numeric_atoms","value":7611,"base":4}},"right_expr":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"numeric_atoms","value":2959,"base":4},"right_expr":{"type":"numeric_atoms","value":2140,"base":4}}},"used_operators":["Nsiff2A1zJ","XIIwhv8d0m","JclMnS0uGI"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","B5M0gjZbta","UMwdvZNt44","MRPaB8lBjK","vkpjKywKVM","9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1360","layer":2},{"info":"number node, value=7611","layer":2},{"info":"compute binary expreesion, left_input=1360, right_input=7611, op_id = XIIwhv8d0m binary_op_definition= 'a⫌⩉⩟b = { (((a↬179)⇮⋭(b⇡⇂b))⇉⇱⇎) }', output=-50","layer":1},{"info":"number node, value=2959","layer":2},{"info":"number node, value=2140","layer":2},{"info":"compute binary expreesion, left_input=2959, right_input=2140, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=2140","layer":1},{"info":"compute binary expreesion, left_input=-50, right_input=2140, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯111100⫌⩉⩟⪩⨒∯1312323)⊴⪩⨒∯232033⨔⇊⪩⨒∯201130=NaN","reverse_text":"NaN=(⪩⨒∯111100⫌⩉⩟⪩⨒∯1312323)⊴⪩⨒∯232033⨔⇊⪩⨒∯201130","cot":[{"info":"⪩⨒∯111100⫌⩉⩟⪩⨒∯1312323=⪩⨒∯-302","layer":1},{"info":"⪩⨒∯232033⨔⇊⪩⨒∯201130=⪩⨒∯201130","layer":1},{"info":"⪩⨒∯-302⊴⪩⨒∯201130=NaN","layer":0}]}
{"id":103,"expression_no_base_symbol":"$3690$⊋$2561$⪘⫢($2143$∈)","expression":"⪩⨒∯321222⊋⪩⨒∯220001⪘⫢(⪩⨒∯201133∈)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2395,"operation_count":3,"complexity_ratio":798.3333333333334,"tree":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"binary","operator":"⊋","left_expr":{"type":"numeric_atoms","value":3690,"base":4},"right_expr":{"type":"numeric_atoms","value":2561,"base":4}},"right_expr":{"type":"unary","operator":"∈","unary_expr":{"type":"numeric_atoms","value":2143,"base":4}}},"used_operators":["oacrs7FA3X","W4tP9CfskL","ztP7wcbY7m"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu","rysDP5nf3Z","XPYlsWDdGa","8w2t5hMYqp","f6k1SAg4EE","14qkJME0vr"],"result":"⪩⨒∯2300311100010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3690","layer":2},{"info":"number node, value=2561","layer":2},{"info":"compute binary expreesion, left_input=3690, right_input=2561, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=23177792","layer":1},{"info":"number node, value=2143","layer":2},{"info":"compute unary expreesion, input=2143, op_id = ztP7wcbY7m, unary_op_definition = 'a∈ = { ((⊄⩳↩250)-(a⊦⊿)) , if ((⪲⇎a)>320 or (a⪒777)>25 or a!=39) ; a , else }', output=5758","layer":1},{"info":"compute binary expreesion, left_input=23177792, right_input=5758, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=46355460","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯321222⊋⪩⨒∯220001⪘⫢(⪩⨒∯201133∈)=⪩⨒∯2300311100010","reverse_text":"⪩⨒∯2300311100010=⪩⨒∯321222⊋⪩⨒∯220001⪘⫢(⪩⨒∯201133∈)","cot":[{"info":"⪩⨒∯321222⊋⪩⨒∯220001=⪩⨒∯1120122221000","layer":1},{"info":"⪩⨒∯201133∈=⪩⨒∯1121332","layer":1},{"info":"⪩⨒∯1120122221000⪘⫢⪩⨒∯1121332=⪩⨒∯2300311100010","layer":0}]}
{"id":104,"expression_no_base_symbol":"(⨈⪑$2251$)⨵⪆($2113$⩅⪻⪻)","expression":"(⨈⪑⪩⨒∯203023)⨵⪆(⪩⨒∯201001⩅⪻⪻)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":212,"operation_count":3,"complexity_ratio":70.66666666666667,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"unary","operator":"⨈⪑","unary_expr":{"type":"numeric_atoms","value":2251,"base":4}},"right_expr":{"type":"unary","operator":"⩅⪻⪻","unary_expr":{"type":"numeric_atoms","value":2113,"base":4}}},"used_operators":["2DQ55sFlQl","mp94q5OcYM","kHoXpA7yos"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","YjI8oCXuph","09Ly4LVMIf","Bmrmz2XGnR","kbkesczE7y","i8ToyICDmI","IWmyXbctLI","SUmda5xLS4","KPf6cnQVty","8HhzD0ZcuI","9Isq31Ruls"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2251","layer":2},{"info":"compute unary expreesion, input=2251, op_id = mp94q5OcYM, unary_op_definition = '⨈⪑a = { (((⫇a)⫃⨇(89⪮%⊝a))≬⋮((a≚⊃≕a)∲⫓(a⪮%⊝117))) }', output=868","layer":1},{"info":"number node, value=2113","layer":2},{"info":"compute unary expreesion, input=2113, op_id = kHoXpA7yos, unary_op_definition = 'a⩅⪻⪻ = { (a⪄((a∌↝a)⨽(a∺≝⩲a))) }', output=-312149","layer":1},{"info":"compute binary expreesion, left_input=868, right_input=-312149, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⨈⪑⪩⨒∯203023)⨵⪆(⪩⨒∯201001⩅⪻⪻)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⨈⪑⪩⨒∯203023)⨵⪆(⪩⨒∯201001⩅⪻⪻)","cot":[{"info":"⨈⪑⪩⨒∯203023=⪩⨒∯31210","layer":1},{"info":"⪩⨒∯201001⩅⪻⪻=⪩⨒∯-1030031111","layer":1},{"info":"⪩⨒∯31210⨵⪆⪩⨒∯-1030031111=⪩⨒∯2200","layer":0}]}
{"id":105,"expression_no_base_symbol":"∤(⫯$2251$)","expression":"∤(⫯⪩⨒∯203023)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":56,"operation_count":2,"complexity_ratio":28.0,"tree":{"type":"unary","operator":"∤","unary_expr":{"type":"unary","operator":"⫯","unary_expr":{"type":"numeric_atoms","value":2251,"base":4}}},"used_operators":["k2HlF1dBQh","H6BK1Evt7c"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","tifHPKVTfV","8w2t5hMYqp","2Wsdkap16l","KbjG8mgYpV","sJAwomhLZr","Ph9nP6C5qx","AYdpE9sXAk","X99M06cbEe"],"result":"⪩⨒∯21","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2251","layer":2},{"info":"compute unary expreesion, input=2251, op_id = H6BK1Evt7c, unary_op_definition = '⫯a = { ((a⩠)∠↢(⨂⪏⇭a)) , if (a≧⫂∧919)>20 ; ((a⩹a)≫≃) , else }', output=-79754","layer":1},{"info":"compute unary expreesion, input=-79754, op_id = k2HlF1dBQh, unary_op_definition = '∤a = { (((a⇼⇔∾a)+(a-a))-(⊄⩳↩3)) }', output=9","layer":0}],"base":4,"result_base":4,"text":"∤(⫯⪩⨒∯203023)=⪩⨒∯21","reverse_text":"⪩⨒∯21=∤(⫯⪩⨒∯203023)","cot":[{"info":"⫯⪩⨒∯203023=⪩⨒∯-103132022","layer":1},{"info":"∤⪩⨒∯-103132022=⪩⨒∯21","layer":0}]}
{"id":106,"expression_no_base_symbol":"($5395$≠≀$5167$)∳⫺(∑⇻≧$7113$)","expression":"(⪩⨒∯1110103≠≀⪩⨒∯1100233)∳⫺(∑⇻≧⪩⨒∯1233021)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":54,"operation_count":3,"complexity_ratio":18.0,"tree":{"type":"binary","operator":"∳⫺","left_expr":{"type":"binary","operator":"≠≀","left_expr":{"type":"numeric_atoms","value":5395,"base":4},"right_expr":{"type":"numeric_atoms","value":5167,"base":4}},"right_expr":{"type":"unary","operator":"∑⇻≧","unary_expr":{"type":"numeric_atoms","value":7113,"base":4}}},"used_operators":["AzXXKTstlj","IwW236VD4Y","l1M9WJ3V7u"],"dependent_operators":["F4yD0voBRQ","Tcnh7f0tEr","ZvLB05nZmT","eLAdDNolq6","NTOWxs364D","sdazOOVcIp","2DDjHMKMc0","2td37pGCOC","23Mk6UjR3U","EBcxylXtPf","xUOZtlo3hN"],"result":"⪩⨒∯-21303222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5395","layer":2},{"info":"number node, value=5167","layer":2},{"info":"compute binary expreesion, left_input=5395, right_input=5167, op_id = IwW236VD4Y binary_op_definition= 'a≠≀b = { (⩦⩻⨪(a⩚⊴⇥b)) , if (≤/b)>10 ; ((a⪨≂a)⪨≂(a⋝⋈⪟356)) , else }', output=-10484","layer":1},{"info":"number node, value=7113","layer":2},{"info":"compute unary expreesion, input=7113, op_id = l1M9WJ3V7u, unary_op_definition = '∑⇻≧a = { (⨞⊢a) , if (a⫌⩹⨱)<644 ; (426⋷a) , else }', output=-852","layer":1},{"info":"compute binary expreesion, left_input=-10484, right_input=-852, op_id = AzXXKTstlj binary_op_definition= 'a∳⫺b = { (a≣⋋) , if (b⫳≱↱947)==166 ; (a⇣⩺⋵b) , else }', output=-40170","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1110103≠≀⪩⨒∯1100233)∳⫺(∑⇻≧⪩⨒∯1233021)=⪩⨒∯-21303222","reverse_text":"⪩⨒∯-21303222=(⪩⨒∯1110103≠≀⪩⨒∯1100233)∳⫺(∑⇻≧⪩⨒∯1233021)","cot":[{"info":"⪩⨒∯1110103≠≀⪩⨒∯1100233=⪩⨒∯-2203310","layer":1},{"info":"∑⇻≧⪩⨒∯1233021=⪩⨒∯-31110","layer":1},{"info":"⪩⨒∯-2203310∳⫺⪩⨒∯-31110=⪩⨒∯-21303222","layer":0}]}
{"id":107,"expression_no_base_symbol":"(⇾⩊⇾$1139$)⨵⪆(≦∁$1020$)","expression":"(⇾⩊⇾⪩⨒∯101303)⨵⪆(≦∁⪩⨒∯33330)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15,"operation_count":3,"complexity_ratio":5.0,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"unary","operator":"⇾⩊⇾","unary_expr":{"type":"numeric_atoms","value":1139,"base":4}},"right_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":1020,"base":4}}},"used_operators":["2DQ55sFlQl","bx9Z9DAK5y","9ICcGScMcE"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","BjRHVeLaeN","8w2t5hMYqp","QMFrweE19q","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1139","layer":2},{"info":"compute unary expreesion, input=1139, op_id = bx9Z9DAK5y, unary_op_definition = '⇾⩊⇾a = { (⊄⩳↩((a+259)⫡⨏(a⫩⊇))) }', output=-16737","layer":1},{"info":"number node, value=1020","layer":2},{"info":"compute unary expreesion, input=1020, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=1020","layer":1},{"info":"compute binary expreesion, left_input=-16737, right_input=1020, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⇾⩊⇾⪩⨒∯101303)⨵⪆(≦∁⪩⨒∯33330)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⇾⩊⇾⪩⨒∯101303)⨵⪆(≦∁⪩⨒∯33330)","cot":[{"info":"⇾⩊⇾⪩⨒∯101303=⪩⨒∯-10011201","layer":1},{"info":"≦∁⪩⨒∯33330=⪩⨒∯33330","layer":1},{"info":"⪩⨒∯-10011201⨵⪆⪩⨒∯33330=⪩⨒∯2200","layer":0}]}
{"id":108,"expression_no_base_symbol":"$5329$↺$1377$⨳⩥⨓$2839$⊋$2103$","expression":"⪩⨒∯1103101↺⪩⨒∯111201⨳⩥⨓⪩⨒∯230113⊋⪩⨒∯200313","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1584,"operation_count":3,"complexity_ratio":528.0,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":5329,"base":4},"right_expr":{"type":"numeric_atoms","value":1377,"base":4}},"right_expr":{"type":"binary","operator":"⊋","left_expr":{"type":"numeric_atoms","value":2839,"base":4},"right_expr":{"type":"numeric_atoms","value":2103,"base":4}}},"used_operators":["nCS4ZIUYfx","7j4O788W3g","W4tP9CfskL"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd","2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu"],"result":"⪩⨒∯233311010023","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5329","layer":2},{"info":"number node, value=1377","layer":2},{"info":"compute binary expreesion, left_input=5329, right_input=1377, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1377","layer":1},{"info":"number node, value=2839","layer":2},{"info":"number node, value=2103","layer":2},{"info":"compute binary expreesion, left_input=2839, right_input=2103, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=12539500","layer":1},{"info":"compute binary expreesion, left_input=1377, right_input=12539500, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=12538123","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1103101↺⪩⨒∯111201⨳⩥⨓⪩⨒∯230113⊋⪩⨒∯200313=⪩⨒∯233311010023","reverse_text":"⪩⨒∯233311010023=⪩⨒∯1103101↺⪩⨒∯111201⨳⩥⨓⪩⨒∯230113⊋⪩⨒∯200313","cot":[{"info":"⪩⨒∯1103101↺⪩⨒∯111201=⪩⨒∯111201","layer":1},{"info":"⪩⨒∯230113⊋⪩⨒∯200313=⪩⨒∯233311121230","layer":1},{"info":"⪩⨒∯111201⨳⩥⨓⪩⨒∯233311121230=⪩⨒∯233311010023","layer":0}]}
{"id":109,"expression_no_base_symbol":"$1683$≥⨤⩑$7057$⋳⪒($1172$⩺⪪$2320$)","expression":"⪩⨒∯122103≥⨤⩑⪩⨒∯1232101⋳⪒(⪩⨒∯102110⩺⪪⪩⨒∯210100)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":142,"operation_count":3,"complexity_ratio":47.333333333333336,"tree":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"binary","operator":"≥⨤⩑","left_expr":{"type":"numeric_atoms","value":1683,"base":4},"right_expr":{"type":"numeric_atoms","value":7057,"base":4}},"right_expr":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"numeric_atoms","value":1172,"base":4},"right_expr":{"type":"numeric_atoms","value":2320,"base":4}}},"used_operators":["12rbrZMWeM","gJLn6v0xnP","uvdQJvN4PV"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","mp7IySMOzn","aA7tF3KVD3","QvoQhV0rrE","Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U"],"result":"⪩⨒∯332133","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1683","layer":2},{"info":"number node, value=7057","layer":2},{"info":"compute binary expreesion, left_input=1683, right_input=7057, op_id = gJLn6v0xnP binary_op_definition= 'a≥⨤⩑b = { (b⇷a) , if (b⪘⨀)>356 ; (702∠⫱488) , else }', output=1234","layer":1},{"info":"number node, value=1172","layer":2},{"info":"number node, value=2320","layer":2},{"info":"compute binary expreesion, left_input=1172, right_input=2320, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=-1818","layer":1},{"info":"compute binary expreesion, left_input=1234, right_input=-1818, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=3999","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯122103≥⨤⩑⪩⨒∯1232101⋳⪒(⪩⨒∯102110⩺⪪⪩⨒∯210100)=⪩⨒∯332133","reverse_text":"⪩⨒∯332133=⪩⨒∯122103≥⨤⩑⪩⨒∯1232101⋳⪒(⪩⨒∯102110⩺⪪⪩⨒∯210100)","cot":[{"info":"⪩⨒∯122103≥⨤⩑⪩⨒∯1232101=⪩⨒∯103102","layer":1},{"info":"⪩⨒∯102110⩺⪪⪩⨒∯210100=⪩⨒∯-130122","layer":1},{"info":"⪩⨒∯103102⋳⪒⪩⨒∯-130122=⪩⨒∯332133","layer":0}]}
{"id":110,"expression_no_base_symbol":"$1258$⊔$3264$⨭⪣$2080$⩚⊴⇥$3666$","expression":"⪩⨒∯103222⊔⪩⨒∯303000⨭⪣⪩⨒∯200200⩚⊴⇥⪩⨒∯321102","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":54,"operation_count":3,"complexity_ratio":18.0,"tree":{"type":"binary","operator":"⨭⪣","left_expr":{"type":"binary","operator":"⊔","left_expr":{"type":"numeric_atoms","value":1258,"base":4},"right_expr":{"type":"numeric_atoms","value":3264,"base":4}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":2080,"base":4},"right_expr":{"type":"numeric_atoms","value":3666,"base":4}}},"used_operators":["kn8WO9XteQ","E4l6HwMY31","NTOWxs364D"],"dependent_operators":["vRio1gEz1j","61wBmkZwlr","SWo3A1KBJH","8jW3W4yZS5","LkLIoiE525","Y7wcNGrDQJ","PPChnnnBFF","W4YGzv6Whe","DpFCA1CohY","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","QMFrweE19q","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⪩⨒∯3230311","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1258","layer":2},{"info":"number node, value=3264","layer":2},{"info":"compute binary expreesion, left_input=1258, right_input=3264, op_id = E4l6HwMY31 binary_op_definition= 'a⊔b = { (((a≧⫂∧b)∲⫓(⋗⩬⋾b))⫡⨏((b⪒a)≧⫂∧(a+64))) }', output=16436","layer":1},{"info":"number node, value=2080","layer":2},{"info":"number node, value=3666","layer":2},{"info":"compute binary expreesion, left_input=2080, right_input=3666, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-5867","layer":1},{"info":"compute binary expreesion, left_input=16436, right_input=-5867, op_id = kn8WO9XteQ binary_op_definition= 'a⨭⪣b = { ((486⇩)⩵∡(a∣a)) , if (b⇯⋐)>445 or (≋b)>319 or b<=69 ; (↯⪼(⇋↷b)) , else }', output=15157","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯103222⊔⪩⨒∯303000⨭⪣⪩⨒∯200200⩚⊴⇥⪩⨒∯321102=⪩⨒∯3230311","reverse_text":"⪩⨒∯3230311=⪩⨒∯103222⊔⪩⨒∯303000⨭⪣⪩⨒∯200200⩚⊴⇥⪩⨒∯321102","cot":[{"info":"⪩⨒∯103222⊔⪩⨒∯303000=⪩⨒∯10000310","layer":1},{"info":"⪩⨒∯200200⩚⊴⇥⪩⨒∯321102=⪩⨒∯-1123223","layer":1},{"info":"⪩⨒∯10000310⨭⪣⪩⨒∯-1123223=⪩⨒∯3230311","layer":0}]}
{"id":111,"expression_no_base_symbol":"($8192$⩹$1153$)⩠","expression":"(⪩⨒∯2000000⩹⪩⨒∯102001)⩠","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":31,"operation_count":2,"complexity_ratio":15.5,"tree":{"type":"unary","operator":"⩠","unary_expr":{"type":"binary","operator":"⩹","left_expr":{"type":"numeric_atoms","value":8192,"base":4},"right_expr":{"type":"numeric_atoms","value":1153,"base":4}}},"used_operators":["sJAwomhLZr","2Wsdkap16l"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","k8jYdgA6NY","eH2TOUuTDT","W4YGzv6Whe","Z2TMIBDE3Q","COABgblf1C","rysDP5nf3Z","NTOWxs364D","23Mk6UjR3U","XIabStNQrY","2DDjHMKMc0","12rbrZMWeM","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=8192","layer":2},{"info":"number node, value=1153","layer":2},{"info":"compute binary expreesion, left_input=8192, right_input=1153, op_id = 2Wsdkap16l binary_op_definition= 'a⩹b = { (b-((b⨳⩥⨓b)⨸⪁(1⋝⋈⪟b))) , if (b⇋≉)!=246 ; (((a⇋≉)⨰(a⋷a))⋳⪒((a⩚⊴⇥a)⨳⩥⨓(a≧⫂∧a))) , else }', output=1151","layer":1},{"info":"compute unary expreesion, input=1151, op_id = sJAwomhLZr, unary_op_definition = 'a⩠ = { (((a+a)⊭↱(a⪨≂a))∲⫓((a⩤)%(a⪐))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2000000⩹⪩⨒∯102001)⩠=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯2000000⩹⪩⨒∯102001)⩠","cot":[{"info":"⪩⨒∯2000000⩹⪩⨒∯102001=⪩⨒∯101333","layer":1},{"info":"⪩⨒∯101333⩠=⪩⨒∯0","layer":0}]}
{"id":112,"expression_no_base_symbol":"$1009$⪍↜⋙$2295$⨳⩥⨓(⋃$3534$)","expression":"⪩⨒∯33301⪍↜⋙⪩⨒∯203313⨳⩥⨓(⋃⪩⨒∯313032)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":25,"operation_count":3,"complexity_ratio":8.333333333333334,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⪍↜⋙","left_expr":{"type":"numeric_atoms","value":1009,"base":4},"right_expr":{"type":"numeric_atoms","value":2295,"base":4}},"right_expr":{"type":"unary","operator":"⋃","unary_expr":{"type":"numeric_atoms","value":3534,"base":4}}},"used_operators":["nCS4ZIUYfx","L05ObWFQCd","3mBM5G4a3l"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","DZ8iAZOCBD","tifHPKVTfV","EBcxylXtPf","QMFrweE19q","g55IO6H4Gj"],"result":"⪩⨒∯10102310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1009","layer":2},{"info":"number node, value=2295","layer":2},{"info":"compute binary expreesion, left_input=1009, right_input=2295, op_id = L05ObWFQCd binary_op_definition= 'a⪍↜⋙b = { ((a-b)⊉≛↸(a⫡⨏b)) , if (a⫌⩹⨱)!=88 ; ((a⫡⨏b)⇼⇔∾(a⫌⩹⨱)) , else }', output=-10418","layer":1},{"info":"number node, value=3534","layer":2},{"info":"compute unary expreesion, input=3534, op_id = 3mBM5G4a3l, unary_op_definition = '⋃a = { (51⨸⪁a) }', output=7170","layer":1},{"info":"compute binary expreesion, left_input=-10418, right_input=7170, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=17588","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯33301⪍↜⋙⪩⨒∯203313⨳⩥⨓(⋃⪩⨒∯313032)=⪩⨒∯10102310","reverse_text":"⪩⨒∯10102310=⪩⨒∯33301⪍↜⋙⪩⨒∯203313⨳⩥⨓(⋃⪩⨒∯313032)","cot":[{"info":"⪩⨒∯33301⪍↜⋙⪩⨒∯203313=⪩⨒∯-2202302","layer":1},{"info":"⋃⪩⨒∯313032=⪩⨒∯1300002","layer":1},{"info":"⪩⨒∯-2202302⨳⩥⨓⪩⨒∯1300002=⪩⨒∯10102310","layer":0}]}
{"id":113,"expression_no_base_symbol":"$1702$∇⊂⋱$6816$⪥$2287$∌$2367$","expression":"⪩⨒∯122212∇⊂⋱⪩⨒∯1222200⪥⪩⨒∯203233∌⪩⨒∯210333","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":30,"operation_count":3,"complexity_ratio":10.0,"tree":{"type":"binary","operator":"⪥","left_expr":{"type":"binary","operator":"∇⊂⋱","left_expr":{"type":"numeric_atoms","value":1702,"base":4},"right_expr":{"type":"numeric_atoms","value":6816,"base":4}},"right_expr":{"type":"binary","operator":"∌","left_expr":{"type":"numeric_atoms","value":2287,"base":4},"right_expr":{"type":"numeric_atoms","value":2367,"base":4}}},"used_operators":["QbnwKVWMIQ","nhYeJWJD5X","8cLx32lpNA"],"dependent_operators":["WR6HLWljOP","nhYeJWJD5X","f6k1SAg4EE","jLgFTUHLKL","PPChnnnBFF","P8v4zCKN1o","23Mk6UjR3U","f6k1SAg4EE","AF7qkfDlqP","nCS4ZIUYfx","N41Kp7NANJ","7j4O788W3g","t8gj7n24qd"],"result":"⪩⨒∯-1310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1702","layer":2},{"info":"number node, value=6816","layer":2},{"info":"compute binary expreesion, left_input=1702, right_input=6816, op_id = nhYeJWJD5X binary_op_definition= 'a∇⊂⋱b = { (b⪒b) , if a<143 ; ((⨑⩽⪐a)⋷(∥⊫(a⨳⩥⨓a))) , else }', output=2858","layer":1},{"info":"number node, value=2287","layer":2},{"info":"number node, value=2367","layer":2},{"info":"compute binary expreesion, left_input=2287, right_input=2367, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-2367","layer":1},{"info":"compute binary expreesion, left_input=2858, right_input=-2367, op_id = QbnwKVWMIQ binary_op_definition= 'a⪥b = { (b∇⊂⋱(58∣a)) , if (b↢721)<125 ; (↩(508⪒a)) , else }', output=-116","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯122212∇⊂⋱⪩⨒∯1222200⪥⪩⨒∯203233∌⪩⨒∯210333=⪩⨒∯-1310","reverse_text":"⪩⨒∯-1310=⪩⨒∯122212∇⊂⋱⪩⨒∯1222200⪥⪩⨒∯203233∌⪩⨒∯210333","cot":[{"info":"⪩⨒∯122212∇⊂⋱⪩⨒∯1222200=⪩⨒∯230222","layer":1},{"info":"⪩⨒∯203233∌⪩⨒∯210333=⪩⨒∯-210333","layer":1},{"info":"⪩⨒∯230222⪥⪩⨒∯-210333=⪩⨒∯-1310","layer":0}]}
{"id":114,"expression_no_base_symbol":"$2846$⩘$1109$∙∹∝$5580$⫥∨⫟$4938$","expression":"⪩⨒∯230132⩘⪩⨒∯101111∙∹∝⪩⨒∯1113030⫥∨⫟⪩⨒∯1031022","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":257,"operation_count":3,"complexity_ratio":85.66666666666667,"tree":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"binary","operator":"⩘","left_expr":{"type":"numeric_atoms","value":2846,"base":4},"right_expr":{"type":"numeric_atoms","value":1109,"base":4}},"right_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":5580,"base":4},"right_expr":{"type":"numeric_atoms","value":4938,"base":4}}},"used_operators":["HmxsFra2vL","cHh1gJQ2o6","KYD54nUTWz"],"dependent_operators":["BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","23Mk6UjR3U","eRqsBgTDFp","zVYPLywUTj","bPywburJMS","KPf6cnQVty","YbVcJGFEVW","5twsqlHp2o","8HhzD0ZcuI","rGHVDoGpnC"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2846","layer":2},{"info":"number node, value=1109","layer":2},{"info":"compute binary expreesion, left_input=2846, right_input=1109, op_id = cHh1gJQ2o6 binary_op_definition= 'a⩘b = { (((b⋷b)↼⊘⨖(a⊢6))∺≝⩲((a⪒⊣⊆619)≃(a⊪))) }', output=160","layer":1},{"info":"number node, value=5580","layer":2},{"info":"number node, value=4938","layer":2},{"info":"compute binary expreesion, left_input=5580, right_input=4938, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=nan, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯230132⩘⪩⨒∯101111∙∹∝⪩⨒∯1113030⫥∨⫟⪩⨒∯1031022=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯230132⩘⪩⨒∯101111∙∹∝⪩⨒∯1113030⫥∨⫟⪩⨒∯1031022","cot":[{"info":"⪩⨒∯230132⩘⪩⨒∯101111=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯1113030⫥∨⫟⪩⨒∯1031022=NaN","layer":1},{"info":"⪩⨒∯2200∙∹∝NaN=⪩⨒∯0","layer":0}]}
{"id":115,"expression_no_base_symbol":"$3504$⫣⪄⊒$1951$≚⋢","expression":"⪩⨒∯312300⫣⪄⊒⪩⨒∯132133≚⋢","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":120,"operation_count":2,"complexity_ratio":60.0,"tree":{"type":"unary","operator":"≚⋢","unary_expr":{"type":"binary","operator":"⫣⪄⊒","left_expr":{"type":"numeric_atoms","value":3504,"base":4},"right_expr":{"type":"numeric_atoms","value":1951,"base":4}}},"used_operators":["MahUMFw56D","RabNbG55vr"],"dependent_operators":["3ViojmjbAp","NTOWxs364D","DbCuESL50I","fOIeswaMU4","g7Hmc5v1ko","KPf6cnQVty","j9kHMeSvPp","k8jYdgA6NY","2DDjHMKMc0","8WDwsbhb0R","cTDWOvIxvz","IWmyXbctLI"],"result":"⪩⨒∯-1121","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3504","layer":2},{"info":"number node, value=1951","layer":2},{"info":"compute binary expreesion, left_input=3504, right_input=1951, op_id = RabNbG55vr binary_op_definition= 'a⫣⪄⊒b = { ((a⪮%⊝(153⪭a))%(⋼∭⪍(b⩚⊴⇥34))) , if b>769 ; ((∂⩏⊆(b⩟))∺≝⩲((b∝a)⋝⋈⪟(a⩌⋺b))) , else }', output=-5210","layer":1},{"info":"compute unary expreesion, input=-5210, op_id = MahUMFw56D, unary_op_definition = 'a≚⋢ = { (a⨓86) }', output=-89","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯312300⫣⪄⊒⪩⨒∯132133≚⋢=⪩⨒∯-1121","reverse_text":"⪩⨒∯-1121=⪩⨒∯312300⫣⪄⊒⪩⨒∯132133≚⋢","cot":[{"info":"⪩⨒∯312300⫣⪄⊒⪩⨒∯132133=⪩⨒∯-1101122","layer":1},{"info":"⪩⨒∯-1101122≚⋢=⪩⨒∯-1121","layer":0}]}
{"id":116,"expression_no_base_symbol":"($3654$⫳≱↱$3100$)≹⇙⪍($2486$≀⩗∶$2918$)","expression":"(⪩⨒∯321012⫳≱↱⪩⨒∯300130)≹⇙⪍(⪩⨒∯212312≀⩗∶⪩⨒∯231212)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":398,"operation_count":3,"complexity_ratio":132.66666666666666,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⫳≱↱","left_expr":{"type":"numeric_atoms","value":3654,"base":4},"right_expr":{"type":"numeric_atoms","value":3100,"base":4}},"right_expr":{"type":"binary","operator":"≀⩗∶","left_expr":{"type":"numeric_atoms","value":2486,"base":4},"right_expr":{"type":"numeric_atoms","value":2918,"base":4}}},"used_operators":["AHs5Up7iyr","ZvLB05nZmT","8INZBEW696"],"dependent_operators":["dWAJyo7jo9","2Wsdkap16l","FyVja0WsTP","wEfv7U73WA","bJkvcejdHO","HmxsFra2vL","8cLx32lpNA","KPf6cnQVty","2DlMacCsIx","l07mrZUIn9"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3654","layer":2},{"info":"number node, value=3100","layer":2},{"info":"compute binary expreesion, left_input=3654, right_input=3100, op_id = ZvLB05nZmT binary_op_definition= 'a⫳≱↱b = { (((a⩹b)⇐≅)∌((a∙∹∝345)⊱⇼⊻(b≎⊠⪸a))) }', output=-204","layer":1},{"info":"number node, value=2486","layer":2},{"info":"number node, value=2918","layer":2},{"info":"compute binary expreesion, left_input=2486, right_input=2918, op_id = 8INZBEW696 binary_op_definition= 'a≀⩗∶b = { (a⩨b) , if (a∺≝⩲555)<251 ; (306↪⪝) , else }', output=-3","layer":1},{"info":"compute binary expreesion, left_input=-204, right_input=-3, op_id = AHs5Up7iyr binary_op_definition= 'a≹⇙⪍b = {a, if b == 0; (a≹⇙⪍(b-1))⪢(b), if b > 0 and abs(b) < 1000; -(a≹⇙⪍(b+1))⪢(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯321012⫳≱↱⪩⨒∯300130)≹⇙⪍(⪩⨒∯212312≀⩗∶⪩⨒∯231212)=NaN","reverse_text":"NaN=(⪩⨒∯321012⫳≱↱⪩⨒∯300130)≹⇙⪍(⪩⨒∯212312≀⩗∶⪩⨒∯231212)","cot":[{"info":"⪩⨒∯321012⫳≱↱⪩⨒∯300130=⪩⨒∯-3030","layer":1},{"info":"⪩⨒∯212312≀⩗∶⪩⨒∯231212=⪩⨒∯-3","layer":1},{"info":"⪩⨒∯-3030≹⇙⪍⪩⨒∯-3=NaN","layer":0}]}
{"id":117,"expression_no_base_symbol":"(∤$1533$)∺≝⩲($1578$⫰⋱$2279$)","expression":"(∤⪩⨒∯113331)∺≝⩲(⪩⨒∯120222⫰⋱⪩⨒∯203213)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":25,"operation_count":3,"complexity_ratio":8.333333333333334,"tree":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"unary","operator":"∤","unary_expr":{"type":"numeric_atoms","value":1533,"base":4}},"right_expr":{"type":"binary","operator":"⫰⋱","left_expr":{"type":"numeric_atoms","value":1578,"base":4},"right_expr":{"type":"numeric_atoms","value":2279,"base":4}}},"used_operators":["KPf6cnQVty","k2HlF1dBQh","6o9Blt3TJ6"],"dependent_operators":["BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl","W4YGzv6Whe","rysDP5nf3Z","tifHPKVTfV","8w2t5hMYqp","W4YGzv6Whe","nCS4ZIUYfx","Qy55tPpLXF"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1533","layer":2},{"info":"compute unary expreesion, input=1533, op_id = k2HlF1dBQh, unary_op_definition = '∤a = { (((a⇼⇔∾a)+(a-a))-(⊄⩳↩3)) }', output=9","layer":1},{"info":"number node, value=1578","layer":2},{"info":"number node, value=2279","layer":2},{"info":"compute binary expreesion, left_input=1578, right_input=2279, op_id = 6o9Blt3TJ6 binary_op_definition= 'a⫰⋱b = { ((a+b)⨳⩥⨓(b⋥≓≎b)) }', output=-1545","layer":1},{"info":"compute binary expreesion, left_input=9, right_input=-1545, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":0}],"base":4,"result_base":4,"text":"(∤⪩⨒∯113331)∺≝⩲(⪩⨒∯120222⫰⋱⪩⨒∯203213)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(∤⪩⨒∯113331)∺≝⩲(⪩⨒∯120222⫰⋱⪩⨒∯203213)","cot":[{"info":"∤⪩⨒∯113331=⪩⨒∯21","layer":1},{"info":"⪩⨒∯120222⫰⋱⪩⨒∯203213=⪩⨒∯-120021","layer":1},{"info":"⪩⨒∯21∺≝⩲⪩⨒∯-120021=⪩⨒∯2200","layer":0}]}
{"id":118,"expression_no_base_symbol":"($2984$⋥⋵⩄$1326$)⨑⩅≇($1515$≨$6506$)","expression":"(⪩⨒∯232220⋥⋵⩄⪩⨒∯110232)⨑⩅≇(⪩⨒∯113223≨⪩⨒∯1211222)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":12816,"operation_count":3,"complexity_ratio":4272.0,"tree":{"type":"binary","operator":"⨑⩅≇","left_expr":{"type":"binary","operator":"⋥⋵⩄","left_expr":{"type":"numeric_atoms","value":2984,"base":4},"right_expr":{"type":"numeric_atoms","value":1326,"base":4}},"right_expr":{"type":"binary","operator":"≨","left_expr":{"type":"numeric_atoms","value":1515,"base":4},"right_expr":{"type":"numeric_atoms","value":6506,"base":4}}},"used_operators":["h92wMvzauj","7t3wd0Fuz7","0KMCeP1Jsh"],"dependent_operators":["s3Fd5m9Dh2","3sJ7IOPOlU","nREPSIbpBE","9Isq31Ruls","umQnsF7QlU","8HhzD0ZcuI","u6S6b8DprG","DmTXOeWf9t","AFVx7xoS7T","jLgFTUHLKL","oacrs7FA3X","xNBdhnnwKq","IWmyXbctLI","2td37pGCOC","AFVx7xoS7T","jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC"],"result":"⪩⨒∯-11103","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2984","layer":2},{"info":"number node, value=1326","layer":2},{"info":"compute binary expreesion, left_input=2984, right_input=1326, op_id = 7t3wd0Fuz7 binary_op_definition= 'a⋥⋵⩄b = { ((⩦⩻⨪a)⇌⫙⪟(b⪮%⊝b)) }', output=113","layer":1},{"info":"number node, value=1515","layer":2},{"info":"number node, value=6506","layer":2},{"info":"compute binary expreesion, left_input=1515, right_input=6506, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-12674","layer":1},{"info":"compute binary expreesion, left_input=113, right_input=-12674, op_id = h92wMvzauj binary_op_definition= 'a⨑⩅≇b = { (((a⪇≇⋚b)⊬⨰(b⨽582))∌↝a) , if (↽≂a)<10 or (b⊭∹↮)==22 ; ((a⊲⩕⊾(↩a))⪕((a⨚243)⇌⫙⪟(b⪘⫢b))) , else }', output=-339","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯232220⋥⋵⩄⪩⨒∯110232)⨑⩅≇(⪩⨒∯113223≨⪩⨒∯1211222)=⪩⨒∯-11103","reverse_text":"⪩⨒∯-11103=(⪩⨒∯232220⋥⋵⩄⪩⨒∯110232)⨑⩅≇(⪩⨒∯113223≨⪩⨒∯1211222)","cot":[{"info":"⪩⨒∯232220⋥⋵⩄⪩⨒∯110232=⪩⨒∯1301","layer":1},{"info":"⪩⨒∯113223≨⪩⨒∯1211222=⪩⨒∯-3012002","layer":1},{"info":"⪩⨒∯1301⨑⩅≇⪩⨒∯-3012002=⪩⨒∯-11103","layer":0}]}
{"id":119,"expression_no_base_symbol":"($3023$⨰$2114$)⪟⇏($4789$⨫⇇↔$3818$)","expression":"(⪩⨒∯233033⨰⪩⨒∯201002)⪟⇏(⪩⨒∯1022311⨫⇇↔⪩⨒∯323222)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":62,"operation_count":3,"complexity_ratio":20.666666666666668,"tree":{"type":"binary","operator":"⪟⇏","left_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":3023,"base":4},"right_expr":{"type":"numeric_atoms","value":2114,"base":4}},"right_expr":{"type":"binary","operator":"⨫⇇↔","left_expr":{"type":"numeric_atoms","value":4789,"base":4},"right_expr":{"type":"numeric_atoms","value":3818,"base":4}}},"used_operators":["GODebY97qR","eewbuw0ToL","LXhwmt4mBO"],"dependent_operators":["gx7XJ7hdpj","XnXgA4xnOs","wEfv7U73WA","2DQ55sFlQl","f6k1SAg4EE","oacrs7FA3X","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","d7ASUq0ydm","DZ8iAZOCBD","rJVOvQCfKK"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3023","layer":2},{"info":"number node, value=2114","layer":2},{"info":"compute binary expreesion, left_input=3023, right_input=2114, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=919","layer":1},{"info":"number node, value=4789","layer":2},{"info":"number node, value=3818","layer":2},{"info":"compute binary expreesion, left_input=4789, right_input=3818, op_id = LXhwmt4mBO binary_op_definition= 'a⨫⇇↔b = { ((9⊉≛↸b)⫯⪬∳(a⨎a)) }', output=-527","layer":1},{"info":"compute binary expreesion, left_input=919, right_input=-527, op_id = GODebY97qR binary_op_definition= 'a⪟⇏b = { ((b⨑≵⋬b)⫸⇳(440⪒a)) , if (b⇐≅)<189 ; ((219⨑≵⋬a)⪘⫢(b⨵⪆b)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯233033⨰⪩⨒∯201002)⪟⇏(⪩⨒∯1022311⨫⇇↔⪩⨒∯323222)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯233033⨰⪩⨒∯201002)⪟⇏(⪩⨒∯1022311⨫⇇↔⪩⨒∯323222)","cot":[{"info":"⪩⨒∯233033⨰⪩⨒∯201002=⪩⨒∯32113","layer":1},{"info":"⪩⨒∯1022311⨫⇇↔⪩⨒∯323222=⪩⨒∯-20033","layer":1},{"info":"⪩⨒∯32113⪟⇏⪩⨒∯-20033=⪩⨒∯0","layer":0}]}
{"id":120,"expression_no_base_symbol":"($5300$⪔⊥$1087$)∴($1009$⇣⩺⋵$6505$)","expression":"(⪩⨒∯1102310⪔⊥⪩⨒∯100333)∴(⪩⨒∯33301⇣⩺⋵⪩⨒∯1211221)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":67,"operation_count":3,"complexity_ratio":22.333333333333332,"tree":{"type":"binary","operator":"∴","left_expr":{"type":"binary","operator":"⪔⊥","left_expr":{"type":"numeric_atoms","value":5300,"base":4},"right_expr":{"type":"numeric_atoms","value":1087,"base":4}},"right_expr":{"type":"binary","operator":"⇣⩺⋵","left_expr":{"type":"numeric_atoms","value":1009,"base":4},"right_expr":{"type":"numeric_atoms","value":6505,"base":4}}},"used_operators":["hrf7POJlIJ","HJ9erzHUuu","F4yD0voBRQ"],"dependent_operators":["g55IO6H4Gj","P8v4zCKN1o","23Mk6UjR3U","eLAdDNolq6","rysDP5nf3Z","7j4O788W3g","tifHPKVTfV","8w2t5hMYqp","sdazOOVcIp","2td37pGCOC","COABgblf1C","NTOWxs364D","KPf6cnQVty","8jW3W4yZS5","12rbrZMWeM","g55IO6H4Gj","2DlMacCsIx"],"result":"⪩⨒∯21212012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5300","layer":2},{"info":"number node, value=1087","layer":2},{"info":"compute binary expreesion, left_input=5300, right_input=1087, op_id = HJ9erzHUuu binary_op_definition= 'a⪔⊥b = { (⩦⩻⨪(≤/(315⇼⇔∾a))) , if b<175 ; ((⊄⩳↩(b-b))⇼⇔∾((b⪨≂a)⊭↱(a↺b))) , else }', output=18827","layer":1},{"info":"number node, value=1009","layer":2},{"info":"number node, value=6505","layer":2},{"info":"compute binary expreesion, left_input=1009, right_input=6505, op_id = F4yD0voBRQ binary_op_definition= 'a⇣⩺⋵b = { (((a⩨565)∺≝⩲(5⨸⪁a))⩚⊴⇥(↯⪼(a⋳⪒b))) }', output=-8912","layer":1},{"info":"compute binary expreesion, left_input=18827, right_input=-8912, op_id = hrf7POJlIJ binary_op_definition= 'a∴b = { ((∥⊫(22⋷b))⨸⪁a) }', output=39302","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1102310⪔⊥⪩⨒∯100333)∴(⪩⨒∯33301⇣⩺⋵⪩⨒∯1211221)=⪩⨒∯21212012","reverse_text":"⪩⨒∯21212012=(⪩⨒∯1102310⪔⊥⪩⨒∯100333)∴(⪩⨒∯33301⇣⩺⋵⪩⨒∯1211221)","cot":[{"info":"⪩⨒∯1102310⪔⊥⪩⨒∯100333=⪩⨒∯10212023","layer":1},{"info":"⪩⨒∯33301⇣⩺⋵⪩⨒∯1211221=⪩⨒∯-2023100","layer":1},{"info":"⪩⨒∯10212023∴⪩⨒∯-2023100=⪩⨒∯21212012","layer":0}]}
{"id":121,"expression_no_base_symbol":"$4317$⩇∃⫛$1672$⪥⨬⪅","expression":"⪩⨒∯1003131⩇∃⫛⪩⨒∯122020⪥⨬⪅","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":552,"operation_count":2,"complexity_ratio":276.0,"tree":{"type":"unary","operator":"⪥⨬⪅","unary_expr":{"type":"binary","operator":"⩇∃⫛","left_expr":{"type":"numeric_atoms","value":4317,"base":4},"right_expr":{"type":"numeric_atoms","value":1672,"base":4}}},"used_operators":["zNRQejTB5A","1aApVXNlOP"],"dependent_operators":["d7ASUq0ydm","Uaa54Peajs","3EYGwJThht","y4ImoPnbV5","JwTKLfZU96","rJVOvQCfKK","uWAJUKEvyW","9FxExcQeMw","rysDP5nf3Z","e1ybzncUwg","Qy55tPpLXF","DZ8iAZOCBD","2DQ55sFlQl","t8gj7n24qd","2DDjHMKMc0","Z2TMIBDE3Q","14qkJME0vr","f6k1SAg4EE","Ph9nP6C5qx","eewbuw0ToL","u6S6b8DprG"],"result":"⪩⨒∯-13121","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4317","layer":2},{"info":"number node, value=1672","layer":2},{"info":"compute binary expreesion, left_input=4317, right_input=1672, op_id = 1aApVXNlOP binary_op_definition= 'a⩇∃⫛b = { (((b⊉≛↸a)⩤)⨰((362⩷∴b)⋥≓≎(↽≂a))) , if (a⊦⊿)>7 and b<=506 and (-a)==737 ; (((b⩤)⪒(b≧⫂∧a))⋝⋈⪟((a⨵⪆a)-(≉a))) , else }', output=-2172","layer":1},{"info":"compute unary expreesion, input=-2172, op_id = zNRQejTB5A, unary_op_definition = 'a⪥⨬⪅ = { (((a⨎1)⊹∫⫚(a⇄a))⫯⪬∳((a∽a)↳≱(∂a))) }', output=-473","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1003131⩇∃⫛⪩⨒∯122020⪥⨬⪅=⪩⨒∯-13121","reverse_text":"⪩⨒∯-13121=⪩⨒∯1003131⩇∃⫛⪩⨒∯122020⪥⨬⪅","cot":[{"info":"⪩⨒∯1003131⩇∃⫛⪩⨒∯122020=⪩⨒∯-201330","layer":1},{"info":"⪩⨒∯-201330⪥⨬⪅=⪩⨒∯-13121","layer":0}]}
{"id":122,"expression_no_base_symbol":"(⫟$1391$)⩼⇪↪$4452$↞⋁$1847$","expression":"(⫟⪩⨒∯111233)⩼⇪↪⪩⨒∯1011210↞⋁⪩⨒∯130313","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":223,"operation_count":3,"complexity_ratio":74.33333333333333,"tree":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"unary","operator":"⫟","unary_expr":{"type":"numeric_atoms","value":1391,"base":4}},"right_expr":{"type":"binary","operator":"↞⋁","left_expr":{"type":"numeric_atoms","value":4452,"base":4},"right_expr":{"type":"numeric_atoms","value":1847,"base":4}}},"used_operators":["ocnLzx9CaJ","z4E1FaHLuy","RqrPlJkxDo"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q","9FxExcQeMw","W4YGzv6Whe","Qy55tPpLXF","BjRHVeLaeN","sdazOOVcIp","Ph9nP6C5qx","t8gj7n24qd","EBcxylXtPf","f6k1SAg4EE","2DDjHMKMc0","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx","QMFrweE19q","Uaa54Peajs","CArV6hThFE","13rbtpv6ld"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1391","layer":2},{"info":"compute unary expreesion, input=1391, op_id = z4E1FaHLuy, unary_op_definition = '⫟a = { (((-a)⪨≂(a⨸⪁a))≧⫂∧((a⩷∴a)⨰(a⫡⨏a))) , if (a⫌⩹⨱)>=11 ; (((a+263)⋝⋈⪟(a⨳⩥⨓a))⪒((a⋥≓≎a)⫩⊇)) , else }', output=-3266","layer":1},{"info":"number node, value=4452","layer":2},{"info":"number node, value=1847","layer":2},{"info":"compute binary expreesion, left_input=4452, right_input=1847, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-3266, right_input=nan, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⫟⪩⨒∯111233)⩼⇪↪⪩⨒∯1011210↞⋁⪩⨒∯130313=NaN","reverse_text":"NaN=(⫟⪩⨒∯111233)⩼⇪↪⪩⨒∯1011210↞⋁⪩⨒∯130313","cot":[{"info":"⫟⪩⨒∯111233=⪩⨒∯-303002","layer":1},{"info":"⪩⨒∯1011210↞⋁⪩⨒∯130313=NaN","layer":1},{"info":"⪩⨒∯-303002⩼⇪↪NaN=NaN","layer":0}]}
{"id":123,"expression_no_base_symbol":"$1847$⊋$3147$⩇∃⫛$1418$∳⫺$1045$","expression":"⪩⨒∯130313⊋⪩⨒∯301023⩇∃⫛⪩⨒∯112022∳⫺⪩⨒∯100111","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2620,"operation_count":3,"complexity_ratio":873.3333333333334,"tree":{"type":"binary","operator":"⩇∃⫛","left_expr":{"type":"binary","operator":"⊋","left_expr":{"type":"numeric_atoms","value":1847,"base":4},"right_expr":{"type":"numeric_atoms","value":3147,"base":4}},"right_expr":{"type":"binary","operator":"∳⫺","left_expr":{"type":"numeric_atoms","value":1418,"base":4},"right_expr":{"type":"numeric_atoms","value":1045,"base":4}}},"used_operators":["1aApVXNlOP","W4tP9CfskL","AzXXKTstlj"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","e1ybzncUwg","Qy55tPpLXF","DZ8iAZOCBD","2DQ55sFlQl","t8gj7n24qd","2DDjHMKMc0","Z2TMIBDE3Q","14qkJME0vr","f6k1SAg4EE","Ph9nP6C5qx","eewbuw0ToL","u6S6b8DprG","2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu","F4yD0voBRQ","Tcnh7f0tEr","ZvLB05nZmT"],"result":"⪩⨒∯-1312000131010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1847","layer":2},{"info":"number node, value=3147","layer":2},{"info":"compute binary expreesion, left_input=1847, right_input=3147, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=-30934852","layer":1},{"info":"number node, value=1418","layer":2},{"info":"number node, value=1045","layer":2},{"info":"compute binary expreesion, left_input=1418, right_input=1045, op_id = AzXXKTstlj binary_op_definition= 'a∳⫺b = { (a≣⋋) , if (b⫳≱↱947)==166 ; (a⇣⩺⋵b) , else }', output=-260","layer":1},{"info":"compute binary expreesion, left_input=-30934852, right_input=-260, op_id = 1aApVXNlOP binary_op_definition= 'a⩇∃⫛b = { (((b⊉≛↸a)⩤)⨰((362⩷∴b)⋥≓≎(↽≂a))) , if (a⊦⊿)>7 and b<=506 and (-a)==737 ; (((b⩤)⪒(b≧⫂∧a))⋝⋈⪟((a⨵⪆a)-(≉a))) , else }', output=-30934852","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯130313⊋⪩⨒∯301023⩇∃⫛⪩⨒∯112022∳⫺⪩⨒∯100111=⪩⨒∯-1312000131010","reverse_text":"⪩⨒∯-1312000131010=⪩⨒∯130313⊋⪩⨒∯301023⩇∃⫛⪩⨒∯112022∳⫺⪩⨒∯100111","cot":[{"info":"⪩⨒∯130313⊋⪩⨒∯301023=⪩⨒∯-1312000131010","layer":1},{"info":"⪩⨒∯112022∳⫺⪩⨒∯100111=⪩⨒∯-10010","layer":1},{"info":"⪩⨒∯-1312000131010⩇∃⫛⪩⨒∯-10010=⪩⨒∯-1312000131010","layer":0}]}
{"id":124,"expression_no_base_symbol":"$1763$↤⩊$1175$≁($3870$⨜⨶$4079$)","expression":"⪩⨒∯123203↤⩊⪩⨒∯102113≁(⪩⨒∯330132⨜⨶⪩⨒∯333233)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":225,"operation_count":3,"complexity_ratio":75.0,"tree":{"type":"binary","operator":"≁","left_expr":{"type":"binary","operator":"↤⩊","left_expr":{"type":"numeric_atoms","value":1763,"base":4},"right_expr":{"type":"numeric_atoms","value":1175,"base":4}},"right_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":3870,"base":4},"right_expr":{"type":"numeric_atoms","value":4079,"base":4}}},"used_operators":["8N2wDY1A35","13rbtpv6ld","HiPekx5b7W"],"dependent_operators":["B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v","s1XTVnmDOJ","wEfv7U73WA","9cloC0Ngie","KPf6cnQVty","KYD54nUTWz","k8jYdgA6NY","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1763","layer":2},{"info":"number node, value=1175","layer":2},{"info":"compute binary expreesion, left_input=1763, right_input=1175, op_id = 13rbtpv6ld binary_op_definition= 'a↤⩊b = { ((a⫥∨⫟63)⇐≅) , if (a∺≝⩲71)<727 ; ((b%b)⊕∕(b≓∲14)) , else }', output=nan","layer":1},{"info":"number node, value=3870","layer":2},{"info":"number node, value=4079","layer":2},{"info":"compute binary expreesion, left_input=3870, right_input=4079, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-7902","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-7902, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯123203↤⩊⪩⨒∯102113≁(⪩⨒∯330132⨜⨶⪩⨒∯333233)=NaN","reverse_text":"NaN=⪩⨒∯123203↤⩊⪩⨒∯102113≁(⪩⨒∯330132⨜⨶⪩⨒∯333233)","cot":[{"info":"⪩⨒∯123203↤⩊⪩⨒∯102113=NaN","layer":1},{"info":"⪩⨒∯330132⨜⨶⪩⨒∯333233=⪩⨒∯-1323132","layer":1},{"info":"NaN≁⪩⨒∯-1323132=NaN","layer":0}]}
{"id":125,"expression_no_base_symbol":"$8342$⊬⨰$4993$+($2017$/$2275$)","expression":"⪩⨒∯2002112⊬⨰⪩⨒∯1032001+(⪩⨒∯133201/⪩⨒∯203203)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":11,"operation_count":3,"complexity_ratio":3.6666666666666665,"tree":{"type":"binary","operator":"+","left_expr":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"numeric_atoms","value":8342,"base":4},"right_expr":{"type":"numeric_atoms","value":4993,"base":4}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":2017,"base":4},"right_expr":{"type":"numeric_atoms","value":2275,"base":4}}},"used_operators":["W4YGzv6Whe","s3Fd5m9Dh2","XhwjNDsVaA"],"dependent_operators":["23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","rysDP5nf3Z"],"result":"⪩⨒∯12221322","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8342","layer":2},{"info":"number node, value=4993","layer":2},{"info":"compute binary expreesion, left_input=8342, right_input=4993, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=27258","layer":1},{"info":"number node, value=2017","layer":2},{"info":"number node, value=2275","layer":2},{"info":"compute binary expreesion, left_input=2017, right_input=2275, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute binary expreesion, left_input=27258, right_input=0, op_id = W4YGzv6Whe binary_op_definition= 'None', output=27258","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯2002112⊬⨰⪩⨒∯1032001+(⪩⨒∯133201/⪩⨒∯203203)=⪩⨒∯12221322","reverse_text":"⪩⨒∯12221322=⪩⨒∯2002112⊬⨰⪩⨒∯1032001+(⪩⨒∯133201/⪩⨒∯203203)","cot":[{"info":"⪩⨒∯2002112⊬⨰⪩⨒∯1032001=⪩⨒∯12221322","layer":1},{"info":"⪩⨒∯133201/⪩⨒∯203203=⪩⨒∯0","layer":1},{"info":"⪩⨒∯12221322+⪩⨒∯0=⪩⨒∯12221322","layer":0}]}
{"id":126,"expression_no_base_symbol":"(↑$5629$)⪪($2632$⩅⪻⪻)","expression":"(↑⪩⨒∯1113331)⪪(⪩⨒∯221020⩅⪻⪻)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":886,"operation_count":3,"complexity_ratio":295.3333333333333,"tree":{"type":"binary","operator":"⪪","left_expr":{"type":"unary","operator":"↑","unary_expr":{"type":"numeric_atoms","value":5629,"base":4}},"right_expr":{"type":"unary","operator":"⩅⪻⪻","unary_expr":{"type":"numeric_atoms","value":2632,"base":4}}},"used_operators":["xD69zh8xqp","tR7O2zTn5j","kHoXpA7yos"],"dependent_operators":["FU0Cs4j7VP","JclMnS0uGI","oRDoc9rAEX","RygbFNSyEJ","2DlMacCsIx","SUmda5xLS4","KPf6cnQVty","8HhzD0ZcuI","9Isq31Ruls"],"result":"⪩⨒∯-12013321","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5629","layer":2},{"info":"compute unary expreesion, input=5629, op_id = tR7O2zTn5j, unary_op_definition = '↑a = { ((a⩨a)⊋≦⊧(a≦↸a)) }', output=192","layer":1},{"info":"number node, value=2632","layer":2},{"info":"compute unary expreesion, input=2632, op_id = kHoXpA7yos, unary_op_definition = 'a⩅⪻⪻ = { (a⪄((a∌↝a)⨽(a∺≝⩲a))) }', output=-388961","layer":1},{"info":"compute binary expreesion, left_input=192, right_input=-388961, op_id = xD69zh8xqp binary_op_definition= 'a⪪b = { ((b⨔⇊a)↛⩡⫤) }', output=-25081","layer":0}],"base":4,"result_base":4,"text":"(↑⪩⨒∯1113331)⪪(⪩⨒∯221020⩅⪻⪻)=⪩⨒∯-12013321","reverse_text":"⪩⨒∯-12013321=(↑⪩⨒∯1113331)⪪(⪩⨒∯221020⩅⪻⪻)","cot":[{"info":"↑⪩⨒∯1113331=⪩⨒∯3000","layer":1},{"info":"⪩⨒∯221020⩅⪻⪻=⪩⨒∯-1132331201","layer":1},{"info":"⪩⨒∯3000⪪⪩⨒∯-1132331201=⪩⨒∯-12013321","layer":0}]}
{"id":127,"expression_no_base_symbol":"($7240$⫢⨠$3517$)⋕⪉⪜($1440$⪘⫢$4410$)","expression":"(⪩⨒∯1301020⫢⨠⪩⨒∯312331)⋕⪉⪜(⪩⨒∯112200⪘⫢⪩⨒∯1010322)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":103,"operation_count":3,"complexity_ratio":34.333333333333336,"tree":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"binary","operator":"⫢⨠","left_expr":{"type":"numeric_atoms","value":7240,"base":4},"right_expr":{"type":"numeric_atoms","value":3517,"base":4}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1440,"base":4},"right_expr":{"type":"numeric_atoms","value":4410,"base":4}}},"used_operators":["z6LnFrNh4i","xlXykHWxX1","oacrs7FA3X"],"dependent_operators":["sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z","KFSx94NKJn","e1ybzncUwg","zR4jO40bMj","g7Hmc5v1ko","k2HlF1dBQh","2DlMacCsIx","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⪩⨒∯3030","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7240","layer":2},{"info":"number node, value=3517","layer":2},{"info":"compute binary expreesion, left_input=7240, right_input=3517, op_id = xlXykHWxX1 binary_op_definition= 'a⫢⨠b = { (((b⩨a)⪶≀⋏(a⩌⋺b))⩒⫫(∤(≉a))) }', output=160","layer":1},{"info":"number node, value=1440","layer":2},{"info":"number node, value=4410","layer":2},{"info":"compute binary expreesion, left_input=1440, right_input=4410, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=2756","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=2756, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=204","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1301020⫢⨠⪩⨒∯312331)⋕⪉⪜(⪩⨒∯112200⪘⫢⪩⨒∯1010322)=⪩⨒∯3030","reverse_text":"⪩⨒∯3030=(⪩⨒∯1301020⫢⨠⪩⨒∯312331)⋕⪉⪜(⪩⨒∯112200⪘⫢⪩⨒∯1010322)","cot":[{"info":"⪩⨒∯1301020⫢⨠⪩⨒∯312331=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯112200⪘⫢⪩⨒∯1010322=⪩⨒∯223010","layer":1},{"info":"⪩⨒∯2200⋕⪉⪜⪩⨒∯223010=⪩⨒∯3030","layer":0}]}
{"id":128,"expression_no_base_symbol":"($6459$⇍⊗$1023$)⪥($2309$⨰$1364$)","expression":"(⪩⨒∯1210323⇍⊗⪩⨒∯33333)⪥(⪩⨒∯210011⨰⪩⨒∯111110)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":504,"operation_count":3,"complexity_ratio":168.0,"tree":{"type":"binary","operator":"⪥","left_expr":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"numeric_atoms","value":6459,"base":4},"right_expr":{"type":"numeric_atoms","value":1023,"base":4}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":2309,"base":4},"right_expr":{"type":"numeric_atoms","value":1364,"base":4}}},"used_operators":["QbnwKVWMIQ","5uvYHDjeKN","eewbuw0ToL"],"dependent_operators":["WR6HLWljOP","nhYeJWJD5X","f6k1SAg4EE","jLgFTUHLKL","PPChnnnBFF","Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯321130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6459","layer":2},{"info":"number node, value=1023","layer":2},{"info":"compute binary expreesion, left_input=6459, right_input=1023, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=-244","layer":1},{"info":"number node, value=2309","layer":2},{"info":"number node, value=1364","layer":2},{"info":"compute binary expreesion, left_input=2309, right_input=1364, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=955","layer":1},{"info":"compute binary expreesion, left_input=-244, right_input=955, op_id = QbnwKVWMIQ binary_op_definition= 'a⪥b = { (b∇⊂⋱(58∣a)) , if (b↢721)<125 ; (↩(508⪒a)) , else }', output=3676","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1210323⇍⊗⪩⨒∯33333)⪥(⪩⨒∯210011⨰⪩⨒∯111110)=⪩⨒∯321130","reverse_text":"⪩⨒∯321130=(⪩⨒∯1210323⇍⊗⪩⨒∯33333)⪥(⪩⨒∯210011⨰⪩⨒∯111110)","cot":[{"info":"⪩⨒∯1210323⇍⊗⪩⨒∯33333=⪩⨒∯-3310","layer":1},{"info":"⪩⨒∯210011⨰⪩⨒∯111110=⪩⨒∯32323","layer":1},{"info":"⪩⨒∯-3310⪥⪩⨒∯32323=⪩⨒∯321130","layer":0}]}
{"id":129,"expression_no_base_symbol":"↨(∨∊⋏$3176$)","expression":"↨(∨∊⋏⪩⨒∯301220)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":231,"operation_count":2,"complexity_ratio":115.5,"tree":{"type":"unary","operator":"↨","unary_expr":{"type":"unary","operator":"∨∊⋏","unary_expr":{"type":"numeric_atoms","value":3176,"base":4}}},"used_operators":["jiX4gk2v2Q","R5aXW34M0v"],"dependent_operators":["rGHVDoGpnC","oZj3VtZNQx","L05ObWFQCd","YjI8oCXuph","9ICcGScMcE","g7Hmc5v1ko","ocnLzx9CaJ","2DDjHMKMc0","hrf7POJlIJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3176","layer":2},{"info":"compute unary expreesion, input=3176, op_id = R5aXW34M0v, unary_op_definition = '∨∊⋏a = { (((101⋝⋈⪟206)⪍↜⋙(≦∁a))⩼⇪↪((a⩌⋺a)∴(⫇a))) }', output=63023","layer":1},{"info":"compute unary expreesion, input=63023, op_id = jiX4gk2v2Q, unary_op_definition = '↨a = { ((203≀⫉a)⨟⋌⩍a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"↨(∨∊⋏⪩⨒∯301220)=NaN","reverse_text":"NaN=↨(∨∊⋏⪩⨒∯301220)","cot":[{"info":"∨∊⋏⪩⨒∯301220=⪩⨒∯33120233","layer":1},{"info":"↨⪩⨒∯33120233=NaN","layer":0}]}
{"id":130,"expression_no_base_symbol":"⇁⨣⪵($1377$⪷)","expression":"⇁⨣⪵(⪩⨒∯111201⪷)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1384,"operation_count":2,"complexity_ratio":692.0,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"unary","operator":"⪷","unary_expr":{"type":"numeric_atoms","value":1377,"base":4}}},"used_operators":["inkyxCbjAn","Qctrpi3WzA"],"dependent_operators":["B5M0gjZbta","Nsiff2A1zJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1377","layer":2},{"info":"compute unary expreesion, input=1377, op_id = Qctrpi3WzA, unary_op_definition = 'a⪷ = { (a⊴a) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇁⨣⪵(⪩⨒∯111201⪷)=NaN","reverse_text":"NaN=⇁⨣⪵(⪩⨒∯111201⪷)","cot":[{"info":"⪩⨒∯111201⪷=NaN","layer":1},{"info":"⇁⨣⪵NaN=NaN","layer":0}]}
{"id":131,"expression_no_base_symbol":"($4467$⫳≱↱$3329$)∑⇟⊟$5860$≨$4485$","expression":"(⪩⨒∯1011303⫳≱↱⪩⨒∯310001)∑⇟⊟⪩⨒∯1123210≨⪩⨒∯1012011","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":380,"operation_count":3,"complexity_ratio":126.66666666666667,"tree":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"binary","operator":"⫳≱↱","left_expr":{"type":"numeric_atoms","value":4467,"base":4},"right_expr":{"type":"numeric_atoms","value":3329,"base":4}},"right_expr":{"type":"binary","operator":"≨","left_expr":{"type":"numeric_atoms","value":5860,"base":4},"right_expr":{"type":"numeric_atoms","value":4485,"base":4}}},"used_operators":["U7g4x0WXJJ","ZvLB05nZmT","0KMCeP1Jsh"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","2Wsdkap16l","FyVja0WsTP","wEfv7U73WA","bJkvcejdHO","HmxsFra2vL","8cLx32lpNA","jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4467","layer":2},{"info":"number node, value=3329","layer":2},{"info":"compute binary expreesion, left_input=4467, right_input=3329, op_id = ZvLB05nZmT binary_op_definition= 'a⫳≱↱b = { (((a⩹b)⇐≅)∌((a∙∹∝345)⊱⇼⊻(b≎⊠⪸a))) }', output=-204","layer":1},{"info":"number node, value=5860","layer":2},{"info":"number node, value=4485","layer":2},{"info":"compute binary expreesion, left_input=5860, right_input=4485, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-56124","layer":1},{"info":"compute binary expreesion, left_input=-204, right_input=-56124, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1011303⫳≱↱⪩⨒∯310001)∑⇟⊟⪩⨒∯1123210≨⪩⨒∯1012011=NaN","reverse_text":"NaN=(⪩⨒∯1011303⫳≱↱⪩⨒∯310001)∑⇟⊟⪩⨒∯1123210≨⪩⨒∯1012011","cot":[{"info":"⪩⨒∯1011303⫳≱↱⪩⨒∯310001=⪩⨒∯-3030","layer":1},{"info":"⪩⨒∯1123210≨⪩⨒∯1012011=⪩⨒∯-31230330","layer":1},{"info":"⪩⨒∯-3030∑⇟⊟⪩⨒∯-31230330=NaN","layer":0}]}
{"id":132,"expression_no_base_symbol":"⊤⊝$7797$∠↢$2707$","expression":"⊤⊝⪩⨒∯1321311∠↢⪩⨒∯222103","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":18,"operation_count":2,"complexity_ratio":9.0,"tree":{"type":"unary","operator":"⊤⊝","unary_expr":{"type":"binary","operator":"∠↢","left_expr":{"type":"numeric_atoms","value":7797,"base":4},"right_expr":{"type":"numeric_atoms","value":2707,"base":4}}},"used_operators":["rXAclfmB4M","KbjG8mgYpV"],"dependent_operators":["sdazOOVcIp","rysDP5nf3Z","NTOWxs364D","XPYlsWDdGa","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","nCS4ZIUYfx","COABgblf1C"],"result":"⪩⨒∯-201201122","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7797","layer":2},{"info":"number node, value=2707","layer":2},{"info":"compute binary expreesion, left_input=7797, right_input=2707, op_id = KbjG8mgYpV binary_op_definition= 'a∠↢b = { (a⊭↱((159⨳⩥⨓16)-(b⨸⪁a))) , if (b==488 or (⨞⊢a)==254) ; (⪲⇎((-b)⫡⨏(b⩚⊴⇥a))) , else }', output=-68004","layer":1},{"info":"compute unary expreesion, input=-68004, op_id = rXAclfmB4M, unary_op_definition = '⊤⊝a = { (a⪨≂700) }', output=-137306","layer":0}],"base":4,"result_base":4,"text":"⊤⊝⪩⨒∯1321311∠↢⪩⨒∯222103=⪩⨒∯-201201122","reverse_text":"⪩⨒∯-201201122=⊤⊝⪩⨒∯1321311∠↢⪩⨒∯222103","cot":[{"info":"⪩⨒∯1321311∠↢⪩⨒∯222103=⪩⨒∯-100212210","layer":1},{"info":"⊤⊝⪩⨒∯-100212210=⪩⨒∯-201201122","layer":0}]}
{"id":133,"expression_no_base_symbol":"$4888$⪎↠$4950$∣($7449$⨭⪣$2266$)","expression":"⪩⨒∯1030120⪎↠⪩⨒∯1031112∣(⪩⨒∯1310121⨭⪣⪩⨒∯203122)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":44,"operation_count":3,"complexity_ratio":14.666666666666666,"tree":{"type":"binary","operator":"∣","left_expr":{"type":"binary","operator":"⪎↠","left_expr":{"type":"numeric_atoms","value":4888,"base":4},"right_expr":{"type":"numeric_atoms","value":4950,"base":4}},"right_expr":{"type":"binary","operator":"⨭⪣","left_expr":{"type":"numeric_atoms","value":7449,"base":4},"right_expr":{"type":"numeric_atoms","value":2266,"base":4}}},"used_operators":["PPChnnnBFF","3tVxb0NHM4","kn8WO9XteQ"],"dependent_operators":["eLAdDNolq6","eH2TOUuTDT","Ph9nP6C5qx","i8ToyICDmI","P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM","vRio1gEz1j","61wBmkZwlr","SWo3A1KBJH","8jW3W4yZS5","LkLIoiE525","Y7wcNGrDQJ","PPChnnnBFF"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4888","layer":2},{"info":"number node, value=4950","layer":2},{"info":"compute binary expreesion, left_input=4888, right_input=4950, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=160","layer":1},{"info":"number node, value=7449","layer":2},{"info":"number node, value=2266","layer":2},{"info":"compute binary expreesion, left_input=7449, right_input=2266, op_id = kn8WO9XteQ binary_op_definition= 'a⨭⪣b = { ((486⇩)⩵∡(a∣a)) , if (b⇯⋐)>445 or (≋b)>319 or b<=69 ; (↯⪼(⇋↷b)) , else }', output=6170","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=6170, op_id = PPChnnnBFF binary_op_definition= 'a∣b = { (≤/((a⪐)≧⫂∧(a∲⫓b))) , if (b⪐)<590 ; a , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1030120⪎↠⪩⨒∯1031112∣(⪩⨒∯1310121⨭⪣⪩⨒∯203122)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⪩⨒∯1030120⪎↠⪩⨒∯1031112∣(⪩⨒∯1310121⨭⪣⪩⨒∯203122)","cot":[{"info":"⪩⨒∯1030120⪎↠⪩⨒∯1031112=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯1310121⨭⪣⪩⨒∯203122=⪩⨒∯1200122","layer":1},{"info":"⪩⨒∯2200∣⪩⨒∯1200122=⪩⨒∯2200","layer":0}]}
{"id":134,"expression_no_base_symbol":"(≘$3549$)⪪$1265$⨜⨶$3889$","expression":"(≘⪩⨒∯313131)⪪⪩⨒∯103301⨜⨶⪩⨒∯330301","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":292,"operation_count":3,"complexity_ratio":97.33333333333333,"tree":{"type":"binary","operator":"⪪","left_expr":{"type":"unary","operator":"≘","unary_expr":{"type":"numeric_atoms","value":3549,"base":4}},"right_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":1265,"base":4},"right_expr":{"type":"numeric_atoms","value":3889,"base":4}}},"used_operators":["xD69zh8xqp","tcjXMdvYtA","HiPekx5b7W"],"dependent_operators":["FU0Cs4j7VP","JclMnS0uGI","XTarYq4gQB","xRrnTEsQ6j","oPMjh9089D","BUOGQAYlQx","oacrs7FA3X","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3549","layer":2},{"info":"compute unary expreesion, input=3549, op_id = tcjXMdvYtA, unary_op_definition = '≘a = { ((⊀(⪝⪂⫅a))⫁⪎(a⪘⫢(⋂a))) }', output=7826329","layer":1},{"info":"number node, value=1265","layer":2},{"info":"number node, value=3889","layer":2},{"info":"compute binary expreesion, left_input=1265, right_input=3889, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-7522","layer":1},{"info":"compute binary expreesion, left_input=7826329, right_input=-7522, op_id = xD69zh8xqp binary_op_definition= 'a⪪b = { ((b⨔⇊a)↛⩡⫤) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(≘⪩⨒∯313131)⪪⪩⨒∯103301⨜⨶⪩⨒∯330301=NaN","reverse_text":"NaN=(≘⪩⨒∯313131)⪪⪩⨒∯103301⨜⨶⪩⨒∯330301","cot":[{"info":"≘⪩⨒∯313131=⪩⨒∯131312232121","layer":1},{"info":"⪩⨒∯103301⨜⨶⪩⨒∯330301=⪩⨒∯-1311202","layer":1},{"info":"⪩⨒∯131312232121⪪⪩⨒∯-1311202=NaN","layer":0}]}
{"id":135,"expression_no_base_symbol":"(⫟$7506$)↡⊰⫅($2053$⇪⋭)","expression":"(⫟⪩⨒∯1311102)↡⊰⫅(⪩⨒∯200011⇪⋭)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":74,"operation_count":3,"complexity_ratio":24.666666666666668,"tree":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"unary","operator":"⫟","unary_expr":{"type":"numeric_atoms","value":7506,"base":4}},"right_expr":{"type":"unary","operator":"⇪⋭","unary_expr":{"type":"numeric_atoms","value":2053,"base":4}}},"used_operators":["VCtxkLNOzz","z4E1FaHLuy","Z8Yg6dlDSp"],"dependent_operators":["Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn","9FxExcQeMw","W4YGzv6Whe","Qy55tPpLXF","BjRHVeLaeN","sdazOOVcIp","Ph9nP6C5qx","t8gj7n24qd","EBcxylXtPf","f6k1SAg4EE","2DDjHMKMc0","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx","QMFrweE19q","T2fj7uvVaJ","5KTvxBwnZo","inkyxCbjAn"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7506","layer":2},{"info":"compute unary expreesion, input=7506, op_id = z4E1FaHLuy, unary_op_definition = '⫟a = { (((-a)⪨≂(a⨸⪁a))≧⫂∧((a⩷∴a)⨰(a⫡⨏a))) , if (a⫌⩹⨱)>=11 ; (((a+263)⋝⋈⪟(a⨳⩥⨓a))⪒((a⋥≓≎a)⫩⊇)) , else }', output=-21611","layer":1},{"info":"number node, value=2053","layer":2},{"info":"compute unary expreesion, input=2053, op_id = Z8Yg6dlDSp, unary_op_definition = 'a⇪⋭ = { ((a≒∊a)⋓(⇁⨣⪵a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-21611, right_input=nan, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⫟⪩⨒∯1311102)↡⊰⫅(⪩⨒∯200011⇪⋭)=NaN","reverse_text":"NaN=(⫟⪩⨒∯1311102)↡⊰⫅(⪩⨒∯200011⇪⋭)","cot":[{"info":"⫟⪩⨒∯1311102=⪩⨒∯-11101223","layer":1},{"info":"⪩⨒∯200011⇪⋭=NaN","layer":1},{"info":"⪩⨒∯-11101223↡⊰⫅NaN=NaN","layer":0}]}
{"id":136,"expression_no_base_symbol":"↨$2465$∇⊂⋱$3212$","expression":"↨⪩⨒∯212201∇⊂⋱⪩⨒∯302030","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":176,"operation_count":2,"complexity_ratio":88.0,"tree":{"type":"unary","operator":"↨","unary_expr":{"type":"binary","operator":"∇⊂⋱","left_expr":{"type":"numeric_atoms","value":2465,"base":4},"right_expr":{"type":"numeric_atoms","value":3212,"base":4}}},"used_operators":["jiX4gk2v2Q","nhYeJWJD5X"],"dependent_operators":["rGHVDoGpnC","oZj3VtZNQx","P8v4zCKN1o","23Mk6UjR3U","f6k1SAg4EE","AF7qkfDlqP","nCS4ZIUYfx"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2465","layer":2},{"info":"number node, value=3212","layer":2},{"info":"compute binary expreesion, left_input=2465, right_input=3212, op_id = nhYeJWJD5X binary_op_definition= 'a∇⊂⋱b = { (b⪒b) , if a<143 ; ((⨑⩽⪐a)⋷(∥⊫(a⨳⩥⨓a))) , else }', output=4384","layer":1},{"info":"compute unary expreesion, input=4384, op_id = jiX4gk2v2Q, unary_op_definition = '↨a = { ((203≀⫉a)⨟⋌⩍a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"↨⪩⨒∯212201∇⊂⋱⪩⨒∯302030=NaN","reverse_text":"NaN=↨⪩⨒∯212201∇⊂⋱⪩⨒∯302030","cot":[{"info":"⪩⨒∯212201∇⊂⋱⪩⨒∯302030=⪩⨒∯1010200","layer":1},{"info":"↨⪩⨒∯1010200=NaN","layer":0}]}
{"id":137,"expression_no_base_symbol":"⊤⊝$5719$⨳⩥⨓$1281$","expression":"⊤⊝⪩⨒∯1121113⨳⩥⨓⪩⨒∯110001","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8,"operation_count":2,"complexity_ratio":4.0,"tree":{"type":"unary","operator":"⊤⊝","unary_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":5719,"base":4},"right_expr":{"type":"numeric_atoms","value":1281,"base":4}}},"used_operators":["rXAclfmB4M","nCS4ZIUYfx"],"dependent_operators":["sdazOOVcIp","W4YGzv6Whe","rysDP5nf3Z"],"result":"⪩⨒∯-2132332","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5719","layer":2},{"info":"number node, value=1281","layer":2},{"info":"compute binary expreesion, left_input=5719, right_input=1281, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-4438","layer":1},{"info":"compute unary expreesion, input=-4438, op_id = rXAclfmB4M, unary_op_definition = '⊤⊝a = { (a⪨≂700) }', output=-10174","layer":0}],"base":4,"result_base":4,"text":"⊤⊝⪩⨒∯1121113⨳⩥⨓⪩⨒∯110001=⪩⨒∯-2132332","reverse_text":"⪩⨒∯-2132332=⊤⊝⪩⨒∯1121113⨳⩥⨓⪩⨒∯110001","cot":[{"info":"⪩⨒∯1121113⨳⩥⨓⪩⨒∯110001=⪩⨒∯-1011112","layer":1},{"info":"⊤⊝⪩⨒∯-1011112=⪩⨒∯-2132332","layer":0}]}
{"id":138,"expression_no_base_symbol":"$1265$∺≝⩲$2890$⊨(∂$3597$)","expression":"⪩⨒∯103301∺≝⩲⪩⨒∯231022⊨(∂⪩⨒∯320031)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":18,"operation_count":3,"complexity_ratio":6.0,"tree":{"type":"binary","operator":"⊨","left_expr":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"numeric_atoms","value":1265,"base":4},"right_expr":{"type":"numeric_atoms","value":2890,"base":4}},"right_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":3597,"base":4}}},"used_operators":["vg4gO5BX6G","KPf6cnQVty","Uaa54Peajs"],"dependent_operators":["NTOWxs364D","JLbD19bQDL","xUOZtlo3hN","AF7qkfDlqP","BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1265","layer":2},{"info":"number node, value=2890","layer":2},{"info":"compute binary expreesion, left_input=1265, right_input=2890, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":1},{"info":"number node, value=3597","layer":2},{"info":"compute unary expreesion, input=3597, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=nan, op_id = vg4gO5BX6G binary_op_definition= 'a⊨b = { (⨞⊢(b⪠⩆⊳)) , if a<=416 ; (⨑⩽⪐(a⩚⊴⇥a)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯103301∺≝⩲⪩⨒∯231022⊨(∂⪩⨒∯320031)=NaN","reverse_text":"NaN=⪩⨒∯103301∺≝⩲⪩⨒∯231022⊨(∂⪩⨒∯320031)","cot":[{"info":"⪩⨒∯103301∺≝⩲⪩⨒∯231022=⪩⨒∯2200","layer":1},{"info":"∂⪩⨒∯320031=NaN","layer":1},{"info":"⪩⨒∯2200⊨NaN=NaN","layer":0}]}
{"id":139,"expression_no_base_symbol":"($1327$≀⫉$2211$)⇍⊗$5107$≹⇙⪍$2963$","expression":"(⪩⨒∯110233≀⫉⪩⨒∯202203)⇍⊗⪩⨒∯1033303≹⇙⪍⪩⨒∯232103","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":204,"operation_count":3,"complexity_ratio":68.0,"tree":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"binary","operator":"≀⫉","left_expr":{"type":"numeric_atoms","value":1327,"base":4},"right_expr":{"type":"numeric_atoms","value":2211,"base":4}},"right_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":5107,"base":4},"right_expr":{"type":"numeric_atoms","value":2963,"base":4}}},"used_operators":["5uvYHDjeKN","oZj3VtZNQx","AHs5Up7iyr"],"dependent_operators":["Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o","9FxExcQeMw","Tcnh7f0tEr","jBncVCNhdl","FyVja0WsTP","Ikt5ks8PT7","EWw2JM7wp4","cTDWOvIxvz","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1327","layer":2},{"info":"number node, value=2211","layer":2},{"info":"compute binary expreesion, left_input=1327, right_input=2211, op_id = oZj3VtZNQx binary_op_definition= 'a≀⫉b = { (((55≣⋋)∝(a⩷∴a))⊱⇼⊻((a⪉⨛b)⩧⪆(b⋭≵475))) }', output=2822","layer":1},{"info":"number node, value=5107","layer":2},{"info":"number node, value=2963","layer":2},{"info":"compute binary expreesion, left_input=5107, right_input=2963, op_id = AHs5Up7iyr binary_op_definition= 'a≹⇙⪍b = {a, if b == 0; (a≹⇙⪍(b-1))⪢(b), if b > 0 and abs(b) < 1000; -(a≹⇙⪍(b+1))⪢(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=2822, right_input=nan, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯110233≀⫉⪩⨒∯202203)⇍⊗⪩⨒∯1033303≹⇙⪍⪩⨒∯232103=NaN","reverse_text":"NaN=(⪩⨒∯110233≀⫉⪩⨒∯202203)⇍⊗⪩⨒∯1033303≹⇙⪍⪩⨒∯232103","cot":[{"info":"⪩⨒∯110233≀⫉⪩⨒∯202203=⪩⨒∯230012","layer":1},{"info":"⪩⨒∯1033303≹⇙⪍⪩⨒∯232103=NaN","layer":1},{"info":"⪩⨒∯230012⇍⊗NaN=NaN","layer":0}]}
{"id":140,"expression_no_base_symbol":"($5096$⇗⋫)⨜⨶($1491$%$6295$)","expression":"(⪩⨒∯1033220⇗⋫)⨜⨶(⪩⨒∯113103%⪩⨒∯1202113)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":27,"operation_count":3,"complexity_ratio":9.0,"tree":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"unary","operator":"⇗⋫","unary_expr":{"type":"numeric_atoms","value":5096,"base":4}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":1491,"base":4},"right_expr":{"type":"numeric_atoms","value":6295,"base":4}}},"used_operators":["HiPekx5b7W","hpqmaQFPrd","k8jYdgA6NY"],"dependent_operators":["N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","rxpJgHHUmx","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5096","layer":2},{"info":"compute unary expreesion, input=5096, op_id = hpqmaQFPrd, unary_op_definition = 'a⇗⋫ = { (a≭a) }', output=nan","layer":1},{"info":"number node, value=1491","layer":2},{"info":"number node, value=6295","layer":2},{"info":"compute binary expreesion, left_input=1491, right_input=6295, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1491","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1491, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1033220⇗⋫)⨜⨶(⪩⨒∯113103%⪩⨒∯1202113)=NaN","reverse_text":"NaN=(⪩⨒∯1033220⇗⋫)⨜⨶(⪩⨒∯113103%⪩⨒∯1202113)","cot":[{"info":"⪩⨒∯1033220⇗⋫=NaN","layer":1},{"info":"⪩⨒∯113103%⪩⨒∯1202113=⪩⨒∯113103","layer":1},{"info":"NaN⨜⨶⪩⨒∯113103=NaN","layer":0}]}
{"id":141,"expression_no_base_symbol":"⇋⊎⋝($1229$⊹∫⫚$3352$)","expression":"⇋⊎⋝(⪩⨒∯103031⊹∫⫚⪩⨒∯310120)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":97,"operation_count":2,"complexity_ratio":48.5,"tree":{"type":"unary","operator":"⇋⊎⋝","unary_expr":{"type":"binary","operator":"⊹∫⫚","left_expr":{"type":"numeric_atoms","value":1229,"base":4},"right_expr":{"type":"numeric_atoms","value":3352,"base":4}}},"used_operators":["CzM2PEoXns","uWAJUKEvyW"],"dependent_operators":["dWAJyo7jo9","BiWNJpBvwn","w2P8NbNXyL","vg4gO5BX6G","k8jYdgA6NY","g55IO6H4Gj","2td37pGCOC","jLgFTUHLKL"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1229","layer":2},{"info":"number node, value=3352","layer":2},{"info":"compute binary expreesion, left_input=1229, right_input=3352, op_id = uWAJUKEvyW binary_op_definition= 'a⊹∫⫚b = { (↩(a⊨b)) , if (⩦⩻⨪a)==479 or (b⊉↱≁467)==779 ; ((b⨸⪁b)%(b⩍⋽⫝̸187)) , else }', output=-56","layer":1},{"info":"compute unary expreesion, input=-56, op_id = CzM2PEoXns, unary_op_definition = '⇋⊎⋝a = { (a⪢a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇋⊎⋝(⪩⨒∯103031⊹∫⫚⪩⨒∯310120)=NaN","reverse_text":"NaN=⇋⊎⋝(⪩⨒∯103031⊹∫⫚⪩⨒∯310120)","cot":[{"info":"⪩⨒∯103031⊹∫⫚⪩⨒∯310120=⪩⨒∯-320","layer":1},{"info":"⇋⊎⋝⪩⨒∯-320=NaN","layer":0}]}
{"id":142,"expression_no_base_symbol":"($6843$⋛$1805$)⨐($4479$≄⊠$1702$)","expression":"(⪩⨒∯1222323⋛⪩⨒∯130031)⨐(⪩⨒∯1011333≄⊠⪩⨒∯122212)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":326,"operation_count":3,"complexity_ratio":108.66666666666667,"tree":{"type":"binary","operator":"⨐","left_expr":{"type":"binary","operator":"⋛","left_expr":{"type":"numeric_atoms","value":6843,"base":4},"right_expr":{"type":"numeric_atoms","value":1805,"base":4}},"right_expr":{"type":"binary","operator":"≄⊠","left_expr":{"type":"numeric_atoms","value":4479,"base":4},"right_expr":{"type":"numeric_atoms","value":1702,"base":4}}},"used_operators":["Noe24qw2ks","YbUVn0Rbpy","vXNesLlMH1"],"dependent_operators":["u6S6b8DprG","2DQ55sFlQl","QMFrweE19q","d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA","d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI"],"result":"⪩⨒∯202132122","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6843","layer":2},{"info":"number node, value=1805","layer":2},{"info":"compute binary expreesion, left_input=6843, right_input=1805, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-70605","layer":1},{"info":"number node, value=4479","layer":2},{"info":"number node, value=1702","layer":2},{"info":"compute binary expreesion, left_input=4479, right_input=1702, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=31900","layer":1},{"info":"compute binary expreesion, left_input=-70605, right_input=31900, op_id = Noe24qw2ks binary_op_definition= 'a⨐b = { (↽≂a) , if (a⨵⪆301)>43 ; (b⫡⨏a) , else }', output=141210","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1222323⋛⪩⨒∯130031)⨐(⪩⨒∯1011333≄⊠⪩⨒∯122212)=⪩⨒∯202132122","reverse_text":"⪩⨒∯202132122=(⪩⨒∯1222323⋛⪩⨒∯130031)⨐(⪩⨒∯1011333≄⊠⪩⨒∯122212)","cot":[{"info":"⪩⨒∯1222323⋛⪩⨒∯130031=⪩⨒∯-101033031","layer":1},{"info":"⪩⨒∯1011333≄⊠⪩⨒∯122212=⪩⨒∯13302130","layer":1},{"info":"⪩⨒∯-101033031⨐⪩⨒∯13302130=⪩⨒∯202132122","layer":0}]}
{"id":143,"expression_no_base_symbol":"≯($1986$∙∹∝$4686$)","expression":"≯(⪩⨒∯133002∙∹∝⪩⨒∯1021032)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16,"operation_count":2,"complexity_ratio":8.0,"tree":{"type":"unary","operator":"≯","unary_expr":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"numeric_atoms","value":1986,"base":4},"right_expr":{"type":"numeric_atoms","value":4686,"base":4}}},"used_operators":["keWfFq85dY","HmxsFra2vL"],"dependent_operators":["g55IO6H4Gj","JLbD19bQDL","BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1986","layer":2},{"info":"number node, value=4686","layer":2},{"info":"compute binary expreesion, left_input=1986, right_input=4686, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = keWfFq85dY, unary_op_definition = '≯a = { ((a⨸⪁a)⪠⩆⊳) }', output=0","layer":0}],"base":4,"result_base":4,"text":"≯(⪩⨒∯133002∙∹∝⪩⨒∯1021032)=⪩⨒∯0","reverse_text":"⪩⨒∯0=≯(⪩⨒∯133002∙∹∝⪩⨒∯1021032)","cot":[{"info":"⪩⨒∯133002∙∹∝⪩⨒∯1021032=⪩⨒∯0","layer":1},{"info":"≯⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":144,"expression_no_base_symbol":"$3316$⊝⪿⪼$3994$↰","expression":"⪩⨒∯303310⊝⪿⪼⪩⨒∯332122↰","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":26,"operation_count":2,"complexity_ratio":13.0,"tree":{"type":"unary","operator":"↰","unary_expr":{"type":"binary","operator":"⊝⪿⪼","left_expr":{"type":"numeric_atoms","value":3316,"base":4},"right_expr":{"type":"numeric_atoms","value":3994,"base":4}}},"used_operators":["bl5wxAcryP","3Oe9XWJUTD"],"dependent_operators":["nCS4ZIUYfx","Z2TMIBDE3Q","NTOWxs364D","Qy55tPpLXF","8w2t5hMYqp","t8gj7n24qd","eewbuw0ToL","QMFrweE19q"],"result":"⪩⨒∯32202303","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3316","layer":2},{"info":"number node, value=3994","layer":2},{"info":"compute binary expreesion, left_input=3316, right_input=3994, op_id = 3Oe9XWJUTD binary_op_definition= 'a⊝⪿⪼b = { ((⊄⩳↩(480⩚⊴⇥a))⫡⨏((a⨰b)⋥≓≎(-b))) }', output=59672","layer":1},{"info":"compute unary expreesion, input=59672, op_id = bl5wxAcryP, unary_op_definition = 'a↰ = { ((a⨳⩥⨓101)⩤) }', output=59571","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯303310⊝⪿⪼⪩⨒∯332122↰=⪩⨒∯32202303","reverse_text":"⪩⨒∯32202303=⪩⨒∯303310⊝⪿⪼⪩⨒∯332122↰","cot":[{"info":"⪩⨒∯303310⊝⪿⪼⪩⨒∯332122=⪩⨒∯32210120","layer":1},{"info":"⪩⨒∯32210120↰=⪩⨒∯32202303","layer":0}]}
{"id":145,"expression_no_base_symbol":"($9898$≁$1911$)⫞⩸⩒(⫛⫱⨽$6549$)","expression":"(⪩⨒∯2122222≁⪩⨒∯131313)⫞⩸⩒(⫛⫱⨽⪩⨒∯1212111)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1492,"operation_count":3,"complexity_ratio":497.3333333333333,"tree":{"type":"binary","operator":"⫞⩸⩒","left_expr":{"type":"binary","operator":"≁","left_expr":{"type":"numeric_atoms","value":9898,"base":4},"right_expr":{"type":"numeric_atoms","value":1911,"base":4}},"right_expr":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"numeric_atoms","value":6549,"base":4}}},"used_operators":["XGcMNugi78","8N2wDY1A35","DlLNRPXxWL"],"dependent_operators":["VJ330n2nnx","JclMnS0uGI","SWo3A1KBJH","rJVOvQCfKK","B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v","rGHVDoGpnC"],"result":"⪩⨒∯13332113","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=9898","layer":2},{"info":"number node, value=1911","layer":2},{"info":"compute binary expreesion, left_input=9898, right_input=1911, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=32663","layer":1},{"info":"number node, value=6549","layer":2},{"info":"compute unary expreesion, input=6549, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=32663, right_input=0, op_id = XGcMNugi78 binary_op_definition= 'a⫞⩸⩒b = { (a⨎b) , if ((⇋↷b)>164 and (a↬⩅∪)<=12 and (b⨔⇊430)!=387) ; a , else }', output=32663","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2122222≁⪩⨒∯131313)⫞⩸⩒(⫛⫱⨽⪩⨒∯1212111)=⪩⨒∯13332113","reverse_text":"⪩⨒∯13332113=(⪩⨒∯2122222≁⪩⨒∯131313)⫞⩸⩒(⫛⫱⨽⪩⨒∯1212111)","cot":[{"info":"⪩⨒∯2122222≁⪩⨒∯131313=⪩⨒∯13332113","layer":1},{"info":"⫛⫱⨽⪩⨒∯1212111=⪩⨒∯0","layer":1},{"info":"⪩⨒∯13332113⫞⩸⩒⪩⨒∯0=⪩⨒∯13332113","layer":0}]}
{"id":146,"expression_no_base_symbol":"$1624$≴⪞⇿$5780$⪎⩰","expression":"⪩⨒∯121120≴⪞⇿⪩⨒∯1122110⪎⩰","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1389,"operation_count":2,"complexity_ratio":694.5,"tree":{"type":"unary","operator":"⪎⩰","unary_expr":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"numeric_atoms","value":1624,"base":4},"right_expr":{"type":"numeric_atoms","value":5780,"base":4}}},"used_operators":["2ufhKmSs5H","lvlrscuwVU"],"dependent_operators":["DpFCA1CohY","N41Kp7NANJ","sdazOOVcIp","EBcxylXtPf","f6k1SAg4EE","COABgblf1C","DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP"],"result":"⪩⨒∯-202","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1624","layer":2},{"info":"number node, value=5780","layer":2},{"info":"compute binary expreesion, left_input=1624, right_input=5780, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=3650636","layer":1},{"info":"compute unary expreesion, input=3650636, op_id = 2ufhKmSs5H, unary_op_definition = 'a⪎⩰ = { (17≋⫹) , if a>=326 and a!=597 ; (((a⪒a)⫌⩹⨱)⊭↱(⋗⩬⋾(756⪨≂a))) , else }', output=-34","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯121120≴⪞⇿⪩⨒∯1122110⪎⩰=⪩⨒∯-202","reverse_text":"⪩⨒∯-202=⪩⨒∯121120≴⪞⇿⪩⨒∯1122110⪎⩰","cot":[{"info":"⪩⨒∯121120≴⪞⇿⪩⨒∯1122110=⪩⨒∯31323101030","layer":1},{"info":"⪩⨒∯31323101030⪎⩰=⪩⨒∯-202","layer":0}]}
{"id":147,"expression_no_base_symbol":"(⩷⨜⫀$1128$)⪘⫢$2704$⊢$1217$","expression":"(⩷⨜⫀⪩⨒∯101220)⪘⫢⪩⨒∯222100⊢⪩⨒∯103001","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":40,"operation_count":3,"complexity_ratio":13.333333333333334,"tree":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"unary","operator":"⩷⨜⫀","unary_expr":{"type":"numeric_atoms","value":1128,"base":4}},"right_expr":{"type":"binary","operator":"⊢","left_expr":{"type":"numeric_atoms","value":2704,"base":4},"right_expr":{"type":"numeric_atoms","value":1217,"base":4}}},"used_operators":["oacrs7FA3X","CDi0ktkjQ4","5twsqlHp2o"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","ruOEQAzv1W","nhYeJWJD5X","P8v4zCKN1o","Qy55tPpLXF","BjRHVeLaeN","DZ8iAZOCBD","7j4O788W3g","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","14qkJME0vr","D4vGDi5EA2","2td37pGCOC"],"result":"⪩⨒∯-1","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1128","layer":2},{"info":"compute unary expreesion, input=1128, op_id = CDi0ktkjQ4, unary_op_definition = '⩷⨜⫀a = { (a∇⊂⋱383) , if a<1 ; (↔a) , else }', output=-855","layer":1},{"info":"number node, value=2704","layer":2},{"info":"number node, value=1217","layer":2},{"info":"compute binary expreesion, left_input=2704, right_input=1217, op_id = 5twsqlHp2o binary_op_definition= 'a⊢b = { (((225⫩⊇)⊉≛↸(∥⊫a))⨵⪆(25⊉≛↸(b⋥≓≎47))) , if (a≦≮≮)==364 ; (((b⊦⊿)⪨≂(⩦⩻⨪b))↺((⨞⊢a)⪨≂(-1))) , else }', output=-5652","layer":1},{"info":"compute binary expreesion, left_input=-855, right_input=-5652, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=-1","layer":0}],"base":4,"result_base":4,"text":"(⩷⨜⫀⪩⨒∯101220)⪘⫢⪩⨒∯222100⊢⪩⨒∯103001=⪩⨒∯-1","reverse_text":"⪩⨒∯-1=(⩷⨜⫀⪩⨒∯101220)⪘⫢⪩⨒∯222100⊢⪩⨒∯103001","cot":[{"info":"⩷⨜⫀⪩⨒∯101220=⪩⨒∯-31113","layer":1},{"info":"⪩⨒∯222100⊢⪩⨒∯103001=⪩⨒∯-1120110","layer":1},{"info":"⪩⨒∯-31113⪘⫢⪩⨒∯-1120110=⪩⨒∯-1","layer":0}]}
{"id":148,"expression_no_base_symbol":"($4089$≧⫂∧$6257$)⊮⊟↴$1647$⊮⊟↴$3207$","expression":"(⪩⨒∯333321≧⫂∧⪩⨒∯1201301)⊮⊟↴⪩⨒∯121233⊮⊟↴⪩⨒∯302013","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":87,"operation_count":3,"complexity_ratio":29.0,"tree":{"type":"binary","operator":"⊮⊟↴","left_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":4089,"base":4},"right_expr":{"type":"numeric_atoms","value":6257,"base":4}},"right_expr":{"type":"binary","operator":"⊮⊟↴","left_expr":{"type":"numeric_atoms","value":1647,"base":4},"right_expr":{"type":"numeric_atoms","value":3207,"base":4}}},"used_operators":["QDVgd2eftb","Ph9nP6C5qx"],"dependent_operators":["XhwjNDsVaA","C6VvDP6HwP","WkeUrDK8WX","kuIXHzHcAH","3Oe9XWJUTD","rJVOvQCfKK","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4089","layer":2},{"info":"number node, value=6257","layer":2},{"info":"compute binary expreesion, left_input=4089, right_input=6257, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=5784","layer":1},{"info":"number node, value=1647","layer":2},{"info":"number node, value=3207","layer":2},{"info":"compute binary expreesion, left_input=1647, right_input=3207, op_id = QDVgd2eftb binary_op_definition= 'a⊮⊟↴b = { ((⩰267)⪨⊡(b⊝⪿⪼a)) , if a!=19 ; ((b⨎372)/(b⪑⩈)) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=5784, right_input=0, op_id = QDVgd2eftb binary_op_definition= 'a⊮⊟↴b = { ((⩰267)⪨⊡(b⊝⪿⪼a)) , if a!=19 ; ((b⨎372)/(b⪑⩈)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯333321≧⫂∧⪩⨒∯1201301)⊮⊟↴⪩⨒∯121233⊮⊟↴⪩⨒∯302013=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯333321≧⫂∧⪩⨒∯1201301)⊮⊟↴⪩⨒∯121233⊮⊟↴⪩⨒∯302013","cot":[{"info":"⪩⨒∯333321≧⫂∧⪩⨒∯1201301=⪩⨒∯1122120","layer":1},{"info":"⪩⨒∯121233⊮⊟↴⪩⨒∯302013=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1122120⊮⊟↴⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":149,"expression_no_base_symbol":"($3507$⫑%∭)∓⋝($1736$∛$2668$)","expression":"(⪩⨒∯312303⫑%∭)∓⋝(⪩⨒∯123020∛⪩⨒∯221230)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1086,"operation_count":3,"complexity_ratio":362.0,"tree":{"type":"binary","operator":"∓⋝","left_expr":{"type":"unary","operator":"⫑%∭","unary_expr":{"type":"numeric_atoms","value":3507,"base":4}},"right_expr":{"type":"binary","operator":"∛","left_expr":{"type":"numeric_atoms","value":1736,"base":4},"right_expr":{"type":"numeric_atoms","value":2668,"base":4}}},"used_operators":["PoHhknlbAi","xUx7qlDO4z","w2537kitQq"],"dependent_operators":["DZ8iAZOCBD","DbCuESL50I","mqXw5SEYmG","2MzE1hQ0cz","GODebY97qR","qWUSsah53b","XhwjNDsVaA","oZj3VtZNQx","KYD54nUTWz","nREPSIbpBE","rGHVDoGpnC","DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3507","layer":2},{"info":"compute unary expreesion, input=3507, op_id = xUx7qlDO4z, unary_op_definition = 'a⫑%∭ = { (((a⨟⋌⩍23)⫥∨⫟(a≀⫉a))/((a⨚141)⪟⇏(⫡⇟⇯a))) }', output=nan","layer":1},{"info":"number node, value=1736","layer":2},{"info":"number node, value=2668","layer":2},{"info":"compute binary expreesion, left_input=1736, right_input=2668, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=-670","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-670, op_id = PoHhknlbAi binary_op_definition= 'a∓⋝b = { (((a⊉≛↸a)⫸⊐(⋼∭⪍b))∩⋅) }', output=67","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯312303⫑%∭)∓⋝(⪩⨒∯123020∛⪩⨒∯221230)=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=(⪩⨒∯312303⫑%∭)∓⋝(⪩⨒∯123020∛⪩⨒∯221230)","cot":[{"info":"⪩⨒∯312303⫑%∭=NaN","layer":1},{"info":"⪩⨒∯123020∛⪩⨒∯221230=⪩⨒∯-22132","layer":1},{"info":"NaN∓⋝⪩⨒∯-22132=⪩⨒∯1003","layer":0}]}
{"id":150,"expression_no_base_symbol":"($1552$⪘⫢$2345$)⋹⋡⊁(⇾⩊⇾$2925$)","expression":"(⪩⨒∯120100⪘⫢⪩⨒∯210221)⋹⋡⊁(⇾⩊⇾⪩⨒∯231231)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":50,"operation_count":3,"complexity_ratio":16.666666666666668,"tree":{"type":"binary","operator":"⋹⋡⊁","left_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1552,"base":4},"right_expr":{"type":"numeric_atoms","value":2345,"base":4}},"right_expr":{"type":"unary","operator":"⇾⩊⇾","unary_expr":{"type":"numeric_atoms","value":2925,"base":4}}},"used_operators":["As8RqfVLgs","oacrs7FA3X","bx9Z9DAK5y"],"dependent_operators":["ljTHtUsqzn","WkeUrDK8WX","fu6greOZ01","xRrnTEsQ6j","oPMjh9089D","ivGwdmUAux","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","W4YGzv6Whe","BjRHVeLaeN","8w2t5hMYqp","QMFrweE19q"],"result":"⪩⨒∯11300122","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1552","layer":2},{"info":"number node, value=2345","layer":2},{"info":"compute binary expreesion, left_input=1552, right_input=2345, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=2980","layer":1},{"info":"number node, value=2925","layer":2},{"info":"compute unary expreesion, input=2925, op_id = bx9Z9DAK5y, unary_op_definition = '⇾⩊⇾a = { (⊄⩳↩((a+259)⫡⨏(a⫩⊇))) }', output=-32811","layer":1},{"info":"compute binary expreesion, left_input=2980, right_input=-32811, op_id = As8RqfVLgs binary_op_definition= 'a⋹⋡⊁b = { ((a⨐⩸⫘247)⫁⪎(⩰b)) , if (⫵↿b)==517 or b>135 ; (⊀(≀↧⇸a)) , else }', output=23578","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯120100⪘⫢⪩⨒∯210221)⋹⋡⊁(⇾⩊⇾⪩⨒∯231231)=⪩⨒∯11300122","reverse_text":"⪩⨒∯11300122=(⪩⨒∯120100⪘⫢⪩⨒∯210221)⋹⋡⊁(⇾⩊⇾⪩⨒∯231231)","cot":[{"info":"⪩⨒∯120100⪘⫢⪩⨒∯210221=⪩⨒∯232210","layer":1},{"info":"⇾⩊⇾⪩⨒∯231231=⪩⨒∯-20000223","layer":1},{"info":"⪩⨒∯232210⋹⋡⊁⪩⨒∯-20000223=⪩⨒∯11300122","layer":0}]}
{"id":151,"expression_no_base_symbol":"≦∁$1073$⫁⪎$1360$","expression":"≦∁⪩⨒∯100301⫁⪎⪩⨒∯111100","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":36,"operation_count":2,"complexity_ratio":18.0,"tree":{"type":"unary","operator":"≦∁","unary_expr":{"type":"binary","operator":"⫁⪎","left_expr":{"type":"numeric_atoms","value":1073,"base":4},"right_expr":{"type":"numeric_atoms","value":1360,"base":4}}},"used_operators":["9ICcGScMcE","xRrnTEsQ6j"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","P8v4zCKN1o","Qy55tPpLXF","tifHPKVTfV","sdazOOVcIp","2DDjHMKMc0","i8ToyICDmI"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1073","layer":2},{"info":"number node, value=1360","layer":2},{"info":"compute binary expreesion, left_input=1073, right_input=1360, op_id = xRrnTEsQ6j binary_op_definition= 'a⫁⪎b = { ((b⋝⋈⪟a)⇼⇔∾a) , if (∥⊫b)!=57 ; ((191∲⫓a)⋥≓≎(a⪨≂368)) , else }', output=-287","layer":1},{"info":"compute unary expreesion, input=-287, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=67","layer":0}],"base":4,"result_base":4,"text":"≦∁⪩⨒∯100301⫁⪎⪩⨒∯111100=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=≦∁⪩⨒∯100301⫁⪎⪩⨒∯111100","cot":[{"info":"⪩⨒∯100301⫁⪎⪩⨒∯111100=⪩⨒∯-10133","layer":1},{"info":"≦∁⪩⨒∯-10133=⪩⨒∯1003","layer":0}]}
{"id":152,"expression_no_base_symbol":"$4117$∙⊟$6543$⊍⩺⋍$1592$⪃⊛⇣$3319$","expression":"⪩⨒∯1000111∙⊟⪩⨒∯1212033⊍⩺⋍⪩⨒∯120320⪃⊛⇣⪩⨒∯303313","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4967,"operation_count":3,"complexity_ratio":1655.6666666666667,"tree":{"type":"binary","operator":"⊍⩺⋍","left_expr":{"type":"binary","operator":"∙⊟","left_expr":{"type":"numeric_atoms","value":4117,"base":4},"right_expr":{"type":"numeric_atoms","value":6543,"base":4}},"right_expr":{"type":"binary","operator":"⪃⊛⇣","left_expr":{"type":"numeric_atoms","value":1592,"base":4},"right_expr":{"type":"numeric_atoms","value":3319,"base":4}}},"used_operators":["OXDGMFPWZM","SxTAKzQCrw","rrgAzCduG9"],"dependent_operators":["kn8WO9XteQ","inkyxCbjAn","13rbtpv6ld","6iOiAJX1F8","oWn0xqSxBt","3Oe9XWJUTD","4CyGpkTkEk","CArV6hThFE","PPChnnnBFF","Ez1Nq5fNfI","AHs5Up7iyr","2DDjHMKMc0","7IPrd9c3lf","8cLx32lpNA"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4117","layer":2},{"info":"number node, value=6543","layer":2},{"info":"compute binary expreesion, left_input=4117, right_input=6543, op_id = SxTAKzQCrw binary_op_definition= 'a∙⊟b = { (⩪∧⨌(a⫲⨊)) , if (b∐⫣)<386 ; ((a∣a)⊝⪿⪼(⊙↵-a)) , else }', output=63367","layer":1},{"info":"number node, value=1592","layer":2},{"info":"number node, value=3319","layer":2},{"info":"compute binary expreesion, left_input=1592, right_input=3319, op_id = rrgAzCduG9 binary_op_definition= 'a⪃⊛⇣b = { ((b∌b)⊵↤) , if b==348 ; ((a≹⇙⪍a)⪬(a⋝⋈⪟a)) , else }', output=1234","layer":1},{"info":"compute binary expreesion, left_input=63367, right_input=1234, op_id = OXDGMFPWZM binary_op_definition= 'a⊍⩺⋍b = { ((⇁⨣⪵659)↤⩊(b⨭⪣a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1000111∙⊟⪩⨒∯1212033⊍⩺⋍⪩⨒∯120320⪃⊛⇣⪩⨒∯303313=NaN","reverse_text":"NaN=⪩⨒∯1000111∙⊟⪩⨒∯1212033⊍⩺⋍⪩⨒∯120320⪃⊛⇣⪩⨒∯303313","cot":[{"info":"⪩⨒∯1000111∙⊟⪩⨒∯1212033=⪩⨒∯33132013","layer":1},{"info":"⪩⨒∯120320⪃⊛⇣⪩⨒∯303313=⪩⨒∯103102","layer":1},{"info":"⪩⨒∯33132013⊍⩺⋍⪩⨒∯103102=NaN","layer":0}]}
{"id":153,"expression_no_base_symbol":"($2263$⨑≵⋬$1061$)⩁⩘($4043$∷$1000$)","expression":"(⪩⨒∯203113⨑≵⋬⪩⨒∯100211)⩁⩘(⪩⨒∯333023∷⪩⨒∯33220)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":40,"operation_count":3,"complexity_ratio":13.333333333333334,"tree":{"type":"binary","operator":"⩁⩘","left_expr":{"type":"binary","operator":"⨑≵⋬","left_expr":{"type":"numeric_atoms","value":2263,"base":4},"right_expr":{"type":"numeric_atoms","value":1061,"base":4}},"right_expr":{"type":"binary","operator":"∷","left_expr":{"type":"numeric_atoms","value":4043,"base":4},"right_expr":{"type":"numeric_atoms","value":1000,"base":4}}},"used_operators":["gub5Cegaqo","XnXgA4xnOs","D3AQDKkPcf"],"dependent_operators":["DpFCA1CohY","IWmyXbctLI","eewbuw0ToL","AF7qkfDlqP","QMFrweE19q","9FxExcQeMw","NTOWxs364D","7j4O788W3g"],"result":"⪩⨒∯1031110","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2263","layer":2},{"info":"number node, value=1061","layer":2},{"info":"compute binary expreesion, left_input=2263, right_input=1061, op_id = XnXgA4xnOs binary_op_definition= 'a⨑≵⋬b = { ((a⨰b)⫡⨏(⨑⩽⪐b)) }', output=5267","layer":1},{"info":"number node, value=4043","layer":2},{"info":"number node, value=1000","layer":2},{"info":"compute binary expreesion, left_input=4043, right_input=1000, op_id = D3AQDKkPcf binary_op_definition= 'a∷b = { (a⩚⊴⇥673) , if (b⩷∴24)<=112 ; (a↺b) , else }', output=1000","layer":1},{"info":"compute binary expreesion, left_input=5267, right_input=1000, op_id = gub5Cegaqo binary_op_definition= 'a⩁⩘b = { ((b⪮%⊝b)⪮%⊝(⋗⩬⋾a)) }', output=4948","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯203113⨑≵⋬⪩⨒∯100211)⩁⩘(⪩⨒∯333023∷⪩⨒∯33220)=⪩⨒∯1031110","reverse_text":"⪩⨒∯1031110=(⪩⨒∯203113⨑≵⋬⪩⨒∯100211)⩁⩘(⪩⨒∯333023∷⪩⨒∯33220)","cot":[{"info":"⪩⨒∯203113⨑≵⋬⪩⨒∯100211=⪩⨒∯1102103","layer":1},{"info":"⪩⨒∯333023∷⪩⨒∯33220=⪩⨒∯33220","layer":1},{"info":"⪩⨒∯1102103⩁⩘⪩⨒∯33220=⪩⨒∯1031110","layer":0}]}
{"id":154,"expression_no_base_symbol":"$4967$⫔⩽⩺$3180$⫔⩽⩺($6481$⪁$6256$)","expression":"⪩⨒∯1031213⫔⩽⩺⪩⨒∯301230⫔⩽⩺(⪩⨒∯1211101⪁⪩⨒∯1201300)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":439719952,"operation_count":3,"complexity_ratio":146573317.33333334,"tree":{"type":"binary","operator":"⫔⩽⩺","left_expr":{"type":"binary","operator":"⫔⩽⩺","left_expr":{"type":"numeric_atoms","value":4967,"base":4},"right_expr":{"type":"numeric_atoms","value":3180,"base":4}},"right_expr":{"type":"binary","operator":"⪁","left_expr":{"type":"numeric_atoms","value":6481,"base":4},"right_expr":{"type":"numeric_atoms","value":6256,"base":4}}},"used_operators":["i9eR4S00cU","I7sXao9hZE"],"dependent_operators":["Tw270M8GLb","fu6greOZ01","dWAJyo7jo9","wxb3vTeyAj","nlCqmYiOvY"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4967","layer":2},{"info":"number node, value=3180","layer":2},{"info":"compute binary expreesion, left_input=4967, right_input=3180, op_id = i9eR4S00cU binary_op_definition= 'a⫔⩽⩺b = { (⨰⫟⨤(a⨐⩸⫘b)) }', output=nan","layer":1},{"info":"number node, value=6481","layer":2},{"info":"number node, value=6256","layer":2},{"info":"compute binary expreesion, left_input=6481, right_input=6256, op_id = I7sXao9hZE binary_op_definition= 'a⪁b = { (((⫶⊄≣b)⨽⪊≇)⪢a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = i9eR4S00cU binary_op_definition= 'a⫔⩽⩺b = { (⨰⫟⨤(a⨐⩸⫘b)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1031213⫔⩽⩺⪩⨒∯301230⫔⩽⩺(⪩⨒∯1211101⪁⪩⨒∯1201300)=NaN","reverse_text":"NaN=⪩⨒∯1031213⫔⩽⩺⪩⨒∯301230⫔⩽⩺(⪩⨒∯1211101⪁⪩⨒∯1201300)","cot":[{"info":"⪩⨒∯1031213⫔⩽⩺⪩⨒∯301230=NaN","layer":1},{"info":"⪩⨒∯1211101⪁⪩⨒∯1201300=NaN","layer":1},{"info":"NaN⫔⩽⩺NaN=NaN","layer":0}]}
{"id":155,"expression_no_base_symbol":"($3982$⇗⋫)⩦($3762$⨽$5882$)","expression":"(⪩⨒∯332032⇗⋫)⩦(⪩⨒∯322302⨽⪩⨒∯1123322)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3787,"operation_count":3,"complexity_ratio":1262.3333333333333,"tree":{"type":"binary","operator":"⩦","left_expr":{"type":"unary","operator":"⇗⋫","unary_expr":{"type":"numeric_atoms","value":3982,"base":4}},"right_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":3762,"base":4},"right_expr":{"type":"numeric_atoms","value":5882,"base":4}}},"used_operators":["0kmYd0q39Y","hpqmaQFPrd","8HhzD0ZcuI"],"dependent_operators":["N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q","rxpJgHHUmx","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3982","layer":2},{"info":"compute unary expreesion, input=3982, op_id = hpqmaQFPrd, unary_op_definition = 'a⇗⋫ = { (a≭a) }', output=nan","layer":1},{"info":"number node, value=3762","layer":2},{"info":"number node, value=5882","layer":2},{"info":"compute binary expreesion, left_input=3762, right_input=5882, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-42474264","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-42474264, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯332032⇗⋫)⩦(⪩⨒∯322302⨽⪩⨒∯1123322)=NaN","reverse_text":"NaN=(⪩⨒∯332032⇗⋫)⩦(⪩⨒∯322302⨽⪩⨒∯1123322)","cot":[{"info":"⪩⨒∯332032⇗⋫=NaN","layer":1},{"info":"⪩⨒∯322302⨽⪩⨒∯1123322=⪩⨒∯-2202001230120","layer":1},{"info":"NaN⩦⪩⨒∯-2202001230120=NaN","layer":0}]}
{"id":156,"expression_no_base_symbol":"(⊀$2533$)⨪↰⇹$2069$≄⊠$6544$","expression":"(⊀⪩⨒∯213211)⨪↰⇹⪩⨒∯200111≄⊠⪩⨒∯1212100","highest_n_order":4,"priority_hierarchical_complexity":1,"normalized_expansion_degree":9945,"operation_count":3,"complexity_ratio":3315.0,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"unary","operator":"⊀","unary_expr":{"type":"numeric_atoms","value":2533,"base":4}},"right_expr":{"type":"binary","operator":"≄⊠","left_expr":{"type":"numeric_atoms","value":2069,"base":4},"right_expr":{"type":"numeric_atoms","value":6544,"base":4}}},"used_operators":["tmPS8pqC7x","oPMjh9089D","vXNesLlMH1"],"dependent_operators":["rJVOvQCfKK","Qy55tPpLXF","XIabStNQrY","tifHPKVTfV","glklzrTFfD","sdazOOVcIp","8w2t5hMYqp","Ph9nP6C5qx","g55IO6H4Gj","2td37pGCOC","QMFrweE19q","d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI"],"result":"⪩⨒∯2122032","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2533","layer":2},{"info":"compute unary expreesion, input=2533, op_id = oPMjh9089D, unary_op_definition = '⊀a = { (((⩦⩻⨪67)⪨≂(a⋥≓≎63))⇋≉) , if (a⇼⇔∾9)<290 ; (((⊄⩳↩a)⨁⊸⫻)⫡⨏((a≧⫂∧a)⨸⪁(a≧⫂∧a))) , else }', output=9870","layer":1},{"info":"number node, value=2069","layer":2},{"info":"number node, value=6544","layer":2},{"info":"compute binary expreesion, left_input=2069, right_input=6544, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=109372","layer":1},{"info":"compute binary expreesion, left_input=9870, right_input=109372, op_id = tmPS8pqC7x binary_op_definition= 'a⨪↰⇹b = {a, if a == 0; (b)⨎((a-1)⨪↰⇹b), if a > 0 and abs(a) < 1000000; -(b)⨎((a+1)⨪↰⇹b), if a < 0 and abs(a) < 1000000; NaN, else}', output=9870","layer":0}],"base":4,"result_base":4,"text":"(⊀⪩⨒∯213211)⨪↰⇹⪩⨒∯200111≄⊠⪩⨒∯1212100=⪩⨒∯2122032","reverse_text":"⪩⨒∯2122032=(⊀⪩⨒∯213211)⨪↰⇹⪩⨒∯200111≄⊠⪩⨒∯1212100","cot":[{"info":"⊀⪩⨒∯213211=⪩⨒∯2122032","layer":1},{"info":"⪩⨒∯200111≄⊠⪩⨒∯1212100=⪩⨒∯122230330","layer":1},{"info":"⪩⨒∯2122032⨪↰⇹⪩⨒∯122230330=⪩⨒∯2122032","layer":0}]}
{"id":157,"expression_no_base_symbol":"⇠($5270$⫸⊐$5371$)","expression":"⇠(⪩⨒∯1102112⫸⊐⪩⨒∯1103323)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":33,"operation_count":2,"complexity_ratio":16.5,"tree":{"type":"unary","operator":"⇠","unary_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":5270,"base":4},"right_expr":{"type":"numeric_atoms","value":5371,"base":4}}},"used_operators":["18saOjeKKm","mqXw5SEYmG"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"⪩⨒∯-11021331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5270","layer":2},{"info":"number node, value=5371","layer":2},{"info":"compute binary expreesion, left_input=5270, right_input=5371, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=21359","layer":1},{"info":"compute unary expreesion, input=21359, op_id = 18saOjeKKm, unary_op_definition = '⇠a = { ((a⨳⩥⨓242)∲⫓(229⪨≂a)) }', output=-21117","layer":0}],"base":4,"result_base":4,"text":"⇠(⪩⨒∯1102112⫸⊐⪩⨒∯1103323)=⪩⨒∯-11021331","reverse_text":"⪩⨒∯-11021331=⇠(⪩⨒∯1102112⫸⊐⪩⨒∯1103323)","cot":[{"info":"⪩⨒∯1102112⫸⊐⪩⨒∯1103323=⪩⨒∯11031233","layer":1},{"info":"⇠⪩⨒∯11031233=⪩⨒∯-11021331","layer":0}]}
{"id":158,"expression_no_base_symbol":"(≇⪴$4600$)⇀∌","expression":"(≇⪴⪩⨒∯1013320)⇀∌","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":296,"operation_count":2,"complexity_ratio":148.0,"tree":{"type":"unary","operator":"⇀∌","unary_expr":{"type":"unary","operator":"≇⪴","unary_expr":{"type":"numeric_atoms","value":4600,"base":4}}},"used_operators":["2k53nXOpI5","zoVPnxeHJ3"],"dependent_operators":["Q3PJZHRvZv","ddLRYrp01A","AcOhelriW5","7t3wd0Fuz7","3tVxb0NHM4","7j4O788W3g","Ph9nP6C5qx","f6k1SAg4EE","14qkJME0vr","g55IO6H4Gj","COABgblf1C"],"result":"⪩⨒∯1301","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4600","layer":2},{"info":"compute unary expreesion, input=4600, op_id = zoVPnxeHJ3, unary_op_definition = '≇⪴a = { ((a⪒a)↺(a⨸⪁a)) , if (a⊭↱741)>=792 ; ((a≧⫂∧a)⊦⊿) , else }', output=-12460","layer":1},{"info":"compute unary expreesion, input=-12460, op_id = 2k53nXOpI5, unary_op_definition = 'a⇀∌ = { ((a⪎↠(⨣⨃⇪a))⋥⋵⩄(a∊∟⩊(⊥a))) }', output=113","layer":0}],"base":4,"result_base":4,"text":"(≇⪴⪩⨒∯1013320)⇀∌=⪩⨒∯1301","reverse_text":"⪩⨒∯1301=(≇⪴⪩⨒∯1013320)⇀∌","cot":[{"info":"≇⪴⪩⨒∯1013320=⪩⨒∯-3002230","layer":1},{"info":"⪩⨒∯-3002230⇀∌=⪩⨒∯1301","layer":0}]}
{"id":159,"expression_no_base_symbol":"(⇉-⫰$3671$)↼⊘⨖($4493$⨐⩸⫘$3590$)","expression":"(⇉-⫰⪩⨒∯321113)↼⊘⨖(⪩⨒∯1012031⨐⩸⫘⪩⨒∯320012)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15,"operation_count":3,"complexity_ratio":5.0,"tree":{"type":"binary","operator":"↼⊘⨖","left_expr":{"type":"unary","operator":"⇉-⫰","unary_expr":{"type":"numeric_atoms","value":3671,"base":4}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":4493,"base":4},"right_expr":{"type":"numeric_atoms","value":3590,"base":4}}},"used_operators":["bPywburJMS","IGFM8TAlm9","fu6greOZ01"],"dependent_operators":["9FxExcQeMw","P8v4zCKN1o","t8gj7n24qd","eH2TOUuTDT","eewbuw0ToL","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3671","layer":2},{"info":"compute unary expreesion, input=3671, op_id = IGFM8TAlm9, unary_op_definition = '⇉-⫰a = { ((a⨰a)⪐) }', output=20","layer":1},{"info":"number node, value=4493","layer":2},{"info":"number node, value=3590","layer":2},{"info":"compute binary expreesion, left_input=4493, right_input=3590, op_id = fu6greOZ01 binary_op_definition= 'a⨐⩸⫘b = {a, if b == 0; (a⨐⩸⫘(b-1))⨓(b), if b > 0 and abs(b) < 1000; -(a⨐⩸⫘(b+1))⨓(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=20, right_input=nan, op_id = bPywburJMS binary_op_definition= 'a↼⊘⨖b = { (-a) , if (∥⊫b)==149 ; (b⩷∴95) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⇉-⫰⪩⨒∯321113)↼⊘⨖(⪩⨒∯1012031⨐⩸⫘⪩⨒∯320012)=NaN","reverse_text":"NaN=(⇉-⫰⪩⨒∯321113)↼⊘⨖(⪩⨒∯1012031⨐⩸⫘⪩⨒∯320012)","cot":[{"info":"⇉-⫰⪩⨒∯321113=⪩⨒∯110","layer":1},{"info":"⪩⨒∯1012031⨐⩸⫘⪩⨒∯320012=NaN","layer":1},{"info":"⪩⨒∯110↼⊘⨖NaN=NaN","layer":0}]}
{"id":160,"expression_no_base_symbol":"⫯(↴⪽⋼$3713$)","expression":"⫯(↴⪽⋼⪩⨒∯322001)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":49,"operation_count":2,"complexity_ratio":24.5,"tree":{"type":"unary","operator":"⫯","unary_expr":{"type":"unary","operator":"↴⪽⋼","unary_expr":{"type":"numeric_atoms","value":3713,"base":4}}},"used_operators":["H6BK1Evt7c","5TUYCnJO6w"],"dependent_operators":["2Wsdkap16l","KbjG8mgYpV","sJAwomhLZr","Ph9nP6C5qx","AYdpE9sXAk","X99M06cbEe","MGuIdZPyUC","UqFzSgLMvQ","k7HXdKtiEU","yyfyN0ffXY","pRsWfj4Fpp","diKm42VcIt"],"result":"⪩⨒∯-202131212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3713","layer":2},{"info":"compute unary expreesion, input=3713, op_id = 5TUYCnJO6w, unary_op_definition = '↴⪽⋼a = { a , if ((∡a)<5 or (⇘a)>=19 or (⊲⪭a)==199) ; (((a↙a)⇡)⇉⇉) , else }', output=3713","layer":1},{"info":"compute unary expreesion, input=3713, op_id = H6BK1Evt7c, unary_op_definition = '⫯a = { ((a⩠)∠↢(⨂⪏⇭a)) , if (a≧⫂∧919)>20 ; ((a⩹a)≫≃) , else }', output=-141158","layer":0}],"base":4,"result_base":4,"text":"⫯(↴⪽⋼⪩⨒∯322001)=⪩⨒∯-202131212","reverse_text":"⪩⨒∯-202131212=⫯(↴⪽⋼⪩⨒∯322001)","cot":[{"info":"↴⪽⋼⪩⨒∯322001=⪩⨒∯322001","layer":1},{"info":"⫯⪩⨒∯322001=⪩⨒∯-202131212","layer":0}]}
{"id":161,"expression_no_base_symbol":"∓(⪁⇼$1318$)","expression":"∓(⪁⇼⪩⨒∯110212)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":28,"operation_count":2,"complexity_ratio":14.0,"tree":{"type":"unary","operator":"∓","unary_expr":{"type":"unary","operator":"⪁⇼","unary_expr":{"type":"numeric_atoms","value":1318,"base":4}}},"used_operators":["OwUj7dcsQK","ZNVVrZ94lY"],"dependent_operators":["DpFCA1CohY","12rbrZMWeM","nCS4ZIUYfx","QMFrweE19q","sdazOOVcIp","2DQ55sFlQl","tifHPKVTfV"],"result":"⪩⨒∯-2233002","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1318","layer":2},{"info":"compute unary expreesion, input=1318, op_id = ZNVVrZ94lY, unary_op_definition = '⪁⇼a = { ((a⨵⪆a)⪨≂(a⇼⇔∾a)) }', output=422","layer":1},{"info":"compute unary expreesion, input=422, op_id = OwUj7dcsQK, unary_op_definition = '∓a = { (⋗⩬⋾((a⋳⪒554)⨳⩥⨓(a⫡⨏a))) }', output=-11202","layer":0}],"base":4,"result_base":4,"text":"∓(⪁⇼⪩⨒∯110212)=⪩⨒∯-2233002","reverse_text":"⪩⨒∯-2233002=∓(⪁⇼⪩⨒∯110212)","cot":[{"info":"⪁⇼⪩⨒∯110212=⪩⨒∯12212","layer":1},{"info":"∓⪩⨒∯12212=⪩⨒∯-2233002","layer":0}]}
{"id":162,"expression_no_base_symbol":"↓⇌(⇈$8126$)","expression":"↓⇌(⇈⪩⨒∯1332332)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1020,"operation_count":2,"complexity_ratio":510.0,"tree":{"type":"unary","operator":"↓⇌","unary_expr":{"type":"unary","operator":"⇈","unary_expr":{"type":"numeric_atoms","value":8126,"base":4}}},"used_operators":["PxpmPgHHJV","SLLxy00UIr"],"dependent_operators":["23Mk6UjR3U","glklzrTFfD","Z2TMIBDE3Q","Qy55tPpLXF","DZ8iAZOCBD","tifHPKVTfV","Tw270M8GLb","8HhzD0ZcuI","jCPkEVoL5K","ZcwmYACASQ"],"result":"⪩⨒∯-31332","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=8126","layer":2},{"info":"compute unary expreesion, input=8126, op_id = SLLxy00UIr, unary_op_definition = '⇈a = { (((⨰⫟⨤60)⋥≓≎(a⫍⨯↯))⇻⋧≁((a⇼⇔∾a)⨽(323⊉≛↸a))) }', output=-447","layer":1},{"info":"compute unary expreesion, input=-447, op_id = PxpmPgHHJV, unary_op_definition = '↓⇌a = { (a⋷507) , if a>=68 and (a⩤)>=87 ; (a⨁⊸⫻) , else }', output=-894","layer":0}],"base":4,"result_base":4,"text":"↓⇌(⇈⪩⨒∯1332332)=⪩⨒∯-31332","reverse_text":"⪩⨒∯-31332=↓⇌(⇈⪩⨒∯1332332)","cot":[{"info":"⇈⪩⨒∯1332332=⪩⨒∯-12333","layer":1},{"info":"↓⇌⪩⨒∯-12333=⪩⨒∯-31332","layer":0}]}
{"id":163,"expression_no_base_symbol":"(⫛⫱⨽$1354$)⪨⊡$2277$⨟⋌⩍$6230$","expression":"(⫛⫱⨽⪩⨒∯111022)⪨⊡⪩⨒∯203211⨟⋌⩍⪩⨒∯1201112","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1435,"operation_count":3,"complexity_ratio":478.3333333333333,"tree":{"type":"binary","operator":"⪨⊡","left_expr":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"numeric_atoms","value":1354,"base":4}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":2277,"base":4},"right_expr":{"type":"numeric_atoms","value":6230,"base":4}}},"used_operators":["kuIXHzHcAH","DlLNRPXxWL","rGHVDoGpnC"],"dependent_operators":["JLbD19bQDL","glklzrTFfD","eewbuw0ToL","AF7qkfDlqP","rGHVDoGpnC","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1354","layer":2},{"info":"compute unary expreesion, input=1354, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"number node, value=2277","layer":2},{"info":"number node, value=6230","layer":2},{"info":"compute binary expreesion, left_input=2277, right_input=6230, op_id = rGHVDoGpnC binary_op_definition= 'a⨟⋌⩍b = {a, if b == 0; (a⨟⋌⩍(b-1))≣⋋, if b > 0 and abs(b) < 1000; -(a⨟⋌⩍(b+1))≣⋋, if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = kuIXHzHcAH binary_op_definition= 'a⪨⊡b = { (⨑⩽⪐(b⨁⊸⫻)) , if (⨑⩽⪐b)>42 ; ((a⨰b)⪠⩆⊳) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⫛⫱⨽⪩⨒∯111022)⪨⊡⪩⨒∯203211⨟⋌⩍⪩⨒∯1201112=NaN","reverse_text":"NaN=(⫛⫱⨽⪩⨒∯111022)⪨⊡⪩⨒∯203211⨟⋌⩍⪩⨒∯1201112","cot":[{"info":"⫛⫱⨽⪩⨒∯111022=⪩⨒∯0","layer":1},{"info":"⪩⨒∯203211⨟⋌⩍⪩⨒∯1201112=NaN","layer":1},{"info":"⪩⨒∯0⪨⊡NaN=NaN","layer":0}]}
{"id":164,"expression_no_base_symbol":"⇘($4072$⫰⋱$3644$)","expression":"⇘(⪩⨒∯333220⫰⋱⪩⨒∯320330)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8129,"operation_count":2,"complexity_ratio":4064.5,"tree":{"type":"unary","operator":"⇘","unary_expr":{"type":"binary","operator":"⫰⋱","left_expr":{"type":"numeric_atoms","value":4072,"base":4},"right_expr":{"type":"numeric_atoms","value":3644,"base":4}}},"used_operators":["MGuIdZPyUC","6o9Blt3TJ6"],"dependent_operators":["eLxqMNBOBk","86A5ENbKR9","9HNa5Wba9A","E4l6HwMY31","40aOVDgCDB","bF6eod5Gvf","AFVx7xoS7T","f6k1SAg4EE","5twsqlHp2o","oacrs7FA3X","W4YGzv6Whe","nCS4ZIUYfx","Qy55tPpLXF"],"result":"⪩⨒∯-201003312302303","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4072","layer":2},{"info":"number node, value=3644","layer":2},{"info":"compute binary expreesion, left_input=4072, right_input=3644, op_id = 6o9Blt3TJ6 binary_op_definition= 'a⫰⋱b = { ((a+b)⨳⩥⨓(b⋥≓≎b)) }', output=-4039","layer":1},{"info":"compute unary expreesion, input=-4039, op_id = MGuIdZPyUC, unary_op_definition = '⇘a = { (⪸((⫓⪴a)→⨶⪴(a⪘⫢a))) , if (⫓⪴a)>35 ; (((a*a)⊢)⊔((a⊢a)⇌⫙⪟(193⪒a))) , else }', output=-554658995","layer":0}],"base":4,"result_base":4,"text":"⇘(⪩⨒∯333220⫰⋱⪩⨒∯320330)=⪩⨒∯-201003312302303","reverse_text":"⪩⨒∯-201003312302303=⇘(⪩⨒∯333220⫰⋱⪩⨒∯320330)","cot":[{"info":"⪩⨒∯333220⫰⋱⪩⨒∯320330=⪩⨒∯-333013","layer":1},{"info":"⇘⪩⨒∯-333013=⪩⨒∯-201003312302303","layer":0}]}
{"id":165,"expression_no_base_symbol":"$1721$⩒⫫$2458$≀⩗∶$2349$∇⊂⋱$3488$","expression":"⪩⨒∯122321⩒⫫⪩⨒∯212122≀⩗∶⪩⨒∯210231∇⊂⋱⪩⨒∯312200","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":51,"operation_count":3,"complexity_ratio":17.0,"tree":{"type":"binary","operator":"≀⩗∶","left_expr":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"numeric_atoms","value":1721,"base":4},"right_expr":{"type":"numeric_atoms","value":2458,"base":4}},"right_expr":{"type":"binary","operator":"∇⊂⋱","left_expr":{"type":"numeric_atoms","value":2349,"base":4},"right_expr":{"type":"numeric_atoms","value":3488,"base":4}}},"used_operators":["8INZBEW696","KFSx94NKJn","nhYeJWJD5X"],"dependent_operators":["KPf6cnQVty","2DlMacCsIx","l07mrZUIn9","NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","P8v4zCKN1o","23Mk6UjR3U","f6k1SAg4EE","AF7qkfDlqP","nCS4ZIUYfx"],"result":"⪩⨒∯-12","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1721","layer":2},{"info":"number node, value=2458","layer":2},{"info":"compute binary expreesion, left_input=1721, right_input=2458, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=1419","layer":1},{"info":"number node, value=2349","layer":2},{"info":"number node, value=3488","layer":2},{"info":"compute binary expreesion, left_input=2349, right_input=3488, op_id = nhYeJWJD5X binary_op_definition= 'a∇⊂⋱b = { (b⪒b) , if a<143 ; ((⨑⩽⪐a)⋷(∥⊫(a⨳⩥⨓a))) , else }', output=4152","layer":1},{"info":"compute binary expreesion, left_input=1419, right_input=4152, op_id = 8INZBEW696 binary_op_definition= 'a≀⩗∶b = { (a⩨b) , if (a∺≝⩲555)<251 ; (306↪⪝) , else }', output=-6","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯122321⩒⫫⪩⨒∯212122≀⩗∶⪩⨒∯210231∇⊂⋱⪩⨒∯312200=⪩⨒∯-12","reverse_text":"⪩⨒∯-12=⪩⨒∯122321⩒⫫⪩⨒∯212122≀⩗∶⪩⨒∯210231∇⊂⋱⪩⨒∯312200","cot":[{"info":"⪩⨒∯122321⩒⫫⪩⨒∯212122=⪩⨒∯112023","layer":1},{"info":"⪩⨒∯210231∇⊂⋱⪩⨒∯312200=⪩⨒∯1000320","layer":1},{"info":"⪩⨒∯112023≀⩗∶⪩⨒∯1000320=⪩⨒∯-12","layer":0}]}
{"id":166,"expression_no_base_symbol":"$2487$∓⋝$4688$⊾⪯⋞$4542$⨐$1431$","expression":"⪩⨒∯212313∓⋝⪩⨒∯1021100⊾⪯⋞⪩⨒∯1012332⨐⪩⨒∯112113","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":95,"operation_count":3,"complexity_ratio":31.666666666666668,"tree":{"type":"binary","operator":"⊾⪯⋞","left_expr":{"type":"binary","operator":"∓⋝","left_expr":{"type":"numeric_atoms","value":2487,"base":4},"right_expr":{"type":"numeric_atoms","value":4688,"base":4}},"right_expr":{"type":"binary","operator":"⨐","left_expr":{"type":"numeric_atoms","value":4542,"base":4},"right_expr":{"type":"numeric_atoms","value":1431,"base":4}}},"used_operators":["HK0tfVPux8","PoHhknlbAi","Noe24qw2ks"],"dependent_operators":["s3Fd5m9Dh2","KFSx94NKJn","MmTdOpaElr","XnXgA4xnOs","fOIeswaMU4","YSKBFp38Pu","oacrs7FA3X","xNBdhnnwKq","DZ8iAZOCBD","DbCuESL50I","mqXw5SEYmG","2MzE1hQ0cz","u6S6b8DprG","2DQ55sFlQl","QMFrweE19q"],"result":"⪩⨒∯-30310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2487","layer":2},{"info":"number node, value=4688","layer":2},{"info":"compute binary expreesion, left_input=2487, right_input=4688, op_id = PoHhknlbAi binary_op_definition= 'a∓⋝b = { (((a⊉≛↸a)⫸⊐(⋼∭⪍b))∩⋅) }', output=67","layer":1},{"info":"number node, value=4542","layer":2},{"info":"number node, value=1431","layer":2},{"info":"compute binary expreesion, left_input=4542, right_input=1431, op_id = Noe24qw2ks binary_op_definition= 'a⨐b = { (↽≂a) , if (a⨵⪆301)>43 ; (b⫡⨏a) , else }', output=-9084","layer":1},{"info":"compute binary expreesion, left_input=67, right_input=-9084, op_id = HK0tfVPux8 binary_op_definition= 'a⊾⪯⋞b = { ((121⊭∹↮)⊬⨰(a⨑≵⋬b)) , if (a⩟)==395 or (a⨱∎)>94 ; ((b⪘⫢b)⩒⫫(a⇤b)) , else }', output=-820","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯212313∓⋝⪩⨒∯1021100⊾⪯⋞⪩⨒∯1012332⨐⪩⨒∯112113=⪩⨒∯-30310","reverse_text":"⪩⨒∯-30310=⪩⨒∯212313∓⋝⪩⨒∯1021100⊾⪯⋞⪩⨒∯1012332⨐⪩⨒∯112113","cot":[{"info":"⪩⨒∯212313∓⋝⪩⨒∯1021100=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯1012332⨐⪩⨒∯112113=⪩⨒∯-2031330","layer":1},{"info":"⪩⨒∯1003⊾⪯⋞⪩⨒∯-2031330=⪩⨒∯-30310","layer":0}]}
{"id":167,"expression_no_base_symbol":"↓⇌($7756$⨝⩣∺)","expression":"↓⇌(⪩⨒∯1321030⨝⩣∺)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":2,"complexity_ratio":3.0,"tree":{"type":"unary","operator":"↓⇌","unary_expr":{"type":"unary","operator":"⨝⩣∺","unary_expr":{"type":"numeric_atoms","value":7756,"base":4}}},"used_operators":["PxpmPgHHJV","ancx8kZcWl"],"dependent_operators":["23Mk6UjR3U","glklzrTFfD","Z2TMIBDE3Q","DZ8iAZOCBD","t8gj7n24qd"],"result":"⪩⨒∯-13210300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7756","layer":2},{"info":"compute unary expreesion, input=7756, op_id = ancx8kZcWl, unary_op_definition = 'a⨝⩣∺ = { (-(a⊉≛↸a)) }', output=-15512","layer":1},{"info":"compute unary expreesion, input=-15512, op_id = PxpmPgHHJV, unary_op_definition = '↓⇌a = { (a⋷507) , if a>=68 and (a⩤)>=87 ; (a⨁⊸⫻) , else }', output=-31024","layer":0}],"base":4,"result_base":4,"text":"↓⇌(⪩⨒∯1321030⨝⩣∺)=⪩⨒∯-13210300","reverse_text":"⪩⨒∯-13210300=↓⇌(⪩⨒∯1321030⨝⩣∺)","cot":[{"info":"⪩⨒∯1321030⨝⩣∺=⪩⨒∯-3302120","layer":1},{"info":"↓⇌⪩⨒∯-3302120=⪩⨒∯-13210300","layer":0}]}
{"id":168,"expression_no_base_symbol":"$1263$↬$1194$∖$6942$⇴$2348$","expression":"⪩⨒∯103233↬⪩⨒∯102222∖⪩⨒∯1230132⇴⪩⨒∯210230","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3806,"operation_count":3,"complexity_ratio":1268.6666666666667,"tree":{"type":"binary","operator":"∖","left_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":1263,"base":4},"right_expr":{"type":"numeric_atoms","value":1194,"base":4}},"right_expr":{"type":"binary","operator":"⇴","left_expr":{"type":"numeric_atoms","value":6942,"base":4},"right_expr":{"type":"numeric_atoms","value":2348,"base":4}}},"used_operators":["tXD093vOjl","B5M0gjZbta","4JB6nKBMSY"],"dependent_operators":["rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC","rGHVDoGpnC","sdazOOVcIp","NTOWxs364D","COABgblf1C"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1263","layer":2},{"info":"number node, value=1194","layer":2},{"info":"compute binary expreesion, left_input=1263, right_input=1194, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":1},{"info":"number node, value=6942","layer":2},{"info":"number node, value=2348","layer":2},{"info":"compute binary expreesion, left_input=6942, right_input=2348, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=45962","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=45962, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯103233↬⪩⨒∯102222∖⪩⨒∯1230132⇴⪩⨒∯210230=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯103233↬⪩⨒∯102222∖⪩⨒∯1230132⇴⪩⨒∯210230","cot":[{"info":"⪩⨒∯103233↬⪩⨒∯102222=NaN","layer":1},{"info":"⪩⨒∯1230132⇴⪩⨒∯210230=⪩⨒∯23032022","layer":1},{"info":"NaN∖⪩⨒∯23032022=⪩⨒∯0","layer":0}]}
{"id":169,"expression_no_base_symbol":"($2783$⩵∡$2945$)∼($1164$⋅⇍$1950$)","expression":"(⪩⨒∯223133⩵∡⪩⨒∯232001)∼(⪩⨒∯102030⋅⇍⪩⨒∯132132)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":171,"operation_count":3,"complexity_ratio":57.0,"tree":{"type":"binary","operator":"∼","left_expr":{"type":"binary","operator":"⩵∡","left_expr":{"type":"numeric_atoms","value":2783,"base":4},"right_expr":{"type":"numeric_atoms","value":2945,"base":4}},"right_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":1164,"base":4},"right_expr":{"type":"numeric_atoms","value":1950,"base":4}}},"used_operators":["DyGG3AbaNP","Y7wcNGrDQJ","AdZkA7nFnk"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","NTOWxs364D","glklzrTFfD","tifHPKVTfV","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2783","layer":2},{"info":"number node, value=2945","layer":2},{"info":"compute binary expreesion, left_input=2783, right_input=2945, op_id = Y7wcNGrDQJ binary_op_definition= 'a⩵∡b = { ((b⇼⇔∾a)⩚⊴⇥(a⨁⊸⫻)) }', output=-2742","layer":1},{"info":"number node, value=1164","layer":2},{"info":"number node, value=1950","layer":2},{"info":"compute binary expreesion, left_input=1164, right_input=1950, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"compute binary expreesion, left_input=-2742, right_input=-22, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯223133⩵∡⪩⨒∯232001)∼(⪩⨒∯102030⋅⇍⪩⨒∯132132)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯223133⩵∡⪩⨒∯232001)∼(⪩⨒∯102030⋅⇍⪩⨒∯132132)","cot":[{"info":"⪩⨒∯223133⩵∡⪩⨒∯232001=⪩⨒∯-222312","layer":1},{"info":"⪩⨒∯102030⋅⇍⪩⨒∯132132=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯-222312∼⪩⨒∯-112=⪩⨒∯0","layer":0}]}
{"id":170,"expression_no_base_symbol":"$1360$⋕⪉⪜$1609$⊨$3868$≒∊$2046$","expression":"⪩⨒∯111100⋕⪉⪜⪩⨒∯121021⊨⪩⨒∯330130≒∊⪩⨒∯133332","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":45,"operation_count":3,"complexity_ratio":15.0,"tree":{"type":"binary","operator":"⊨","left_expr":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"numeric_atoms","value":1360,"base":4},"right_expr":{"type":"numeric_atoms","value":1609,"base":4}},"right_expr":{"type":"binary","operator":"≒∊","left_expr":{"type":"numeric_atoms","value":3868,"base":4},"right_expr":{"type":"numeric_atoms","value":2046,"base":4}}},"used_operators":["vg4gO5BX6G","z6LnFrNh4i","5KTvxBwnZo"],"dependent_operators":["NTOWxs364D","JLbD19bQDL","xUOZtlo3hN","AF7qkfDlqP","sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z","3EYGwJThht","dWAJyo7jo9","Z2TMIBDE3Q","bjFbhXSADs","3DZMoQKiUl"],"result":"⪩⨒∯2333033","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1360","layer":2},{"info":"number node, value=1609","layer":2},{"info":"compute binary expreesion, left_input=1360, right_input=1609, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=2802","layer":1},{"info":"number node, value=3868","layer":2},{"info":"number node, value=2046","layer":2},{"info":"compute binary expreesion, left_input=3868, right_input=2046, op_id = 5KTvxBwnZo binary_op_definition= 'a≒∊b = { (≱⇩⩕(a⪢a)) , if (a⩤)==117 ; ((b⪊≅)⇄a) , else }', output=-3384","layer":1},{"info":"compute binary expreesion, left_input=2802, right_input=-3384, op_id = vg4gO5BX6G binary_op_definition= 'a⊨b = { (⨞⊢(b⪠⩆⊳)) , if a<=416 ; (⨑⩽⪐(a⩚⊴⇥a)) , else }', output=12239","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯111100⋕⪉⪜⪩⨒∯121021⊨⪩⨒∯330130≒∊⪩⨒∯133332=⪩⨒∯2333033","reverse_text":"⪩⨒∯2333033=⪩⨒∯111100⋕⪉⪜⪩⨒∯121021⊨⪩⨒∯330130≒∊⪩⨒∯133332","cot":[{"info":"⪩⨒∯111100⋕⪉⪜⪩⨒∯121021=⪩⨒∯223302","layer":1},{"info":"⪩⨒∯330130≒∊⪩⨒∯133332=⪩⨒∯-310320","layer":1},{"info":"⪩⨒∯223302⊨⪩⨒∯-310320=⪩⨒∯2333033","layer":0}]}
{"id":171,"expression_no_base_symbol":"⪹($4183$∠↢$1777$)","expression":"⪹(⪩⨒∯1001113∠↢⪩⨒∯123301)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":15,"operation_count":2,"complexity_ratio":7.5,"tree":{"type":"unary","operator":"⪹","unary_expr":{"type":"binary","operator":"∠↢","left_expr":{"type":"numeric_atoms","value":4183,"base":4},"right_expr":{"type":"numeric_atoms","value":1777,"base":4}}},"used_operators":["USyYr0JgAa","KbjG8mgYpV"],"dependent_operators":["tifHPKVTfV","rysDP5nf3Z","NTOWxs364D","XPYlsWDdGa","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","nCS4ZIUYfx","COABgblf1C"],"result":"⪩⨒∯21330010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4183","layer":2},{"info":"number node, value=1777","layer":2},{"info":"compute binary expreesion, left_input=4183, right_input=1777, op_id = KbjG8mgYpV binary_op_definition= 'a∠↢b = { (a⊭↱((159⨳⩥⨓16)-(b⨸⪁a))) , if (b==488 or (⨞⊢a)==254) ; (⪲⇎((-b)⫡⨏(b⩚⊴⇥a))) , else }', output=-40528","layer":1},{"info":"compute unary expreesion, input=-40528, op_id = USyYr0JgAa, unary_op_definition = '⪹a = { (a⇼⇔∾180) }', output=40708","layer":0}],"base":4,"result_base":4,"text":"⪹(⪩⨒∯1001113∠↢⪩⨒∯123301)=⪩⨒∯21330010","reverse_text":"⪩⨒∯21330010=⪹(⪩⨒∯1001113∠↢⪩⨒∯123301)","cot":[{"info":"⪩⨒∯1001113∠↢⪩⨒∯123301=⪩⨒∯-21321100","layer":1},{"info":"⪹⪩⨒∯-21321100=⪩⨒∯21330010","layer":0}]}
{"id":172,"expression_no_base_symbol":"($1023$⊍)⨵⪆(≯$1301$)","expression":"(⪩⨒∯33333⊍)⨵⪆(≯⪩⨒∯110111)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":24,"operation_count":3,"complexity_ratio":8.0,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"unary","operator":"⊍","unary_expr":{"type":"numeric_atoms","value":1023,"base":4}},"right_expr":{"type":"unary","operator":"≯","unary_expr":{"type":"numeric_atoms","value":1301,"base":4}}},"used_operators":["2DQ55sFlQl","3nqY3DE9mg","keWfFq85dY"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","8w2t5hMYqp","AF7qkfDlqP","12rbrZMWeM","g55IO6H4Gj","JLbD19bQDL"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1023","layer":2},{"info":"compute unary expreesion, input=1023, op_id = 3nqY3DE9mg, unary_op_definition = 'a⊍ = { (⊄⩳↩(⨑⩽⪐(a⋳⪒a))) }', output=1389","layer":1},{"info":"number node, value=1301","layer":2},{"info":"compute unary expreesion, input=1301, op_id = keWfFq85dY, unary_op_definition = '≯a = { ((a⨸⪁a)⪠⩆⊳) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=1389, right_input=0, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯33333⊍)⨵⪆(≯⪩⨒∯110111)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⪩⨒∯33333⊍)⨵⪆(≯⪩⨒∯110111)","cot":[{"info":"⪩⨒∯33333⊍=⪩⨒∯111231","layer":1},{"info":"≯⪩⨒∯110111=⪩⨒∯0","layer":1},{"info":"⪩⨒∯111231⨵⪆⪩⨒∯0=⪩⨒∯2200","layer":0}]}
{"id":173,"expression_no_base_symbol":"$2555$≳⇉$3544$⨐⩸⫘$2100$∑⇟⊟$8291$","expression":"⪩⨒∯213323≳⇉⪩⨒∯313120⨐⩸⫘⪩⨒∯200310∑⇟⊟⪩⨒∯2001203","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":122280261,"operation_count":3,"complexity_ratio":40760087.0,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"≳⇉","left_expr":{"type":"numeric_atoms","value":2555,"base":4},"right_expr":{"type":"numeric_atoms","value":3544,"base":4}},"right_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":2100,"base":4},"right_expr":{"type":"numeric_atoms","value":8291,"base":4}}},"used_operators":["fu6greOZ01","V0kx6qeWkN","U7g4x0WXJJ"],"dependent_operators":["3ViojmjbAp","KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2555","layer":2},{"info":"number node, value=3544","layer":2},{"info":"compute binary expreesion, left_input=2555, right_input=3544, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":1},{"info":"number node, value=2100","layer":2},{"info":"number node, value=8291","layer":2},{"info":"compute binary expreesion, left_input=2100, right_input=8291, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = fu6greOZ01 binary_op_definition= 'a⨐⩸⫘b = {a, if b == 0; (a⨐⩸⫘(b-1))⨓(b), if b > 0 and abs(b) < 1000; -(a⨐⩸⫘(b+1))⨓(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯213323≳⇉⪩⨒∯313120⨐⩸⫘⪩⨒∯200310∑⇟⊟⪩⨒∯2001203=NaN","reverse_text":"NaN=⪩⨒∯213323≳⇉⪩⨒∯313120⨐⩸⫘⪩⨒∯200310∑⇟⊟⪩⨒∯2001203","cot":[{"info":"⪩⨒∯213323≳⇉⪩⨒∯313120=NaN","layer":1},{"info":"⪩⨒∯200310∑⇟⊟⪩⨒∯2001203=NaN","layer":1},{"info":"NaN⨐⩸⫘NaN=NaN","layer":0}]}
{"id":174,"expression_no_base_symbol":"($2162$-$2214$)∷","expression":"(⪩⨒∯201302-⪩⨒∯202212)∷","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8,"operation_count":2,"complexity_ratio":4.0,"tree":{"type":"unary","operator":"∷","unary_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":2162,"base":4},"right_expr":{"type":"numeric_atoms","value":2214,"base":4}}},"used_operators":["nFAOW8KTqp","rysDP5nf3Z"],"dependent_operators":["D4vGDi5EA2","t8gj7n24qd","2DDjHMKMc0"],"result":"⪩⨒∯-2130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2162","layer":2},{"info":"number node, value=2214","layer":2},{"info":"compute binary expreesion, left_input=2162, right_input=2214, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-52","layer":1},{"info":"compute unary expreesion, input=-52, op_id = nFAOW8KTqp, unary_op_definition = 'a∷ = { ((-(a⋝⋈⪟a))≦≮≮) }', output=-156","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯201302-⪩⨒∯202212)∷=⪩⨒∯-2130","reverse_text":"⪩⨒∯-2130=(⪩⨒∯201302-⪩⨒∯202212)∷","cot":[{"info":"⪩⨒∯201302-⪩⨒∯202212=⪩⨒∯-310","layer":1},{"info":"⪩⨒∯-310∷=⪩⨒∯-2130","layer":0}]}
{"id":175,"expression_no_base_symbol":"($1791$⇼⇔∾$7155$)⪔$5187$⪛$2246$","expression":"(⪩⨒∯123333⇼⇔∾⪩⨒∯1233303)⪔⪩⨒∯1101003⪛⪩⨒∯203012","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":798,"operation_count":3,"complexity_ratio":266.0,"tree":{"type":"binary","operator":"⪔","left_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":1791,"base":4},"right_expr":{"type":"numeric_atoms","value":7155,"base":4}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":5187,"base":4},"right_expr":{"type":"numeric_atoms","value":2246,"base":4}}},"used_operators":["GjBEYRfMaF","tifHPKVTfV","uFcxV4UQCh"],"dependent_operators":["YjI8oCXuph","8INZBEW696","dWAJyo7jo9","nREPSIbpBE","2DDjHMKMc0","IWmyXbctLI","PoHhknlbAi","rysDP5nf3Z","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⪩⨒∯13002","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1791","layer":2},{"info":"number node, value=7155","layer":2},{"info":"compute binary expreesion, left_input=1791, right_input=7155, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=5364","layer":1},{"info":"number node, value=5187","layer":2},{"info":"number node, value=2246","layer":2},{"info":"compute binary expreesion, left_input=5187, right_input=2246, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=695","layer":1},{"info":"compute binary expreesion, left_input=5364, right_input=695, op_id = GjBEYRfMaF binary_op_definition= 'a⪔b = { (((⫇a)∓⋝(61⪢b))⪮%⊝((b⋝⋈⪟b)⨚(a≀⩗∶a))) }', output=450","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯123333⇼⇔∾⪩⨒∯1233303)⪔⪩⨒∯1101003⪛⪩⨒∯203012=⪩⨒∯13002","reverse_text":"⪩⨒∯13002=(⪩⨒∯123333⇼⇔∾⪩⨒∯1233303)⪔⪩⨒∯1101003⪛⪩⨒∯203012","cot":[{"info":"⪩⨒∯123333⇼⇔∾⪩⨒∯1233303=⪩⨒∯1103310","layer":1},{"info":"⪩⨒∯1101003⪛⪩⨒∯203012=⪩⨒∯22313","layer":1},{"info":"⪩⨒∯1103310⪔⪩⨒∯22313=⪩⨒∯13002","layer":0}]}
{"id":176,"expression_no_base_symbol":"⊤⊝$1342$⇻⋧≁$1483$","expression":"⊤⊝⪩⨒∯110332⇻⋧≁⪩⨒∯113023","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1374,"operation_count":2,"complexity_ratio":687.0,"tree":{"type":"unary","operator":"⊤⊝","unary_expr":{"type":"binary","operator":"⇻⋧≁","left_expr":{"type":"numeric_atoms","value":1342,"base":4},"right_expr":{"type":"numeric_atoms","value":1483,"base":4}}},"used_operators":["rXAclfmB4M","jCPkEVoL5K"],"dependent_operators":["sdazOOVcIp","eLxqMNBOBk","XnXgA4xnOs","3EYGwJThht","XTarYq4gQB","59igzFyhWz","dfKe02y8D2","X99M06cbEe"],"result":"⪩⨒∯-202100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1342","layer":2},{"info":"number node, value=1483","layer":2},{"info":"compute binary expreesion, left_input=1342, right_input=1483, op_id = jCPkEVoL5K binary_op_definition= 'a⇻⋧≁b = { ((⫓⪴a)⫚↹⊑(54≫≃)) , if (a∵≐)<=35 or a>411 ; ((⪝⪂⫅b)⇄(290⨑≵⋬a)) , else }', output=-447","layer":1},{"info":"compute unary expreesion, input=-447, op_id = rXAclfmB4M, unary_op_definition = '⊤⊝a = { (a⪨≂700) }', output=-2192","layer":0}],"base":4,"result_base":4,"text":"⊤⊝⪩⨒∯110332⇻⋧≁⪩⨒∯113023=⪩⨒∯-202100","reverse_text":"⪩⨒∯-202100=⊤⊝⪩⨒∯110332⇻⋧≁⪩⨒∯113023","cot":[{"info":"⪩⨒∯110332⇻⋧≁⪩⨒∯113023=⪩⨒∯-12333","layer":1},{"info":"⊤⊝⪩⨒∯-12333=⪩⨒∯-202100","layer":0}]}
{"id":177,"expression_no_base_symbol":"$1184$⨽∌$1559$⨳⩥⨓($1385$⩤)","expression":"⪩⨒∯102200⨽∌⪩⨒∯120113⨳⩥⨓(⪩⨒∯111221⩤)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":61,"operation_count":3,"complexity_ratio":20.333333333333332,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⨽∌","left_expr":{"type":"numeric_atoms","value":1184,"base":4},"right_expr":{"type":"numeric_atoms","value":1559,"base":4}},"right_expr":{"type":"unary","operator":"⩤","unary_expr":{"type":"numeric_atoms","value":1385,"base":4}}},"used_operators":["nCS4ZIUYfx","9samAPKr6k","Z2TMIBDE3Q"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯-111221","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1184","layer":2},{"info":"number node, value=1559","layer":2},{"info":"compute binary expreesion, left_input=1184, right_input=1559, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":1},{"info":"number node, value=1385","layer":2},{"info":"compute unary expreesion, input=1385, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-1385","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-1385, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-1385","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102200⨽∌⪩⨒∯120113⨳⩥⨓(⪩⨒∯111221⩤)=⪩⨒∯-111221","reverse_text":"⪩⨒∯-111221=⪩⨒∯102200⨽∌⪩⨒∯120113⨳⩥⨓(⪩⨒∯111221⩤)","cot":[{"info":"⪩⨒∯102200⨽∌⪩⨒∯120113=⪩⨒∯0","layer":1},{"info":"⪩⨒∯111221⩤=⪩⨒∯-111221","layer":1},{"info":"⪩⨒∯0⨳⩥⨓⪩⨒∯-111221=⪩⨒∯-111221","layer":0}]}
{"id":178,"expression_no_base_symbol":"⩪∧⨌($8815$⋐⇩⊬)","expression":"⩪∧⨌(⪩⨒∯2021233⋐⇩⊬)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":10,"operation_count":2,"complexity_ratio":5.0,"tree":{"type":"unary","operator":"⩪∧⨌","unary_expr":{"type":"unary","operator":"⋐⇩⊬","unary_expr":{"type":"numeric_atoms","value":8815,"base":4}}},"used_operators":["6iOiAJX1F8","JuuLT1NoCs"],"dependent_operators":["P8v4zCKN1o","23Mk6UjR3U","7j4O788W3g","f6k1SAg4EE","g55IO6H4Gj","mp7IySMOzn","JclMnS0uGI","ddLRYrp01A"],"result":"⪩⨒∯111201112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8815","layer":2},{"info":"compute unary expreesion, input=8815, op_id = JuuLT1NoCs, unary_op_definition = 'a⋐⇩⊬ = { (a⨔⇊a) , if (a∊∟⩊189)<=582 ; (a⇷a) , else }', output=8815","layer":1},{"info":"compute unary expreesion, input=8815, op_id = 6iOiAJX1F8, unary_op_definition = '⩪∧⨌a = { (∥⊫a) , if ((a⋷517)==285 and (a⪒780)<=108) ; ((a↺a)⨸⪁(a⨸⪁a)) , else }', output=88150","layer":0}],"base":4,"result_base":4,"text":"⩪∧⨌(⪩⨒∯2021233⋐⇩⊬)=⪩⨒∯111201112","reverse_text":"⪩⨒∯111201112=⩪∧⨌(⪩⨒∯2021233⋐⇩⊬)","cot":[{"info":"⪩⨒∯2021233⋐⇩⊬=⪩⨒∯2021233","layer":1},{"info":"⩪∧⨌⪩⨒∯2021233=⪩⨒∯111201112","layer":0}]}
{"id":179,"expression_no_base_symbol":"⨈⫕($3495$∖$3000$)","expression":"⨈⫕(⪩⨒∯312213∖⪩⨒∯232320)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":807,"operation_count":2,"complexity_ratio":403.5,"tree":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"binary","operator":"∖","left_expr":{"type":"numeric_atoms","value":3495,"base":4},"right_expr":{"type":"numeric_atoms","value":3000,"base":4}}},"used_operators":["megm06wKyl","tXD093vOjl"],"dependent_operators":["8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q","rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC"],"result":"⪩⨒∯-111","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3495","layer":2},{"info":"number node, value=3000","layer":2},{"info":"compute binary expreesion, left_input=3495, right_input=3000, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = megm06wKyl, unary_op_definition = '⨈⫕a = { (((a+a)⊦⊿)+⇶⊼123) , if (a⩤)!=46 and a==442 and (+⊝⨔a)!=531 ; (↯⪼(⊥(8⨁⊸⫻))) , else }', output=-21","layer":0}],"base":4,"result_base":4,"text":"⨈⫕(⪩⨒∯312213∖⪩⨒∯232320)=⪩⨒∯-111","reverse_text":"⪩⨒∯-111=⨈⫕(⪩⨒∯312213∖⪩⨒∯232320)","cot":[{"info":"⪩⨒∯312213∖⪩⨒∯232320=⪩⨒∯0","layer":1},{"info":"⨈⫕⪩⨒∯0=⪩⨒∯-111","layer":0}]}
{"id":180,"expression_no_base_symbol":"$1679$⊋$2149$⩢≌","expression":"⪩⨒∯122033⊋⪩⨒∯201211⩢≌","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1123,"operation_count":2,"complexity_ratio":561.5,"tree":{"type":"unary","operator":"⩢≌","unary_expr":{"type":"binary","operator":"⊋","left_expr":{"type":"numeric_atoms","value":1679,"base":4},"right_expr":{"type":"numeric_atoms","value":2149,"base":4}}},"used_operators":["D617RFjZIq","W4tP9CfskL"],"dependent_operators":["hTbEZDJLEm","o20kRiQErp","2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu"],"result":"⪩⨒∯1301","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1679","layer":2},{"info":"number node, value=2149","layer":2},{"info":"compute binary expreesion, left_input=1679, right_input=2149, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=-7132188","layer":1},{"info":"compute unary expreesion, input=-7132188, op_id = D617RFjZIq, unary_op_definition = 'a⩢≌ = { ((a∸)∟) }', output=113","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯122033⊋⪩⨒∯201211⩢≌=⪩⨒∯1301","reverse_text":"⪩⨒∯1301=⪩⨒∯122033⊋⪩⨒∯201211⩢≌","cot":[{"info":"⪩⨒∯122033⊋⪩⨒∯201211=⪩⨒∯-123031100130","layer":1},{"info":"⪩⨒∯-123031100130⩢≌=⪩⨒∯1301","layer":0}]}
{"id":181,"expression_no_base_symbol":"($1447$⩁)⪛(⊄⩳↩$3814$)","expression":"(⪩⨒∯112213⩁)⪛(⊄⩳↩⪩⨒∯323212)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":30,"operation_count":3,"complexity_ratio":10.0,"tree":{"type":"binary","operator":"⪛","left_expr":{"type":"unary","operator":"⩁","unary_expr":{"type":"numeric_atoms","value":1447,"base":4}},"right_expr":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":3814,"base":4}}},"used_operators":["uFcxV4UQCh","5GqDbVmqXU","8w2t5hMYqp"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","7j4O788W3g","jLgFTUHLKL","8cLx32lpNA","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-2021130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1447","layer":2},{"info":"compute unary expreesion, input=1447, op_id = 5GqDbVmqXU, unary_op_definition = 'a⩁ = { ((↩a)∌(a↺a)) }', output=-8796","layer":1},{"info":"number node, value=3814","layer":2},{"info":"compute unary expreesion, input=3814, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-11442","layer":1},{"info":"compute binary expreesion, left_input=-8796, right_input=-11442, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=-8796","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯112213⩁)⪛(⊄⩳↩⪩⨒∯323212)=⪩⨒∯-2021130","reverse_text":"⪩⨒∯-2021130=(⪩⨒∯112213⩁)⪛(⊄⩳↩⪩⨒∯323212)","cot":[{"info":"⪩⨒∯112213⩁=⪩⨒∯-2021130","layer":1},{"info":"⊄⩳↩⪩⨒∯323212=⪩⨒∯-2302302","layer":1},{"info":"⪩⨒∯-2021130⪛⪩⨒∯-2302302=⪩⨒∯-2021130","layer":0}]}
{"id":182,"expression_no_base_symbol":"($1370$⨟⋌⩍$5556$)⪎↠($5145$⋭≵$1433$)","expression":"(⪩⨒∯111122⨟⋌⩍⪩⨒∯1112310)⪎↠(⪩⨒∯1100121⋭≵⪩⨒∯112121)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":63,"operation_count":3,"complexity_ratio":21.0,"tree":{"type":"binary","operator":"⪎↠","left_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":1370,"base":4},"right_expr":{"type":"numeric_atoms","value":5556,"base":4}},"right_expr":{"type":"binary","operator":"⋭≵","left_expr":{"type":"numeric_atoms","value":5145,"base":4},"right_expr":{"type":"numeric_atoms","value":1433,"base":4}}},"used_operators":["3tVxb0NHM4","rGHVDoGpnC","jBncVCNhdl"],"dependent_operators":["P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM","Tcnh7f0tEr","RygbFNSyEJ","gx7XJ7hdpj","9ICcGScMcE","C6VvDP6HwP","mqXw5SEYmG","7IPrd9c3lf","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1370","layer":2},{"info":"number node, value=5556","layer":2},{"info":"compute binary expreesion, left_input=1370, right_input=5556, op_id = rGHVDoGpnC binary_op_definition= 'a⨟⋌⩍b = {a, if b == 0; (a⨟⋌⩍(b-1))≣⋋, if b > 0 and abs(b) < 1000; -(a⨟⋌⩍(b+1))≣⋋, if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"number node, value=5145","layer":2},{"info":"number node, value=1433","layer":2},{"info":"compute binary expreesion, left_input=5145, right_input=1433, op_id = jBncVCNhdl binary_op_definition= 'a⋭≵b = { ((156≦↸a)⊭↱(≦∁b)) , if (b⫸⊐434)<=441 and (a⫸⇳180)>=132 ; ((a⪑⩈)⊵↤) , else }', output=67","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=67, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯111122⨟⋌⩍⪩⨒∯1112310)⪎↠(⪩⨒∯1100121⋭≵⪩⨒∯112121)=NaN","reverse_text":"NaN=(⪩⨒∯111122⨟⋌⩍⪩⨒∯1112310)⪎↠(⪩⨒∯1100121⋭≵⪩⨒∯112121)","cot":[{"info":"⪩⨒∯111122⨟⋌⩍⪩⨒∯1112310=NaN","layer":1},{"info":"⪩⨒∯1100121⋭≵⪩⨒∯112121=⪩⨒∯1003","layer":1},{"info":"NaN⪎↠⪩⨒∯1003=NaN","layer":0}]}
{"id":183,"expression_no_base_symbol":"($1021$⫥∨⫟$1324$)⪇≇⋚($3563$⨘⋶⪀)","expression":"(⪩⨒∯33331⫥∨⫟⪩⨒∯110230)⪇≇⋚(⪩⨒∯313223⨘⋶⪀)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":246,"operation_count":3,"complexity_ratio":82.0,"tree":{"type":"binary","operator":"⪇≇⋚","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1021,"base":4},"right_expr":{"type":"numeric_atoms","value":1324,"base":4}},"right_expr":{"type":"unary","operator":"⨘⋶⪀","unary_expr":{"type":"numeric_atoms","value":3563,"base":4}}},"used_operators":["3sJ7IOPOlU","KYD54nUTWz","XVKwrhznBb"],"dependent_operators":["DZ8iAZOCBD","JLbD19bQDL","xUOZtlo3hN","8HhzD0ZcuI","rGHVDoGpnC","TpPTUOHfaN","FyVja0WsTP","UqFzSgLMvQ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1021","layer":2},{"info":"number node, value=1324","layer":2},{"info":"compute binary expreesion, left_input=1021, right_input=1324, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=3563","layer":2},{"info":"compute unary expreesion, input=3563, op_id = XVKwrhznBb, unary_op_definition = 'a⨘⋶⪀ = { ((326+⇶⊼a)⊱⇼⊻(a⇡)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = 3sJ7IOPOlU binary_op_definition= 'a⪇≇⋚b = { ((⨞⊢(a⊉≛↸b))⪠⩆⊳) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯33331⫥∨⫟⪩⨒∯110230)⪇≇⋚(⪩⨒∯313223⨘⋶⪀)=NaN","reverse_text":"NaN=(⪩⨒∯33331⫥∨⫟⪩⨒∯110230)⪇≇⋚(⪩⨒∯313223⨘⋶⪀)","cot":[{"info":"⪩⨒∯33331⫥∨⫟⪩⨒∯110230=NaN","layer":1},{"info":"⪩⨒∯313223⨘⋶⪀=NaN","layer":1},{"info":"NaN⪇≇⋚NaN=NaN","layer":0}]}
{"id":184,"expression_no_base_symbol":"($5029$≠≀$6919$)⫏⊷","expression":"(⪩⨒∯1032211≠≀⪩⨒∯1230013)⫏⊷","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":29444,"operation_count":2,"complexity_ratio":14722.0,"tree":{"type":"unary","operator":"⫏⊷","unary_expr":{"type":"binary","operator":"≠≀","left_expr":{"type":"numeric_atoms","value":5029,"base":4},"right_expr":{"type":"numeric_atoms","value":6919,"base":4}}},"used_operators":["dcShxvzhyw","IwW236VD4Y"],"dependent_operators":["FU0Cs4j7VP","7YooWSwCyH","HK0tfVPux8","eLAdDNolq6","NTOWxs364D","sdazOOVcIp","2DDjHMKMc0","2td37pGCOC"],"result":"⪩⨒∯331220","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5029","layer":2},{"info":"number node, value=6919","layer":2},{"info":"compute binary expreesion, left_input=5029, right_input=6919, op_id = IwW236VD4Y binary_op_definition= 'a≠≀b = { (⩦⩻⨪(a⩚⊴⇥b)) , if (≤/b)>10 ; ((a⪨≂a)⪨≂(a⋝⋈⪟356)) , else }', output=-9752","layer":1},{"info":"compute unary expreesion, input=-9752, op_id = dcShxvzhyw, unary_op_definition = 'a⫏⊷ = { ((224∪⫐a)⊾⪯⋞(a↛⩡⫤)) }', output=3944","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1032211≠≀⪩⨒∯1230013)⫏⊷=⪩⨒∯331220","reverse_text":"⪩⨒∯331220=(⪩⨒∯1032211≠≀⪩⨒∯1230013)⫏⊷","cot":[{"info":"⪩⨒∯1032211≠≀⪩⨒∯1230013=⪩⨒∯-2120120","layer":1},{"info":"⪩⨒∯-2120120⫏⊷=⪩⨒∯331220","layer":0}]}
{"id":185,"expression_no_base_symbol":"($2117$⪉⨛$1471$)⨸($1288$⋅⇍$1547$)","expression":"(⪩⨒∯201011⪉⨛⪩⨒∯112333)⨸(⪩⨒∯110020⋅⇍⪩⨒∯120023)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5233,"operation_count":3,"complexity_ratio":1744.3333333333333,"tree":{"type":"binary","operator":"⨸","left_expr":{"type":"binary","operator":"⪉⨛","left_expr":{"type":"numeric_atoms","value":2117,"base":4},"right_expr":{"type":"numeric_atoms","value":1471,"base":4}},"right_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":1288,"base":4},"right_expr":{"type":"numeric_atoms","value":1547,"base":4}}},"used_operators":["KmoU8R5UQR","EWw2JM7wp4","AdZkA7nFnk"],"dependent_operators":["ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl","NTOWxs364D","tifHPKVTfV","12rbrZMWeM","i8ToyICDmI","eewbuw0ToL","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6"],"result":"⪩⨒∯2133032","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2117","layer":2},{"info":"number node, value=1471","layer":2},{"info":"compute binary expreesion, left_input=2117, right_input=1471, op_id = EWw2JM7wp4 binary_op_definition= 'a⪉⨛b = { (((82⇼⇔∾a)⩚⊴⇥a)⩚⊴⇥((b∲⫓a)⋳⪒(a⨰b))) }', output=5095","layer":1},{"info":"number node, value=1288","layer":2},{"info":"number node, value=1547","layer":2},{"info":"compute binary expreesion, left_input=1288, right_input=1547, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"compute binary expreesion, left_input=5095, right_input=-22, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=10190","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯201011⪉⨛⪩⨒∯112333)⨸(⪩⨒∯110020⋅⇍⪩⨒∯120023)=⪩⨒∯2133032","reverse_text":"⪩⨒∯2133032=(⪩⨒∯201011⪉⨛⪩⨒∯112333)⨸(⪩⨒∯110020⋅⇍⪩⨒∯120023)","cot":[{"info":"⪩⨒∯201011⪉⨛⪩⨒∯112333=⪩⨒∯1033213","layer":1},{"info":"⪩⨒∯110020⋅⇍⪩⨒∯120023=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯1033213⨸⪩⨒∯-112=⪩⨒∯2133032","layer":0}]}
{"id":186,"expression_no_base_symbol":"(↯⪼$1409$)⪬($1698$≒∊$1006$)","expression":"(↯⪼⪩⨒∯112001)⪬(⪩⨒∯122202≒∊⪩⨒∯33232)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":606,"operation_count":3,"complexity_ratio":202.0,"tree":{"type":"binary","operator":"⪬","left_expr":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"numeric_atoms","value":1409,"base":4}},"right_expr":{"type":"binary","operator":"≒∊","left_expr":{"type":"numeric_atoms","value":1698,"base":4},"right_expr":{"type":"numeric_atoms","value":1006,"base":4}}},"used_operators":["Ez1Nq5fNfI","8jW3W4yZS5","5KTvxBwnZo"],"dependent_operators":["eRqsBgTDFp","mp7IySMOzn","JL8yIekQnl","QvoQhV0rrE","kbkesczE7y","eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","3EYGwJThht","dWAJyo7jo9","Z2TMIBDE3Q","bjFbhXSADs","3DZMoQKiUl"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1409","layer":2},{"info":"compute unary expreesion, input=1409, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":1},{"info":"number node, value=1698","layer":2},{"info":"number node, value=1006","layer":2},{"info":"compute binary expreesion, left_input=1698, right_input=1006, op_id = 5KTvxBwnZo binary_op_definition= 'a≒∊b = { (≱⇩⩕(a⪢a)) , if (a⩤)==117 ; ((b⪊≅)⇄a) , else }', output=-1214","layer":1},{"info":"compute binary expreesion, left_input=-21, right_input=-1214, op_id = Ez1Nq5fNfI binary_op_definition= 'a⪬b = { (((514⋫)⪒⊣⊆(b≬⋮a))∠⫱(1⇷(b≬⋮32))) }', output=1234","layer":0}],"base":4,"result_base":4,"text":"(↯⪼⪩⨒∯112001)⪬(⪩⨒∯122202≒∊⪩⨒∯33232)=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=(↯⪼⪩⨒∯112001)⪬(⪩⨒∯122202≒∊⪩⨒∯33232)","cot":[{"info":"↯⪼⪩⨒∯112001=⪩⨒∯-111","layer":1},{"info":"⪩⨒∯122202≒∊⪩⨒∯33232=⪩⨒∯-102332","layer":1},{"info":"⪩⨒∯-111⪬⪩⨒∯-102332=⪩⨒∯103102","layer":0}]}
{"id":187,"expression_no_base_symbol":"∂⩏⊆$1218$⋛$3515$","expression":"∂⩏⊆⪩⨒∯103002⋛⪩⨒∯312323","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":265,"operation_count":2,"complexity_ratio":132.5,"tree":{"type":"unary","operator":"∂⩏⊆","unary_expr":{"type":"binary","operator":"⋛","left_expr":{"type":"numeric_atoms","value":1218,"base":4},"right_expr":{"type":"numeric_atoms","value":3515,"base":4}}},"used_operators":["8WDwsbhb0R","YbUVn0Rbpy"],"dependent_operators":["14qkJME0vr","eLAdDNolq6","d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA"],"result":"⪩⨒∯131231302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1218","layer":2},{"info":"number node, value=3515","layer":2},{"info":"compute binary expreesion, left_input=1218, right_input=3515, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-121230","layer":1},{"info":"compute unary expreesion, input=-121230, op_id = 8WDwsbhb0R, unary_op_definition = '∂⩏⊆a = { (≤/a) , if a<=92 ; (a⊦⊿) , else }', output=121714","layer":0}],"base":4,"result_base":4,"text":"∂⩏⊆⪩⨒∯103002⋛⪩⨒∯312323=⪩⨒∯131231302","reverse_text":"⪩⨒∯131231302=∂⩏⊆⪩⨒∯103002⋛⪩⨒∯312323","cot":[{"info":"⪩⨒∯103002⋛⪩⨒∯312323=⪩⨒∯-131212032","layer":1},{"info":"∂⩏⊆⪩⨒∯-131212032=⪩⨒∯131231302","layer":0}]}
{"id":188,"expression_no_base_symbol":"(⊬↢$5819$)⪎↠$1190$⪎↠$2519$","expression":"(⊬↢⪩⨒∯1122323)⪎↠⪩⨒∯102212⪎↠⪩⨒∯213113","highest_n_order":3,"priority_hierarchical_complexity":1,"normalized_expansion_degree":5887,"operation_count":3,"complexity_ratio":1962.3333333333333,"tree":{"type":"binary","operator":"⪎↠","left_expr":{"type":"unary","operator":"⊬↢","unary_expr":{"type":"numeric_atoms","value":5819,"base":4}},"right_expr":{"type":"binary","operator":"⪎↠","left_expr":{"type":"numeric_atoms","value":1190,"base":4},"right_expr":{"type":"numeric_atoms","value":2519,"base":4}}},"used_operators":["3tVxb0NHM4","WPoGxAaPR1"],"dependent_operators":["P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM","XGcMNugi78","d7ASUq0ydm","OwUj7dcsQK","FyVja0WsTP","1eCjFl0mb9","j6NVkjMzuk","SL6IHkK8vl","MRPaB8lBjK","yyfyN0ffXY","3Oe9XWJUTD","3tVxb0NHM4","8cLx32lpNA"],"result":"⪩⨒∯100332","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5819","layer":2},{"info":"compute unary expreesion, input=5819, op_id = WPoGxAaPR1, unary_op_definition = '⊬↢a = { (((a⫞⩸⩒a)⊝⪿⪼(a⫯⪬∳a))⪎↠((a⨀⨒)↸(∐⩳⋚a))) , if (∓a)>278 ; (((a↙a)⊱⇼⊻(a∌480))⇉⇱⇎) , else }', output=218","layer":1},{"info":"number node, value=1190","layer":2},{"info":"number node, value=2519","layer":2},{"info":"compute binary expreesion, left_input=1190, right_input=2519, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=160","layer":1},{"info":"compute binary expreesion, left_input=218, right_input=160, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=1086","layer":0}],"base":4,"result_base":4,"text":"(⊬↢⪩⨒∯1122323)⪎↠⪩⨒∯102212⪎↠⪩⨒∯213113=⪩⨒∯100332","reverse_text":"⪩⨒∯100332=(⊬↢⪩⨒∯1122323)⪎↠⪩⨒∯102212⪎↠⪩⨒∯213113","cot":[{"info":"⊬↢⪩⨒∯1122323=⪩⨒∯3122","layer":1},{"info":"⪩⨒∯102212⪎↠⪩⨒∯213113=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯3122⪎↠⪩⨒∯2200=⪩⨒∯100332","layer":0}]}
{"id":189,"expression_no_base_symbol":"⊖(⊬↢$6032$)","expression":"⊖(⊬↢⪩⨒∯1132100)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6093,"operation_count":2,"complexity_ratio":3046.5,"tree":{"type":"unary","operator":"⊖","unary_expr":{"type":"unary","operator":"⊬↢","unary_expr":{"type":"numeric_atoms","value":6032,"base":4}}},"used_operators":["U6pG0PXrV3","WPoGxAaPR1"],"dependent_operators":["tifHPKVTfV","i8ToyICDmI","D4vGDi5EA2","nCS4ZIUYfx","XGcMNugi78","d7ASUq0ydm","OwUj7dcsQK","FyVja0WsTP","1eCjFl0mb9","j6NVkjMzuk","SL6IHkK8vl","MRPaB8lBjK","yyfyN0ffXY","3Oe9XWJUTD","3tVxb0NHM4","8cLx32lpNA"],"result":"⪩⨒∯-22032","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6032","layer":2},{"info":"compute unary expreesion, input=6032, op_id = WPoGxAaPR1, unary_op_definition = '⊬↢a = { (((a⫞⩸⩒a)⊝⪿⪼(a⫯⪬∳a))⪎↠((a⨀⨒)↸(∐⩳⋚a))) , if (∓a)>278 ; (((a↙a)⊱⇼⊻(a∌480))⇉⇱⇎) , else }', output=218","layer":1},{"info":"compute unary expreesion, input=218, op_id = U6pG0PXrV3, unary_op_definition = '⊖a = { (((a⇼⇔∾a)⨳⩥⨓(a≦≮≮))∲⫓a) }', output=-654","layer":0}],"base":4,"result_base":4,"text":"⊖(⊬↢⪩⨒∯1132100)=⪩⨒∯-22032","reverse_text":"⪩⨒∯-22032=⊖(⊬↢⪩⨒∯1132100)","cot":[{"info":"⊬↢⪩⨒∯1132100=⪩⨒∯3122","layer":1},{"info":"⊖⪩⨒∯3122=⪩⨒∯-22032","layer":0}]}
{"id":190,"expression_no_base_symbol":"$4824$⨻⩈⩔$3933$∠↢$3029$⨓$3132$","expression":"⪩⨒∯1023120⨻⩈⩔⪩⨒∯331131∠↢⪩⨒∯233111⨓⪩⨒∯300330","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3262,"operation_count":3,"complexity_ratio":1087.3333333333333,"tree":{"type":"binary","operator":"∠↢","left_expr":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"numeric_atoms","value":4824,"base":4},"right_expr":{"type":"numeric_atoms","value":3933,"base":4}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":3029,"base":4},"right_expr":{"type":"numeric_atoms","value":3132,"base":4}}},"used_operators":["KbjG8mgYpV","nEsXyWgiOK","3ViojmjbAp"],"dependent_operators":["rysDP5nf3Z","NTOWxs364D","XPYlsWDdGa","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","nCS4ZIUYfx","COABgblf1C","D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⪩⨒∯-102200100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4824","layer":2},{"info":"number node, value=3933","layer":2},{"info":"compute binary expreesion, left_input=4824, right_input=3933, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=30191","layer":1},{"info":"number node, value=3029","layer":2},{"info":"number node, value=3132","layer":2},{"info":"compute binary expreesion, left_input=3029, right_input=3132, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-3135","layer":1},{"info":"compute binary expreesion, left_input=30191, right_input=-3135, op_id = KbjG8mgYpV binary_op_definition= 'a∠↢b = { (a⊭↱((159⨳⩥⨓16)-(b⨸⪁a))) , if (b==488 or (⨞⊢a)==254) ; (⪲⇎((-b)⫡⨏(b⩚⊴⇥a))) , else }', output=-75792","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1023120⨻⩈⩔⪩⨒∯331131∠↢⪩⨒∯233111⨓⪩⨒∯300330=⪩⨒∯-102200100","reverse_text":"⪩⨒∯-102200100=⪩⨒∯1023120⨻⩈⩔⪩⨒∯331131∠↢⪩⨒∯233111⨓⪩⨒∯300330","cot":[{"info":"⪩⨒∯1023120⨻⩈⩔⪩⨒∯331131=⪩⨒∯13113233","layer":1},{"info":"⪩⨒∯233111⨓⪩⨒∯300330=⪩⨒∯-300333","layer":1},{"info":"⪩⨒∯13113233∠↢⪩⨒∯-300333=⪩⨒∯-102200100","layer":0}]}
{"id":191,"expression_no_base_symbol":"$5442$↳∿⪆$5975$⫃⨇$1096$≹⇙⪍$3793$","expression":"⪩⨒∯1111002↳∿⪆⪩⨒∯1131113⫃⨇⪩⨒∯101020≹⇙⪍⪩⨒∯323101","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2495,"operation_count":3,"complexity_ratio":831.6666666666666,"tree":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"binary","operator":"↳∿⪆","left_expr":{"type":"numeric_atoms","value":5442,"base":4},"right_expr":{"type":"numeric_atoms","value":5975,"base":4}},"right_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":1096,"base":4},"right_expr":{"type":"numeric_atoms","value":3793,"base":4}}},"used_operators":["09Ly4LVMIf","Cw4SuJJGHO","AHs5Up7iyr"],"dependent_operators":["9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG","hyuBjUqXlG","bF6eod5Gvf","nEsXyWgiOK","ruOEQAzv1W","Tw270M8GLb","QMFrweE19q","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5442","layer":2},{"info":"number node, value=5975","layer":2},{"info":"compute binary expreesion, left_input=5442, right_input=5975, op_id = Cw4SuJJGHO binary_op_definition= 'a↳∿⪆b = { ((⨰⫟⨤(↔15))⨻⩈⩔((b⪛⫼133)⫡⨏(b→⨶⪴a))) }', output=nan","layer":1},{"info":"number node, value=1096","layer":2},{"info":"number node, value=3793","layer":2},{"info":"compute binary expreesion, left_input=1096, right_input=3793, op_id = AHs5Up7iyr binary_op_definition= 'a≹⇙⪍b = {a, if b == 0; (a≹⇙⪍(b-1))⪢(b), if b > 0 and abs(b) < 1000; -(a≹⇙⪍(b+1))⪢(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1111002↳∿⪆⪩⨒∯1131113⫃⨇⪩⨒∯101020≹⇙⪍⪩⨒∯323101=NaN","reverse_text":"NaN=⪩⨒∯1111002↳∿⪆⪩⨒∯1131113⫃⨇⪩⨒∯101020≹⇙⪍⪩⨒∯323101","cot":[{"info":"⪩⨒∯1111002↳∿⪆⪩⨒∯1131113=NaN","layer":1},{"info":"⪩⨒∯101020≹⇙⪍⪩⨒∯323101=NaN","layer":1},{"info":"NaN⫃⨇NaN=NaN","layer":0}]}
{"id":192,"expression_no_base_symbol":"$1019$⩷∴$1301$⨭⪣($6580$⊬⫿⊭)","expression":"⪩⨒∯33323⩷∴⪩⨒∯110111⨭⪣(⪩⨒∯1212310⊬⫿⊭)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":63,"operation_count":3,"complexity_ratio":21.0,"tree":{"type":"binary","operator":"⨭⪣","left_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":1019,"base":4},"right_expr":{"type":"numeric_atoms","value":1301,"base":4}},"right_expr":{"type":"unary","operator":"⊬⫿⊭","unary_expr":{"type":"numeric_atoms","value":6580,"base":4}}},"used_operators":["kn8WO9XteQ","9FxExcQeMw","v0DYgG9ikt"],"dependent_operators":["vRio1gEz1j","61wBmkZwlr","SWo3A1KBJH","8jW3W4yZS5","LkLIoiE525","Y7wcNGrDQJ","PPChnnnBFF","rysDP5nf3Z","eLAdDNolq6","P8v4zCKN1o","7j4O788W3g","8w2t5hMYqp","2DQ55sFlQl","2DDjHMKMc0","xUOZtlo3hN","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","u6S6b8DprG"],"result":"⪩⨒∯-3013","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1019","layer":2},{"info":"number node, value=1301","layer":2},{"info":"compute binary expreesion, left_input=1019, right_input=1301, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-596","layer":1},{"info":"number node, value=6580","layer":2},{"info":"compute unary expreesion, input=6580, op_id = v0DYgG9ikt, unary_op_definition = 'a⊬⫿⊭ = { ((⨑⩽⪐(≤/a))↺((⨞⊢a)⨰(↽≂188))) , if a<119 ; (((∥⊫a)⨳⩥⨓(a⨵⪆a))↺(⊄⩳↩(a⋝⋈⪟a))) , else }', output=-19740","layer":1},{"info":"compute binary expreesion, left_input=-596, right_input=-19740, op_id = kn8WO9XteQ binary_op_definition= 'a⨭⪣b = { ((486⇩)⩵∡(a∣a)) , if (b⇯⋐)>445 or (≋b)>319 or b<=69 ; (↯⪼(⇋↷b)) , else }', output=-199","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯33323⩷∴⪩⨒∯110111⨭⪣(⪩⨒∯1212310⊬⫿⊭)=⪩⨒∯-3013","reverse_text":"⪩⨒∯-3013=⪩⨒∯33323⩷∴⪩⨒∯110111⨭⪣(⪩⨒∯1212310⊬⫿⊭)","cot":[{"info":"⪩⨒∯33323⩷∴⪩⨒∯110111=⪩⨒∯-21110","layer":1},{"info":"⪩⨒∯1212310⊬⫿⊭=⪩⨒∯-10310130","layer":1},{"info":"⪩⨒∯-21110⨭⪣⪩⨒∯-10310130=⪩⨒∯-3013","layer":0}]}
{"id":193,"expression_no_base_symbol":"⇠$2245$⨔⇊$4455$","expression":"⇠⪩⨒∯203011⨔⇊⪩⨒∯1011213","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":10,"operation_count":2,"complexity_ratio":5.0,"tree":{"type":"unary","operator":"⇠","unary_expr":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"numeric_atoms","value":2245,"base":4},"right_expr":{"type":"numeric_atoms","value":4455,"base":4}}},"used_operators":["18saOjeKKm","JclMnS0uGI"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","nCS4ZIUYfx","9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI"],"result":"⪩⨒∯-1001311","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2245","layer":2},{"info":"number node, value=4455","layer":2},{"info":"compute binary expreesion, left_input=2245, right_input=4455, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=4455","layer":1},{"info":"compute unary expreesion, input=4455, op_id = 18saOjeKKm, unary_op_definition = '⇠a = { ((a⨳⩥⨓242)∲⫓(229⪨≂a)) }', output=-4213","layer":0}],"base":4,"result_base":4,"text":"⇠⪩⨒∯203011⨔⇊⪩⨒∯1011213=⪩⨒∯-1001311","reverse_text":"⪩⨒∯-1001311=⇠⪩⨒∯203011⨔⇊⪩⨒∯1011213","cot":[{"info":"⪩⨒∯203011⨔⇊⪩⨒∯1011213=⪩⨒∯1011213","layer":1},{"info":"⇠⪩⨒∯1011213=⪩⨒∯-1001311","layer":0}]}
{"id":194,"expression_no_base_symbol":"$4455$⇡⇂$2257$⩦($2273$⨻⩈⩔$3096$)","expression":"⪩⨒∯1011213⇡⇂⪩⨒∯203101⩦(⪩⨒∯203201⨻⩈⩔⪩⨒∯300120)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":12498,"operation_count":3,"complexity_ratio":4166.0,"tree":{"type":"binary","operator":"⩦","left_expr":{"type":"binary","operator":"⇡⇂","left_expr":{"type":"numeric_atoms","value":4455,"base":4},"right_expr":{"type":"numeric_atoms","value":2257,"base":4}},"right_expr":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"numeric_atoms","value":2273,"base":4},"right_expr":{"type":"numeric_atoms","value":3096,"base":4}}},"used_operators":["0kmYd0q39Y","UMwdvZNt44","nEsXyWgiOK"],"dependent_operators":["N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q","9FxExcQeMw","23Mk6UjR3U","z4E1FaHLuy","3tj9sqzovi","fu6greOZ01","AHs5Up7iyr","lvlrscuwVU","KPf6cnQVty","uBihLCJcMX","12rbrZMWeM","WPoGxAaPR1","D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4455","layer":2},{"info":"number node, value=2257","layer":2},{"info":"compute binary expreesion, left_input=4455, right_input=2257, op_id = UMwdvZNt44 binary_op_definition= 'a⇡⇂b = { (((b≹⇙⪍b)⋳⪒(b⋷a))∺≝⩲(⫟(a⩷∴43))) , if (⊬↢a)==727 or (a⇔⨋)<18 ; ((604≴⪞⇿(≻⋜b))⨐⩸⫘a) , else }', output=nan","layer":1},{"info":"number node, value=2273","layer":2},{"info":"number node, value=3096","layer":2},{"info":"compute binary expreesion, left_input=2273, right_input=3096, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=9783","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=9783, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1011213⇡⇂⪩⨒∯203101⩦(⪩⨒∯203201⨻⩈⩔⪩⨒∯300120)=NaN","reverse_text":"NaN=⪩⨒∯1011213⇡⇂⪩⨒∯203101⩦(⪩⨒∯203201⨻⩈⩔⪩⨒∯300120)","cot":[{"info":"⪩⨒∯1011213⇡⇂⪩⨒∯203101=NaN","layer":1},{"info":"⪩⨒∯203201⨻⩈⩔⪩⨒∯300120=⪩⨒∯2120313","layer":1},{"info":"NaN⩦⪩⨒∯2120313=NaN","layer":0}]}
{"id":195,"expression_no_base_symbol":"→⩰($7669$⊾⪯⋞$1878$)","expression":"→⩰(⪩⨒∯1313311⊾⪯⋞⪩⨒∯131112)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3771,"operation_count":2,"complexity_ratio":1885.5,"tree":{"type":"unary","operator":"→⩰","unary_expr":{"type":"binary","operator":"⊾⪯⋞","left_expr":{"type":"numeric_atoms","value":7669,"base":4},"right_expr":{"type":"numeric_atoms","value":1878,"base":4}}},"used_operators":["o8Pngz0Tml","HK0tfVPux8"],"dependent_operators":["9FxExcQeMw","4X4GscPmMf","YbUVn0Rbpy","Nsiff2A1zJ","l1M9WJ3V7u","eewbuw0ToL","s3Fd5m9Dh2","KFSx94NKJn","MmTdOpaElr","XnXgA4xnOs","fOIeswaMU4","YSKBFp38Pu","oacrs7FA3X","xNBdhnnwKq"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7669","layer":2},{"info":"number node, value=1878","layer":2},{"info":"compute binary expreesion, left_input=7669, right_input=1878, op_id = HK0tfVPux8 binary_op_definition= 'a⊾⪯⋞b = { ((121⊭∹↮)⊬⨰(a⨑≵⋬b)) , if (a⩟)==395 or (a⨱∎)>94 ; ((b⪘⫢b)⩒⫫(a⇤b)) , else }', output=3330","layer":1},{"info":"compute unary expreesion, input=3330, op_id = o8Pngz0Tml, unary_op_definition = '→⩰a = { ((∑⇻≧(a⋛a))⨰((a⊴a)⩷∴(a⨕⋳))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"→⩰(⪩⨒∯1313311⊾⪯⋞⪩⨒∯131112)=NaN","reverse_text":"NaN=→⩰(⪩⨒∯1313311⊾⪯⋞⪩⨒∯131112)","cot":[{"info":"⪩⨒∯1313311⊾⪯⋞⪩⨒∯131112=⪩⨒∯310002","layer":1},{"info":"→⩰⪩⨒∯310002=NaN","layer":0}]}
{"id":196,"expression_no_base_symbol":"($3952$⊬⨰$1280$)⇂≾⫗(∐⩳⋚$3767$)","expression":"(⪩⨒∯331300⊬⨰⪩⨒∯110000)⇂≾⫗(∐⩳⋚⪩⨒∯322313)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":238,"operation_count":3,"complexity_ratio":79.33333333333333,"tree":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"numeric_atoms","value":3952,"base":4},"right_expr":{"type":"numeric_atoms","value":1280,"base":4}},"right_expr":{"type":"unary","operator":"∐⩳⋚","unary_expr":{"type":"numeric_atoms","value":3767,"base":4}}},"used_operators":["aBQ6xLxuTc","s3Fd5m9Dh2","SL6IHkK8vl"],"dependent_operators":["g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U","23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","s3Fd5m9Dh2","zR4jO40bMj","18saOjeKKm","k7HXdKtiEU","z4E1FaHLuy","XTarYq4gQB","xRrnTEsQ6j","Ph9nP6C5qx","f6k1SAg4EE","D3AQDKkPcf"],"result":"⪩⨒∯-22210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3952","layer":2},{"info":"number node, value=1280","layer":2},{"info":"compute binary expreesion, left_input=3952, right_input=1280, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=8016","layer":1},{"info":"number node, value=3767","layer":2},{"info":"compute unary expreesion, input=3767, op_id = SL6IHkK8vl, unary_op_definition = '∐⩳⋚a = { (⊲⪭((⇠a)⪶≀⋏(a⪒a))) , if (⫟a)==290 ; ((⪝⪂⫅(105⫁⪎a))⊬⨰(a≧⫂∧(a∷a))) , else }', output=550434","layer":1},{"info":"compute binary expreesion, left_input=8016, right_input=550434, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-676","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯331300⊬⨰⪩⨒∯110000)⇂≾⫗(∐⩳⋚⪩⨒∯322313)=⪩⨒∯-22210","reverse_text":"⪩⨒∯-22210=(⪩⨒∯331300⊬⨰⪩⨒∯110000)⇂≾⫗(∐⩳⋚⪩⨒∯322313)","cot":[{"info":"⪩⨒∯331300⊬⨰⪩⨒∯110000=⪩⨒∯1331100","layer":1},{"info":"∐⩳⋚⪩⨒∯322313=⪩⨒∯2012120202","layer":1},{"info":"⪩⨒∯1331100⇂≾⫗⪩⨒∯2012120202=⪩⨒∯-22210","layer":0}]}
{"id":197,"expression_no_base_symbol":"($1870$⫳≱↱$4692$)⨳⩥⨓$1035$⨸$2094$","expression":"(⪩⨒∯131032⫳≱↱⪩⨒∯1021110)⨳⩥⨓⪩⨒∯100023⨸⪩⨒∯200232","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1458,"operation_count":3,"complexity_ratio":486.0,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⫳≱↱","left_expr":{"type":"numeric_atoms","value":1870,"base":4},"right_expr":{"type":"numeric_atoms","value":4692,"base":4}},"right_expr":{"type":"binary","operator":"⨸","left_expr":{"type":"numeric_atoms","value":1035,"base":4},"right_expr":{"type":"numeric_atoms","value":2094,"base":4}}},"used_operators":["nCS4ZIUYfx","ZvLB05nZmT","KmoU8R5UQR"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","2Wsdkap16l","FyVja0WsTP","wEfv7U73WA","bJkvcejdHO","HmxsFra2vL","8cLx32lpNA","ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl"],"result":"⪩⨒∯203202","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1870","layer":2},{"info":"number node, value=4692","layer":2},{"info":"compute binary expreesion, left_input=1870, right_input=4692, op_id = ZvLB05nZmT binary_op_definition= 'a⫳≱↱b = { (((a⩹b)⇐≅)∌((a∙∹∝345)⊱⇼⊻(b≎⊠⪸a))) }', output=-204","layer":1},{"info":"number node, value=1035","layer":2},{"info":"number node, value=2094","layer":2},{"info":"compute binary expreesion, left_input=1035, right_input=2094, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=2070","layer":1},{"info":"compute binary expreesion, left_input=-204, right_input=2070, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=2274","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯131032⫳≱↱⪩⨒∯1021110)⨳⩥⨓⪩⨒∯100023⨸⪩⨒∯200232=⪩⨒∯203202","reverse_text":"⪩⨒∯203202=(⪩⨒∯131032⫳≱↱⪩⨒∯1021110)⨳⩥⨓⪩⨒∯100023⨸⪩⨒∯200232","cot":[{"info":"⪩⨒∯131032⫳≱↱⪩⨒∯1021110=⪩⨒∯-3030","layer":1},{"info":"⪩⨒∯100023⨸⪩⨒∯200232=⪩⨒∯200112","layer":1},{"info":"⪩⨒∯-3030⨳⩥⨓⪩⨒∯200112=⪩⨒∯203202","layer":0}]}
{"id":198,"expression_no_base_symbol":"$2342$⨎$4016$⪐","expression":"⪩⨒∯210212⨎⪩⨒∯332300⪐","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3,"operation_count":2,"complexity_ratio":1.5,"tree":{"type":"unary","operator":"⪐","unary_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":2342,"base":4},"right_expr":{"type":"numeric_atoms","value":4016,"base":4}}},"used_operators":["eH2TOUuTDT","rJVOvQCfKK"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"⪩⨒∯1331200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2342","layer":2},{"info":"number node, value=4016","layer":2},{"info":"compute binary expreesion, left_input=2342, right_input=4016, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=4016","layer":1},{"info":"compute unary expreesion, input=4016, op_id = eH2TOUuTDT, unary_op_definition = 'a⪐ = { (a+a) , if (-a)!=532 or a<368 ; (-a) , else }', output=8032","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯210212⨎⪩⨒∯332300⪐=⪩⨒∯1331200","reverse_text":"⪩⨒∯1331200=⪩⨒∯210212⨎⪩⨒∯332300⪐","cot":[{"info":"⪩⨒∯210212⨎⪩⨒∯332300=⪩⨒∯332300","layer":1},{"info":"⪩⨒∯332300⪐=⪩⨒∯1331200","layer":0}]}
{"id":199,"expression_no_base_symbol":"∓($5671$≝⊰⇂)","expression":"∓(⪩⨒∯1120213≝⊰⇂)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1442,"operation_count":2,"complexity_ratio":721.0,"tree":{"type":"unary","operator":"∓","unary_expr":{"type":"unary","operator":"≝⊰⇂","unary_expr":{"type":"numeric_atoms","value":5671,"base":4}}},"used_operators":["OwUj7dcsQK","htSmYCowi5"],"dependent_operators":["DpFCA1CohY","12rbrZMWeM","nCS4ZIUYfx","QMFrweE19q","9FxExcQeMw","DlLNRPXxWL"],"result":"⪩⨒∯-1030020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5671","layer":2},{"info":"compute unary expreesion, input=5671, op_id = htSmYCowi5, unary_op_definition = 'a≝⊰⇂ = { (a⩷∴51) , if a<491 ; (⫛⫱⨽a) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = OwUj7dcsQK, unary_op_definition = '∓a = { (⋗⩬⋾((a⋳⪒554)⨳⩥⨓(a⫡⨏a))) }', output=-4872","layer":0}],"base":4,"result_base":4,"text":"∓(⪩⨒∯1120213≝⊰⇂)=⪩⨒∯-1030020","reverse_text":"⪩⨒∯-1030020=∓(⪩⨒∯1120213≝⊰⇂)","cot":[{"info":"⪩⨒∯1120213≝⊰⇂=⪩⨒∯0","layer":1},{"info":"∓⪩⨒∯0=⪩⨒∯-1030020","layer":0}]}
{"id":200,"expression_no_base_symbol":"$1045$⩖⊿$5894$↡⊰⫅(≀↧⇸$1173$)","expression":"⪩⨒∯100111⩖⊿⪩⨒∯1130012↡⊰⫅(≀↧⇸⪩⨒∯102111)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":32893,"operation_count":3,"complexity_ratio":10964.333333333334,"tree":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"binary","operator":"⩖⊿","left_expr":{"type":"numeric_atoms","value":1045,"base":4},"right_expr":{"type":"numeric_atoms","value":5894,"base":4}},"right_expr":{"type":"unary","operator":"≀↧⇸","unary_expr":{"type":"numeric_atoms","value":1173,"base":4}}},"used_operators":["VCtxkLNOzz","RZ5CV9rWsJ","ljTHtUsqzn"],"dependent_operators":["Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn","HJ9erzHUuu","IWmyXbctLI","8cLx32lpNA","XPYlsWDdGa","23Mk6UjR3U"],"result":"⪩⨒∯1021110","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1045","layer":2},{"info":"number node, value=5894","layer":2},{"info":"compute binary expreesion, left_input=1045, right_input=5894, op_id = RZ5CV9rWsJ binary_op_definition= 'a⩖⊿b = { ((b⪔⊥a)⪮%⊝(a∌125)) }', output=42890","layer":1},{"info":"number node, value=1173","layer":2},{"info":"compute unary expreesion, input=1173, op_id = ljTHtUsqzn, unary_op_definition = '≀↧⇸a = { (⪲⇎(a⋷a)) }', output=2346","layer":1},{"info":"compute binary expreesion, left_input=42890, right_input=2346, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=4692","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯100111⩖⊿⪩⨒∯1130012↡⊰⫅(≀↧⇸⪩⨒∯102111)=⪩⨒∯1021110","reverse_text":"⪩⨒∯1021110=⪩⨒∯100111⩖⊿⪩⨒∯1130012↡⊰⫅(≀↧⇸⪩⨒∯102111)","cot":[{"info":"⪩⨒∯100111⩖⊿⪩⨒∯1130012=⪩⨒∯22132022","layer":1},{"info":"≀↧⇸⪩⨒∯102111=⪩⨒∯210222","layer":1},{"info":"⪩⨒∯22132022↡⊰⫅⪩⨒∯210222=⪩⨒∯1021110","layer":0}]}
{"id":201,"expression_no_base_symbol":"(⨆≐≲$4021$)⪎↠(∓⪦$3435$)","expression":"(⨆≐≲⪩⨒∯332311)⪎↠(∓⪦⪩⨒∯311223)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":153,"operation_count":3,"complexity_ratio":51.0,"tree":{"type":"binary","operator":"⪎↠","left_expr":{"type":"unary","operator":"⨆≐≲","unary_expr":{"type":"numeric_atoms","value":4021,"base":4}},"right_expr":{"type":"unary","operator":"∓⪦","unary_expr":{"type":"numeric_atoms","value":3435,"base":4}}},"used_operators":["3tVxb0NHM4","Bi9z9uYZqW","D309nIvmXG"],"dependent_operators":["P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM","SWo3A1KBJH","SUmda5xLS4","bx9Z9DAK5y","P8v4zCKN1o","sdazOOVcIp","Ph9nP6C5qx","eewbuw0ToL"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4021","layer":2},{"info":"compute unary expreesion, input=4021, op_id = Bi9z9uYZqW, unary_op_definition = '⨆≐≲a = { (⇋↷(⇾⩊⇾(a⪄a))) }', output=43672344","layer":1},{"info":"number node, value=3435","layer":2},{"info":"compute unary expreesion, input=3435, op_id = D309nIvmXG, unary_op_definition = '∓⪦a = { (((a≧⫂∧a)⨰(a⨰a))⨰(∥⊫(343⪨≂a))) }', output=3027","layer":1},{"info":"compute binary expreesion, left_input=43672344, right_input=3027, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⨆≐≲⪩⨒∯332311)⪎↠(∓⪦⪩⨒∯311223)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⨆≐≲⪩⨒∯332311)⪎↠(∓⪦⪩⨒∯311223)","cot":[{"info":"⨆≐≲⪩⨒∯332311=⪩⨒∯2212212030120","layer":1},{"info":"∓⪦⪩⨒∯311223=⪩⨒∯233103","layer":1},{"info":"⪩⨒∯2212212030120⪎↠⪩⨒∯233103=⪩⨒∯2200","layer":0}]}
{"id":202,"expression_no_base_symbol":"($2270$⊲⩕⊾$1419$)≎⪠($4568$∕⩚$1010$)","expression":"(⪩⨒∯203132⊲⩕⊾⪩⨒∯112023)≎⪠(⪩⨒∯1013120∕⩚⪩⨒∯33302)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":23713,"operation_count":3,"complexity_ratio":7904.333333333333,"tree":{"type":"binary","operator":"≎⪠","left_expr":{"type":"binary","operator":"⊲⩕⊾","left_expr":{"type":"numeric_atoms","value":2270,"base":4},"right_expr":{"type":"numeric_atoms","value":1419,"base":4}},"right_expr":{"type":"binary","operator":"∕⩚","left_expr":{"type":"numeric_atoms","value":4568,"base":4},"right_expr":{"type":"numeric_atoms","value":1010,"base":4}}},"used_operators":["aNhz54LH3e","DmTXOeWf9t","z9ffQ9n5Zr"],"dependent_operators":["bl5wxAcryP","RygbFNSyEJ","SLLxy00UIr","AcOhelriW5","ctOc4cKSDt","cHh1gJQ2o6","KYD54nUTWz","kbkesczE7y","BUOGQAYlQx","PPChnnnBFF","23Mk6UjR3U","DZ8iAZOCBD","BjRHVeLaeN","QMFrweE19q","AF7qkfDlqP","COABgblf1C","3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr"],"result":"⪩⨒∯10301212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2270","layer":2},{"info":"number node, value=1419","layer":2},{"info":"compute binary expreesion, left_input=2270, right_input=1419, op_id = DmTXOeWf9t binary_op_definition= 'a⊲⩕⊾b = { (((a⊉≛↸b)⊭↱(⨑⩽⪐b))⫡⨏((a⫩⊇)⋷(a⊉≛↸b))) }', output=-47140","layer":1},{"info":"number node, value=4568","layer":2},{"info":"number node, value=1010","layer":2},{"info":"compute binary expreesion, left_input=4568, right_input=1010, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-4571","layer":1},{"info":"compute binary expreesion, left_input=-47140, right_input=-4571, op_id = aNhz54LH3e binary_op_definition= 'a≎⪠b = { (((a⫥∨⫟11)≦↸(657∣a))⩘((⇈a)≬⋮(a↰))) , if a==21 ; (∟⋨(⋂(⨣⨃⇪b))) , else }', output=19558","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯203132⊲⩕⊾⪩⨒∯112023)≎⪠(⪩⨒∯1013120∕⩚⪩⨒∯33302)=⪩⨒∯10301212","reverse_text":"⪩⨒∯10301212=(⪩⨒∯203132⊲⩕⊾⪩⨒∯112023)≎⪠(⪩⨒∯1013120∕⩚⪩⨒∯33302)","cot":[{"info":"⪩⨒∯203132⊲⩕⊾⪩⨒∯112023=⪩⨒∯-23200210","layer":1},{"info":"⪩⨒∯1013120∕⩚⪩⨒∯33302=⪩⨒∯-1013123","layer":1},{"info":"⪩⨒∯-23200210≎⪠⪩⨒∯-1013123=⪩⨒∯10301212","layer":0}]}
{"id":203,"expression_no_base_symbol":"↴⪽⋼$3845$⋥≓≎$1704$","expression":"↴⪽⋼⪩⨒∯330011⋥≓≎⪩⨒∯122220","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":135,"operation_count":2,"complexity_ratio":67.5,"tree":{"type":"unary","operator":"↴⪽⋼","unary_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":3845,"base":4},"right_expr":{"type":"numeric_atoms","value":1704,"base":4}}},"used_operators":["5TUYCnJO6w","Qy55tPpLXF"],"dependent_operators":["MGuIdZPyUC","UqFzSgLMvQ","k7HXdKtiEU","yyfyN0ffXY","pRsWfj4Fpp","diKm42VcIt","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯20233232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3845","layer":2},{"info":"number node, value=1704","layer":2},{"info":"compute binary expreesion, left_input=3845, right_input=1704, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-404","layer":1},{"info":"compute unary expreesion, input=-404, op_id = 5TUYCnJO6w, unary_op_definition = '↴⪽⋼a = { a , if ((∡a)<5 or (⇘a)>=19 or (⊲⪭a)==199) ; (((a↙a)⇡)⇉⇉) , else }', output=35822","layer":0}],"base":4,"result_base":4,"text":"↴⪽⋼⪩⨒∯330011⋥≓≎⪩⨒∯122220=⪩⨒∯20233232","reverse_text":"⪩⨒∯20233232=↴⪽⋼⪩⨒∯330011⋥≓≎⪩⨒∯122220","cot":[{"info":"⪩⨒∯330011⋥≓≎⪩⨒∯122220=⪩⨒∯-12110","layer":1},{"info":"↴⪽⋼⪩⨒∯-12110=⪩⨒∯20233232","layer":0}]}
{"id":204,"expression_no_base_symbol":"($3739$≬⋮$2989$)⩼⇪↪($3838$↙$3980$)","expression":"(⪩⨒∯322123≬⋮⪩⨒∯232231)⩼⇪↪(⪩⨒∯323332↙⪩⨒∯332030)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4008,"operation_count":3,"complexity_ratio":1336.0,"tree":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"binary","operator":"≬⋮","left_expr":{"type":"numeric_atoms","value":3739,"base":4},"right_expr":{"type":"numeric_atoms","value":2989,"base":4}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":3838,"base":4},"right_expr":{"type":"numeric_atoms","value":3980,"base":4}}},"used_operators":["ocnLzx9CaJ","kbkesczE7y","yyfyN0ffXY"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q","P8v4zCKN1o","rysDP5nf3Z","7j4O788W3g","XIabStNQrY","t8gj7n24qd","i8ToyICDmI","tmPS8pqC7x","DpFCA1CohY"],"result":"⪩⨒∯110220311","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3739","layer":2},{"info":"number node, value=2989","layer":2},{"info":"compute binary expreesion, left_input=3739, right_input=2989, op_id = kbkesczE7y binary_op_definition= 'a≬⋮b = { (((-a)∲⫓(b⇋≉))↺(∥⊫(b-b))) }', output=868","layer":1},{"info":"number node, value=3838","layer":2},{"info":"number node, value=3980","layer":2},{"info":"compute binary expreesion, left_input=3838, right_input=3980, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-11940","layer":1},{"info":"compute binary expreesion, left_input=868, right_input=-11940, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=84533","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯322123≬⋮⪩⨒∯232231)⩼⇪↪(⪩⨒∯323332↙⪩⨒∯332030)=⪩⨒∯110220311","reverse_text":"⪩⨒∯110220311=(⪩⨒∯322123≬⋮⪩⨒∯232231)⩼⇪↪(⪩⨒∯323332↙⪩⨒∯332030)","cot":[{"info":"⪩⨒∯322123≬⋮⪩⨒∯232231=⪩⨒∯31210","layer":1},{"info":"⪩⨒∯323332↙⪩⨒∯332030=⪩⨒∯-2322210","layer":1},{"info":"⪩⨒∯31210⩼⇪↪⪩⨒∯-2322210=⪩⨒∯110220311","layer":0}]}
{"id":205,"expression_no_base_symbol":"↣≠⋷$2807$⪬$5592$","expression":"↣≠⋷⪩⨒∯223313⪬⪩⨒∯1113120","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":572,"operation_count":2,"complexity_ratio":286.0,"tree":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"binary","operator":"⪬","left_expr":{"type":"numeric_atoms","value":2807,"base":4},"right_expr":{"type":"numeric_atoms","value":5592,"base":4}}},"used_operators":["Asc51vEJeQ","Ez1Nq5fNfI"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","eRqsBgTDFp","mp7IySMOzn","JL8yIekQnl","QvoQhV0rrE","kbkesczE7y"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2807","layer":2},{"info":"number node, value=5592","layer":2},{"info":"compute binary expreesion, left_input=2807, right_input=5592, op_id = Ez1Nq5fNfI binary_op_definition= 'a⪬b = { (((514⋫)⪒⊣⊆(b≬⋮a))∠⫱(1⇷(b≬⋮32))) }', output=1234","layer":1},{"info":"compute unary expreesion, input=1234, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"↣≠⋷⪩⨒∯223313⪬⪩⨒∯1113120=NaN","reverse_text":"NaN=↣≠⋷⪩⨒∯223313⪬⪩⨒∯1113120","cot":[{"info":"⪩⨒∯223313⪬⪩⨒∯1113120=⪩⨒∯103102","layer":1},{"info":"↣≠⋷⪩⨒∯103102=NaN","layer":0}]}
{"id":206,"expression_no_base_symbol":"$4866$≁↽≥$4193$↼⊘⨖$4640$≴⪞⇿$1311$","expression":"⪩⨒∯1030002≁↽≥⪩⨒∯1001201↼⊘⨖⪩⨒∯1020200≴⪞⇿⪩⨒∯110133","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4432,"operation_count":3,"complexity_ratio":1477.3333333333333,"tree":{"type":"binary","operator":"↼⊘⨖","left_expr":{"type":"binary","operator":"≁↽≥","left_expr":{"type":"numeric_atoms","value":4866,"base":4},"right_expr":{"type":"numeric_atoms","value":4193,"base":4}},"right_expr":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"numeric_atoms","value":4640,"base":4},"right_expr":{"type":"numeric_atoms","value":1311,"base":4}}},"used_operators":["bPywburJMS","ncHt1X6cMc","lvlrscuwVU"],"dependent_operators":["9FxExcQeMw","P8v4zCKN1o","t8gj7n24qd","oWn0xqSxBt","3Oe9XWJUTD","DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP"],"result":"⪩⨒∯10202333301322","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4866","layer":2},{"info":"number node, value=4193","layer":2},{"info":"compute binary expreesion, left_input=4866, right_input=4193, op_id = ncHt1X6cMc binary_op_definition= 'a≁↽≥b = { (a⊝⪿⪼b) , if b>=116 ; (⊙↵-b) , else }', output=64716","layer":1},{"info":"number node, value=4640","layer":2},{"info":"number node, value=1311","layer":2},{"info":"compute binary expreesion, left_input=4640, right_input=1311, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=38141612","layer":1},{"info":"compute binary expreesion, left_input=64716, right_input=38141612, op_id = bPywburJMS binary_op_definition= 'a↼⊘⨖b = { (-a) , if (∥⊫b)==149 ; (b⩷∴95) , else }', output=76283002","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1030002≁↽≥⪩⨒∯1001201↼⊘⨖⪩⨒∯1020200≴⪞⇿⪩⨒∯110133=⪩⨒∯10202333301322","reverse_text":"⪩⨒∯10202333301322=⪩⨒∯1030002≁↽≥⪩⨒∯1001201↼⊘⨖⪩⨒∯1020200≴⪞⇿⪩⨒∯110133","cot":[{"info":"⪩⨒∯1030002≁↽≥⪩⨒∯1001201=⪩⨒∯33303030","layer":1},{"info":"⪩⨒∯1020200≴⪞⇿⪩⨒∯110133=⪩⨒∯2101133322230","layer":1},{"info":"⪩⨒∯33303030↼⊘⨖⪩⨒∯2101133322230=⪩⨒∯10202333301322","layer":0}]}
{"id":207,"expression_no_base_symbol":"($1342$⪁$1707$)⨂≜(↴⪽⋼$4313$)","expression":"(⪩⨒∯110332⪁⪩⨒∯122223)⨂≜(↴⪽⋼⪩⨒∯1003121)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":37278768,"operation_count":3,"complexity_ratio":12426256.0,"tree":{"type":"binary","operator":"⨂≜","left_expr":{"type":"binary","operator":"⪁","left_expr":{"type":"numeric_atoms","value":1342,"base":4},"right_expr":{"type":"numeric_atoms","value":1707,"base":4}},"right_expr":{"type":"unary","operator":"↴⪽⋼","unary_expr":{"type":"numeric_atoms","value":4313,"base":4}}},"used_operators":["k1SHOSEABc","I7sXao9hZE","5TUYCnJO6w"],"dependent_operators":["9FxExcQeMw","HiPekx5b7W","eLxqMNBOBk","JclMnS0uGI","COABgblf1C","U7g4x0WXJJ","dWAJyo7jo9","wxb3vTeyAj","nlCqmYiOvY","MGuIdZPyUC","UqFzSgLMvQ","k7HXdKtiEU","yyfyN0ffXY","pRsWfj4Fpp","diKm42VcIt"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1342","layer":2},{"info":"number node, value=1707","layer":2},{"info":"compute binary expreesion, left_input=1342, right_input=1707, op_id = I7sXao9hZE binary_op_definition= 'a⪁b = { (((⫶⊄≣b)⨽⪊≇)⪢a) }', output=nan","layer":1},{"info":"number node, value=4313","layer":2},{"info":"compute unary expreesion, input=4313, op_id = 5TUYCnJO6w, unary_op_definition = '↴⪽⋼a = { a , if ((∡a)<5 or (⇘a)>=19 or (⊲⪭a)==199) ; (((a↙a)⇡)⇉⇉) , else }', output=4313","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=4313, op_id = k1SHOSEABc binary_op_definition= 'a⨂≜b = { ((37⊭↱(⫓⪴a))⩷∴((111⨜⨶78)⨔⇊(a∑⇟⊟b))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯110332⪁⪩⨒∯122223)⨂≜(↴⪽⋼⪩⨒∯1003121)=NaN","reverse_text":"NaN=(⪩⨒∯110332⪁⪩⨒∯122223)⨂≜(↴⪽⋼⪩⨒∯1003121)","cot":[{"info":"⪩⨒∯110332⪁⪩⨒∯122223=NaN","layer":1},{"info":"↴⪽⋼⪩⨒∯1003121=⪩⨒∯1003121","layer":1},{"info":"NaN⨂≜⪩⨒∯1003121=NaN","layer":0}]}
{"id":208,"expression_no_base_symbol":"(⫖→$8799$)⨎⋸⪻","expression":"(⫖→⪩⨒∯2021133)⨎⋸⪻","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9007,"operation_count":2,"complexity_ratio":4503.5,"tree":{"type":"unary","operator":"⨎⋸⪻","unary_expr":{"type":"unary","operator":"⫖→","unary_expr":{"type":"numeric_atoms","value":8799,"base":4}}},"used_operators":["Dk5vyLCiGd","U4ylXWHChL"],"dependent_operators":["IWmyXbctLI","tmPS8pqC7x","Ikt5ks8PT7","AFVx7xoS7T","o20kRiQErp"],"result":"⪩⨒∯22132","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8799","layer":2},{"info":"compute unary expreesion, input=8799, op_id = U4ylXWHChL, unary_op_definition = '⫖→a = { (((a⨪↰⇹a)⇌⫙⪟(a⩧⪆a))∸) }', output=177","layer":1},{"info":"compute unary expreesion, input=177, op_id = Dk5vyLCiGd, unary_op_definition = 'a⨎⋸⪻ = { (a⪮%⊝26) }', output=670","layer":0}],"base":4,"result_base":4,"text":"(⫖→⪩⨒∯2021133)⨎⋸⪻=⪩⨒∯22132","reverse_text":"⪩⨒∯22132=(⫖→⪩⨒∯2021133)⨎⋸⪻","cot":[{"info":"⫖→⪩⨒∯2021133=⪩⨒∯2301","layer":1},{"info":"⪩⨒∯2301⨎⋸⪻=⪩⨒∯22132","layer":0}]}
{"id":209,"expression_no_base_symbol":"($6685$⪘⨀)⨻⩈⩔($2780$⪡$5810$)","expression":"(⪩⨒∯1220131⪘⨀)⨻⩈⩔(⪩⨒∯223130⪡⪩⨒∯1122302)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":107,"operation_count":3,"complexity_ratio":35.666666666666664,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"unary","operator":"⪘⨀","unary_expr":{"type":"numeric_atoms","value":6685,"base":4}},"right_expr":{"type":"binary","operator":"⪡","left_expr":{"type":"numeric_atoms","value":2780,"base":4},"right_expr":{"type":"numeric_atoms","value":5810,"base":4}}},"used_operators":["nEsXyWgiOK","aA7tF3KVD3","oraRL2iQuh"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","bl5wxAcryP","L05ObWFQCd","XhwjNDsVaA","2Wsdkap16l","ljTHtUsqzn","k8jYdgA6NY","8WDwsbhb0R"],"result":"⪩⨒∯-2232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6685","layer":2},{"info":"compute unary expreesion, input=6685, op_id = aA7tF3KVD3, unary_op_definition = 'a⪘⨀ = { ((104/a)⪍↜⋙(a↰)) }', output=-13951","layer":1},{"info":"number node, value=2780","layer":2},{"info":"number node, value=5810","layer":2},{"info":"compute binary expreesion, left_input=2780, right_input=5810, op_id = oraRL2iQuh binary_op_definition= 'a⪡b = { (107%(a⩹b)) , if a>=49 ; (≀↧⇸(∂⩏⊆a)) , else }', output=107","layer":1},{"info":"compute binary expreesion, left_input=-13951, right_input=107, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=-174","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1220131⪘⨀)⨻⩈⩔(⪩⨒∯223130⪡⪩⨒∯1122302)=⪩⨒∯-2232","reverse_text":"⪩⨒∯-2232=(⪩⨒∯1220131⪘⨀)⨻⩈⩔(⪩⨒∯223130⪡⪩⨒∯1122302)","cot":[{"info":"⪩⨒∯1220131⪘⨀=⪩⨒∯-3121333","layer":1},{"info":"⪩⨒∯223130⪡⪩⨒∯1122302=⪩⨒∯1223","layer":1},{"info":"⪩⨒∯-3121333⨻⩈⩔⪩⨒∯1223=⪩⨒∯-2232","layer":0}]}
{"id":210,"expression_no_base_symbol":"$1195$↡⊰⫅$1979$≬⋮($6062$-$1357$)","expression":"⪩⨒∯102223↡⊰⫅⪩⨒∯132323≬⋮(⪩⨒∯1132232-⪩⨒∯111031)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":27735,"operation_count":3,"complexity_ratio":9245.0,"tree":{"type":"binary","operator":"≬⋮","left_expr":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"numeric_atoms","value":1195,"base":4},"right_expr":{"type":"numeric_atoms","value":1979,"base":4}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":6062,"base":4},"right_expr":{"type":"numeric_atoms","value":1357,"base":4}}},"used_operators":["kbkesczE7y","VCtxkLNOzz","rysDP5nf3Z"],"dependent_operators":["P8v4zCKN1o","rysDP5nf3Z","7j4O788W3g","XIabStNQrY","t8gj7n24qd","i8ToyICDmI","Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn"],"result":"⪩⨒∯31210","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1195","layer":2},{"info":"number node, value=1979","layer":2},{"info":"compute binary expreesion, left_input=1195, right_input=1979, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=3958","layer":1},{"info":"number node, value=6062","layer":2},{"info":"number node, value=1357","layer":2},{"info":"compute binary expreesion, left_input=6062, right_input=1357, op_id = rysDP5nf3Z binary_op_definition= 'None', output=4705","layer":1},{"info":"compute binary expreesion, left_input=3958, right_input=4705, op_id = kbkesczE7y binary_op_definition= 'a≬⋮b = { (((-a)∲⫓(b⇋≉))↺(∥⊫(b-b))) }', output=868","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102223↡⊰⫅⪩⨒∯132323≬⋮(⪩⨒∯1132232-⪩⨒∯111031)=⪩⨒∯31210","reverse_text":"⪩⨒∯31210=⪩⨒∯102223↡⊰⫅⪩⨒∯132323≬⋮(⪩⨒∯1132232-⪩⨒∯111031)","cot":[{"info":"⪩⨒∯102223↡⊰⫅⪩⨒∯132323=⪩⨒∯331312","layer":1},{"info":"⪩⨒∯1132232-⪩⨒∯111031=⪩⨒∯1021201","layer":1},{"info":"⪩⨒∯331312≬⋮⪩⨒∯1021201=⪩⨒∯31210","layer":0}]}
{"id":211,"expression_no_base_symbol":"(⩩$3968$)⊋≦⊧$2153$↓$4658$","expression":"(⩩⪩⨒∯332000)⊋≦⊧⪩⨒∯201221↓⪩⨒∯1020302","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":70432,"operation_count":3,"complexity_ratio":23477.333333333332,"tree":{"type":"binary","operator":"⊋≦⊧","left_expr":{"type":"unary","operator":"⩩","unary_expr":{"type":"numeric_atoms","value":3968,"base":4}},"right_expr":{"type":"binary","operator":"↓","left_expr":{"type":"numeric_atoms","value":2153,"base":4},"right_expr":{"type":"numeric_atoms","value":4658,"base":4}}},"used_operators":["oRDoc9rAEX","kMhfGuqI2H","Af076pWI7l"],"dependent_operators":["DZ8iAZOCBD","tifHPKVTfV","sdazOOVcIp","glklzrTFfD","DIvbN7qnHd","12rbrZMWeM","Ph9nP6C5qx","eewbuw0ToL","2td37pGCOC","6aG7x05OhS","z63VuFQld9","lFBm8KRb8F","f6k1SAg4EE","ZGCBLdVRRX","nhYeJWJD5X","mp7IySMOzn","Noe24qw2ks","lvlrscuwVU","T2fj7uvVaJ","PoHhknlbAi"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3968","layer":2},{"info":"compute unary expreesion, input=3968, op_id = kMhfGuqI2H, unary_op_definition = '⩩a = { (⇜(a⫩)) , if (⇵⪽a)!=444 ; ((a⪒a)∧) , else }', output=nan","layer":1},{"info":"number node, value=2153","layer":2},{"info":"number node, value=4658","layer":2},{"info":"compute binary expreesion, left_input=2153, right_input=4658, op_id = Af076pWI7l binary_op_definition= 'a↓b = { (((b⇷b)∓⋝b)⨐((462≴⪞⇿a)∇⊂⋱(a⋓a))) }', output=-134","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-134, op_id = oRDoc9rAEX binary_op_definition= 'a⊋≦⊧b = { (((24⊉≛↸a)⊉≛↸(⩦⩻⨪b))⊉≛↸((a⊠≄⫣)⪨≂(b⇼⇔∾a))) , if a<=128 ; (((a⇼⇔∾b)⨁⊸⫻)⇼⇔∾((22⋳⪒a)⨰(a≧⫂∧a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⩩⪩⨒∯332000)⊋≦⊧⪩⨒∯201221↓⪩⨒∯1020302=NaN","reverse_text":"NaN=(⩩⪩⨒∯332000)⊋≦⊧⪩⨒∯201221↓⪩⨒∯1020302","cot":[{"info":"⩩⪩⨒∯332000=NaN","layer":1},{"info":"⪩⨒∯201221↓⪩⨒∯1020302=⪩⨒∯-2012","layer":1},{"info":"NaN⊋≦⊧⪩⨒∯-2012=NaN","layer":0}]}
{"id":212,"expression_no_base_symbol":"≔$4488$⨸$6121$","expression":"≔⪩⨒∯1012020⨸⪩⨒∯1133221","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4635,"operation_count":2,"complexity_ratio":2317.5,"tree":{"type":"unary","operator":"≔","unary_expr":{"type":"binary","operator":"⨸","left_expr":{"type":"numeric_atoms","value":4488,"base":4},"right_expr":{"type":"numeric_atoms","value":6121,"base":4}}},"used_operators":["8FLs4eVsLt","KmoU8R5UQR"],"dependent_operators":["uPb5QRN0te","VwlE7vj6HS","3mBM5G4a3l","8HhzD0ZcuI","BUOGQAYlQx","AYdpE9sXAk","ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl"],"result":"⪩⨒∯-331002302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4488","layer":2},{"info":"number node, value=6121","layer":2},{"info":"compute binary expreesion, left_input=4488, right_input=6121, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=8976","layer":1},{"info":"compute unary expreesion, input=8976, op_id = 8FLs4eVsLt, unary_op_definition = '≔a = { (⋃(⋂a)) , if (⨂⪏⇭a)<=427 or (a↫)>=16 ; ((a⨽194)↯⫤) , else }', output=-250034","layer":0}],"base":4,"result_base":4,"text":"≔⪩⨒∯1012020⨸⪩⨒∯1133221=⪩⨒∯-331002302","reverse_text":"⪩⨒∯-331002302=≔⪩⨒∯1012020⨸⪩⨒∯1133221","cot":[{"info":"⪩⨒∯1012020⨸⪩⨒∯1133221=⪩⨒∯2030100","layer":1},{"info":"≔⪩⨒∯2030100=⪩⨒∯-331002302","layer":0}]}
{"id":213,"expression_no_base_symbol":"$2155$∌$1181$⨻⩈⩔($2789$↠)","expression":"⪩⨒∯201223∌⪩⨒∯102131⨻⩈⩔(⪩⨒∯223211↠)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":86,"operation_count":3,"complexity_ratio":28.666666666666668,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"binary","operator":"∌","left_expr":{"type":"numeric_atoms","value":2155,"base":4},"right_expr":{"type":"numeric_atoms","value":1181,"base":4}},"right_expr":{"type":"unary","operator":"↠","unary_expr":{"type":"numeric_atoms","value":2789,"base":4}}},"used_operators":["nEsXyWgiOK","8cLx32lpNA","LBdsKIvxzf"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","N41Kp7NANJ","7j4O788W3g","t8gj7n24qd","d7ASUq0ydm","rysDP5nf3Z","Noe24qw2ks","xRrnTEsQ6j","dfKe02y8D2","Tw270M8GLb"],"result":"⪩⨒∯-2232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2155","layer":2},{"info":"number node, value=1181","layer":2},{"info":"compute binary expreesion, left_input=2155, right_input=1181, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-1181","layer":1},{"info":"number node, value=2789","layer":2},{"info":"compute unary expreesion, input=2789, op_id = LBdsKIvxzf, unary_op_definition = 'a↠ = { ((⨰⫟⨤603)⨐(a⫯⪬∳a)) , if (a⫁⪎18)<=15 ; (167⫚↹⊑(a-a)) , else }', output=-447","layer":1},{"info":"compute binary expreesion, left_input=-1181, right_input=-447, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=-174","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯201223∌⪩⨒∯102131⨻⩈⩔(⪩⨒∯223211↠)=⪩⨒∯-2232","reverse_text":"⪩⨒∯-2232=⪩⨒∯201223∌⪩⨒∯102131⨻⩈⩔(⪩⨒∯223211↠)","cot":[{"info":"⪩⨒∯201223∌⪩⨒∯102131=⪩⨒∯-102131","layer":1},{"info":"⪩⨒∯223211↠=⪩⨒∯-12333","layer":1},{"info":"⪩⨒∯-102131⨻⩈⩔⪩⨒∯-12333=⪩⨒∯-2232","layer":0}]}
{"id":214,"expression_no_base_symbol":"($3392$≦≮≮)≦↸($1571$⩹$6548$)","expression":"(⪩⨒∯311000≦≮≮)≦↸(⪩⨒∯120203⩹⪩⨒∯1212110)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":36,"operation_count":3,"complexity_ratio":12.0,"tree":{"type":"binary","operator":"≦↸","left_expr":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":3392,"base":4}},"right_expr":{"type":"binary","operator":"⩹","left_expr":{"type":"numeric_atoms","value":1571,"base":4},"right_expr":{"type":"numeric_atoms","value":6548,"base":4}}},"used_operators":["RygbFNSyEJ","D4vGDi5EA2","2Wsdkap16l"],"dependent_operators":["eLAdDNolq6","e1ybzncUwg","DZ8iAZOCBD","XIabStNQrY","12rbrZMWeM","2DDjHMKMc0","g55IO6H4Gj","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","NTOWxs364D","23Mk6UjR3U","XIabStNQrY","2DDjHMKMc0","12rbrZMWeM","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx"],"result":"⪩⨒∯1330011","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3392","layer":2},{"info":"compute unary expreesion, input=3392, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-10176","layer":1},{"info":"number node, value=1571","layer":2},{"info":"number node, value=6548","layer":2},{"info":"compute binary expreesion, left_input=1571, right_input=6548, op_id = 2Wsdkap16l binary_op_definition= 'a⩹b = { (b-((b⨳⩥⨓b)⨸⪁(1⋝⋈⪟b))) , if (b⇋≉)!=246 ; (((a⇋≉)⨰(a⋷a))⋳⪒((a⩚⊴⇥a)⨳⩥⨓(a≧⫂∧a))) , else }', output=6546","layer":1},{"info":"compute binary expreesion, left_input=-10176, right_input=6546, op_id = RygbFNSyEJ binary_op_definition= 'a≦↸b = { (((≤/a)⋳⪒(b⊉≛↸a))⋝⋈⪟((a⇋≉)⨸⪁(≉a))) }', output=7941","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯311000≦≮≮)≦↸(⪩⨒∯120203⩹⪩⨒∯1212110)=⪩⨒∯1330011","reverse_text":"⪩⨒∯1330011=(⪩⨒∯311000≦≮≮)≦↸(⪩⨒∯120203⩹⪩⨒∯1212110)","cot":[{"info":"⪩⨒∯311000≦≮≮=⪩⨒∯-2133000","layer":1},{"info":"⪩⨒∯120203⩹⪩⨒∯1212110=⪩⨒∯1212102","layer":1},{"info":"⪩⨒∯-2133000≦↸⪩⨒∯1212102=⪩⨒∯1330011","layer":0}]}
{"id":215,"expression_no_base_symbol":"⇐($4251$∌$2958$)","expression":"⇐(⪩⨒∯1002123∌⪩⨒∯232032)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":44,"operation_count":2,"complexity_ratio":22.0,"tree":{"type":"unary","operator":"⇐","unary_expr":{"type":"binary","operator":"∌","left_expr":{"type":"numeric_atoms","value":4251,"base":4},"right_expr":{"type":"numeric_atoms","value":2958,"base":4}}},"used_operators":["nmZMaaE0Q9","8cLx32lpNA"],"dependent_operators":["23Mk6UjR3U","ocnLzx9CaJ","SWo3A1KBJH","nREPSIbpBE","k8jYdgA6NY","u6S6b8DprG","N41Kp7NANJ","7j4O788W3g","t8gj7n24qd"],"result":"⪩⨒∯-1032120","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4251","layer":2},{"info":"number node, value=2958","layer":2},{"info":"compute binary expreesion, left_input=4251, right_input=2958, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-2958","layer":1},{"info":"compute unary expreesion, input=-2958, op_id = nmZMaaE0Q9, unary_op_definition = '⇐a = { (((⇋↷a)⋷(a⩼⇪↪a))%(↽≂(a⨚a))) }', output=-5016","layer":0}],"base":4,"result_base":4,"text":"⇐(⪩⨒∯1002123∌⪩⨒∯232032)=⪩⨒∯-1032120","reverse_text":"⪩⨒∯-1032120=⇐(⪩⨒∯1002123∌⪩⨒∯232032)","cot":[{"info":"⪩⨒∯1002123∌⪩⨒∯232032=⪩⨒∯-232032","layer":1},{"info":"⇐⪩⨒∯-232032=⪩⨒∯-1032120","layer":0}]}
{"id":216,"expression_no_base_symbol":"$2179$⊹∫⫚$3364$⪇≇⋚$2382$⋥⋵⩄$1019$","expression":"⪩⨒∯202003⊹∫⫚⪩⨒∯310210⪇≇⋚⪩⨒∯211032⋥⋵⩄⪩⨒∯33323","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":76,"operation_count":3,"complexity_ratio":25.333333333333332,"tree":{"type":"binary","operator":"⪇≇⋚","left_expr":{"type":"binary","operator":"⊹∫⫚","left_expr":{"type":"numeric_atoms","value":2179,"base":4},"right_expr":{"type":"numeric_atoms","value":3364,"base":4}},"right_expr":{"type":"binary","operator":"⋥⋵⩄","left_expr":{"type":"numeric_atoms","value":2382,"base":4},"right_expr":{"type":"numeric_atoms","value":1019,"base":4}}},"used_operators":["3sJ7IOPOlU","uWAJUKEvyW","7t3wd0Fuz7"],"dependent_operators":["DZ8iAZOCBD","JLbD19bQDL","xUOZtlo3hN","BiWNJpBvwn","w2P8NbNXyL","vg4gO5BX6G","k8jYdgA6NY","g55IO6H4Gj","2td37pGCOC","jLgFTUHLKL","IWmyXbctLI","2td37pGCOC","AFVx7xoS7T"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2179","layer":2},{"info":"number node, value=3364","layer":2},{"info":"compute binary expreesion, left_input=2179, right_input=3364, op_id = uWAJUKEvyW binary_op_definition= 'a⊹∫⫚b = { (↩(a⊨b)) , if (⩦⩻⨪a)==479 or (b⊉↱≁467)==779 ; ((b⨸⪁b)%(b⩍⋽⫝̸187)) , else }', output=-8","layer":1},{"info":"number node, value=2382","layer":2},{"info":"number node, value=1019","layer":2},{"info":"compute binary expreesion, left_input=2382, right_input=1019, op_id = 7t3wd0Fuz7 binary_op_definition= 'a⋥⋵⩄b = { ((⩦⩻⨪a)⇌⫙⪟(b⪮%⊝b)) }', output=113","layer":1},{"info":"compute binary expreesion, left_input=-8, right_input=113, op_id = 3sJ7IOPOlU binary_op_definition= 'a⪇≇⋚b = { ((⨞⊢(a⊉≛↸b))⪠⩆⊳) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯202003⊹∫⫚⪩⨒∯310210⪇≇⋚⪩⨒∯211032⋥⋵⩄⪩⨒∯33323=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯202003⊹∫⫚⪩⨒∯310210⪇≇⋚⪩⨒∯211032⋥⋵⩄⪩⨒∯33323","cot":[{"info":"⪩⨒∯202003⊹∫⫚⪩⨒∯310210=⪩⨒∯-20","layer":1},{"info":"⪩⨒∯211032⋥⋵⩄⪩⨒∯33323=⪩⨒∯1301","layer":1},{"info":"⪩⨒∯-20⪇≇⋚⪩⨒∯1301=⪩⨒∯0","layer":0}]}
{"id":217,"expression_no_base_symbol":"($1757$⊉≛↸$1614$)↓(⨴⫝$1690$)","expression":"(⪩⨒∯123131⊉≛↸⪩⨒∯121032)↓(⨴⫝⪩⨒∯122122)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2119,"operation_count":3,"complexity_ratio":706.3333333333334,"tree":{"type":"binary","operator":"↓","left_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":1757,"base":4},"right_expr":{"type":"numeric_atoms","value":1614,"base":4}},"right_expr":{"type":"unary","operator":"⨴⫝","unary_expr":{"type":"numeric_atoms","value":1690,"base":4}}},"used_operators":["Af076pWI7l","DZ8iAZOCBD","SVb2v531z1"],"dependent_operators":["nhYeJWJD5X","mp7IySMOzn","Noe24qw2ks","lvlrscuwVU","T2fj7uvVaJ","PoHhknlbAi","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","oDCm7WA9JY","XnXgA4xnOs","ocnLzx9CaJ","3sJ7IOPOlU","9cloC0Ngie","SWo3A1KBJH","jWTQ2TZYIH","pRsWfj4Fpp","DyGG3AbaNP","5obUd6DV38","8HhzD0ZcuI","YbUVn0Rbpy","AdZkA7nFnk","SIgE0bArFf"],"result":"⪩⨒∯-2012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1757","layer":2},{"info":"number node, value=1614","layer":2},{"info":"compute binary expreesion, left_input=1757, right_input=1614, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=3514","layer":1},{"info":"number node, value=1690","layer":2},{"info":"compute unary expreesion, input=1690, op_id = SVb2v531z1, unary_op_definition = '⨴⫝a = { ((⪨⨬(⇋↷a))≬⇓((a⋅⇍a)⨑≵⋬(∡178))) , if (a⪇≇⋚963)!=62 ; (((541⋛107)⩼⇪↪(⪭⩑⪱a))⋻⩜⩜((a⊕∕a)∼(459⨽6))) , else }', output=2828198","layer":1},{"info":"compute binary expreesion, left_input=3514, right_input=2828198, op_id = Af076pWI7l binary_op_definition= 'a↓b = { (((b⇷b)∓⋝b)⨐((462≴⪞⇿a)∇⊂⋱(a⋓a))) }', output=-134","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯123131⊉≛↸⪩⨒∯121032)↓(⨴⫝⪩⨒∯122122)=⪩⨒∯-2012","reverse_text":"⪩⨒∯-2012=(⪩⨒∯123131⊉≛↸⪩⨒∯121032)↓(⨴⫝⪩⨒∯122122)","cot":[{"info":"⪩⨒∯123131⊉≛↸⪩⨒∯121032=⪩⨒∯312322","layer":1},{"info":"⨴⫝⪩⨒∯122122=⪩⨒∯22302132212","layer":1},{"info":"⪩⨒∯312322↓⪩⨒∯22302132212=⪩⨒∯-2012","layer":0}]}
{"id":218,"expression_no_base_symbol":"≋($2122$∙⊟$2503$)","expression":"≋(⪩⨒∯201022∙⊟⪩⨒∯213013)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2195,"operation_count":2,"complexity_ratio":1097.5,"tree":{"type":"unary","operator":"≋","unary_expr":{"type":"binary","operator":"∙⊟","left_expr":{"type":"numeric_atoms","value":2122,"base":4},"right_expr":{"type":"numeric_atoms","value":2503,"base":4}}},"used_operators":["61wBmkZwlr","SxTAKzQCrw"],"dependent_operators":["7j4O788W3g","6iOiAJX1F8","oWn0xqSxBt","3Oe9XWJUTD","4CyGpkTkEk","CArV6hThFE","PPChnnnBFF"],"result":"⪩⨒∯21020320","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2122","layer":2},{"info":"number node, value=2503","layer":2},{"info":"compute binary expreesion, left_input=2122, right_input=2503, op_id = SxTAKzQCrw binary_op_definition= 'a∙⊟b = { (⩪∧⨌(a⫲⨊)) , if (b∐⫣)<386 ; ((a∣a)⊝⪿⪼(⊙↵-a)) , else }', output=37432","layer":1},{"info":"compute unary expreesion, input=37432, op_id = 61wBmkZwlr, unary_op_definition = '≋a = { (a↺a) }', output=37432","layer":0}],"base":4,"result_base":4,"text":"≋(⪩⨒∯201022∙⊟⪩⨒∯213013)=⪩⨒∯21020320","reverse_text":"⪩⨒∯21020320=≋(⪩⨒∯201022∙⊟⪩⨒∯213013)","cot":[{"info":"⪩⨒∯201022∙⊟⪩⨒∯213013=⪩⨒∯21020320","layer":1},{"info":"≋⪩⨒∯21020320=⪩⨒∯21020320","layer":0}]}
{"id":219,"expression_no_base_symbol":"(⊵⊁$1149$)∕⩚($3036$+$1110$)","expression":"(⊵⊁⪩⨒∯101331)∕⩚(⪩⨒∯233130+⪩⨒∯101112)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5867,"operation_count":3,"complexity_ratio":1955.6666666666667,"tree":{"type":"binary","operator":"∕⩚","left_expr":{"type":"unary","operator":"⊵⊁","unary_expr":{"type":"numeric_atoms","value":1149,"base":4}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":3036,"base":4},"right_expr":{"type":"numeric_atoms","value":1110,"base":4}}},"used_operators":["z9ffQ9n5Zr","AvED76WdY7","W4YGzv6Whe"],"dependent_operators":["3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr","uBihLCJcMX","k8jYdgA6NY"],"result":"⪩⨒∯-1123003","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1149","layer":2},{"info":"compute unary expreesion, input=1149, op_id = AvED76WdY7, unary_op_definition = '⊵⊁a = { (a⇔⨋) , if a>58 ; (a%a) , else }', output=5824","layer":1},{"info":"number node, value=3036","layer":2},{"info":"number node, value=1110","layer":2},{"info":"compute binary expreesion, left_input=3036, right_input=1110, op_id = W4YGzv6Whe binary_op_definition= 'None', output=4146","layer":1},{"info":"compute binary expreesion, left_input=5824, right_input=4146, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-5827","layer":0}],"base":4,"result_base":4,"text":"(⊵⊁⪩⨒∯101331)∕⩚(⪩⨒∯233130+⪩⨒∯101112)=⪩⨒∯-1123003","reverse_text":"⪩⨒∯-1123003=(⊵⊁⪩⨒∯101331)∕⩚(⪩⨒∯233130+⪩⨒∯101112)","cot":[{"info":"⊵⊁⪩⨒∯101331=⪩⨒∯1123000","layer":1},{"info":"⪩⨒∯233130+⪩⨒∯101112=⪩⨒∯1000302","layer":1},{"info":"⪩⨒∯1123000∕⩚⪩⨒∯1000302=⪩⨒∯-1123003","layer":0}]}
{"id":220,"expression_no_base_symbol":"(∮$6619$)⊘","expression":"(∮⪩⨒∯1213123)⊘","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":327,"operation_count":2,"complexity_ratio":163.5,"tree":{"type":"unary","operator":"⊘","unary_expr":{"type":"unary","operator":"∮","unary_expr":{"type":"numeric_atoms","value":6619,"base":4}}},"used_operators":["gu96TGCTMs","CqXKPLVYql"],"dependent_operators":["XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","2Wsdkap16l","eLxqMNBOBk","KbjG8mgYpV","MmTdOpaElr","JclMnS0uGI","bJkvcejdHO","eewbuw0ToL"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6619","layer":2},{"info":"compute unary expreesion, input=6619, op_id = CqXKPLVYql, unary_op_definition = '∮a = { ((a⩹a)⨰(⫓⪴488)) , if (a<=186 and a<741 and (a⨱∎)<232) ; ((a≎⊠⪸a)⨔⇊(973∠↢a)) , else }', output=67","layer":1},{"info":"compute unary expreesion, input=67, op_id = gu96TGCTMs, unary_op_definition = 'a⊘ = { ((a⨰a)/(∥⊫a)) , if (⨑⩽⪐a)!=520 or (a≧⫂∧486)>62 or (⊄⩳↩a)>=602 ; ((-240)⩚⊴⇥a) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(∮⪩⨒∯1213123)⊘=⪩⨒∯0","reverse_text":"⪩⨒∯0=(∮⪩⨒∯1213123)⊘","cot":[{"info":"∮⪩⨒∯1213123=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯1003⊘=⪩⨒∯0","layer":0}]}
{"id":221,"expression_no_base_symbol":"($3637$⇮⋭$8142$)∋($1788$⨪↰⇹$1684$)","expression":"(⪩⨒∯320311⇮⋭⪩⨒∯1333032)∋(⪩⨒∯123330⨪↰⇹⪩⨒∯122110)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1945,"operation_count":3,"complexity_ratio":648.3333333333334,"tree":{"type":"binary","operator":"∋","left_expr":{"type":"binary","operator":"⇮⋭","left_expr":{"type":"numeric_atoms","value":3637,"base":4},"right_expr":{"type":"numeric_atoms","value":8142,"base":4}},"right_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":1788,"base":4},"right_expr":{"type":"numeric_atoms","value":1684,"base":4}}},"used_operators":["ukq6epAj5P","vkpjKywKVM","tmPS8pqC7x"],"dependent_operators":["SUmda5xLS4","61wBmkZwlr","KbjG8mgYpV","nhYeJWJD5X","U6pG0PXrV3","tifHPKVTfV","bJkvcejdHO","40aOVDgCDB","YbVcJGFEVW","rJVOvQCfKK"],"result":"⪩⨒∯31311113210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3637","layer":2},{"info":"number node, value=8142","layer":2},{"info":"compute binary expreesion, left_input=3637, right_input=8142, op_id = vkpjKywKVM binary_op_definition= 'a⇮⋭b = { (((⊖b)⊢)≎⊠⪸((a≃b)⇼⇔∾(47∇⊂⋱106))) }', output=-473","layer":1},{"info":"number node, value=1788","layer":2},{"info":"number node, value=1684","layer":2},{"info":"compute binary expreesion, left_input=1788, right_input=1684, op_id = tmPS8pqC7x binary_op_definition= 'a⨪↰⇹b = {a, if a == 0; (b)⨎((a-1)⨪↰⇹b), if a > 0 and abs(a) < 1000000; -(b)⨎((a+1)⨪↰⇹b), if a < 0 and abs(a) < 1000000; NaN, else}', output=1788","layer":1},{"info":"compute binary expreesion, left_input=-473, right_input=1788, op_id = ukq6epAj5P binary_op_definition= 'a∋b = { ((≋a)∠↢(b⪄a)) }', output=3626468","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯320311⇮⋭⪩⨒∯1333032)∋(⪩⨒∯123330⨪↰⇹⪩⨒∯122110)=⪩⨒∯31311113210","reverse_text":"⪩⨒∯31311113210=(⪩⨒∯320311⇮⋭⪩⨒∯1333032)∋(⪩⨒∯123330⨪↰⇹⪩⨒∯122110)","cot":[{"info":"⪩⨒∯320311⇮⋭⪩⨒∯1333032=⪩⨒∯-13121","layer":1},{"info":"⪩⨒∯123330⨪↰⇹⪩⨒∯122110=⪩⨒∯123330","layer":1},{"info":"⪩⨒∯-13121∋⪩⨒∯123330=⪩⨒∯31311113210","layer":0}]}
{"id":222,"expression_no_base_symbol":"(⨣⨃⇪$5743$)≓∲(≔$2652$)","expression":"(⨣⨃⇪⪩⨒∯1121233)≓∲(≔⪩⨒∯221130)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":89,"operation_count":3,"complexity_ratio":29.666666666666668,"tree":{"type":"binary","operator":"≓∲","left_expr":{"type":"unary","operator":"⨣⨃⇪","unary_expr":{"type":"numeric_atoms","value":5743,"base":4}},"right_expr":{"type":"unary","operator":"≔","unary_expr":{"type":"numeric_atoms","value":2652,"base":4}}},"used_operators":["s1XTVnmDOJ","AcOhelriW5","8FLs4eVsLt"],"dependent_operators":["HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu","s3Fd5m9Dh2","liw5iZPkLH","yyfyN0ffXY","uPb5QRN0te","VwlE7vj6HS","3mBM5G4a3l","8HhzD0ZcuI","BUOGQAYlQx","AYdpE9sXAk"],"result":"⪩⨒∯20010220222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5743","layer":2},{"info":"compute unary expreesion, input=5743, op_id = AcOhelriW5, unary_op_definition = '⨣⨃⇪a = { (⨡↴(172⊬⨰(3↙a))) }', output=1405","layer":1},{"info":"number node, value=2652","layer":2},{"info":"compute unary expreesion, input=2652, op_id = 8FLs4eVsLt, unary_op_definition = '≔a = { (⋃(⋂a)) , if (⨂⪏⇭a)<=427 or (a↫)>=16 ; ((a⨽194)↯⫤) , else }', output=-72962","layer":1},{"info":"compute binary expreesion, left_input=1405, right_input=-72962, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=2116138","layer":0}],"base":4,"result_base":4,"text":"(⨣⨃⇪⪩⨒∯1121233)≓∲(≔⪩⨒∯221130)=⪩⨒∯20010220222","reverse_text":"⪩⨒∯20010220222=(⨣⨃⇪⪩⨒∯1121233)≓∲(≔⪩⨒∯221130)","cot":[{"info":"⨣⨃⇪⪩⨒∯1121233=⪩⨒∯111331","layer":1},{"info":"≔⪩⨒∯221130=⪩⨒∯-101310002","layer":1},{"info":"⪩⨒∯111331≓∲⪩⨒∯-101310002=⪩⨒∯20010220222","layer":0}]}
{"id":223,"expression_no_base_symbol":"($1304$⇯⋐)∊∟⩊($1344$⫚↹⊑$8133$)","expression":"(⪩⨒∯110120⇯⋐)∊∟⩊(⪩⨒∯111000⫚↹⊑⪩⨒∯1333011)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":131,"operation_count":3,"complexity_ratio":43.666666666666664,"tree":{"type":"binary","operator":"∊∟⩊","left_expr":{"type":"unary","operator":"⇯⋐","unary_expr":{"type":"numeric_atoms","value":1304,"base":4}},"right_expr":{"type":"binary","operator":"⫚↹⊑","left_expr":{"type":"numeric_atoms","value":1344,"base":4},"right_expr":{"type":"numeric_atoms","value":8133,"base":4}}},"used_operators":["ddLRYrp01A","LkLIoiE525","dfKe02y8D2"],"dependent_operators":["59igzFyhWz","A8NUZmVepG","3sJ7IOPOlU","P8v4zCKN1o","DZ8iAZOCBD","7j4O788W3g","tifHPKVTfV","eewbuw0ToL","QMFrweE19q","2DQ55sFlQl","DIvbN7qnHd","t8gj7n24qd","12rbrZMWeM","g55IO6H4Gj"],"result":"⪩⨒∯233","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1304","layer":2},{"info":"compute unary expreesion, input=1304, op_id = LkLIoiE525, unary_op_definition = 'a⇯⋐ = { (((a↺a)⊉≛↸(∥⊫a))⨰((17⫡⨏a)⇼⇔∾a)) }', output=4790","layer":1},{"info":"number node, value=1344","layer":2},{"info":"number node, value=8133","layer":2},{"info":"compute binary expreesion, left_input=1344, right_input=8133, op_id = dfKe02y8D2 binary_op_definition= 'a⫚↹⊑b = { ((126⊠≄⫣)⋳⪒((-b)⨵⪆(a⨸⪁b))) }', output=-447","layer":1},{"info":"compute binary expreesion, left_input=4790, right_input=-447, op_id = ddLRYrp01A binary_op_definition= 'a∊∟⩊b = { b , if (b∵≐)>=166 or (a⪇≇⋚4)==505 ; (↥a) , else }', output=47","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯110120⇯⋐)∊∟⩊(⪩⨒∯111000⫚↹⊑⪩⨒∯1333011)=⪩⨒∯233","reverse_text":"⪩⨒∯233=(⪩⨒∯110120⇯⋐)∊∟⩊(⪩⨒∯111000⫚↹⊑⪩⨒∯1333011)","cot":[{"info":"⪩⨒∯110120⇯⋐=⪩⨒∯1022312","layer":1},{"info":"⪩⨒∯111000⫚↹⊑⪩⨒∯1333011=⪩⨒∯-12333","layer":1},{"info":"⪩⨒∯1022312∊∟⩊⪩⨒∯-12333=⪩⨒∯233","layer":0}]}
{"id":224,"expression_no_base_symbol":"⊤⊝($4780$∛≔)","expression":"⊤⊝(⪩⨒∯1022230∛≔)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34846,"operation_count":2,"complexity_ratio":17423.0,"tree":{"type":"unary","operator":"⊤⊝","unary_expr":{"type":"unary","operator":"∛≔","unary_expr":{"type":"numeric_atoms","value":4780,"base":4}}},"used_operators":["rXAclfmB4M","mGnSCrte3L"],"dependent_operators":["sdazOOVcIp","d7ASUq0ydm","OKKcZfAt5B","212REbPD9h","gx7XJ7hdpj","nEsXyWgiOK","oWn0xqSxBt"],"result":"-Inf","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4780","layer":2},{"info":"compute unary expreesion, input=4780, op_id = mGnSCrte3L, unary_op_definition = 'a∛≔ = { (((⊙↵-a)⋾⨃∁(a⨻⩈⩔a))≝⊿(a⫸⇳(a⫯⪬∳a))) }', output=-inf","layer":1},{"info":"compute unary expreesion, input=-inf, op_id = rXAclfmB4M, unary_op_definition = '⊤⊝a = { (a⪨≂700) }', output=-inf","layer":0}],"base":4,"result_base":4,"text":"⊤⊝(⪩⨒∯1022230∛≔)=-Inf","reverse_text":"-Inf=⊤⊝(⪩⨒∯1022230∛≔)","cot":[{"info":"⪩⨒∯1022230∛≔=-Inf","layer":1},{"info":"⊤⊝-Inf=-Inf","layer":0}]}
{"id":225,"expression_no_base_symbol":"$6299$⪕$4451$⫔⩽⩺$7186$↓$1161$","expression":"⪩⨒∯1202123⪕⪩⨒∯1011203⫔⩽⩺⪩⨒∯1300102↓⪩⨒∯102021","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":36738,"operation_count":3,"complexity_ratio":12246.0,"tree":{"type":"binary","operator":"⫔⩽⩺","left_expr":{"type":"binary","operator":"⪕","left_expr":{"type":"numeric_atoms","value":6299,"base":4},"right_expr":{"type":"numeric_atoms","value":4451,"base":4}},"right_expr":{"type":"binary","operator":"↓","left_expr":{"type":"numeric_atoms","value":7186,"base":4},"right_expr":{"type":"numeric_atoms","value":1161,"base":4}}},"used_operators":["i9eR4S00cU","umQnsF7QlU","Af076pWI7l"],"dependent_operators":["Tw270M8GLb","fu6greOZ01","P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF","nhYeJWJD5X","mp7IySMOzn","Noe24qw2ks","lvlrscuwVU","T2fj7uvVaJ","PoHhknlbAi"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6299","layer":2},{"info":"number node, value=4451","layer":2},{"info":"compute binary expreesion, left_input=6299, right_input=4451, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=9048","layer":1},{"info":"number node, value=7186","layer":2},{"info":"number node, value=1161","layer":2},{"info":"compute binary expreesion, left_input=7186, right_input=1161, op_id = Af076pWI7l binary_op_definition= 'a↓b = { (((b⇷b)∓⋝b)⨐((462≴⪞⇿a)∇⊂⋱(a⋓a))) }', output=-134","layer":1},{"info":"compute binary expreesion, left_input=9048, right_input=-134, op_id = i9eR4S00cU binary_op_definition= 'a⫔⩽⩺b = { (⨰⫟⨤(a⨐⩸⫘b)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1202123⪕⪩⨒∯1011203⫔⩽⩺⪩⨒∯1300102↓⪩⨒∯102021=NaN","reverse_text":"NaN=⪩⨒∯1202123⪕⪩⨒∯1011203⫔⩽⩺⪩⨒∯1300102↓⪩⨒∯102021","cot":[{"info":"⪩⨒∯1202123⪕⪩⨒∯1011203=⪩⨒∯2031120","layer":1},{"info":"⪩⨒∯1300102↓⪩⨒∯102021=⪩⨒∯-2012","layer":1},{"info":"⪩⨒∯2031120⫔⩽⩺⪩⨒∯-2012=NaN","layer":0}]}
{"id":226,"expression_no_base_symbol":"($4547$∼$2034$)⨑⩅≇($3987$⊝⪿⪼$2533$)","expression":"(⪩⨒∯1013003∼⪩⨒∯133302)⨑⩅≇(⪩⨒∯332103⊝⪿⪼⪩⨒∯213211)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":215,"operation_count":3,"complexity_ratio":71.66666666666667,"tree":{"type":"binary","operator":"⨑⩅≇","left_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":4547,"base":4},"right_expr":{"type":"numeric_atoms","value":2034,"base":4}},"right_expr":{"type":"binary","operator":"⊝⪿⪼","left_expr":{"type":"numeric_atoms","value":3987,"base":4},"right_expr":{"type":"numeric_atoms","value":2533,"base":4}}},"used_operators":["h92wMvzauj","DyGG3AbaNP","3Oe9XWJUTD"],"dependent_operators":["s3Fd5m9Dh2","3sJ7IOPOlU","nREPSIbpBE","9Isq31Ruls","umQnsF7QlU","8HhzD0ZcuI","u6S6b8DprG","DmTXOeWf9t","AFVx7xoS7T","jLgFTUHLKL","oacrs7FA3X","xNBdhnnwKq","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","NTOWxs364D","Qy55tPpLXF","8w2t5hMYqp","t8gj7n24qd","eewbuw0ToL","QMFrweE19q"],"result":"⪩⨒∯32213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4547","layer":2},{"info":"number node, value=2034","layer":2},{"info":"compute binary expreesion, left_input=4547, right_input=2034, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":1},{"info":"number node, value=3987","layer":2},{"info":"number node, value=2533","layer":2},{"info":"compute binary expreesion, left_input=3987, right_input=2533, op_id = 3Oe9XWJUTD binary_op_definition= 'a⊝⪿⪼b = { ((⊄⩳↩(480⩚⊴⇥a))⫡⨏((a⨰b)⋥≓≎(-b))) }', output=56609","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=56609, op_id = h92wMvzauj binary_op_definition= 'a⨑⩅≇b = { (((a⪇≇⋚b)⊬⨰(b⨽582))∌↝a) , if (↽≂a)<10 or (b⊭∹↮)==22 ; ((a⊲⩕⊾(↩a))⪕((a⨚243)⇌⫙⪟(b⪘⫢b))) , else }', output=935","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1013003∼⪩⨒∯133302)⨑⩅≇(⪩⨒∯332103⊝⪿⪼⪩⨒∯213211)=⪩⨒∯32213","reverse_text":"⪩⨒∯32213=(⪩⨒∯1013003∼⪩⨒∯133302)⨑⩅≇(⪩⨒∯332103⊝⪿⪼⪩⨒∯213211)","cot":[{"info":"⪩⨒∯1013003∼⪩⨒∯133302=NaN","layer":1},{"info":"⪩⨒∯332103⊝⪿⪼⪩⨒∯213211=⪩⨒∯31310201","layer":1},{"info":"NaN⨑⩅≇⪩⨒∯31310201=⪩⨒∯32213","layer":0}]}
{"id":227,"expression_no_base_symbol":"($1122$≨$1904$)⇡⇂($6489$⪉⨛$3418$)","expression":"(⪩⨒∯101202≨⪩⨒∯131300)⇡⇂(⪩⨒∯1211121⪉⨛⪩⨒∯311122)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":85082,"operation_count":3,"complexity_ratio":28360.666666666668,"tree":{"type":"binary","operator":"⇡⇂","left_expr":{"type":"binary","operator":"≨","left_expr":{"type":"numeric_atoms","value":1122,"base":4},"right_expr":{"type":"numeric_atoms","value":1904,"base":4}},"right_expr":{"type":"binary","operator":"⪉⨛","left_expr":{"type":"numeric_atoms","value":6489,"base":4},"right_expr":{"type":"numeric_atoms","value":3418,"base":4}}},"used_operators":["UMwdvZNt44","0KMCeP1Jsh","EWw2JM7wp4"],"dependent_operators":["9FxExcQeMw","23Mk6UjR3U","z4E1FaHLuy","3tj9sqzovi","fu6greOZ01","AHs5Up7iyr","lvlrscuwVU","KPf6cnQVty","uBihLCJcMX","12rbrZMWeM","WPoGxAaPR1","jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC","NTOWxs364D","tifHPKVTfV","12rbrZMWeM","i8ToyICDmI","eewbuw0ToL"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1122","layer":2},{"info":"number node, value=1904","layer":2},{"info":"compute binary expreesion, left_input=1122, right_input=1904, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-8744","layer":1},{"info":"number node, value=6489","layer":2},{"info":"number node, value=3418","layer":2},{"info":"compute binary expreesion, left_input=6489, right_input=3418, op_id = EWw2JM7wp4 binary_op_definition= 'a⪉⨛b = { (((82⇼⇔∾a)⩚⊴⇥a)⩚⊴⇥((b∲⫓a)⋳⪒(a⨰b))) }', output=16264","layer":1},{"info":"compute binary expreesion, left_input=-8744, right_input=16264, op_id = UMwdvZNt44 binary_op_definition= 'a⇡⇂b = { (((b≹⇙⪍b)⋳⪒(b⋷a))∺≝⩲(⫟(a⩷∴43))) , if (⊬↢a)==727 or (a⇔⨋)<18 ; ((604≴⪞⇿(≻⋜b))⨐⩸⫘a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101202≨⪩⨒∯131300)⇡⇂(⪩⨒∯1211121⪉⨛⪩⨒∯311122)=NaN","reverse_text":"NaN=(⪩⨒∯101202≨⪩⨒∯131300)⇡⇂(⪩⨒∯1211121⪉⨛⪩⨒∯311122)","cot":[{"info":"⪩⨒∯101202≨⪩⨒∯131300=⪩⨒∯-2020220","layer":1},{"info":"⪩⨒∯1211121⪉⨛⪩⨒∯311122=⪩⨒∯3332020","layer":1},{"info":"⪩⨒∯-2020220⇡⇂⪩⨒∯3332020=NaN","layer":0}]}
{"id":228,"expression_no_base_symbol":"⩷⨜⫀($4081$≄⊠$7029$)","expression":"⩷⨜⫀(⪩⨒∯333301≄⊠⪩⨒∯1231311)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":65,"operation_count":2,"complexity_ratio":32.5,"tree":{"type":"unary","operator":"⩷⨜⫀","unary_expr":{"type":"binary","operator":"≄⊠","left_expr":{"type":"numeric_atoms","value":4081,"base":4},"right_expr":{"type":"numeric_atoms","value":7029,"base":4}}},"used_operators":["CDi0ktkjQ4","vXNesLlMH1"],"dependent_operators":["ruOEQAzv1W","nhYeJWJD5X","d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI"],"result":"⪩⨒∯-130201323","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4081","layer":2},{"info":"number node, value=7029","layer":2},{"info":"compute binary expreesion, left_input=4081, right_input=7029, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=117132","layer":1},{"info":"compute unary expreesion, input=117132, op_id = CDi0ktkjQ4, unary_op_definition = '⩷⨜⫀a = { (a∇⊂⋱383) , if a<1 ; (↔a) , else }', output=-116859","layer":0}],"base":4,"result_base":4,"text":"⩷⨜⫀(⪩⨒∯333301≄⊠⪩⨒∯1231311)=⪩⨒∯-130201323","reverse_text":"⪩⨒∯-130201323=⩷⨜⫀(⪩⨒∯333301≄⊠⪩⨒∯1231311)","cot":[{"info":"⪩⨒∯333301≄⊠⪩⨒∯1231311=⪩⨒∯130212030","layer":1},{"info":"⩷⨜⫀⪩⨒∯130212030=⪩⨒∯-130201323","layer":0}]}
{"id":229,"expression_no_base_symbol":"($2978$⋻⩜⩜$2296$)⪎↠($4359$∕⩚$5584$)","expression":"(⪩⨒∯232202⋻⩜⩜⪩⨒∯203320)⪎↠(⪩⨒∯1010013∕⩚⪩⨒∯1113100)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":36534,"operation_count":3,"complexity_ratio":12178.0,"tree":{"type":"binary","operator":"⪎↠","left_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":2978,"base":4},"right_expr":{"type":"numeric_atoms","value":2296,"base":4}},"right_expr":{"type":"binary","operator":"∕⩚","left_expr":{"type":"numeric_atoms","value":4359,"base":4},"right_expr":{"type":"numeric_atoms","value":5584,"base":4}}},"used_operators":["3tVxb0NHM4","oDCm7WA9JY","z9ffQ9n5Zr"],"dependent_operators":["P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2978","layer":2},{"info":"number node, value=2296","layer":2},{"info":"compute binary expreesion, left_input=2978, right_input=2296, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=5956","layer":1},{"info":"number node, value=4359","layer":2},{"info":"number node, value=5584","layer":2},{"info":"compute binary expreesion, left_input=4359, right_input=5584, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-4362","layer":1},{"info":"compute binary expreesion, left_input=5956, right_input=-4362, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯232202⋻⩜⩜⪩⨒∯203320)⪎↠(⪩⨒∯1010013∕⩚⪩⨒∯1113100)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⪩⨒∯232202⋻⩜⩜⪩⨒∯203320)⪎↠(⪩⨒∯1010013∕⩚⪩⨒∯1113100)","cot":[{"info":"⪩⨒∯232202⋻⩜⩜⪩⨒∯203320=⪩⨒∯1131010","layer":1},{"info":"⪩⨒∯1010013∕⩚⪩⨒∯1113100=⪩⨒∯-1010022","layer":1},{"info":"⪩⨒∯1131010⪎↠⪩⨒∯-1010022=⪩⨒∯2200","layer":0}]}
{"id":230,"expression_no_base_symbol":"$2321$⨚⇆$4538$⪠⩆⊳","expression":"⪩⨒∯210101⨚⇆⪩⨒∯1012322⪠⩆⊳","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16284,"operation_count":2,"complexity_ratio":8142.0,"tree":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"numeric_atoms","value":2321,"base":4},"right_expr":{"type":"numeric_atoms","value":4538,"base":4}}},"used_operators":["JLbD19bQDL","lwHaAYXP2r"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2321","layer":2},{"info":"number node, value=4538","layer":2},{"info":"compute binary expreesion, left_input=2321, right_input=4538, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = JLbD19bQDL, unary_op_definition = 'a⪠⩆⊳ = { ((a+a)-((a-a)+(a+a))) , if ((-a)!=71 or a<=364) ; (-((a+a)+(a-a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯210101⨚⇆⪩⨒∯1012322⪠⩆⊳=NaN","reverse_text":"NaN=⪩⨒∯210101⨚⇆⪩⨒∯1012322⪠⩆⊳","cot":[{"info":"⪩⨒∯210101⨚⇆⪩⨒∯1012322=NaN","layer":1},{"info":"NaN⪠⩆⊳=NaN","layer":0}]}
{"id":231,"expression_no_base_symbol":"⊖∈($3102$∀⊥⇻)","expression":"⊖∈(⪩⨒∯300132∀⊥⇻)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":70,"operation_count":2,"complexity_ratio":35.0,"tree":{"type":"unary","operator":"⊖∈","unary_expr":{"type":"unary","operator":"∀⊥⇻","unary_expr":{"type":"numeric_atoms","value":3102,"base":4}}},"used_operators":["YFxL8Sc2Zy","k4iM1060OG"],"dependent_operators":["zVYPLywUTj","sdazOOVcIp","ancx8kZcWl","YSKBFp38Pu","QvoQhV0rrE","XhwjNDsVaA","3Oe9XWJUTD"],"result":"⪩⨒∯-1113122","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3102","layer":2},{"info":"compute unary expreesion, input=3102, op_id = k4iM1060OG, unary_op_definition = 'a∀⊥⇻ = { ((a∠⫱a)/(a⊝⪿⪼a)) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = YFxL8Sc2Zy, unary_op_definition = '⊖∈a = { a , if (a⨝⩣∺)>=369 ; ((a⊪)⪨≂(a⇤a)) , else }', output=-5594","layer":0}],"base":4,"result_base":4,"text":"⊖∈(⪩⨒∯300132∀⊥⇻)=⪩⨒∯-1113122","reverse_text":"⪩⨒∯-1113122=⊖∈(⪩⨒∯300132∀⊥⇻)","cot":[{"info":"⪩⨒∯300132∀⊥⇻=⪩⨒∯0","layer":1},{"info":"⊖∈⪩⨒∯0=⪩⨒∯-1113122","layer":0}]}
{"id":232,"expression_no_base_symbol":"($5540$⪄$2559$)∩⋅","expression":"(⪩⨒∯1112210⪄⪩⨒∯213333)∩⋅","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":97,"operation_count":2,"complexity_ratio":48.5,"tree":{"type":"unary","operator":"∩⋅","unary_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":5540,"base":4},"right_expr":{"type":"numeric_atoms","value":2559,"base":4}}},"used_operators":["2MzE1hQ0cz","SUmda5xLS4"],"dependent_operators":["Qy55tPpLXF","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5540","layer":2},{"info":"number node, value=2559","layer":2},{"info":"compute binary expreesion, left_input=5540, right_input=2559, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-826245","layer":1},{"info":"compute unary expreesion, input=-826245, op_id = 2MzE1hQ0cz, unary_op_definition = 'a∩⋅ = { (a⋥≓≎44) }', output=67","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1112210⪄⪩⨒∯213333)∩⋅=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=(⪩⨒∯1112210⪄⪩⨒∯213333)∩⋅","cot":[{"info":"⪩⨒∯1112210⪄⪩⨒∯213333=⪩⨒∯-3021232011","layer":1},{"info":"⪩⨒∯-3021232011∩⋅=⪩⨒∯1003","layer":0}]}
{"id":233,"expression_no_base_symbol":"($2228$⨕⋳)↓$2682$↢$1508$","expression":"(⪩⨒∯202310⨕⋳)↓⪩⨒∯221322↢⪩⨒∯113210","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":31174,"operation_count":3,"complexity_ratio":10391.333333333334,"tree":{"type":"binary","operator":"↓","left_expr":{"type":"unary","operator":"⨕⋳","unary_expr":{"type":"numeric_atoms","value":2228,"base":4}},"right_expr":{"type":"binary","operator":"↢","left_expr":{"type":"numeric_atoms","value":2682,"base":4},"right_expr":{"type":"numeric_atoms","value":1508,"base":4}}},"used_operators":["Af076pWI7l","4X4GscPmMf","WR6HLWljOP"],"dependent_operators":["nhYeJWJD5X","mp7IySMOzn","Noe24qw2ks","lvlrscuwVU","T2fj7uvVaJ","PoHhknlbAi","9bazX3JMtO","nhYeJWJD5X","DbCuESL50I","3EYGwJThht","w2P8NbNXyL","uFcxV4UQCh","bJkvcejdHO","BUOGQAYlQx","cTDWOvIxvz","hrf7POJlIJ","eLAdDNolq6","g55IO6H4Gj","7j4O788W3g","12rbrZMWeM","f6k1SAg4EE","i8ToyICDmI","COABgblf1C"],"result":"⪩⨒∯-2012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2228","layer":2},{"info":"compute unary expreesion, input=2228, op_id = 4X4GscPmMf, unary_op_definition = 'a⨕⋳ = { ((⋼∭⪍(a∴a))⊉↱≁(⋂(a↹⊜60))) , if (a∝72)!=68 ; (((a≎⊠⪸503)⇄(a∇⊂⋱a))⪛a) , else }', output=115692","layer":1},{"info":"number node, value=2682","layer":2},{"info":"number node, value=1508","layer":2},{"info":"compute binary expreesion, left_input=2682, right_input=1508, op_id = WR6HLWljOP binary_op_definition= 'a↢b = { ((a∲⫓a)⪒(≤/a)) , if (a⊭↱114)<=535 ; ((a⋳⪒749)↺(b⨸⪁a)) , else }', output=2198","layer":1},{"info":"compute binary expreesion, left_input=115692, right_input=2198, op_id = Af076pWI7l binary_op_definition= 'a↓b = { (((b⇷b)∓⋝b)⨐((462≴⪞⇿a)∇⊂⋱(a⋓a))) }', output=-134","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯202310⨕⋳)↓⪩⨒∯221322↢⪩⨒∯113210=⪩⨒∯-2012","reverse_text":"⪩⨒∯-2012=(⪩⨒∯202310⨕⋳)↓⪩⨒∯221322↢⪩⨒∯113210","cot":[{"info":"⪩⨒∯202310⨕⋳=⪩⨒∯130033230","layer":1},{"info":"⪩⨒∯221322↢⪩⨒∯113210=⪩⨒∯202112","layer":1},{"info":"⪩⨒∯130033230↓⪩⨒∯202112=⪩⨒∯-2012","layer":0}]}
{"id":234,"expression_no_base_symbol":"$1134$⇼⇔∾$4366$⫦⪉($1152$⫿)","expression":"⪩⨒∯101232⇼⇔∾⪩⨒∯1010032⫦⪉(⪩⨒∯102000⫿)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":29,"operation_count":3,"complexity_ratio":9.666666666666666,"tree":{"type":"binary","operator":"⫦⪉","left_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":1134,"base":4},"right_expr":{"type":"numeric_atoms","value":4366,"base":4}},"right_expr":{"type":"unary","operator":"⫿","unary_expr":{"type":"numeric_atoms","value":1152,"base":4}}},"used_operators":["wscyQdcy20","tifHPKVTfV","9tKT6PmtkH"],"dependent_operators":["W4YGzv6Whe","B3sABdIn96","9HNa5Wba9A","g7Hmc5v1ko","nREPSIbpBE","D3AQDKkPcf","rysDP5nf3Z","t8gj7n24qd","DpFCA1CohY","9ICcGScMcE","f6k1SAg4EE"],"result":"⪩⨒∯-120130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1134","layer":2},{"info":"number node, value=4366","layer":2},{"info":"compute binary expreesion, left_input=1134, right_input=4366, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=3232","layer":1},{"info":"number node, value=1152","layer":2},{"info":"compute unary expreesion, input=1152, op_id = 9tKT6PmtkH, unary_op_definition = 'a⫿ = { (≦∁a) , if (⋗⩬⋾a)<1 ; (a⪒a) , else }', output=1152","layer":1},{"info":"compute binary expreesion, left_input=3232, right_input=1152, op_id = wscyQdcy20 binary_op_definition= 'a⫦⪉b = { ((a⩌⋺206)⪹) , if (a∷677)>=23 ; ((b+a)*(b⨚b)) , else }', output=-1564","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯101232⇼⇔∾⪩⨒∯1010032⫦⪉(⪩⨒∯102000⫿)=⪩⨒∯-120130","reverse_text":"⪩⨒∯-120130=⪩⨒∯101232⇼⇔∾⪩⨒∯1010032⫦⪉(⪩⨒∯102000⫿)","cot":[{"info":"⪩⨒∯101232⇼⇔∾⪩⨒∯1010032=⪩⨒∯302200","layer":1},{"info":"⪩⨒∯102000⫿=⪩⨒∯102000","layer":1},{"info":"⪩⨒∯302200⫦⪉⪩⨒∯102000=⪩⨒∯-120130","layer":0}]}
{"id":235,"expression_no_base_symbol":"+⊝⨔($6479$⫒⫫$1295$)","expression":"+⊝⨔(⪩⨒∯1211033⫒⫫⪩⨒∯110033)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":24,"operation_count":2,"complexity_ratio":12.0,"tree":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"binary","operator":"⫒⫫","left_expr":{"type":"numeric_atoms","value":6479,"base":4},"right_expr":{"type":"numeric_atoms","value":1295,"base":4}}},"used_operators":["DhbWaqg5eL","6Ko8hGgeMq"],"dependent_operators":["dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","jdwGQqwJi5","AHs5Up7iyr","AFVx7xoS7T"],"result":"⪩⨒∯113302","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6479","layer":2},{"info":"number node, value=1295","layer":2},{"info":"compute binary expreesion, left_input=6479, right_input=1295, op_id = 6Ko8hGgeMq binary_op_definition= 'a⫒⫫b = { (b≹⇙⪍a) , if (a∁)>135 ; (b⇌⫙⪟a) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = DhbWaqg5eL, unary_op_definition = '+⊝⨔a = { ((⪲⇎(⨑⩽⪐14))⨁⊸⫻) , if (a⫸⊐100)!=276 or (a⩷∴98)>390 ; (((a⪐)⪢(a⫸⊐221))+((a⩨a)⪘⫢(-370))) , else }', output=1522","layer":0}],"base":4,"result_base":4,"text":"+⊝⨔(⪩⨒∯1211033⫒⫫⪩⨒∯110033)=⪩⨒∯113302","reverse_text":"⪩⨒∯113302=+⊝⨔(⪩⨒∯1211033⫒⫫⪩⨒∯110033)","cot":[{"info":"⪩⨒∯1211033⫒⫫⪩⨒∯110033=NaN","layer":1},{"info":"+⊝⨔NaN=⪩⨒∯113302","layer":0}]}
{"id":236,"expression_no_base_symbol":"$2415$∺≝⩲$7627$⩘(⨴⫝$1604$)","expression":"⪩⨒∯211233∺≝⩲⪩⨒∯1313023⩘(⨴⫝⪩⨒∯121010)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1924,"operation_count":3,"complexity_ratio":641.3333333333334,"tree":{"type":"binary","operator":"⩘","left_expr":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"numeric_atoms","value":2415,"base":4},"right_expr":{"type":"numeric_atoms","value":7627,"base":4}},"right_expr":{"type":"unary","operator":"⨴⫝","unary_expr":{"type":"numeric_atoms","value":1604,"base":4}}},"used_operators":["cHh1gJQ2o6","KPf6cnQVty","SVb2v531z1"],"dependent_operators":["23Mk6UjR3U","eRqsBgTDFp","zVYPLywUTj","bPywburJMS","KPf6cnQVty","YbVcJGFEVW","5twsqlHp2o","BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl","oDCm7WA9JY","XnXgA4xnOs","ocnLzx9CaJ","3sJ7IOPOlU","9cloC0Ngie","SWo3A1KBJH","jWTQ2TZYIH","pRsWfj4Fpp","DyGG3AbaNP","5obUd6DV38","8HhzD0ZcuI","YbUVn0Rbpy","AdZkA7nFnk","SIgE0bArFf"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2415","layer":2},{"info":"number node, value=7627","layer":2},{"info":"compute binary expreesion, left_input=2415, right_input=7627, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":1},{"info":"number node, value=1604","layer":2},{"info":"compute unary expreesion, input=1604, op_id = SVb2v531z1, unary_op_definition = '⨴⫝a = { ((⪨⨬(⇋↷a))≬⇓((a⋅⇍a)⨑≵⋬(∡178))) , if (a⪇≇⋚963)!=62 ; (((541⋛107)⩼⇪↪(⪭⩑⪱a))⋻⩜⩜((a⊕∕a)∼(459⨽6))) , else }', output=2828198","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=2828198, op_id = cHh1gJQ2o6 binary_op_definition= 'a⩘b = { (((b⋷b)↼⊘⨖(a⊢6))∺≝⩲((a⪒⊣⊆619)≃(a⊪))) }', output=160","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯211233∺≝⩲⪩⨒∯1313023⩘(⨴⫝⪩⨒∯121010)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⪩⨒∯211233∺≝⩲⪩⨒∯1313023⩘(⨴⫝⪩⨒∯121010)","cot":[{"info":"⪩⨒∯211233∺≝⩲⪩⨒∯1313023=⪩⨒∯2200","layer":1},{"info":"⨴⫝⪩⨒∯121010=⪩⨒∯22302132212","layer":1},{"info":"⪩⨒∯2200⩘⪩⨒∯22302132212=⪩⨒∯2200","layer":0}]}
{"id":237,"expression_no_base_symbol":"($1401$⨒$4655$)⋾⨃∁(⇖$1566$)","expression":"(⪩⨒∯111321⨒⪩⨒∯1020233)⋾⨃∁(⇖⪩⨒∯120132)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":50,"operation_count":3,"complexity_ratio":16.666666666666668,"tree":{"type":"binary","operator":"⋾⨃∁","left_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":1401,"base":4},"right_expr":{"type":"numeric_atoms","value":4655,"base":4}},"right_expr":{"type":"unary","operator":"⇖","unary_expr":{"type":"numeric_atoms","value":1566,"base":4}}},"used_operators":["212REbPD9h","y75s1iXyHd","tfWHHpNKUN"],"dependent_operators":["eLxqMNBOBk","Qy55tPpLXF","w2P8NbNXyL","2DQ55sFlQl","f6k1SAg4EE","srAu1WTS94","oacrs7FA3X","7qqUquhhSb","2DQ55sFlQl"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1401","layer":2},{"info":"number node, value=4655","layer":2},{"info":"compute binary expreesion, left_input=1401, right_input=4655, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-8034","layer":1},{"info":"number node, value=1566","layer":2},{"info":"compute unary expreesion, input=1566, op_id = tfWHHpNKUN, unary_op_definition = '⇖a = { (221⨵⪆a) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=-8034, right_input=160, op_id = 212REbPD9h binary_op_definition= 'a⋾⨃∁b = { ((430⊉↱≁b)⨵⪆b) , if (a⪒898)>=359 ; ((⫓⪴b)⊉↱≁(26⋥≓≎b)) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯111321⨒⪩⨒∯1020233)⋾⨃∁(⇖⪩⨒∯120132)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⪩⨒∯111321⨒⪩⨒∯1020233)⋾⨃∁(⇖⪩⨒∯120132)","cot":[{"info":"⪩⨒∯111321⨒⪩⨒∯1020233=⪩⨒∯-1331202","layer":1},{"info":"⇖⪩⨒∯120132=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯-1331202⋾⨃∁⪩⨒∯2200=⪩⨒∯2200","layer":0}]}
{"id":238,"expression_no_base_symbol":"($3310$+⪬∐$5587$)⫘($4287$∙∹∝$4571$)","expression":"(⪩⨒∯303232+⪬∐⪩⨒∯1113103)⫘(⪩⨒∯1002333∙∹∝⪩⨒∯1013123)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":10158,"operation_count":3,"complexity_ratio":3386.0,"tree":{"type":"binary","operator":"⫘","left_expr":{"type":"binary","operator":"+⪬∐","left_expr":{"type":"numeric_atoms","value":3310,"base":4},"right_expr":{"type":"numeric_atoms","value":5587,"base":4}},"right_expr":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"numeric_atoms","value":4287,"base":4},"right_expr":{"type":"numeric_atoms","value":4571,"base":4}}},"used_operators":["48vC8HMD2b","2GS7woTJqF","HmxsFra2vL"],"dependent_operators":["OwUj7dcsQK","7j4O788W3g","tfWHHpNKUN","3ViojmjbAp","dfKe02y8D2","tcjXMdvYtA","D4vGDi5EA2","86A5ENbKR9","X99M06cbEe","g55IO6H4Gj","D4vGDi5EA2","BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI"],"result":"⪩⨒∯2213000232233","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3310","layer":2},{"info":"number node, value=5587","layer":2},{"info":"compute binary expreesion, left_input=3310, right_input=5587, op_id = 2GS7woTJqF binary_op_definition= 'a+⪬∐b = { (a≦≮≮) , if b!=63 ; (b⨸⪁575) , else }', output=-9930","layer":1},{"info":"number node, value=4287","layer":2},{"info":"number node, value=4571","layer":2},{"info":"compute binary expreesion, left_input=4287, right_input=4571, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-9930, right_input=0, op_id = 48vC8HMD2b binary_op_definition= 'a⫘b = { ((≘(b⨓a))≫≃) , if ((⇖a)!=319 or (a↺926)<190) ; ((∓a)⫚↹⊑(⪸(a≦≮≮))) , else }', output=43781039","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯303232+⪬∐⪩⨒∯1113103)⫘(⪩⨒∯1002333∙∹∝⪩⨒∯1013123)=⪩⨒∯2213000232233","reverse_text":"⪩⨒∯2213000232233=(⪩⨒∯303232+⪬∐⪩⨒∯1113103)⫘(⪩⨒∯1002333∙∹∝⪩⨒∯1013123)","cot":[{"info":"⪩⨒∯303232+⪬∐⪩⨒∯1113103=⪩⨒∯-2123022","layer":1},{"info":"⪩⨒∯1002333∙∹∝⪩⨒∯1013123=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-2123022⫘⪩⨒∯0=⪩⨒∯2213000232233","layer":0}]}
{"id":239,"expression_no_base_symbol":"($1045$⊹≧⊝)↹⊜($1456$⫸⇳$4449$)","expression":"(⪩⨒∯100111⊹≧⊝)↹⊜(⪩⨒∯112300⫸⇳⪩⨒∯1011201)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":53,"operation_count":3,"complexity_ratio":17.666666666666668,"tree":{"type":"binary","operator":"↹⊜","left_expr":{"type":"unary","operator":"⊹≧⊝","unary_expr":{"type":"numeric_atoms","value":1045,"base":4}},"right_expr":{"type":"binary","operator":"⫸⇳","left_expr":{"type":"numeric_atoms","value":1456,"base":4},"right_expr":{"type":"numeric_atoms","value":4449,"base":4}}},"used_operators":["9bazX3JMtO","LxFB4K6j0n","gx7XJ7hdpj"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","23Mk6UjR3U","tifHPKVTfV","eH2TOUuTDT","DIvbN7qnHd","NTOWxs364D","P8v4zCKN1o","XPYlsWDdGa","DZ8iAZOCBD","t8gj7n24qd","g55IO6H4Gj","eewbuw0ToL","i8ToyICDmI","COABgblf1C","DpFCA1CohY","7j4O788W3g","tifHPKVTfV","2DQ55sFlQl","DIvbN7qnHd","12rbrZMWeM","t8gj7n24qd","14qkJME0vr","g55IO6H4Gj","eewbuw0ToL"],"result":"⪩⨒∯-1200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1045","layer":2},{"info":"compute unary expreesion, input=1045, op_id = LxFB4K6j0n, unary_op_definition = 'a⊹≧⊝ = { (((∥⊫a)⊭↱(a⩚⊴⇥a))⊉≛↸(⪲⇎(⪲⇎a))) , if a!=566 ; (-((a∲⫓a)⨸⪁(a⨰a))) , else }', output=-4180","layer":1},{"info":"number node, value=1456","layer":2},{"info":"number node, value=4449","layer":2},{"info":"compute binary expreesion, left_input=1456, right_input=4449, op_id = gx7XJ7hdpj binary_op_definition= 'a⫸⇳b = { (((494⋳⪒b)⇼⇔∾(⋗⩬⋾a))↺((b⊦⊿)⨸⪁(b⨵⪆b))) , if a==116 ; (-((a⨰a)⊠≄⫣)) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-4180, right_input=0, op_id = 9bazX3JMtO binary_op_definition= 'a↹⊜b = { (((a⊠≄⫣)⩷∴(b-a))⩷∴((a⋷b)⇼⇔∾(b⪐))) }', output=-96","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100111⊹≧⊝)↹⊜(⪩⨒∯112300⫸⇳⪩⨒∯1011201)=⪩⨒∯-1200","reverse_text":"⪩⨒∯-1200=(⪩⨒∯100111⊹≧⊝)↹⊜(⪩⨒∯112300⫸⇳⪩⨒∯1011201)","cot":[{"info":"⪩⨒∯100111⊹≧⊝=⪩⨒∯-1001110","layer":1},{"info":"⪩⨒∯112300⫸⇳⪩⨒∯1011201=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-1001110↹⊜⪩⨒∯0=⪩⨒∯-1200","layer":0}]}
{"id":240,"expression_no_base_symbol":"≸($1747$⨚⇆$2382$)","expression":"≸(⪩⨒∯123103⨚⇆⪩⨒∯211032)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":12314,"operation_count":2,"complexity_ratio":6157.0,"tree":{"type":"unary","operator":"≸","unary_expr":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"numeric_atoms","value":1747,"base":4},"right_expr":{"type":"numeric_atoms","value":2382,"base":4}}},"used_operators":["eOf03JbCpp","lwHaAYXP2r"],"dependent_operators":["WmT3o8z6ya","l07mrZUIn9","NTOWxs364D","RygbFNSyEJ","tifHPKVTfV","oRDoc9rAEX","IwW236VD4Y","1aApVXNlOP","Z5m6OM72h2","mqXw5SEYmG","IWmyXbctLI","gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1747","layer":2},{"info":"number node, value=2382","layer":2},{"info":"compute binary expreesion, left_input=1747, right_input=2382, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = eOf03JbCpp, unary_op_definition = '≸a = { (29∘((630⊋≦⊧a)⩚⊴⇥(a≦↸a))) , if (a⋘⨑⨽)>2 ; (((a⪮%⊝a)⇼⇔∾(a↪⪝))⫸⊐((a⪮%⊝a)≠≀(3⩇∃⫛a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"≸(⪩⨒∯123103⨚⇆⪩⨒∯211032)=NaN","reverse_text":"NaN=≸(⪩⨒∯123103⨚⇆⪩⨒∯211032)","cot":[{"info":"⪩⨒∯123103⨚⇆⪩⨒∯211032=NaN","layer":1},{"info":"≸NaN=NaN","layer":0}]}
{"id":241,"expression_no_base_symbol":"⩒∊($1062$⩹$4762$)","expression":"⩒∊(⪩⨒∯100212⩹⪩⨒∯1022122)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":21,"operation_count":2,"complexity_ratio":10.5,"tree":{"type":"unary","operator":"⩒∊","unary_expr":{"type":"binary","operator":"⩹","left_expr":{"type":"numeric_atoms","value":1062,"base":4},"right_expr":{"type":"numeric_atoms","value":4762,"base":4}}},"used_operators":["qazvmhNBbN","2Wsdkap16l"],"dependent_operators":["AF7qkfDlqP","f6k1SAg4EE","eLAdDNolq6","rysDP5nf3Z","NTOWxs364D","23Mk6UjR3U","XIabStNQrY","2DDjHMKMc0","12rbrZMWeM","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx"],"result":"⪩⨒∯2020323","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1062","layer":2},{"info":"number node, value=4762","layer":2},{"info":"compute binary expreesion, left_input=1062, right_input=4762, op_id = 2Wsdkap16l binary_op_definition= 'a⩹b = { (b-((b⨳⩥⨓b)⨸⪁(1⋝⋈⪟b))) , if (b⇋≉)!=246 ; (((a⇋≉)⨰(a⋷a))⋳⪒((a⩚⊴⇥a)⨳⩥⨓(a≧⫂∧a))) , else }', output=4760","layer":1},{"info":"compute unary expreesion, input=4760, op_id = qazvmhNBbN, unary_op_definition = '⩒∊a = { ((≤/a)⪒(⨑⩽⪐a)) }', output=8763","layer":0}],"base":4,"result_base":4,"text":"⩒∊(⪩⨒∯100212⩹⪩⨒∯1022122)=⪩⨒∯2020323","reverse_text":"⪩⨒∯2020323=⩒∊(⪩⨒∯100212⩹⪩⨒∯1022122)","cot":[{"info":"⪩⨒∯100212⩹⪩⨒∯1022122=⪩⨒∯1022120","layer":1},{"info":"⩒∊⪩⨒∯1022120=⪩⨒∯2020323","layer":0}]}
{"id":242,"expression_no_base_symbol":"≉($4651$⫏⊷)","expression":"≉(⪩⨒∯1020223⫏⊷)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":14146,"operation_count":2,"complexity_ratio":7073.0,"tree":{"type":"unary","operator":"≉","unary_expr":{"type":"unary","operator":"⫏⊷","unary_expr":{"type":"numeric_atoms","value":4651,"base":4}}},"used_operators":["e1ybzncUwg","dcShxvzhyw"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","FU0Cs4j7VP","7YooWSwCyH","HK0tfVPux8"],"result":"⪩⨒∯-30310","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4651","layer":2},{"info":"compute unary expreesion, input=4651, op_id = dcShxvzhyw, unary_op_definition = 'a⫏⊷ = { ((224∪⫐a)⊾⪯⋞(a↛⩡⫤)) }', output=-820","layer":1},{"info":"compute unary expreesion, input=-820, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=-820","layer":0}],"base":4,"result_base":4,"text":"≉(⪩⨒∯1020223⫏⊷)=⪩⨒∯-30310","reverse_text":"⪩⨒∯-30310=≉(⪩⨒∯1020223⫏⊷)","cot":[{"info":"⪩⨒∯1020223⫏⊷=⪩⨒∯-30310","layer":1},{"info":"≉⪩⨒∯-30310=⪩⨒∯-30310","layer":0}]}
{"id":243,"expression_no_base_symbol":"$1801$⋾⨃∁$1258$⪕($1034$⩚⊴⇥$2496$)","expression":"⪩⨒∯130021⋾⨃∁⪩⨒∯103222⪕(⪩⨒∯100022⩚⊴⇥⪩⨒∯213000)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1299,"operation_count":3,"complexity_ratio":433.0,"tree":{"type":"binary","operator":"⪕","left_expr":{"type":"binary","operator":"⋾⨃∁","left_expr":{"type":"numeric_atoms","value":1801,"base":4},"right_expr":{"type":"numeric_atoms","value":1258,"base":4}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":1034,"base":4},"right_expr":{"type":"numeric_atoms","value":2496,"base":4}}},"used_operators":["umQnsF7QlU","212REbPD9h","NTOWxs364D"],"dependent_operators":["P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF","eLxqMNBOBk","Qy55tPpLXF","w2P8NbNXyL","2DQ55sFlQl","f6k1SAg4EE","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⪩⨒∯32213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1801","layer":2},{"info":"number node, value=1258","layer":2},{"info":"compute binary expreesion, left_input=1801, right_input=1258, op_id = 212REbPD9h binary_op_definition= 'a⋾⨃∁b = { ((430⊉↱≁b)⨵⪆b) , if (a⪒898)>=359 ; ((⫓⪴b)⊉↱≁(26⋥≓≎b)) , else }', output=15810450","layer":1},{"info":"number node, value=1034","layer":2},{"info":"number node, value=2496","layer":2},{"info":"compute binary expreesion, left_input=1034, right_input=2496, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-3651","layer":1},{"info":"compute binary expreesion, left_input=15810450, right_input=-3651, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=935","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯130021⋾⨃∁⪩⨒∯103222⪕(⪩⨒∯100022⩚⊴⇥⪩⨒∯213000)=⪩⨒∯32213","reverse_text":"⪩⨒∯32213=⪩⨒∯130021⋾⨃∁⪩⨒∯103222⪕(⪩⨒∯100022⩚⊴⇥⪩⨒∯213000)","cot":[{"info":"⪩⨒∯130021⋾⨃∁⪩⨒∯103222=⪩⨒∯330103332102","layer":1},{"info":"⪩⨒∯100022⩚⊴⇥⪩⨒∯213000=⪩⨒∯-321003","layer":1},{"info":"⪩⨒∯330103332102⪕⪩⨒∯-321003=⪩⨒∯32213","layer":0}]}
{"id":244,"expression_no_base_symbol":"⊥($1993$⩒⫫$1946$)","expression":"⊥(⪩⨒∯133021⩒⫫⪩⨒∯132122)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":25,"operation_count":2,"complexity_ratio":12.5,"tree":{"type":"unary","operator":"⊥","unary_expr":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"numeric_atoms","value":1993,"base":4},"right_expr":{"type":"numeric_atoms","value":1946,"base":4}}},"used_operators":["Q3PJZHRvZv","KFSx94NKJn"],"dependent_operators":["fu6greOZ01","NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1993","layer":2},{"info":"number node, value=1946","layer":2},{"info":"compute binary expreesion, left_input=1993, right_input=1946, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=1691","layer":1},{"info":"compute unary expreesion, input=1691, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⊥(⪩⨒∯133021⩒⫫⪩⨒∯132122)=NaN","reverse_text":"NaN=⊥(⪩⨒∯133021⩒⫫⪩⨒∯132122)","cot":[{"info":"⪩⨒∯133021⩒⫫⪩⨒∯132122=⪩⨒∯122123","layer":1},{"info":"⊥⪩⨒∯122123=NaN","layer":0}]}
{"id":245,"expression_no_base_symbol":"($1179$⩒⫫$2595$)↞⋁($3760$⨑≵⋬$2398$)","expression":"(⪩⨒∯102123⩒⫫⪩⨒∯220203)↞⋁(⪩⨒∯322300⨑≵⋬⪩⨒∯211132)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":215,"operation_count":3,"complexity_ratio":71.66666666666667,"tree":{"type":"binary","operator":"↞⋁","left_expr":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"numeric_atoms","value":1179,"base":4},"right_expr":{"type":"numeric_atoms","value":2595,"base":4}},"right_expr":{"type":"binary","operator":"⨑≵⋬","left_expr":{"type":"numeric_atoms","value":3760,"base":4},"right_expr":{"type":"numeric_atoms","value":2398,"base":4}}},"used_operators":["RqrPlJkxDo","KFSx94NKJn","XnXgA4xnOs"],"dependent_operators":["Uaa54Peajs","CArV6hThFE","13rbtpv6ld","NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","eewbuw0ToL","AF7qkfDlqP","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1179","layer":2},{"info":"number node, value=2595","layer":2},{"info":"compute binary expreesion, left_input=1179, right_input=2595, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=877","layer":1},{"info":"number node, value=3760","layer":2},{"info":"number node, value=2398","layer":2},{"info":"compute binary expreesion, left_input=3760, right_input=2398, op_id = XnXgA4xnOs binary_op_definition= 'a⨑≵⋬b = { ((a⨰b)⫡⨏(⨑⩽⪐b)) }', output=3393","layer":1},{"info":"compute binary expreesion, left_input=877, right_input=3393, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯102123⩒⫫⪩⨒∯220203)↞⋁(⪩⨒∯322300⨑≵⋬⪩⨒∯211132)=NaN","reverse_text":"NaN=(⪩⨒∯102123⩒⫫⪩⨒∯220203)↞⋁(⪩⨒∯322300⨑≵⋬⪩⨒∯211132)","cot":[{"info":"⪩⨒∯102123⩒⫫⪩⨒∯220203=⪩⨒∯31231","layer":1},{"info":"⪩⨒∯322300⨑≵⋬⪩⨒∯211132=⪩⨒∯311001","layer":1},{"info":"⪩⨒∯31231↞⋁⪩⨒∯311001=NaN","layer":0}]}
{"id":246,"expression_no_base_symbol":"($1597$⪛⫼$1192$)⪮%⊝(⫓⪴$4261$)","expression":"(⪩⨒∯120331⪛⫼⪩⨒∯102220)⪮%⊝(⫓⪴⪩⨒∯1002211)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4381,"operation_count":3,"complexity_ratio":1460.3333333333333,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"binary","operator":"⪛⫼","left_expr":{"type":"numeric_atoms","value":1597,"base":4},"right_expr":{"type":"numeric_atoms","value":1192,"base":4}},"right_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":4261,"base":4}}},"used_operators":["IWmyXbctLI","hyuBjUqXlG","eLxqMNBOBk"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","HJ9erzHUuu","9ICcGScMcE","DO4fhlbJSI","BX1lVwlMe0","Noe24qw2ks","uFcxV4UQCh","A8NUZmVepG","vg4gO5BX6G","dfKe02y8D2","hrf7POJlIJ","mqXw5SEYmG","QMFrweE19q","wztAlM01eG","9HNa5Wba9A"],"result":"⪩⨒∯203030","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1597","layer":2},{"info":"number node, value=1192","layer":2},{"info":"compute binary expreesion, left_input=1597, right_input=1192, op_id = hyuBjUqXlG binary_op_definition= 'a⪛⫼b = { (((↸⊣b)⫡⨏(⊿b))⫸⊐(≦∁(↥a))) , if (a⇟⨁⪰)!=192 ; (((b⊨a)⪛b)⨐((37⪔⊥b)∴(11⫚↹⊑395))) , else }', output=968","layer":1},{"info":"number node, value=4261","layer":2},{"info":"compute unary expreesion, input=4261, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=18156121","layer":1},{"info":"compute binary expreesion, left_input=968, right_input=18156121, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=2252","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯120331⪛⫼⪩⨒∯102220)⪮%⊝(⫓⪴⪩⨒∯1002211)=⪩⨒∯203030","reverse_text":"⪩⨒∯203030=(⪩⨒∯120331⪛⫼⪩⨒∯102220)⪮%⊝(⫓⪴⪩⨒∯1002211)","cot":[{"info":"⪩⨒∯120331⪛⫼⪩⨒∯102220=⪩⨒∯33020","layer":1},{"info":"⫓⪴⪩⨒∯1002211=⪩⨒∯1011100221121","layer":1},{"info":"⪩⨒∯33020⪮%⊝⪩⨒∯1011100221121=⪩⨒∯203030","layer":0}]}
{"id":247,"expression_no_base_symbol":"($1530$⩍⋽⫝̸$4757$)⊕∕($1334$⪨≂$1135$)","expression":"(⪩⨒∯113322⩍⋽⫝̸⪩⨒∯1022111)⊕∕(⪩⨒∯110312⪨≂⪩⨒∯101233)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":10,"operation_count":3,"complexity_ratio":3.3333333333333335,"tree":{"type":"binary","operator":"⊕∕","left_expr":{"type":"binary","operator":"⩍⋽⫝̸","left_expr":{"type":"numeric_atoms","value":1530,"base":4},"right_expr":{"type":"numeric_atoms","value":4757,"base":4}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":1334,"base":4},"right_expr":{"type":"numeric_atoms","value":1135,"base":4}}},"used_operators":["9cloC0Ngie","BiWNJpBvwn","sdazOOVcIp"],"dependent_operators":["Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf","Ph9nP6C5qx","xUOZtlo3hN","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯323203","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1530","layer":2},{"info":"number node, value=4757","layer":2},{"info":"compute binary expreesion, left_input=1530, right_input=4757, op_id = BiWNJpBvwn binary_op_definition= 'a⩍⋽⫝̸b = { ((⨞⊢508)≧⫂∧(a≧⫂∧b)) }', output=3811","layer":1},{"info":"number node, value=1334","layer":2},{"info":"number node, value=1135","layer":2},{"info":"compute binary expreesion, left_input=1334, right_input=1135, op_id = sdazOOVcIp binary_op_definition= 'a⪨≂b = { (((a-117)-b)-((145-b)-(a-a))) , if (-b)==187 ; ((-(b-102))-((b-a)-a)) , else }', output=500","layer":1},{"info":"compute binary expreesion, left_input=3811, right_input=500, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=3811","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯113322⩍⋽⫝̸⪩⨒∯1022111)⊕∕(⪩⨒∯110312⪨≂⪩⨒∯101233)=⪩⨒∯323203","reverse_text":"⪩⨒∯323203=(⪩⨒∯113322⩍⋽⫝̸⪩⨒∯1022111)⊕∕(⪩⨒∯110312⪨≂⪩⨒∯101233)","cot":[{"info":"⪩⨒∯113322⩍⋽⫝̸⪩⨒∯1022111=⪩⨒∯323203","layer":1},{"info":"⪩⨒∯110312⪨≂⪩⨒∯101233=⪩⨒∯13310","layer":1},{"info":"⪩⨒∯323203⊕∕⪩⨒∯13310=⪩⨒∯323203","layer":0}]}
{"id":248,"expression_no_base_symbol":"($1455$⋥≓≎$1380$)⫯⪬∳$1083$∊∟⩊$9516$","expression":"(⪩⨒∯112233⋥≓≎⪩⨒∯111210)⫯⪬∳⪩⨒∯100323∊∟⩊⪩⨒∯2110230","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":17,"operation_count":3,"complexity_ratio":5.666666666666667,"tree":{"type":"binary","operator":"⫯⪬∳","left_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":1455,"base":4},"right_expr":{"type":"numeric_atoms","value":1380,"base":4}},"right_expr":{"type":"binary","operator":"∊∟⩊","left_expr":{"type":"numeric_atoms","value":1083,"base":4},"right_expr":{"type":"numeric_atoms","value":9516,"base":4}}},"used_operators":["d7ASUq0ydm","Qy55tPpLXF","ddLRYrp01A"],"dependent_operators":["Qy55tPpLXF","BjRHVeLaeN","8w2t5hMYqp","Ph9nP6C5qx","eewbuw0ToL","D4vGDi5EA2","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","59igzFyhWz","A8NUZmVepG","3sJ7IOPOlU"],"result":"⪩⨒∯-223221","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1455","layer":2},{"info":"number node, value=1380","layer":2},{"info":"compute binary expreesion, left_input=1455, right_input=1380, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=1338","layer":1},{"info":"number node, value=1083","layer":2},{"info":"number node, value=9516","layer":2},{"info":"compute binary expreesion, left_input=1083, right_input=9516, op_id = ddLRYrp01A binary_op_definition= 'a∊∟⩊b = { b , if (b∵≐)>=166 or (a⪇≇⋚4)==505 ; (↥a) , else }', output=9516","layer":1},{"info":"compute binary expreesion, left_input=1338, right_input=9516, op_id = d7ASUq0ydm binary_op_definition= 'a⫯⪬∳b = { ((b⋥≓≎a)≧⫂∧(⊄⩳↩a)) , if (a≦≮≮)!=65 ; ((b⫩⊇)⋥≓≎(a⨰b)) , else }', output=-2793","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯112233⋥≓≎⪩⨒∯111210)⫯⪬∳⪩⨒∯100323∊∟⩊⪩⨒∯2110230=⪩⨒∯-223221","reverse_text":"⪩⨒∯-223221=(⪩⨒∯112233⋥≓≎⪩⨒∯111210)⫯⪬∳⪩⨒∯100323∊∟⩊⪩⨒∯2110230","cot":[{"info":"⪩⨒∯112233⋥≓≎⪩⨒∯111210=⪩⨒∯110322","layer":1},{"info":"⪩⨒∯100323∊∟⩊⪩⨒∯2110230=⪩⨒∯2110230","layer":1},{"info":"⪩⨒∯110322⫯⪬∳⪩⨒∯2110230=⪩⨒∯-223221","layer":0}]}
{"id":249,"expression_no_base_symbol":"$2010$↞⋁$4940$⨼⩣(⊥$5988$)","expression":"⪩⨒∯133122↞⋁⪩⨒∯1031030⨼⩣(⊥⪩⨒∯1131210)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":517,"operation_count":3,"complexity_ratio":172.33333333333334,"tree":{"type":"binary","operator":"⨼⩣","left_expr":{"type":"binary","operator":"↞⋁","left_expr":{"type":"numeric_atoms","value":2010,"base":4},"right_expr":{"type":"numeric_atoms","value":4940,"base":4}},"right_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":5988,"base":4}}},"used_operators":["JxwMv5le6e","RqrPlJkxDo","Q3PJZHRvZv"],"dependent_operators":["uFcxV4UQCh","cHh1gJQ2o6","SL6IHkK8vl","KYD54nUTWz","pRsWfj4Fpp","CArV6hThFE","Uaa54Peajs","CArV6hThFE","13rbtpv6ld","fu6greOZ01"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2010","layer":2},{"info":"number node, value=4940","layer":2},{"info":"compute binary expreesion, left_input=2010, right_input=4940, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":1},{"info":"number node, value=5988","layer":2},{"info":"compute unary expreesion, input=5988, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = JxwMv5le6e binary_op_definition= 'a⨼⩣b = { ((∐⩳⋚(b⩘a))⪛((∡129)⫥∨⫟(a⫲⨊))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯133122↞⋁⪩⨒∯1031030⨼⩣(⊥⪩⨒∯1131210)=NaN","reverse_text":"NaN=⪩⨒∯133122↞⋁⪩⨒∯1031030⨼⩣(⊥⪩⨒∯1131210)","cot":[{"info":"⪩⨒∯133122↞⋁⪩⨒∯1031030=NaN","layer":1},{"info":"⊥⪩⨒∯1131210=NaN","layer":1},{"info":"NaN⨼⩣NaN=NaN","layer":0}]}
{"id":250,"expression_no_base_symbol":"⇜($1255$⊝⪿⪼$1601$)","expression":"⇜(⪩⨒∯103213⊝⪿⪼⪩⨒∯121001)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":344,"operation_count":2,"complexity_ratio":172.0,"tree":{"type":"unary","operator":"⇜","unary_expr":{"type":"binary","operator":"⊝⪿⪼","left_expr":{"type":"numeric_atoms","value":1255,"base":4},"right_expr":{"type":"numeric_atoms","value":1601,"base":4}}},"used_operators":["lFBm8KRb8F","3Oe9XWJUTD"],"dependent_operators":["s3Fd5m9Dh2","DlLNRPXxWL","ZvLB05nZmT","6o9Blt3TJ6","f6k1SAg4EE","1h0rLqGiFr","NTOWxs364D","Qy55tPpLXF","8w2t5hMYqp","t8gj7n24qd","eewbuw0ToL","QMFrweE19q"],"result":"⪩⨒∯-230330000","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1255","layer":2},{"info":"number node, value=1601","layer":2},{"info":"compute binary expreesion, left_input=1255, right_input=1601, op_id = 3Oe9XWJUTD binary_op_definition= 'a⊝⪿⪼b = { ((⊄⩳↩(480⩚⊴⇥a))⫡⨏((a⨰b)⋥≓≎(-b))) }', output=22957","layer":1},{"info":"compute unary expreesion, input=22957, op_id = lFBm8KRb8F, unary_op_definition = '⇜a = { ((a⫳≱↱a)⊬⨰(a⪒a)) , if a>51 ; ((⩷10)⫰⋱(⫛⫱⨽a)) , else }', output=-184064","layer":0}],"base":4,"result_base":4,"text":"⇜(⪩⨒∯103213⊝⪿⪼⪩⨒∯121001)=⪩⨒∯-230330000","reverse_text":"⪩⨒∯-230330000=⇜(⪩⨒∯103213⊝⪿⪼⪩⨒∯121001)","cot":[{"info":"⪩⨒∯103213⊝⪿⪼⪩⨒∯121001=⪩⨒∯11212231","layer":1},{"info":"⇜⪩⨒∯11212231=⪩⨒∯-230330000","layer":0}]}
{"id":251,"expression_no_base_symbol":"$2631$∊∟⩊$1854$⨫⇇↔($2923$⨒$2350$)","expression":"⪩⨒∯221013∊∟⩊⪩⨒∯130332⨫⇇↔(⪩⨒∯231223⨒⪩⨒∯210232)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":35,"operation_count":3,"complexity_ratio":11.666666666666666,"tree":{"type":"binary","operator":"⨫⇇↔","left_expr":{"type":"binary","operator":"∊∟⩊","left_expr":{"type":"numeric_atoms","value":2631,"base":4},"right_expr":{"type":"numeric_atoms","value":1854,"base":4}},"right_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":2923,"base":4},"right_expr":{"type":"numeric_atoms","value":2350,"base":4}}},"used_operators":["LXhwmt4mBO","ddLRYrp01A","y75s1iXyHd"],"dependent_operators":["d7ASUq0ydm","DZ8iAZOCBD","rJVOvQCfKK","59igzFyhWz","A8NUZmVepG","3sJ7IOPOlU","srAu1WTS94","oacrs7FA3X","7qqUquhhSb"],"result":"⪩⨒∯-20033","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2631","layer":2},{"info":"number node, value=1854","layer":2},{"info":"compute binary expreesion, left_input=2631, right_input=1854, op_id = ddLRYrp01A binary_op_definition= 'a∊∟⩊b = { b , if (b∵≐)>=166 or (a⪇≇⋚4)==505 ; (↥a) , else }', output=1854","layer":1},{"info":"number node, value=2923","layer":2},{"info":"number node, value=2350","layer":2},{"info":"compute binary expreesion, left_input=2923, right_input=2350, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-17166","layer":1},{"info":"compute binary expreesion, left_input=1854, right_input=-17166, op_id = LXhwmt4mBO binary_op_definition= 'a⨫⇇↔b = { ((9⊉≛↸b)⫯⪬∳(a⨎a)) }', output=-527","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯221013∊∟⩊⪩⨒∯130332⨫⇇↔(⪩⨒∯231223⨒⪩⨒∯210232)=⪩⨒∯-20033","reverse_text":"⪩⨒∯-20033=⪩⨒∯221013∊∟⩊⪩⨒∯130332⨫⇇↔(⪩⨒∯231223⨒⪩⨒∯210232)","cot":[{"info":"⪩⨒∯221013∊∟⩊⪩⨒∯130332=⪩⨒∯130332","layer":1},{"info":"⪩⨒∯231223⨒⪩⨒∯210232=⪩⨒∯-10030032","layer":1},{"info":"⪩⨒∯130332⨫⇇↔⪩⨒∯-10030032=⪩⨒∯-20033","layer":0}]}
{"id":252,"expression_no_base_symbol":"($3350$⪚$2357$)⪬($4311$⫒⫫$4519$)","expression":"(⪩⨒∯310112⪚⪩⨒∯210311)⪬(⪩⨒∯1003113⫒⫫⪩⨒∯1012213)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":594,"operation_count":3,"complexity_ratio":198.0,"tree":{"type":"binary","operator":"⪬","left_expr":{"type":"binary","operator":"⪚","left_expr":{"type":"numeric_atoms","value":3350,"base":4},"right_expr":{"type":"numeric_atoms","value":2357,"base":4}},"right_expr":{"type":"binary","operator":"⫒⫫","left_expr":{"type":"numeric_atoms","value":4311,"base":4},"right_expr":{"type":"numeric_atoms","value":4519,"base":4}}},"used_operators":["Ez1Nq5fNfI","HrjLwUk87U","6Ko8hGgeMq"],"dependent_operators":["eRqsBgTDFp","mp7IySMOzn","JL8yIekQnl","QvoQhV0rrE","kbkesczE7y","9FxExcQeMw","rysDP5nf3Z","NTOWxs364D","DZ8iAZOCBD","tifHPKVTfV","eH2TOUuTDT","2DDjHMKMc0","jdwGQqwJi5","AHs5Up7iyr","AFVx7xoS7T"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3350","layer":2},{"info":"number node, value=2357","layer":2},{"info":"compute binary expreesion, left_input=3350, right_input=2357, op_id = HrjLwUk87U binary_op_definition= 'a⪚b = { (((317⩚⊴⇥a)⋝⋈⪟(518-95))⊉≛↸((97⪐)⩷∴(b⇼⇔∾a))) }', output=1630","layer":1},{"info":"number node, value=4311","layer":2},{"info":"number node, value=4519","layer":2},{"info":"compute binary expreesion, left_input=4311, right_input=4519, op_id = 6Ko8hGgeMq binary_op_definition= 'a⫒⫫b = { (b≹⇙⪍a) , if (a∁)>135 ; (b⇌⫙⪟a) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1630, right_input=nan, op_id = Ez1Nq5fNfI binary_op_definition= 'a⪬b = { (((514⋫)⪒⊣⊆(b≬⋮a))∠⫱(1⇷(b≬⋮32))) }', output=1234","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯310112⪚⪩⨒∯210311)⪬(⪩⨒∯1003113⫒⫫⪩⨒∯1012213)=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=(⪩⨒∯310112⪚⪩⨒∯210311)⪬(⪩⨒∯1003113⫒⫫⪩⨒∯1012213)","cot":[{"info":"⪩⨒∯310112⪚⪩⨒∯210311=⪩⨒∯121132","layer":1},{"info":"⪩⨒∯1003113⫒⫫⪩⨒∯1012213=NaN","layer":1},{"info":"⪩⨒∯121132⪬NaN=⪩⨒∯103102","layer":0}]}
{"id":253,"expression_no_base_symbol":"⇋↷($5806$⊍⩺⋍$1109$)","expression":"⇋↷(⪩⨒∯1122232⊍⩺⋍⪩⨒∯101111)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":215,"operation_count":2,"complexity_ratio":107.5,"tree":{"type":"unary","operator":"⇋↷","unary_expr":{"type":"binary","operator":"⊍⩺⋍","left_expr":{"type":"numeric_atoms","value":5806,"base":4},"right_expr":{"type":"numeric_atoms","value":1109,"base":4}}},"used_operators":["SWo3A1KBJH","OXDGMFPWZM"],"dependent_operators":["XPYlsWDdGa","23Mk6UjR3U","2DQ55sFlQl","u6S6b8DprG","kn8WO9XteQ","inkyxCbjAn","13rbtpv6ld"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5806","layer":2},{"info":"number node, value=1109","layer":2},{"info":"compute binary expreesion, left_input=5806, right_input=1109, op_id = OXDGMFPWZM binary_op_definition= 'a⊍⩺⋍b = { ((⇁⨣⪵659)↤⩊(b⨭⪣a)) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = SWo3A1KBJH, unary_op_definition = '⇋↷a = { (⪲⇎((↽≂a)⋷(a⨵⪆a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇋↷(⪩⨒∯1122232⊍⩺⋍⪩⨒∯101111)=NaN","reverse_text":"NaN=⇋↷(⪩⨒∯1122232⊍⩺⋍⪩⨒∯101111)","cot":[{"info":"⪩⨒∯1122232⊍⩺⋍⪩⨒∯101111=NaN","layer":1},{"info":"⇋↷NaN=NaN","layer":0}]}
{"id":254,"expression_no_base_symbol":"($7296$⊾⪯⋞$1492$)⨼⩣(↴⪽⋼$5070$)","expression":"(⪩⨒∯1302000⊾⪯⋞⪩⨒∯113110)⨼⩣(↴⪽⋼⪩⨒∯1033032)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":429,"operation_count":3,"complexity_ratio":143.0,"tree":{"type":"binary","operator":"⨼⩣","left_expr":{"type":"binary","operator":"⊾⪯⋞","left_expr":{"type":"numeric_atoms","value":7296,"base":4},"right_expr":{"type":"numeric_atoms","value":1492,"base":4}},"right_expr":{"type":"unary","operator":"↴⪽⋼","unary_expr":{"type":"numeric_atoms","value":5070,"base":4}}},"used_operators":["JxwMv5le6e","HK0tfVPux8","5TUYCnJO6w"],"dependent_operators":["uFcxV4UQCh","cHh1gJQ2o6","SL6IHkK8vl","KYD54nUTWz","pRsWfj4Fpp","CArV6hThFE","s3Fd5m9Dh2","KFSx94NKJn","MmTdOpaElr","XnXgA4xnOs","fOIeswaMU4","YSKBFp38Pu","oacrs7FA3X","xNBdhnnwKq","MGuIdZPyUC","UqFzSgLMvQ","k7HXdKtiEU","yyfyN0ffXY","pRsWfj4Fpp","diKm42VcIt"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7296","layer":2},{"info":"number node, value=1492","layer":2},{"info":"compute binary expreesion, left_input=7296, right_input=1492, op_id = HK0tfVPux8 binary_op_definition= 'a⊾⪯⋞b = { ((121⊭∹↮)⊬⨰(a⨑≵⋬b)) , if (a⩟)==395 or (a⨱∎)>94 ; ((b⪘⫢b)⩒⫫(a⇤b)) , else }', output=2558","layer":1},{"info":"number node, value=5070","layer":2},{"info":"compute unary expreesion, input=5070, op_id = 5TUYCnJO6w, unary_op_definition = '↴⪽⋼a = { a , if ((∡a)<5 or (⇘a)>=19 or (⊲⪭a)==199) ; (((a↙a)⇡)⇉⇉) , else }', output=5070","layer":1},{"info":"compute binary expreesion, left_input=2558, right_input=5070, op_id = JxwMv5le6e binary_op_definition= 'a⨼⩣b = { ((∐⩳⋚(b⩘a))⪛((∡129)⫥∨⫟(a⫲⨊))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1302000⊾⪯⋞⪩⨒∯113110)⨼⩣(↴⪽⋼⪩⨒∯1033032)=NaN","reverse_text":"NaN=(⪩⨒∯1302000⊾⪯⋞⪩⨒∯113110)⨼⩣(↴⪽⋼⪩⨒∯1033032)","cot":[{"info":"⪩⨒∯1302000⊾⪯⋞⪩⨒∯113110=⪩⨒∯213332","layer":1},{"info":"↴⪽⋼⪩⨒∯1033032=⪩⨒∯1033032","layer":1},{"info":"⪩⨒∯213332⨼⩣⪩⨒∯1033032=NaN","layer":0}]}
{"id":255,"expression_no_base_symbol":"(⊙↵-$1985$)⫡⨏$1966$↞⋁$7937$","expression":"(⊙↵-⪩⨒∯133001)⫡⨏⪩⨒∯132232↞⋁⪩⨒∯1330001","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2212,"operation_count":3,"complexity_ratio":737.3333333333334,"tree":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":1985,"base":4}},"right_expr":{"type":"binary","operator":"↞⋁","left_expr":{"type":"numeric_atoms","value":1966,"base":4},"right_expr":{"type":"numeric_atoms","value":7937,"base":4}}},"used_operators":["QMFrweE19q","oWn0xqSxBt","RqrPlJkxDo"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","Uaa54Peajs","CArV6hThFE","13rbtpv6ld"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1985","layer":2},{"info":"compute unary expreesion, input=1985, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"number node, value=1966","layer":2},{"info":"number node, value=7937","layer":2},{"info":"compute binary expreesion, left_input=1966, right_input=7937, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-1, right_input=nan, op_id = QMFrweE19q binary_op_definition= 'a⫡⨏b = { 497 , if (-b)==408 and (-a)>=56 ; (((a+783)+(a+a))+((b+a)+(a+b))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⊙↵-⪩⨒∯133001)⫡⨏⪩⨒∯132232↞⋁⪩⨒∯1330001=NaN","reverse_text":"NaN=(⊙↵-⪩⨒∯133001)⫡⨏⪩⨒∯132232↞⋁⪩⨒∯1330001","cot":[{"info":"⊙↵-⪩⨒∯133001=⪩⨒∯-1","layer":1},{"info":"⪩⨒∯132232↞⋁⪩⨒∯1330001=NaN","layer":1},{"info":"⪩⨒∯-1⫡⨏NaN=NaN","layer":0}]}
{"id":256,"expression_no_base_symbol":"($1574$⪡$7060$)⩁⩘($1104$→⨶⪴$1820$)","expression":"(⪩⨒∯120212⪡⪩⨒∯1232110)⩁⩘(⪩⨒∯101100→⨶⪴⪩⨒∯130130)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":38,"operation_count":3,"complexity_ratio":12.666666666666666,"tree":{"type":"binary","operator":"⩁⩘","left_expr":{"type":"binary","operator":"⪡","left_expr":{"type":"numeric_atoms","value":1574,"base":4},"right_expr":{"type":"numeric_atoms","value":7060,"base":4}},"right_expr":{"type":"binary","operator":"→⨶⪴","left_expr":{"type":"numeric_atoms","value":1104,"base":4},"right_expr":{"type":"numeric_atoms","value":1820,"base":4}}},"used_operators":["gub5Cegaqo","oraRL2iQuh","bF6eod5Gvf"],"dependent_operators":["DpFCA1CohY","IWmyXbctLI","2Wsdkap16l","ljTHtUsqzn","k8jYdgA6NY","8WDwsbhb0R","8w2t5hMYqp","9FxExcQeMw"],"result":"⪩⨒∯-11012130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1574","layer":2},{"info":"number node, value=7060","layer":2},{"info":"compute binary expreesion, left_input=1574, right_input=7060, op_id = oraRL2iQuh binary_op_definition= 'a⪡b = { (107%(a⩹b)) , if a>=49 ; (≀↧⇸(∂⩏⊆a)) , else }', output=107","layer":1},{"info":"number node, value=1104","layer":2},{"info":"number node, value=1820","layer":2},{"info":"compute binary expreesion, left_input=1104, right_input=1820, op_id = bF6eod5Gvf binary_op_definition= 'a→⨶⪴b = { (a⩷∴b) , if b<109 ; (⊄⩳↩b) , else }', output=-5460","layer":1},{"info":"compute binary expreesion, left_input=107, right_input=-5460, op_id = gub5Cegaqo binary_op_definition= 'a⩁⩘b = { ((b⪮%⊝b)⪮%⊝(⋗⩬⋾a)) }', output=-20892","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯120212⪡⪩⨒∯1232110)⩁⩘(⪩⨒∯101100→⨶⪴⪩⨒∯130130)=⪩⨒∯-11012130","reverse_text":"⪩⨒∯-11012130=(⪩⨒∯120212⪡⪩⨒∯1232110)⩁⩘(⪩⨒∯101100→⨶⪴⪩⨒∯130130)","cot":[{"info":"⪩⨒∯120212⪡⪩⨒∯1232110=⪩⨒∯1223","layer":1},{"info":"⪩⨒∯101100→⨶⪴⪩⨒∯130130=⪩⨒∯-1111110","layer":1},{"info":"⪩⨒∯1223⩁⩘⪩⨒∯-1111110=⪩⨒∯-11012130","layer":0}]}
{"id":257,"expression_no_base_symbol":"⊑($3128$⪄$1036$)","expression":"⊑(⪩⨒∯300320⪄⪩⨒∯100030)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":504,"operation_count":2,"complexity_ratio":252.0,"tree":{"type":"unary","operator":"⊑","unary_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":3128,"base":4},"right_expr":{"type":"numeric_atoms","value":1036,"base":4}}},"used_operators":["IkUmn0D7oy","SUmda5xLS4"],"dependent_operators":["oRDoc9rAEX","AdZkA7nFnk","megm06wKyl","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⪩⨒∯3000","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3128","layer":2},{"info":"number node, value=1036","layer":2},{"info":"compute binary expreesion, left_input=3128, right_input=1036, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-463177","layer":1},{"info":"compute unary expreesion, input=-463177, op_id = IkUmn0D7oy, unary_op_definition = '⊑a = { ((a⋅⇍254)⊋≦⊧(⨈⫕a)) }', output=192","layer":0}],"base":4,"result_base":4,"text":"⊑(⪩⨒∯300320⪄⪩⨒∯100030)=⪩⨒∯3000","reverse_text":"⪩⨒∯3000=⊑(⪩⨒∯300320⪄⪩⨒∯100030)","cot":[{"info":"⪩⨒∯300320⪄⪩⨒∯100030=⪩⨒∯-1301011021","layer":1},{"info":"⊑⪩⨒∯-1301011021=⪩⨒∯3000","layer":0}]}
{"id":258,"expression_no_base_symbol":"$1160$⨓$1372$⨭⪣$2050$⪥$3003$","expression":"⪩⨒∯102020⨓⪩⨒∯111130⨭⪣⪩⨒∯200002⪥⪩⨒∯232323","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1441,"operation_count":3,"complexity_ratio":480.3333333333333,"tree":{"type":"binary","operator":"⨭⪣","left_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":1160,"base":4},"right_expr":{"type":"numeric_atoms","value":1372,"base":4}},"right_expr":{"type":"binary","operator":"⪥","left_expr":{"type":"numeric_atoms","value":2050,"base":4},"right_expr":{"type":"numeric_atoms","value":3003,"base":4}}},"used_operators":["kn8WO9XteQ","3ViojmjbAp","QbnwKVWMIQ"],"dependent_operators":["vRio1gEz1j","61wBmkZwlr","SWo3A1KBJH","8jW3W4yZS5","LkLIoiE525","Y7wcNGrDQJ","PPChnnnBFF","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","WR6HLWljOP","nhYeJWJD5X","f6k1SAg4EE","jLgFTUHLKL","PPChnnnBFF"],"result":"⪩⨒∯21010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1160","layer":2},{"info":"number node, value=1372","layer":2},{"info":"compute binary expreesion, left_input=1160, right_input=1372, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1375","layer":1},{"info":"number node, value=2050","layer":2},{"info":"number node, value=3003","layer":2},{"info":"compute binary expreesion, left_input=2050, right_input=3003, op_id = QbnwKVWMIQ binary_op_definition= 'a⪥b = { (b∇⊂⋱(58∣a)) , if (b↢721)<125 ; (↩(508⪒a)) , else }', output=12852","layer":1},{"info":"compute binary expreesion, left_input=-1375, right_input=12852, op_id = kn8WO9XteQ binary_op_definition= 'a⨭⪣b = { ((486⇩)⩵∡(a∣a)) , if (b⇯⋐)>445 or (≋b)>319 or b<=69 ; (↯⪼(⇋↷b)) , else }', output=580","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102020⨓⪩⨒∯111130⨭⪣⪩⨒∯200002⪥⪩⨒∯232323=⪩⨒∯21010","reverse_text":"⪩⨒∯21010=⪩⨒∯102020⨓⪩⨒∯111130⨭⪣⪩⨒∯200002⪥⪩⨒∯232323","cot":[{"info":"⪩⨒∯102020⨓⪩⨒∯111130=⪩⨒∯-111133","layer":1},{"info":"⪩⨒∯200002⪥⪩⨒∯232323=⪩⨒∯3020310","layer":1},{"info":"⪩⨒∯-111133⨭⪣⪩⨒∯3020310=⪩⨒∯21010","layer":0}]}
{"id":259,"expression_no_base_symbol":"($1991$⇣⩺⋵$2593$)⊝⪿⪼(⇋⊎⋝$6798$)","expression":"(⪩⨒∯133013⇣⩺⋵⪩⨒∯220201)⊝⪿⪼(⇋⊎⋝⪩⨒∯1222032)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6877,"operation_count":3,"complexity_ratio":2292.3333333333335,"tree":{"type":"binary","operator":"⊝⪿⪼","left_expr":{"type":"binary","operator":"⇣⩺⋵","left_expr":{"type":"numeric_atoms","value":1991,"base":4},"right_expr":{"type":"numeric_atoms","value":2593,"base":4}},"right_expr":{"type":"unary","operator":"⇋⊎⋝","unary_expr":{"type":"numeric_atoms","value":6798,"base":4}}},"used_operators":["3Oe9XWJUTD","F4yD0voBRQ","CzM2PEoXns"],"dependent_operators":["NTOWxs364D","Qy55tPpLXF","8w2t5hMYqp","t8gj7n24qd","eewbuw0ToL","QMFrweE19q","NTOWxs364D","KPf6cnQVty","8jW3W4yZS5","12rbrZMWeM","g55IO6H4Gj","2DlMacCsIx","dWAJyo7jo9"],"result":"⪩⨒∯1132100","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1991","layer":2},{"info":"number node, value=2593","layer":2},{"info":"compute binary expreesion, left_input=1991, right_input=2593, op_id = F4yD0voBRQ binary_op_definition= 'a⇣⩺⋵b = { (((a⩨565)∺≝⩲(5⨸⪁a))⩚⊴⇥(↯⪼(a⋳⪒b))) }', output=-260","layer":1},{"info":"number node, value=6798","layer":2},{"info":"compute unary expreesion, input=6798, op_id = CzM2PEoXns, unary_op_definition = '⇋⊎⋝a = { (a⪢a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-260, right_input=nan, op_id = 3Oe9XWJUTD binary_op_definition= 'a⊝⪿⪼b = { ((⊄⩳↩(480⩚⊴⇥a))⫡⨏((a⨰b)⋥≓≎(-b))) }', output=6032","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯133013⇣⩺⋵⪩⨒∯220201)⊝⪿⪼(⇋⊎⋝⪩⨒∯1222032)=⪩⨒∯1132100","reverse_text":"⪩⨒∯1132100=(⪩⨒∯133013⇣⩺⋵⪩⨒∯220201)⊝⪿⪼(⇋⊎⋝⪩⨒∯1222032)","cot":[{"info":"⪩⨒∯133013⇣⩺⋵⪩⨒∯220201=⪩⨒∯-10010","layer":1},{"info":"⇋⊎⋝⪩⨒∯1222032=NaN","layer":1},{"info":"⪩⨒∯-10010⊝⪿⪼NaN=⪩⨒∯1132100","layer":0}]}
{"id":260,"expression_no_base_symbol":"($2601$%$8416$)⨽$1695$⪎↠$8601$","expression":"(⪩⨒∯220221%⪩⨒∯2003200)⨽⪩⨒∯122133⪎↠⪩⨒∯2012121","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2621,"operation_count":3,"complexity_ratio":873.6666666666666,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":2601,"base":4},"right_expr":{"type":"numeric_atoms","value":8416,"base":4}},"right_expr":{"type":"binary","operator":"⪎↠","left_expr":{"type":"numeric_atoms","value":1695,"base":4},"right_expr":{"type":"numeric_atoms","value":8601,"base":4}}},"used_operators":["8HhzD0ZcuI","k8jYdgA6NY","3tVxb0NHM4"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","rysDP5nf3Z","P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM"],"result":"⪩⨒∯-1031122301301","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2601","layer":2},{"info":"number node, value=8416","layer":2},{"info":"compute binary expreesion, left_input=2601, right_input=8416, op_id = k8jYdgA6NY binary_op_definition= 'None', output=2601","layer":1},{"info":"number node, value=1695","layer":2},{"info":"number node, value=8601","layer":2},{"info":"compute binary expreesion, left_input=1695, right_input=8601, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=160","layer":1},{"info":"compute binary expreesion, left_input=2601, right_input=160, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-20294769","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯220221%⪩⨒∯2003200)⨽⪩⨒∯122133⪎↠⪩⨒∯2012121=⪩⨒∯-1031122301301","reverse_text":"⪩⨒∯-1031122301301=(⪩⨒∯220221%⪩⨒∯2003200)⨽⪩⨒∯122133⪎↠⪩⨒∯2012121","cot":[{"info":"⪩⨒∯220221%⪩⨒∯2003200=⪩⨒∯220221","layer":1},{"info":"⪩⨒∯122133⪎↠⪩⨒∯2012121=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯220221⨽⪩⨒∯2200=⪩⨒∯-1031122301301","layer":0}]}
{"id":261,"expression_no_base_symbol":"$1537$∛$1023$∠↢$1021$⩌⋺$6100$","expression":"⪩⨒∯120001∛⪩⨒∯33333∠↢⪩⨒∯33331⩌⋺⪩⨒∯1133110","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":89,"operation_count":3,"complexity_ratio":29.666666666666668,"tree":{"type":"binary","operator":"∠↢","left_expr":{"type":"binary","operator":"∛","left_expr":{"type":"numeric_atoms","value":1537,"base":4},"right_expr":{"type":"numeric_atoms","value":1023,"base":4}},"right_expr":{"type":"binary","operator":"⩌⋺","left_expr":{"type":"numeric_atoms","value":1021,"base":4},"right_expr":{"type":"numeric_atoms","value":6100,"base":4}}},"used_operators":["KbjG8mgYpV","w2537kitQq","g7Hmc5v1ko"],"dependent_operators":["rysDP5nf3Z","NTOWxs364D","XPYlsWDdGa","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","nCS4ZIUYfx","COABgblf1C","DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc","9FxExcQeMw","W4YGzv6Whe","NTOWxs364D","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","i8ToyICDmI","QMFrweE19q"],"result":"⪩⨒∯120330322","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1537","layer":2},{"info":"number node, value=1023","layer":2},{"info":"compute binary expreesion, left_input=1537, right_input=1023, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=67","layer":1},{"info":"number node, value=1021","layer":2},{"info":"number node, value=6100","layer":2},{"info":"compute binary expreesion, left_input=1021, right_input=6100, op_id = g7Hmc5v1ko binary_op_definition= 'a⩌⋺b = { ((⨞⊢(b⨵⪆b))∲⫓((a⪨≂b)⪨≂(b⩷∴919))) , if (b⫡⨏102)>364 and (-b)==524 ; (b⇼⇔∾((a+a)⩚⊴⇥(-a))) , else }', output=-7242","layer":1},{"info":"compute binary expreesion, left_input=67, right_input=-7242, op_id = KbjG8mgYpV binary_op_definition= 'a∠↢b = { (a⊭↱((159⨳⩥⨓16)-(b⨸⪁a))) , if (b==488 or (⨞⊢a)==254) ; (⪲⇎((-b)⫡⨏(b⩚⊴⇥a))) , else }', output=102202","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯120001∛⪩⨒∯33333∠↢⪩⨒∯33331⩌⋺⪩⨒∯1133110=⪩⨒∯120330322","reverse_text":"⪩⨒∯120330322=⪩⨒∯120001∛⪩⨒∯33333∠↢⪩⨒∯33331⩌⋺⪩⨒∯1133110","cot":[{"info":"⪩⨒∯120001∛⪩⨒∯33333=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯33331⩌⋺⪩⨒∯1133110=⪩⨒∯-1301022","layer":1},{"info":"⪩⨒∯1003∠↢⪩⨒∯-1301022=⪩⨒∯120330322","layer":0}]}
{"id":262,"expression_no_base_symbol":"($1716$⪃↞⩐)⊋≦⊧$2188$⋓$1958$","expression":"(⪩⨒∯122310⪃↞⩐)⊋≦⊧⪩⨒∯202030⋓⪩⨒∯132212","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":750,"operation_count":3,"complexity_ratio":250.0,"tree":{"type":"binary","operator":"⊋≦⊧","left_expr":{"type":"unary","operator":"⪃↞⩐","unary_expr":{"type":"numeric_atoms","value":1716,"base":4}},"right_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":2188,"base":4},"right_expr":{"type":"numeric_atoms","value":1958,"base":4}}},"used_operators":["oRDoc9rAEX","grXIztHqDa","T2fj7uvVaJ"],"dependent_operators":["DZ8iAZOCBD","tifHPKVTfV","sdazOOVcIp","glklzrTFfD","DIvbN7qnHd","12rbrZMWeM","Ph9nP6C5qx","eewbuw0ToL","2td37pGCOC","IwW236VD4Y","bF6eod5Gvf","l07mrZUIn9","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⪩⨒∯3300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1716","layer":2},{"info":"compute unary expreesion, input=1716, op_id = grXIztHqDa, unary_op_definition = 'a⪃↞⩐ = { ((a→⨶⪴a)≠≀(a↪⪝)) }', output=10602","layer":1},{"info":"number node, value=2188","layer":2},{"info":"number node, value=1958","layer":2},{"info":"compute binary expreesion, left_input=2188, right_input=1958, op_id = T2fj7uvVaJ binary_op_definition= 'a⋓b = { (((60⪒b)⊭∹↮)%((a⪘⫢68)⪘⫢(⨵≀≌a))) , if (b>=803 and b<=372 and b<242) ; (16⪢((b⊠≄⫣)⋷(a⫌⩹⨱))) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=10602, right_input=0, op_id = oRDoc9rAEX binary_op_definition= 'a⊋≦⊧b = { (((24⊉≛↸a)⊉≛↸(⩦⩻⨪b))⊉≛↸((a⊠≄⫣)⪨≂(b⇼⇔∾a))) , if a<=128 ; (((a⇼⇔∾b)⨁⊸⫻)⇼⇔∾((22⋳⪒a)⨰(a≧⫂∧a))) , else }', output=240","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯122310⪃↞⩐)⊋≦⊧⪩⨒∯202030⋓⪩⨒∯132212=⪩⨒∯3300","reverse_text":"⪩⨒∯3300=(⪩⨒∯122310⪃↞⩐)⊋≦⊧⪩⨒∯202030⋓⪩⨒∯132212","cot":[{"info":"⪩⨒∯122310⪃↞⩐=⪩⨒∯2211222","layer":1},{"info":"⪩⨒∯202030⋓⪩⨒∯132212=⪩⨒∯0","layer":1},{"info":"⪩⨒∯2211222⊋≦⊧⪩⨒∯0=⪩⨒∯3300","layer":0}]}
{"id":263,"expression_no_base_symbol":"(⫓⪴$3176$)⪄$4657$⇄$2135$","expression":"(⫓⪴⪩⨒∯301220)⪄⪩⨒∯1020301⇄⪩⨒∯201113","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3276,"operation_count":3,"complexity_ratio":1092.0,"tree":{"type":"binary","operator":"⪄","left_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":3176,"base":4}},"right_expr":{"type":"binary","operator":"⇄","left_expr":{"type":"numeric_atoms","value":4657,"base":4},"right_expr":{"type":"numeric_atoms","value":2135,"base":4}}},"used_operators":["SUmda5xLS4","eLxqMNBOBk","3EYGwJThht"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","9HNa5Wba9A","eLAdDNolq6","DZ8iAZOCBD","i8ToyICDmI"],"result":"⪩⨒∯-1120332311312321","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3176","layer":2},{"info":"compute unary expreesion, input=3176, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=10086976","layer":1},{"info":"number node, value=4657","layer":2},{"info":"number node, value=2135","layer":2},{"info":"compute binary expreesion, left_input=4657, right_input=2135, op_id = 3EYGwJThht binary_op_definition= 'a⇄b = { ((≤/b)∲⫓(a⊉≛↸b)) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=10086976, right_input=0, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-1492868537","layer":0}],"base":4,"result_base":4,"text":"(⫓⪴⪩⨒∯301220)⪄⪩⨒∯1020301⇄⪩⨒∯201113=⪩⨒∯-1120332311312321","reverse_text":"⪩⨒∯-1120332311312321=(⫓⪴⪩⨒∯301220)⪄⪩⨒∯1020301⇄⪩⨒∯201113","cot":[{"info":"⫓⪴⪩⨒∯301220=⪩⨒∯212132221000","layer":1},{"info":"⪩⨒∯1020301⇄⪩⨒∯201113=⪩⨒∯0","layer":1},{"info":"⪩⨒∯212132221000⪄⪩⨒∯0=⪩⨒∯-1120332311312321","layer":0}]}
{"id":264,"expression_no_base_symbol":"$4156$≀⩗∶$4306$↛⩡⫤","expression":"⪩⨒∯1000330≀⩗∶⪩⨒∯1003102↛⩡⫤","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":87,"operation_count":2,"complexity_ratio":43.5,"tree":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"binary","operator":"≀⩗∶","left_expr":{"type":"numeric_atoms","value":4156,"base":4},"right_expr":{"type":"numeric_atoms","value":4306,"base":4}}},"used_operators":["FU0Cs4j7VP","8INZBEW696"],"dependent_operators":["8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X","KPf6cnQVty","2DlMacCsIx","l07mrZUIn9"],"result":"⪩⨒∯3","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4156","layer":2},{"info":"number node, value=4306","layer":2},{"info":"compute binary expreesion, left_input=4156, right_input=4306, op_id = 8INZBEW696 binary_op_definition= 'a≀⩗∶b = { (a⩨b) , if (a∺≝⩲555)<251 ; (306↪⪝) , else }', output=-3","layer":1},{"info":"compute unary expreesion, input=-3, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=3","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1000330≀⩗∶⪩⨒∯1003102↛⩡⫤=⪩⨒∯3","reverse_text":"⪩⨒∯3=⪩⨒∯1000330≀⩗∶⪩⨒∯1003102↛⩡⫤","cot":[{"info":"⪩⨒∯1000330≀⩗∶⪩⨒∯1003102=⪩⨒∯-3","layer":1},{"info":"⪩⨒∯-3↛⩡⫤=⪩⨒∯3","layer":0}]}
{"id":265,"expression_no_base_symbol":"(⇘$5249$)⪎↠($4932$≓∲$1483$)","expression":"(⇘⪩⨒∯1102001)⪎↠(⪩⨒∯1031010≓∲⪩⨒∯113023)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":10604,"operation_count":3,"complexity_ratio":3534.6666666666665,"tree":{"type":"binary","operator":"⪎↠","left_expr":{"type":"unary","operator":"⇘","unary_expr":{"type":"numeric_atoms","value":5249,"base":4}},"right_expr":{"type":"binary","operator":"≓∲","left_expr":{"type":"numeric_atoms","value":4932,"base":4},"right_expr":{"type":"numeric_atoms","value":1483,"base":4}}},"used_operators":["3tVxb0NHM4","MGuIdZPyUC","s1XTVnmDOJ"],"dependent_operators":["P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM","eLxqMNBOBk","86A5ENbKR9","9HNa5Wba9A","E4l6HwMY31","40aOVDgCDB","bF6eod5Gvf","AFVx7xoS7T","f6k1SAg4EE","5twsqlHp2o","oacrs7FA3X","HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5249","layer":2},{"info":"compute unary expreesion, input=5249, op_id = MGuIdZPyUC, unary_op_definition = '⇘a = { (⪸((⫓⪴a)→⨶⪴(a⪘⫢a))) , if (⫓⪴a)>35 ; (((a*a)⊢)⊔((a⊢a)⇌⫙⪟(193⪒a))) , else }', output=309322","layer":1},{"info":"number node, value=4932","layer":2},{"info":"number node, value=1483","layer":2},{"info":"compute binary expreesion, left_input=4932, right_input=1483, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=50103","layer":1},{"info":"compute binary expreesion, left_input=309322, right_input=50103, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⇘⪩⨒∯1102001)⪎↠(⪩⨒∯1031010≓∲⪩⨒∯113023)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⇘⪩⨒∯1102001)⪎↠(⪩⨒∯1031010≓∲⪩⨒∯113023)","cot":[{"info":"⇘⪩⨒∯1102001=⪩⨒∯1023201022","layer":1},{"info":"⪩⨒∯1031010≓∲⪩⨒∯113023=⪩⨒∯30032313","layer":1},{"info":"⪩⨒∯1023201022⪎↠⪩⨒∯30032313=⪩⨒∯2200","layer":0}]}
{"id":266,"expression_no_base_symbol":"(⋼∭⪍$1730$)⪨≂(∂$1934$)","expression":"(⋼∭⪍⪩⨒∯123002)⪨≂(∂⪩⨒∯132032)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":17,"operation_count":3,"complexity_ratio":5.666666666666667,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"unary","operator":"⋼∭⪍","unary_expr":{"type":"numeric_atoms","value":1730,"base":4}},"right_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":1934,"base":4}}},"used_operators":["sdazOOVcIp","DbCuESL50I","Uaa54Peajs"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","e1ybzncUwg","sdazOOVcIp","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","u6S6b8DprG","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1730","layer":2},{"info":"compute unary expreesion, input=1730, op_id = DbCuESL50I, unary_op_definition = '⋼∭⪍a = { (≉((a∲⫓a)⪨≂(a⪒a))) , if (↽≂a)>481 ; (↽≂((↽≂435)≧⫂∧(↽≂a))) , else }', output=-5180","layer":1},{"info":"number node, value=1934","layer":2},{"info":"compute unary expreesion, input=1934, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-5180, right_input=nan, op_id = sdazOOVcIp binary_op_definition= 'a⪨≂b = { (((a-117)-b)-((145-b)-(a-a))) , if (-b)==187 ; ((-(b-102))-((b-a)-a)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⋼∭⪍⪩⨒∯123002)⪨≂(∂⪩⨒∯132032)=NaN","reverse_text":"NaN=(⋼∭⪍⪩⨒∯123002)⪨≂(∂⪩⨒∯132032)","cot":[{"info":"⋼∭⪍⪩⨒∯123002=⪩⨒∯-1100330","layer":1},{"info":"∂⪩⨒∯132032=NaN","layer":1},{"info":"⪩⨒∯-1100330⪨≂NaN=NaN","layer":0}]}
{"id":267,"expression_no_base_symbol":"(⊁⨺$1111$)⫰⋱$3939$⪪$1711$","expression":"(⊁⨺⪩⨒∯101113)⫰⋱⪩⨒∯331203⪪⪩⨒∯122233","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11970,"operation_count":3,"complexity_ratio":3990.0,"tree":{"type":"binary","operator":"⫰⋱","left_expr":{"type":"unary","operator":"⊁⨺","unary_expr":{"type":"numeric_atoms","value":1111,"base":4}},"right_expr":{"type":"binary","operator":"⪪","left_expr":{"type":"numeric_atoms","value":3939,"base":4},"right_expr":{"type":"numeric_atoms","value":1711,"base":4}}},"used_operators":["6o9Blt3TJ6","PxiHyQbrIp","xD69zh8xqp"],"dependent_operators":["W4YGzv6Whe","nCS4ZIUYfx","Qy55tPpLXF","rysDP5nf3Z","e1ybzncUwg","XPYlsWDdGa","23Mk6UjR3U","7j4O788W3g","2td37pGCOC","2DQ55sFlQl","xUOZtlo3hN","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","FU0Cs4j7VP","JclMnS0uGI"],"result":"⪩⨒∯2100033001","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1111","layer":2},{"info":"compute unary expreesion, input=1111, op_id = PxiHyQbrIp, unary_op_definition = '⊁⨺a = { (((⨞⊢a)⋷(3↺a))⨵⪆((⪲⇎a)-(≉a))) , if a>5 ; (((a↺a)⨳⩥⨓(⩦⩻⨪a))⨳⩥⨓((a∲⫓a)⫡⨏(≉a))) , else }', output=160","layer":1},{"info":"number node, value=3939","layer":2},{"info":"number node, value=1711","layer":2},{"info":"compute binary expreesion, left_input=3939, right_input=1711, op_id = xD69zh8xqp binary_op_definition= 'a⪪b = { ((b⨔⇊a)↛⩡⫤) }', output=-590878","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=-590878, op_id = 6o9Blt3TJ6 binary_op_definition= 'a⫰⋱b = { ((a+b)⨳⩥⨓(b⋥≓≎b)) }', output=590785","layer":0}],"base":4,"result_base":4,"text":"(⊁⨺⪩⨒∯101113)⫰⋱⪩⨒∯331203⪪⪩⨒∯122233=⪩⨒∯2100033001","reverse_text":"⪩⨒∯2100033001=(⊁⨺⪩⨒∯101113)⫰⋱⪩⨒∯331203⪪⪩⨒∯122233","cot":[{"info":"⊁⨺⪩⨒∯101113=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯331203⪪⪩⨒∯122233=⪩⨒∯-2100100132","layer":1},{"info":"⪩⨒∯2200⫰⋱⪩⨒∯-2100100132=⪩⨒∯2100033001","layer":0}]}
{"id":268,"expression_no_base_symbol":"$1606$⨜⨶$2021$↙($2675$⪗)","expression":"⪩⨒∯121012⨜⨶⪩⨒∯133211↙(⪩⨒∯221303⪗)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2701,"operation_count":3,"complexity_ratio":900.3333333333334,"tree":{"type":"binary","operator":"↙","left_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":1606,"base":4},"right_expr":{"type":"numeric_atoms","value":2021,"base":4}},"right_expr":{"type":"unary","operator":"⪗","unary_expr":{"type":"numeric_atoms","value":2675,"base":4}}},"used_operators":["yyfyN0ffXY","HiPekx5b7W","VEQNXA0ZBg"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","dWAJyo7jo9"],"result":"⪩⨒∯-323022","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1606","layer":2},{"info":"number node, value=2021","layer":2},{"info":"compute binary expreesion, left_input=1606, right_input=2021, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-3786","layer":1},{"info":"number node, value=2675","layer":2},{"info":"compute unary expreesion, input=2675, op_id = VEQNXA0ZBg, unary_op_definition = 'a⪗ = { (a⪢a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-3786, right_input=nan, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-3786","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯121012⨜⨶⪩⨒∯133211↙(⪩⨒∯221303⪗)=⪩⨒∯-323022","reverse_text":"⪩⨒∯-323022=⪩⨒∯121012⨜⨶⪩⨒∯133211↙(⪩⨒∯221303⪗)","cot":[{"info":"⪩⨒∯121012⨜⨶⪩⨒∯133211=⪩⨒∯-323022","layer":1},{"info":"⪩⨒∯221303⪗=NaN","layer":1},{"info":"⪩⨒∯-323022↙NaN=⪩⨒∯-323022","layer":0}]}
{"id":269,"expression_no_base_symbol":"($3782$⨽$1015$)⨸($3775$⋻⩜⩜$2350$)","expression":"(⪩⨒∯323012⨽⪩⨒∯33313)⨸(⪩⨒∯322333⋻⩜⩜⪩⨒∯210232)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":36809,"operation_count":3,"complexity_ratio":12269.666666666666,"tree":{"type":"binary","operator":"⨸","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":3782,"base":4},"right_expr":{"type":"numeric_atoms","value":1015,"base":4}},"right_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":3775,"base":4},"right_expr":{"type":"numeric_atoms","value":2350,"base":4}}},"used_operators":["KmoU8R5UQR","8HhzD0ZcuI","oDCm7WA9JY"],"dependent_operators":["ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3782","layer":2},{"info":"number node, value=1015","layer":2},{"info":"compute binary expreesion, left_input=3782, right_input=1015, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-42912303","layer":1},{"info":"number node, value=3775","layer":2},{"info":"number node, value=2350","layer":2},{"info":"compute binary expreesion, left_input=3775, right_input=2350, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=7550","layer":1},{"info":"compute binary expreesion, left_input=-42912303, right_input=7550, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯323012⨽⪩⨒∯33313)⨸(⪩⨒∯322333⋻⩜⩜⪩⨒∯210232)=NaN","reverse_text":"NaN=(⪩⨒∯323012⨽⪩⨒∯33313)⨸(⪩⨒∯322333⋻⩜⩜⪩⨒∯210232)","cot":[{"info":"⪩⨒∯323012⨽⪩⨒∯33313=⪩⨒∯-2203230220233","layer":1},{"info":"⪩⨒∯322333⋻⩜⩜⪩⨒∯210232=⪩⨒∯1311332","layer":1},{"info":"⪩⨒∯-2203230220233⨸⪩⨒∯1311332=NaN","layer":0}]}
{"id":270,"expression_no_base_symbol":"⇁⨣⪵$1207$⋥≓≎$1175$","expression":"⇁⨣⪵⪩⨒∯102313⋥≓≎⪩⨒∯102113","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5,"operation_count":2,"complexity_ratio":2.5,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":1207,"base":4},"right_expr":{"type":"numeric_atoms","value":1175,"base":4}}},"used_operators":["inkyxCbjAn","Qy55tPpLXF"],"dependent_operators":["B5M0gjZbta","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1207","layer":2},{"info":"number node, value=1175","layer":2},{"info":"compute binary expreesion, left_input=1207, right_input=1175, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=1176","layer":1},{"info":"compute unary expreesion, input=1176, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇁⨣⪵⪩⨒∯102313⋥≓≎⪩⨒∯102113=NaN","reverse_text":"NaN=⇁⨣⪵⪩⨒∯102313⋥≓≎⪩⨒∯102113","cot":[{"info":"⪩⨒∯102313⋥≓≎⪩⨒∯102113=⪩⨒∯102120","layer":1},{"info":"⇁⨣⪵⪩⨒∯102120=NaN","layer":0}]}
{"id":271,"expression_no_base_symbol":"$7527$⪔⊥$6462$≬⋮$7365$⋕⪉⪜$3459$","expression":"⪩⨒∯1311213⪔⊥⪩⨒∯1210332≬⋮⪩⨒∯1303011⋕⪉⪜⪩⨒∯312003","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":60,"operation_count":3,"complexity_ratio":20.0,"tree":{"type":"binary","operator":"≬⋮","left_expr":{"type":"binary","operator":"⪔⊥","left_expr":{"type":"numeric_atoms","value":7527,"base":4},"right_expr":{"type":"numeric_atoms","value":6462,"base":4}},"right_expr":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"numeric_atoms","value":7365,"base":4},"right_expr":{"type":"numeric_atoms","value":3459,"base":4}}},"used_operators":["kbkesczE7y","HJ9erzHUuu","z6LnFrNh4i"],"dependent_operators":["P8v4zCKN1o","rysDP5nf3Z","7j4O788W3g","XIabStNQrY","t8gj7n24qd","i8ToyICDmI","eLAdDNolq6","rysDP5nf3Z","7j4O788W3g","tifHPKVTfV","8w2t5hMYqp","sdazOOVcIp","2td37pGCOC","COABgblf1C","sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z"],"result":"⪩⨒∯31210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7527","layer":2},{"info":"number node, value=6462","layer":2},{"info":"compute binary expreesion, left_input=7527, right_input=6462, op_id = HJ9erzHUuu binary_op_definition= 'a⪔⊥b = { (⩦⩻⨪(≤/(315⇼⇔∾a))) , if b<175 ; ((⊄⩳↩(b-b))⇼⇔∾((b⪨≂a)⊭↱(a↺b))) , else }', output=16985","layer":1},{"info":"number node, value=7365","layer":2},{"info":"number node, value=3459","layer":2},{"info":"compute binary expreesion, left_input=7365, right_input=3459, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=2802","layer":1},{"info":"compute binary expreesion, left_input=16985, right_input=2802, op_id = kbkesczE7y binary_op_definition= 'a≬⋮b = { (((-a)∲⫓(b⇋≉))↺(∥⊫(b-b))) }', output=868","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1311213⪔⊥⪩⨒∯1210332≬⋮⪩⨒∯1303011⋕⪉⪜⪩⨒∯312003=⪩⨒∯31210","reverse_text":"⪩⨒∯31210=⪩⨒∯1311213⪔⊥⪩⨒∯1210332≬⋮⪩⨒∯1303011⋕⪉⪜⪩⨒∯312003","cot":[{"info":"⪩⨒∯1311213⪔⊥⪩⨒∯1210332=⪩⨒∯10021121","layer":1},{"info":"⪩⨒∯1303011⋕⪉⪜⪩⨒∯312003=⪩⨒∯223302","layer":1},{"info":"⪩⨒∯10021121≬⋮⪩⨒∯223302=⪩⨒∯31210","layer":0}]}
{"id":272,"expression_no_base_symbol":"⇖⫷⫕($1815$⪉⨛$1065$)","expression":"⇖⫷⫕(⪩⨒∯130113⪉⨛⪩⨒∯100221)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":819,"operation_count":2,"complexity_ratio":409.5,"tree":{"type":"unary","operator":"⇖⫷⫕","unary_expr":{"type":"binary","operator":"⪉⨛","left_expr":{"type":"numeric_atoms","value":1815,"base":4},"right_expr":{"type":"numeric_atoms","value":1065,"base":4}}},"used_operators":["UHmRx3INFg","EWw2JM7wp4"],"dependent_operators":["DE7zCoGJt9","FyVja0WsTP","oZj3VtZNQx","DyGG3AbaNP","NTOWxs364D","tifHPKVTfV","12rbrZMWeM","i8ToyICDmI","eewbuw0ToL"],"result":"⪩⨒∯230012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1815","layer":2},{"info":"number node, value=1065","layer":2},{"info":"compute binary expreesion, left_input=1815, right_input=1065, op_id = EWw2JM7wp4 binary_op_definition= 'a⪉⨛b = { (((82⇼⇔∾a)⩚⊴⇥a)⩚⊴⇥((b∲⫓a)⋳⪒(a⨰b))) }', output=4595","layer":1},{"info":"compute unary expreesion, input=4595, op_id = UHmRx3INFg, unary_op_definition = '⇖⫷⫕a = { ((a∼125)≀⫉(↞≼(a⊱⇼⊻51))) }', output=2822","layer":0}],"base":4,"result_base":4,"text":"⇖⫷⫕(⪩⨒∯130113⪉⨛⪩⨒∯100221)=⪩⨒∯230012","reverse_text":"⪩⨒∯230012=⇖⫷⫕(⪩⨒∯130113⪉⨛⪩⨒∯100221)","cot":[{"info":"⪩⨒∯130113⪉⨛⪩⨒∯100221=⪩⨒∯1013303","layer":1},{"info":"⇖⫷⫕⪩⨒∯1013303=⪩⨒∯230012","layer":0}]}
{"id":273,"expression_no_base_symbol":"$1357$⨪↰⇹$6928$≃($3663$⋅⇍$1093$)","expression":"⪩⨒∯111031⨪↰⇹⪩⨒∯1230100≃(⪩⨒∯321033⋅⇍⪩⨒∯101011)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1379,"operation_count":3,"complexity_ratio":459.6666666666667,"tree":{"type":"binary","operator":"≃","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":1357,"base":4},"right_expr":{"type":"numeric_atoms","value":6928,"base":4}},"right_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":3663,"base":4},"right_expr":{"type":"numeric_atoms","value":1093,"base":4}}},"used_operators":["YbVcJGFEVW","tmPS8pqC7x","AdZkA7nFnk"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","23Mk6UjR3U","JLbD19bQDL","7j4O788W3g","glklzrTFfD","tifHPKVTfV","t8gj7n24qd","i8ToyICDmI","COABgblf1C","rJVOvQCfKK","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6"],"result":"⪩⨒∯300","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1357","layer":2},{"info":"number node, value=6928","layer":2},{"info":"compute binary expreesion, left_input=1357, right_input=6928, op_id = tmPS8pqC7x binary_op_definition= 'a⨪↰⇹b = {a, if a == 0; (b)⨎((a-1)⨪↰⇹b), if a > 0 and abs(a) < 1000000; -(b)⨎((a+1)⨪↰⇹b), if a < 0 and abs(a) < 1000000; NaN, else}', output=1357","layer":1},{"info":"number node, value=3663","layer":2},{"info":"number node, value=1093","layer":2},{"info":"compute binary expreesion, left_input=3663, right_input=1093, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"compute binary expreesion, left_input=1357, right_input=-22, op_id = YbVcJGFEVW binary_op_definition= 'a≃b = { (((13⋥≓≎b)⋷(a⇼⇔∾b))⨁⊸⫻) , if ((b⨁⊸⫻)>=162 or (b⪠⩆⊳)<=569) ; ((-(17⋷a))↺((a⩷∴a)⊭↱(b∲⫓a))) , else }', output=48","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯111031⨪↰⇹⪩⨒∯1230100≃(⪩⨒∯321033⋅⇍⪩⨒∯101011)=⪩⨒∯300","reverse_text":"⪩⨒∯300=⪩⨒∯111031⨪↰⇹⪩⨒∯1230100≃(⪩⨒∯321033⋅⇍⪩⨒∯101011)","cot":[{"info":"⪩⨒∯111031⨪↰⇹⪩⨒∯1230100=⪩⨒∯111031","layer":1},{"info":"⪩⨒∯321033⋅⇍⪩⨒∯101011=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯111031≃⪩⨒∯-112=⪩⨒∯300","layer":0}]}
{"id":274,"expression_no_base_symbol":"⨣⨃⇪(≯$4744$)","expression":"⨣⨃⇪(≯⪩⨒∯1022020)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":23,"operation_count":2,"complexity_ratio":11.5,"tree":{"type":"unary","operator":"⨣⨃⇪","unary_expr":{"type":"unary","operator":"≯","unary_expr":{"type":"numeric_atoms","value":4744,"base":4}}},"used_operators":["AcOhelriW5","keWfFq85dY"],"dependent_operators":["s3Fd5m9Dh2","liw5iZPkLH","yyfyN0ffXY","g55IO6H4Gj","JLbD19bQDL"],"result":"⪩⨒∯111331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4744","layer":2},{"info":"compute unary expreesion, input=4744, op_id = keWfFq85dY, unary_op_definition = '≯a = { ((a⨸⪁a)⪠⩆⊳) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = AcOhelriW5, unary_op_definition = '⨣⨃⇪a = { (⨡↴(172⊬⨰(3↙a))) }', output=1405","layer":0}],"base":4,"result_base":4,"text":"⨣⨃⇪(≯⪩⨒∯1022020)=⪩⨒∯111331","reverse_text":"⪩⨒∯111331=⨣⨃⇪(≯⪩⨒∯1022020)","cot":[{"info":"≯⪩⨒∯1022020=⪩⨒∯0","layer":1},{"info":"⨣⨃⇪⪩⨒∯0=⪩⨒∯111331","layer":0}]}
{"id":275,"expression_no_base_symbol":"($4736$∛$2576$)∘($1955$⨎$2736$)","expression":"(⪩⨒∯1022000∛⪩⨒∯220100)∘(⪩⨒∯132203⨎⪩⨒∯222300)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":99,"operation_count":3,"complexity_ratio":33.0,"tree":{"type":"binary","operator":"∘","left_expr":{"type":"binary","operator":"∛","left_expr":{"type":"numeric_atoms","value":4736,"base":4},"right_expr":{"type":"numeric_atoms","value":2576,"base":4}},"right_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":1955,"base":4},"right_expr":{"type":"numeric_atoms","value":2736,"base":4}}},"used_operators":["Z5m6OM72h2","w2537kitQq","rJVOvQCfKK"],"dependent_operators":["eH2TOUuTDT","rysDP5nf3Z","DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"⪩⨒∯-110330","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4736","layer":2},{"info":"number node, value=2576","layer":2},{"info":"compute binary expreesion, left_input=4736, right_input=2576, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=-670","layer":1},{"info":"number node, value=1955","layer":2},{"info":"number node, value=2736","layer":2},{"info":"compute binary expreesion, left_input=1955, right_input=2736, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=2736","layer":1},{"info":"compute binary expreesion, left_input=-670, right_input=2736, op_id = Z5m6OM72h2 binary_op_definition= 'a∘b = { (380-a) , if b<=483 ; (a⪐) , else }', output=-1340","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1022000∛⪩⨒∯220100)∘(⪩⨒∯132203⨎⪩⨒∯222300)=⪩⨒∯-110330","reverse_text":"⪩⨒∯-110330=(⪩⨒∯1022000∛⪩⨒∯220100)∘(⪩⨒∯132203⨎⪩⨒∯222300)","cot":[{"info":"⪩⨒∯1022000∛⪩⨒∯220100=⪩⨒∯-22132","layer":1},{"info":"⪩⨒∯132203⨎⪩⨒∯222300=⪩⨒∯222300","layer":1},{"info":"⪩⨒∯-22132∘⪩⨒∯222300=⪩⨒∯-110330","layer":0}]}
{"id":276,"expression_no_base_symbol":"$1092$∛$2671$⪔($1318$⨸⪁$4092$)","expression":"⪩⨒∯101010∛⪩⨒∯221233⪔(⪩⨒∯110212⨸⪁⪩⨒∯333330)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11002,"operation_count":3,"complexity_ratio":3667.3333333333335,"tree":{"type":"binary","operator":"⪔","left_expr":{"type":"binary","operator":"∛","left_expr":{"type":"numeric_atoms","value":1092,"base":4},"right_expr":{"type":"numeric_atoms","value":2671,"base":4}},"right_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":1318,"base":4},"right_expr":{"type":"numeric_atoms","value":4092,"base":4}}},"used_operators":["GjBEYRfMaF","w2537kitQq","g55IO6H4Gj"],"dependent_operators":["YjI8oCXuph","8INZBEW696","dWAJyo7jo9","nREPSIbpBE","2DDjHMKMc0","IWmyXbctLI","PoHhknlbAi","DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc","W4YGzv6Whe"],"result":"⪩⨒∯13002","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1092","layer":2},{"info":"number node, value=2671","layer":2},{"info":"compute binary expreesion, left_input=1092, right_input=2671, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=-670","layer":1},{"info":"number node, value=1318","layer":2},{"info":"number node, value=4092","layer":2},{"info":"compute binary expreesion, left_input=1318, right_input=4092, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=10820","layer":1},{"info":"compute binary expreesion, left_input=-670, right_input=10820, op_id = GjBEYRfMaF binary_op_definition= 'a⪔b = { (((⫇a)∓⋝(61⪢b))⪮%⊝((b⋝⋈⪟b)⨚(a≀⩗∶a))) }', output=450","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯101010∛⪩⨒∯221233⪔(⪩⨒∯110212⨸⪁⪩⨒∯333330)=⪩⨒∯13002","reverse_text":"⪩⨒∯13002=⪩⨒∯101010∛⪩⨒∯221233⪔(⪩⨒∯110212⨸⪁⪩⨒∯333330)","cot":[{"info":"⪩⨒∯101010∛⪩⨒∯221233=⪩⨒∯-22132","layer":1},{"info":"⪩⨒∯110212⨸⪁⪩⨒∯333330=⪩⨒∯2221010","layer":1},{"info":"⪩⨒∯-22132⪔⪩⨒∯2221010=⪩⨒∯13002","layer":0}]}
{"id":277,"expression_no_base_symbol":"$2503$⩌⋺$2305$⊴$1626$⨂≜$1446$","expression":"⪩⨒∯213013⩌⋺⪩⨒∯210001⊴⪩⨒∯121122⨂≜⪩⨒∯112212","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1673,"operation_count":3,"complexity_ratio":557.6666666666666,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"⩌⋺","left_expr":{"type":"numeric_atoms","value":2503,"base":4},"right_expr":{"type":"numeric_atoms","value":2305,"base":4}},"right_expr":{"type":"binary","operator":"⨂≜","left_expr":{"type":"numeric_atoms","value":1626,"base":4},"right_expr":{"type":"numeric_atoms","value":1446,"base":4}}},"used_operators":["Nsiff2A1zJ","g7Hmc5v1ko","k1SHOSEABc"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","9FxExcQeMw","W4YGzv6Whe","NTOWxs364D","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","i8ToyICDmI","QMFrweE19q","9FxExcQeMw","HiPekx5b7W","eLxqMNBOBk","JclMnS0uGI","COABgblf1C","U7g4x0WXJJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2503","layer":2},{"info":"number node, value=2305","layer":2},{"info":"compute binary expreesion, left_input=2503, right_input=2305, op_id = g7Hmc5v1ko binary_op_definition= 'a⩌⋺b = { ((⨞⊢(b⨵⪆b))∲⫓((a⪨≂b)⪨≂(b⩷∴919))) , if (b⫡⨏102)>364 and (-b)==524 ; (b⇼⇔∾((a+a)⩚⊴⇥(-a))) , else }', output=-4929","layer":1},{"info":"number node, value=1626","layer":2},{"info":"number node, value=1446","layer":2},{"info":"compute binary expreesion, left_input=1626, right_input=1446, op_id = k1SHOSEABc binary_op_definition= 'a⨂≜b = { ((37⊭↱(⫓⪴a))⩷∴((111⨜⨶78)⨔⇊(a∑⇟⊟b))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-4929, right_input=nan, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯213013⩌⋺⪩⨒∯210001⊴⪩⨒∯121122⨂≜⪩⨒∯112212=NaN","reverse_text":"NaN=⪩⨒∯213013⩌⋺⪩⨒∯210001⊴⪩⨒∯121122⨂≜⪩⨒∯112212","cot":[{"info":"⪩⨒∯213013⩌⋺⪩⨒∯210001=⪩⨒∯-1031001","layer":1},{"info":"⪩⨒∯121122⨂≜⪩⨒∯112212=NaN","layer":1},{"info":"⪩⨒∯-1031001⊴NaN=NaN","layer":0}]}
{"id":278,"expression_no_base_symbol":"↥≼⋛$1565$⨰$1320$","expression":"↥≼⋛⪩⨒∯120131⨰⪩⨒∯110220","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":15,"operation_count":2,"complexity_ratio":7.5,"tree":{"type":"unary","operator":"↥≼⋛","unary_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":1565,"base":4},"right_expr":{"type":"numeric_atoms","value":1320,"base":4}}},"used_operators":["x5lMkHmzsq","eewbuw0ToL"],"dependent_operators":["eLAdDNolq6","9FxExcQeMw","Qy55tPpLXF","7j4O788W3g","Z2TMIBDE3Q","nCS4ZIUYfx","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-1301","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1565","layer":2},{"info":"number node, value=1320","layer":2},{"info":"compute binary expreesion, left_input=1565, right_input=1320, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=255","layer":1},{"info":"compute unary expreesion, input=255, op_id = x5lMkHmzsq, unary_op_definition = '↥≼⋛a = { ((a⩤)⋥≓≎(a⨳⩥⨓a)) , if a<111 ; ((a⩷∴285)↺(≤/597)) , else }', output=-113","layer":0}],"base":4,"result_base":4,"text":"↥≼⋛⪩⨒∯120131⨰⪩⨒∯110220=⪩⨒∯-1301","reverse_text":"⪩⨒∯-1301=↥≼⋛⪩⨒∯120131⨰⪩⨒∯110220","cot":[{"info":"⪩⨒∯120131⨰⪩⨒∯110220=⪩⨒∯3333","layer":1},{"info":"↥≼⋛⪩⨒∯3333=⪩⨒∯-1301","layer":0}]}
{"id":279,"expression_no_base_symbol":"($2295$⨸⪁$7411$)⨰($3235$⋫)","expression":"(⪩⨒∯203313⨸⪁⪩⨒∯1303303)⨰(⪩⨒∯302203⋫)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3244,"operation_count":3,"complexity_ratio":1081.3333333333333,"tree":{"type":"binary","operator":"⨰","left_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":2295,"base":4},"right_expr":{"type":"numeric_atoms","value":7411,"base":4}},"right_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":3235,"base":4}}},"used_operators":["eewbuw0ToL","g55IO6H4Gj","JL8yIekQnl"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","tmPS8pqC7x"],"result":"⪩⨒∯3330323","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2295","layer":2},{"info":"number node, value=7411","layer":2},{"info":"compute binary expreesion, left_input=2295, right_input=7411, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=19412","layer":1},{"info":"number node, value=3235","layer":2},{"info":"compute unary expreesion, input=3235, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=3235","layer":1},{"info":"compute binary expreesion, left_input=19412, right_input=3235, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=16187","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯203313⨸⪁⪩⨒∯1303303)⨰(⪩⨒∯302203⋫)=⪩⨒∯3330323","reverse_text":"⪩⨒∯3330323=(⪩⨒∯203313⨸⪁⪩⨒∯1303303)⨰(⪩⨒∯302203⋫)","cot":[{"info":"⪩⨒∯203313⨸⪁⪩⨒∯1303303=⪩⨒∯10233110","layer":1},{"info":"⪩⨒∯302203⋫=⪩⨒∯302203","layer":1},{"info":"⪩⨒∯10233110⨰⪩⨒∯302203=⪩⨒∯3330323","layer":0}]}
{"id":280,"expression_no_base_symbol":"⇨$1667$⋕⪉⪜$6236$","expression":"⇨⪩⨒∯122003⋕⪉⪜⪩⨒∯1201130","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":27,"operation_count":2,"complexity_ratio":13.5,"tree":{"type":"unary","operator":"⇨","unary_expr":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"numeric_atoms","value":1667,"base":4},"right_expr":{"type":"numeric_atoms","value":6236,"base":4}}},"used_operators":["G9tJMlZ94a","z6LnFrNh4i"],"dependent_operators":["k8jYdgA6NY","sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1667","layer":2},{"info":"number node, value=6236","layer":2},{"info":"compute binary expreesion, left_input=1667, right_input=6236, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=204","layer":1},{"info":"compute unary expreesion, input=204, op_id = G9tJMlZ94a, unary_op_definition = '⇨a = { (a%a) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⇨⪩⨒∯122003⋕⪉⪜⪩⨒∯1201130=⪩⨒∯0","reverse_text":"⪩⨒∯0=⇨⪩⨒∯122003⋕⪉⪜⪩⨒∯1201130","cot":[{"info":"⪩⨒∯122003⋕⪉⪜⪩⨒∯1201130=⪩⨒∯3030","layer":1},{"info":"⇨⪩⨒∯3030=⪩⨒∯0","layer":0}]}
{"id":281,"expression_no_base_symbol":"$3316$⩵∡$3061$+$2741$≒∊$6007$","expression":"⪩⨒∯303310⩵∡⪩⨒∯233311+⪩⨒∯222311≒∊⪩⨒∯1131313","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":14,"operation_count":3,"complexity_ratio":4.666666666666667,"tree":{"type":"binary","operator":"+","left_expr":{"type":"binary","operator":"⩵∡","left_expr":{"type":"numeric_atoms","value":3316,"base":4},"right_expr":{"type":"numeric_atoms","value":3061,"base":4}},"right_expr":{"type":"binary","operator":"≒∊","left_expr":{"type":"numeric_atoms","value":2741,"base":4},"right_expr":{"type":"numeric_atoms","value":6007,"base":4}}},"used_operators":["W4YGzv6Whe","Y7wcNGrDQJ","5KTvxBwnZo"],"dependent_operators":["NTOWxs364D","glklzrTFfD","tifHPKVTfV","3EYGwJThht","dWAJyo7jo9","Z2TMIBDE3Q","bjFbhXSADs","3DZMoQKiUl"],"result":"⪩⨒∯-1130331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3316","layer":2},{"info":"number node, value=3061","layer":2},{"info":"compute binary expreesion, left_input=3316, right_input=3061, op_id = Y7wcNGrDQJ binary_op_definition= 'a⩵∡b = { ((b⇼⇔∾a)⩚⊴⇥(a⨁⊸⫻)) }', output=-3692","layer":1},{"info":"number node, value=2741","layer":2},{"info":"number node, value=6007","layer":2},{"info":"compute binary expreesion, left_input=2741, right_input=6007, op_id = 5KTvxBwnZo binary_op_definition= 'a≒∊b = { (≱⇩⩕(a⪢a)) , if (a⩤)==117 ; ((b⪊≅)⇄a) , else }', output=-2257","layer":1},{"info":"compute binary expreesion, left_input=-3692, right_input=-2257, op_id = W4YGzv6Whe binary_op_definition= 'None', output=-5949","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯303310⩵∡⪩⨒∯233311+⪩⨒∯222311≒∊⪩⨒∯1131313=⪩⨒∯-1130331","reverse_text":"⪩⨒∯-1130331=⪩⨒∯303310⩵∡⪩⨒∯233311+⪩⨒∯222311≒∊⪩⨒∯1131313","cot":[{"info":"⪩⨒∯303310⩵∡⪩⨒∯233311=⪩⨒∯-321230","layer":1},{"info":"⪩⨒∯222311≒∊⪩⨒∯1131313=⪩⨒∯-203101","layer":1},{"info":"⪩⨒∯-321230+⪩⨒∯-203101=⪩⨒∯-1130331","layer":0}]}
{"id":282,"expression_no_base_symbol":"(⪓⩚$4025$)↹⊜(≑⋹$3519$)","expression":"(⪓⩚⪩⨒∯332321)↹⊜(≑⋹⪩⨒∯312333)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3494,"operation_count":3,"complexity_ratio":1164.6666666666667,"tree":{"type":"binary","operator":"↹⊜","left_expr":{"type":"unary","operator":"⪓⩚","unary_expr":{"type":"numeric_atoms","value":4025,"base":4}},"right_expr":{"type":"unary","operator":"≑⋹","unary_expr":{"type":"numeric_atoms","value":3519,"base":4}}},"used_operators":["9bazX3JMtO","u0R0Locfp2","6B9nyZLogK"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","23Mk6UjR3U","tifHPKVTfV","eH2TOUuTDT","DIvbN7qnHd","6o9Blt3TJ6","mp7IySMOzn","Nsiff2A1zJ","aBQ6xLxuTc","zR4jO40bMj","RabNbG55vr","ocnLzx9CaJ","3ViojmjbAp","FlXk3pOYe8","o20kRiQErp","4JB6nKBMSY","2td37pGCOC","COABgblf1C"],"result":"⪩⨒∯-3033300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4025","layer":2},{"info":"compute unary expreesion, input=4025, op_id = u0R0Locfp2, unary_op_definition = '⪓⩚a = { (a⫰⋱a) , if (a⊴910)>461 ; (240⇷213) , else }', output=426","layer":1},{"info":"number node, value=3519","layer":2},{"info":"compute unary expreesion, input=3519, op_id = 6B9nyZLogK, unary_op_definition = '≑⋹a = { (((a⨓a)⫣⪄⊒(148∸))⇴(⩦⩻⨪(a⇂≾⫗a))) , if a<188 ; (⩎⋉((a⩼⇪↪a)⊭↱(a⪶≀⋏172))) , else }', output=1650","layer":1},{"info":"compute binary expreesion, left_input=426, right_input=1650, op_id = 9bazX3JMtO binary_op_definition= 'a↹⊜b = { (((a⊠≄⫣)⩷∴(b-a))⩷∴((a⋷b)⇼⇔∾(b⪐))) }', output=-13296","layer":0}],"base":4,"result_base":4,"text":"(⪓⩚⪩⨒∯332321)↹⊜(≑⋹⪩⨒∯312333)=⪩⨒∯-3033300","reverse_text":"⪩⨒∯-3033300=(⪓⩚⪩⨒∯332321)↹⊜(≑⋹⪩⨒∯312333)","cot":[{"info":"⪓⩚⪩⨒∯332321=⪩⨒∯12222","layer":1},{"info":"≑⋹⪩⨒∯312333=⪩⨒∯121302","layer":1},{"info":"⪩⨒∯12222↹⊜⪩⨒∯121302=⪩⨒∯-3033300","layer":0}]}
{"id":283,"expression_no_base_symbol":"(⇐$1011$)⊭↱$3958$∺≝⩲$2888$","expression":"(⇐⪩⨒∯33303)⊭↱⪩⨒∯331312∺≝⩲⪩⨒∯231020","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":66,"operation_count":3,"complexity_ratio":22.0,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"unary","operator":"⇐","unary_expr":{"type":"numeric_atoms","value":1011,"base":4}},"right_expr":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"numeric_atoms","value":3958,"base":4},"right_expr":{"type":"numeric_atoms","value":2888,"base":4}}},"used_operators":["COABgblf1C","nmZMaaE0Q9","KPf6cnQVty"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","23Mk6UjR3U","ocnLzx9CaJ","SWo3A1KBJH","nREPSIbpBE","k8jYdgA6NY","u6S6b8DprG","BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl"],"result":"⪩⨒∯-321103","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1011","layer":2},{"info":"compute unary expreesion, input=1011, op_id = nmZMaaE0Q9, unary_op_definition = '⇐a = { (((⇋↷a)⋷(a⩼⇪↪a))%(↽≂(a⨚a))) }', output=1996","layer":1},{"info":"number node, value=3958","layer":2},{"info":"number node, value=2888","layer":2},{"info":"compute binary expreesion, left_input=3958, right_input=2888, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=1996, right_input=160, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-3667","layer":0}],"base":4,"result_base":4,"text":"(⇐⪩⨒∯33303)⊭↱⪩⨒∯331312∺≝⩲⪩⨒∯231020=⪩⨒∯-321103","reverse_text":"⪩⨒∯-321103=(⇐⪩⨒∯33303)⊭↱⪩⨒∯331312∺≝⩲⪩⨒∯231020","cot":[{"info":"⇐⪩⨒∯33303=⪩⨒∯133030","layer":1},{"info":"⪩⨒∯331312∺≝⩲⪩⨒∯231020=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯133030⊭↱⪩⨒∯2200=⪩⨒∯-321103","layer":0}]}
{"id":284,"expression_no_base_symbol":"($3222$+⪬∐$1204$)⪣⫩","expression":"(⪩⨒∯302112+⪬∐⪩⨒∯102310)⪣⫩","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7,"operation_count":2,"complexity_ratio":3.5,"tree":{"type":"unary","operator":"⪣⫩","unary_expr":{"type":"binary","operator":"+⪬∐","left_expr":{"type":"numeric_atoms","value":3222,"base":4},"right_expr":{"type":"numeric_atoms","value":1204,"base":4}}},"used_operators":["iuk5sVOGFA","2GS7woTJqF"],"dependent_operators":["W4YGzv6Whe","Qy55tPpLXF","XPYlsWDdGa","23Mk6UjR3U","Ph9nP6C5qx","i8ToyICDmI","g55IO6H4Gj","D4vGDi5EA2"],"result":"⪩⨒∯32101","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3222","layer":2},{"info":"number node, value=1204","layer":2},{"info":"compute binary expreesion, left_input=3222, right_input=1204, op_id = 2GS7woTJqF binary_op_definition= 'a+⪬∐b = { (a≦≮≮) , if b!=63 ; (b⨸⪁575) , else }', output=-9666","layer":1},{"info":"compute unary expreesion, input=-9666, op_id = iuk5sVOGFA, unary_op_definition = 'a⪣⫩ = { ((a⋥≓≎a)⋷(a+a)) , if a>=275 ; ((a∲⫓a)≧⫂∧(⪲⇎693)) , else }', output=913","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯302112+⪬∐⪩⨒∯102310)⪣⫩=⪩⨒∯32101","reverse_text":"⪩⨒∯32101=(⪩⨒∯302112+⪬∐⪩⨒∯102310)⪣⫩","cot":[{"info":"⪩⨒∯302112+⪬∐⪩⨒∯102310=⪩⨒∯-2113002","layer":1},{"info":"⪩⨒∯-2113002⪣⫩=⪩⨒∯32101","layer":0}]}
{"id":285,"expression_no_base_symbol":"($2066$/$1258$)⩵∡$2848$∛$1535$","expression":"(⪩⨒∯200102/⪩⨒∯103222)⩵∡⪩⨒∯230200∛⪩⨒∯113333","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":78,"operation_count":3,"complexity_ratio":26.0,"tree":{"type":"binary","operator":"⩵∡","left_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":2066,"base":4},"right_expr":{"type":"numeric_atoms","value":1258,"base":4}},"right_expr":{"type":"binary","operator":"∛","left_expr":{"type":"numeric_atoms","value":2848,"base":4},"right_expr":{"type":"numeric_atoms","value":1535,"base":4}}},"used_operators":["Y7wcNGrDQJ","XhwjNDsVaA","w2537kitQq"],"dependent_operators":["NTOWxs364D","glklzrTFfD","tifHPKVTfV","rysDP5nf3Z","DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc"],"result":"⪩⨒∯-321","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2066","layer":2},{"info":"number node, value=1258","layer":2},{"info":"compute binary expreesion, left_input=2066, right_input=1258, op_id = XhwjNDsVaA binary_op_definition= 'None', output=1","layer":1},{"info":"number node, value=2848","layer":2},{"info":"number node, value=1535","layer":2},{"info":"compute binary expreesion, left_input=2848, right_input=1535, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=67","layer":1},{"info":"compute binary expreesion, left_input=1, right_input=67, op_id = Y7wcNGrDQJ binary_op_definition= 'a⩵∡b = { ((b⇼⇔∾a)⩚⊴⇥(a⨁⊸⫻)) }', output=-57","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯200102/⪩⨒∯103222)⩵∡⪩⨒∯230200∛⪩⨒∯113333=⪩⨒∯-321","reverse_text":"⪩⨒∯-321=(⪩⨒∯200102/⪩⨒∯103222)⩵∡⪩⨒∯230200∛⪩⨒∯113333","cot":[{"info":"⪩⨒∯200102/⪩⨒∯103222=⪩⨒∯1","layer":1},{"info":"⪩⨒∯230200∛⪩⨒∯113333=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯1⩵∡⪩⨒∯1003=⪩⨒∯-321","layer":0}]}
{"id":286,"expression_no_base_symbol":"($1553$⫳≱↱$1090$)↦","expression":"(⪩⨒∯120101⫳≱↱⪩⨒∯101002)↦","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":388,"operation_count":2,"complexity_ratio":194.0,"tree":{"type":"unary","operator":"↦","unary_expr":{"type":"binary","operator":"⫳≱↱","left_expr":{"type":"numeric_atoms","value":1553,"base":4},"right_expr":{"type":"numeric_atoms","value":1090,"base":4}}},"used_operators":["fFznvYxMfW","ZvLB05nZmT"],"dependent_operators":["L05ObWFQCd","d7ASUq0ydm","inkyxCbjAn","9HNa5Wba9A","AHs5Up7iyr","xRrnTEsQ6j","vkpjKywKVM","Z5m6OM72h2","eewbuw0ToL","uWAJUKEvyW","2Wsdkap16l","FyVja0WsTP","wEfv7U73WA","bJkvcejdHO","HmxsFra2vL","8cLx32lpNA"],"result":"⪩⨒∯-110","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1553","layer":2},{"info":"number node, value=1090","layer":2},{"info":"compute binary expreesion, left_input=1553, right_input=1090, op_id = ZvLB05nZmT binary_op_definition= 'a⫳≱↱b = { (((a⩹b)⇐≅)∌((a∙∹∝345)⊱⇼⊻(b≎⊠⪸a))) }', output=-204","layer":1},{"info":"compute unary expreesion, input=-204, op_id = fFznvYxMfW, unary_op_definition = 'a↦ = { (((a⊹∫⫚a)*177)⊹∫⫚((579⨰53)⪍↜⋙a)) , if a<72 ; ((⇁⨣⪵(a⫯⪬∳a))⫁⪎((a∘a)≹⇙⪍(a⇮⋭a))) , else }', output=-20","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯120101⫳≱↱⪩⨒∯101002)↦=⪩⨒∯-110","reverse_text":"⪩⨒∯-110=(⪩⨒∯120101⫳≱↱⪩⨒∯101002)↦","cot":[{"info":"⪩⨒∯120101⫳≱↱⪩⨒∯101002=⪩⨒∯-3030","layer":1},{"info":"⪩⨒∯-3030↦=⪩⨒∯-110","layer":0}]}
{"id":287,"expression_no_base_symbol":"($8571$⩤)⇴∐($1600$≃$2276$)","expression":"(⪩⨒∯2011323⩤)⇴∐(⪩⨒∯121000≃⪩⨒∯203210)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":40,"operation_count":3,"complexity_ratio":13.333333333333334,"tree":{"type":"binary","operator":"⇴∐","left_expr":{"type":"unary","operator":"⩤","unary_expr":{"type":"numeric_atoms","value":8571,"base":4}},"right_expr":{"type":"binary","operator":"≃","left_expr":{"type":"numeric_atoms","value":1600,"base":4},"right_expr":{"type":"numeric_atoms","value":2276,"base":4}}},"used_operators":["HnzytWxmAO","Z2TMIBDE3Q","YbVcJGFEVW"],"dependent_operators":["2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ","rysDP5nf3Z","t8gj7n24qd","9FxExcQeMw","Qy55tPpLXF","23Mk6UjR3U","JLbD19bQDL","7j4O788W3g","glklzrTFfD","tifHPKVTfV","t8gj7n24qd","i8ToyICDmI","COABgblf1C"],"result":"⪩⨒∯-1310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8571","layer":2},{"info":"compute unary expreesion, input=8571, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-8571","layer":1},{"info":"number node, value=1600","layer":2},{"info":"number node, value=2276","layer":2},{"info":"compute binary expreesion, left_input=1600, right_input=2276, op_id = YbVcJGFEVW binary_op_definition= 'a≃b = { (((13⋥≓≎b)⋷(a⇼⇔∾b))⨁⊸⫻) , if ((b⨁⊸⫻)>=162 or (b⪠⩆⊳)<=569) ; ((-(17⋷a))↺((a⩷∴a)⊭↱(b∲⫓a))) , else }', output=-6440","layer":1},{"info":"compute binary expreesion, left_input=-8571, right_input=-6440, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=-116","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2011323⩤)⇴∐(⪩⨒∯121000≃⪩⨒∯203210)=⪩⨒∯-1310","reverse_text":"⪩⨒∯-1310=(⪩⨒∯2011323⩤)⇴∐(⪩⨒∯121000≃⪩⨒∯203210)","cot":[{"info":"⪩⨒∯2011323⩤=⪩⨒∯-2011323","layer":1},{"info":"⪩⨒∯121000≃⪩⨒∯203210=⪩⨒∯-1210220","layer":1},{"info":"⪩⨒∯-2011323⇴∐⪩⨒∯-1210220=⪩⨒∯-1310","layer":0}]}
{"id":288,"expression_no_base_symbol":"($2344$⇴$1629$)⨽∌($2473$∙⊟$1312$)","expression":"(⪩⨒∯210220⇴⪩⨒∯121131)⨽∌(⪩⨒∯212221∙⊟⪩⨒∯110200)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2615,"operation_count":3,"complexity_ratio":871.6666666666666,"tree":{"type":"binary","operator":"⨽∌","left_expr":{"type":"binary","operator":"⇴","left_expr":{"type":"numeric_atoms","value":2344,"base":4},"right_expr":{"type":"numeric_atoms","value":1629,"base":4}},"right_expr":{"type":"binary","operator":"∙⊟","left_expr":{"type":"numeric_atoms","value":2473,"base":4},"right_expr":{"type":"numeric_atoms","value":1312,"base":4}}},"used_operators":["9samAPKr6k","4JB6nKBMSY","SxTAKzQCrw"],"dependent_operators":["YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu","sdazOOVcIp","NTOWxs364D","COABgblf1C","6iOiAJX1F8","oWn0xqSxBt","3Oe9XWJUTD","4CyGpkTkEk","CArV6hThFE","PPChnnnBFF"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2344","layer":2},{"info":"number node, value=1629","layer":2},{"info":"compute binary expreesion, left_input=2344, right_input=1629, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=16936","layer":1},{"info":"number node, value=2473","layer":2},{"info":"number node, value=1312","layer":2},{"info":"compute binary expreesion, left_input=2473, right_input=1312, op_id = SxTAKzQCrw binary_op_definition= 'a∙⊟b = { (⩪∧⨌(a⫲⨊)) , if (b∐⫣)<386 ; ((a∣a)⊝⪿⪼(⊙↵-a)) , else }', output=41995","layer":1},{"info":"compute binary expreesion, left_input=16936, right_input=41995, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯210220⇴⪩⨒∯121131)⨽∌(⪩⨒∯212221∙⊟⪩⨒∯110200)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯210220⇴⪩⨒∯121131)⨽∌(⪩⨒∯212221∙⊟⪩⨒∯110200)","cot":[{"info":"⪩⨒∯210220⇴⪩⨒∯121131=⪩⨒∯10020220","layer":1},{"info":"⪩⨒∯212221∙⊟⪩⨒∯110200=⪩⨒∯22100023","layer":1},{"info":"⪩⨒∯10020220⨽∌⪩⨒∯22100023=⪩⨒∯0","layer":0}]}
{"id":289,"expression_no_base_symbol":"$5620$⪪$6141$*$1462$⪒⊣⊆$7318$","expression":"⪩⨒∯1113310⪪⪩⨒∯1133331*⪩⨒∯112312⪒⊣⊆⪩⨒∯1302112","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19920,"operation_count":3,"complexity_ratio":6640.0,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"⪪","left_expr":{"type":"numeric_atoms","value":5620,"base":4},"right_expr":{"type":"numeric_atoms","value":6141,"base":4}},"right_expr":{"type":"binary","operator":"⪒⊣⊆","left_expr":{"type":"numeric_atoms","value":1462,"base":4},"right_expr":{"type":"numeric_atoms","value":7318,"base":4}}},"used_operators":["9HNa5Wba9A","xD69zh8xqp","eRqsBgTDFp"],"dependent_operators":["W4YGzv6Whe","FU0Cs4j7VP","JclMnS0uGI","sdazOOVcIp","W4YGzv6Whe"],"result":"-Inf","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5620","layer":2},{"info":"number node, value=6141","layer":2},{"info":"compute binary expreesion, left_input=5620, right_input=6141, op_id = xD69zh8xqp binary_op_definition= 'a⪪b = { ((b⨔⇊a)↛⩡⫤) }', output=-844709","layer":1},{"info":"number node, value=1462","layer":2},{"info":"number node, value=7318","layer":2},{"info":"compute binary expreesion, left_input=1462, right_input=7318, op_id = eRqsBgTDFp binary_op_definition= 'a⪒⊣⊆b = { (b⪨≂a) , if a<=17 ; (a+a) , else }', output=2924","layer":1},{"info":"compute binary expreesion, left_input=-844709, right_input=2924, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=-inf","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1113310⪪⪩⨒∯1133331*⪩⨒∯112312⪒⊣⊆⪩⨒∯1302112=-Inf","reverse_text":"-Inf=⪩⨒∯1113310⪪⪩⨒∯1133331*⪩⨒∯112312⪒⊣⊆⪩⨒∯1302112","cot":[{"info":"⪩⨒∯1113310⪪⪩⨒∯1133331=⪩⨒∯-3032032211","layer":1},{"info":"⪩⨒∯112312⪒⊣⊆⪩⨒∯1302112=⪩⨒∯231230","layer":1},{"info":"⪩⨒∯-3032032211*⪩⨒∯231230=-Inf","layer":0}]}
{"id":290,"expression_no_base_symbol":"$3759$⊬⨰$2265$≭$8040$≴⪞⇿$3320$","expression":"⪩⨒∯322233⊬⨰⪩⨒∯203121≭⪩⨒∯1331220≴⪞⇿⪩⨒∯303320","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7812,"operation_count":3,"complexity_ratio":2604.0,"tree":{"type":"binary","operator":"≭","left_expr":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"numeric_atoms","value":3759,"base":4},"right_expr":{"type":"numeric_atoms","value":2265,"base":4}},"right_expr":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"numeric_atoms","value":8040,"base":4},"right_expr":{"type":"numeric_atoms","value":3320,"base":4}}},"used_operators":["rxpJgHHUmx","s3Fd5m9Dh2","lvlrscuwVU"],"dependent_operators":["AHs5Up7iyr","23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3759","layer":2},{"info":"number node, value=2265","layer":2},{"info":"compute binary expreesion, left_input=3759, right_input=2265, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=11763","layer":1},{"info":"number node, value=8040","layer":2},{"info":"number node, value=3320","layer":2},{"info":"compute binary expreesion, left_input=8040, right_input=3320, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=120652812","layer":1},{"info":"compute binary expreesion, left_input=11763, right_input=120652812, op_id = rxpJgHHUmx binary_op_definition= 'a≭b = {-22, if b == 0; (a)≹⇙⪍(a≭(b-1)), if b > 0 and abs(b) < 100; -(a)≹⇙⪍(a≭(b+1)), if b < 0 and abs(b) < 100; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯322233⊬⨰⪩⨒∯203121≭⪩⨒∯1331220≴⪞⇿⪩⨒∯303320=NaN","reverse_text":"NaN=⪩⨒∯322233⊬⨰⪩⨒∯203121≭⪩⨒∯1331220≴⪞⇿⪩⨒∯303320","cot":[{"info":"⪩⨒∯322233⊬⨰⪩⨒∯203121=⪩⨒∯2313303","layer":1},{"info":"⪩⨒∯1331220≴⪞⇿⪩⨒∯303320=⪩⨒∯13030100100030","layer":1},{"info":"⪩⨒∯2313303≭⪩⨒∯13030100100030=NaN","layer":0}]}
{"id":291,"expression_no_base_symbol":"$9711$⨔⇊$1002$∳⫺($1002$⊢)","expression":"⪩⨒∯2113233⨔⇊⪩⨒∯33222∳⫺(⪩⨒∯33222⊢)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":61,"operation_count":3,"complexity_ratio":20.333333333333332,"tree":{"type":"binary","operator":"∳⫺","left_expr":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"numeric_atoms","value":9711,"base":4},"right_expr":{"type":"numeric_atoms","value":1002,"base":4}},"right_expr":{"type":"unary","operator":"⊢","unary_expr":{"type":"numeric_atoms","value":1002,"base":4}}},"used_operators":["AzXXKTstlj","JclMnS0uGI","40aOVDgCDB"],"dependent_operators":["F4yD0voBRQ","Tcnh7f0tEr","ZvLB05nZmT","9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI","NTOWxs364D"],"result":"⪩⨒∯-10010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=9711","layer":2},{"info":"number node, value=1002","layer":2},{"info":"compute binary expreesion, left_input=9711, right_input=1002, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=1002","layer":1},{"info":"number node, value=1002","layer":2},{"info":"compute unary expreesion, input=1002, op_id = 40aOVDgCDB, unary_op_definition = 'a⊢ = { a , if a<=675 ; (a⩚⊴⇥126) , else }', output=-1249","layer":1},{"info":"compute binary expreesion, left_input=1002, right_input=-1249, op_id = AzXXKTstlj binary_op_definition= 'a∳⫺b = { (a≣⋋) , if (b⫳≱↱947)==166 ; (a⇣⩺⋵b) , else }', output=-260","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯2113233⨔⇊⪩⨒∯33222∳⫺(⪩⨒∯33222⊢)=⪩⨒∯-10010","reverse_text":"⪩⨒∯-10010=⪩⨒∯2113233⨔⇊⪩⨒∯33222∳⫺(⪩⨒∯33222⊢)","cot":[{"info":"⪩⨒∯2113233⨔⇊⪩⨒∯33222=⪩⨒∯33222","layer":1},{"info":"⪩⨒∯33222⊢=⪩⨒∯-103201","layer":1},{"info":"⪩⨒∯33222∳⫺⪩⨒∯-103201=⪩⨒∯-10010","layer":0}]}
{"id":292,"expression_no_base_symbol":"≛(⨩∲⋌$2116$)","expression":"≛(⨩∲⋌⪩⨒∯201010)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":32,"operation_count":2,"complexity_ratio":16.0,"tree":{"type":"unary","operator":"≛","unary_expr":{"type":"unary","operator":"⨩∲⋌","unary_expr":{"type":"numeric_atoms","value":2116,"base":4}}},"used_operators":["W7eaUhjymW","aSik1wnThz"],"dependent_operators":["W4YGzv6Whe","NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","DZ8iAZOCBD","JLbD19bQDL","sdazOOVcIp","2DDjHMKMc0","f6k1SAg4EE","eewbuw0ToL","COABgblf1C","rysDP5nf3Z","Ph9nP6C5qx","Z2TMIBDE3Q"],"result":"⪩⨒∯-1112023","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2116","layer":2},{"info":"compute unary expreesion, input=2116, op_id = aSik1wnThz, unary_op_definition = '⨩∲⋌a = { ((759≧⫂∧(236-a))⩤) }', output=-2639","layer":1},{"info":"compute unary expreesion, input=-2639, op_id = W7eaUhjymW, unary_op_definition = '≛a = { (((a+a)⊉≛↸(a⪠⩆⊳))⊭↱((a⪒a)⩚⊴⇥(a⋝⋈⪟a))) , if (a⫩⊇)>7 or a==273 ; (((a-a)⪒(a⪨≂a))⊉≛↸((a⨰a)⋝⋈⪟(a+a))) , else }', output=-5515","layer":0}],"base":4,"result_base":4,"text":"≛(⨩∲⋌⪩⨒∯201010)=⪩⨒∯-1112023","reverse_text":"⪩⨒∯-1112023=≛(⨩∲⋌⪩⨒∯201010)","cot":[{"info":"⨩∲⋌⪩⨒∯201010=⪩⨒∯-221033","layer":1},{"info":"≛⪩⨒∯-221033=⪩⨒∯-1112023","layer":0}]}
{"id":293,"expression_no_base_symbol":"(⫓⪴$2329$)⨥⫆($1610$⨉)","expression":"(⫓⪴⪩⨒∯210121)⨥⫆(⪩⨒∯121022⨉)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3963,"operation_count":3,"complexity_ratio":1321.0,"tree":{"type":"binary","operator":"⨥⫆","left_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":2329,"base":4}},"right_expr":{"type":"unary","operator":"⨉","unary_expr":{"type":"numeric_atoms","value":1610,"base":4}}},"used_operators":["yXekIHxTD4","eLxqMNBOBk","aMUSaJuDRU"],"dependent_operators":["eRqsBgTDFp","ancx8kZcWl","oacrs7FA3X","9HNa5Wba9A","tmPS8pqC7x","g55IO6H4Gj","qWUSsah53b"],"result":"⪩⨒∯2223130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2329","layer":2},{"info":"compute unary expreesion, input=2329, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=5424241","layer":1},{"info":"number node, value=1610","layer":2},{"info":"compute unary expreesion, input=1610, op_id = aMUSaJuDRU, unary_op_definition = 'a⨉ = { ((⫡⇟⇯148)⨸⪁(a⨪↰⇹a)) }', output=5548","layer":1},{"info":"compute binary expreesion, left_input=5424241, right_input=5548, op_id = yXekIHxTD4 binary_op_definition= 'a⨥⫆b = { (b⨝⩣∺) , if (a⪒⊣⊆344)<109 ; (b⪘⫢a) , else }', output=10972","layer":0}],"base":4,"result_base":4,"text":"(⫓⪴⪩⨒∯210121)⨥⫆(⪩⨒∯121022⨉)=⪩⨒∯2223130","reverse_text":"⪩⨒∯2223130=(⫓⪴⪩⨒∯210121)⨥⫆(⪩⨒∯121022⨉)","cot":[{"info":"⫓⪴⪩⨒∯210121=⪩⨒∯110230101301","layer":1},{"info":"⪩⨒∯121022⨉=⪩⨒∯1112230","layer":1},{"info":"⪩⨒∯110230101301⨥⫆⪩⨒∯1112230=⪩⨒∯2223130","layer":0}]}
{"id":294,"expression_no_base_symbol":"∂(↔$2065$)","expression":"∂(↔⪩⨒∯200101)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":424,"operation_count":2,"complexity_ratio":212.0,"tree":{"type":"unary","operator":"∂","unary_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":2065,"base":4}}},"used_operators":["Uaa54Peajs","ruOEQAzv1W"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp"],"result":"⪩⨒∯113320","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2065","layer":2},{"info":"compute unary expreesion, input=2065, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-1792","layer":1},{"info":"compute unary expreesion, input=-1792, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=1528","layer":0}],"base":4,"result_base":4,"text":"∂(↔⪩⨒∯200101)=⪩⨒∯113320","reverse_text":"⪩⨒∯113320=∂(↔⪩⨒∯200101)","cot":[{"info":"↔⪩⨒∯200101=⪩⨒∯-130000","layer":1},{"info":"∂⪩⨒∯-130000=⪩⨒∯113320","layer":0}]}
{"id":295,"expression_no_base_symbol":"↨⩢⫨($2733$≧⫂∧$6456$)","expression":"↨⩢⫨(⪩⨒∯222231≧⫂∧⪩⨒∯1210320)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":68,"operation_count":2,"complexity_ratio":34.0,"tree":{"type":"unary","operator":"↨⩢⫨","unary_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":2733,"base":4},"right_expr":{"type":"numeric_atoms","value":6456,"base":4}}},"used_operators":["Z5CJsN7DuW","Ph9nP6C5qx"],"dependent_operators":["Noe24qw2ks","gu96TGCTMs","8jW3W4yZS5","AFVx7xoS7T","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2733","layer":2},{"info":"number node, value=6456","layer":2},{"info":"compute binary expreesion, left_input=2733, right_input=6456, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=5983","layer":1},{"info":"compute unary expreesion, input=5983, op_id = Z5CJsN7DuW, unary_op_definition = '↨⩢⫨a = { (((211⨐a)⇌⫙⪟(↯⪼a))⊘) }', output=0","layer":0}],"base":4,"result_base":4,"text":"↨⩢⫨(⪩⨒∯222231≧⫂∧⪩⨒∯1210320)=⪩⨒∯0","reverse_text":"⪩⨒∯0=↨⩢⫨(⪩⨒∯222231≧⫂∧⪩⨒∯1210320)","cot":[{"info":"⪩⨒∯222231≧⫂∧⪩⨒∯1210320=⪩⨒∯1131133","layer":1},{"info":"↨⩢⫨⪩⨒∯1131133=⪩⨒∯0","layer":0}]}
{"id":296,"expression_no_base_symbol":"($3276$⫭)⊹≧⊝","expression":"(⪩⨒∯303030⫭)⊹≧⊝","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":32,"operation_count":2,"complexity_ratio":16.0,"tree":{"type":"unary","operator":"⊹≧⊝","unary_expr":{"type":"unary","operator":"⫭","unary_expr":{"type":"numeric_atoms","value":3276,"base":4}}},"used_operators":["LxFB4K6j0n","t4WUHVGj7f"],"dependent_operators":["NTOWxs364D","P8v4zCKN1o","XPYlsWDdGa","DZ8iAZOCBD","t8gj7n24qd","g55IO6H4Gj","eewbuw0ToL","i8ToyICDmI","COABgblf1C","NTOWxs364D","2DDjHMKMc0","xUOZtlo3hN","g55IO6H4Gj"],"result":"⪩⨒∯-21311110","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3276","layer":2},{"info":"compute unary expreesion, input=3276, op_id = t4WUHVGj7f, unary_op_definition = 'a⫭ = { (⨞⊢((a⨸⪁147)⩚⊴⇥(a⋝⋈⪟a))) }', output=10069","layer":1},{"info":"compute unary expreesion, input=10069, op_id = LxFB4K6j0n, unary_op_definition = 'a⊹≧⊝ = { (((∥⊫a)⊭↱(a⩚⊴⇥a))⊉≛↸(⪲⇎(⪲⇎a))) , if a!=566 ; (-((a∲⫓a)⨸⪁(a⨰a))) , else }', output=-40276","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯303030⫭)⊹≧⊝=⪩⨒∯-21311110","reverse_text":"⪩⨒∯-21311110=(⪩⨒∯303030⫭)⊹≧⊝","cot":[{"info":"⪩⨒∯303030⫭=⪩⨒∯2131111","layer":1},{"info":"⪩⨒∯2131111⊹≧⊝=⪩⨒∯-21311110","layer":0}]}
{"id":297,"expression_no_base_symbol":"($4661$∕⩚$2992$)⇔⨋","expression":"(⪩⨒∯1020311∕⩚⪩⨒∯232300)⇔⨋","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4693,"operation_count":2,"complexity_ratio":2346.5,"tree":{"type":"unary","operator":"⇔⨋","unary_expr":{"type":"binary","operator":"∕⩚","left_expr":{"type":"numeric_atoms","value":4661,"base":4},"right_expr":{"type":"numeric_atoms","value":2992,"base":4}}},"used_operators":["uBihLCJcMX","z9ffQ9n5Zr"],"dependent_operators":["N41Kp7NANJ","7j4O788W3g","glklzrTFfD","tifHPKVTfV","12rbrZMWeM","f6k1SAg4EE","D4vGDi5EA2","nCS4ZIUYfx","QMFrweE19q","3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr"],"result":"⪩⨒∯10133","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4661","layer":2},{"info":"number node, value=2992","layer":2},{"info":"compute binary expreesion, left_input=4661, right_input=2992, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-4664","layer":1},{"info":"compute unary expreesion, input=-4664, op_id = uBihLCJcMX, unary_op_definition = 'a⇔⨋ = { (((a⨁⊸⫻)⋳⪒a)⪒((a≦≮≮)⨁⊸⫻)) , if a<217 ; (((a≋⫹)⨳⩥⨓(a↺a))⋳⪒((a⨳⩥⨓a)⫡⨏(a⇼⇔∾a))) , else }', output=287","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1020311∕⩚⪩⨒∯232300)⇔⨋=⪩⨒∯10133","reverse_text":"⪩⨒∯10133=(⪩⨒∯1020311∕⩚⪩⨒∯232300)⇔⨋","cot":[{"info":"⪩⨒∯1020311∕⩚⪩⨒∯232300=⪩⨒∯-1020320","layer":1},{"info":"⪩⨒∯-1020320⇔⨋=⪩⨒∯10133","layer":0}]}
{"id":298,"expression_no_base_symbol":"$1893$+⪬∐$1112$≒∊($1077$⨑≵⋬$1496$)","expression":"⪩⨒∯131211+⪬∐⪩⨒∯101120≒∊(⪩⨒∯100311⨑≵⋬⪩⨒∯113120)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":36,"operation_count":3,"complexity_ratio":12.0,"tree":{"type":"binary","operator":"≒∊","left_expr":{"type":"binary","operator":"+⪬∐","left_expr":{"type":"numeric_atoms","value":1893,"base":4},"right_expr":{"type":"numeric_atoms","value":1112,"base":4}},"right_expr":{"type":"binary","operator":"⨑≵⋬","left_expr":{"type":"numeric_atoms","value":1077,"base":4},"right_expr":{"type":"numeric_atoms","value":1496,"base":4}}},"used_operators":["5KTvxBwnZo","2GS7woTJqF","XnXgA4xnOs"],"dependent_operators":["3EYGwJThht","dWAJyo7jo9","Z2TMIBDE3Q","bjFbhXSADs","3DZMoQKiUl","g55IO6H4Gj","D4vGDi5EA2","eewbuw0ToL","AF7qkfDlqP","QMFrweE19q"],"result":"⪩⨒∯1200103","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1893","layer":2},{"info":"number node, value=1112","layer":2},{"info":"compute binary expreesion, left_input=1893, right_input=1112, op_id = 2GS7woTJqF binary_op_definition= 'a+⪬∐b = { (a≦≮≮) , if b!=63 ; (b⨸⪁575) , else }', output=-5679","layer":1},{"info":"number node, value=1077","layer":2},{"info":"number node, value=1496","layer":2},{"info":"compute binary expreesion, left_input=1077, right_input=1496, op_id = XnXgA4xnOs binary_op_definition= 'a⨑≵⋬b = { ((a⨰b)⫡⨏(⨑⩽⪐b)) }', output=-3708","layer":1},{"info":"compute binary expreesion, left_input=-5679, right_input=-3708, op_id = 5KTvxBwnZo binary_op_definition= 'a≒∊b = { (≱⇩⩕(a⪢a)) , if (a⩤)==117 ; ((b⪊≅)⇄a) , else }', output=6163","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯131211+⪬∐⪩⨒∯101120≒∊(⪩⨒∯100311⨑≵⋬⪩⨒∯113120)=⪩⨒∯1200103","reverse_text":"⪩⨒∯1200103=⪩⨒∯131211+⪬∐⪩⨒∯101120≒∊(⪩⨒∯100311⨑≵⋬⪩⨒∯113120)","cot":[{"info":"⪩⨒∯131211+⪬∐⪩⨒∯101120=⪩⨒∯-1120233","layer":1},{"info":"⪩⨒∯100311⨑≵⋬⪩⨒∯113120=⪩⨒∯-321330","layer":1},{"info":"⪩⨒∯-1120233≒∊⪩⨒∯-321330=⪩⨒∯1200103","layer":0}]}
{"id":299,"expression_no_base_symbol":"$2454$⨂≜$1111$⪐","expression":"⪩⨒∯212112⨂≜⪩⨒∯101113⪐","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2489,"operation_count":2,"complexity_ratio":1244.5,"tree":{"type":"unary","operator":"⪐","unary_expr":{"type":"binary","operator":"⨂≜","left_expr":{"type":"numeric_atoms","value":2454,"base":4},"right_expr":{"type":"numeric_atoms","value":1111,"base":4}}},"used_operators":["eH2TOUuTDT","k1SHOSEABc"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","9FxExcQeMw","HiPekx5b7W","eLxqMNBOBk","JclMnS0uGI","COABgblf1C","U7g4x0WXJJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2454","layer":2},{"info":"number node, value=1111","layer":2},{"info":"compute binary expreesion, left_input=2454, right_input=1111, op_id = k1SHOSEABc binary_op_definition= 'a⨂≜b = { ((37⊭↱(⫓⪴a))⩷∴((111⨜⨶78)⨔⇊(a∑⇟⊟b))) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = eH2TOUuTDT, unary_op_definition = 'a⪐ = { (a+a) , if (-a)!=532 or a<368 ; (-a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯212112⨂≜⪩⨒∯101113⪐=NaN","reverse_text":"NaN=⪩⨒∯212112⨂≜⪩⨒∯101113⪐","cot":[{"info":"⪩⨒∯212112⨂≜⪩⨒∯101113=NaN","layer":1},{"info":"NaN⪐=NaN","layer":0}]}
{"id":300,"expression_no_base_symbol":"⪫⨮⊛($3958$⫳≱↱$9104$)","expression":"⪫⨮⊛(⪩⨒∯331312⫳≱↱⪩⨒∯2032100)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":310,"operation_count":2,"complexity_ratio":155.0,"tree":{"type":"unary","operator":"⪫⨮⊛","unary_expr":{"type":"binary","operator":"⫳≱↱","left_expr":{"type":"numeric_atoms","value":3958,"base":4},"right_expr":{"type":"numeric_atoms","value":9104,"base":4}}},"used_operators":["w5FWba1tyO","ZvLB05nZmT"],"dependent_operators":["s3Fd5m9Dh2","RZ5CV9rWsJ","SUmda5xLS4","kn8WO9XteQ","hTbEZDJLEm","Tw270M8GLb","2Wsdkap16l","FyVja0WsTP","wEfv7U73WA","bJkvcejdHO","HmxsFra2vL","8cLx32lpNA"],"result":"⪩⨒∯-3030","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3958","layer":2},{"info":"number node, value=9104","layer":2},{"info":"compute binary expreesion, left_input=3958, right_input=9104, op_id = ZvLB05nZmT binary_op_definition= 'a⫳≱↱b = { (((a⩹b)⇐≅)∌((a∙∹∝345)⊱⇼⊻(b≎⊠⪸a))) }', output=-204","layer":1},{"info":"compute unary expreesion, input=-204, op_id = w5FWba1tyO, unary_op_definition = '⪫⨮⊛a = { a , if (a⨭⪣527)<=182 ; ((⨰⫟⨤(a⪄a))⩖⊿((a⊬⨰a)∟)) , else }', output=-204","layer":0}],"base":4,"result_base":4,"text":"⪫⨮⊛(⪩⨒∯331312⫳≱↱⪩⨒∯2032100)=⪩⨒∯-3030","reverse_text":"⪩⨒∯-3030=⪫⨮⊛(⪩⨒∯331312⫳≱↱⪩⨒∯2032100)","cot":[{"info":"⪩⨒∯331312⫳≱↱⪩⨒∯2032100=⪩⨒∯-3030","layer":1},{"info":"⪫⨮⊛⪩⨒∯-3030=⪩⨒∯-3030","layer":0}]}
{"id":301,"expression_no_base_symbol":"$1990$∌$8639$⪕($2191$⊎←↗)","expression":"⪩⨒∯133012∌⪩⨒∯2012333⪕(⪩⨒∯202033⊎←↗)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":21,"operation_count":3,"complexity_ratio":7.0,"tree":{"type":"binary","operator":"⪕","left_expr":{"type":"binary","operator":"∌","left_expr":{"type":"numeric_atoms","value":1990,"base":4},"right_expr":{"type":"numeric_atoms","value":8639,"base":4}},"right_expr":{"type":"unary","operator":"⊎←↗","unary_expr":{"type":"numeric_atoms","value":2191,"base":4}}},"used_operators":["umQnsF7QlU","8cLx32lpNA","dwb5p0fa6d"],"dependent_operators":["P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF","N41Kp7NANJ","7j4O788W3g","t8gj7n24qd","sdazOOVcIp","COABgblf1C"],"result":"⪩⨒∯32213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1990","layer":2},{"info":"number node, value=8639","layer":2},{"info":"compute binary expreesion, left_input=1990, right_input=8639, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-8639","layer":1},{"info":"number node, value=2191","layer":2},{"info":"compute unary expreesion, input=2191, op_id = dwb5p0fa6d, unary_op_definition = 'a⊎←↗ = { (a⊭↱340) , if (a⪨≂940)!=203 ; (a⊭↱a) , else }', output=-3697","layer":1},{"info":"compute binary expreesion, left_input=-8639, right_input=-3697, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=935","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯133012∌⪩⨒∯2012333⪕(⪩⨒∯202033⊎←↗)=⪩⨒∯32213","reverse_text":"⪩⨒∯32213=⪩⨒∯133012∌⪩⨒∯2012333⪕(⪩⨒∯202033⊎←↗)","cot":[{"info":"⪩⨒∯133012∌⪩⨒∯2012333=⪩⨒∯-2012333","layer":1},{"info":"⪩⨒∯202033⊎←↗=⪩⨒∯-321301","layer":1},{"info":"⪩⨒∯-2012333⪕⪩⨒∯-321301=⪩⨒∯32213","layer":0}]}
{"id":302,"expression_no_base_symbol":"$3627$≭$1459$∠⫱($1488$⪉⨛$2349$)","expression":"⪩⨒∯320223≭⪩⨒∯112303∠⫱(⪩⨒∯113100⪉⨛⪩⨒∯210231)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":36,"operation_count":3,"complexity_ratio":12.0,"tree":{"type":"binary","operator":"∠⫱","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":3627,"base":4},"right_expr":{"type":"numeric_atoms","value":1459,"base":4}},"right_expr":{"type":"binary","operator":"⪉⨛","left_expr":{"type":"numeric_atoms","value":1488,"base":4},"right_expr":{"type":"numeric_atoms","value":2349,"base":4}}},"used_operators":["QvoQhV0rrE","rxpJgHHUmx","EWw2JM7wp4"],"dependent_operators":["eLAdDNolq6","DZ8iAZOCBD","7j4O788W3g","tifHPKVTfV","AF7qkfDlqP","AHs5Up7iyr","NTOWxs364D","tifHPKVTfV","12rbrZMWeM","i8ToyICDmI","eewbuw0ToL"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3627","layer":2},{"info":"number node, value=1459","layer":2},{"info":"compute binary expreesion, left_input=3627, right_input=1459, op_id = rxpJgHHUmx binary_op_definition= 'a≭b = {-22, if b == 0; (a)≹⇙⪍(a≭(b-1)), if b > 0 and abs(b) < 100; -(a)≹⇙⪍(a≭(b+1)), if b < 0 and abs(b) < 100; NaN, else}', output=nan","layer":1},{"info":"number node, value=1488","layer":2},{"info":"number node, value=2349","layer":2},{"info":"compute binary expreesion, left_input=1488, right_input=2349, op_id = EWw2JM7wp4 binary_op_definition= 'a⪉⨛b = { (((82⇼⇔∾a)⩚⊴⇥a)⩚⊴⇥((b∲⫓a)⋳⪒(a⨰b))) }', output=2330","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2330, op_id = QvoQhV0rrE binary_op_definition= 'a∠⫱b = { ((⨑⩽⪐a)↺(617⊉≛↸a)) , if (≤/b)<=3 ; (b⇼⇔∾a) , else }', output=1234","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯320223≭⪩⨒∯112303∠⫱(⪩⨒∯113100⪉⨛⪩⨒∯210231)=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=⪩⨒∯320223≭⪩⨒∯112303∠⫱(⪩⨒∯113100⪉⨛⪩⨒∯210231)","cot":[{"info":"⪩⨒∯320223≭⪩⨒∯112303=NaN","layer":1},{"info":"⪩⨒∯113100⪉⨛⪩⨒∯210231=⪩⨒∯210122","layer":1},{"info":"NaN∠⫱⪩⨒∯210122=⪩⨒∯103102","layer":0}]}
{"id":303,"expression_no_base_symbol":"($3831$⪘⫢$3169$)⊬⨰($1326$⩨$5858$)","expression":"(⪩⨒∯323313⪘⫢⪩⨒∯301201)⊬⨰(⪩⨒∯110232⩨⪩⨒∯1123202)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":31,"operation_count":3,"complexity_ratio":10.333333333333334,"tree":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":3831,"base":4},"right_expr":{"type":"numeric_atoms","value":3169,"base":4}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":1326,"base":4},"right_expr":{"type":"numeric_atoms","value":5858,"base":4}}},"used_operators":["s3Fd5m9Dh2","oacrs7FA3X","2DlMacCsIx"],"dependent_operators":["23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⪩⨒∯1210202","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3831","layer":2},{"info":"number node, value=3169","layer":2},{"info":"compute binary expreesion, left_input=3831, right_input=3169, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=7538","layer":1},{"info":"number node, value=1326","layer":2},{"info":"number node, value=5858","layer":2},{"info":"compute binary expreesion, left_input=1326, right_input=5858, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-12","layer":1},{"info":"compute binary expreesion, left_input=7538, right_input=-12, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=6434","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯323313⪘⫢⪩⨒∯301201)⊬⨰(⪩⨒∯110232⩨⪩⨒∯1123202)=⪩⨒∯1210202","reverse_text":"⪩⨒∯1210202=(⪩⨒∯323313⪘⫢⪩⨒∯301201)⊬⨰(⪩⨒∯110232⩨⪩⨒∯1123202)","cot":[{"info":"⪩⨒∯323313⪘⫢⪩⨒∯301201=⪩⨒∯1311302","layer":1},{"info":"⪩⨒∯110232⩨⪩⨒∯1123202=⪩⨒∯-30","layer":1},{"info":"⪩⨒∯1311302⊬⨰⪩⨒∯-30=⪩⨒∯1210202","layer":0}]}
{"id":304,"expression_no_base_symbol":"∓⪦(⨵≀≌$5152$)","expression":"∓⪦(⨵≀≌⪩⨒∯1100200)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":32,"operation_count":2,"complexity_ratio":16.0,"tree":{"type":"unary","operator":"∓⪦","unary_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":5152,"base":4}}},"used_operators":["D309nIvmXG","srAu1WTS94"],"dependent_operators":["P8v4zCKN1o","sdazOOVcIp","Ph9nP6C5qx","eewbuw0ToL","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A"],"result":"⪩⨒∯-13330232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5152","layer":2},{"info":"compute unary expreesion, input=5152, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-15456","layer":1},{"info":"compute unary expreesion, input=-15456, op_id = D309nIvmXG, unary_op_definition = '∓⪦a = { (((a≧⫂∧a)⨰(a⨰a))⨰(∥⊫(343⪨≂a))) }', output=-32558","layer":0}],"base":4,"result_base":4,"text":"∓⪦(⨵≀≌⪩⨒∯1100200)=⪩⨒∯-13330232","reverse_text":"⪩⨒∯-13330232=∓⪦(⨵≀≌⪩⨒∯1100200)","cot":[{"info":"⨵≀≌⪩⨒∯1100200=⪩⨒∯-3301200","layer":1},{"info":"∓⪦⪩⨒∯-3301200=⪩⨒∯-13330232","layer":0}]}
{"id":305,"expression_no_base_symbol":"≦∁$3990$≭$6764$","expression":"≦∁⪩⨒∯332112≭⪩⨒∯1221230","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2,"operation_count":2,"complexity_ratio":1.0,"tree":{"type":"unary","operator":"≦∁","unary_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":3990,"base":4},"right_expr":{"type":"numeric_atoms","value":6764,"base":4}}},"used_operators":["9ICcGScMcE","rxpJgHHUmx"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3990","layer":2},{"info":"number node, value=6764","layer":2},{"info":"compute binary expreesion, left_input=3990, right_input=6764, op_id = rxpJgHHUmx binary_op_definition= 'a≭b = {-22, if b == 0; (a)≹⇙⪍(a≭(b-1)), if b > 0 and abs(b) < 100; -(a)≹⇙⪍(a≭(b+1)), if b < 0 and abs(b) < 100; NaN, else}', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"≦∁⪩⨒∯332112≭⪩⨒∯1221230=NaN","reverse_text":"NaN=≦∁⪩⨒∯332112≭⪩⨒∯1221230","cot":[{"info":"⪩⨒∯332112≭⪩⨒∯1221230=NaN","layer":1},{"info":"≦∁NaN=NaN","layer":0}]}
{"id":306,"expression_no_base_symbol":"$3476$⫘$1090$↺$4887$≁↽≥$6995$","expression":"⪩⨒∯312110⫘⪩⨒∯101002↺⪩⨒∯1030113≁↽≥⪩⨒∯1231103","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3717,"operation_count":3,"complexity_ratio":1239.0,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"⫘","left_expr":{"type":"numeric_atoms","value":3476,"base":4},"right_expr":{"type":"numeric_atoms","value":1090,"base":4}},"right_expr":{"type":"binary","operator":"≁↽≥","left_expr":{"type":"numeric_atoms","value":4887,"base":4},"right_expr":{"type":"numeric_atoms","value":6995,"base":4}}},"used_operators":["7j4O788W3g","48vC8HMD2b","ncHt1X6cMc"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","OwUj7dcsQK","7j4O788W3g","tfWHHpNKUN","3ViojmjbAp","dfKe02y8D2","tcjXMdvYtA","D4vGDi5EA2","86A5ENbKR9","X99M06cbEe","oWn0xqSxBt","3Oe9XWJUTD"],"result":"⪩⨒∯110110211","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3476","layer":2},{"info":"number node, value=1090","layer":2},{"info":"compute binary expreesion, left_input=3476, right_input=1090, op_id = 48vC8HMD2b binary_op_definition= 'a⫘b = { ((≘(b⨓a))≫≃) , if ((⇖a)!=319 or (a↺926)<190) ; ((∓a)⫚↹⊑(⪸(a≦≮≮))) , else }', output=4092181","layer":1},{"info":"number node, value=4887","layer":2},{"info":"number node, value=6995","layer":2},{"info":"compute binary expreesion, left_input=4887, right_input=6995, op_id = ncHt1X6cMc binary_op_definition= 'a≁↽≥b = { (a⊝⪿⪼b) , if b>=116 ; (⊙↵-b) , else }', output=83237","layer":1},{"info":"compute binary expreesion, left_input=4092181, right_input=83237, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=83237","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯312110⫘⪩⨒∯101002↺⪩⨒∯1030113≁↽≥⪩⨒∯1231103=⪩⨒∯110110211","reverse_text":"⪩⨒∯110110211=⪩⨒∯312110⫘⪩⨒∯101002↺⪩⨒∯1030113≁↽≥⪩⨒∯1231103","cot":[{"info":"⪩⨒∯312110⫘⪩⨒∯101002=⪩⨒∯33213010111","layer":1},{"info":"⪩⨒∯1030113≁↽≥⪩⨒∯1231103=⪩⨒∯110110211","layer":1},{"info":"⪩⨒∯33213010111↺⪩⨒∯110110211=⪩⨒∯110110211","layer":0}]}
{"id":307,"expression_no_base_symbol":"$1178$⇡⇂$3193$*($4914$⋖∅⋲)","expression":"⪩⨒∯102122⇡⇂⪩⨒∯301321*(⪩⨒∯1030302⋖∅⋲)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":18914,"operation_count":3,"complexity_ratio":6304.666666666667,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"⇡⇂","left_expr":{"type":"numeric_atoms","value":1178,"base":4},"right_expr":{"type":"numeric_atoms","value":3193,"base":4}},"right_expr":{"type":"unary","operator":"⋖∅⋲","unary_expr":{"type":"numeric_atoms","value":4914,"base":4}}},"used_operators":["9HNa5Wba9A","UMwdvZNt44","L95AwlJzhO"],"dependent_operators":["W4YGzv6Whe","9FxExcQeMw","23Mk6UjR3U","z4E1FaHLuy","3tj9sqzovi","fu6greOZ01","AHs5Up7iyr","lvlrscuwVU","KPf6cnQVty","uBihLCJcMX","12rbrZMWeM","WPoGxAaPR1","gx7XJ7hdpj","3nqY3DE9mg","XTarYq4gQB","y4ImoPnbV5","i8ToyICDmI","xNBdhnnwKq"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1178","layer":2},{"info":"number node, value=3193","layer":2},{"info":"compute binary expreesion, left_input=1178, right_input=3193, op_id = UMwdvZNt44 binary_op_definition= 'a⇡⇂b = { (((b≹⇙⪍b)⋳⪒(b⋷a))∺≝⩲(⫟(a⩷∴43))) , if (⊬↢a)==727 or (a⇔⨋)<18 ; ((604≴⪞⇿(≻⋜b))⨐⩸⫘a) , else }', output=nan","layer":1},{"info":"number node, value=4914","layer":2},{"info":"compute unary expreesion, input=4914, op_id = L95AwlJzhO, unary_op_definition = 'a⋖∅⋲ = { ((⪝⪂⫅431)⊍) , if (a∲⫓500)>7 ; ((a∽304)⫸⇳(a⊭∹↮)) , else }', output=-384231","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-384231, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102122⇡⇂⪩⨒∯301321*(⪩⨒∯1030302⋖∅⋲)=NaN","reverse_text":"NaN=⪩⨒∯102122⇡⇂⪩⨒∯301321*(⪩⨒∯1030302⋖∅⋲)","cot":[{"info":"⪩⨒∯102122⇡⇂⪩⨒∯301321=NaN","layer":1},{"info":"⪩⨒∯1030302⋖∅⋲=⪩⨒∯-1131303213","layer":1},{"info":"NaN*⪩⨒∯-1131303213=NaN","layer":0}]}
{"id":308,"expression_no_base_symbol":"$2543$⇣⩺⋵$3435$⨽⪊≇","expression":"⪩⨒∯213233⇣⩺⋵⪩⨒∯311223⨽⪊≇","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":66,"operation_count":2,"complexity_ratio":33.0,"tree":{"type":"unary","operator":"⨽⪊≇","unary_expr":{"type":"binary","operator":"⇣⩺⋵","left_expr":{"type":"numeric_atoms","value":2543,"base":4},"right_expr":{"type":"numeric_atoms","value":3435,"base":4}}},"used_operators":["nlCqmYiOvY","F4yD0voBRQ"],"dependent_operators":["W4YGzv6Whe","sdazOOVcIp","XIabStNQrY","NTOWxs364D","KPf6cnQVty","8jW3W4yZS5","12rbrZMWeM","g55IO6H4Gj","2DlMacCsIx"],"result":"⪩⨒∯-100112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2543","layer":2},{"info":"number node, value=3435","layer":2},{"info":"compute binary expreesion, left_input=2543, right_input=3435, op_id = F4yD0voBRQ binary_op_definition= 'a⇣⩺⋵b = { (((a⩨565)∺≝⩲(5⨸⪁a))⩚⊴⇥(↯⪼(a⋳⪒b))) }', output=-260","layer":1},{"info":"compute unary expreesion, input=-260, op_id = nlCqmYiOvY, unary_op_definition = 'a⨽⪊≇ = { ((a⇋≉)⪨≂(a+216)) }', output=-1046","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯213233⇣⩺⋵⪩⨒∯311223⨽⪊≇=⪩⨒∯-100112","reverse_text":"⪩⨒∯-100112=⪩⨒∯213233⇣⩺⋵⪩⨒∯311223⨽⪊≇","cot":[{"info":"⪩⨒∯213233⇣⩺⋵⪩⨒∯311223=⪩⨒∯-10010","layer":1},{"info":"⪩⨒∯-10010⨽⪊≇=⪩⨒∯-100112","layer":0}]}
{"id":309,"expression_no_base_symbol":"$1190$≠≀$7639$∽$1308$⇡⇂$1695$","expression":"⪩⨒∯102212≠≀⪩⨒∯1313113∽⪩⨒∯110130⇡⇂⪩⨒∯122133","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8337,"operation_count":3,"complexity_ratio":2779.0,"tree":{"type":"binary","operator":"∽","left_expr":{"type":"binary","operator":"≠≀","left_expr":{"type":"numeric_atoms","value":1190,"base":4},"right_expr":{"type":"numeric_atoms","value":7639,"base":4}},"right_expr":{"type":"binary","operator":"⇡⇂","left_expr":{"type":"numeric_atoms","value":1308,"base":4},"right_expr":{"type":"numeric_atoms","value":1695,"base":4}}},"used_operators":["y4ImoPnbV5","IwW236VD4Y","UMwdvZNt44"],"dependent_operators":["NTOWxs364D","QMFrweE19q","eLAdDNolq6","NTOWxs364D","sdazOOVcIp","2DDjHMKMc0","2td37pGCOC","9FxExcQeMw","23Mk6UjR3U","z4E1FaHLuy","3tj9sqzovi","fu6greOZ01","AHs5Up7iyr","lvlrscuwVU","KPf6cnQVty","uBihLCJcMX","12rbrZMWeM","WPoGxAaPR1"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1190","layer":2},{"info":"number node, value=7639","layer":2},{"info":"compute binary expreesion, left_input=1190, right_input=7639, op_id = IwW236VD4Y binary_op_definition= 'a≠≀b = { (⩦⩻⨪(a⩚⊴⇥b)) , if (≤/b)>10 ; ((a⪨≂a)⪨≂(a⋝⋈⪟356)) , else }', output=-2074","layer":1},{"info":"number node, value=1308","layer":2},{"info":"number node, value=1695","layer":2},{"info":"compute binary expreesion, left_input=1308, right_input=1695, op_id = UMwdvZNt44 binary_op_definition= 'a⇡⇂b = { (((b≹⇙⪍b)⋳⪒(b⋷a))∺≝⩲(⫟(a⩷∴43))) , if (⊬↢a)==727 or (a⇔⨋)<18 ; ((604≴⪞⇿(≻⋜b))⨐⩸⫘a) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-2074, right_input=nan, op_id = y4ImoPnbV5 binary_op_definition= 'a∽b = { ((a⩚⊴⇥b)⫡⨏b) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102212≠≀⪩⨒∯1313113∽⪩⨒∯110130⇡⇂⪩⨒∯122133=NaN","reverse_text":"NaN=⪩⨒∯102212≠≀⪩⨒∯1313113∽⪩⨒∯110130⇡⇂⪩⨒∯122133","cot":[{"info":"⪩⨒∯102212≠≀⪩⨒∯1313113=⪩⨒∯-200122","layer":1},{"info":"⪩⨒∯110130⇡⇂⪩⨒∯122133=NaN","layer":1},{"info":"⪩⨒∯-200122∽NaN=NaN","layer":0}]}
{"id":310,"expression_no_base_symbol":"($1772$⪭≯$1915$)⨚⇆$1431$≹⇙⪍$4253$","expression":"(⪩⨒∯123230⪭≯⪩⨒∯131323)⨚⇆⪩⨒∯112113≹⇙⪍⪩⨒∯1002131","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":375,"operation_count":3,"complexity_ratio":125.0,"tree":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"binary","operator":"⪭≯","left_expr":{"type":"numeric_atoms","value":1772,"base":4},"right_expr":{"type":"numeric_atoms","value":1915,"base":4}},"right_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":1431,"base":4},"right_expr":{"type":"numeric_atoms","value":4253,"base":4}}},"used_operators":["lwHaAYXP2r","XAx5wpdLa6","AHs5Up7iyr"],"dependent_operators":["gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi","9samAPKr6k","HJ9erzHUuu","TpPTUOHfaN","DbCuESL50I","s1XTVnmDOJ","61wBmkZwlr","Z5CJsN7DuW","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1772","layer":2},{"info":"number node, value=1915","layer":2},{"info":"compute binary expreesion, left_input=1772, right_input=1915, op_id = XAx5wpdLa6 binary_op_definition= 'a⪭≯b = { (((b⨽∌374)⪔⊥(⋼∭⪍b))+⇶⊼((≋a)≓∲(↨⩢⫨a))) }', output=nan","layer":1},{"info":"number node, value=1431","layer":2},{"info":"number node, value=4253","layer":2},{"info":"compute binary expreesion, left_input=1431, right_input=4253, op_id = AHs5Up7iyr binary_op_definition= 'a≹⇙⪍b = {a, if b == 0; (a≹⇙⪍(b-1))⪢(b), if b > 0 and abs(b) < 1000; -(a≹⇙⪍(b+1))⪢(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯123230⪭≯⪩⨒∯131323)⨚⇆⪩⨒∯112113≹⇙⪍⪩⨒∯1002131=NaN","reverse_text":"NaN=(⪩⨒∯123230⪭≯⪩⨒∯131323)⨚⇆⪩⨒∯112113≹⇙⪍⪩⨒∯1002131","cot":[{"info":"⪩⨒∯123230⪭≯⪩⨒∯131323=NaN","layer":1},{"info":"⪩⨒∯112113≹⇙⪍⪩⨒∯1002131=NaN","layer":1},{"info":"NaN⨚⇆NaN=NaN","layer":0}]}
{"id":311,"expression_no_base_symbol":"(∤$5583$)⨓$5219$⨼⩣$2479$","expression":"(∤⪩⨒∯1113033)⨓⪩⨒∯1101203⨼⩣⪩⨒∯212233","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":395,"operation_count":3,"complexity_ratio":131.66666666666666,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"unary","operator":"∤","unary_expr":{"type":"numeric_atoms","value":5583,"base":4}},"right_expr":{"type":"binary","operator":"⨼⩣","left_expr":{"type":"numeric_atoms","value":5219,"base":4},"right_expr":{"type":"numeric_atoms","value":2479,"base":4}}},"used_operators":["3ViojmjbAp","k2HlF1dBQh","JxwMv5le6e"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","rysDP5nf3Z","tifHPKVTfV","8w2t5hMYqp","uFcxV4UQCh","cHh1gJQ2o6","SL6IHkK8vl","KYD54nUTWz","pRsWfj4Fpp","CArV6hThFE"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5583","layer":2},{"info":"compute unary expreesion, input=5583, op_id = k2HlF1dBQh, unary_op_definition = '∤a = { (((a⇼⇔∾a)+(a-a))-(⊄⩳↩3)) }', output=9","layer":1},{"info":"number node, value=5219","layer":2},{"info":"number node, value=2479","layer":2},{"info":"compute binary expreesion, left_input=5219, right_input=2479, op_id = JxwMv5le6e binary_op_definition= 'a⨼⩣b = { ((∐⩳⋚(b⩘a))⪛((∡129)⫥∨⫟(a⫲⨊))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=9, right_input=nan, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(∤⪩⨒∯1113033)⨓⪩⨒∯1101203⨼⩣⪩⨒∯212233=NaN","reverse_text":"NaN=(∤⪩⨒∯1113033)⨓⪩⨒∯1101203⨼⩣⪩⨒∯212233","cot":[{"info":"∤⪩⨒∯1113033=⪩⨒∯21","layer":1},{"info":"⪩⨒∯1101203⨼⩣⪩⨒∯212233=NaN","layer":1},{"info":"⪩⨒∯21⨓NaN=NaN","layer":0}]}
{"id":312,"expression_no_base_symbol":"($1705$*$1529$)⩒⫫($1508$⩺⪪$2033$)","expression":"(⪩⨒∯122221*⪩⨒∯113321)⩒⫫(⪩⨒∯113210⩺⪪⪩⨒∯133301)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1679,"operation_count":3,"complexity_ratio":559.6666666666666,"tree":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1705,"base":4},"right_expr":{"type":"numeric_atoms","value":1529,"base":4}},"right_expr":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"numeric_atoms","value":1508,"base":4},"right_expr":{"type":"numeric_atoms","value":2033,"base":4}}},"used_operators":["KFSx94NKJn","9HNa5Wba9A","uvdQJvN4PV"],"dependent_operators":["NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","W4YGzv6Whe","Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U"],"result":"⪩⨒∯21330120303","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1705","layer":2},{"info":"number node, value=1529","layer":2},{"info":"compute binary expreesion, left_input=1705, right_input=1529, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=2606945","layer":1},{"info":"number node, value=1508","layer":2},{"info":"number node, value=2033","layer":2},{"info":"compute binary expreesion, left_input=1508, right_input=2033, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=-1818","layer":1},{"info":"compute binary expreesion, left_input=2606945, right_input=-1818, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=2606643","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯122221*⪩⨒∯113321)⩒⫫(⪩⨒∯113210⩺⪪⪩⨒∯133301)=⪩⨒∯21330120303","reverse_text":"⪩⨒∯21330120303=(⪩⨒∯122221*⪩⨒∯113321)⩒⫫(⪩⨒∯113210⩺⪪⪩⨒∯133301)","cot":[{"info":"⪩⨒∯122221*⪩⨒∯113321=⪩⨒∯21330131201","layer":1},{"info":"⪩⨒∯113210⩺⪪⪩⨒∯133301=⪩⨒∯-130122","layer":1},{"info":"⪩⨒∯21330131201⩒⫫⪩⨒∯-130122=⪩⨒∯21330120303","layer":0}]}
{"id":313,"expression_no_base_symbol":"⋗⩴⪓$2265$⫁⪎$1641$","expression":"⋗⩴⪓⪩⨒∯203121⫁⪎⪩⨒∯121221","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":676,"operation_count":2,"complexity_ratio":338.0,"tree":{"type":"unary","operator":"⋗⩴⪓","unary_expr":{"type":"binary","operator":"⫁⪎","left_expr":{"type":"numeric_atoms","value":2265,"base":4},"right_expr":{"type":"numeric_atoms","value":1641,"base":4}}},"used_operators":["nOKPl9n5zu","xRrnTEsQ6j"],"dependent_operators":["Qtd6bqUJcN","tifHPKVTfV","tmPS8pqC7x","jLgFTUHLKL","wztAlM01eG","P8v4zCKN1o","Qy55tPpLXF","tifHPKVTfV","sdazOOVcIp","2DDjHMKMc0","i8ToyICDmI"],"result":"⪩⨒∯10201","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2265","layer":2},{"info":"number node, value=1641","layer":2},{"info":"compute binary expreesion, left_input=2265, right_input=1641, op_id = xRrnTEsQ6j binary_op_definition= 'a⫁⪎b = { ((b⋝⋈⪟a)⇼⇔∾a) , if (∥⊫b)!=57 ; ((191∲⫓a)⋥≓≎(a⪨≂368)) , else }', output=624","layer":1},{"info":"compute unary expreesion, input=624, op_id = nOKPl9n5zu, unary_op_definition = '⋗⩴⪓a = { (↩a) , if (↸⊣a)>=41 ; (a⇼⇔∾(≪(a⨪↰⇹a))) , else }', output=289","layer":0}],"base":4,"result_base":4,"text":"⋗⩴⪓⪩⨒∯203121⫁⪎⪩⨒∯121221=⪩⨒∯10201","reverse_text":"⪩⨒∯10201=⋗⩴⪓⪩⨒∯203121⫁⪎⪩⨒∯121221","cot":[{"info":"⪩⨒∯203121⫁⪎⪩⨒∯121221=⪩⨒∯21300","layer":1},{"info":"⋗⩴⪓⪩⨒∯21300=⪩⨒∯10201","layer":0}]}
{"id":314,"expression_no_base_symbol":"($1532$⇴∐$3697$)⪶≀⋏(⩰$2862$)","expression":"(⪩⨒∯113330⇴∐⪩⨒∯321301)⪶≀⋏(⩰⪩⨒∯230232)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":44,"operation_count":3,"complexity_ratio":14.666666666666666,"tree":{"type":"binary","operator":"⪶≀⋏","left_expr":{"type":"binary","operator":"⇴∐","left_expr":{"type":"numeric_atoms","value":1532,"base":4},"right_expr":{"type":"numeric_atoms","value":3697,"base":4}},"right_expr":{"type":"unary","operator":"⩰","unary_expr":{"type":"numeric_atoms","value":2862,"base":4}}},"used_operators":["zR4jO40bMj","HnzytWxmAO","WkeUrDK8WX"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","NTOWxs364D","glklzrTFfD","2DDjHMKMc0","g55IO6H4Gj","eewbuw0ToL","2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ","W4YGzv6Whe","xUOZtlo3hN","Z2TMIBDE3Q","g55IO6H4Gj","i8ToyICDmI"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1532","layer":2},{"info":"number node, value=3697","layer":2},{"info":"compute binary expreesion, left_input=1532, right_input=3697, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=nan","layer":1},{"info":"number node, value=2862","layer":2},{"info":"compute unary expreesion, input=2862, op_id = WkeUrDK8WX, unary_op_definition = '⩰a = { (((a⨸⪁500)⩤)+(a∲⫓(⨞⊢a))) }', output=-3862","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-3862, op_id = zR4jO40bMj binary_op_definition= 'a⪶≀⋏b = { (((b⨸⪁b)⨸⪁(a-a))⋝⋈⪟(b⋝⋈⪟(b+b))) , if a<244 ; (((b⩚⊴⇥a)⨁⊸⫻)⨰a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯113330⇴∐⪩⨒∯321301)⪶≀⋏(⩰⪩⨒∯230232)=NaN","reverse_text":"NaN=(⪩⨒∯113330⇴∐⪩⨒∯321301)⪶≀⋏(⩰⪩⨒∯230232)","cot":[{"info":"⪩⨒∯113330⇴∐⪩⨒∯321301=NaN","layer":1},{"info":"⩰⪩⨒∯230232=⪩⨒∯-330112","layer":1},{"info":"NaN⪶≀⋏⪩⨒∯-330112=NaN","layer":0}]}
{"id":315,"expression_no_base_symbol":"$4963$+⪬∐$1165$∀⇚≩($1072$≃$6865$)","expression":"⪩⨒∯1031203+⪬∐⪩⨒∯102031∀⇚≩(⪩⨒∯100300≃⪩⨒∯1223101)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":104245,"operation_count":3,"complexity_ratio":34748.333333333336,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"+⪬∐","left_expr":{"type":"numeric_atoms","value":4963,"base":4},"right_expr":{"type":"numeric_atoms","value":1165,"base":4}},"right_expr":{"type":"binary","operator":"≃","left_expr":{"type":"numeric_atoms","value":1072,"base":4},"right_expr":{"type":"numeric_atoms","value":6865,"base":4}}},"used_operators":["LRNGc0VcxI","2GS7woTJqF","YbVcJGFEVW"],"dependent_operators":["X99M06cbEe","g55IO6H4Gj","D4vGDi5EA2","9FxExcQeMw","Qy55tPpLXF","23Mk6UjR3U","JLbD19bQDL","7j4O788W3g","glklzrTFfD","tifHPKVTfV","t8gj7n24qd","i8ToyICDmI","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4963","layer":2},{"info":"number node, value=1165","layer":2},{"info":"compute binary expreesion, left_input=4963, right_input=1165, op_id = 2GS7woTJqF binary_op_definition= 'a+⪬∐b = { (a≦≮≮) , if b!=63 ; (b⨸⪁575) , else }', output=-14889","layer":1},{"info":"number node, value=1072","layer":2},{"info":"number node, value=6865","layer":2},{"info":"compute binary expreesion, left_input=1072, right_input=6865, op_id = YbVcJGFEVW binary_op_definition= 'a≃b = { (((13⋥≓≎b)⋷(a⇼⇔∾b))⨁⊸⫻) , if ((b⨁⊸⫻)>=162 or (b⪠⩆⊳)<=569) ; ((-(17⋷a))↺((a⩷∴a)⊭↱(b∲⫓a))) , else }', output=-4328","layer":1},{"info":"compute binary expreesion, left_input=-14889, right_input=-4328, op_id = LRNGc0VcxI binary_op_definition= 'a∀⇚≩b = {b, if a == 0; ((a-1)∀⇚≩b)≫≃, if a > 0 and abs(a) < 1000000; -((a+1)∀⇚≩b)≫≃, if a < 0 and abs(a) < 1000000; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1031203+⪬∐⪩⨒∯102031∀⇚≩(⪩⨒∯100300≃⪩⨒∯1223101)=NaN","reverse_text":"NaN=⪩⨒∯1031203+⪬∐⪩⨒∯102031∀⇚≩(⪩⨒∯100300≃⪩⨒∯1223101)","cot":[{"info":"⪩⨒∯1031203+⪬∐⪩⨒∯102031=⪩⨒∯-3220221","layer":1},{"info":"⪩⨒∯100300≃⪩⨒∯1223101=⪩⨒∯-1003220","layer":1},{"info":"⪩⨒∯-3220221∀⇚≩⪩⨒∯-1003220=NaN","layer":0}]}
{"id":316,"expression_no_base_symbol":"$2017$∛$6997$⩺⪪($2277$⊪)","expression":"⪩⨒∯133201∛⪩⨒∯1231111⩺⪪(⪩⨒∯203211⊪)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":254,"operation_count":3,"complexity_ratio":84.66666666666667,"tree":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"binary","operator":"∛","left_expr":{"type":"numeric_atoms","value":2017,"base":4},"right_expr":{"type":"numeric_atoms","value":6997,"base":4}},"right_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":2277,"base":4}}},"used_operators":["uvdQJvN4PV","w2537kitQq","zVYPLywUTj"],"dependent_operators":["Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U","DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL"],"result":"⪩⨒∯-11113322","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2017","layer":2},{"info":"number node, value=6997","layer":2},{"info":"compute binary expreesion, left_input=2017, right_input=6997, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=-670","layer":1},{"info":"number node, value=2277","layer":2},{"info":"compute unary expreesion, input=2277, op_id = zVYPLywUTj, unary_op_definition = 'a⊪ = { (((a*a)+(18⨵⪆91))⪨≂((62⋥≓≎a)*(a⪒a))) , if (≉a)<304 or (a⫩⊇)==292 ; ((⊄⩳↩(a⪠⩆⊳))*((a/a)≧⫂∧(21*a))) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-670, right_input=0, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=-22010","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯133201∛⪩⨒∯1231111⩺⪪(⪩⨒∯203211⊪)=⪩⨒∯-11113322","reverse_text":"⪩⨒∯-11113322=⪩⨒∯133201∛⪩⨒∯1231111⩺⪪(⪩⨒∯203211⊪)","cot":[{"info":"⪩⨒∯133201∛⪩⨒∯1231111=⪩⨒∯-22132","layer":1},{"info":"⪩⨒∯203211⊪=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-22132⩺⪪⪩⨒∯0=⪩⨒∯-11113322","layer":0}]}
{"id":317,"expression_no_base_symbol":"∑⇻≧$1528$≓∲$1996$","expression":"∑⇻≧⪩⨒∯113320≓∲⪩⨒∯133030","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":52,"operation_count":2,"complexity_ratio":26.0,"tree":{"type":"unary","operator":"∑⇻≧","unary_expr":{"type":"binary","operator":"≓∲","left_expr":{"type":"numeric_atoms","value":1528,"base":4},"right_expr":{"type":"numeric_atoms","value":1996,"base":4}}},"used_operators":["l1M9WJ3V7u","s1XTVnmDOJ"],"dependent_operators":["23Mk6UjR3U","EBcxylXtPf","xUOZtlo3hN","HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu"],"result":"⪩⨒∯-31110","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1528","layer":2},{"info":"number node, value=1996","layer":2},{"info":"compute binary expreesion, left_input=1528, right_input=1996, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=16063","layer":1},{"info":"compute unary expreesion, input=16063, op_id = l1M9WJ3V7u, unary_op_definition = '∑⇻≧a = { (⨞⊢a) , if (a⫌⩹⨱)<644 ; (426⋷a) , else }', output=-852","layer":0}],"base":4,"result_base":4,"text":"∑⇻≧⪩⨒∯113320≓∲⪩⨒∯133030=⪩⨒∯-31110","reverse_text":"⪩⨒∯-31110=∑⇻≧⪩⨒∯113320≓∲⪩⨒∯133030","cot":[{"info":"⪩⨒∯113320≓∲⪩⨒∯133030=⪩⨒∯3322333","layer":1},{"info":"∑⇻≧⪩⨒∯3322333=⪩⨒∯-31110","layer":0}]}
{"id":318,"expression_no_base_symbol":"($1014$⫌⩉⩟$1922$)≀⫉$2785$⨚$3002$","expression":"(⪩⨒∯33312⫌⩉⩟⪩⨒∯132002)≀⫉⪩⨒∯223201⨚⪩⨒∯232322","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11827,"operation_count":3,"complexity_ratio":3942.3333333333335,"tree":{"type":"binary","operator":"≀⫉","left_expr":{"type":"binary","operator":"⫌⩉⩟","left_expr":{"type":"numeric_atoms","value":1014,"base":4},"right_expr":{"type":"numeric_atoms","value":1922,"base":4}},"right_expr":{"type":"binary","operator":"⨚","left_expr":{"type":"numeric_atoms","value":2785,"base":4},"right_expr":{"type":"numeric_atoms","value":3002,"base":4}}},"used_operators":["oZj3VtZNQx","XIIwhv8d0m","nREPSIbpBE"],"dependent_operators":["9FxExcQeMw","Tcnh7f0tEr","jBncVCNhdl","FyVja0WsTP","Ikt5ks8PT7","EWw2JM7wp4","cTDWOvIxvz","B5M0gjZbta","UMwdvZNt44","MRPaB8lBjK","vkpjKywKVM","BjRHVeLaeN","12rbrZMWeM"],"result":"⪩⨒∯230012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1014","layer":2},{"info":"number node, value=1922","layer":2},{"info":"compute binary expreesion, left_input=1014, right_input=1922, op_id = XIIwhv8d0m binary_op_definition= 'a⫌⩉⩟b = { (((a↬179)⇮⋭(b⇡⇂b))⇉⇱⇎) }', output=-50","layer":1},{"info":"number node, value=2785","layer":2},{"info":"number node, value=3002","layer":2},{"info":"compute binary expreesion, left_input=2785, right_input=3002, op_id = nREPSIbpBE binary_op_definition= 'a⨚b = { (((b⋳⪒a)⋳⪒31)⫩⊇) }', output=-5504","layer":1},{"info":"compute binary expreesion, left_input=-50, right_input=-5504, op_id = oZj3VtZNQx binary_op_definition= 'a≀⫉b = { (((55≣⋋)∝(a⩷∴a))⊱⇼⊻((a⪉⨛b)⩧⪆(b⋭≵475))) }', output=2822","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯33312⫌⩉⩟⪩⨒∯132002)≀⫉⪩⨒∯223201⨚⪩⨒∯232322=⪩⨒∯230012","reverse_text":"⪩⨒∯230012=(⪩⨒∯33312⫌⩉⩟⪩⨒∯132002)≀⫉⪩⨒∯223201⨚⪩⨒∯232322","cot":[{"info":"⪩⨒∯33312⫌⩉⩟⪩⨒∯132002=⪩⨒∯-302","layer":1},{"info":"⪩⨒∯223201⨚⪩⨒∯232322=⪩⨒∯-1112000","layer":1},{"info":"⪩⨒∯-302≀⫉⪩⨒∯-1112000=⪩⨒∯230012","layer":0}]}
{"id":319,"expression_no_base_symbol":"↥(⇁⨣⪵$1558$)","expression":"↥(⇁⨣⪵⪩⨒∯120112)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2,"operation_count":2,"complexity_ratio":1.0,"tree":{"type":"unary","operator":"↥","unary_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":1558,"base":4}}},"used_operators":["A8NUZmVepG","inkyxCbjAn"],"dependent_operators":["k8jYdgA6NY","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1558","layer":2},{"info":"compute unary expreesion, input=1558, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"↥(⇁⨣⪵⪩⨒∯120112)=NaN","reverse_text":"NaN=↥(⇁⨣⪵⪩⨒∯120112)","cot":[{"info":"⇁⨣⪵⪩⨒∯120112=NaN","layer":1},{"info":"↥NaN=NaN","layer":0}]}
{"id":320,"expression_no_base_symbol":"($1297$⊬⫿⊭)∽$1775$⨰$4668$","expression":"(⪩⨒∯110101⊬⫿⊭)∽⪩⨒∯123233⨰⪩⨒∯1020330","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":32,"operation_count":3,"complexity_ratio":10.666666666666666,"tree":{"type":"binary","operator":"∽","left_expr":{"type":"unary","operator":"⊬⫿⊭","unary_expr":{"type":"numeric_atoms","value":1297,"base":4}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":1775,"base":4},"right_expr":{"type":"numeric_atoms","value":4668,"base":4}}},"used_operators":["y4ImoPnbV5","v0DYgG9ikt","eewbuw0ToL"],"dependent_operators":["NTOWxs364D","QMFrweE19q","eLAdDNolq6","P8v4zCKN1o","7j4O788W3g","8w2t5hMYqp","2DQ55sFlQl","2DDjHMKMc0","xUOZtlo3hN","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","u6S6b8DprG","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯12321322","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1297","layer":2},{"info":"compute unary expreesion, input=1297, op_id = v0DYgG9ikt, unary_op_definition = 'a⊬⫿⊭ = { ((⨑⩽⪐(≤/a))↺((⨞⊢a)⨰(↽≂188))) , if a<119 ; (((∥⊫a)⨳⩥⨓(a⨵⪆a))↺(⊄⩳↩(a⋝⋈⪟a))) , else }', output=-3891","layer":1},{"info":"number node, value=1775","layer":2},{"info":"number node, value=4668","layer":2},{"info":"compute binary expreesion, left_input=1775, right_input=4668, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-2883","layer":1},{"info":"compute binary expreesion, left_input=-3891, right_input=-2883, op_id = y4ImoPnbV5 binary_op_definition= 'a∽b = { ((a⩚⊴⇥b)⫡⨏b) }', output=28282","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯110101⊬⫿⊭)∽⪩⨒∯123233⨰⪩⨒∯1020330=⪩⨒∯12321322","reverse_text":"⪩⨒∯12321322=(⪩⨒∯110101⊬⫿⊭)∽⪩⨒∯123233⨰⪩⨒∯1020330","cot":[{"info":"⪩⨒∯110101⊬⫿⊭=⪩⨒∯-330303","layer":1},{"info":"⪩⨒∯123233⨰⪩⨒∯1020330=⪩⨒∯-231003","layer":1},{"info":"⪩⨒∯-330303∽⪩⨒∯-231003=⪩⨒∯12321322","layer":0}]}
{"id":321,"expression_no_base_symbol":"⇖($2434$⇍⊗$2078$)","expression":"⇖(⪩⨒∯212002⇍⊗⪩⨒∯200132)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":41,"operation_count":2,"complexity_ratio":20.5,"tree":{"type":"unary","operator":"⇖","unary_expr":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"numeric_atoms","value":2434,"base":4},"right_expr":{"type":"numeric_atoms","value":2078,"base":4}}},"used_operators":["tfWHHpNKUN","5uvYHDjeKN"],"dependent_operators":["2DQ55sFlQl","Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2434","layer":2},{"info":"number node, value=2078","layer":2},{"info":"compute binary expreesion, left_input=2434, right_input=2078, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=-244","layer":1},{"info":"compute unary expreesion, input=-244, op_id = tfWHHpNKUN, unary_op_definition = '⇖a = { (221⨵⪆a) }', output=160","layer":0}],"base":4,"result_base":4,"text":"⇖(⪩⨒∯212002⇍⊗⪩⨒∯200132)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⇖(⪩⨒∯212002⇍⊗⪩⨒∯200132)","cot":[{"info":"⪩⨒∯212002⇍⊗⪩⨒∯200132=⪩⨒∯-3310","layer":1},{"info":"⇖⪩⨒∯-3310=⪩⨒∯2200","layer":0}]}
{"id":322,"expression_no_base_symbol":"($8700$⫰⋱$1052$)+⇶⊼($6770$≓∲$1270$)","expression":"(⪩⨒∯2013330⫰⋱⪩⨒∯100130)+⇶⊼(⪩⨒∯1221302≓∲⪩⨒∯103312)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":59,"operation_count":3,"complexity_ratio":19.666666666666668,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"binary","operator":"⫰⋱","left_expr":{"type":"numeric_atoms","value":8700,"base":4},"right_expr":{"type":"numeric_atoms","value":1052,"base":4}},"right_expr":{"type":"binary","operator":"≓∲","left_expr":{"type":"numeric_atoms","value":6770,"base":4},"right_expr":{"type":"numeric_atoms","value":1270,"base":4}}},"used_operators":["TpPTUOHfaN","6o9Blt3TJ6","s1XTVnmDOJ"],"dependent_operators":["AHs5Up7iyr","W4YGzv6Whe","nCS4ZIUYfx","Qy55tPpLXF","HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8700","layer":2},{"info":"number node, value=1052","layer":2},{"info":"compute binary expreesion, left_input=8700, right_input=1052, op_id = 6o9Blt3TJ6 binary_op_definition= 'a⫰⋱b = { ((a+b)⨳⩥⨓(b⋥≓≎b)) }', output=-8667","layer":1},{"info":"number node, value=6770","layer":2},{"info":"number node, value=1270","layer":2},{"info":"compute binary expreesion, left_input=6770, right_input=1270, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=68483","layer":1},{"info":"compute binary expreesion, left_input=-8667, right_input=68483, op_id = TpPTUOHfaN binary_op_definition= 'a+⇶⊼b = {b, if b == 0; (a)≹⇙⪍(a+⇶⊼(b-1)), if b > 0 and abs(b) < 100; -(a)≹⇙⪍(a+⇶⊼(b+1)), if b < 0 and abs(b) < 100; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2013330⫰⋱⪩⨒∯100130)+⇶⊼(⪩⨒∯1221302≓∲⪩⨒∯103312)=NaN","reverse_text":"NaN=(⪩⨒∯2013330⫰⋱⪩⨒∯100130)+⇶⊼(⪩⨒∯1221302≓∲⪩⨒∯103312)","cot":[{"info":"⪩⨒∯2013330⫰⋱⪩⨒∯100130=⪩⨒∯-2013123","layer":1},{"info":"⪩⨒∯1221302≓∲⪩⨒∯103312=⪩⨒∯100232003","layer":1},{"info":"⪩⨒∯-2013123+⇶⊼⪩⨒∯100232003=NaN","layer":0}]}
{"id":323,"expression_no_base_symbol":"$4898$⪝$3798$⇮⋭$7108$∺≝⩲$1005$","expression":"⪩⨒∯1030202⪝⪩⨒∯323112⇮⋭⪩⨒∯1233010∺≝⩲⪩⨒∯33231","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":734,"operation_count":3,"complexity_ratio":244.66666666666666,"tree":{"type":"binary","operator":"⇮⋭","left_expr":{"type":"binary","operator":"⪝","left_expr":{"type":"numeric_atoms","value":4898,"base":4},"right_expr":{"type":"numeric_atoms","value":3798,"base":4}},"right_expr":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"numeric_atoms","value":7108,"base":4},"right_expr":{"type":"numeric_atoms","value":1005,"base":4}}},"used_operators":["vkpjKywKVM","wicAB68Tmb","KPf6cnQVty"],"dependent_operators":["nhYeJWJD5X","U6pG0PXrV3","tifHPKVTfV","bJkvcejdHO","40aOVDgCDB","YbVcJGFEVW","L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X","BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl"],"result":"⪩⨒∯132112200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4898","layer":2},{"info":"number node, value=3798","layer":2},{"info":"compute binary expreesion, left_input=4898, right_input=3798, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=-4799","layer":1},{"info":"number node, value=7108","layer":2},{"info":"number node, value=1005","layer":2},{"info":"compute binary expreesion, left_input=7108, right_input=1005, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=-4799, right_input=160, op_id = vkpjKywKVM binary_op_definition= 'a⇮⋭b = { (((⊖b)⊢)≎⊠⪸((a≃b)⇼⇔∾(47∇⊂⋱106))) }', output=124320","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1030202⪝⪩⨒∯323112⇮⋭⪩⨒∯1233010∺≝⩲⪩⨒∯33231=⪩⨒∯132112200","reverse_text":"⪩⨒∯132112200=⪩⨒∯1030202⪝⪩⨒∯323112⇮⋭⪩⨒∯1233010∺≝⩲⪩⨒∯33231","cot":[{"info":"⪩⨒∯1030202⪝⪩⨒∯323112=⪩⨒∯-1022333","layer":1},{"info":"⪩⨒∯1233010∺≝⩲⪩⨒∯33231=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯-1022333⇮⋭⪩⨒∯2200=⪩⨒∯132112200","layer":0}]}
{"id":324,"expression_no_base_symbol":"$1832$≳⇉$1547$⫃⨇$4569$≎⪠$2243$","expression":"⪩⨒∯130220≳⇉⪩⨒∯120023⫃⨇⪩⨒∯1013121≎⪠⪩⨒∯203003","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":42827671,"operation_count":3,"complexity_ratio":14275890.333333334,"tree":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"binary","operator":"≳⇉","left_expr":{"type":"numeric_atoms","value":1832,"base":4},"right_expr":{"type":"numeric_atoms","value":1547,"base":4}},"right_expr":{"type":"binary","operator":"≎⪠","left_expr":{"type":"numeric_atoms","value":4569,"base":4},"right_expr":{"type":"numeric_atoms","value":2243,"base":4}}},"used_operators":["09Ly4LVMIf","V0kx6qeWkN","aNhz54LH3e"],"dependent_operators":["9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG","KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls","bl5wxAcryP","RygbFNSyEJ","SLLxy00UIr","AcOhelriW5","ctOc4cKSDt","cHh1gJQ2o6","KYD54nUTWz","kbkesczE7y","BUOGQAYlQx","PPChnnnBFF"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1832","layer":2},{"info":"number node, value=1547","layer":2},{"info":"compute binary expreesion, left_input=1832, right_input=1547, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":1},{"info":"number node, value=4569","layer":2},{"info":"number node, value=2243","layer":2},{"info":"compute binary expreesion, left_input=4569, right_input=2243, op_id = aNhz54LH3e binary_op_definition= 'a≎⪠b = { (((a⫥∨⫟11)≦↸(657∣a))⩘((⇈a)≬⋮(a↰))) , if a==21 ; (∟⋨(⋂(⨣⨃⇪b))) , else }', output=19558","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=19558, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯130220≳⇉⪩⨒∯120023⫃⨇⪩⨒∯1013121≎⪠⪩⨒∯203003=NaN","reverse_text":"NaN=⪩⨒∯130220≳⇉⪩⨒∯120023⫃⨇⪩⨒∯1013121≎⪠⪩⨒∯203003","cot":[{"info":"⪩⨒∯130220≳⇉⪩⨒∯120023=NaN","layer":1},{"info":"⪩⨒∯1013121≎⪠⪩⨒∯203003=⪩⨒∯10301212","layer":1},{"info":"NaN⫃⨇⪩⨒∯10301212=NaN","layer":0}]}
{"id":325,"expression_no_base_symbol":"($3233$⪄$5821$)⫥∨⫟($1825$⨀⨒)","expression":"(⪩⨒∯302201⪄⪩⨒∯1122331)⫥∨⫟(⪩⨒∯130201⨀⨒)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":296,"operation_count":3,"complexity_ratio":98.66666666666667,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":3233,"base":4},"right_expr":{"type":"numeric_atoms","value":5821,"base":4}},"right_expr":{"type":"unary","operator":"⨀⨒","unary_expr":{"type":"numeric_atoms","value":1825,"base":4}}},"used_operators":["KYD54nUTWz","SUmda5xLS4","j6NVkjMzuk"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","E4l6HwMY31","Ikt5ks8PT7","HmxsFra2vL","oacrs7FA3X"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3233","layer":2},{"info":"number node, value=5821","layer":2},{"info":"compute binary expreesion, left_input=3233, right_input=5821, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-497857","layer":1},{"info":"number node, value=1825","layer":2},{"info":"compute unary expreesion, input=1825, op_id = j6NVkjMzuk, unary_op_definition = 'a⨀⨒ = { ((a⪘⫢a)⊔(a⪘⫢a)) , if a!=184 ; ((a⩧⪆a)∙∹∝a) , else }', output=22282","layer":1},{"info":"compute binary expreesion, left_input=-497857, right_input=22282, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯302201⪄⪩⨒∯1122331)⫥∨⫟(⪩⨒∯130201⨀⨒)=NaN","reverse_text":"NaN=(⪩⨒∯302201⪄⪩⨒∯1122331)⫥∨⫟(⪩⨒∯130201⨀⨒)","cot":[{"info":"⪩⨒∯302201⪄⪩⨒∯1122331=⪩⨒∯-1321203001","layer":1},{"info":"⪩⨒∯130201⨀⨒=⪩⨒∯11130022","layer":1},{"info":"⪩⨒∯-1321203001⫥∨⫟⪩⨒∯11130022=NaN","layer":0}]}
{"id":326,"expression_no_base_symbol":"($5178$∙∹∝$1417$)⊴$2297$∣$4381$","expression":"(⪩⨒∯1100322∙∹∝⪩⨒∯112021)⊴⪩⨒∯203321∣⪩⨒∯1010131","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2311,"operation_count":3,"complexity_ratio":770.3333333333334,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"numeric_atoms","value":5178,"base":4},"right_expr":{"type":"numeric_atoms","value":1417,"base":4}},"right_expr":{"type":"binary","operator":"∣","left_expr":{"type":"numeric_atoms","value":2297,"base":4},"right_expr":{"type":"numeric_atoms","value":4381,"base":4}}},"used_operators":["Nsiff2A1zJ","HmxsFra2vL","PPChnnnBFF"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","eLAdDNolq6","eH2TOUuTDT","Ph9nP6C5qx","i8ToyICDmI"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5178","layer":2},{"info":"number node, value=1417","layer":2},{"info":"compute binary expreesion, left_input=5178, right_input=1417, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":1},{"info":"number node, value=2297","layer":2},{"info":"number node, value=4381","layer":2},{"info":"compute binary expreesion, left_input=2297, right_input=4381, op_id = PPChnnnBFF binary_op_definition= 'a∣b = { (≤/((a⪐)≧⫂∧(a∲⫓b))) , if (b⪐)<590 ; a , else }', output=2297","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=2297, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1100322∙∹∝⪩⨒∯112021)⊴⪩⨒∯203321∣⪩⨒∯1010131=NaN","reverse_text":"NaN=(⪩⨒∯1100322∙∹∝⪩⨒∯112021)⊴⪩⨒∯203321∣⪩⨒∯1010131","cot":[{"info":"⪩⨒∯1100322∙∹∝⪩⨒∯112021=⪩⨒∯0","layer":1},{"info":"⪩⨒∯203321∣⪩⨒∯1010131=⪩⨒∯203321","layer":1},{"info":"⪩⨒∯0⊴⪩⨒∯203321=NaN","layer":0}]}
{"id":327,"expression_no_base_symbol":"$2127$∥⊢⊲$1628$∖(⇺⋃$1975$)","expression":"⪩⨒∯201033∥⊢⊲⪩⨒∯121130∖(⇺⋃⪩⨒∯132313)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":233,"operation_count":3,"complexity_ratio":77.66666666666667,"tree":{"type":"binary","operator":"∖","left_expr":{"type":"binary","operator":"∥⊢⊲","left_expr":{"type":"numeric_atoms","value":2127,"base":4},"right_expr":{"type":"numeric_atoms","value":1628,"base":4}},"right_expr":{"type":"unary","operator":"⇺⋃","unary_expr":{"type":"numeric_atoms","value":1975,"base":4}}},"used_operators":["tXD093vOjl","v1UQAVDJRr","E5v5B3UAjG"],"dependent_operators":["rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC","EBcxylXtPf","rGHVDoGpnC","bl5wxAcryP","Q3PJZHRvZv","gub5Cegaqo","8INZBEW696","kuIXHzHcAH","7YooWSwCyH"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2127","layer":2},{"info":"number node, value=1628","layer":2},{"info":"compute binary expreesion, left_input=2127, right_input=1628, op_id = v1UQAVDJRr binary_op_definition= 'a∥⊢⊲b = { (a⨟⋌⩍b) , if (a⫌⩹⨱)>=49 ; b , else }', output=nan","layer":1},{"info":"number node, value=1975","layer":2},{"info":"compute unary expreesion, input=1975, op_id = E5v5B3UAjG, unary_op_definition = '⇺⋃a = { (((a≀⩗∶a)∪⫐(a⩁⩘229))⪨⊡(⊥(a↰))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯201033∥⊢⊲⪩⨒∯121130∖(⇺⋃⪩⨒∯132313)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯201033∥⊢⊲⪩⨒∯121130∖(⇺⋃⪩⨒∯132313)","cot":[{"info":"⪩⨒∯201033∥⊢⊲⪩⨒∯121130=NaN","layer":1},{"info":"⇺⋃⪩⨒∯132313=NaN","layer":1},{"info":"NaN∖NaN=⪩⨒∯0","layer":0}]}
{"id":328,"expression_no_base_symbol":"($1021$⩧⪆$1540$)≁↽≥(∐⩳⋚$2492$)","expression":"(⪩⨒∯33331⩧⪆⪩⨒∯120010)≁↽≥(∐⩳⋚⪩⨒∯212330)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":194,"operation_count":3,"complexity_ratio":64.66666666666667,"tree":{"type":"binary","operator":"≁↽≥","left_expr":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"numeric_atoms","value":1021,"base":4},"right_expr":{"type":"numeric_atoms","value":1540,"base":4}},"right_expr":{"type":"unary","operator":"∐⩳⋚","unary_expr":{"type":"numeric_atoms","value":2492,"base":4}}},"used_operators":["ncHt1X6cMc","Ikt5ks8PT7","SL6IHkK8vl"],"dependent_operators":["oWn0xqSxBt","3Oe9XWJUTD","eewbuw0ToL","t8gj7n24qd","s3Fd5m9Dh2","zR4jO40bMj","18saOjeKKm","k7HXdKtiEU","z4E1FaHLuy","XTarYq4gQB","xRrnTEsQ6j","Ph9nP6C5qx","f6k1SAg4EE","D3AQDKkPcf"],"result":"⪩⨒∯-3031300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1021","layer":2},{"info":"number node, value=1540","layer":2},{"info":"compute binary expreesion, left_input=1021, right_input=1540, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-1540","layer":1},{"info":"number node, value=2492","layer":2},{"info":"compute unary expreesion, input=2492, op_id = SL6IHkK8vl, unary_op_definition = '∐⩳⋚a = { (⊲⪭((⇠a)⪶≀⋏(a⪒a))) , if (⫟a)==290 ; ((⪝⪂⫅(105⫁⪎a))⊬⨰(a≧⫂∧(a∷a))) , else }', output=357909","layer":1},{"info":"compute binary expreesion, left_input=-1540, right_input=357909, op_id = ncHt1X6cMc binary_op_definition= 'a≁↽≥b = { (a⊝⪿⪼b) , if b>=116 ; (⊙↵-b) , else }', output=-13168","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯33331⩧⪆⪩⨒∯120010)≁↽≥(∐⩳⋚⪩⨒∯212330)=⪩⨒∯-3031300","reverse_text":"⪩⨒∯-3031300=(⪩⨒∯33331⩧⪆⪩⨒∯120010)≁↽≥(∐⩳⋚⪩⨒∯212330)","cot":[{"info":"⪩⨒∯33331⩧⪆⪩⨒∯120010=⪩⨒∯-120010","layer":1},{"info":"∐⩳⋚⪩⨒∯212330=⪩⨒∯1113120111","layer":1},{"info":"⪩⨒∯-120010≁↽≥⪩⨒∯1113120111=⪩⨒∯-3031300","layer":0}]}
{"id":329,"expression_no_base_symbol":"⩦⩻⨪(⨮↦↱$1099$)","expression":"⩦⩻⨪(⨮↦↱⪩⨒∯101023)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":655,"operation_count":2,"complexity_ratio":327.5,"tree":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"unary","operator":"⨮↦↱","unary_expr":{"type":"numeric_atoms","value":1099,"base":4}}},"used_operators":["2td37pGCOC","sYcpBQ0cFf"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","OKKcZfAt5B","WR6HLWljOP","umQnsF7QlU","8HhzD0ZcuI","BUOGQAYlQx","bx9Z9DAK5y","wztAlM01eG"],"result":"⪩⨒∯-10021313133","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1099","layer":2},{"info":"compute unary expreesion, input=1099, op_id = sYcpBQ0cFf, unary_op_definition = '⨮↦↱a = { ((⇾⩊⇾a)⪕(a≝⊿a)) , if (↸⊣a)>398 ; ((a↢a)⨽(⋂a)) , else }', output=-1088991","layer":1},{"info":"compute unary expreesion, input=-1088991, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=-1088991","layer":0}],"base":4,"result_base":4,"text":"⩦⩻⨪(⨮↦↱⪩⨒∯101023)=⪩⨒∯-10021313133","reverse_text":"⪩⨒∯-10021313133=⩦⩻⨪(⨮↦↱⪩⨒∯101023)","cot":[{"info":"⨮↦↱⪩⨒∯101023=⪩⨒∯-10021313133","layer":1},{"info":"⩦⩻⨪⪩⨒∯-10021313133=⪩⨒∯-10021313133","layer":0}]}
{"id":330,"expression_no_base_symbol":"(⊆⋠$1620$)⋭≵$1565$∛$2470$","expression":"(⊆⋠⪩⨒∯121110)⋭≵⪩⨒∯120131∛⪩⨒∯212212","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":169,"operation_count":3,"complexity_ratio":56.333333333333336,"tree":{"type":"binary","operator":"⋭≵","left_expr":{"type":"unary","operator":"⊆⋠","unary_expr":{"type":"numeric_atoms","value":1620,"base":4}},"right_expr":{"type":"binary","operator":"∛","left_expr":{"type":"numeric_atoms","value":1565,"base":4},"right_expr":{"type":"numeric_atoms","value":2470,"base":4}}},"used_operators":["jBncVCNhdl","EBhcHTkKd8","w2537kitQq"],"dependent_operators":["RygbFNSyEJ","gx7XJ7hdpj","9ICcGScMcE","C6VvDP6HwP","mqXw5SEYmG","7IPrd9c3lf","COABgblf1C","YjI8oCXuph","VwlE7vj6HS","e1ybzncUwg","SUmda5xLS4","vg4gO5BX6G","KipPnG1M2J","DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc"],"result":"⪩⨒∯202","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1620","layer":2},{"info":"compute unary expreesion, input=1620, op_id = EBhcHTkKd8, unary_op_definition = '⊆⋠a = { ((a⊨a)↯⫤) , if (≉a)>=63 ; ((⫇a)⪄(a∀⋜↑)) , else }', output=0","layer":1},{"info":"number node, value=1565","layer":2},{"info":"number node, value=2470","layer":2},{"info":"compute binary expreesion, left_input=1565, right_input=2470, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=-670","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-670, op_id = jBncVCNhdl binary_op_definition= 'a⋭≵b = { ((156≦↸a)⊭↱(≦∁b)) , if (b⫸⊐434)<=441 and (a⫸⇳180)>=132 ; ((a⪑⩈)⊵↤) , else }', output=34","layer":0}],"base":4,"result_base":4,"text":"(⊆⋠⪩⨒∯121110)⋭≵⪩⨒∯120131∛⪩⨒∯212212=⪩⨒∯202","reverse_text":"⪩⨒∯202=(⊆⋠⪩⨒∯121110)⋭≵⪩⨒∯120131∛⪩⨒∯212212","cot":[{"info":"⊆⋠⪩⨒∯121110=⪩⨒∯0","layer":1},{"info":"⪩⨒∯120131∛⪩⨒∯212212=⪩⨒∯-22132","layer":1},{"info":"⪩⨒∯0⋭≵⪩⨒∯-22132=⪩⨒∯202","layer":0}]}
{"id":331,"expression_no_base_symbol":"($7717$⪕$1922$)⨜⨶(⪁⇼$3250$)","expression":"(⪩⨒∯1320211⪕⪩⨒∯132002)⨜⨶(⪁⇼⪩⨒∯302302)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":38,"operation_count":3,"complexity_ratio":12.666666666666666,"tree":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"binary","operator":"⪕","left_expr":{"type":"numeric_atoms","value":7717,"base":4},"right_expr":{"type":"numeric_atoms","value":1922,"base":4}},"right_expr":{"type":"unary","operator":"⪁⇼","unary_expr":{"type":"numeric_atoms","value":3250,"base":4}}},"used_operators":["HiPekx5b7W","umQnsF7QlU","ZNVVrZ94lY"],"dependent_operators":["N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF","sdazOOVcIp","2DQ55sFlQl","tifHPKVTfV"],"result":"⪩⨒∯203333311","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7717","layer":2},{"info":"number node, value=1922","layer":2},{"info":"compute binary expreesion, left_input=7717, right_input=1922, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=14413","layer":1},{"info":"number node, value=3250","layer":2},{"info":"compute unary expreesion, input=3250, op_id = ZNVVrZ94lY, unary_op_definition = '⪁⇼a = { ((a⨵⪆a)⪨≂(a⇼⇔∾a)) }', output=422","layer":1},{"info":"compute binary expreesion, left_input=14413, right_input=422, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=147445","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1320211⪕⪩⨒∯132002)⨜⨶(⪁⇼⪩⨒∯302302)=⪩⨒∯203333311","reverse_text":"⪩⨒∯203333311=(⪩⨒∯1320211⪕⪩⨒∯132002)⨜⨶(⪁⇼⪩⨒∯302302)","cot":[{"info":"⪩⨒∯1320211⪕⪩⨒∯132002=⪩⨒∯3201031","layer":1},{"info":"⪁⇼⪩⨒∯302302=⪩⨒∯12212","layer":1},{"info":"⪩⨒∯3201031⨜⨶⪩⨒∯12212=⪩⨒∯203333311","layer":0}]}
{"id":332,"expression_no_base_symbol":"(⫖→$6055$)∀⇚≩$1719$⫁$1861$","expression":"(⫖→⪩⨒∯1132213)∀⇚≩⪩⨒∯122313⫁⪩⨒∯131011","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7589,"operation_count":3,"complexity_ratio":2529.6666666666665,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"unary","operator":"⫖→","unary_expr":{"type":"numeric_atoms","value":6055,"base":4}},"right_expr":{"type":"binary","operator":"⫁","left_expr":{"type":"numeric_atoms","value":1719,"base":4},"right_expr":{"type":"numeric_atoms","value":1861,"base":4}}},"used_operators":["LRNGc0VcxI","U4ylXWHChL","0ajvFaJAv0"],"dependent_operators":["X99M06cbEe","tmPS8pqC7x","Ikt5ks8PT7","AFVx7xoS7T","o20kRiQErp","cHh1gJQ2o6","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6055","layer":2},{"info":"compute unary expreesion, input=6055, op_id = U4ylXWHChL, unary_op_definition = '⫖→a = { (((a⨪↰⇹a)⇌⫙⪟(a⩧⪆a))∸) }', output=177","layer":1},{"info":"number node, value=1719","layer":2},{"info":"number node, value=1861","layer":2},{"info":"compute binary expreesion, left_input=1719, right_input=1861, op_id = 0ajvFaJAv0 binary_op_definition= 'a⫁b = { (a≹⇙⪍6) , if a==154 ; (b⩘b) , else }', output=160","layer":1},{"info":"compute binary expreesion, left_input=177, right_input=160, op_id = LRNGc0VcxI binary_op_definition= 'a∀⇚≩b = {b, if a == 0; ((a-1)∀⇚≩b)≫≃, if a > 0 and abs(a) < 1000000; -((a+1)∀⇚≩b)≫≃, if a < 0 and abs(a) < 1000000; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⫖→⪩⨒∯1132213)∀⇚≩⪩⨒∯122313⫁⪩⨒∯131011=NaN","reverse_text":"NaN=(⫖→⪩⨒∯1132213)∀⇚≩⪩⨒∯122313⫁⪩⨒∯131011","cot":[{"info":"⫖→⪩⨒∯1132213=⪩⨒∯2301","layer":1},{"info":"⪩⨒∯122313⫁⪩⨒∯131011=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯2301∀⇚≩⪩⨒∯2200=NaN","layer":0}]}
{"id":333,"expression_no_base_symbol":"≸($5395$⋅⇍$3046$)","expression":"≸(⪩⨒∯1110103⋅⇍⪩⨒∯233212)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":64,"operation_count":2,"complexity_ratio":32.0,"tree":{"type":"unary","operator":"≸","unary_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":5395,"base":4},"right_expr":{"type":"numeric_atoms","value":3046,"base":4}}},"used_operators":["eOf03JbCpp","AdZkA7nFnk"],"dependent_operators":["WmT3o8z6ya","l07mrZUIn9","NTOWxs364D","RygbFNSyEJ","tifHPKVTfV","oRDoc9rAEX","IwW236VD4Y","1aApVXNlOP","Z5m6OM72h2","mqXw5SEYmG","IWmyXbctLI","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6"],"result":"⪩⨒∯11133","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5395","layer":2},{"info":"number node, value=3046","layer":2},{"info":"compute binary expreesion, left_input=5395, right_input=3046, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"compute unary expreesion, input=-22, op_id = eOf03JbCpp, unary_op_definition = '≸a = { (29∘((630⊋≦⊧a)⩚⊴⇥(a≦↸a))) , if (a⋘⨑⨽)>2 ; (((a⪮%⊝a)⇼⇔∾(a↪⪝))⫸⊐((a⪮%⊝a)≠≀(3⩇∃⫛a))) , else }', output=351","layer":0}],"base":4,"result_base":4,"text":"≸(⪩⨒∯1110103⋅⇍⪩⨒∯233212)=⪩⨒∯11133","reverse_text":"⪩⨒∯11133=≸(⪩⨒∯1110103⋅⇍⪩⨒∯233212)","cot":[{"info":"⪩⨒∯1110103⋅⇍⪩⨒∯233212=⪩⨒∯-112","layer":1},{"info":"≸⪩⨒∯-112=⪩⨒∯11133","layer":0}]}
{"id":334,"expression_no_base_symbol":"($4110$⫦⪉$2538$)⩌⋺($1299$∪⫐$5930$)","expression":"(⪩⨒∯1000032⫦⪉⪩⨒∯213222)⩌⋺(⪩⨒∯110103∪⫐⪩⨒∯1130222)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":34,"operation_count":3,"complexity_ratio":11.333333333333334,"tree":{"type":"binary","operator":"⩌⋺","left_expr":{"type":"binary","operator":"⫦⪉","left_expr":{"type":"numeric_atoms","value":4110,"base":4},"right_expr":{"type":"numeric_atoms","value":2538,"base":4}},"right_expr":{"type":"binary","operator":"∪⫐","left_expr":{"type":"numeric_atoms","value":1299,"base":4},"right_expr":{"type":"numeric_atoms","value":5930,"base":4}}},"used_operators":["g7Hmc5v1ko","wscyQdcy20","7YooWSwCyH"],"dependent_operators":["9FxExcQeMw","W4YGzv6Whe","NTOWxs364D","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","i8ToyICDmI","QMFrweE19q","W4YGzv6Whe","B3sABdIn96","9HNa5Wba9A","g7Hmc5v1ko","nREPSIbpBE","D3AQDKkPcf","rJVOvQCfKK","2DDjHMKMc0"],"result":"⪩⨒∯131230","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4110","layer":2},{"info":"number node, value=2538","layer":2},{"info":"compute binary expreesion, left_input=4110, right_input=2538, op_id = wscyQdcy20 binary_op_definition= 'a⫦⪉b = { ((a⩌⋺206)⪹) , if (a∷677)>=23 ; ((b+a)*(b⨚b)) , else }', output=-3320","layer":1},{"info":"number node, value=1299","layer":2},{"info":"number node, value=5930","layer":2},{"info":"compute binary expreesion, left_input=1299, right_input=5930, op_id = 7YooWSwCyH binary_op_definition= 'a∪⫐b = { ((a⋝⋈⪟b)⨎a) }', output=1299","layer":1},{"info":"compute binary expreesion, left_input=-3320, right_input=1299, op_id = g7Hmc5v1ko binary_op_definition= 'a⩌⋺b = { ((⨞⊢(b⨵⪆b))∲⫓((a⪨≂b)⪨≂(b⩷∴919))) , if (b⫡⨏102)>364 and (-b)==524 ; (b⇼⇔∾((a+a)⩚⊴⇥(-a))) , else }', output=1900","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1000032⫦⪉⪩⨒∯213222)⩌⋺(⪩⨒∯110103∪⫐⪩⨒∯1130222)=⪩⨒∯131230","reverse_text":"⪩⨒∯131230=(⪩⨒∯1000032⫦⪉⪩⨒∯213222)⩌⋺(⪩⨒∯110103∪⫐⪩⨒∯1130222)","cot":[{"info":"⪩⨒∯1000032⫦⪉⪩⨒∯213222=⪩⨒∯-303320","layer":1},{"info":"⪩⨒∯110103∪⫐⪩⨒∯1130222=⪩⨒∯110103","layer":1},{"info":"⪩⨒∯-303320⩌⋺⪩⨒∯110103=⪩⨒∯131230","layer":0}]}
{"id":335,"expression_no_base_symbol":"($3772$≥⨤⩑$1299$)⪝($2857$⫰⋱$1642$)","expression":"(⪩⨒∯322330≥⨤⩑⪩⨒∯110103)⪝(⪩⨒∯230221⫰⋱⪩⨒∯121222)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":438,"operation_count":3,"complexity_ratio":146.0,"tree":{"type":"binary","operator":"⪝","left_expr":{"type":"binary","operator":"≥⨤⩑","left_expr":{"type":"numeric_atoms","value":3772,"base":4},"right_expr":{"type":"numeric_atoms","value":1299,"base":4}},"right_expr":{"type":"binary","operator":"⫰⋱","left_expr":{"type":"numeric_atoms","value":2857,"base":4},"right_expr":{"type":"numeric_atoms","value":1642,"base":4}}},"used_operators":["wicAB68Tmb","gJLn6v0xnP","6o9Blt3TJ6"],"dependent_operators":["L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X","mp7IySMOzn","aA7tF3KVD3","QvoQhV0rrE","W4YGzv6Whe","nCS4ZIUYfx","Qy55tPpLXF"],"result":"⪩⨒∯-10003313","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3772","layer":2},{"info":"number node, value=1299","layer":2},{"info":"compute binary expreesion, left_input=3772, right_input=1299, op_id = gJLn6v0xnP binary_op_definition= 'a≥⨤⩑b = { (b⇷a) , if (b⪘⨀)>356 ; (702∠⫱488) , else }', output=1234","layer":1},{"info":"number node, value=2857","layer":2},{"info":"number node, value=1642","layer":2},{"info":"compute binary expreesion, left_input=2857, right_input=1642, op_id = 6o9Blt3TJ6 binary_op_definition= 'a⫰⋱b = { ((a+b)⨳⩥⨓(b⋥≓≎b)) }', output=-2824","layer":1},{"info":"compute binary expreesion, left_input=1234, right_input=-2824, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=-16631","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯322330≥⨤⩑⪩⨒∯110103)⪝(⪩⨒∯230221⫰⋱⪩⨒∯121222)=⪩⨒∯-10003313","reverse_text":"⪩⨒∯-10003313=(⪩⨒∯322330≥⨤⩑⪩⨒∯110103)⪝(⪩⨒∯230221⫰⋱⪩⨒∯121222)","cot":[{"info":"⪩⨒∯322330≥⨤⩑⪩⨒∯110103=⪩⨒∯103102","layer":1},{"info":"⪩⨒∯230221⫰⋱⪩⨒∯121222=⪩⨒∯-230020","layer":1},{"info":"⪩⨒∯103102⪝⪩⨒∯-230020=⪩⨒∯-10003313","layer":0}]}
{"id":336,"expression_no_base_symbol":"(≱⇩⩕$1200$)⫯⪬∳$4067$∓⋝$1725$","expression":"(≱⇩⩕⪩⨒∯102300)⫯⪬∳⪩⨒∯333203∓⋝⪩⨒∯122331","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":75,"operation_count":3,"complexity_ratio":25.0,"tree":{"type":"binary","operator":"⫯⪬∳","left_expr":{"type":"unary","operator":"≱⇩⩕","unary_expr":{"type":"numeric_atoms","value":1200,"base":4}},"right_expr":{"type":"binary","operator":"∓⋝","left_expr":{"type":"numeric_atoms","value":4067,"base":4},"right_expr":{"type":"numeric_atoms","value":1725,"base":4}}},"used_operators":["d7ASUq0ydm","3DZMoQKiUl","PoHhknlbAi"],"dependent_operators":["Qy55tPpLXF","BjRHVeLaeN","8w2t5hMYqp","Ph9nP6C5qx","eewbuw0ToL","D4vGDi5EA2","AFVx7xoS7T","12rbrZMWeM","xNBdhnnwKq","DZ8iAZOCBD","DbCuESL50I","mqXw5SEYmG","2MzE1hQ0cz"],"result":"⪩⨒∯20103","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1200","layer":2},{"info":"compute unary expreesion, input=1200, op_id = 3DZMoQKiUl, unary_op_definition = '≱⇩⩕a = { (((a⋳⪒a)⊭∹↮)⇌⫙⪟a) }', output=113","layer":1},{"info":"number node, value=4067","layer":2},{"info":"number node, value=1725","layer":2},{"info":"compute binary expreesion, left_input=4067, right_input=1725, op_id = PoHhknlbAi binary_op_definition= 'a∓⋝b = { (((a⊉≛↸a)⫸⊐(⋼∭⪍b))∩⋅) }', output=67","layer":1},{"info":"compute binary expreesion, left_input=113, right_input=67, op_id = d7ASUq0ydm binary_op_definition= 'a⫯⪬∳b = { ((b⋥≓≎a)≧⫂∧(⊄⩳↩a)) , if (a≦≮≮)!=65 ; ((b⫩⊇)⋥≓≎(a⨰b)) , else }', output=531","layer":0}],"base":4,"result_base":4,"text":"(≱⇩⩕⪩⨒∯102300)⫯⪬∳⪩⨒∯333203∓⋝⪩⨒∯122331=⪩⨒∯20103","reverse_text":"⪩⨒∯20103=(≱⇩⩕⪩⨒∯102300)⫯⪬∳⪩⨒∯333203∓⋝⪩⨒∯122331","cot":[{"info":"≱⇩⩕⪩⨒∯102300=⪩⨒∯1301","layer":1},{"info":"⪩⨒∯333203∓⋝⪩⨒∯122331=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯1301⫯⪬∳⪩⨒∯1003=⪩⨒∯20103","layer":0}]}
{"id":337,"expression_no_base_symbol":"(⨈⪑$1493$)∖($8344$∴≳≥)","expression":"(⨈⪑⪩⨒∯113111)∖(⪩⨒∯2002120∴≳≥)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2887,"operation_count":3,"complexity_ratio":962.3333333333334,"tree":{"type":"binary","operator":"∖","left_expr":{"type":"unary","operator":"⨈⪑","unary_expr":{"type":"numeric_atoms","value":1493,"base":4}},"right_expr":{"type":"unary","operator":"∴≳≥","unary_expr":{"type":"numeric_atoms","value":8344,"base":4}}},"used_operators":["tXD093vOjl","mp94q5OcYM","a3N2hFLK0J"],"dependent_operators":["rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC","YjI8oCXuph","09Ly4LVMIf","Bmrmz2XGnR","kbkesczE7y","i8ToyICDmI","IWmyXbctLI","g55IO6H4Gj","DpFCA1CohY","xUOZtlo3hN"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1493","layer":2},{"info":"compute unary expreesion, input=1493, op_id = mp94q5OcYM, unary_op_definition = '⨈⪑a = { (((⫇a)⫃⨇(89⪮%⊝a))≬⋮((a≚⊃≕a)∲⫓(a⪮%⊝117))) }', output=868","layer":1},{"info":"number node, value=8344","layer":2},{"info":"compute unary expreesion, input=8344, op_id = a3N2hFLK0J, unary_op_definition = 'a∴≳≥ = { (⨞⊢a) , if (⋗⩬⋾a)==641 ; (a⨸⪁a) , else }', output=33376","layer":1},{"info":"compute binary expreesion, left_input=868, right_input=33376, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⨈⪑⪩⨒∯113111)∖(⪩⨒∯2002120∴≳≥)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⨈⪑⪩⨒∯113111)∖(⪩⨒∯2002120∴≳≥)","cot":[{"info":"⨈⪑⪩⨒∯113111=⪩⨒∯31210","layer":1},{"info":"⪩⨒∯2002120∴≳≥=⪩⨒∯20021200","layer":1},{"info":"⪩⨒∯31210∖⪩⨒∯20021200=⪩⨒∯0","layer":0}]}
{"id":338,"expression_no_base_symbol":"($1315$⫰⋱$1191$)⊱⇼⊻($2342$⫲≸⪮$1167$)","expression":"(⪩⨒∯110203⫰⋱⪩⨒∯102213)⊱⇼⊻(⪩⨒∯210212⫲≸⪮⪩⨒∯102033)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2357,"operation_count":3,"complexity_ratio":785.6666666666666,"tree":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"binary","operator":"⫰⋱","left_expr":{"type":"numeric_atoms","value":1315,"base":4},"right_expr":{"type":"numeric_atoms","value":1191,"base":4}},"right_expr":{"type":"binary","operator":"⫲≸⪮","left_expr":{"type":"numeric_atoms","value":2342,"base":4},"right_expr":{"type":"numeric_atoms","value":1167,"base":4}}},"used_operators":["FyVja0WsTP","6o9Blt3TJ6","P3lXMJvFrc"],"dependent_operators":["W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","W4YGzv6Whe","nCS4ZIUYfx","Qy55tPpLXF","tmPS8pqC7x","oWn0xqSxBt","DbCuESL50I"],"result":"⪩⨒∯1103110","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1315","layer":2},{"info":"number node, value=1191","layer":2},{"info":"compute binary expreesion, left_input=1315, right_input=1191, op_id = 6o9Blt3TJ6 binary_op_definition= 'a⫰⋱b = { ((a+b)⨳⩥⨓(b⋥≓≎b)) }', output=-1282","layer":1},{"info":"number node, value=2342","layer":2},{"info":"number node, value=1167","layer":2},{"info":"compute binary expreesion, left_input=2342, right_input=1167, op_id = P3lXMJvFrc binary_op_definition= 'a⫲≸⪮b = { (⋼∭⪍a) , if (⊙↵-b)>333 ; (a⨪↰⇹b) , else }', output=2342","layer":1},{"info":"compute binary expreesion, left_input=-1282, right_input=2342, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=5332","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯110203⫰⋱⪩⨒∯102213)⊱⇼⊻(⪩⨒∯210212⫲≸⪮⪩⨒∯102033)=⪩⨒∯1103110","reverse_text":"⪩⨒∯1103110=(⪩⨒∯110203⫰⋱⪩⨒∯102213)⊱⇼⊻(⪩⨒∯210212⫲≸⪮⪩⨒∯102033)","cot":[{"info":"⪩⨒∯110203⫰⋱⪩⨒∯102213=⪩⨒∯-110002","layer":1},{"info":"⪩⨒∯210212⫲≸⪮⪩⨒∯102033=⪩⨒∯210212","layer":1},{"info":"⪩⨒∯-110002⊱⇼⊻⪩⨒∯210212=⪩⨒∯1103110","layer":0}]}
{"id":339,"expression_no_base_symbol":"($8714$⩹$6824$)⨥⫆($1289$⋛$1543$)","expression":"(⪩⨒∯2020022⩹⪩⨒∯1222220)⨥⫆(⪩⨒∯110021⋛⪩⨒∯120013)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":286,"operation_count":3,"complexity_ratio":95.33333333333333,"tree":{"type":"binary","operator":"⨥⫆","left_expr":{"type":"binary","operator":"⩹","left_expr":{"type":"numeric_atoms","value":8714,"base":4},"right_expr":{"type":"numeric_atoms","value":6824,"base":4}},"right_expr":{"type":"binary","operator":"⋛","left_expr":{"type":"numeric_atoms","value":1289,"base":4},"right_expr":{"type":"numeric_atoms","value":1543,"base":4}}},"used_operators":["yXekIHxTD4","2Wsdkap16l","YbUVn0Rbpy"],"dependent_operators":["eRqsBgTDFp","ancx8kZcWl","oacrs7FA3X","rysDP5nf3Z","NTOWxs364D","23Mk6UjR3U","XIabStNQrY","2DDjHMKMc0","12rbrZMWeM","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx","d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA"],"result":"⪩⨒∯-1","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8714","layer":2},{"info":"number node, value=6824","layer":2},{"info":"compute binary expreesion, left_input=8714, right_input=6824, op_id = 2Wsdkap16l binary_op_definition= 'a⩹b = { (b-((b⨳⩥⨓b)⨸⪁(1⋝⋈⪟b))) , if (b⇋≉)!=246 ; (((a⇋≉)⨰(a⋷a))⋳⪒((a⩚⊴⇥a)⨳⩥⨓(a≧⫂∧a))) , else }', output=6822","layer":1},{"info":"number node, value=1289","layer":2},{"info":"number node, value=1543","layer":2},{"info":"compute binary expreesion, left_input=1289, right_input=1543, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-120591","layer":1},{"info":"compute binary expreesion, left_input=6822, right_input=-120591, op_id = yXekIHxTD4 binary_op_definition= 'a⨥⫆b = { (b⨝⩣∺) , if (a⪒⊣⊆344)<109 ; (b⪘⫢a) , else }', output=-1","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2020022⩹⪩⨒∯1222220)⨥⫆(⪩⨒∯110021⋛⪩⨒∯120013)=⪩⨒∯-1","reverse_text":"⪩⨒∯-1=(⪩⨒∯2020022⩹⪩⨒∯1222220)⨥⫆(⪩⨒∯110021⋛⪩⨒∯120013)","cot":[{"info":"⪩⨒∯2020022⩹⪩⨒∯1222220=⪩⨒∯1222212","layer":1},{"info":"⪩⨒∯110021⋛⪩⨒∯120013=⪩⨒∯-131130033","layer":1},{"info":"⪩⨒∯1222212⨥⫆⪩⨒∯-131130033=⪩⨒∯-1","layer":0}]}
{"id":340,"expression_no_base_symbol":"⨰⫟⨤(⋎⨆$1642$)","expression":"⨰⫟⨤(⋎⨆⪩⨒∯121222)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":921,"operation_count":2,"complexity_ratio":460.5,"tree":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"unary","operator":"⋎⨆","unary_expr":{"type":"numeric_atoms","value":1642,"base":4}}},"used_operators":["Tw270M8GLb","E64sFOc4tB"],"dependent_operators":["sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","PxiHyQbrIp","l07mrZUIn9","3sJ7IOPOlU","liw5iZPkLH"],"result":"⪩⨒∯101020311312","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1642","layer":2},{"info":"compute unary expreesion, input=1642, op_id = E64sFOc4tB, unary_op_definition = '⋎⨆a = { (a⪇≇⋚a) , if (⊁⨺a)>31 and (⨡↴a)>=90 ; (136↪⪝) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=4492662","layer":0}],"base":4,"result_base":4,"text":"⨰⫟⨤(⋎⨆⪩⨒∯121222)=⪩⨒∯101020311312","reverse_text":"⪩⨒∯101020311312=⨰⫟⨤(⋎⨆⪩⨒∯121222)","cot":[{"info":"⋎⨆⪩⨒∯121222=⪩⨒∯0","layer":1},{"info":"⨰⫟⨤⪩⨒∯0=⪩⨒∯101020311312","layer":0}]}
{"id":341,"expression_no_base_symbol":"⊈($5218$≚⊃≕$5820$)","expression":"⊈(⪩⨒∯1101202≚⊃≕⪩⨒∯1122330)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":21,"operation_count":2,"complexity_ratio":10.5,"tree":{"type":"unary","operator":"⊈","unary_expr":{"type":"binary","operator":"≚⊃≕","left_expr":{"type":"numeric_atoms","value":5218,"base":4},"right_expr":{"type":"numeric_atoms","value":5820,"base":4}}},"used_operators":["RHru8klgy8","Bmrmz2XGnR"],"dependent_operators":["12rbrZMWeM","xUOZtlo3hN","9FxExcQeMw","Qy55tPpLXF","7j4O788W3g","sdazOOVcIp","8w2t5hMYqp","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q"],"result":"⪩⨒∯-3301","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5218","layer":2},{"info":"number node, value=5820","layer":2},{"info":"compute binary expreesion, left_input=5218, right_input=5820, op_id = Bmrmz2XGnR binary_op_definition= 'a≚⊃≕b = { (-((⊄⩳↩b)⪨≂(a⩷∴b))) , if ((b⫡⨏524)<690 or (⨞⊢a)>=395) ; ((⊄⩳↩(b⋥≓≎a))⋥≓≎((a↺a)⪨≂(479⨸⪁a))) , else }', output=67","layer":1},{"info":"compute unary expreesion, input=67, op_id = RHru8klgy8, unary_op_definition = '⊈a = { (a⋳⪒a) , if a==61 ; (⨞⊢a) , else }', output=-241","layer":0}],"base":4,"result_base":4,"text":"⊈(⪩⨒∯1101202≚⊃≕⪩⨒∯1122330)=⪩⨒∯-3301","reverse_text":"⪩⨒∯-3301=⊈(⪩⨒∯1101202≚⊃≕⪩⨒∯1122330)","cot":[{"info":"⪩⨒∯1101202≚⊃≕⪩⨒∯1122330=⪩⨒∯1003","layer":1},{"info":"⊈⪩⨒∯1003=⪩⨒∯-3301","layer":0}]}
{"id":342,"expression_no_base_symbol":"⩩($4163$∣$2633$)","expression":"⩩(⪩⨒∯1001003∣⪩⨒∯221021)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5100,"operation_count":2,"complexity_ratio":2550.0,"tree":{"type":"unary","operator":"⩩","unary_expr":{"type":"binary","operator":"∣","left_expr":{"type":"numeric_atoms","value":4163,"base":4},"right_expr":{"type":"numeric_atoms","value":2633,"base":4}}},"used_operators":["kMhfGuqI2H","PPChnnnBFF"],"dependent_operators":["6aG7x05OhS","z63VuFQld9","lFBm8KRb8F","f6k1SAg4EE","ZGCBLdVRRX","eLAdDNolq6","eH2TOUuTDT","Ph9nP6C5qx","i8ToyICDmI"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4163","layer":2},{"info":"number node, value=2633","layer":2},{"info":"compute binary expreesion, left_input=4163, right_input=2633, op_id = PPChnnnBFF binary_op_definition= 'a∣b = { (≤/((a⪐)≧⫂∧(a∲⫓b))) , if (b⪐)<590 ; a , else }', output=4163","layer":1},{"info":"compute unary expreesion, input=4163, op_id = kMhfGuqI2H, unary_op_definition = '⩩a = { (⇜(a⫩)) , if (⇵⪽a)!=444 ; ((a⪒a)∧) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⩩(⪩⨒∯1001003∣⪩⨒∯221021)=NaN","reverse_text":"NaN=⩩(⪩⨒∯1001003∣⪩⨒∯221021)","cot":[{"info":"⪩⨒∯1001003∣⪩⨒∯221021=⪩⨒∯1001003","layer":1},{"info":"⩩⪩⨒∯1001003=NaN","layer":0}]}
{"id":343,"expression_no_base_symbol":"($1911$⫔⩽⩺$2894$)⪝(⊽$4708$)","expression":"(⪩⨒∯131313⫔⩽⩺⪩⨒∯231032)⪝(⊽⪩⨒∯1021210)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":453,"operation_count":3,"complexity_ratio":151.0,"tree":{"type":"binary","operator":"⪝","left_expr":{"type":"binary","operator":"⫔⩽⩺","left_expr":{"type":"numeric_atoms","value":1911,"base":4},"right_expr":{"type":"numeric_atoms","value":2894,"base":4}},"right_expr":{"type":"unary","operator":"⊽","unary_expr":{"type":"numeric_atoms","value":4708,"base":4}}},"used_operators":["wicAB68Tmb","i9eR4S00cU","QxG7OkqoLX"],"dependent_operators":["L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X","Tw270M8GLb","fu6greOZ01","g55IO6H4Gj","VJ330n2nnx","z63VuFQld9"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1911","layer":2},{"info":"number node, value=2894","layer":2},{"info":"compute binary expreesion, left_input=1911, right_input=2894, op_id = i9eR4S00cU binary_op_definition= 'a⫔⩽⩺b = { (⨰⫟⨤(a⨐⩸⫘b)) }', output=nan","layer":1},{"info":"number node, value=4708","layer":2},{"info":"compute unary expreesion, input=4708, op_id = QxG7OkqoLX, unary_op_definition = '⊽a = { (a⨸⪁761) , if (a↬⩅∪)<402 ; (a∧) , else }', output=10938","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=10938, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯131313⫔⩽⩺⪩⨒∯231032)⪝(⊽⪩⨒∯1021210)=NaN","reverse_text":"NaN=(⪩⨒∯131313⫔⩽⩺⪩⨒∯231032)⪝(⊽⪩⨒∯1021210)","cot":[{"info":"⪩⨒∯131313⫔⩽⩺⪩⨒∯231032=NaN","layer":1},{"info":"⊽⪩⨒∯1021210=⪩⨒∯2222322","layer":1},{"info":"NaN⪝⪩⨒∯2222322=NaN","layer":0}]}
{"id":344,"expression_no_base_symbol":"⩦⊞($7994$⨒$1815$)","expression":"⩦⊞(⪩⨒∯1330322⨒⪩⨒∯130113)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":27,"operation_count":2,"complexity_ratio":13.5,"tree":{"type":"unary","operator":"⩦⊞","unary_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":7994,"base":4},"right_expr":{"type":"numeric_atoms","value":1815,"base":4}}},"used_operators":["u7fv1HBiaC","y75s1iXyHd"],"dependent_operators":["eLAdDNolq6","Qy55tPpLXF","7j4O788W3g","AF7qkfDlqP","srAu1WTS94","oacrs7FA3X","7qqUquhhSb"],"result":"⪩⨒∯-113100020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7994","layer":2},{"info":"number node, value=1815","layer":2},{"info":"compute binary expreesion, left_input=7994, right_input=1815, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-47592","layer":1},{"info":"compute unary expreesion, input=-47592, op_id = u7fv1HBiaC, unary_op_definition = '⩦⊞a = { (⨑⩽⪐a) , if a>=405 ; ((≤/395)⋥≓≎(a↺a)) , else }', output=-95240","layer":0}],"base":4,"result_base":4,"text":"⩦⊞(⪩⨒∯1330322⨒⪩⨒∯130113)=⪩⨒∯-113100020","reverse_text":"⪩⨒∯-113100020=⩦⊞(⪩⨒∯1330322⨒⪩⨒∯130113)","cot":[{"info":"⪩⨒∯1330322⨒⪩⨒∯130113=⪩⨒∯-23213220","layer":1},{"info":"⩦⊞⪩⨒∯-23213220=⪩⨒∯-113100020","layer":0}]}
{"id":345,"expression_no_base_symbol":"($5634$⋾⨃∁$9262$)⊋($7533$⪭$2729$)","expression":"(⪩⨒∯1120002⋾⨃∁⪩⨒∯2100232)⊋(⪩⨒∯1311231⪭⪩⨒∯222221)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9372,"operation_count":3,"complexity_ratio":3124.0,"tree":{"type":"binary","operator":"⊋","left_expr":{"type":"binary","operator":"⋾⨃∁","left_expr":{"type":"numeric_atoms","value":5634,"base":4},"right_expr":{"type":"numeric_atoms","value":9262,"base":4}},"right_expr":{"type":"binary","operator":"⪭","left_expr":{"type":"numeric_atoms","value":7533,"base":4},"right_expr":{"type":"numeric_atoms","value":2729,"base":4}}},"used_operators":["W4tP9CfskL","212REbPD9h","j9kHMeSvPp"],"dependent_operators":["2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu","eLxqMNBOBk","Qy55tPpLXF","w2P8NbNXyL","2DQ55sFlQl","f6k1SAg4EE","COABgblf1C","xUOZtlo3hN"],"result":"⪩⨒∯-1103222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5634","layer":2},{"info":"number node, value=9262","layer":2},{"info":"compute binary expreesion, left_input=5634, right_input=9262, op_id = 212REbPD9h binary_op_definition= 'a⋾⨃∁b = { ((430⊉↱≁b)⨵⪆b) , if (a⪒898)>=359 ; ((⫓⪴b)⊉↱≁(26⋥≓≎b)) , else }', output=857735202","layer":1},{"info":"number node, value=7533","layer":2},{"info":"number node, value=2729","layer":2},{"info":"compute binary expreesion, left_input=7533, right_input=2729, op_id = j9kHMeSvPp binary_op_definition= 'a⪭b = { (⨞⊢a) , if a<649 ; (b⊭↱b) , else }', output=5","layer":1},{"info":"compute binary expreesion, left_input=857735202, right_input=5, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=-5354","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1120002⋾⨃∁⪩⨒∯2100232)⊋(⪩⨒∯1311231⪭⪩⨒∯222221)=⪩⨒∯-1103222","reverse_text":"⪩⨒∯-1103222=(⪩⨒∯1120002⋾⨃∁⪩⨒∯2100232)⊋(⪩⨒∯1311231⪭⪩⨒∯222221)","cot":[{"info":"⪩⨒∯1120002⋾⨃∁⪩⨒∯2100232=⪩⨒∯303020000000202","layer":1},{"info":"⪩⨒∯1311231⪭⪩⨒∯222221=⪩⨒∯11","layer":1},{"info":"⪩⨒∯303020000000202⊋⪩⨒∯11=⪩⨒∯-1103222","layer":0}]}
{"id":346,"expression_no_base_symbol":"($2863$⊘)⩇∃⫛(⊥$1815$)","expression":"(⪩⨒∯230233⊘)⩇∃⫛(⊥⪩⨒∯130113)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":32,"operation_count":3,"complexity_ratio":10.666666666666666,"tree":{"type":"binary","operator":"⩇∃⫛","left_expr":{"type":"unary","operator":"⊘","unary_expr":{"type":"numeric_atoms","value":2863,"base":4}},"right_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":1815,"base":4}}},"used_operators":["1aApVXNlOP","gu96TGCTMs","Q3PJZHRvZv"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","e1ybzncUwg","Qy55tPpLXF","DZ8iAZOCBD","2DQ55sFlQl","t8gj7n24qd","2DDjHMKMc0","Z2TMIBDE3Q","14qkJME0vr","f6k1SAg4EE","Ph9nP6C5qx","eewbuw0ToL","u6S6b8DprG","XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","fu6greOZ01"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2863","layer":2},{"info":"compute unary expreesion, input=2863, op_id = gu96TGCTMs, unary_op_definition = 'a⊘ = { ((a⨰a)/(∥⊫a)) , if (⨑⩽⪐a)!=520 or (a≧⫂∧486)>62 or (⊄⩳↩a)>=602 ; ((-240)⩚⊴⇥a) , else }', output=0","layer":1},{"info":"number node, value=1815","layer":2},{"info":"compute unary expreesion, input=1815, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = 1aApVXNlOP binary_op_definition= 'a⩇∃⫛b = { (((b⊉≛↸a)⩤)⨰((362⩷∴b)⋥≓≎(↽≂a))) , if (a⊦⊿)>7 and b<=506 and (-a)==737 ; (((b⩤)⪒(b≧⫂∧a))⋝⋈⪟((a⨵⪆a)-(≉a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯230233⊘)⩇∃⫛(⊥⪩⨒∯130113)=NaN","reverse_text":"NaN=(⪩⨒∯230233⊘)⩇∃⫛(⊥⪩⨒∯130113)","cot":[{"info":"⪩⨒∯230233⊘=⪩⨒∯0","layer":1},{"info":"⊥⪩⨒∯130113=NaN","layer":1},{"info":"⪩⨒∯0⩇∃⫛NaN=NaN","layer":0}]}
{"id":347,"expression_no_base_symbol":"$3062$≀⩗∶$3651$∽$3073$⪔⊥$4832$","expression":"⪩⨒∯233312≀⩗∶⪩⨒∯321003∽⪩⨒∯300001⪔⊥⪩⨒∯1023200","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":42,"operation_count":3,"complexity_ratio":14.0,"tree":{"type":"binary","operator":"∽","left_expr":{"type":"binary","operator":"≀⩗∶","left_expr":{"type":"numeric_atoms","value":3062,"base":4},"right_expr":{"type":"numeric_atoms","value":3651,"base":4}},"right_expr":{"type":"binary","operator":"⪔⊥","left_expr":{"type":"numeric_atoms","value":3073,"base":4},"right_expr":{"type":"numeric_atoms","value":4832,"base":4}}},"used_operators":["y4ImoPnbV5","8INZBEW696","HJ9erzHUuu"],"dependent_operators":["NTOWxs364D","QMFrweE19q","KPf6cnQVty","2DlMacCsIx","l07mrZUIn9","eLAdDNolq6","rysDP5nf3Z","7j4O788W3g","tifHPKVTfV","8w2t5hMYqp","sdazOOVcIp","2td37pGCOC","COABgblf1C"],"result":"⪩⨒∯-1232312","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3062","layer":2},{"info":"number node, value=3651","layer":2},{"info":"compute binary expreesion, left_input=3062, right_input=3651, op_id = 8INZBEW696 binary_op_definition= 'a≀⩗∶b = { (a⩨b) , if (a∺≝⩲555)<251 ; (306↪⪝) , else }', output=-3","layer":1},{"info":"number node, value=3073","layer":2},{"info":"number node, value=4832","layer":2},{"info":"compute binary expreesion, left_input=3073, right_input=4832, op_id = HJ9erzHUuu binary_op_definition= 'a⪔⊥b = { (⩦⩻⨪(≤/(315⇼⇔∾a))) , if b<175 ; ((⊄⩳↩(b-b))⇼⇔∾((b⪨≂a)⊭↱(a↺b))) , else }', output=2429","layer":1},{"info":"compute binary expreesion, left_input=-3, right_input=2429, op_id = y4ImoPnbV5 binary_op_definition= 'a∽b = { ((a⩚⊴⇥b)⫡⨏b) }', output=-7094","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯233312≀⩗∶⪩⨒∯321003∽⪩⨒∯300001⪔⊥⪩⨒∯1023200=⪩⨒∯-1232312","reverse_text":"⪩⨒∯-1232312=⪩⨒∯233312≀⩗∶⪩⨒∯321003∽⪩⨒∯300001⪔⊥⪩⨒∯1023200","cot":[{"info":"⪩⨒∯233312≀⩗∶⪩⨒∯321003=⪩⨒∯-3","layer":1},{"info":"⪩⨒∯300001⪔⊥⪩⨒∯1023200=⪩⨒∯211331","layer":1},{"info":"⪩⨒∯-3∽⪩⨒∯211331=⪩⨒∯-1232312","layer":0}]}
{"id":348,"expression_no_base_symbol":"($1424$≚⋢)⨂≜($5459$⋕⪉⪜$4425$)","expression":"(⪩⨒∯112100≚⋢)⨂≜(⪩⨒∯1111103⋕⪉⪜⪩⨒∯1011021)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":242,"operation_count":3,"complexity_ratio":80.66666666666667,"tree":{"type":"binary","operator":"⨂≜","left_expr":{"type":"unary","operator":"≚⋢","unary_expr":{"type":"numeric_atoms","value":1424,"base":4}},"right_expr":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"numeric_atoms","value":5459,"base":4},"right_expr":{"type":"numeric_atoms","value":4425,"base":4}}},"used_operators":["k1SHOSEABc","MahUMFw56D","z6LnFrNh4i"],"dependent_operators":["9FxExcQeMw","HiPekx5b7W","eLxqMNBOBk","JclMnS0uGI","COABgblf1C","U7g4x0WXJJ","3ViojmjbAp","sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1424","layer":2},{"info":"compute unary expreesion, input=1424, op_id = MahUMFw56D, unary_op_definition = 'a≚⋢ = { (a⨓86) }', output=-89","layer":1},{"info":"number node, value=5459","layer":2},{"info":"number node, value=4425","layer":2},{"info":"compute binary expreesion, left_input=5459, right_input=4425, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=2802","layer":1},{"info":"compute binary expreesion, left_input=-89, right_input=2802, op_id = k1SHOSEABc binary_op_definition= 'a⨂≜b = { ((37⊭↱(⫓⪴a))⩷∴((111⨜⨶78)⨔⇊(a∑⇟⊟b))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯112100≚⋢)⨂≜(⪩⨒∯1111103⋕⪉⪜⪩⨒∯1011021)=NaN","reverse_text":"NaN=(⪩⨒∯112100≚⋢)⨂≜(⪩⨒∯1111103⋕⪉⪜⪩⨒∯1011021)","cot":[{"info":"⪩⨒∯112100≚⋢=⪩⨒∯-1121","layer":1},{"info":"⪩⨒∯1111103⋕⪉⪜⪩⨒∯1011021=⪩⨒∯223302","layer":1},{"info":"⪩⨒∯-1121⨂≜⪩⨒∯223302=NaN","layer":0}]}
{"id":349,"expression_no_base_symbol":"$4971$⨑≵⋬$1588$⫃⨇$5375$⫢⨠$1408$","expression":"⪩⨒∯1031223⨑≵⋬⪩⨒∯120310⫃⨇⪩⨒∯1103333⫢⨠⪩⨒∯112000","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":92,"operation_count":3,"complexity_ratio":30.666666666666668,"tree":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"binary","operator":"⨑≵⋬","left_expr":{"type":"numeric_atoms","value":4971,"base":4},"right_expr":{"type":"numeric_atoms","value":1588,"base":4}},"right_expr":{"type":"binary","operator":"⫢⨠","left_expr":{"type":"numeric_atoms","value":5375,"base":4},"right_expr":{"type":"numeric_atoms","value":1408,"base":4}}},"used_operators":["09Ly4LVMIf","XnXgA4xnOs","xlXykHWxX1"],"dependent_operators":["9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG","eewbuw0ToL","AF7qkfDlqP","QMFrweE19q","KFSx94NKJn","e1ybzncUwg","zR4jO40bMj","g7Hmc5v1ko","k2HlF1dBQh","2DlMacCsIx"],"result":"⪩⨒∯-22200","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4971","layer":2},{"info":"number node, value=1588","layer":2},{"info":"compute binary expreesion, left_input=4971, right_input=1588, op_id = XnXgA4xnOs binary_op_definition= 'a⨑≵⋬b = { ((a⨰b)⫡⨏(⨑⩽⪐b)) }', output=15118","layer":1},{"info":"number node, value=5375","layer":2},{"info":"number node, value=1408","layer":2},{"info":"compute binary expreesion, left_input=5375, right_input=1408, op_id = xlXykHWxX1 binary_op_definition= 'a⫢⨠b = { (((b⩨a)⪶≀⋏(a⩌⋺b))⩒⫫(∤(≉a))) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=15118, right_input=160, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=-672","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1031223⨑≵⋬⪩⨒∯120310⫃⨇⪩⨒∯1103333⫢⨠⪩⨒∯112000=⪩⨒∯-22200","reverse_text":"⪩⨒∯-22200=⪩⨒∯1031223⨑≵⋬⪩⨒∯120310⫃⨇⪩⨒∯1103333⫢⨠⪩⨒∯112000","cot":[{"info":"⪩⨒∯1031223⨑≵⋬⪩⨒∯120310=⪩⨒∯3230032","layer":1},{"info":"⪩⨒∯1103333⫢⨠⪩⨒∯112000=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯3230032⫃⨇⪩⨒∯2200=⪩⨒∯-22200","layer":0}]}
{"id":350,"expression_no_base_symbol":"(⊬↢$3853$)∌($2747$⪚$2779$)","expression":"(⊬↢⪩⨒∯330031)∌(⪩⨒∯222323⪚⪩⨒∯223123)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3927,"operation_count":3,"complexity_ratio":1309.0,"tree":{"type":"binary","operator":"∌","left_expr":{"type":"unary","operator":"⊬↢","unary_expr":{"type":"numeric_atoms","value":3853,"base":4}},"right_expr":{"type":"binary","operator":"⪚","left_expr":{"type":"numeric_atoms","value":2747,"base":4},"right_expr":{"type":"numeric_atoms","value":2779,"base":4}}},"used_operators":["8cLx32lpNA","WPoGxAaPR1","HrjLwUk87U"],"dependent_operators":["N41Kp7NANJ","7j4O788W3g","t8gj7n24qd","XGcMNugi78","d7ASUq0ydm","OwUj7dcsQK","FyVja0WsTP","1eCjFl0mb9","j6NVkjMzuk","SL6IHkK8vl","MRPaB8lBjK","yyfyN0ffXY","3Oe9XWJUTD","3tVxb0NHM4","8cLx32lpNA","9FxExcQeMw","rysDP5nf3Z","NTOWxs364D","DZ8iAZOCBD","tifHPKVTfV","eH2TOUuTDT","2DDjHMKMc0"],"result":"⪩⨒∯12210","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3853","layer":2},{"info":"compute unary expreesion, input=3853, op_id = WPoGxAaPR1, unary_op_definition = '⊬↢a = { (((a⫞⩸⩒a)⊝⪿⪼(a⫯⪬∳a))⪎↠((a⨀⨒)↸(∐⩳⋚a))) , if (∓a)>278 ; (((a↙a)⊱⇼⊻(a∌480))⇉⇱⇎) , else }', output=218","layer":1},{"info":"number node, value=2747","layer":2},{"info":"number node, value=2779","layer":2},{"info":"compute binary expreesion, left_input=2747, right_input=2779, op_id = HrjLwUk87U binary_op_definition= 'a⪚b = { (((317⩚⊴⇥a)⋝⋈⪟(518-95))⊉≛↸((97⪐)⩷∴(b⇼⇔∾a))) }', output=-420","layer":1},{"info":"compute binary expreesion, left_input=218, right_input=-420, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=420","layer":0}],"base":4,"result_base":4,"text":"(⊬↢⪩⨒∯330031)∌(⪩⨒∯222323⪚⪩⨒∯223123)=⪩⨒∯12210","reverse_text":"⪩⨒∯12210=(⊬↢⪩⨒∯330031)∌(⪩⨒∯222323⪚⪩⨒∯223123)","cot":[{"info":"⊬↢⪩⨒∯330031=⪩⨒∯3122","layer":1},{"info":"⪩⨒∯222323⪚⪩⨒∯223123=⪩⨒∯-12210","layer":1},{"info":"⪩⨒∯3122∌⪩⨒∯-12210=⪩⨒∯12210","layer":0}]}
{"id":351,"expression_no_base_symbol":"⨴⫝$1818$⫘$3776$","expression":"⨴⫝⪩⨒∯130122⫘⪩⨒∯323000","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3854,"operation_count":2,"complexity_ratio":1927.0,"tree":{"type":"unary","operator":"⨴⫝","unary_expr":{"type":"binary","operator":"⫘","left_expr":{"type":"numeric_atoms","value":1818,"base":4},"right_expr":{"type":"numeric_atoms","value":3776,"base":4}}},"used_operators":["SVb2v531z1","48vC8HMD2b"],"dependent_operators":["oDCm7WA9JY","XnXgA4xnOs","ocnLzx9CaJ","3sJ7IOPOlU","9cloC0Ngie","SWo3A1KBJH","jWTQ2TZYIH","pRsWfj4Fpp","DyGG3AbaNP","5obUd6DV38","8HhzD0ZcuI","YbUVn0Rbpy","AdZkA7nFnk","SIgE0bArFf","OwUj7dcsQK","7j4O788W3g","tfWHHpNKUN","3ViojmjbAp","dfKe02y8D2","tcjXMdvYtA","D4vGDi5EA2","86A5ENbKR9","X99M06cbEe"],"result":"⪩⨒∯22302132212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1818","layer":2},{"info":"number node, value=3776","layer":2},{"info":"compute binary expreesion, left_input=1818, right_input=3776, op_id = 48vC8HMD2b binary_op_definition= 'a⫘b = { ((≘(b⨓a))≫≃) , if ((⇖a)!=319 or (a↺926)<190) ; ((∓a)⫚↹⊑(⪸(a≦≮≮))) , else }', output=2142373","layer":1},{"info":"compute unary expreesion, input=2142373, op_id = SVb2v531z1, unary_op_definition = '⨴⫝a = { ((⪨⨬(⇋↷a))≬⇓((a⋅⇍a)⨑≵⋬(∡178))) , if (a⪇≇⋚963)!=62 ; (((541⋛107)⩼⇪↪(⪭⩑⪱a))⋻⩜⩜((a⊕∕a)∼(459⨽6))) , else }', output=2828198","layer":0}],"base":4,"result_base":4,"text":"⨴⫝⪩⨒∯130122⫘⪩⨒∯323000=⪩⨒∯22302132212","reverse_text":"⪩⨒∯22302132212=⨴⫝⪩⨒∯130122⫘⪩⨒∯323000","cot":[{"info":"⪩⨒∯130122⫘⪩⨒∯323000=⪩⨒∯20023002211","layer":1},{"info":"⨴⫝⪩⨒∯20023002211=⪩⨒∯22302132212","layer":0}]}
{"id":352,"expression_no_base_symbol":"$1297$⇡⇂$3735$↬⩅∪","expression":"⪩⨒∯110101⇡⇂⪩⨒∯322113↬⩅∪","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":18843,"operation_count":2,"complexity_ratio":9421.5,"tree":{"type":"unary","operator":"↬⩅∪","unary_expr":{"type":"binary","operator":"⇡⇂","left_expr":{"type":"numeric_atoms","value":1297,"base":4},"right_expr":{"type":"numeric_atoms","value":3735,"base":4}}},"used_operators":["VJ330n2nnx","UMwdvZNt44"],"dependent_operators":["D4vGDi5EA2","23Mk6UjR3U","u6S6b8DprG","9FxExcQeMw","23Mk6UjR3U","z4E1FaHLuy","3tj9sqzovi","fu6greOZ01","AHs5Up7iyr","lvlrscuwVU","KPf6cnQVty","uBihLCJcMX","12rbrZMWeM","WPoGxAaPR1"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1297","layer":2},{"info":"number node, value=3735","layer":2},{"info":"compute binary expreesion, left_input=1297, right_input=3735, op_id = UMwdvZNt44 binary_op_definition= 'a⇡⇂b = { (((b≹⇙⪍b)⋳⪒(b⋷a))∺≝⩲(⫟(a⩷∴43))) , if (⊬↢a)==727 or (a⇔⨋)<18 ; ((604≴⪞⇿(≻⋜b))⨐⩸⫘a) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = VJ330n2nnx, unary_op_definition = 'a↬⩅∪ = { (a≦≮≮) , if (↽≂a)!=185 or a>=376 or a<=585 ; (a⋷a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯110101⇡⇂⪩⨒∯322113↬⩅∪=NaN","reverse_text":"NaN=⪩⨒∯110101⇡⇂⪩⨒∯322113↬⩅∪","cot":[{"info":"⪩⨒∯110101⇡⇂⪩⨒∯322113=NaN","layer":1},{"info":"NaN↬⩅∪=NaN","layer":0}]}
{"id":353,"expression_no_base_symbol":"$3333$⩘$2321$⇷$3920$⩁⩘$1380$","expression":"⪩⨒∯310011⩘⪩⨒∯210101⇷⪩⨒∯331100⩁⩘⪩⨒∯111210","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2363,"operation_count":3,"complexity_ratio":787.6666666666666,"tree":{"type":"binary","operator":"⇷","left_expr":{"type":"binary","operator":"⩘","left_expr":{"type":"numeric_atoms","value":3333,"base":4},"right_expr":{"type":"numeric_atoms","value":2321,"base":4}},"right_expr":{"type":"binary","operator":"⩁⩘","left_expr":{"type":"numeric_atoms","value":3920,"base":4},"right_expr":{"type":"numeric_atoms","value":1380,"base":4}}},"used_operators":["mp7IySMOzn","cHh1gJQ2o6","gub5Cegaqo"],"dependent_operators":["DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","23Mk6UjR3U","eRqsBgTDFp","zVYPLywUTj","bPywburJMS","KPf6cnQVty","YbVcJGFEVW","5twsqlHp2o","DpFCA1CohY","IWmyXbctLI"],"result":"⪩⨒∯3022020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3333","layer":2},{"info":"number node, value=2321","layer":2},{"info":"compute binary expreesion, left_input=3333, right_input=2321, op_id = cHh1gJQ2o6 binary_op_definition= 'a⩘b = { (((b⋷b)↼⊘⨖(a⊢6))∺≝⩲((a⪒⊣⊆619)≃(a⊪))) }', output=160","layer":1},{"info":"number node, value=3920","layer":2},{"info":"number node, value=1380","layer":2},{"info":"compute binary expreesion, left_input=3920, right_input=1380, op_id = gub5Cegaqo binary_op_definition= 'a⩁⩘b = { ((b⪮%⊝b)⪮%⊝(⋗⩬⋾a)) }', output=6468","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=6468, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=12936","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯310011⩘⪩⨒∯210101⇷⪩⨒∯331100⩁⩘⪩⨒∯111210=⪩⨒∯3022020","reverse_text":"⪩⨒∯3022020=⪩⨒∯310011⩘⪩⨒∯210101⇷⪩⨒∯331100⩁⩘⪩⨒∯111210","cot":[{"info":"⪩⨒∯310011⩘⪩⨒∯210101=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯331100⩁⩘⪩⨒∯111210=⪩⨒∯1211010","layer":1},{"info":"⪩⨒∯2200⇷⪩⨒∯1211010=⪩⨒∯3022020","layer":0}]}
{"id":354,"expression_no_base_symbol":"($7203$⫌⩉⩟$3810$)⫃⨇$4607$⋅⇍$1331$","expression":"(⪩⨒∯1300203⫌⩉⩟⪩⨒∯323202)⫃⨇⪩⨒∯1013333⋅⇍⪩⨒∯110303","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":26695,"operation_count":3,"complexity_ratio":8898.333333333334,"tree":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"binary","operator":"⫌⩉⩟","left_expr":{"type":"numeric_atoms","value":7203,"base":4},"right_expr":{"type":"numeric_atoms","value":3810,"base":4}},"right_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":4607,"base":4},"right_expr":{"type":"numeric_atoms","value":1331,"base":4}}},"used_operators":["09Ly4LVMIf","XIIwhv8d0m","AdZkA7nFnk"],"dependent_operators":["9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG","B5M0gjZbta","UMwdvZNt44","MRPaB8lBjK","vkpjKywKVM","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6"],"result":"⪩⨒∯320","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7203","layer":2},{"info":"number node, value=3810","layer":2},{"info":"compute binary expreesion, left_input=7203, right_input=3810, op_id = XIIwhv8d0m binary_op_definition= 'a⫌⩉⩟b = { (((a↬179)⇮⋭(b⇡⇂b))⇉⇱⇎) }', output=-50","layer":1},{"info":"number node, value=4607","layer":2},{"info":"number node, value=1331","layer":2},{"info":"compute binary expreesion, left_input=4607, right_input=1331, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"compute binary expreesion, left_input=-50, right_input=-22, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=56","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1300203⫌⩉⩟⪩⨒∯323202)⫃⨇⪩⨒∯1013333⋅⇍⪩⨒∯110303=⪩⨒∯320","reverse_text":"⪩⨒∯320=(⪩⨒∯1300203⫌⩉⩟⪩⨒∯323202)⫃⨇⪩⨒∯1013333⋅⇍⪩⨒∯110303","cot":[{"info":"⪩⨒∯1300203⫌⩉⩟⪩⨒∯323202=⪩⨒∯-302","layer":1},{"info":"⪩⨒∯1013333⋅⇍⪩⨒∯110303=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯-302⫃⨇⪩⨒∯-112=⪩⨒∯320","layer":0}]}
{"id":355,"expression_no_base_symbol":"≛$6042$∠↢$3739$","expression":"≛⪩⨒∯1132122∠↢⪩⨒∯322123","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":41,"operation_count":2,"complexity_ratio":20.5,"tree":{"type":"unary","operator":"≛","unary_expr":{"type":"binary","operator":"∠↢","left_expr":{"type":"numeric_atoms","value":6042,"base":4},"right_expr":{"type":"numeric_atoms","value":3739,"base":4}}},"used_operators":["W7eaUhjymW","KbjG8mgYpV"],"dependent_operators":["W4YGzv6Whe","NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","DZ8iAZOCBD","JLbD19bQDL","sdazOOVcIp","2DDjHMKMc0","f6k1SAg4EE","eewbuw0ToL","COABgblf1C","rysDP5nf3Z","NTOWxs364D","XPYlsWDdGa","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","nCS4ZIUYfx","COABgblf1C"],"result":"⪩⨒∯-210320331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6042","layer":2},{"info":"number node, value=3739","layer":2},{"info":"compute binary expreesion, left_input=6042, right_input=3739, op_id = KbjG8mgYpV binary_op_definition= 'a∠↢b = { (a⊭↱((159⨳⩥⨓16)-(b⨸⪁a))) , if (b==488 or (⨞⊢a)==254) ; (⪲⇎((-b)⫡⨏(b⩚⊴⇥a))) , else }', output=-75432","layer":1},{"info":"compute unary expreesion, input=-75432, op_id = W7eaUhjymW, unary_op_definition = '≛a = { (((a+a)⊉≛↸(a⪠⩆⊳))⊭↱((a⪒a)⩚⊴⇥(a⋝⋈⪟a))) , if (a⫩⊇)>7 or a==273 ; (((a-a)⪒(a⪨≂a))⊉≛↸((a⨰a)⋝⋈⪟(a+a))) , else }', output=-151101","layer":0}],"base":4,"result_base":4,"text":"≛⪩⨒∯1132122∠↢⪩⨒∯322123=⪩⨒∯-210320331","reverse_text":"⪩⨒∯-210320331=≛⪩⨒∯1132122∠↢⪩⨒∯322123","cot":[{"info":"⪩⨒∯1132122∠↢⪩⨒∯322123=⪩⨒∯-102122220","layer":1},{"info":"≛⪩⨒∯-102122220=⪩⨒∯-210320331","layer":0}]}
{"id":356,"expression_no_base_symbol":"∷≠($4276$⪮%⊝$1890$)","expression":"∷≠(⪩⨒∯1002310⪮%⊝⪩⨒∯131202)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":11,"operation_count":2,"complexity_ratio":5.5,"tree":{"type":"unary","operator":"∷≠","unary_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":4276,"base":4},"right_expr":{"type":"numeric_atoms","value":1890,"base":4}}},"used_operators":["QiR2Oyf5Xj","IWmyXbctLI"],"dependent_operators":["7j4O788W3g","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⪩⨒∯2022210","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4276","layer":2},{"info":"number node, value=1890","layer":2},{"info":"compute binary expreesion, left_input=4276, right_input=1890, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=8868","layer":1},{"info":"compute unary expreesion, input=8868, op_id = QiR2Oyf5Xj, unary_op_definition = '∷≠a = { (71↺a) }', output=8868","layer":0}],"base":4,"result_base":4,"text":"∷≠(⪩⨒∯1002310⪮%⊝⪩⨒∯131202)=⪩⨒∯2022210","reverse_text":"⪩⨒∯2022210=∷≠(⪩⨒∯1002310⪮%⊝⪩⨒∯131202)","cot":[{"info":"⪩⨒∯1002310⪮%⊝⪩⨒∯131202=⪩⨒∯2022210","layer":1},{"info":"∷≠⪩⨒∯2022210=⪩⨒∯2022210","layer":0}]}
{"id":357,"expression_no_base_symbol":"$3665$⋳⪒$1466$≥⨤⩑($8239$⇔⨋)","expression":"⪩⨒∯321101⋳⪒⪩⨒∯112322≥⨤⩑(⪩⨒∯2000233⇔⨋)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":43,"operation_count":3,"complexity_ratio":14.333333333333334,"tree":{"type":"binary","operator":"≥⨤⩑","left_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":3665,"base":4},"right_expr":{"type":"numeric_atoms","value":1466,"base":4}},"right_expr":{"type":"unary","operator":"⇔⨋","unary_expr":{"type":"numeric_atoms","value":8239,"base":4}}},"used_operators":["gJLn6v0xnP","12rbrZMWeM","uBihLCJcMX"],"dependent_operators":["mp7IySMOzn","aA7tF3KVD3","QvoQhV0rrE","rysDP5nf3Z","t8gj7n24qd","N41Kp7NANJ","7j4O788W3g","glklzrTFfD","tifHPKVTfV","12rbrZMWeM","f6k1SAg4EE","D4vGDi5EA2","nCS4ZIUYfx","QMFrweE19q"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3665","layer":2},{"info":"number node, value=1466","layer":2},{"info":"compute binary expreesion, left_input=3665, right_input=1466, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=5577","layer":1},{"info":"number node, value=8239","layer":2},{"info":"compute unary expreesion, input=8239, op_id = uBihLCJcMX, unary_op_definition = 'a⇔⨋ = { (((a⨁⊸⫻)⋳⪒a)⪒((a≦≮≮)⨁⊸⫻)) , if a<217 ; (((a≋⫹)⨳⩥⨓(a↺a))⋳⪒((a⨳⩥⨓a)⫡⨏(a⇼⇔∾a))) , else }', output=48364","layer":1},{"info":"compute binary expreesion, left_input=5577, right_input=48364, op_id = gJLn6v0xnP binary_op_definition= 'a≥⨤⩑b = { (b⇷a) , if (b⪘⨀)>356 ; (702∠⫱488) , else }', output=1234","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯321101⋳⪒⪩⨒∯112322≥⨤⩑(⪩⨒∯2000233⇔⨋)=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=⪩⨒∯321101⋳⪒⪩⨒∯112322≥⨤⩑(⪩⨒∯2000233⇔⨋)","cot":[{"info":"⪩⨒∯321101⋳⪒⪩⨒∯112322=⪩⨒∯1113021","layer":1},{"info":"⪩⨒∯2000233⇔⨋=⪩⨒∯23303230","layer":1},{"info":"⪩⨒∯1113021≥⨤⩑⪩⨒∯23303230=⪩⨒∯103102","layer":0}]}
{"id":358,"expression_no_base_symbol":"($1169$⩼⇪↪$4049$)⨔⇊(∥⊫$2037$)","expression":"(⪩⨒∯102101⩼⇪↪⪩⨒∯333101)⨔⇊(∥⊫⪩⨒∯133311)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":17,"operation_count":3,"complexity_ratio":5.666666666666667,"tree":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"numeric_atoms","value":1169,"base":4},"right_expr":{"type":"numeric_atoms","value":4049,"base":4}},"right_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":2037,"base":4}}},"used_operators":["JclMnS0uGI","ocnLzx9CaJ","P8v4zCKN1o"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI","9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯231121","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1169","layer":2},{"info":"number node, value=4049","layer":2},{"info":"compute binary expreesion, left_input=1169, right_input=4049, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=-26788","layer":1},{"info":"number node, value=2037","layer":2},{"info":"compute unary expreesion, input=2037, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=2905","layer":1},{"info":"compute binary expreesion, left_input=-26788, right_input=2905, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=2905","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯102101⩼⇪↪⪩⨒∯333101)⨔⇊(∥⊫⪩⨒∯133311)=⪩⨒∯231121","reverse_text":"⪩⨒∯231121=(⪩⨒∯102101⩼⇪↪⪩⨒∯333101)⨔⇊(∥⊫⪩⨒∯133311)","cot":[{"info":"⪩⨒∯102101⩼⇪↪⪩⨒∯333101=⪩⨒∯-12202210","layer":1},{"info":"∥⊫⪩⨒∯133311=⪩⨒∯231121","layer":1},{"info":"⪩⨒∯-12202210⨔⇊⪩⨒∯231121=⪩⨒∯231121","layer":0}]}
{"id":359,"expression_no_base_symbol":"≇⪴($1213$⩅⪻⪻)","expression":"≇⪴(⪩⨒∯102331⩅⪻⪻)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":145,"operation_count":2,"complexity_ratio":72.5,"tree":{"type":"unary","operator":"≇⪴","unary_expr":{"type":"unary","operator":"⩅⪻⪻","unary_expr":{"type":"numeric_atoms","value":1213,"base":4}}},"used_operators":["zoVPnxeHJ3","kHoXpA7yos"],"dependent_operators":["7j4O788W3g","Ph9nP6C5qx","f6k1SAg4EE","14qkJME0vr","g55IO6H4Gj","COABgblf1C","SUmda5xLS4","KPf6cnQVty","8HhzD0ZcuI","9Isq31Ruls"],"result":"⪩⨒∯-2232300110","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1213","layer":2},{"info":"compute unary expreesion, input=1213, op_id = kHoXpA7yos, unary_op_definition = 'a⩅⪻⪻ = { (a⪄((a∌↝a)⨽(a∺≝⩲a))) }', output=-178949","layer":1},{"info":"compute unary expreesion, input=-178949, op_id = zoVPnxeHJ3, unary_op_definition = '≇⪴a = { ((a⪒a)↺(a⨸⪁a)) , if (a⊭↱741)>=792 ; ((a≧⫂∧a)⊦⊿) , else }', output=-715796","layer":0}],"base":4,"result_base":4,"text":"≇⪴(⪩⨒∯102331⩅⪻⪻)=⪩⨒∯-2232300110","reverse_text":"⪩⨒∯-2232300110=≇⪴(⪩⨒∯102331⩅⪻⪻)","cot":[{"info":"⪩⨒∯102331⩅⪻⪻=⪩⨒∯-223230011","layer":1},{"info":"≇⪴⪩⨒∯-223230011=⪩⨒∯-2232300110","layer":0}]}
{"id":360,"expression_no_base_symbol":"($4076$≳⇉$1805$)⪍↜⋙($1451$⨎$3018$)","expression":"(⪩⨒∯333230≳⇉⪩⨒∯130031)⪍↜⋙(⪩⨒∯112223⨎⪩⨒∯233022)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":55573766,"operation_count":3,"complexity_ratio":18524588.666666668,"tree":{"type":"binary","operator":"⪍↜⋙","left_expr":{"type":"binary","operator":"≳⇉","left_expr":{"type":"numeric_atoms","value":4076,"base":4},"right_expr":{"type":"numeric_atoms","value":1805,"base":4}},"right_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":1451,"base":4},"right_expr":{"type":"numeric_atoms","value":3018,"base":4}}},"used_operators":["L05ObWFQCd","V0kx6qeWkN","rJVOvQCfKK"],"dependent_operators":["rysDP5nf3Z","DZ8iAZOCBD","tifHPKVTfV","EBcxylXtPf","QMFrweE19q","KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4076","layer":2},{"info":"number node, value=1805","layer":2},{"info":"compute binary expreesion, left_input=4076, right_input=1805, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":1},{"info":"number node, value=1451","layer":2},{"info":"number node, value=3018","layer":2},{"info":"compute binary expreesion, left_input=1451, right_input=3018, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=3018","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=3018, op_id = L05ObWFQCd binary_op_definition= 'a⪍↜⋙b = { ((a-b)⊉≛↸(a⫡⨏b)) , if (a⫌⩹⨱)!=88 ; ((a⫡⨏b)⇼⇔∾(a⫌⩹⨱)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯333230≳⇉⪩⨒∯130031)⪍↜⋙(⪩⨒∯112223⨎⪩⨒∯233022)=NaN","reverse_text":"NaN=(⪩⨒∯333230≳⇉⪩⨒∯130031)⪍↜⋙(⪩⨒∯112223⨎⪩⨒∯233022)","cot":[{"info":"⪩⨒∯333230≳⇉⪩⨒∯130031=NaN","layer":1},{"info":"⪩⨒∯112223⨎⪩⨒∯233022=⪩⨒∯233022","layer":1},{"info":"NaN⪍↜⋙⪩⨒∯233022=NaN","layer":0}]}
{"id":361,"expression_no_base_symbol":"$1934$⪥$4272$⋾⨃∁($8093$∕⩚$3522$)","expression":"⪩⨒∯132032⪥⪩⨒∯1002300⋾⨃∁(⪩⨒∯1332131∕⩚⪩⨒∯313002)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16256,"operation_count":3,"complexity_ratio":5418.666666666667,"tree":{"type":"binary","operator":"⋾⨃∁","left_expr":{"type":"binary","operator":"⪥","left_expr":{"type":"numeric_atoms","value":1934,"base":4},"right_expr":{"type":"numeric_atoms","value":4272,"base":4}},"right_expr":{"type":"binary","operator":"∕⩚","left_expr":{"type":"numeric_atoms","value":8093,"base":4},"right_expr":{"type":"numeric_atoms","value":3522,"base":4}}},"used_operators":["212REbPD9h","QbnwKVWMIQ","z9ffQ9n5Zr"],"dependent_operators":["eLxqMNBOBk","Qy55tPpLXF","w2P8NbNXyL","2DQ55sFlQl","f6k1SAg4EE","WR6HLWljOP","nhYeJWJD5X","f6k1SAg4EE","jLgFTUHLKL","PPChnnnBFF","3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr"],"result":"⪩⨒∯213010232030202","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1934","layer":2},{"info":"number node, value=4272","layer":2},{"info":"compute binary expreesion, left_input=1934, right_input=4272, op_id = QbnwKVWMIQ binary_op_definition= 'a⪥b = { (b∇⊂⋱(58∣a)) , if (b↢721)<125 ; (↩(508⪒a)) , else }', output=12388","layer":1},{"info":"number node, value=8093","layer":2},{"info":"number node, value=3522","layer":2},{"info":"compute binary expreesion, left_input=8093, right_input=3522, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-8096","layer":1},{"info":"compute binary expreesion, left_input=12388, right_input=-8096, op_id = 212REbPD9h binary_op_definition= 'a⋾⨃∁b = { ((430⊉↱≁b)⨵⪆b) , if (a⪒898)>=359 ; ((⫓⪴b)⊉↱≁(26⋥≓≎b)) , else }', output=655549218","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯132032⪥⪩⨒∯1002300⋾⨃∁(⪩⨒∯1332131∕⩚⪩⨒∯313002)=⪩⨒∯213010232030202","reverse_text":"⪩⨒∯213010232030202=⪩⨒∯132032⪥⪩⨒∯1002300⋾⨃∁(⪩⨒∯1332131∕⩚⪩⨒∯313002)","cot":[{"info":"⪩⨒∯132032⪥⪩⨒∯1002300=⪩⨒∯3001210","layer":1},{"info":"⪩⨒∯1332131∕⩚⪩⨒∯313002=⪩⨒∯-1332200","layer":1},{"info":"⪩⨒∯3001210⋾⨃∁⪩⨒∯-1332200=⪩⨒∯213010232030202","layer":0}]}
{"id":362,"expression_no_base_symbol":"(≸$3205$)⫁⪎($3590$⨒$4691$)","expression":"(≸⪩⨒∯302011)⫁⪎(⪩⨒∯320012⨒⪩⨒∯1021103)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":87,"operation_count":3,"complexity_ratio":29.0,"tree":{"type":"binary","operator":"⫁⪎","left_expr":{"type":"unary","operator":"≸","unary_expr":{"type":"numeric_atoms","value":3205,"base":4}},"right_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":3590,"base":4},"right_expr":{"type":"numeric_atoms","value":4691,"base":4}}},"used_operators":["xRrnTEsQ6j","eOf03JbCpp","y75s1iXyHd"],"dependent_operators":["P8v4zCKN1o","Qy55tPpLXF","tifHPKVTfV","sdazOOVcIp","2DDjHMKMc0","i8ToyICDmI","WmT3o8z6ya","l07mrZUIn9","NTOWxs364D","RygbFNSyEJ","tifHPKVTfV","oRDoc9rAEX","IwW236VD4Y","1aApVXNlOP","Z5m6OM72h2","mqXw5SEYmG","IWmyXbctLI","srAu1WTS94","oacrs7FA3X","7qqUquhhSb"],"result":"⪩⨒∯11023222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3205","layer":2},{"info":"compute unary expreesion, input=3205, op_id = eOf03JbCpp, unary_op_definition = '≸a = { (29∘((630⊋≦⊧a)⩚⊴⇥(a≦↸a))) , if (a⋘⨑⨽)>2 ; (((a⪮%⊝a)⇼⇔∾(a↪⪝))⫸⊐((a⪮%⊝a)≠≀(3⩇∃⫛a))) , else }', output=58","layer":1},{"info":"number node, value=3590","layer":2},{"info":"number node, value=4691","layer":2},{"info":"compute binary expreesion, left_input=3590, right_input=4691, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-21168","layer":1},{"info":"compute binary expreesion, left_input=58, right_input=-21168, op_id = xRrnTEsQ6j binary_op_definition= 'a⫁⪎b = { ((b⋝⋈⪟a)⇼⇔∾a) , if (∥⊫b)!=57 ; ((191∲⫓a)⋥≓≎(a⪨≂368)) , else }', output=21226","layer":0}],"base":4,"result_base":4,"text":"(≸⪩⨒∯302011)⫁⪎(⪩⨒∯320012⨒⪩⨒∯1021103)=⪩⨒∯11023222","reverse_text":"⪩⨒∯11023222=(≸⪩⨒∯302011)⫁⪎(⪩⨒∯320012⨒⪩⨒∯1021103)","cot":[{"info":"≸⪩⨒∯302011=⪩⨒∯322","layer":1},{"info":"⪩⨒∯320012⨒⪩⨒∯1021103=⪩⨒∯-11022300","layer":1},{"info":"⪩⨒∯322⫁⪎⪩⨒∯-11022300=⪩⨒∯11023222","layer":0}]}
{"id":363,"expression_no_base_symbol":"$1802$⊴$1285$≬⇓(↨⩢⫨$2192$)","expression":"⪩⨒∯130022⊴⪩⨒∯110011≬⇓(↨⩢⫨⪩⨒∯202100)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2309,"operation_count":3,"complexity_ratio":769.6666666666666,"tree":{"type":"binary","operator":"≬⇓","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1802,"base":4},"right_expr":{"type":"numeric_atoms","value":1285,"base":4}},"right_expr":{"type":"unary","operator":"↨⩢⫨","unary_expr":{"type":"numeric_atoms","value":2192,"base":4}}},"used_operators":["jWTQ2TZYIH","Nsiff2A1zJ","Z5CJsN7DuW"],"dependent_operators":["AdZkA7nFnk","zVYPLywUTj","XTarYq4gQB","dWAJyo7jo9","14qkJME0vr","Noe24qw2ks","gu96TGCTMs","8jW3W4yZS5","AFVx7xoS7T"],"result":"⪩⨒∯-112","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1802","layer":2},{"info":"number node, value=1285","layer":2},{"info":"compute binary expreesion, left_input=1802, right_input=1285, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=2192","layer":2},{"info":"compute unary expreesion, input=2192, op_id = Z5CJsN7DuW, unary_op_definition = '↨⩢⫨a = { (((211⨐a)⇌⫙⪟(↯⪼a))⊘) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=0, op_id = jWTQ2TZYIH binary_op_definition= 'a≬⇓b = { (a⊪) , if a<=154 or (⪝⪂⫅a)>=41 ; (a⋅⇍b) , else }', output=-22","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯130022⊴⪩⨒∯110011≬⇓(↨⩢⫨⪩⨒∯202100)=⪩⨒∯-112","reverse_text":"⪩⨒∯-112=⪩⨒∯130022⊴⪩⨒∯110011≬⇓(↨⩢⫨⪩⨒∯202100)","cot":[{"info":"⪩⨒∯130022⊴⪩⨒∯110011=NaN","layer":1},{"info":"↨⩢⫨⪩⨒∯202100=⪩⨒∯0","layer":1},{"info":"NaN≬⇓⪩⨒∯0=⪩⨒∯-112","layer":0}]}
{"id":364,"expression_no_base_symbol":"$5725$⩧⪆$1246$⩺⪪(∥⊫$1388$)","expression":"⪩⨒∯1121131⩧⪆⪩⨒∯103132⩺⪪(∥⊫⪩⨒∯111230)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":129,"operation_count":3,"complexity_ratio":43.0,"tree":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"numeric_atoms","value":5725,"base":4},"right_expr":{"type":"numeric_atoms","value":1246,"base":4}},"right_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":1388,"base":4}}},"used_operators":["uvdQJvN4PV","Ikt5ks8PT7","P8v4zCKN1o"],"dependent_operators":["Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U","eewbuw0ToL","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-130122","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5725","layer":2},{"info":"number node, value=1246","layer":2},{"info":"compute binary expreesion, left_input=5725, right_input=1246, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-1246","layer":1},{"info":"number node, value=1388","layer":2},{"info":"compute unary expreesion, input=1388, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=2256","layer":1},{"info":"compute binary expreesion, left_input=-1246, right_input=2256, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=-1818","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1121131⩧⪆⪩⨒∯103132⩺⪪(∥⊫⪩⨒∯111230)=⪩⨒∯-130122","reverse_text":"⪩⨒∯-130122=⪩⨒∯1121131⩧⪆⪩⨒∯103132⩺⪪(∥⊫⪩⨒∯111230)","cot":[{"info":"⪩⨒∯1121131⩧⪆⪩⨒∯103132=⪩⨒∯-103132","layer":1},{"info":"∥⊫⪩⨒∯111230=⪩⨒∯203100","layer":1},{"info":"⪩⨒∯-103132⩺⪪⪩⨒∯203100=⪩⨒∯-130122","layer":0}]}
{"id":365,"expression_no_base_symbol":"($1738$⋭≵$3481$)⨟⋌⩍$2201$⫁$1386$","expression":"(⪩⨒∯123022⋭≵⪩⨒∯312121)⨟⋌⩍⪩⨒∯202121⫁⪩⨒∯111222","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":859,"operation_count":3,"complexity_ratio":286.3333333333333,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"⋭≵","left_expr":{"type":"numeric_atoms","value":1738,"base":4},"right_expr":{"type":"numeric_atoms","value":3481,"base":4}},"right_expr":{"type":"binary","operator":"⫁","left_expr":{"type":"numeric_atoms","value":2201,"base":4},"right_expr":{"type":"numeric_atoms","value":1386,"base":4}}},"used_operators":["rGHVDoGpnC","jBncVCNhdl","0ajvFaJAv0"],"dependent_operators":["Tcnh7f0tEr","RygbFNSyEJ","gx7XJ7hdpj","9ICcGScMcE","C6VvDP6HwP","mqXw5SEYmG","7IPrd9c3lf","COABgblf1C","cHh1gJQ2o6","AHs5Up7iyr"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1738","layer":2},{"info":"number node, value=3481","layer":2},{"info":"compute binary expreesion, left_input=1738, right_input=3481, op_id = jBncVCNhdl binary_op_definition= 'a⋭≵b = { ((156≦↸a)⊭↱(≦∁b)) , if (b⫸⊐434)<=441 and (a⫸⇳180)>=132 ; ((a⪑⩈)⊵↤) , else }', output=67","layer":1},{"info":"number node, value=2201","layer":2},{"info":"number node, value=1386","layer":2},{"info":"compute binary expreesion, left_input=2201, right_input=1386, op_id = 0ajvFaJAv0 binary_op_definition= 'a⫁b = { (a≹⇙⪍6) , if a==154 ; (b⩘b) , else }', output=160","layer":1},{"info":"compute binary expreesion, left_input=67, right_input=160, op_id = rGHVDoGpnC binary_op_definition= 'a⨟⋌⩍b = {a, if b == 0; (a⨟⋌⩍(b-1))≣⋋, if b > 0 and abs(b) < 1000; -(a⨟⋌⩍(b+1))≣⋋, if b < 0 and abs(b) < 1000; NaN, else}', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯123022⋭≵⪩⨒∯312121)⨟⋌⩍⪩⨒∯202121⫁⪩⨒∯111222=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯123022⋭≵⪩⨒∯312121)⨟⋌⩍⪩⨒∯202121⫁⪩⨒∯111222","cot":[{"info":"⪩⨒∯123022⋭≵⪩⨒∯312121=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯202121⫁⪩⨒∯111222=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯1003⨟⋌⩍⪩⨒∯2200=⪩⨒∯0","layer":0}]}
{"id":366,"expression_no_base_symbol":"($3403$⇚⪠)⊬⨰($7944$⋐⇩⊬)","expression":"(⪩⨒∯311023⇚⪠)⊬⨰(⪩⨒∯1330020⋐⇩⊬)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3431,"operation_count":3,"complexity_ratio":1143.6666666666667,"tree":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"unary","operator":"⇚⪠","unary_expr":{"type":"numeric_atoms","value":3403,"base":4}},"right_expr":{"type":"unary","operator":"⋐⇩⊬","unary_expr":{"type":"numeric_atoms","value":7944,"base":4}}},"used_operators":["s3Fd5m9Dh2","Loh9y4A90B","JuuLT1NoCs"],"dependent_operators":["23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","Z5m6OM72h2","9HNa5Wba9A","ztP7wcbY7m","mp7IySMOzn","JclMnS0uGI","ddLRYrp01A"],"result":"⪩⨒∯1120131333302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3403","layer":2},{"info":"compute unary expreesion, input=3403, op_id = Loh9y4A90B, unary_op_definition = 'a⇚⪠ = { ((a∘(a∈))*a) }', output=23160818","layer":1},{"info":"number node, value=7944","layer":2},{"info":"compute unary expreesion, input=7944, op_id = JuuLT1NoCs, unary_op_definition = 'a⋐⇩⊬ = { (a⨔⇊a) , if (a∊∟⩊189)<=582 ; (a⇷a) , else }', output=7944","layer":1},{"info":"compute binary expreesion, left_input=23160818, right_input=7944, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=23191538","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯311023⇚⪠)⊬⨰(⪩⨒∯1330020⋐⇩⊬)=⪩⨒∯1120131333302","reverse_text":"⪩⨒∯1120131333302=(⪩⨒∯311023⇚⪠)⊬⨰(⪩⨒∯1330020⋐⇩⊬)","cot":[{"info":"⪩⨒∯311023⇚⪠=⪩⨒∯1120112133302","layer":1},{"info":"⪩⨒∯1330020⋐⇩⊬=⪩⨒∯1330020","layer":1},{"info":"⪩⨒∯1120112133302⊬⨰⪩⨒∯1330020=⪩⨒∯1120131333302","layer":0}]}
{"id":367,"expression_no_base_symbol":"∡($2913$⊹≧⊝)","expression":"∡(⪩⨒∯231201⊹≧⊝)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":29,"operation_count":2,"complexity_ratio":14.5,"tree":{"type":"unary","operator":"∡","unary_expr":{"type":"unary","operator":"⊹≧⊝","unary_expr":{"type":"numeric_atoms","value":2913,"base":4}}},"used_operators":["pRsWfj4Fpp","LxFB4K6j0n"],"dependent_operators":["D4vGDi5EA2","DZ8iAZOCBD","2DDjHMKMc0","NTOWxs364D","P8v4zCKN1o","XPYlsWDdGa","DZ8iAZOCBD","t8gj7n24qd","g55IO6H4Gj","eewbuw0ToL","i8ToyICDmI","COABgblf1C"],"result":"⪩⨒∯101010120","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2913","layer":2},{"info":"compute unary expreesion, input=2913, op_id = LxFB4K6j0n, unary_op_definition = 'a⊹≧⊝ = { (((∥⊫a)⊭↱(a⩚⊴⇥a))⊉≛↸(⪲⇎(⪲⇎a))) , if a!=566 ; (-((a∲⫓a)⨸⪁(a⨰a))) , else }', output=-11652","layer":1},{"info":"compute unary expreesion, input=-11652, op_id = pRsWfj4Fpp, unary_op_definition = '∡a = { ((a≦≮≮)⊉≛↸(a⋝⋈⪟a)) }', output=69912","layer":0}],"base":4,"result_base":4,"text":"∡(⪩⨒∯231201⊹≧⊝)=⪩⨒∯101010120","reverse_text":"⪩⨒∯101010120=∡(⪩⨒∯231201⊹≧⊝)","cot":[{"info":"⪩⨒∯231201⊹≧⊝=⪩⨒∯-2312010","layer":1},{"info":"∡⪩⨒∯-2312010=⪩⨒∯101010120","layer":0}]}
{"id":368,"expression_no_base_symbol":"$2260$⩧⪆$1404$⋫","expression":"⪩⨒∯203110⩧⪆⪩⨒∯111330⋫","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1405,"operation_count":2,"complexity_ratio":702.5,"tree":{"type":"unary","operator":"⋫","unary_expr":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"numeric_atoms","value":2260,"base":4},"right_expr":{"type":"numeric_atoms","value":1404,"base":4}}},"used_operators":["JL8yIekQnl","Ikt5ks8PT7"],"dependent_operators":["tmPS8pqC7x","eewbuw0ToL","t8gj7n24qd"],"result":"⪩⨒∯-111330","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2260","layer":2},{"info":"number node, value=1404","layer":2},{"info":"compute binary expreesion, left_input=2260, right_input=1404, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-1404","layer":1},{"info":"compute unary expreesion, input=-1404, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=-1404","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯203110⩧⪆⪩⨒∯111330⋫=⪩⨒∯-111330","reverse_text":"⪩⨒∯-111330=⪩⨒∯203110⩧⪆⪩⨒∯111330⋫","cot":[{"info":"⪩⨒∯203110⩧⪆⪩⨒∯111330=⪩⨒∯-111330","layer":1},{"info":"⪩⨒∯-111330⋫=⪩⨒∯-111330","layer":0}]}
{"id":369,"expression_no_base_symbol":"⫵↿(⊢≑≆$4814$)","expression":"⫵↿(⊢≑≆⪩⨒∯1023032)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":38,"operation_count":2,"complexity_ratio":19.0,"tree":{"type":"unary","operator":"⫵↿","unary_expr":{"type":"unary","operator":"⊢≑≆","unary_expr":{"type":"numeric_atoms","value":4814,"base":4}}},"used_operators":["ivGwdmUAux","27wFxooxGf"],"dependent_operators":["LXhwmt4mBO","09Ly4LVMIf","LRNGc0VcxI","y4ImoPnbV5","8jW3W4yZS5","G9tJMlZ94a","eLAdDNolq6","9FxExcQeMw","Ph9nP6C5qx","g55IO6H4Gj"],"result":"⪩⨒∯2021","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4814","layer":2},{"info":"compute unary expreesion, input=4814, op_id = 27wFxooxGf, unary_op_definition = '⊢≑≆a = { a , if (≤/a)==126 and a<49 ; ((559⨸⪁a)≧⫂∧(349⩷∴a)) , else }', output=19708","layer":1},{"info":"compute unary expreesion, input=19708, op_id = ivGwdmUAux, unary_op_definition = '⫵↿a = { ((a⫃⨇256)∽(a∀⇚≩66)) , if (⇨a)>=1 ; (↯⪼(a⨫⇇↔a)) , else }', output=137","layer":0}],"base":4,"result_base":4,"text":"⫵↿(⊢≑≆⪩⨒∯1023032)=⪩⨒∯2021","reverse_text":"⪩⨒∯2021=⫵↿(⊢≑≆⪩⨒∯1023032)","cot":[{"info":"⊢≑≆⪩⨒∯1023032=⪩⨒∯10303330","layer":1},{"info":"⫵↿⪩⨒∯10303330=⪩⨒∯2021","layer":0}]}
{"id":370,"expression_no_base_symbol":"($6384$→⨶⪴$7936$)∌$2516$⪔⊥$1005$","expression":"(⪩⨒∯1203300→⨶⪴⪩⨒∯1330000)∌⪩⨒∯213110⪔⊥⪩⨒∯33231","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":27,"operation_count":3,"complexity_ratio":9.0,"tree":{"type":"binary","operator":"∌","left_expr":{"type":"binary","operator":"→⨶⪴","left_expr":{"type":"numeric_atoms","value":6384,"base":4},"right_expr":{"type":"numeric_atoms","value":7936,"base":4}},"right_expr":{"type":"binary","operator":"⪔⊥","left_expr":{"type":"numeric_atoms","value":2516,"base":4},"right_expr":{"type":"numeric_atoms","value":1005,"base":4}}},"used_operators":["8cLx32lpNA","bF6eod5Gvf","HJ9erzHUuu"],"dependent_operators":["N41Kp7NANJ","7j4O788W3g","t8gj7n24qd","8w2t5hMYqp","9FxExcQeMw","eLAdDNolq6","rysDP5nf3Z","7j4O788W3g","tifHPKVTfV","8w2t5hMYqp","sdazOOVcIp","2td37pGCOC","COABgblf1C"],"result":"⪩⨒∯-11310000","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6384","layer":2},{"info":"number node, value=7936","layer":2},{"info":"compute binary expreesion, left_input=6384, right_input=7936, op_id = bF6eod5Gvf binary_op_definition= 'a→⨶⪴b = { (a⩷∴b) , if b<109 ; (⊄⩳↩b) , else }', output=-23808","layer":1},{"info":"number node, value=2516","layer":2},{"info":"number node, value=1005","layer":2},{"info":"compute binary expreesion, left_input=2516, right_input=1005, op_id = HJ9erzHUuu binary_op_definition= 'a⪔⊥b = { (⩦⩻⨪(≤/(315⇼⇔∾a))) , if b<175 ; ((⊄⩳↩(b-b))⇼⇔∾((b⪨≂a)⊭↱(a↺b))) , else }', output=7855","layer":1},{"info":"compute binary expreesion, left_input=-23808, right_input=7855, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-23808","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1203300→⨶⪴⪩⨒∯1330000)∌⪩⨒∯213110⪔⊥⪩⨒∯33231=⪩⨒∯-11310000","reverse_text":"⪩⨒∯-11310000=(⪩⨒∯1203300→⨶⪴⪩⨒∯1330000)∌⪩⨒∯213110⪔⊥⪩⨒∯33231","cot":[{"info":"⪩⨒∯1203300→⨶⪴⪩⨒∯1330000=⪩⨒∯-11310000","layer":1},{"info":"⪩⨒∯213110⪔⊥⪩⨒∯33231=⪩⨒∯1322233","layer":1},{"info":"⪩⨒∯-11310000∌⪩⨒∯1322233=⪩⨒∯-11310000","layer":0}]}
{"id":371,"expression_no_base_symbol":"(⇋↷$1016$)⩧⪆(⫛⫱⨽$2744$)","expression":"(⇋↷⪩⨒∯33320)⩧⪆(⫛⫱⨽⪩⨒∯222320)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1431,"operation_count":3,"complexity_ratio":477.0,"tree":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"unary","operator":"⇋↷","unary_expr":{"type":"numeric_atoms","value":1016,"base":4}},"right_expr":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"numeric_atoms","value":2744,"base":4}}},"used_operators":["Ikt5ks8PT7","SWo3A1KBJH","DlLNRPXxWL"],"dependent_operators":["eewbuw0ToL","t8gj7n24qd","XPYlsWDdGa","23Mk6UjR3U","2DQ55sFlQl","u6S6b8DprG","rGHVDoGpnC"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1016","layer":2},{"info":"compute unary expreesion, input=1016, op_id = SWo3A1KBJH, unary_op_definition = '⇋↷a = { (⪲⇎((↽≂a)⋷(a⨵⪆a))) }', output=8128","layer":1},{"info":"number node, value=2744","layer":2},{"info":"compute unary expreesion, input=2744, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=8128, right_input=0, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⇋↷⪩⨒∯33320)⩧⪆(⫛⫱⨽⪩⨒∯222320)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⇋↷⪩⨒∯33320)⩧⪆(⫛⫱⨽⪩⨒∯222320)","cot":[{"info":"⇋↷⪩⨒∯33320=⪩⨒∯1333000","layer":1},{"info":"⫛⫱⨽⪩⨒∯222320=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1333000⩧⪆⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":372,"expression_no_base_symbol":"$1438$≌$2740$⩘","expression":"⪩⨒∯112132≌⪩⨒∯222310⩘","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2913,"operation_count":2,"complexity_ratio":1456.5,"tree":{"type":"unary","operator":"⩘","unary_expr":{"type":"binary","operator":"≌","left_expr":{"type":"numeric_atoms","value":1438,"base":4},"right_expr":{"type":"numeric_atoms","value":2740,"base":4}}},"used_operators":["wvHyciQT5X","lyWz822IDG"],"dependent_operators":["9ICcGScMcE","dfKe02y8D2","B5M0gjZbta","W7eaUhjymW","CpSg5vQTgA","w2P8NbNXyL","0kmYd0q39Y","3sJ7IOPOlU","Bmrmz2XGnR","WkeUrDK8WX","03sUfWo75k","5twsqlHp2o","oacrs7FA3X","aMUSaJuDRU"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1438","layer":2},{"info":"number node, value=2740","layer":2},{"info":"compute binary expreesion, left_input=1438, right_input=2740, op_id = lyWz822IDG binary_op_definition= 'a≌b = { (≛((132⩦9)⊉↱≁(a⪇≇⋚a))) , if (a⪘⫢419)==234 ; (((⩰124)≚⊃≕(b⨴∎))⊢((16⨉)↬(a⊟⇱))) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = wvHyciQT5X, unary_op_definition = 'a⩘ = { (≦∁(a⫚↹⊑129)) }', output=67","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯112132≌⪩⨒∯222310⩘=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=⪩⨒∯112132≌⪩⨒∯222310⩘","cot":[{"info":"⪩⨒∯112132≌⪩⨒∯222310=NaN","layer":1},{"info":"NaN⩘=⪩⨒∯1003","layer":0}]}
{"id":373,"expression_no_base_symbol":"($1141$⪗)↬⩅∪","expression":"(⪩⨒∯101311⪗)↬⩅∪","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1147,"operation_count":2,"complexity_ratio":573.5,"tree":{"type":"unary","operator":"↬⩅∪","unary_expr":{"type":"unary","operator":"⪗","unary_expr":{"type":"numeric_atoms","value":1141,"base":4}}},"used_operators":["VJ330n2nnx","VEQNXA0ZBg"],"dependent_operators":["D4vGDi5EA2","23Mk6UjR3U","u6S6b8DprG","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1141","layer":2},{"info":"compute unary expreesion, input=1141, op_id = VEQNXA0ZBg, unary_op_definition = 'a⪗ = { (a⪢a) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = VJ330n2nnx, unary_op_definition = 'a↬⩅∪ = { (a≦≮≮) , if (↽≂a)!=185 or a>=376 or a<=585 ; (a⋷a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101311⪗)↬⩅∪=NaN","reverse_text":"NaN=(⪩⨒∯101311⪗)↬⩅∪","cot":[{"info":"⪩⨒∯101311⪗=NaN","layer":1},{"info":"NaN↬⩅∪=NaN","layer":0}]}
{"id":374,"expression_no_base_symbol":"($4853$⨒$5596$)⋆⋳","expression":"(⪩⨒∯1023311⨒⪩⨒∯1113130)⋆⋳","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":31,"operation_count":2,"complexity_ratio":15.5,"tree":{"type":"unary","operator":"⋆⋳","unary_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":4853,"base":4},"right_expr":{"type":"numeric_atoms","value":5596,"base":4}}},"used_operators":["6MpZysEj17","y75s1iXyHd"],"dependent_operators":["9FxExcQeMw","7j4O788W3g","DIvbN7qnHd","srAu1WTS94","oacrs7FA3X","7qqUquhhSb"],"result":"⪩⨒∯32001310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4853","layer":2},{"info":"number node, value=5596","layer":2},{"info":"compute binary expreesion, left_input=4853, right_input=5596, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-28746","layer":1},{"info":"compute unary expreesion, input=-28746, op_id = 6MpZysEj17, unary_op_definition = 'a⋆⋳ = { ((a⊠≄⫣)⩷∴(a↺a)) }', output=57460","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1023311⨒⪩⨒∯1113130)⋆⋳=⪩⨒∯32001310","reverse_text":"⪩⨒∯32001310=(⪩⨒∯1023311⨒⪩⨒∯1113130)⋆⋳","cot":[{"info":"⪩⨒∯1023311⨒⪩⨒∯1113130=⪩⨒∯-13001022","layer":1},{"info":"⪩⨒∯-13001022⋆⋳=⪩⨒∯32001310","layer":0}]}
{"id":375,"expression_no_base_symbol":"(⫯$3583$)∺≝⩲($2101$⊴$7807$)","expression":"(⫯⪩⨒∯313333)∺≝⩲(⪩⨒∯200311⊴⪩⨒∯1321333)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7870,"operation_count":3,"complexity_ratio":2623.3333333333335,"tree":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"unary","operator":"⫯","unary_expr":{"type":"numeric_atoms","value":3583,"base":4}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":2101,"base":4},"right_expr":{"type":"numeric_atoms","value":7807,"base":4}}},"used_operators":["KPf6cnQVty","H6BK1Evt7c","Nsiff2A1zJ"],"dependent_operators":["BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl","2Wsdkap16l","KbjG8mgYpV","sJAwomhLZr","Ph9nP6C5qx","AYdpE9sXAk","X99M06cbEe","dWAJyo7jo9","14qkJME0vr"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3583","layer":2},{"info":"compute unary expreesion, input=3583, op_id = H6BK1Evt7c, unary_op_definition = '⫯a = { ((a⩠)∠↢(⨂⪏⇭a)) , if (a≧⫂∧919)>20 ; ((a⩹a)≫≃) , else }', output=-135698","layer":1},{"info":"number node, value=2101","layer":2},{"info":"number node, value=7807","layer":2},{"info":"compute binary expreesion, left_input=2101, right_input=7807, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-135698, right_input=nan, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⫯⪩⨒∯313333)∺≝⩲(⪩⨒∯200311⊴⪩⨒∯1321333)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⫯⪩⨒∯313333)∺≝⩲(⪩⨒∯200311⊴⪩⨒∯1321333)","cot":[{"info":"⫯⪩⨒∯313333=⪩⨒∯-201020102","layer":1},{"info":"⪩⨒∯200311⊴⪩⨒∯1321333=NaN","layer":1},{"info":"⪩⨒∯-201020102∺≝⩲NaN=⪩⨒∯2200","layer":0}]}
{"id":376,"expression_no_base_symbol":"($4335$⪛$3157$)↑","expression":"(⪩⨒∯1003233⪛⪩⨒∯301111)↑","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":11,"operation_count":2,"complexity_ratio":5.5,"tree":{"type":"unary","operator":"↑","unary_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":4335,"base":4},"right_expr":{"type":"numeric_atoms","value":3157,"base":4}}},"used_operators":["BThhyOhh10","uFcxV4UQCh"],"dependent_operators":["i8ToyICDmI","3EYGwJThht","xNBdhnnwKq","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⪩⨒∯3132","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4335","layer":2},{"info":"number node, value=3157","layer":2},{"info":"compute binary expreesion, left_input=4335, right_input=3157, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1178","layer":1},{"info":"compute unary expreesion, input=1178, op_id = BThhyOhh10, unary_op_definition = 'a↑ = { ((a∲⫓a)⇄(262⊭∹↮)) }', output=222","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1003233⪛⪩⨒∯301111)↑=⪩⨒∯3132","reverse_text":"⪩⨒∯3132=(⪩⨒∯1003233⪛⪩⨒∯301111)↑","cot":[{"info":"⪩⨒∯1003233⪛⪩⨒∯301111=⪩⨒∯102122","layer":1},{"info":"⪩⨒∯102122↑=⪩⨒∯3132","layer":0}]}
{"id":377,"expression_no_base_symbol":"⨩∲⋌($1270$⪍↜⋙$1445$)","expression":"⨩∲⋌(⪩⨒∯103312⪍↜⋙⪩⨒∯112211)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":22,"operation_count":2,"complexity_ratio":11.0,"tree":{"type":"unary","operator":"⨩∲⋌","unary_expr":{"type":"binary","operator":"⪍↜⋙","left_expr":{"type":"numeric_atoms","value":1270,"base":4},"right_expr":{"type":"numeric_atoms","value":1445,"base":4}}},"used_operators":["aSik1wnThz","L05ObWFQCd"],"dependent_operators":["rysDP5nf3Z","Ph9nP6C5qx","Z2TMIBDE3Q","rysDP5nf3Z","DZ8iAZOCBD","tifHPKVTfV","EBcxylXtPf","QMFrweE19q"],"result":"⪩⨒∯-2120322","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1270","layer":2},{"info":"number node, value=1445","layer":2},{"info":"compute binary expreesion, left_input=1270, right_input=1445, op_id = L05ObWFQCd binary_op_definition= 'a⪍↜⋙b = { ((a-b)⊉≛↸(a⫡⨏b)) , if (a⫌⩹⨱)!=88 ; ((a⫡⨏b)⇼⇔∾(a⫌⩹⨱)) , else }', output=-10023","layer":1},{"info":"compute unary expreesion, input=-10023, op_id = aSik1wnThz, unary_op_definition = '⨩∲⋌a = { ((759≧⫂∧(236-a))⩤) }', output=-9786","layer":0}],"base":4,"result_base":4,"text":"⨩∲⋌(⪩⨒∯103312⪍↜⋙⪩⨒∯112211)=⪩⨒∯-2120322","reverse_text":"⪩⨒∯-2120322=⨩∲⋌(⪩⨒∯103312⪍↜⋙⪩⨒∯112211)","cot":[{"info":"⪩⨒∯103312⪍↜⋙⪩⨒∯112211=⪩⨒∯-2130213","layer":1},{"info":"⨩∲⋌⪩⨒∯-2130213=⪩⨒∯-2120322","layer":0}]}
{"id":378,"expression_no_base_symbol":"($3534$⩭)⨭⪣$1066$⪛$4868$","expression":"(⪩⨒∯313032⩭)⨭⪣⪩⨒∯100222⪛⪩⨒∯1030010","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":23233,"operation_count":3,"complexity_ratio":7744.333333333333,"tree":{"type":"binary","operator":"⨭⪣","left_expr":{"type":"unary","operator":"⩭","unary_expr":{"type":"numeric_atoms","value":3534,"base":4}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":1066,"base":4},"right_expr":{"type":"numeric_atoms","value":4868,"base":4}}},"used_operators":["kn8WO9XteQ","yIPP7u6H5x","uFcxV4UQCh"],"dependent_operators":["vRio1gEz1j","61wBmkZwlr","SWo3A1KBJH","8jW3W4yZS5","LkLIoiE525","Y7wcNGrDQJ","PPChnnnBFF","nOKPl9n5zu","SUmda5xLS4","9HNa5Wba9A","fu6greOZ01","3tVxb0NHM4","GjBEYRfMaF","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3534","layer":2},{"info":"compute unary expreesion, input=3534, op_id = yIPP7u6H5x, unary_op_definition = 'a⩭ = { (((a⨐⩸⫘a)⪎↠(696*a))⪔(224⪄(⋗⩴⪓a))) }', output=nan","layer":1},{"info":"number node, value=1066","layer":2},{"info":"number node, value=4868","layer":2},{"info":"compute binary expreesion, left_input=1066, right_input=4868, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1066","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1066, op_id = kn8WO9XteQ binary_op_definition= 'a⨭⪣b = { ((486⇩)⩵∡(a∣a)) , if (b⇯⋐)>445 or (≋b)>319 or b<=69 ; (↯⪼(⇋↷b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯313032⩭)⨭⪣⪩⨒∯100222⪛⪩⨒∯1030010=NaN","reverse_text":"NaN=(⪩⨒∯313032⩭)⨭⪣⪩⨒∯100222⪛⪩⨒∯1030010","cot":[{"info":"⪩⨒∯313032⩭=NaN","layer":1},{"info":"⪩⨒∯100222⪛⪩⨒∯1030010=⪩⨒∯100222","layer":1},{"info":"NaN⨭⪣⪩⨒∯100222=NaN","layer":0}]}
{"id":379,"expression_no_base_symbol":"⇜⊴$5448$⫢⨠$1413$","expression":"⇜⊴⪩⨒∯1111020⫢⨠⪩⨒∯112011","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":144,"operation_count":2,"complexity_ratio":72.0,"tree":{"type":"unary","operator":"⇜⊴","unary_expr":{"type":"binary","operator":"⫢⨠","left_expr":{"type":"numeric_atoms","value":5448,"base":4},"right_expr":{"type":"numeric_atoms","value":1413,"base":4}}},"used_operators":["XwDhCwWbUn","xlXykHWxX1"],"dependent_operators":["WR6HLWljOP","JclMnS0uGI","D309nIvmXG","w2P8NbNXyL","YbVcJGFEVW","DmTXOeWf9t","4CyGpkTkEk","cTDWOvIxvz","jLgFTUHLKL","COABgblf1C","hrf7POJlIJ","KFSx94NKJn","e1ybzncUwg","zR4jO40bMj","g7Hmc5v1ko","k2HlF1dBQh","2DlMacCsIx"],"result":"⪩⨒∯112122","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5448","layer":2},{"info":"number node, value=1413","layer":2},{"info":"compute binary expreesion, left_input=5448, right_input=1413, op_id = xlXykHWxX1 binary_op_definition= 'a⫢⨠b = { (((b⩨a)⪶≀⋏(a⩌⋺b))⩒⫫(∤(≉a))) }', output=160","layer":1},{"info":"compute unary expreesion, input=160, op_id = XwDhCwWbUn, unary_op_definition = '⇜⊴a = { (↩(∓⪦(a≃a))) , if ((a∐⫣)>271 and (a∴779)<=132) ; ((a↢(a⨔⇊a))⊲⩕⊾((a∝a)⊉↱≁(a⊭↱19))) , else }', output=1434","layer":0}],"base":4,"result_base":4,"text":"⇜⊴⪩⨒∯1111020⫢⨠⪩⨒∯112011=⪩⨒∯112122","reverse_text":"⪩⨒∯112122=⇜⊴⪩⨒∯1111020⫢⨠⪩⨒∯112011","cot":[{"info":"⪩⨒∯1111020⫢⨠⪩⨒∯112011=⪩⨒∯2200","layer":1},{"info":"⇜⊴⪩⨒∯2200=⪩⨒∯112122","layer":0}]}
{"id":380,"expression_no_base_symbol":"$5419$⨿$3044$⫯⪬∳($1631$∲⫓$6945$)","expression":"⪩⨒∯1110223⨿⪩⨒∯233210⫯⪬∳(⪩⨒∯121133∲⫓⪩⨒∯1230201)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":235,"operation_count":3,"complexity_ratio":78.33333333333333,"tree":{"type":"binary","operator":"⫯⪬∳","left_expr":{"type":"binary","operator":"⨿","left_expr":{"type":"numeric_atoms","value":5419,"base":4},"right_expr":{"type":"numeric_atoms","value":3044,"base":4}},"right_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":1631,"base":4},"right_expr":{"type":"numeric_atoms","value":6945,"base":4}}},"used_operators":["d7ASUq0ydm","abYXlopdE0","i8ToyICDmI"],"dependent_operators":["Qy55tPpLXF","BjRHVeLaeN","8w2t5hMYqp","Ph9nP6C5qx","eewbuw0ToL","D4vGDi5EA2","gJLn6v0xnP","KFSx94NKJn","jWTQ2TZYIH","yXekIHxTD4","KYD54nUTWz","i8ToyICDmI","PoHhknlbAi","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯13210","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5419","layer":2},{"info":"number node, value=3044","layer":2},{"info":"compute binary expreesion, left_input=5419, right_input=3044, op_id = abYXlopdE0 binary_op_definition= 'a⨿b = { (((a∲⫓409)≬⇓(a⩒⫫a))∓⋝((146⫥∨⫟b)≥⨤⩑(219⨥⫆b))) }', output=-319","layer":1},{"info":"number node, value=1631","layer":2},{"info":"number node, value=6945","layer":2},{"info":"compute binary expreesion, left_input=1631, right_input=6945, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-319, right_input=0, op_id = d7ASUq0ydm binary_op_definition= 'a⫯⪬∳b = { ((b⋥≓≎a)≧⫂∧(⊄⩳↩a)) , if (a≦≮≮)!=65 ; ((b⫩⊇)⋥≓≎(a⨰b)) , else }', output=484","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1110223⨿⪩⨒∯233210⫯⪬∳(⪩⨒∯121133∲⫓⪩⨒∯1230201)=⪩⨒∯13210","reverse_text":"⪩⨒∯13210=⪩⨒∯1110223⨿⪩⨒∯233210⫯⪬∳(⪩⨒∯121133∲⫓⪩⨒∯1230201)","cot":[{"info":"⪩⨒∯1110223⨿⪩⨒∯233210=⪩⨒∯-10333","layer":1},{"info":"⪩⨒∯121133∲⫓⪩⨒∯1230201=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-10333⫯⪬∳⪩⨒∯0=⪩⨒∯13210","layer":0}]}
{"id":381,"expression_no_base_symbol":"(⨭⩧⫛$1135$)⨂≜($2591$⨁⊸⫻)","expression":"(⨭⩧⫛⪩⨒∯101233)⨂≜(⪩⨒∯220133⨁⊸⫻)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":61,"operation_count":3,"complexity_ratio":20.333333333333332,"tree":{"type":"binary","operator":"⨂≜","left_expr":{"type":"unary","operator":"⨭⩧⫛","unary_expr":{"type":"numeric_atoms","value":1135,"base":4}},"right_expr":{"type":"unary","operator":"⨁⊸⫻","unary_expr":{"type":"numeric_atoms","value":2591,"base":4}}},"used_operators":["k1SHOSEABc","g21JL6JxX7","glklzrTFfD"],"dependent_operators":["9FxExcQeMw","HiPekx5b7W","eLxqMNBOBk","JclMnS0uGI","COABgblf1C","U7g4x0WXJJ","Ikt5ks8PT7","Asc51vEJeQ","A8NUZmVepG","W4YGzv6Whe","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1135","layer":2},{"info":"compute unary expreesion, input=1135, op_id = g21JL6JxX7, unary_op_definition = '⨭⩧⫛a = { ((↥a)⩧⪆(↣≠⋷a)) }', output=nan","layer":1},{"info":"number node, value=2591","layer":2},{"info":"compute unary expreesion, input=2591, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=2591","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2591, op_id = k1SHOSEABc binary_op_definition= 'a⨂≜b = { ((37⊭↱(⫓⪴a))⩷∴((111⨜⨶78)⨔⇊(a∑⇟⊟b))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⨭⩧⫛⪩⨒∯101233)⨂≜(⪩⨒∯220133⨁⊸⫻)=NaN","reverse_text":"NaN=(⨭⩧⫛⪩⨒∯101233)⨂≜(⪩⨒∯220133⨁⊸⫻)","cot":[{"info":"⨭⩧⫛⪩⨒∯101233=NaN","layer":1},{"info":"⪩⨒∯220133⨁⊸⫻=⪩⨒∯220133","layer":1},{"info":"NaN⨂≜⪩⨒∯220133=NaN","layer":0}]}
{"id":382,"expression_no_base_symbol":"$2795$≄⊠$6424$≬⋮$6039$⫲≸⪮$8146$","expression":"⪩⨒∯223223≄⊠⪩⨒∯1210120≬⋮⪩⨒∯1132113⫲≸⪮⪩⨒∯1333102","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6110,"operation_count":3,"complexity_ratio":2036.6666666666667,"tree":{"type":"binary","operator":"≬⋮","left_expr":{"type":"binary","operator":"≄⊠","left_expr":{"type":"numeric_atoms","value":2795,"base":4},"right_expr":{"type":"numeric_atoms","value":6424,"base":4}},"right_expr":{"type":"binary","operator":"⫲≸⪮","left_expr":{"type":"numeric_atoms","value":6039,"base":4},"right_expr":{"type":"numeric_atoms","value":8146,"base":4}}},"used_operators":["kbkesczE7y","vXNesLlMH1","P3lXMJvFrc"],"dependent_operators":["P8v4zCKN1o","rysDP5nf3Z","7j4O788W3g","XIabStNQrY","t8gj7n24qd","i8ToyICDmI","d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI","tmPS8pqC7x","oWn0xqSxBt","DbCuESL50I"],"result":"⪩⨒∯31210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2795","layer":2},{"info":"number node, value=6424","layer":2},{"info":"compute binary expreesion, left_input=2795, right_input=6424, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=107452","layer":1},{"info":"number node, value=6039","layer":2},{"info":"number node, value=8146","layer":2},{"info":"compute binary expreesion, left_input=6039, right_input=8146, op_id = P3lXMJvFrc binary_op_definition= 'a⫲≸⪮b = { (⋼∭⪍a) , if (⊙↵-b)>333 ; (a⨪↰⇹b) , else }', output=6039","layer":1},{"info":"compute binary expreesion, left_input=107452, right_input=6039, op_id = kbkesczE7y binary_op_definition= 'a≬⋮b = { (((-a)∲⫓(b⇋≉))↺(∥⊫(b-b))) }', output=868","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯223223≄⊠⪩⨒∯1210120≬⋮⪩⨒∯1132113⫲≸⪮⪩⨒∯1333102=⪩⨒∯31210","reverse_text":"⪩⨒∯31210=⪩⨒∯223223≄⊠⪩⨒∯1210120≬⋮⪩⨒∯1132113⫲≸⪮⪩⨒∯1333102","cot":[{"info":"⪩⨒∯223223≄⊠⪩⨒∯1210120=⪩⨒∯122032330","layer":1},{"info":"⪩⨒∯1132113⫲≸⪮⪩⨒∯1333102=⪩⨒∯1132113","layer":1},{"info":"⪩⨒∯122032330≬⋮⪩⨒∯1132113=⪩⨒∯31210","layer":0}]}
{"id":383,"expression_no_base_symbol":"(⋣$1283$)⫢⨠$3839$⫣⪄⊒$3629$","expression":"(⋣⪩⨒∯110003)⫢⨠⪩⨒∯323333⫣⪄⊒⪩⨒∯320231","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":281,"operation_count":3,"complexity_ratio":93.66666666666667,"tree":{"type":"binary","operator":"⫢⨠","left_expr":{"type":"unary","operator":"⋣","unary_expr":{"type":"numeric_atoms","value":1283,"base":4}},"right_expr":{"type":"binary","operator":"⫣⪄⊒","left_expr":{"type":"numeric_atoms","value":3839,"base":4},"right_expr":{"type":"numeric_atoms","value":3629,"base":4}}},"used_operators":["xlXykHWxX1","zQWRhDnn8F","RabNbG55vr"],"dependent_operators":["KFSx94NKJn","e1ybzncUwg","zR4jO40bMj","g7Hmc5v1ko","k2HlF1dBQh","2DlMacCsIx","vRio1gEz1j","x5lMkHmzsq","3EYGwJThht","DbCuESL50I","XTarYq4gQB","IGFM8TAlm9","sdazOOVcIp","8HhzD0ZcuI","keWfFq85dY","NTOWxs364D","DbCuESL50I","fOIeswaMU4","g7Hmc5v1ko","KPf6cnQVty","j9kHMeSvPp","k8jYdgA6NY","2DDjHMKMc0","8WDwsbhb0R","cTDWOvIxvz","IWmyXbctLI"],"result":"⪩⨒∯23330300202","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1283","layer":2},{"info":"compute unary expreesion, input=1283, op_id = zQWRhDnn8F, unary_op_definition = '⋣a = { ((⋼∭⪍203)⇄(≯(a⨽a))) , if (a⇩)==859 ; (↥≼⋛((⪝⪂⫅a)⪨≂(⇉-⫰26))) , else }', output=-377107","layer":1},{"info":"number node, value=3839","layer":2},{"info":"number node, value=3629","layer":2},{"info":"compute binary expreesion, left_input=3839, right_input=3629, op_id = RabNbG55vr binary_op_definition= 'a⫣⪄⊒b = { ((a⪮%⊝(153⪭a))%(⋼∭⪍(b⩚⊴⇥34))) , if b>769 ; ((∂⩏⊆(b⩟))∺≝⩲((b∝a)⋝⋈⪟(a⩌⋺b))) , else }', output=-14608","layer":1},{"info":"compute binary expreesion, left_input=-377107, right_input=-14608, op_id = xlXykHWxX1 binary_op_definition= 'a⫢⨠b = { (((b⩨a)⪶≀⋏(a⩌⋺b))⩒⫫(∤(≉a))) }', output=3132450","layer":0}],"base":4,"result_base":4,"text":"(⋣⪩⨒∯110003)⫢⨠⪩⨒∯323333⫣⪄⊒⪩⨒∯320231=⪩⨒∯23330300202","reverse_text":"⪩⨒∯23330300202=(⋣⪩⨒∯110003)⫢⨠⪩⨒∯323333⫣⪄⊒⪩⨒∯320231","cot":[{"info":"⋣⪩⨒∯110003=⪩⨒∯-1130010103","layer":1},{"info":"⪩⨒∯323333⫣⪄⊒⪩⨒∯320231=⪩⨒∯-3210100","layer":1},{"info":"⪩⨒∯-1130010103⫢⨠⪩⨒∯-3210100=⪩⨒∯23330300202","layer":0}]}
{"id":384,"expression_no_base_symbol":"$2965$≥⨤⩑$9692$⋻⩜⩜($1042$-$2213$)","expression":"⪩⨒∯232111≥⨤⩑⪩⨒∯2113130⋻⩜⩜(⪩⨒∯100102-⪩⨒∯202211)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16410,"operation_count":3,"complexity_ratio":5470.0,"tree":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"binary","operator":"≥⨤⩑","left_expr":{"type":"numeric_atoms","value":2965,"base":4},"right_expr":{"type":"numeric_atoms","value":9692,"base":4}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1042,"base":4},"right_expr":{"type":"numeric_atoms","value":2213,"base":4}}},"used_operators":["oDCm7WA9JY","gJLn6v0xnP","rysDP5nf3Z"],"dependent_operators":["mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","mp7IySMOzn","aA7tF3KVD3","QvoQhV0rrE"],"result":"⪩⨒∯212210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2965","layer":2},{"info":"number node, value=9692","layer":2},{"info":"compute binary expreesion, left_input=2965, right_input=9692, op_id = gJLn6v0xnP binary_op_definition= 'a≥⨤⩑b = { (b⇷a) , if (b⪘⨀)>356 ; (702∠⫱488) , else }', output=1234","layer":1},{"info":"number node, value=1042","layer":2},{"info":"number node, value=2213","layer":2},{"info":"compute binary expreesion, left_input=1042, right_input=2213, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-1171","layer":1},{"info":"compute binary expreesion, left_input=1234, right_input=-1171, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=2468","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯232111≥⨤⩑⪩⨒∯2113130⋻⩜⩜(⪩⨒∯100102-⪩⨒∯202211)=⪩⨒∯212210","reverse_text":"⪩⨒∯212210=⪩⨒∯232111≥⨤⩑⪩⨒∯2113130⋻⩜⩜(⪩⨒∯100102-⪩⨒∯202211)","cot":[{"info":"⪩⨒∯232111≥⨤⩑⪩⨒∯2113130=⪩⨒∯103102","layer":1},{"info":"⪩⨒∯100102-⪩⨒∯202211=⪩⨒∯-102103","layer":1},{"info":"⪩⨒∯103102⋻⩜⩜⪩⨒∯-102103=⪩⨒∯212210","layer":0}]}
{"id":385,"expression_no_base_symbol":"⋼∭⪍$3001$⪚$4963$","expression":"⋼∭⪍⪩⨒∯232321⪚⪩⨒∯1031203","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34,"operation_count":2,"complexity_ratio":17.0,"tree":{"type":"unary","operator":"⋼∭⪍","unary_expr":{"type":"binary","operator":"⪚","left_expr":{"type":"numeric_atoms","value":3001,"base":4},"right_expr":{"type":"numeric_atoms","value":4963,"base":4}}},"used_operators":["DbCuESL50I","HrjLwUk87U"],"dependent_operators":["e1ybzncUwg","sdazOOVcIp","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","u6S6b8DprG","9FxExcQeMw","rysDP5nf3Z","NTOWxs364D","DZ8iAZOCBD","tifHPKVTfV","eH2TOUuTDT","2DDjHMKMc0"],"result":"⪩⨒∯-12033222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3001","layer":2},{"info":"number node, value=4963","layer":2},{"info":"compute binary expreesion, left_input=3001, right_input=4963, op_id = HrjLwUk87U binary_op_definition= 'a⪚b = { (((317⩚⊴⇥a)⋝⋈⪟(518-95))⊉≛↸((97⪐)⩷∴(b⇼⇔∾a))) }', output=-4280","layer":1},{"info":"compute unary expreesion, input=-4280, op_id = DbCuESL50I, unary_op_definition = '⋼∭⪍a = { (≉((a∲⫓a)⪨≂(a⪒a))) , if (↽≂a)>481 ; (↽≂((↽≂435)≧⫂∧(↽≂a))) , else }', output=-25578","layer":0}],"base":4,"result_base":4,"text":"⋼∭⪍⪩⨒∯232321⪚⪩⨒∯1031203=⪩⨒∯-12033222","reverse_text":"⪩⨒∯-12033222=⋼∭⪍⪩⨒∯232321⪚⪩⨒∯1031203","cot":[{"info":"⪩⨒∯232321⪚⪩⨒∯1031203=⪩⨒∯-1002320","layer":1},{"info":"⋼∭⪍⪩⨒∯-1002320=⪩⨒∯-12033222","layer":0}]}
{"id":386,"expression_no_base_symbol":"(⊀$4058$)⇼⇔∾$8146$⇤$4539$","expression":"(⊀⪩⨒∯333122)⇼⇔∾⪩⨒∯1333102⇤⪩⨒∯1012323","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":37,"operation_count":3,"complexity_ratio":12.333333333333334,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"unary","operator":"⊀","unary_expr":{"type":"numeric_atoms","value":4058,"base":4}},"right_expr":{"type":"binary","operator":"⇤","left_expr":{"type":"numeric_atoms","value":8146,"base":4},"right_expr":{"type":"numeric_atoms","value":4539,"base":4}}},"used_operators":["tifHPKVTfV","oPMjh9089D","YSKBFp38Pu"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","Qy55tPpLXF","XIabStNQrY","tifHPKVTfV","glklzrTFfD","sdazOOVcIp","8w2t5hMYqp","Ph9nP6C5qx","g55IO6H4Gj","2td37pGCOC","QMFrweE19q","rysDP5nf3Z","XPYlsWDdGa","tifHPKVTfV","2DQ55sFlQl","2DDjHMKMc0","xUOZtlo3hN","QMFrweE19q"],"result":"⪩⨒∯-102230003","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4058","layer":2},{"info":"compute unary expreesion, input=4058, op_id = oPMjh9089D, unary_op_definition = '⊀a = { (((⩦⩻⨪67)⪨≂(a⋥≓≎63))⇋≉) , if (a⇼⇔∾9)<290 ; (((⊄⩳↩a)⨁⊸⫻)⫡⨏((a≧⫂∧a)⨸⪁(a≧⫂∧a))) , else }', output=15970","layer":1},{"info":"number node, value=8146","layer":2},{"info":"number node, value=4539","layer":2},{"info":"compute binary expreesion, left_input=8146, right_input=4539, op_id = YSKBFp38Pu binary_op_definition= 'a⇤b = { (((b-523)⇼⇔∾(⨞⊢a))⫡⨏((⪲⇎a)⨵⪆(336⋝⋈⪟a))) }', output=-60577","layer":1},{"info":"compute binary expreesion, left_input=15970, right_input=-60577, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-76547","layer":0}],"base":4,"result_base":4,"text":"(⊀⪩⨒∯333122)⇼⇔∾⪩⨒∯1333102⇤⪩⨒∯1012323=⪩⨒∯-102230003","reverse_text":"⪩⨒∯-102230003=(⊀⪩⨒∯333122)⇼⇔∾⪩⨒∯1333102⇤⪩⨒∯1012323","cot":[{"info":"⊀⪩⨒∯333122=⪩⨒∯3321202","layer":1},{"info":"⪩⨒∯1333102⇤⪩⨒∯1012323=⪩⨒∯-32302201","layer":1},{"info":"⪩⨒∯3321202⇼⇔∾⪩⨒∯-32302201=⪩⨒∯-102230003","layer":0}]}
{"id":387,"expression_no_base_symbol":"≑⋹($8946$∷$3351$)","expression":"≑⋹(⪩⨒∯2023302∷⪩⨒∯310113)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":108,"operation_count":2,"complexity_ratio":54.0,"tree":{"type":"unary","operator":"≑⋹","unary_expr":{"type":"binary","operator":"∷","left_expr":{"type":"numeric_atoms","value":8946,"base":4},"right_expr":{"type":"numeric_atoms","value":3351,"base":4}}},"used_operators":["6B9nyZLogK","D3AQDKkPcf"],"dependent_operators":["aBQ6xLxuTc","zR4jO40bMj","RabNbG55vr","ocnLzx9CaJ","3ViojmjbAp","FlXk3pOYe8","o20kRiQErp","4JB6nKBMSY","2td37pGCOC","COABgblf1C","9FxExcQeMw","NTOWxs364D","7j4O788W3g"],"result":"⪩⨒∯121302","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=8946","layer":2},{"info":"number node, value=3351","layer":2},{"info":"compute binary expreesion, left_input=8946, right_input=3351, op_id = D3AQDKkPcf binary_op_definition= 'a∷b = { (a⩚⊴⇥673) , if (b⩷∴24)<=112 ; (a↺b) , else }', output=3351","layer":1},{"info":"compute unary expreesion, input=3351, op_id = 6B9nyZLogK, unary_op_definition = '≑⋹a = { (((a⨓a)⫣⪄⊒(148∸))⇴(⩦⩻⨪(a⇂≾⫗a))) , if a<188 ; (⩎⋉((a⩼⇪↪a)⊭↱(a⪶≀⋏172))) , else }', output=1650","layer":0}],"base":4,"result_base":4,"text":"≑⋹(⪩⨒∯2023302∷⪩⨒∯310113)=⪩⨒∯121302","reverse_text":"⪩⨒∯121302=≑⋹(⪩⨒∯2023302∷⪩⨒∯310113)","cot":[{"info":"⪩⨒∯2023302∷⪩⨒∯310113=⪩⨒∯310113","layer":1},{"info":"≑⋹⪩⨒∯310113=⪩⨒∯121302","layer":0}]}
{"id":388,"expression_no_base_symbol":"∜⨇($2286$⨪↰⇹$1040$)","expression":"∜⨇(⪩⨒∯203232⨪↰⇹⪩⨒∯100100)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2343,"operation_count":2,"complexity_ratio":1171.5,"tree":{"type":"unary","operator":"∜⨇","unary_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":2286,"base":4},"right_expr":{"type":"numeric_atoms","value":1040,"base":4}}},"used_operators":["uFPyJr306J","tmPS8pqC7x"],"dependent_operators":["fG6uBQFnGz","pRsWfj4Fpp","rGHVDoGpnC","Y7wcNGrDQJ","NNaDxxp6OQ","rJVOvQCfKK"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2286","layer":2},{"info":"number node, value=1040","layer":2},{"info":"compute binary expreesion, left_input=2286, right_input=1040, op_id = tmPS8pqC7x binary_op_definition= 'a⨪↰⇹b = {a, if a == 0; (b)⨎((a-1)⨪↰⇹b), if a > 0 and abs(a) < 1000000; -(b)⨎((a+1)⨪↰⇹b), if a < 0 and abs(a) < 1000000; NaN, else}', output=2286","layer":1},{"info":"compute unary expreesion, input=2286, op_id = uFPyJr306J, unary_op_definition = '∜⨇a = { (a⨟⋌⩍a) , if (a⫽⇹≛)!=2 or (↩⪖a)==528 or (∡a)>=548 ; (132⩵∡a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"∜⨇(⪩⨒∯203232⨪↰⇹⪩⨒∯100100)=NaN","reverse_text":"NaN=∜⨇(⪩⨒∯203232⨪↰⇹⪩⨒∯100100)","cot":[{"info":"⪩⨒∯203232⨪↰⇹⪩⨒∯100100=⪩⨒∯203232","layer":1},{"info":"∜⨇⪩⨒∯203232=NaN","layer":0}]}
{"id":389,"expression_no_base_symbol":"$3116$⩺⪪$4438$∷(∥⊫$1351$)","expression":"⪩⨒∯300230⩺⪪⪩⨒∯1011112∷(∥⊫⪩⨒∯111013)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":132,"operation_count":3,"complexity_ratio":44.0,"tree":{"type":"binary","operator":"∷","left_expr":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"numeric_atoms","value":3116,"base":4},"right_expr":{"type":"numeric_atoms","value":4438,"base":4}},"right_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":1351,"base":4}}},"used_operators":["D3AQDKkPcf","uvdQJvN4PV","P8v4zCKN1o"],"dependent_operators":["9FxExcQeMw","NTOWxs364D","7j4O788W3g","Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯202223","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3116","layer":2},{"info":"number node, value=4438","layer":2},{"info":"compute binary expreesion, left_input=3116, right_input=4438, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=-1818","layer":1},{"info":"number node, value=1351","layer":2},{"info":"compute unary expreesion, input=1351, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=2219","layer":1},{"info":"compute binary expreesion, left_input=-1818, right_input=2219, op_id = D3AQDKkPcf binary_op_definition= 'a∷b = { (a⩚⊴⇥673) , if (b⩷∴24)<=112 ; (a↺b) , else }', output=2219","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯300230⩺⪪⪩⨒∯1011112∷(∥⊫⪩⨒∯111013)=⪩⨒∯202223","reverse_text":"⪩⨒∯202223=⪩⨒∯300230⩺⪪⪩⨒∯1011112∷(∥⊫⪩⨒∯111013)","cot":[{"info":"⪩⨒∯300230⩺⪪⪩⨒∯1011112=⪩⨒∯-130122","layer":1},{"info":"∥⊫⪩⨒∯111013=⪩⨒∯202223","layer":1},{"info":"⪩⨒∯-130122∷⪩⨒∯202223=⪩⨒∯202223","layer":0}]}
{"id":390,"expression_no_base_symbol":"($8396$/$1630$)⩦($1217$+$2383$)","expression":"(⪩⨒∯2003030/⪩⨒∯121132)⩦(⪩⨒∯103001+⪩⨒∯211033)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":21,"operation_count":3,"complexity_ratio":7.0,"tree":{"type":"binary","operator":"⩦","left_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":8396,"base":4},"right_expr":{"type":"numeric_atoms","value":1630,"base":4}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":1217,"base":4},"right_expr":{"type":"numeric_atoms","value":2383,"base":4}}},"used_operators":["0kmYd0q39Y","XhwjNDsVaA","W4YGzv6Whe"],"dependent_operators":["N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q","rysDP5nf3Z"],"result":"⪩⨒∯22","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=8396","layer":2},{"info":"number node, value=1630","layer":2},{"info":"compute binary expreesion, left_input=8396, right_input=1630, op_id = XhwjNDsVaA binary_op_definition= 'None', output=5","layer":1},{"info":"number node, value=1217","layer":2},{"info":"number node, value=2383","layer":2},{"info":"compute binary expreesion, left_input=1217, right_input=2383, op_id = W4YGzv6Whe binary_op_definition= 'None', output=3600","layer":1},{"info":"compute binary expreesion, left_input=5, right_input=3600, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=10","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2003030/⪩⨒∯121132)⩦(⪩⨒∯103001+⪩⨒∯211033)=⪩⨒∯22","reverse_text":"⪩⨒∯22=(⪩⨒∯2003030/⪩⨒∯121132)⩦(⪩⨒∯103001+⪩⨒∯211033)","cot":[{"info":"⪩⨒∯2003030/⪩⨒∯121132=⪩⨒∯11","layer":1},{"info":"⪩⨒∯103001+⪩⨒∯211033=⪩⨒∯320100","layer":1},{"info":"⪩⨒∯11⩦⪩⨒∯320100=⪩⨒∯22","layer":0}]}
{"id":391,"expression_no_base_symbol":"(↘$1054$)⊋≦⊧$2804$∳⫺$5485$","expression":"(↘⪩⨒∯100132)⊋≦⊧⪩⨒∯223310∳⫺⪩⨒∯1111231","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":83,"operation_count":3,"complexity_ratio":27.666666666666668,"tree":{"type":"binary","operator":"⊋≦⊧","left_expr":{"type":"unary","operator":"↘","unary_expr":{"type":"numeric_atoms","value":1054,"base":4}},"right_expr":{"type":"binary","operator":"∳⫺","left_expr":{"type":"numeric_atoms","value":2804,"base":4},"right_expr":{"type":"numeric_atoms","value":5485,"base":4}}},"used_operators":["oRDoc9rAEX","LdNpr8hQHL","AzXXKTstlj"],"dependent_operators":["DZ8iAZOCBD","tifHPKVTfV","sdazOOVcIp","glklzrTFfD","DIvbN7qnHd","12rbrZMWeM","Ph9nP6C5qx","eewbuw0ToL","2td37pGCOC","uFcxV4UQCh","F4yD0voBRQ","Tcnh7f0tEr","ZvLB05nZmT"],"result":"⪩⨒∯23320","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1054","layer":2},{"info":"compute unary expreesion, input=1054, op_id = LdNpr8hQHL, unary_op_definition = '↘a = { (a⪛392) }', output=270","layer":1},{"info":"number node, value=2804","layer":2},{"info":"number node, value=5485","layer":2},{"info":"compute binary expreesion, left_input=2804, right_input=5485, op_id = AzXXKTstlj binary_op_definition= 'a∳⫺b = { (a≣⋋) , if (b⫳≱↱947)==166 ; (a⇣⩺⋵b) , else }', output=-260","layer":1},{"info":"compute binary expreesion, left_input=270, right_input=-260, op_id = oRDoc9rAEX binary_op_definition= 'a⊋≦⊧b = { (((24⊉≛↸a)⊉≛↸(⩦⩻⨪b))⊉≛↸((a⊠≄⫣)⪨≂(b⇼⇔∾a))) , if a<=128 ; (((a⇼⇔∾b)⨁⊸⫻)⇼⇔∾((22⋳⪒a)⨰(a≧⫂∧a))) , else }', output=760","layer":0}],"base":4,"result_base":4,"text":"(↘⪩⨒∯100132)⊋≦⊧⪩⨒∯223310∳⫺⪩⨒∯1111231=⪩⨒∯23320","reverse_text":"⪩⨒∯23320=(↘⪩⨒∯100132)⊋≦⊧⪩⨒∯223310∳⫺⪩⨒∯1111231","cot":[{"info":"↘⪩⨒∯100132=⪩⨒∯10032","layer":1},{"info":"⪩⨒∯223310∳⫺⪩⨒∯1111231=⪩⨒∯-10010","layer":1},{"info":"⪩⨒∯10032⊋≦⊧⪩⨒∯-10010=⪩⨒∯23320","layer":0}]}
{"id":392,"expression_no_base_symbol":"⊢≑≆($2681$⋓$4648$)","expression":"⊢≑≆(⪩⨒∯221321⋓⪩⨒∯1020220)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":23,"operation_count":2,"complexity_ratio":11.5,"tree":{"type":"unary","operator":"⊢≑≆","unary_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":2681,"base":4},"right_expr":{"type":"numeric_atoms","value":4648,"base":4}}},"used_operators":["27wFxooxGf","T2fj7uvVaJ"],"dependent_operators":["eLAdDNolq6","9FxExcQeMw","Ph9nP6C5qx","g55IO6H4Gj","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⪩⨒∯3001","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2681","layer":2},{"info":"number node, value=4648","layer":2},{"info":"compute binary expreesion, left_input=2681, right_input=4648, op_id = T2fj7uvVaJ binary_op_definition= 'a⋓b = { (((60⪒b)⊭∹↮)%((a⪘⫢68)⪘⫢(⨵≀≌a))) , if (b>=803 and b<=372 and b<242) ; (16⪢((b⊠≄⫣)⋷(a⫌⩹⨱))) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = 27wFxooxGf, unary_op_definition = '⊢≑≆a = { a , if (≤/a)==126 and a<49 ; ((559⨸⪁a)≧⫂∧(349⩷∴a)) , else }', output=193","layer":0}],"base":4,"result_base":4,"text":"⊢≑≆(⪩⨒∯221321⋓⪩⨒∯1020220)=⪩⨒∯3001","reverse_text":"⪩⨒∯3001=⊢≑≆(⪩⨒∯221321⋓⪩⨒∯1020220)","cot":[{"info":"⪩⨒∯221321⋓⪩⨒∯1020220=⪩⨒∯0","layer":1},{"info":"⊢≑≆⪩⨒∯0=⪩⨒∯3001","layer":0}]}
{"id":393,"expression_no_base_symbol":"$3356$⪘⫢$1598$↺$2622$∳⫺$5189$","expression":"⪩⨒∯310130⪘⫢⪩⨒∯120332↺⪩⨒∯220332∳⫺⪩⨒∯1101011","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":74,"operation_count":3,"complexity_ratio":24.666666666666668,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":3356,"base":4},"right_expr":{"type":"numeric_atoms","value":1598,"base":4}},"right_expr":{"type":"binary","operator":"∳⫺","left_expr":{"type":"numeric_atoms","value":2622,"base":4},"right_expr":{"type":"numeric_atoms","value":5189,"base":4}}},"used_operators":["7j4O788W3g","oacrs7FA3X","AzXXKTstlj"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","F4yD0voBRQ","Tcnh7f0tEr","ZvLB05nZmT"],"result":"⪩⨒∯-10010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3356","layer":2},{"info":"number node, value=1598","layer":2},{"info":"compute binary expreesion, left_input=3356, right_input=1598, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=6588","layer":1},{"info":"number node, value=2622","layer":2},{"info":"number node, value=5189","layer":2},{"info":"compute binary expreesion, left_input=2622, right_input=5189, op_id = AzXXKTstlj binary_op_definition= 'a∳⫺b = { (a≣⋋) , if (b⫳≱↱947)==166 ; (a⇣⩺⋵b) , else }', output=-260","layer":1},{"info":"compute binary expreesion, left_input=6588, right_input=-260, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=-260","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯310130⪘⫢⪩⨒∯120332↺⪩⨒∯220332∳⫺⪩⨒∯1101011=⪩⨒∯-10010","reverse_text":"⪩⨒∯-10010=⪩⨒∯310130⪘⫢⪩⨒∯120332↺⪩⨒∯220332∳⫺⪩⨒∯1101011","cot":[{"info":"⪩⨒∯310130⪘⫢⪩⨒∯120332=⪩⨒∯1212330","layer":1},{"info":"⪩⨒∯220332∳⫺⪩⨒∯1101011=⪩⨒∯-10010","layer":1},{"info":"⪩⨒∯1212330↺⪩⨒∯-10010=⪩⨒∯-10010","layer":0}]}
{"id":394,"expression_no_base_symbol":"$1998$∣$3916$⊋≦⊧($2171$∖$4037$)","expression":"⪩⨒∯133032∣⪩⨒∯331030⊋≦⊧(⪩⨒∯201323∖⪩⨒∯333011)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":525,"operation_count":3,"complexity_ratio":175.0,"tree":{"type":"binary","operator":"⊋≦⊧","left_expr":{"type":"binary","operator":"∣","left_expr":{"type":"numeric_atoms","value":1998,"base":4},"right_expr":{"type":"numeric_atoms","value":3916,"base":4}},"right_expr":{"type":"binary","operator":"∖","left_expr":{"type":"numeric_atoms","value":2171,"base":4},"right_expr":{"type":"numeric_atoms","value":4037,"base":4}}},"used_operators":["oRDoc9rAEX","PPChnnnBFF","tXD093vOjl"],"dependent_operators":["DZ8iAZOCBD","tifHPKVTfV","sdazOOVcIp","glklzrTFfD","DIvbN7qnHd","12rbrZMWeM","Ph9nP6C5qx","eewbuw0ToL","2td37pGCOC","eLAdDNolq6","eH2TOUuTDT","Ph9nP6C5qx","i8ToyICDmI","rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC"],"result":"⪩⨒∯3300","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1998","layer":2},{"info":"number node, value=3916","layer":2},{"info":"compute binary expreesion, left_input=1998, right_input=3916, op_id = PPChnnnBFF binary_op_definition= 'a∣b = { (≤/((a⪐)≧⫂∧(a∲⫓b))) , if (b⪐)<590 ; a , else }', output=1998","layer":1},{"info":"number node, value=2171","layer":2},{"info":"number node, value=4037","layer":2},{"info":"compute binary expreesion, left_input=2171, right_input=4037, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=1998, right_input=0, op_id = oRDoc9rAEX binary_op_definition= 'a⊋≦⊧b = { (((24⊉≛↸a)⊉≛↸(⩦⩻⨪b))⊉≛↸((a⊠≄⫣)⪨≂(b⇼⇔∾a))) , if a<=128 ; (((a⇼⇔∾b)⨁⊸⫻)⇼⇔∾((22⋳⪒a)⨰(a≧⫂∧a))) , else }', output=240","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯133032∣⪩⨒∯331030⊋≦⊧(⪩⨒∯201323∖⪩⨒∯333011)=⪩⨒∯3300","reverse_text":"⪩⨒∯3300=⪩⨒∯133032∣⪩⨒∯331030⊋≦⊧(⪩⨒∯201323∖⪩⨒∯333011)","cot":[{"info":"⪩⨒∯133032∣⪩⨒∯331030=⪩⨒∯133032","layer":1},{"info":"⪩⨒∯201323∖⪩⨒∯333011=⪩⨒∯0","layer":1},{"info":"⪩⨒∯133032⊋≦⊧⪩⨒∯0=⪩⨒∯3300","layer":0}]}
{"id":395,"expression_no_base_symbol":"($1391$⋾⨃∁$5152$)⪔⊥($4260$⨸⪁$5273$)","expression":"(⪩⨒∯111233⋾⨃∁⪩⨒∯1100200)⪔⊥(⪩⨒∯1002210⨸⪁⪩⨒∯1102121)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5203,"operation_count":3,"complexity_ratio":1734.3333333333333,"tree":{"type":"binary","operator":"⪔⊥","left_expr":{"type":"binary","operator":"⋾⨃∁","left_expr":{"type":"numeric_atoms","value":1391,"base":4},"right_expr":{"type":"numeric_atoms","value":5152,"base":4}},"right_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":4260,"base":4},"right_expr":{"type":"numeric_atoms","value":5273,"base":4}}},"used_operators":["HJ9erzHUuu","212REbPD9h","g55IO6H4Gj"],"dependent_operators":["eLAdDNolq6","rysDP5nf3Z","7j4O788W3g","tifHPKVTfV","8w2t5hMYqp","sdazOOVcIp","2td37pGCOC","COABgblf1C","eLxqMNBOBk","Qy55tPpLXF","w2P8NbNXyL","2DQ55sFlQl","f6k1SAg4EE","W4YGzv6Whe"],"result":"⪩⨒∯333101010023031","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1391","layer":2},{"info":"number node, value=5152","layer":2},{"info":"compute binary expreesion, left_input=1391, right_input=5152, op_id = 212REbPD9h binary_op_definition= 'a⋾⨃∁b = { ((430⊉↱≁b)⨵⪆b) , if (a⪒898)>=359 ; ((⫓⪴b)⊉↱≁(26⋥≓≎b)) , else }', output=265369122","layer":1},{"info":"number node, value=4260","layer":2},{"info":"number node, value=5273","layer":2},{"info":"compute binary expreesion, left_input=4260, right_input=5273, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=19066","layer":1},{"info":"compute binary expreesion, left_input=265369122, right_input=19066, op_id = HJ9erzHUuu binary_op_definition= 'a⪔⊥b = { (⩦⩻⨪(≤/(315⇼⇔∾a))) , if b<175 ; ((⊄⩳↩(b-b))⇼⇔∾((b⪨≂a)⊭↱(a↺b))) , else }', output=1061438157","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯111233⋾⨃∁⪩⨒∯1100200)⪔⊥(⪩⨒∯1002210⨸⪁⪩⨒∯1102121)=⪩⨒∯333101010023031","reverse_text":"⪩⨒∯333101010023031=(⪩⨒∯111233⋾⨃∁⪩⨒∯1100200)⪔⊥(⪩⨒∯1002210⨸⪁⪩⨒∯1102121)","cot":[{"info":"⪩⨒∯111233⋾⨃∁⪩⨒∯1100200=⪩⨒∯33310103120202","layer":1},{"info":"⪩⨒∯1002210⨸⪁⪩⨒∯1102121=⪩⨒∯10221322","layer":1},{"info":"⪩⨒∯33310103120202⪔⊥⪩⨒∯10221322=⪩⨒∯333101010023031","layer":0}]}
{"id":396,"expression_no_base_symbol":"↞≼($1431$⊦⊿)","expression":"↞≼(⪩⨒∯112113⊦⊿)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":21,"operation_count":2,"complexity_ratio":10.5,"tree":{"type":"unary","operator":"↞≼","unary_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":1431,"base":4}}},"used_operators":["DE7zCoGJt9","14qkJME0vr"],"dependent_operators":["W4YGzv6Whe","D4vGDi5EA2","23Mk6UjR3U","BjRHVeLaeN","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","u6S6b8DprG","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯-20220332","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1431","layer":2},{"info":"compute unary expreesion, input=1431, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-4372","layer":1},{"info":"compute unary expreesion, input=-4372, op_id = DE7zCoGJt9, unary_op_definition = '↞≼a = { (↽≂(197⨰(a⨸⪁a))) , if (a⨸⪁373)!=224 ; (((591⋷a)≧⫂∧(a+a))⨸⪁((a⫩⊇)≦≮≮)) , else }', output=-35390","layer":0}],"base":4,"result_base":4,"text":"↞≼(⪩⨒∯112113⊦⊿)=⪩⨒∯-20220332","reverse_text":"⪩⨒∯-20220332=↞≼(⪩⨒∯112113⊦⊿)","cot":[{"info":"⪩⨒∯112113⊦⊿=⪩⨒∯-1010110","layer":1},{"info":"↞≼⪩⨒∯-1010110=⪩⨒∯-20220332","layer":0}]}
{"id":397,"expression_no_base_symbol":"∂(≻⋜$6320$)","expression":"∂(≻⋜⪩⨒∯1202300)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34079,"operation_count":2,"complexity_ratio":17039.5,"tree":{"type":"unary","operator":"∂","unary_expr":{"type":"unary","operator":"≻⋜","unary_expr":{"type":"numeric_atoms","value":6320,"base":4}}},"used_operators":["Uaa54Peajs","3tj9sqzovi"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","XGcMNugi78","dWAJyo7jo9","Tw270M8GLb","Y7wcNGrDQJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6320","layer":2},{"info":"compute unary expreesion, input=6320, op_id = 3tj9sqzovi, unary_op_definition = '≻⋜a = { (((a⩵∡a)⫞⩸⩒(⨰⫟⨤a))⪢a) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"∂(≻⋜⪩⨒∯1202300)=NaN","reverse_text":"NaN=∂(≻⋜⪩⨒∯1202300)","cot":[{"info":"≻⋜⪩⨒∯1202300=NaN","layer":1},{"info":"∂NaN=NaN","layer":0}]}
{"id":398,"expression_no_base_symbol":"($6185$*$1111$)≦↸($6168$⊢$1392$)","expression":"(⪩⨒∯1200221*⪩⨒∯101113)≦↸(⪩⨒∯1200120⊢⪩⨒∯111300)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1158,"operation_count":3,"complexity_ratio":386.0,"tree":{"type":"binary","operator":"≦↸","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":6185,"base":4},"right_expr":{"type":"numeric_atoms","value":1111,"base":4}},"right_expr":{"type":"binary","operator":"⊢","left_expr":{"type":"numeric_atoms","value":6168,"base":4},"right_expr":{"type":"numeric_atoms","value":1392,"base":4}}},"used_operators":["RygbFNSyEJ","9HNa5Wba9A","5twsqlHp2o"],"dependent_operators":["eLAdDNolq6","e1ybzncUwg","DZ8iAZOCBD","XIabStNQrY","12rbrZMWeM","2DDjHMKMc0","g55IO6H4Gj","W4YGzv6Whe","P8v4zCKN1o","Qy55tPpLXF","BjRHVeLaeN","DZ8iAZOCBD","7j4O788W3g","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","14qkJME0vr","D4vGDi5EA2","2td37pGCOC"],"result":"⪩⨒∯-122031131012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6185","layer":2},{"info":"number node, value=1111","layer":2},{"info":"compute binary expreesion, left_input=6185, right_input=1111, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=6871535","layer":1},{"info":"number node, value=6168","layer":2},{"info":"number node, value=1392","layer":2},{"info":"compute binary expreesion, left_input=6168, right_input=1392, op_id = 5twsqlHp2o binary_op_definition= 'a⊢b = { (((225⫩⊇)⊉≛↸(∥⊫a))⨵⪆(25⊉≛↸(b⋥≓≎47))) , if (a≦≮≮)==364 ; (((b⊦⊿)⪨≂(⩦⩻⨪b))↺((⨞⊢a)⪨≂(-1))) , else }', output=-12580","layer":1},{"info":"compute binary expreesion, left_input=6871535, right_input=-12580, op_id = RygbFNSyEJ binary_op_definition= 'a≦↸b = { (((≤/a)⋳⪒(b⊉≛↸a))⋝⋈⪟((a⇋≉)⨸⪁(≉a))) }', output=-6870854","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1200221*⪩⨒∯101113)≦↸(⪩⨒∯1200120⊢⪩⨒∯111300)=⪩⨒∯-122031131012","reverse_text":"⪩⨒∯-122031131012=(⪩⨒∯1200221*⪩⨒∯101113)≦↸(⪩⨒∯1200120⊢⪩⨒∯111300)","cot":[{"info":"⪩⨒∯1200221*⪩⨒∯101113=⪩⨒∯122031213233","layer":1},{"info":"⪩⨒∯1200120⊢⪩⨒∯111300=⪩⨒∯-3010210","layer":1},{"info":"⪩⨒∯122031213233≦↸⪩⨒∯-3010210=⪩⨒∯-122031131012","layer":0}]}
{"id":399,"expression_no_base_symbol":"(⊤⊝$3086$)⪟⇏($5090$⪨≂$2944$)","expression":"(⊤⊝⪩⨒∯300032)⪟⇏(⪩⨒∯1033202⪨≂⪩⨒∯232000)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":37,"operation_count":3,"complexity_ratio":12.333333333333334,"tree":{"type":"binary","operator":"⪟⇏","left_expr":{"type":"unary","operator":"⊤⊝","unary_expr":{"type":"numeric_atoms","value":3086,"base":4}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":5090,"base":4},"right_expr":{"type":"numeric_atoms","value":2944,"base":4}}},"used_operators":["GODebY97qR","rXAclfmB4M","sdazOOVcIp"],"dependent_operators":["gx7XJ7hdpj","XnXgA4xnOs","wEfv7U73WA","2DQ55sFlQl","f6k1SAg4EE","oacrs7FA3X","sdazOOVcIp","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯-1","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3086","layer":2},{"info":"compute unary expreesion, input=3086, op_id = rXAclfmB4M, unary_op_definition = '⊤⊝a = { (a⪨≂700) }', output=4874","layer":1},{"info":"number node, value=5090","layer":2},{"info":"number node, value=2944","layer":2},{"info":"compute binary expreesion, left_input=5090, right_input=2944, op_id = sdazOOVcIp binary_op_definition= 'a⪨≂b = { (((a-117)-b)-((145-b)-(a-a))) , if (-b)==187 ; ((-(b-102))-((b-a)-a)) , else }', output=4394","layer":1},{"info":"compute binary expreesion, left_input=4874, right_input=4394, op_id = GODebY97qR binary_op_definition= 'a⪟⇏b = { ((b⨑≵⋬b)⫸⇳(440⪒a)) , if (b⇐≅)<189 ; ((219⨑≵⋬a)⪘⫢(b⨵⪆b)) , else }', output=-1","layer":0}],"base":4,"result_base":4,"text":"(⊤⊝⪩⨒∯300032)⪟⇏(⪩⨒∯1033202⪨≂⪩⨒∯232000)=⪩⨒∯-1","reverse_text":"⪩⨒∯-1=(⊤⊝⪩⨒∯300032)⪟⇏(⪩⨒∯1033202⪨≂⪩⨒∯232000)","cot":[{"info":"⊤⊝⪩⨒∯300032=⪩⨒∯1030022","layer":1},{"info":"⪩⨒∯1033202⪨≂⪩⨒∯232000=⪩⨒∯1010222","layer":1},{"info":"⪩⨒∯1030022⪟⇏⪩⨒∯1010222=⪩⨒∯-1","layer":0}]}
{"id":400,"expression_no_base_symbol":"⨝⨆$2673$≳⇉$4714$","expression":"⨝⨆⪩⨒∯221301≳⇉⪩⨒∯1021222","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":352757580,"operation_count":2,"complexity_ratio":176378790.0,"tree":{"type":"unary","operator":"⨝⨆","unary_expr":{"type":"binary","operator":"≳⇉","left_expr":{"type":"numeric_atoms","value":2673,"base":4},"right_expr":{"type":"numeric_atoms","value":4714,"base":4}}},"used_operators":["bQ67fsrMVf","V0kx6qeWkN"],"dependent_operators":["tifHPKVTfV","KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2673","layer":2},{"info":"number node, value=4714","layer":2},{"info":"compute binary expreesion, left_input=2673, right_input=4714, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = bQ67fsrMVf, unary_op_definition = '⨝⨆a = { (209⇼⇔∾a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⨝⨆⪩⨒∯221301≳⇉⪩⨒∯1021222=NaN","reverse_text":"NaN=⨝⨆⪩⨒∯221301≳⇉⪩⨒∯1021222","cot":[{"info":"⪩⨒∯221301≳⇉⪩⨒∯1021222=NaN","layer":1},{"info":"⨝⨆NaN=NaN","layer":0}]}
{"id":401,"expression_no_base_symbol":"(⊿$1577$)↹⊜($1340$⊋≦⊧$3208$)","expression":"(⊿⪩⨒∯120221)↹⊜(⪩⨒∯110330⊋≦⊧⪩⨒∯302020)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":64,"operation_count":3,"complexity_ratio":21.333333333333332,"tree":{"type":"binary","operator":"↹⊜","left_expr":{"type":"unary","operator":"⊿","unary_expr":{"type":"numeric_atoms","value":1577,"base":4}},"right_expr":{"type":"binary","operator":"⊋≦⊧","left_expr":{"type":"numeric_atoms","value":1340,"base":4},"right_expr":{"type":"numeric_atoms","value":3208,"base":4}}},"used_operators":["9bazX3JMtO","DO4fhlbJSI","oRDoc9rAEX"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","23Mk6UjR3U","tifHPKVTfV","eH2TOUuTDT","DIvbN7qnHd","9FxExcQeMw","e1ybzncUwg","XPYlsWDdGa","sdazOOVcIp","2DQ55sFlQl","12rbrZMWeM","DZ8iAZOCBD","tifHPKVTfV","sdazOOVcIp","glklzrTFfD","DIvbN7qnHd","12rbrZMWeM","Ph9nP6C5qx","eewbuw0ToL","2td37pGCOC"],"result":"⪩⨒∯20121000","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1577","layer":2},{"info":"compute unary expreesion, input=1577, op_id = DO4fhlbJSI, unary_op_definition = '⊿a = { ((⪲⇎(a⨵⪆a))⩷∴((≉a)⋳⪒(a⪨≂a))) }', output=-7046","layer":1},{"info":"number node, value=1340","layer":2},{"info":"number node, value=3208","layer":2},{"info":"compute binary expreesion, left_input=1340, right_input=3208, op_id = oRDoc9rAEX binary_op_definition= 'a⊋≦⊧b = { (((24⊉≛↸a)⊉≛↸(⩦⩻⨪b))⊉≛↸((a⊠≄⫣)⪨≂(b⇼⇔∾a))) , if a<=128 ; (((a⇼⇔∾b)⨁⊸⫻)⇼⇔∾((22⋳⪒a)⨰(a≧⫂∧a))) , else }', output=-4308","layer":1},{"info":"compute binary expreesion, left_input=-7046, right_input=-4308, op_id = 9bazX3JMtO binary_op_definition= 'a↹⊜b = { (((a⊠≄⫣)⩷∴(b-a))⩷∴((a⋷b)⇼⇔∾(b⪐))) }', output=34368","layer":0}],"base":4,"result_base":4,"text":"(⊿⪩⨒∯120221)↹⊜(⪩⨒∯110330⊋≦⊧⪩⨒∯302020)=⪩⨒∯20121000","reverse_text":"⪩⨒∯20121000=(⊿⪩⨒∯120221)↹⊜(⪩⨒∯110330⊋≦⊧⪩⨒∯302020)","cot":[{"info":"⊿⪩⨒∯120221=⪩⨒∯-1232012","layer":1},{"info":"⪩⨒∯110330⊋≦⊧⪩⨒∯302020=⪩⨒∯-1003110","layer":1},{"info":"⪩⨒∯-1232012↹⊜⪩⨒∯-1003110=⪩⨒∯20121000","layer":0}]}
{"id":402,"expression_no_base_symbol":"($1725$⪔⊥$5225$)⋕⪉⪜($5032$∺≝⩲$2319$)","expression":"(⪩⨒∯122331⪔⊥⪩⨒∯1101221)⋕⪉⪜(⪩⨒∯1032220∺≝⩲⪩⨒∯210033)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":54,"operation_count":3,"complexity_ratio":18.0,"tree":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"binary","operator":"⪔⊥","left_expr":{"type":"numeric_atoms","value":1725,"base":4},"right_expr":{"type":"numeric_atoms","value":5225,"base":4}},"right_expr":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"numeric_atoms","value":5032,"base":4},"right_expr":{"type":"numeric_atoms","value":2319,"base":4}}},"used_operators":["z6LnFrNh4i","HJ9erzHUuu","KPf6cnQVty"],"dependent_operators":["sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z","eLAdDNolq6","rysDP5nf3Z","7j4O788W3g","tifHPKVTfV","8w2t5hMYqp","sdazOOVcIp","2td37pGCOC","COABgblf1C","BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl"],"result":"⪩⨒∯3030","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1725","layer":2},{"info":"number node, value=5225","layer":2},{"info":"compute binary expreesion, left_input=1725, right_input=5225, op_id = HJ9erzHUuu binary_op_definition= 'a⪔⊥b = { (⩦⩻⨪(≤/(315⇼⇔∾a))) , if b<175 ; ((⊄⩳↩(b-b))⇼⇔∾((b⪨≂a)⊭↱(a↺b))) , else }', output=-3749","layer":1},{"info":"number node, value=5032","layer":2},{"info":"number node, value=2319","layer":2},{"info":"compute binary expreesion, left_input=5032, right_input=2319, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=-3749, right_input=160, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=204","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯122331⪔⊥⪩⨒∯1101221)⋕⪉⪜(⪩⨒∯1032220∺≝⩲⪩⨒∯210033)=⪩⨒∯3030","reverse_text":"⪩⨒∯3030=(⪩⨒∯122331⪔⊥⪩⨒∯1101221)⋕⪉⪜(⪩⨒∯1032220∺≝⩲⪩⨒∯210033)","cot":[{"info":"⪩⨒∯122331⪔⊥⪩⨒∯1101221=⪩⨒∯-322211","layer":1},{"info":"⪩⨒∯1032220∺≝⩲⪩⨒∯210033=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯-322211⋕⪉⪜⪩⨒∯2200=⪩⨒∯3030","layer":0}]}
{"id":403,"expression_no_base_symbol":"$1079$↞⋁$7565$⋷$5813$⨔≚≋$1537$","expression":"⪩⨒∯100313↞⋁⪩⨒∯1312031⋷⪩⨒∯1122311⨔≚≋⪩⨒∯120001","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":226,"operation_count":3,"complexity_ratio":75.33333333333333,"tree":{"type":"binary","operator":"⋷","left_expr":{"type":"binary","operator":"↞⋁","left_expr":{"type":"numeric_atoms","value":1079,"base":4},"right_expr":{"type":"numeric_atoms","value":7565,"base":4}},"right_expr":{"type":"binary","operator":"⨔≚≋","left_expr":{"type":"numeric_atoms","value":5813,"base":4},"right_expr":{"type":"numeric_atoms","value":1537,"base":4}}},"used_operators":["23Mk6UjR3U","RqrPlJkxDo","Z57zeUYC9z"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","Uaa54Peajs","CArV6hThFE","13rbtpv6ld","zR4jO40bMj","QvoQhV0rrE","RHru8klgy8","3tVxb0NHM4","f6k1SAg4EE","IWmyXbctLI"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1079","layer":2},{"info":"number node, value=7565","layer":2},{"info":"compute binary expreesion, left_input=1079, right_input=7565, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":1},{"info":"number node, value=5813","layer":2},{"info":"number node, value=1537","layer":2},{"info":"compute binary expreesion, left_input=5813, right_input=1537, op_id = Z57zeUYC9z binary_op_definition= 'a⨔≚≋b = { ((⊈(b⪎↠b))⪶≀⋏((29⪒b)∠⫱(a⪮%⊝521))) }', output=9872","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=9872, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯100313↞⋁⪩⨒∯1312031⋷⪩⨒∯1122311⨔≚≋⪩⨒∯120001=NaN","reverse_text":"NaN=⪩⨒∯100313↞⋁⪩⨒∯1312031⋷⪩⨒∯1122311⨔≚≋⪩⨒∯120001","cot":[{"info":"⪩⨒∯100313↞⋁⪩⨒∯1312031=NaN","layer":1},{"info":"⪩⨒∯1122311⨔≚≋⪩⨒∯120001=⪩⨒∯2122100","layer":1},{"info":"NaN⋷⪩⨒∯2122100=NaN","layer":0}]}
{"id":404,"expression_no_base_symbol":"$1051$⇴∐$1020$≎⊠⪸$4584$∌↝$7679$","expression":"⪩⨒∯100123⇴∐⪩⨒∯33330≎⊠⪸⪩⨒∯1013220∌↝⪩⨒∯1313333","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":55,"operation_count":3,"complexity_ratio":18.333333333333332,"tree":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"binary","operator":"⇴∐","left_expr":{"type":"numeric_atoms","value":1051,"base":4},"right_expr":{"type":"numeric_atoms","value":1020,"base":4}},"right_expr":{"type":"binary","operator":"∌↝","left_expr":{"type":"numeric_atoms","value":4584,"base":4},"right_expr":{"type":"numeric_atoms","value":7679,"base":4}}},"used_operators":["bJkvcejdHO","HnzytWxmAO","9Isq31Ruls"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ","DpFCA1CohY","NTOWxs364D","Qy55tPpLXF","23Mk6UjR3U","EBcxylXtPf","xUOZtlo3hN","t8gj7n24qd","2DDjHMKMc0","Ph9nP6C5qx","i8ToyICDmI"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1051","layer":2},{"info":"number node, value=1020","layer":2},{"info":"compute binary expreesion, left_input=1051, right_input=1020, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=nan","layer":1},{"info":"number node, value=4584","layer":2},{"info":"number node, value=7679","layer":2},{"info":"compute binary expreesion, left_input=4584, right_input=7679, op_id = 9Isq31Ruls binary_op_definition= 'a∌↝b = { ((⋗⩬⋾b)∲⫓(⨞⊢(a⩚⊴⇥145))) , if (b⫌⩹⨱)>=130 ; ((-a)⋷((a≧⫂∧a)⋝⋈⪟(50⋥≓≎196))) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=0, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯100123⇴∐⪩⨒∯33330≎⊠⪸⪩⨒∯1013220∌↝⪩⨒∯1313333=NaN","reverse_text":"NaN=⪩⨒∯100123⇴∐⪩⨒∯33330≎⊠⪸⪩⨒∯1013220∌↝⪩⨒∯1313333","cot":[{"info":"⪩⨒∯100123⇴∐⪩⨒∯33330=NaN","layer":1},{"info":"⪩⨒∯1013220∌↝⪩⨒∯1313333=⪩⨒∯0","layer":1},{"info":"NaN≎⊠⪸⪩⨒∯0=NaN","layer":0}]}
{"id":405,"expression_no_base_symbol":"⋼∭⪍($1947$⪭$2812$)","expression":"⋼∭⪍(⪩⨒∯132123⪭⪩⨒∯223330)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16,"operation_count":2,"complexity_ratio":8.0,"tree":{"type":"unary","operator":"⋼∭⪍","unary_expr":{"type":"binary","operator":"⪭","left_expr":{"type":"numeric_atoms","value":1947,"base":4},"right_expr":{"type":"numeric_atoms","value":2812,"base":4}}},"used_operators":["DbCuESL50I","j9kHMeSvPp"],"dependent_operators":["e1ybzncUwg","sdazOOVcIp","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","u6S6b8DprG","COABgblf1C","xUOZtlo3hN"],"result":"⪩⨒∯33012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1947","layer":2},{"info":"number node, value=2812","layer":2},{"info":"compute binary expreesion, left_input=1947, right_input=2812, op_id = j9kHMeSvPp binary_op_definition= 'a⪭b = { (⨞⊢a) , if a<649 ; (b⊭↱b) , else }', output=5","layer":1},{"info":"compute unary expreesion, input=5, op_id = DbCuESL50I, unary_op_definition = '⋼∭⪍a = { (≉((a∲⫓a)⪨≂(a⪒a))) , if (↽≂a)>481 ; (↽≂((↽≂435)≧⫂∧(↽≂a))) , else }', output=966","layer":0}],"base":4,"result_base":4,"text":"⋼∭⪍(⪩⨒∯132123⪭⪩⨒∯223330)=⪩⨒∯33012","reverse_text":"⪩⨒∯33012=⋼∭⪍(⪩⨒∯132123⪭⪩⨒∯223330)","cot":[{"info":"⪩⨒∯132123⪭⪩⨒∯223330=⪩⨒∯11","layer":1},{"info":"⋼∭⪍⪩⨒∯11=⪩⨒∯33012","layer":0}]}
{"id":406,"expression_no_base_symbol":"($7443$∣$4740$)∥⊢⊲($3654$⇴∐$2299$)","expression":"(⪩⨒∯1310103∣⪩⨒∯1022010)∥⊢⊲(⪩⨒∯321012⇴∐⪩⨒∯203323)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":35,"operation_count":3,"complexity_ratio":11.666666666666666,"tree":{"type":"binary","operator":"∥⊢⊲","left_expr":{"type":"binary","operator":"∣","left_expr":{"type":"numeric_atoms","value":7443,"base":4},"right_expr":{"type":"numeric_atoms","value":4740,"base":4}},"right_expr":{"type":"binary","operator":"⇴∐","left_expr":{"type":"numeric_atoms","value":3654,"base":4},"right_expr":{"type":"numeric_atoms","value":2299,"base":4}}},"used_operators":["v1UQAVDJRr","PPChnnnBFF","HnzytWxmAO"],"dependent_operators":["EBcxylXtPf","rGHVDoGpnC","eLAdDNolq6","eH2TOUuTDT","Ph9nP6C5qx","i8ToyICDmI","2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7443","layer":2},{"info":"number node, value=4740","layer":2},{"info":"compute binary expreesion, left_input=7443, right_input=4740, op_id = PPChnnnBFF binary_op_definition= 'a∣b = { (≤/((a⪐)≧⫂∧(a∲⫓b))) , if (b⪐)<590 ; a , else }', output=7443","layer":1},{"info":"number node, value=3654","layer":2},{"info":"number node, value=2299","layer":2},{"info":"compute binary expreesion, left_input=3654, right_input=2299, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=7443, right_input=nan, op_id = v1UQAVDJRr binary_op_definition= 'a∥⊢⊲b = { (a⨟⋌⩍b) , if (a⫌⩹⨱)>=49 ; b , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1310103∣⪩⨒∯1022010)∥⊢⊲(⪩⨒∯321012⇴∐⪩⨒∯203323)=NaN","reverse_text":"NaN=(⪩⨒∯1310103∣⪩⨒∯1022010)∥⊢⊲(⪩⨒∯321012⇴∐⪩⨒∯203323)","cot":[{"info":"⪩⨒∯1310103∣⪩⨒∯1022010=⪩⨒∯1310103","layer":1},{"info":"⪩⨒∯321012⇴∐⪩⨒∯203323=NaN","layer":1},{"info":"⪩⨒∯1310103∥⊢⊲NaN=NaN","layer":0}]}
{"id":407,"expression_no_base_symbol":"(⊁⨺$3299$)⪢($2523$⨑≵⋬$4484$)","expression":"(⊁⨺⪩⨒∯303203)⪢(⪩⨒∯213123⨑≵⋬⪩⨒∯1012010)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":17423,"operation_count":3,"complexity_ratio":5807.666666666667,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"unary","operator":"⊁⨺","unary_expr":{"type":"numeric_atoms","value":3299,"base":4}},"right_expr":{"type":"binary","operator":"⨑≵⋬","left_expr":{"type":"numeric_atoms","value":2523,"base":4},"right_expr":{"type":"numeric_atoms","value":4484,"base":4}}},"used_operators":["dWAJyo7jo9","PxiHyQbrIp","XnXgA4xnOs"],"dependent_operators":["k8jYdgA6NY","rysDP5nf3Z","e1ybzncUwg","XPYlsWDdGa","23Mk6UjR3U","7j4O788W3g","2td37pGCOC","2DQ55sFlQl","xUOZtlo3hN","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","eewbuw0ToL","AF7qkfDlqP","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3299","layer":2},{"info":"compute unary expreesion, input=3299, op_id = PxiHyQbrIp, unary_op_definition = '⊁⨺a = { (((⨞⊢a)⋷(3↺a))⨵⪆((⪲⇎a)-(≉a))) , if a>5 ; (((a↺a)⨳⩥⨓(⩦⩻⨪a))⨳⩥⨓((a∲⫓a)⫡⨏(≉a))) , else }', output=160","layer":1},{"info":"number node, value=2523","layer":2},{"info":"number node, value=4484","layer":2},{"info":"compute binary expreesion, left_input=2523, right_input=4484, op_id = XnXgA4xnOs binary_op_definition= 'a⨑≵⋬b = { ((a⨰b)⫡⨏(⨑⩽⪐b)) }', output=-17394","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=-17394, op_id = dWAJyo7jo9 binary_op_definition= 'a⪢b = {b, if b == 0; (a)%(a⪢(b-1)), if b > 0 and abs(b) < 1000000; -(a)%(a⪢(b+1)), if b < 0 and abs(b) < 1000000; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⊁⨺⪩⨒∯303203)⪢(⪩⨒∯213123⨑≵⋬⪩⨒∯1012010)=NaN","reverse_text":"NaN=(⊁⨺⪩⨒∯303203)⪢(⪩⨒∯213123⨑≵⋬⪩⨒∯1012010)","cot":[{"info":"⊁⨺⪩⨒∯303203=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯213123⨑≵⋬⪩⨒∯1012010=⪩⨒∯-10033302","layer":1},{"info":"⪩⨒∯2200⪢⪩⨒∯-10033302=NaN","layer":0}]}
{"id":408,"expression_no_base_symbol":"⇁⨣⪵(⩩$4798$)","expression":"⇁⨣⪵(⩩⪩⨒∯1022332)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5735,"operation_count":2,"complexity_ratio":2867.5,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"unary","operator":"⩩","unary_expr":{"type":"numeric_atoms","value":4798,"base":4}}},"used_operators":["inkyxCbjAn","kMhfGuqI2H"],"dependent_operators":["B5M0gjZbta","6aG7x05OhS","z63VuFQld9","lFBm8KRb8F","f6k1SAg4EE","ZGCBLdVRRX"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4798","layer":2},{"info":"compute unary expreesion, input=4798, op_id = kMhfGuqI2H, unary_op_definition = '⩩a = { (⇜(a⫩)) , if (⇵⪽a)!=444 ; ((a⪒a)∧) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇁⨣⪵(⩩⪩⨒∯1022332)=NaN","reverse_text":"NaN=⇁⨣⪵(⩩⪩⨒∯1022332)","cot":[{"info":"⩩⪩⨒∯1022332=NaN","layer":1},{"info":"⇁⨣⪵NaN=NaN","layer":0}]}
{"id":409,"expression_no_base_symbol":"(↞≼$2354$)⩚⊴⇥($1015$⇀∌)","expression":"(↞≼⪩⨒∯210302)⩚⊴⇥(⪩⨒∯33313⇀∌)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":87,"operation_count":3,"complexity_ratio":29.0,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"unary","operator":"↞≼","unary_expr":{"type":"numeric_atoms","value":2354,"base":4}},"right_expr":{"type":"unary","operator":"⇀∌","unary_expr":{"type":"numeric_atoms","value":1015,"base":4}}},"used_operators":["NTOWxs364D","DE7zCoGJt9","2k53nXOpI5"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","D4vGDi5EA2","23Mk6UjR3U","BjRHVeLaeN","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","u6S6b8DprG","Q3PJZHRvZv","ddLRYrp01A","AcOhelriW5","7t3wd0Fuz7","3tVxb0NHM4"],"result":"⪩⨒∯-10203130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2354","layer":2},{"info":"compute unary expreesion, input=2354, op_id = DE7zCoGJt9, unary_op_definition = '↞≼a = { (↽≂(197⨰(a⨸⪁a))) , if (a⨸⪁373)!=224 ; (((591⋷a)≧⫂∧(a+a))⨸⪁((a⫩⊇)≦≮≮)) , else }', output=18418","layer":1},{"info":"number node, value=1015","layer":2},{"info":"compute unary expreesion, input=1015, op_id = 2k53nXOpI5, unary_op_definition = 'a⇀∌ = { ((a⪎↠(⨣⨃⇪a))⋥⋵⩄(a∊∟⩊(⊥a))) }', output=113","layer":1},{"info":"compute binary expreesion, left_input=18418, right_input=113, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-18652","layer":0}],"base":4,"result_base":4,"text":"(↞≼⪩⨒∯210302)⩚⊴⇥(⪩⨒∯33313⇀∌)=⪩⨒∯-10203130","reverse_text":"⪩⨒∯-10203130=(↞≼⪩⨒∯210302)⩚⊴⇥(⪩⨒∯33313⇀∌)","cot":[{"info":"↞≼⪩⨒∯210302=⪩⨒∯10133302","layer":1},{"info":"⪩⨒∯33313⇀∌=⪩⨒∯1301","layer":1},{"info":"⪩⨒∯10133302⩚⊴⇥⪩⨒∯1301=⪩⨒∯-10203130","layer":0}]}
{"id":410,"expression_no_base_symbol":"$1754$⋅⇍$1835$⊉≛↸(⊵⊁$1797$)","expression":"⪩⨒∯123122⋅⇍⪩⨒∯130223⊉≛↸(⊵⊁⪩⨒∯130011)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":33,"operation_count":3,"complexity_ratio":11.0,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":1754,"base":4},"right_expr":{"type":"numeric_atoms","value":1835,"base":4}},"right_expr":{"type":"unary","operator":"⊵⊁","unary_expr":{"type":"numeric_atoms","value":1797,"base":4}}},"used_operators":["DZ8iAZOCBD","AdZkA7nFnk","AvED76WdY7"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6","uBihLCJcMX","k8jYdgA6NY"],"result":"⪩⨒∯-230","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1754","layer":2},{"info":"number node, value=1835","layer":2},{"info":"compute binary expreesion, left_input=1754, right_input=1835, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"number node, value=1797","layer":2},{"info":"compute unary expreesion, input=1797, op_id = AvED76WdY7, unary_op_definition = '⊵⊁a = { (a⇔⨋) , if a>58 ; (a%a) , else }', output=9712","layer":1},{"info":"compute binary expreesion, left_input=-22, right_input=9712, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=-44","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯123122⋅⇍⪩⨒∯130223⊉≛↸(⊵⊁⪩⨒∯130011)=⪩⨒∯-230","reverse_text":"⪩⨒∯-230=⪩⨒∯123122⋅⇍⪩⨒∯130223⊉≛↸(⊵⊁⪩⨒∯130011)","cot":[{"info":"⪩⨒∯123122⋅⇍⪩⨒∯130223=⪩⨒∯-112","layer":1},{"info":"⊵⊁⪩⨒∯130011=⪩⨒∯2113300","layer":1},{"info":"⪩⨒∯-112⊉≛↸⪩⨒∯2113300=⪩⨒∯-230","layer":0}]}
{"id":411,"expression_no_base_symbol":"($1681$⨸⪁$2804$)∵≐","expression":"(⪩⨒∯122101⨸⪁⪩⨒∯223310)∵≐","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8,"operation_count":2,"complexity_ratio":4.0,"tree":{"type":"unary","operator":"∵≐","unary_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":1681,"base":4},"right_expr":{"type":"numeric_atoms","value":2804,"base":4}}},"used_operators":["59igzFyhWz","g55IO6H4Gj"],"dependent_operators":["W4YGzv6Whe","DZ8iAZOCBD","8w2t5hMYqp","Ph9nP6C5qx","12rbrZMWeM","W4YGzv6Whe"],"result":"⪩⨒∯1331120","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1681","layer":2},{"info":"number node, value=2804","layer":2},{"info":"compute binary expreesion, left_input=1681, right_input=2804, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=8970","layer":1},{"info":"compute unary expreesion, input=8970, op_id = 59igzFyhWz, unary_op_definition = 'a∵≐ = { ((a⊉≛↸31)⋳⪒(101+a)) , if a<=828 ; ((⊄⩳↩a)≧⫂∧(a≧⫂∧a)) , else }', output=8024","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯122101⨸⪁⪩⨒∯223310)∵≐=⪩⨒∯1331120","reverse_text":"⪩⨒∯1331120=(⪩⨒∯122101⨸⪁⪩⨒∯223310)∵≐","cot":[{"info":"⪩⨒∯122101⨸⪁⪩⨒∯223310=⪩⨒∯2030022","layer":1},{"info":"⪩⨒∯2030022∵≐=⪩⨒∯1331120","layer":0}]}
{"id":412,"expression_no_base_symbol":"($3594$⋥≓≎$1225$)⊬⫿⊭","expression":"(⪩⨒∯320022⋥≓≎⪩⨒∯103021)⊬⫿⊭","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":22,"operation_count":2,"complexity_ratio":11.0,"tree":{"type":"unary","operator":"⊬⫿⊭","unary_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":3594,"base":4},"right_expr":{"type":"numeric_atoms","value":1225,"base":4}}},"used_operators":["v0DYgG9ikt","Qy55tPpLXF"],"dependent_operators":["eLAdDNolq6","P8v4zCKN1o","7j4O788W3g","8w2t5hMYqp","2DQ55sFlQl","2DDjHMKMc0","xUOZtlo3hN","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","u6S6b8DprG","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯110223","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3594","layer":2},{"info":"number node, value=1225","layer":2},{"info":"compute binary expreesion, left_input=3594, right_input=1225, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-1111","layer":1},{"info":"compute unary expreesion, input=-1111, op_id = v0DYgG9ikt, unary_op_definition = 'a⊬⫿⊭ = { ((⨑⩽⪐(≤/a))↺((⨞⊢a)⨰(↽≂188))) , if a<119 ; (((∥⊫a)⨳⩥⨓(a⨵⪆a))↺(⊄⩳↩(a⋝⋈⪟a))) , else }', output=1323","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯320022⋥≓≎⪩⨒∯103021)⊬⫿⊭=⪩⨒∯110223","reverse_text":"⪩⨒∯110223=(⪩⨒∯320022⋥≓≎⪩⨒∯103021)⊬⫿⊭","cot":[{"info":"⪩⨒∯320022⋥≓≎⪩⨒∯103021=⪩⨒∯-101113","layer":1},{"info":"⪩⨒∯-101113⊬⫿⊭=⪩⨒∯110223","layer":0}]}
{"id":413,"expression_no_base_symbol":"(⋗⩴⪓$7890$)→⨶⪴(⩷$7823$)","expression":"(⋗⩴⪓⪩⨒∯1323102)→⨶⪴(⩷⪩⨒∯1322033)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7956,"operation_count":3,"complexity_ratio":2652.0,"tree":{"type":"binary","operator":"→⨶⪴","left_expr":{"type":"unary","operator":"⋗⩴⪓","unary_expr":{"type":"numeric_atoms","value":7890,"base":4}},"right_expr":{"type":"unary","operator":"⩷","unary_expr":{"type":"numeric_atoms","value":7823,"base":4}}},"used_operators":["bF6eod5Gvf","nOKPl9n5zu","1h0rLqGiFr"],"dependent_operators":["8w2t5hMYqp","9FxExcQeMw","Qtd6bqUJcN","tifHPKVTfV","tmPS8pqC7x","jLgFTUHLKL","wztAlM01eG","14qkJME0vr","g55IO6H4Gj","7j4O788W3g"],"result":"⪩⨒∯222131210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7890","layer":2},{"info":"compute unary expreesion, input=7890, op_id = nOKPl9n5zu, unary_op_definition = '⋗⩴⪓a = { (↩a) , if (↸⊣a)>=41 ; (a⇼⇔∾(≪(a⨪↰⇹a))) , else }', output=-6977","layer":1},{"info":"number node, value=7823","layer":2},{"info":"compute unary expreesion, input=7823, op_id = 1h0rLqGiFr, unary_op_definition = '⩷a = { (((a⊦⊿)↺(a⨸⪁a))⊦⊿) }', output=-93955","layer":1},{"info":"compute binary expreesion, left_input=-6977, right_input=-93955, op_id = bF6eod5Gvf binary_op_definition= 'a→⨶⪴b = { (a⩷∴b) , if b<109 ; (⊄⩳↩b) , else }', output=173924","layer":0}],"base":4,"result_base":4,"text":"(⋗⩴⪓⪩⨒∯1323102)→⨶⪴(⩷⪩⨒∯1322033)=⪩⨒∯222131210","reverse_text":"⪩⨒∯222131210=(⋗⩴⪓⪩⨒∯1323102)→⨶⪴(⩷⪩⨒∯1322033)","cot":[{"info":"⋗⩴⪓⪩⨒∯1323102=⪩⨒∯-1231001","layer":1},{"info":"⩷⪩⨒∯1322033=⪩⨒∯-112330003","layer":1},{"info":"⪩⨒∯-1231001→⨶⪴⪩⨒∯-112330003=⪩⨒∯222131210","layer":0}]}
{"id":414,"expression_no_base_symbol":"($2269$%$2327$)⪟⇏(≔$1303$)","expression":"(⪩⨒∯203131%⪩⨒∯210113)⪟⇏(≔⪩⨒∯110113)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":64,"operation_count":3,"complexity_ratio":21.333333333333332,"tree":{"type":"binary","operator":"⪟⇏","left_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":2269,"base":4},"right_expr":{"type":"numeric_atoms","value":2327,"base":4}},"right_expr":{"type":"unary","operator":"≔","unary_expr":{"type":"numeric_atoms","value":1303,"base":4}}},"used_operators":["GODebY97qR","k8jYdgA6NY","8FLs4eVsLt"],"dependent_operators":["gx7XJ7hdpj","XnXgA4xnOs","wEfv7U73WA","2DQ55sFlQl","f6k1SAg4EE","oacrs7FA3X","rysDP5nf3Z","uPb5QRN0te","VwlE7vj6HS","3mBM5G4a3l","8HhzD0ZcuI","BUOGQAYlQx","AYdpE9sXAk"],"result":"⪩⨒∯-1","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2269","layer":2},{"info":"number node, value=2327","layer":2},{"info":"compute binary expreesion, left_input=2269, right_input=2327, op_id = k8jYdgA6NY binary_op_definition= 'None', output=2269","layer":1},{"info":"number node, value=1303","layer":2},{"info":"compute unary expreesion, input=1303, op_id = 8FLs4eVsLt, unary_op_definition = '≔a = { (⋃(⋂a)) , if (⨂⪏⇭a)<=427 or (a↫)>=16 ; ((a⨽194)↯⫤) , else }', output=-35190","layer":1},{"info":"compute binary expreesion, left_input=2269, right_input=-35190, op_id = GODebY97qR binary_op_definition= 'a⪟⇏b = { ((b⨑≵⋬b)⫸⇳(440⪒a)) , if (b⇐≅)<189 ; ((219⨑≵⋬a)⪘⫢(b⨵⪆b)) , else }', output=-1","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯203131%⪩⨒∯210113)⪟⇏(≔⪩⨒∯110113)=⪩⨒∯-1","reverse_text":"⪩⨒∯-1=(⪩⨒∯203131%⪩⨒∯210113)⪟⇏(≔⪩⨒∯110113)","cot":[{"info":"⪩⨒∯203131%⪩⨒∯210113=⪩⨒∯203131","layer":1},{"info":"≔⪩⨒∯110113=⪩⨒∯-20211312","layer":1},{"info":"⪩⨒∯203131⪟⇏⪩⨒∯-20211312=⪩⨒∯-1","layer":0}]}
{"id":415,"expression_no_base_symbol":"⨣⨃⇪($2908$⨵⪆$3013$)","expression":"⨣⨃⇪(⪩⨒∯231130⨵⪆⪩⨒∯233011)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":15,"operation_count":2,"complexity_ratio":7.5,"tree":{"type":"unary","operator":"⨣⨃⇪","unary_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":2908,"base":4},"right_expr":{"type":"numeric_atoms","value":3013,"base":4}}},"used_operators":["AcOhelriW5","2DQ55sFlQl"],"dependent_operators":["s3Fd5m9Dh2","liw5iZPkLH","yyfyN0ffXY","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯111331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2908","layer":2},{"info":"number node, value=3013","layer":2},{"info":"compute binary expreesion, left_input=2908, right_input=3013, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"compute unary expreesion, input=160, op_id = AcOhelriW5, unary_op_definition = '⨣⨃⇪a = { (⨡↴(172⊬⨰(3↙a))) }', output=1405","layer":0}],"base":4,"result_base":4,"text":"⨣⨃⇪(⪩⨒∯231130⨵⪆⪩⨒∯233011)=⪩⨒∯111331","reverse_text":"⪩⨒∯111331=⨣⨃⇪(⪩⨒∯231130⨵⪆⪩⨒∯233011)","cot":[{"info":"⪩⨒∯231130⨵⪆⪩⨒∯233011=⪩⨒∯2200","layer":1},{"info":"⨣⨃⇪⪩⨒∯2200=⪩⨒∯111331","layer":0}]}
{"id":416,"expression_no_base_symbol":"$3896$⨔⇊$3088$∲⫓$1334$⊲⩕⊾$4319$","expression":"⪩⨒∯330320⨔⇊⪩⨒∯300100∲⫓⪩⨒∯110312⊲⩕⊾⪩⨒∯1003133","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":27,"operation_count":3,"complexity_ratio":9.0,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"numeric_atoms","value":3896,"base":4},"right_expr":{"type":"numeric_atoms","value":3088,"base":4}},"right_expr":{"type":"binary","operator":"⊲⩕⊾","left_expr":{"type":"numeric_atoms","value":1334,"base":4},"right_expr":{"type":"numeric_atoms","value":4319,"base":4}}},"used_operators":["i8ToyICDmI","JclMnS0uGI","DmTXOeWf9t"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI","23Mk6UjR3U","DZ8iAZOCBD","BjRHVeLaeN","QMFrweE19q","AF7qkfDlqP","COABgblf1C"],"result":"⪩⨒∯300100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3896","layer":2},{"info":"number node, value=3088","layer":2},{"info":"compute binary expreesion, left_input=3896, right_input=3088, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=3088","layer":1},{"info":"number node, value=1334","layer":2},{"info":"number node, value=4319","layer":2},{"info":"compute binary expreesion, left_input=1334, right_input=4319, op_id = DmTXOeWf9t binary_op_definition= 'a⊲⩕⊾b = { (((a⊉≛↸b)⊭↱(⨑⩽⪐b))⫡⨏((a⫩⊇)⋷(a⊉≛↸b))) }', output=-61164","layer":1},{"info":"compute binary expreesion, left_input=3088, right_input=-61164, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=3088","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯330320⨔⇊⪩⨒∯300100∲⫓⪩⨒∯110312⊲⩕⊾⪩⨒∯1003133=⪩⨒∯300100","reverse_text":"⪩⨒∯300100=⪩⨒∯330320⨔⇊⪩⨒∯300100∲⫓⪩⨒∯110312⊲⩕⊾⪩⨒∯1003133","cot":[{"info":"⪩⨒∯330320⨔⇊⪩⨒∯300100=⪩⨒∯300100","layer":1},{"info":"⪩⨒∯110312⊲⩕⊾⪩⨒∯1003133=⪩⨒∯-32323230","layer":1},{"info":"⪩⨒∯300100∲⫓⪩⨒∯-32323230=⪩⨒∯300100","layer":0}]}
{"id":417,"expression_no_base_symbol":"($7360$⨚⇆$1162$)⇞","expression":"(⪩⨒∯1303000⨚⇆⪩⨒∯102022)⇞","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":51566,"operation_count":2,"complexity_ratio":25783.0,"tree":{"type":"unary","operator":"⇞","unary_expr":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"numeric_atoms","value":7360,"base":4},"right_expr":{"type":"numeric_atoms","value":1162,"base":4}}},"used_operators":["5JYyxRJd4f","lwHaAYXP2r"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","DZ8iAZOCBD","tifHPKVTfV","Ph9nP6C5qx","xUOZtlo3hN","g55IO6H4Gj","i8ToyICDmI","QMFrweE19q","gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7360","layer":2},{"info":"number node, value=1162","layer":2},{"info":"compute binary expreesion, left_input=7360, right_input=1162, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = 5JYyxRJd4f, unary_op_definition = 'a⇞ = { (a≧⫂∧((a⩷∴a)⨸⪁(a-a))) , if a<7 ; ((⨞⊢(a∲⫓a))⫡⨏(a⊉≛↸(a⇼⇔∾a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1303000⨚⇆⪩⨒∯102022)⇞=NaN","reverse_text":"NaN=(⪩⨒∯1303000⨚⇆⪩⨒∯102022)⇞","cot":[{"info":"⪩⨒∯1303000⨚⇆⪩⨒∯102022=NaN","layer":1},{"info":"NaN⇞=NaN","layer":0}]}
{"id":418,"expression_no_base_symbol":"($7699$⩅⪻⪻)⋝⋈⪟($1093$↡⊰⫅$2552$)","expression":"(⪩⨒∯1320103⩅⪻⪻)⋝⋈⪟(⪩⨒∯101011↡⊰⫅⪩⨒∯213320)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":35877,"operation_count":3,"complexity_ratio":11959.0,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"unary","operator":"⩅⪻⪻","unary_expr":{"type":"numeric_atoms","value":7699,"base":4}},"right_expr":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"numeric_atoms","value":1093,"base":4},"right_expr":{"type":"numeric_atoms","value":2552,"base":4}}},"used_operators":["2DDjHMKMc0","kHoXpA7yos","VCtxkLNOzz"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","SUmda5xLS4","KPf6cnQVty","8HhzD0ZcuI","9Isq31Ruls","Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn"],"result":"⪩⨒∯-10112002331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7699","layer":2},{"info":"compute unary expreesion, input=7699, op_id = kHoXpA7yos, unary_op_definition = 'a⩅⪻⪻ = { (a⪄((a∌↝a)⨽(a∺≝⩲a))) }', output=-1138877","layer":1},{"info":"number node, value=1093","layer":2},{"info":"number node, value=2552","layer":2},{"info":"compute binary expreesion, left_input=1093, right_input=2552, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=5104","layer":1},{"info":"compute binary expreesion, left_input=-1138877, right_input=5104, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=-1138877","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1320103⩅⪻⪻)⋝⋈⪟(⪩⨒∯101011↡⊰⫅⪩⨒∯213320)=⪩⨒∯-10112002331","reverse_text":"⪩⨒∯-10112002331=(⪩⨒∯1320103⩅⪻⪻)⋝⋈⪟(⪩⨒∯101011↡⊰⫅⪩⨒∯213320)","cot":[{"info":"⪩⨒∯1320103⩅⪻⪻=⪩⨒∯-10112002331","layer":1},{"info":"⪩⨒∯101011↡⊰⫅⪩⨒∯213320=⪩⨒∯1033300","layer":1},{"info":"⪩⨒∯-10112002331⋝⋈⪟⪩⨒∯1033300=⪩⨒∯-10112002331","layer":0}]}
{"id":419,"expression_no_base_symbol":"(∐⩳⋚$1042$)⩼⇪↪($2026$⨒$2424$)","expression":"(∐⩳⋚⪩⨒∯100102)⩼⇪↪(⪩⨒∯133222⨒⪩⨒∯211320)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":203,"operation_count":3,"complexity_ratio":67.66666666666667,"tree":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"unary","operator":"∐⩳⋚","unary_expr":{"type":"numeric_atoms","value":1042,"base":4}},"right_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":2026,"base":4},"right_expr":{"type":"numeric_atoms","value":2424,"base":4}}},"used_operators":["ocnLzx9CaJ","SL6IHkK8vl","y75s1iXyHd"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q","s3Fd5m9Dh2","zR4jO40bMj","18saOjeKKm","k7HXdKtiEU","z4E1FaHLuy","XTarYq4gQB","xRrnTEsQ6j","Ph9nP6C5qx","f6k1SAg4EE","D3AQDKkPcf","srAu1WTS94","oacrs7FA3X","7qqUquhhSb"],"result":"⪩⨒∯1113303013","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1042","layer":2},{"info":"compute unary expreesion, input=1042, op_id = SL6IHkK8vl, unary_op_definition = '∐⩳⋚a = { (⊲⪭((⇠a)⪶≀⋏(a⪒a))) , if (⫟a)==290 ; ((⪝⪂⫅(105⫁⪎a))⊬⨰(a≧⫂∧(a∷a))) , else }', output=138959","layer":1},{"info":"number node, value=2026","layer":2},{"info":"number node, value=2424","layer":2},{"info":"compute binary expreesion, left_input=2026, right_input=2424, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-11784","layer":1},{"info":"compute binary expreesion, left_input=138959, right_input=-11784, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=359623","layer":0}],"base":4,"result_base":4,"text":"(∐⩳⋚⪩⨒∯100102)⩼⇪↪(⪩⨒∯133222⨒⪩⨒∯211320)=⪩⨒∯1113303013","reverse_text":"⪩⨒∯1113303013=(∐⩳⋚⪩⨒∯100102)⩼⇪↪(⪩⨒∯133222⨒⪩⨒∯211320)","cot":[{"info":"∐⩳⋚⪩⨒∯100102=⪩⨒∯201323033","layer":1},{"info":"⪩⨒∯133222⨒⪩⨒∯211320=⪩⨒∯-2320020","layer":1},{"info":"⪩⨒∯201323033⩼⇪↪⪩⨒∯-2320020=⪩⨒∯1113303013","layer":0}]}
{"id":420,"expression_no_base_symbol":"⇺⋃($7509$⨽⪊≇)","expression":"⇺⋃(⪩⨒∯1311111⨽⪊≇)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":64,"operation_count":2,"complexity_ratio":32.0,"tree":{"type":"unary","operator":"⇺⋃","unary_expr":{"type":"unary","operator":"⨽⪊≇","unary_expr":{"type":"numeric_atoms","value":7509,"base":4}}},"used_operators":["E5v5B3UAjG","nlCqmYiOvY"],"dependent_operators":["bl5wxAcryP","Q3PJZHRvZv","gub5Cegaqo","8INZBEW696","kuIXHzHcAH","7YooWSwCyH","W4YGzv6Whe","sdazOOVcIp","XIabStNQrY"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7509","layer":2},{"info":"compute unary expreesion, input=7509, op_id = nlCqmYiOvY, unary_op_definition = 'a⨽⪊≇ = { ((a⇋≉)⪨≂(a+216)) }', output=14492","layer":1},{"info":"compute unary expreesion, input=14492, op_id = E5v5B3UAjG, unary_op_definition = '⇺⋃a = { (((a≀⩗∶a)∪⫐(a⩁⩘229))⪨⊡(⊥(a↰))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇺⋃(⪩⨒∯1311111⨽⪊≇)=NaN","reverse_text":"NaN=⇺⋃(⪩⨒∯1311111⨽⪊≇)","cot":[{"info":"⪩⨒∯1311111⨽⪊≇=⪩⨒∯3202130","layer":1},{"info":"⇺⋃⪩⨒∯3202130=NaN","layer":0}]}
{"id":421,"expression_no_base_symbol":"(⊗$3451$)⩚⊴⇥($1586$%$6212$)","expression":"(⊗⪩⨒∯311323)⩚⊴⇥(⪩⨒∯120302%⪩⨒∯1201010)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":28,"operation_count":3,"complexity_ratio":9.333333333333334,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"unary","operator":"⊗","unary_expr":{"type":"numeric_atoms","value":3451,"base":4}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":1586,"base":4},"right_expr":{"type":"numeric_atoms","value":6212,"base":4}}},"used_operators":["NTOWxs364D","RhiyfpczSx","k8jYdgA6NY"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","nhYeJWJD5X","sJAwomhLZr","Z5m6OM72h2","HrjLwUk87U","rysDP5nf3Z"],"result":"⪩⨒∯1101023","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3451","layer":2},{"info":"compute unary expreesion, input=3451, op_id = RhiyfpczSx, unary_op_definition = '⊗a = { (64∇⊂⋱a) , if (a⪚13)>=164 ; (a∘(a⩠)) , else }', output=-6902","layer":1},{"info":"number node, value=1586","layer":2},{"info":"number node, value=6212","layer":2},{"info":"compute binary expreesion, left_input=1586, right_input=6212, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1586","layer":1},{"info":"compute binary expreesion, left_input=-6902, right_input=1586, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=5195","layer":0}],"base":4,"result_base":4,"text":"(⊗⪩⨒∯311323)⩚⊴⇥(⪩⨒∯120302%⪩⨒∯1201010)=⪩⨒∯1101023","reverse_text":"⪩⨒∯1101023=(⊗⪩⨒∯311323)⩚⊴⇥(⪩⨒∯120302%⪩⨒∯1201010)","cot":[{"info":"⊗⪩⨒∯311323=⪩⨒∯-1223312","layer":1},{"info":"⪩⨒∯120302%⪩⨒∯1201010=⪩⨒∯120302","layer":1},{"info":"⪩⨒∯-1223312⩚⊴⇥⪩⨒∯120302=⪩⨒∯1101023","layer":0}]}
{"id":422,"expression_no_base_symbol":"(↽≂$6167$)⊔(∜⨇$5470$)","expression":"(↽≂⪩⨒∯1200113)⊔(∜⨇⪩⨒∯1111132)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":79,"operation_count":3,"complexity_ratio":26.333333333333332,"tree":{"type":"binary","operator":"⊔","left_expr":{"type":"unary","operator":"↽≂","unary_expr":{"type":"numeric_atoms","value":6167,"base":4}},"right_expr":{"type":"unary","operator":"∜⨇","unary_expr":{"type":"numeric_atoms","value":5470,"base":4}}},"used_operators":["E4l6HwMY31","u6S6b8DprG","uFPyJr306J"],"dependent_operators":["W4YGzv6Whe","DpFCA1CohY","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","QMFrweE19q","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","fG6uBQFnGz","pRsWfj4Fpp","rGHVDoGpnC","Y7wcNGrDQJ","NNaDxxp6OQ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6167","layer":2},{"info":"compute unary expreesion, input=6167, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-12334","layer":1},{"info":"number node, value=5470","layer":2},{"info":"compute unary expreesion, input=5470, op_id = uFPyJr306J, unary_op_definition = '∜⨇a = { (a⨟⋌⩍a) , if (a⫽⇹≛)!=2 or (↩⪖a)==528 or (∡a)>=548 ; (132⩵∡a) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-12334, right_input=nan, op_id = E4l6HwMY31 binary_op_definition= 'a⊔b = { (((a≧⫂∧b)∲⫓(⋗⩬⋾b))⫡⨏((b⪒a)≧⫂∧(a+64))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(↽≂⪩⨒∯1200113)⊔(∜⨇⪩⨒∯1111132)=NaN","reverse_text":"NaN=(↽≂⪩⨒∯1200113)⊔(∜⨇⪩⨒∯1111132)","cot":[{"info":"↽≂⪩⨒∯1200113=⪩⨒∯-3000232","layer":1},{"info":"∜⨇⪩⨒∯1111132=NaN","layer":1},{"info":"⪩⨒∯-3000232⊔NaN=NaN","layer":0}]}
{"id":423,"expression_no_base_symbol":"$1851$⪝$4317$≁$1924$≁↽≥$5807$","expression":"⪩⨒∯130323⪝⪩⨒∯1003131≁⪩⨒∯132010≁↽≥⪩⨒∯1122233","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":507,"operation_count":3,"complexity_ratio":169.0,"tree":{"type":"binary","operator":"≁","left_expr":{"type":"binary","operator":"⪝","left_expr":{"type":"numeric_atoms","value":1851,"base":4},"right_expr":{"type":"numeric_atoms","value":4317,"base":4}},"right_expr":{"type":"binary","operator":"≁↽≥","left_expr":{"type":"numeric_atoms","value":1924,"base":4},"right_expr":{"type":"numeric_atoms","value":5807,"base":4}}},"used_operators":["8N2wDY1A35","wicAB68Tmb","ncHt1X6cMc"],"dependent_operators":["B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v","L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X","oWn0xqSxBt","3Oe9XWJUTD"],"result":"⪩⨒∯3200010233","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1851","layer":2},{"info":"number node, value=4317","layer":2},{"info":"compute binary expreesion, left_input=1851, right_input=4317, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=237","layer":1},{"info":"number node, value=1924","layer":2},{"info":"number node, value=5807","layer":2},{"info":"compute binary expreesion, left_input=1924, right_input=5807, op_id = ncHt1X6cMc binary_op_definition= 'a≁↽≥b = { (a⊝⪿⪼b) , if b>=116 ; (⊙↵-b) , else }', output=38792","layer":1},{"info":"compute binary expreesion, left_input=237, right_input=38792, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=917807","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯130323⪝⪩⨒∯1003131≁⪩⨒∯132010≁↽≥⪩⨒∯1122233=⪩⨒∯3200010233","reverse_text":"⪩⨒∯3200010233=⪩⨒∯130323⪝⪩⨒∯1003131≁⪩⨒∯132010≁↽≥⪩⨒∯1122233","cot":[{"info":"⪩⨒∯130323⪝⪩⨒∯1003131=⪩⨒∯3231","layer":1},{"info":"⪩⨒∯132010≁↽≥⪩⨒∯1122233=⪩⨒∯21132020","layer":1},{"info":"⪩⨒∯3231≁⪩⨒∯21132020=⪩⨒∯3200010233","layer":0}]}
{"id":424,"expression_no_base_symbol":"⪲⇎$1169$∝$1187$","expression":"⪲⇎⪩⨒∯102101∝⪩⨒∯102203","highest_n_order":1,"priority_hierarchical_complexity":1,"normalized_expansion_degree":11,"operation_count":2,"complexity_ratio":5.5,"tree":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"binary","operator":"∝","left_expr":{"type":"numeric_atoms","value":1169,"base":4},"right_expr":{"type":"numeric_atoms","value":1187,"base":4}}},"used_operators":["XPYlsWDdGa","cTDWOvIxvz"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","7j4O788W3g","W4YGzv6Whe","COABgblf1C"],"result":"⪩⨒∯210230","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1169","layer":2},{"info":"number node, value=1187","layer":2},{"info":"compute binary expreesion, left_input=1169, right_input=1187, op_id = cTDWOvIxvz binary_op_definition= 'a∝b = { ((b↺a)+(b⊭↱b)) }', output=1174","layer":1},{"info":"compute unary expreesion, input=1174, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=2348","layer":0}],"base":4,"result_base":4,"text":"⪲⇎⪩⨒∯102101∝⪩⨒∯102203=⪩⨒∯210230","reverse_text":"⪩⨒∯210230=⪲⇎⪩⨒∯102101∝⪩⨒∯102203","cot":[{"info":"⪩⨒∯102101∝⪩⨒∯102203=⪩⨒∯102112","layer":1},{"info":"⪲⇎⪩⨒∯102112=⪩⨒∯210230","layer":0}]}
{"id":425,"expression_no_base_symbol":"(≤/$3170$)⩨$4744$⋕⪉⪜$2762$","expression":"(≤/⪩⨒∯301202)⩨⪩⨒∯1022020⋕⪉⪜⪩⨒∯223022","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":33,"operation_count":3,"complexity_ratio":11.0,"tree":{"type":"binary","operator":"⩨","left_expr":{"type":"unary","operator":"≤/","unary_expr":{"type":"numeric_atoms","value":3170,"base":4}},"right_expr":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"numeric_atoms","value":4744,"base":4},"right_expr":{"type":"numeric_atoms","value":2762,"base":4}}},"used_operators":["2DlMacCsIx","eLAdDNolq6","z6LnFrNh4i"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","rysDP5nf3Z","sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z"],"result":"⪩⨒∯12","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3170","layer":2},{"info":"compute unary expreesion, input=3170, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-2686","layer":1},{"info":"number node, value=4744","layer":2},{"info":"number node, value=2762","layer":2},{"info":"compute binary expreesion, left_input=4744, right_input=2762, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=2802","layer":1},{"info":"compute binary expreesion, left_input=-2686, right_input=2802, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=6","layer":0}],"base":4,"result_base":4,"text":"(≤/⪩⨒∯301202)⩨⪩⨒∯1022020⋕⪉⪜⪩⨒∯223022=⪩⨒∯12","reverse_text":"⪩⨒∯12=(≤/⪩⨒∯301202)⩨⪩⨒∯1022020⋕⪉⪜⪩⨒∯223022","cot":[{"info":"≤/⪩⨒∯301202=⪩⨒∯-221332","layer":1},{"info":"⪩⨒∯1022020⋕⪉⪜⪩⨒∯223022=⪩⨒∯223302","layer":1},{"info":"⪩⨒∯-221332⩨⪩⨒∯223302=⪩⨒∯12","layer":0}]}
{"id":426,"expression_no_base_symbol":"(≸$3183$)∣($2860$⊝⪿⪼$4038$)","expression":"(≸⪩⨒∯301233)∣(⪩⨒∯230230⊝⪿⪼⪩⨒∯333012)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":82,"operation_count":3,"complexity_ratio":27.333333333333332,"tree":{"type":"binary","operator":"∣","left_expr":{"type":"unary","operator":"≸","unary_expr":{"type":"numeric_atoms","value":3183,"base":4}},"right_expr":{"type":"binary","operator":"⊝⪿⪼","left_expr":{"type":"numeric_atoms","value":2860,"base":4},"right_expr":{"type":"numeric_atoms","value":4038,"base":4}}},"used_operators":["PPChnnnBFF","eOf03JbCpp","3Oe9XWJUTD"],"dependent_operators":["eLAdDNolq6","eH2TOUuTDT","Ph9nP6C5qx","i8ToyICDmI","WmT3o8z6ya","l07mrZUIn9","NTOWxs364D","RygbFNSyEJ","tifHPKVTfV","oRDoc9rAEX","IwW236VD4Y","1aApVXNlOP","Z5m6OM72h2","mqXw5SEYmG","IWmyXbctLI","NTOWxs364D","Qy55tPpLXF","8w2t5hMYqp","t8gj7n24qd","eewbuw0ToL","QMFrweE19q"],"result":"⪩⨒∯322","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3183","layer":2},{"info":"compute unary expreesion, input=3183, op_id = eOf03JbCpp, unary_op_definition = '≸a = { (29∘((630⊋≦⊧a)⩚⊴⇥(a≦↸a))) , if (a⋘⨑⨽)>2 ; (((a⪮%⊝a)⇼⇔∾(a↪⪝))⫸⊐((a⪮%⊝a)≠≀(3⩇∃⫛a))) , else }', output=58","layer":1},{"info":"number node, value=2860","layer":2},{"info":"number node, value=4038","layer":2},{"info":"compute binary expreesion, left_input=2860, right_input=4038, op_id = 3Oe9XWJUTD binary_op_definition= 'a⊝⪿⪼b = { ((⊄⩳↩(480⩚⊴⇥a))⫡⨏((a⨰b)⋥≓≎(-b))) }', output=52832","layer":1},{"info":"compute binary expreesion, left_input=58, right_input=52832, op_id = PPChnnnBFF binary_op_definition= 'a∣b = { (≤/((a⪐)≧⫂∧(a∲⫓b))) , if (b⪐)<590 ; a , else }', output=58","layer":0}],"base":4,"result_base":4,"text":"(≸⪩⨒∯301233)∣(⪩⨒∯230230⊝⪿⪼⪩⨒∯333012)=⪩⨒∯322","reverse_text":"⪩⨒∯322=(≸⪩⨒∯301233)∣(⪩⨒∯230230⊝⪿⪼⪩⨒∯333012)","cot":[{"info":"≸⪩⨒∯301233=⪩⨒∯322","layer":1},{"info":"⪩⨒∯230230⊝⪿⪼⪩⨒∯333012=⪩⨒∯30321200","layer":1},{"info":"⪩⨒∯322∣⪩⨒∯30321200=⪩⨒∯322","layer":0}]}
{"id":427,"expression_no_base_symbol":"(⋎⨆$2362$)⇍⊗($1128$⩵∡$1462$)","expression":"(⋎⨆⪩⨒∯210322)⇍⊗(⪩⨒∯101220⩵∡⪩⨒∯112312)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":491,"operation_count":3,"complexity_ratio":163.66666666666666,"tree":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"unary","operator":"⋎⨆","unary_expr":{"type":"numeric_atoms","value":2362,"base":4}},"right_expr":{"type":"binary","operator":"⩵∡","left_expr":{"type":"numeric_atoms","value":1128,"base":4},"right_expr":{"type":"numeric_atoms","value":1462,"base":4}}},"used_operators":["5uvYHDjeKN","E64sFOc4tB","Y7wcNGrDQJ"],"dependent_operators":["Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o","PxiHyQbrIp","l07mrZUIn9","3sJ7IOPOlU","liw5iZPkLH","NTOWxs364D","glklzrTFfD","tifHPKVTfV"],"result":"⪩⨒∯-3310","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2362","layer":2},{"info":"compute unary expreesion, input=2362, op_id = E64sFOc4tB, unary_op_definition = '⋎⨆a = { (a⪇≇⋚a) , if (⊁⨺a)>31 and (⨡↴a)>=90 ; (136↪⪝) , else }', output=0","layer":1},{"info":"number node, value=1128","layer":2},{"info":"number node, value=1462","layer":2},{"info":"compute binary expreesion, left_input=1128, right_input=1462, op_id = Y7wcNGrDQJ binary_op_definition= 'a⩵∡b = { ((b⇼⇔∾a)⩚⊴⇥(a⨁⊸⫻)) }', output=-915","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-915, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=-244","layer":0}],"base":4,"result_base":4,"text":"(⋎⨆⪩⨒∯210322)⇍⊗(⪩⨒∯101220⩵∡⪩⨒∯112312)=⪩⨒∯-3310","reverse_text":"⪩⨒∯-3310=(⋎⨆⪩⨒∯210322)⇍⊗(⪩⨒∯101220⩵∡⪩⨒∯112312)","cot":[{"info":"⋎⨆⪩⨒∯210322=⪩⨒∯0","layer":1},{"info":"⪩⨒∯101220⩵∡⪩⨒∯112312=⪩⨒∯-32103","layer":1},{"info":"⪩⨒∯0⇍⊗⪩⨒∯-32103=⪩⨒∯-3310","layer":0}]}
{"id":428,"expression_no_base_symbol":"($6419$∧)⨸($1002$⇴$5880$)","expression":"(⪩⨒∯1210103∧)⨸(⪩⨒∯33222⇴⪩⨒∯1123320)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":132,"operation_count":3,"complexity_ratio":44.0,"tree":{"type":"binary","operator":"⨸","left_expr":{"type":"unary","operator":"∧","unary_expr":{"type":"numeric_atoms","value":6419,"base":4}},"right_expr":{"type":"binary","operator":"⇴","left_expr":{"type":"numeric_atoms","value":1002,"base":4},"right_expr":{"type":"numeric_atoms","value":5880,"base":4}}},"used_operators":["KmoU8R5UQR","z63VuFQld9","4JB6nKBMSY"],"dependent_operators":["ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl","B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","sdazOOVcIp","NTOWxs364D","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6419","layer":2},{"info":"compute unary expreesion, input=6419, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=nan","layer":1},{"info":"number node, value=1002","layer":2},{"info":"number node, value=5880","layer":2},{"info":"compute binary expreesion, left_input=1002, right_input=5880, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=17386","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=17386, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1210103∧)⨸(⪩⨒∯33222⇴⪩⨒∯1123320)=NaN","reverse_text":"NaN=(⪩⨒∯1210103∧)⨸(⪩⨒∯33222⇴⪩⨒∯1123320)","cot":[{"info":"⪩⨒∯1210103∧=NaN","layer":1},{"info":"⪩⨒∯33222⇴⪩⨒∯1123320=⪩⨒∯10033222","layer":1},{"info":"NaN⨸⪩⨒∯10033222=NaN","layer":0}]}
{"id":429,"expression_no_base_symbol":"⪲⇎$1251$⪪$1314$","expression":"⪲⇎⪩⨒∯103203⪪⪩⨒∯110202","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3890,"operation_count":2,"complexity_ratio":1945.0,"tree":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"binary","operator":"⪪","left_expr":{"type":"numeric_atoms","value":1251,"base":4},"right_expr":{"type":"numeric_atoms","value":1314,"base":4}}},"used_operators":["XPYlsWDdGa","xD69zh8xqp"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","FU0Cs4j7VP","JclMnS0uGI"],"result":"⪩⨒∯-1122110330","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1251","layer":2},{"info":"number node, value=1314","layer":2},{"info":"compute binary expreesion, left_input=1251, right_input=1314, op_id = xD69zh8xqp binary_op_definition= 'a⪪b = { ((b⨔⇊a)↛⩡⫤) }', output=-184990","layer":1},{"info":"compute unary expreesion, input=-184990, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=-369980","layer":0}],"base":4,"result_base":4,"text":"⪲⇎⪩⨒∯103203⪪⪩⨒∯110202=⪩⨒∯-1122110330","reverse_text":"⪩⨒∯-1122110330=⪲⇎⪩⨒∯103203⪪⪩⨒∯110202","cot":[{"info":"⪩⨒∯103203⪪⪩⨒∯110202=⪩⨒∯-231022132","layer":1},{"info":"⪲⇎⪩⨒∯-231022132=⪩⨒∯-1122110330","layer":0}]}
{"id":430,"expression_no_base_symbol":"($3280$≴⪞⇿$2103$)≎⪠($5906$≠≀$1175$)","expression":"(⪩⨒∯303100≴⪞⇿⪩⨒∯200313)≎⪠(⪩⨒∯1130102≠≀⪩⨒∯102113)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":22160,"operation_count":3,"complexity_ratio":7386.666666666667,"tree":{"type":"binary","operator":"≎⪠","left_expr":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"numeric_atoms","value":3280,"base":4},"right_expr":{"type":"numeric_atoms","value":2103,"base":4}},"right_expr":{"type":"binary","operator":"≠≀","left_expr":{"type":"numeric_atoms","value":5906,"base":4},"right_expr":{"type":"numeric_atoms","value":1175,"base":4}}},"used_operators":["aNhz54LH3e","lvlrscuwVU","IwW236VD4Y"],"dependent_operators":["bl5wxAcryP","RygbFNSyEJ","SLLxy00UIr","AcOhelriW5","ctOc4cKSDt","cHh1gJQ2o6","KYD54nUTWz","kbkesczE7y","BUOGQAYlQx","PPChnnnBFF","DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP","eLAdDNolq6","NTOWxs364D","sdazOOVcIp","2DDjHMKMc0","2td37pGCOC"],"result":"⪩⨒∯10301212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3280","layer":2},{"info":"number node, value=2103","layer":2},{"info":"compute binary expreesion, left_input=3280, right_input=2103, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=18084332","layer":1},{"info":"number node, value=5906","layer":2},{"info":"number node, value=1175","layer":2},{"info":"compute binary expreesion, left_input=5906, right_input=1175, op_id = IwW236VD4Y binary_op_definition= 'a≠≀b = { (⩦⩻⨪(a⩚⊴⇥b)) , if (≤/b)>10 ; ((a⪨≂a)⪨≂(a⋝⋈⪟356)) , else }', output=-11506","layer":1},{"info":"compute binary expreesion, left_input=18084332, right_input=-11506, op_id = aNhz54LH3e binary_op_definition= 'a≎⪠b = { (((a⫥∨⫟11)≦↸(657∣a))⩘((⇈a)≬⋮(a↰))) , if a==21 ; (∟⋨(⋂(⨣⨃⇪b))) , else }', output=19558","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯303100≴⪞⇿⪩⨒∯200313)≎⪠(⪩⨒∯1130102≠≀⪩⨒∯102113)=⪩⨒∯10301212","reverse_text":"⪩⨒∯10301212=(⪩⨒∯303100≴⪞⇿⪩⨒∯200313)≎⪠(⪩⨒∯1130102≠≀⪩⨒∯102113)","cot":[{"info":"⪩⨒∯303100≴⪞⇿⪩⨒∯200313=⪩⨒∯1010333013230","layer":1},{"info":"⪩⨒∯1130102≠≀⪩⨒∯102113=⪩⨒∯-2303302","layer":1},{"info":"⪩⨒∯1010333013230≎⪠⪩⨒∯-2303302=⪩⨒∯10301212","layer":0}]}
{"id":431,"expression_no_base_symbol":"($2090$⫃⨇$3987$)⋣⋖(⋣$1316$)","expression":"(⪩⨒∯200222⫃⨇⪩⨒∯332103)⋣⋖(⋣⪩⨒∯110210)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3599,"operation_count":3,"complexity_ratio":1199.6666666666667,"tree":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"numeric_atoms","value":2090,"base":4},"right_expr":{"type":"numeric_atoms","value":3987,"base":4}},"right_expr":{"type":"unary","operator":"⋣","unary_expr":{"type":"numeric_atoms","value":1316,"base":4}}},"used_operators":["J0M6qkBnIM","09Ly4LVMIf","zQWRhDnn8F"],"dependent_operators":["VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2","9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG","vRio1gEz1j","x5lMkHmzsq","3EYGwJThht","DbCuESL50I","XTarYq4gQB","IGFM8TAlm9","sdazOOVcIp","8HhzD0ZcuI","keWfFq85dY"],"result":"⪩⨒∯-20033","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2090","layer":2},{"info":"number node, value=3987","layer":2},{"info":"compute binary expreesion, left_input=2090, right_input=3987, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=-15980","layer":1},{"info":"number node, value=1316","layer":2},{"info":"compute unary expreesion, input=1316, op_id = zQWRhDnn8F, unary_op_definition = '⋣a = { ((⋼∭⪍203)⇄(≯(a⨽a))) , if (a⇩)==859 ; (↥≼⋛((⪝⪂⫅a)⪨≂(⇉-⫰26))) , else }', output=-386809","layer":1},{"info":"compute binary expreesion, left_input=-15980, right_input=-386809, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=-527","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯200222⫃⨇⪩⨒∯332103)⋣⋖(⋣⪩⨒∯110210)=⪩⨒∯-20033","reverse_text":"⪩⨒∯-20033=(⪩⨒∯200222⫃⨇⪩⨒∯332103)⋣⋖(⋣⪩⨒∯110210)","cot":[{"info":"⪩⨒∯200222⫃⨇⪩⨒∯332103=⪩⨒∯-3321230","layer":1},{"info":"⋣⪩⨒∯110210=⪩⨒∯-1132123321","layer":1},{"info":"⪩⨒∯-3321230⋣⋖⪩⨒∯-1132123321=⪩⨒∯-20033","layer":0}]}
{"id":432,"expression_no_base_symbol":"⊽($5477$⋳⪒$4450$)","expression":"⊽(⪩⨒∯1111211⋳⪒⪩⨒∯1011202)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16,"operation_count":2,"complexity_ratio":8.0,"tree":{"type":"unary","operator":"⊽","unary_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":5477,"base":4},"right_expr":{"type":"numeric_atoms","value":4450,"base":4}}},"used_operators":["QxG7OkqoLX","12rbrZMWeM"],"dependent_operators":["g55IO6H4Gj","VJ330n2nnx","z63VuFQld9","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯3122010","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5477","layer":2},{"info":"number node, value=4450","layer":2},{"info":"compute binary expreesion, left_input=5477, right_input=4450, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=6217","layer":1},{"info":"compute unary expreesion, input=6217, op_id = QxG7OkqoLX, unary_op_definition = '⊽a = { (a⨸⪁761) , if (a↬⩅∪)<402 ; (a∧) , else }', output=13956","layer":0}],"base":4,"result_base":4,"text":"⊽(⪩⨒∯1111211⋳⪒⪩⨒∯1011202)=⪩⨒∯3122010","reverse_text":"⪩⨒∯3122010=⊽(⪩⨒∯1111211⋳⪒⪩⨒∯1011202)","cot":[{"info":"⪩⨒∯1111211⋳⪒⪩⨒∯1011202=⪩⨒∯1201021","layer":1},{"info":"⊽⪩⨒∯1201021=⪩⨒∯3122010","layer":0}]}
{"id":433,"expression_no_base_symbol":"$5811$≦↸$7995$↳∿⪆$2189$↳≱$1301$","expression":"⪩⨒∯1122303≦↸⪩⨒∯1330323↳∿⪆⪩⨒∯202031↳≱⪩⨒∯110111","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2495,"operation_count":3,"complexity_ratio":831.6666666666666,"tree":{"type":"binary","operator":"↳∿⪆","left_expr":{"type":"binary","operator":"≦↸","left_expr":{"type":"numeric_atoms","value":5811,"base":4},"right_expr":{"type":"numeric_atoms","value":7995,"base":4}},"right_expr":{"type":"binary","operator":"↳≱","left_expr":{"type":"numeric_atoms","value":2189,"base":4},"right_expr":{"type":"numeric_atoms","value":1301,"base":4}}},"used_operators":["Cw4SuJJGHO","RygbFNSyEJ","JwTKLfZU96"],"dependent_operators":["hyuBjUqXlG","bF6eod5Gvf","nEsXyWgiOK","ruOEQAzv1W","Tw270M8GLb","QMFrweE19q","eLAdDNolq6","e1ybzncUwg","DZ8iAZOCBD","XIabStNQrY","12rbrZMWeM","2DDjHMKMc0","g55IO6H4Gj","DhbWaqg5eL","WR6HLWljOP","XhwjNDsVaA","T2fj7uvVaJ","7YooWSwCyH","B3sABdIn96"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5811","layer":2},{"info":"number node, value=7995","layer":2},{"info":"compute binary expreesion, left_input=5811, right_input=7995, op_id = RygbFNSyEJ binary_op_definition= 'a≦↸b = { (((≤/a)⋳⪒(b⊉≛↸a))⋝⋈⪟((a⇋≉)⨸⪁(≉a))) }', output=-26931","layer":1},{"info":"number node, value=2189","layer":2},{"info":"number node, value=1301","layer":2},{"info":"compute binary expreesion, left_input=2189, right_input=1301, op_id = JwTKLfZU96 binary_op_definition= 'a↳≱b = { (((a∪⫐104)↢(147/b))⋓((+⊝⨔b)⪹)) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-26931, right_input=0, op_id = Cw4SuJJGHO binary_op_definition= 'a↳∿⪆b = { ((⨰⫟⨤(↔15))⨻⩈⩔((b⪛⫼133)⫡⨏(b→⨶⪴a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1122303≦↸⪩⨒∯1330323↳∿⪆⪩⨒∯202031↳≱⪩⨒∯110111=NaN","reverse_text":"NaN=⪩⨒∯1122303≦↸⪩⨒∯1330323↳∿⪆⪩⨒∯202031↳≱⪩⨒∯110111","cot":[{"info":"⪩⨒∯1122303≦↸⪩⨒∯1330323=⪩⨒∯-12210303","layer":1},{"info":"⪩⨒∯202031↳≱⪩⨒∯110111=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-12210303↳∿⪆⪩⨒∯0=NaN","layer":0}]}
{"id":434,"expression_no_base_symbol":"(+⊝⨔$6079$)≴⪞⇿(≦∁$3380$)","expression":"(+⊝⨔⪩⨒∯1132333)≴⪞⇿(≦∁⪩⨒∯310310)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1325,"operation_count":3,"complexity_ratio":441.6666666666667,"tree":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":6079,"base":4}},"right_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":3380,"base":4}}},"used_operators":["lvlrscuwVU","DhbWaqg5eL","9ICcGScMcE"],"dependent_operators":["DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"⪩⨒∯23321301230","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6079","layer":2},{"info":"compute unary expreesion, input=6079, op_id = DhbWaqg5eL, unary_op_definition = '+⊝⨔a = { ((⪲⇎(⨑⩽⪐14))⨁⊸⫻) , if (a⫸⊐100)!=276 or (a⩷∴98)>390 ; (((a⪐)⪢(a⫸⊐221))+((a⩨a)⪘⫢(-370))) , else }', output=1522","layer":1},{"info":"number node, value=3380","layer":2},{"info":"compute unary expreesion, input=3380, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=3380","layer":1},{"info":"compute binary expreesion, left_input=1522, right_input=3380, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=3120236","layer":0}],"base":4,"result_base":4,"text":"(+⊝⨔⪩⨒∯1132333)≴⪞⇿(≦∁⪩⨒∯310310)=⪩⨒∯23321301230","reverse_text":"⪩⨒∯23321301230=(+⊝⨔⪩⨒∯1132333)≴⪞⇿(≦∁⪩⨒∯310310)","cot":[{"info":"+⊝⨔⪩⨒∯1132333=⪩⨒∯113302","layer":1},{"info":"≦∁⪩⨒∯310310=⪩⨒∯310310","layer":1},{"info":"⪩⨒∯113302≴⪞⇿⪩⨒∯310310=⪩⨒∯23321301230","layer":0}]}
{"id":435,"expression_no_base_symbol":"$4853$⋳⪒$7104$↸$2851$⋕⪉⪜$2648$","expression":"⪩⨒∯1023311⋳⪒⪩⨒∯1233000↸⪩⨒∯230203⋕⪉⪜⪩⨒∯221120","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2353,"operation_count":3,"complexity_ratio":784.3333333333334,"tree":{"type":"binary","operator":"↸","left_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":4853,"base":4},"right_expr":{"type":"numeric_atoms","value":7104,"base":4}},"right_expr":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"numeric_atoms","value":2851,"base":4},"right_expr":{"type":"numeric_atoms","value":2648,"base":4}}},"used_operators":["1eCjFl0mb9","12rbrZMWeM","z6LnFrNh4i"],"dependent_operators":["9HNa5Wba9A","61wBmkZwlr","rJVOvQCfKK","rysDP5nf3Z","t8gj7n24qd","sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z"],"result":"⪩⨒∯210023","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4853","layer":2},{"info":"number node, value=7104","layer":2},{"info":"compute binary expreesion, left_input=4853, right_input=7104, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=2315","layer":1},{"info":"number node, value=2851","layer":2},{"info":"number node, value=2648","layer":2},{"info":"compute binary expreesion, left_input=2851, right_input=2648, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=2802","layer":1},{"info":"compute binary expreesion, left_input=2315, right_input=2802, op_id = 1eCjFl0mb9 binary_op_definition= 'a↸b = { ((b*a)⨎(≋a)) }', output=2315","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1023311⋳⪒⪩⨒∯1233000↸⪩⨒∯230203⋕⪉⪜⪩⨒∯221120=⪩⨒∯210023","reverse_text":"⪩⨒∯210023=⪩⨒∯1023311⋳⪒⪩⨒∯1233000↸⪩⨒∯230203⋕⪉⪜⪩⨒∯221120","cot":[{"info":"⪩⨒∯1023311⋳⪒⪩⨒∯1233000=⪩⨒∯210023","layer":1},{"info":"⪩⨒∯230203⋕⪉⪜⪩⨒∯221120=⪩⨒∯223302","layer":1},{"info":"⪩⨒∯210023↸⪩⨒∯223302=⪩⨒∯210023","layer":0}]}
{"id":436,"expression_no_base_symbol":"$1000$∌$1077$⨽$5019$↳≱$5503$","expression":"⪩⨒∯33220∌⪩⨒∯100311⨽⪩⨒∯1032123↳≱⪩⨒∯1111333","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1172,"operation_count":3,"complexity_ratio":390.6666666666667,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"binary","operator":"∌","left_expr":{"type":"numeric_atoms","value":1000,"base":4},"right_expr":{"type":"numeric_atoms","value":1077,"base":4}},"right_expr":{"type":"binary","operator":"↳≱","left_expr":{"type":"numeric_atoms","value":5019,"base":4},"right_expr":{"type":"numeric_atoms","value":5503,"base":4}}},"used_operators":["8HhzD0ZcuI","8cLx32lpNA","JwTKLfZU96"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","N41Kp7NANJ","7j4O788W3g","t8gj7n24qd","DhbWaqg5eL","WR6HLWljOP","XhwjNDsVaA","T2fj7uvVaJ","7YooWSwCyH","B3sABdIn96"],"result":"⪩⨒∯-31101033021","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1000","layer":2},{"info":"number node, value=1077","layer":2},{"info":"compute binary expreesion, left_input=1000, right_input=1077, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-1077","layer":1},{"info":"number node, value=5019","layer":2},{"info":"number node, value=5503","layer":2},{"info":"compute binary expreesion, left_input=5019, right_input=5503, op_id = JwTKLfZU96 binary_op_definition= 'a↳≱b = { (((a∪⫐104)↢(147/b))⋓((+⊝⨔b)⪹)) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-1077, right_input=0, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-3478473","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯33220∌⪩⨒∯100311⨽⪩⨒∯1032123↳≱⪩⨒∯1111333=⪩⨒∯-31101033021","reverse_text":"⪩⨒∯-31101033021=⪩⨒∯33220∌⪩⨒∯100311⨽⪩⨒∯1032123↳≱⪩⨒∯1111333","cot":[{"info":"⪩⨒∯33220∌⪩⨒∯100311=⪩⨒∯-100311","layer":1},{"info":"⪩⨒∯1032123↳≱⪩⨒∯1111333=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-100311⨽⪩⨒∯0=⪩⨒∯-31101033021","layer":0}]}
{"id":437,"expression_no_base_symbol":"($2413$⋻⩜⩜$5944$)∷","expression":"(⪩⨒∯211231⋻⩜⩜⪩⨒∯1130320)∷","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":83229,"operation_count":2,"complexity_ratio":41614.5,"tree":{"type":"unary","operator":"∷","unary_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":2413,"base":4},"right_expr":{"type":"numeric_atoms","value":5944,"base":4}}},"used_operators":["nFAOW8KTqp","oDCm7WA9JY"],"dependent_operators":["D4vGDi5EA2","t8gj7n24qd","2DDjHMKMc0","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE"],"result":"⪩⨒∯3202032","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2413","layer":2},{"info":"number node, value=5944","layer":2},{"info":"compute binary expreesion, left_input=2413, right_input=5944, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=4826","layer":1},{"info":"compute unary expreesion, input=4826, op_id = nFAOW8KTqp, unary_op_definition = 'a∷ = { ((-(a⋝⋈⪟a))≦≮≮) }', output=14478","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯211231⋻⩜⩜⪩⨒∯1130320)∷=⪩⨒∯3202032","reverse_text":"⪩⨒∯3202032=(⪩⨒∯211231⋻⩜⩜⪩⨒∯1130320)∷","cot":[{"info":"⪩⨒∯211231⋻⩜⩜⪩⨒∯1130320=⪩⨒∯1023122","layer":1},{"info":"⪩⨒∯1023122∷=⪩⨒∯3202032","layer":0}]}
{"id":438,"expression_no_base_symbol":"⪲⇎($2620$⪒$1518$)","expression":"⪲⇎(⪩⨒∯220330⪒⪩⨒∯113232)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5,"operation_count":2,"complexity_ratio":2.5,"tree":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":2620,"base":4},"right_expr":{"type":"numeric_atoms","value":1518,"base":4}}},"used_operators":["XPYlsWDdGa","f6k1SAg4EE"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-2001110","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2620","layer":2},{"info":"number node, value=1518","layer":2},{"info":"compute binary expreesion, left_input=2620, right_input=1518, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-4138","layer":1},{"info":"compute unary expreesion, input=-4138, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=-8276","layer":0}],"base":4,"result_base":4,"text":"⪲⇎(⪩⨒∯220330⪒⪩⨒∯113232)=⪩⨒∯-2001110","reverse_text":"⪩⨒∯-2001110=⪲⇎(⪩⨒∯220330⪒⪩⨒∯113232)","cot":[{"info":"⪩⨒∯220330⪒⪩⨒∯113232=⪩⨒∯-1000222","layer":1},{"info":"⪲⇎⪩⨒∯-1000222=⪩⨒∯-2001110","layer":0}]}
{"id":439,"expression_no_base_symbol":"(⩏⊷≩$3861$)⪍↜⋙$1022$⋕⪉⪜$4039$","expression":"(⩏⊷≩⪩⨒∯330111)⪍↜⋙⪩⨒∯33332⋕⪉⪜⪩⨒∯333013","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":60,"operation_count":3,"complexity_ratio":20.0,"tree":{"type":"binary","operator":"⪍↜⋙","left_expr":{"type":"unary","operator":"⩏⊷≩","unary_expr":{"type":"numeric_atoms","value":3861,"base":4}},"right_expr":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"numeric_atoms","value":1022,"base":4},"right_expr":{"type":"numeric_atoms","value":4039,"base":4}}},"used_operators":["L05ObWFQCd","uOZ1tnYMDE","z6LnFrNh4i"],"dependent_operators":["rysDP5nf3Z","DZ8iAZOCBD","tifHPKVTfV","EBcxylXtPf","QMFrweE19q","23Mk6UjR3U","12rbrZMWeM","sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z"],"result":"⪩⨒∯3201202","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3861","layer":2},{"info":"compute unary expreesion, input=3861, op_id = uOZ1tnYMDE, unary_op_definition = '⩏⊷≩a = { ((a⋳⪒20)⋷(a⋳⪒17)) }', output=7421","layer":1},{"info":"number node, value=1022","layer":2},{"info":"number node, value=4039","layer":2},{"info":"compute binary expreesion, left_input=1022, right_input=4039, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=204","layer":1},{"info":"compute binary expreesion, left_input=7421, right_input=204, op_id = L05ObWFQCd binary_op_definition= 'a⪍↜⋙b = { ((a-b)⊉≛↸(a⫡⨏b)) , if (a⫌⩹⨱)!=88 ; ((a⫡⨏b)⇼⇔∾(a⫌⩹⨱)) , else }', output=14434","layer":0}],"base":4,"result_base":4,"text":"(⩏⊷≩⪩⨒∯330111)⪍↜⋙⪩⨒∯33332⋕⪉⪜⪩⨒∯333013=⪩⨒∯3201202","reverse_text":"⪩⨒∯3201202=(⩏⊷≩⪩⨒∯330111)⪍↜⋙⪩⨒∯33332⋕⪉⪜⪩⨒∯333013","cot":[{"info":"⩏⊷≩⪩⨒∯330111=⪩⨒∯1303331","layer":1},{"info":"⪩⨒∯33332⋕⪉⪜⪩⨒∯333013=⪩⨒∯3030","layer":1},{"info":"⪩⨒∯1303331⪍↜⋙⪩⨒∯3030=⪩⨒∯3201202","layer":0}]}
{"id":440,"expression_no_base_symbol":"(∜⨇$3062$)≓∲$2745$⨂≜$2029$","expression":"(∜⨇⪩⨒∯233312)≓∲⪩⨒∯222321⨂≜⪩⨒∯133231","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2875,"operation_count":3,"complexity_ratio":958.3333333333334,"tree":{"type":"binary","operator":"≓∲","left_expr":{"type":"unary","operator":"∜⨇","unary_expr":{"type":"numeric_atoms","value":3062,"base":4}},"right_expr":{"type":"binary","operator":"⨂≜","left_expr":{"type":"numeric_atoms","value":2745,"base":4},"right_expr":{"type":"numeric_atoms","value":2029,"base":4}}},"used_operators":["s1XTVnmDOJ","uFPyJr306J","k1SHOSEABc"],"dependent_operators":["HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu","fG6uBQFnGz","pRsWfj4Fpp","rGHVDoGpnC","Y7wcNGrDQJ","NNaDxxp6OQ","9FxExcQeMw","HiPekx5b7W","eLxqMNBOBk","JclMnS0uGI","COABgblf1C","U7g4x0WXJJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3062","layer":2},{"info":"compute unary expreesion, input=3062, op_id = uFPyJr306J, unary_op_definition = '∜⨇a = { (a⨟⋌⩍a) , if (a⫽⇹≛)!=2 or (↩⪖a)==528 or (∡a)>=548 ; (132⩵∡a) , else }', output=nan","layer":1},{"info":"number node, value=2745","layer":2},{"info":"number node, value=2029","layer":2},{"info":"compute binary expreesion, left_input=2745, right_input=2029, op_id = k1SHOSEABc binary_op_definition= 'a⨂≜b = { ((37⊭↱(⫓⪴a))⩷∴((111⨜⨶78)⨔⇊(a∑⇟⊟b))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(∜⨇⪩⨒∯233312)≓∲⪩⨒∯222321⨂≜⪩⨒∯133231=NaN","reverse_text":"NaN=(∜⨇⪩⨒∯233312)≓∲⪩⨒∯222321⨂≜⪩⨒∯133231","cot":[{"info":"∜⨇⪩⨒∯233312=NaN","layer":1},{"info":"⪩⨒∯222321⨂≜⪩⨒∯133231=NaN","layer":1},{"info":"NaN≓∲NaN=NaN","layer":0}]}
{"id":441,"expression_no_base_symbol":"$6132$⨜⨶$5816$⊬⨰($1631$⇴∐$6037$)","expression":"⪩⨒∯1133310⨜⨶⪩⨒∯1122320⊬⨰(⪩⨒∯121133⇴∐⪩⨒∯1132111)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":59,"operation_count":3,"complexity_ratio":19.666666666666668,"tree":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":6132,"base":4},"right_expr":{"type":"numeric_atoms","value":5816,"base":4}},"right_expr":{"type":"binary","operator":"⇴∐","left_expr":{"type":"numeric_atoms","value":1631,"base":4},"right_expr":{"type":"numeric_atoms","value":6037,"base":4}}},"used_operators":["s3Fd5m9Dh2","HiPekx5b7W","HnzytWxmAO"],"dependent_operators":["23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6132","layer":2},{"info":"number node, value=5816","layer":2},{"info":"compute binary expreesion, left_input=6132, right_input=5816, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-11376","layer":1},{"info":"number node, value=1631","layer":2},{"info":"number node, value=6037","layer":2},{"info":"compute binary expreesion, left_input=1631, right_input=6037, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-11376, right_input=nan, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1133310⨜⨶⪩⨒∯1122320⊬⨰(⪩⨒∯121133⇴∐⪩⨒∯1132111)=NaN","reverse_text":"NaN=⪩⨒∯1133310⨜⨶⪩⨒∯1122320⊬⨰(⪩⨒∯121133⇴∐⪩⨒∯1132111)","cot":[{"info":"⪩⨒∯1133310⨜⨶⪩⨒∯1122320=⪩⨒∯-2301300","layer":1},{"info":"⪩⨒∯121133⇴∐⪩⨒∯1132111=NaN","layer":1},{"info":"⪩⨒∯-2301300⊬⨰NaN=NaN","layer":0}]}
{"id":442,"expression_no_base_symbol":"($2813$≀⫉$1831$)⊱⇼⊻($1468$∷$3070$)","expression":"(⪩⨒∯223331≀⫉⪩⨒∯130213)⊱⇼⊻(⪩⨒∯112330∷⪩⨒∯233332)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":173,"operation_count":3,"complexity_ratio":57.666666666666664,"tree":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"binary","operator":"≀⫉","left_expr":{"type":"numeric_atoms","value":2813,"base":4},"right_expr":{"type":"numeric_atoms","value":1831,"base":4}},"right_expr":{"type":"binary","operator":"∷","left_expr":{"type":"numeric_atoms","value":1468,"base":4},"right_expr":{"type":"numeric_atoms","value":3070,"base":4}}},"used_operators":["FyVja0WsTP","oZj3VtZNQx","D3AQDKkPcf"],"dependent_operators":["W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","9FxExcQeMw","Tcnh7f0tEr","jBncVCNhdl","FyVja0WsTP","Ikt5ks8PT7","EWw2JM7wp4","cTDWOvIxvz","9FxExcQeMw","NTOWxs364D","7j4O788W3g"],"result":"⪩⨒∯12302","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2813","layer":2},{"info":"number node, value=1831","layer":2},{"info":"compute binary expreesion, left_input=2813, right_input=1831, op_id = oZj3VtZNQx binary_op_definition= 'a≀⫉b = { (((55≣⋋)∝(a⩷∴a))⊱⇼⊻((a⪉⨛b)⩧⪆(b⋭≵475))) }', output=2822","layer":1},{"info":"number node, value=1468","layer":2},{"info":"number node, value=3070","layer":2},{"info":"compute binary expreesion, left_input=1468, right_input=3070, op_id = D3AQDKkPcf binary_op_definition= 'a∷b = { (a⩚⊴⇥673) , if (b⩷∴24)<=112 ; (a↺b) , else }', output=3070","layer":1},{"info":"compute binary expreesion, left_input=2822, right_input=3070, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯223331≀⫉⪩⨒∯130213)⊱⇼⊻(⪩⨒∯112330∷⪩⨒∯233332)=⪩⨒∯12302","reverse_text":"⪩⨒∯12302=(⪩⨒∯223331≀⫉⪩⨒∯130213)⊱⇼⊻(⪩⨒∯112330∷⪩⨒∯233332)","cot":[{"info":"⪩⨒∯223331≀⫉⪩⨒∯130213=⪩⨒∯230012","layer":1},{"info":"⪩⨒∯112330∷⪩⨒∯233332=⪩⨒∯233332","layer":1},{"info":"⪩⨒∯230012⊱⇼⊻⪩⨒∯233332=⪩⨒∯12302","layer":0}]}
{"id":443,"expression_no_base_symbol":"(↞≼$2963$)⇼⇔∾($2539$⇗⋫)","expression":"(↞≼⪩⨒∯232103)⇼⇔∾(⪩⨒∯213223⇗⋫)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":18,"operation_count":3,"complexity_ratio":6.0,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"unary","operator":"↞≼","unary_expr":{"type":"numeric_atoms","value":2963,"base":4}},"right_expr":{"type":"unary","operator":"⇗⋫","unary_expr":{"type":"numeric_atoms","value":2539,"base":4}}},"used_operators":["tifHPKVTfV","DE7zCoGJt9","hpqmaQFPrd"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","D4vGDi5EA2","23Mk6UjR3U","BjRHVeLaeN","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","u6S6b8DprG","rxpJgHHUmx"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2963","layer":2},{"info":"compute unary expreesion, input=2963, op_id = DE7zCoGJt9, unary_op_definition = '↞≼a = { (↽≂(197⨰(a⨸⪁a))) , if (a⨸⪁373)!=224 ; (((591⋷a)≧⫂∧(a+a))⨸⪁((a⫩⊇)≦≮≮)) , else }', output=23290","layer":1},{"info":"number node, value=2539","layer":2},{"info":"compute unary expreesion, input=2539, op_id = hpqmaQFPrd, unary_op_definition = 'a⇗⋫ = { (a≭a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=23290, right_input=nan, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(↞≼⪩⨒∯232103)⇼⇔∾(⪩⨒∯213223⇗⋫)=NaN","reverse_text":"NaN=(↞≼⪩⨒∯232103)⇼⇔∾(⪩⨒∯213223⇗⋫)","cot":[{"info":"↞≼⪩⨒∯232103=⪩⨒∯11223322","layer":1},{"info":"⪩⨒∯213223⇗⋫=NaN","layer":1},{"info":"⪩⨒∯11223322⇼⇔∾NaN=NaN","layer":0}]}
{"id":444,"expression_no_base_symbol":"(≤/$1154$)⫗⊷⫓($3319$⨟⋌⩍$2814$)","expression":"(≤/⪩⨒∯102002)⫗⊷⫓(⪩⨒∯303313⨟⋌⩍⪩⨒∯223332)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":87545,"operation_count":3,"complexity_ratio":29181.666666666668,"tree":{"type":"binary","operator":"⫗⊷⫓","left_expr":{"type":"unary","operator":"≤/","unary_expr":{"type":"numeric_atoms","value":1154,"base":4}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":3319,"base":4},"right_expr":{"type":"numeric_atoms","value":2814,"base":4}}},"used_operators":["zashukvMKz","eLAdDNolq6","rGHVDoGpnC"],"dependent_operators":["xD69zh8xqp","Uaa54Peajs","BjRHVeLaeN","QiR2Oyf5Xj","k1SHOSEABc","Asc51vEJeQ","oRDoc9rAEX","bJkvcejdHO","8INZBEW696","Af076pWI7l","rysDP5nf3Z","Tcnh7f0tEr"],"result":"⪩⨒∯-2012","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1154","layer":2},{"info":"compute unary expreesion, input=1154, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-670","layer":1},{"info":"number node, value=3319","layer":2},{"info":"number node, value=2814","layer":2},{"info":"compute binary expreesion, left_input=3319, right_input=2814, op_id = rGHVDoGpnC binary_op_definition= 'a⨟⋌⩍b = {a, if b == 0; (a⨟⋌⩍(b-1))≣⋋, if b > 0 and abs(b) < 1000; -(a⨟⋌⩍(b+1))≣⋋, if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-670, right_input=nan, op_id = zashukvMKz binary_op_definition= 'a⫗⊷⫓b = { ((∂(b⨂≜a))⫩⊇) , if (↣≠⋷b)<=196 ; ((∷≠(a⊋≦⊧b))↓((b≎⊠⪸a)⪪(a≀⩗∶b))) , else }', output=-134","layer":0}],"base":4,"result_base":4,"text":"(≤/⪩⨒∯102002)⫗⊷⫓(⪩⨒∯303313⨟⋌⩍⪩⨒∯223332)=⪩⨒∯-2012","reverse_text":"⪩⨒∯-2012=(≤/⪩⨒∯102002)⫗⊷⫓(⪩⨒∯303313⨟⋌⩍⪩⨒∯223332)","cot":[{"info":"≤/⪩⨒∯102002=⪩⨒∯-22132","layer":1},{"info":"⪩⨒∯303313⨟⋌⩍⪩⨒∯223332=NaN","layer":1},{"info":"⪩⨒∯-22132⫗⊷⫓NaN=⪩⨒∯-2012","layer":0}]}
{"id":445,"expression_no_base_symbol":"(↔$5720$)≁($1294$⩵∡$2086$)","expression":"(↔⪩⨒∯1121120)≁(⪩⨒∯110032⩵∡⪩⨒∯200212)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":96,"operation_count":3,"complexity_ratio":32.0,"tree":{"type":"binary","operator":"≁","left_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":5720,"base":4}},"right_expr":{"type":"binary","operator":"⩵∡","left_expr":{"type":"numeric_atoms","value":1294,"base":4},"right_expr":{"type":"numeric_atoms","value":2086,"base":4}}},"used_operators":["8N2wDY1A35","ruOEQAzv1W","Y7wcNGrDQJ"],"dependent_operators":["B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","NTOWxs364D","glklzrTFfD","tifHPKVTfV"],"result":"⪩⨒∯-12310131","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5720","layer":2},{"info":"compute unary expreesion, input=5720, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-5447","layer":1},{"info":"number node, value=1294","layer":2},{"info":"number node, value=2086","layer":2},{"info":"compute binary expreesion, left_input=1294, right_input=2086, op_id = Y7wcNGrDQJ binary_op_definition= 'a⩵∡b = { ((b⇼⇔∾a)⩚⊴⇥(a⨁⊸⫻)) }', output=-623","layer":1},{"info":"compute binary expreesion, left_input=-5447, right_input=-623, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=-27933","layer":0}],"base":4,"result_base":4,"text":"(↔⪩⨒∯1121120)≁(⪩⨒∯110032⩵∡⪩⨒∯200212)=⪩⨒∯-12310131","reverse_text":"⪩⨒∯-12310131=(↔⪩⨒∯1121120)≁(⪩⨒∯110032⩵∡⪩⨒∯200212)","cot":[{"info":"↔⪩⨒∯1121120=⪩⨒∯-1111013","layer":1},{"info":"⪩⨒∯110032⩵∡⪩⨒∯200212=⪩⨒∯-21233","layer":1},{"info":"⪩⨒∯-1111013≁⪩⨒∯-21233=⪩⨒∯-12310131","layer":0}]}
{"id":446,"expression_no_base_symbol":"($1045$∝$4753$)⊨($5642$≭$3387$)","expression":"(⪩⨒∯100111∝⪩⨒∯1022101)⊨(⪩⨒∯1120022≭⪩⨒∯310323)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":20,"operation_count":3,"complexity_ratio":6.666666666666667,"tree":{"type":"binary","operator":"⊨","left_expr":{"type":"binary","operator":"∝","left_expr":{"type":"numeric_atoms","value":1045,"base":4},"right_expr":{"type":"numeric_atoms","value":4753,"base":4}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":5642,"base":4},"right_expr":{"type":"numeric_atoms","value":3387,"base":4}}},"used_operators":["vg4gO5BX6G","cTDWOvIxvz","rxpJgHHUmx"],"dependent_operators":["NTOWxs364D","JLbD19bQDL","xUOZtlo3hN","AF7qkfDlqP","7j4O788W3g","W4YGzv6Whe","COABgblf1C","AHs5Up7iyr"],"result":"⪩⨒∯1101233","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1045","layer":2},{"info":"number node, value=4753","layer":2},{"info":"compute binary expreesion, left_input=1045, right_input=4753, op_id = cTDWOvIxvz binary_op_definition= 'a∝b = { ((b↺a)+(b⊭↱b)) }', output=1050","layer":1},{"info":"number node, value=5642","layer":2},{"info":"number node, value=3387","layer":2},{"info":"compute binary expreesion, left_input=5642, right_input=3387, op_id = rxpJgHHUmx binary_op_definition= 'a≭b = {-22, if b == 0; (a)≹⇙⪍(a≭(b-1)), if b > 0 and abs(b) < 100; -(a)≹⇙⪍(a≭(b+1)), if b < 0 and abs(b) < 100; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1050, right_input=nan, op_id = vg4gO5BX6G binary_op_definition= 'a⊨b = { (⨞⊢(b⪠⩆⊳)) , if a<=416 ; (⨑⩽⪐(a⩚⊴⇥a)) , else }', output=5231","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100111∝⪩⨒∯1022101)⊨(⪩⨒∯1120022≭⪩⨒∯310323)=⪩⨒∯1101233","reverse_text":"⪩⨒∯1101233=(⪩⨒∯100111∝⪩⨒∯1022101)⊨(⪩⨒∯1120022≭⪩⨒∯310323)","cot":[{"info":"⪩⨒∯100111∝⪩⨒∯1022101=⪩⨒∯100122","layer":1},{"info":"⪩⨒∯1120022≭⪩⨒∯310323=NaN","layer":1},{"info":"⪩⨒∯100122⊨NaN=⪩⨒∯1101233","layer":0}]}
{"id":447,"expression_no_base_symbol":"($2221$≳⇉$2263$)∑⇟⊟(⩩$1619$)","expression":"(⪩⨒∯202231≳⇉⪩⨒∯203113)∑⇟⊟(⩩⪩⨒∯121103)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":51293497,"operation_count":3,"complexity_ratio":17097832.333333332,"tree":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"binary","operator":"≳⇉","left_expr":{"type":"numeric_atoms","value":2221,"base":4},"right_expr":{"type":"numeric_atoms","value":2263,"base":4}},"right_expr":{"type":"unary","operator":"⩩","unary_expr":{"type":"numeric_atoms","value":1619,"base":4}}},"used_operators":["U7g4x0WXJJ","V0kx6qeWkN","kMhfGuqI2H"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls","6aG7x05OhS","z63VuFQld9","lFBm8KRb8F","f6k1SAg4EE","ZGCBLdVRRX"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2221","layer":2},{"info":"number node, value=2263","layer":2},{"info":"compute binary expreesion, left_input=2221, right_input=2263, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":1},{"info":"number node, value=1619","layer":2},{"info":"compute unary expreesion, input=1619, op_id = kMhfGuqI2H, unary_op_definition = '⩩a = { (⇜(a⫩)) , if (⇵⪽a)!=444 ; ((a⪒a)∧) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯202231≳⇉⪩⨒∯203113)∑⇟⊟(⩩⪩⨒∯121103)=NaN","reverse_text":"NaN=(⪩⨒∯202231≳⇉⪩⨒∯203113)∑⇟⊟(⩩⪩⨒∯121103)","cot":[{"info":"⪩⨒∯202231≳⇉⪩⨒∯203113=NaN","layer":1},{"info":"⩩⪩⨒∯121103=NaN","layer":1},{"info":"NaN∑⇟⊟NaN=NaN","layer":0}]}
{"id":448,"expression_no_base_symbol":"(⨡↴$1026$)⨪↰⇹($1035$⪒$2121$)","expression":"(⨡↴⪩⨒∯100002)⨪↰⇹(⪩⨒∯100023⪒⪩⨒∯201021)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2083,"operation_count":3,"complexity_ratio":694.3333333333334,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"unary","operator":"⨡↴","unary_expr":{"type":"numeric_atoms","value":1026,"base":4}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":1035,"base":4},"right_expr":{"type":"numeric_atoms","value":2121,"base":4}}},"used_operators":["tmPS8pqC7x","liw5iZPkLH","f6k1SAg4EE"],"dependent_operators":["rJVOvQCfKK","W4YGzv6Whe","P8v4zCKN1o","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯200123","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1026","layer":2},{"info":"compute unary expreesion, input=1026, op_id = liw5iZPkLH, unary_op_definition = '⨡↴a = { (∥⊫(a+181)) }', output=2075","layer":1},{"info":"number node, value=1035","layer":2},{"info":"number node, value=2121","layer":2},{"info":"compute binary expreesion, left_input=1035, right_input=2121, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-3156","layer":1},{"info":"compute binary expreesion, left_input=2075, right_input=-3156, op_id = tmPS8pqC7x binary_op_definition= 'a⨪↰⇹b = {a, if a == 0; (b)⨎((a-1)⨪↰⇹b), if a > 0 and abs(a) < 1000000; -(b)⨎((a+1)⨪↰⇹b), if a < 0 and abs(a) < 1000000; NaN, else}', output=2075","layer":0}],"base":4,"result_base":4,"text":"(⨡↴⪩⨒∯100002)⨪↰⇹(⪩⨒∯100023⪒⪩⨒∯201021)=⪩⨒∯200123","reverse_text":"⪩⨒∯200123=(⨡↴⪩⨒∯100002)⨪↰⇹(⪩⨒∯100023⪒⪩⨒∯201021)","cot":[{"info":"⨡↴⪩⨒∯100002=⪩⨒∯200123","layer":1},{"info":"⪩⨒∯100023⪒⪩⨒∯201021=⪩⨒∯-301110","layer":1},{"info":"⪩⨒∯200123⨪↰⇹⪩⨒∯-301110=⪩⨒∯200123","layer":0}]}
{"id":449,"expression_no_base_symbol":"⨭⩧⫛($1011$⪄$1273$)","expression":"⨭⩧⫛(⪩⨒∯33303⪄⪩⨒∯103321)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3056,"operation_count":2,"complexity_ratio":1528.0,"tree":{"type":"unary","operator":"⨭⩧⫛","unary_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":1011,"base":4},"right_expr":{"type":"numeric_atoms","value":1273,"base":4}}},"used_operators":["g21JL6JxX7","SUmda5xLS4"],"dependent_operators":["Ikt5ks8PT7","Asc51vEJeQ","A8NUZmVepG","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1011","layer":2},{"info":"number node, value=1273","layer":2},{"info":"compute binary expreesion, left_input=1011, right_input=1273, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-150809","layer":1},{"info":"compute unary expreesion, input=-150809, op_id = g21JL6JxX7, unary_op_definition = '⨭⩧⫛a = { ((↥a)⩧⪆(↣≠⋷a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⨭⩧⫛(⪩⨒∯33303⪄⪩⨒∯103321)=NaN","reverse_text":"NaN=⨭⩧⫛(⪩⨒∯33303⪄⪩⨒∯103321)","cot":[{"info":"⪩⨒∯33303⪄⪩⨒∯103321=⪩⨒∯-210310121","layer":1},{"info":"⨭⩧⫛⪩⨒∯-210310121=NaN","layer":0}]}
{"id":450,"expression_no_base_symbol":"∨∊⋏($7186$⪛$3059$)","expression":"∨∊⋏(⪩⨒∯1300102⪛⪩⨒∯233303)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":73,"operation_count":2,"complexity_ratio":36.5,"tree":{"type":"unary","operator":"∨∊⋏","unary_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":7186,"base":4},"right_expr":{"type":"numeric_atoms","value":3059,"base":4}}},"used_operators":["R5aXW34M0v","uFcxV4UQCh"],"dependent_operators":["L05ObWFQCd","YjI8oCXuph","9ICcGScMcE","g7Hmc5v1ko","ocnLzx9CaJ","2DDjHMKMc0","hrf7POJlIJ","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⪩⨒∯3002033","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7186","layer":2},{"info":"number node, value=3059","layer":2},{"info":"compute binary expreesion, left_input=7186, right_input=3059, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1068","layer":1},{"info":"compute unary expreesion, input=1068, op_id = R5aXW34M0v, unary_op_definition = '∨∊⋏a = { (((101⋝⋈⪟206)⪍↜⋙(≦∁a))⩼⇪↪((a⩌⋺a)∴(⫇a))) }', output=12431","layer":0}],"base":4,"result_base":4,"text":"∨∊⋏(⪩⨒∯1300102⪛⪩⨒∯233303)=⪩⨒∯3002033","reverse_text":"⪩⨒∯3002033=∨∊⋏(⪩⨒∯1300102⪛⪩⨒∯233303)","cot":[{"info":"⪩⨒∯1300102⪛⪩⨒∯233303=⪩⨒∯100230","layer":1},{"info":"∨∊⋏⪩⨒∯100230=⪩⨒∯3002033","layer":0}]}
{"id":451,"expression_no_base_symbol":"$1507$≎⪠$1852$⫢⨠(∂⩏⊆$1563$)","expression":"⪩⨒∯113203≎⪠⪩⨒∯130330⫢⨠(∂⩏⊆⪩⨒∯120123)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19175,"operation_count":3,"complexity_ratio":6391.666666666667,"tree":{"type":"binary","operator":"⫢⨠","left_expr":{"type":"binary","operator":"≎⪠","left_expr":{"type":"numeric_atoms","value":1507,"base":4},"right_expr":{"type":"numeric_atoms","value":1852,"base":4}},"right_expr":{"type":"unary","operator":"∂⩏⊆","unary_expr":{"type":"numeric_atoms","value":1563,"base":4}}},"used_operators":["xlXykHWxX1","aNhz54LH3e","8WDwsbhb0R"],"dependent_operators":["KFSx94NKJn","e1ybzncUwg","zR4jO40bMj","g7Hmc5v1ko","k2HlF1dBQh","2DlMacCsIx","bl5wxAcryP","RygbFNSyEJ","SLLxy00UIr","AcOhelriW5","ctOc4cKSDt","cHh1gJQ2o6","KYD54nUTWz","kbkesczE7y","BUOGQAYlQx","PPChnnnBFF","14qkJME0vr","eLAdDNolq6"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1507","layer":2},{"info":"number node, value=1852","layer":2},{"info":"compute binary expreesion, left_input=1507, right_input=1852, op_id = aNhz54LH3e binary_op_definition= 'a≎⪠b = { (((a⫥∨⫟11)≦↸(657∣a))⩘((⇈a)≬⋮(a↰))) , if a==21 ; (∟⋨(⋂(⨣⨃⇪b))) , else }', output=19558","layer":1},{"info":"number node, value=1563","layer":2},{"info":"compute unary expreesion, input=1563, op_id = 8WDwsbhb0R, unary_op_definition = '∂⩏⊆a = { (≤/a) , if a<=92 ; (a⊦⊿) , else }', output=-4768","layer":1},{"info":"compute binary expreesion, left_input=19558, right_input=-4768, op_id = xlXykHWxX1 binary_op_definition= 'a⫢⨠b = { (((b⩨a)⪶≀⋏(a⩌⋺b))⩒⫫(∤(≉a))) }', output=160","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯113203≎⪠⪩⨒∯130330⫢⨠(∂⩏⊆⪩⨒∯120123)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⪩⨒∯113203≎⪠⪩⨒∯130330⫢⨠(∂⩏⊆⪩⨒∯120123)","cot":[{"info":"⪩⨒∯113203≎⪠⪩⨒∯130330=⪩⨒∯10301212","layer":1},{"info":"∂⩏⊆⪩⨒∯120123=⪩⨒∯-1022200","layer":1},{"info":"⪩⨒∯10301212⫢⨠⪩⨒∯-1022200=⪩⨒∯2200","layer":0}]}
{"id":452,"expression_no_base_symbol":"$1311$⨽$5260$⩵∡$4218$⨼⩣$4743$","expression":"⪩⨒∯110133⨽⪩⨒∯1102030⩵∡⪩⨒∯1001322⨼⩣⪩⨒∯1022013","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1705,"operation_count":3,"complexity_ratio":568.3333333333334,"tree":{"type":"binary","operator":"⩵∡","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1311,"base":4},"right_expr":{"type":"numeric_atoms","value":5260,"base":4}},"right_expr":{"type":"binary","operator":"⨼⩣","left_expr":{"type":"numeric_atoms","value":4218,"base":4},"right_expr":{"type":"numeric_atoms","value":4743,"base":4}}},"used_operators":["Y7wcNGrDQJ","8HhzD0ZcuI","JxwMv5le6e"],"dependent_operators":["NTOWxs364D","glklzrTFfD","tifHPKVTfV","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","uFcxV4UQCh","cHh1gJQ2o6","SL6IHkK8vl","KYD54nUTWz","pRsWfj4Fpp","CArV6hThFE"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1311","layer":2},{"info":"number node, value=5260","layer":2},{"info":"compute binary expreesion, left_input=1311, right_input=5260, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-5170629","layer":1},{"info":"number node, value=4218","layer":2},{"info":"number node, value=4743","layer":2},{"info":"compute binary expreesion, left_input=4218, right_input=4743, op_id = JxwMv5le6e binary_op_definition= 'a⨼⩣b = { ((∐⩳⋚(b⩘a))⪛((∡129)⫥∨⫟(a⫲⨊))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-5170629, right_input=nan, op_id = Y7wcNGrDQJ binary_op_definition= 'a⩵∡b = { ((b⇼⇔∾a)⩚⊴⇥(a⨁⊸⫻)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯110133⨽⪩⨒∯1102030⩵∡⪩⨒∯1001322⨼⩣⪩⨒∯1022013=NaN","reverse_text":"NaN=⪩⨒∯110133⨽⪩⨒∯1102030⩵∡⪩⨒∯1001322⨼⩣⪩⨒∯1022013","cot":[{"info":"⪩⨒∯110133⨽⪩⨒∯1102030=⪩⨒∯-103232113011","layer":1},{"info":"⪩⨒∯1001322⨼⩣⪩⨒∯1022013=NaN","layer":1},{"info":"⪩⨒∯-103232113011⩵∡NaN=NaN","layer":0}]}
{"id":453,"expression_no_base_symbol":"($2198$⇴∐$3415$)⨂≜($2813$≳⇉$1165$)","expression":"(⪩⨒∯202112⇴∐⪩⨒∯311113)⨂≜(⪩⨒∯223331≳⇉⪩⨒∯102031)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":19301679,"operation_count":3,"complexity_ratio":6433893.0,"tree":{"type":"binary","operator":"⨂≜","left_expr":{"type":"binary","operator":"⇴∐","left_expr":{"type":"numeric_atoms","value":2198,"base":4},"right_expr":{"type":"numeric_atoms","value":3415,"base":4}},"right_expr":{"type":"binary","operator":"≳⇉","left_expr":{"type":"numeric_atoms","value":2813,"base":4},"right_expr":{"type":"numeric_atoms","value":1165,"base":4}}},"used_operators":["k1SHOSEABc","HnzytWxmAO","V0kx6qeWkN"],"dependent_operators":["9FxExcQeMw","HiPekx5b7W","eLxqMNBOBk","JclMnS0uGI","COABgblf1C","U7g4x0WXJJ","2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ","KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2198","layer":2},{"info":"number node, value=3415","layer":2},{"info":"compute binary expreesion, left_input=2198, right_input=3415, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=nan","layer":1},{"info":"number node, value=2813","layer":2},{"info":"number node, value=1165","layer":2},{"info":"compute binary expreesion, left_input=2813, right_input=1165, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = k1SHOSEABc binary_op_definition= 'a⨂≜b = { ((37⊭↱(⫓⪴a))⩷∴((111⨜⨶78)⨔⇊(a∑⇟⊟b))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯202112⇴∐⪩⨒∯311113)⨂≜(⪩⨒∯223331≳⇉⪩⨒∯102031)=NaN","reverse_text":"NaN=(⪩⨒∯202112⇴∐⪩⨒∯311113)⨂≜(⪩⨒∯223331≳⇉⪩⨒∯102031)","cot":[{"info":"⪩⨒∯202112⇴∐⪩⨒∯311113=NaN","layer":1},{"info":"⪩⨒∯223331≳⇉⪩⨒∯102031=NaN","layer":1},{"info":"NaN⨂≜NaN=NaN","layer":0}]}
{"id":454,"expression_no_base_symbol":"($1222$⇷$1184$)⨥⫆($6249$⋷$2919$)","expression":"(⪩⨒∯103012⇷⪩⨒∯102200)⨥⫆(⪩⨒∯1201221⋷⪩⨒∯231213)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":17126,"operation_count":3,"complexity_ratio":5708.666666666667,"tree":{"type":"binary","operator":"⨥⫆","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":1222,"base":4},"right_expr":{"type":"numeric_atoms","value":1184,"base":4}},"right_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":6249,"base":4},"right_expr":{"type":"numeric_atoms","value":2919,"base":4}}},"used_operators":["yXekIHxTD4","mp7IySMOzn","23Mk6UjR3U"],"dependent_operators":["eRqsBgTDFp","ancx8kZcWl","oacrs7FA3X","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1222","layer":2},{"info":"number node, value=1184","layer":2},{"info":"compute binary expreesion, left_input=1222, right_input=1184, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=2368","layer":1},{"info":"number node, value=6249","layer":2},{"info":"number node, value=2919","layer":2},{"info":"compute binary expreesion, left_input=6249, right_input=2919, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-411","layer":1},{"info":"compute binary expreesion, left_input=2368, right_input=-411, op_id = yXekIHxTD4 binary_op_definition= 'a⨥⫆b = { (b⨝⩣∺) , if (a⪒⊣⊆344)<109 ; (b⪘⫢a) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯103012⇷⪩⨒∯102200)⨥⫆(⪩⨒∯1201221⋷⪩⨒∯231213)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯103012⇷⪩⨒∯102200)⨥⫆(⪩⨒∯1201221⋷⪩⨒∯231213)","cot":[{"info":"⪩⨒∯103012⇷⪩⨒∯102200=⪩⨒∯211000","layer":1},{"info":"⪩⨒∯1201221⋷⪩⨒∯231213=⪩⨒∯-12123","layer":1},{"info":"⪩⨒∯211000⨥⫆⪩⨒∯-12123=⪩⨒∯0","layer":0}]}
{"id":455,"expression_no_base_symbol":"($3933$⩷∴$2310$)⩅⪻⪻","expression":"(⪩⨒∯331131⩷∴⪩⨒∯210012)⩅⪻⪻","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":137,"operation_count":2,"complexity_ratio":68.5,"tree":{"type":"unary","operator":"⩅⪻⪻","unary_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":3933,"base":4},"right_expr":{"type":"numeric_atoms","value":2310,"base":4}}},"used_operators":["kHoXpA7yos","9FxExcQeMw"],"dependent_operators":["SUmda5xLS4","KPf6cnQVty","8HhzD0ZcuI","9Isq31Ruls","rysDP5nf3Z"],"result":"⪩⨒∯-1303333121","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3933","layer":2},{"info":"number node, value=2310","layer":2},{"info":"compute binary expreesion, left_input=3933, right_input=2310, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=3214","layer":1},{"info":"compute unary expreesion, input=3214, op_id = kHoXpA7yos, unary_op_definition = 'a⩅⪻⪻ = { (a⪄((a∌↝a)⨽(a∺≝⩲a))) }', output=-475097","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯331131⩷∴⪩⨒∯210012)⩅⪻⪻=⪩⨒∯-1303333121","reverse_text":"⪩⨒∯-1303333121=(⪩⨒∯331131⩷∴⪩⨒∯210012)⩅⪻⪻","cot":[{"info":"⪩⨒∯331131⩷∴⪩⨒∯210012=⪩⨒∯302032","layer":1},{"info":"⪩⨒∯302032⩅⪻⪻=⪩⨒∯-1303333121","layer":0}]}
{"id":456,"expression_no_base_symbol":"(⇈$4254$)⊔$1569$⨻⩈⩔$8926$","expression":"(⇈⪩⨒∯1002132)⊔⪩⨒∯120201⨻⩈⩔⪩⨒∯2023132","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1146,"operation_count":3,"complexity_ratio":382.0,"tree":{"type":"binary","operator":"⊔","left_expr":{"type":"unary","operator":"⇈","unary_expr":{"type":"numeric_atoms","value":4254,"base":4}},"right_expr":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"numeric_atoms","value":1569,"base":4},"right_expr":{"type":"numeric_atoms","value":8926,"base":4}}},"used_operators":["E4l6HwMY31","SLLxy00UIr","nEsXyWgiOK"],"dependent_operators":["W4YGzv6Whe","DpFCA1CohY","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","QMFrweE19q","Qy55tPpLXF","DZ8iAZOCBD","tifHPKVTfV","Tw270M8GLb","8HhzD0ZcuI","jCPkEVoL5K","ZcwmYACASQ","D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG"],"result":"⪩⨒∯3003303","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4254","layer":2},{"info":"compute unary expreesion, input=4254, op_id = SLLxy00UIr, unary_op_definition = '⇈a = { (((⨰⫟⨤60)⋥≓≎(a⫍⨯↯))⇻⋧≁((a⇼⇔∾a)⨽(323⊉≛↸a))) }', output=-447","layer":1},{"info":"number node, value=1569","layer":2},{"info":"number node, value=8926","layer":2},{"info":"compute binary expreesion, left_input=1569, right_input=8926, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=4151","layer":1},{"info":"compute binary expreesion, left_input=-447, right_input=4151, op_id = E4l6HwMY31 binary_op_definition= 'a⊔b = { (((a≧⫂∧b)∲⫓(⋗⩬⋾b))⫡⨏((b⪒a)≧⫂∧(a+64))) }', output=12531","layer":0}],"base":4,"result_base":4,"text":"(⇈⪩⨒∯1002132)⊔⪩⨒∯120201⨻⩈⩔⪩⨒∯2023132=⪩⨒∯3003303","reverse_text":"⪩⨒∯3003303=(⇈⪩⨒∯1002132)⊔⪩⨒∯120201⨻⩈⩔⪩⨒∯2023132","cot":[{"info":"⇈⪩⨒∯1002132=⪩⨒∯-12333","layer":1},{"info":"⪩⨒∯120201⨻⩈⩔⪩⨒∯2023132=⪩⨒∯1000313","layer":1},{"info":"⪩⨒∯-12333⊔⪩⨒∯1000313=⪩⨒∯3003303","layer":0}]}
{"id":457,"expression_no_base_symbol":"($2841$⫃⨇$4044$)⪪(↪⫪⫘$5911$)","expression":"(⪩⨒∯230121⫃⨇⪩⨒∯333030)⪪(↪⫪⫘⪩⨒∯1130113)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":632,"operation_count":3,"complexity_ratio":210.66666666666666,"tree":{"type":"binary","operator":"⪪","left_expr":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"numeric_atoms","value":2841,"base":4},"right_expr":{"type":"numeric_atoms","value":4044,"base":4}},"right_expr":{"type":"unary","operator":"↪⫪⫘","unary_expr":{"type":"numeric_atoms","value":5911,"base":4}}},"used_operators":["xD69zh8xqp","09Ly4LVMIf","9dWsAM3GFt"],"dependent_operators":["FU0Cs4j7VP","JclMnS0uGI","9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG","DyGG3AbaNP","nREPSIbpBE","rysDP5nf3Z"],"result":"⪩⨒∯-1200332","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2841","layer":2},{"info":"number node, value=4044","layer":2},{"info":"compute binary expreesion, left_input=2841, right_input=4044, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=-16208","layer":1},{"info":"number node, value=5911","layer":2},{"info":"compute unary expreesion, input=5911, op_id = 9dWsAM3GFt, unary_op_definition = '↪⫪⫘a = { ((a⨚283)∼(a-a)) }', output=20","layer":1},{"info":"compute binary expreesion, left_input=-16208, right_input=20, op_id = xD69zh8xqp binary_op_definition= 'a⪪b = { ((b⨔⇊a)↛⩡⫤) }', output=-6206","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯230121⫃⨇⪩⨒∯333030)⪪(↪⫪⫘⪩⨒∯1130113)=⪩⨒∯-1200332","reverse_text":"⪩⨒∯-1200332=(⪩⨒∯230121⫃⨇⪩⨒∯333030)⪪(↪⫪⫘⪩⨒∯1130113)","cot":[{"info":"⪩⨒∯230121⫃⨇⪩⨒∯333030=⪩⨒∯-3331100","layer":1},{"info":"↪⫪⫘⪩⨒∯1130113=⪩⨒∯110","layer":1},{"info":"⪩⨒∯-3331100⪪⪩⨒∯110=⪩⨒∯-1200332","layer":0}]}
{"id":458,"expression_no_base_symbol":"↽≂($2165$≬⋮$1032$)","expression":"↽≂(⪩⨒∯201311≬⋮⪩⨒∯100020)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16,"operation_count":2,"complexity_ratio":8.0,"tree":{"type":"unary","operator":"↽≂","unary_expr":{"type":"binary","operator":"≬⋮","left_expr":{"type":"numeric_atoms","value":2165,"base":4},"right_expr":{"type":"numeric_atoms","value":1032,"base":4}}},"used_operators":["u6S6b8DprG","kbkesczE7y"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","P8v4zCKN1o","rysDP5nf3Z","7j4O788W3g","XIabStNQrY","t8gj7n24qd","i8ToyICDmI"],"result":"⪩⨒∯-123020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2165","layer":2},{"info":"number node, value=1032","layer":2},{"info":"compute binary expreesion, left_input=2165, right_input=1032, op_id = kbkesczE7y binary_op_definition= 'a≬⋮b = { (((-a)∲⫓(b⇋≉))↺(∥⊫(b-b))) }', output=868","layer":1},{"info":"compute unary expreesion, input=868, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-1736","layer":0}],"base":4,"result_base":4,"text":"↽≂(⪩⨒∯201311≬⋮⪩⨒∯100020)=⪩⨒∯-123020","reverse_text":"⪩⨒∯-123020=↽≂(⪩⨒∯201311≬⋮⪩⨒∯100020)","cot":[{"info":"⪩⨒∯201311≬⋮⪩⨒∯100020=⪩⨒∯31210","layer":1},{"info":"↽≂⪩⨒∯31210=⪩⨒∯-123020","layer":0}]}
{"id":459,"expression_no_base_symbol":"$1830$⨸$9212$⩒⫫$5969$⫞⩸⩒$5371$","expression":"⪩⨒∯130212⨸⪩⨒∯2033330⩒⫫⪩⨒∯1131101⫞⩸⩒⪩⨒∯1103323","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1981,"operation_count":3,"complexity_ratio":660.3333333333334,"tree":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"binary","operator":"⨸","left_expr":{"type":"numeric_atoms","value":1830,"base":4},"right_expr":{"type":"numeric_atoms","value":9212,"base":4}},"right_expr":{"type":"binary","operator":"⫞⩸⩒","left_expr":{"type":"numeric_atoms","value":5969,"base":4},"right_expr":{"type":"numeric_atoms","value":5371,"base":4}}},"used_operators":["KFSx94NKJn","KmoU8R5UQR","XGcMNugi78"],"dependent_operators":["NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl","VJ330n2nnx","JclMnS0uGI","SWo3A1KBJH","rJVOvQCfKK"],"result":"⪩⨒∯310132","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1830","layer":2},{"info":"number node, value=9212","layer":2},{"info":"compute binary expreesion, left_input=1830, right_input=9212, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=3660","layer":1},{"info":"number node, value=5969","layer":2},{"info":"number node, value=5371","layer":2},{"info":"compute binary expreesion, left_input=5969, right_input=5371, op_id = XGcMNugi78 binary_op_definition= 'a⫞⩸⩒b = { (a⨎b) , if ((⇋↷b)>164 and (a↬⩅∪)<=12 and (b⨔⇊430)!=387) ; a , else }', output=5371","layer":1},{"info":"compute binary expreesion, left_input=3660, right_input=5371, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=3358","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯130212⨸⪩⨒∯2033330⩒⫫⪩⨒∯1131101⫞⩸⩒⪩⨒∯1103323=⪩⨒∯310132","reverse_text":"⪩⨒∯310132=⪩⨒∯130212⨸⪩⨒∯2033330⩒⫫⪩⨒∯1131101⫞⩸⩒⪩⨒∯1103323","cot":[{"info":"⪩⨒∯130212⨸⪩⨒∯2033330=⪩⨒∯321030","layer":1},{"info":"⪩⨒∯1131101⫞⩸⩒⪩⨒∯1103323=⪩⨒∯1103323","layer":1},{"info":"⪩⨒∯321030⩒⫫⪩⨒∯1103323=⪩⨒∯310132","layer":0}]}
{"id":460,"expression_no_base_symbol":"($1426$⇮⋭$1344$)⇴$1976$∌$4509$","expression":"(⪩⨒∯112102⇮⋭⪩⨒∯111000)⇴⪩⨒∯132320∌⪩⨒∯1012131","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":62,"operation_count":3,"complexity_ratio":20.666666666666668,"tree":{"type":"binary","operator":"⇴","left_expr":{"type":"binary","operator":"⇮⋭","left_expr":{"type":"numeric_atoms","value":1426,"base":4},"right_expr":{"type":"numeric_atoms","value":1344,"base":4}},"right_expr":{"type":"binary","operator":"∌","left_expr":{"type":"numeric_atoms","value":1976,"base":4},"right_expr":{"type":"numeric_atoms","value":4509,"base":4}}},"used_operators":["4JB6nKBMSY","vkpjKywKVM","8cLx32lpNA"],"dependent_operators":["sdazOOVcIp","NTOWxs364D","COABgblf1C","nhYeJWJD5X","U6pG0PXrV3","tifHPKVTfV","bJkvcejdHO","40aOVDgCDB","YbVcJGFEVW","N41Kp7NANJ","7j4O788W3g","t8gj7n24qd"],"result":"⪩⨒∯-2333102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1426","layer":2},{"info":"number node, value=1344","layer":2},{"info":"compute binary expreesion, left_input=1426, right_input=1344, op_id = vkpjKywKVM binary_op_definition= 'a⇮⋭b = { (((⊖b)⊢)≎⊠⪸((a≃b)⇼⇔∾(47∇⊂⋱106))) }', output=-473","layer":1},{"info":"number node, value=1976","layer":2},{"info":"number node, value=4509","layer":2},{"info":"compute binary expreesion, left_input=1976, right_input=4509, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-4509","layer":1},{"info":"compute binary expreesion, left_input=-473, right_input=-4509, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=-12242","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯112102⇮⋭⪩⨒∯111000)⇴⪩⨒∯132320∌⪩⨒∯1012131=⪩⨒∯-2333102","reverse_text":"⪩⨒∯-2333102=(⪩⨒∯112102⇮⋭⪩⨒∯111000)⇴⪩⨒∯132320∌⪩⨒∯1012131","cot":[{"info":"⪩⨒∯112102⇮⋭⪩⨒∯111000=⪩⨒∯-13121","layer":1},{"info":"⪩⨒∯132320∌⪩⨒∯1012131=⪩⨒∯-1012131","layer":1},{"info":"⪩⨒∯-13121⇴⪩⨒∯-1012131=⪩⨒∯-2333102","layer":0}]}
{"id":461,"expression_no_base_symbol":"($8649$⫡⨏$1585$)⩹$1069$≧⫂∧$1443$","expression":"(⪩⨒∯2013021⫡⨏⪩⨒∯120301)⩹⪩⨒∯100231≧⫂∧⪩⨒∯112203","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":21,"operation_count":3,"complexity_ratio":7.0,"tree":{"type":"binary","operator":"⩹","left_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":8649,"base":4},"right_expr":{"type":"numeric_atoms","value":1585,"base":4}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":1069,"base":4},"right_expr":{"type":"numeric_atoms","value":1443,"base":4}}},"used_operators":["2Wsdkap16l","QMFrweE19q","Ph9nP6C5qx"],"dependent_operators":["rysDP5nf3Z","NTOWxs364D","23Mk6UjR3U","XIabStNQrY","2DDjHMKMc0","12rbrZMWeM","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯33020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8649","layer":2},{"info":"number node, value=1585","layer":2},{"info":"compute binary expreesion, left_input=8649, right_input=1585, op_id = QMFrweE19q binary_op_definition= 'a⫡⨏b = { 497 , if (-b)==408 and (-a)>=56 ; (((a+783)+(a+a))+((b+a)+(a+b))) , else }', output=47198","layer":1},{"info":"number node, value=1069","layer":2},{"info":"number node, value=1443","layer":2},{"info":"compute binary expreesion, left_input=1069, right_input=1443, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=970","layer":1},{"info":"compute binary expreesion, left_input=47198, right_input=970, op_id = 2Wsdkap16l binary_op_definition= 'a⩹b = { (b-((b⨳⩥⨓b)⨸⪁(1⋝⋈⪟b))) , if (b⇋≉)!=246 ; (((a⇋≉)⨰(a⋷a))⋳⪒((a⩚⊴⇥a)⨳⩥⨓(a≧⫂∧a))) , else }', output=968","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2013021⫡⨏⪩⨒∯120301)⩹⪩⨒∯100231≧⫂∧⪩⨒∯112203=⪩⨒∯33020","reverse_text":"⪩⨒∯33020=(⪩⨒∯2013021⫡⨏⪩⨒∯120301)⩹⪩⨒∯100231≧⫂∧⪩⨒∯112203","cot":[{"info":"⪩⨒∯2013021⫡⨏⪩⨒∯120301=⪩⨒∯23201132","layer":1},{"info":"⪩⨒∯100231≧⫂∧⪩⨒∯112203=⪩⨒∯33022","layer":1},{"info":"⪩⨒∯23201132⩹⪩⨒∯33022=⪩⨒∯33020","layer":0}]}
{"id":462,"expression_no_base_symbol":"⪫⨮⊛(⊑$5240$)","expression":"⪫⨮⊛(⊑⪩⨒∯1101320)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":410,"operation_count":2,"complexity_ratio":205.0,"tree":{"type":"unary","operator":"⪫⨮⊛","unary_expr":{"type":"unary","operator":"⊑","unary_expr":{"type":"numeric_atoms","value":5240,"base":4}}},"used_operators":["w5FWba1tyO","IkUmn0D7oy"],"dependent_operators":["s3Fd5m9Dh2","RZ5CV9rWsJ","SUmda5xLS4","kn8WO9XteQ","hTbEZDJLEm","Tw270M8GLb","oRDoc9rAEX","AdZkA7nFnk","megm06wKyl"],"result":"⪩⨒∯3000","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5240","layer":2},{"info":"compute unary expreesion, input=5240, op_id = IkUmn0D7oy, unary_op_definition = '⊑a = { ((a⋅⇍254)⊋≦⊧(⨈⫕a)) }', output=192","layer":1},{"info":"compute unary expreesion, input=192, op_id = w5FWba1tyO, unary_op_definition = '⪫⨮⊛a = { a , if (a⨭⪣527)<=182 ; ((⨰⫟⨤(a⪄a))⩖⊿((a⊬⨰a)∟)) , else }', output=192","layer":0}],"base":4,"result_base":4,"text":"⪫⨮⊛(⊑⪩⨒∯1101320)=⪩⨒∯3000","reverse_text":"⪩⨒∯3000=⪫⨮⊛(⊑⪩⨒∯1101320)","cot":[{"info":"⊑⪩⨒∯1101320=⪩⨒∯3000","layer":1},{"info":"⪫⨮⊛⪩⨒∯3000=⪩⨒∯3000","layer":0}]}
{"id":463,"expression_no_base_symbol":"⋼∭⪍(≋$2438$)","expression":"⋼∭⪍(≋⪩⨒∯212012)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":13,"operation_count":2,"complexity_ratio":6.5,"tree":{"type":"unary","operator":"⋼∭⪍","unary_expr":{"type":"unary","operator":"≋","unary_expr":{"type":"numeric_atoms","value":2438,"base":4}}},"used_operators":["DbCuESL50I","61wBmkZwlr"],"dependent_operators":["e1ybzncUwg","sdazOOVcIp","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","u6S6b8DprG","7j4O788W3g"],"result":"⪩⨒∯-1331030","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2438","layer":2},{"info":"compute unary expreesion, input=2438, op_id = 61wBmkZwlr, unary_op_definition = '≋a = { (a↺a) }', output=2438","layer":1},{"info":"compute unary expreesion, input=2438, op_id = DbCuESL50I, unary_op_definition = '⋼∭⪍a = { (≉((a∲⫓a)⪨≂(a⪒a))) , if (↽≂a)>481 ; (↽≂((↽≂435)≧⫂∧(↽≂a))) , else }', output=-8012","layer":0}],"base":4,"result_base":4,"text":"⋼∭⪍(≋⪩⨒∯212012)=⪩⨒∯-1331030","reverse_text":"⪩⨒∯-1331030=⋼∭⪍(≋⪩⨒∯212012)","cot":[{"info":"≋⪩⨒∯212012=⪩⨒∯212012","layer":1},{"info":"⋼∭⪍⪩⨒∯212012=⪩⨒∯-1331030","layer":0}]}
{"id":464,"expression_no_base_symbol":"$5597$⊕∕$5410$↱$5599$⪕$2420$","expression":"⪩⨒∯1113131⊕∕⪩⨒∯1110202↱⪩⨒∯1113133⪕⪩⨒∯211310","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":58,"operation_count":3,"complexity_ratio":19.333333333333332,"tree":{"type":"binary","operator":"↱","left_expr":{"type":"binary","operator":"⊕∕","left_expr":{"type":"numeric_atoms","value":5597,"base":4},"right_expr":{"type":"numeric_atoms","value":5410,"base":4}},"right_expr":{"type":"binary","operator":"⪕","left_expr":{"type":"numeric_atoms","value":5599,"base":4},"right_expr":{"type":"numeric_atoms","value":2420,"base":4}}},"used_operators":["SR5kFfdi6N","9cloC0Ngie","umQnsF7QlU"],"dependent_operators":["k4iM1060OG","eOf03JbCpp","2GS7woTJqF","XnXgA4xnOs","ddLRYrp01A","Noe24qw2ks","bF6eod5Gvf","Nsiff2A1zJ","j9kHMeSvPp","pRsWfj4Fpp","apS25hmuAe","Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf","P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF"],"result":"⪩⨒∯-12331203","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5597","layer":2},{"info":"number node, value=5410","layer":2},{"info":"compute binary expreesion, left_input=5597, right_input=5410, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=5597","layer":1},{"info":"number node, value=5599","layer":2},{"info":"number node, value=2420","layer":2},{"info":"compute binary expreesion, left_input=5599, right_input=2420, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=9679","layer":1},{"info":"compute binary expreesion, left_input=5597, right_input=9679, op_id = SR5kFfdi6N binary_op_definition= 'a↱b = { ((≸a)⊴((b∊∟⩊b)⨐(a+⪬∐830))) , if (a==35 or (b∀⊥⇻)>46) ; ((≅≯⇸b)→⨶⪴((∡b)⪭(b⨑≵⋬499))) , else }', output=-28515","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1113131⊕∕⪩⨒∯1110202↱⪩⨒∯1113133⪕⪩⨒∯211310=⪩⨒∯-12331203","reverse_text":"⪩⨒∯-12331203=⪩⨒∯1113131⊕∕⪩⨒∯1110202↱⪩⨒∯1113133⪕⪩⨒∯211310","cot":[{"info":"⪩⨒∯1113131⊕∕⪩⨒∯1110202=⪩⨒∯1113131","layer":1},{"info":"⪩⨒∯1113133⪕⪩⨒∯211310=⪩⨒∯2113033","layer":1},{"info":"⪩⨒∯1113131↱⪩⨒∯2113033=⪩⨒∯-12331203","layer":0}]}
{"id":465,"expression_no_base_symbol":"(⊥$5591$)⨻⩈⩔$1698$⪥$2249$","expression":"(⊥⪩⨒∯1113113)⨻⩈⩔⪩⨒∯122202⪥⪩⨒∯203021","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":113,"operation_count":3,"complexity_ratio":37.666666666666664,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":5591,"base":4}},"right_expr":{"type":"binary","operator":"⪥","left_expr":{"type":"numeric_atoms","value":1698,"base":4},"right_expr":{"type":"numeric_atoms","value":2249,"base":4}}},"used_operators":["nEsXyWgiOK","Q3PJZHRvZv","QbnwKVWMIQ"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","fu6greOZ01","WR6HLWljOP","nhYeJWJD5X","f6k1SAg4EE","jLgFTUHLKL","PPChnnnBFF"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5591","layer":2},{"info":"compute unary expreesion, input=5591, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"number node, value=1698","layer":2},{"info":"number node, value=2249","layer":2},{"info":"compute binary expreesion, left_input=1698, right_input=2249, op_id = QbnwKVWMIQ binary_op_definition= 'a⪥b = { (b∇⊂⋱(58∣a)) , if (b↢721)<125 ; (↩(508⪒a)) , else }', output=11444","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=11444, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⊥⪩⨒∯1113113)⨻⩈⩔⪩⨒∯122202⪥⪩⨒∯203021=NaN","reverse_text":"NaN=(⊥⪩⨒∯1113113)⨻⩈⩔⪩⨒∯122202⪥⪩⨒∯203021","cot":[{"info":"⊥⪩⨒∯1113113=NaN","layer":1},{"info":"⪩⨒∯122202⪥⪩⨒∯203021=⪩⨒∯2302310","layer":1},{"info":"NaN⨻⩈⩔⪩⨒∯2302310=NaN","layer":0}]}
{"id":466,"expression_no_base_symbol":"≸($1113$⫦⪉$8363$)","expression":"≸(⪩⨒∯101121⫦⪉⪩⨒∯2002223)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":82,"operation_count":2,"complexity_ratio":41.0,"tree":{"type":"unary","operator":"≸","unary_expr":{"type":"binary","operator":"⫦⪉","left_expr":{"type":"numeric_atoms","value":1113,"base":4},"right_expr":{"type":"numeric_atoms","value":8363,"base":4}}},"used_operators":["eOf03JbCpp","wscyQdcy20"],"dependent_operators":["WmT3o8z6ya","l07mrZUIn9","NTOWxs364D","RygbFNSyEJ","tifHPKVTfV","oRDoc9rAEX","IwW236VD4Y","1aApVXNlOP","Z5m6OM72h2","mqXw5SEYmG","IWmyXbctLI","W4YGzv6Whe","B3sABdIn96","9HNa5Wba9A","g7Hmc5v1ko","nREPSIbpBE","D3AQDKkPcf"],"result":"⪩⨒∯322","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1113","layer":2},{"info":"number node, value=8363","layer":2},{"info":"compute binary expreesion, left_input=1113, right_input=8363, op_id = wscyQdcy20 binary_op_definition= 'a⫦⪉b = { ((a⩌⋺206)⪹) , if (a∷677)>=23 ; ((b+a)*(b⨚b)) , else }', output=2674","layer":1},{"info":"compute unary expreesion, input=2674, op_id = eOf03JbCpp, unary_op_definition = '≸a = { (29∘((630⊋≦⊧a)⩚⊴⇥(a≦↸a))) , if (a⋘⨑⨽)>2 ; (((a⪮%⊝a)⇼⇔∾(a↪⪝))⫸⊐((a⪮%⊝a)≠≀(3⩇∃⫛a))) , else }', output=58","layer":0}],"base":4,"result_base":4,"text":"≸(⪩⨒∯101121⫦⪉⪩⨒∯2002223)=⪩⨒∯322","reverse_text":"⪩⨒∯322=≸(⪩⨒∯101121⫦⪉⪩⨒∯2002223)","cot":[{"info":"⪩⨒∯101121⫦⪉⪩⨒∯2002223=⪩⨒∯221302","layer":1},{"info":"≸⪩⨒∯221302=⪩⨒∯322","layer":0}]}
{"id":467,"expression_no_base_symbol":"$1314$⋛$9780$⪍↜⋙$5294$∛$1423$","expression":"⪩⨒∯110202⋛⪩⨒∯2120310⪍↜⋙⪩⨒∯1102232∛⪩⨒∯112033","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":352,"operation_count":3,"complexity_ratio":117.33333333333333,"tree":{"type":"binary","operator":"⪍↜⋙","left_expr":{"type":"binary","operator":"⋛","left_expr":{"type":"numeric_atoms","value":1314,"base":4},"right_expr":{"type":"numeric_atoms","value":9780,"base":4}},"right_expr":{"type":"binary","operator":"∛","left_expr":{"type":"numeric_atoms","value":5294,"base":4},"right_expr":{"type":"numeric_atoms","value":1423,"base":4}}},"used_operators":["L05ObWFQCd","YbUVn0Rbpy","w2537kitQq"],"dependent_operators":["rysDP5nf3Z","DZ8iAZOCBD","tifHPKVTfV","EBcxylXtPf","QMFrweE19q","d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA","DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc"],"result":"⪩⨒∯2102231101","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1314","layer":2},{"info":"number node, value=9780","layer":2},{"info":"compute binary expreesion, left_input=1314, right_input=9780, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-120366","layer":1},{"info":"number node, value=5294","layer":2},{"info":"number node, value=1423","layer":2},{"info":"compute binary expreesion, left_input=5294, right_input=1423, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=67","layer":1},{"info":"compute binary expreesion, left_input=-120366, right_input=67, op_id = L05ObWFQCd binary_op_definition= 'a⪍↜⋙b = { ((a-b)⊉≛↸(a⫡⨏b)) , if (a⫌⩹⨱)!=88 ; ((a⫡⨏b)⇼⇔∾(a⫌⩹⨱)) , else }', output=600913","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯110202⋛⪩⨒∯2120310⪍↜⋙⪩⨒∯1102232∛⪩⨒∯112033=⪩⨒∯2102231101","reverse_text":"⪩⨒∯2102231101=⪩⨒∯110202⋛⪩⨒∯2120310⪍↜⋙⪩⨒∯1102232∛⪩⨒∯112033","cot":[{"info":"⪩⨒∯110202⋛⪩⨒∯2120310=⪩⨒∯-131120232","layer":1},{"info":"⪩⨒∯1102232∛⪩⨒∯112033=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯-131120232⪍↜⋙⪩⨒∯1003=⪩⨒∯2102231101","layer":0}]}
{"id":468,"expression_no_base_symbol":"($2879$⪚⩙≫)⫚↹⊑(⩰$1123$)","expression":"(⪩⨒∯230333⪚⩙≫)⫚↹⊑(⩰⪩⨒∯101203)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":38,"operation_count":3,"complexity_ratio":12.666666666666666,"tree":{"type":"binary","operator":"⫚↹⊑","left_expr":{"type":"unary","operator":"⪚⩙≫","unary_expr":{"type":"numeric_atoms","value":2879,"base":4}},"right_expr":{"type":"unary","operator":"⩰","unary_expr":{"type":"numeric_atoms","value":1123,"base":4}}},"used_operators":["dfKe02y8D2","4n53wtyJvv","WkeUrDK8WX"],"dependent_operators":["2DQ55sFlQl","DIvbN7qnHd","t8gj7n24qd","12rbrZMWeM","g55IO6H4Gj","Uaa54Peajs","nCS4ZIUYfx","WR6HLWljOP","W4YGzv6Whe","xUOZtlo3hN","Z2TMIBDE3Q","g55IO6H4Gj","i8ToyICDmI"],"result":"⪩⨒∯-12333","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2879","layer":2},{"info":"compute unary expreesion, input=2879, op_id = 4n53wtyJvv, unary_op_definition = 'a⪚⩙≫ = { ((316↢a)⨳⩥⨓(∂255)) }', output=nan","layer":1},{"info":"number node, value=1123","layer":2},{"info":"compute unary expreesion, input=1123, op_id = WkeUrDK8WX, unary_op_definition = '⩰a = { (((a⨸⪁500)⩤)+(a∲⫓(⨞⊢a))) }', output=-2123","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-2123, op_id = dfKe02y8D2 binary_op_definition= 'a⫚↹⊑b = { ((126⊠≄⫣)⋳⪒((-b)⨵⪆(a⨸⪁b))) }', output=-447","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯230333⪚⩙≫)⫚↹⊑(⩰⪩⨒∯101203)=⪩⨒∯-12333","reverse_text":"⪩⨒∯-12333=(⪩⨒∯230333⪚⩙≫)⫚↹⊑(⩰⪩⨒∯101203)","cot":[{"info":"⪩⨒∯230333⪚⩙≫=NaN","layer":1},{"info":"⩰⪩⨒∯101203=⪩⨒∯-201023","layer":1},{"info":"NaN⫚↹⊑⪩⨒∯-201023=⪩⨒∯-12333","layer":0}]}
{"id":469,"expression_no_base_symbol":"∜⨇($1789$⫸⇳$3723$)","expression":"∜⨇(⪩⨒∯123331⫸⇳⪩⨒∯322023)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":64,"operation_count":2,"complexity_ratio":32.0,"tree":{"type":"unary","operator":"∜⨇","unary_expr":{"type":"binary","operator":"⫸⇳","left_expr":{"type":"numeric_atoms","value":1789,"base":4},"right_expr":{"type":"numeric_atoms","value":3723,"base":4}}},"used_operators":["uFPyJr306J","gx7XJ7hdpj"],"dependent_operators":["fG6uBQFnGz","pRsWfj4Fpp","rGHVDoGpnC","Y7wcNGrDQJ","NNaDxxp6OQ","DpFCA1CohY","7j4O788W3g","tifHPKVTfV","2DQ55sFlQl","DIvbN7qnHd","12rbrZMWeM","t8gj7n24qd","14qkJME0vr","g55IO6H4Gj","eewbuw0ToL"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1789","layer":2},{"info":"number node, value=3723","layer":2},{"info":"compute binary expreesion, left_input=1789, right_input=3723, op_id = gx7XJ7hdpj binary_op_definition= 'a⫸⇳b = { (((494⋳⪒b)⇼⇔∾(⋗⩬⋾a))↺((b⊦⊿)⨸⪁(b⨵⪆b))) , if a==116 ; (-((a⨰a)⊠≄⫣)) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = uFPyJr306J, unary_op_definition = '∜⨇a = { (a⨟⋌⩍a) , if (a⫽⇹≛)!=2 or (↩⪖a)==528 or (∡a)>=548 ; (132⩵∡a) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"∜⨇(⪩⨒∯123331⫸⇳⪩⨒∯322023)=⪩⨒∯0","reverse_text":"⪩⨒∯0=∜⨇(⪩⨒∯123331⫸⇳⪩⨒∯322023)","cot":[{"info":"⪩⨒∯123331⫸⇳⪩⨒∯322023=⪩⨒∯0","layer":1},{"info":"∜⨇⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":470,"expression_no_base_symbol":"(⨣⨃⇪$4314$)⊹≧⊝","expression":"(⨣⨃⇪⪩⨒∯1003122)⊹≧⊝","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":35,"operation_count":2,"complexity_ratio":17.5,"tree":{"type":"unary","operator":"⊹≧⊝","unary_expr":{"type":"unary","operator":"⨣⨃⇪","unary_expr":{"type":"numeric_atoms","value":4314,"base":4}}},"used_operators":["LxFB4K6j0n","AcOhelriW5"],"dependent_operators":["NTOWxs364D","P8v4zCKN1o","XPYlsWDdGa","DZ8iAZOCBD","t8gj7n24qd","g55IO6H4Gj","eewbuw0ToL","i8ToyICDmI","COABgblf1C","s3Fd5m9Dh2","liw5iZPkLH","yyfyN0ffXY"],"result":"⪩⨒∯-1113310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4314","layer":2},{"info":"compute unary expreesion, input=4314, op_id = AcOhelriW5, unary_op_definition = '⨣⨃⇪a = { (⨡↴(172⊬⨰(3↙a))) }', output=1405","layer":1},{"info":"compute unary expreesion, input=1405, op_id = LxFB4K6j0n, unary_op_definition = 'a⊹≧⊝ = { (((∥⊫a)⊭↱(a⩚⊴⇥a))⊉≛↸(⪲⇎(⪲⇎a))) , if a!=566 ; (-((a∲⫓a)⨸⪁(a⨰a))) , else }', output=-5620","layer":0}],"base":4,"result_base":4,"text":"(⨣⨃⇪⪩⨒∯1003122)⊹≧⊝=⪩⨒∯-1113310","reverse_text":"⪩⨒∯-1113310=(⨣⨃⇪⪩⨒∯1003122)⊹≧⊝","cot":[{"info":"⨣⨃⇪⪩⨒∯1003122=⪩⨒∯111331","layer":1},{"info":"⪩⨒∯111331⊹≧⊝=⪩⨒∯-1113310","layer":0}]}
{"id":471,"expression_no_base_symbol":"($1695$⊭↱$1441$)⊦⊿","expression":"(⪩⨒∯122133⊭↱⪩⨒∯112201)⊦⊿","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":12,"operation_count":2,"complexity_ratio":6.0,"tree":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":1695,"base":4},"right_expr":{"type":"numeric_atoms","value":1441,"base":4}}},"used_operators":["14qkJME0vr","COABgblf1C"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯112112","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1695","layer":2},{"info":"number node, value=1441","layer":2},{"info":"compute binary expreesion, left_input=1695, right_input=1441, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-503","layer":1},{"info":"compute unary expreesion, input=-503, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=1430","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯122133⊭↱⪩⨒∯112201)⊦⊿=⪩⨒∯112112","reverse_text":"⪩⨒∯112112=(⪩⨒∯122133⊭↱⪩⨒∯112201)⊦⊿","cot":[{"info":"⪩⨒∯122133⊭↱⪩⨒∯112201=⪩⨒∯-13313","layer":1},{"info":"⪩⨒∯-13313⊦⊿=⪩⨒∯112112","layer":0}]}
{"id":472,"expression_no_base_symbol":"($7334$⫚↹⊑$3353$)⇣⩺⋵($4445$⊭↱$1679$)","expression":"(⪩⨒∯1302212⫚↹⊑⪩⨒∯310121)⇣⩺⋵(⪩⨒∯1011131⊭↱⪩⨒∯122033)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":78,"operation_count":3,"complexity_ratio":26.0,"tree":{"type":"binary","operator":"⇣⩺⋵","left_expr":{"type":"binary","operator":"⫚↹⊑","left_expr":{"type":"numeric_atoms","value":7334,"base":4},"right_expr":{"type":"numeric_atoms","value":3353,"base":4}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":4445,"base":4},"right_expr":{"type":"numeric_atoms","value":1679,"base":4}}},"used_operators":["F4yD0voBRQ","dfKe02y8D2","COABgblf1C"],"dependent_operators":["NTOWxs364D","KPf6cnQVty","8jW3W4yZS5","12rbrZMWeM","g55IO6H4Gj","2DlMacCsIx","2DQ55sFlQl","DIvbN7qnHd","t8gj7n24qd","12rbrZMWeM","g55IO6H4Gj","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-10010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7334","layer":2},{"info":"number node, value=3353","layer":2},{"info":"compute binary expreesion, left_input=7334, right_input=3353, op_id = dfKe02y8D2 binary_op_definition= 'a⫚↹⊑b = { ((126⊠≄⫣)⋳⪒((-b)⨵⪆(a⨸⪁b))) }', output=-447","layer":1},{"info":"number node, value=4445","layer":2},{"info":"number node, value=1679","layer":2},{"info":"compute binary expreesion, left_input=4445, right_input=1679, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-5527","layer":1},{"info":"compute binary expreesion, left_input=-447, right_input=-5527, op_id = F4yD0voBRQ binary_op_definition= 'a⇣⩺⋵b = { (((a⩨565)∺≝⩲(5⨸⪁a))⩚⊴⇥(↯⪼(a⋳⪒b))) }', output=-260","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1302212⫚↹⊑⪩⨒∯310121)⇣⩺⋵(⪩⨒∯1011131⊭↱⪩⨒∯122033)=⪩⨒∯-10010","reverse_text":"⪩⨒∯-10010=(⪩⨒∯1302212⫚↹⊑⪩⨒∯310121)⇣⩺⋵(⪩⨒∯1011131⊭↱⪩⨒∯122033)","cot":[{"info":"⪩⨒∯1302212⫚↹⊑⪩⨒∯310121=⪩⨒∯-12333","layer":1},{"info":"⪩⨒∯1011131⊭↱⪩⨒∯122033=⪩⨒∯-1112113","layer":1},{"info":"⪩⨒∯-12333⇣⩺⋵⪩⨒∯-1112113=⪩⨒∯-10010","layer":0}]}
{"id":473,"expression_no_base_symbol":"($2971$∴≳≥)≬⇓(⊬↢$3484$)","expression":"(⪩⨒∯232123∴≳≥)≬⇓(⊬↢⪩⨒∯312130)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3543,"operation_count":3,"complexity_ratio":1181.0,"tree":{"type":"binary","operator":"≬⇓","left_expr":{"type":"unary","operator":"∴≳≥","unary_expr":{"type":"numeric_atoms","value":2971,"base":4}},"right_expr":{"type":"unary","operator":"⊬↢","unary_expr":{"type":"numeric_atoms","value":3484,"base":4}}},"used_operators":["jWTQ2TZYIH","a3N2hFLK0J","WPoGxAaPR1"],"dependent_operators":["AdZkA7nFnk","zVYPLywUTj","XTarYq4gQB","g55IO6H4Gj","DpFCA1CohY","xUOZtlo3hN","XGcMNugi78","d7ASUq0ydm","OwUj7dcsQK","FyVja0WsTP","1eCjFl0mb9","j6NVkjMzuk","SL6IHkK8vl","MRPaB8lBjK","yyfyN0ffXY","3Oe9XWJUTD","3tVxb0NHM4","8cLx32lpNA"],"result":"⪩⨒∯-112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2971","layer":2},{"info":"compute unary expreesion, input=2971, op_id = a3N2hFLK0J, unary_op_definition = 'a∴≳≥ = { (⨞⊢a) , if (⋗⩬⋾a)==641 ; (a⨸⪁a) , else }', output=11884","layer":1},{"info":"number node, value=3484","layer":2},{"info":"compute unary expreesion, input=3484, op_id = WPoGxAaPR1, unary_op_definition = '⊬↢a = { (((a⫞⩸⩒a)⊝⪿⪼(a⫯⪬∳a))⪎↠((a⨀⨒)↸(∐⩳⋚a))) , if (∓a)>278 ; (((a↙a)⊱⇼⊻(a∌480))⇉⇱⇎) , else }', output=218","layer":1},{"info":"compute binary expreesion, left_input=11884, right_input=218, op_id = jWTQ2TZYIH binary_op_definition= 'a≬⇓b = { (a⊪) , if a<=154 or (⪝⪂⫅a)>=41 ; (a⋅⇍b) , else }', output=-22","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯232123∴≳≥)≬⇓(⊬↢⪩⨒∯312130)=⪩⨒∯-112","reverse_text":"⪩⨒∯-112=(⪩⨒∯232123∴≳≥)≬⇓(⊬↢⪩⨒∯312130)","cot":[{"info":"⪩⨒∯232123∴≳≥=⪩⨒∯2321230","layer":1},{"info":"⊬↢⪩⨒∯312130=⪩⨒∯3122","layer":1},{"info":"⪩⨒∯2321230≬⇓⪩⨒∯3122=⪩⨒∯-112","layer":0}]}
{"id":474,"expression_no_base_symbol":"($7290$⩘⨬⇊)∙∹∝($1892$⫳≱↱$2400$)","expression":"(⪩⨒∯1301322⩘⨬⇊)∙∹∝(⪩⨒∯131210⫳≱↱⪩⨒∯211200)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2434,"operation_count":3,"complexity_ratio":811.3333333333334,"tree":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"unary","operator":"⩘⨬⇊","unary_expr":{"type":"numeric_atoms","value":7290,"base":4}},"right_expr":{"type":"binary","operator":"⫳≱↱","left_expr":{"type":"numeric_atoms","value":1892,"base":4},"right_expr":{"type":"numeric_atoms","value":2400,"base":4}}},"used_operators":["HmxsFra2vL","XXmTpEpWTW","ZvLB05nZmT"],"dependent_operators":["BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","rxpJgHHUmx","HnzytWxmAO","8cLx32lpNA","2Wsdkap16l","FyVja0WsTP","wEfv7U73WA","bJkvcejdHO","HmxsFra2vL","8cLx32lpNA"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7290","layer":2},{"info":"compute unary expreesion, input=7290, op_id = XXmTpEpWTW, unary_op_definition = 'a⩘⨬⇊ = { ((a⇴∐a)∌(a≭31)) }', output=nan","layer":1},{"info":"number node, value=1892","layer":2},{"info":"number node, value=2400","layer":2},{"info":"compute binary expreesion, left_input=1892, right_input=2400, op_id = ZvLB05nZmT binary_op_definition= 'a⫳≱↱b = { (((a⩹b)⇐≅)∌((a∙∹∝345)⊱⇼⊻(b≎⊠⪸a))) }', output=-204","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-204, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1301322⩘⨬⇊)∙∹∝(⪩⨒∯131210⫳≱↱⪩⨒∯211200)=NaN","reverse_text":"NaN=(⪩⨒∯1301322⩘⨬⇊)∙∹∝(⪩⨒∯131210⫳≱↱⪩⨒∯211200)","cot":[{"info":"⪩⨒∯1301322⩘⨬⇊=NaN","layer":1},{"info":"⪩⨒∯131210⫳≱↱⪩⨒∯211200=⪩⨒∯-3030","layer":1},{"info":"NaN∙∹∝⪩⨒∯-3030=NaN","layer":0}]}
{"id":475,"expression_no_base_symbol":"($1358$≦≮≮)*$1137$∓⋝$2883$","expression":"(⪩⨒∯111032≦≮≮)*⪩⨒∯101301∓⋝⪩⨒∯231003","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":107,"operation_count":3,"complexity_ratio":35.666666666666664,"tree":{"type":"binary","operator":"*","left_expr":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":1358,"base":4}},"right_expr":{"type":"binary","operator":"∓⋝","left_expr":{"type":"numeric_atoms","value":1137,"base":4},"right_expr":{"type":"numeric_atoms","value":2883,"base":4}}},"used_operators":["9HNa5Wba9A","D4vGDi5EA2","PoHhknlbAi"],"dependent_operators":["W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd","DZ8iAZOCBD","DbCuESL50I","mqXw5SEYmG","2MzE1hQ0cz"],"result":"⪩⨒∯-1002220332","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1358","layer":2},{"info":"compute unary expreesion, input=1358, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-4074","layer":1},{"info":"number node, value=1137","layer":2},{"info":"number node, value=2883","layer":2},{"info":"compute binary expreesion, left_input=1137, right_input=2883, op_id = PoHhknlbAi binary_op_definition= 'a∓⋝b = { (((a⊉≛↸a)⫸⊐(⋼∭⪍b))∩⋅) }', output=67","layer":1},{"info":"compute binary expreesion, left_input=-4074, right_input=67, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=-272958","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯111032≦≮≮)*⪩⨒∯101301∓⋝⪩⨒∯231003=⪩⨒∯-1002220332","reverse_text":"⪩⨒∯-1002220332=(⪩⨒∯111032≦≮≮)*⪩⨒∯101301∓⋝⪩⨒∯231003","cot":[{"info":"⪩⨒∯111032≦≮≮=⪩⨒∯-333222","layer":1},{"info":"⪩⨒∯101301∓⋝⪩⨒∯231003=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯-333222*⪩⨒∯1003=⪩⨒∯-1002220332","layer":0}]}
{"id":476,"expression_no_base_symbol":"$1441$⫗⊷⫓$6270$⨎$3048$≌$3657$","expression":"⪩⨒∯112201⫗⊷⫓⪩⨒∯1201332⨎⪩⨒∯233220≌⪩⨒∯321021","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4435,"operation_count":3,"complexity_ratio":1478.3333333333333,"tree":{"type":"binary","operator":"⨎","left_expr":{"type":"binary","operator":"⫗⊷⫓","left_expr":{"type":"numeric_atoms","value":1441,"base":4},"right_expr":{"type":"numeric_atoms","value":6270,"base":4}},"right_expr":{"type":"binary","operator":"≌","left_expr":{"type":"numeric_atoms","value":3048,"base":4},"right_expr":{"type":"numeric_atoms","value":3657,"base":4}}},"used_operators":["rJVOvQCfKK","zashukvMKz","lyWz822IDG"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","xD69zh8xqp","Uaa54Peajs","BjRHVeLaeN","QiR2Oyf5Xj","k1SHOSEABc","Asc51vEJeQ","oRDoc9rAEX","bJkvcejdHO","8INZBEW696","Af076pWI7l","B5M0gjZbta","W7eaUhjymW","CpSg5vQTgA","w2P8NbNXyL","0kmYd0q39Y","3sJ7IOPOlU","Bmrmz2XGnR","WkeUrDK8WX","03sUfWo75k","5twsqlHp2o","oacrs7FA3X","aMUSaJuDRU"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1441","layer":2},{"info":"number node, value=6270","layer":2},{"info":"compute binary expreesion, left_input=1441, right_input=6270, op_id = zashukvMKz binary_op_definition= 'a⫗⊷⫓b = { ((∂(b⨂≜a))⫩⊇) , if (↣≠⋷b)<=196 ; ((∷≠(a⊋≦⊧b))↓((b≎⊠⪸a)⪪(a≀⩗∶b))) , else }', output=-134","layer":1},{"info":"number node, value=3048","layer":2},{"info":"number node, value=3657","layer":2},{"info":"compute binary expreesion, left_input=3048, right_input=3657, op_id = lyWz822IDG binary_op_definition= 'a≌b = { (≛((132⩦9)⊉↱≁(a⪇≇⋚a))) , if (a⪘⫢419)==234 ; (((⩰124)≚⊃≕(b⨴∎))⊢((16⨉)↬(a⊟⇱))) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-134, right_input=nan, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯112201⫗⊷⫓⪩⨒∯1201332⨎⪩⨒∯233220≌⪩⨒∯321021=NaN","reverse_text":"NaN=⪩⨒∯112201⫗⊷⫓⪩⨒∯1201332⨎⪩⨒∯233220≌⪩⨒∯321021","cot":[{"info":"⪩⨒∯112201⫗⊷⫓⪩⨒∯1201332=⪩⨒∯-2012","layer":1},{"info":"⪩⨒∯233220≌⪩⨒∯321021=NaN","layer":1},{"info":"⪩⨒∯-2012⨎NaN=NaN","layer":0}]}
{"id":477,"expression_no_base_symbol":"($6176$⊍⩺⋍$4109$)⋭≵(⨰⫟⨤$1124$)","expression":"(⪩⨒∯1200200⊍⩺⋍⪩⨒∯1000031)⋭≵(⨰⫟⨤⪩⨒∯101210)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3903,"operation_count":3,"complexity_ratio":1301.0,"tree":{"type":"binary","operator":"⋭≵","left_expr":{"type":"binary","operator":"⊍⩺⋍","left_expr":{"type":"numeric_atoms","value":6176,"base":4},"right_expr":{"type":"numeric_atoms","value":4109,"base":4}},"right_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":1124,"base":4}}},"used_operators":["jBncVCNhdl","OXDGMFPWZM","Tw270M8GLb"],"dependent_operators":["RygbFNSyEJ","gx7XJ7hdpj","9ICcGScMcE","C6VvDP6HwP","mqXw5SEYmG","7IPrd9c3lf","COABgblf1C","kn8WO9XteQ","inkyxCbjAn","13rbtpv6ld","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6176","layer":2},{"info":"number node, value=4109","layer":2},{"info":"compute binary expreesion, left_input=6176, right_input=4109, op_id = OXDGMFPWZM binary_op_definition= 'a⊍⩺⋍b = { ((⇁⨣⪵659)↤⩊(b⨭⪣a)) }', output=nan","layer":1},{"info":"number node, value=1124","layer":2},{"info":"compute unary expreesion, input=1124, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = jBncVCNhdl binary_op_definition= 'a⋭≵b = { ((156≦↸a)⊭↱(≦∁b)) , if (b⫸⊐434)<=441 and (a⫸⇳180)>=132 ; ((a⪑⩈)⊵↤) , else }', output=67","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1200200⊍⩺⋍⪩⨒∯1000031)⋭≵(⨰⫟⨤⪩⨒∯101210)=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=(⪩⨒∯1200200⊍⩺⋍⪩⨒∯1000031)⋭≵(⨰⫟⨤⪩⨒∯101210)","cot":[{"info":"⪩⨒∯1200200⊍⩺⋍⪩⨒∯1000031=NaN","layer":1},{"info":"⨰⫟⨤⪩⨒∯101210=NaN","layer":1},{"info":"NaN⋭≵NaN=⪩⨒∯1003","layer":0}]}
{"id":478,"expression_no_base_symbol":"⨭⩧⫛(⊊≼∋$1864$)","expression":"⨭⩧⫛(⊊≼∋⪩⨒∯131020)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":201711,"operation_count":2,"complexity_ratio":100855.5,"tree":{"type":"unary","operator":"⨭⩧⫛","unary_expr":{"type":"unary","operator":"⊊≼∋","unary_expr":{"type":"numeric_atoms","value":1864,"base":4}}},"used_operators":["g21JL6JxX7","FWz7pXsQhA"],"dependent_operators":["Ikt5ks8PT7","Asc51vEJeQ","A8NUZmVepG","B5M0gjZbta","jCPkEVoL5K"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1864","layer":2},{"info":"compute unary expreesion, input=1864, op_id = FWz7pXsQhA, unary_op_definition = '⊊≼∋a = { (a↬a) , if a<=50 ; (a⇻⋧≁a) , else }', output=-447","layer":1},{"info":"compute unary expreesion, input=-447, op_id = g21JL6JxX7, unary_op_definition = '⨭⩧⫛a = { ((↥a)⩧⪆(↣≠⋷a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⨭⩧⫛(⊊≼∋⪩⨒∯131020)=NaN","reverse_text":"NaN=⨭⩧⫛(⊊≼∋⪩⨒∯131020)","cot":[{"info":"⊊≼∋⪩⨒∯131020=⪩⨒∯-12333","layer":1},{"info":"⨭⩧⫛⪩⨒∯-12333=NaN","layer":0}]}
{"id":479,"expression_no_base_symbol":"$2024$⊋$1835$⪒(↩⪖$1358$)","expression":"⪩⨒∯133220⊋⪩⨒∯130223⪒(↩⪖⪩⨒∯111032)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":508,"operation_count":3,"complexity_ratio":169.33333333333334,"tree":{"type":"binary","operator":"⪒","left_expr":{"type":"binary","operator":"⊋","left_expr":{"type":"numeric_atoms","value":2024,"base":4},"right_expr":{"type":"numeric_atoms","value":1835,"base":4}},"right_expr":{"type":"unary","operator":"↩⪖","unary_expr":{"type":"numeric_atoms","value":1358,"base":4}}},"used_operators":["f6k1SAg4EE","W4tP9CfskL","fG6uBQFnGz"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu","rysDP5nf3Z","DpFCA1CohY","e1ybzncUwg","XIabStNQrY","eH2TOUuTDT","2DQ55sFlQl","Ph9nP6C5qx","Z2TMIBDE3Q","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"⪩⨒∯-30022211112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2024","layer":2},{"info":"number node, value=1835","layer":2},{"info":"compute binary expreesion, left_input=2024, right_input=1835, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=3200208","layer":1},{"info":"number node, value=1358","layer":2},{"info":"compute unary expreesion, input=1358, op_id = fG6uBQFnGz, unary_op_definition = '↩⪖a = { (((a-a)⨵⪆(a⪐))⫡⨏(a⩤)) , if (a⇋≉)==322 ; (((≉487)⨳⩥⨓(⋗⩬⋾a))⨸⪁((a⊦⊿)≧⫂∧(a∲⫓a))) , else }', output=-11130","layer":1},{"info":"compute binary expreesion, left_input=3200208, right_input=-11130, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-3189078","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯133220⊋⪩⨒∯130223⪒(↩⪖⪩⨒∯111032)=⪩⨒∯-30022211112","reverse_text":"⪩⨒∯-30022211112=⪩⨒∯133220⊋⪩⨒∯130223⪒(↩⪖⪩⨒∯111032)","cot":[{"info":"⪩⨒∯133220⊋⪩⨒∯130223=⪩⨒∯30031103100","layer":1},{"info":"↩⪖⪩⨒∯111032=⪩⨒∯-2231322","layer":1},{"info":"⪩⨒∯30031103100⪒⪩⨒∯-2231322=⪩⨒∯-30022211112","layer":0}]}
{"id":480,"expression_no_base_symbol":"($1769$⇴$2309$)⊊","expression":"(⪩⨒∯123221⇴⪩⨒∯210011)⊊","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":248,"operation_count":2,"complexity_ratio":124.0,"tree":{"type":"unary","operator":"⊊","unary_expr":{"type":"binary","operator":"⇴","left_expr":{"type":"numeric_atoms","value":1769,"base":4},"right_expr":{"type":"numeric_atoms","value":2309,"base":4}}},"used_operators":["W9R8I5fN5A","4JB6nKBMSY"],"dependent_operators":["DlLNRPXxWL","aBQ6xLxuTc","8n5YIzOsVS","oZj3VtZNQx","MahUMFw56D","hyuBjUqXlG","aA7tF3KVD3","2DDjHMKMc0","QMFrweE19q","SxTAKzQCrw","8cLx32lpNA","sdazOOVcIp","NTOWxs364D","COABgblf1C"],"result":"⪩⨒∯112030233","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1769","layer":2},{"info":"number node, value=2309","layer":2},{"info":"compute binary expreesion, left_input=1769, right_input=2309, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=14846","layer":1},{"info":"compute unary expreesion, input=14846, op_id = W9R8I5fN5A, unary_op_definition = 'a⊊ = { (((⫛⫱⨽a)∙⊟a)∌((a⇂≾⫗536)⋝⋈⪟(a⫡⨏a))) , if ((a≚⋢)==7 or (a⪘⨀)==15) ; ((a≀⫉(6⪛⫼a))⫠↝⫳) , else }', output=90927","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯123221⇴⪩⨒∯210011)⊊=⪩⨒∯112030233","reverse_text":"⪩⨒∯112030233=(⪩⨒∯123221⇴⪩⨒∯210011)⊊","cot":[{"info":"⪩⨒∯123221⇴⪩⨒∯210011=⪩⨒∯3213332","layer":1},{"info":"⪩⨒∯3213332⊊=⪩⨒∯112030233","layer":0}]}
{"id":481,"expression_no_base_symbol":"⨣⨃⇪(⪹$1472$)","expression":"⨣⨃⇪(⪹⪩⨒∯113000)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16,"operation_count":2,"complexity_ratio":8.0,"tree":{"type":"unary","operator":"⨣⨃⇪","unary_expr":{"type":"unary","operator":"⪹","unary_expr":{"type":"numeric_atoms","value":1472,"base":4}}},"used_operators":["AcOhelriW5","USyYr0JgAa"],"dependent_operators":["s3Fd5m9Dh2","liw5iZPkLH","yyfyN0ffXY","tifHPKVTfV"],"result":"⪩⨒∯111331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1472","layer":2},{"info":"compute unary expreesion, input=1472, op_id = USyYr0JgAa, unary_op_definition = '⪹a = { (a⇼⇔∾180) }', output=-1292","layer":1},{"info":"compute unary expreesion, input=-1292, op_id = AcOhelriW5, unary_op_definition = '⨣⨃⇪a = { (⨡↴(172⊬⨰(3↙a))) }', output=1405","layer":0}],"base":4,"result_base":4,"text":"⨣⨃⇪(⪹⪩⨒∯113000)=⪩⨒∯111331","reverse_text":"⪩⨒∯111331=⨣⨃⇪(⪹⪩⨒∯113000)","cot":[{"info":"⪹⪩⨒∯113000=⪩⨒∯-110030","layer":1},{"info":"⨣⨃⇪⪩⨒∯-110030=⪩⨒∯111331","layer":0}]}
{"id":482,"expression_no_base_symbol":"⫓⪴$1021$⨸$4710$","expression":"⫓⪴⪩⨒∯33331⨸⪩⨒∯1021212","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3174,"operation_count":2,"complexity_ratio":1587.0,"tree":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"binary","operator":"⨸","left_expr":{"type":"numeric_atoms","value":1021,"base":4},"right_expr":{"type":"numeric_atoms","value":4710,"base":4}}},"used_operators":["eLxqMNBOBk","KmoU8R5UQR"],"dependent_operators":["9HNa5Wba9A","ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl"],"result":"⪩⨒∯33322000210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1021","layer":2},{"info":"number node, value=4710","layer":2},{"info":"compute binary expreesion, left_input=1021, right_input=4710, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=2042","layer":1},{"info":"compute unary expreesion, input=2042, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=4169764","layer":0}],"base":4,"result_base":4,"text":"⫓⪴⪩⨒∯33331⨸⪩⨒∯1021212=⪩⨒∯33322000210","reverse_text":"⪩⨒∯33322000210=⫓⪴⪩⨒∯33331⨸⪩⨒∯1021212","cot":[{"info":"⪩⨒∯33331⨸⪩⨒∯1021212=⪩⨒∯133322","layer":1},{"info":"⫓⪴⪩⨒∯133322=⪩⨒∯33322000210","layer":0}]}
{"id":483,"expression_no_base_symbol":"$1357$∥⊢⊲$5400$⨶","expression":"⪩⨒∯111031∥⊢⊲⪩⨒∯1110120⨶","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":15,"operation_count":2,"complexity_ratio":7.5,"tree":{"type":"unary","operator":"⨶","unary_expr":{"type":"binary","operator":"∥⊢⊲","left_expr":{"type":"numeric_atoms","value":1357,"base":4},"right_expr":{"type":"numeric_atoms","value":5400,"base":4}}},"used_operators":["rFxw8gIMmB","v1UQAVDJRr"],"dependent_operators":["f6k1SAg4EE","Qy55tPpLXF","EBcxylXtPf","rGHVDoGpnC"],"result":"⪩⨒∯-2012","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1357","layer":2},{"info":"number node, value=5400","layer":2},{"info":"compute binary expreesion, left_input=1357, right_input=5400, op_id = v1UQAVDJRr binary_op_definition= 'a∥⊢⊲b = { (a⨟⋌⩍b) , if (a⫌⩹⨱)>=49 ; b , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = rFxw8gIMmB, unary_op_definition = 'a⨶ = { ((a⋥≓≎303)⪒(a⋥≓≎537)) }', output=-134","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯111031∥⊢⊲⪩⨒∯1110120⨶=⪩⨒∯-2012","reverse_text":"⪩⨒∯-2012=⪩⨒∯111031∥⊢⊲⪩⨒∯1110120⨶","cot":[{"info":"⪩⨒∯111031∥⊢⊲⪩⨒∯1110120=NaN","layer":1},{"info":"NaN⨶=⪩⨒∯-2012","layer":0}]}
{"id":484,"expression_no_base_symbol":"(⋗⩬⋾$8659$)⫲≸⪮($3274$⋅⇍$1066$)","expression":"(⋗⩬⋾⪩⨒∯2013103)⫲≸⪮(⪩⨒∯303022⋅⇍⪩⨒∯100222)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":25984,"operation_count":3,"complexity_ratio":8661.333333333334,"tree":{"type":"binary","operator":"⫲≸⪮","left_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":8659,"base":4}},"right_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":3274,"base":4},"right_expr":{"type":"numeric_atoms","value":1066,"base":4}}},"used_operators":["P3lXMJvFrc","DpFCA1CohY","AdZkA7nFnk"],"dependent_operators":["tmPS8pqC7x","oWn0xqSxBt","DbCuESL50I","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6"],"result":"⪩⨒∯12111321","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8659","layer":2},{"info":"compute unary expreesion, input=8659, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-25977","layer":1},{"info":"number node, value=3274","layer":2},{"info":"number node, value=1066","layer":2},{"info":"compute binary expreesion, left_input=3274, right_input=1066, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"compute binary expreesion, left_input=-25977, right_input=-22, op_id = P3lXMJvFrc binary_op_definition= 'a⫲≸⪮b = { (⋼∭⪍a) , if (⊙↵-b)>333 ; (a⨪↰⇹b) , else }', output=25977","layer":0}],"base":4,"result_base":4,"text":"(⋗⩬⋾⪩⨒∯2013103)⫲≸⪮(⪩⨒∯303022⋅⇍⪩⨒∯100222)=⪩⨒∯12111321","reverse_text":"⪩⨒∯12111321=(⋗⩬⋾⪩⨒∯2013103)⫲≸⪮(⪩⨒∯303022⋅⇍⪩⨒∯100222)","cot":[{"info":"⋗⩬⋾⪩⨒∯2013103=⪩⨒∯-12111321","layer":1},{"info":"⪩⨒∯303022⋅⇍⪩⨒∯100222=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯-12111321⫲≸⪮⪩⨒∯-112=⪩⨒∯12111321","layer":0}]}
{"id":485,"expression_no_base_symbol":"(→⩰$5483$)≁↽≥($1611$⪉⨛$4203$)","expression":"(→⩰⪩⨒∯1111223)≁↽≥(⪩⨒∯121023⪉⨛⪩⨒∯1001223)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5912,"operation_count":3,"complexity_ratio":1970.6666666666667,"tree":{"type":"binary","operator":"≁↽≥","left_expr":{"type":"unary","operator":"→⩰","unary_expr":{"type":"numeric_atoms","value":5483,"base":4}},"right_expr":{"type":"binary","operator":"⪉⨛","left_expr":{"type":"numeric_atoms","value":1611,"base":4},"right_expr":{"type":"numeric_atoms","value":4203,"base":4}}},"used_operators":["ncHt1X6cMc","o8Pngz0Tml","EWw2JM7wp4"],"dependent_operators":["oWn0xqSxBt","3Oe9XWJUTD","9FxExcQeMw","4X4GscPmMf","YbUVn0Rbpy","Nsiff2A1zJ","l1M9WJ3V7u","eewbuw0ToL","NTOWxs364D","tifHPKVTfV","12rbrZMWeM","i8ToyICDmI","eewbuw0ToL"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5483","layer":2},{"info":"compute unary expreesion, input=5483, op_id = o8Pngz0Tml, unary_op_definition = '→⩰a = { ((∑⇻≧(a⋛a))⨰((a⊴a)⩷∴(a⨕⋳))) }', output=nan","layer":1},{"info":"number node, value=1611","layer":2},{"info":"number node, value=4203","layer":2},{"info":"compute binary expreesion, left_input=1611, right_input=4203, op_id = EWw2JM7wp4 binary_op_definition= 'a⪉⨛b = { (((82⇼⇔∾a)⩚⊴⇥a)⩚⊴⇥((b∲⫓a)⋳⪒(a⨰b))) }', output=845","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=845, op_id = ncHt1X6cMc binary_op_definition= 'a≁↽≥b = { (a⊝⪿⪼b) , if b>=116 ; (⊙↵-b) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(→⩰⪩⨒∯1111223)≁↽≥(⪩⨒∯121023⪉⨛⪩⨒∯1001223)=NaN","reverse_text":"NaN=(→⩰⪩⨒∯1111223)≁↽≥(⪩⨒∯121023⪉⨛⪩⨒∯1001223)","cot":[{"info":"→⩰⪩⨒∯1111223=NaN","layer":1},{"info":"⪩⨒∯121023⪉⨛⪩⨒∯1001223=⪩⨒∯31031","layer":1},{"info":"NaN≁↽≥⪩⨒∯31031=NaN","layer":0}]}
{"id":486,"expression_no_base_symbol":"$6021$⪥$1140$⨳⩥⨓$3544$⪡$2509$","expression":"⪩⨒∯1132011⪥⪩⨒∯101310⨳⩥⨓⪩⨒∯313120⪡⪩⨒∯213031","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":40,"operation_count":3,"complexity_ratio":13.333333333333334,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⪥","left_expr":{"type":"numeric_atoms","value":6021,"base":4},"right_expr":{"type":"numeric_atoms","value":1140,"base":4}},"right_expr":{"type":"binary","operator":"⪡","left_expr":{"type":"numeric_atoms","value":3544,"base":4},"right_expr":{"type":"numeric_atoms","value":2509,"base":4}}},"used_operators":["nCS4ZIUYfx","QbnwKVWMIQ","oraRL2iQuh"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","WR6HLWljOP","nhYeJWJD5X","f6k1SAg4EE","jLgFTUHLKL","PPChnnnBFF","2Wsdkap16l","ljTHtUsqzn","k8jYdgA6NY","8WDwsbhb0R"],"result":"⪩⨒∯-12333111","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6021","layer":2},{"info":"number node, value=1140","layer":2},{"info":"compute binary expreesion, left_input=6021, right_input=1140, op_id = QbnwKVWMIQ binary_op_definition= 'a⪥b = { (b∇⊂⋱(58∣a)) , if (b↢721)<125 ; (↩(508⪒a)) , else }', output=28736","layer":1},{"info":"number node, value=3544","layer":2},{"info":"number node, value=2509","layer":2},{"info":"compute binary expreesion, left_input=3544, right_input=2509, op_id = oraRL2iQuh binary_op_definition= 'a⪡b = { (107%(a⩹b)) , if a>=49 ; (≀↧⇸(∂⩏⊆a)) , else }', output=107","layer":1},{"info":"compute binary expreesion, left_input=28736, right_input=107, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-28629","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1132011⪥⪩⨒∯101310⨳⩥⨓⪩⨒∯313120⪡⪩⨒∯213031=⪩⨒∯-12333111","reverse_text":"⪩⨒∯-12333111=⪩⨒∯1132011⪥⪩⨒∯101310⨳⩥⨓⪩⨒∯313120⪡⪩⨒∯213031","cot":[{"info":"⪩⨒∯1132011⪥⪩⨒∯101310=⪩⨒∯13001000","layer":1},{"info":"⪩⨒∯313120⪡⪩⨒∯213031=⪩⨒∯1223","layer":1},{"info":"⪩⨒∯13001000⨳⩥⨓⪩⨒∯1223=⪩⨒∯-12333111","layer":0}]}
{"id":487,"expression_no_base_symbol":"($1387$≄⊠$3897$)∋($2122$∠↢$1135$)","expression":"(⪩⨒∯111223≄⊠⪩⨒∯330321)∋(⪩⨒∯201022∠↢⪩⨒∯101233)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":179,"operation_count":3,"complexity_ratio":59.666666666666664,"tree":{"type":"binary","operator":"∋","left_expr":{"type":"binary","operator":"≄⊠","left_expr":{"type":"numeric_atoms","value":1387,"base":4},"right_expr":{"type":"numeric_atoms","value":3897,"base":4}},"right_expr":{"type":"binary","operator":"∠↢","left_expr":{"type":"numeric_atoms","value":2122,"base":4},"right_expr":{"type":"numeric_atoms","value":1135,"base":4}}},"used_operators":["ukq6epAj5P","vXNesLlMH1","KbjG8mgYpV"],"dependent_operators":["SUmda5xLS4","61wBmkZwlr","KbjG8mgYpV","d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI","rysDP5nf3Z","NTOWxs364D","XPYlsWDdGa","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","nCS4ZIUYfx","COABgblf1C"],"result":"⪩⨒∯-1032302100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1387","layer":2},{"info":"number node, value=3897","layer":2},{"info":"compute binary expreesion, left_input=1387, right_input=3897, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=67020","layer":1},{"info":"number node, value=2122","layer":2},{"info":"number node, value=1135","layer":2},{"info":"compute binary expreesion, left_input=2122, right_input=1135, op_id = KbjG8mgYpV binary_op_definition= 'a∠↢b = { (a⊭↱((159⨳⩥⨓16)-(b⨸⪁a))) , if (b==488 or (⨞⊢a)==254) ; (⪲⇎((-b)⫡⨏(b⩚⊴⇥a))) , else }', output=-23296","layer":1},{"info":"compute binary expreesion, left_input=67020, right_input=-23296, op_id = ukq6epAj5P binary_op_definition= 'a∋b = { ((≋a)∠↢(b⪄a)) }', output=-322704","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯111223≄⊠⪩⨒∯330321)∋(⪩⨒∯201022∠↢⪩⨒∯101233)=⪩⨒∯-1032302100","reverse_text":"⪩⨒∯-1032302100=(⪩⨒∯111223≄⊠⪩⨒∯330321)∋(⪩⨒∯201022∠↢⪩⨒∯101233)","cot":[{"info":"⪩⨒∯111223≄⊠⪩⨒∯330321=⪩⨒∯100113030","layer":1},{"info":"⪩⨒∯201022∠↢⪩⨒∯101233=⪩⨒∯-11230000","layer":1},{"info":"⪩⨒∯100113030∋⪩⨒∯-11230000=⪩⨒∯-1032302100","layer":0}]}
{"id":488,"expression_no_base_symbol":"$7272$↹⊜$9019$⊎←↗","expression":"⪩⨒∯1301220↹⊜⪩⨒∯2030323⊎←↗","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34,"operation_count":2,"complexity_ratio":17.0,"tree":{"type":"unary","operator":"⊎←↗","unary_expr":{"type":"binary","operator":"↹⊜","left_expr":{"type":"numeric_atoms","value":7272,"base":4},"right_expr":{"type":"numeric_atoms","value":9019,"base":4}}},"used_operators":["dwb5p0fa6d","9bazX3JMtO"],"dependent_operators":["sdazOOVcIp","COABgblf1C","9FxExcQeMw","rysDP5nf3Z","23Mk6UjR3U","tifHPKVTfV","eH2TOUuTDT","DIvbN7qnHd"],"result":"⪩⨒∯22232211","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7272","layer":2},{"info":"number node, value=9019","layer":2},{"info":"compute binary expreesion, left_input=7272, right_input=9019, op_id = 9bazX3JMtO binary_op_definition= 'a↹⊜b = { (((a⊠≄⫣)⩷∴(b-a))⩷∴((a⋷b)⇼⇔∾(b⪐))) }', output=-21628","layer":1},{"info":"compute unary expreesion, input=-21628, op_id = dwb5p0fa6d, unary_op_definition = 'a⊎←↗ = { (a⊭↱340) , if (a⪨≂940)!=203 ; (a⊭↱a) , else }', output=43941","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1301220↹⊜⪩⨒∯2030323⊎←↗=⪩⨒∯22232211","reverse_text":"⪩⨒∯22232211=⪩⨒∯1301220↹⊜⪩⨒∯2030323⊎←↗","cot":[{"info":"⪩⨒∯1301220↹⊜⪩⨒∯2030323=⪩⨒∯-11101330","layer":1},{"info":"⪩⨒∯-11101330⊎←↗=⪩⨒∯22232211","layer":0}]}
{"id":489,"expression_no_base_symbol":"⪫⨮⊛($4675$⋹)","expression":"⪫⨮⊛(⪩⨒∯1021003⋹)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":69,"operation_count":2,"complexity_ratio":34.5,"tree":{"type":"unary","operator":"⪫⨮⊛","unary_expr":{"type":"unary","operator":"⋹","unary_expr":{"type":"numeric_atoms","value":4675,"base":4}}},"used_operators":["w5FWba1tyO","opAxDRczMr"],"dependent_operators":["s3Fd5m9Dh2","RZ5CV9rWsJ","SUmda5xLS4","kn8WO9XteQ","hTbEZDJLEm","Tw270M8GLb","13rbtpv6ld","mp7IySMOzn","z63VuFQld9","aN9a90urxU","27wFxooxGf","SVb2v531z1","eewbuw0ToL"],"result":"⪩⨒∯-110","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4675","layer":2},{"info":"compute unary expreesion, input=4675, op_id = opAxDRczMr, unary_op_definition = 'a⋹ = { ((⨴⫝a)⇷(a↤⩊a)) , if (a≃⋄)<20 or (⊢≑≆a)<=20 ; ((a⨰a)∧) , else }', output=-20","layer":1},{"info":"compute unary expreesion, input=-20, op_id = w5FWba1tyO, unary_op_definition = '⪫⨮⊛a = { a , if (a⨭⪣527)<=182 ; ((⨰⫟⨤(a⪄a))⩖⊿((a⊬⨰a)∟)) , else }', output=-20","layer":0}],"base":4,"result_base":4,"text":"⪫⨮⊛(⪩⨒∯1021003⋹)=⪩⨒∯-110","reverse_text":"⪩⨒∯-110=⪫⨮⊛(⪩⨒∯1021003⋹)","cot":[{"info":"⪩⨒∯1021003⋹=⪩⨒∯-110","layer":1},{"info":"⪫⨮⊛⪩⨒∯-110=⪩⨒∯-110","layer":0}]}
{"id":490,"expression_no_base_symbol":"↸⊣($4914$⊎←↗)","expression":"↸⊣(⪩⨒∯1030302⊎←↗)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":21,"operation_count":2,"complexity_ratio":10.5,"tree":{"type":"unary","operator":"↸⊣","unary_expr":{"type":"unary","operator":"⊎←↗","unary_expr":{"type":"numeric_atoms","value":4914,"base":4}}},"used_operators":["wztAlM01eG","dwb5p0fa6d"],"dependent_operators":["N41Kp7NANJ","XPYlsWDdGa","7j4O788W3g","DZ8iAZOCBD","8w2t5hMYqp","12rbrZMWeM","f6k1SAg4EE","sdazOOVcIp","COABgblf1C"],"result":"⪩⨒∯10131232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4914","layer":2},{"info":"compute unary expreesion, input=4914, op_id = dwb5p0fa6d, unary_op_definition = 'a⊎←↗ = { (a⊭↱340) , if (a⪨≂940)!=203 ; (a⊭↱a) , else }', output=-9143","layer":1},{"info":"compute unary expreesion, input=-9143, op_id = wztAlM01eG, unary_op_definition = '↸⊣a = { ((⊄⩳↩a)↺(a≋⫹)) , if (⪲⇎a)<33 ; ((a⪒a)⊉≛↸(a⋳⪒a)) , else }', output=18286","layer":0}],"base":4,"result_base":4,"text":"↸⊣(⪩⨒∯1030302⊎←↗)=⪩⨒∯10131232","reverse_text":"⪩⨒∯10131232=↸⊣(⪩⨒∯1030302⊎←↗)","cot":[{"info":"⪩⨒∯1030302⊎←↗=⪩⨒∯-2032313","layer":1},{"info":"↸⊣⪩⨒∯-2032313=⪩⨒∯10131232","layer":0}]}
{"id":491,"expression_no_base_symbol":"⊖∈($4193$⊹≧⊝)","expression":"⊖∈(⪩⨒∯1001201⊹≧⊝)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":50377,"operation_count":2,"complexity_ratio":25188.5,"tree":{"type":"unary","operator":"⊖∈","unary_expr":{"type":"unary","operator":"⊹≧⊝","unary_expr":{"type":"numeric_atoms","value":4193,"base":4}}},"used_operators":["YFxL8Sc2Zy","LxFB4K6j0n"],"dependent_operators":["zVYPLywUTj","sdazOOVcIp","ancx8kZcWl","YSKBFp38Pu","NTOWxs364D","P8v4zCKN1o","XPYlsWDdGa","DZ8iAZOCBD","t8gj7n24qd","g55IO6H4Gj","eewbuw0ToL","i8ToyICDmI","COABgblf1C"],"result":"Inf","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4193","layer":2},{"info":"compute unary expreesion, input=4193, op_id = LxFB4K6j0n, unary_op_definition = 'a⊹≧⊝ = { (((∥⊫a)⊭↱(a⩚⊴⇥a))⊉≛↸(⪲⇎(⪲⇎a))) , if a!=566 ; (-((a∲⫓a)⨸⪁(a⨰a))) , else }', output=-16772","layer":1},{"info":"compute unary expreesion, input=-16772, op_id = YFxL8Sc2Zy, unary_op_definition = '⊖∈a = { a , if (a⨝⩣∺)>=369 ; ((a⊪)⪨≂(a⇤a)) , else }', output=inf","layer":0}],"base":4,"result_base":4,"text":"⊖∈(⪩⨒∯1001201⊹≧⊝)=Inf","reverse_text":"Inf=⊖∈(⪩⨒∯1001201⊹≧⊝)","cot":[{"info":"⪩⨒∯1001201⊹≧⊝=⪩⨒∯-10012010","layer":1},{"info":"⊖∈⪩⨒∯-10012010=Inf","layer":0}]}
{"id":492,"expression_no_base_symbol":"$2066$→⨶⪴$6877$⪛$6732$∺≝⩲$4164$","expression":"⪩⨒∯200102→⨶⪴⪩⨒∯1223131⪛⪩⨒∯1221030∺≝⩲⪩⨒∯1001010","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":143,"operation_count":3,"complexity_ratio":47.666666666666664,"tree":{"type":"binary","operator":"⪛","left_expr":{"type":"binary","operator":"→⨶⪴","left_expr":{"type":"numeric_atoms","value":2066,"base":4},"right_expr":{"type":"numeric_atoms","value":6877,"base":4}},"right_expr":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"numeric_atoms","value":6732,"base":4},"right_expr":{"type":"numeric_atoms","value":4164,"base":4}}},"used_operators":["uFcxV4UQCh","bF6eod5Gvf","KPf6cnQVty"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","8w2t5hMYqp","9FxExcQeMw","BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl"],"result":"⪩⨒∯21","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2066","layer":2},{"info":"number node, value=6877","layer":2},{"info":"compute binary expreesion, left_input=2066, right_input=6877, op_id = bF6eod5Gvf binary_op_definition= 'a→⨶⪴b = { (a⩷∴b) , if b<109 ; (⊄⩳↩b) , else }', output=-20631","layer":1},{"info":"number node, value=6732","layer":2},{"info":"number node, value=4164","layer":2},{"info":"compute binary expreesion, left_input=6732, right_input=4164, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=-20631, right_input=160, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=9","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯200102→⨶⪴⪩⨒∯1223131⪛⪩⨒∯1221030∺≝⩲⪩⨒∯1001010=⪩⨒∯21","reverse_text":"⪩⨒∯21=⪩⨒∯200102→⨶⪴⪩⨒∯1223131⪛⪩⨒∯1221030∺≝⩲⪩⨒∯1001010","cot":[{"info":"⪩⨒∯200102→⨶⪴⪩⨒∯1223131=⪩⨒∯-11002113","layer":1},{"info":"⪩⨒∯1221030∺≝⩲⪩⨒∯1001010=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯-11002113⪛⪩⨒∯2200=⪩⨒∯21","layer":0}]}
{"id":493,"expression_no_base_symbol":"(⇁⨣⪵$1293$)⋹","expression":"(⇁⨣⪵⪩⨒∯110031)⋹","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":15,"operation_count":2,"complexity_ratio":7.5,"tree":{"type":"unary","operator":"⋹","unary_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":1293,"base":4}}},"used_operators":["opAxDRczMr","inkyxCbjAn"],"dependent_operators":["13rbtpv6ld","mp7IySMOzn","z63VuFQld9","aN9a90urxU","27wFxooxGf","SVb2v531z1","eewbuw0ToL","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1293","layer":2},{"info":"compute unary expreesion, input=1293, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = opAxDRczMr, unary_op_definition = 'a⋹ = { ((⨴⫝a)⇷(a↤⩊a)) , if (a≃⋄)<20 or (⊢≑≆a)<=20 ; ((a⨰a)∧) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⇁⨣⪵⪩⨒∯110031)⋹=NaN","reverse_text":"NaN=(⇁⨣⪵⪩⨒∯110031)⋹","cot":[{"info":"⇁⨣⪵⪩⨒∯110031=NaN","layer":1},{"info":"NaN⋹=NaN","layer":0}]}
{"id":494,"expression_no_base_symbol":"($6407$∲⫓$1781$)⇀∌","expression":"(⪩⨒∯1210013∲⫓⪩⨒∯123311)⇀∌","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":57,"operation_count":2,"complexity_ratio":28.5,"tree":{"type":"unary","operator":"⇀∌","unary_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":6407,"base":4},"right_expr":{"type":"numeric_atoms","value":1781,"base":4}}},"used_operators":["2k53nXOpI5","i8ToyICDmI"],"dependent_operators":["Q3PJZHRvZv","ddLRYrp01A","AcOhelriW5","7t3wd0Fuz7","3tVxb0NHM4","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6407","layer":2},{"info":"number node, value=1781","layer":2},{"info":"compute binary expreesion, left_input=6407, right_input=1781, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = 2k53nXOpI5, unary_op_definition = 'a⇀∌ = { ((a⪎↠(⨣⨃⇪a))⋥⋵⩄(a∊∟⩊(⊥a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1210013∲⫓⪩⨒∯123311)⇀∌=NaN","reverse_text":"NaN=(⪩⨒∯1210013∲⫓⪩⨒∯123311)⇀∌","cot":[{"info":"⪩⨒∯1210013∲⫓⪩⨒∯123311=⪩⨒∯0","layer":1},{"info":"⪩⨒∯0⇀∌=NaN","layer":0}]}
{"id":495,"expression_no_base_symbol":"(≦∁$3303$)⪢($1346$⨒$1208$)","expression":"(≦∁⪩⨒∯303213)⪢(⪩⨒∯111002⨒⪩⨒∯102320)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7725,"operation_count":3,"complexity_ratio":2575.0,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":3303,"base":4}},"right_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":1346,"base":4},"right_expr":{"type":"numeric_atoms","value":1208,"base":4}}},"used_operators":["dWAJyo7jo9","9ICcGScMcE","y75s1iXyHd"],"dependent_operators":["k8jYdgA6NY","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","srAu1WTS94","oacrs7FA3X","7qqUquhhSb"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3303","layer":2},{"info":"compute unary expreesion, input=3303, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=3303","layer":1},{"info":"number node, value=1346","layer":2},{"info":"number node, value=1208","layer":2},{"info":"compute binary expreesion, left_input=1346, right_input=1208, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-7704","layer":1},{"info":"compute binary expreesion, left_input=3303, right_input=-7704, op_id = dWAJyo7jo9 binary_op_definition= 'a⪢b = {b, if b == 0; (a)%(a⪢(b-1)), if b > 0 and abs(b) < 1000000; -(a)%(a⪢(b+1)), if b < 0 and abs(b) < 1000000; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"(≦∁⪩⨒∯303213)⪢(⪩⨒∯111002⨒⪩⨒∯102320)=NaN","reverse_text":"NaN=(≦∁⪩⨒∯303213)⪢(⪩⨒∯111002⨒⪩⨒∯102320)","cot":[{"info":"≦∁⪩⨒∯303213=⪩⨒∯303213","layer":1},{"info":"⪩⨒∯111002⨒⪩⨒∯102320=⪩⨒∯-1320120","layer":1},{"info":"⪩⨒∯303213⪢⪩⨒∯-1320120=NaN","layer":0}]}
{"id":496,"expression_no_base_symbol":"≸($5726$↬$1584$)","expression":"≸(⪩⨒∯1121132↬⪩⨒∯120300)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":55,"operation_count":2,"complexity_ratio":27.5,"tree":{"type":"unary","operator":"≸","unary_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":5726,"base":4},"right_expr":{"type":"numeric_atoms","value":1584,"base":4}}},"used_operators":["eOf03JbCpp","B5M0gjZbta"],"dependent_operators":["WmT3o8z6ya","l07mrZUIn9","NTOWxs364D","RygbFNSyEJ","tifHPKVTfV","oRDoc9rAEX","IwW236VD4Y","1aApVXNlOP","Z5m6OM72h2","mqXw5SEYmG","IWmyXbctLI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5726","layer":2},{"info":"number node, value=1584","layer":2},{"info":"compute binary expreesion, left_input=5726, right_input=1584, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = eOf03JbCpp, unary_op_definition = '≸a = { (29∘((630⊋≦⊧a)⩚⊴⇥(a≦↸a))) , if (a⋘⨑⨽)>2 ; (((a⪮%⊝a)⇼⇔∾(a↪⪝))⫸⊐((a⪮%⊝a)≠≀(3⩇∃⫛a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"≸(⪩⨒∯1121132↬⪩⨒∯120300)=NaN","reverse_text":"NaN=≸(⪩⨒∯1121132↬⪩⨒∯120300)","cot":[{"info":"⪩⨒∯1121132↬⪩⨒∯120300=NaN","layer":1},{"info":"≸NaN=NaN","layer":0}]}
{"id":497,"expression_no_base_symbol":"$3703$⩘$5461$*$2733$⇮⋭$4311$","expression":"⪩⨒∯321313⩘⪩⨒∯1111111*⪩⨒∯222231⇮⋭⪩⨒∯1003113","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":303,"operation_count":3,"complexity_ratio":101.0,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"⩘","left_expr":{"type":"numeric_atoms","value":3703,"base":4},"right_expr":{"type":"numeric_atoms","value":5461,"base":4}},"right_expr":{"type":"binary","operator":"⇮⋭","left_expr":{"type":"numeric_atoms","value":2733,"base":4},"right_expr":{"type":"numeric_atoms","value":4311,"base":4}}},"used_operators":["9HNa5Wba9A","cHh1gJQ2o6","vkpjKywKVM"],"dependent_operators":["W4YGzv6Whe","23Mk6UjR3U","eRqsBgTDFp","zVYPLywUTj","bPywburJMS","KPf6cnQVty","YbVcJGFEVW","5twsqlHp2o","nhYeJWJD5X","U6pG0PXrV3","tifHPKVTfV","bJkvcejdHO","40aOVDgCDB","YbVcJGFEVW"],"result":"⪩⨒∯-102132200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3703","layer":2},{"info":"number node, value=5461","layer":2},{"info":"compute binary expreesion, left_input=3703, right_input=5461, op_id = cHh1gJQ2o6 binary_op_definition= 'a⩘b = { (((b⋷b)↼⊘⨖(a⊢6))∺≝⩲((a⪒⊣⊆619)≃(a⊪))) }', output=160","layer":1},{"info":"number node, value=2733","layer":2},{"info":"number node, value=4311","layer":2},{"info":"compute binary expreesion, left_input=2733, right_input=4311, op_id = vkpjKywKVM binary_op_definition= 'a⇮⋭b = { (((⊖b)⊢)≎⊠⪸((a≃b)⇼⇔∾(47∇⊂⋱106))) }', output=-473","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=-473, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=-75680","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯321313⩘⪩⨒∯1111111*⪩⨒∯222231⇮⋭⪩⨒∯1003113=⪩⨒∯-102132200","reverse_text":"⪩⨒∯-102132200=⪩⨒∯321313⩘⪩⨒∯1111111*⪩⨒∯222231⇮⋭⪩⨒∯1003113","cot":[{"info":"⪩⨒∯321313⩘⪩⨒∯1111111=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯222231⇮⋭⪩⨒∯1003113=⪩⨒∯-13121","layer":1},{"info":"⪩⨒∯2200*⪩⨒∯-13121=⪩⨒∯-102132200","layer":0}]}
{"id":498,"expression_no_base_symbol":"(⨩∲⋌$1590$)⫚↹⊑$2069$∘$1869$","expression":"(⨩∲⋌⪩⨒∯120312)⫚↹⊑⪩⨒∯200111∘⪩⨒∯131031","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":21,"operation_count":3,"complexity_ratio":7.0,"tree":{"type":"binary","operator":"⫚↹⊑","left_expr":{"type":"unary","operator":"⨩∲⋌","unary_expr":{"type":"numeric_atoms","value":1590,"base":4}},"right_expr":{"type":"binary","operator":"∘","left_expr":{"type":"numeric_atoms","value":2069,"base":4},"right_expr":{"type":"numeric_atoms","value":1869,"base":4}}},"used_operators":["dfKe02y8D2","aSik1wnThz","Z5m6OM72h2"],"dependent_operators":["2DQ55sFlQl","DIvbN7qnHd","t8gj7n24qd","12rbrZMWeM","g55IO6H4Gj","rysDP5nf3Z","Ph9nP6C5qx","Z2TMIBDE3Q","eH2TOUuTDT","rysDP5nf3Z"],"result":"⪩⨒∯-12333","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1590","layer":2},{"info":"compute unary expreesion, input=1590, op_id = aSik1wnThz, unary_op_definition = '⨩∲⋌a = { ((759≧⫂∧(236-a))⩤) }', output=-2113","layer":1},{"info":"number node, value=2069","layer":2},{"info":"number node, value=1869","layer":2},{"info":"compute binary expreesion, left_input=2069, right_input=1869, op_id = Z5m6OM72h2 binary_op_definition= 'a∘b = { (380-a) , if b<=483 ; (a⪐) , else }', output=4138","layer":1},{"info":"compute binary expreesion, left_input=-2113, right_input=4138, op_id = dfKe02y8D2 binary_op_definition= 'a⫚↹⊑b = { ((126⊠≄⫣)⋳⪒((-b)⨵⪆(a⨸⪁b))) }', output=-447","layer":0}],"base":4,"result_base":4,"text":"(⨩∲⋌⪩⨒∯120312)⫚↹⊑⪩⨒∯200111∘⪩⨒∯131031=⪩⨒∯-12333","reverse_text":"⪩⨒∯-12333=(⨩∲⋌⪩⨒∯120312)⫚↹⊑⪩⨒∯200111∘⪩⨒∯131031","cot":[{"info":"⨩∲⋌⪩⨒∯120312=⪩⨒∯-201001","layer":1},{"info":"⪩⨒∯200111∘⪩⨒∯131031=⪩⨒∯1000222","layer":1},{"info":"⪩⨒∯-201001⫚↹⊑⪩⨒∯1000222=⪩⨒∯-12333","layer":0}]}
{"id":499,"expression_no_base_symbol":"$6426$∘$1642$∖$4008$⫁⪎$2024$","expression":"⪩⨒∯1210122∘⪩⨒∯121222∖⪩⨒∯332220⫁⪎⪩⨒∯133220","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":353,"operation_count":3,"complexity_ratio":117.66666666666667,"tree":{"type":"binary","operator":"∖","left_expr":{"type":"binary","operator":"∘","left_expr":{"type":"numeric_atoms","value":6426,"base":4},"right_expr":{"type":"numeric_atoms","value":1642,"base":4}},"right_expr":{"type":"binary","operator":"⫁⪎","left_expr":{"type":"numeric_atoms","value":4008,"base":4},"right_expr":{"type":"numeric_atoms","value":2024,"base":4}}},"used_operators":["tXD093vOjl","Z5m6OM72h2","xRrnTEsQ6j"],"dependent_operators":["rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC","eH2TOUuTDT","rysDP5nf3Z","P8v4zCKN1o","Qy55tPpLXF","tifHPKVTfV","sdazOOVcIp","2DDjHMKMc0","i8ToyICDmI"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6426","layer":2},{"info":"number node, value=1642","layer":2},{"info":"compute binary expreesion, left_input=6426, right_input=1642, op_id = Z5m6OM72h2 binary_op_definition= 'a∘b = { (380-a) , if b<=483 ; (a⪐) , else }', output=12852","layer":1},{"info":"number node, value=4008","layer":2},{"info":"number node, value=2024","layer":2},{"info":"compute binary expreesion, left_input=4008, right_input=2024, op_id = xRrnTEsQ6j binary_op_definition= 'a⫁⪎b = { ((b⋝⋈⪟a)⇼⇔∾a) , if (∥⊫b)!=57 ; ((191∲⫓a)⋥≓≎(a⪨≂368)) , else }', output=1984","layer":1},{"info":"compute binary expreesion, left_input=12852, right_input=1984, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1210122∘⪩⨒∯121222∖⪩⨒∯332220⫁⪎⪩⨒∯133220=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯1210122∘⪩⨒∯121222∖⪩⨒∯332220⫁⪎⪩⨒∯133220","cot":[{"info":"⪩⨒∯1210122∘⪩⨒∯121222=⪩⨒∯3020310","layer":1},{"info":"⪩⨒∯332220⫁⪎⪩⨒∯133220=⪩⨒∯133000","layer":1},{"info":"⪩⨒∯3020310∖⪩⨒∯133000=⪩⨒∯0","layer":0}]}
{"id":500,"expression_no_base_symbol":"∮($1425$⩢≌)","expression":"∮(⪩⨒∯112101⩢≌)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":741,"operation_count":2,"complexity_ratio":370.5,"tree":{"type":"unary","operator":"∮","unary_expr":{"type":"unary","operator":"⩢≌","unary_expr":{"type":"numeric_atoms","value":1425,"base":4}}},"used_operators":["CqXKPLVYql","D617RFjZIq"],"dependent_operators":["2Wsdkap16l","eLxqMNBOBk","KbjG8mgYpV","MmTdOpaElr","JclMnS0uGI","bJkvcejdHO","eewbuw0ToL","hTbEZDJLEm","o20kRiQErp"],"result":"⪩⨒∯-322013013","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1425","layer":2},{"info":"compute unary expreesion, input=1425, op_id = D617RFjZIq, unary_op_definition = 'a⩢≌ = { ((a∸)∟) }', output=113","layer":1},{"info":"compute unary expreesion, input=113, op_id = CqXKPLVYql, unary_op_definition = '∮a = { ((a⩹a)⨰(⫓⪴488)) , if (a<=186 and a<741 and (a⨱∎)<232) ; ((a≎⊠⪸a)⨔⇊(973∠↢a)) , else }', output=-238023","layer":0}],"base":4,"result_base":4,"text":"∮(⪩⨒∯112101⩢≌)=⪩⨒∯-322013013","reverse_text":"⪩⨒∯-322013013=∮(⪩⨒∯112101⩢≌)","cot":[{"info":"⪩⨒∯112101⩢≌=⪩⨒∯1301","layer":1},{"info":"∮⪩⨒∯1301=⪩⨒∯-322013013","layer":0}]}
{"id":501,"expression_no_base_symbol":"($3118$≝⊰⇂)⫒⫫$3881$⫣⪄⊒$1111$","expression":"(⪩⨒∯300232≝⊰⇂)⫒⫫⪩⨒∯330221⫣⪄⊒⪩⨒∯101113","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1463,"operation_count":3,"complexity_ratio":487.6666666666667,"tree":{"type":"binary","operator":"⫒⫫","left_expr":{"type":"unary","operator":"≝⊰⇂","unary_expr":{"type":"numeric_atoms","value":3118,"base":4}},"right_expr":{"type":"binary","operator":"⫣⪄⊒","left_expr":{"type":"numeric_atoms","value":3881,"base":4},"right_expr":{"type":"numeric_atoms","value":1111,"base":4}}},"used_operators":["6Ko8hGgeMq","htSmYCowi5","RabNbG55vr"],"dependent_operators":["jdwGQqwJi5","AHs5Up7iyr","AFVx7xoS7T","9FxExcQeMw","DlLNRPXxWL","NTOWxs364D","DbCuESL50I","fOIeswaMU4","g7Hmc5v1ko","KPf6cnQVty","j9kHMeSvPp","k8jYdgA6NY","2DDjHMKMc0","8WDwsbhb0R","cTDWOvIxvz","IWmyXbctLI"],"result":"⪩⨒∯1301","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3118","layer":2},{"info":"compute unary expreesion, input=3118, op_id = htSmYCowi5, unary_op_definition = 'a≝⊰⇂ = { (a⩷∴51) , if a<491 ; (⫛⫱⨽a) , else }', output=0","layer":1},{"info":"number node, value=3881","layer":2},{"info":"number node, value=1111","layer":2},{"info":"compute binary expreesion, left_input=3881, right_input=1111, op_id = RabNbG55vr binary_op_definition= 'a⫣⪄⊒b = { ((a⪮%⊝(153⪭a))%(⋼∭⪍(b⩚⊴⇥34))) , if b>769 ; ((∂⩏⊆(b⩟))∺≝⩲((b∝a)⋝⋈⪟(a⩌⋺b))) , else }', output=-6910","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-6910, op_id = 6Ko8hGgeMq binary_op_definition= 'a⫒⫫b = { (b≹⇙⪍a) , if (a∁)>135 ; (b⇌⫙⪟a) , else }', output=113","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯300232≝⊰⇂)⫒⫫⪩⨒∯330221⫣⪄⊒⪩⨒∯101113=⪩⨒∯1301","reverse_text":"⪩⨒∯1301=(⪩⨒∯300232≝⊰⇂)⫒⫫⪩⨒∯330221⫣⪄⊒⪩⨒∯101113","cot":[{"info":"⪩⨒∯300232≝⊰⇂=⪩⨒∯0","layer":1},{"info":"⪩⨒∯330221⫣⪄⊒⪩⨒∯101113=⪩⨒∯-1223332","layer":1},{"info":"⪩⨒∯0⫒⫫⪩⨒∯-1223332=⪩⨒∯1301","layer":0}]}
{"id":502,"expression_no_base_symbol":"⊢≑≆($4335$∙⊟$2319$)","expression":"⊢≑≆(⪩⨒∯1003233∙⊟⪩⨒∯210033)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4417,"operation_count":2,"complexity_ratio":2208.5,"tree":{"type":"unary","operator":"⊢≑≆","unary_expr":{"type":"binary","operator":"∙⊟","left_expr":{"type":"numeric_atoms","value":4335,"base":4},"right_expr":{"type":"numeric_atoms","value":2319,"base":4}}},"used_operators":["27wFxooxGf","SxTAKzQCrw"],"dependent_operators":["eLAdDNolq6","9FxExcQeMw","Ph9nP6C5qx","g55IO6H4Gj","6iOiAJX1F8","oWn0xqSxBt","3Oe9XWJUTD","4CyGpkTkEk","CArV6hThFE","PPChnnnBFF"],"result":"⪩⨒∯1000300220","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4335","layer":2},{"info":"number node, value=2319","layer":2},{"info":"compute binary expreesion, left_input=4335, right_input=2319, op_id = SxTAKzQCrw binary_op_definition= 'a∙⊟b = { (⩪∧⨌(a⫲⨊)) , if (b∐⫣)<386 ; ((a∣a)⊝⪿⪼(⊙↵-a)) , else }', output=66201","layer":1},{"info":"compute unary expreesion, input=66201, op_id = 27wFxooxGf, unary_op_definition = '⊢≑≆a = { a , if (≤/a)==126 and a<49 ; ((559⨸⪁a)≧⫂∧(349⩷∴a)) , else }', output=265256","layer":0}],"base":4,"result_base":4,"text":"⊢≑≆(⪩⨒∯1003233∙⊟⪩⨒∯210033)=⪩⨒∯1000300220","reverse_text":"⪩⨒∯1000300220=⊢≑≆(⪩⨒∯1003233∙⊟⪩⨒∯210033)","cot":[{"info":"⪩⨒∯1003233∙⊟⪩⨒∯210033=⪩⨒∯100022121","layer":1},{"info":"⊢≑≆⪩⨒∯100022121=⪩⨒∯1000300220","layer":0}]}
{"id":503,"expression_no_base_symbol":"$1828$⋅⇍$1364$+$2260$⫌⩉⩟$4942$","expression":"⪩⨒∯130210⋅⇍⪩⨒∯111110+⪩⨒∯203110⫌⩉⩟⪩⨒∯1031032","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":34376,"operation_count":3,"complexity_ratio":11458.666666666666,"tree":{"type":"binary","operator":"+","left_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":1828,"base":4},"right_expr":{"type":"numeric_atoms","value":1364,"base":4}},"right_expr":{"type":"binary","operator":"⫌⩉⩟","left_expr":{"type":"numeric_atoms","value":2260,"base":4},"right_expr":{"type":"numeric_atoms","value":4942,"base":4}}},"used_operators":["W4YGzv6Whe","AdZkA7nFnk","XIIwhv8d0m"],"dependent_operators":["g55IO6H4Gj","NTOWxs364D","eLAdDNolq6","B5M0gjZbta","UMwdvZNt44","MRPaB8lBjK","vkpjKywKVM"],"result":"⪩⨒∯-1020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1828","layer":2},{"info":"number node, value=1364","layer":2},{"info":"compute binary expreesion, left_input=1828, right_input=1364, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"number node, value=2260","layer":2},{"info":"number node, value=4942","layer":2},{"info":"compute binary expreesion, left_input=2260, right_input=4942, op_id = XIIwhv8d0m binary_op_definition= 'a⫌⩉⩟b = { (((a↬179)⇮⋭(b⇡⇂b))⇉⇱⇎) }', output=-50","layer":1},{"info":"compute binary expreesion, left_input=-22, right_input=-50, op_id = W4YGzv6Whe binary_op_definition= 'None', output=-72","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯130210⋅⇍⪩⨒∯111110+⪩⨒∯203110⫌⩉⩟⪩⨒∯1031032=⪩⨒∯-1020","reverse_text":"⪩⨒∯-1020=⪩⨒∯130210⋅⇍⪩⨒∯111110+⪩⨒∯203110⫌⩉⩟⪩⨒∯1031032","cot":[{"info":"⪩⨒∯130210⋅⇍⪩⨒∯111110=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯203110⫌⩉⩟⪩⨒∯1031032=⪩⨒∯-302","layer":1},{"info":"⪩⨒∯-112+⪩⨒∯-302=⪩⨒∯-1020","layer":0}]}
{"id":504,"expression_no_base_symbol":"($2713$/$2920$)⇷($4145$⩁)","expression":"(⪩⨒∯222121/⪩⨒∯231220)⇷(⪩⨒∯1000301⩁)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":33,"operation_count":3,"complexity_ratio":11.0,"tree":{"type":"binary","operator":"⇷","left_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":2713,"base":4},"right_expr":{"type":"numeric_atoms","value":2920,"base":4}},"right_expr":{"type":"unary","operator":"⩁","unary_expr":{"type":"numeric_atoms","value":4145,"base":4}}},"used_operators":["mp7IySMOzn","XhwjNDsVaA","5GqDbVmqXU"],"dependent_operators":["DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","rysDP5nf3Z","7j4O788W3g","jLgFTUHLKL","8cLx32lpNA"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2713","layer":2},{"info":"number node, value=2920","layer":2},{"info":"compute binary expreesion, left_input=2713, right_input=2920, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"number node, value=4145","layer":2},{"info":"compute unary expreesion, input=4145, op_id = 5GqDbVmqXU, unary_op_definition = 'a⩁ = { ((↩a)∌(a↺a)) }', output=-30380","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-30380, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯222121/⪩⨒∯231220)⇷(⪩⨒∯1000301⩁)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯222121/⪩⨒∯231220)⇷(⪩⨒∯1000301⩁)","cot":[{"info":"⪩⨒∯222121/⪩⨒∯231220=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1000301⩁=⪩⨒∯-13122230","layer":1},{"info":"⪩⨒∯0⇷⪩⨒∯-13122230=⪩⨒∯0","layer":0}]}
{"id":505,"expression_no_base_symbol":"⊗($3940$⨪↰⇹$4755$)","expression":"⊗(⪩⨒∯331210⨪↰⇹⪩⨒∯1022103)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3964,"operation_count":2,"complexity_ratio":1982.0,"tree":{"type":"unary","operator":"⊗","unary_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":3940,"base":4},"right_expr":{"type":"numeric_atoms","value":4755,"base":4}}},"used_operators":["RhiyfpczSx","tmPS8pqC7x"],"dependent_operators":["nhYeJWJD5X","sJAwomhLZr","Z5m6OM72h2","HrjLwUk87U","rJVOvQCfKK"],"result":"⪩⨒∯-1323020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3940","layer":2},{"info":"number node, value=4755","layer":2},{"info":"compute binary expreesion, left_input=3940, right_input=4755, op_id = tmPS8pqC7x binary_op_definition= 'a⨪↰⇹b = {a, if a == 0; (b)⨎((a-1)⨪↰⇹b), if a > 0 and abs(a) < 1000000; -(b)⨎((a+1)⨪↰⇹b), if a < 0 and abs(a) < 1000000; NaN, else}', output=3940","layer":1},{"info":"compute unary expreesion, input=3940, op_id = RhiyfpczSx, unary_op_definition = '⊗a = { (64∇⊂⋱a) , if (a⪚13)>=164 ; (a∘(a⩠)) , else }', output=-7880","layer":0}],"base":4,"result_base":4,"text":"⊗(⪩⨒∯331210⨪↰⇹⪩⨒∯1022103)=⪩⨒∯-1323020","reverse_text":"⪩⨒∯-1323020=⊗(⪩⨒∯331210⨪↰⇹⪩⨒∯1022103)","cot":[{"info":"⪩⨒∯331210⨪↰⇹⪩⨒∯1022103=⪩⨒∯331210","layer":1},{"info":"⊗⪩⨒∯331210=⪩⨒∯-1323020","layer":0}]}
{"id":506,"expression_no_base_symbol":"($1120$≝⊿$1022$)⨐($3999$∊∟⩊$2420$)","expression":"(⪩⨒∯101200≝⊿⪩⨒∯33332)⨐(⪩⨒∯332133∊∟⩊⪩⨒∯211310)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19,"operation_count":3,"complexity_ratio":6.333333333333333,"tree":{"type":"binary","operator":"⨐","left_expr":{"type":"binary","operator":"≝⊿","left_expr":{"type":"numeric_atoms","value":1120,"base":4},"right_expr":{"type":"numeric_atoms","value":1022,"base":4}},"right_expr":{"type":"binary","operator":"∊∟⩊","left_expr":{"type":"numeric_atoms","value":3999,"base":4},"right_expr":{"type":"numeric_atoms","value":2420,"base":4}}},"used_operators":["Noe24qw2ks","OKKcZfAt5B","ddLRYrp01A"],"dependent_operators":["u6S6b8DprG","2DQ55sFlQl","QMFrweE19q","12rbrZMWeM","59igzFyhWz","A8NUZmVepG","3sJ7IOPOlU"],"result":"⪩⨒∯1303202","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1120","layer":2},{"info":"number node, value=1022","layer":2},{"info":"compute binary expreesion, left_input=1120, right_input=1022, op_id = OKKcZfAt5B binary_op_definition= 'a≝⊿b = { ((82⋳⪒b)⋳⪒a) }', output=-3697","layer":1},{"info":"number node, value=3999","layer":2},{"info":"number node, value=2420","layer":2},{"info":"compute binary expreesion, left_input=3999, right_input=2420, op_id = ddLRYrp01A binary_op_definition= 'a∊∟⩊b = { b , if (b∵≐)>=166 or (a⪇≇⋚4)==505 ; (↥a) , else }', output=2420","layer":1},{"info":"compute binary expreesion, left_input=-3697, right_input=2420, op_id = Noe24qw2ks binary_op_definition= 'a⨐b = { (↽≂a) , if (a⨵⪆301)>43 ; (b⫡⨏a) , else }', output=7394","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101200≝⊿⪩⨒∯33332)⨐(⪩⨒∯332133∊∟⩊⪩⨒∯211310)=⪩⨒∯1303202","reverse_text":"⪩⨒∯1303202=(⪩⨒∯101200≝⊿⪩⨒∯33332)⨐(⪩⨒∯332133∊∟⩊⪩⨒∯211310)","cot":[{"info":"⪩⨒∯101200≝⊿⪩⨒∯33332=⪩⨒∯-321301","layer":1},{"info":"⪩⨒∯332133∊∟⩊⪩⨒∯211310=⪩⨒∯211310","layer":1},{"info":"⪩⨒∯-321301⨐⪩⨒∯211310=⪩⨒∯1303202","layer":0}]}
{"id":507,"expression_no_base_symbol":"$3329$∪⫐$2976$∕⩚(↴⪽⋼$2459$)","expression":"⪩⨒∯310001∪⫐⪩⨒∯232200∕⩚(↴⪽⋼⪩⨒∯212123)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3349,"operation_count":3,"complexity_ratio":1116.3333333333333,"tree":{"type":"binary","operator":"∕⩚","left_expr":{"type":"binary","operator":"∪⫐","left_expr":{"type":"numeric_atoms","value":3329,"base":4},"right_expr":{"type":"numeric_atoms","value":2976,"base":4}},"right_expr":{"type":"unary","operator":"↴⪽⋼","unary_expr":{"type":"numeric_atoms","value":2459,"base":4}}},"used_operators":["z9ffQ9n5Zr","7YooWSwCyH","5TUYCnJO6w"],"dependent_operators":["3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr","rJVOvQCfKK","2DDjHMKMc0","MGuIdZPyUC","UqFzSgLMvQ","k7HXdKtiEU","yyfyN0ffXY","pRsWfj4Fpp","diKm42VcIt"],"result":"⪩⨒∯-310010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3329","layer":2},{"info":"number node, value=2976","layer":2},{"info":"compute binary expreesion, left_input=3329, right_input=2976, op_id = 7YooWSwCyH binary_op_definition= 'a∪⫐b = { ((a⋝⋈⪟b)⨎a) }', output=3329","layer":1},{"info":"number node, value=2459","layer":2},{"info":"compute unary expreesion, input=2459, op_id = 5TUYCnJO6w, unary_op_definition = '↴⪽⋼a = { a , if ((∡a)<5 or (⇘a)>=19 or (⊲⪭a)==199) ; (((a↙a)⇡)⇉⇉) , else }', output=2459","layer":1},{"info":"compute binary expreesion, left_input=3329, right_input=2459, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-3332","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯310001∪⫐⪩⨒∯232200∕⩚(↴⪽⋼⪩⨒∯212123)=⪩⨒∯-310010","reverse_text":"⪩⨒∯-310010=⪩⨒∯310001∪⫐⪩⨒∯232200∕⩚(↴⪽⋼⪩⨒∯212123)","cot":[{"info":"⪩⨒∯310001∪⫐⪩⨒∯232200=⪩⨒∯310001","layer":1},{"info":"↴⪽⋼⪩⨒∯212123=⪩⨒∯212123","layer":1},{"info":"⪩⨒∯310001∕⩚⪩⨒∯212123=⪩⨒∯-310010","layer":0}]}
{"id":508,"expression_no_base_symbol":"≪($1456$∁)","expression":"≪(⪩⨒∯112300∁)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":44,"operation_count":2,"complexity_ratio":22.0,"tree":{"type":"unary","operator":"≪","unary_expr":{"type":"unary","operator":"∁","unary_expr":{"type":"numeric_atoms","value":1456,"base":4}}},"used_operators":["Qtd6bqUJcN","jdwGQqwJi5"],"dependent_operators":["3nqY3DE9mg","09Ly4LVMIf","wEfv7U73WA","tifHPKVTfV","ruOEQAzv1W","iuk5sVOGFA","2DDjHMKMc0"],"result":"⪩⨒∯32101","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1456","layer":2},{"info":"compute unary expreesion, input=1456, op_id = jdwGQqwJi5, unary_op_definition = 'a∁ = { (a⋝⋈⪟a) }', output=1456","layer":1},{"info":"compute unary expreesion, input=1456, op_id = Qtd6bqUJcN, unary_op_definition = '≪a = { ((431⫃⨇a)⪣⫩) , if (a⊍)!=211 or (a⇐≅)==294 ; (↔(a⇼⇔∾a)) , else }', output=913","layer":0}],"base":4,"result_base":4,"text":"≪(⪩⨒∯112300∁)=⪩⨒∯32101","reverse_text":"⪩⨒∯32101=≪(⪩⨒∯112300∁)","cot":[{"info":"⪩⨒∯112300∁=⪩⨒∯112300","layer":1},{"info":"≪⪩⨒∯112300=⪩⨒∯32101","layer":0}]}
{"id":509,"expression_no_base_symbol":"$5322$⨑⩅≇$1765$⋘⨑⨽","expression":"⪩⨒∯1103022⨑⩅≇⪩⨒∯123211⋘⨑⨽","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1831,"operation_count":2,"complexity_ratio":915.5,"tree":{"type":"unary","operator":"⋘⨑⨽","unary_expr":{"type":"binary","operator":"⨑⩅≇","left_expr":{"type":"numeric_atoms","value":5322,"base":4},"right_expr":{"type":"numeric_atoms","value":1765,"base":4}}},"used_operators":["WmT3o8z6ya","h92wMvzauj"],"dependent_operators":["W4YGzv6Whe","DpFCA1CohY","N41Kp7NANJ","8w2t5hMYqp","QMFrweE19q","s3Fd5m9Dh2","3sJ7IOPOlU","nREPSIbpBE","9Isq31Ruls","umQnsF7QlU","8HhzD0ZcuI","u6S6b8DprG","DmTXOeWf9t","AFVx7xoS7T","jLgFTUHLKL","oacrs7FA3X","xNBdhnnwKq"],"result":"⪩⨒∯-103103013","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5322","layer":2},{"info":"number node, value=1765","layer":2},{"info":"compute binary expreesion, left_input=5322, right_input=1765, op_id = h92wMvzauj binary_op_definition= 'a⨑⩅≇b = { (((a⪇≇⋚b)⊬⨰(b⨽582))∌↝a) , if (↽≂a)<10 or (b⊭∹↮)==22 ; ((a⊲⩕⊾(↩a))⪕((a⨚243)⇌⫙⪟(b⪘⫢b))) , else }', output=-15966","layer":1},{"info":"compute unary expreesion, input=-15966, op_id = WmT3o8z6ya, unary_op_definition = 'a⋘⨑⨽ = { ((a⫡⨏a)+(a≋⫹)) , if (⊄⩳↩a)!=44 ; (⋗⩬⋾(394+a)) , else }', output=-79047","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1103022⨑⩅≇⪩⨒∯123211⋘⨑⨽=⪩⨒∯-103103013","reverse_text":"⪩⨒∯-103103013=⪩⨒∯1103022⨑⩅≇⪩⨒∯123211⋘⨑⨽","cot":[{"info":"⪩⨒∯1103022⨑⩅≇⪩⨒∯123211=⪩⨒∯-3321132","layer":1},{"info":"⪩⨒∯-3321132⋘⨑⨽=⪩⨒∯-103103013","layer":0}]}
{"id":510,"expression_no_base_symbol":"$4919$⇣⩺⋵$7447$+(⊀$2573$)","expression":"⪩⨒∯1030313⇣⩺⋵⪩⨒∯1310113+(⊀⪩⨒∯220031)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":75,"operation_count":3,"complexity_ratio":25.0,"tree":{"type":"binary","operator":"+","left_expr":{"type":"binary","operator":"⇣⩺⋵","left_expr":{"type":"numeric_atoms","value":4919,"base":4},"right_expr":{"type":"numeric_atoms","value":7447,"base":4}},"right_expr":{"type":"unary","operator":"⊀","unary_expr":{"type":"numeric_atoms","value":2573,"base":4}}},"used_operators":["W4YGzv6Whe","F4yD0voBRQ","oPMjh9089D"],"dependent_operators":["NTOWxs364D","KPf6cnQVty","8jW3W4yZS5","12rbrZMWeM","g55IO6H4Gj","2DlMacCsIx","Qy55tPpLXF","XIabStNQrY","tifHPKVTfV","glklzrTFfD","sdazOOVcIp","8w2t5hMYqp","Ph9nP6C5qx","g55IO6H4Gj","2td37pGCOC","QMFrweE19q"],"result":"⪩⨒∯2120222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4919","layer":2},{"info":"number node, value=7447","layer":2},{"info":"compute binary expreesion, left_input=4919, right_input=7447, op_id = F4yD0voBRQ binary_op_definition= 'a⇣⩺⋵b = { (((a⩨565)∺≝⩲(5⨸⪁a))⩚⊴⇥(↯⪼(a⋳⪒b))) }', output=-260","layer":1},{"info":"number node, value=2573","layer":2},{"info":"compute unary expreesion, input=2573, op_id = oPMjh9089D, unary_op_definition = '⊀a = { (((⩦⩻⨪67)⪨≂(a⋥≓≎63))⇋≉) , if (a⇼⇔∾9)<290 ; (((⊄⩳↩a)⨁⊸⫻)⫡⨏((a≧⫂∧a)⨸⪁(a≧⫂∧a))) , else }', output=10030","layer":1},{"info":"compute binary expreesion, left_input=-260, right_input=10030, op_id = W4YGzv6Whe binary_op_definition= 'None', output=9770","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1030313⇣⩺⋵⪩⨒∯1310113+(⊀⪩⨒∯220031)=⪩⨒∯2120222","reverse_text":"⪩⨒∯2120222=⪩⨒∯1030313⇣⩺⋵⪩⨒∯1310113+(⊀⪩⨒∯220031)","cot":[{"info":"⪩⨒∯1030313⇣⩺⋵⪩⨒∯1310113=⪩⨒∯-10010","layer":1},{"info":"⊀⪩⨒∯220031=⪩⨒∯2130232","layer":1},{"info":"⪩⨒∯-10010+⪩⨒∯2130232=⪩⨒∯2120222","layer":0}]}
{"id":511,"expression_no_base_symbol":"$5628$∑⇟⊟$5851$⪍↜⋙$3262$⫒⫫$1769$","expression":"⪩⨒∯1113330∑⇟⊟⪩⨒∯1123123⪍↜⋙⪩⨒∯302332⫒⫫⪩⨒∯123221","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":22,"operation_count":3,"complexity_ratio":7.333333333333333,"tree":{"type":"binary","operator":"⪍↜⋙","left_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":5628,"base":4},"right_expr":{"type":"numeric_atoms","value":5851,"base":4}},"right_expr":{"type":"binary","operator":"⫒⫫","left_expr":{"type":"numeric_atoms","value":3262,"base":4},"right_expr":{"type":"numeric_atoms","value":1769,"base":4}}},"used_operators":["L05ObWFQCd","U7g4x0WXJJ","6Ko8hGgeMq"],"dependent_operators":["rysDP5nf3Z","DZ8iAZOCBD","tifHPKVTfV","EBcxylXtPf","QMFrweE19q","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","jdwGQqwJi5","AHs5Up7iyr","AFVx7xoS7T"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5628","layer":2},{"info":"number node, value=5851","layer":2},{"info":"compute binary expreesion, left_input=5628, right_input=5851, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"number node, value=3262","layer":2},{"info":"number node, value=1769","layer":2},{"info":"compute binary expreesion, left_input=3262, right_input=1769, op_id = 6Ko8hGgeMq binary_op_definition= 'a⫒⫫b = { (b≹⇙⪍a) , if (a∁)>135 ; (b⇌⫙⪟a) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = L05ObWFQCd binary_op_definition= 'a⪍↜⋙b = { ((a-b)⊉≛↸(a⫡⨏b)) , if (a⫌⩹⨱)!=88 ; ((a⫡⨏b)⇼⇔∾(a⫌⩹⨱)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1113330∑⇟⊟⪩⨒∯1123123⪍↜⋙⪩⨒∯302332⫒⫫⪩⨒∯123221=NaN","reverse_text":"NaN=⪩⨒∯1113330∑⇟⊟⪩⨒∯1123123⪍↜⋙⪩⨒∯302332⫒⫫⪩⨒∯123221","cot":[{"info":"⪩⨒∯1113330∑⇟⊟⪩⨒∯1123123=NaN","layer":1},{"info":"⪩⨒∯302332⫒⫫⪩⨒∯123221=NaN","layer":1},{"info":"NaN⪍↜⋙NaN=NaN","layer":0}]}
{"id":512,"expression_no_base_symbol":"⨛(⊁⨺$3208$)","expression":"⨛(⊁⨺⪩⨒∯302020)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":52,"operation_count":2,"complexity_ratio":26.0,"tree":{"type":"unary","operator":"⨛","unary_expr":{"type":"unary","operator":"⊁⨺","unary_expr":{"type":"numeric_atoms","value":3208,"base":4}}},"used_operators":["CoMdbyAt7R","PxiHyQbrIp"],"dependent_operators":["U6pG0PXrV3","DyGG3AbaNP","liw5iZPkLH","3DZMoQKiUl","rysDP5nf3Z","e1ybzncUwg","XPYlsWDdGa","23Mk6UjR3U","7j4O788W3g","2td37pGCOC","2DQ55sFlQl","xUOZtlo3hN","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3208","layer":2},{"info":"compute unary expreesion, input=3208, op_id = PxiHyQbrIp, unary_op_definition = '⊁⨺a = { (((⨞⊢a)⋷(3↺a))⨵⪆((⪲⇎a)-(≉a))) , if a>5 ; (((a↺a)⨳⩥⨓(⩦⩻⨪a))⨳⩥⨓((a∲⫓a)⫡⨏(≉a))) , else }', output=160","layer":1},{"info":"compute unary expreesion, input=160, op_id = CoMdbyAt7R, unary_op_definition = '⨛a = { (⊖((≱⇩⩕a)∼(⨡↴a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⨛(⊁⨺⪩⨒∯302020)=NaN","reverse_text":"NaN=⨛(⊁⨺⪩⨒∯302020)","cot":[{"info":"⊁⨺⪩⨒∯302020=⪩⨒∯2200","layer":1},{"info":"⨛⪩⨒∯2200=NaN","layer":0}]}
{"id":513,"expression_no_base_symbol":"($1056$⪛$3150$)⪒⊣⊆(≸$3223$)","expression":"(⪩⨒∯100200⪛⪩⨒∯301032)⪒⊣⊆(≸⪩⨒∯302113)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":64,"operation_count":3,"complexity_ratio":21.333333333333332,"tree":{"type":"binary","operator":"⪒⊣⊆","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":1056,"base":4},"right_expr":{"type":"numeric_atoms","value":3150,"base":4}},"right_expr":{"type":"unary","operator":"≸","unary_expr":{"type":"numeric_atoms","value":3223,"base":4}}},"used_operators":["eRqsBgTDFp","uFcxV4UQCh","eOf03JbCpp"],"dependent_operators":["sdazOOVcIp","W4YGzv6Whe","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","WmT3o8z6ya","l07mrZUIn9","NTOWxs364D","RygbFNSyEJ","tifHPKVTfV","oRDoc9rAEX","IwW236VD4Y","1aApVXNlOP","Z5m6OM72h2","mqXw5SEYmG","IWmyXbctLI"],"result":"⪩⨒∯201000","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1056","layer":2},{"info":"number node, value=3150","layer":2},{"info":"compute binary expreesion, left_input=1056, right_input=3150, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1056","layer":1},{"info":"number node, value=3223","layer":2},{"info":"compute unary expreesion, input=3223, op_id = eOf03JbCpp, unary_op_definition = '≸a = { (29∘((630⊋≦⊧a)⩚⊴⇥(a≦↸a))) , if (a⋘⨑⨽)>2 ; (((a⪮%⊝a)⇼⇔∾(a↪⪝))⫸⊐((a⪮%⊝a)≠≀(3⩇∃⫛a))) , else }', output=58","layer":1},{"info":"compute binary expreesion, left_input=1056, right_input=58, op_id = eRqsBgTDFp binary_op_definition= 'a⪒⊣⊆b = { (b⪨≂a) , if a<=17 ; (a+a) , else }', output=2112","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100200⪛⪩⨒∯301032)⪒⊣⊆(≸⪩⨒∯302113)=⪩⨒∯201000","reverse_text":"⪩⨒∯201000=(⪩⨒∯100200⪛⪩⨒∯301032)⪒⊣⊆(≸⪩⨒∯302113)","cot":[{"info":"⪩⨒∯100200⪛⪩⨒∯301032=⪩⨒∯100200","layer":1},{"info":"≸⪩⨒∯302113=⪩⨒∯322","layer":1},{"info":"⪩⨒∯100200⪒⊣⊆⪩⨒∯322=⪩⨒∯201000","layer":0}]}
{"id":514,"expression_no_base_symbol":"⩦⩻⨪$1503$≥⨤⩑$1002$","expression":"⩦⩻⨪⪩⨒∯113133≥⨤⩑⪩⨒∯33222","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":12,"operation_count":2,"complexity_ratio":6.0,"tree":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"binary","operator":"≥⨤⩑","left_expr":{"type":"numeric_atoms","value":1503,"base":4},"right_expr":{"type":"numeric_atoms","value":1002,"base":4}}},"used_operators":["2td37pGCOC","gJLn6v0xnP"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","mp7IySMOzn","aA7tF3KVD3","QvoQhV0rrE"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1503","layer":2},{"info":"number node, value=1002","layer":2},{"info":"compute binary expreesion, left_input=1503, right_input=1002, op_id = gJLn6v0xnP binary_op_definition= 'a≥⨤⩑b = { (b⇷a) , if (b⪘⨀)>356 ; (702∠⫱488) , else }', output=1234","layer":1},{"info":"compute unary expreesion, input=1234, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=1234","layer":0}],"base":4,"result_base":4,"text":"⩦⩻⨪⪩⨒∯113133≥⨤⩑⪩⨒∯33222=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=⩦⩻⨪⪩⨒∯113133≥⨤⩑⪩⨒∯33222","cot":[{"info":"⪩⨒∯113133≥⨤⩑⪩⨒∯33222=⪩⨒∯103102","layer":1},{"info":"⩦⩻⨪⪩⨒∯103102=⪩⨒∯103102","layer":0}]}
{"id":515,"expression_no_base_symbol":"($1510$∕⩚$5655$)⋥≓≎(⊥$1449$)","expression":"(⪩⨒∯113212∕⩚⪩⨒∯1120113)⋥≓≎(⊥⪩⨒∯112221)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1528,"operation_count":3,"complexity_ratio":509.3333333333333,"tree":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"binary","operator":"∕⩚","left_expr":{"type":"numeric_atoms","value":1510,"base":4},"right_expr":{"type":"numeric_atoms","value":5655,"base":4}},"right_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":1449,"base":4}}},"used_operators":["Qy55tPpLXF","z9ffQ9n5Zr","Q3PJZHRvZv"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr","fu6greOZ01"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1510","layer":2},{"info":"number node, value=5655","layer":2},{"info":"compute binary expreesion, left_input=1510, right_input=5655, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-1513","layer":1},{"info":"number node, value=1449","layer":2},{"info":"compute unary expreesion, input=1449, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-1513, right_input=nan, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=67","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯113212∕⩚⪩⨒∯1120113)⋥≓≎(⊥⪩⨒∯112221)=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=(⪩⨒∯113212∕⩚⪩⨒∯1120113)⋥≓≎(⊥⪩⨒∯112221)","cot":[{"info":"⪩⨒∯113212∕⩚⪩⨒∯1120113=⪩⨒∯-113221","layer":1},{"info":"⊥⪩⨒∯112221=NaN","layer":1},{"info":"⪩⨒∯-113221⋥≓≎NaN=⪩⨒∯1003","layer":0}]}
{"id":516,"expression_no_base_symbol":"↪⫪⫘($1926$⪓⨏)","expression":"↪⫪⫘(⪩⨒∯132012⪓⨏)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2112,"operation_count":2,"complexity_ratio":1056.0,"tree":{"type":"unary","operator":"↪⫪⫘","unary_expr":{"type":"unary","operator":"⪓⨏","unary_expr":{"type":"numeric_atoms","value":1926,"base":4}}},"used_operators":["9dWsAM3GFt","4X9JU4Jbn6"],"dependent_operators":["DyGG3AbaNP","nREPSIbpBE","rysDP5nf3Z","gJLn6v0xnP","nOKPl9n5zu","W9R8I5fN5A","rxpJgHHUmx","inkyxCbjAn","z63VuFQld9","AcOhelriW5","3sJ7IOPOlU","CoMdbyAt7R","cHh1gJQ2o6","xlXykHWxX1","Nsiff2A1zJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1926","layer":2},{"info":"compute unary expreesion, input=1926, op_id = 4X9JU4Jbn6, unary_op_definition = 'a⪓⨏ = { (((⨣⨃⇪a)≭(a⊊))⫢⨠((a⪇≇⋚a)⩘(413≥⨤⩑a))) , if (⇁⨣⪵a)<1 ; ((⋗⩴⪓(191∧))⫢⨠(⨛(a⊴a))) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = 9dWsAM3GFt, unary_op_definition = '↪⫪⫘a = { ((a⨚283)∼(a-a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"↪⫪⫘(⪩⨒∯132012⪓⨏)=NaN","reverse_text":"NaN=↪⫪⫘(⪩⨒∯132012⪓⨏)","cot":[{"info":"⪩⨒∯132012⪓⨏=NaN","layer":1},{"info":"↪⫪⫘NaN=NaN","layer":0}]}
{"id":517,"expression_no_base_symbol":"↘$3567$⫞⩸⩒$3785$","expression":"↘⪩⨒∯313233⫞⩸⩒⪩⨒∯323021","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":28,"operation_count":2,"complexity_ratio":14.0,"tree":{"type":"unary","operator":"↘","unary_expr":{"type":"binary","operator":"⫞⩸⩒","left_expr":{"type":"numeric_atoms","value":3567,"base":4},"right_expr":{"type":"numeric_atoms","value":3785,"base":4}}},"used_operators":["LdNpr8hQHL","XGcMNugi78"],"dependent_operators":["uFcxV4UQCh","VJ330n2nnx","JclMnS0uGI","SWo3A1KBJH","rJVOvQCfKK"],"result":"⪩⨒∯10001","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3567","layer":2},{"info":"number node, value=3785","layer":2},{"info":"compute binary expreesion, left_input=3567, right_input=3785, op_id = XGcMNugi78 binary_op_definition= 'a⫞⩸⩒b = { (a⨎b) , if ((⇋↷b)>164 and (a↬⩅∪)<=12 and (b⨔⇊430)!=387) ; a , else }', output=3785","layer":1},{"info":"compute unary expreesion, input=3785, op_id = LdNpr8hQHL, unary_op_definition = '↘a = { (a⪛392) }', output=257","layer":0}],"base":4,"result_base":4,"text":"↘⪩⨒∯313233⫞⩸⩒⪩⨒∯323021=⪩⨒∯10001","reverse_text":"⪩⨒∯10001=↘⪩⨒∯313233⫞⩸⩒⪩⨒∯323021","cot":[{"info":"⪩⨒∯313233⫞⩸⩒⪩⨒∯323021=⪩⨒∯323021","layer":1},{"info":"↘⪩⨒∯323021=⪩⨒∯10001","layer":0}]}
{"id":518,"expression_no_base_symbol":"⩒∊($1139$⋻⩜⩜$6679$)","expression":"⩒∊(⪩⨒∯101303⋻⩜⩜⪩⨒∯1220113)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":93520,"operation_count":2,"complexity_ratio":46760.0,"tree":{"type":"unary","operator":"⩒∊","unary_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":1139,"base":4},"right_expr":{"type":"numeric_atoms","value":6679,"base":4}}},"used_operators":["qazvmhNBbN","oDCm7WA9JY"],"dependent_operators":["AF7qkfDlqP","f6k1SAg4EE","eLAdDNolq6","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE"],"result":"⪩⨒∯323113","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1139","layer":2},{"info":"number node, value=6679","layer":2},{"info":"compute binary expreesion, left_input=1139, right_input=6679, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=2278","layer":1},{"info":"compute unary expreesion, input=2278, op_id = qazvmhNBbN, unary_op_definition = '⩒∊a = { ((≤/a)⪒(⨑⩽⪐a)) }', output=3799","layer":0}],"base":4,"result_base":4,"text":"⩒∊(⪩⨒∯101303⋻⩜⩜⪩⨒∯1220113)=⪩⨒∯323113","reverse_text":"⪩⨒∯323113=⩒∊(⪩⨒∯101303⋻⩜⩜⪩⨒∯1220113)","cot":[{"info":"⪩⨒∯101303⋻⩜⩜⪩⨒∯1220113=⪩⨒∯203212","layer":1},{"info":"⩒∊⪩⨒∯203212=⪩⨒∯323113","layer":0}]}
{"id":519,"expression_no_base_symbol":"($6689$⪛$6386$)⫯⪬∳$1120$⋹⋡⊁$1140$","expression":"(⪩⨒∯1220201⪛⪩⨒∯1203302)⫯⪬∳⪩⨒∯101200⋹⋡⊁⪩⨒∯101310","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":62550,"operation_count":3,"complexity_ratio":20850.0,"tree":{"type":"binary","operator":"⫯⪬∳","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":6689,"base":4},"right_expr":{"type":"numeric_atoms","value":6386,"base":4}},"right_expr":{"type":"binary","operator":"⋹⋡⊁","left_expr":{"type":"numeric_atoms","value":1120,"base":4},"right_expr":{"type":"numeric_atoms","value":1140,"base":4}}},"used_operators":["d7ASUq0ydm","uFcxV4UQCh","As8RqfVLgs"],"dependent_operators":["Qy55tPpLXF","BjRHVeLaeN","8w2t5hMYqp","Ph9nP6C5qx","eewbuw0ToL","D4vGDi5EA2","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","ljTHtUsqzn","WkeUrDK8WX","fu6greOZ01","xRrnTEsQ6j","oPMjh9089D","ivGwdmUAux"],"result":"⪩⨒∯-11112","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6689","layer":2},{"info":"number node, value=6386","layer":2},{"info":"compute binary expreesion, left_input=6689, right_input=6386, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=303","layer":1},{"info":"number node, value=1120","layer":2},{"info":"number node, value=1140","layer":2},{"info":"compute binary expreesion, left_input=1120, right_input=1140, op_id = As8RqfVLgs binary_op_definition= 'a⋹⋡⊁b = { ((a⨐⩸⫘247)⫁⪎(⩰b)) , if (⫵↿b)==517 or b>135 ; (⊀(≀↧⇸a)) , else }', output=1890","layer":1},{"info":"compute binary expreesion, left_input=303, right_input=1890, op_id = d7ASUq0ydm binary_op_definition= 'a⫯⪬∳b = { ((b⋥≓≎a)≧⫂∧(⊄⩳↩a)) , if (a≦≮≮)!=65 ; ((b⫩⊇)⋥≓≎(a⨰b)) , else }', output=-342","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1220201⪛⪩⨒∯1203302)⫯⪬∳⪩⨒∯101200⋹⋡⊁⪩⨒∯101310=⪩⨒∯-11112","reverse_text":"⪩⨒∯-11112=(⪩⨒∯1220201⪛⪩⨒∯1203302)⫯⪬∳⪩⨒∯101200⋹⋡⊁⪩⨒∯101310","cot":[{"info":"⪩⨒∯1220201⪛⪩⨒∯1203302=⪩⨒∯10233","layer":1},{"info":"⪩⨒∯101200⋹⋡⊁⪩⨒∯101310=⪩⨒∯131202","layer":1},{"info":"⪩⨒∯10233⫯⪬∳⪩⨒∯131202=⪩⨒∯-11112","layer":0}]}
{"id":520,"expression_no_base_symbol":"($1011$⪕$2986$)⇂≾⫗($1226$⨽∌$2158$)","expression":"(⪩⨒∯33303⪕⪩⨒∯232222)⇂≾⫗(⪩⨒∯103022⨽∌⪩⨒∯201232)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":136,"operation_count":3,"complexity_ratio":45.333333333333336,"tree":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"binary","operator":"⪕","left_expr":{"type":"numeric_atoms","value":1011,"base":4},"right_expr":{"type":"numeric_atoms","value":2986,"base":4}},"right_expr":{"type":"binary","operator":"⨽∌","left_expr":{"type":"numeric_atoms","value":1226,"base":4},"right_expr":{"type":"numeric_atoms","value":2158,"base":4}}},"used_operators":["aBQ6xLxuTc","umQnsF7QlU","9samAPKr6k"],"dependent_operators":["g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U","P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF","YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu"],"result":"⪩⨒∯-21130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1011","layer":2},{"info":"number node, value=2986","layer":2},{"info":"compute binary expreesion, left_input=1011, right_input=2986, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=-55","layer":1},{"info":"number node, value=1226","layer":2},{"info":"number node, value=2158","layer":2},{"info":"compute binary expreesion, left_input=1226, right_input=2158, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-55, right_input=0, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-604","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯33303⪕⪩⨒∯232222)⇂≾⫗(⪩⨒∯103022⨽∌⪩⨒∯201232)=⪩⨒∯-21130","reverse_text":"⪩⨒∯-21130=(⪩⨒∯33303⪕⪩⨒∯232222)⇂≾⫗(⪩⨒∯103022⨽∌⪩⨒∯201232)","cot":[{"info":"⪩⨒∯33303⪕⪩⨒∯232222=⪩⨒∯-313","layer":1},{"info":"⪩⨒∯103022⨽∌⪩⨒∯201232=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-313⇂≾⫗⪩⨒∯0=⪩⨒∯-21130","layer":0}]}
{"id":521,"expression_no_base_symbol":"($2584$∝$4554$)⨐⩸⫘(⪡⇡≛$6306$)","expression":"(⪩⨒∯220120∝⪩⨒∯1013022)⨐⩸⫘(⪡⇡≛⪩⨒∯1202202)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":42,"operation_count":3,"complexity_ratio":14.0,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"∝","left_expr":{"type":"numeric_atoms","value":2584,"base":4},"right_expr":{"type":"numeric_atoms","value":4554,"base":4}},"right_expr":{"type":"unary","operator":"⪡⇡≛","unary_expr":{"type":"numeric_atoms","value":6306,"base":4}}},"used_operators":["fu6greOZ01","cTDWOvIxvz","qL4PrbW1Dq"],"dependent_operators":["3ViojmjbAp","7j4O788W3g","W4YGzv6Whe","COABgblf1C","oacrs7FA3X","apS25hmuAe","iuk5sVOGFA","8cLx32lpNA","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2584","layer":2},{"info":"number node, value=4554","layer":2},{"info":"compute binary expreesion, left_input=2584, right_input=4554, op_id = cTDWOvIxvz binary_op_definition= 'a∝b = { ((b↺a)+(b⊭↱b)) }', output=2589","layer":1},{"info":"number node, value=6306","layer":2},{"info":"compute unary expreesion, input=6306, op_id = qL4PrbW1Dq, unary_op_definition = '⪡⇡≛a = { (a∌a) , if (a⪘⫢111)>=396 or (≅≯⇸a)!=229 or (a⪣⫩)<228 ; (a≫≃) , else }', output=-6306","layer":1},{"info":"compute binary expreesion, left_input=2589, right_input=-6306, op_id = fu6greOZ01 binary_op_definition= 'a⨐⩸⫘b = {a, if b == 0; (a⨐⩸⫘(b-1))⨓(b), if b > 0 and abs(b) < 1000; -(a⨐⩸⫘(b+1))⨓(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯220120∝⪩⨒∯1013022)⨐⩸⫘(⪡⇡≛⪩⨒∯1202202)=NaN","reverse_text":"NaN=(⪩⨒∯220120∝⪩⨒∯1013022)⨐⩸⫘(⪡⇡≛⪩⨒∯1202202)","cot":[{"info":"⪩⨒∯220120∝⪩⨒∯1013022=⪩⨒∯220131","layer":1},{"info":"⪡⇡≛⪩⨒∯1202202=⪩⨒∯-1202202","layer":1},{"info":"⪩⨒∯220131⨐⩸⫘⪩⨒∯-1202202=NaN","layer":0}]}
{"id":522,"expression_no_base_symbol":"($1101$⪒$4592$)⪭≯($3238$⋅⇍$1058$)","expression":"(⪩⨒∯101031⪒⪩⨒∯1013300)⪭≯(⪩⨒∯302212⋅⇍⪩⨒∯100202)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5853,"operation_count":3,"complexity_ratio":1951.0,"tree":{"type":"binary","operator":"⪭≯","left_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":1101,"base":4},"right_expr":{"type":"numeric_atoms","value":4592,"base":4}},"right_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":3238,"base":4},"right_expr":{"type":"numeric_atoms","value":1058,"base":4}}},"used_operators":["XAx5wpdLa6","f6k1SAg4EE","AdZkA7nFnk"],"dependent_operators":["9samAPKr6k","HJ9erzHUuu","TpPTUOHfaN","DbCuESL50I","s1XTVnmDOJ","61wBmkZwlr","Z5CJsN7DuW","W4YGzv6Whe","t8gj7n24qd","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1101","layer":2},{"info":"number node, value=4592","layer":2},{"info":"compute binary expreesion, left_input=1101, right_input=4592, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-5693","layer":1},{"info":"number node, value=3238","layer":2},{"info":"number node, value=1058","layer":2},{"info":"compute binary expreesion, left_input=3238, right_input=1058, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"compute binary expreesion, left_input=-5693, right_input=-22, op_id = XAx5wpdLa6 binary_op_definition= 'a⪭≯b = { (((b⨽∌374)⪔⊥(⋼∭⪍b))+⇶⊼((≋a)≓∲(↨⩢⫨a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101031⪒⪩⨒∯1013300)⪭≯(⪩⨒∯302212⋅⇍⪩⨒∯100202)=NaN","reverse_text":"NaN=(⪩⨒∯101031⪒⪩⨒∯1013300)⪭≯(⪩⨒∯302212⋅⇍⪩⨒∯100202)","cot":[{"info":"⪩⨒∯101031⪒⪩⨒∯1013300=⪩⨒∯-1120331","layer":1},{"info":"⪩⨒∯302212⋅⇍⪩⨒∯100202=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯-1120331⪭≯⪩⨒∯-112=NaN","layer":0}]}
{"id":523,"expression_no_base_symbol":"($5250$⪄$4173$)⪡(≋$4790$)","expression":"(⪩⨒∯1102002⪄⪩⨒∯1001031)⪡(≋⪩⨒∯1022312)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":103,"operation_count":3,"complexity_ratio":34.333333333333336,"tree":{"type":"binary","operator":"⪡","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":5250,"base":4},"right_expr":{"type":"numeric_atoms","value":4173,"base":4}},"right_expr":{"type":"unary","operator":"≋","unary_expr":{"type":"numeric_atoms","value":4790,"base":4}}},"used_operators":["oraRL2iQuh","SUmda5xLS4","61wBmkZwlr"],"dependent_operators":["2Wsdkap16l","ljTHtUsqzn","k8jYdgA6NY","8WDwsbhb0R","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","7j4O788W3g"],"result":"⪩⨒∯12001313302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5250","layer":2},{"info":"number node, value=4173","layer":2},{"info":"compute binary expreesion, left_input=5250, right_input=4173, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-789781","layer":1},{"info":"number node, value=4790","layer":2},{"info":"compute unary expreesion, input=4790, op_id = 61wBmkZwlr, unary_op_definition = '≋a = { (a↺a) }', output=4790","layer":1},{"info":"compute binary expreesion, left_input=-789781, right_input=4790, op_id = oraRL2iQuh binary_op_definition= 'a⪡b = { (107%(a⩹b)) , if a>=49 ; (≀↧⇸(∂⩏⊆a)) , else }', output=1580530","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1102002⪄⪩⨒∯1001031)⪡(≋⪩⨒∯1022312)=⪩⨒∯12001313302","reverse_text":"⪩⨒∯12001313302=(⪩⨒∯1102002⪄⪩⨒∯1001031)⪡(≋⪩⨒∯1022312)","cot":[{"info":"⪩⨒∯1102002⪄⪩⨒∯1001031=⪩⨒∯-3000310111","layer":1},{"info":"≋⪩⨒∯1022312=⪩⨒∯1022312","layer":1},{"info":"⪩⨒∯-3000310111⪡⪩⨒∯1022312=⪩⨒∯12001313302","layer":0}]}
{"id":524,"expression_no_base_symbol":"($2783$⊲⩕⊾$9497$)≁$1274$⋹⋡⊁$6921$","expression":"(⪩⨒∯223133⊲⩕⊾⪩⨒∯2110121)≁⪩⨒∯103322⋹⋡⊁⪩⨒∯1230021","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":62628,"operation_count":3,"complexity_ratio":20876.0,"tree":{"type":"binary","operator":"≁","left_expr":{"type":"binary","operator":"⊲⩕⊾","left_expr":{"type":"numeric_atoms","value":2783,"base":4},"right_expr":{"type":"numeric_atoms","value":9497,"base":4}},"right_expr":{"type":"binary","operator":"⋹⋡⊁","left_expr":{"type":"numeric_atoms","value":1274,"base":4},"right_expr":{"type":"numeric_atoms","value":6921,"base":4}}},"used_operators":["8N2wDY1A35","DmTXOeWf9t","As8RqfVLgs"],"dependent_operators":["B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v","23Mk6UjR3U","DZ8iAZOCBD","BjRHVeLaeN","QMFrweE19q","AF7qkfDlqP","COABgblf1C","ljTHtUsqzn","WkeUrDK8WX","fu6greOZ01","xRrnTEsQ6j","oPMjh9089D","ivGwdmUAux"],"result":"⪩⨒∯221232113","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2783","layer":2},{"info":"number node, value=9497","layer":2},{"info":"compute binary expreesion, left_input=2783, right_input=9497, op_id = DmTXOeWf9t binary_op_definition= 'a⊲⩕⊾b = { (((a⊉≛↸b)⊭↱(⨑⩽⪐b))⫡⨏((a⫩⊇)⋷(a⊉≛↸b))) }', output=-136128","layer":1},{"info":"number node, value=1274","layer":2},{"info":"number node, value=6921","layer":2},{"info":"compute binary expreesion, left_input=1274, right_input=6921, op_id = As8RqfVLgs binary_op_definition= 'a⋹⋡⊁b = { ((a⨐⩸⫘247)⫁⪎(⩰b)) , if (⫵↿b)==517 or b>135 ; (⊀(≀↧⇸a)) , else }', output=7671","layer":1},{"info":"compute binary expreesion, left_input=-136128, right_input=7671, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=170903","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯223133⊲⩕⊾⪩⨒∯2110121)≁⪩⨒∯103322⋹⋡⊁⪩⨒∯1230021=⪩⨒∯221232113","reverse_text":"⪩⨒∯221232113=(⪩⨒∯223133⊲⩕⊾⪩⨒∯2110121)≁⪩⨒∯103322⋹⋡⊁⪩⨒∯1230021","cot":[{"info":"⪩⨒∯223133⊲⩕⊾⪩⨒∯2110121=⪩⨒∯-201033000","layer":1},{"info":"⪩⨒∯103322⋹⋡⊁⪩⨒∯1230021=⪩⨒∯1313313","layer":1},{"info":"⪩⨒∯-201033000≁⪩⨒∯1313313=⪩⨒∯221232113","layer":0}]}
{"id":525,"expression_no_base_symbol":"↞≼($4782$⪭≯$1744$)","expression":"↞≼(⪩⨒∯1022232⪭≯⪩⨒∯123100)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":198,"operation_count":2,"complexity_ratio":99.0,"tree":{"type":"unary","operator":"↞≼","unary_expr":{"type":"binary","operator":"⪭≯","left_expr":{"type":"numeric_atoms","value":4782,"base":4},"right_expr":{"type":"numeric_atoms","value":1744,"base":4}}},"used_operators":["DE7zCoGJt9","XAx5wpdLa6"],"dependent_operators":["W4YGzv6Whe","D4vGDi5EA2","23Mk6UjR3U","BjRHVeLaeN","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","u6S6b8DprG","9samAPKr6k","HJ9erzHUuu","TpPTUOHfaN","DbCuESL50I","s1XTVnmDOJ","61wBmkZwlr","Z5CJsN7DuW"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4782","layer":2},{"info":"number node, value=1744","layer":2},{"info":"compute binary expreesion, left_input=4782, right_input=1744, op_id = XAx5wpdLa6 binary_op_definition= 'a⪭≯b = { (((b⨽∌374)⪔⊥(⋼∭⪍b))+⇶⊼((≋a)≓∲(↨⩢⫨a))) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = DE7zCoGJt9, unary_op_definition = '↞≼a = { (↽≂(197⨰(a⨸⪁a))) , if (a⨸⪁373)!=224 ; (((591⋷a)≧⫂∧(a+a))⨸⪁((a⫩⊇)≦≮≮)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"↞≼(⪩⨒∯1022232⪭≯⪩⨒∯123100)=NaN","reverse_text":"NaN=↞≼(⪩⨒∯1022232⪭≯⪩⨒∯123100)","cot":[{"info":"⪩⨒∯1022232⪭≯⪩⨒∯123100=NaN","layer":1},{"info":"↞≼NaN=NaN","layer":0}]}
{"id":526,"expression_no_base_symbol":"($1407$⫃⨇$2323$)⇚⪠","expression":"(⪩⨒∯111333⫃⨇⪩⨒∯210103)⇚⪠","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9352,"operation_count":2,"complexity_ratio":4676.0,"tree":{"type":"unary","operator":"⇚⪠","unary_expr":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"numeric_atoms","value":1407,"base":4},"right_expr":{"type":"numeric_atoms","value":2323,"base":4}}},"used_operators":["Loh9y4A90B","09Ly4LVMIf"],"dependent_operators":["Z5m6OM72h2","9HNa5Wba9A","ztP7wcbY7m","9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG"],"result":"⪩⨒∯-11121021313200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1407","layer":2},{"info":"number node, value=2323","layer":2},{"info":"compute binary expreesion, left_input=1407, right_input=2323, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=-9324","layer":1},{"info":"compute unary expreesion, input=-9324, op_id = Loh9y4A90B, unary_op_definition = 'a⇚⪠ = { ((a∘(a∈))*a) }', output=-90480096","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯111333⫃⨇⪩⨒∯210103)⇚⪠=⪩⨒∯-11121021313200","reverse_text":"⪩⨒∯-11121021313200=(⪩⨒∯111333⫃⨇⪩⨒∯210103)⇚⪠","cot":[{"info":"⪩⨒∯111333⫃⨇⪩⨒∯210103=⪩⨒∯-2101230","layer":1},{"info":"⪩⨒∯-2101230⇚⪠=⪩⨒∯-11121021313200","layer":0}]}
{"id":527,"expression_no_base_symbol":"$3730$⊱⇼⊻$7140$↱($3248$↛⩡⫤)","expression":"⪩⨒∯322102⊱⇼⊻⪩⨒∯1233210↱(⪩⨒∯302300↛⩡⫤)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9937,"operation_count":3,"complexity_ratio":3312.3333333333335,"tree":{"type":"binary","operator":"↱","left_expr":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"numeric_atoms","value":3730,"base":4},"right_expr":{"type":"numeric_atoms","value":7140,"base":4}},"right_expr":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"numeric_atoms","value":3248,"base":4}}},"used_operators":["SR5kFfdi6N","FyVja0WsTP","FU0Cs4j7VP"],"dependent_operators":["k4iM1060OG","eOf03JbCpp","2GS7woTJqF","XnXgA4xnOs","ddLRYrp01A","Noe24qw2ks","bF6eod5Gvf","Nsiff2A1zJ","j9kHMeSvPp","pRsWfj4Fpp","apS25hmuAe","W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X"],"result":"⪩⨒∯-32302201320","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3730","layer":2},{"info":"number node, value=7140","layer":2},{"info":"compute binary expreesion, left_input=3730, right_input=7140, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":1},{"info":"number node, value=3248","layer":2},{"info":"compute unary expreesion, input=3248, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-486537","layer":1},{"info":"compute binary expreesion, left_input=434, right_input=-486537, op_id = SR5kFfdi6N binary_op_definition= 'a↱b = { ((≸a)⊴((b∊∟⩊b)⨐(a+⪬∐830))) , if (a==35 or (b∀⊥⇻)>46) ; ((≅≯⇸b)→⨶⪴((∡b)⪭(b⨑≵⋬499))) , else }', output=-3876984","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯322102⊱⇼⊻⪩⨒∯1233210↱(⪩⨒∯302300↛⩡⫤)=⪩⨒∯-32302201320","reverse_text":"⪩⨒∯-32302201320=⪩⨒∯322102⊱⇼⊻⪩⨒∯1233210↱(⪩⨒∯302300↛⩡⫤)","cot":[{"info":"⪩⨒∯322102⊱⇼⊻⪩⨒∯1233210=⪩⨒∯12302","layer":1},{"info":"⪩⨒∯302300↛⩡⫤=⪩⨒∯-1312302021","layer":1},{"info":"⪩⨒∯12302↱⪩⨒∯-1312302021=⪩⨒∯-32302201320","layer":0}]}
{"id":528,"expression_no_base_symbol":"($1040$≦↸$3656$)≌($2918$⊠≄⫣)","expression":"(⪩⨒∯100100≦↸⪩⨒∯321020)≌(⪩⨒∯231212⊠≄⫣)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":156,"operation_count":3,"complexity_ratio":52.0,"tree":{"type":"binary","operator":"≌","left_expr":{"type":"binary","operator":"≦↸","left_expr":{"type":"numeric_atoms","value":1040,"base":4},"right_expr":{"type":"numeric_atoms","value":3656,"base":4}},"right_expr":{"type":"unary","operator":"⊠≄⫣","unary_expr":{"type":"numeric_atoms","value":2918,"base":4}}},"used_operators":["lyWz822IDG","RygbFNSyEJ","DIvbN7qnHd"],"dependent_operators":["B5M0gjZbta","W7eaUhjymW","CpSg5vQTgA","w2P8NbNXyL","0kmYd0q39Y","3sJ7IOPOlU","Bmrmz2XGnR","WkeUrDK8WX","03sUfWo75k","5twsqlHp2o","oacrs7FA3X","aMUSaJuDRU","eLAdDNolq6","e1ybzncUwg","DZ8iAZOCBD","XIabStNQrY","12rbrZMWeM","2DDjHMKMc0","g55IO6H4Gj","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯2031320","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1040","layer":2},{"info":"number node, value=3656","layer":2},{"info":"compute binary expreesion, left_input=1040, right_input=3656, op_id = RygbFNSyEJ binary_op_definition= 'a≦↸b = { (((≤/a)⋳⪒(b⊉≛↸a))⋝⋈⪟((a⇋≉)⨸⪁(≉a))) }', output=-8711","layer":1},{"info":"number node, value=2918","layer":2},{"info":"compute unary expreesion, input=2918, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-8711, right_input=0, op_id = lyWz822IDG binary_op_definition= 'a≌b = { (≛((132⩦9)⊉↱≁(a⪇≇⋚a))) , if (a⪘⫢419)==234 ; (((⩰124)≚⊃≕(b⨴∎))⊢((16⨉)↬(a⊟⇱))) , else }', output=9080","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100100≦↸⪩⨒∯321020)≌(⪩⨒∯231212⊠≄⫣)=⪩⨒∯2031320","reverse_text":"⪩⨒∯2031320=(⪩⨒∯100100≦↸⪩⨒∯321020)≌(⪩⨒∯231212⊠≄⫣)","cot":[{"info":"⪩⨒∯100100≦↸⪩⨒∯321020=⪩⨒∯-2020013","layer":1},{"info":"⪩⨒∯231212⊠≄⫣=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-2020013≌⪩⨒∯0=⪩⨒∯2031320","layer":0}]}
{"id":529,"expression_no_base_symbol":"$1948$⊕∕$1029$⊹∫⫚$2572$⪢$2123$","expression":"⪩⨒∯132130⊕∕⪩⨒∯100011⊹∫⫚⪩⨒∯220030⪢⪩⨒∯201023","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3349,"operation_count":3,"complexity_ratio":1116.3333333333333,"tree":{"type":"binary","operator":"⊹∫⫚","left_expr":{"type":"binary","operator":"⊕∕","left_expr":{"type":"numeric_atoms","value":1948,"base":4},"right_expr":{"type":"numeric_atoms","value":1029,"base":4}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":2572,"base":4},"right_expr":{"type":"numeric_atoms","value":2123,"base":4}}},"used_operators":["uWAJUKEvyW","9cloC0Ngie","dWAJyo7jo9"],"dependent_operators":["BiWNJpBvwn","w2P8NbNXyL","vg4gO5BX6G","k8jYdgA6NY","g55IO6H4Gj","2td37pGCOC","jLgFTUHLKL","Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1948","layer":2},{"info":"number node, value=1029","layer":2},{"info":"compute binary expreesion, left_input=1948, right_input=1029, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=1948","layer":1},{"info":"number node, value=2572","layer":2},{"info":"number node, value=2123","layer":2},{"info":"compute binary expreesion, left_input=2572, right_input=2123, op_id = dWAJyo7jo9 binary_op_definition= 'a⪢b = {b, if b == 0; (a)%(a⪢(b-1)), if b > 0 and abs(b) < 1000000; -(a)%(a⪢(b+1)), if b < 0 and abs(b) < 1000000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1948, right_input=nan, op_id = uWAJUKEvyW binary_op_definition= 'a⊹∫⫚b = { (↩(a⊨b)) , if (⩦⩻⨪a)==479 or (b⊉↱≁467)==779 ; ((b⨸⪁b)%(b⩍⋽⫝̸187)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯132130⊕∕⪩⨒∯100011⊹∫⫚⪩⨒∯220030⪢⪩⨒∯201023=NaN","reverse_text":"NaN=⪩⨒∯132130⊕∕⪩⨒∯100011⊹∫⫚⪩⨒∯220030⪢⪩⨒∯201023","cot":[{"info":"⪩⨒∯132130⊕∕⪩⨒∯100011=⪩⨒∯132130","layer":1},{"info":"⪩⨒∯220030⪢⪩⨒∯201023=NaN","layer":1},{"info":"⪩⨒∯132130⊹∫⫚NaN=NaN","layer":0}]}
{"id":530,"expression_no_base_symbol":"($2709$⩧⪆$1604$)↬$2535$∇⊂⋱$2127$","expression":"(⪩⨒∯222111⩧⪆⪩⨒∯121010)↬⪩⨒∯213213∇⊂⋱⪩⨒∯201033","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15,"operation_count":3,"complexity_ratio":5.0,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"numeric_atoms","value":2709,"base":4},"right_expr":{"type":"numeric_atoms","value":1604,"base":4}},"right_expr":{"type":"binary","operator":"∇⊂⋱","left_expr":{"type":"numeric_atoms","value":2535,"base":4},"right_expr":{"type":"numeric_atoms","value":2127,"base":4}}},"used_operators":["B5M0gjZbta","Ikt5ks8PT7","nhYeJWJD5X"],"dependent_operators":["rGHVDoGpnC","eewbuw0ToL","t8gj7n24qd","P8v4zCKN1o","23Mk6UjR3U","f6k1SAg4EE","AF7qkfDlqP","nCS4ZIUYfx"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2709","layer":2},{"info":"number node, value=1604","layer":2},{"info":"compute binary expreesion, left_input=2709, right_input=1604, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-1604","layer":1},{"info":"number node, value=2535","layer":2},{"info":"number node, value=2127","layer":2},{"info":"compute binary expreesion, left_input=2535, right_input=2127, op_id = nhYeJWJD5X binary_op_definition= 'a∇⊂⋱b = { (b⪒b) , if a<143 ; ((⨑⩽⪐a)⋷(∥⊫(a⨳⩥⨓a))) , else }', output=4524","layer":1},{"info":"compute binary expreesion, left_input=-1604, right_input=4524, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯222111⩧⪆⪩⨒∯121010)↬⪩⨒∯213213∇⊂⋱⪩⨒∯201033=NaN","reverse_text":"NaN=(⪩⨒∯222111⩧⪆⪩⨒∯121010)↬⪩⨒∯213213∇⊂⋱⪩⨒∯201033","cot":[{"info":"⪩⨒∯222111⩧⪆⪩⨒∯121010=⪩⨒∯-121010","layer":1},{"info":"⪩⨒∯213213∇⊂⋱⪩⨒∯201033=⪩⨒∯1012230","layer":1},{"info":"⪩⨒∯-121010↬⪩⨒∯1012230=NaN","layer":0}]}
{"id":531,"expression_no_base_symbol":"(≸$2981$)⫉⨲⊜$1952$↢$2943$","expression":"(≸⪩⨒∯232211)⫉⨲⊜⪩⨒∯132200↢⪩⨒∯231333","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":104,"operation_count":3,"complexity_ratio":34.666666666666664,"tree":{"type":"binary","operator":"⫉⨲⊜","left_expr":{"type":"unary","operator":"≸","unary_expr":{"type":"numeric_atoms","value":2981,"base":4}},"right_expr":{"type":"binary","operator":"↢","left_expr":{"type":"numeric_atoms","value":1952,"base":4},"right_expr":{"type":"numeric_atoms","value":2943,"base":4}}},"used_operators":["WhqkvtTD3t","eOf03JbCpp","WR6HLWljOP"],"dependent_operators":["eewbuw0ToL","zVYPLywUTj","WmT3o8z6ya","l07mrZUIn9","NTOWxs364D","RygbFNSyEJ","tifHPKVTfV","oRDoc9rAEX","IwW236VD4Y","1aApVXNlOP","Z5m6OM72h2","mqXw5SEYmG","IWmyXbctLI","eLAdDNolq6","g55IO6H4Gj","7j4O788W3g","12rbrZMWeM","f6k1SAg4EE","i8ToyICDmI","COABgblf1C"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2981","layer":2},{"info":"compute unary expreesion, input=2981, op_id = eOf03JbCpp, unary_op_definition = '≸a = { (29∘((630⊋≦⊧a)⩚⊴⇥(a≦↸a))) , if (a⋘⨑⨽)>2 ; (((a⪮%⊝a)⇼⇔∾(a↪⪝))⫸⊐((a⪮%⊝a)≠≀(3⩇∃⫛a))) , else }', output=58","layer":1},{"info":"number node, value=1952","layer":2},{"info":"number node, value=2943","layer":2},{"info":"compute binary expreesion, left_input=1952, right_input=2943, op_id = WR6HLWljOP binary_op_definition= 'a↢b = { ((a∲⫓a)⪒(≤/a)) , if (a⊭↱114)<=535 ; ((a⋳⪒749)↺(b⨸⪁a)) , else }', output=1468","layer":1},{"info":"compute binary expreesion, left_input=58, right_input=1468, op_id = WhqkvtTD3t binary_op_definition= 'a⫉⨲⊜b = { (b⨰120) , if b<=7 ; (a⊪) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(≸⪩⨒∯232211)⫉⨲⊜⪩⨒∯132200↢⪩⨒∯231333=⪩⨒∯0","reverse_text":"⪩⨒∯0=(≸⪩⨒∯232211)⫉⨲⊜⪩⨒∯132200↢⪩⨒∯231333","cot":[{"info":"≸⪩⨒∯232211=⪩⨒∯322","layer":1},{"info":"⪩⨒∯132200↢⪩⨒∯231333=⪩⨒∯112330","layer":1},{"info":"⪩⨒∯322⫉⨲⊜⪩⨒∯112330=⪩⨒∯0","layer":0}]}
{"id":532,"expression_no_base_symbol":"(⇖⫷⫕$5197$)⋥⋵⩄($1188$⨳⩥⨓$2305$)","expression":"(⇖⫷⫕⪩⨒∯1101031)⋥⋵⩄(⪩⨒∯102210⨳⩥⨓⪩⨒∯210001)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":835,"operation_count":3,"complexity_ratio":278.3333333333333,"tree":{"type":"binary","operator":"⋥⋵⩄","left_expr":{"type":"unary","operator":"⇖⫷⫕","unary_expr":{"type":"numeric_atoms","value":5197,"base":4}},"right_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":1188,"base":4},"right_expr":{"type":"numeric_atoms","value":2305,"base":4}}},"used_operators":["7t3wd0Fuz7","UHmRx3INFg","nCS4ZIUYfx"],"dependent_operators":["IWmyXbctLI","2td37pGCOC","AFVx7xoS7T","DE7zCoGJt9","FyVja0WsTP","oZj3VtZNQx","DyGG3AbaNP","W4YGzv6Whe","rysDP5nf3Z"],"result":"⪩⨒∯1301","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5197","layer":2},{"info":"compute unary expreesion, input=5197, op_id = UHmRx3INFg, unary_op_definition = '⇖⫷⫕a = { ((a∼125)≀⫉(↞≼(a⊱⇼⊻51))) }', output=2822","layer":1},{"info":"number node, value=1188","layer":2},{"info":"number node, value=2305","layer":2},{"info":"compute binary expreesion, left_input=1188, right_input=2305, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=1117","layer":1},{"info":"compute binary expreesion, left_input=2822, right_input=1117, op_id = 7t3wd0Fuz7 binary_op_definition= 'a⋥⋵⩄b = { ((⩦⩻⨪a)⇌⫙⪟(b⪮%⊝b)) }', output=113","layer":0}],"base":4,"result_base":4,"text":"(⇖⫷⫕⪩⨒∯1101031)⋥⋵⩄(⪩⨒∯102210⨳⩥⨓⪩⨒∯210001)=⪩⨒∯1301","reverse_text":"⪩⨒∯1301=(⇖⫷⫕⪩⨒∯1101031)⋥⋵⩄(⪩⨒∯102210⨳⩥⨓⪩⨒∯210001)","cot":[{"info":"⇖⫷⫕⪩⨒∯1101031=⪩⨒∯230012","layer":1},{"info":"⪩⨒∯102210⨳⩥⨓⪩⨒∯210001=⪩⨒∯101131","layer":1},{"info":"⪩⨒∯230012⋥⋵⩄⪩⨒∯101131=⪩⨒∯1301","layer":0}]}
{"id":533,"expression_no_base_symbol":"$6355$≁$6205$⩠","expression":"⪩⨒∯1203103≁⪩⨒∯1200331⩠","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":87,"operation_count":2,"complexity_ratio":43.5,"tree":{"type":"unary","operator":"⩠","unary_expr":{"type":"binary","operator":"≁","left_expr":{"type":"numeric_atoms","value":6355,"base":4},"right_expr":{"type":"numeric_atoms","value":6205,"base":4}}},"used_operators":["sJAwomhLZr","8N2wDY1A35"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","k8jYdgA6NY","eH2TOUuTDT","W4YGzv6Whe","Z2TMIBDE3Q","COABgblf1C","B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6355","layer":2},{"info":"number node, value=6205","layer":2},{"info":"compute binary expreesion, left_input=6355, right_input=6205, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=135719","layer":1},{"info":"compute unary expreesion, input=135719, op_id = sJAwomhLZr, unary_op_definition = 'a⩠ = { (((a+a)⊭↱(a⪨≂a))∲⫓((a⩤)%(a⪐))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1203103≁⪩⨒∯1200331⩠=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯1203103≁⪩⨒∯1200331⩠","cot":[{"info":"⪩⨒∯1203103≁⪩⨒∯1200331=⪩⨒∯201020213","layer":1},{"info":"⪩⨒∯201020213⩠=⪩⨒∯0","layer":0}]}
{"id":534,"expression_no_base_symbol":"($1483$⋭≵$1852$)≥⨤⩑$4858$⨚$2307$","expression":"(⪩⨒∯113023⋭≵⪩⨒∯130330)≥⨤⩑⪩⨒∯1023322⨚⪩⨒∯210003","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":82,"operation_count":3,"complexity_ratio":27.333333333333332,"tree":{"type":"binary","operator":"≥⨤⩑","left_expr":{"type":"binary","operator":"⋭≵","left_expr":{"type":"numeric_atoms","value":1483,"base":4},"right_expr":{"type":"numeric_atoms","value":1852,"base":4}},"right_expr":{"type":"binary","operator":"⨚","left_expr":{"type":"numeric_atoms","value":4858,"base":4},"right_expr":{"type":"numeric_atoms","value":2307,"base":4}}},"used_operators":["gJLn6v0xnP","jBncVCNhdl","nREPSIbpBE"],"dependent_operators":["mp7IySMOzn","aA7tF3KVD3","QvoQhV0rrE","RygbFNSyEJ","gx7XJ7hdpj","9ICcGScMcE","C6VvDP6HwP","mqXw5SEYmG","7IPrd9c3lf","COABgblf1C","BjRHVeLaeN","12rbrZMWeM"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1483","layer":2},{"info":"number node, value=1852","layer":2},{"info":"compute binary expreesion, left_input=1483, right_input=1852, op_id = jBncVCNhdl binary_op_definition= 'a⋭≵b = { ((156≦↸a)⊭↱(≦∁b)) , if (b⫸⊐434)<=441 and (a⫸⇳180)>=132 ; ((a⪑⩈)⊵↤) , else }', output=67","layer":1},{"info":"number node, value=4858","layer":2},{"info":"number node, value=2307","layer":2},{"info":"compute binary expreesion, left_input=4858, right_input=2307, op_id = nREPSIbpBE binary_op_definition= 'a⨚b = { (((b⋳⪒a)⋳⪒31)⫩⊇) }', output=1422","layer":1},{"info":"compute binary expreesion, left_input=67, right_input=1422, op_id = gJLn6v0xnP binary_op_definition= 'a≥⨤⩑b = { (b⇷a) , if (b⪘⨀)>356 ; (702∠⫱488) , else }', output=1234","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯113023⋭≵⪩⨒∯130330)≥⨤⩑⪩⨒∯1023322⨚⪩⨒∯210003=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=(⪩⨒∯113023⋭≵⪩⨒∯130330)≥⨤⩑⪩⨒∯1023322⨚⪩⨒∯210003","cot":[{"info":"⪩⨒∯113023⋭≵⪩⨒∯130330=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯1023322⨚⪩⨒∯210003=⪩⨒∯112032","layer":1},{"info":"⪩⨒∯1003≥⨤⩑⪩⨒∯112032=⪩⨒∯103102","layer":0}]}
{"id":535,"expression_no_base_symbol":"⇜$1868$⨥⫆$2764$","expression":"⇜⪩⨒∯131030⨥⫆⪩⨒∯223030","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":335,"operation_count":2,"complexity_ratio":167.5,"tree":{"type":"unary","operator":"⇜","unary_expr":{"type":"binary","operator":"⨥⫆","left_expr":{"type":"numeric_atoms","value":1868,"base":4},"right_expr":{"type":"numeric_atoms","value":2764,"base":4}}},"used_operators":["lFBm8KRb8F","yXekIHxTD4"],"dependent_operators":["s3Fd5m9Dh2","DlLNRPXxWL","ZvLB05nZmT","6o9Blt3TJ6","f6k1SAg4EE","1h0rLqGiFr","eRqsBgTDFp","ancx8kZcWl","oacrs7FA3X"],"result":"⪩⨒∯-22221320","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1868","layer":2},{"info":"number node, value=2764","layer":2},{"info":"compute binary expreesion, left_input=1868, right_input=2764, op_id = yXekIHxTD4 binary_op_definition= 'a⨥⫆b = { (b⨝⩣∺) , if (a⪒⊣⊆344)<109 ; (b⪘⫢a) , else }', output=5404","layer":1},{"info":"compute unary expreesion, input=5404, op_id = lFBm8KRb8F, unary_op_definition = '⇜a = { ((a⫳≱↱a)⊬⨰(a⪒a)) , if a>51 ; ((⩷10)⫰⋱(⫛⫱⨽a)) , else }', output=-43640","layer":0}],"base":4,"result_base":4,"text":"⇜⪩⨒∯131030⨥⫆⪩⨒∯223030=⪩⨒∯-22221320","reverse_text":"⪩⨒∯-22221320=⇜⪩⨒∯131030⨥⫆⪩⨒∯223030","cot":[{"info":"⪩⨒∯131030⨥⫆⪩⨒∯223030=⪩⨒∯1110130","layer":1},{"info":"⇜⪩⨒∯1110130=⪩⨒∯-22221320","layer":0}]}
{"id":536,"expression_no_base_symbol":"≑⋹($7712$⋝⋈⪟$2012$)","expression":"≑⋹(⪩⨒∯1320200⋝⋈⪟⪩⨒∯133130)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":109,"operation_count":2,"complexity_ratio":54.5,"tree":{"type":"unary","operator":"≑⋹","unary_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":7712,"base":4},"right_expr":{"type":"numeric_atoms","value":2012,"base":4}}},"used_operators":["6B9nyZLogK","2DDjHMKMc0"],"dependent_operators":["aBQ6xLxuTc","zR4jO40bMj","RabNbG55vr","ocnLzx9CaJ","3ViojmjbAp","FlXk3pOYe8","o20kRiQErp","4JB6nKBMSY","2td37pGCOC","COABgblf1C","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯121302","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7712","layer":2},{"info":"number node, value=2012","layer":2},{"info":"compute binary expreesion, left_input=7712, right_input=2012, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=7712","layer":1},{"info":"compute unary expreesion, input=7712, op_id = 6B9nyZLogK, unary_op_definition = '≑⋹a = { (((a⨓a)⫣⪄⊒(148∸))⇴(⩦⩻⨪(a⇂≾⫗a))) , if a<188 ; (⩎⋉((a⩼⇪↪a)⊭↱(a⪶≀⋏172))) , else }', output=1650","layer":0}],"base":4,"result_base":4,"text":"≑⋹(⪩⨒∯1320200⋝⋈⪟⪩⨒∯133130)=⪩⨒∯121302","reverse_text":"⪩⨒∯121302=≑⋹(⪩⨒∯1320200⋝⋈⪟⪩⨒∯133130)","cot":[{"info":"⪩⨒∯1320200⋝⋈⪟⪩⨒∯133130=⪩⨒∯1320200","layer":1},{"info":"≑⋹⪩⨒∯1320200=⪩⨒∯121302","layer":0}]}
{"id":537,"expression_no_base_symbol":"$1623$≚⊃≕$2275$≃($3035$⊪)","expression":"⪩⨒∯121113≚⊃≕⪩⨒∯203203≃(⪩⨒∯233123⊪)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":72,"operation_count":3,"complexity_ratio":24.0,"tree":{"type":"binary","operator":"≃","left_expr":{"type":"binary","operator":"≚⊃≕","left_expr":{"type":"numeric_atoms","value":1623,"base":4},"right_expr":{"type":"numeric_atoms","value":2275,"base":4}},"right_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":3035,"base":4}}},"used_operators":["YbVcJGFEVW","Bmrmz2XGnR","zVYPLywUTj"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","23Mk6UjR3U","JLbD19bQDL","7j4O788W3g","glklzrTFfD","tifHPKVTfV","t8gj7n24qd","i8ToyICDmI","COABgblf1C","9FxExcQeMw","Qy55tPpLXF","7j4O788W3g","sdazOOVcIp","8w2t5hMYqp","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL"],"result":"⪩⨒∯-1100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1623","layer":2},{"info":"number node, value=2275","layer":2},{"info":"compute binary expreesion, left_input=1623, right_input=2275, op_id = Bmrmz2XGnR binary_op_definition= 'a≚⊃≕b = { (-((⊄⩳↩b)⪨≂(a⩷∴b))) , if ((b⫡⨏524)<690 or (⨞⊢a)>=395) ; ((⊄⩳↩(b⋥≓≎a))⋥≓≎((a↺a)⪨≂(479⨸⪁a))) , else }', output=67","layer":1},{"info":"number node, value=3035","layer":2},{"info":"compute unary expreesion, input=3035, op_id = zVYPLywUTj, unary_op_definition = 'a⊪ = { (((a*a)+(18⨵⪆91))⪨≂((62⋥≓≎a)*(a⪒a))) , if (≉a)<304 or (a⫩⊇)==292 ; ((⊄⩳↩(a⪠⩆⊳))*((a/a)≧⫂∧(21*a))) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=67, right_input=0, op_id = YbVcJGFEVW binary_op_definition= 'a≃b = { (((13⋥≓≎b)⋷(a⇼⇔∾b))⨁⊸⫻) , if ((b⨁⊸⫻)>=162 or (b⪠⩆⊳)<=569) ; ((-(17⋷a))↺((a⩷∴a)⊭↱(b∲⫓a))) , else }', output=-80","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯121113≚⊃≕⪩⨒∯203203≃(⪩⨒∯233123⊪)=⪩⨒∯-1100","reverse_text":"⪩⨒∯-1100=⪩⨒∯121113≚⊃≕⪩⨒∯203203≃(⪩⨒∯233123⊪)","cot":[{"info":"⪩⨒∯121113≚⊃≕⪩⨒∯203203=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯233123⊪=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1003≃⪩⨒∯0=⪩⨒∯-1100","layer":0}]}
{"id":538,"expression_no_base_symbol":"∡$2172$⊔$6807$","expression":"∡⪩⨒∯201330⊔⪩⨒∯1222113","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":27,"operation_count":2,"complexity_ratio":13.5,"tree":{"type":"unary","operator":"∡","unary_expr":{"type":"binary","operator":"⊔","left_expr":{"type":"numeric_atoms","value":2172,"base":4},"right_expr":{"type":"numeric_atoms","value":6807,"base":4}}},"used_operators":["pRsWfj4Fpp","E4l6HwMY31"],"dependent_operators":["D4vGDi5EA2","DZ8iAZOCBD","2DDjHMKMc0","W4YGzv6Whe","DpFCA1CohY","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","QMFrweE19q"],"result":"⪩⨒∯-20302023","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2172","layer":2},{"info":"number node, value=6807","layer":2},{"info":"compute binary expreesion, left_input=2172, right_input=6807, op_id = E4l6HwMY31 binary_op_definition= 'a⊔b = { (((a≧⫂∧b)∲⫓(⋗⩬⋾b))⫡⨏((b⪒a)≧⫂∧(a+64))) }', output=35979","layer":1},{"info":"compute unary expreesion, input=35979, op_id = pRsWfj4Fpp, unary_op_definition = '∡a = { ((a≦≮≮)⊉≛↸(a⋝⋈⪟a)) }', output=-35979","layer":0}],"base":4,"result_base":4,"text":"∡⪩⨒∯201330⊔⪩⨒∯1222113=⪩⨒∯-20302023","reverse_text":"⪩⨒∯-20302023=∡⪩⨒∯201330⊔⪩⨒∯1222113","cot":[{"info":"⪩⨒∯201330⊔⪩⨒∯1222113=⪩⨒∯20302023","layer":1},{"info":"∡⪩⨒∯20302023=⪩⨒∯-20302023","layer":0}]}
{"id":539,"expression_no_base_symbol":"⫶⊄≣($4426$⨱∎)","expression":"⫶⊄≣(⪩⨒∯1011022⨱∎)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":27,"operation_count":2,"complexity_ratio":13.5,"tree":{"type":"unary","operator":"⫶⊄≣","unary_expr":{"type":"unary","operator":"⨱∎","unary_expr":{"type":"numeric_atoms","value":4426,"base":4}}},"used_operators":["wxb3vTeyAj","MmTdOpaElr"],"dependent_operators":["eLAdDNolq6","3nqY3DE9mg","8HhzD0ZcuI","tifHPKVTfV"],"result":"⪩⨒∯-123302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4426","layer":2},{"info":"compute unary expreesion, input=4426, op_id = MmTdOpaElr, unary_op_definition = 'a⨱∎ = { (a⇼⇔∾a) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = wxb3vTeyAj, unary_op_definition = '⫶⊄≣a = { (≤/((a⨽a)⊍)) }', output=-1778","layer":0}],"base":4,"result_base":4,"text":"⫶⊄≣(⪩⨒∯1011022⨱∎)=⪩⨒∯-123302","reverse_text":"⪩⨒∯-123302=⫶⊄≣(⪩⨒∯1011022⨱∎)","cot":[{"info":"⪩⨒∯1011022⨱∎=⪩⨒∯0","layer":1},{"info":"⫶⊄≣⪩⨒∯0=⪩⨒∯-123302","layer":0}]}
{"id":540,"expression_no_base_symbol":"$4257$≎⪠$3354$∲⫓$4385$≦↸$2109$","expression":"⪩⨒∯1002201≎⪠⪩⨒∯310122∲⫓⪩⨒∯1010201≦↸⪩⨒∯200331","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19127,"operation_count":3,"complexity_ratio":6375.666666666667,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"≎⪠","left_expr":{"type":"numeric_atoms","value":4257,"base":4},"right_expr":{"type":"numeric_atoms","value":3354,"base":4}},"right_expr":{"type":"binary","operator":"≦↸","left_expr":{"type":"numeric_atoms","value":4385,"base":4},"right_expr":{"type":"numeric_atoms","value":2109,"base":4}}},"used_operators":["i8ToyICDmI","aNhz54LH3e","RygbFNSyEJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","bl5wxAcryP","RygbFNSyEJ","SLLxy00UIr","AcOhelriW5","ctOc4cKSDt","cHh1gJQ2o6","KYD54nUTWz","kbkesczE7y","BUOGQAYlQx","PPChnnnBFF","eLAdDNolq6","e1ybzncUwg","DZ8iAZOCBD","XIabStNQrY","12rbrZMWeM","2DDjHMKMc0","g55IO6H4Gj"],"result":"⪩⨒∯10301212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4257","layer":2},{"info":"number node, value=3354","layer":2},{"info":"compute binary expreesion, left_input=4257, right_input=3354, op_id = aNhz54LH3e binary_op_definition= 'a≎⪠b = { (((a⫥∨⫟11)≦↸(657∣a))⩘((⇈a)≬⋮(a↰))) , if a==21 ; (∟⋨(⋂(⨣⨃⇪b))) , else }', output=19558","layer":1},{"info":"number node, value=4385","layer":2},{"info":"number node, value=2109","layer":2},{"info":"compute binary expreesion, left_input=4385, right_input=2109, op_id = RygbFNSyEJ binary_op_definition= 'a≦↸b = { (((≤/a)⋳⪒(b⊉≛↸a))⋝⋈⪟((a⇋≉)⨸⪁(≉a))) }', output=-12307","layer":1},{"info":"compute binary expreesion, left_input=19558, right_input=-12307, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=19558","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1002201≎⪠⪩⨒∯310122∲⫓⪩⨒∯1010201≦↸⪩⨒∯200331=⪩⨒∯10301212","reverse_text":"⪩⨒∯10301212=⪩⨒∯1002201≎⪠⪩⨒∯310122∲⫓⪩⨒∯1010201≦↸⪩⨒∯200331","cot":[{"info":"⪩⨒∯1002201≎⪠⪩⨒∯310122=⪩⨒∯10301212","layer":1},{"info":"⪩⨒∯1010201≦↸⪩⨒∯200331=⪩⨒∯-3000103","layer":1},{"info":"⪩⨒∯10301212∲⫓⪩⨒∯-3000103=⪩⨒∯10301212","layer":0}]}
{"id":541,"expression_no_base_symbol":"⪁⇼($5442$∷$2088$)","expression":"⪁⇼(⪩⨒∯1111002∷⪩⨒∯200220)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":10,"operation_count":2,"complexity_ratio":5.0,"tree":{"type":"unary","operator":"⪁⇼","unary_expr":{"type":"binary","operator":"∷","left_expr":{"type":"numeric_atoms","value":5442,"base":4},"right_expr":{"type":"numeric_atoms","value":2088,"base":4}}},"used_operators":["ZNVVrZ94lY","D3AQDKkPcf"],"dependent_operators":["sdazOOVcIp","2DQ55sFlQl","tifHPKVTfV","9FxExcQeMw","NTOWxs364D","7j4O788W3g"],"result":"⪩⨒∯12212","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5442","layer":2},{"info":"number node, value=2088","layer":2},{"info":"compute binary expreesion, left_input=5442, right_input=2088, op_id = D3AQDKkPcf binary_op_definition= 'a∷b = { (a⩚⊴⇥673) , if (b⩷∴24)<=112 ; (a↺b) , else }', output=2088","layer":1},{"info":"compute unary expreesion, input=2088, op_id = ZNVVrZ94lY, unary_op_definition = '⪁⇼a = { ((a⨵⪆a)⪨≂(a⇼⇔∾a)) }', output=422","layer":0}],"base":4,"result_base":4,"text":"⪁⇼(⪩⨒∯1111002∷⪩⨒∯200220)=⪩⨒∯12212","reverse_text":"⪩⨒∯12212=⪁⇼(⪩⨒∯1111002∷⪩⨒∯200220)","cot":[{"info":"⪩⨒∯1111002∷⪩⨒∯200220=⪩⨒∯200220","layer":1},{"info":"⪁⇼⪩⨒∯200220=⪩⨒∯12212","layer":0}]}
{"id":542,"expression_no_base_symbol":"($1069$⨚⇆$2058$)⪪($1763$⊾⪯⋞$1002$)","expression":"(⪩⨒∯100231⨚⇆⪩⨒∯200022)⪪(⪩⨒∯123203⊾⪯⋞⪩⨒∯33222)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7635,"operation_count":3,"complexity_ratio":2545.0,"tree":{"type":"binary","operator":"⪪","left_expr":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"numeric_atoms","value":1069,"base":4},"right_expr":{"type":"numeric_atoms","value":2058,"base":4}},"right_expr":{"type":"binary","operator":"⊾⪯⋞","left_expr":{"type":"numeric_atoms","value":1763,"base":4},"right_expr":{"type":"numeric_atoms","value":1002,"base":4}}},"used_operators":["xD69zh8xqp","lwHaAYXP2r","HK0tfVPux8"],"dependent_operators":["FU0Cs4j7VP","JclMnS0uGI","gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi","s3Fd5m9Dh2","KFSx94NKJn","MmTdOpaElr","XnXgA4xnOs","fOIeswaMU4","YSKBFp38Pu","oacrs7FA3X","xNBdhnnwKq"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1069","layer":2},{"info":"number node, value=2058","layer":2},{"info":"compute binary expreesion, left_input=1069, right_input=2058, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":1},{"info":"number node, value=1763","layer":2},{"info":"number node, value=1002","layer":2},{"info":"compute binary expreesion, left_input=1763, right_input=1002, op_id = HK0tfVPux8 binary_op_definition= 'a⊾⪯⋞b = { ((121⊭∹↮)⊬⨰(a⨑≵⋬b)) , if (a⩟)==395 or (a⨱∎)>94 ; ((b⪘⫢b)⩒⫫(a⇤b)) , else }', output=1578","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1578, op_id = xD69zh8xqp binary_op_definition= 'a⪪b = { ((b⨔⇊a)↛⩡⫤) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100231⨚⇆⪩⨒∯200022)⪪(⪩⨒∯123203⊾⪯⋞⪩⨒∯33222)=NaN","reverse_text":"NaN=(⪩⨒∯100231⨚⇆⪩⨒∯200022)⪪(⪩⨒∯123203⊾⪯⋞⪩⨒∯33222)","cot":[{"info":"⪩⨒∯100231⨚⇆⪩⨒∯200022=NaN","layer":1},{"info":"⪩⨒∯123203⊾⪯⋞⪩⨒∯33222=⪩⨒∯120222","layer":1},{"info":"NaN⪪⪩⨒∯120222=NaN","layer":0}]}
{"id":543,"expression_no_base_symbol":"(⊊≼∋$2998$)⊨$6971$⨚$4914$","expression":"(⊊≼∋⪩⨒∯232312)⊨⪩⨒∯1230323⨚⪩⨒∯1030302","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3049,"operation_count":3,"complexity_ratio":1016.3333333333334,"tree":{"type":"binary","operator":"⊨","left_expr":{"type":"unary","operator":"⊊≼∋","unary_expr":{"type":"numeric_atoms","value":2998,"base":4}},"right_expr":{"type":"binary","operator":"⨚","left_expr":{"type":"numeric_atoms","value":6971,"base":4},"right_expr":{"type":"numeric_atoms","value":4914,"base":4}}},"used_operators":["vg4gO5BX6G","FWz7pXsQhA","nREPSIbpBE"],"dependent_operators":["NTOWxs364D","JLbD19bQDL","xUOZtlo3hN","AF7qkfDlqP","B5M0gjZbta","jCPkEVoL5K","BjRHVeLaeN","12rbrZMWeM"],"result":"⪩⨒∯-2232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2998","layer":2},{"info":"compute unary expreesion, input=2998, op_id = FWz7pXsQhA, unary_op_definition = '⊊≼∋a = { (a↬a) , if a<=50 ; (a⇻⋧≁a) , else }', output=-447","layer":1},{"info":"number node, value=6971","layer":2},{"info":"number node, value=4914","layer":2},{"info":"compute binary expreesion, left_input=6971, right_input=4914, op_id = nREPSIbpBE binary_op_definition= 'a⨚b = { (((b⋳⪒a)⋳⪒31)⫩⊇) }', output=-4780","layer":1},{"info":"compute binary expreesion, left_input=-447, right_input=-4780, op_id = vg4gO5BX6G binary_op_definition= 'a⊨b = { (⨞⊢(b⪠⩆⊳)) , if a<=416 ; (⨑⩽⪐(a⩚⊴⇥a)) , else }', output=-174","layer":0}],"base":4,"result_base":4,"text":"(⊊≼∋⪩⨒∯232312)⊨⪩⨒∯1230323⨚⪩⨒∯1030302=⪩⨒∯-2232","reverse_text":"⪩⨒∯-2232=(⊊≼∋⪩⨒∯232312)⊨⪩⨒∯1230323⨚⪩⨒∯1030302","cot":[{"info":"⊊≼∋⪩⨒∯232312=⪩⨒∯-12333","layer":1},{"info":"⪩⨒∯1230323⨚⪩⨒∯1030302=⪩⨒∯-1022230","layer":1},{"info":"⪩⨒∯-12333⊨⪩⨒∯-1022230=⪩⨒∯-2232","layer":0}]}
{"id":544,"expression_no_base_symbol":"$3346$⇂≾⫗$2367$∠⫱(⇋↷$2929$)","expression":"⪩⨒∯310102⇂≾⫗⪩⨒∯210333∠⫱(⇋↷⪩⨒∯231301)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":78,"operation_count":3,"complexity_ratio":26.0,"tree":{"type":"binary","operator":"∠⫱","left_expr":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"numeric_atoms","value":3346,"base":4},"right_expr":{"type":"numeric_atoms","value":2367,"base":4}},"right_expr":{"type":"unary","operator":"⇋↷","unary_expr":{"type":"numeric_atoms","value":2929,"base":4}}},"used_operators":["QvoQhV0rrE","aBQ6xLxuTc","SWo3A1KBJH"],"dependent_operators":["eLAdDNolq6","DZ8iAZOCBD","7j4O788W3g","tifHPKVTfV","AF7qkfDlqP","g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U","XPYlsWDdGa","23Mk6UjR3U","2DQ55sFlQl","u6S6b8DprG"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3346","layer":2},{"info":"number node, value=2367","layer":2},{"info":"compute binary expreesion, left_input=3346, right_input=2367, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-676","layer":1},{"info":"number node, value=2929","layer":2},{"info":"compute unary expreesion, input=2929, op_id = SWo3A1KBJH, unary_op_definition = '⇋↷a = { (⪲⇎((↽≂a)⋷(a⨵⪆a))) }', output=23432","layer":1},{"info":"compute binary expreesion, left_input=-676, right_input=23432, op_id = QvoQhV0rrE binary_op_definition= 'a∠⫱b = { ((⨑⩽⪐a)↺(617⊉≛↸a)) , if (≤/b)<=3 ; (b⇼⇔∾a) , else }', output=1234","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯310102⇂≾⫗⪩⨒∯210333∠⫱(⇋↷⪩⨒∯231301)=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=⪩⨒∯310102⇂≾⫗⪩⨒∯210333∠⫱(⇋↷⪩⨒∯231301)","cot":[{"info":"⪩⨒∯310102⇂≾⫗⪩⨒∯210333=⪩⨒∯-22210","layer":1},{"info":"⇋↷⪩⨒∯231301=⪩⨒∯11232020","layer":1},{"info":"⪩⨒∯-22210∠⫱⪩⨒∯11232020=⪩⨒∯103102","layer":0}]}
{"id":545,"expression_no_base_symbol":"∑⇻≧$2148$⫉⨲⊜$1587$","expression":"∑⇻≧⪩⨒∯201210⫉⨲⊜⪩⨒∯120303","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":35,"operation_count":2,"complexity_ratio":17.5,"tree":{"type":"unary","operator":"∑⇻≧","unary_expr":{"type":"binary","operator":"⫉⨲⊜","left_expr":{"type":"numeric_atoms","value":2148,"base":4},"right_expr":{"type":"numeric_atoms","value":1587,"base":4}}},"used_operators":["l1M9WJ3V7u","WhqkvtTD3t"],"dependent_operators":["23Mk6UjR3U","EBcxylXtPf","xUOZtlo3hN","eewbuw0ToL","zVYPLywUTj"],"result":"⪩⨒∯-31110","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2148","layer":2},{"info":"number node, value=1587","layer":2},{"info":"compute binary expreesion, left_input=2148, right_input=1587, op_id = WhqkvtTD3t binary_op_definition= 'a⫉⨲⊜b = { (b⨰120) , if b<=7 ; (a⊪) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = l1M9WJ3V7u, unary_op_definition = '∑⇻≧a = { (⨞⊢a) , if (a⫌⩹⨱)<644 ; (426⋷a) , else }', output=-852","layer":0}],"base":4,"result_base":4,"text":"∑⇻≧⪩⨒∯201210⫉⨲⊜⪩⨒∯120303=⪩⨒∯-31110","reverse_text":"⪩⨒∯-31110=∑⇻≧⪩⨒∯201210⫉⨲⊜⪩⨒∯120303","cot":[{"info":"⪩⨒∯201210⫉⨲⊜⪩⨒∯120303=⪩⨒∯0","layer":1},{"info":"∑⇻≧⪩⨒∯0=⪩⨒∯-31110","layer":0}]}
{"id":546,"expression_no_base_symbol":"⪫⨮⊛($3349$⨜⨶$3034$)","expression":"⪫⨮⊛(⪩⨒∯310111⨜⨶⪩⨒∯233122)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":119885,"operation_count":2,"complexity_ratio":59942.5,"tree":{"type":"unary","operator":"⪫⨮⊛","unary_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":3349,"base":4},"right_expr":{"type":"numeric_atoms","value":3034,"base":4}}},"used_operators":["w5FWba1tyO","HiPekx5b7W"],"dependent_operators":["s3Fd5m9Dh2","RZ5CV9rWsJ","SUmda5xLS4","kn8WO9XteQ","hTbEZDJLEm","Tw270M8GLb","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3349","layer":2},{"info":"number node, value=3034","layer":2},{"info":"compute binary expreesion, left_input=3349, right_input=3034, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-5812","layer":1},{"info":"compute unary expreesion, input=-5812, op_id = w5FWba1tyO, unary_op_definition = '⪫⨮⊛a = { a , if (a⨭⪣527)<=182 ; ((⨰⫟⨤(a⪄a))⩖⊿((a⊬⨰a)∟)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪫⨮⊛(⪩⨒∯310111⨜⨶⪩⨒∯233122)=NaN","reverse_text":"NaN=⪫⨮⊛(⪩⨒∯310111⨜⨶⪩⨒∯233122)","cot":[{"info":"⪩⨒∯310111⨜⨶⪩⨒∯233122=⪩⨒∯-1122310","layer":1},{"info":"⪫⨮⊛⪩⨒∯-1122310=NaN","layer":0}]}
{"id":547,"expression_no_base_symbol":"(↔$1708$)⨐($3442$⨕⋳)","expression":"(↔⪩⨒∯122230)⨐(⪩⨒∯311302⨕⋳)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":104,"operation_count":3,"complexity_ratio":34.666666666666664,"tree":{"type":"binary","operator":"⨐","left_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":1708,"base":4}},"right_expr":{"type":"unary","operator":"⨕⋳","unary_expr":{"type":"numeric_atoms","value":3442,"base":4}}},"used_operators":["Noe24qw2ks","ruOEQAzv1W","4X4GscPmMf"],"dependent_operators":["u6S6b8DprG","2DQ55sFlQl","QMFrweE19q","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","9bazX3JMtO","nhYeJWJD5X","DbCuESL50I","3EYGwJThht","w2P8NbNXyL","uFcxV4UQCh","bJkvcejdHO","BUOGQAYlQx","cTDWOvIxvz","hrf7POJlIJ"],"result":"⪩⨒∯230312","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1708","layer":2},{"info":"compute unary expreesion, input=1708, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-1435","layer":1},{"info":"number node, value=3442","layer":2},{"info":"compute unary expreesion, input=3442, op_id = 4X4GscPmMf, unary_op_definition = 'a⨕⋳ = { ((⋼∭⪍(a∴a))⊉↱≁(⋂(a↹⊜60))) , if (a∝72)!=68 ; (((a≎⊠⪸503)⇄(a∇⊂⋱a))⪛a) , else }', output=222524","layer":1},{"info":"compute binary expreesion, left_input=-1435, right_input=222524, op_id = Noe24qw2ks binary_op_definition= 'a⨐b = { (↽≂a) , if (a⨵⪆301)>43 ; (b⫡⨏a) , else }', output=2870","layer":0}],"base":4,"result_base":4,"text":"(↔⪩⨒∯122230)⨐(⪩⨒∯311302⨕⋳)=⪩⨒∯230312","reverse_text":"⪩⨒∯230312=(↔⪩⨒∯122230)⨐(⪩⨒∯311302⨕⋳)","cot":[{"info":"↔⪩⨒∯122230=⪩⨒∯-112123","layer":1},{"info":"⪩⨒∯311302⨕⋳=⪩⨒∯312110330","layer":1},{"info":"⪩⨒∯-112123⨐⪩⨒∯312110330=⪩⨒∯230312","layer":0}]}
{"id":548,"expression_no_base_symbol":"$1514$⩧⪆$5237$⫚↹⊑$3949$⪃⊛⇣$2255$","expression":"⪩⨒∯113222⩧⪆⪩⨒∯1101311⫚↹⊑⪩⨒∯331231⪃⊛⇣⪩⨒∯203033","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":588,"operation_count":3,"complexity_ratio":196.0,"tree":{"type":"binary","operator":"⫚↹⊑","left_expr":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"numeric_atoms","value":1514,"base":4},"right_expr":{"type":"numeric_atoms","value":5237,"base":4}},"right_expr":{"type":"binary","operator":"⪃⊛⇣","left_expr":{"type":"numeric_atoms","value":3949,"base":4},"right_expr":{"type":"numeric_atoms","value":2255,"base":4}}},"used_operators":["dfKe02y8D2","Ikt5ks8PT7","rrgAzCduG9"],"dependent_operators":["2DQ55sFlQl","DIvbN7qnHd","t8gj7n24qd","12rbrZMWeM","g55IO6H4Gj","eewbuw0ToL","t8gj7n24qd","Ez1Nq5fNfI","AHs5Up7iyr","2DDjHMKMc0","7IPrd9c3lf","8cLx32lpNA"],"result":"⪩⨒∯-12333","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1514","layer":2},{"info":"number node, value=5237","layer":2},{"info":"compute binary expreesion, left_input=1514, right_input=5237, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-5237","layer":1},{"info":"number node, value=3949","layer":2},{"info":"number node, value=2255","layer":2},{"info":"compute binary expreesion, left_input=3949, right_input=2255, op_id = rrgAzCduG9 binary_op_definition= 'a⪃⊛⇣b = { ((b∌b)⊵↤) , if b==348 ; ((a≹⇙⪍a)⪬(a⋝⋈⪟a)) , else }', output=1234","layer":1},{"info":"compute binary expreesion, left_input=-5237, right_input=1234, op_id = dfKe02y8D2 binary_op_definition= 'a⫚↹⊑b = { ((126⊠≄⫣)⋳⪒((-b)⨵⪆(a⨸⪁b))) }', output=-447","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯113222⩧⪆⪩⨒∯1101311⫚↹⊑⪩⨒∯331231⪃⊛⇣⪩⨒∯203033=⪩⨒∯-12333","reverse_text":"⪩⨒∯-12333=⪩⨒∯113222⩧⪆⪩⨒∯1101311⫚↹⊑⪩⨒∯331231⪃⊛⇣⪩⨒∯203033","cot":[{"info":"⪩⨒∯113222⩧⪆⪩⨒∯1101311=⪩⨒∯-1101311","layer":1},{"info":"⪩⨒∯331231⪃⊛⇣⪩⨒∯203033=⪩⨒∯103102","layer":1},{"info":"⪩⨒∯-1101311⫚↹⊑⪩⨒∯103102=⪩⨒∯-12333","layer":0}]}
{"id":549,"expression_no_base_symbol":"(⊤⊝$1894$)≨(⩒∊$4228$)","expression":"(⊤⊝⪩⨒∯131212)≨(⩒∊⪩⨒∯1002010)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":83,"operation_count":3,"complexity_ratio":27.666666666666668,"tree":{"type":"binary","operator":"≨","left_expr":{"type":"unary","operator":"⊤⊝","unary_expr":{"type":"numeric_atoms","value":1894,"base":4}},"right_expr":{"type":"unary","operator":"⩒∊","unary_expr":{"type":"numeric_atoms","value":4228,"base":4}}},"used_operators":["0KMCeP1Jsh","rXAclfmB4M","qazvmhNBbN"],"dependent_operators":["jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC","sdazOOVcIp","AF7qkfDlqP","f6k1SAg4EE","eLAdDNolq6"],"result":"⪩⨒∯-11132120","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1894","layer":2},{"info":"compute unary expreesion, input=1894, op_id = rXAclfmB4M, unary_op_definition = '⊤⊝a = { (a⪨≂700) }', output=2490","layer":1},{"info":"number node, value=4228","layer":2},{"info":"compute unary expreesion, input=4228, op_id = qazvmhNBbN, unary_op_definition = '⩒∊a = { ((≤/a)⪒(⨑⩽⪐a)) }', output=7699","layer":1},{"info":"compute binary expreesion, left_input=2490, right_input=7699, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-22424","layer":0}],"base":4,"result_base":4,"text":"(⊤⊝⪩⨒∯131212)≨(⩒∊⪩⨒∯1002010)=⪩⨒∯-11132120","reverse_text":"⪩⨒∯-11132120=(⊤⊝⪩⨒∯131212)≨(⩒∊⪩⨒∯1002010)","cot":[{"info":"⊤⊝⪩⨒∯131212=⪩⨒∯212322","layer":1},{"info":"⩒∊⪩⨒∯1002010=⪩⨒∯1320103","layer":1},{"info":"⪩⨒∯212322≨⪩⨒∯1320103=⪩⨒∯-11132120","layer":0}]}
{"id":550,"expression_no_base_symbol":"≻⋜($7945$⊍⩺⋍$1485$)","expression":"≻⋜(⪩⨒∯1330021⊍⩺⋍⪩⨒∯113031)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":244,"operation_count":2,"complexity_ratio":122.0,"tree":{"type":"unary","operator":"≻⋜","unary_expr":{"type":"binary","operator":"⊍⩺⋍","left_expr":{"type":"numeric_atoms","value":7945,"base":4},"right_expr":{"type":"numeric_atoms","value":1485,"base":4}}},"used_operators":["3tj9sqzovi","OXDGMFPWZM"],"dependent_operators":["XGcMNugi78","dWAJyo7jo9","Tw270M8GLb","Y7wcNGrDQJ","kn8WO9XteQ","inkyxCbjAn","13rbtpv6ld"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7945","layer":2},{"info":"number node, value=1485","layer":2},{"info":"compute binary expreesion, left_input=7945, right_input=1485, op_id = OXDGMFPWZM binary_op_definition= 'a⊍⩺⋍b = { ((⇁⨣⪵659)↤⩊(b⨭⪣a)) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = 3tj9sqzovi, unary_op_definition = '≻⋜a = { (((a⩵∡a)⫞⩸⩒(⨰⫟⨤a))⪢a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"≻⋜(⪩⨒∯1330021⊍⩺⋍⪩⨒∯113031)=NaN","reverse_text":"NaN=≻⋜(⪩⨒∯1330021⊍⩺⋍⪩⨒∯113031)","cot":[{"info":"⪩⨒∯1330021⊍⩺⋍⪩⨒∯113031=NaN","layer":1},{"info":"≻⋜NaN=NaN","layer":0}]}
{"id":551,"expression_no_base_symbol":"($1096$∪⫐$3663$)⩚⊴⇥$1240$⫒⫫$3009$","expression":"(⪩⨒∯101020∪⫐⪩⨒∯321033)⩚⊴⇥⪩⨒∯103120⫒⫫⪩⨒∯233001","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11,"operation_count":3,"complexity_ratio":3.6666666666666665,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"binary","operator":"∪⫐","left_expr":{"type":"numeric_atoms","value":1096,"base":4},"right_expr":{"type":"numeric_atoms","value":3663,"base":4}},"right_expr":{"type":"binary","operator":"⫒⫫","left_expr":{"type":"numeric_atoms","value":1240,"base":4},"right_expr":{"type":"numeric_atoms","value":3009,"base":4}}},"used_operators":["NTOWxs364D","7YooWSwCyH","6Ko8hGgeMq"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rJVOvQCfKK","2DDjHMKMc0","jdwGQqwJi5","AHs5Up7iyr","AFVx7xoS7T"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1096","layer":2},{"info":"number node, value=3663","layer":2},{"info":"compute binary expreesion, left_input=1096, right_input=3663, op_id = 7YooWSwCyH binary_op_definition= 'a∪⫐b = { ((a⋝⋈⪟b)⨎a) }', output=1096","layer":1},{"info":"number node, value=1240","layer":2},{"info":"number node, value=3009","layer":2},{"info":"compute binary expreesion, left_input=1240, right_input=3009, op_id = 6Ko8hGgeMq binary_op_definition= 'a⫒⫫b = { (b≹⇙⪍a) , if (a∁)>135 ; (b⇌⫙⪟a) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1096, right_input=nan, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101020∪⫐⪩⨒∯321033)⩚⊴⇥⪩⨒∯103120⫒⫫⪩⨒∯233001=NaN","reverse_text":"NaN=(⪩⨒∯101020∪⫐⪩⨒∯321033)⩚⊴⇥⪩⨒∯103120⫒⫫⪩⨒∯233001","cot":[{"info":"⪩⨒∯101020∪⫐⪩⨒∯321033=⪩⨒∯101020","layer":1},{"info":"⪩⨒∯103120⫒⫫⪩⨒∯233001=NaN","layer":1},{"info":"⪩⨒∯101020⩚⊴⇥NaN=NaN","layer":0}]}
{"id":552,"expression_no_base_symbol":"(∤↝$1257$)⫘($2387$↬$4308$)","expression":"(∤↝⪩⨒∯103221)⫘(⪩⨒∯211103↬⪩⨒∯1003110)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1476,"operation_count":3,"complexity_ratio":492.0,"tree":{"type":"binary","operator":"⫘","left_expr":{"type":"unary","operator":"∤↝","unary_expr":{"type":"numeric_atoms","value":1257,"base":4}},"right_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":2387,"base":4},"right_expr":{"type":"numeric_atoms","value":4308,"base":4}}},"used_operators":["48vC8HMD2b","3UMq87Qwqg","B5M0gjZbta"],"dependent_operators":["OwUj7dcsQK","7j4O788W3g","tfWHHpNKUN","3ViojmjbAp","dfKe02y8D2","tcjXMdvYtA","D4vGDi5EA2","86A5ENbKR9","X99M06cbEe","s3Fd5m9Dh2","YjI8oCXuph","7j4O788W3g","k7HXdKtiEU","ocnLzx9CaJ","Noe24qw2ks","fG6uBQFnGz","cTDWOvIxvz","jLgFTUHLKL","rGHVDoGpnC"],"result":"⪩⨒∯11221332031","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1257","layer":2},{"info":"compute unary expreesion, input=1257, op_id = 3UMq87Qwqg, unary_op_definition = '∤↝a = { a , if ((a⊬⨰244)<=56 or (⫇a)>308 or (a⨐673)<=60) ; (((↩⪖a)⩼⇪↪(57∝206))↺(↩(⊲⪭a))) , else }', output=1257","layer":1},{"info":"number node, value=2387","layer":2},{"info":"number node, value=4308","layer":2},{"info":"compute binary expreesion, left_input=2387, right_input=4308, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1257, right_input=nan, op_id = 48vC8HMD2b binary_op_definition= 'a⫘b = { ((≘(b⨓a))≫≃) , if ((⇖a)!=319 or (a↺926)<190) ; ((∓a)⫚↹⊑(⪸(a≦≮≮))) , else }', output=1482637","layer":0}],"base":4,"result_base":4,"text":"(∤↝⪩⨒∯103221)⫘(⪩⨒∯211103↬⪩⨒∯1003110)=⪩⨒∯11221332031","reverse_text":"⪩⨒∯11221332031=(∤↝⪩⨒∯103221)⫘(⪩⨒∯211103↬⪩⨒∯1003110)","cot":[{"info":"∤↝⪩⨒∯103221=⪩⨒∯103221","layer":1},{"info":"⪩⨒∯211103↬⪩⨒∯1003110=NaN","layer":1},{"info":"⪩⨒∯103221⫘NaN=⪩⨒∯11221332031","layer":0}]}
{"id":553,"expression_no_base_symbol":"∓$3192$≹⇙⪍$5708$","expression":"∓⪩⨒∯301320≹⇙⪍⪩⨒∯1121030","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":21,"operation_count":2,"complexity_ratio":10.5,"tree":{"type":"unary","operator":"∓","unary_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":3192,"base":4},"right_expr":{"type":"numeric_atoms","value":5708,"base":4}}},"used_operators":["OwUj7dcsQK","AHs5Up7iyr"],"dependent_operators":["DpFCA1CohY","12rbrZMWeM","nCS4ZIUYfx","QMFrweE19q","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3192","layer":2},{"info":"number node, value=5708","layer":2},{"info":"compute binary expreesion, left_input=3192, right_input=5708, op_id = AHs5Up7iyr binary_op_definition= 'a≹⇙⪍b = {a, if b == 0; (a≹⇙⪍(b-1))⪢(b), if b > 0 and abs(b) < 1000; -(a≹⇙⪍(b+1))⪢(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = OwUj7dcsQK, unary_op_definition = '∓a = { (⋗⩬⋾((a⋳⪒554)⨳⩥⨓(a⫡⨏a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"∓⪩⨒∯301320≹⇙⪍⪩⨒∯1121030=NaN","reverse_text":"NaN=∓⪩⨒∯301320≹⇙⪍⪩⨒∯1121030","cot":[{"info":"⪩⨒∯301320≹⇙⪍⪩⨒∯1121030=NaN","layer":1},{"info":"∓NaN=NaN","layer":0}]}
{"id":554,"expression_no_base_symbol":"$6625$⇄$3753$/(⫎≠⋺$2036$)","expression":"⪩⨒∯1213201⇄⪩⨒∯322221/(⫎≠⋺⪩⨒∯133310)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":21,"operation_count":3,"complexity_ratio":7.0,"tree":{"type":"binary","operator":"/","left_expr":{"type":"binary","operator":"⇄","left_expr":{"type":"numeric_atoms","value":6625,"base":4},"right_expr":{"type":"numeric_atoms","value":3753,"base":4}},"right_expr":{"type":"unary","operator":"⫎≠⋺","unary_expr":{"type":"numeric_atoms","value":2036,"base":4}}},"used_operators":["XhwjNDsVaA","3EYGwJThht","LYeZOJ0nQG"],"dependent_operators":["rysDP5nf3Z","eLAdDNolq6","DZ8iAZOCBD","i8ToyICDmI","9FxExcQeMw","NTOWxs364D","P8v4zCKN1o","tifHPKVTfV","i8ToyICDmI","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6625","layer":2},{"info":"number node, value=3753","layer":2},{"info":"compute binary expreesion, left_input=6625, right_input=3753, op_id = 3EYGwJThht binary_op_definition= 'a⇄b = { ((≤/b)∲⫓(a⊉≛↸b)) }', output=0","layer":1},{"info":"number node, value=2036","layer":2},{"info":"compute unary expreesion, input=2036, op_id = LYeZOJ0nQG, unary_op_definition = '⫎≠⋺a = { ((655⩚⊴⇥a)∲⫓(∥⊫86)) , if (a⩷∴509)>=9 ; ((1⊭↱337)⇼⇔∾(a⩷∴a)) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=0, op_id = XhwjNDsVaA binary_op_definition= 'None', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1213201⇄⪩⨒∯322221/(⫎≠⋺⪩⨒∯133310)=NaN","reverse_text":"NaN=⪩⨒∯1213201⇄⪩⨒∯322221/(⫎≠⋺⪩⨒∯133310)","cot":[{"info":"⪩⨒∯1213201⇄⪩⨒∯322221=⪩⨒∯0","layer":1},{"info":"⫎≠⋺⪩⨒∯133310=⪩⨒∯0","layer":1},{"info":"⪩⨒∯0/⪩⨒∯0=NaN","layer":0}]}
{"id":555,"expression_no_base_symbol":"($4015$⫣⪄⊒$6173$)↞⋁(⨛$3499$)","expression":"(⪩⨒∯332233⫣⪄⊒⪩⨒∯1200131)↞⋁(⨛⪩⨒∯312223)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":247,"operation_count":3,"complexity_ratio":82.33333333333333,"tree":{"type":"binary","operator":"↞⋁","left_expr":{"type":"binary","operator":"⫣⪄⊒","left_expr":{"type":"numeric_atoms","value":4015,"base":4},"right_expr":{"type":"numeric_atoms","value":6173,"base":4}},"right_expr":{"type":"unary","operator":"⨛","unary_expr":{"type":"numeric_atoms","value":3499,"base":4}}},"used_operators":["RqrPlJkxDo","RabNbG55vr","CoMdbyAt7R"],"dependent_operators":["Uaa54Peajs","CArV6hThFE","13rbtpv6ld","NTOWxs364D","DbCuESL50I","fOIeswaMU4","g7Hmc5v1ko","KPf6cnQVty","j9kHMeSvPp","k8jYdgA6NY","2DDjHMKMc0","8WDwsbhb0R","cTDWOvIxvz","IWmyXbctLI","U6pG0PXrV3","DyGG3AbaNP","liw5iZPkLH","3DZMoQKiUl"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4015","layer":2},{"info":"number node, value=6173","layer":2},{"info":"compute binary expreesion, left_input=4015, right_input=6173, op_id = RabNbG55vr binary_op_definition= 'a⫣⪄⊒b = { ((a⪮%⊝(153⪭a))%(⋼∭⪍(b⩚⊴⇥34))) , if b>769 ; ((∂⩏⊆(b⩟))∺≝⩲((b∝a)⋝⋈⪟(a⩌⋺b))) , else }', output=-29520","layer":1},{"info":"number node, value=3499","layer":2},{"info":"compute unary expreesion, input=3499, op_id = CoMdbyAt7R, unary_op_definition = '⨛a = { (⊖((≱⇩⩕a)∼(⨡↴a))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-29520, right_input=nan, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯332233⫣⪄⊒⪩⨒∯1200131)↞⋁(⨛⪩⨒∯312223)=NaN","reverse_text":"NaN=(⪩⨒∯332233⫣⪄⊒⪩⨒∯1200131)↞⋁(⨛⪩⨒∯312223)","cot":[{"info":"⪩⨒∯332233⫣⪄⊒⪩⨒∯1200131=⪩⨒∯-13031100","layer":1},{"info":"⨛⪩⨒∯312223=NaN","layer":1},{"info":"⪩⨒∯-13031100↞⋁NaN=NaN","layer":0}]}
{"id":556,"expression_no_base_symbol":"(⊊≼∋$1622$)⩘$7973$⨐$1586$","expression":"(⊊≼∋⪩⨒∯121112)⩘⪩⨒∯1330211⨐⪩⨒∯120302","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3076,"operation_count":3,"complexity_ratio":1025.3333333333333,"tree":{"type":"binary","operator":"⩘","left_expr":{"type":"unary","operator":"⊊≼∋","unary_expr":{"type":"numeric_atoms","value":1622,"base":4}},"right_expr":{"type":"binary","operator":"⨐","left_expr":{"type":"numeric_atoms","value":7973,"base":4},"right_expr":{"type":"numeric_atoms","value":1586,"base":4}}},"used_operators":["cHh1gJQ2o6","FWz7pXsQhA","Noe24qw2ks"],"dependent_operators":["23Mk6UjR3U","eRqsBgTDFp","zVYPLywUTj","bPywburJMS","KPf6cnQVty","YbVcJGFEVW","5twsqlHp2o","B5M0gjZbta","jCPkEVoL5K","u6S6b8DprG","2DQ55sFlQl","QMFrweE19q"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1622","layer":2},{"info":"compute unary expreesion, input=1622, op_id = FWz7pXsQhA, unary_op_definition = '⊊≼∋a = { (a↬a) , if a<=50 ; (a⇻⋧≁a) , else }', output=-447","layer":1},{"info":"number node, value=7973","layer":2},{"info":"number node, value=1586","layer":2},{"info":"compute binary expreesion, left_input=7973, right_input=1586, op_id = Noe24qw2ks binary_op_definition= 'a⨐b = { (↽≂a) , if (a⨵⪆301)>43 ; (b⫡⨏a) , else }', output=-15946","layer":1},{"info":"compute binary expreesion, left_input=-447, right_input=-15946, op_id = cHh1gJQ2o6 binary_op_definition= 'a⩘b = { (((b⋷b)↼⊘⨖(a⊢6))∺≝⩲((a⪒⊣⊆619)≃(a⊪))) }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⊊≼∋⪩⨒∯121112)⩘⪩⨒∯1330211⨐⪩⨒∯120302=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⊊≼∋⪩⨒∯121112)⩘⪩⨒∯1330211⨐⪩⨒∯120302","cot":[{"info":"⊊≼∋⪩⨒∯121112=⪩⨒∯-12333","layer":1},{"info":"⪩⨒∯1330211⨐⪩⨒∯120302=⪩⨒∯-3321022","layer":1},{"info":"⪩⨒∯-12333⩘⪩⨒∯-3321022=⪩⨒∯2200","layer":0}]}
{"id":557,"expression_no_base_symbol":"($1525$⩒⫫$2299$)⪝($1003$∺≝⩲$1680$)","expression":"(⪩⨒∯113311⩒⫫⪩⨒∯203323)⪝(⪩⨒∯33223∺≝⩲⪩⨒∯122100)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":454,"operation_count":3,"complexity_ratio":151.33333333333334,"tree":{"type":"binary","operator":"⪝","left_expr":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"numeric_atoms","value":1525,"base":4},"right_expr":{"type":"numeric_atoms","value":2299,"base":4}},"right_expr":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"numeric_atoms","value":1003,"base":4},"right_expr":{"type":"numeric_atoms","value":1680,"base":4}}},"used_operators":["wicAB68Tmb","KFSx94NKJn","KPf6cnQVty"],"dependent_operators":["L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X","NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl"],"result":"⪩⨒∯-1020223","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1525","layer":2},{"info":"number node, value=2299","layer":2},{"info":"compute binary expreesion, left_input=1525, right_input=2299, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=1223","layer":1},{"info":"number node, value=1003","layer":2},{"info":"number node, value=1680","layer":2},{"info":"compute binary expreesion, left_input=1003, right_input=1680, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=1223, right_input=160, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=-4651","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯113311⩒⫫⪩⨒∯203323)⪝(⪩⨒∯33223∺≝⩲⪩⨒∯122100)=⪩⨒∯-1020223","reverse_text":"⪩⨒∯-1020223=(⪩⨒∯113311⩒⫫⪩⨒∯203323)⪝(⪩⨒∯33223∺≝⩲⪩⨒∯122100)","cot":[{"info":"⪩⨒∯113311⩒⫫⪩⨒∯203323=⪩⨒∯103013","layer":1},{"info":"⪩⨒∯33223∺≝⩲⪩⨒∯122100=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯103013⪝⪩⨒∯2200=⪩⨒∯-1020223","layer":0}]}
{"id":558,"expression_no_base_symbol":"⊖∈($4707$⊅)","expression":"⊖∈(⪩⨒∯1021203⊅)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":181,"operation_count":2,"complexity_ratio":90.5,"tree":{"type":"unary","operator":"⊖∈","unary_expr":{"type":"unary","operator":"⊅","unary_expr":{"type":"numeric_atoms","value":4707,"base":4}}},"used_operators":["YFxL8Sc2Zy","7p6YLioM7f"],"dependent_operators":["zVYPLywUTj","sdazOOVcIp","ancx8kZcWl","YSKBFp38Pu","SUmda5xLS4","vg4gO5BX6G","HrjLwUk87U"],"result":"⪩⨒∯-2031302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4707","layer":2},{"info":"compute unary expreesion, input=4707, op_id = 7p6YLioM7f, unary_op_definition = 'a⊅ = { ((a⪄a)⊨(517⪚a)) }', output=-174","layer":1},{"info":"compute unary expreesion, input=-174, op_id = YFxL8Sc2Zy, unary_op_definition = '⊖∈a = { a , if (a⨝⩣∺)>=369 ; ((a⊪)⪨≂(a⇤a)) , else }', output=-9074","layer":0}],"base":4,"result_base":4,"text":"⊖∈(⪩⨒∯1021203⊅)=⪩⨒∯-2031302","reverse_text":"⪩⨒∯-2031302=⊖∈(⪩⨒∯1021203⊅)","cot":[{"info":"⪩⨒∯1021203⊅=⪩⨒∯-2232","layer":1},{"info":"⊖∈⪩⨒∯-2232=⪩⨒∯-2031302","layer":0}]}
{"id":559,"expression_no_base_symbol":"(⇺⋃$2541$)⇔⨋","expression":"(⇺⋃⪩⨒∯213231)⇔⨋","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":82,"operation_count":2,"complexity_ratio":41.0,"tree":{"type":"unary","operator":"⇔⨋","unary_expr":{"type":"unary","operator":"⇺⋃","unary_expr":{"type":"numeric_atoms","value":2541,"base":4}}},"used_operators":["uBihLCJcMX","E5v5B3UAjG"],"dependent_operators":["N41Kp7NANJ","7j4O788W3g","glklzrTFfD","tifHPKVTfV","12rbrZMWeM","f6k1SAg4EE","D4vGDi5EA2","nCS4ZIUYfx","QMFrweE19q","bl5wxAcryP","Q3PJZHRvZv","gub5Cegaqo","8INZBEW696","kuIXHzHcAH","7YooWSwCyH"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2541","layer":2},{"info":"compute unary expreesion, input=2541, op_id = E5v5B3UAjG, unary_op_definition = '⇺⋃a = { (((a≀⩗∶a)∪⫐(a⩁⩘229))⪨⊡(⊥(a↰))) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = uBihLCJcMX, unary_op_definition = 'a⇔⨋ = { (((a⨁⊸⫻)⋳⪒a)⪒((a≦≮≮)⨁⊸⫻)) , if a<217 ; (((a≋⫹)⨳⩥⨓(a↺a))⋳⪒((a⨳⩥⨓a)⫡⨏(a⇼⇔∾a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⇺⋃⪩⨒∯213231)⇔⨋=NaN","reverse_text":"NaN=(⇺⋃⪩⨒∯213231)⇔⨋","cot":[{"info":"⇺⋃⪩⨒∯213231=NaN","layer":1},{"info":"NaN⇔⨋=NaN","layer":0}]}
{"id":560,"expression_no_base_symbol":"($3485$⪚$5964$)↞⋁($1242$⩟)","expression":"(⪩⨒∯312131⪚⪩⨒∯1131030)↞⋁(⪩⨒∯103122⩟)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":37,"operation_count":3,"complexity_ratio":12.333333333333334,"tree":{"type":"binary","operator":"↞⋁","left_expr":{"type":"binary","operator":"⪚","left_expr":{"type":"numeric_atoms","value":3485,"base":4},"right_expr":{"type":"numeric_atoms","value":5964,"base":4}},"right_expr":{"type":"unary","operator":"⩟","unary_expr":{"type":"numeric_atoms","value":1242,"base":4}}},"used_operators":["RqrPlJkxDo","HrjLwUk87U","fOIeswaMU4"],"dependent_operators":["Uaa54Peajs","CArV6hThFE","13rbtpv6ld","9FxExcQeMw","rysDP5nf3Z","NTOWxs364D","DZ8iAZOCBD","tifHPKVTfV","eH2TOUuTDT","2DDjHMKMc0","W4YGzv6Whe","Qy55tPpLXF","8w2t5hMYqp","12rbrZMWeM"],"result":"⪩⨒∯-1103002","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3485","layer":2},{"info":"number node, value=5964","layer":2},{"info":"compute binary expreesion, left_input=3485, right_input=5964, op_id = HrjLwUk87U binary_op_definition= 'a⪚b = { (((317⩚⊴⇥a)⋝⋈⪟(518-95))⊉≛↸((97⪐)⩷∴(b⇼⇔∾a))) }', output=-5314","layer":1},{"info":"number node, value=1242","layer":2},{"info":"compute unary expreesion, input=1242, op_id = fOIeswaMU4, unary_op_definition = 'a⩟ = { (⊄⩳↩((a⋳⪒a)+(155⋥≓≎a))) }', output=-9951","layer":1},{"info":"compute binary expreesion, left_input=-5314, right_input=-9951, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=-5314","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯312131⪚⪩⨒∯1131030)↞⋁(⪩⨒∯103122⩟)=⪩⨒∯-1103002","reverse_text":"⪩⨒∯-1103002=(⪩⨒∯312131⪚⪩⨒∯1131030)↞⋁(⪩⨒∯103122⩟)","cot":[{"info":"⪩⨒∯312131⪚⪩⨒∯1131030=⪩⨒∯-1103002","layer":1},{"info":"⪩⨒∯103122⩟=⪩⨒∯-2123133","layer":1},{"info":"⪩⨒∯-1103002↞⋁⪩⨒∯-2123133=⪩⨒∯-1103002","layer":0}]}
{"id":561,"expression_no_base_symbol":"$2592$∌$3604$*($1546$-$4113$)","expression":"⪩⨒∯220200∌⪩⨒∯320110*(⪩⨒∯120022-⪩⨒∯1000101)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2569,"operation_count":3,"complexity_ratio":856.3333333333334,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"∌","left_expr":{"type":"numeric_atoms","value":2592,"base":4},"right_expr":{"type":"numeric_atoms","value":3604,"base":4}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1546,"base":4},"right_expr":{"type":"numeric_atoms","value":4113,"base":4}}},"used_operators":["9HNa5Wba9A","8cLx32lpNA","rysDP5nf3Z"],"dependent_operators":["W4YGzv6Whe","N41Kp7NANJ","7j4O788W3g","t8gj7n24qd"],"result":"⪩⨒∯203102222030","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2592","layer":2},{"info":"number node, value=3604","layer":2},{"info":"compute binary expreesion, left_input=2592, right_input=3604, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-3604","layer":1},{"info":"number node, value=1546","layer":2},{"info":"number node, value=4113","layer":2},{"info":"compute binary expreesion, left_input=1546, right_input=4113, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-2567","layer":1},{"info":"compute binary expreesion, left_input=-3604, right_input=-2567, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=9251468","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯220200∌⪩⨒∯320110*(⪩⨒∯120022-⪩⨒∯1000101)=⪩⨒∯203102222030","reverse_text":"⪩⨒∯203102222030=⪩⨒∯220200∌⪩⨒∯320110*(⪩⨒∯120022-⪩⨒∯1000101)","cot":[{"info":"⪩⨒∯220200∌⪩⨒∯320110=⪩⨒∯-320110","layer":1},{"info":"⪩⨒∯120022-⪩⨒∯1000101=⪩⨒∯-220013","layer":1},{"info":"⪩⨒∯-320110*⪩⨒∯-220013=⪩⨒∯203102222030","layer":0}]}
{"id":562,"expression_no_base_symbol":"↨⩢⫨($1669$⊉≛↸$1403$)","expression":"↨⩢⫨(⪩⨒∯122011⊉≛↸⪩⨒∯111323)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":69,"operation_count":2,"complexity_ratio":34.5,"tree":{"type":"unary","operator":"↨⩢⫨","unary_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":1669,"base":4},"right_expr":{"type":"numeric_atoms","value":1403,"base":4}}},"used_operators":["Z5CJsN7DuW","DZ8iAZOCBD"],"dependent_operators":["Noe24qw2ks","gu96TGCTMs","8jW3W4yZS5","AFVx7xoS7T","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1669","layer":2},{"info":"number node, value=1403","layer":2},{"info":"compute binary expreesion, left_input=1669, right_input=1403, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=3338","layer":1},{"info":"compute unary expreesion, input=3338, op_id = Z5CJsN7DuW, unary_op_definition = '↨⩢⫨a = { (((211⨐a)⇌⫙⪟(↯⪼a))⊘) }', output=0","layer":0}],"base":4,"result_base":4,"text":"↨⩢⫨(⪩⨒∯122011⊉≛↸⪩⨒∯111323)=⪩⨒∯0","reverse_text":"⪩⨒∯0=↨⩢⫨(⪩⨒∯122011⊉≛↸⪩⨒∯111323)","cot":[{"info":"⪩⨒∯122011⊉≛↸⪩⨒∯111323=⪩⨒∯310022","layer":1},{"info":"↨⩢⫨⪩⨒∯310022=⪩⨒∯0","layer":0}]}
{"id":563,"expression_no_base_symbol":"($5750$→⨶⪴$2895$)→⨶⪴(⊙↵-$5125$)","expression":"(⪩⨒∯1121312→⨶⪴⪩⨒∯231033)→⨶⪴(⊙↵-⪩⨒∯1100011)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5180,"operation_count":3,"complexity_ratio":1726.6666666666667,"tree":{"type":"binary","operator":"→⨶⪴","left_expr":{"type":"binary","operator":"→⨶⪴","left_expr":{"type":"numeric_atoms","value":5750,"base":4},"right_expr":{"type":"numeric_atoms","value":2895,"base":4}},"right_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":5125,"base":4}}},"used_operators":["bF6eod5Gvf","oWn0xqSxBt"],"dependent_operators":["8w2t5hMYqp","9FxExcQeMw","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"⪩⨒∯-10033320","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5750","layer":2},{"info":"number node, value=2895","layer":2},{"info":"compute binary expreesion, left_input=5750, right_input=2895, op_id = bF6eod5Gvf binary_op_definition= 'a→⨶⪴b = { (a⩷∴b) , if b<109 ; (⊄⩳↩b) , else }', output=-8685","layer":1},{"info":"number node, value=5125","layer":2},{"info":"compute unary expreesion, input=5125, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute binary expreesion, left_input=-8685, right_input=-1, op_id = bF6eod5Gvf binary_op_definition= 'a→⨶⪴b = { (a⩷∴b) , if b<109 ; (⊄⩳↩b) , else }', output=-17400","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1121312→⨶⪴⪩⨒∯231033)→⨶⪴(⊙↵-⪩⨒∯1100011)=⪩⨒∯-10033320","reverse_text":"⪩⨒∯-10033320=(⪩⨒∯1121312→⨶⪴⪩⨒∯231033)→⨶⪴(⊙↵-⪩⨒∯1100011)","cot":[{"info":"⪩⨒∯1121312→⨶⪴⪩⨒∯231033=⪩⨒∯-2013231","layer":1},{"info":"⊙↵-⪩⨒∯1100011=⪩⨒∯-1","layer":1},{"info":"⪩⨒∯-2013231→⨶⪴⪩⨒∯-1=⪩⨒∯-10033320","layer":0}]}
{"id":564,"expression_no_base_symbol":"↞≼($2554$⊭↱$5660$)","expression":"↞≼(⪩⨒∯213322⊭↱⪩⨒∯1120130)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":21,"operation_count":2,"complexity_ratio":10.5,"tree":{"type":"unary","operator":"↞≼","unary_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":2554,"base":4},"right_expr":{"type":"numeric_atoms","value":5660,"base":4}}},"used_operators":["DE7zCoGJt9","COABgblf1C"],"dependent_operators":["W4YGzv6Whe","D4vGDi5EA2","23Mk6UjR3U","BjRHVeLaeN","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","u6S6b8DprG","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯30002222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2554","layer":2},{"info":"number node, value=5660","layer":2},{"info":"compute binary expreesion, left_input=2554, right_input=5660, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=6217","layer":1},{"info":"compute unary expreesion, input=6217, op_id = DE7zCoGJt9, unary_op_definition = '↞≼a = { (↽≂(197⨰(a⨸⪁a))) , if (a⨸⪁373)!=224 ; (((591⋷a)≧⫂∧(a+a))⨸⪁((a⫩⊇)≦≮≮)) , else }', output=49322","layer":0}],"base":4,"result_base":4,"text":"↞≼(⪩⨒∯213322⊭↱⪩⨒∯1120130)=⪩⨒∯30002222","reverse_text":"⪩⨒∯30002222=↞≼(⪩⨒∯213322⊭↱⪩⨒∯1120130)","cot":[{"info":"⪩⨒∯213322⊭↱⪩⨒∯1120130=⪩⨒∯1201021","layer":1},{"info":"↞≼⪩⨒∯1201021=⪩⨒∯30002222","layer":0}]}
{"id":565,"expression_no_base_symbol":"$5556$⪶≀⋏$2800$≬⇓($5085$-$1887$)","expression":"⪩⨒∯1112310⪶≀⋏⪩⨒∯223300≬⇓(⪩⨒∯1033131-⪩⨒∯131133)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":67680,"operation_count":3,"complexity_ratio":22560.0,"tree":{"type":"binary","operator":"≬⇓","left_expr":{"type":"binary","operator":"⪶≀⋏","left_expr":{"type":"numeric_atoms","value":5556,"base":4},"right_expr":{"type":"numeric_atoms","value":2800,"base":4}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":5085,"base":4},"right_expr":{"type":"numeric_atoms","value":1887,"base":4}}},"used_operators":["jWTQ2TZYIH","zR4jO40bMj","rysDP5nf3Z"],"dependent_operators":["AdZkA7nFnk","zVYPLywUTj","XTarYq4gQB","W4YGzv6Whe","rysDP5nf3Z","NTOWxs364D","glklzrTFfD","2DDjHMKMc0","g55IO6H4Gj","eewbuw0ToL"],"result":"Inf","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5556","layer":2},{"info":"number node, value=2800","layer":2},{"info":"compute binary expreesion, left_input=5556, right_input=2800, op_id = zR4jO40bMj binary_op_definition= 'a⪶≀⋏b = { (((b⨸⪁b)⨸⪁(a-a))⋝⋈⪟(b⋝⋈⪟(b+b))) , if a<244 ; (((b⩚⊴⇥a)⨁⊸⫻)⨰a) , else }', output=-22500","layer":1},{"info":"number node, value=5085","layer":2},{"info":"number node, value=1887","layer":2},{"info":"compute binary expreesion, left_input=5085, right_input=1887, op_id = rysDP5nf3Z binary_op_definition= 'None', output=3198","layer":1},{"info":"compute binary expreesion, left_input=-22500, right_input=3198, op_id = jWTQ2TZYIH binary_op_definition= 'a≬⇓b = { (a⊪) , if a<=154 or (⪝⪂⫅a)>=41 ; (a⋅⇍b) , else }', output=inf","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1112310⪶≀⋏⪩⨒∯223300≬⇓(⪩⨒∯1033131-⪩⨒∯131133)=Inf","reverse_text":"Inf=⪩⨒∯1112310⪶≀⋏⪩⨒∯223300≬⇓(⪩⨒∯1033131-⪩⨒∯131133)","cot":[{"info":"⪩⨒∯1112310⪶≀⋏⪩⨒∯223300=⪩⨒∯-11133210","layer":1},{"info":"⪩⨒∯1033131-⪩⨒∯131133=⪩⨒∯301332","layer":1},{"info":"⪩⨒∯-11133210≬⇓⪩⨒∯301332=Inf","layer":0}]}
{"id":566,"expression_no_base_symbol":"(↓⇌$1120$)⨌↪","expression":"(↓⇌⪩⨒∯101200)⨌↪","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":14,"operation_count":2,"complexity_ratio":7.0,"tree":{"type":"unary","operator":"⨌↪","unary_expr":{"type":"unary","operator":"↓⇌","unary_expr":{"type":"numeric_atoms","value":1120,"base":4}}},"used_operators":["cWQsF5MvuD","PxpmPgHHJV"],"dependent_operators":["8w2t5hMYqp","2DQ55sFlQl","i8ToyICDmI","QMFrweE19q","23Mk6UjR3U","glklzrTFfD","Z2TMIBDE3Q"],"result":"⪩⨒∯-13200","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1120","layer":2},{"info":"compute unary expreesion, input=1120, op_id = PxpmPgHHJV, unary_op_definition = '↓⇌a = { (a⋷507) , if a>=68 and (a⩤)>=87 ; (a⨁⊸⫻) , else }', output=1120","layer":1},{"info":"compute unary expreesion, input=1120, op_id = cWQsF5MvuD, unary_op_definition = 'a⨌↪ = { (⊄⩳↩((a∲⫓a)⨵⪆(a⫡⨏a))) }', output=-480","layer":0}],"base":4,"result_base":4,"text":"(↓⇌⪩⨒∯101200)⨌↪=⪩⨒∯-13200","reverse_text":"⪩⨒∯-13200=(↓⇌⪩⨒∯101200)⨌↪","cot":[{"info":"↓⇌⪩⨒∯101200=⪩⨒∯101200","layer":1},{"info":"⪩⨒∯101200⨌↪=⪩⨒∯-13200","layer":0}]}
{"id":567,"expression_no_base_symbol":"($8487$↬$2379$)≃⋄","expression":"(⪩⨒∯2010213↬⪩⨒∯211023)≃⋄","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":24,"operation_count":2,"complexity_ratio":12.0,"tree":{"type":"unary","operator":"≃⋄","unary_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":8487,"base":4},"right_expr":{"type":"numeric_atoms","value":2379,"base":4}}},"used_operators":["aN9a90urxU","B5M0gjZbta"],"dependent_operators":["uFcxV4UQCh","jLgFTUHLKL","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=8487","layer":2},{"info":"number node, value=2379","layer":2},{"info":"compute binary expreesion, left_input=8487, right_input=2379, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = aN9a90urxU, unary_op_definition = 'a≃⋄ = { (↩(252⪛a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2010213↬⪩⨒∯211023)≃⋄=NaN","reverse_text":"NaN=(⪩⨒∯2010213↬⪩⨒∯211023)≃⋄","cot":[{"info":"⪩⨒∯2010213↬⪩⨒∯211023=NaN","layer":1},{"info":"NaN≃⋄=NaN","layer":0}]}
{"id":568,"expression_no_base_symbol":"(≪$1229$)⩍⋽⫝̸($2856$≧⫂∧$1361$)","expression":"(≪⪩⨒∯103031)⩍⋽⫝̸(⪩⨒∯230220≧⫂∧⪩⨒∯111101)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":46,"operation_count":3,"complexity_ratio":15.333333333333334,"tree":{"type":"binary","operator":"⩍⋽⫝̸","left_expr":{"type":"unary","operator":"≪","unary_expr":{"type":"numeric_atoms","value":1229,"base":4}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":2856,"base":4},"right_expr":{"type":"numeric_atoms","value":1361,"base":4}}},"used_operators":["BiWNJpBvwn","Qtd6bqUJcN","Ph9nP6C5qx"],"dependent_operators":["Ph9nP6C5qx","xUOZtlo3hN","3nqY3DE9mg","09Ly4LVMIf","wEfv7U73WA","tifHPKVTfV","ruOEQAzv1W","iuk5sVOGFA","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯-322","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1229","layer":2},{"info":"compute unary expreesion, input=1229, op_id = Qtd6bqUJcN, unary_op_definition = '≪a = { ((431⫃⨇a)⪣⫩) , if (a⊍)!=211 or (a⇐≅)==294 ; (↔(a⇼⇔∾a)) , else }', output=913","layer":1},{"info":"number node, value=2856","layer":2},{"info":"number node, value=1361","layer":2},{"info":"compute binary expreesion, left_input=2856, right_input=1361, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=888","layer":1},{"info":"compute binary expreesion, left_input=913, right_input=888, op_id = BiWNJpBvwn binary_op_definition= 'a⩍⋽⫝̸b = { ((⨞⊢508)≧⫂∧(a≧⫂∧b)) }', output=-58","layer":0}],"base":4,"result_base":4,"text":"(≪⪩⨒∯103031)⩍⋽⫝̸(⪩⨒∯230220≧⫂∧⪩⨒∯111101)=⪩⨒∯-322","reverse_text":"⪩⨒∯-322=(≪⪩⨒∯103031)⩍⋽⫝̸(⪩⨒∯230220≧⫂∧⪩⨒∯111101)","cot":[{"info":"≪⪩⨒∯103031=⪩⨒∯32101","layer":1},{"info":"⪩⨒∯230220≧⫂∧⪩⨒∯111101=⪩⨒∯31320","layer":1},{"info":"⪩⨒∯32101⩍⋽⫝̸⪩⨒∯31320=⪩⨒∯-322","layer":0}]}
{"id":569,"expression_no_base_symbol":"($5169$∴≳≥)⋥≓≎(≉$1494$)","expression":"(⪩⨒∯1100301∴≳≥)⋥≓≎(≉⪩⨒∯113112)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"unary","operator":"∴≳≥","unary_expr":{"type":"numeric_atoms","value":5169,"base":4}},"right_expr":{"type":"unary","operator":"≉","unary_expr":{"type":"numeric_atoms","value":1494,"base":4}}},"used_operators":["Qy55tPpLXF","a3N2hFLK0J","e1ybzncUwg"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","g55IO6H4Gj","DpFCA1CohY","xUOZtlo3hN","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-10003101","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5169","layer":2},{"info":"compute unary expreesion, input=5169, op_id = a3N2hFLK0J, unary_op_definition = 'a∴≳≥ = { (⨞⊢a) , if (⋗⩬⋾a)==641 ; (a⨸⪁a) , else }', output=20676","layer":1},{"info":"number node, value=1494","layer":2},{"info":"compute unary expreesion, input=1494, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=2025","layer":1},{"info":"compute binary expreesion, left_input=20676, right_input=2025, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-16593","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1100301∴≳≥)⋥≓≎(≉⪩⨒∯113112)=⪩⨒∯-10003101","reverse_text":"⪩⨒∯-10003101=(⪩⨒∯1100301∴≳≥)⋥≓≎(≉⪩⨒∯113112)","cot":[{"info":"⪩⨒∯1100301∴≳≥=⪩⨒∯11003010","layer":1},{"info":"≉⪩⨒∯113112=⪩⨒∯133221","layer":1},{"info":"⪩⨒∯11003010⋥≓≎⪩⨒∯133221=⪩⨒∯-10003101","layer":0}]}
{"id":570,"expression_no_base_symbol":"($2597$*$2974$)≚⋢","expression":"(⪩⨒∯220211*⪩⨒∯232132)≚⋢","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2689,"operation_count":2,"complexity_ratio":1344.5,"tree":{"type":"unary","operator":"≚⋢","unary_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":2597,"base":4},"right_expr":{"type":"numeric_atoms","value":2974,"base":4}}},"used_operators":["MahUMFw56D","9HNa5Wba9A"],"dependent_operators":["3ViojmjbAp","W4YGzv6Whe"],"result":"⪩⨒∯-1121","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2597","layer":2},{"info":"number node, value=2974","layer":2},{"info":"compute binary expreesion, left_input=2597, right_input=2974, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=7723478","layer":1},{"info":"compute unary expreesion, input=7723478, op_id = MahUMFw56D, unary_op_definition = 'a≚⋢ = { (a⨓86) }', output=-89","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯220211*⪩⨒∯232132)≚⋢=⪩⨒∯-1121","reverse_text":"⪩⨒∯-1121=(⪩⨒∯220211*⪩⨒∯232132)≚⋢","cot":[{"info":"⪩⨒∯220211*⪩⨒∯232132=⪩⨒∯131131213112","layer":1},{"info":"⪩⨒∯131131213112≚⋢=⪩⨒∯-1121","layer":0}]}
{"id":571,"expression_no_base_symbol":"($2393$⨑≵⋬$1125$)⊋$7301$⪚$1015$","expression":"(⪩⨒∯211121⨑≵⋬⪩⨒∯101211)⊋⪩⨒∯1302011⪚⪩⨒∯33313","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13483,"operation_count":3,"complexity_ratio":4494.333333333333,"tree":{"type":"binary","operator":"⊋","left_expr":{"type":"binary","operator":"⨑≵⋬","left_expr":{"type":"numeric_atoms","value":2393,"base":4},"right_expr":{"type":"numeric_atoms","value":1125,"base":4}},"right_expr":{"type":"binary","operator":"⪚","left_expr":{"type":"numeric_atoms","value":7301,"base":4},"right_expr":{"type":"numeric_atoms","value":1015,"base":4}}},"used_operators":["W4tP9CfskL","XnXgA4xnOs","HrjLwUk87U"],"dependent_operators":["2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu","eewbuw0ToL","AF7qkfDlqP","QMFrweE19q","9FxExcQeMw","rysDP5nf3Z","NTOWxs364D","DZ8iAZOCBD","tifHPKVTfV","eH2TOUuTDT","2DDjHMKMc0"],"result":"⪩⨒∯-212310102000300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2393","layer":2},{"info":"number node, value=1125","layer":2},{"info":"compute binary expreesion, left_input=2393, right_input=1125, op_id = XnXgA4xnOs binary_op_definition= 'a⨑≵⋬b = { ((a⨰b)⫡⨏(⨑⩽⪐b)) }', output=5469","layer":1},{"info":"number node, value=7301","layer":2},{"info":"number node, value=1015","layer":2},{"info":"compute binary expreesion, left_input=7301, right_input=1015, op_id = HrjLwUk87U binary_op_definition= 'a⪚b = { (((317⩚⊴⇥a)⋝⋈⪟(518-95))⊉≛↸((97⪐)⩷∴(b⇼⇔∾a))) }', output=12216","layer":1},{"info":"compute binary expreesion, left_input=5469, right_input=12216, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=-651239472","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯211121⨑≵⋬⪩⨒∯101211)⊋⪩⨒∯1302011⪚⪩⨒∯33313=⪩⨒∯-212310102000300","reverse_text":"⪩⨒∯-212310102000300=(⪩⨒∯211121⨑≵⋬⪩⨒∯101211)⊋⪩⨒∯1302011⪚⪩⨒∯33313","cot":[{"info":"⪩⨒∯211121⨑≵⋬⪩⨒∯101211=⪩⨒∯1111131","layer":1},{"info":"⪩⨒∯1302011⪚⪩⨒∯33313=⪩⨒∯2332320","layer":1},{"info":"⪩⨒∯1111131⊋⪩⨒∯2332320=⪩⨒∯-212310102000300","layer":0}]}
{"id":572,"expression_no_base_symbol":"($1277$∖$1121$)⋻⩜⩜$4988$⨚$2945$","expression":"(⪩⨒∯103331∖⪩⨒∯101201)⋻⩜⩜⪩⨒∯1031330⨚⪩⨒∯232001","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":12476,"operation_count":3,"complexity_ratio":4158.666666666667,"tree":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"binary","operator":"∖","left_expr":{"type":"numeric_atoms","value":1277,"base":4},"right_expr":{"type":"numeric_atoms","value":1121,"base":4}},"right_expr":{"type":"binary","operator":"⨚","left_expr":{"type":"numeric_atoms","value":4988,"base":4},"right_expr":{"type":"numeric_atoms","value":2945,"base":4}}},"used_operators":["oDCm7WA9JY","tXD093vOjl","nREPSIbpBE"],"dependent_operators":["mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC","BjRHVeLaeN","12rbrZMWeM"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1277","layer":2},{"info":"number node, value=1121","layer":2},{"info":"compute binary expreesion, left_input=1277, right_input=1121, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":1},{"info":"number node, value=4988","layer":2},{"info":"number node, value=2945","layer":2},{"info":"compute binary expreesion, left_input=4988, right_input=2945, op_id = nREPSIbpBE binary_op_definition= 'a⨚b = { (((b⋳⪒a)⋳⪒31)⫩⊇) }', output=-870","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-870, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯103331∖⪩⨒∯101201)⋻⩜⩜⪩⨒∯1031330⨚⪩⨒∯232001=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯103331∖⪩⨒∯101201)⋻⩜⩜⪩⨒∯1031330⨚⪩⨒∯232001","cot":[{"info":"⪩⨒∯103331∖⪩⨒∯101201=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1031330⨚⪩⨒∯232001=⪩⨒∯-31212","layer":1},{"info":"⪩⨒∯0⋻⩜⩜⪩⨒∯-31212=⪩⨒∯0","layer":0}]}
{"id":573,"expression_no_base_symbol":"(⋼∭⪍$1257$)⊎←↗","expression":"(⋼∭⪍⪩⨒∯103221)⊎←↗","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":22,"operation_count":2,"complexity_ratio":11.0,"tree":{"type":"unary","operator":"⊎←↗","unary_expr":{"type":"unary","operator":"⋼∭⪍","unary_expr":{"type":"numeric_atoms","value":1257,"base":4}}},"used_operators":["dwb5p0fa6d","DbCuESL50I"],"dependent_operators":["sdazOOVcIp","COABgblf1C","e1ybzncUwg","sdazOOVcIp","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","u6S6b8DprG"],"result":"⪩⨒∯1301131","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1257","layer":2},{"info":"compute unary expreesion, input=1257, op_id = DbCuESL50I, unary_op_definition = '⋼∭⪍a = { (≉((a∲⫓a)⪨≂(a⪒a))) , if (↽≂a)>481 ; (↽≂((↽≂435)≧⫂∧(↽≂a))) , else }', output=-3288","layer":1},{"info":"compute unary expreesion, input=-3288, op_id = dwb5p0fa6d, unary_op_definition = 'a⊎←↗ = { (a⊭↱340) , if (a⪨≂940)!=203 ; (a⊭↱a) , else }', output=7261","layer":0}],"base":4,"result_base":4,"text":"(⋼∭⪍⪩⨒∯103221)⊎←↗=⪩⨒∯1301131","reverse_text":"⪩⨒∯1301131=(⋼∭⪍⪩⨒∯103221)⊎←↗","cot":[{"info":"⋼∭⪍⪩⨒∯103221=⪩⨒∯-303120","layer":1},{"info":"⪩⨒∯-303120⊎←↗=⪩⨒∯1301131","layer":0}]}
{"id":574,"expression_no_base_symbol":"$5280$≁↽≥$2855$⊉≛↸$1663$⇴∐$6581$","expression":"⪩⨒∯1102200≁↽≥⪩⨒∯230213⊉≛↸⪩⨒∯121333⇴∐⪩⨒∯1212311","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":52,"operation_count":3,"complexity_ratio":17.333333333333332,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"binary","operator":"≁↽≥","left_expr":{"type":"numeric_atoms","value":5280,"base":4},"right_expr":{"type":"numeric_atoms","value":2855,"base":4}},"right_expr":{"type":"binary","operator":"⇴∐","left_expr":{"type":"numeric_atoms","value":1663,"base":4},"right_expr":{"type":"numeric_atoms","value":6581,"base":4}}},"used_operators":["DZ8iAZOCBD","ncHt1X6cMc","HnzytWxmAO"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","oWn0xqSxBt","3Oe9XWJUTD","2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ"],"result":"⪩⨒∯203202030","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5280","layer":2},{"info":"number node, value=2855","layer":2},{"info":"compute binary expreesion, left_input=5280, right_input=2855, op_id = ncHt1X6cMc binary_op_definition= 'a≁↽≥b = { (a⊝⪿⪼b) , if b>=116 ; (⊙↵-b) , else }', output=72774","layer":1},{"info":"number node, value=1663","layer":2},{"info":"number node, value=6581","layer":2},{"info":"compute binary expreesion, left_input=1663, right_input=6581, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=72774, right_input=nan, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=145548","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1102200≁↽≥⪩⨒∯230213⊉≛↸⪩⨒∯121333⇴∐⪩⨒∯1212311=⪩⨒∯203202030","reverse_text":"⪩⨒∯203202030=⪩⨒∯1102200≁↽≥⪩⨒∯230213⊉≛↸⪩⨒∯121333⇴∐⪩⨒∯1212311","cot":[{"info":"⪩⨒∯1102200≁↽≥⪩⨒∯230213=⪩⨒∯101301012","layer":1},{"info":"⪩⨒∯121333⇴∐⪩⨒∯1212311=NaN","layer":1},{"info":"⪩⨒∯101301012⊉≛↸NaN=⪩⨒∯203202030","layer":0}]}
{"id":575,"expression_no_base_symbol":"(∟⋨$1182$)⩅⪻⪻","expression":"(∟⋨⪩⨒∯102132)⩅⪻⪻","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2004,"operation_count":2,"complexity_ratio":1002.0,"tree":{"type":"unary","operator":"⩅⪻⪻","unary_expr":{"type":"unary","operator":"∟⋨","unary_expr":{"type":"numeric_atoms","value":1182,"base":4}}},"used_operators":["kHoXpA7yos","ctOc4cKSDt"],"dependent_operators":["SUmda5xLS4","KPf6cnQVty","8HhzD0ZcuI","9Isq31Ruls","eLAdDNolq6","tmPS8pqC7x"],"result":"⪩⨒∯332023","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1182","layer":2},{"info":"compute unary expreesion, input=1182, op_id = ctOc4cKSDt, unary_op_definition = '∟⋨a = { (≤/(a⨪↰⇹a)) }', output=-698","layer":1},{"info":"compute unary expreesion, input=-698, op_id = kHoXpA7yos, unary_op_definition = 'a⩅⪻⪻ = { (a⪄((a∌↝a)⨽(a∺≝⩲a))) }', output=3979","layer":0}],"base":4,"result_base":4,"text":"(∟⋨⪩⨒∯102132)⩅⪻⪻=⪩⨒∯332023","reverse_text":"⪩⨒∯332023=(∟⋨⪩⨒∯102132)⩅⪻⪻","cot":[{"info":"∟⋨⪩⨒∯102132=⪩⨒∯-22322","layer":1},{"info":"⪩⨒∯-22322⩅⪻⪻=⪩⨒∯332023","layer":0}]}
{"id":576,"expression_no_base_symbol":"≦∁$1863$↡⊰⫅$3045$","expression":"≦∁⪩⨒∯131013↡⊰⫅⪩⨒∯233211","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":42646,"operation_count":2,"complexity_ratio":21323.0,"tree":{"type":"unary","operator":"≦∁","unary_expr":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"numeric_atoms","value":1863,"base":4},"right_expr":{"type":"numeric_atoms","value":3045,"base":4}}},"used_operators":["9ICcGScMcE","VCtxkLNOzz"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn"],"result":"⪩⨒∯1133022","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1863","layer":2},{"info":"number node, value=3045","layer":2},{"info":"compute binary expreesion, left_input=1863, right_input=3045, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=6090","layer":1},{"info":"compute unary expreesion, input=6090, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=6090","layer":0}],"base":4,"result_base":4,"text":"≦∁⪩⨒∯131013↡⊰⫅⪩⨒∯233211=⪩⨒∯1133022","reverse_text":"⪩⨒∯1133022=≦∁⪩⨒∯131013↡⊰⫅⪩⨒∯233211","cot":[{"info":"⪩⨒∯131013↡⊰⫅⪩⨒∯233211=⪩⨒∯1133022","layer":1},{"info":"≦∁⪩⨒∯1133022=⪩⨒∯1133022","layer":0}]}
{"id":577,"expression_no_base_symbol":"($1234$⇉⇉)∺≝⩲($1170$⪒$3236$)","expression":"(⪩⨒∯103102⇉⇉)∺≝⩲(⪩⨒∯102102⪒⪩⨒∯302210)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":71,"operation_count":3,"complexity_ratio":23.666666666666668,"tree":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"unary","operator":"⇉⇉","unary_expr":{"type":"numeric_atoms","value":1234,"base":4}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":1170,"base":4},"right_expr":{"type":"numeric_atoms","value":3236,"base":4}}},"used_operators":["KPf6cnQVty","diKm42VcIt","f6k1SAg4EE"],"dependent_operators":["BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl","RygbFNSyEJ","XPYlsWDdGa","k8jYdgA6NY","xUOZtlo3hN","AFVx7xoS7T","iuk5sVOGFA","86A5ENbKR9","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1234","layer":2},{"info":"compute unary expreesion, input=1234, op_id = diKm42VcIt, unary_op_definition = 'a⇉⇉ = { (⪸(⨞⊢(a≦↸a))) , if (a⪣⫩)!=30 ; (a%(⪲⇎(a⇌⫙⪟156))) , else }', output=-69168","layer":1},{"info":"number node, value=1170","layer":2},{"info":"number node, value=3236","layer":2},{"info":"compute binary expreesion, left_input=1170, right_input=3236, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-4406","layer":1},{"info":"compute binary expreesion, left_input=-69168, right_input=-4406, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯103102⇉⇉)∺≝⩲(⪩⨒∯102102⪒⪩⨒∯302210)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⪩⨒∯103102⇉⇉)∺≝⩲(⪩⨒∯102102⪒⪩⨒∯302210)","cot":[{"info":"⪩⨒∯103102⇉⇉=⪩⨒∯-100320300","layer":1},{"info":"⪩⨒∯102102⪒⪩⨒∯302210=⪩⨒∯-1010312","layer":1},{"info":"⪩⨒∯-100320300∺≝⩲⪩⨒∯-1010312=⪩⨒∯2200","layer":0}]}
{"id":578,"expression_no_base_symbol":"⊄⩳↩($7799$⫚↹⊑$3679$)","expression":"⊄⩳↩(⪩⨒∯1321313⫚↹⊑⪩⨒∯321133)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":18,"operation_count":2,"complexity_ratio":9.0,"tree":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"binary","operator":"⫚↹⊑","left_expr":{"type":"numeric_atoms","value":7799,"base":4},"right_expr":{"type":"numeric_atoms","value":3679,"base":4}}},"used_operators":["8w2t5hMYqp","dfKe02y8D2"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","2DQ55sFlQl","DIvbN7qnHd","t8gj7n24qd","12rbrZMWeM","g55IO6H4Gj"],"result":"⪩⨒∯110331","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7799","layer":2},{"info":"number node, value=3679","layer":2},{"info":"compute binary expreesion, left_input=7799, right_input=3679, op_id = dfKe02y8D2 binary_op_definition= 'a⫚↹⊑b = { ((126⊠≄⫣)⋳⪒((-b)⨵⪆(a⨸⪁b))) }', output=-447","layer":1},{"info":"compute unary expreesion, input=-447, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=1341","layer":0}],"base":4,"result_base":4,"text":"⊄⩳↩(⪩⨒∯1321313⫚↹⊑⪩⨒∯321133)=⪩⨒∯110331","reverse_text":"⪩⨒∯110331=⊄⩳↩(⪩⨒∯1321313⫚↹⊑⪩⨒∯321133)","cot":[{"info":"⪩⨒∯1321313⫚↹⊑⪩⨒∯321133=⪩⨒∯-12333","layer":1},{"info":"⊄⩳↩⪩⨒∯-12333=⪩⨒∯110331","layer":0}]}
{"id":579,"expression_no_base_symbol":"($8470$≳⇉$1638$)↼⊘⨖($1460$⫚↹⊑$3649$)","expression":"(⪩⨒∯2010112≳⇉⪩⨒∯121212)↼⊘⨖(⪩⨒∯112310⫚↹⊑⪩⨒∯321001)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":35799725,"operation_count":3,"complexity_ratio":11933241.666666666,"tree":{"type":"binary","operator":"↼⊘⨖","left_expr":{"type":"binary","operator":"≳⇉","left_expr":{"type":"numeric_atoms","value":8470,"base":4},"right_expr":{"type":"numeric_atoms","value":1638,"base":4}},"right_expr":{"type":"binary","operator":"⫚↹⊑","left_expr":{"type":"numeric_atoms","value":1460,"base":4},"right_expr":{"type":"numeric_atoms","value":3649,"base":4}}},"used_operators":["bPywburJMS","V0kx6qeWkN","dfKe02y8D2"],"dependent_operators":["9FxExcQeMw","P8v4zCKN1o","t8gj7n24qd","KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls","2DQ55sFlQl","DIvbN7qnHd","t8gj7n24qd","12rbrZMWeM","g55IO6H4Gj"],"result":"⪩⨒∯-101130","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=8470","layer":2},{"info":"number node, value=1638","layer":2},{"info":"compute binary expreesion, left_input=8470, right_input=1638, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":1},{"info":"number node, value=1460","layer":2},{"info":"number node, value=3649","layer":2},{"info":"compute binary expreesion, left_input=1460, right_input=3649, op_id = dfKe02y8D2 binary_op_definition= 'a⫚↹⊑b = { ((126⊠≄⫣)⋳⪒((-b)⨵⪆(a⨸⪁b))) }', output=-447","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-447, op_id = bPywburJMS binary_op_definition= 'a↼⊘⨖b = { (-a) , if (∥⊫b)==149 ; (b⩷∴95) , else }', output=-1116","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2010112≳⇉⪩⨒∯121212)↼⊘⨖(⪩⨒∯112310⫚↹⊑⪩⨒∯321001)=⪩⨒∯-101130","reverse_text":"⪩⨒∯-101130=(⪩⨒∯2010112≳⇉⪩⨒∯121212)↼⊘⨖(⪩⨒∯112310⫚↹⊑⪩⨒∯321001)","cot":[{"info":"⪩⨒∯2010112≳⇉⪩⨒∯121212=NaN","layer":1},{"info":"⪩⨒∯112310⫚↹⊑⪩⨒∯321001=⪩⨒∯-12333","layer":1},{"info":"NaN↼⊘⨖⪩⨒∯-12333=⪩⨒∯-101130","layer":0}]}
{"id":580,"expression_no_base_symbol":"$2357$⊔$2766$⊍⩺⋍$3126$≨$1062$","expression":"⪩⨒∯210311⊔⪩⨒∯223032⊍⩺⋍⪩⨒∯300312≨⪩⨒∯100212","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":301,"operation_count":3,"complexity_ratio":100.33333333333333,"tree":{"type":"binary","operator":"⊍⩺⋍","left_expr":{"type":"binary","operator":"⊔","left_expr":{"type":"numeric_atoms","value":2357,"base":4},"right_expr":{"type":"numeric_atoms","value":2766,"base":4}},"right_expr":{"type":"binary","operator":"≨","left_expr":{"type":"numeric_atoms","value":3126,"base":4},"right_expr":{"type":"numeric_atoms","value":1062,"base":4}}},"used_operators":["OXDGMFPWZM","E4l6HwMY31","0KMCeP1Jsh"],"dependent_operators":["kn8WO9XteQ","inkyxCbjAn","13rbtpv6ld","W4YGzv6Whe","DpFCA1CohY","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","QMFrweE19q","jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2357","layer":2},{"info":"number node, value=2766","layer":2},{"info":"compute binary expreesion, left_input=2357, right_input=2766, op_id = E4l6HwMY31 binary_op_definition= 'a⊔b = { (((a≧⫂∧b)∲⫓(⋗⩬⋾b))⫡⨏((b⪒a)≧⫂∧(a+64))) }', output=16144","layer":1},{"info":"number node, value=3126","layer":2},{"info":"number node, value=1062","layer":2},{"info":"compute binary expreesion, left_input=3126, right_input=1062, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-28784","layer":1},{"info":"compute binary expreesion, left_input=16144, right_input=-28784, op_id = OXDGMFPWZM binary_op_definition= 'a⊍⩺⋍b = { ((⇁⨣⪵659)↤⩊(b⨭⪣a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯210311⊔⪩⨒∯223032⊍⩺⋍⪩⨒∯300312≨⪩⨒∯100212=NaN","reverse_text":"NaN=⪩⨒∯210311⊔⪩⨒∯223032⊍⩺⋍⪩⨒∯300312≨⪩⨒∯100212","cot":[{"info":"⪩⨒∯210311⊔⪩⨒∯223032=⪩⨒∯3330100","layer":1},{"info":"⪩⨒∯300312≨⪩⨒∯100212=⪩⨒∯-13001300","layer":1},{"info":"⪩⨒∯3330100⊍⩺⋍⪩⨒∯-13001300=NaN","layer":0}]}
{"id":581,"expression_no_base_symbol":"(⋠∜$4830$)⫚↹⊑($7361$⪁$2014$)","expression":"(⋠∜⪩⨒∯1023132)⫚↹⊑(⪩⨒∯1303001⪁⪩⨒∯133132)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5709150,"operation_count":3,"complexity_ratio":1903050.0,"tree":{"type":"binary","operator":"⫚↹⊑","left_expr":{"type":"unary","operator":"⋠∜","unary_expr":{"type":"numeric_atoms","value":4830,"base":4}},"right_expr":{"type":"binary","operator":"⪁","left_expr":{"type":"numeric_atoms","value":7361,"base":4},"right_expr":{"type":"numeric_atoms","value":2014,"base":4}}},"used_operators":["dfKe02y8D2","ZJpFhNJr3x","I7sXao9hZE"],"dependent_operators":["2DQ55sFlQl","DIvbN7qnHd","t8gj7n24qd","12rbrZMWeM","g55IO6H4Gj","X99M06cbEe","4CyGpkTkEk","Qy55tPpLXF","dWAJyo7jo9","wxb3vTeyAj","nlCqmYiOvY"],"result":"⪩⨒∯-12333","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4830","layer":2},{"info":"compute unary expreesion, input=4830, op_id = ZJpFhNJr3x, unary_op_definition = '⋠∜a = { ((a∐⫣)⋥≓≎(a≫≃)) }', output=21604","layer":1},{"info":"number node, value=7361","layer":2},{"info":"number node, value=2014","layer":2},{"info":"compute binary expreesion, left_input=7361, right_input=2014, op_id = I7sXao9hZE binary_op_definition= 'a⪁b = { (((⫶⊄≣b)⨽⪊≇)⪢a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=21604, right_input=nan, op_id = dfKe02y8D2 binary_op_definition= 'a⫚↹⊑b = { ((126⊠≄⫣)⋳⪒((-b)⨵⪆(a⨸⪁b))) }', output=-447","layer":0}],"base":4,"result_base":4,"text":"(⋠∜⪩⨒∯1023132)⫚↹⊑(⪩⨒∯1303001⪁⪩⨒∯133132)=⪩⨒∯-12333","reverse_text":"⪩⨒∯-12333=(⋠∜⪩⨒∯1023132)⫚↹⊑(⪩⨒∯1303001⪁⪩⨒∯133132)","cot":[{"info":"⋠∜⪩⨒∯1023132=⪩⨒∯11101210","layer":1},{"info":"⪩⨒∯1303001⪁⪩⨒∯133132=NaN","layer":1},{"info":"⪩⨒∯11101210⫚↹⊑NaN=⪩⨒∯-12333","layer":0}]}
{"id":582,"expression_no_base_symbol":"(⇜⊴$3386$)⇂≾⫗(⇖⫷⫕$1492$)","expression":"(⇜⊴⪩⨒∯310322)⇂≾⫗(⇖⫷⫕⪩⨒∯113110)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":869,"operation_count":3,"complexity_ratio":289.6666666666667,"tree":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"unary","operator":"⇜⊴","unary_expr":{"type":"numeric_atoms","value":3386,"base":4}},"right_expr":{"type":"unary","operator":"⇖⫷⫕","unary_expr":{"type":"numeric_atoms","value":1492,"base":4}}},"used_operators":["aBQ6xLxuTc","XwDhCwWbUn","UHmRx3INFg"],"dependent_operators":["g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U","WR6HLWljOP","JclMnS0uGI","D309nIvmXG","w2P8NbNXyL","YbVcJGFEVW","DmTXOeWf9t","4CyGpkTkEk","cTDWOvIxvz","jLgFTUHLKL","COABgblf1C","hrf7POJlIJ","DE7zCoGJt9","FyVja0WsTP","oZj3VtZNQx","DyGG3AbaNP"],"result":"⪩⨒∯-22132","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3386","layer":2},{"info":"compute unary expreesion, input=3386, op_id = XwDhCwWbUn, unary_op_definition = '⇜⊴a = { (↩(∓⪦(a≃a))) , if ((a∐⫣)>271 and (a∴779)<=132) ; ((a↢(a⨔⇊a))⊲⩕⊾((a∝a)⊉↱≁(a⊭↱19))) , else }', output=-785382","layer":1},{"info":"number node, value=1492","layer":2},{"info":"compute unary expreesion, input=1492, op_id = UHmRx3INFg, unary_op_definition = '⇖⫷⫕a = { ((a∼125)≀⫉(↞≼(a⊱⇼⊻51))) }', output=2822","layer":1},{"info":"compute binary expreesion, left_input=-785382, right_input=2822, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-670","layer":0}],"base":4,"result_base":4,"text":"(⇜⊴⪩⨒∯310322)⇂≾⫗(⇖⫷⫕⪩⨒∯113110)=⪩⨒∯-22132","reverse_text":"⪩⨒∯-22132=(⇜⊴⪩⨒∯310322)⇂≾⫗(⇖⫷⫕⪩⨒∯113110)","cot":[{"info":"⇜⊴⪩⨒∯310322=⪩⨒∯-2333233212","layer":1},{"info":"⇖⫷⫕⪩⨒∯113110=⪩⨒∯230012","layer":1},{"info":"⪩⨒∯-2333233212⇂≾⫗⪩⨒∯230012=⪩⨒∯-22132","layer":0}]}
{"id":583,"expression_no_base_symbol":"⩎⋉($3994$⩺⋐⫨)","expression":"⩎⋉(⪩⨒∯332122⩺⋐⫨)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":639,"operation_count":2,"complexity_ratio":319.5,"tree":{"type":"unary","operator":"⩎⋉","unary_expr":{"type":"unary","operator":"⩺⋐⫨","unary_expr":{"type":"numeric_atoms","value":3994,"base":4}}},"used_operators":["FlXk3pOYe8","yS9ePUuUdn"],"dependent_operators":["KbjG8mgYpV","wztAlM01eG","JclMnS0uGI","XhwjNDsVaA","W7eaUhjymW","9ICcGScMcE","fG6uBQFnGz","8w2t5hMYqp","Bmrmz2XGnR","Noe24qw2ks","1aApVXNlOP","i8ToyICDmI","nCS4ZIUYfx","2DlMacCsIx","hrf7POJlIJ","9samAPKr6k","j9kHMeSvPp","Tcnh7f0tEr"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3994","layer":2},{"info":"compute unary expreesion, input=3994, op_id = yS9ePUuUdn, unary_op_definition = 'a⩺⋐⫨ = { ((a≣⋋)⨽∌(a⪭a)) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = FlXk3pOYe8, unary_op_definition = '⩎⋉a = { (((a/a)∲⫓(≛a))∴((a⩨a)⨳⩥⨓(⊄⩳↩a))) , if (a⩇∃⫛268)<=24 or a==244 or (↩⪖a)>=4 ; (((a⨔⇊a)∠↢(↸⊣a))≚⊃≕((≦∁a)⨐461)) , else }', output=67","layer":0}],"base":4,"result_base":4,"text":"⩎⋉(⪩⨒∯332122⩺⋐⫨)=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=⩎⋉(⪩⨒∯332122⩺⋐⫨)","cot":[{"info":"⪩⨒∯332122⩺⋐⫨=⪩⨒∯0","layer":1},{"info":"⩎⋉⪩⨒∯0=⪩⨒∯1003","layer":0}]}
{"id":584,"expression_no_base_symbol":"($1741$⨸⪁$1772$)≚⊃≕($1581$⪛$2902$)","expression":"(⪩⨒∯123031⨸⪁⪩⨒∯123230)≚⊃≕(⪩⨒∯120231⪛⪩⨒∯231112)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":26,"operation_count":3,"complexity_ratio":8.666666666666666,"tree":{"type":"binary","operator":"≚⊃≕","left_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":1741,"base":4},"right_expr":{"type":"numeric_atoms","value":1772,"base":4}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":1581,"base":4},"right_expr":{"type":"numeric_atoms","value":2902,"base":4}}},"used_operators":["Bmrmz2XGnR","g55IO6H4Gj","uFcxV4UQCh"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","7j4O788W3g","sdazOOVcIp","8w2t5hMYqp","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","W4YGzv6Whe","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1741","layer":2},{"info":"number node, value=1772","layer":2},{"info":"compute binary expreesion, left_input=1741, right_input=1772, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=7026","layer":1},{"info":"number node, value=1581","layer":2},{"info":"number node, value=2902","layer":2},{"info":"compute binary expreesion, left_input=1581, right_input=2902, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1581","layer":1},{"info":"compute binary expreesion, left_input=7026, right_input=1581, op_id = Bmrmz2XGnR binary_op_definition= 'a≚⊃≕b = { (-((⊄⩳↩b)⪨≂(a⩷∴b))) , if ((b⫡⨏524)<690 or (⨞⊢a)>=395) ; ((⊄⩳↩(b⋥≓≎a))⋥≓≎((a↺a)⪨≂(479⨸⪁a))) , else }', output=67","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯123031⨸⪁⪩⨒∯123230)≚⊃≕(⪩⨒∯120231⪛⪩⨒∯231112)=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=(⪩⨒∯123031⨸⪁⪩⨒∯123230)≚⊃≕(⪩⨒∯120231⪛⪩⨒∯231112)","cot":[{"info":"⪩⨒∯123031⨸⪁⪩⨒∯123230=⪩⨒∯1231302","layer":1},{"info":"⪩⨒∯120231⪛⪩⨒∯231112=⪩⨒∯120231","layer":1},{"info":"⪩⨒∯1231302≚⊃≕⪩⨒∯120231=⪩⨒∯1003","layer":0}]}
{"id":585,"expression_no_base_symbol":"($1210$⪇≇⋚$4638$)≧⫂∧($1167$⊋≦⊧$1634$)","expression":"(⪩⨒∯102322⪇≇⋚⪩⨒∯1020132)≧⫂∧(⪩⨒∯102033⊋≦⊧⪩⨒∯121202)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":31,"operation_count":3,"complexity_ratio":10.333333333333334,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"⪇≇⋚","left_expr":{"type":"numeric_atoms","value":1210,"base":4},"right_expr":{"type":"numeric_atoms","value":4638,"base":4}},"right_expr":{"type":"binary","operator":"⊋≦⊧","left_expr":{"type":"numeric_atoms","value":1167,"base":4},"right_expr":{"type":"numeric_atoms","value":1634,"base":4}}},"used_operators":["Ph9nP6C5qx","3sJ7IOPOlU","oRDoc9rAEX"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","DZ8iAZOCBD","JLbD19bQDL","xUOZtlo3hN","DZ8iAZOCBD","tifHPKVTfV","sdazOOVcIp","glklzrTFfD","DIvbN7qnHd","12rbrZMWeM","Ph9nP6C5qx","eewbuw0ToL","2td37pGCOC"],"result":"⪩⨒∯220001","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1210","layer":2},{"info":"number node, value=4638","layer":2},{"info":"compute binary expreesion, left_input=1210, right_input=4638, op_id = 3sJ7IOPOlU binary_op_definition= 'a⪇≇⋚b = { ((⨞⊢(a⊉≛↸b))⪠⩆⊳) }', output=0","layer":1},{"info":"number node, value=1167","layer":2},{"info":"number node, value=1634","layer":2},{"info":"compute binary expreesion, left_input=1167, right_input=1634, op_id = oRDoc9rAEX binary_op_definition= 'a⊋≦⊧b = { (((24⊉≛↸a)⊉≛↸(⩦⩻⨪b))⊉≛↸((a⊠≄⫣)⪨≂(b⇼⇔∾a))) , if a<=128 ; (((a⇼⇔∾b)⨁⊸⫻)⇼⇔∾((22⋳⪒a)⨰(a≧⫂∧a))) , else }', output=-2561","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-2561, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=2561","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯102322⪇≇⋚⪩⨒∯1020132)≧⫂∧(⪩⨒∯102033⊋≦⊧⪩⨒∯121202)=⪩⨒∯220001","reverse_text":"⪩⨒∯220001=(⪩⨒∯102322⪇≇⋚⪩⨒∯1020132)≧⫂∧(⪩⨒∯102033⊋≦⊧⪩⨒∯121202)","cot":[{"info":"⪩⨒∯102322⪇≇⋚⪩⨒∯1020132=⪩⨒∯0","layer":1},{"info":"⪩⨒∯102033⊋≦⊧⪩⨒∯121202=⪩⨒∯-220001","layer":1},{"info":"⪩⨒∯0≧⫂∧⪩⨒∯-220001=⪩⨒∯220001","layer":0}]}
{"id":586,"expression_no_base_symbol":"($1250$↺$3021$)⩺⪪($3464$%$3182$)","expression":"(⪩⨒∯103202↺⪩⨒∯233031)⩺⪪(⪩⨒∯312020%⪩⨒∯301232)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":128,"operation_count":3,"complexity_ratio":42.666666666666664,"tree":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":1250,"base":4},"right_expr":{"type":"numeric_atoms","value":3021,"base":4}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":3464,"base":4},"right_expr":{"type":"numeric_atoms","value":3182,"base":4}}},"used_operators":["uvdQJvN4PV","7j4O788W3g","k8jYdgA6NY"],"dependent_operators":["Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z"],"result":"⪩⨒∯-22322302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1250","layer":2},{"info":"number node, value=3021","layer":2},{"info":"compute binary expreesion, left_input=1250, right_input=3021, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=3021","layer":1},{"info":"number node, value=3464","layer":2},{"info":"number node, value=3182","layer":2},{"info":"compute binary expreesion, left_input=3464, right_input=3182, op_id = k8jYdgA6NY binary_op_definition= 'None', output=282","layer":1},{"info":"compute binary expreesion, left_input=3021, right_input=282, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=-44722","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯103202↺⪩⨒∯233031)⩺⪪(⪩⨒∯312020%⪩⨒∯301232)=⪩⨒∯-22322302","reverse_text":"⪩⨒∯-22322302=(⪩⨒∯103202↺⪩⨒∯233031)⩺⪪(⪩⨒∯312020%⪩⨒∯301232)","cot":[{"info":"⪩⨒∯103202↺⪩⨒∯233031=⪩⨒∯233031","layer":1},{"info":"⪩⨒∯312020%⪩⨒∯301232=⪩⨒∯10122","layer":1},{"info":"⪩⨒∯233031⩺⪪⪩⨒∯10122=⪩⨒∯-22322302","layer":0}]}
{"id":587,"expression_no_base_symbol":"⊑($1586$⊀⩕)","expression":"⊑(⪩⨒∯120302⊀⩕)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1668,"operation_count":2,"complexity_ratio":834.0,"tree":{"type":"unary","operator":"⊑","unary_expr":{"type":"unary","operator":"⊀⩕","unary_expr":{"type":"numeric_atoms","value":1586,"base":4}}},"used_operators":["IkUmn0D7oy","r0FS3hW4cC"],"dependent_operators":["oRDoc9rAEX","AdZkA7nFnk","megm06wKyl","rGHVDoGpnC","nhYeJWJD5X"],"result":"⪩⨒∯3000","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1586","layer":2},{"info":"compute unary expreesion, input=1586, op_id = r0FS3hW4cC, unary_op_definition = 'a⊀⩕ = { (a⨟⋌⩍(181∇⊂⋱a)) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = IkUmn0D7oy, unary_op_definition = '⊑a = { ((a⋅⇍254)⊋≦⊧(⨈⫕a)) }', output=192","layer":0}],"base":4,"result_base":4,"text":"⊑(⪩⨒∯120302⊀⩕)=⪩⨒∯3000","reverse_text":"⪩⨒∯3000=⊑(⪩⨒∯120302⊀⩕)","cot":[{"info":"⪩⨒∯120302⊀⩕=⪩⨒∯0","layer":1},{"info":"⊑⪩⨒∯0=⪩⨒∯3000","layer":0}]}
{"id":588,"expression_no_base_symbol":"⋠∜(⩦⩻⨪$4324$)","expression":"⋠∜(⩦⩻⨪⪩⨒∯1003210)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":24,"operation_count":2,"complexity_ratio":12.0,"tree":{"type":"unary","operator":"⋠∜","unary_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":4324,"base":4}}},"used_operators":["ZJpFhNJr3x","2td37pGCOC"],"dependent_operators":["X99M06cbEe","4CyGpkTkEk","Qy55tPpLXF","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯10301330","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4324","layer":2},{"info":"compute unary expreesion, input=4324, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=4324","layer":1},{"info":"compute unary expreesion, input=4324, op_id = ZJpFhNJr3x, unary_op_definition = '⋠∜a = { ((a∐⫣)⋥≓≎(a≫≃)) }', output=19580","layer":0}],"base":4,"result_base":4,"text":"⋠∜(⩦⩻⨪⪩⨒∯1003210)=⪩⨒∯10301330","reverse_text":"⪩⨒∯10301330=⋠∜(⩦⩻⨪⪩⨒∯1003210)","cot":[{"info":"⩦⩻⨪⪩⨒∯1003210=⪩⨒∯1003210","layer":1},{"info":"⋠∜⪩⨒∯1003210=⪩⨒∯10301330","layer":0}]}
{"id":589,"expression_no_base_symbol":"($1044$⊭↱$1564$)↓($5537$⫽⇹≛)","expression":"(⪩⨒∯100110⊭↱⪩⨒∯120130)↓(⪩⨒∯1112201⫽⇹≛)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4141,"operation_count":3,"complexity_ratio":1380.3333333333333,"tree":{"type":"binary","operator":"↓","left_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":1044,"base":4},"right_expr":{"type":"numeric_atoms","value":1564,"base":4}},"right_expr":{"type":"unary","operator":"⫽⇹≛","unary_expr":{"type":"numeric_atoms","value":5537,"base":4}}},"used_operators":["Af076pWI7l","COABgblf1C","NNaDxxp6OQ"],"dependent_operators":["nhYeJWJD5X","mp7IySMOzn","Noe24qw2ks","lvlrscuwVU","T2fj7uvVaJ","PoHhknlbAi","W4YGzv6Whe","t8gj7n24qd","KbjG8mgYpV","AdZkA7nFnk","IWmyXbctLI"],"result":"⪩⨒∯1021310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1044","layer":2},{"info":"number node, value=1564","layer":2},{"info":"compute binary expreesion, left_input=1044, right_input=1564, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=1045","layer":1},{"info":"number node, value=5537","layer":2},{"info":"compute unary expreesion, input=5537, op_id = NNaDxxp6OQ, unary_op_definition = 'a⫽⇹≛ = { ((113⋅⇍170)⪮%⊝(a∠↢a)) }', output=272","layer":1},{"info":"compute binary expreesion, left_input=1045, right_input=272, op_id = Af076pWI7l binary_op_definition= 'a↓b = { (((b⇷b)∓⋝b)⨐((462≴⪞⇿a)∇⊂⋱(a⋓a))) }', output=4724","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100110⊭↱⪩⨒∯120130)↓(⪩⨒∯1112201⫽⇹≛)=⪩⨒∯1021310","reverse_text":"⪩⨒∯1021310=(⪩⨒∯100110⊭↱⪩⨒∯120130)↓(⪩⨒∯1112201⫽⇹≛)","cot":[{"info":"⪩⨒∯100110⊭↱⪩⨒∯120130=⪩⨒∯100111","layer":1},{"info":"⪩⨒∯1112201⫽⇹≛=⪩⨒∯10100","layer":1},{"info":"⪩⨒∯100111↓⪩⨒∯10100=⪩⨒∯1021310","layer":0}]}
{"id":590,"expression_no_base_symbol":"⩪∧⨌(∂⩏⊆$5415$)","expression":"⩪∧⨌(∂⩏⊆⪩⨒∯1110213)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":14,"operation_count":2,"complexity_ratio":7.0,"tree":{"type":"unary","operator":"⩪∧⨌","unary_expr":{"type":"unary","operator":"∂⩏⊆","unary_expr":{"type":"numeric_atoms","value":5415,"base":4}}},"used_operators":["6iOiAJX1F8","8WDwsbhb0R"],"dependent_operators":["P8v4zCKN1o","23Mk6UjR3U","7j4O788W3g","f6k1SAg4EE","g55IO6H4Gj","14qkJME0vr","eLAdDNolq6"],"result":"⪩⨒∯-213312220","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5415","layer":2},{"info":"compute unary expreesion, input=5415, op_id = 8WDwsbhb0R, unary_op_definition = '∂⩏⊆a = { (≤/a) , if a<=92 ; (a⊦⊿) , else }', output=-16324","layer":1},{"info":"compute unary expreesion, input=-16324, op_id = 6iOiAJX1F8, unary_op_definition = '⩪∧⨌a = { (∥⊫a) , if ((a⋷517)==285 and (a⪒780)<=108) ; ((a↺a)⨸⪁(a⨸⪁a)) , else }', output=-163240","layer":0}],"base":4,"result_base":4,"text":"⩪∧⨌(∂⩏⊆⪩⨒∯1110213)=⪩⨒∯-213312220","reverse_text":"⪩⨒∯-213312220=⩪∧⨌(∂⩏⊆⪩⨒∯1110213)","cot":[{"info":"∂⩏⊆⪩⨒∯1110213=⪩⨒∯-3333010","layer":1},{"info":"⩪∧⨌⪩⨒∯-3333010=⪩⨒∯-213312220","layer":0}]}
{"id":591,"expression_no_base_symbol":"∜⨇($3431$≎⪠$1721$)","expression":"∜⨇(⪩⨒∯311213≎⪠⪩⨒∯122321)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":19162,"operation_count":2,"complexity_ratio":9581.0,"tree":{"type":"unary","operator":"∜⨇","unary_expr":{"type":"binary","operator":"≎⪠","left_expr":{"type":"numeric_atoms","value":3431,"base":4},"right_expr":{"type":"numeric_atoms","value":1721,"base":4}}},"used_operators":["uFPyJr306J","aNhz54LH3e"],"dependent_operators":["fG6uBQFnGz","pRsWfj4Fpp","rGHVDoGpnC","Y7wcNGrDQJ","NNaDxxp6OQ","bl5wxAcryP","RygbFNSyEJ","SLLxy00UIr","AcOhelriW5","ctOc4cKSDt","cHh1gJQ2o6","KYD54nUTWz","kbkesczE7y","BUOGQAYlQx","PPChnnnBFF"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3431","layer":2},{"info":"number node, value=1721","layer":2},{"info":"compute binary expreesion, left_input=3431, right_input=1721, op_id = aNhz54LH3e binary_op_definition= 'a≎⪠b = { (((a⫥∨⫟11)≦↸(657∣a))⩘((⇈a)≬⋮(a↰))) , if a==21 ; (∟⋨(⋂(⨣⨃⇪b))) , else }', output=19558","layer":1},{"info":"compute unary expreesion, input=19558, op_id = uFPyJr306J, unary_op_definition = '∜⨇a = { (a⨟⋌⩍a) , if (a⫽⇹≛)!=2 or (↩⪖a)==528 or (∡a)>=548 ; (132⩵∡a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"∜⨇(⪩⨒∯311213≎⪠⪩⨒∯122321)=NaN","reverse_text":"NaN=∜⨇(⪩⨒∯311213≎⪠⪩⨒∯122321)","cot":[{"info":"⪩⨒∯311213≎⪠⪩⨒∯122321=⪩⨒∯10301212","layer":1},{"info":"∜⨇⪩⨒∯10301212=NaN","layer":0}]}
{"id":592,"expression_no_base_symbol":"$3054$⪨⊡$1461$∐⫣","expression":"⪩⨒∯233232⪨⊡⪩⨒∯112311∐⫣","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":22,"operation_count":2,"complexity_ratio":11.0,"tree":{"type":"unary","operator":"∐⫣","unary_expr":{"type":"binary","operator":"⪨⊡","left_expr":{"type":"numeric_atoms","value":3054,"base":4},"right_expr":{"type":"numeric_atoms","value":1461,"base":4}}},"used_operators":["4CyGpkTkEk","kuIXHzHcAH"],"dependent_operators":["XPYlsWDdGa","eewbuw0ToL","e1ybzncUwg","JLbD19bQDL","glklzrTFfD","eewbuw0ToL","AF7qkfDlqP"],"result":"⪩⨒∯20213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3054","layer":2},{"info":"number node, value=1461","layer":2},{"info":"compute binary expreesion, left_input=3054, right_input=1461, op_id = kuIXHzHcAH binary_op_definition= 'a⪨⊡b = { (⨑⩽⪐(b⨁⊸⫻)) , if (⨑⩽⪐b)>42 ; ((a⨰b)⪠⩆⊳) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = 4CyGpkTkEk, unary_op_definition = 'a∐⫣ = { (≉(⪲⇎(a⨰a))) }', output=551","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯233232⪨⊡⪩⨒∯112311∐⫣=⪩⨒∯20213","reverse_text":"⪩⨒∯20213=⪩⨒∯233232⪨⊡⪩⨒∯112311∐⫣","cot":[{"info":"⪩⨒∯233232⪨⊡⪩⨒∯112311=⪩⨒∯0","layer":1},{"info":"⪩⨒∯0∐⫣=⪩⨒∯20213","layer":0}]}
{"id":593,"expression_no_base_symbol":"$3321$⇌⫙⪟$2272$⇼⇔∾(≻⋜$3164$)","expression":"⪩⨒∯303321⇌⫙⪟⪩⨒∯203200⇼⇔∾(≻⋜⪩⨒∯301130)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15138,"operation_count":3,"complexity_ratio":5046.0,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"binary","operator":"⇌⫙⪟","left_expr":{"type":"numeric_atoms","value":3321,"base":4},"right_expr":{"type":"numeric_atoms","value":2272,"base":4}},"right_expr":{"type":"unary","operator":"≻⋜","unary_expr":{"type":"numeric_atoms","value":3164,"base":4}}},"used_operators":["tifHPKVTfV","AFVx7xoS7T","3tj9sqzovi"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","DpFCA1CohY","DZ8iAZOCBD","tifHPKVTfV","2DQ55sFlQl","12rbrZMWeM","xUOZtlo3hN","eewbuw0ToL","XGcMNugi78","dWAJyo7jo9","Tw270M8GLb","Y7wcNGrDQJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3321","layer":2},{"info":"number node, value=2272","layer":2},{"info":"compute binary expreesion, left_input=3321, right_input=2272, op_id = AFVx7xoS7T binary_op_definition= 'a⇌⫙⪟b = { (⨞⊢(a⇼⇔∾(a⋳⪒a))) , if (⨞⊢b)<133 ; ((a⋳⪒(b⨰261))⇼⇔∾((⋗⩬⋾b)⊉≛↸(a⨵⪆75))) , else }', output=113","layer":1},{"info":"number node, value=3164","layer":2},{"info":"compute unary expreesion, input=3164, op_id = 3tj9sqzovi, unary_op_definition = '≻⋜a = { (((a⩵∡a)⫞⩸⩒(⨰⫟⨤a))⪢a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=113, right_input=nan, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯303321⇌⫙⪟⪩⨒∯203200⇼⇔∾(≻⋜⪩⨒∯301130)=NaN","reverse_text":"NaN=⪩⨒∯303321⇌⫙⪟⪩⨒∯203200⇼⇔∾(≻⋜⪩⨒∯301130)","cot":[{"info":"⪩⨒∯303321⇌⫙⪟⪩⨒∯203200=⪩⨒∯1301","layer":1},{"info":"≻⋜⪩⨒∯301130=NaN","layer":1},{"info":"⪩⨒∯1301⇼⇔∾NaN=NaN","layer":0}]}
{"id":594,"expression_no_base_symbol":"⨵≀≌($8178$⋻⩜⩜$3734$)","expression":"⨵≀≌(⪩⨒∯1333302⋻⩜⩜⪩⨒∯322112)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":52285,"operation_count":2,"complexity_ratio":26142.5,"tree":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":8178,"base":4},"right_expr":{"type":"numeric_atoms","value":3734,"base":4}}},"used_operators":["srAu1WTS94","oDCm7WA9JY"],"dependent_operators":["glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE"],"result":"⪩⨒∯-23332230","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8178","layer":2},{"info":"number node, value=3734","layer":2},{"info":"compute binary expreesion, left_input=8178, right_input=3734, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=16356","layer":1},{"info":"compute unary expreesion, input=16356, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-49068","layer":0}],"base":4,"result_base":4,"text":"⨵≀≌(⪩⨒∯1333302⋻⩜⩜⪩⨒∯322112)=⪩⨒∯-23332230","reverse_text":"⪩⨒∯-23332230=⨵≀≌(⪩⨒∯1333302⋻⩜⩜⪩⨒∯322112)","cot":[{"info":"⪩⨒∯1333302⋻⩜⩜⪩⨒∯322112=⪩⨒∯3333210","layer":1},{"info":"⨵≀≌⪩⨒∯3333210=⪩⨒∯-23332230","layer":0}]}
{"id":595,"expression_no_base_symbol":"$5733$⨐⩸⫘$7583$∪⫐(⨝⨆$1257$)","expression":"⪩⨒∯1121211⨐⩸⫘⪩⨒∯1312133∪⫐(⨝⨆⪩⨒∯103221)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7,"operation_count":3,"complexity_ratio":2.3333333333333335,"tree":{"type":"binary","operator":"∪⫐","left_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":5733,"base":4},"right_expr":{"type":"numeric_atoms","value":7583,"base":4}},"right_expr":{"type":"unary","operator":"⨝⨆","unary_expr":{"type":"numeric_atoms","value":1257,"base":4}}},"used_operators":["7YooWSwCyH","fu6greOZ01","bQ67fsrMVf"],"dependent_operators":["rJVOvQCfKK","2DDjHMKMc0","3ViojmjbAp","tifHPKVTfV"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5733","layer":2},{"info":"number node, value=7583","layer":2},{"info":"compute binary expreesion, left_input=5733, right_input=7583, op_id = fu6greOZ01 binary_op_definition= 'a⨐⩸⫘b = {a, if b == 0; (a⨐⩸⫘(b-1))⨓(b), if b > 0 and abs(b) < 1000; -(a⨐⩸⫘(b+1))⨓(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"number node, value=1257","layer":2},{"info":"compute unary expreesion, input=1257, op_id = bQ67fsrMVf, unary_op_definition = '⨝⨆a = { (209⇼⇔∾a) }', output=1048","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1048, op_id = 7YooWSwCyH binary_op_definition= 'a∪⫐b = { ((a⋝⋈⪟b)⨎a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1121211⨐⩸⫘⪩⨒∯1312133∪⫐(⨝⨆⪩⨒∯103221)=NaN","reverse_text":"NaN=⪩⨒∯1121211⨐⩸⫘⪩⨒∯1312133∪⫐(⨝⨆⪩⨒∯103221)","cot":[{"info":"⪩⨒∯1121211⨐⩸⫘⪩⨒∯1312133=NaN","layer":1},{"info":"⨝⨆⪩⨒∯103221=⪩⨒∯100120","layer":1},{"info":"NaN∪⫐⪩⨒∯100120=NaN","layer":0}]}
{"id":596,"expression_no_base_symbol":"($3305$⪒$1841$)⩷∴(∷≠$1879$)","expression":"(⪩⨒∯303221⪒⪩⨒∯130301)⩷∴(∷≠⪩⨒∯131113)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11,"operation_count":3,"complexity_ratio":3.6666666666666665,"tree":{"type":"binary","operator":"⩷∴","left_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":3305,"base":4},"right_expr":{"type":"numeric_atoms","value":1841,"base":4}},"right_expr":{"type":"unary","operator":"∷≠","unary_expr":{"type":"numeric_atoms","value":1879,"base":4}}},"used_operators":["9FxExcQeMw","f6k1SAg4EE","QiR2Oyf5Xj"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","7j4O788W3g"],"result":"⪩⨒∯-3130002","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3305","layer":2},{"info":"number node, value=1841","layer":2},{"info":"compute binary expreesion, left_input=3305, right_input=1841, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-5146","layer":1},{"info":"number node, value=1879","layer":2},{"info":"compute unary expreesion, input=1879, op_id = QiR2Oyf5Xj, unary_op_definition = '∷≠a = { (71↺a) }', output=1879","layer":1},{"info":"compute binary expreesion, left_input=-5146, right_input=1879, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-14082","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯303221⪒⪩⨒∯130301)⩷∴(∷≠⪩⨒∯131113)=⪩⨒∯-3130002","reverse_text":"⪩⨒∯-3130002=(⪩⨒∯303221⪒⪩⨒∯130301)⩷∴(∷≠⪩⨒∯131113)","cot":[{"info":"⪩⨒∯303221⪒⪩⨒∯130301=⪩⨒∯-1100122","layer":1},{"info":"∷≠⪩⨒∯131113=⪩⨒∯131113","layer":1},{"info":"⪩⨒∯-1100122⩷∴⪩⨒∯131113=⪩⨒∯-3130002","layer":0}]}
{"id":597,"expression_no_base_symbol":"$3591$⪔⊥$1161$≄⊠($3337$⩧⪆$4929$)","expression":"⪩⨒∯320013⪔⊥⪩⨒∯102021≄⊠(⪩⨒∯310021⩧⪆⪩⨒∯1031001)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":99,"operation_count":3,"complexity_ratio":33.0,"tree":{"type":"binary","operator":"≄⊠","left_expr":{"type":"binary","operator":"⪔⊥","left_expr":{"type":"numeric_atoms","value":3591,"base":4},"right_expr":{"type":"numeric_atoms","value":1161,"base":4}},"right_expr":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"numeric_atoms","value":3337,"base":4},"right_expr":{"type":"numeric_atoms","value":4929,"base":4}}},"used_operators":["vXNesLlMH1","HJ9erzHUuu","Ikt5ks8PT7"],"dependent_operators":["d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI","eLAdDNolq6","rysDP5nf3Z","7j4O788W3g","tifHPKVTfV","8w2t5hMYqp","sdazOOVcIp","2td37pGCOC","COABgblf1C","eewbuw0ToL","t8gj7n24qd"],"result":"⪩⨒∯113130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3591","layer":2},{"info":"number node, value=1161","layer":2},{"info":"compute binary expreesion, left_input=3591, right_input=1161, op_id = HJ9erzHUuu binary_op_definition= 'a⪔⊥b = { (⩦⩻⨪(≤/(315⇼⇔∾a))) , if b<175 ; ((⊄⩳↩(b-b))⇼⇔∾((b⪨≂a)⊭↱(a↺b))) , else }', output=11843","layer":1},{"info":"number node, value=3337","layer":2},{"info":"number node, value=4929","layer":2},{"info":"compute binary expreesion, left_input=3337, right_input=4929, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-4929","layer":1},{"info":"compute binary expreesion, left_input=11843, right_input=-4929, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=1500","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯320013⪔⊥⪩⨒∯102021≄⊠(⪩⨒∯310021⩧⪆⪩⨒∯1031001)=⪩⨒∯113130","reverse_text":"⪩⨒∯113130=⪩⨒∯320013⪔⊥⪩⨒∯102021≄⊠(⪩⨒∯310021⩧⪆⪩⨒∯1031001)","cot":[{"info":"⪩⨒∯320013⪔⊥⪩⨒∯102021=⪩⨒∯2321003","layer":1},{"info":"⪩⨒∯310021⩧⪆⪩⨒∯1031001=⪩⨒∯-1031001","layer":1},{"info":"⪩⨒∯2321003≄⊠⪩⨒∯-1031001=⪩⨒∯113130","layer":0}]}
{"id":598,"expression_no_base_symbol":"($1143$⊋$1874$)⫣⪄⊒$3691$⪃⊛⇣$1065$","expression":"(⪩⨒∯101313⊋⪩⨒∯131102)⫣⪄⊒⪩⨒∯321223⪃⊛⇣⪩⨒∯100221","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4424,"operation_count":3,"complexity_ratio":1474.6666666666667,"tree":{"type":"binary","operator":"⫣⪄⊒","left_expr":{"type":"binary","operator":"⊋","left_expr":{"type":"numeric_atoms","value":1143,"base":4},"right_expr":{"type":"numeric_atoms","value":1874,"base":4}},"right_expr":{"type":"binary","operator":"⪃⊛⇣","left_expr":{"type":"numeric_atoms","value":3691,"base":4},"right_expr":{"type":"numeric_atoms","value":1065,"base":4}}},"used_operators":["RabNbG55vr","W4tP9CfskL","rrgAzCduG9"],"dependent_operators":["NTOWxs364D","DbCuESL50I","fOIeswaMU4","g7Hmc5v1ko","KPf6cnQVty","j9kHMeSvPp","k8jYdgA6NY","2DDjHMKMc0","8WDwsbhb0R","cTDWOvIxvz","IWmyXbctLI","2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu","Ez1Nq5fNfI","AHs5Up7iyr","2DDjHMKMc0","7IPrd9c3lf","8cLx32lpNA"],"result":"⪩⨒∯-123010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1143","layer":2},{"info":"number node, value=1874","layer":2},{"info":"compute binary expreesion, left_input=1143, right_input=1874, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=-9928816","layer":1},{"info":"number node, value=3691","layer":2},{"info":"number node, value=1065","layer":2},{"info":"compute binary expreesion, left_input=3691, right_input=1065, op_id = rrgAzCduG9 binary_op_definition= 'a⪃⊛⇣b = { ((b∌b)⊵↤) , if b==348 ; ((a≹⇙⪍a)⪬(a⋝⋈⪟a)) , else }', output=1234","layer":1},{"info":"compute binary expreesion, left_input=-9928816, right_input=1234, op_id = RabNbG55vr binary_op_definition= 'a⫣⪄⊒b = { ((a⪮%⊝(153⪭a))%(⋼∭⪍(b⩚⊴⇥34))) , if b>769 ; ((∂⩏⊆(b⩟))∺≝⩲((b∝a)⋝⋈⪟(a⩌⋺b))) , else }', output=-1732","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101313⊋⪩⨒∯131102)⫣⪄⊒⪩⨒∯321223⪃⊛⇣⪩⨒∯100221=⪩⨒∯-123010","reverse_text":"⪩⨒∯-123010=(⪩⨒∯101313⊋⪩⨒∯131102)⫣⪄⊒⪩⨒∯321223⪃⊛⇣⪩⨒∯100221","cot":[{"info":"⪩⨒∯101313⊋⪩⨒∯131102=⪩⨒∯-211320001300","layer":1},{"info":"⪩⨒∯321223⪃⊛⇣⪩⨒∯100221=⪩⨒∯103102","layer":1},{"info":"⪩⨒∯-211320001300⫣⪄⊒⪩⨒∯103102=⪩⨒∯-123010","layer":0}]}
{"id":599,"expression_no_base_symbol":"$1380$+⪬∐$3300$⫔⩽⩺$1836$⋾⨃∁$4819$","expression":"⪩⨒∯111210+⪬∐⪩⨒∯303210⫔⩽⩺⪩⨒∯130230⋾⨃∁⪩⨒∯1023103","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4881,"operation_count":3,"complexity_ratio":1627.0,"tree":{"type":"binary","operator":"⫔⩽⩺","left_expr":{"type":"binary","operator":"+⪬∐","left_expr":{"type":"numeric_atoms","value":1380,"base":4},"right_expr":{"type":"numeric_atoms","value":3300,"base":4}},"right_expr":{"type":"binary","operator":"⋾⨃∁","left_expr":{"type":"numeric_atoms","value":1836,"base":4},"right_expr":{"type":"numeric_atoms","value":4819,"base":4}}},"used_operators":["i9eR4S00cU","2GS7woTJqF","212REbPD9h"],"dependent_operators":["Tw270M8GLb","fu6greOZ01","g55IO6H4Gj","D4vGDi5EA2","eLxqMNBOBk","Qy55tPpLXF","w2P8NbNXyL","2DQ55sFlQl","f6k1SAg4EE"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1380","layer":2},{"info":"number node, value=3300","layer":2},{"info":"compute binary expreesion, left_input=1380, right_input=3300, op_id = 2GS7woTJqF binary_op_definition= 'a+⪬∐b = { (a≦≮≮) , if b!=63 ; (b⨸⪁575) , else }', output=-4140","layer":1},{"info":"number node, value=1836","layer":2},{"info":"number node, value=4819","layer":2},{"info":"compute binary expreesion, left_input=1836, right_input=4819, op_id = 212REbPD9h binary_op_definition= 'a⋾⨃∁b = { ((430⊉↱≁b)⨵⪆b) , if (a⪒898)>=359 ; ((⫓⪴b)⊉↱≁(26⋥≓≎b)) , else }', output=232169688","layer":1},{"info":"compute binary expreesion, left_input=-4140, right_input=232169688, op_id = i9eR4S00cU binary_op_definition= 'a⫔⩽⩺b = { (⨰⫟⨤(a⨐⩸⫘b)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯111210+⪬∐⪩⨒∯303210⫔⩽⩺⪩⨒∯130230⋾⨃∁⪩⨒∯1023103=NaN","reverse_text":"NaN=⪩⨒∯111210+⪬∐⪩⨒∯303210⫔⩽⩺⪩⨒∯130230⋾⨃∁⪩⨒∯1023103","cot":[{"info":"⪩⨒∯111210+⪬∐⪩⨒∯303210=⪩⨒∯-1000230","layer":1},{"info":"⪩⨒∯130230⋾⨃∁⪩⨒∯1023103=⪩⨒∯31311222003120","layer":1},{"info":"⪩⨒∯-1000230⫔⩽⩺⪩⨒∯31311222003120=NaN","layer":0}]}
{"id":600,"expression_no_base_symbol":"($1033$∷)∛($5341$⩘$5529$)","expression":"(⪩⨒∯100021∷)∛(⪩⨒∯1103131⩘⪩⨒∯1112121)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":152,"operation_count":3,"complexity_ratio":50.666666666666664,"tree":{"type":"binary","operator":"∛","left_expr":{"type":"unary","operator":"∷","unary_expr":{"type":"numeric_atoms","value":1033,"base":4}},"right_expr":{"type":"binary","operator":"⩘","left_expr":{"type":"numeric_atoms","value":5341,"base":4},"right_expr":{"type":"numeric_atoms","value":5529,"base":4}}},"used_operators":["w2537kitQq","nFAOW8KTqp","cHh1gJQ2o6"],"dependent_operators":["DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc","D4vGDi5EA2","t8gj7n24qd","2DDjHMKMc0","23Mk6UjR3U","eRqsBgTDFp","zVYPLywUTj","bPywburJMS","KPf6cnQVty","YbVcJGFEVW","5twsqlHp2o"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1033","layer":2},{"info":"compute unary expreesion, input=1033, op_id = nFAOW8KTqp, unary_op_definition = 'a∷ = { ((-(a⋝⋈⪟a))≦≮≮) }', output=3099","layer":1},{"info":"number node, value=5341","layer":2},{"info":"number node, value=5529","layer":2},{"info":"compute binary expreesion, left_input=5341, right_input=5529, op_id = cHh1gJQ2o6 binary_op_definition= 'a⩘b = { (((b⋷b)↼⊘⨖(a⊢6))∺≝⩲((a⪒⊣⊆619)≃(a⊪))) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=3099, right_input=160, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=67","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100021∷)∛(⪩⨒∯1103131⩘⪩⨒∯1112121)=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=(⪩⨒∯100021∷)∛(⪩⨒∯1103131⩘⪩⨒∯1112121)","cot":[{"info":"⪩⨒∯100021∷=⪩⨒∯300123","layer":1},{"info":"⪩⨒∯1103131⩘⪩⨒∯1112121=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯300123∛⪩⨒∯2200=⪩⨒∯1003","layer":0}]}
{"id":601,"expression_no_base_symbol":"(∜⨇$1646$)+$1033$⇴∐$2833$","expression":"(∜⨇⪩⨒∯121232)+⪩⨒∯100021⇴∐⪩⨒∯230101","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":84,"operation_count":3,"complexity_ratio":28.0,"tree":{"type":"binary","operator":"+","left_expr":{"type":"unary","operator":"∜⨇","unary_expr":{"type":"numeric_atoms","value":1646,"base":4}},"right_expr":{"type":"binary","operator":"⇴∐","left_expr":{"type":"numeric_atoms","value":1033,"base":4},"right_expr":{"type":"numeric_atoms","value":2833,"base":4}}},"used_operators":["W4YGzv6Whe","uFPyJr306J","HnzytWxmAO"],"dependent_operators":["fG6uBQFnGz","pRsWfj4Fpp","rGHVDoGpnC","Y7wcNGrDQJ","NNaDxxp6OQ","2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1646","layer":2},{"info":"compute unary expreesion, input=1646, op_id = uFPyJr306J, unary_op_definition = '∜⨇a = { (a⨟⋌⩍a) , if (a⫽⇹≛)!=2 or (↩⪖a)==528 or (∡a)>=548 ; (132⩵∡a) , else }', output=nan","layer":1},{"info":"number node, value=1033","layer":2},{"info":"number node, value=2833","layer":2},{"info":"compute binary expreesion, left_input=1033, right_input=2833, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = W4YGzv6Whe binary_op_definition= 'None', output=nan","layer":0}],"base":4,"result_base":4,"text":"(∜⨇⪩⨒∯121232)+⪩⨒∯100021⇴∐⪩⨒∯230101=NaN","reverse_text":"NaN=(∜⨇⪩⨒∯121232)+⪩⨒∯100021⇴∐⪩⨒∯230101","cot":[{"info":"∜⨇⪩⨒∯121232=NaN","layer":1},{"info":"⪩⨒∯100021⇴∐⪩⨒∯230101=NaN","layer":1},{"info":"NaN+NaN=NaN","layer":0}]}
{"id":602,"expression_no_base_symbol":"$2926$⨟⋌⩍$2176$≥⨤⩑(⪲⇎$5862$)","expression":"⪩⨒∯231232⨟⋌⩍⪩⨒∯202000≥⨤⩑(⪲⇎⪩⨒∯1123212)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":12,"operation_count":3,"complexity_ratio":4.0,"tree":{"type":"binary","operator":"≥⨤⩑","left_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":2926,"base":4},"right_expr":{"type":"numeric_atoms","value":2176,"base":4}},"right_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":5862,"base":4}}},"used_operators":["gJLn6v0xnP","rGHVDoGpnC","XPYlsWDdGa"],"dependent_operators":["mp7IySMOzn","aA7tF3KVD3","QvoQhV0rrE","Tcnh7f0tEr","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2926","layer":2},{"info":"number node, value=2176","layer":2},{"info":"compute binary expreesion, left_input=2926, right_input=2176, op_id = rGHVDoGpnC binary_op_definition= 'a⨟⋌⩍b = {a, if b == 0; (a⨟⋌⩍(b-1))≣⋋, if b > 0 and abs(b) < 1000; -(a⨟⋌⩍(b+1))≣⋋, if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"number node, value=5862","layer":2},{"info":"compute unary expreesion, input=5862, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=11724","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=11724, op_id = gJLn6v0xnP binary_op_definition= 'a≥⨤⩑b = { (b⇷a) , if (b⪘⨀)>356 ; (702∠⫱488) , else }', output=1234","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯231232⨟⋌⩍⪩⨒∯202000≥⨤⩑(⪲⇎⪩⨒∯1123212)=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=⪩⨒∯231232⨟⋌⩍⪩⨒∯202000≥⨤⩑(⪲⇎⪩⨒∯1123212)","cot":[{"info":"⪩⨒∯231232⨟⋌⩍⪩⨒∯202000=NaN","layer":1},{"info":"⪲⇎⪩⨒∯1123212=⪩⨒∯2313030","layer":1},{"info":"NaN≥⨤⩑⪩⨒∯2313030=⪩⨒∯103102","layer":0}]}
{"id":603,"expression_no_base_symbol":"(∥⊫$1322$)≠≀(⊤⊝$1055$)","expression":"(∥⊫⪩⨒∯110222)≠≀(⊤⊝⪩⨒∯100133)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":22,"operation_count":3,"complexity_ratio":7.333333333333333,"tree":{"type":"binary","operator":"≠≀","left_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":1322,"base":4}},"right_expr":{"type":"unary","operator":"⊤⊝","unary_expr":{"type":"numeric_atoms","value":1055,"base":4}}},"used_operators":["IwW236VD4Y","P8v4zCKN1o","rXAclfmB4M"],"dependent_operators":["eLAdDNolq6","NTOWxs364D","sdazOOVcIp","2DDjHMKMc0","2td37pGCOC","W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp"],"result":"⪩⨒∯-333222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1322","layer":2},{"info":"compute unary expreesion, input=1322, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=2190","layer":1},{"info":"number node, value=1055","layer":2},{"info":"compute unary expreesion, input=1055, op_id = rXAclfmB4M, unary_op_definition = '⊤⊝a = { (a⪨≂700) }', output=812","layer":1},{"info":"compute binary expreesion, left_input=2190, right_input=812, op_id = IwW236VD4Y binary_op_definition= 'a≠≀b = { (⩦⩻⨪(a⩚⊴⇥b)) , if (≤/b)>10 ; ((a⪨≂a)⪨≂(a⋝⋈⪟356)) , else }', output=-4074","layer":0}],"base":4,"result_base":4,"text":"(∥⊫⪩⨒∯110222)≠≀(⊤⊝⪩⨒∯100133)=⪩⨒∯-333222","reverse_text":"⪩⨒∯-333222=(∥⊫⪩⨒∯110222)≠≀(⊤⊝⪩⨒∯100133)","cot":[{"info":"∥⊫⪩⨒∯110222=⪩⨒∯202032","layer":1},{"info":"⊤⊝⪩⨒∯100133=⪩⨒∯30230","layer":1},{"info":"⪩⨒∯202032≠≀⪩⨒∯30230=⪩⨒∯-333222","layer":0}]}
{"id":604,"expression_no_base_symbol":"∨∊⋏(+⊝⨔$1820$)","expression":"∨∊⋏(+⊝⨔⪩⨒∯130130)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":108,"operation_count":2,"complexity_ratio":54.0,"tree":{"type":"unary","operator":"∨∊⋏","unary_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":1820,"base":4}}},"used_operators":["R5aXW34M0v","DhbWaqg5eL"],"dependent_operators":["L05ObWFQCd","YjI8oCXuph","9ICcGScMcE","g7Hmc5v1ko","ocnLzx9CaJ","2DDjHMKMc0","hrf7POJlIJ","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe"],"result":"⪩⨒∯11230133","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1820","layer":2},{"info":"compute unary expreesion, input=1820, op_id = DhbWaqg5eL, unary_op_definition = '+⊝⨔a = { ((⪲⇎(⨑⩽⪐14))⨁⊸⫻) , if (a⫸⊐100)!=276 or (a⩷∴98)>390 ; (((a⪐)⪢(a⫸⊐221))+((a⩨a)⪘⫢(-370))) , else }', output=1522","layer":1},{"info":"compute unary expreesion, input=1522, op_id = R5aXW34M0v, unary_op_definition = '∨∊⋏a = { (((101⋝⋈⪟206)⪍↜⋙(≦∁a))⩼⇪↪((a⩌⋺a)∴(⫇a))) }', output=23327","layer":0}],"base":4,"result_base":4,"text":"∨∊⋏(+⊝⨔⪩⨒∯130130)=⪩⨒∯11230133","reverse_text":"⪩⨒∯11230133=∨∊⋏(+⊝⨔⪩⨒∯130130)","cot":[{"info":"+⊝⨔⪩⨒∯130130=⪩⨒∯113302","layer":1},{"info":"∨∊⋏⪩⨒∯113302=⪩⨒∯11230133","layer":0}]}
{"id":605,"expression_no_base_symbol":"+⊝⨔(⪨⨬$2604$)","expression":"+⊝⨔(⪨⨬⪩⨒∯220230)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":42,"operation_count":2,"complexity_ratio":21.0,"tree":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"unary","operator":"⪨⨬","unary_expr":{"type":"numeric_atoms","value":2604,"base":4}}},"used_operators":["DhbWaqg5eL","5obUd6DV38"],"dependent_operators":["dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","T2fj7uvVaJ","nlCqmYiOvY"],"result":"⪩⨒∯113302","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2604","layer":2},{"info":"compute unary expreesion, input=2604, op_id = 5obUd6DV38, unary_op_definition = '⪨⨬a = { ((a⋓a)⨽⪊≇) }', output=-526","layer":1},{"info":"compute unary expreesion, input=-526, op_id = DhbWaqg5eL, unary_op_definition = '+⊝⨔a = { ((⪲⇎(⨑⩽⪐14))⨁⊸⫻) , if (a⫸⊐100)!=276 or (a⩷∴98)>390 ; (((a⪐)⪢(a⫸⊐221))+((a⩨a)⪘⫢(-370))) , else }', output=1522","layer":0}],"base":4,"result_base":4,"text":"+⊝⨔(⪨⨬⪩⨒∯220230)=⪩⨒∯113302","reverse_text":"⪩⨒∯113302=+⊝⨔(⪨⨬⪩⨒∯220230)","cot":[{"info":"⪨⨬⪩⨒∯220230=⪩⨒∯-20032","layer":1},{"info":"+⊝⨔⪩⨒∯-20032=⪩⨒∯113302","layer":0}]}
{"id":606,"expression_no_base_symbol":"∥⊫($1518$⇉⇱⇎)","expression":"∥⊫(⪩⨒∯113232⇉⇱⇎)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":42,"operation_count":2,"complexity_ratio":21.0,"tree":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"unary","operator":"⇉⇱⇎","unary_expr":{"type":"numeric_atoms","value":1518,"base":4}}},"used_operators":["P8v4zCKN1o","MRPaB8lBjK"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","QiR2Oyf5Xj","uFcxV4UQCh","EWw2JM7wp4","t8gj7n24qd","keWfFq85dY"],"result":"⪩⨒∯-313","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1518","layer":2},{"info":"compute unary expreesion, input=1518, op_id = MRPaB8lBjK, unary_op_definition = 'a⇉⇱⇎ = { (((a/a)⪉⨛(≯757))⪛(∷≠(-a))) }', output=-1300","layer":1},{"info":"compute unary expreesion, input=-1300, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=-55","layer":0}],"base":4,"result_base":4,"text":"∥⊫(⪩⨒∯113232⇉⇱⇎)=⪩⨒∯-313","reverse_text":"⪩⨒∯-313=∥⊫(⪩⨒∯113232⇉⇱⇎)","cot":[{"info":"⪩⨒∯113232⇉⇱⇎=⪩⨒∯-110110","layer":1},{"info":"∥⊫⪩⨒∯-110110=⪩⨒∯-313","layer":0}]}
{"id":607,"expression_no_base_symbol":"$5637$⋣⋖$3596$⊲⩕⊾($1005$≧⫂∧$2121$)","expression":"⪩⨒∯1120011⋣⋖⪩⨒∯320030⊲⩕⊾(⪩⨒∯33231≧⫂∧⪩⨒∯201021)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":27,"operation_count":3,"complexity_ratio":9.0,"tree":{"type":"binary","operator":"⊲⩕⊾","left_expr":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"numeric_atoms","value":5637,"base":4},"right_expr":{"type":"numeric_atoms","value":3596,"base":4}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":1005,"base":4},"right_expr":{"type":"numeric_atoms","value":2121,"base":4}}},"used_operators":["DmTXOeWf9t","J0M6qkBnIM","Ph9nP6C5qx"],"dependent_operators":["23Mk6UjR3U","DZ8iAZOCBD","BjRHVeLaeN","QMFrweE19q","AF7qkfDlqP","COABgblf1C","VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯-121032012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5637","layer":2},{"info":"number node, value=3596","layer":2},{"info":"compute binary expreesion, left_input=5637, right_input=3596, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=5637","layer":1},{"info":"number node, value=1005","layer":2},{"info":"number node, value=2121","layer":2},{"info":"compute binary expreesion, left_input=1005, right_input=2121, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=1648","layer":1},{"info":"compute binary expreesion, left_input=5637, right_input=1648, op_id = DmTXOeWf9t binary_op_definition= 'a⊲⩕⊾b = { (((a⊉≛↸b)⊭↱(⨑⩽⪐b))⫡⨏((a⫩⊇)⋷(a⊉≛↸b))) }', output=-103302","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1120011⋣⋖⪩⨒∯320030⊲⩕⊾(⪩⨒∯33231≧⫂∧⪩⨒∯201021)=⪩⨒∯-121032012","reverse_text":"⪩⨒∯-121032012=⪩⨒∯1120011⋣⋖⪩⨒∯320030⊲⩕⊾(⪩⨒∯33231≧⫂∧⪩⨒∯201021)","cot":[{"info":"⪩⨒∯1120011⋣⋖⪩⨒∯320030=⪩⨒∯1120011","layer":1},{"info":"⪩⨒∯33231≧⫂∧⪩⨒∯201021=⪩⨒∯121300","layer":1},{"info":"⪩⨒∯1120011⊲⩕⊾⪩⨒∯121300=⪩⨒∯-121032012","layer":0}]}
{"id":608,"expression_no_base_symbol":"(⨩∲⋌$1876$)≃$5509$⩁⩘$1062$","expression":"(⨩∲⋌⪩⨒∯131110)≃⪩⨒∯1112011⩁⩘⪩⨒∯100212","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":42,"operation_count":3,"complexity_ratio":14.0,"tree":{"type":"binary","operator":"≃","left_expr":{"type":"unary","operator":"⨩∲⋌","unary_expr":{"type":"numeric_atoms","value":1876,"base":4}},"right_expr":{"type":"binary","operator":"⩁⩘","left_expr":{"type":"numeric_atoms","value":5509,"base":4},"right_expr":{"type":"numeric_atoms","value":1062,"base":4}}},"used_operators":["YbVcJGFEVW","aSik1wnThz","gub5Cegaqo"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","23Mk6UjR3U","JLbD19bQDL","7j4O788W3g","glklzrTFfD","tifHPKVTfV","t8gj7n24qd","i8ToyICDmI","COABgblf1C","rysDP5nf3Z","Ph9nP6C5qx","Z2TMIBDE3Q","DpFCA1CohY","IWmyXbctLI"],"result":"⪩⨒∯1022222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1876","layer":2},{"info":"compute unary expreesion, input=1876, op_id = aSik1wnThz, unary_op_definition = '⨩∲⋌a = { ((759≧⫂∧(236-a))⩤) }', output=-2399","layer":1},{"info":"number node, value=5509","layer":2},{"info":"number node, value=1062","layer":2},{"info":"compute binary expreesion, left_input=5509, right_input=1062, op_id = gub5Cegaqo binary_op_definition= 'a⩁⩘b = { ((b⪮%⊝b)⪮%⊝(⋗⩬⋾a)) }', output=5196","layer":1},{"info":"compute binary expreesion, left_input=-2399, right_input=5196, op_id = YbVcJGFEVW binary_op_definition= 'a≃b = { (((13⋥≓≎b)⋷(a⇼⇔∾b))⨁⊸⫻) , if ((b⨁⊸⫻)>=162 or (b⪠⩆⊳)<=569) ; ((-(17⋷a))↺((a⩷∴a)⊭↱(b∲⫓a))) , else }', output=4778","layer":0}],"base":4,"result_base":4,"text":"(⨩∲⋌⪩⨒∯131110)≃⪩⨒∯1112011⩁⩘⪩⨒∯100212=⪩⨒∯1022222","reverse_text":"⪩⨒∯1022222=(⨩∲⋌⪩⨒∯131110)≃⪩⨒∯1112011⩁⩘⪩⨒∯100212","cot":[{"info":"⨩∲⋌⪩⨒∯131110=⪩⨒∯-211133","layer":1},{"info":"⪩⨒∯1112011⩁⩘⪩⨒∯100212=⪩⨒∯1101030","layer":1},{"info":"⪩⨒∯-211133≃⪩⨒∯1101030=⪩⨒∯1022222","layer":0}]}
{"id":609,"expression_no_base_symbol":"($1504$⪑⩈)∝$1580$⪘⫢$6633$","expression":"(⪩⨒∯113200⪑⩈)∝⪩⨒∯120230⪘⫢⪩⨒∯1213221","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":52,"operation_count":3,"complexity_ratio":17.333333333333332,"tree":{"type":"binary","operator":"∝","left_expr":{"type":"unary","operator":"⪑⩈","unary_expr":{"type":"numeric_atoms","value":1504,"base":4}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1580,"base":4},"right_expr":{"type":"numeric_atoms","value":6633,"base":4}}},"used_operators":["cTDWOvIxvz","C6VvDP6HwP","oacrs7FA3X"],"dependent_operators":["7j4O788W3g","W4YGzv6Whe","COABgblf1C","9FxExcQeMw","NTOWxs364D","tifHPKVTfV","sdazOOVcIp","Z2TMIBDE3Q","i8ToyICDmI","eewbuw0ToL","2td37pGCOC","QMFrweE19q","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⪩⨒∯2331123","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1504","layer":2},{"info":"compute unary expreesion, input=1504, op_id = C6VvDP6HwP, unary_op_definition = 'a⪑⩈ = { (((a⫡⨏a)⩚⊴⇥(477⪨≂185))⇼⇔∾(⩦⩻⨪(a∲⫓a))) , if (a⨰851)>=379 ; (((a⩷∴a)⩤)⨰a) , else }', output=12118","layer":1},{"info":"number node, value=1580","layer":2},{"info":"number node, value=6633","layer":2},{"info":"compute binary expreesion, left_input=1580, right_input=6633, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=3036","layer":1},{"info":"compute binary expreesion, left_input=12118, right_input=3036, op_id = cTDWOvIxvz binary_op_definition= 'a∝b = { ((b↺a)+(b⊭↱b)) }', output=12123","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯113200⪑⩈)∝⪩⨒∯120230⪘⫢⪩⨒∯1213221=⪩⨒∯2331123","reverse_text":"⪩⨒∯2331123=(⪩⨒∯113200⪑⩈)∝⪩⨒∯120230⪘⫢⪩⨒∯1213221","cot":[{"info":"⪩⨒∯113200⪑⩈=⪩⨒∯2331112","layer":1},{"info":"⪩⨒∯120230⪘⫢⪩⨒∯1213221=⪩⨒∯233130","layer":1},{"info":"⪩⨒∯2331112∝⪩⨒∯233130=⪩⨒∯2331123","layer":0}]}
{"id":610,"expression_no_base_symbol":"$3102$≴⪞⇿$1908$⪮%⊝(⇋↷$5904$)","expression":"⪩⨒∯300132≴⪞⇿⪩⨒∯131310⪮%⊝(⇋↷⪩⨒∯1130100)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2881,"operation_count":3,"complexity_ratio":960.3333333333334,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"numeric_atoms","value":3102,"base":4},"right_expr":{"type":"numeric_atoms","value":1908,"base":4}},"right_expr":{"type":"unary","operator":"⇋↷","unary_expr":{"type":"numeric_atoms","value":5904,"base":4}}},"used_operators":["IWmyXbctLI","lvlrscuwVU","SWo3A1KBJH"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP","XPYlsWDdGa","23Mk6UjR3U","2DQ55sFlQl","u6S6b8DprG"],"result":"⪩⨒∯1322013312310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3102","layer":2},{"info":"number node, value=1908","layer":2},{"info":"compute binary expreesion, left_input=3102, right_input=1908, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=16006716","layer":1},{"info":"number node, value=5904","layer":2},{"info":"compute unary expreesion, input=5904, op_id = SWo3A1KBJH, unary_op_definition = '⇋↷a = { (⪲⇎((↽≂a)⋷(a⨵⪆a))) }', output=47232","layer":1},{"info":"compute binary expreesion, left_input=16006716, right_input=47232, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=32013748","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯300132≴⪞⇿⪩⨒∯131310⪮%⊝(⇋↷⪩⨒∯1130100)=⪩⨒∯1322013312310","reverse_text":"⪩⨒∯1322013312310=⪩⨒∯300132≴⪞⇿⪩⨒∯131310⪮%⊝(⇋↷⪩⨒∯1130100)","cot":[{"info":"⪩⨒∯300132≴⪞⇿⪩⨒∯131310=⪩⨒∯331003320330","layer":1},{"info":"⇋↷⪩⨒∯1130100=⪩⨒∯23202000","layer":1},{"info":"⪩⨒∯331003320330⪮%⊝⪩⨒∯23202000=⪩⨒∯1322013312310","layer":0}]}
{"id":611,"expression_no_base_symbol":"($1371$∈)⪥(⨙⪌$3343$)","expression":"(⪩⨒∯111123∈)⪥(⨙⪌⪩⨒∯310033)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":949,"operation_count":3,"complexity_ratio":316.3333333333333,"tree":{"type":"binary","operator":"⪥","left_expr":{"type":"unary","operator":"∈","unary_expr":{"type":"numeric_atoms","value":1371,"base":4}},"right_expr":{"type":"unary","operator":"⨙⪌","unary_expr":{"type":"numeric_atoms","value":3343,"base":4}}},"used_operators":["QbnwKVWMIQ","ztP7wcbY7m","vEGLkm4Z2k"],"dependent_operators":["WR6HLWljOP","nhYeJWJD5X","f6k1SAg4EE","jLgFTUHLKL","PPChnnnBFF","rysDP5nf3Z","XPYlsWDdGa","8w2t5hMYqp","f6k1SAg4EE","14qkJME0vr","tmPS8pqC7x","kbkesczE7y","D3AQDKkPcf","cTDWOvIxvz","2MzE1hQ0cz","oacrs7FA3X"],"result":"⪩⨒∯10133310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1371","layer":2},{"info":"compute unary expreesion, input=1371, op_id = ztP7wcbY7m, unary_op_definition = 'a∈ = { ((⊄⩳↩250)-(a⊦⊿)) , if ((⪲⇎a)>320 or (a⪒777)>25 or a!=39) ; a , else }', output=3442","layer":1},{"info":"number node, value=3343","layer":2},{"info":"compute unary expreesion, input=3343, op_id = vEGLkm4Z2k, unary_op_definition = '⨙⪌a = { (((a⪘⫢a)∷(a≬⋮a))⨪↰⇹(a∝(a∩⋅))) }', output=868","layer":1},{"info":"compute binary expreesion, left_input=3442, right_input=868, op_id = QbnwKVWMIQ binary_op_definition= 'a⪥b = { (b∇⊂⋱(58∣a)) , if (b↢721)<125 ; (↩(508⪒a)) , else }', output=18420","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯111123∈)⪥(⨙⪌⪩⨒∯310033)=⪩⨒∯10133310","reverse_text":"⪩⨒∯10133310=(⪩⨒∯111123∈)⪥(⨙⪌⪩⨒∯310033)","cot":[{"info":"⪩⨒∯111123∈=⪩⨒∯311302","layer":1},{"info":"⨙⪌⪩⨒∯310033=⪩⨒∯31210","layer":1},{"info":"⪩⨒∯311302⪥⪩⨒∯31210=⪩⨒∯10133310","layer":0}]}
{"id":612,"expression_no_base_symbol":"($1219$⇣⩺⋵$1344$)⩇∃⫛(≉$5163$)","expression":"(⪩⨒∯103003⇣⩺⋵⪩⨒∯111000)⩇∃⫛(≉⪩⨒∯1100223)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":71,"operation_count":3,"complexity_ratio":23.666666666666668,"tree":{"type":"binary","operator":"⩇∃⫛","left_expr":{"type":"binary","operator":"⇣⩺⋵","left_expr":{"type":"numeric_atoms","value":1219,"base":4},"right_expr":{"type":"numeric_atoms","value":1344,"base":4}},"right_expr":{"type":"unary","operator":"≉","unary_expr":{"type":"numeric_atoms","value":5163,"base":4}}},"used_operators":["1aApVXNlOP","F4yD0voBRQ","e1ybzncUwg"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","e1ybzncUwg","Qy55tPpLXF","DZ8iAZOCBD","2DQ55sFlQl","t8gj7n24qd","2DDjHMKMc0","Z2TMIBDE3Q","14qkJME0vr","f6k1SAg4EE","Ph9nP6C5qx","eewbuw0ToL","u6S6b8DprG","NTOWxs364D","KPf6cnQVty","8jW3W4yZS5","12rbrZMWeM","g55IO6H4Gj","2DlMacCsIx","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-10010","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1219","layer":2},{"info":"number node, value=1344","layer":2},{"info":"compute binary expreesion, left_input=1219, right_input=1344, op_id = F4yD0voBRQ binary_op_definition= 'a⇣⩺⋵b = { (((a⩨565)∺≝⩲(5⨸⪁a))⩚⊴⇥(↯⪼(a⋳⪒b))) }', output=-260","layer":1},{"info":"number node, value=5163","layer":2},{"info":"compute unary expreesion, input=5163, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=5694","layer":1},{"info":"compute binary expreesion, left_input=-260, right_input=5694, op_id = 1aApVXNlOP binary_op_definition= 'a⩇∃⫛b = { (((b⊉≛↸a)⩤)⨰((362⩷∴b)⋥≓≎(↽≂a))) , if (a⊦⊿)>7 and b<=506 and (-a)==737 ; (((b⩤)⪒(b≧⫂∧a))⋝⋈⪟((a⨵⪆a)-(≉a))) , else }', output=-260","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯103003⇣⩺⋵⪩⨒∯111000)⩇∃⫛(≉⪩⨒∯1100223)=⪩⨒∯-10010","reverse_text":"⪩⨒∯-10010=(⪩⨒∯103003⇣⩺⋵⪩⨒∯111000)⩇∃⫛(≉⪩⨒∯1100223)","cot":[{"info":"⪩⨒∯103003⇣⩺⋵⪩⨒∯111000=⪩⨒∯-10010","layer":1},{"info":"≉⪩⨒∯1100223=⪩⨒∯1120332","layer":1},{"info":"⪩⨒∯-10010⩇∃⫛⪩⨒∯1120332=⪩⨒∯-10010","layer":0}]}
{"id":613,"expression_no_base_symbol":"⪫⨮⊛($1569$⩇∃⫛$1293$)","expression":"⪫⨮⊛(⪩⨒∯120201⩇∃⫛⪩⨒∯110031)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":13,"operation_count":2,"complexity_ratio":6.5,"tree":{"type":"unary","operator":"⪫⨮⊛","unary_expr":{"type":"binary","operator":"⩇∃⫛","left_expr":{"type":"numeric_atoms","value":1569,"base":4},"right_expr":{"type":"numeric_atoms","value":1293,"base":4}}},"used_operators":["w5FWba1tyO","1aApVXNlOP"],"dependent_operators":["s3Fd5m9Dh2","RZ5CV9rWsJ","SUmda5xLS4","kn8WO9XteQ","hTbEZDJLEm","Tw270M8GLb","9FxExcQeMw","rysDP5nf3Z","e1ybzncUwg","Qy55tPpLXF","DZ8iAZOCBD","2DQ55sFlQl","t8gj7n24qd","2DDjHMKMc0","Z2TMIBDE3Q","14qkJME0vr","f6k1SAg4EE","Ph9nP6C5qx","eewbuw0ToL","u6S6b8DprG"],"result":"⪩⨒∯3011","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1569","layer":2},{"info":"number node, value=1293","layer":2},{"info":"compute binary expreesion, left_input=1569, right_input=1293, op_id = 1aApVXNlOP binary_op_definition= 'a⩇∃⫛b = { (((b⊉≛↸a)⩤)⨰((362⩷∴b)⋥≓≎(↽≂a))) , if (a⊦⊿)>7 and b<=506 and (-a)==737 ; (((b⩤)⪒(b≧⫂∧a))⋝⋈⪟((a⨵⪆a)-(≉a))) , else }', output=197","layer":1},{"info":"compute unary expreesion, input=197, op_id = w5FWba1tyO, unary_op_definition = '⪫⨮⊛a = { a , if (a⨭⪣527)<=182 ; ((⨰⫟⨤(a⪄a))⩖⊿((a⊬⨰a)∟)) , else }', output=197","layer":0}],"base":4,"result_base":4,"text":"⪫⨮⊛(⪩⨒∯120201⩇∃⫛⪩⨒∯110031)=⪩⨒∯3011","reverse_text":"⪩⨒∯3011=⪫⨮⊛(⪩⨒∯120201⩇∃⫛⪩⨒∯110031)","cot":[{"info":"⪩⨒∯120201⩇∃⫛⪩⨒∯110031=⪩⨒∯3011","layer":1},{"info":"⪫⨮⊛⪩⨒∯3011=⪩⨒∯3011","layer":0}]}
{"id":614,"expression_no_base_symbol":"⊆⋠($2023$⇼⇔∾$1294$)","expression":"⊆⋠(⪩⨒∯133213⇼⇔∾⪩⨒∯110032)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":108,"operation_count":2,"complexity_ratio":54.0,"tree":{"type":"unary","operator":"⊆⋠","unary_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":2023,"base":4},"right_expr":{"type":"numeric_atoms","value":1294,"base":4}}},"used_operators":["EBhcHTkKd8","tifHPKVTfV"],"dependent_operators":["YjI8oCXuph","VwlE7vj6HS","e1ybzncUwg","SUmda5xLS4","vg4gO5BX6G","KipPnG1M2J","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯-10101301","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2023","layer":2},{"info":"number node, value=1294","layer":2},{"info":"compute binary expreesion, left_input=2023, right_input=1294, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-729","layer":1},{"info":"compute unary expreesion, input=-729, op_id = EBhcHTkKd8, unary_op_definition = '⊆⋠a = { ((a⊨a)↯⫤) , if (≉a)>=63 ; ((⫇a)⪄(a∀⋜↑)) , else }', output=-17521","layer":0}],"base":4,"result_base":4,"text":"⊆⋠(⪩⨒∯133213⇼⇔∾⪩⨒∯110032)=⪩⨒∯-10101301","reverse_text":"⪩⨒∯-10101301=⊆⋠(⪩⨒∯133213⇼⇔∾⪩⨒∯110032)","cot":[{"info":"⪩⨒∯133213⇼⇔∾⪩⨒∯110032=⪩⨒∯-23121","layer":1},{"info":"⊆⋠⪩⨒∯-23121=⪩⨒∯-10101301","layer":0}]}
{"id":615,"expression_no_base_symbol":"(⨈⪑$8584$)∳⫺$1229$≁$3635$","expression":"(⨈⪑⪩⨒∯2012020)∳⫺⪩⨒∯103031≁⪩⨒∯320303","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":188,"operation_count":3,"complexity_ratio":62.666666666666664,"tree":{"type":"binary","operator":"∳⫺","left_expr":{"type":"unary","operator":"⨈⪑","unary_expr":{"type":"numeric_atoms","value":8584,"base":4}},"right_expr":{"type":"binary","operator":"≁","left_expr":{"type":"numeric_atoms","value":1229,"base":4},"right_expr":{"type":"numeric_atoms","value":3635,"base":4}}},"used_operators":["AzXXKTstlj","mp94q5OcYM","8N2wDY1A35"],"dependent_operators":["F4yD0voBRQ","Tcnh7f0tEr","ZvLB05nZmT","YjI8oCXuph","09Ly4LVMIf","Bmrmz2XGnR","kbkesczE7y","i8ToyICDmI","IWmyXbctLI","B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v"],"result":"⪩⨒∯-203102200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8584","layer":2},{"info":"compute unary expreesion, input=8584, op_id = mp94q5OcYM, unary_op_definition = '⨈⪑a = { (((⫇a)⫃⨇(89⪮%⊝a))≬⋮((a≚⊃≕a)∲⫓(a⪮%⊝117))) }', output=868","layer":1},{"info":"number node, value=1229","layer":2},{"info":"number node, value=3635","layer":2},{"info":"compute binary expreesion, left_input=1229, right_input=3635, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=74039","layer":1},{"info":"compute binary expreesion, left_input=868, right_input=74039, op_id = AzXXKTstlj binary_op_definition= 'a∳⫺b = { (a≣⋋) , if (b⫳≱↱947)==166 ; (a⇣⩺⋵b) , else }', output=-144544","layer":0}],"base":4,"result_base":4,"text":"(⨈⪑⪩⨒∯2012020)∳⫺⪩⨒∯103031≁⪩⨒∯320303=⪩⨒∯-203102200","reverse_text":"⪩⨒∯-203102200=(⨈⪑⪩⨒∯2012020)∳⫺⪩⨒∯103031≁⪩⨒∯320303","cot":[{"info":"⨈⪑⪩⨒∯2012020=⪩⨒∯31210","layer":1},{"info":"⪩⨒∯103031≁⪩⨒∯320303=⪩⨒∯102010313","layer":1},{"info":"⪩⨒∯31210∳⫺⪩⨒∯102010313=⪩⨒∯-203102200","layer":0}]}
{"id":616,"expression_no_base_symbol":"$4012$⊉↱≁$4198$≧⫂∧$1306$⋛$1860$","expression":"⪩⨒∯332230⊉↱≁⪩⨒∯1001212≧⫂∧⪩⨒∯110122⋛⪩⨒∯131010","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":291,"operation_count":3,"complexity_ratio":97.0,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"⊉↱≁","left_expr":{"type":"numeric_atoms","value":4012,"base":4},"right_expr":{"type":"numeric_atoms","value":4198,"base":4}},"right_expr":{"type":"binary","operator":"⋛","left_expr":{"type":"numeric_atoms","value":1306,"base":4},"right_expr":{"type":"numeric_atoms","value":1860,"base":4}}},"used_operators":["Ph9nP6C5qx","w2P8NbNXyL","YbUVn0Rbpy"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","9FxExcQeMw","e1ybzncUwg","sdazOOVcIp","t8gj7n24qd","eewbuw0ToL","d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA"],"result":"⪩⨒∯201002112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4012","layer":2},{"info":"number node, value=4198","layer":2},{"info":"compute binary expreesion, left_input=4012, right_input=4198, op_id = w2P8NbNXyL binary_op_definition= 'a⊉↱≁b = { ((≉(a⨰b))⪨≂((145⩷∴a)⪨≂(-b))) }', output=14880","layer":1},{"info":"number node, value=1306","layer":2},{"info":"number node, value=1860","layer":2},{"info":"compute binary expreesion, left_input=1306, right_input=1860, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-120438","layer":1},{"info":"compute binary expreesion, left_input=14880, right_input=-120438, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=135318","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯332230⊉↱≁⪩⨒∯1001212≧⫂∧⪩⨒∯110122⋛⪩⨒∯131010=⪩⨒∯201002112","reverse_text":"⪩⨒∯201002112=⪩⨒∯332230⊉↱≁⪩⨒∯1001212≧⫂∧⪩⨒∯110122⋛⪩⨒∯131010","cot":[{"info":"⪩⨒∯332230⊉↱≁⪩⨒∯1001212=⪩⨒∯3220200","layer":1},{"info":"⪩⨒∯110122⋛⪩⨒∯131010=⪩⨒∯-131121312","layer":1},{"info":"⪩⨒∯3220200≧⫂∧⪩⨒∯-131121312=⪩⨒∯201002112","layer":0}]}
{"id":617,"expression_no_base_symbol":"($1026$⨔⇊$1116$)⋹","expression":"(⪩⨒∯100002⨔⇊⪩⨒∯101130)⋹","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":69,"operation_count":2,"complexity_ratio":34.5,"tree":{"type":"unary","operator":"⋹","unary_expr":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"numeric_atoms","value":1026,"base":4},"right_expr":{"type":"numeric_atoms","value":1116,"base":4}}},"used_operators":["opAxDRczMr","JclMnS0uGI"],"dependent_operators":["13rbtpv6ld","mp7IySMOzn","z63VuFQld9","aN9a90urxU","27wFxooxGf","SVb2v531z1","eewbuw0ToL","9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI"],"result":"⪩⨒∯-110","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1026","layer":2},{"info":"number node, value=1116","layer":2},{"info":"compute binary expreesion, left_input=1026, right_input=1116, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=1116","layer":1},{"info":"compute unary expreesion, input=1116, op_id = opAxDRczMr, unary_op_definition = 'a⋹ = { ((⨴⫝a)⇷(a↤⩊a)) , if (a≃⋄)<20 or (⊢≑≆a)<=20 ; ((a⨰a)∧) , else }', output=-20","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100002⨔⇊⪩⨒∯101130)⋹=⪩⨒∯-110","reverse_text":"⪩⨒∯-110=(⪩⨒∯100002⨔⇊⪩⨒∯101130)⋹","cot":[{"info":"⪩⨒∯100002⨔⇊⪩⨒∯101130=⪩⨒∯101130","layer":1},{"info":"⪩⨒∯101130⋹=⪩⨒∯-110","layer":0}]}
{"id":618,"expression_no_base_symbol":"≇⪴($3071$⨓$1155$)","expression":"≇⪴(⪩⨒∯233333⨓⪩⨒∯102003)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1175,"operation_count":2,"complexity_ratio":587.5,"tree":{"type":"unary","operator":"≇⪴","unary_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":3071,"base":4},"right_expr":{"type":"numeric_atoms","value":1155,"base":4}}},"used_operators":["zoVPnxeHJ3","3ViojmjbAp"],"dependent_operators":["7j4O788W3g","Ph9nP6C5qx","f6k1SAg4EE","14qkJME0vr","g55IO6H4Gj","COABgblf1C","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⪩⨒∯-1020120","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3071","layer":2},{"info":"number node, value=1155","layer":2},{"info":"compute binary expreesion, left_input=3071, right_input=1155, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1158","layer":1},{"info":"compute unary expreesion, input=-1158, op_id = zoVPnxeHJ3, unary_op_definition = '≇⪴a = { ((a⪒a)↺(a⨸⪁a)) , if (a⊭↱741)>=792 ; ((a≧⫂∧a)⊦⊿) , else }', output=-4632","layer":0}],"base":4,"result_base":4,"text":"≇⪴(⪩⨒∯233333⨓⪩⨒∯102003)=⪩⨒∯-1020120","reverse_text":"⪩⨒∯-1020120=≇⪴(⪩⨒∯233333⨓⪩⨒∯102003)","cot":[{"info":"⪩⨒∯233333⨓⪩⨒∯102003=⪩⨒∯-102012","layer":1},{"info":"≇⪴⪩⨒∯-102012=⪩⨒∯-1020120","layer":0}]}
{"id":619,"expression_no_base_symbol":"$6436$∀⇚≩$1704$⪭≯$2993$≴⪞⇿$5334$","expression":"⪩⨒∯1210210∀⇚≩⪩⨒∯122220⪭≯⪩⨒∯232301≴⪞⇿⪩⨒∯1103112","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":47990,"operation_count":3,"complexity_ratio":15996.666666666666,"tree":{"type":"binary","operator":"⪭≯","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":6436,"base":4},"right_expr":{"type":"numeric_atoms","value":1704,"base":4}},"right_expr":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"numeric_atoms","value":2993,"base":4},"right_expr":{"type":"numeric_atoms","value":5334,"base":4}}},"used_operators":["XAx5wpdLa6","LRNGc0VcxI","lvlrscuwVU"],"dependent_operators":["9samAPKr6k","HJ9erzHUuu","TpPTUOHfaN","DbCuESL50I","s1XTVnmDOJ","61wBmkZwlr","Z5CJsN7DuW","X99M06cbEe","DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6436","layer":2},{"info":"number node, value=1704","layer":2},{"info":"compute binary expreesion, left_input=6436, right_input=1704, op_id = LRNGc0VcxI binary_op_definition= 'a∀⇚≩b = {b, if a == 0; ((a-1)∀⇚≩b)≫≃, if a > 0 and abs(a) < 1000000; -((a+1)∀⇚≩b)≫≃, if a < 0 and abs(a) < 1000000; NaN, else}', output=nan","layer":1},{"info":"number node, value=2993","layer":2},{"info":"number node, value=5334","layer":2},{"info":"compute binary expreesion, left_input=2993, right_input=5334, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=14797034","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=14797034, op_id = XAx5wpdLa6 binary_op_definition= 'a⪭≯b = { (((b⨽∌374)⪔⊥(⋼∭⪍b))+⇶⊼((≋a)≓∲(↨⩢⫨a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1210210∀⇚≩⪩⨒∯122220⪭≯⪩⨒∯232301≴⪞⇿⪩⨒∯1103112=NaN","reverse_text":"NaN=⪩⨒∯1210210∀⇚≩⪩⨒∯122220⪭≯⪩⨒∯232301≴⪞⇿⪩⨒∯1103112","cot":[{"info":"⪩⨒∯1210210∀⇚≩⪩⨒∯122220=NaN","layer":1},{"info":"⪩⨒∯232301≴⪞⇿⪩⨒∯1103112=⪩⨒∯320130203222","layer":1},{"info":"NaN⪭≯⪩⨒∯320130203222=NaN","layer":0}]}
{"id":620,"expression_no_base_symbol":"$2058$∘$1171$∌↝($3248$⊭↱$5348$)","expression":"⪩⨒∯200022∘⪩⨒∯102103∌↝(⪩⨒∯302300⊭↱⪩⨒∯1103210)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":25,"operation_count":3,"complexity_ratio":8.333333333333334,"tree":{"type":"binary","operator":"∌↝","left_expr":{"type":"binary","operator":"∘","left_expr":{"type":"numeric_atoms","value":2058,"base":4},"right_expr":{"type":"numeric_atoms","value":1171,"base":4}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":3248,"base":4},"right_expr":{"type":"numeric_atoms","value":5348,"base":4}}},"used_operators":["9Isq31Ruls","Z5m6OM72h2","COABgblf1C"],"dependent_operators":["DpFCA1CohY","NTOWxs364D","Qy55tPpLXF","23Mk6UjR3U","EBcxylXtPf","xUOZtlo3hN","t8gj7n24qd","2DDjHMKMc0","Ph9nP6C5qx","i8ToyICDmI","eH2TOUuTDT","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2058","layer":2},{"info":"number node, value=1171","layer":2},{"info":"compute binary expreesion, left_input=2058, right_input=1171, op_id = Z5m6OM72h2 binary_op_definition= 'a∘b = { (380-a) , if b<=483 ; (a⪐) , else }', output=4116","layer":1},{"info":"number node, value=3248","layer":2},{"info":"number node, value=5348","layer":2},{"info":"compute binary expreesion, left_input=3248, right_input=5348, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=4205","layer":1},{"info":"compute binary expreesion, left_input=4116, right_input=4205, op_id = 9Isq31Ruls binary_op_definition= 'a∌↝b = { ((⋗⩬⋾b)∲⫓(⨞⊢(a⩚⊴⇥145))) , if (b⫌⩹⨱)>=130 ; ((-a)⋷((a≧⫂∧a)⋝⋈⪟(50⋥≓≎196))) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯200022∘⪩⨒∯102103∌↝(⪩⨒∯302300⊭↱⪩⨒∯1103210)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯200022∘⪩⨒∯102103∌↝(⪩⨒∯302300⊭↱⪩⨒∯1103210)","cot":[{"info":"⪩⨒∯200022∘⪩⨒∯102103=⪩⨒∯1000110","layer":1},{"info":"⪩⨒∯302300⊭↱⪩⨒∯1103210=⪩⨒∯1001231","layer":1},{"info":"⪩⨒∯1000110∌↝⪩⨒∯1001231=⪩⨒∯0","layer":0}]}
{"id":621,"expression_no_base_symbol":"($1463$⋻⩜⩜$9182$)⪃⊛⇣(⩏⊷≩$2921$)","expression":"(⪩⨒∯112313⋻⩜⩜⪩⨒∯2033132)⪃⊛⇣(⩏⊷≩⪩⨒∯231221)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":129143,"operation_count":3,"complexity_ratio":43047.666666666664,"tree":{"type":"binary","operator":"⪃⊛⇣","left_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":1463,"base":4},"right_expr":{"type":"numeric_atoms","value":9182,"base":4}},"right_expr":{"type":"unary","operator":"⩏⊷≩","unary_expr":{"type":"numeric_atoms","value":2921,"base":4}}},"used_operators":["rrgAzCduG9","oDCm7WA9JY","uOZ1tnYMDE"],"dependent_operators":["Ez1Nq5fNfI","AHs5Up7iyr","2DDjHMKMc0","7IPrd9c3lf","8cLx32lpNA","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","23Mk6UjR3U","12rbrZMWeM"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1463","layer":2},{"info":"number node, value=9182","layer":2},{"info":"compute binary expreesion, left_input=1463, right_input=9182, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=2926","layer":1},{"info":"number node, value=2921","layer":2},{"info":"compute unary expreesion, input=2921, op_id = uOZ1tnYMDE, unary_op_definition = '⩏⊷≩a = { ((a⋳⪒20)⋷(a⋳⪒17)) }', output=5541","layer":1},{"info":"compute binary expreesion, left_input=2926, right_input=5541, op_id = rrgAzCduG9 binary_op_definition= 'a⪃⊛⇣b = { ((b∌b)⊵↤) , if b==348 ; ((a≹⇙⪍a)⪬(a⋝⋈⪟a)) , else }', output=1234","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯112313⋻⩜⩜⪩⨒∯2033132)⪃⊛⇣(⩏⊷≩⪩⨒∯231221)=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=(⪩⨒∯112313⋻⩜⩜⪩⨒∯2033132)⪃⊛⇣(⩏⊷≩⪩⨒∯231221)","cot":[{"info":"⪩⨒∯112313⋻⩜⩜⪩⨒∯2033132=⪩⨒∯231232","layer":1},{"info":"⩏⊷≩⪩⨒∯231221=⪩⨒∯1112211","layer":1},{"info":"⪩⨒∯231232⪃⊛⇣⪩⨒∯1112211=⪩⨒∯103102","layer":0}]}
{"id":622,"expression_no_base_symbol":"($8082$⊋$5653$)⇍⊗($5675$⩘$2724$)","expression":"(⪩⨒∯1332102⊋⪩⨒∯1120111)⇍⊗(⪩⨒∯1120223⩘⪩⨒∯222210)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5519,"operation_count":3,"complexity_ratio":1839.6666666666667,"tree":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"binary","operator":"⊋","left_expr":{"type":"numeric_atoms","value":8082,"base":4},"right_expr":{"type":"numeric_atoms","value":5653,"base":4}},"right_expr":{"type":"binary","operator":"⩘","left_expr":{"type":"numeric_atoms","value":5675,"base":4},"right_expr":{"type":"numeric_atoms","value":2724,"base":4}}},"used_operators":["5uvYHDjeKN","W4tP9CfskL","cHh1gJQ2o6"],"dependent_operators":["Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o","2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu","23Mk6UjR3U","eRqsBgTDFp","zVYPLywUTj","bPywburJMS","KPf6cnQVty","YbVcJGFEVW","5twsqlHp2o"],"result":"⪩⨒∯-3310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8082","layer":2},{"info":"number node, value=5653","layer":2},{"info":"compute binary expreesion, left_input=8082, right_input=5653, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=110023440","layer":1},{"info":"number node, value=5675","layer":2},{"info":"number node, value=2724","layer":2},{"info":"compute binary expreesion, left_input=5675, right_input=2724, op_id = cHh1gJQ2o6 binary_op_definition= 'a⩘b = { (((b⋷b)↼⊘⨖(a⊢6))∺≝⩲((a⪒⊣⊆619)≃(a⊪))) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=110023440, right_input=160, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=-244","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1332102⊋⪩⨒∯1120111)⇍⊗(⪩⨒∯1120223⩘⪩⨒∯222210)=⪩⨒∯-3310","reverse_text":"⪩⨒∯-3310=(⪩⨒∯1332102⊋⪩⨒∯1120111)⇍⊗(⪩⨒∯1120223⩘⪩⨒∯222210)","cot":[{"info":"⪩⨒∯1332102⊋⪩⨒∯1120111=⪩⨒∯12203231030100","layer":1},{"info":"⪩⨒∯1120223⩘⪩⨒∯222210=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯12203231030100⇍⊗⪩⨒∯2200=⪩⨒∯-3310","layer":0}]}
{"id":623,"expression_no_base_symbol":"⋃($6096$⩒⫫$1454$)","expression":"⋃(⪩⨒∯1133100⩒⫫⪩⨒∯112232)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":27,"operation_count":2,"complexity_ratio":13.5,"tree":{"type":"unary","operator":"⋃","unary_expr":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"numeric_atoms","value":6096,"base":4},"right_expr":{"type":"numeric_atoms","value":1454,"base":4}}},"used_operators":["3mBM5G4a3l","KFSx94NKJn"],"dependent_operators":["g55IO6H4Gj","NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP"],"result":"⪩⨒∯2312222","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6096","layer":2},{"info":"number node, value=1454","layer":2},{"info":"compute binary expreesion, left_input=6096, right_input=1454, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=5794","layer":1},{"info":"compute unary expreesion, input=5794, op_id = 3mBM5G4a3l, unary_op_definition = '⋃a = { (51⨸⪁a) }', output=11690","layer":0}],"base":4,"result_base":4,"text":"⋃(⪩⨒∯1133100⩒⫫⪩⨒∯112232)=⪩⨒∯2312222","reverse_text":"⪩⨒∯2312222=⋃(⪩⨒∯1133100⩒⫫⪩⨒∯112232)","cot":[{"info":"⪩⨒∯1133100⩒⫫⪩⨒∯112232=⪩⨒∯1122202","layer":1},{"info":"⋃⪩⨒∯1122202=⪩⨒∯2312222","layer":0}]}
{"id":624,"expression_no_base_symbol":"(⨂⪏⇭$1445$)⨒$2023$↬$2448$","expression":"(⨂⪏⇭⪩⨒∯112211)⨒⪩⨒∯133213↬⪩⨒∯212100","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":31,"operation_count":3,"complexity_ratio":10.333333333333334,"tree":{"type":"binary","operator":"⨒","left_expr":{"type":"unary","operator":"⨂⪏⇭","unary_expr":{"type":"numeric_atoms","value":1445,"base":4}},"right_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":2023,"base":4},"right_expr":{"type":"numeric_atoms","value":2448,"base":4}}},"used_operators":["y75s1iXyHd","AYdpE9sXAk","B5M0gjZbta"],"dependent_operators":["srAu1WTS94","oacrs7FA3X","7qqUquhhSb","eewbuw0ToL","NTOWxs364D","EBcxylXtPf","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1445","layer":2},{"info":"compute unary expreesion, input=1445, op_id = AYdpE9sXAk, unary_op_definition = '⨂⪏⇭a = { (a⨰((85⩚⊴⇥a)⫌⩹⨱)) }', output=3356","layer":1},{"info":"number node, value=2023","layer":2},{"info":"number node, value=2448","layer":2},{"info":"compute binary expreesion, left_input=2023, right_input=2448, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=3356, right_input=nan, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⨂⪏⇭⪩⨒∯112211)⨒⪩⨒∯133213↬⪩⨒∯212100=NaN","reverse_text":"NaN=(⨂⪏⇭⪩⨒∯112211)⨒⪩⨒∯133213↬⪩⨒∯212100","cot":[{"info":"⨂⪏⇭⪩⨒∯112211=⪩⨒∯310130","layer":1},{"info":"⪩⨒∯133213↬⪩⨒∯212100=NaN","layer":1},{"info":"⪩⨒∯310130⨒NaN=NaN","layer":0}]}
{"id":625,"expression_no_base_symbol":"($1650$⩨$2004$)⊱⇼⊻($3858$⨫⇇↔$2255$)","expression":"(⪩⨒∯121302⩨⪩⨒∯133110)⊱⇼⊻(⪩⨒∯330102⨫⇇↔⪩⨒∯203033)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":27,"operation_count":3,"complexity_ratio":9.0,"tree":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":1650,"base":4},"right_expr":{"type":"numeric_atoms","value":2004,"base":4}},"right_expr":{"type":"binary","operator":"⨫⇇↔","left_expr":{"type":"numeric_atoms","value":3858,"base":4},"right_expr":{"type":"numeric_atoms","value":2255,"base":4}}},"used_operators":["FyVja0WsTP","2DlMacCsIx","LXhwmt4mBO"],"dependent_operators":["W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","d7ASUq0ydm","DZ8iAZOCBD","rJVOvQCfKK"],"result":"⪩⨒∯223212","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1650","layer":2},{"info":"number node, value=2004","layer":2},{"info":"compute binary expreesion, left_input=1650, right_input=2004, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-3","layer":1},{"info":"number node, value=3858","layer":2},{"info":"number node, value=2255","layer":2},{"info":"compute binary expreesion, left_input=3858, right_input=2255, op_id = LXhwmt4mBO binary_op_definition= 'a⨫⇇↔b = { ((9⊉≛↸b)⫯⪬∳(a⨎a)) }', output=-527","layer":1},{"info":"compute binary expreesion, left_input=-3, right_input=-527, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=2790","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯121302⩨⪩⨒∯133110)⊱⇼⊻(⪩⨒∯330102⨫⇇↔⪩⨒∯203033)=⪩⨒∯223212","reverse_text":"⪩⨒∯223212=(⪩⨒∯121302⩨⪩⨒∯133110)⊱⇼⊻(⪩⨒∯330102⨫⇇↔⪩⨒∯203033)","cot":[{"info":"⪩⨒∯121302⩨⪩⨒∯133110=⪩⨒∯-3","layer":1},{"info":"⪩⨒∯330102⨫⇇↔⪩⨒∯203033=⪩⨒∯-20033","layer":1},{"info":"⪩⨒∯-3⊱⇼⊻⪩⨒∯-20033=⪩⨒∯223212","layer":0}]}
{"id":626,"expression_no_base_symbol":"($3435$⨚$3744$)⊱⇼⊻($1868$⩚⊴⇥$1285$)","expression":"(⪩⨒∯311223⨚⪩⨒∯322200)⊱⇼⊻(⪩⨒∯131030⩚⊴⇥⪩⨒∯110011)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":28,"operation_count":3,"complexity_ratio":9.333333333333334,"tree":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"binary","operator":"⨚","left_expr":{"type":"numeric_atoms","value":3435,"base":4},"right_expr":{"type":"numeric_atoms","value":3744,"base":4}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":1868,"base":4},"right_expr":{"type":"numeric_atoms","value":1285,"base":4}}},"used_operators":["FyVja0WsTP","nREPSIbpBE","NTOWxs364D"],"dependent_operators":["W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","BjRHVeLaeN","12rbrZMWeM","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⪩⨒∯-12110132","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3435","layer":2},{"info":"number node, value=3744","layer":2},{"info":"compute binary expreesion, left_input=3435, right_input=3744, op_id = nREPSIbpBE binary_op_definition= 'a⨚b = { (((b⋳⪒a)⋳⪒31)⫩⊇) }', output=-7172","layer":1},{"info":"number node, value=1868","layer":2},{"info":"number node, value=1285","layer":2},{"info":"compute binary expreesion, left_input=1868, right_input=1285, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-3274","layer":1},{"info":"compute binary expreesion, left_input=-7172, right_input=-3274, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=-25886","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯311223⨚⪩⨒∯322200)⊱⇼⊻(⪩⨒∯131030⩚⊴⇥⪩⨒∯110011)=⪩⨒∯-12110132","reverse_text":"⪩⨒∯-12110132=(⪩⨒∯311223⨚⪩⨒∯322200)⊱⇼⊻(⪩⨒∯131030⩚⊴⇥⪩⨒∯110011)","cot":[{"info":"⪩⨒∯311223⨚⪩⨒∯322200=⪩⨒∯-1300010","layer":1},{"info":"⪩⨒∯131030⩚⊴⇥⪩⨒∯110011=⪩⨒∯-303022","layer":1},{"info":"⪩⨒∯-1300010⊱⇼⊻⪩⨒∯-303022=⪩⨒∯-12110132","layer":0}]}
{"id":627,"expression_no_base_symbol":"∨∊⋏($1161$⇍⊗$2261$)","expression":"∨∊⋏(⪩⨒∯102021⇍⊗⪩⨒∯203111)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":121,"operation_count":2,"complexity_ratio":60.5,"tree":{"type":"unary","operator":"∨∊⋏","unary_expr":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"numeric_atoms","value":1161,"base":4},"right_expr":{"type":"numeric_atoms","value":2261,"base":4}}},"used_operators":["R5aXW34M0v","5uvYHDjeKN"],"dependent_operators":["L05ObWFQCd","YjI8oCXuph","9ICcGScMcE","g7Hmc5v1ko","ocnLzx9CaJ","2DDjHMKMc0","hrf7POJlIJ","Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o"],"result":"⪩⨒∯-10032221","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1161","layer":2},{"info":"number node, value=2261","layer":2},{"info":"compute binary expreesion, left_input=1161, right_input=2261, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=-244","layer":1},{"info":"compute unary expreesion, input=-244, op_id = R5aXW34M0v, unary_op_definition = '∨∊⋏a = { (((101⋝⋈⪟206)⪍↜⋙(≦∁a))⩼⇪↪((a⩌⋺a)∴(⫇a))) }', output=-17321","layer":0}],"base":4,"result_base":4,"text":"∨∊⋏(⪩⨒∯102021⇍⊗⪩⨒∯203111)=⪩⨒∯-10032221","reverse_text":"⪩⨒∯-10032221=∨∊⋏(⪩⨒∯102021⇍⊗⪩⨒∯203111)","cot":[{"info":"⪩⨒∯102021⇍⊗⪩⨒∯203111=⪩⨒∯-3310","layer":1},{"info":"∨∊⋏⪩⨒∯-3310=⪩⨒∯-10032221","layer":0}]}
{"id":628,"expression_no_base_symbol":"($1186$≝⊿$1989$)⫁($4742$∋$1933$)","expression":"(⪩⨒∯102202≝⊿⪩⨒∯133011)⫁(⪩⨒∯1022012∋⪩⨒∯132031)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":220,"operation_count":3,"complexity_ratio":73.33333333333333,"tree":{"type":"binary","operator":"⫁","left_expr":{"type":"binary","operator":"≝⊿","left_expr":{"type":"numeric_atoms","value":1186,"base":4},"right_expr":{"type":"numeric_atoms","value":1989,"base":4}},"right_expr":{"type":"binary","operator":"∋","left_expr":{"type":"numeric_atoms","value":4742,"base":4},"right_expr":{"type":"numeric_atoms","value":1933,"base":4}}},"used_operators":["0ajvFaJAv0","OKKcZfAt5B","ukq6epAj5P"],"dependent_operators":["cHh1gJQ2o6","AHs5Up7iyr","12rbrZMWeM","SUmda5xLS4","61wBmkZwlr","KbjG8mgYpV"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1186","layer":2},{"info":"number node, value=1989","layer":2},{"info":"compute binary expreesion, left_input=1186, right_input=1989, op_id = OKKcZfAt5B binary_op_definition= 'a≝⊿b = { ((82⋳⪒b)⋳⪒a) }', output=-5697","layer":1},{"info":"number node, value=4742","layer":2},{"info":"number node, value=1933","layer":2},{"info":"compute binary expreesion, left_input=4742, right_input=1933, op_id = ukq6epAj5P binary_op_definition= 'a∋b = { ((≋a)∠↢(b⪄a)) }', output=4198088","layer":1},{"info":"compute binary expreesion, left_input=-5697, right_input=4198088, op_id = 0ajvFaJAv0 binary_op_definition= 'a⫁b = { (a≹⇙⪍6) , if a==154 ; (b⩘b) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯102202≝⊿⪩⨒∯133011)⫁(⪩⨒∯1022012∋⪩⨒∯132031)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⪩⨒∯102202≝⊿⪩⨒∯133011)⫁(⪩⨒∯1022012∋⪩⨒∯132031)","cot":[{"info":"⪩⨒∯102202≝⊿⪩⨒∯133011=⪩⨒∯-1121001","layer":1},{"info":"⪩⨒∯1022012∋⪩⨒∯132031=⪩⨒∯100000323020","layer":1},{"info":"⪩⨒∯-1121001⫁⪩⨒∯100000323020=⪩⨒∯2200","layer":0}]}
{"id":629,"expression_no_base_symbol":"⪸$7099$⨔⇊$6418$","expression":"⪸⪩⨒∯1232323⨔⇊⪩⨒∯1210102","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":29,"operation_count":2,"complexity_ratio":14.5,"tree":{"type":"unary","operator":"⪸","unary_expr":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"numeric_atoms","value":7099,"base":4},"right_expr":{"type":"numeric_atoms","value":6418,"base":4}}},"used_operators":["86A5ENbKR9","JclMnS0uGI"],"dependent_operators":["Qy55tPpLXF","23Mk6UjR3U","tifHPKVTfV","sdazOOVcIp","g55IO6H4Gj","AF7qkfDlqP","QMFrweE19q","9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI"],"result":"⪩⨒∯-122211201","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7099","layer":2},{"info":"number node, value=6418","layer":2},{"info":"compute binary expreesion, left_input=7099, right_input=6418, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=6418","layer":1},{"info":"compute unary expreesion, input=6418, op_id = 86A5ENbKR9, unary_op_definition = '⪸a = { (((220⪨≂51)⇼⇔∾(a⫡⨏303))⋷((a⨸⪁a)⋥≓≎(⨑⩽⪐a))) }', output=-108897","layer":0}],"base":4,"result_base":4,"text":"⪸⪩⨒∯1232323⨔⇊⪩⨒∯1210102=⪩⨒∯-122211201","reverse_text":"⪩⨒∯-122211201=⪸⪩⨒∯1232323⨔⇊⪩⨒∯1210102","cot":[{"info":"⪩⨒∯1232323⨔⇊⪩⨒∯1210102=⪩⨒∯1210102","layer":1},{"info":"⪸⪩⨒∯1210102=⪩⨒∯-122211201","layer":0}]}
{"id":630,"expression_no_base_symbol":"∂($1254$-$1560$)","expression":"∂(⪩⨒∯103212-⪩⨒∯120120)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":418,"operation_count":2,"complexity_ratio":209.0,"tree":{"type":"unary","operator":"∂","unary_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1254,"base":4},"right_expr":{"type":"numeric_atoms","value":1560,"base":4}}},"used_operators":["Uaa54Peajs","rysDP5nf3Z"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"⪩⨒∯222","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1254","layer":2},{"info":"number node, value=1560","layer":2},{"info":"compute binary expreesion, left_input=1254, right_input=1560, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-306","layer":1},{"info":"compute unary expreesion, input=-306, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=42","layer":0}],"base":4,"result_base":4,"text":"∂(⪩⨒∯103212-⪩⨒∯120120)=⪩⨒∯222","reverse_text":"⪩⨒∯222=∂(⪩⨒∯103212-⪩⨒∯120120)","cot":[{"info":"⪩⨒∯103212-⪩⨒∯120120=⪩⨒∯-10302","layer":1},{"info":"∂⪩⨒∯-10302=⪩⨒∯222","layer":0}]}
{"id":631,"expression_no_base_symbol":"⫶⊄≣($1375$⨀⨒)","expression":"⫶⊄≣(⪩⨒∯111133⨀⨒)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16056,"operation_count":2,"complexity_ratio":8028.0,"tree":{"type":"unary","operator":"⫶⊄≣","unary_expr":{"type":"unary","operator":"⨀⨒","unary_expr":{"type":"numeric_atoms","value":1375,"base":4}}},"used_operators":["wxb3vTeyAj","j6NVkjMzuk"],"dependent_operators":["eLAdDNolq6","3nqY3DE9mg","8HhzD0ZcuI","E4l6HwMY31","Ikt5ks8PT7","HmxsFra2vL","oacrs7FA3X"],"result":"Inf","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1375","layer":2},{"info":"compute unary expreesion, input=1375, op_id = j6NVkjMzuk, unary_op_definition = 'a⨀⨒ = { ((a⪘⫢a)⊔(a⪘⫢a)) , if a!=184 ; ((a⩧⪆a)∙∹∝a) , else }', output=15982","layer":1},{"info":"compute unary expreesion, input=15982, op_id = wxb3vTeyAj, unary_op_definition = '⫶⊄≣a = { (≤/((a⨽a)⊍)) }', output=inf","layer":0}],"base":4,"result_base":4,"text":"⫶⊄≣(⪩⨒∯111133⨀⨒)=Inf","reverse_text":"Inf=⫶⊄≣(⪩⨒∯111133⨀⨒)","cot":[{"info":"⪩⨒∯111133⨀⨒=⪩⨒∯3321232","layer":1},{"info":"⫶⊄≣⪩⨒∯3321232=Inf","layer":0}]}
{"id":632,"expression_no_base_symbol":"(⋗⩬⋾$1437$)↳≱($1551$⨻⩈⩔$1258$)","expression":"(⋗⩬⋾⪩⨒∯112131)↳≱(⪩⨒∯120033⨻⩈⩔⪩⨒∯103222)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":199,"operation_count":3,"complexity_ratio":66.33333333333333,"tree":{"type":"binary","operator":"↳≱","left_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":1437,"base":4}},"right_expr":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"numeric_atoms","value":1551,"base":4},"right_expr":{"type":"numeric_atoms","value":1258,"base":4}}},"used_operators":["JwTKLfZU96","DpFCA1CohY","nEsXyWgiOK"],"dependent_operators":["DhbWaqg5eL","WR6HLWljOP","XhwjNDsVaA","T2fj7uvVaJ","7YooWSwCyH","B3sABdIn96","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1437","layer":2},{"info":"compute unary expreesion, input=1437, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-4311","layer":1},{"info":"number node, value=1551","layer":2},{"info":"number node, value=1258","layer":2},{"info":"compute binary expreesion, left_input=1551, right_input=1258, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=4007","layer":1},{"info":"compute binary expreesion, left_input=-4311, right_input=4007, op_id = JwTKLfZU96 binary_op_definition= 'a↳≱b = { (((a∪⫐104)↢(147/b))⋓((+⊝⨔b)⪹)) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⋗⩬⋾⪩⨒∯112131)↳≱(⪩⨒∯120033⨻⩈⩔⪩⨒∯103222)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⋗⩬⋾⪩⨒∯112131)↳≱(⪩⨒∯120033⨻⩈⩔⪩⨒∯103222)","cot":[{"info":"⋗⩬⋾⪩⨒∯112131=⪩⨒∯-1003113","layer":1},{"info":"⪩⨒∯120033⨻⩈⩔⪩⨒∯103222=⪩⨒∯332213","layer":1},{"info":"⪩⨒∯-1003113↳≱⪩⨒∯332213=⪩⨒∯0","layer":0}]}
{"id":633,"expression_no_base_symbol":"≸≮($2285$⩺⪪$1636$)","expression":"≸≮(⪩⨒∯203231⩺⪪⪩⨒∯121210)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":147,"operation_count":2,"complexity_ratio":73.5,"tree":{"type":"unary","operator":"≸≮","unary_expr":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"numeric_atoms","value":2285,"base":4},"right_expr":{"type":"numeric_atoms","value":1636,"base":4}}},"used_operators":["AljMvE3RRm","uvdQJvN4PV"],"dependent_operators":["3UMq87Qwqg","QiR2Oyf5Xj","Z57zeUYC9z","6o9Blt3TJ6","kbkesczE7y","oPMjh9089D","Nsiff2A1zJ","7qqUquhhSb","Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U"],"result":"⪩⨒∯221200131","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2285","layer":2},{"info":"number node, value=1636","layer":2},{"info":"compute binary expreesion, left_input=2285, right_input=1636, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=-11282","layer":1},{"info":"compute unary expreesion, input=-11282, op_id = AljMvE3RRm, unary_op_definition = '≸≮a = { (a⊴((a⨔≚≋a)⫰⋱(∤↝a))) , if (a>367 and (a≬⋮702)!=1) ; (⊀((∷≠a)⩉⊫⨁)) , else }', output=170013","layer":0}],"base":4,"result_base":4,"text":"≸≮(⪩⨒∯203231⩺⪪⪩⨒∯121210)=⪩⨒∯221200131","reverse_text":"⪩⨒∯221200131=≸≮(⪩⨒∯203231⩺⪪⪩⨒∯121210)","cot":[{"info":"⪩⨒∯203231⩺⪪⪩⨒∯121210=⪩⨒∯-2300102","layer":1},{"info":"≸≮⪩⨒∯-2300102=⪩⨒∯221200131","layer":0}]}
{"id":634,"expression_no_base_symbol":"(⇋↷$5992$)⊬⨰(⫵↿$1700$)","expression":"(⇋↷⪩⨒∯1131220)⊬⨰(⫵↿⪩⨒∯122210)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":44,"operation_count":3,"complexity_ratio":14.666666666666666,"tree":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"unary","operator":"⇋↷","unary_expr":{"type":"numeric_atoms","value":5992,"base":4}},"right_expr":{"type":"unary","operator":"⫵↿","unary_expr":{"type":"numeric_atoms","value":1700,"base":4}}},"used_operators":["s3Fd5m9Dh2","SWo3A1KBJH","ivGwdmUAux"],"dependent_operators":["23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","XPYlsWDdGa","23Mk6UjR3U","2DQ55sFlQl","u6S6b8DprG","LXhwmt4mBO","09Ly4LVMIf","LRNGc0VcxI","y4ImoPnbV5","8jW3W4yZS5","G9tJMlZ94a"],"result":"⪩⨒∯23211010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5992","layer":2},{"info":"compute unary expreesion, input=5992, op_id = SWo3A1KBJH, unary_op_definition = '⇋↷a = { (⪲⇎((↽≂a)⋷(a⨵⪆a))) }', output=47936","layer":1},{"info":"number node, value=1700","layer":2},{"info":"compute unary expreesion, input=1700, op_id = ivGwdmUAux, unary_op_definition = '⫵↿a = { ((a⫃⨇256)∽(a∀⇚≩66)) , if (⇨a)>=1 ; (↯⪼(a⨫⇇↔a)) , else }', output=137","layer":1},{"info":"compute binary expreesion, left_input=47936, right_input=137, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=47428","layer":0}],"base":4,"result_base":4,"text":"(⇋↷⪩⨒∯1131220)⊬⨰(⫵↿⪩⨒∯122210)=⪩⨒∯23211010","reverse_text":"⪩⨒∯23211010=(⇋↷⪩⨒∯1131220)⊬⨰(⫵↿⪩⨒∯122210)","cot":[{"info":"⇋↷⪩⨒∯1131220=⪩⨒∯23231000","layer":1},{"info":"⫵↿⪩⨒∯122210=⪩⨒∯2021","layer":1},{"info":"⪩⨒∯23231000⊬⨰⪩⨒∯2021=⪩⨒∯23211010","layer":0}]}
{"id":635,"expression_no_base_symbol":"($5062$⊀⩕)⨻⩈⩔$2867$⇂≾⫗$2110$","expression":"(⪩⨒∯1033012⊀⩕)⨻⩈⩔⪩⨒∯230303⇂≾⫗⪩⨒∯200332","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1386,"operation_count":3,"complexity_ratio":462.0,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"unary","operator":"⊀⩕","unary_expr":{"type":"numeric_atoms","value":5062,"base":4}},"right_expr":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"numeric_atoms","value":2867,"base":4},"right_expr":{"type":"numeric_atoms","value":2110,"base":4}}},"used_operators":["nEsXyWgiOK","r0FS3hW4cC","aBQ6xLxuTc"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","rGHVDoGpnC","nhYeJWJD5X","g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U"],"result":"⪩⨒∯-2232","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5062","layer":2},{"info":"compute unary expreesion, input=5062, op_id = r0FS3hW4cC, unary_op_definition = 'a⊀⩕ = { (a⨟⋌⩍(181∇⊂⋱a)) }', output=0","layer":1},{"info":"number node, value=2867","layer":2},{"info":"number node, value=2110","layer":2},{"info":"compute binary expreesion, left_input=2867, right_input=2110, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-676","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-676, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=-174","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1033012⊀⩕)⨻⩈⩔⪩⨒∯230303⇂≾⫗⪩⨒∯200332=⪩⨒∯-2232","reverse_text":"⪩⨒∯-2232=(⪩⨒∯1033012⊀⩕)⨻⩈⩔⪩⨒∯230303⇂≾⫗⪩⨒∯200332","cot":[{"info":"⪩⨒∯1033012⊀⩕=⪩⨒∯0","layer":1},{"info":"⪩⨒∯230303⇂≾⫗⪩⨒∯200332=⪩⨒∯-22210","layer":1},{"info":"⪩⨒∯0⨻⩈⩔⪩⨒∯-22210=⪩⨒∯-2232","layer":0}]}
{"id":636,"expression_no_base_symbol":"($8518$⨎$6714$)⨔⇊($4984$≣⋋)","expression":"(⪩⨒∯2011012⨎⪩⨒∯1220322)⨔⇊(⪩⨒∯1031320≣⋋)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":516,"operation_count":3,"complexity_ratio":172.0,"tree":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":8518,"base":4},"right_expr":{"type":"numeric_atoms","value":6714,"base":4}},"right_expr":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"numeric_atoms","value":4984,"base":4}}},"used_operators":["JclMnS0uGI","rJVOvQCfKK","Tcnh7f0tEr"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=8518","layer":2},{"info":"number node, value=6714","layer":2},{"info":"compute binary expreesion, left_input=8518, right_input=6714, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=6714","layer":1},{"info":"number node, value=4984","layer":2},{"info":"compute unary expreesion, input=4984, op_id = Tcnh7f0tEr, unary_op_definition = 'a≣⋋ = { ((a/a)⋥≓≎(a⨪↰⇹248)) , if (a⪢148)<38 ; ((511*a)⊠≄⫣) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=6714, right_input=0, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2011012⨎⪩⨒∯1220322)⨔⇊(⪩⨒∯1031320≣⋋)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯2011012⨎⪩⨒∯1220322)⨔⇊(⪩⨒∯1031320≣⋋)","cot":[{"info":"⪩⨒∯2011012⨎⪩⨒∯1220322=⪩⨒∯1220322","layer":1},{"info":"⪩⨒∯1031320≣⋋=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1220322⨔⇊⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":637,"expression_no_base_symbol":"$4028$≠≀$3014$⋆⋳","expression":"⪩⨒∯332330≠≀⪩⨒∯233012⋆⋳","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":24,"operation_count":2,"complexity_ratio":12.0,"tree":{"type":"unary","operator":"⋆⋳","unary_expr":{"type":"binary","operator":"≠≀","left_expr":{"type":"numeric_atoms","value":4028,"base":4},"right_expr":{"type":"numeric_atoms","value":3014,"base":4}}},"used_operators":["6MpZysEj17","IwW236VD4Y"],"dependent_operators":["9FxExcQeMw","7j4O788W3g","DIvbN7qnHd","eLAdDNolq6","NTOWxs364D","sdazOOVcIp","2DDjHMKMc0","2td37pGCOC"],"result":"⪩⨒∯3301230","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4028","layer":2},{"info":"number node, value=3014","layer":2},{"info":"compute binary expreesion, left_input=4028, right_input=3014, op_id = IwW236VD4Y binary_op_definition= 'a≠≀b = { (⩦⩻⨪(a⩚⊴⇥b)) , if (≤/b)>10 ; ((a⪨≂a)⪨≂(a⋝⋈⪟356)) , else }', output=-7750","layer":1},{"info":"compute unary expreesion, input=-7750, op_id = 6MpZysEj17, unary_op_definition = 'a⋆⋳ = { ((a⊠≄⫣)⩷∴(a↺a)) }', output=15468","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯332330≠≀⪩⨒∯233012⋆⋳=⪩⨒∯3301230","reverse_text":"⪩⨒∯3301230=⪩⨒∯332330≠≀⪩⨒∯233012⋆⋳","cot":[{"info":"⪩⨒∯332330≠≀⪩⨒∯233012=⪩⨒∯-1321012","layer":1},{"info":"⪩⨒∯-1321012⋆⋳=⪩⨒∯3301230","layer":0}]}
{"id":638,"expression_no_base_symbol":"($2205$⨪↰⇹$6689$)⨼⩣($1870$⩧⪆$1248$)","expression":"(⪩⨒∯202131⨪↰⇹⪩⨒∯1220201)⨼⩣(⪩⨒∯131032⩧⪆⪩⨒∯103200)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6307,"operation_count":3,"complexity_ratio":2102.3333333333335,"tree":{"type":"binary","operator":"⨼⩣","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":2205,"base":4},"right_expr":{"type":"numeric_atoms","value":6689,"base":4}},"right_expr":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"numeric_atoms","value":1870,"base":4},"right_expr":{"type":"numeric_atoms","value":1248,"base":4}}},"used_operators":["JxwMv5le6e","tmPS8pqC7x","Ikt5ks8PT7"],"dependent_operators":["uFcxV4UQCh","cHh1gJQ2o6","SL6IHkK8vl","KYD54nUTWz","pRsWfj4Fpp","CArV6hThFE","rJVOvQCfKK","eewbuw0ToL","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2205","layer":2},{"info":"number node, value=6689","layer":2},{"info":"compute binary expreesion, left_input=2205, right_input=6689, op_id = tmPS8pqC7x binary_op_definition= 'a⨪↰⇹b = {a, if a == 0; (b)⨎((a-1)⨪↰⇹b), if a > 0 and abs(a) < 1000000; -(b)⨎((a+1)⨪↰⇹b), if a < 0 and abs(a) < 1000000; NaN, else}', output=2205","layer":1},{"info":"number node, value=1870","layer":2},{"info":"number node, value=1248","layer":2},{"info":"compute binary expreesion, left_input=1870, right_input=1248, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-1248","layer":1},{"info":"compute binary expreesion, left_input=2205, right_input=-1248, op_id = JxwMv5le6e binary_op_definition= 'a⨼⩣b = { ((∐⩳⋚(b⩘a))⪛((∡129)⫥∨⫟(a⫲⨊))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯202131⨪↰⇹⪩⨒∯1220201)⨼⩣(⪩⨒∯131032⩧⪆⪩⨒∯103200)=NaN","reverse_text":"NaN=(⪩⨒∯202131⨪↰⇹⪩⨒∯1220201)⨼⩣(⪩⨒∯131032⩧⪆⪩⨒∯103200)","cot":[{"info":"⪩⨒∯202131⨪↰⇹⪩⨒∯1220201=⪩⨒∯202131","layer":1},{"info":"⪩⨒∯131032⩧⪆⪩⨒∯103200=⪩⨒∯-103200","layer":1},{"info":"⪩⨒∯202131⨼⩣⪩⨒∯-103200=NaN","layer":0}]}
{"id":639,"expression_no_base_symbol":"(⊆⋠$4209$)↺$4549$⪛⫼$1970$","expression":"(⊆⋠⪩⨒∯1001301)↺⪩⨒∯1013011⪛⫼⪩⨒∯132302","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":200,"operation_count":3,"complexity_ratio":66.66666666666667,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"unary","operator":"⊆⋠","unary_expr":{"type":"numeric_atoms","value":4209,"base":4}},"right_expr":{"type":"binary","operator":"⪛⫼","left_expr":{"type":"numeric_atoms","value":4549,"base":4},"right_expr":{"type":"numeric_atoms","value":1970,"base":4}}},"used_operators":["7j4O788W3g","EBhcHTkKd8","hyuBjUqXlG"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","YjI8oCXuph","VwlE7vj6HS","e1ybzncUwg","SUmda5xLS4","vg4gO5BX6G","KipPnG1M2J","HJ9erzHUuu","9ICcGScMcE","DO4fhlbJSI","BX1lVwlMe0","Noe24qw2ks","uFcxV4UQCh","A8NUZmVepG","vg4gO5BX6G","dfKe02y8D2","hrf7POJlIJ","mqXw5SEYmG","QMFrweE19q","wztAlM01eG"],"result":"⪩⨒∯33020","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4209","layer":2},{"info":"compute unary expreesion, input=4209, op_id = EBhcHTkKd8, unary_op_definition = '⊆⋠a = { ((a⊨a)↯⫤) , if (≉a)>=63 ; ((⫇a)⪄(a∀⋜↑)) , else }', output=0","layer":1},{"info":"number node, value=4549","layer":2},{"info":"number node, value=1970","layer":2},{"info":"compute binary expreesion, left_input=4549, right_input=1970, op_id = hyuBjUqXlG binary_op_definition= 'a⪛⫼b = { (((↸⊣b)⫡⨏(⊿b))⫸⊐(≦∁(↥a))) , if (a⇟⨁⪰)!=192 ; (((b⊨a)⪛b)⨐((37⪔⊥b)∴(11⫚↹⊑395))) , else }', output=968","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=968, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=968","layer":0}],"base":4,"result_base":4,"text":"(⊆⋠⪩⨒∯1001301)↺⪩⨒∯1013011⪛⫼⪩⨒∯132302=⪩⨒∯33020","reverse_text":"⪩⨒∯33020=(⊆⋠⪩⨒∯1001301)↺⪩⨒∯1013011⪛⫼⪩⨒∯132302","cot":[{"info":"⊆⋠⪩⨒∯1001301=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1013011⪛⫼⪩⨒∯132302=⪩⨒∯33020","layer":1},{"info":"⪩⨒∯0↺⪩⨒∯33020=⪩⨒∯33020","layer":0}]}
{"id":640,"expression_no_base_symbol":"(⨦⪝$3416$)⊝⪿⪼($1436$⇌⫙⪟$1794$)","expression":"(⨦⪝⪩⨒∯311120)⊝⪿⪼(⪩⨒∯112130⇌⫙⪟⪩⨒∯130002)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":66,"operation_count":3,"complexity_ratio":22.0,"tree":{"type":"binary","operator":"⊝⪿⪼","left_expr":{"type":"unary","operator":"⨦⪝","unary_expr":{"type":"numeric_atoms","value":3416,"base":4}},"right_expr":{"type":"binary","operator":"⇌⫙⪟","left_expr":{"type":"numeric_atoms","value":1436,"base":4},"right_expr":{"type":"numeric_atoms","value":1794,"base":4}}},"used_operators":["3Oe9XWJUTD","SUjycxNXIR","AFVx7xoS7T"],"dependent_operators":["NTOWxs364D","Qy55tPpLXF","8w2t5hMYqp","t8gj7n24qd","eewbuw0ToL","QMFrweE19q","V0kx6qeWkN","rJVOvQCfKK","rxpJgHHUmx","AcOhelriW5","SpZWOsLKZJ","LYeZOJ0nQG","HmxsFra2vL","AvED76WdY7","DpFCA1CohY","DZ8iAZOCBD","tifHPKVTfV","2DQ55sFlQl","12rbrZMWeM","xUOZtlo3hN","eewbuw0ToL"],"result":"⪩⨒∯-10132120","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3416","layer":2},{"info":"compute unary expreesion, input=3416, op_id = SUjycxNXIR, unary_op_definition = '⨦⪝a = { (⫎≠⋺((a≳⇉a)⨎(⊵⊁a))) , if (a∙∹∝10)>301 ; ((⨣⨃⇪(a≭a))⊚⫡⫭) , else }', output=-1884","layer":1},{"info":"number node, value=1436","layer":2},{"info":"number node, value=1794","layer":2},{"info":"compute binary expreesion, left_input=1436, right_input=1794, op_id = AFVx7xoS7T binary_op_definition= 'a⇌⫙⪟b = { (⨞⊢(a⇼⇔∾(a⋳⪒a))) , if (⨞⊢b)<133 ; ((a⋳⪒(b⨰261))⇼⇔∾((⋗⩬⋾b)⊉≛↸(a⨵⪆75))) , else }', output=113","layer":1},{"info":"compute binary expreesion, left_input=-1884, right_input=113, op_id = 3Oe9XWJUTD binary_op_definition= 'a⊝⪿⪼b = { ((⊄⩳↩(480⩚⊴⇥a))⫡⨏((a⨰b)⋥≓≎(-b))) }', output=-18328","layer":0}],"base":4,"result_base":4,"text":"(⨦⪝⪩⨒∯311120)⊝⪿⪼(⪩⨒∯112130⇌⫙⪟⪩⨒∯130002)=⪩⨒∯-10132120","reverse_text":"⪩⨒∯-10132120=(⨦⪝⪩⨒∯311120)⊝⪿⪼(⪩⨒∯112130⇌⫙⪟⪩⨒∯130002)","cot":[{"info":"⨦⪝⪩⨒∯311120=⪩⨒∯-131130","layer":1},{"info":"⪩⨒∯112130⇌⫙⪟⪩⨒∯130002=⪩⨒∯1301","layer":1},{"info":"⪩⨒∯-131130⊝⪿⪼⪩⨒∯1301=⪩⨒∯-10132120","layer":0}]}
{"id":641,"expression_no_base_symbol":"($1331$∪⫐$1991$)≨(≔$2059$)","expression":"(⪩⨒∯110303∪⫐⪩⨒∯133013)≨(≔⪩⨒∯200023)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":110,"operation_count":3,"complexity_ratio":36.666666666666664,"tree":{"type":"binary","operator":"≨","left_expr":{"type":"binary","operator":"∪⫐","left_expr":{"type":"numeric_atoms","value":1331,"base":4},"right_expr":{"type":"numeric_atoms","value":1991,"base":4}},"right_expr":{"type":"unary","operator":"≔","unary_expr":{"type":"numeric_atoms","value":2059,"base":4}}},"used_operators":["0KMCeP1Jsh","7YooWSwCyH","8FLs4eVsLt"],"dependent_operators":["jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC","rJVOvQCfKK","2DDjHMKMc0","uPb5QRN0te","VwlE7vj6HS","3mBM5G4a3l","8HhzD0ZcuI","BUOGQAYlQx","AYdpE9sXAk"],"result":"⪩⨒∯-2221102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1331","layer":2},{"info":"number node, value=1991","layer":2},{"info":"compute binary expreesion, left_input=1331, right_input=1991, op_id = 7YooWSwCyH binary_op_definition= 'a∪⫐b = { ((a⋝⋈⪟b)⨎a) }', output=1331","layer":1},{"info":"number node, value=2059","layer":2},{"info":"compute unary expreesion, input=2059, op_id = 8FLs4eVsLt, unary_op_definition = '≔a = { (⋃(⋂a)) , if (⨂⪏⇭a)<=427 or (a↫)>=16 ; ((a⨽194)↯⫤) , else }', output=-56358","layer":1},{"info":"compute binary expreesion, left_input=1331, right_input=-56358, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-10834","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯110303∪⫐⪩⨒∯133013)≨(≔⪩⨒∯200023)=⪩⨒∯-2221102","reverse_text":"⪩⨒∯-2221102=(⪩⨒∯110303∪⫐⪩⨒∯133013)≨(≔⪩⨒∯200023)","cot":[{"info":"⪩⨒∯110303∪⫐⪩⨒∯133013=⪩⨒∯110303","layer":1},{"info":"≔⪩⨒∯200023=⪩⨒∯-31300212","layer":1},{"info":"⪩⨒∯110303≨⪩⨒∯-31300212=⪩⨒∯-2221102","layer":0}]}
{"id":642,"expression_no_base_symbol":"(⊖$1039$)⇻⋧≁($3774$⪭$3270$)","expression":"(⊖⪩⨒∯100033)⇻⋧≁(⪩⨒∯322332⪭⪩⨒∯303012)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":49,"operation_count":3,"complexity_ratio":16.333333333333332,"tree":{"type":"binary","operator":"⇻⋧≁","left_expr":{"type":"unary","operator":"⊖","unary_expr":{"type":"numeric_atoms","value":1039,"base":4}},"right_expr":{"type":"binary","operator":"⪭","left_expr":{"type":"numeric_atoms","value":3774,"base":4},"right_expr":{"type":"numeric_atoms","value":3270,"base":4}}},"used_operators":["jCPkEVoL5K","U6pG0PXrV3","j9kHMeSvPp"],"dependent_operators":["eLxqMNBOBk","XnXgA4xnOs","3EYGwJThht","XTarYq4gQB","59igzFyhWz","dfKe02y8D2","X99M06cbEe","tifHPKVTfV","i8ToyICDmI","D4vGDi5EA2","nCS4ZIUYfx","COABgblf1C","xUOZtlo3hN"],"result":"⪩⨒∯-12333","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1039","layer":2},{"info":"compute unary expreesion, input=1039, op_id = U6pG0PXrV3, unary_op_definition = '⊖a = { (((a⇼⇔∾a)⨳⩥⨓(a≦≮≮))∲⫓a) }', output=0","layer":1},{"info":"number node, value=3774","layer":2},{"info":"number node, value=3270","layer":2},{"info":"compute binary expreesion, left_input=3774, right_input=3270, op_id = j9kHMeSvPp binary_op_definition= 'a⪭b = { (⨞⊢a) , if a<649 ; (b⊭↱b) , else }', output=5","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=5, op_id = jCPkEVoL5K binary_op_definition= 'a⇻⋧≁b = { ((⫓⪴a)⫚↹⊑(54≫≃)) , if (a∵≐)<=35 or a>411 ; ((⪝⪂⫅b)⇄(290⨑≵⋬a)) , else }', output=-447","layer":0}],"base":4,"result_base":4,"text":"(⊖⪩⨒∯100033)⇻⋧≁(⪩⨒∯322332⪭⪩⨒∯303012)=⪩⨒∯-12333","reverse_text":"⪩⨒∯-12333=(⊖⪩⨒∯100033)⇻⋧≁(⪩⨒∯322332⪭⪩⨒∯303012)","cot":[{"info":"⊖⪩⨒∯100033=⪩⨒∯0","layer":1},{"info":"⪩⨒∯322332⪭⪩⨒∯303012=⪩⨒∯11","layer":1},{"info":"⪩⨒∯0⇻⋧≁⪩⨒∯11=⪩⨒∯-12333","layer":0}]}
{"id":643,"expression_no_base_symbol":"$2738$≴⪞⇿$2955$⋝⋈⪟$1474$≚⊃≕$7577$","expression":"⪩⨒∯222302≴⪞⇿⪩⨒∯232023⋝⋈⪟⪩⨒∯113002≚⊃≕⪩⨒∯1312121","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2524,"operation_count":3,"complexity_ratio":841.3333333333334,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"numeric_atoms","value":2738,"base":4},"right_expr":{"type":"numeric_atoms","value":2955,"base":4}},"right_expr":{"type":"binary","operator":"≚⊃≕","left_expr":{"type":"numeric_atoms","value":1474,"base":4},"right_expr":{"type":"numeric_atoms","value":7577,"base":4}}},"used_operators":["2DDjHMKMc0","lvlrscuwVU","Bmrmz2XGnR"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP","9FxExcQeMw","Qy55tPpLXF","7j4O788W3g","sdazOOVcIp","8w2t5hMYqp","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q"],"result":"⪩⨒∯232112331230","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2738","layer":2},{"info":"number node, value=2955","layer":2},{"info":"compute binary expreesion, left_input=2738, right_input=2955, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=12152684","layer":1},{"info":"number node, value=1474","layer":2},{"info":"number node, value=7577","layer":2},{"info":"compute binary expreesion, left_input=1474, right_input=7577, op_id = Bmrmz2XGnR binary_op_definition= 'a≚⊃≕b = { (-((⊄⩳↩b)⪨≂(a⩷∴b))) , if ((b⫡⨏524)<690 or (⨞⊢a)>=395) ; ((⊄⩳↩(b⋥≓≎a))⋥≓≎((a↺a)⪨≂(479⨸⪁a))) , else }', output=-23279","layer":1},{"info":"compute binary expreesion, left_input=12152684, right_input=-23279, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=12152684","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯222302≴⪞⇿⪩⨒∯232023⋝⋈⪟⪩⨒∯113002≚⊃≕⪩⨒∯1312121=⪩⨒∯232112331230","reverse_text":"⪩⨒∯232112331230=⪩⨒∯222302≴⪞⇿⪩⨒∯232023⋝⋈⪟⪩⨒∯113002≚⊃≕⪩⨒∯1312121","cot":[{"info":"⪩⨒∯222302≴⪞⇿⪩⨒∯232023=⪩⨒∯232112331230","layer":1},{"info":"⪩⨒∯113002≚⊃≕⪩⨒∯1312121=⪩⨒∯-11223233","layer":1},{"info":"⪩⨒∯232112331230⋝⋈⪟⪩⨒∯-11223233=⪩⨒∯232112331230","layer":0}]}
{"id":644,"expression_no_base_symbol":"($3073$⩚⊴⇥$2379$)⪝($1004$∲⫓$1998$)","expression":"(⪩⨒∯300001⩚⊴⇥⪩⨒∯211023)⪝(⪩⨒∯33230∲⫓⪩⨒∯133032)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":428,"operation_count":3,"complexity_ratio":142.66666666666666,"tree":{"type":"binary","operator":"⪝","left_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":3073,"base":4},"right_expr":{"type":"numeric_atoms","value":2379,"base":4}},"right_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":1004,"base":4},"right_expr":{"type":"numeric_atoms","value":1998,"base":4}}},"used_operators":["wicAB68Tmb","NTOWxs364D","i8ToyICDmI"],"dependent_operators":["L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-31110203","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3073","layer":2},{"info":"number node, value=2379","layer":2},{"info":"compute binary expreesion, left_input=3073, right_input=2379, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-5573","layer":1},{"info":"number node, value=1004","layer":2},{"info":"number node, value=1998","layer":2},{"info":"compute binary expreesion, left_input=1004, right_input=1998, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-5573, right_input=0, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=-54563","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯300001⩚⊴⇥⪩⨒∯211023)⪝(⪩⨒∯33230∲⫓⪩⨒∯133032)=⪩⨒∯-31110203","reverse_text":"⪩⨒∯-31110203=(⪩⨒∯300001⩚⊴⇥⪩⨒∯211023)⪝(⪩⨒∯33230∲⫓⪩⨒∯133032)","cot":[{"info":"⪩⨒∯300001⩚⊴⇥⪩⨒∯211023=⪩⨒∯-1113011","layer":1},{"info":"⪩⨒∯33230∲⫓⪩⨒∯133032=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-1113011⪝⪩⨒∯0=⪩⨒∯-31110203","layer":0}]}
{"id":645,"expression_no_base_symbol":"∓$3075$↓$3414$","expression":"∓⪩⨒∯300003↓⪩⨒∯311112","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":48113,"operation_count":2,"complexity_ratio":24056.5,"tree":{"type":"unary","operator":"∓","unary_expr":{"type":"binary","operator":"↓","left_expr":{"type":"numeric_atoms","value":3075,"base":4},"right_expr":{"type":"numeric_atoms","value":3414,"base":4}}},"used_operators":["OwUj7dcsQK","Af076pWI7l"],"dependent_operators":["DpFCA1CohY","12rbrZMWeM","nCS4ZIUYfx","QMFrweE19q","nhYeJWJD5X","mp7IySMOzn","Noe24qw2ks","lvlrscuwVU","T2fj7uvVaJ","PoHhknlbAi"],"result":"⪩⨒∯-230232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3075","layer":2},{"info":"number node, value=3414","layer":2},{"info":"compute binary expreesion, left_input=3075, right_input=3414, op_id = Af076pWI7l binary_op_definition= 'a↓b = { (((b⇷b)∓⋝b)⨐((462≴⪞⇿a)∇⊂⋱(a⋓a))) }', output=-134","layer":1},{"info":"compute unary expreesion, input=-134, op_id = OwUj7dcsQK, unary_op_definition = '∓a = { (⋗⩬⋾((a⋳⪒554)⨳⩥⨓(a⫡⨏a))) }', output=-2862","layer":0}],"base":4,"result_base":4,"text":"∓⪩⨒∯300003↓⪩⨒∯311112=⪩⨒∯-230232","reverse_text":"⪩⨒∯-230232=∓⪩⨒∯300003↓⪩⨒∯311112","cot":[{"info":"⪩⨒∯300003↓⪩⨒∯311112=⪩⨒∯-2012","layer":1},{"info":"∓⪩⨒∯-2012=⪩⨒∯-230232","layer":0}]}
{"id":646,"expression_no_base_symbol":"($6728$⇣⩺⋵$2754$)→⨶⪴($2226$⋝⋈⪟$1581$)","expression":"(⪩⨒∯1221020⇣⩺⋵⪩⨒∯223002)→⨶⪴(⪩⨒∯202302⋝⋈⪟⪩⨒∯120231)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":63,"operation_count":3,"complexity_ratio":21.0,"tree":{"type":"binary","operator":"→⨶⪴","left_expr":{"type":"binary","operator":"⇣⩺⋵","left_expr":{"type":"numeric_atoms","value":6728,"base":4},"right_expr":{"type":"numeric_atoms","value":2754,"base":4}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":2226,"base":4},"right_expr":{"type":"numeric_atoms","value":1581,"base":4}}},"used_operators":["bF6eod5Gvf","F4yD0voBRQ","2DDjHMKMc0"],"dependent_operators":["8w2t5hMYqp","9FxExcQeMw","NTOWxs364D","KPf6cnQVty","8jW3W4yZS5","12rbrZMWeM","g55IO6H4Gj","2DlMacCsIx","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-1220112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6728","layer":2},{"info":"number node, value=2754","layer":2},{"info":"compute binary expreesion, left_input=6728, right_input=2754, op_id = F4yD0voBRQ binary_op_definition= 'a⇣⩺⋵b = { (((a⩨565)∺≝⩲(5⨸⪁a))⩚⊴⇥(↯⪼(a⋳⪒b))) }', output=-260","layer":1},{"info":"number node, value=2226","layer":2},{"info":"number node, value=1581","layer":2},{"info":"compute binary expreesion, left_input=2226, right_input=1581, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=2226","layer":1},{"info":"compute binary expreesion, left_input=-260, right_input=2226, op_id = bF6eod5Gvf binary_op_definition= 'a→⨶⪴b = { (a⩷∴b) , if b<109 ; (⊄⩳↩b) , else }', output=-6678","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1221020⇣⩺⋵⪩⨒∯223002)→⨶⪴(⪩⨒∯202302⋝⋈⪟⪩⨒∯120231)=⪩⨒∯-1220112","reverse_text":"⪩⨒∯-1220112=(⪩⨒∯1221020⇣⩺⋵⪩⨒∯223002)→⨶⪴(⪩⨒∯202302⋝⋈⪟⪩⨒∯120231)","cot":[{"info":"⪩⨒∯1221020⇣⩺⋵⪩⨒∯223002=⪩⨒∯-10010","layer":1},{"info":"⪩⨒∯202302⋝⋈⪟⪩⨒∯120231=⪩⨒∯202302","layer":1},{"info":"⪩⨒∯-10010→⨶⪴⪩⨒∯202302=⪩⨒∯-1220112","layer":0}]}
{"id":647,"expression_no_base_symbol":"($2143$%$2273$)⨻⩈⩔$6594$≄⊠$3574$","expression":"(⪩⨒∯201133%⪩⨒∯203201)⨻⩈⩔⪩⨒∯1213002≄⊠⪩⨒∯313312","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":170,"operation_count":3,"complexity_ratio":56.666666666666664,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":2143,"base":4},"right_expr":{"type":"numeric_atoms","value":2273,"base":4}},"right_expr":{"type":"binary","operator":"≄⊠","left_expr":{"type":"numeric_atoms","value":6594,"base":4},"right_expr":{"type":"numeric_atoms","value":3574,"base":4}}},"used_operators":["nEsXyWgiOK","k8jYdgA6NY","vXNesLlMH1"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","rysDP5nf3Z","d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI"],"result":"⪩⨒∯2020213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2143","layer":2},{"info":"number node, value=2273","layer":2},{"info":"compute binary expreesion, left_input=2143, right_input=2273, op_id = k8jYdgA6NY binary_op_definition= 'None', output=2143","layer":1},{"info":"number node, value=6594","layer":2},{"info":"number node, value=3574","layer":2},{"info":"compute binary expreesion, left_input=6594, right_input=3574, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=61852","layer":1},{"info":"compute binary expreesion, left_input=2143, right_input=61852, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=8743","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯201133%⪩⨒∯203201)⨻⩈⩔⪩⨒∯1213002≄⊠⪩⨒∯313312=⪩⨒∯2020213","reverse_text":"⪩⨒∯2020213=(⪩⨒∯201133%⪩⨒∯203201)⨻⩈⩔⪩⨒∯1213002≄⊠⪩⨒∯313312","cot":[{"info":"⪩⨒∯201133%⪩⨒∯203201=⪩⨒∯201133","layer":1},{"info":"⪩⨒∯1213002≄⊠⪩⨒∯313312=⪩⨒∯33012130","layer":1},{"info":"⪩⨒∯201133⨻⩈⩔⪩⨒∯33012130=⪩⨒∯2020213","layer":0}]}
{"id":648,"expression_no_base_symbol":"($3013$≓∲$5365$)⨭⪣$1138$≝⊿$6238$","expression":"(⪩⨒∯233011≓∲⪩⨒∯1103311)⨭⪣⪩⨒∯101302≝⊿⪩⨒∯1201132","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":98,"operation_count":3,"complexity_ratio":32.666666666666664,"tree":{"type":"binary","operator":"⨭⪣","left_expr":{"type":"binary","operator":"≓∲","left_expr":{"type":"numeric_atoms","value":3013,"base":4},"right_expr":{"type":"numeric_atoms","value":5365,"base":4}},"right_expr":{"type":"binary","operator":"≝⊿","left_expr":{"type":"numeric_atoms","value":1138,"base":4},"right_expr":{"type":"numeric_atoms","value":6238,"base":4}}},"used_operators":["kn8WO9XteQ","s1XTVnmDOJ","OKKcZfAt5B"],"dependent_operators":["vRio1gEz1j","61wBmkZwlr","SWo3A1KBJH","8jW3W4yZS5","LkLIoiE525","Y7wcNGrDQJ","PPChnnnBFF","HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu","12rbrZMWeM"],"result":"⪩⨒∯13033002","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3013","layer":2},{"info":"number node, value=5365","layer":2},{"info":"compute binary expreesion, left_input=3013, right_input=5365, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=30913","layer":1},{"info":"number node, value=1138","layer":2},{"info":"number node, value=6238","layer":2},{"info":"compute binary expreesion, left_input=1138, right_input=6238, op_id = OKKcZfAt5B binary_op_definition= 'a≝⊿b = { ((82⋳⪒b)⋳⪒a) }', output=-14147","layer":1},{"info":"compute binary expreesion, left_input=30913, right_input=-14147, op_id = kn8WO9XteQ binary_op_definition= 'a⨭⪣b = { ((486⇩)⩵∡(a∣a)) , if (b⇯⋐)>445 or (≋b)>319 or b<=69 ; (↯⪼(⇋↷b)) , else }', output=29634","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯233011≓∲⪩⨒∯1103311)⨭⪣⪩⨒∯101302≝⊿⪩⨒∯1201132=⪩⨒∯13033002","reverse_text":"⪩⨒∯13033002=(⪩⨒∯233011≓∲⪩⨒∯1103311)⨭⪣⪩⨒∯101302≝⊿⪩⨒∯1201132","cot":[{"info":"⪩⨒∯233011≓∲⪩⨒∯1103311=⪩⨒∯13203001","layer":1},{"info":"⪩⨒∯101302≝⊿⪩⨒∯1201132=⪩⨒∯-3131003","layer":1},{"info":"⪩⨒∯13203001⨭⪣⪩⨒∯-3131003=⪩⨒∯13033002","layer":0}]}
{"id":649,"expression_no_base_symbol":"⊙↵-$2827$⇂≾⫗$3266$","expression":"⊙↵-⪩⨒∯230023⇂≾⫗⪩⨒∯303002","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":766,"operation_count":2,"complexity_ratio":383.0,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"numeric_atoms","value":2827,"base":4},"right_expr":{"type":"numeric_atoms","value":3266,"base":4}}},"used_operators":["oWn0xqSxBt","aBQ6xLxuTc"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U"],"result":"⪩⨒∯3010","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2827","layer":2},{"info":"number node, value=3266","layer":2},{"info":"compute binary expreesion, left_input=2827, right_input=3266, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-676","layer":1},{"info":"compute unary expreesion, input=-676, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=196","layer":0}],"base":4,"result_base":4,"text":"⊙↵-⪩⨒∯230023⇂≾⫗⪩⨒∯303002=⪩⨒∯3010","reverse_text":"⪩⨒∯3010=⊙↵-⪩⨒∯230023⇂≾⫗⪩⨒∯303002","cot":[{"info":"⪩⨒∯230023⇂≾⫗⪩⨒∯303002=⪩⨒∯-22210","layer":1},{"info":"⊙↵-⪩⨒∯-22210=⪩⨒∯3010","layer":0}]}
{"id":650,"expression_no_base_symbol":"($4073$⩚⊴⇥$1699$)⨸(⊈$3498$)","expression":"(⪩⨒∯333221⩚⊴⇥⪩⨒∯122203)⨸(⊈⪩⨒∯312222)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6008,"operation_count":3,"complexity_ratio":2002.6666666666667,"tree":{"type":"binary","operator":"⨸","left_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":4073,"base":4},"right_expr":{"type":"numeric_atoms","value":1699,"base":4}},"right_expr":{"type":"unary","operator":"⊈","unary_expr":{"type":"numeric_atoms","value":3498,"base":4}}},"used_operators":["KmoU8R5UQR","NTOWxs364D","RHru8klgy8"],"dependent_operators":["ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","12rbrZMWeM","xUOZtlo3hN"],"result":"⪩⨒∯2320022","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4073","layer":2},{"info":"number node, value=1699","layer":2},{"info":"compute binary expreesion, left_input=4073, right_input=1699, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-5893","layer":1},{"info":"number node, value=3498","layer":2},{"info":"compute unary expreesion, input=3498, op_id = RHru8klgy8, unary_op_definition = '⊈a = { (a⋳⪒a) , if a==61 ; (⨞⊢a) , else }', output=-3672","layer":1},{"info":"compute binary expreesion, left_input=-5893, right_input=-3672, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=11786","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯333221⩚⊴⇥⪩⨒∯122203)⨸(⊈⪩⨒∯312222)=⪩⨒∯2320022","reverse_text":"⪩⨒∯2320022=(⪩⨒∯333221⩚⊴⇥⪩⨒∯122203)⨸(⊈⪩⨒∯312222)","cot":[{"info":"⪩⨒∯333221⩚⊴⇥⪩⨒∯122203=⪩⨒∯-1130011","layer":1},{"info":"⊈⪩⨒∯312222=⪩⨒∯-321120","layer":1},{"info":"⪩⨒∯-1130011⨸⪩⨒∯-321120=⪩⨒∯2320022","layer":0}]}
{"id":651,"expression_no_base_symbol":"↨⩢⫨($7117$⊍⩺⋍$6935$)","expression":"↨⩢⫨(⪩⨒∯1233031⊍⩺⋍⪩⨒∯1230113)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":274,"operation_count":2,"complexity_ratio":137.0,"tree":{"type":"unary","operator":"↨⩢⫨","unary_expr":{"type":"binary","operator":"⊍⩺⋍","left_expr":{"type":"numeric_atoms","value":7117,"base":4},"right_expr":{"type":"numeric_atoms","value":6935,"base":4}}},"used_operators":["Z5CJsN7DuW","OXDGMFPWZM"],"dependent_operators":["Noe24qw2ks","gu96TGCTMs","8jW3W4yZS5","AFVx7xoS7T","kn8WO9XteQ","inkyxCbjAn","13rbtpv6ld"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7117","layer":2},{"info":"number node, value=6935","layer":2},{"info":"compute binary expreesion, left_input=7117, right_input=6935, op_id = OXDGMFPWZM binary_op_definition= 'a⊍⩺⋍b = { ((⇁⨣⪵659)↤⩊(b⨭⪣a)) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = Z5CJsN7DuW, unary_op_definition = '↨⩢⫨a = { (((211⨐a)⇌⫙⪟(↯⪼a))⊘) }', output=0","layer":0}],"base":4,"result_base":4,"text":"↨⩢⫨(⪩⨒∯1233031⊍⩺⋍⪩⨒∯1230113)=⪩⨒∯0","reverse_text":"⪩⨒∯0=↨⩢⫨(⪩⨒∯1233031⊍⩺⋍⪩⨒∯1230113)","cot":[{"info":"⪩⨒∯1233031⊍⩺⋍⪩⨒∯1230113=NaN","layer":1},{"info":"↨⩢⫨NaN=⪩⨒∯0","layer":0}]}
{"id":652,"expression_no_base_symbol":"(⨞⊢$4164$)⊵↤","expression":"(⨞⊢⪩⨒∯1001010)⊵↤","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":17,"operation_count":2,"complexity_ratio":8.5,"tree":{"type":"unary","operator":"⊵↤","unary_expr":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":4164,"base":4}}},"used_operators":["7IPrd9c3lf","xUOZtlo3hN"],"dependent_operators":["eLAdDNolq6","W4YGzv6Whe","9FxExcQeMw","Qy55tPpLXF","BjRHVeLaeN","tifHPKVTfV","2DDjHMKMc0","f6k1SAg4EE","Z2TMIBDE3Q","eewbuw0ToL","QMFrweE19q","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯12022131","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4164","layer":2},{"info":"compute unary expreesion, input=4164, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-4338","layer":1},{"info":"compute unary expreesion, input=-4338, op_id = 7IPrd9c3lf, unary_op_definition = 'a⊵↤ = { (((a⪒a)+a)⇼⇔∾((a⫡⨏a)⩤)) , if (a!=425 and (≤/a)>523) ; (((a⫩⊇)⨰(a⋥≓≎a))⋥≓≎((a⩷∴a)⋝⋈⪟(a⩷∴a))) , else }', output=25245","layer":0}],"base":4,"result_base":4,"text":"(⨞⊢⪩⨒∯1001010)⊵↤=⪩⨒∯12022131","reverse_text":"⪩⨒∯12022131=(⨞⊢⪩⨒∯1001010)⊵↤","cot":[{"info":"⨞⊢⪩⨒∯1001010=⪩⨒∯-1003302","layer":1},{"info":"⪩⨒∯-1003302⊵↤=⪩⨒∯12022131","layer":0}]}
{"id":653,"expression_no_base_symbol":"($1643$⪉⨛$1141$)≨($1287$⇴$4841$)","expression":"(⪩⨒∯121223⪉⨛⪩⨒∯101311)≨(⪩⨒∯110013⇴⪩⨒∯1023221)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":107,"operation_count":3,"complexity_ratio":35.666666666666664,"tree":{"type":"binary","operator":"≨","left_expr":{"type":"binary","operator":"⪉⨛","left_expr":{"type":"numeric_atoms","value":1643,"base":4},"right_expr":{"type":"numeric_atoms","value":1141,"base":4}},"right_expr":{"type":"binary","operator":"⇴","left_expr":{"type":"numeric_atoms","value":1287,"base":4},"right_expr":{"type":"numeric_atoms","value":4841,"base":4}}},"used_operators":["0KMCeP1Jsh","EWw2JM7wp4","4JB6nKBMSY"],"dependent_operators":["jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC","NTOWxs364D","tifHPKVTfV","12rbrZMWeM","i8ToyICDmI","eewbuw0ToL","sdazOOVcIp","NTOWxs364D","COABgblf1C"],"result":"⪩⨒∯-21022302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1643","layer":2},{"info":"number node, value=1141","layer":2},{"info":"compute binary expreesion, left_input=1643, right_input=1141, op_id = EWw2JM7wp4 binary_op_definition= 'a⪉⨛b = { (((82⇼⇔∾a)⩚⊴⇥a)⩚⊴⇥((b∲⫓a)⋳⪒(a⨰b))) }', output=4003","layer":1},{"info":"number node, value=1287","layer":2},{"info":"number node, value=4841","layer":2},{"info":"compute binary expreesion, left_input=1287, right_input=4841, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=17018","layer":1},{"info":"compute binary expreesion, left_input=4003, right_input=17018, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-37554","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯121223⪉⨛⪩⨒∯101311)≨(⪩⨒∯110013⇴⪩⨒∯1023221)=⪩⨒∯-21022302","reverse_text":"⪩⨒∯-21022302=(⪩⨒∯121223⪉⨛⪩⨒∯101311)≨(⪩⨒∯110013⇴⪩⨒∯1023221)","cot":[{"info":"⪩⨒∯121223⪉⨛⪩⨒∯101311=⪩⨒∯332203","layer":1},{"info":"⪩⨒∯110013⇴⪩⨒∯1023221=⪩⨒∯10021322","layer":1},{"info":"⪩⨒∯332203≨⪩⨒∯10021322=⪩⨒∯-21022302","layer":0}]}
{"id":654,"expression_no_base_symbol":"$3655$∓⋝$4238$≃$3853$⊢$8696$","expression":"⪩⨒∯321013∓⋝⪩⨒∯1002032≃⪩⨒∯330031⊢⪩⨒∯2013320","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":79,"operation_count":3,"complexity_ratio":26.333333333333332,"tree":{"type":"binary","operator":"≃","left_expr":{"type":"binary","operator":"∓⋝","left_expr":{"type":"numeric_atoms","value":3655,"base":4},"right_expr":{"type":"numeric_atoms","value":4238,"base":4}},"right_expr":{"type":"binary","operator":"⊢","left_expr":{"type":"numeric_atoms","value":3853,"base":4},"right_expr":{"type":"numeric_atoms","value":8696,"base":4}}},"used_operators":["YbVcJGFEVW","PoHhknlbAi","5twsqlHp2o"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","23Mk6UjR3U","JLbD19bQDL","7j4O788W3g","glklzrTFfD","tifHPKVTfV","t8gj7n24qd","i8ToyICDmI","COABgblf1C","DZ8iAZOCBD","DbCuESL50I","mqXw5SEYmG","2MzE1hQ0cz","P8v4zCKN1o","Qy55tPpLXF","BjRHVeLaeN","DZ8iAZOCBD","7j4O788W3g","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","14qkJME0vr","D4vGDi5EA2","2td37pGCOC"],"result":"⪩⨒∯13300100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3655","layer":2},{"info":"number node, value=4238","layer":2},{"info":"compute binary expreesion, left_input=3655, right_input=4238, op_id = PoHhknlbAi binary_op_definition= 'a∓⋝b = { (((a⊉≛↸a)⫸⊐(⋼∭⪍b))∩⋅) }', output=67","layer":1},{"info":"number node, value=3853","layer":2},{"info":"number node, value=8696","layer":2},{"info":"compute binary expreesion, left_input=3853, right_input=8696, op_id = 5twsqlHp2o binary_op_definition= 'a⊢b = { (((225⫩⊇)⊉≛↸(∥⊫a))⨵⪆(25⊉≛↸(b⋥≓≎47))) , if (a≦≮≮)==364 ; (((b⊦⊿)⪨≂(⩦⩻⨪b))↺((⨞⊢a)⪨≂(-1))) , else }', output=-7950","layer":1},{"info":"compute binary expreesion, left_input=67, right_input=-7950, op_id = YbVcJGFEVW binary_op_definition= 'a≃b = { (((13⋥≓≎b)⋷(a⇼⇔∾b))⨁⊸⫻) , if ((b⨁⊸⫻)>=162 or (b⪠⩆⊳)<=569) ; ((-(17⋷a))↺((a⩷∴a)⊭↱(b∲⫓a))) , else }', output=31760","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯321013∓⋝⪩⨒∯1002032≃⪩⨒∯330031⊢⪩⨒∯2013320=⪩⨒∯13300100","reverse_text":"⪩⨒∯13300100=⪩⨒∯321013∓⋝⪩⨒∯1002032≃⪩⨒∯330031⊢⪩⨒∯2013320","cot":[{"info":"⪩⨒∯321013∓⋝⪩⨒∯1002032=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯330031⊢⪩⨒∯2013320=⪩⨒∯-1330032","layer":1},{"info":"⪩⨒∯1003≃⪩⨒∯-1330032=⪩⨒∯13300100","layer":0}]}
{"id":655,"expression_no_base_symbol":"(⇨$3620$)⊋$3107$≚⊃≕$1217$","expression":"(⇨⪩⨒∯320210)⊋⪩⨒∯300203≚⊃≕⪩⨒∯103001","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":97,"operation_count":3,"complexity_ratio":32.333333333333336,"tree":{"type":"binary","operator":"⊋","left_expr":{"type":"unary","operator":"⇨","unary_expr":{"type":"numeric_atoms","value":3620,"base":4}},"right_expr":{"type":"binary","operator":"≚⊃≕","left_expr":{"type":"numeric_atoms","value":3107,"base":4},"right_expr":{"type":"numeric_atoms","value":1217,"base":4}}},"used_operators":["W4tP9CfskL","G9tJMlZ94a","Bmrmz2XGnR"],"dependent_operators":["2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu","k8jYdgA6NY","9FxExcQeMw","Qy55tPpLXF","7j4O788W3g","sdazOOVcIp","8w2t5hMYqp","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q"],"result":"⪩⨒∯-1000102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3620","layer":2},{"info":"compute unary expreesion, input=3620, op_id = G9tJMlZ94a, unary_op_definition = '⇨a = { (a%a) }', output=0","layer":1},{"info":"number node, value=3107","layer":2},{"info":"number node, value=1217","layer":2},{"info":"compute binary expreesion, left_input=3107, right_input=1217, op_id = Bmrmz2XGnR binary_op_definition= 'a≚⊃≕b = { (-((⊄⩳↩b)⪨≂(a⩷∴b))) , if ((b⫡⨏524)<690 or (⨞⊢a)>=395) ; ((⊄⩳↩(b⋥≓≎a))⋥≓≎((a↺a)⪨≂(479⨸⪁a))) , else }', output=67","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=67, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=-4114","layer":0}],"base":4,"result_base":4,"text":"(⇨⪩⨒∯320210)⊋⪩⨒∯300203≚⊃≕⪩⨒∯103001=⪩⨒∯-1000102","reverse_text":"⪩⨒∯-1000102=(⇨⪩⨒∯320210)⊋⪩⨒∯300203≚⊃≕⪩⨒∯103001","cot":[{"info":"⇨⪩⨒∯320210=⪩⨒∯0","layer":1},{"info":"⪩⨒∯300203≚⊃≕⪩⨒∯103001=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯0⊋⪩⨒∯1003=⪩⨒∯-1000102","layer":0}]}
{"id":656,"expression_no_base_symbol":"$6589$⩼⇪↪$1168$∷($2001$⊟⇱)","expression":"⪩⨒∯1212331⩼⇪↪⪩⨒∯102100∷(⪩⨒∯133101⊟⇱)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":23,"operation_count":3,"complexity_ratio":7.666666666666667,"tree":{"type":"binary","operator":"∷","left_expr":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"numeric_atoms","value":6589,"base":4},"right_expr":{"type":"numeric_atoms","value":1168,"base":4}},"right_expr":{"type":"unary","operator":"⊟⇱","unary_expr":{"type":"numeric_atoms","value":2001,"base":4}}},"used_operators":["D3AQDKkPcf","ocnLzx9CaJ","03sUfWo75k"],"dependent_operators":["9FxExcQeMw","NTOWxs364D","7j4O788W3g","9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q","IWmyXbctLI"],"result":"⪩⨒∯1003132","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6589","layer":2},{"info":"number node, value=1168","layer":2},{"info":"compute binary expreesion, left_input=6589, right_input=1168, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=4219","layer":1},{"info":"number node, value=2001","layer":2},{"info":"compute unary expreesion, input=2001, op_id = 03sUfWo75k, unary_op_definition = 'a⊟⇱ = { (a⪮%⊝a) }', output=4318","layer":1},{"info":"compute binary expreesion, left_input=4219, right_input=4318, op_id = D3AQDKkPcf binary_op_definition= 'a∷b = { (a⩚⊴⇥673) , if (b⩷∴24)<=112 ; (a↺b) , else }', output=4318","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1212331⩼⇪↪⪩⨒∯102100∷(⪩⨒∯133101⊟⇱)=⪩⨒∯1003132","reverse_text":"⪩⨒∯1003132=⪩⨒∯1212331⩼⇪↪⪩⨒∯102100∷(⪩⨒∯133101⊟⇱)","cot":[{"info":"⪩⨒∯1212331⩼⇪↪⪩⨒∯102100=⪩⨒∯1001323","layer":1},{"info":"⪩⨒∯133101⊟⇱=⪩⨒∯1003132","layer":1},{"info":"⪩⨒∯1001323∷⪩⨒∯1003132=⪩⨒∯1003132","layer":0}]}
{"id":657,"expression_no_base_symbol":"(⩪∧⨌$1294$)⨜⨶($6693$⪛⫼$2768$)","expression":"(⩪∧⨌⪩⨒∯110032)⨜⨶(⪩⨒∯1220211⪛⫼⪩⨒∯223100)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":244,"operation_count":3,"complexity_ratio":81.33333333333333,"tree":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"unary","operator":"⩪∧⨌","unary_expr":{"type":"numeric_atoms","value":1294,"base":4}},"right_expr":{"type":"binary","operator":"⪛⫼","left_expr":{"type":"numeric_atoms","value":6693,"base":4},"right_expr":{"type":"numeric_atoms","value":2768,"base":4}}},"used_operators":["HiPekx5b7W","6iOiAJX1F8","hyuBjUqXlG"],"dependent_operators":["N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","P8v4zCKN1o","23Mk6UjR3U","7j4O788W3g","f6k1SAg4EE","g55IO6H4Gj","HJ9erzHUuu","9ICcGScMcE","DO4fhlbJSI","BX1lVwlMe0","Noe24qw2ks","uFcxV4UQCh","A8NUZmVepG","vg4gO5BX6G","dfKe02y8D2","hrf7POJlIJ","mqXw5SEYmG","QMFrweE19q","wztAlM01eG"],"result":"⪩⨒∯-122100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1294","layer":2},{"info":"compute unary expreesion, input=1294, op_id = 6iOiAJX1F8, unary_op_definition = '⩪∧⨌a = { (∥⊫a) , if ((a⋷517)==285 and (a⪒780)<=108) ; ((a↺a)⨸⪁(a⨸⪁a)) , else }', output=12940","layer":1},{"info":"number node, value=6693","layer":2},{"info":"number node, value=2768","layer":2},{"info":"compute binary expreesion, left_input=6693, right_input=2768, op_id = hyuBjUqXlG binary_op_definition= 'a⪛⫼b = { (((↸⊣b)⫡⨏(⊿b))⫸⊐(≦∁(↥a))) , if (a⇟⨁⪰)!=192 ; (((b⊨a)⪛b)⨐((37⪔⊥b)∴(11⫚↹⊑395))) , else }', output=968","layer":1},{"info":"compute binary expreesion, left_input=12940, right_input=968, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-1680","layer":0}],"base":4,"result_base":4,"text":"(⩪∧⨌⪩⨒∯110032)⨜⨶(⪩⨒∯1220211⪛⫼⪩⨒∯223100)=⪩⨒∯-122100","reverse_text":"⪩⨒∯-122100=(⩪∧⨌⪩⨒∯110032)⨜⨶(⪩⨒∯1220211⪛⫼⪩⨒∯223100)","cot":[{"info":"⩪∧⨌⪩⨒∯110032=⪩⨒∯3022030","layer":1},{"info":"⪩⨒∯1220211⪛⫼⪩⨒∯223100=⪩⨒∯33020","layer":1},{"info":"⪩⨒∯3022030⨜⨶⪩⨒∯33020=⪩⨒∯-122100","layer":0}]}
{"id":658,"expression_no_base_symbol":"(⨭⩧⫛$1365$)∛$4413$⫞⩸⩒$3669$","expression":"(⨭⩧⫛⪩⨒∯111111)∛⪩⨒∯1010331⫞⩸⩒⪩⨒∯321111","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":152,"operation_count":3,"complexity_ratio":50.666666666666664,"tree":{"type":"binary","operator":"∛","left_expr":{"type":"unary","operator":"⨭⩧⫛","unary_expr":{"type":"numeric_atoms","value":1365,"base":4}},"right_expr":{"type":"binary","operator":"⫞⩸⩒","left_expr":{"type":"numeric_atoms","value":4413,"base":4},"right_expr":{"type":"numeric_atoms","value":3669,"base":4}}},"used_operators":["w2537kitQq","g21JL6JxX7","XGcMNugi78"],"dependent_operators":["DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc","Ikt5ks8PT7","Asc51vEJeQ","A8NUZmVepG","VJ330n2nnx","JclMnS0uGI","SWo3A1KBJH","rJVOvQCfKK"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1365","layer":2},{"info":"compute unary expreesion, input=1365, op_id = g21JL6JxX7, unary_op_definition = '⨭⩧⫛a = { ((↥a)⩧⪆(↣≠⋷a)) }', output=nan","layer":1},{"info":"number node, value=4413","layer":2},{"info":"number node, value=3669","layer":2},{"info":"compute binary expreesion, left_input=4413, right_input=3669, op_id = XGcMNugi78 binary_op_definition= 'a⫞⩸⩒b = { (a⨎b) , if ((⇋↷b)>164 and (a↬⩅∪)<=12 and (b⨔⇊430)!=387) ; a , else }', output=3669","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=3669, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⨭⩧⫛⪩⨒∯111111)∛⪩⨒∯1010331⫞⩸⩒⪩⨒∯321111=NaN","reverse_text":"NaN=(⨭⩧⫛⪩⨒∯111111)∛⪩⨒∯1010331⫞⩸⩒⪩⨒∯321111","cot":[{"info":"⨭⩧⫛⪩⨒∯111111=NaN","layer":1},{"info":"⪩⨒∯1010331⫞⩸⩒⪩⨒∯321111=⪩⨒∯321111","layer":1},{"info":"NaN∛⪩⨒∯321111=NaN","layer":0}]}
{"id":659,"expression_no_base_symbol":"($3011$⨽$3309$)⊀⩕","expression":"(⪩⨒∯233003⨽⪩⨒∯303231)⊀⩕","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4279,"operation_count":2,"complexity_ratio":2139.5,"tree":{"type":"unary","operator":"⊀⩕","unary_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":3011,"base":4},"right_expr":{"type":"numeric_atoms","value":3309,"base":4}}},"used_operators":["r0FS3hW4cC","8HhzD0ZcuI"],"dependent_operators":["rGHVDoGpnC","nhYeJWJD5X","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3011","layer":2},{"info":"number node, value=3309","layer":2},{"info":"compute binary expreesion, left_input=3011, right_input=3309, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-27206976","layer":1},{"info":"compute unary expreesion, input=-27206976, op_id = r0FS3hW4cC, unary_op_definition = 'a⊀⩕ = { (a⨟⋌⩍(181∇⊂⋱a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯233003⨽⪩⨒∯303231)⊀⩕=NaN","reverse_text":"NaN=(⪩⨒∯233003⨽⪩⨒∯303231)⊀⩕","cot":[{"info":"⪩⨒∯233003⨽⪩⨒∯303231=⪩⨒∯-1213302111000","layer":1},{"info":"⪩⨒∯-1213302111000⊀⩕=NaN","layer":0}]}
{"id":660,"expression_no_base_symbol":"(⇤←$1572$)⇂≾⫗($1110$⨳⩥⨓$6739$)","expression":"(⇤←⪩⨒∯120210)⇂≾⫗(⪩⨒∯101112⨳⩥⨓⪩⨒∯1221103)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":113,"operation_count":3,"complexity_ratio":37.666666666666664,"tree":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"unary","operator":"⇤←","unary_expr":{"type":"numeric_atoms","value":1572,"base":4}},"right_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":1110,"base":4},"right_expr":{"type":"numeric_atoms","value":6739,"base":4}}},"used_operators":["aBQ6xLxuTc","jfAgQ2OQeM","nCS4ZIUYfx"],"dependent_operators":["g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U","NTOWxs364D","FyVja0WsTP","zVYPLywUTj","nCS4ZIUYfx","W4YGzv6Whe","rysDP5nf3Z"],"result":"⪩⨒∯-21310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1572","layer":2},{"info":"compute unary expreesion, input=1572, op_id = jfAgQ2OQeM, unary_op_definition = '⇤←a = { (a⨳⩥⨓((a⩚⊴⇥238)⊱⇼⊻(a⊪))) }', output=-6494","layer":1},{"info":"number node, value=1110","layer":2},{"info":"number node, value=6739","layer":2},{"info":"compute binary expreesion, left_input=1110, right_input=6739, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=5629","layer":1},{"info":"compute binary expreesion, left_input=-6494, right_input=5629, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-628","layer":0}],"base":4,"result_base":4,"text":"(⇤←⪩⨒∯120210)⇂≾⫗(⪩⨒∯101112⨳⩥⨓⪩⨒∯1221103)=⪩⨒∯-21310","reverse_text":"⪩⨒∯-21310=(⇤←⪩⨒∯120210)⇂≾⫗(⪩⨒∯101112⨳⩥⨓⪩⨒∯1221103)","cot":[{"info":"⇤←⪩⨒∯120210=⪩⨒∯-1211132","layer":1},{"info":"⪩⨒∯101112⨳⩥⨓⪩⨒∯1221103=⪩⨒∯1113331","layer":1},{"info":"⪩⨒∯-1211132⇂≾⫗⪩⨒∯1113331=⪩⨒∯-21310","layer":0}]}
{"id":661,"expression_no_base_symbol":"$2381$→⨶⪴$2493$⇼⇔∾($4837$⫔⩽⩺$6535$)","expression":"⪩⨒∯211031→⨶⪴⪩⨒∯212331⇼⇔∾(⪩⨒∯1023211⫔⩽⩺⪩⨒∯1212013)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":35,"operation_count":3,"complexity_ratio":11.666666666666666,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"binary","operator":"→⨶⪴","left_expr":{"type":"numeric_atoms","value":2381,"base":4},"right_expr":{"type":"numeric_atoms","value":2493,"base":4}},"right_expr":{"type":"binary","operator":"⫔⩽⩺","left_expr":{"type":"numeric_atoms","value":4837,"base":4},"right_expr":{"type":"numeric_atoms","value":6535,"base":4}}},"used_operators":["tifHPKVTfV","bF6eod5Gvf","i9eR4S00cU"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","8w2t5hMYqp","9FxExcQeMw","Tw270M8GLb","fu6greOZ01"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2381","layer":2},{"info":"number node, value=2493","layer":2},{"info":"compute binary expreesion, left_input=2381, right_input=2493, op_id = bF6eod5Gvf binary_op_definition= 'a→⨶⪴b = { (a⩷∴b) , if b<109 ; (⊄⩳↩b) , else }', output=-7479","layer":1},{"info":"number node, value=4837","layer":2},{"info":"number node, value=6535","layer":2},{"info":"compute binary expreesion, left_input=4837, right_input=6535, op_id = i9eR4S00cU binary_op_definition= 'a⫔⩽⩺b = { (⨰⫟⨤(a⨐⩸⫘b)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-7479, right_input=nan, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯211031→⨶⪴⪩⨒∯212331⇼⇔∾(⪩⨒∯1023211⫔⩽⩺⪩⨒∯1212013)=NaN","reverse_text":"NaN=⪩⨒∯211031→⨶⪴⪩⨒∯212331⇼⇔∾(⪩⨒∯1023211⫔⩽⩺⪩⨒∯1212013)","cot":[{"info":"⪩⨒∯211031→⨶⪴⪩⨒∯212331=⪩⨒∯-1310313","layer":1},{"info":"⪩⨒∯1023211⫔⩽⩺⪩⨒∯1212013=NaN","layer":1},{"info":"⪩⨒∯-1310313⇼⇔∾NaN=NaN","layer":0}]}
{"id":662,"expression_no_base_symbol":"$1404$≁$2823$∕⩚$2184$⨰$2900$","expression":"⪩⨒∯111330≁⪩⨒∯230013∕⩚⪩⨒∯202020⨰⪩⨒∯231110","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":92,"operation_count":3,"complexity_ratio":30.666666666666668,"tree":{"type":"binary","operator":"∕⩚","left_expr":{"type":"binary","operator":"≁","left_expr":{"type":"numeric_atoms","value":1404,"base":4},"right_expr":{"type":"numeric_atoms","value":2823,"base":4}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":2184,"base":4},"right_expr":{"type":"numeric_atoms","value":2900,"base":4}}},"used_operators":["z9ffQ9n5Zr","8N2wDY1A35","eewbuw0ToL"],"dependent_operators":["3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr","B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-13213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1404","layer":2},{"info":"number node, value=2823","layer":2},{"info":"compute binary expreesion, left_input=1404, right_input=2823, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=54551","layer":1},{"info":"number node, value=2184","layer":2},{"info":"number node, value=2900","layer":2},{"info":"compute binary expreesion, left_input=2184, right_input=2900, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-706","layer":1},{"info":"compute binary expreesion, left_input=54551, right_input=-706, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-487","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯111330≁⪩⨒∯230013∕⩚⪩⨒∯202020⨰⪩⨒∯231110=⪩⨒∯-13213","reverse_text":"⪩⨒∯-13213=⪩⨒∯111330≁⪩⨒∯230013∕⩚⪩⨒∯202020⨰⪩⨒∯231110","cot":[{"info":"⪩⨒∯111330≁⪩⨒∯230013=⪩⨒∯31110113","layer":1},{"info":"⪩⨒∯202020⨰⪩⨒∯231110=⪩⨒∯-23002","layer":1},{"info":"⪩⨒∯31110113∕⩚⪩⨒∯-23002=⪩⨒∯-13213","layer":0}]}
{"id":663,"expression_no_base_symbol":"($1608$-$2129$)⩣⫁∢($4201$-$1220$)","expression":"(⪩⨒∯121020-⪩⨒∯201101)⩣⫁∢(⪩⨒∯1001221-⪩⨒∯103010)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":23,"operation_count":3,"complexity_ratio":7.666666666666667,"tree":{"type":"binary","operator":"⩣⫁∢","left_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1608,"base":4},"right_expr":{"type":"numeric_atoms","value":2129,"base":4}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":4201,"base":4},"right_expr":{"type":"numeric_atoms","value":1220,"base":4}}},"used_operators":["JDUIKTTSIa","rysDP5nf3Z"],"dependent_operators":["sdazOOVcIp","eewbuw0ToL","AF7qkfDlqP","u6S6b8DprG"],"result":"⪩⨒∯221121","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1608","layer":2},{"info":"number node, value=2129","layer":2},{"info":"compute binary expreesion, left_input=1608, right_input=2129, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-521","layer":1},{"info":"number node, value=4201","layer":2},{"info":"number node, value=1220","layer":2},{"info":"compute binary expreesion, left_input=4201, right_input=1220, op_id = rysDP5nf3Z binary_op_definition= 'None', output=2981","layer":1},{"info":"compute binary expreesion, left_input=-521, right_input=2981, op_id = JDUIKTTSIa binary_op_definition= 'a⩣⫁∢b = { (⨑⩽⪐((a⪨≂b)⨰(↽≂b))) }', output=2649","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯121020-⪩⨒∯201101)⩣⫁∢(⪩⨒∯1001221-⪩⨒∯103010)=⪩⨒∯221121","reverse_text":"⪩⨒∯221121=(⪩⨒∯121020-⪩⨒∯201101)⩣⫁∢(⪩⨒∯1001221-⪩⨒∯103010)","cot":[{"info":"⪩⨒∯121020-⪩⨒∯201101=⪩⨒∯-20021","layer":1},{"info":"⪩⨒∯1001221-⪩⨒∯103010=⪩⨒∯232211","layer":1},{"info":"⪩⨒∯-20021⩣⫁∢⪩⨒∯232211=⪩⨒∯221121","layer":0}]}
{"id":664,"expression_no_base_symbol":"$3827$⩁⩘$1954$↼⊘⨖($5971$⫳≱↱$2479$)","expression":"⪩⨒∯323303⩁⩘⪩⨒∯132202↼⊘⨖(⪩⨒∯1131103⫳≱↱⪩⨒∯212233)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":336,"operation_count":3,"complexity_ratio":112.0,"tree":{"type":"binary","operator":"↼⊘⨖","left_expr":{"type":"binary","operator":"⩁⩘","left_expr":{"type":"numeric_atoms","value":3827,"base":4},"right_expr":{"type":"numeric_atoms","value":1954,"base":4}},"right_expr":{"type":"binary","operator":"⫳≱↱","left_expr":{"type":"numeric_atoms","value":5971,"base":4},"right_expr":{"type":"numeric_atoms","value":2479,"base":4}}},"used_operators":["bPywburJMS","gub5Cegaqo","ZvLB05nZmT"],"dependent_operators":["9FxExcQeMw","P8v4zCKN1o","t8gj7n24qd","DpFCA1CohY","IWmyXbctLI","2Wsdkap16l","FyVja0WsTP","wEfv7U73WA","bJkvcejdHO","HmxsFra2vL","8cLx32lpNA"],"result":"⪩⨒∯-21312","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3827","layer":2},{"info":"number node, value=1954","layer":2},{"info":"compute binary expreesion, left_input=3827, right_input=1954, op_id = gub5Cegaqo binary_op_definition= 'a⩁⩘b = { ((b⪮%⊝b)⪮%⊝(⋗⩬⋾a)) }', output=8764","layer":1},{"info":"number node, value=5971","layer":2},{"info":"number node, value=2479","layer":2},{"info":"compute binary expreesion, left_input=5971, right_input=2479, op_id = ZvLB05nZmT binary_op_definition= 'a⫳≱↱b = { (((a⩹b)⇐≅)∌((a∙∹∝345)⊱⇼⊻(b≎⊠⪸a))) }', output=-204","layer":1},{"info":"compute binary expreesion, left_input=8764, right_input=-204, op_id = bPywburJMS binary_op_definition= 'a↼⊘⨖b = { (-a) , if (∥⊫b)==149 ; (b⩷∴95) , else }', output=-630","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯323303⩁⩘⪩⨒∯132202↼⊘⨖(⪩⨒∯1131103⫳≱↱⪩⨒∯212233)=⪩⨒∯-21312","reverse_text":"⪩⨒∯-21312=⪩⨒∯323303⩁⩘⪩⨒∯132202↼⊘⨖(⪩⨒∯1131103⫳≱↱⪩⨒∯212233)","cot":[{"info":"⪩⨒∯323303⩁⩘⪩⨒∯132202=⪩⨒∯2020330","layer":1},{"info":"⪩⨒∯1131103⫳≱↱⪩⨒∯212233=⪩⨒∯-3030","layer":1},{"info":"⪩⨒∯2020330↼⊘⨖⪩⨒∯-3030=⪩⨒∯-21312","layer":0}]}
{"id":665,"expression_no_base_symbol":"$5933$↢$2039$≓∲($1374$↸$5229$)","expression":"⪩⨒∯1130231↢⪩⨒∯133313≓∲(⪩⨒∯111132↸⪩⨒∯1101231)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1439,"operation_count":3,"complexity_ratio":479.6666666666667,"tree":{"type":"binary","operator":"≓∲","left_expr":{"type":"binary","operator":"↢","left_expr":{"type":"numeric_atoms","value":5933,"base":4},"right_expr":{"type":"numeric_atoms","value":2039,"base":4}},"right_expr":{"type":"binary","operator":"↸","left_expr":{"type":"numeric_atoms","value":1374,"base":4},"right_expr":{"type":"numeric_atoms","value":5229,"base":4}}},"used_operators":["s1XTVnmDOJ","WR6HLWljOP","1eCjFl0mb9"],"dependent_operators":["HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu","eLAdDNolq6","g55IO6H4Gj","7j4O788W3g","12rbrZMWeM","f6k1SAg4EE","i8ToyICDmI","COABgblf1C","9HNa5Wba9A","61wBmkZwlr","rJVOvQCfKK"],"result":"⪩⨒∯31133221","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5933","layer":2},{"info":"number node, value=2039","layer":2},{"info":"compute binary expreesion, left_input=5933, right_input=2039, op_id = WR6HLWljOP binary_op_definition= 'a↢b = { ((a∲⫓a)⪒(≤/a)) , if (a⊭↱114)<=535 ; ((a⋳⪒749)↺(b⨸⪁a)) , else }', output=5449","layer":1},{"info":"number node, value=1374","layer":2},{"info":"number node, value=5229","layer":2},{"info":"compute binary expreesion, left_input=1374, right_input=5229, op_id = 1eCjFl0mb9 binary_op_definition= 'a↸b = { ((b*a)⨎(≋a)) }', output=1374","layer":1},{"info":"compute binary expreesion, left_input=5449, right_input=1374, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=55273","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1130231↢⪩⨒∯133313≓∲(⪩⨒∯111132↸⪩⨒∯1101231)=⪩⨒∯31133221","reverse_text":"⪩⨒∯31133221=⪩⨒∯1130231↢⪩⨒∯133313≓∲(⪩⨒∯111132↸⪩⨒∯1101231)","cot":[{"info":"⪩⨒∯1130231↢⪩⨒∯133313=⪩⨒∯1111021","layer":1},{"info":"⪩⨒∯111132↸⪩⨒∯1101231=⪩⨒∯111132","layer":1},{"info":"⪩⨒∯1111021≓∲⪩⨒∯111132=⪩⨒∯31133221","layer":0}]}
{"id":666,"expression_no_base_symbol":"(⨝⨆$1865$)⊉≛↸$1198$⊕∕$2639$","expression":"(⨝⨆⪩⨒∯131021)⊉≛↸⪩⨒∯102232⊕∕⪩⨒∯221033","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5,"operation_count":3,"complexity_ratio":1.6666666666666667,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"unary","operator":"⨝⨆","unary_expr":{"type":"numeric_atoms","value":1865,"base":4}},"right_expr":{"type":"binary","operator":"⊕∕","left_expr":{"type":"numeric_atoms","value":1198,"base":4},"right_expr":{"type":"numeric_atoms","value":2639,"base":4}}},"used_operators":["DZ8iAZOCBD","bQ67fsrMVf","9cloC0Ngie"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","tifHPKVTfV","Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf"],"result":"⪩⨒∯303300","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1865","layer":2},{"info":"compute unary expreesion, input=1865, op_id = bQ67fsrMVf, unary_op_definition = '⨝⨆a = { (209⇼⇔∾a) }', output=1656","layer":1},{"info":"number node, value=1198","layer":2},{"info":"number node, value=2639","layer":2},{"info":"compute binary expreesion, left_input=1198, right_input=2639, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=1198","layer":1},{"info":"compute binary expreesion, left_input=1656, right_input=1198, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=3312","layer":0}],"base":4,"result_base":4,"text":"(⨝⨆⪩⨒∯131021)⊉≛↸⪩⨒∯102232⊕∕⪩⨒∯221033=⪩⨒∯303300","reverse_text":"⪩⨒∯303300=(⨝⨆⪩⨒∯131021)⊉≛↸⪩⨒∯102232⊕∕⪩⨒∯221033","cot":[{"info":"⨝⨆⪩⨒∯131021=⪩⨒∯121320","layer":1},{"info":"⪩⨒∯102232⊕∕⪩⨒∯221033=⪩⨒∯102232","layer":1},{"info":"⪩⨒∯121320⊉≛↸⪩⨒∯102232=⪩⨒∯303300","layer":0}]}
{"id":667,"expression_no_base_symbol":"($1223$≬⋮$1818$)∌$2246$↳∿⪆$1968$","expression":"(⪩⨒∯103013≬⋮⪩⨒∯130122)∌⪩⨒∯203012↳∿⪆⪩⨒∯132300","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2417,"operation_count":3,"complexity_ratio":805.6666666666666,"tree":{"type":"binary","operator":"∌","left_expr":{"type":"binary","operator":"≬⋮","left_expr":{"type":"numeric_atoms","value":1223,"base":4},"right_expr":{"type":"numeric_atoms","value":1818,"base":4}},"right_expr":{"type":"binary","operator":"↳∿⪆","left_expr":{"type":"numeric_atoms","value":2246,"base":4},"right_expr":{"type":"numeric_atoms","value":1968,"base":4}}},"used_operators":["8cLx32lpNA","kbkesczE7y","Cw4SuJJGHO"],"dependent_operators":["N41Kp7NANJ","7j4O788W3g","t8gj7n24qd","P8v4zCKN1o","rysDP5nf3Z","7j4O788W3g","XIabStNQrY","t8gj7n24qd","i8ToyICDmI","hyuBjUqXlG","bF6eod5Gvf","nEsXyWgiOK","ruOEQAzv1W","Tw270M8GLb","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1223","layer":2},{"info":"number node, value=1818","layer":2},{"info":"compute binary expreesion, left_input=1223, right_input=1818, op_id = kbkesczE7y binary_op_definition= 'a≬⋮b = { (((-a)∲⫓(b⇋≉))↺(∥⊫(b-b))) }', output=868","layer":1},{"info":"number node, value=2246","layer":2},{"info":"number node, value=1968","layer":2},{"info":"compute binary expreesion, left_input=2246, right_input=1968, op_id = Cw4SuJJGHO binary_op_definition= 'a↳∿⪆b = { ((⨰⫟⨤(↔15))⨻⩈⩔((b⪛⫼133)⫡⨏(b→⨶⪴a))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=868, right_input=nan, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯103013≬⋮⪩⨒∯130122)∌⪩⨒∯203012↳∿⪆⪩⨒∯132300=NaN","reverse_text":"NaN=(⪩⨒∯103013≬⋮⪩⨒∯130122)∌⪩⨒∯203012↳∿⪆⪩⨒∯132300","cot":[{"info":"⪩⨒∯103013≬⋮⪩⨒∯130122=⪩⨒∯31210","layer":1},{"info":"⪩⨒∯203012↳∿⪆⪩⨒∯132300=NaN","layer":1},{"info":"⪩⨒∯31210∌NaN=NaN","layer":0}]}
{"id":668,"expression_no_base_symbol":"(⨂⪏⇭$4395$)⫚⫇","expression":"(⨂⪏⇭⪩⨒∯1010223)⫚⫇","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":25,"operation_count":2,"complexity_ratio":12.5,"tree":{"type":"unary","operator":"⫚⫇","unary_expr":{"type":"unary","operator":"⨂⪏⇭","unary_expr":{"type":"numeric_atoms","value":4395,"base":4}}},"used_operators":["SdCjLnB6rR","AYdpE9sXAk"],"dependent_operators":["Ph9nP6C5qx","xUOZtlo3hN","g55IO6H4Gj","2td37pGCOC","eewbuw0ToL","NTOWxs364D","EBcxylXtPf"],"result":"⪩⨒∯11212200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4395","layer":2},{"info":"compute unary expreesion, input=4395, op_id = AYdpE9sXAk, unary_op_definition = '⨂⪏⇭a = { (a⨰((85⩚⊴⇥a)⫌⩹⨱)) }', output=12206","layer":1},{"info":"compute unary expreesion, input=12206, op_id = SdCjLnB6rR, unary_op_definition = 'a⫚⫇ = { ((⨞⊢87)⨸⪁((⩦⩻⨪a)≧⫂∧a)) }', output=22944","layer":0}],"base":4,"result_base":4,"text":"(⨂⪏⇭⪩⨒∯1010223)⫚⫇=⪩⨒∯11212200","reverse_text":"⪩⨒∯11212200=(⨂⪏⇭⪩⨒∯1010223)⫚⫇","cot":[{"info":"⨂⪏⇭⪩⨒∯1010223=⪩⨒∯2332232","layer":1},{"info":"⪩⨒∯2332232⫚⫇=⪩⨒∯11212200","layer":0}]}
{"id":669,"expression_no_base_symbol":"$7177$≴⪞⇿$2242$↙(↞≼$1278$)","expression":"⪩⨒∯1300021≴⪞⇿⪩⨒∯203002↙(↞≼⪩⨒∯103332)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16767,"operation_count":3,"complexity_ratio":5589.0,"tree":{"type":"binary","operator":"↙","left_expr":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"numeric_atoms","value":7177,"base":4},"right_expr":{"type":"numeric_atoms","value":2242,"base":4}},"right_expr":{"type":"unary","operator":"↞≼","unary_expr":{"type":"numeric_atoms","value":1278,"base":4}}},"used_operators":["yyfyN0ffXY","lvlrscuwVU","DE7zCoGJt9"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP","W4YGzv6Whe","D4vGDi5EA2","23Mk6UjR3U","BjRHVeLaeN","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","u6S6b8DprG"],"result":"⪩⨒∯-13023312","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7177","layer":2},{"info":"number node, value=2242","layer":2},{"info":"compute binary expreesion, left_input=7177, right_input=2242, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=95330666","layer":1},{"info":"number node, value=1278","layer":2},{"info":"compute unary expreesion, input=1278, op_id = DE7zCoGJt9, unary_op_definition = '↞≼a = { (↽≂(197⨰(a⨸⪁a))) , if (a⨸⪁373)!=224 ; (((591⋷a)≧⫂∧(a+a))⨸⪁((a⫩⊇)≦≮≮)) , else }', output=9810","layer":1},{"info":"compute binary expreesion, left_input=95330666, right_input=9810, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-29430","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1300021≴⪞⇿⪩⨒∯203002↙(↞≼⪩⨒∯103332)=⪩⨒∯-13023312","reverse_text":"⪩⨒∯-13023312=⪩⨒∯1300021≴⪞⇿⪩⨒∯203002↙(↞≼⪩⨒∯103332)","cot":[{"info":"⪩⨒∯1300021≴⪞⇿⪩⨒∯203002=⪩⨒∯11223222011222","layer":1},{"info":"↞≼⪩⨒∯103332=⪩⨒∯2121102","layer":1},{"info":"⪩⨒∯11223222011222↙⪩⨒∯2121102=⪩⨒∯-13023312","layer":0}]}
{"id":670,"expression_no_base_symbol":"($1023$⋛$2643$)⪪$9122$⫣⪄⊒$3755$","expression":"(⪩⨒∯33333⋛⪩⨒∯221103)⪪⪩⨒∯2032202⫣⪄⊒⪩⨒∯322223","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":647,"operation_count":3,"complexity_ratio":215.66666666666666,"tree":{"type":"binary","operator":"⪪","left_expr":{"type":"binary","operator":"⋛","left_expr":{"type":"numeric_atoms","value":1023,"base":4},"right_expr":{"type":"numeric_atoms","value":2643,"base":4}},"right_expr":{"type":"binary","operator":"⫣⪄⊒","left_expr":{"type":"numeric_atoms","value":9122,"base":4},"right_expr":{"type":"numeric_atoms","value":3755,"base":4}}},"used_operators":["xD69zh8xqp","YbUVn0Rbpy","RabNbG55vr"],"dependent_operators":["FU0Cs4j7VP","JclMnS0uGI","d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA","NTOWxs364D","DbCuESL50I","fOIeswaMU4","g7Hmc5v1ko","KPf6cnQVty","j9kHMeSvPp","k8jYdgA6NY","2DDjHMKMc0","8WDwsbhb0R","cTDWOvIxvz","IWmyXbctLI"],"result":"⪩⨒∯-1200332","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1023","layer":2},{"info":"number node, value=2643","layer":2},{"info":"compute binary expreesion, left_input=1023, right_input=2643, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-122985","layer":1},{"info":"number node, value=9122","layer":2},{"info":"number node, value=3755","layer":2},{"info":"compute binary expreesion, left_input=9122, right_input=3755, op_id = RabNbG55vr binary_op_definition= 'a⫣⪄⊒b = { ((a⪮%⊝(153⪭a))%(⋼∭⪍(b⩚⊴⇥34))) , if b>769 ; ((∂⩏⊆(b⩟))∺≝⩲((b∝a)⋝⋈⪟(a⩌⋺b))) , else }', output=-4798","layer":1},{"info":"compute binary expreesion, left_input=-122985, right_input=-4798, op_id = xD69zh8xqp binary_op_definition= 'a⪪b = { ((b⨔⇊a)↛⩡⫤) }', output=-6206","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯33333⋛⪩⨒∯221103)⪪⪩⨒∯2032202⫣⪄⊒⪩⨒∯322223=⪩⨒∯-1200332","reverse_text":"⪩⨒∯-1200332=(⪩⨒∯33333⋛⪩⨒∯221103)⪪⪩⨒∯2032202⫣⪄⊒⪩⨒∯322223","cot":[{"info":"⪩⨒∯33333⋛⪩⨒∯221103=⪩⨒∯-132001221","layer":1},{"info":"⪩⨒∯2032202⫣⪄⊒⪩⨒∯322223=⪩⨒∯-1022332","layer":1},{"info":"⪩⨒∯-132001221⪪⪩⨒∯-1022332=⪩⨒∯-1200332","layer":0}]}
{"id":671,"expression_no_base_symbol":"↓⇌($7686$⪡$1384$)","expression":"↓⇌(⪩⨒∯1320012⪡⪩⨒∯111220)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":15,"operation_count":2,"complexity_ratio":7.5,"tree":{"type":"unary","operator":"↓⇌","unary_expr":{"type":"binary","operator":"⪡","left_expr":{"type":"numeric_atoms","value":7686,"base":4},"right_expr":{"type":"numeric_atoms","value":1384,"base":4}}},"used_operators":["PxpmPgHHJV","oraRL2iQuh"],"dependent_operators":["23Mk6UjR3U","glklzrTFfD","Z2TMIBDE3Q","2Wsdkap16l","ljTHtUsqzn","k8jYdgA6NY","8WDwsbhb0R"],"result":"⪩⨒∯1223","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=7686","layer":2},{"info":"number node, value=1384","layer":2},{"info":"compute binary expreesion, left_input=7686, right_input=1384, op_id = oraRL2iQuh binary_op_definition= 'a⪡b = { (107%(a⩹b)) , if a>=49 ; (≀↧⇸(∂⩏⊆a)) , else }', output=107","layer":1},{"info":"compute unary expreesion, input=107, op_id = PxpmPgHHJV, unary_op_definition = '↓⇌a = { (a⋷507) , if a>=68 and (a⩤)>=87 ; (a⨁⊸⫻) , else }', output=107","layer":0}],"base":4,"result_base":4,"text":"↓⇌(⪩⨒∯1320012⪡⪩⨒∯111220)=⪩⨒∯1223","reverse_text":"⪩⨒∯1223=↓⇌(⪩⨒∯1320012⪡⪩⨒∯111220)","cot":[{"info":"⪩⨒∯1320012⪡⪩⨒∯111220=⪩⨒∯1223","layer":1},{"info":"↓⇌⪩⨒∯1223=⪩⨒∯1223","layer":0}]}
{"id":672,"expression_no_base_symbol":"($1072$⨭⪣$2684$)≳⇉$2991$⋕⪉⪜$1546$","expression":"(⪩⨒∯100300⨭⪣⪩⨒∯221330)≳⇉⪩⨒∯232233⋕⪉⪜⪩⨒∯120022","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":128867799,"operation_count":3,"complexity_ratio":42955933.0,"tree":{"type":"binary","operator":"≳⇉","left_expr":{"type":"binary","operator":"⨭⪣","left_expr":{"type":"numeric_atoms","value":1072,"base":4},"right_expr":{"type":"numeric_atoms","value":2684,"base":4}},"right_expr":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"numeric_atoms","value":2991,"base":4},"right_expr":{"type":"numeric_atoms","value":1546,"base":4}}},"used_operators":["V0kx6qeWkN","kn8WO9XteQ","z6LnFrNh4i"],"dependent_operators":["KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls","vRio1gEz1j","61wBmkZwlr","SWo3A1KBJH","8jW3W4yZS5","LkLIoiE525","Y7wcNGrDQJ","PPChnnnBFF","sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1072","layer":2},{"info":"number node, value=2684","layer":2},{"info":"compute binary expreesion, left_input=1072, right_input=2684, op_id = kn8WO9XteQ binary_op_definition= 'a⨭⪣b = { ((486⇩)⩵∡(a∣a)) , if (b⇯⋐)>445 or (≋b)>319 or b<=69 ; (↯⪼(⇋↷b)) , else }', output=-207","layer":1},{"info":"number node, value=2991","layer":2},{"info":"number node, value=1546","layer":2},{"info":"compute binary expreesion, left_input=2991, right_input=1546, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=2802","layer":1},{"info":"compute binary expreesion, left_input=-207, right_input=2802, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100300⨭⪣⪩⨒∯221330)≳⇉⪩⨒∯232233⋕⪉⪜⪩⨒∯120022=NaN","reverse_text":"NaN=(⪩⨒∯100300⨭⪣⪩⨒∯221330)≳⇉⪩⨒∯232233⋕⪉⪜⪩⨒∯120022","cot":[{"info":"⪩⨒∯100300⨭⪣⪩⨒∯221330=⪩⨒∯-3033","layer":1},{"info":"⪩⨒∯232233⋕⪉⪜⪩⨒∯120022=⪩⨒∯223302","layer":1},{"info":"⪩⨒∯-3033≳⇉⪩⨒∯223302=NaN","layer":0}]}
{"id":673,"expression_no_base_symbol":"(⊥$1130$)⇷$5839$⨔⇊$6764$","expression":"(⊥⪩⨒∯101222)⇷⪩⨒∯1123033⨔⇊⪩⨒∯1221230","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⇷","left_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":1130,"base":4}},"right_expr":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"numeric_atoms","value":5839,"base":4},"right_expr":{"type":"numeric_atoms","value":6764,"base":4}}},"used_operators":["mp7IySMOzn","Q3PJZHRvZv","JclMnS0uGI"],"dependent_operators":["DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","fu6greOZ01","9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI"],"result":"⪩⨒∯3103120","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1130","layer":2},{"info":"compute unary expreesion, input=1130, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"number node, value=5839","layer":2},{"info":"number node, value=6764","layer":2},{"info":"compute binary expreesion, left_input=5839, right_input=6764, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=6764","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=6764, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=13528","layer":0}],"base":4,"result_base":4,"text":"(⊥⪩⨒∯101222)⇷⪩⨒∯1123033⨔⇊⪩⨒∯1221230=⪩⨒∯3103120","reverse_text":"⪩⨒∯3103120=(⊥⪩⨒∯101222)⇷⪩⨒∯1123033⨔⇊⪩⨒∯1221230","cot":[{"info":"⊥⪩⨒∯101222=NaN","layer":1},{"info":"⪩⨒∯1123033⨔⇊⪩⨒∯1221230=⪩⨒∯1221230","layer":1},{"info":"NaN⇷⪩⨒∯1221230=⪩⨒∯3103120","layer":0}]}
{"id":674,"expression_no_base_symbol":"$1561$∌$6988$⇍⊗$2720$⫞⩸⩒$6513$","expression":"⪩⨒∯120121∌⪩⨒∯1231030⇍⊗⪩⨒∯222200⫞⩸⩒⪩⨒∯1211301","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":57,"operation_count":3,"complexity_ratio":19.0,"tree":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"binary","operator":"∌","left_expr":{"type":"numeric_atoms","value":1561,"base":4},"right_expr":{"type":"numeric_atoms","value":6988,"base":4}},"right_expr":{"type":"binary","operator":"⫞⩸⩒","left_expr":{"type":"numeric_atoms","value":2720,"base":4},"right_expr":{"type":"numeric_atoms","value":6513,"base":4}}},"used_operators":["5uvYHDjeKN","8cLx32lpNA","XGcMNugi78"],"dependent_operators":["Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o","N41Kp7NANJ","7j4O788W3g","t8gj7n24qd","VJ330n2nnx","JclMnS0uGI","SWo3A1KBJH","rJVOvQCfKK"],"result":"⪩⨒∯-3310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1561","layer":2},{"info":"number node, value=6988","layer":2},{"info":"compute binary expreesion, left_input=1561, right_input=6988, op_id = 8cLx32lpNA binary_op_definition= 'a∌b = { (248↺a) , if (a≋⫹)>=60 ; (-b) , else }', output=-6988","layer":1},{"info":"number node, value=2720","layer":2},{"info":"number node, value=6513","layer":2},{"info":"compute binary expreesion, left_input=2720, right_input=6513, op_id = XGcMNugi78 binary_op_definition= 'a⫞⩸⩒b = { (a⨎b) , if ((⇋↷b)>164 and (a↬⩅∪)<=12 and (b⨔⇊430)!=387) ; a , else }', output=6513","layer":1},{"info":"compute binary expreesion, left_input=-6988, right_input=6513, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=-244","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯120121∌⪩⨒∯1231030⇍⊗⪩⨒∯222200⫞⩸⩒⪩⨒∯1211301=⪩⨒∯-3310","reverse_text":"⪩⨒∯-3310=⪩⨒∯120121∌⪩⨒∯1231030⇍⊗⪩⨒∯222200⫞⩸⩒⪩⨒∯1211301","cot":[{"info":"⪩⨒∯120121∌⪩⨒∯1231030=⪩⨒∯-1231030","layer":1},{"info":"⪩⨒∯222200⫞⩸⩒⪩⨒∯1211301=⪩⨒∯1211301","layer":1},{"info":"⪩⨒∯-1231030⇍⊗⪩⨒∯1211301=⪩⨒∯-3310","layer":0}]}
{"id":675,"expression_no_base_symbol":"$2255$⪚$5808$⨔≚≋($1045$⨒$4123$)","expression":"⪩⨒∯203033⪚⪩⨒∯1122300⨔≚≋(⪩⨒∯100111⨒⪩⨒∯1000123)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":76,"operation_count":3,"complexity_ratio":25.333333333333332,"tree":{"type":"binary","operator":"⨔≚≋","left_expr":{"type":"binary","operator":"⪚","left_expr":{"type":"numeric_atoms","value":2255,"base":4},"right_expr":{"type":"numeric_atoms","value":5808,"base":4}},"right_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":1045,"base":4},"right_expr":{"type":"numeric_atoms","value":4123,"base":4}}},"used_operators":["Z57zeUYC9z","HrjLwUk87U","y75s1iXyHd"],"dependent_operators":["zR4jO40bMj","QvoQhV0rrE","RHru8klgy8","3tVxb0NHM4","f6k1SAg4EE","IWmyXbctLI","9FxExcQeMw","rysDP5nf3Z","NTOWxs364D","DZ8iAZOCBD","tifHPKVTfV","eH2TOUuTDT","2DDjHMKMc0","srAu1WTS94","oacrs7FA3X","7qqUquhhSb"],"result":"⪩⨒∯213333220","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2255","layer":2},{"info":"number node, value=5808","layer":2},{"info":"compute binary expreesion, left_input=2255, right_input=5808, op_id = HrjLwUk87U binary_op_definition= 'a⪚b = { (((317⩚⊴⇥a)⋝⋈⪟(518-95))⊉≛↸((97⪐)⩷∴(b⇼⇔∾a))) }', output=-7462","layer":1},{"info":"number node, value=1045","layer":2},{"info":"number node, value=4123","layer":2},{"info":"compute binary expreesion, left_input=1045, right_input=4123, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-5898","layer":1},{"info":"compute binary expreesion, left_input=-7462, right_input=-5898, op_id = Z57zeUYC9z binary_op_definition= 'a⨔≚≋b = { ((⊈(b⪎↠b))⪶≀⋏((29⪒b)∠⫱(a⪮%⊝521))) }', output=163816","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯203033⪚⪩⨒∯1122300⨔≚≋(⪩⨒∯100111⨒⪩⨒∯1000123)=⪩⨒∯213333220","reverse_text":"⪩⨒∯213333220=⪩⨒∯203033⪚⪩⨒∯1122300⨔≚≋(⪩⨒∯100111⨒⪩⨒∯1000123)","cot":[{"info":"⪩⨒∯203033⪚⪩⨒∯1122300=⪩⨒∯-1310212","layer":1},{"info":"⪩⨒∯100111⨒⪩⨒∯1000123=⪩⨒∯-1130022","layer":1},{"info":"⪩⨒∯-1310212⨔≚≋⪩⨒∯-1130022=⪩⨒∯213333220","layer":0}]}
{"id":676,"expression_no_base_symbol":"≀↧⇸(⇋↷$2975$)","expression":"≀↧⇸(⇋↷⪩⨒∯232133)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":13,"operation_count":2,"complexity_ratio":6.5,"tree":{"type":"unary","operator":"≀↧⇸","unary_expr":{"type":"unary","operator":"⇋↷","unary_expr":{"type":"numeric_atoms","value":2975,"base":4}}},"used_operators":["ljTHtUsqzn","SWo3A1KBJH"],"dependent_operators":["XPYlsWDdGa","23Mk6UjR3U","XPYlsWDdGa","23Mk6UjR3U","2DQ55sFlQl","u6S6b8DprG"],"result":"⪩⨒∯23213300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2975","layer":2},{"info":"compute unary expreesion, input=2975, op_id = SWo3A1KBJH, unary_op_definition = '⇋↷a = { (⪲⇎((↽≂a)⋷(a⨵⪆a))) }', output=23800","layer":1},{"info":"compute unary expreesion, input=23800, op_id = ljTHtUsqzn, unary_op_definition = '≀↧⇸a = { (⪲⇎(a⋷a)) }', output=47600","layer":0}],"base":4,"result_base":4,"text":"≀↧⇸(⇋↷⪩⨒∯232133)=⪩⨒∯23213300","reverse_text":"⪩⨒∯23213300=≀↧⇸(⇋↷⪩⨒∯232133)","cot":[{"info":"⇋↷⪩⨒∯232133=⪩⨒∯11303320","layer":1},{"info":"≀↧⇸⪩⨒∯11303320=⪩⨒∯23213300","layer":0}]}
{"id":677,"expression_no_base_symbol":"$1234$⪭≯$2596$*(≋$5956$)","expression":"⪩⨒∯103102⪭≯⪩⨒∯220210*(≋⪩⨒∯1131010)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":186,"operation_count":3,"complexity_ratio":62.0,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"⪭≯","left_expr":{"type":"numeric_atoms","value":1234,"base":4},"right_expr":{"type":"numeric_atoms","value":2596,"base":4}},"right_expr":{"type":"unary","operator":"≋","unary_expr":{"type":"numeric_atoms","value":5956,"base":4}}},"used_operators":["9HNa5Wba9A","XAx5wpdLa6","61wBmkZwlr"],"dependent_operators":["W4YGzv6Whe","9samAPKr6k","HJ9erzHUuu","TpPTUOHfaN","DbCuESL50I","s1XTVnmDOJ","61wBmkZwlr","Z5CJsN7DuW","7j4O788W3g"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1234","layer":2},{"info":"number node, value=2596","layer":2},{"info":"compute binary expreesion, left_input=1234, right_input=2596, op_id = XAx5wpdLa6 binary_op_definition= 'a⪭≯b = { (((b⨽∌374)⪔⊥(⋼∭⪍b))+⇶⊼((≋a)≓∲(↨⩢⫨a))) }', output=nan","layer":1},{"info":"number node, value=5956","layer":2},{"info":"compute unary expreesion, input=5956, op_id = 61wBmkZwlr, unary_op_definition = '≋a = { (a↺a) }', output=5956","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=5956, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯103102⪭≯⪩⨒∯220210*(≋⪩⨒∯1131010)=NaN","reverse_text":"NaN=⪩⨒∯103102⪭≯⪩⨒∯220210*(≋⪩⨒∯1131010)","cot":[{"info":"⪩⨒∯103102⪭≯⪩⨒∯220210=NaN","layer":1},{"info":"≋⪩⨒∯1131010=⪩⨒∯1131010","layer":1},{"info":"NaN*⪩⨒∯1131010=NaN","layer":0}]}
{"id":678,"expression_no_base_symbol":"(↴⪽⋼$1242$)⪕($5422$⊬⫿⊭)","expression":"(↴⪽⋼⪩⨒∯103122)⪕(⪩⨒∯1110232⊬⫿⊭)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":26,"operation_count":3,"complexity_ratio":8.666666666666666,"tree":{"type":"binary","operator":"⪕","left_expr":{"type":"unary","operator":"↴⪽⋼","unary_expr":{"type":"numeric_atoms","value":1242,"base":4}},"right_expr":{"type":"unary","operator":"⊬⫿⊭","unary_expr":{"type":"numeric_atoms","value":5422,"base":4}}},"used_operators":["umQnsF7QlU","5TUYCnJO6w","v0DYgG9ikt"],"dependent_operators":["P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF","MGuIdZPyUC","UqFzSgLMvQ","k7HXdKtiEU","yyfyN0ffXY","pRsWfj4Fpp","diKm42VcIt","eLAdDNolq6","P8v4zCKN1o","7j4O788W3g","8w2t5hMYqp","2DQ55sFlQl","2DDjHMKMc0","xUOZtlo3hN","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","u6S6b8DprG"],"result":"⪩⨒∯32213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1242","layer":2},{"info":"compute unary expreesion, input=1242, op_id = 5TUYCnJO6w, unary_op_definition = '↴⪽⋼a = { a , if ((∡a)<5 or (⇘a)>=19 or (⊲⪭a)==199) ; (((a↙a)⇡)⇉⇉) , else }', output=1242","layer":1},{"info":"number node, value=5422","layer":2},{"info":"compute unary expreesion, input=5422, op_id = v0DYgG9ikt, unary_op_definition = 'a⊬⫿⊭ = { ((⨑⩽⪐(≤/a))↺((⨞⊢a)⨰(↽≂188))) , if a<119 ; (((∥⊫a)⨳⩥⨓(a⨵⪆a))↺(⊄⩳↩(a⋝⋈⪟a))) , else }', output=-16266","layer":1},{"info":"compute binary expreesion, left_input=1242, right_input=-16266, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=935","layer":0}],"base":4,"result_base":4,"text":"(↴⪽⋼⪩⨒∯103122)⪕(⪩⨒∯1110232⊬⫿⊭)=⪩⨒∯32213","reverse_text":"⪩⨒∯32213=(↴⪽⋼⪩⨒∯103122)⪕(⪩⨒∯1110232⊬⫿⊭)","cot":[{"info":"↴⪽⋼⪩⨒∯103122=⪩⨒∯103122","layer":1},{"info":"⪩⨒∯1110232⊬⫿⊭=⪩⨒∯-3332022","layer":1},{"info":"⪩⨒∯103122⪕⪩⨒∯-3332022=⪩⨒∯32213","layer":0}]}
{"id":679,"expression_no_base_symbol":"(⇜⊴$1677$)⊧↖","expression":"(⇜⊴⪩⨒∯122031)⊧↖","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":382184,"operation_count":2,"complexity_ratio":191092.0,"tree":{"type":"unary","operator":"⊧↖","unary_expr":{"type":"unary","operator":"⇜⊴","unary_expr":{"type":"numeric_atoms","value":1677,"base":4}}},"used_operators":["EKiFHuOFxO","XwDhCwWbUn"],"dependent_operators":["5twsqlHp2o","dfKe02y8D2","8HhzD0ZcuI","WR6HLWljOP","JclMnS0uGI","D309nIvmXG","w2P8NbNXyL","YbVcJGFEVW","DmTXOeWf9t","4CyGpkTkEk","cTDWOvIxvz","jLgFTUHLKL","COABgblf1C","hrf7POJlIJ"],"result":"Inf","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1677","layer":2},{"info":"compute unary expreesion, input=1677, op_id = XwDhCwWbUn, unary_op_definition = '⇜⊴a = { (↩(∓⪦(a≃a))) , if ((a∐⫣)>271 and (a∴779)<=132) ; ((a↢(a⨔⇊a))⊲⩕⊾((a∝a)⊉↱≁(a⊭↱19))) , else }', output=-382058","layer":1},{"info":"compute unary expreesion, input=-382058, op_id = EKiFHuOFxO, unary_op_definition = 'a⊧↖ = { ((a⨽a)⊢(a⫚↹⊑79)) }', output=inf","layer":0}],"base":4,"result_base":4,"text":"(⇜⊴⪩⨒∯122031)⊧↖=Inf","reverse_text":"Inf=(⇜⊴⪩⨒∯122031)⊧↖","cot":[{"info":"⇜⊴⪩⨒∯122031=⪩⨒∯-1131101222","layer":1},{"info":"⪩⨒∯-1131101222⊧↖=Inf","layer":0}]}
{"id":680,"expression_no_base_symbol":"$1760$⇌⫙⪟$6067$⇡","expression":"⪩⨒∯123200⇌⫙⪟⪩⨒∯1132303⇡","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":85,"operation_count":2,"complexity_ratio":42.5,"tree":{"type":"unary","operator":"⇡","unary_expr":{"type":"binary","operator":"⇌⫙⪟","left_expr":{"type":"numeric_atoms","value":1760,"base":4},"right_expr":{"type":"numeric_atoms","value":6067,"base":4}}},"used_operators":["UqFzSgLMvQ","AFVx7xoS7T"],"dependent_operators":["3sJ7IOPOlU","sJAwomhLZr","4JB6nKBMSY","k2HlF1dBQh","BiWNJpBvwn","YSKBFp38Pu","DpFCA1CohY","DZ8iAZOCBD","tifHPKVTfV","2DQ55sFlQl","12rbrZMWeM","xUOZtlo3hN","eewbuw0ToL"],"result":"⪩⨒∯-231211","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1760","layer":2},{"info":"number node, value=6067","layer":2},{"info":"compute binary expreesion, left_input=1760, right_input=6067, op_id = AFVx7xoS7T binary_op_definition= 'a⇌⫙⪟b = { (⨞⊢(a⇼⇔∾(a⋳⪒a))) , if (⨞⊢b)<133 ; ((a⋳⪒(b⨰261))⇼⇔∾((⋗⩬⋾b)⊉≛↸(a⨵⪆75))) , else }', output=113","layer":1},{"info":"compute unary expreesion, input=113, op_id = UqFzSgLMvQ, unary_op_definition = 'a⇡ = { (((a⇴a)⪇≇⋚(∤27))⇤((a⩍⋽⫝̸27)⩠)) }', output=-2917","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯123200⇌⫙⪟⪩⨒∯1132303⇡=⪩⨒∯-231211","reverse_text":"⪩⨒∯-231211=⪩⨒∯123200⇌⫙⪟⪩⨒∯1132303⇡","cot":[{"info":"⪩⨒∯123200⇌⫙⪟⪩⨒∯1132303=⪩⨒∯1301","layer":1},{"info":"⪩⨒∯1301⇡=⪩⨒∯-231211","layer":0}]}
{"id":681,"expression_no_base_symbol":"(≋$2479$)⪕(⨛$2268$)","expression":"(≋⪩⨒∯212233)⪕(⨛⪩⨒∯203130)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":56,"operation_count":3,"complexity_ratio":18.666666666666668,"tree":{"type":"binary","operator":"⪕","left_expr":{"type":"unary","operator":"≋","unary_expr":{"type":"numeric_atoms","value":2479,"base":4}},"right_expr":{"type":"unary","operator":"⨛","unary_expr":{"type":"numeric_atoms","value":2268,"base":4}}},"used_operators":["umQnsF7QlU","61wBmkZwlr","CoMdbyAt7R"],"dependent_operators":["P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF","7j4O788W3g","U6pG0PXrV3","DyGG3AbaNP","liw5iZPkLH","3DZMoQKiUl"],"result":"⪩⨒∯32213","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2479","layer":2},{"info":"compute unary expreesion, input=2479, op_id = 61wBmkZwlr, unary_op_definition = '≋a = { (a↺a) }', output=2479","layer":1},{"info":"number node, value=2268","layer":2},{"info":"compute unary expreesion, input=2268, op_id = CoMdbyAt7R, unary_op_definition = '⨛a = { (⊖((≱⇩⩕a)∼(⨡↴a))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=2479, right_input=nan, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=935","layer":0}],"base":4,"result_base":4,"text":"(≋⪩⨒∯212233)⪕(⨛⪩⨒∯203130)=⪩⨒∯32213","reverse_text":"⪩⨒∯32213=(≋⪩⨒∯212233)⪕(⨛⪩⨒∯203130)","cot":[{"info":"≋⪩⨒∯212233=⪩⨒∯212233","layer":1},{"info":"⨛⪩⨒∯203130=NaN","layer":1},{"info":"⪩⨒∯212233⪕NaN=⪩⨒∯32213","layer":0}]}
{"id":682,"expression_no_base_symbol":"($2885$⪠⩆⊳)∝($3529$⫡⨏$3713$)","expression":"(⪩⨒∯231011⪠⩆⊳)∝(⪩⨒∯313021⫡⨏⪩⨒∯322001)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":22,"operation_count":3,"complexity_ratio":7.333333333333333,"tree":{"type":"binary","operator":"∝","left_expr":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"numeric_atoms","value":2885,"base":4}},"right_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":3529,"base":4},"right_expr":{"type":"numeric_atoms","value":3713,"base":4}}},"used_operators":["cTDWOvIxvz","JLbD19bQDL","QMFrweE19q"],"dependent_operators":["7j4O788W3g","W4YGzv6Whe","COABgblf1C","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯11","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2885","layer":2},{"info":"compute unary expreesion, input=2885, op_id = JLbD19bQDL, unary_op_definition = 'a⪠⩆⊳ = { ((a+a)-((a-a)+(a+a))) , if ((-a)!=71 or a<=364) ; (-((a+a)+(a-a))) , else }', output=0","layer":1},{"info":"number node, value=3529","layer":2},{"info":"number node, value=3713","layer":2},{"info":"compute binary expreesion, left_input=3529, right_input=3713, op_id = QMFrweE19q binary_op_definition= 'a⫡⨏b = { 497 , if (-b)==408 and (-a)>=56 ; (((a+783)+(a+a))+((b+a)+(a+b))) , else }', output=25854","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=25854, op_id = cTDWOvIxvz binary_op_definition= 'a∝b = { ((b↺a)+(b⊭↱b)) }', output=5","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯231011⪠⩆⊳)∝(⪩⨒∯313021⫡⨏⪩⨒∯322001)=⪩⨒∯11","reverse_text":"⪩⨒∯11=(⪩⨒∯231011⪠⩆⊳)∝(⪩⨒∯313021⫡⨏⪩⨒∯322001)","cot":[{"info":"⪩⨒∯231011⪠⩆⊳=⪩⨒∯0","layer":1},{"info":"⪩⨒∯313021⫡⨏⪩⨒∯322001=⪩⨒∯12103332","layer":1},{"info":"⪩⨒∯0∝⪩⨒∯12103332=⪩⨒∯11","layer":0}]}
{"id":683,"expression_no_base_symbol":"($1598$∽$8060$)⪛($1638$⋝⋈⪟$2122$)","expression":"(⪩⨒∯120332∽⪩⨒∯1331330)⪛(⪩⨒∯121212⋝⋈⪟⪩⨒∯201022)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":35,"operation_count":3,"complexity_ratio":11.666666666666666,"tree":{"type":"binary","operator":"⪛","left_expr":{"type":"binary","operator":"∽","left_expr":{"type":"numeric_atoms","value":1598,"base":4},"right_expr":{"type":"numeric_atoms","value":8060,"base":4}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":1638,"base":4},"right_expr":{"type":"numeric_atoms","value":2122,"base":4}}},"used_operators":["uFcxV4UQCh","y4ImoPnbV5","2DDjHMKMc0"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","NTOWxs364D","QMFrweE19q","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯30000","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1598","layer":2},{"info":"number node, value=8060","layer":2},{"info":"compute binary expreesion, left_input=1598, right_input=8060, op_id = y4ImoPnbV5 binary_op_definition= 'a∽b = { ((a⩚⊴⇥b)⫡⨏b) }', output=-31992","layer":1},{"info":"number node, value=1638","layer":2},{"info":"number node, value=2122","layer":2},{"info":"compute binary expreesion, left_input=1638, right_input=2122, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=1638","layer":1},{"info":"compute binary expreesion, left_input=-31992, right_input=1638, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=768","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯120332∽⪩⨒∯1331330)⪛(⪩⨒∯121212⋝⋈⪟⪩⨒∯201022)=⪩⨒∯30000","reverse_text":"⪩⨒∯30000=(⪩⨒∯120332∽⪩⨒∯1331330)⪛(⪩⨒∯121212⋝⋈⪟⪩⨒∯201022)","cot":[{"info":"⪩⨒∯120332∽⪩⨒∯1331330=⪩⨒∯-13303320","layer":1},{"info":"⪩⨒∯121212⋝⋈⪟⪩⨒∯201022=⪩⨒∯121212","layer":1},{"info":"⪩⨒∯-13303320⪛⪩⨒∯121212=⪩⨒∯30000","layer":0}]}
{"id":684,"expression_no_base_symbol":"↯⪼(⨂⪏⇭$2074$)","expression":"↯⪼(⨂⪏⇭⪩⨒∯200122)","highest_n_order":2,"priority_hierarchical_complexity":1,"normalized_expansion_degree":47,"operation_count":2,"complexity_ratio":23.5,"tree":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"unary","operator":"⨂⪏⇭","unary_expr":{"type":"numeric_atoms","value":2074,"base":4}}},"used_operators":["8jW3W4yZS5","AYdpE9sXAk"],"dependent_operators":["eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","eewbuw0ToL","NTOWxs364D","EBcxylXtPf"],"result":"⪩⨒∯-111","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2074","layer":2},{"info":"compute unary expreesion, input=2074, op_id = AYdpE9sXAk, unary_op_definition = '⨂⪏⇭a = { (a⨰((85⩚⊴⇥a)⫌⩹⨱)) }', output=5243","layer":1},{"info":"compute unary expreesion, input=5243, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":0}],"base":4,"result_base":4,"text":"↯⪼(⨂⪏⇭⪩⨒∯200122)=⪩⨒∯-111","reverse_text":"⪩⨒∯-111=↯⪼(⨂⪏⇭⪩⨒∯200122)","cot":[{"info":"⨂⪏⇭⪩⨒∯200122=⪩⨒∯1101323","layer":1},{"info":"↯⪼⪩⨒∯1101323=⪩⨒∯-111","layer":0}]}
{"id":685,"expression_no_base_symbol":"⫯($2184$⨸$4151$)","expression":"⫯(⪩⨒∯202020⨸⪩⨒∯1000313)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2343,"operation_count":2,"complexity_ratio":1171.5,"tree":{"type":"unary","operator":"⫯","unary_expr":{"type":"binary","operator":"⨸","left_expr":{"type":"numeric_atoms","value":2184,"base":4},"right_expr":{"type":"numeric_atoms","value":4151,"base":4}}},"used_operators":["H6BK1Evt7c","KmoU8R5UQR"],"dependent_operators":["2Wsdkap16l","KbjG8mgYpV","sJAwomhLZr","Ph9nP6C5qx","AYdpE9sXAk","X99M06cbEe","ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl"],"result":"⪩⨒∯-221023130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2184","layer":2},{"info":"number node, value=4151","layer":2},{"info":"compute binary expreesion, left_input=2184, right_input=4151, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=4368","layer":1},{"info":"compute unary expreesion, input=4368, op_id = H6BK1Evt7c, unary_op_definition = '⫯a = { ((a⩠)∠↢(⨂⪏⇭a)) , if (a≧⫂∧919)>20 ; ((a⩹a)≫≃) , else }', output=-168668","layer":0}],"base":4,"result_base":4,"text":"⫯(⪩⨒∯202020⨸⪩⨒∯1000313)=⪩⨒∯-221023130","reverse_text":"⪩⨒∯-221023130=⫯(⪩⨒∯202020⨸⪩⨒∯1000313)","cot":[{"info":"⪩⨒∯202020⨸⪩⨒∯1000313=⪩⨒∯1010100","layer":1},{"info":"⫯⪩⨒∯1010100=⪩⨒∯-221023130","layer":0}]}
{"id":686,"expression_no_base_symbol":"$4529$⫸⊐$1300$∕⩚$2315$↹⊜$1539$","expression":"⪩⨒∯1012301⫸⊐⪩⨒∯110110∕⩚⪩⨒∯210023↹⊜⪩⨒∯120003","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":64,"operation_count":3,"complexity_ratio":21.333333333333332,"tree":{"type":"binary","operator":"∕⩚","left_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":4529,"base":4},"right_expr":{"type":"numeric_atoms","value":1300,"base":4}},"right_expr":{"type":"binary","operator":"↹⊜","left_expr":{"type":"numeric_atoms","value":2315,"base":4},"right_expr":{"type":"numeric_atoms","value":1539,"base":4}}},"used_operators":["z9ffQ9n5Zr","mqXw5SEYmG","9bazX3JMtO"],"dependent_operators":["3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","9FxExcQeMw","rysDP5nf3Z","23Mk6UjR3U","tifHPKVTfV","eH2TOUuTDT","DIvbN7qnHd"],"result":"⪩⨒∯-13213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4529","layer":2},{"info":"number node, value=1300","layer":2},{"info":"compute binary expreesion, left_input=4529, right_input=1300, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=5075","layer":1},{"info":"number node, value=2315","layer":2},{"info":"number node, value=1539","layer":2},{"info":"compute binary expreesion, left_input=2315, right_input=1539, op_id = 9bazX3JMtO binary_op_definition= 'a↹⊜b = { (((a⊠≄⫣)⩷∴(b-a))⩷∴((a⋷b)⇼⇔∾(b⪐))) }', output=-1622","layer":1},{"info":"compute binary expreesion, left_input=5075, right_input=-1622, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-487","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1012301⫸⊐⪩⨒∯110110∕⩚⪩⨒∯210023↹⊜⪩⨒∯120003=⪩⨒∯-13213","reverse_text":"⪩⨒∯-13213=⪩⨒∯1012301⫸⊐⪩⨒∯110110∕⩚⪩⨒∯210023↹⊜⪩⨒∯120003","cot":[{"info":"⪩⨒∯1012301⫸⊐⪩⨒∯110110=⪩⨒∯1033103","layer":1},{"info":"⪩⨒∯210023↹⊜⪩⨒∯120003=⪩⨒∯-121112","layer":1},{"info":"⪩⨒∯1033103∕⩚⪩⨒∯-121112=⪩⨒∯-13213","layer":0}]}
{"id":687,"expression_no_base_symbol":"$2188$∊∟⩊$8822$-$4011$⨔⇊$1116$","expression":"⪩⨒∯202030∊∟⩊⪩⨒∯2021312-⪩⨒∯332223⨔⇊⪩⨒∯101130","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3,"operation_count":3,"complexity_ratio":1.0,"tree":{"type":"binary","operator":"-","left_expr":{"type":"binary","operator":"∊∟⩊","left_expr":{"type":"numeric_atoms","value":2188,"base":4},"right_expr":{"type":"numeric_atoms","value":8822,"base":4}},"right_expr":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"numeric_atoms","value":4011,"base":4},"right_expr":{"type":"numeric_atoms","value":1116,"base":4}}},"used_operators":["rysDP5nf3Z","ddLRYrp01A","JclMnS0uGI"],"dependent_operators":["59igzFyhWz","A8NUZmVepG","3sJ7IOPOlU","9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI"],"result":"⪩⨒∯1320122","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2188","layer":2},{"info":"number node, value=8822","layer":2},{"info":"compute binary expreesion, left_input=2188, right_input=8822, op_id = ddLRYrp01A binary_op_definition= 'a∊∟⩊b = { b , if (b∵≐)>=166 or (a⪇≇⋚4)==505 ; (↥a) , else }', output=8822","layer":1},{"info":"number node, value=4011","layer":2},{"info":"number node, value=1116","layer":2},{"info":"compute binary expreesion, left_input=4011, right_input=1116, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=1116","layer":1},{"info":"compute binary expreesion, left_input=8822, right_input=1116, op_id = rysDP5nf3Z binary_op_definition= 'None', output=7706","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯202030∊∟⩊⪩⨒∯2021312-⪩⨒∯332223⨔⇊⪩⨒∯101130=⪩⨒∯1320122","reverse_text":"⪩⨒∯1320122=⪩⨒∯202030∊∟⩊⪩⨒∯2021312-⪩⨒∯332223⨔⇊⪩⨒∯101130","cot":[{"info":"⪩⨒∯202030∊∟⩊⪩⨒∯2021312=⪩⨒∯2021312","layer":1},{"info":"⪩⨒∯332223⨔⇊⪩⨒∯101130=⪩⨒∯101130","layer":1},{"info":"⪩⨒∯2021312-⪩⨒∯101130=⪩⨒∯1320122","layer":0}]}
{"id":688,"expression_no_base_symbol":"⊬↢($1862$∋$1838$)","expression":"⊬↢(⪩⨒∯131012∋⪩⨒∯130232)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":164,"operation_count":2,"complexity_ratio":82.0,"tree":{"type":"unary","operator":"⊬↢","unary_expr":{"type":"binary","operator":"∋","left_expr":{"type":"numeric_atoms","value":1862,"base":4},"right_expr":{"type":"numeric_atoms","value":1838,"base":4}}},"used_operators":["WPoGxAaPR1","ukq6epAj5P"],"dependent_operators":["XGcMNugi78","d7ASUq0ydm","OwUj7dcsQK","FyVja0WsTP","1eCjFl0mb9","j6NVkjMzuk","SL6IHkK8vl","MRPaB8lBjK","yyfyN0ffXY","3Oe9XWJUTD","3tVxb0NHM4","8cLx32lpNA","SUmda5xLS4","61wBmkZwlr","KbjG8mgYpV"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1862","layer":2},{"info":"number node, value=1838","layer":2},{"info":"compute binary expreesion, left_input=1862, right_input=1838, op_id = ukq6epAj5P binary_op_definition= 'a∋b = { ((≋a)∠↢(b⪄a)) }', output=3851488","layer":1},{"info":"compute unary expreesion, input=3851488, op_id = WPoGxAaPR1, unary_op_definition = '⊬↢a = { (((a⫞⩸⩒a)⊝⪿⪼(a⫯⪬∳a))⪎↠((a⨀⨒)↸(∐⩳⋚a))) , if (∓a)>278 ; (((a↙a)⊱⇼⊻(a∌480))⇉⇱⇎) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⊬↢(⪩⨒∯131012∋⪩⨒∯130232)=NaN","reverse_text":"NaN=⊬↢(⪩⨒∯131012∋⪩⨒∯130232)","cot":[{"info":"⪩⨒∯131012∋⪩⨒∯130232=⪩⨒∯32230103200","layer":1},{"info":"⊬↢⪩⨒∯32230103200=NaN","layer":0}]}
{"id":689,"expression_no_base_symbol":"⇁⨣⪵(⫟$1593$)","expression":"⇁⨣⪵(⫟⪩⨒∯120321)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":38,"operation_count":2,"complexity_ratio":19.0,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"unary","operator":"⫟","unary_expr":{"type":"numeric_atoms","value":1593,"base":4}}},"used_operators":["inkyxCbjAn","z4E1FaHLuy"],"dependent_operators":["B5M0gjZbta","9FxExcQeMw","W4YGzv6Whe","Qy55tPpLXF","BjRHVeLaeN","sdazOOVcIp","Ph9nP6C5qx","t8gj7n24qd","EBcxylXtPf","f6k1SAg4EE","2DDjHMKMc0","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1593","layer":2},{"info":"compute unary expreesion, input=1593, op_id = z4E1FaHLuy, unary_op_definition = '⫟a = { (((-a)⪨≂(a⨸⪁a))≧⫂∧((a⩷∴a)⨰(a⫡⨏a))) , if (a⫌⩹⨱)>=11 ; (((a+263)⋝⋈⪟(a⨳⩥⨓a))⪒((a⋥≓≎a)⫩⊇)) , else }', output=-3872","layer":1},{"info":"compute unary expreesion, input=-3872, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇁⨣⪵(⫟⪩⨒∯120321)=NaN","reverse_text":"NaN=⇁⨣⪵(⫟⪩⨒∯120321)","cot":[{"info":"⫟⪩⨒∯120321=⪩⨒∯-330200","layer":1},{"info":"⇁⨣⪵⪩⨒∯-330200=NaN","layer":0}]}
{"id":690,"expression_no_base_symbol":"$1357$≄⊠$4330$⇮⋭$3083$⨂≜$1669$","expression":"⪩⨒∯111031≄⊠⪩⨒∯1003222⇮⋭⪩⨒∯300023⨂≜⪩⨒∯122011","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3223,"operation_count":3,"complexity_ratio":1074.3333333333333,"tree":{"type":"binary","operator":"⇮⋭","left_expr":{"type":"binary","operator":"≄⊠","left_expr":{"type":"numeric_atoms","value":1357,"base":4},"right_expr":{"type":"numeric_atoms","value":4330,"base":4}},"right_expr":{"type":"binary","operator":"⨂≜","left_expr":{"type":"numeric_atoms","value":3083,"base":4},"right_expr":{"type":"numeric_atoms","value":1669,"base":4}}},"used_operators":["vkpjKywKVM","vXNesLlMH1","k1SHOSEABc"],"dependent_operators":["nhYeJWJD5X","U6pG0PXrV3","tifHPKVTfV","bJkvcejdHO","40aOVDgCDB","YbVcJGFEVW","d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI","9FxExcQeMw","HiPekx5b7W","eLxqMNBOBk","JclMnS0uGI","COABgblf1C","U7g4x0WXJJ"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1357","layer":2},{"info":"number node, value=4330","layer":2},{"info":"compute binary expreesion, left_input=1357, right_input=4330, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=73948","layer":1},{"info":"number node, value=3083","layer":2},{"info":"number node, value=1669","layer":2},{"info":"compute binary expreesion, left_input=3083, right_input=1669, op_id = k1SHOSEABc binary_op_definition= 'a⨂≜b = { ((37⊭↱(⫓⪴a))⩷∴((111⨜⨶78)⨔⇊(a∑⇟⊟b))) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=73948, right_input=nan, op_id = vkpjKywKVM binary_op_definition= 'a⇮⋭b = { (((⊖b)⊢)≎⊠⪸((a≃b)⇼⇔∾(47∇⊂⋱106))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯111031≄⊠⪩⨒∯1003222⇮⋭⪩⨒∯300023⨂≜⪩⨒∯122011=NaN","reverse_text":"NaN=⪩⨒∯111031≄⊠⪩⨒∯1003222⇮⋭⪩⨒∯300023⨂≜⪩⨒∯122011","cot":[{"info":"⪩⨒∯111031≄⊠⪩⨒∯1003222=⪩⨒∯102003130","layer":1},{"info":"⪩⨒∯300023⨂≜⪩⨒∯122011=NaN","layer":1},{"info":"⪩⨒∯102003130⇮⋭NaN=NaN","layer":0}]}
{"id":691,"expression_no_base_symbol":"($3829$⨸⪁$5571$)⪚⩙≫","expression":"(⪩⨒∯323311⨸⪁⪩⨒∯1113003)⪚⩙≫","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":18,"operation_count":2,"complexity_ratio":9.0,"tree":{"type":"unary","operator":"⪚⩙≫","unary_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":3829,"base":4},"right_expr":{"type":"numeric_atoms","value":5571,"base":4}}},"used_operators":["4n53wtyJvv","g55IO6H4Gj"],"dependent_operators":["Uaa54Peajs","nCS4ZIUYfx","WR6HLWljOP","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3829","layer":2},{"info":"number node, value=5571","layer":2},{"info":"compute binary expreesion, left_input=3829, right_input=5571, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=18800","layer":1},{"info":"compute unary expreesion, input=18800, op_id = 4n53wtyJvv, unary_op_definition = 'a⪚⩙≫ = { ((316↢a)⨳⩥⨓(∂255)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯323311⨸⪁⪩⨒∯1113003)⪚⩙≫=NaN","reverse_text":"NaN=(⪩⨒∯323311⨸⪁⪩⨒∯1113003)⪚⩙≫","cot":[{"info":"⪩⨒∯323311⨸⪁⪩⨒∯1113003=⪩⨒∯10211300","layer":1},{"info":"⪩⨒∯10211300⪚⩙≫=NaN","layer":0}]}
{"id":692,"expression_no_base_symbol":"($2154$⊓⋫)⊲⩕⊾$1203$⨜⨶$4240$","expression":"(⪩⨒∯201222⊓⋫)⊲⩕⊾⪩⨒∯102303⨜⨶⪩⨒∯1002100","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":82,"operation_count":3,"complexity_ratio":27.333333333333332,"tree":{"type":"binary","operator":"⊲⩕⊾","left_expr":{"type":"unary","operator":"⊓⋫","unary_expr":{"type":"numeric_atoms","value":2154,"base":4}},"right_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":1203,"base":4},"right_expr":{"type":"numeric_atoms","value":4240,"base":4}}},"used_operators":["DmTXOeWf9t","IqGBaFP0uj","HiPekx5b7W"],"dependent_operators":["23Mk6UjR3U","DZ8iAZOCBD","BjRHVeLaeN","QMFrweE19q","AF7qkfDlqP","COABgblf1C","2td37pGCOC","sdazOOVcIp","2DDjHMKMc0","f6k1SAg4EE","nCS4ZIUYfx","QMFrweE19q","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"⪩⨒∯131012102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2154","layer":2},{"info":"compute unary expreesion, input=2154, op_id = IqGBaFP0uj, unary_op_definition = 'a⊓⋫ = { (((a⪨≂a)⨳⩥⨓(⩦⩻⨪230))⪒(a⋝⋈⪟(542⫡⨏384))) }', output=-2282","layer":1},{"info":"number node, value=1203","layer":2},{"info":"number node, value=4240","layer":2},{"info":"compute binary expreesion, left_input=1203, right_input=4240, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-8224","layer":1},{"info":"compute binary expreesion, left_input=-2282, right_input=-8224, op_id = DmTXOeWf9t binary_op_definition= 'a⊲⩕⊾b = { (((a⊉≛↸b)⊭↱(⨑⩽⪐b))⫡⨏((a⫩⊇)⋷(a⊉≛↸b))) }', output=119186","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯201222⊓⋫)⊲⩕⊾⪩⨒∯102303⨜⨶⪩⨒∯1002100=⪩⨒∯131012102","reverse_text":"⪩⨒∯131012102=(⪩⨒∯201222⊓⋫)⊲⩕⊾⪩⨒∯102303⨜⨶⪩⨒∯1002100","cot":[{"info":"⪩⨒∯201222⊓⋫=⪩⨒∯-203222","layer":1},{"info":"⪩⨒∯102303⨜⨶⪩⨒∯1002100=⪩⨒∯-2000200","layer":1},{"info":"⪩⨒∯-203222⊲⩕⊾⪩⨒∯-2000200=⪩⨒∯131012102","layer":0}]}
{"id":693,"expression_no_base_symbol":"(≤/$1525$)%($3803$⊦⊿)","expression":"(≤/⪩⨒∯113311)%(⪩⨒∯323123⊦⊿)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"%","left_expr":{"type":"unary","operator":"≤/","unary_expr":{"type":"numeric_atoms","value":1525,"base":4}},"right_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":3803,"base":4}}},"used_operators":["k8jYdgA6NY","eLAdDNolq6","14qkJME0vr"],"dependent_operators":["rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯-100101","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1525","layer":2},{"info":"compute unary expreesion, input=1525, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-1041","layer":1},{"info":"number node, value=3803","layer":2},{"info":"compute unary expreesion, input=3803, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-11488","layer":1},{"info":"compute binary expreesion, left_input=-1041, right_input=-11488, op_id = k8jYdgA6NY binary_op_definition= 'None', output=-1041","layer":0}],"base":4,"result_base":4,"text":"(≤/⪩⨒∯113311)%(⪩⨒∯323123⊦⊿)=⪩⨒∯-100101","reverse_text":"⪩⨒∯-100101=(≤/⪩⨒∯113311)%(⪩⨒∯323123⊦⊿)","cot":[{"info":"≤/⪩⨒∯113311=⪩⨒∯-100101","layer":1},{"info":"⪩⨒∯323123⊦⊿=⪩⨒∯-2303200","layer":1},{"info":"⪩⨒∯-100101%⪩⨒∯-2303200=⪩⨒∯-100101","layer":0}]}
{"id":694,"expression_no_base_symbol":"$1418$≨$6388$⨻⩈⩔$3477$⫞⩸⩒$4423$","expression":"⪩⨒∯112022≨⪩⨒∯1203310⨻⩈⩔⪩⨒∯312111⫞⩸⩒⪩⨒∯1011013","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":177,"operation_count":3,"complexity_ratio":59.0,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"binary","operator":"≨","left_expr":{"type":"numeric_atoms","value":1418,"base":4},"right_expr":{"type":"numeric_atoms","value":6388,"base":4}},"right_expr":{"type":"binary","operator":"⫞⩸⩒","left_expr":{"type":"numeric_atoms","value":3477,"base":4},"right_expr":{"type":"numeric_atoms","value":4423,"base":4}}},"used_operators":["nEsXyWgiOK","0KMCeP1Jsh","XGcMNugi78"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC","VJ330n2nnx","JclMnS0uGI","SWo3A1KBJH","rJVOvQCfKK"],"result":"⪩⨒∯-2232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1418","layer":2},{"info":"number node, value=6388","layer":2},{"info":"compute binary expreesion, left_input=1418, right_input=6388, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-11704","layer":1},{"info":"number node, value=3477","layer":2},{"info":"number node, value=4423","layer":2},{"info":"compute binary expreesion, left_input=3477, right_input=4423, op_id = XGcMNugi78 binary_op_definition= 'a⫞⩸⩒b = { (a⨎b) , if ((⇋↷b)>164 and (a↬⩅∪)<=12 and (b⨔⇊430)!=387) ; a , else }', output=4423","layer":1},{"info":"compute binary expreesion, left_input=-11704, right_input=4423, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=-174","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯112022≨⪩⨒∯1203310⨻⩈⩔⪩⨒∯312111⫞⩸⩒⪩⨒∯1011013=⪩⨒∯-2232","reverse_text":"⪩⨒∯-2232=⪩⨒∯112022≨⪩⨒∯1203310⨻⩈⩔⪩⨒∯312111⫞⩸⩒⪩⨒∯1011013","cot":[{"info":"⪩⨒∯112022≨⪩⨒∯1203310=⪩⨒∯-2312320","layer":1},{"info":"⪩⨒∯312111⫞⩸⩒⪩⨒∯1011013=⪩⨒∯1011013","layer":1},{"info":"⪩⨒∯-2312320⨻⩈⩔⪩⨒∯1011013=⪩⨒∯-2232","layer":0}]}
{"id":695,"expression_no_base_symbol":"($6309$⩼⇪↪$3421$)⫯⪬∳($2172$⊬⨰$8609$)","expression":"(⪩⨒∯1202211⩼⇪↪⪩⨒∯311131)⫯⪬∳(⪩⨒∯201330⊬⨰⪩⨒∯2012201)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":32,"operation_count":3,"complexity_ratio":10.666666666666666,"tree":{"type":"binary","operator":"⫯⪬∳","left_expr":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"numeric_atoms","value":6309,"base":4},"right_expr":{"type":"numeric_atoms","value":3421,"base":4}},"right_expr":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"numeric_atoms","value":2172,"base":4},"right_expr":{"type":"numeric_atoms","value":8609,"base":4}}},"used_operators":["d7ASUq0ydm","ocnLzx9CaJ","s3Fd5m9Dh2"],"dependent_operators":["Qy55tPpLXF","BjRHVeLaeN","8w2t5hMYqp","Ph9nP6C5qx","eewbuw0ToL","D4vGDi5EA2","9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q","23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx"],"result":"⪩⨒∯20300113","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6309","layer":2},{"info":"number node, value=3421","layer":2},{"info":"compute binary expreesion, left_input=6309, right_input=3421, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=-12112","layer":1},{"info":"number node, value=2172","layer":2},{"info":"number node, value=8609","layer":2},{"info":"compute binary expreesion, left_input=2172, right_input=8609, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=35552","layer":1},{"info":"compute binary expreesion, left_input=-12112, right_input=35552, op_id = d7ASUq0ydm binary_op_definition= 'a⫯⪬∳b = { ((b⋥≓≎a)≧⫂∧(⊄⩳↩a)) , if (a≦≮≮)!=65 ; ((b⫩⊇)⋥≓≎(a⨰b)) , else }', output=35863","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1202211⩼⇪↪⪩⨒∯311131)⫯⪬∳(⪩⨒∯201330⊬⨰⪩⨒∯2012201)=⪩⨒∯20300113","reverse_text":"⪩⨒∯20300113=(⪩⨒∯1202211⩼⇪↪⪩⨒∯311131)⫯⪬∳(⪩⨒∯201330⊬⨰⪩⨒∯2012201)","cot":[{"info":"⪩⨒∯1202211⩼⇪↪⪩⨒∯311131=⪩⨒∯-2331100","layer":1},{"info":"⪩⨒∯201330⊬⨰⪩⨒∯2012201=⪩⨒∯20223200","layer":1},{"info":"⪩⨒∯-2331100⫯⪬∳⪩⨒∯20223200=⪩⨒∯20300113","layer":0}]}
{"id":696,"expression_no_base_symbol":"$1782$≄⊠$3070$⩧⪆$3430$⋣⋖$1225$","expression":"⪩⨒∯123312≄⊠⪩⨒∯233332⩧⪆⪩⨒∯311212⋣⋖⪩⨒∯103021","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":60,"operation_count":3,"complexity_ratio":20.0,"tree":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"binary","operator":"≄⊠","left_expr":{"type":"numeric_atoms","value":1782,"base":4},"right_expr":{"type":"numeric_atoms","value":3070,"base":4}},"right_expr":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"numeric_atoms","value":3430,"base":4},"right_expr":{"type":"numeric_atoms","value":1225,"base":4}}},"used_operators":["Ikt5ks8PT7","vXNesLlMH1","J0M6qkBnIM"],"dependent_operators":["eewbuw0ToL","t8gj7n24qd","d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI","VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2"],"result":"⪩⨒∯-311212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1782","layer":2},{"info":"number node, value=3070","layer":2},{"info":"compute binary expreesion, left_input=1782, right_input=3070, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=53788","layer":1},{"info":"number node, value=3430","layer":2},{"info":"number node, value=1225","layer":2},{"info":"compute binary expreesion, left_input=3430, right_input=1225, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=3430","layer":1},{"info":"compute binary expreesion, left_input=53788, right_input=3430, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-3430","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯123312≄⊠⪩⨒∯233332⩧⪆⪩⨒∯311212⋣⋖⪩⨒∯103021=⪩⨒∯-311212","reverse_text":"⪩⨒∯-311212=⪩⨒∯123312≄⊠⪩⨒∯233332⩧⪆⪩⨒∯311212⋣⋖⪩⨒∯103021","cot":[{"info":"⪩⨒∯123312≄⊠⪩⨒∯233332=⪩⨒∯31020130","layer":1},{"info":"⪩⨒∯311212⋣⋖⪩⨒∯103021=⪩⨒∯311212","layer":1},{"info":"⪩⨒∯31020130⩧⪆⪩⨒∯311212=⪩⨒∯-311212","layer":0}]}
{"id":697,"expression_no_base_symbol":"$1652$∀⇚≩$1812$∕⩚$1501$∋$1025$","expression":"⪩⨒∯121310∀⇚≩⪩⨒∯130110∕⩚⪩⨒∯113131∋⪩⨒∯100001","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11690,"operation_count":3,"complexity_ratio":3896.6666666666665,"tree":{"type":"binary","operator":"∕⩚","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":1652,"base":4},"right_expr":{"type":"numeric_atoms","value":1812,"base":4}},"right_expr":{"type":"binary","operator":"∋","left_expr":{"type":"numeric_atoms","value":1501,"base":4},"right_expr":{"type":"numeric_atoms","value":1025,"base":4}}},"used_operators":["z9ffQ9n5Zr","LRNGc0VcxI","ukq6epAj5P"],"dependent_operators":["3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr","X99M06cbEe","SUmda5xLS4","61wBmkZwlr","KbjG8mgYpV"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1652","layer":2},{"info":"number node, value=1812","layer":2},{"info":"compute binary expreesion, left_input=1652, right_input=1812, op_id = LRNGc0VcxI binary_op_definition= 'a∀⇚≩b = {b, if a == 0; ((a-1)∀⇚≩b)≫≃, if a > 0 and abs(a) < 1000000; -((a+1)∀⇚≩b)≫≃, if a < 0 and abs(a) < 1000000; NaN, else}', output=nan","layer":1},{"info":"number node, value=1501","layer":2},{"info":"number node, value=1025","layer":2},{"info":"compute binary expreesion, left_input=1501, right_input=1025, op_id = ukq6epAj5P binary_op_definition= 'a∋b = { ((≋a)∠↢(b⪄a)) }', output=2148180","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2148180, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯121310∀⇚≩⪩⨒∯130110∕⩚⪩⨒∯113131∋⪩⨒∯100001=NaN","reverse_text":"NaN=⪩⨒∯121310∀⇚≩⪩⨒∯130110∕⩚⪩⨒∯113131∋⪩⨒∯100001","cot":[{"info":"⪩⨒∯121310∀⇚≩⪩⨒∯130110=NaN","layer":1},{"info":"⪩⨒∯113131∋⪩⨒∯100001=⪩⨒∯20030131110","layer":1},{"info":"NaN∕⩚⪩⨒∯20030131110=NaN","layer":0}]}
{"id":698,"expression_no_base_symbol":"(⩷⨜⫀$1350$)⊬⨰($3621$⫸⊐$1083$)","expression":"(⩷⨜⫀⪩⨒∯111012)⊬⨰(⪩⨒∯320211⫸⊐⪩⨒∯100323)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":39,"operation_count":3,"complexity_ratio":13.0,"tree":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"unary","operator":"⩷⨜⫀","unary_expr":{"type":"numeric_atoms","value":1350,"base":4}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":3621,"base":4},"right_expr":{"type":"numeric_atoms","value":1083,"base":4}}},"used_operators":["s3Fd5m9Dh2","CDi0ktkjQ4","mqXw5SEYmG"],"dependent_operators":["23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","ruOEQAzv1W","nhYeJWJD5X","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"⪩⨒∯3211102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1350","layer":2},{"info":"compute unary expreesion, input=1350, op_id = CDi0ktkjQ4, unary_op_definition = '⩷⨜⫀a = { (a∇⊂⋱383) , if a<1 ; (↔a) , else }', output=-1077","layer":1},{"info":"number node, value=3621","layer":2},{"info":"number node, value=1083","layer":2},{"info":"compute binary expreesion, left_input=3621, right_input=1083, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=4207","layer":1},{"info":"compute binary expreesion, left_input=-1077, right_input=4207, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=14674","layer":0}],"base":4,"result_base":4,"text":"(⩷⨜⫀⪩⨒∯111012)⊬⨰(⪩⨒∯320211⫸⊐⪩⨒∯100323)=⪩⨒∯3211102","reverse_text":"⪩⨒∯3211102=(⩷⨜⫀⪩⨒∯111012)⊬⨰(⪩⨒∯320211⫸⊐⪩⨒∯100323)","cot":[{"info":"⩷⨜⫀⪩⨒∯111012=⪩⨒∯-100311","layer":1},{"info":"⪩⨒∯320211⫸⊐⪩⨒∯100323=⪩⨒∯1001233","layer":1},{"info":"⪩⨒∯-100311⊬⨰⪩⨒∯1001233=⪩⨒∯3211102","layer":0}]}
{"id":699,"expression_no_base_symbol":"$8195$⫁$7516$⨽∌(⪸$2978$)","expression":"⪩⨒∯2000003⫁⪩⨒∯1311130⨽∌(⪸⪩⨒∯232202)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":537,"operation_count":3,"complexity_ratio":179.0,"tree":{"type":"binary","operator":"⨽∌","left_expr":{"type":"binary","operator":"⫁","left_expr":{"type":"numeric_atoms","value":8195,"base":4},"right_expr":{"type":"numeric_atoms","value":7516,"base":4}},"right_expr":{"type":"unary","operator":"⪸","unary_expr":{"type":"numeric_atoms","value":2978,"base":4}}},"used_operators":["9samAPKr6k","0ajvFaJAv0","86A5ENbKR9"],"dependent_operators":["YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu","cHh1gJQ2o6","AHs5Up7iyr","Qy55tPpLXF","23Mk6UjR3U","tifHPKVTfV","sdazOOVcIp","g55IO6H4Gj","AF7qkfDlqP","QMFrweE19q"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8195","layer":2},{"info":"number node, value=7516","layer":2},{"info":"compute binary expreesion, left_input=8195, right_input=7516, op_id = 0ajvFaJAv0 binary_op_definition= 'a⫁b = { (a≹⇙⪍6) , if a==154 ; (b⩘b) , else }', output=160","layer":1},{"info":"number node, value=2978","layer":2},{"info":"compute unary expreesion, input=2978, op_id = 86A5ENbKR9, unary_op_definition = '⪸a = { (((220⪨≂51)⇼⇔∾(a⫡⨏303))⋷((a⨸⪁a)⋥≓≎(⨑⩽⪐a))) }', output=-50417","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=-50417, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯2000003⫁⪩⨒∯1311130⨽∌(⪸⪩⨒∯232202)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯2000003⫁⪩⨒∯1311130⨽∌(⪸⪩⨒∯232202)","cot":[{"info":"⪩⨒∯2000003⫁⪩⨒∯1311130=⪩⨒∯2200","layer":1},{"info":"⪸⪩⨒∯232202=⪩⨒∯-30103301","layer":1},{"info":"⪩⨒∯2200⨽∌⪩⨒∯-30103301=⪩⨒∯0","layer":0}]}
{"id":700,"expression_no_base_symbol":"($6731$⪕$3410$)⩣⫁∢($1929$∷)","expression":"(⪩⨒∯1221023⪕⪩⨒∯311102)⩣⫁∢(⪩⨒∯132021∷)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":36,"operation_count":3,"complexity_ratio":12.0,"tree":{"type":"binary","operator":"⩣⫁∢","left_expr":{"type":"binary","operator":"⪕","left_expr":{"type":"numeric_atoms","value":6731,"base":4},"right_expr":{"type":"numeric_atoms","value":3410,"base":4}},"right_expr":{"type":"unary","operator":"∷","unary_expr":{"type":"numeric_atoms","value":1929,"base":4}}},"used_operators":["JDUIKTTSIa","umQnsF7QlU","nFAOW8KTqp"],"dependent_operators":["sdazOOVcIp","eewbuw0ToL","AF7qkfDlqP","u6S6b8DprG","P8v4zCKN1o","2td37pGCOC","Qy55tPpLXF","D4vGDi5EA2","t8gj7n24qd","2DDjHMKMc0"],"result":"⪩⨒∯-11103301","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6731","layer":2},{"info":"number node, value=3410","layer":2},{"info":"compute binary expreesion, left_input=6731, right_input=3410, op_id = umQnsF7QlU binary_op_definition= 'a⪕b = { (⩦⩻⨪(∥⊫(b⋥≓≎a))) }', output=10953","layer":1},{"info":"number node, value=1929","layer":2},{"info":"compute unary expreesion, input=1929, op_id = nFAOW8KTqp, unary_op_definition = 'a∷ = { ((-(a⋝⋈⪟a))≦≮≮) }', output=5787","layer":1},{"info":"compute binary expreesion, left_input=10953, right_input=5787, op_id = JDUIKTTSIa binary_op_definition= 'a⩣⫁∢b = { (⨑⩽⪐((a⪨≂b)⨰(↽≂b))) }', output=-21745","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1221023⪕⪩⨒∯311102)⩣⫁∢(⪩⨒∯132021∷)=⪩⨒∯-11103301","reverse_text":"⪩⨒∯-11103301=(⪩⨒∯1221023⪕⪩⨒∯311102)⩣⫁∢(⪩⨒∯132021∷)","cot":[{"info":"⪩⨒∯1221023⪕⪩⨒∯311102=⪩⨒∯2223021","layer":1},{"info":"⪩⨒∯132021∷=⪩⨒∯1122123","layer":1},{"info":"⪩⨒∯2223021⩣⫁∢⪩⨒∯1122123=⪩⨒∯-11103301","layer":0}]}
{"id":701,"expression_no_base_symbol":"↯⪼($3121$⋥≓≎$5175$)","expression":"↯⪼(⪩⨒∯300301⋥≓≎⪩⨒∯1100313)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":35,"operation_count":2,"complexity_ratio":17.5,"tree":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":3121,"base":4},"right_expr":{"type":"numeric_atoms","value":5175,"base":4}}},"used_operators":["8jW3W4yZS5","Qy55tPpLXF"],"dependent_operators":["eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯-111","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3121","layer":2},{"info":"number node, value=5175","layer":2},{"info":"compute binary expreesion, left_input=3121, right_input=5175, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=7262","layer":1},{"info":"compute unary expreesion, input=7262, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":0}],"base":4,"result_base":4,"text":"↯⪼(⪩⨒∯300301⋥≓≎⪩⨒∯1100313)=⪩⨒∯-111","reverse_text":"⪩⨒∯-111=↯⪼(⪩⨒∯300301⋥≓≎⪩⨒∯1100313)","cot":[{"info":"⪩⨒∯300301⋥≓≎⪩⨒∯1100313=⪩⨒∯1301132","layer":1},{"info":"↯⪼⪩⨒∯1301132=⪩⨒∯-111","layer":0}]}
{"id":702,"expression_no_base_symbol":"⫇$1569$⫉⨲⊜$6390$","expression":"⫇⪩⨒∯120201⫉⨲⊜⪩⨒∯1203312","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":39,"operation_count":2,"complexity_ratio":19.5,"tree":{"type":"unary","operator":"⫇","unary_expr":{"type":"binary","operator":"⫉⨲⊜","left_expr":{"type":"numeric_atoms","value":1569,"base":4},"right_expr":{"type":"numeric_atoms","value":6390,"base":4}}},"used_operators":["YjI8oCXuph","WhqkvtTD3t"],"dependent_operators":["rysDP5nf3Z","Qy55tPpLXF","N41Kp7NANJ","23Mk6UjR3U","2DQ55sFlQl","12rbrZMWeM","f6k1SAg4EE","i8ToyICDmI","eewbuw0ToL","zVYPLywUTj"],"result":"⪩⨒∯32302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1569","layer":2},{"info":"number node, value=6390","layer":2},{"info":"compute binary expreesion, left_input=1569, right_input=6390, op_id = WhqkvtTD3t binary_op_definition= 'a⫉⨲⊜b = { (b⨰120) , if b<=7 ; (a⊪) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = YjI8oCXuph, unary_op_definition = '⫇a = { (((a⋥≓≎a)⋷(a⋳⪒a))≋⫹) , if a>62 ; (a-((a⨵⪆101)⪒(786∲⫓a))) , else }', output=946","layer":0}],"base":4,"result_base":4,"text":"⫇⪩⨒∯120201⫉⨲⊜⪩⨒∯1203312=⪩⨒∯32302","reverse_text":"⪩⨒∯32302=⫇⪩⨒∯120201⫉⨲⊜⪩⨒∯1203312","cot":[{"info":"⪩⨒∯120201⫉⨲⊜⪩⨒∯1203312=⪩⨒∯0","layer":1},{"info":"⫇⪩⨒∯0=⪩⨒∯32302","layer":0}]}
{"id":703,"expression_no_base_symbol":"⊖(⪝⪂⫅$1669$)","expression":"⊖(⪝⪂⫅⪩⨒∯122011)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":159,"operation_count":2,"complexity_ratio":79.5,"tree":{"type":"unary","operator":"⊖","unary_expr":{"type":"unary","operator":"⪝⪂⫅","unary_expr":{"type":"numeric_atoms","value":1669,"base":4}}},"used_operators":["U6pG0PXrV3","XTarYq4gQB"],"dependent_operators":["tifHPKVTfV","i8ToyICDmI","D4vGDi5EA2","nCS4ZIUYfx","9HNa5Wba9A","8w2t5hMYqp"],"result":"⪩⨒∯2303230131","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1669","layer":2},{"info":"compute unary expreesion, input=1669, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=-245343","layer":1},{"info":"compute unary expreesion, input=-245343, op_id = U6pG0PXrV3, unary_op_definition = '⊖a = { (((a⇼⇔∾a)⨳⩥⨓(a≦≮≮))∲⫓a) }', output=736029","layer":0}],"base":4,"result_base":4,"text":"⊖(⪝⪂⫅⪩⨒∯122011)=⪩⨒∯2303230131","reverse_text":"⪩⨒∯2303230131=⊖(⪝⪂⫅⪩⨒∯122011)","cot":[{"info":"⪝⪂⫅⪩⨒∯122011=⪩⨒∯-323321133","layer":1},{"info":"⊖⪩⨒∯-323321133=⪩⨒∯2303230131","layer":0}]}
{"id":704,"expression_no_base_symbol":"$1979$≳⇉$1328$⊉≛↸$5553$∑⇟⊟$1161$","expression":"⪩⨒∯132323≳⇉⪩⨒∯110300⊉≛↸⪩⨒∯1112301∑⇟⊟⪩⨒∯102021","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16355721,"operation_count":3,"complexity_ratio":5451907.0,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"binary","operator":"≳⇉","left_expr":{"type":"numeric_atoms","value":1979,"base":4},"right_expr":{"type":"numeric_atoms","value":1328,"base":4}},"right_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":5553,"base":4},"right_expr":{"type":"numeric_atoms","value":1161,"base":4}}},"used_operators":["DZ8iAZOCBD","V0kx6qeWkN","U7g4x0WXJJ"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1979","layer":2},{"info":"number node, value=1328","layer":2},{"info":"compute binary expreesion, left_input=1979, right_input=1328, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":1},{"info":"number node, value=5553","layer":2},{"info":"number node, value=1161","layer":2},{"info":"compute binary expreesion, left_input=5553, right_input=1161, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯132323≳⇉⪩⨒∯110300⊉≛↸⪩⨒∯1112301∑⇟⊟⪩⨒∯102021=NaN","reverse_text":"NaN=⪩⨒∯132323≳⇉⪩⨒∯110300⊉≛↸⪩⨒∯1112301∑⇟⊟⪩⨒∯102021","cot":[{"info":"⪩⨒∯132323≳⇉⪩⨒∯110300=NaN","layer":1},{"info":"⪩⨒∯1112301∑⇟⊟⪩⨒∯102021=NaN","layer":1},{"info":"NaN⊉≛↸NaN=NaN","layer":0}]}
{"id":705,"expression_no_base_symbol":"⊵⊁($3678$↬$1462$)","expression":"⊵⊁(⪩⨒∯321132↬⪩⨒∯112312)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2,"operation_count":2,"complexity_ratio":1.0,"tree":{"type":"unary","operator":"⊵⊁","unary_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":3678,"base":4},"right_expr":{"type":"numeric_atoms","value":1462,"base":4}}},"used_operators":["AvED76WdY7","B5M0gjZbta"],"dependent_operators":["uBihLCJcMX","k8jYdgA6NY","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3678","layer":2},{"info":"number node, value=1462","layer":2},{"info":"compute binary expreesion, left_input=3678, right_input=1462, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = AvED76WdY7, unary_op_definition = '⊵⊁a = { (a⇔⨋) , if a>58 ; (a%a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⊵⊁(⪩⨒∯321132↬⪩⨒∯112312)=NaN","reverse_text":"NaN=⊵⊁(⪩⨒∯321132↬⪩⨒∯112312)","cot":[{"info":"⪩⨒∯321132↬⪩⨒∯112312=NaN","layer":1},{"info":"⊵⊁NaN=NaN","layer":0}]}
{"id":706,"expression_no_base_symbol":"($2013$⇼⇔∾$6310$)∺≝⩲($1169$⨵⪆$4375$)","expression":"(⪩⨒∯133131⇼⇔∾⪩⨒∯1202212)∺≝⩲(⪩⨒∯102101⨵⪆⪩⨒∯1010113)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":12,"operation_count":3,"complexity_ratio":4.0,"tree":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":2013,"base":4},"right_expr":{"type":"numeric_atoms","value":6310,"base":4}},"right_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":1169,"base":4},"right_expr":{"type":"numeric_atoms","value":4375,"base":4}}},"used_operators":["KPf6cnQVty","tifHPKVTfV","2DQ55sFlQl"],"dependent_operators":["BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2013","layer":2},{"info":"number node, value=6310","layer":2},{"info":"compute binary expreesion, left_input=2013, right_input=6310, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=4297","layer":1},{"info":"number node, value=1169","layer":2},{"info":"number node, value=4375","layer":2},{"info":"compute binary expreesion, left_input=1169, right_input=4375, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"compute binary expreesion, left_input=4297, right_input=160, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯133131⇼⇔∾⪩⨒∯1202212)∺≝⩲(⪩⨒∯102101⨵⪆⪩⨒∯1010113)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⪩⨒∯133131⇼⇔∾⪩⨒∯1202212)∺≝⩲(⪩⨒∯102101⨵⪆⪩⨒∯1010113)","cot":[{"info":"⪩⨒∯133131⇼⇔∾⪩⨒∯1202212=⪩⨒∯1003021","layer":1},{"info":"⪩⨒∯102101⨵⪆⪩⨒∯1010113=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯1003021∺≝⩲⪩⨒∯2200=⪩⨒∯2200","layer":0}]}
{"id":707,"expression_no_base_symbol":"$1945$⪟⇏$6583$%(≀↧⇸$1072$)","expression":"⪩⨒∯132121⪟⇏⪩⨒∯1212313%(≀↧⇸⪩⨒∯100300)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":33,"operation_count":3,"complexity_ratio":11.0,"tree":{"type":"binary","operator":"%","left_expr":{"type":"binary","operator":"⪟⇏","left_expr":{"type":"numeric_atoms","value":1945,"base":4},"right_expr":{"type":"numeric_atoms","value":6583,"base":4}},"right_expr":{"type":"unary","operator":"≀↧⇸","unary_expr":{"type":"numeric_atoms","value":1072,"base":4}}},"used_operators":["k8jYdgA6NY","GODebY97qR","ljTHtUsqzn"],"dependent_operators":["rysDP5nf3Z","gx7XJ7hdpj","XnXgA4xnOs","wEfv7U73WA","2DQ55sFlQl","f6k1SAg4EE","oacrs7FA3X","XPYlsWDdGa","23Mk6UjR3U"],"result":"⪩⨒∯201133","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1945","layer":2},{"info":"number node, value=6583","layer":2},{"info":"compute binary expreesion, left_input=1945, right_input=6583, op_id = GODebY97qR binary_op_definition= 'a⪟⇏b = { ((b⨑≵⋬b)⫸⇳(440⪒a)) , if (b⇐≅)<189 ; ((219⨑≵⋬a)⪘⫢(b⨵⪆b)) , else }', output=-1","layer":1},{"info":"number node, value=1072","layer":2},{"info":"compute unary expreesion, input=1072, op_id = ljTHtUsqzn, unary_op_definition = '≀↧⇸a = { (⪲⇎(a⋷a)) }', output=2144","layer":1},{"info":"compute binary expreesion, left_input=-1, right_input=2144, op_id = k8jYdgA6NY binary_op_definition= 'None', output=2143","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯132121⪟⇏⪩⨒∯1212313%(≀↧⇸⪩⨒∯100300)=⪩⨒∯201133","reverse_text":"⪩⨒∯201133=⪩⨒∯132121⪟⇏⪩⨒∯1212313%(≀↧⇸⪩⨒∯100300)","cot":[{"info":"⪩⨒∯132121⪟⇏⪩⨒∯1212313=⪩⨒∯-1","layer":1},{"info":"≀↧⇸⪩⨒∯100300=⪩⨒∯201200","layer":1},{"info":"⪩⨒∯-1%⪩⨒∯201200=⪩⨒∯201133","layer":0}]}
{"id":708,"expression_no_base_symbol":"($5603$⩣⫁∢$2832$)↳≱(↡$1142$)","expression":"(⪩⨒∯1113203⩣⫁∢⪩⨒∯230100)↳≱(↡⪩⨒∯101312)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":122,"operation_count":3,"complexity_ratio":40.666666666666664,"tree":{"type":"binary","operator":"↳≱","left_expr":{"type":"binary","operator":"⩣⫁∢","left_expr":{"type":"numeric_atoms","value":5603,"base":4},"right_expr":{"type":"numeric_atoms","value":2832,"base":4}},"right_expr":{"type":"unary","operator":"↡","unary_expr":{"type":"numeric_atoms","value":1142,"base":4}}},"used_operators":["JwTKLfZU96","JDUIKTTSIa","MXaNJeIAZ3"],"dependent_operators":["DhbWaqg5eL","WR6HLWljOP","XhwjNDsVaA","T2fj7uvVaJ","7YooWSwCyH","B3sABdIn96","sdazOOVcIp","eewbuw0ToL","AF7qkfDlqP","u6S6b8DprG","DpFCA1CohY","23Mk6UjR3U","7j4O788W3g","8w2t5hMYqp","sdazOOVcIp","nCS4ZIUYfx"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5603","layer":2},{"info":"number node, value=2832","layer":2},{"info":"compute binary expreesion, left_input=5603, right_input=2832, op_id = JDUIKTTSIa binary_op_definition= 'a⩣⫁∢b = { (⨑⩽⪐((a⪨≂b)⨰(↽≂b))) }', output=-11045","layer":1},{"info":"number node, value=1142","layer":2},{"info":"compute unary expreesion, input=1142, op_id = MXaNJeIAZ3, unary_op_definition = '↡a = { (((772⨳⩥⨓159)⪨≂(a⋷a))↺(⊄⩳↩(⋗⩬⋾a))) }', output=10278","layer":1},{"info":"compute binary expreesion, left_input=-11045, right_input=10278, op_id = JwTKLfZU96 binary_op_definition= 'a↳≱b = { (((a∪⫐104)↢(147/b))⋓((+⊝⨔b)⪹)) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1113203⩣⫁∢⪩⨒∯230100)↳≱(↡⪩⨒∯101312)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯1113203⩣⫁∢⪩⨒∯230100)↳≱(↡⪩⨒∯101312)","cot":[{"info":"⪩⨒∯1113203⩣⫁∢⪩⨒∯230100=⪩⨒∯-2230211","layer":1},{"info":"↡⪩⨒∯101312=⪩⨒∯2200212","layer":1},{"info":"⪩⨒∯-2230211↳≱⪩⨒∯2200212=⪩⨒∯0","layer":0}]}
{"id":709,"expression_no_base_symbol":"⪝⪂⫅$1068$≦↸$3899$","expression":"⪝⪂⫅⪩⨒∯100230≦↸⪩⨒∯330323","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":171,"operation_count":2,"complexity_ratio":85.5,"tree":{"type":"unary","operator":"⪝⪂⫅","unary_expr":{"type":"binary","operator":"≦↸","left_expr":{"type":"numeric_atoms","value":1068,"base":4},"right_expr":{"type":"numeric_atoms","value":3899,"base":4}}},"used_operators":["XTarYq4gQB","RygbFNSyEJ"],"dependent_operators":["9HNa5Wba9A","8w2t5hMYqp","eLAdDNolq6","e1ybzncUwg","DZ8iAZOCBD","XIabStNQrY","12rbrZMWeM","2DDjHMKMc0","g55IO6H4Gj"],"result":"⪩⨒∯11030010333","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1068","layer":2},{"info":"number node, value=3899","layer":2},{"info":"compute binary expreesion, left_input=1068, right_input=3899, op_id = RygbFNSyEJ binary_op_definition= 'a≦↸b = { (((≤/a)⋳⪒(b⊉≛↸a))⋝⋈⪟((a⇋≉)⨸⪁(≉a))) }', output=-9253","layer":1},{"info":"compute unary expreesion, input=-9253, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=1360191","layer":0}],"base":4,"result_base":4,"text":"⪝⪂⫅⪩⨒∯100230≦↸⪩⨒∯330323=⪩⨒∯11030010333","reverse_text":"⪩⨒∯11030010333=⪝⪂⫅⪩⨒∯100230≦↸⪩⨒∯330323","cot":[{"info":"⪩⨒∯100230≦↸⪩⨒∯330323=⪩⨒∯-2100211","layer":1},{"info":"⪝⪂⫅⪩⨒∯-2100211=⪩⨒∯11030010333","layer":0}]}
{"id":710,"expression_no_base_symbol":"$4852$⩚⊴⇥$4261$⨑≵⋬$4079$∠⫱$1263$","expression":"⪩⨒∯1023310⩚⊴⇥⪩⨒∯1002211⨑≵⋬⪩⨒∯333233∠⫱⪩⨒∯103233","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":29,"operation_count":3,"complexity_ratio":9.666666666666666,"tree":{"type":"binary","operator":"⨑≵⋬","left_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":4852,"base":4},"right_expr":{"type":"numeric_atoms","value":4261,"base":4}},"right_expr":{"type":"binary","operator":"∠⫱","left_expr":{"type":"numeric_atoms","value":4079,"base":4},"right_expr":{"type":"numeric_atoms","value":1263,"base":4}}},"used_operators":["XnXgA4xnOs","NTOWxs364D","QvoQhV0rrE"],"dependent_operators":["eewbuw0ToL","AF7qkfDlqP","QMFrweE19q","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","eLAdDNolq6","DZ8iAZOCBD","7j4O788W3g","tifHPKVTfV","AF7qkfDlqP"],"result":"⪩⨒∯-31002311","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4852","layer":2},{"info":"number node, value=4261","layer":2},{"info":"compute binary expreesion, left_input=4852, right_input=4261, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-9234","layer":1},{"info":"number node, value=4079","layer":2},{"info":"number node, value=1263","layer":2},{"info":"compute binary expreesion, left_input=4079, right_input=1263, op_id = QvoQhV0rrE binary_op_definition= 'a∠⫱b = { ((⨑⩽⪐a)↺(617⊉≛↸a)) , if (≤/b)<=3 ; (b⇼⇔∾a) , else }', output=1234","layer":1},{"info":"compute binary expreesion, left_input=-9234, right_input=1234, op_id = XnXgA4xnOs binary_op_definition= 'a⨑≵⋬b = { ((a⨰b)⫡⨏(⨑⩽⪐b)) }', output=-53429","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1023310⩚⊴⇥⪩⨒∯1002211⨑≵⋬⪩⨒∯333233∠⫱⪩⨒∯103233=⪩⨒∯-31002311","reverse_text":"⪩⨒∯-31002311=⪩⨒∯1023310⩚⊴⇥⪩⨒∯1002211⨑≵⋬⪩⨒∯333233∠⫱⪩⨒∯103233","cot":[{"info":"⪩⨒∯1023310⩚⊴⇥⪩⨒∯1002211=⪩⨒∯-2100102","layer":1},{"info":"⪩⨒∯333233∠⫱⪩⨒∯103233=⪩⨒∯103102","layer":1},{"info":"⪩⨒∯-2100102⨑≵⋬⪩⨒∯103102=⪩⨒∯-31002311","layer":0}]}
{"id":711,"expression_no_base_symbol":"$1164$≦↸$2892$⫳≱↱$3269$⨜⨶$4934$","expression":"⪩⨒∯102030≦↸⪩⨒∯231030⫳≱↱⪩⨒∯303011⨜⨶⪩⨒∯1031012","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":96,"operation_count":3,"complexity_ratio":32.0,"tree":{"type":"binary","operator":"⫳≱↱","left_expr":{"type":"binary","operator":"≦↸","left_expr":{"type":"numeric_atoms","value":1164,"base":4},"right_expr":{"type":"numeric_atoms","value":2892,"base":4}},"right_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":3269,"base":4},"right_expr":{"type":"numeric_atoms","value":4934,"base":4}}},"used_operators":["ZvLB05nZmT","RygbFNSyEJ","HiPekx5b7W"],"dependent_operators":["2Wsdkap16l","FyVja0WsTP","wEfv7U73WA","bJkvcejdHO","HmxsFra2vL","8cLx32lpNA","eLAdDNolq6","e1ybzncUwg","DZ8iAZOCBD","XIabStNQrY","12rbrZMWeM","2DDjHMKMc0","g55IO6H4Gj","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"⪩⨒∯-223302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1164","layer":2},{"info":"number node, value=2892","layer":2},{"info":"compute binary expreesion, left_input=1164, right_input=2892, op_id = RygbFNSyEJ binary_op_definition= 'a≦↸b = { (((≤/a)⋳⪒(b⊉≛↸a))⋝⋈⪟((a⇋≉)⨸⪁(≉a))) }', output=-7431","layer":1},{"info":"number node, value=3269","layer":2},{"info":"number node, value=4934","layer":2},{"info":"compute binary expreesion, left_input=3269, right_input=4934, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-9612","layer":1},{"info":"compute binary expreesion, left_input=-7431, right_input=-9612, op_id = ZvLB05nZmT binary_op_definition= 'a⫳≱↱b = { (((a⩹b)⇐≅)∌((a∙∹∝345)⊱⇼⊻(b≎⊠⪸a))) }', output=-2802","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102030≦↸⪩⨒∯231030⫳≱↱⪩⨒∯303011⨜⨶⪩⨒∯1031012=⪩⨒∯-223302","reverse_text":"⪩⨒∯-223302=⪩⨒∯102030≦↸⪩⨒∯231030⫳≱↱⪩⨒∯303011⨜⨶⪩⨒∯1031012","cot":[{"info":"⪩⨒∯102030≦↸⪩⨒∯231030=⪩⨒∯-1310013","layer":1},{"info":"⪩⨒∯303011⨜⨶⪩⨒∯1031012=⪩⨒∯-2112030","layer":1},{"info":"⪩⨒∯-1310013⫳≱↱⪩⨒∯-2112030=⪩⨒∯-223302","layer":0}]}
{"id":712,"expression_no_base_symbol":"(∓⪦$4223$)/$8609$⋻⩜⩜$2176$","expression":"(∓⪦⪩⨒∯1001333)/⪩⨒∯2012201⋻⩜⩜⪩⨒∯202000","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":30498,"operation_count":3,"complexity_ratio":10166.0,"tree":{"type":"binary","operator":"/","left_expr":{"type":"unary","operator":"∓⪦","unary_expr":{"type":"numeric_atoms","value":4223,"base":4}},"right_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":8609,"base":4},"right_expr":{"type":"numeric_atoms","value":2176,"base":4}}},"used_operators":["XhwjNDsVaA","D309nIvmXG","oDCm7WA9JY"],"dependent_operators":["rysDP5nf3Z","P8v4zCKN1o","sdazOOVcIp","Ph9nP6C5qx","eewbuw0ToL","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4223","layer":2},{"info":"compute unary expreesion, input=4223, op_id = D309nIvmXG, unary_op_definition = '∓⪦a = { (((a≧⫂∧a)⨰(a⨰a))⨰(∥⊫(343⪨≂a))) }', output=3815","layer":1},{"info":"number node, value=8609","layer":2},{"info":"number node, value=2176","layer":2},{"info":"compute binary expreesion, left_input=8609, right_input=2176, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=17218","layer":1},{"info":"compute binary expreesion, left_input=3815, right_input=17218, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":0}],"base":4,"result_base":4,"text":"(∓⪦⪩⨒∯1001333)/⪩⨒∯2012201⋻⩜⩜⪩⨒∯202000=⪩⨒∯0","reverse_text":"⪩⨒∯0=(∓⪦⪩⨒∯1001333)/⪩⨒∯2012201⋻⩜⩜⪩⨒∯202000","cot":[{"info":"∓⪦⪩⨒∯1001333=⪩⨒∯323213","layer":1},{"info":"⪩⨒∯2012201⋻⩜⩜⪩⨒∯202000=⪩⨒∯10031002","layer":1},{"info":"⪩⨒∯323213/⪩⨒∯10031002=⪩⨒∯0","layer":0}]}
{"id":713,"expression_no_base_symbol":"($3057$⨁⊸⫻)⫃⨇$1073$⋣⋖$3248$","expression":"(⪩⨒∯233301⨁⊸⫻)⫃⨇⪩⨒∯100301⋣⋖⪩⨒∯302300","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":14,"operation_count":3,"complexity_ratio":4.666666666666667,"tree":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"unary","operator":"⨁⊸⫻","unary_expr":{"type":"numeric_atoms","value":3057,"base":4}},"right_expr":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"numeric_atoms","value":1073,"base":4},"right_expr":{"type":"numeric_atoms","value":3248,"base":4}}},"used_operators":["09Ly4LVMIf","glklzrTFfD","J0M6qkBnIM"],"dependent_operators":["9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG","W4YGzv6Whe","rysDP5nf3Z","VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2"],"result":"⪩⨒∯-1003210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3057","layer":2},{"info":"compute unary expreesion, input=3057, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=3057","layer":1},{"info":"number node, value=1073","layer":2},{"info":"number node, value=3248","layer":2},{"info":"compute binary expreesion, left_input=1073, right_input=3248, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=1073","layer":1},{"info":"compute binary expreesion, left_input=3057, right_input=1073, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=-4324","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯233301⨁⊸⫻)⫃⨇⪩⨒∯100301⋣⋖⪩⨒∯302300=⪩⨒∯-1003210","reverse_text":"⪩⨒∯-1003210=(⪩⨒∯233301⨁⊸⫻)⫃⨇⪩⨒∯100301⋣⋖⪩⨒∯302300","cot":[{"info":"⪩⨒∯233301⨁⊸⫻=⪩⨒∯233301","layer":1},{"info":"⪩⨒∯100301⋣⋖⪩⨒∯302300=⪩⨒∯100301","layer":1},{"info":"⪩⨒∯233301⫃⨇⪩⨒∯100301=⪩⨒∯-1003210","layer":0}]}
{"id":714,"expression_no_base_symbol":"($2279$∣$1490$)⋕⪉⪜($1662$⪇≇⋚$1424$)","expression":"(⪩⨒∯203213∣⪩⨒∯113102)⋕⪉⪜(⪩⨒∯121332⪇≇⋚⪩⨒∯112100)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":39,"operation_count":3,"complexity_ratio":13.0,"tree":{"type":"binary","operator":"⋕⪉⪜","left_expr":{"type":"binary","operator":"∣","left_expr":{"type":"numeric_atoms","value":2279,"base":4},"right_expr":{"type":"numeric_atoms","value":1490,"base":4}},"right_expr":{"type":"binary","operator":"⪇≇⋚","left_expr":{"type":"numeric_atoms","value":1662,"base":4},"right_expr":{"type":"numeric_atoms","value":1424,"base":4}}},"used_operators":["z6LnFrNh4i","PPChnnnBFF","3sJ7IOPOlU"],"dependent_operators":["sJAwomhLZr","FyVja0WsTP","rysDP5nf3Z","eLAdDNolq6","eH2TOUuTDT","Ph9nP6C5qx","i8ToyICDmI","DZ8iAZOCBD","JLbD19bQDL","xUOZtlo3hN"],"result":"⪩⨒∯223302","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2279","layer":2},{"info":"number node, value=1490","layer":2},{"info":"compute binary expreesion, left_input=2279, right_input=1490, op_id = PPChnnnBFF binary_op_definition= 'a∣b = { (≤/((a⪐)≧⫂∧(a∲⫓b))) , if (b⪐)<590 ; a , else }', output=2279","layer":1},{"info":"number node, value=1662","layer":2},{"info":"number node, value=1424","layer":2},{"info":"compute binary expreesion, left_input=1662, right_input=1424, op_id = 3sJ7IOPOlU binary_op_definition= 'a⪇≇⋚b = { ((⨞⊢(a⊉≛↸b))⪠⩆⊳) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=2279, right_input=0, op_id = z6LnFrNh4i binary_op_definition= 'a⋕⪉⪜b = { ((648⩠)⊱⇼⊻(b-a)) }', output=2802","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯203213∣⪩⨒∯113102)⋕⪉⪜(⪩⨒∯121332⪇≇⋚⪩⨒∯112100)=⪩⨒∯223302","reverse_text":"⪩⨒∯223302=(⪩⨒∯203213∣⪩⨒∯113102)⋕⪉⪜(⪩⨒∯121332⪇≇⋚⪩⨒∯112100)","cot":[{"info":"⪩⨒∯203213∣⪩⨒∯113102=⪩⨒∯203213","layer":1},{"info":"⪩⨒∯121332⪇≇⋚⪩⨒∯112100=⪩⨒∯0","layer":1},{"info":"⪩⨒∯203213⋕⪉⪜⪩⨒∯0=⪩⨒∯223302","layer":0}]}
{"id":715,"expression_no_base_symbol":"$1611$⋅⇍$5124$⋻⩜⩜$1151$⨓$4943$","expression":"⪩⨒∯121023⋅⇍⪩⨒∯1100010⋻⩜⩜⪩⨒∯101333⨓⪩⨒∯1031033","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":74203,"operation_count":3,"complexity_ratio":24734.333333333332,"tree":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":1611,"base":4},"right_expr":{"type":"numeric_atoms","value":5124,"base":4}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":1151,"base":4},"right_expr":{"type":"numeric_atoms","value":4943,"base":4}}},"used_operators":["oDCm7WA9JY","AdZkA7nFnk","3ViojmjbAp"],"dependent_operators":["mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⪩⨒∯-230","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1611","layer":2},{"info":"number node, value=5124","layer":2},{"info":"compute binary expreesion, left_input=1611, right_input=5124, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"number node, value=1151","layer":2},{"info":"number node, value=4943","layer":2},{"info":"compute binary expreesion, left_input=1151, right_input=4943, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-4946","layer":1},{"info":"compute binary expreesion, left_input=-22, right_input=-4946, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=-44","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯121023⋅⇍⪩⨒∯1100010⋻⩜⩜⪩⨒∯101333⨓⪩⨒∯1031033=⪩⨒∯-230","reverse_text":"⪩⨒∯-230=⪩⨒∯121023⋅⇍⪩⨒∯1100010⋻⩜⩜⪩⨒∯101333⨓⪩⨒∯1031033","cot":[{"info":"⪩⨒∯121023⋅⇍⪩⨒∯1100010=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯101333⨓⪩⨒∯1031033=⪩⨒∯-1031102","layer":1},{"info":"⪩⨒∯-112⋻⩜⩜⪩⨒∯-1031102=⪩⨒∯-230","layer":0}]}
{"id":716,"expression_no_base_symbol":"$2013$⊱⇼⊻$1686$⇼⇔∾$5181$∝$1379$","expression":"⪩⨒∯133131⊱⇼⊻⪩⨒∯122112⇼⇔∾⪩⨒∯1100331∝⪩⨒∯111203","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19,"operation_count":3,"complexity_ratio":6.333333333333333,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"numeric_atoms","value":2013,"base":4},"right_expr":{"type":"numeric_atoms","value":1686,"base":4}},"right_expr":{"type":"binary","operator":"∝","left_expr":{"type":"numeric_atoms","value":5181,"base":4},"right_expr":{"type":"numeric_atoms","value":1379,"base":4}}},"used_operators":["tifHPKVTfV","FyVja0WsTP","cTDWOvIxvz"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","7j4O788W3g","W4YGzv6Whe","COABgblf1C"],"result":"⪩⨒∯1022100","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2013","layer":2},{"info":"number node, value=1686","layer":2},{"info":"compute binary expreesion, left_input=2013, right_input=1686, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":1},{"info":"number node, value=5181","layer":2},{"info":"number node, value=1379","layer":2},{"info":"compute binary expreesion, left_input=5181, right_input=1379, op_id = cTDWOvIxvz binary_op_definition= 'a∝b = { ((b↺a)+(b⊭↱b)) }', output=5186","layer":1},{"info":"compute binary expreesion, left_input=434, right_input=5186, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=4752","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯133131⊱⇼⊻⪩⨒∯122112⇼⇔∾⪩⨒∯1100331∝⪩⨒∯111203=⪩⨒∯1022100","reverse_text":"⪩⨒∯1022100=⪩⨒∯133131⊱⇼⊻⪩⨒∯122112⇼⇔∾⪩⨒∯1100331∝⪩⨒∯111203","cot":[{"info":"⪩⨒∯133131⊱⇼⊻⪩⨒∯122112=⪩⨒∯12302","layer":1},{"info":"⪩⨒∯1100331∝⪩⨒∯111203=⪩⨒∯1101002","layer":1},{"info":"⪩⨒∯12302⇼⇔∾⪩⨒∯1101002=⪩⨒∯1022100","layer":0}]}
{"id":717,"expression_no_base_symbol":"($2783$⇍⊗$2374$)⊧↖","expression":"(⪩⨒∯223133⇍⊗⪩⨒∯211012)⊧↖","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":332,"operation_count":2,"complexity_ratio":166.0,"tree":{"type":"unary","operator":"⊧↖","unary_expr":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"numeric_atoms","value":2783,"base":4},"right_expr":{"type":"numeric_atoms","value":2374,"base":4}}},"used_operators":["EKiFHuOFxO","5uvYHDjeKN"],"dependent_operators":["5twsqlHp2o","dfKe02y8D2","8HhzD0ZcuI","Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o"],"result":"⪩⨒∯1112021300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2783","layer":2},{"info":"number node, value=2374","layer":2},{"info":"compute binary expreesion, left_input=2783, right_input=2374, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=-244","layer":1},{"info":"compute unary expreesion, input=-244, op_id = EKiFHuOFxO, unary_op_definition = 'a⊧↖ = { ((a⨽a)⊢(a⫚↹⊑79)) }', output=352880","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯223133⇍⊗⪩⨒∯211012)⊧↖=⪩⨒∯1112021300","reverse_text":"⪩⨒∯1112021300=(⪩⨒∯223133⇍⊗⪩⨒∯211012)⊧↖","cot":[{"info":"⪩⨒∯223133⇍⊗⪩⨒∯211012=⪩⨒∯-3310","layer":1},{"info":"⪩⨒∯-3310⊧↖=⪩⨒∯1112021300","layer":0}]}
{"id":718,"expression_no_base_symbol":"(⋗⩬⋾$9129$)≬⋮($2449$⫲)","expression":"(⋗⩬⋾⪩⨒∯2032221)≬⋮(⪩⨒∯212101⫲)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":30,"operation_count":3,"complexity_ratio":10.0,"tree":{"type":"binary","operator":"≬⋮","left_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":9129,"base":4}},"right_expr":{"type":"unary","operator":"⫲","unary_expr":{"type":"numeric_atoms","value":2449,"base":4}}},"used_operators":["kbkesczE7y","DpFCA1CohY","9xnGDUPbC6"],"dependent_operators":["P8v4zCKN1o","rysDP5nf3Z","7j4O788W3g","XIabStNQrY","t8gj7n24qd","i8ToyICDmI","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","NTOWxs364D","Qy55tPpLXF","DZ8iAZOCBD","8w2t5hMYqp","2DDjHMKMc0","AF7qkfDlqP"],"result":"⪩⨒∯31210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=9129","layer":2},{"info":"compute unary expreesion, input=9129, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-27387","layer":1},{"info":"number node, value=2449","layer":2},{"info":"compute unary expreesion, input=2449, op_id = 9xnGDUPbC6, unary_op_definition = 'a⫲ = { ((272⩚⊴⇥36)⊉≛↸(⨑⩽⪐a)) , if (⊄⩳↩a)<13 ; ((a⩚⊴⇥a)⋝⋈⪟(533⋥≓≎a)) , else }', output=2176","layer":1},{"info":"compute binary expreesion, left_input=-27387, right_input=2176, op_id = kbkesczE7y binary_op_definition= 'a≬⋮b = { (((-a)∲⫓(b⇋≉))↺(∥⊫(b-b))) }', output=868","layer":0}],"base":4,"result_base":4,"text":"(⋗⩬⋾⪩⨒∯2032221)≬⋮(⪩⨒∯212101⫲)=⪩⨒∯31210","reverse_text":"⪩⨒∯31210=(⋗⩬⋾⪩⨒∯2032221)≬⋮(⪩⨒∯212101⫲)","cot":[{"info":"⋗⩬⋾⪩⨒∯2032221=⪩⨒∯-12223323","layer":1},{"info":"⪩⨒∯212101⫲=⪩⨒∯202000","layer":1},{"info":"⪩⨒∯-12223323≬⋮⪩⨒∯202000=⪩⨒∯31210","layer":0}]}
{"id":719,"expression_no_base_symbol":"$2661$⫦⪉$2763$⫔⩽⩺(⇖$4528$)","expression":"⪩⨒∯221211⫦⪉⪩⨒∯223023⫔⩽⩺(⇖⪩⨒∯1012300)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":28128,"operation_count":3,"complexity_ratio":9376.0,"tree":{"type":"binary","operator":"⫔⩽⩺","left_expr":{"type":"binary","operator":"⫦⪉","left_expr":{"type":"numeric_atoms","value":2661,"base":4},"right_expr":{"type":"numeric_atoms","value":2763,"base":4}},"right_expr":{"type":"unary","operator":"⇖","unary_expr":{"type":"numeric_atoms","value":4528,"base":4}}},"used_operators":["i9eR4S00cU","wscyQdcy20","tfWHHpNKUN"],"dependent_operators":["Tw270M8GLb","fu6greOZ01","W4YGzv6Whe","B3sABdIn96","9HNa5Wba9A","g7Hmc5v1ko","nREPSIbpBE","D3AQDKkPcf","2DQ55sFlQl"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2661","layer":2},{"info":"number node, value=2763","layer":2},{"info":"compute binary expreesion, left_input=2661, right_input=2763, op_id = wscyQdcy20 binary_op_definition= 'a⫦⪉b = { ((a⩌⋺206)⪹) , if (a∷677)>=23 ; ((b+a)*(b⨚b)) , else }', output=-422","layer":1},{"info":"number node, value=4528","layer":2},{"info":"compute unary expreesion, input=4528, op_id = tfWHHpNKUN, unary_op_definition = '⇖a = { (221⨵⪆a) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=-422, right_input=160, op_id = i9eR4S00cU binary_op_definition= 'a⫔⩽⩺b = { (⨰⫟⨤(a⨐⩸⫘b)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯221211⫦⪉⪩⨒∯223023⫔⩽⩺(⇖⪩⨒∯1012300)=NaN","reverse_text":"NaN=⪩⨒∯221211⫦⪉⪩⨒∯223023⫔⩽⩺(⇖⪩⨒∯1012300)","cot":[{"info":"⪩⨒∯221211⫦⪉⪩⨒∯223023=⪩⨒∯-12212","layer":1},{"info":"⇖⪩⨒∯1012300=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯-12212⫔⩽⩺⪩⨒∯2200=NaN","layer":0}]}
{"id":720,"expression_no_base_symbol":"⩩($1564$⫣⪄⊒$2001$)","expression":"⩩(⪩⨒∯120130⫣⪄⊒⪩⨒∯133101)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":10354,"operation_count":2,"complexity_ratio":5177.0,"tree":{"type":"unary","operator":"⩩","unary_expr":{"type":"binary","operator":"⫣⪄⊒","left_expr":{"type":"numeric_atoms","value":1564,"base":4},"right_expr":{"type":"numeric_atoms","value":2001,"base":4}}},"used_operators":["kMhfGuqI2H","RabNbG55vr"],"dependent_operators":["6aG7x05OhS","z63VuFQld9","lFBm8KRb8F","f6k1SAg4EE","ZGCBLdVRRX","NTOWxs364D","DbCuESL50I","fOIeswaMU4","g7Hmc5v1ko","KPf6cnQVty","j9kHMeSvPp","k8jYdgA6NY","2DDjHMKMc0","8WDwsbhb0R","cTDWOvIxvz","IWmyXbctLI"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1564","layer":2},{"info":"number node, value=2001","layer":2},{"info":"compute binary expreesion, left_input=1564, right_input=2001, op_id = RabNbG55vr binary_op_definition= 'a⫣⪄⊒b = { ((a⪮%⊝(153⪭a))%(⋼∭⪍(b⩚⊴⇥34))) , if b>769 ; ((∂⩏⊆(b⩟))∺≝⩲((b∝a)⋝⋈⪟(a⩌⋺b))) , else }', output=-9390","layer":1},{"info":"compute unary expreesion, input=-9390, op_id = kMhfGuqI2H, unary_op_definition = '⩩a = { (⇜(a⫩)) , if (⇵⪽a)!=444 ; ((a⪒a)∧) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⩩(⪩⨒∯120130⫣⪄⊒⪩⨒∯133101)=NaN","reverse_text":"NaN=⩩(⪩⨒∯120130⫣⪄⊒⪩⨒∯133101)","cot":[{"info":"⪩⨒∯120130⫣⪄⊒⪩⨒∯133101=⪩⨒∯-2102232","layer":1},{"info":"⩩⪩⨒∯-2102232=NaN","layer":0}]}
{"id":721,"expression_no_base_symbol":"(⋗⩴⪓$1021$)⩹$1714$⪘⫢$1214$","expression":"(⋗⩴⪓⪩⨒∯33331)⩹⪩⨒∯122302⪘⫢⪩⨒∯102332","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1092,"operation_count":3,"complexity_ratio":364.0,"tree":{"type":"binary","operator":"⩹","left_expr":{"type":"unary","operator":"⋗⩴⪓","unary_expr":{"type":"numeric_atoms","value":1021,"base":4}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1714,"base":4},"right_expr":{"type":"numeric_atoms","value":1214,"base":4}}},"used_operators":["2Wsdkap16l","nOKPl9n5zu","oacrs7FA3X"],"dependent_operators":["rysDP5nf3Z","NTOWxs364D","23Mk6UjR3U","XIabStNQrY","2DDjHMKMc0","12rbrZMWeM","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx","Qtd6bqUJcN","tifHPKVTfV","tmPS8pqC7x","jLgFTUHLKL","wztAlM01eG","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⪩⨒∯303212","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1021","layer":2},{"info":"compute unary expreesion, input=1021, op_id = nOKPl9n5zu, unary_op_definition = '⋗⩴⪓a = { (↩a) , if (↸⊣a)>=41 ; (a⇼⇔∾(≪(a⨪↰⇹a))) , else }', output=-108","layer":1},{"info":"number node, value=1714","layer":2},{"info":"number node, value=1214","layer":2},{"info":"compute binary expreesion, left_input=1714, right_input=1214, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=3304","layer":1},{"info":"compute binary expreesion, left_input=-108, right_input=3304, op_id = 2Wsdkap16l binary_op_definition= 'a⩹b = { (b-((b⨳⩥⨓b)⨸⪁(1⋝⋈⪟b))) , if (b⇋≉)!=246 ; (((a⇋≉)⨰(a⋷a))⋳⪒((a⩚⊴⇥a)⨳⩥⨓(a≧⫂∧a))) , else }', output=3302","layer":0}],"base":4,"result_base":4,"text":"(⋗⩴⪓⪩⨒∯33331)⩹⪩⨒∯122302⪘⫢⪩⨒∯102332=⪩⨒∯303212","reverse_text":"⪩⨒∯303212=(⋗⩴⪓⪩⨒∯33331)⩹⪩⨒∯122302⪘⫢⪩⨒∯102332","cot":[{"info":"⋗⩴⪓⪩⨒∯33331=⪩⨒∯-1230","layer":1},{"info":"⪩⨒∯122302⪘⫢⪩⨒∯102332=⪩⨒∯303220","layer":1},{"info":"⪩⨒∯-1230⩹⪩⨒∯303220=⪩⨒∯303212","layer":0}]}
{"id":722,"expression_no_base_symbol":"(⊁⨺$1925$)⇻⋧≁$5848$⪝$2472$","expression":"(⊁⨺⪩⨒∯132011)⇻⋧≁⪩⨒∯1123120⪝⪩⨒∯212220","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":605,"operation_count":3,"complexity_ratio":201.66666666666666,"tree":{"type":"binary","operator":"⇻⋧≁","left_expr":{"type":"unary","operator":"⊁⨺","unary_expr":{"type":"numeric_atoms","value":1925,"base":4}},"right_expr":{"type":"binary","operator":"⪝","left_expr":{"type":"numeric_atoms","value":5848,"base":4},"right_expr":{"type":"numeric_atoms","value":2472,"base":4}}},"used_operators":["jCPkEVoL5K","PxiHyQbrIp","wicAB68Tmb"],"dependent_operators":["eLxqMNBOBk","XnXgA4xnOs","3EYGwJThht","XTarYq4gQB","59igzFyhWz","dfKe02y8D2","X99M06cbEe","rysDP5nf3Z","e1ybzncUwg","XPYlsWDdGa","23Mk6UjR3U","7j4O788W3g","2td37pGCOC","2DQ55sFlQl","xUOZtlo3hN","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1925","layer":2},{"info":"compute unary expreesion, input=1925, op_id = PxiHyQbrIp, unary_op_definition = '⊁⨺a = { (((⨞⊢a)⋷(3↺a))⨵⪆((⪲⇎a)-(≉a))) , if a>5 ; (((a↺a)⨳⩥⨓(⩦⩻⨪a))⨳⩥⨓((a∲⫓a)⫡⨏(≉a))) , else }', output=160","layer":1},{"info":"number node, value=5848","layer":2},{"info":"number node, value=2472","layer":2},{"info":"compute binary expreesion, left_input=5848, right_input=2472, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=-13903","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=-13903, op_id = jCPkEVoL5K binary_op_definition= 'a⇻⋧≁b = { ((⫓⪴a)⫚↹⊑(54≫≃)) , if (a∵≐)<=35 or a>411 ; ((⪝⪂⫅b)⇄(290⨑≵⋬a)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⊁⨺⪩⨒∯132011)⇻⋧≁⪩⨒∯1123120⪝⪩⨒∯212220=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⊁⨺⪩⨒∯132011)⇻⋧≁⪩⨒∯1123120⪝⪩⨒∯212220","cot":[{"info":"⊁⨺⪩⨒∯132011=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯1123120⪝⪩⨒∯212220=⪩⨒∯-3121033","layer":1},{"info":"⪩⨒∯2200⇻⋧≁⪩⨒∯-3121033=⪩⨒∯0","layer":0}]}
{"id":723,"expression_no_base_symbol":"($5823$⨭⪣$4408$)⨱∎","expression":"(⪩⨒∯1122333⨭⪣⪩⨒∯1010320)⨱∎","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":35,"operation_count":2,"complexity_ratio":17.5,"tree":{"type":"unary","operator":"⨱∎","unary_expr":{"type":"binary","operator":"⨭⪣","left_expr":{"type":"numeric_atoms","value":5823,"base":4},"right_expr":{"type":"numeric_atoms","value":4408,"base":4}}},"used_operators":["MmTdOpaElr","kn8WO9XteQ"],"dependent_operators":["tifHPKVTfV","vRio1gEz1j","61wBmkZwlr","SWo3A1KBJH","8jW3W4yZS5","LkLIoiE525","Y7wcNGrDQJ","PPChnnnBFF"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5823","layer":2},{"info":"number node, value=4408","layer":2},{"info":"compute binary expreesion, left_input=5823, right_input=4408, op_id = kn8WO9XteQ binary_op_definition= 'a⨭⪣b = { ((486⇩)⩵∡(a∣a)) , if (b⇯⋐)>445 or (≋b)>319 or b<=69 ; (↯⪼(⇋↷b)) , else }', output=4544","layer":1},{"info":"compute unary expreesion, input=4544, op_id = MmTdOpaElr, unary_op_definition = 'a⨱∎ = { (a⇼⇔∾a) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1122333⨭⪣⪩⨒∯1010320)⨱∎=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯1122333⨭⪣⪩⨒∯1010320)⨱∎","cot":[{"info":"⪩⨒∯1122333⨭⪣⪩⨒∯1010320=⪩⨒∯1013000","layer":1},{"info":"⪩⨒∯1013000⨱∎=⪩⨒∯0","layer":0}]}
{"id":724,"expression_no_base_symbol":"($4734$⇚⪠)⩺⪪$1190$⊝⪿⪼$1890$","expression":"(⪩⨒∯1021332⇚⪠)⩺⪪⪩⨒∯102212⊝⪿⪼⪩⨒∯131202","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4898,"operation_count":3,"complexity_ratio":1632.6666666666667,"tree":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"unary","operator":"⇚⪠","unary_expr":{"type":"numeric_atoms","value":4734,"base":4}},"right_expr":{"type":"binary","operator":"⊝⪿⪼","left_expr":{"type":"numeric_atoms","value":1190,"base":4},"right_expr":{"type":"numeric_atoms","value":1890,"base":4}}},"used_operators":["uvdQJvN4PV","Loh9y4A90B","3Oe9XWJUTD"],"dependent_operators":["Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U","Z5m6OM72h2","9HNa5Wba9A","ztP7wcbY7m","NTOWxs364D","Qy55tPpLXF","8w2t5hMYqp","t8gj7n24qd","eewbuw0ToL","QMFrweE19q"],"result":"⪩⨒∯-222231333232202","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4734","layer":2},{"info":"compute unary expreesion, input=4734, op_id = Loh9y4A90B, unary_op_definition = 'a⇚⪠ = { ((a∘(a∈))*a) }', output=44821512","layer":1},{"info":"number node, value=1190","layer":2},{"info":"number node, value=1890","layer":2},{"info":"compute binary expreesion, left_input=1190, right_input=1890, op_id = 3Oe9XWJUTD binary_op_definition= 'a⊝⪿⪼b = { ((⊄⩳↩(480⩚⊴⇥a))⫡⨏((a⨰b)⋥≓≎(-b))) }', output=27782","layer":1},{"info":"compute binary expreesion, left_input=44821512, right_input=27782, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=-716700578","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1021332⇚⪠)⩺⪪⪩⨒∯102212⊝⪿⪼⪩⨒∯131202=⪩⨒∯-222231333232202","reverse_text":"⪩⨒∯-222231333232202=(⪩⨒∯1021332⇚⪠)⩺⪪⪩⨒∯102212⊝⪿⪼⪩⨒∯131202","cot":[{"info":"⪩⨒∯1021332⇚⪠=⪩⨒∯2222332300020","layer":1},{"info":"⪩⨒∯102212⊝⪿⪼⪩⨒∯131202=⪩⨒∯12302012","layer":1},{"info":"⪩⨒∯2222332300020⩺⪪⪩⨒∯12302012=⪩⨒∯-222231333232202","layer":0}]}
{"id":725,"expression_no_base_symbol":"(∤$2280$)⇄(⫟$2406$)","expression":"(∤⪩⨒∯203220)⇄(⫟⪩⨒∯211212)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":49,"operation_count":3,"complexity_ratio":16.333333333333332,"tree":{"type":"binary","operator":"⇄","left_expr":{"type":"unary","operator":"∤","unary_expr":{"type":"numeric_atoms","value":2280,"base":4}},"right_expr":{"type":"unary","operator":"⫟","unary_expr":{"type":"numeric_atoms","value":2406,"base":4}}},"used_operators":["3EYGwJThht","k2HlF1dBQh","z4E1FaHLuy"],"dependent_operators":["eLAdDNolq6","DZ8iAZOCBD","i8ToyICDmI","W4YGzv6Whe","rysDP5nf3Z","tifHPKVTfV","8w2t5hMYqp","9FxExcQeMw","W4YGzv6Whe","Qy55tPpLXF","BjRHVeLaeN","sdazOOVcIp","Ph9nP6C5qx","t8gj7n24qd","EBcxylXtPf","f6k1SAg4EE","2DDjHMKMc0","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx","QMFrweE19q"],"result":"⪩⨒∯1222023","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2280","layer":2},{"info":"compute unary expreesion, input=2280, op_id = k2HlF1dBQh, unary_op_definition = '∤a = { (((a⇼⇔∾a)+(a-a))-(⊄⩳↩3)) }', output=9","layer":1},{"info":"number node, value=2406","layer":2},{"info":"compute unary expreesion, input=2406, op_id = z4E1FaHLuy, unary_op_definition = '⫟a = { (((-a)⪨≂(a⨸⪁a))≧⫂∧((a⩷∴a)⨰(a⫡⨏a))) , if (a⫌⩹⨱)>=11 ; (((a+263)⋝⋈⪟(a⨳⩥⨓a))⪒((a⋥≓≎a)⫩⊇)) , else }', output=-6311","layer":1},{"info":"compute binary expreesion, left_input=9, right_input=-6311, op_id = 3EYGwJThht binary_op_definition= 'a⇄b = { ((≤/b)∲⫓(a⊉≛↸b)) }', output=6795","layer":0}],"base":4,"result_base":4,"text":"(∤⪩⨒∯203220)⇄(⫟⪩⨒∯211212)=⪩⨒∯1222023","reverse_text":"⪩⨒∯1222023=(∤⪩⨒∯203220)⇄(⫟⪩⨒∯211212)","cot":[{"info":"∤⪩⨒∯203220=⪩⨒∯21","layer":1},{"info":"⫟⪩⨒∯211212=⪩⨒∯-1202213","layer":1},{"info":"⪩⨒∯21⇄⪩⨒∯-1202213=⪩⨒∯1222023","layer":0}]}
{"id":726,"expression_no_base_symbol":"(⫵↿$3547$)⫉⨲⊜($2165$+⪬∐$2101$)","expression":"(⫵↿⪩⨒∯313123)⫉⨲⊜(⪩⨒∯201311+⪬∐⪩⨒∯200311)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":36,"operation_count":3,"complexity_ratio":12.0,"tree":{"type":"binary","operator":"⫉⨲⊜","left_expr":{"type":"unary","operator":"⫵↿","unary_expr":{"type":"numeric_atoms","value":3547,"base":4}},"right_expr":{"type":"binary","operator":"+⪬∐","left_expr":{"type":"numeric_atoms","value":2165,"base":4},"right_expr":{"type":"numeric_atoms","value":2101,"base":4}}},"used_operators":["WhqkvtTD3t","ivGwdmUAux","2GS7woTJqF"],"dependent_operators":["eewbuw0ToL","zVYPLywUTj","LXhwmt4mBO","09Ly4LVMIf","LRNGc0VcxI","y4ImoPnbV5","8jW3W4yZS5","G9tJMlZ94a","g55IO6H4Gj","D4vGDi5EA2"],"result":"⪩⨒∯-1213031","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3547","layer":2},{"info":"compute unary expreesion, input=3547, op_id = ivGwdmUAux, unary_op_definition = '⫵↿a = { ((a⫃⨇256)∽(a∀⇚≩66)) , if (⇨a)>=1 ; (↯⪼(a⨫⇇↔a)) , else }', output=137","layer":1},{"info":"number node, value=2165","layer":2},{"info":"number node, value=2101","layer":2},{"info":"compute binary expreesion, left_input=2165, right_input=2101, op_id = 2GS7woTJqF binary_op_definition= 'a+⪬∐b = { (a≦≮≮) , if b!=63 ; (b⨸⪁575) , else }', output=-6495","layer":1},{"info":"compute binary expreesion, left_input=137, right_input=-6495, op_id = WhqkvtTD3t binary_op_definition= 'a⫉⨲⊜b = { (b⨰120) , if b<=7 ; (a⊪) , else }', output=-6605","layer":0}],"base":4,"result_base":4,"text":"(⫵↿⪩⨒∯313123)⫉⨲⊜(⪩⨒∯201311+⪬∐⪩⨒∯200311)=⪩⨒∯-1213031","reverse_text":"⪩⨒∯-1213031=(⫵↿⪩⨒∯313123)⫉⨲⊜(⪩⨒∯201311+⪬∐⪩⨒∯200311)","cot":[{"info":"⫵↿⪩⨒∯313123=⪩⨒∯2021","layer":1},{"info":"⪩⨒∯201311+⪬∐⪩⨒∯200311=⪩⨒∯-1211133","layer":1},{"info":"⪩⨒∯2021⫉⨲⊜⪩⨒∯-1211133=⪩⨒∯-1213031","layer":0}]}
{"id":727,"expression_no_base_symbol":"(≻⋜$3485$)⨽$1435$≴⪞⇿$3126$","expression":"(≻⋜⪩⨒∯312131)⨽⪩⨒∯112123≴⪞⇿⪩⨒∯300312","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19171,"operation_count":3,"complexity_ratio":6390.333333333333,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"unary","operator":"≻⋜","unary_expr":{"type":"numeric_atoms","value":3485,"base":4}},"right_expr":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"numeric_atoms","value":1435,"base":4},"right_expr":{"type":"numeric_atoms","value":3126,"base":4}}},"used_operators":["8HhzD0ZcuI","3tj9sqzovi","lvlrscuwVU"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","XGcMNugi78","dWAJyo7jo9","Tw270M8GLb","Y7wcNGrDQJ","DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3485","layer":2},{"info":"compute unary expreesion, input=3485, op_id = 3tj9sqzovi, unary_op_definition = '≻⋜a = { (((a⩵∡a)⫞⩸⩒(⨰⫟⨤a))⪢a) }', output=nan","layer":1},{"info":"number node, value=1435","layer":2},{"info":"number node, value=3126","layer":2},{"info":"compute binary expreesion, left_input=1435, right_input=3126, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=2700722","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2700722, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(≻⋜⪩⨒∯312131)⨽⪩⨒∯112123≴⪞⇿⪩⨒∯300312=NaN","reverse_text":"NaN=(≻⋜⪩⨒∯312131)⨽⪩⨒∯112123≴⪞⇿⪩⨒∯300312","cot":[{"info":"≻⋜⪩⨒∯312131=NaN","layer":1},{"info":"⪩⨒∯112123≴⪞⇿⪩⨒∯300312=⪩⨒∯22103112302","layer":1},{"info":"NaN⨽⪩⨒∯22103112302=NaN","layer":0}]}
{"id":728,"expression_no_base_symbol":"($1459$⊔$1318$)⊱⇼⊻($2804$+$1284$)","expression":"(⪩⨒∯112303⊔⪩⨒∯110212)⊱⇼⊻(⪩⨒∯223310+⪩⨒∯110010)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":26,"operation_count":3,"complexity_ratio":8.666666666666666,"tree":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"binary","operator":"⊔","left_expr":{"type":"numeric_atoms","value":1459,"base":4},"right_expr":{"type":"numeric_atoms","value":1318,"base":4}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":2804,"base":4},"right_expr":{"type":"numeric_atoms","value":1284,"base":4}}},"used_operators":["FyVja0WsTP","E4l6HwMY31","W4YGzv6Whe"],"dependent_operators":["W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","W4YGzv6Whe","DpFCA1CohY","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","QMFrweE19q"],"result":"⪩⨒∯12302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1459","layer":2},{"info":"number node, value=1318","layer":2},{"info":"compute binary expreesion, left_input=1459, right_input=1318, op_id = E4l6HwMY31 binary_op_definition= 'a⊔b = { (((a≧⫂∧b)∲⫓(⋗⩬⋾b))⫡⨏((b⪒a)≧⫂∧(a+64))) }', output=7108","layer":1},{"info":"number node, value=2804","layer":2},{"info":"number node, value=1284","layer":2},{"info":"compute binary expreesion, left_input=2804, right_input=1284, op_id = W4YGzv6Whe binary_op_definition= 'None', output=4088","layer":1},{"info":"compute binary expreesion, left_input=7108, right_input=4088, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯112303⊔⪩⨒∯110212)⊱⇼⊻(⪩⨒∯223310+⪩⨒∯110010)=⪩⨒∯12302","reverse_text":"⪩⨒∯12302=(⪩⨒∯112303⊔⪩⨒∯110212)⊱⇼⊻(⪩⨒∯223310+⪩⨒∯110010)","cot":[{"info":"⪩⨒∯112303⊔⪩⨒∯110212=⪩⨒∯1233010","layer":1},{"info":"⪩⨒∯223310+⪩⨒∯110010=⪩⨒∯333320","layer":1},{"info":"⪩⨒∯1233010⊱⇼⊻⪩⨒∯333320=⪩⨒∯12302","layer":0}]}
{"id":729,"expression_no_base_symbol":"$3475$∼$2425$↫","expression":"⪩⨒∯312103∼⪩⨒∯211321↫","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":71,"operation_count":2,"complexity_ratio":35.5,"tree":{"type":"unary","operator":"↫","unary_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":3475,"base":4},"right_expr":{"type":"numeric_atoms","value":2425,"base":4}}},"used_operators":["uPb5QRN0te","DyGG3AbaNP"],"dependent_operators":["i8ToyICDmI","2DQ55sFlQl","t8gj7n24qd","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3475","layer":2},{"info":"number node, value=2425","layer":2},{"info":"compute binary expreesion, left_input=3475, right_input=2425, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = uPb5QRN0te, unary_op_definition = 'a↫ = { (a∲⫓a) , if (-a)>=333 ; (a⨵⪆a) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯312103∼⪩⨒∯211321↫=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⪩⨒∯312103∼⪩⨒∯211321↫","cot":[{"info":"⪩⨒∯312103∼⪩⨒∯211321=NaN","layer":1},{"info":"NaN↫=⪩⨒∯2200","layer":0}]}
{"id":730,"expression_no_base_symbol":"$2901$⊢$1941$⩏","expression":"⪩⨒∯231111⊢⪩⨒∯132111⩏","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":257,"operation_count":2,"complexity_ratio":128.5,"tree":{"type":"unary","operator":"⩏","unary_expr":{"type":"binary","operator":"⊢","left_expr":{"type":"numeric_atoms","value":2901,"base":4},"right_expr":{"type":"numeric_atoms","value":1941,"base":4}}},"used_operators":["iA2gmKZ3Wj","5twsqlHp2o"],"dependent_operators":["z6LnFrNh4i","Tcnh7f0tEr","P8v4zCKN1o","Qy55tPpLXF","BjRHVeLaeN","DZ8iAZOCBD","7j4O788W3g","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","14qkJME0vr","D4vGDi5EA2","2td37pGCOC"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2901","layer":2},{"info":"number node, value=1941","layer":2},{"info":"compute binary expreesion, left_input=2901, right_input=1941, op_id = 5twsqlHp2o binary_op_definition= 'a⊢b = { (((225⫩⊇)⊉≛↸(∥⊫a))⨵⪆(25⊉≛↸(b⋥≓≎47))) , if (a≦≮≮)==364 ; (((b⊦⊿)⪨≂(⩦⩻⨪b))↺((⨞⊢a)⪨≂(-1))) , else }', output=-6046","layer":1},{"info":"compute unary expreesion, input=-6046, op_id = iA2gmKZ3Wj, unary_op_definition = 'a⩏ = { ((a⋕⪉⪜272)≣⋋) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯231111⊢⪩⨒∯132111⩏=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯231111⊢⪩⨒∯132111⩏","cot":[{"info":"⪩⨒∯231111⊢⪩⨒∯132111=⪩⨒∯-1132132","layer":1},{"info":"⪩⨒∯-1132132⩏=⪩⨒∯0","layer":0}]}
{"id":731,"expression_no_base_symbol":"$2958$⨜⨶$1824$⩣⫁∢(↨$4311$)","expression":"⪩⨒∯232032⨜⨶⪩⨒∯130200⩣⫁∢(↨⪩⨒∯1003113)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":209,"operation_count":3,"complexity_ratio":69.66666666666667,"tree":{"type":"binary","operator":"⩣⫁∢","left_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":2958,"base":4},"right_expr":{"type":"numeric_atoms","value":1824,"base":4}},"right_expr":{"type":"unary","operator":"↨","unary_expr":{"type":"numeric_atoms","value":4311,"base":4}}},"used_operators":["JDUIKTTSIa","HiPekx5b7W","jiX4gk2v2Q"],"dependent_operators":["sdazOOVcIp","eewbuw0ToL","AF7qkfDlqP","u6S6b8DprG","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","rGHVDoGpnC","oZj3VtZNQx"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2958","layer":2},{"info":"number node, value=1824","layer":2},{"info":"compute binary expreesion, left_input=2958, right_input=1824, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-3392","layer":1},{"info":"number node, value=4311","layer":2},{"info":"compute unary expreesion, input=4311, op_id = jiX4gk2v2Q, unary_op_definition = '↨a = { ((203≀⫉a)⨟⋌⩍a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-3392, right_input=nan, op_id = JDUIKTTSIa binary_op_definition= 'a⩣⫁∢b = { (⨑⩽⪐((a⪨≂b)⨰(↽≂b))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯232032⨜⨶⪩⨒∯130200⩣⫁∢(↨⪩⨒∯1003113)=NaN","reverse_text":"NaN=⪩⨒∯232032⨜⨶⪩⨒∯130200⩣⫁∢(↨⪩⨒∯1003113)","cot":[{"info":"⪩⨒∯232032⨜⨶⪩⨒∯130200=⪩⨒∯-311000","layer":1},{"info":"↨⪩⨒∯1003113=NaN","layer":1},{"info":"⪩⨒∯-311000⩣⫁∢NaN=NaN","layer":0}]}
{"id":732,"expression_no_base_symbol":"⇠(⨂⪏⇭$1383$)","expression":"⇠(⨂⪏⇭⪩⨒∯111213)","highest_n_order":1,"priority_hierarchical_complexity":1,"normalized_expansion_degree":25,"operation_count":2,"complexity_ratio":12.5,"tree":{"type":"unary","operator":"⇠","unary_expr":{"type":"unary","operator":"⨂⪏⇭","unary_expr":{"type":"numeric_atoms","value":1383,"base":4}}},"used_operators":["18saOjeKKm","AYdpE9sXAk"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","nCS4ZIUYfx","eewbuw0ToL","NTOWxs364D","EBcxylXtPf"],"result":"⪩⨒∯-231300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1383","layer":2},{"info":"compute unary expreesion, input=1383, op_id = AYdpE9sXAk, unary_op_definition = '⨂⪏⇭a = { (a⨰((85⩚⊴⇥a)⫌⩹⨱)) }', output=3170","layer":1},{"info":"compute unary expreesion, input=3170, op_id = 18saOjeKKm, unary_op_definition = '⇠a = { ((a⨳⩥⨓242)∲⫓(229⪨≂a)) }', output=-2928","layer":0}],"base":4,"result_base":4,"text":"⇠(⨂⪏⇭⪩⨒∯111213)=⪩⨒∯-231300","reverse_text":"⪩⨒∯-231300=⇠(⨂⪏⇭⪩⨒∯111213)","cot":[{"info":"⨂⪏⇭⪩⨒∯111213=⪩⨒∯301202","layer":1},{"info":"⇠⪩⨒∯301202=⪩⨒∯-231300","layer":0}]}
{"id":733,"expression_no_base_symbol":"($2836$∀⇚≩$2253$)⫉⨲⊜$5085$⊱⇼⊻$1075$","expression":"(⪩⨒∯230110∀⇚≩⪩⨒∯203031)⫉⨲⊜⪩⨒∯1033131⊱⇼⊻⪩⨒∯100303","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19873,"operation_count":3,"complexity_ratio":6624.333333333333,"tree":{"type":"binary","operator":"⫉⨲⊜","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":2836,"base":4},"right_expr":{"type":"numeric_atoms","value":2253,"base":4}},"right_expr":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"numeric_atoms","value":5085,"base":4},"right_expr":{"type":"numeric_atoms","value":1075,"base":4}}},"used_operators":["WhqkvtTD3t","LRNGc0VcxI","FyVja0WsTP"],"dependent_operators":["eewbuw0ToL","zVYPLywUTj","X99M06cbEe","W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2836","layer":2},{"info":"number node, value=2253","layer":2},{"info":"compute binary expreesion, left_input=2836, right_input=2253, op_id = LRNGc0VcxI binary_op_definition= 'a∀⇚≩b = {b, if a == 0; ((a-1)∀⇚≩b)≫≃, if a > 0 and abs(a) < 1000000; -((a+1)∀⇚≩b)≫≃, if a < 0 and abs(a) < 1000000; NaN, else}', output=nan","layer":1},{"info":"number node, value=5085","layer":2},{"info":"number node, value=1075","layer":2},{"info":"compute binary expreesion, left_input=5085, right_input=1075, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=434, op_id = WhqkvtTD3t binary_op_definition= 'a⫉⨲⊜b = { (b⨰120) , if b<=7 ; (a⊪) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯230110∀⇚≩⪩⨒∯203031)⫉⨲⊜⪩⨒∯1033131⊱⇼⊻⪩⨒∯100303=NaN","reverse_text":"NaN=(⪩⨒∯230110∀⇚≩⪩⨒∯203031)⫉⨲⊜⪩⨒∯1033131⊱⇼⊻⪩⨒∯100303","cot":[{"info":"⪩⨒∯230110∀⇚≩⪩⨒∯203031=NaN","layer":1},{"info":"⪩⨒∯1033131⊱⇼⊻⪩⨒∯100303=⪩⨒∯12302","layer":1},{"info":"NaN⫉⨲⊜⪩⨒∯12302=NaN","layer":0}]}
{"id":734,"expression_no_base_symbol":"($1387$⇴$6624$)⋣⋖($5099$⊭↱$6500$)","expression":"(⪩⨒∯111223⇴⪩⨒∯1213200)⋣⋖(⪩⨒∯1033223⊭↱⪩⨒∯1211210)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":21,"operation_count":3,"complexity_ratio":7.0,"tree":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"binary","operator":"⇴","left_expr":{"type":"numeric_atoms","value":1387,"base":4},"right_expr":{"type":"numeric_atoms","value":6624,"base":4}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":5099,"base":4},"right_expr":{"type":"numeric_atoms","value":6500,"base":4}}},"used_operators":["J0M6qkBnIM","4JB6nKBMSY","COABgblf1C"],"dependent_operators":["VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2","sdazOOVcIp","NTOWxs364D","COABgblf1C","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯11023000","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1387","layer":2},{"info":"number node, value=6624","layer":2},{"info":"compute binary expreesion, left_input=1387, right_input=6624, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=21184","layer":1},{"info":"number node, value=5099","layer":2},{"info":"number node, value=6500","layer":2},{"info":"compute binary expreesion, left_input=5099, right_input=6500, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=2807","layer":1},{"info":"compute binary expreesion, left_input=21184, right_input=2807, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=21184","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯111223⇴⪩⨒∯1213200)⋣⋖(⪩⨒∯1033223⊭↱⪩⨒∯1211210)=⪩⨒∯11023000","reverse_text":"⪩⨒∯11023000=(⪩⨒∯111223⇴⪩⨒∯1213200)⋣⋖(⪩⨒∯1033223⊭↱⪩⨒∯1211210)","cot":[{"info":"⪩⨒∯111223⇴⪩⨒∯1213200=⪩⨒∯11023000","layer":1},{"info":"⪩⨒∯1033223⊭↱⪩⨒∯1211210=⪩⨒∯223313","layer":1},{"info":"⪩⨒∯11023000⋣⋖⪩⨒∯223313=⪩⨒∯11023000","layer":0}]}
{"id":735,"expression_no_base_symbol":"($1078$⫒⫫$5631$)⩼⇪↪$3620$≁$2832$","expression":"(⪩⨒∯100312⫒⫫⪩⨒∯1113333)⩼⇪↪⪩⨒∯320210≁⪩⨒∯230100","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":85,"operation_count":3,"complexity_ratio":28.333333333333332,"tree":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"binary","operator":"⫒⫫","left_expr":{"type":"numeric_atoms","value":1078,"base":4},"right_expr":{"type":"numeric_atoms","value":5631,"base":4}},"right_expr":{"type":"binary","operator":"≁","left_expr":{"type":"numeric_atoms","value":3620,"base":4},"right_expr":{"type":"numeric_atoms","value":2832,"base":4}}},"used_operators":["ocnLzx9CaJ","6Ko8hGgeMq","8N2wDY1A35"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q","jdwGQqwJi5","AHs5Up7iyr","AFVx7xoS7T","B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1078","layer":2},{"info":"number node, value=5631","layer":2},{"info":"compute binary expreesion, left_input=1078, right_input=5631, op_id = 6Ko8hGgeMq binary_op_definition= 'a⫒⫫b = { (b≹⇙⪍a) , if (a∁)>135 ; (b⇌⫙⪟a) , else }', output=nan","layer":1},{"info":"number node, value=3620","layer":2},{"info":"number node, value=2832","layer":2},{"info":"compute binary expreesion, left_input=3620, right_input=2832, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=54767","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=54767, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100312⫒⫫⪩⨒∯1113333)⩼⇪↪⪩⨒∯320210≁⪩⨒∯230100=NaN","reverse_text":"NaN=(⪩⨒∯100312⫒⫫⪩⨒∯1113333)⩼⇪↪⪩⨒∯320210≁⪩⨒∯230100","cot":[{"info":"⪩⨒∯100312⫒⫫⪩⨒∯1113333=NaN","layer":1},{"info":"⪩⨒∯320210≁⪩⨒∯230100=⪩⨒∯31113233","layer":1},{"info":"NaN⩼⇪↪⪩⨒∯31113233=NaN","layer":0}]}
{"id":736,"expression_no_base_symbol":"$3091$⪔⊥$2421$⩒⫫$1884$⊬⨰$3551$","expression":"⪩⨒∯300103⪔⊥⪩⨒∯211311⩒⫫⪩⨒∯131130⊬⨰⪩⨒∯313133","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":52,"operation_count":3,"complexity_ratio":17.333333333333332,"tree":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"binary","operator":"⪔⊥","left_expr":{"type":"numeric_atoms","value":3091,"base":4},"right_expr":{"type":"numeric_atoms","value":2421,"base":4}},"right_expr":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"numeric_atoms","value":1884,"base":4},"right_expr":{"type":"numeric_atoms","value":3551,"base":4}}},"used_operators":["KFSx94NKJn","HJ9erzHUuu","s3Fd5m9Dh2"],"dependent_operators":["NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","eLAdDNolq6","rysDP5nf3Z","7j4O788W3g","tifHPKVTfV","8w2t5hMYqp","sdazOOVcIp","2td37pGCOC","COABgblf1C","23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx"],"result":"⪩⨒∯1231231","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3091","layer":2},{"info":"number node, value=2421","layer":2},{"info":"compute binary expreesion, left_input=3091, right_input=2421, op_id = HJ9erzHUuu binary_op_definition= 'a⪔⊥b = { (⩦⩻⨪(≤/(315⇼⇔∾a))) , if b<175 ; ((⊄⩳↩(b-b))⇼⇔∾((b⪨≂a)⊭↱(a↺b))) , else }', output=7323","layer":1},{"info":"number node, value=1884","layer":2},{"info":"number node, value=3551","layer":2},{"info":"compute binary expreesion, left_input=1884, right_input=3551, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=15032","layer":1},{"info":"compute binary expreesion, left_input=7323, right_input=15032, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=7021","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯300103⪔⊥⪩⨒∯211311⩒⫫⪩⨒∯131130⊬⨰⪩⨒∯313133=⪩⨒∯1231231","reverse_text":"⪩⨒∯1231231=⪩⨒∯300103⪔⊥⪩⨒∯211311⩒⫫⪩⨒∯131130⊬⨰⪩⨒∯313133","cot":[{"info":"⪩⨒∯300103⪔⊥⪩⨒∯211311=⪩⨒∯1302123","layer":1},{"info":"⪩⨒∯131130⊬⨰⪩⨒∯313133=⪩⨒∯3222320","layer":1},{"info":"⪩⨒∯1302123⩒⫫⪩⨒∯3222320=⪩⨒∯1231231","layer":0}]}
{"id":737,"expression_no_base_symbol":"($1828$⨓$4931$)≄⊠(⨡↴$6341$)","expression":"(⪩⨒∯130210⨓⪩⨒∯1031003)≄⊠(⨡↴⪩⨒∯1203011)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5000,"operation_count":3,"complexity_ratio":1666.6666666666667,"tree":{"type":"binary","operator":"≄⊠","left_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":1828,"base":4},"right_expr":{"type":"numeric_atoms","value":4931,"base":4}},"right_expr":{"type":"unary","operator":"⨡↴","unary_expr":{"type":"numeric_atoms","value":6341,"base":4}}},"used_operators":["vXNesLlMH1","3ViojmjbAp","liw5iZPkLH"],"dependent_operators":["d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","P8v4zCKN1o"],"result":"⪩⨒∯132000130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1828","layer":2},{"info":"number node, value=4931","layer":2},{"info":"compute binary expreesion, left_input=1828, right_input=4931, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-4934","layer":1},{"info":"number node, value=6341","layer":2},{"info":"compute unary expreesion, input=6341, op_id = liw5iZPkLH, unary_op_definition = '⨡↴a = { (∥⊫(a+181)) }', output=7390","layer":1},{"info":"compute binary expreesion, left_input=-4934, right_input=7390, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=122908","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯130210⨓⪩⨒∯1031003)≄⊠(⨡↴⪩⨒∯1203011)=⪩⨒∯132000130","reverse_text":"⪩⨒∯132000130=(⪩⨒∯130210⨓⪩⨒∯1031003)≄⊠(⨡↴⪩⨒∯1203011)","cot":[{"info":"⪩⨒∯130210⨓⪩⨒∯1031003=⪩⨒∯-1031012","layer":1},{"info":"⨡↴⪩⨒∯1203011=⪩⨒∯1303132","layer":1},{"info":"⪩⨒∯-1031012≄⊠⪩⨒∯1303132=⪩⨒∯132000130","layer":0}]}
{"id":738,"expression_no_base_symbol":"($5059$⪒⊣⊆$5185$)⨜⨶($3042$⨭⪣$6681$)","expression":"(⪩⨒∯1033003⪒⊣⊆⪩⨒∯1101001)⨜⨶(⪩⨒∯233202⨭⪣⪩⨒∯1220121)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":59,"operation_count":3,"complexity_ratio":19.666666666666668,"tree":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"binary","operator":"⪒⊣⊆","left_expr":{"type":"numeric_atoms","value":5059,"base":4},"right_expr":{"type":"numeric_atoms","value":5185,"base":4}},"right_expr":{"type":"binary","operator":"⨭⪣","left_expr":{"type":"numeric_atoms","value":3042,"base":4},"right_expr":{"type":"numeric_atoms","value":6681,"base":4}}},"used_operators":["HiPekx5b7W","eRqsBgTDFp","kn8WO9XteQ"],"dependent_operators":["N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","sdazOOVcIp","W4YGzv6Whe","vRio1gEz1j","61wBmkZwlr","SWo3A1KBJH","8jW3W4yZS5","LkLIoiE525","Y7wcNGrDQJ","PPChnnnBFF"],"result":"⪩⨒∯-303012","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5059","layer":2},{"info":"number node, value=5185","layer":2},{"info":"compute binary expreesion, left_input=5059, right_input=5185, op_id = eRqsBgTDFp binary_op_definition= 'a⪒⊣⊆b = { (b⪨≂a) , if a<=17 ; (a+a) , else }', output=10118","layer":1},{"info":"number node, value=3042","layer":2},{"info":"number node, value=6681","layer":2},{"info":"compute binary expreesion, left_input=3042, right_input=6681, op_id = kn8WO9XteQ binary_op_definition= 'a⨭⪣b = { ((486⇩)⩵∡(a∣a)) , if (b⇯⋐)>445 or (≋b)>319 or b<=69 ; (↯⪼(⇋↷b)) , else }', output=1763","layer":1},{"info":"compute binary expreesion, left_input=10118, right_input=1763, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-3270","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1033003⪒⊣⊆⪩⨒∯1101001)⨜⨶(⪩⨒∯233202⨭⪣⪩⨒∯1220121)=⪩⨒∯-303012","reverse_text":"⪩⨒∯-303012=(⪩⨒∯1033003⪒⊣⊆⪩⨒∯1101001)⨜⨶(⪩⨒∯233202⨭⪣⪩⨒∯1220121)","cot":[{"info":"⪩⨒∯1033003⪒⊣⊆⪩⨒∯1101001=⪩⨒∯2132012","layer":1},{"info":"⪩⨒∯233202⨭⪣⪩⨒∯1220121=⪩⨒∯123203","layer":1},{"info":"⪩⨒∯2132012⨜⨶⪩⨒∯123203=⪩⨒∯-303012","layer":0}]}
{"id":739,"expression_no_base_symbol":"⊁⨺(⫵↿$1526$)","expression":"⊁⨺(⫵↿⪩⨒∯113312)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":39,"operation_count":2,"complexity_ratio":19.5,"tree":{"type":"unary","operator":"⊁⨺","unary_expr":{"type":"unary","operator":"⫵↿","unary_expr":{"type":"numeric_atoms","value":1526,"base":4}}},"used_operators":["PxiHyQbrIp","ivGwdmUAux"],"dependent_operators":["rysDP5nf3Z","e1ybzncUwg","XPYlsWDdGa","23Mk6UjR3U","7j4O788W3g","2td37pGCOC","2DQ55sFlQl","xUOZtlo3hN","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","LXhwmt4mBO","09Ly4LVMIf","LRNGc0VcxI","y4ImoPnbV5","8jW3W4yZS5","G9tJMlZ94a"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1526","layer":2},{"info":"compute unary expreesion, input=1526, op_id = ivGwdmUAux, unary_op_definition = '⫵↿a = { ((a⫃⨇256)∽(a∀⇚≩66)) , if (⇨a)>=1 ; (↯⪼(a⨫⇇↔a)) , else }', output=137","layer":1},{"info":"compute unary expreesion, input=137, op_id = PxiHyQbrIp, unary_op_definition = '⊁⨺a = { (((⨞⊢a)⋷(3↺a))⨵⪆((⪲⇎a)-(≉a))) , if a>5 ; (((a↺a)⨳⩥⨓(⩦⩻⨪a))⨳⩥⨓((a∲⫓a)⫡⨏(≉a))) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"⊁⨺(⫵↿⪩⨒∯113312)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⊁⨺(⫵↿⪩⨒∯113312)","cot":[{"info":"⫵↿⪩⨒∯113312=⪩⨒∯2021","layer":1},{"info":"⊁⨺⪩⨒∯2021=⪩⨒∯2200","layer":0}]}
{"id":740,"expression_no_base_symbol":"($5264$⪁$2393$)≀⫉$9821$⩇∃⫛$3182$","expression":"(⪩⨒∯1102100⪁⪩⨒∯211121)≀⫉⪩⨒∯2121131⩇∃⫛⪩⨒∯301232","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":87082742,"operation_count":3,"complexity_ratio":29027580.666666668,"tree":{"type":"binary","operator":"≀⫉","left_expr":{"type":"binary","operator":"⪁","left_expr":{"type":"numeric_atoms","value":5264,"base":4},"right_expr":{"type":"numeric_atoms","value":2393,"base":4}},"right_expr":{"type":"binary","operator":"⩇∃⫛","left_expr":{"type":"numeric_atoms","value":9821,"base":4},"right_expr":{"type":"numeric_atoms","value":3182,"base":4}}},"used_operators":["oZj3VtZNQx","I7sXao9hZE","1aApVXNlOP"],"dependent_operators":["9FxExcQeMw","Tcnh7f0tEr","jBncVCNhdl","FyVja0WsTP","Ikt5ks8PT7","EWw2JM7wp4","cTDWOvIxvz","dWAJyo7jo9","wxb3vTeyAj","nlCqmYiOvY","9FxExcQeMw","rysDP5nf3Z","e1ybzncUwg","Qy55tPpLXF","DZ8iAZOCBD","2DQ55sFlQl","t8gj7n24qd","2DDjHMKMc0","Z2TMIBDE3Q","14qkJME0vr","f6k1SAg4EE","Ph9nP6C5qx","eewbuw0ToL","u6S6b8DprG"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5264","layer":2},{"info":"number node, value=2393","layer":2},{"info":"compute binary expreesion, left_input=5264, right_input=2393, op_id = I7sXao9hZE binary_op_definition= 'a⪁b = { (((⫶⊄≣b)⨽⪊≇)⪢a) }', output=nan","layer":1},{"info":"number node, value=9821","layer":2},{"info":"number node, value=3182","layer":2},{"info":"compute binary expreesion, left_input=9821, right_input=3182, op_id = 1aApVXNlOP binary_op_definition= 'a⩇∃⫛b = { (((b⊉≛↸a)⩤)⨰((362⩷∴b)⋥≓≎(↽≂a))) , if (a⊦⊿)>7 and b<=506 and (-a)==737 ; (((b⩤)⪒(b≧⫂∧a))⋝⋈⪟((a⨵⪆a)-(≉a))) , else }', output=-6166","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-6166, op_id = oZj3VtZNQx binary_op_definition= 'a≀⫉b = { (((55≣⋋)∝(a⩷∴a))⊱⇼⊻((a⪉⨛b)⩧⪆(b⋭≵475))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1102100⪁⪩⨒∯211121)≀⫉⪩⨒∯2121131⩇∃⫛⪩⨒∯301232=NaN","reverse_text":"NaN=(⪩⨒∯1102100⪁⪩⨒∯211121)≀⫉⪩⨒∯2121131⩇∃⫛⪩⨒∯301232","cot":[{"info":"⪩⨒∯1102100⪁⪩⨒∯211121=NaN","layer":1},{"info":"⪩⨒∯2121131⩇∃⫛⪩⨒∯301232=⪩⨒∯-1200112","layer":1},{"info":"NaN≀⫉⪩⨒∯-1200112=NaN","layer":0}]}
{"id":741,"expression_no_base_symbol":"⫟(⪲⇎$7653$)","expression":"⫟(⪲⇎⪩⨒∯1313211)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":39,"operation_count":2,"complexity_ratio":19.5,"tree":{"type":"unary","operator":"⫟","unary_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":7653,"base":4}}},"used_operators":["z4E1FaHLuy","XPYlsWDdGa"],"dependent_operators":["9FxExcQeMw","W4YGzv6Whe","Qy55tPpLXF","BjRHVeLaeN","sdazOOVcIp","Ph9nP6C5qx","t8gj7n24qd","EBcxylXtPf","f6k1SAg4EE","2DDjHMKMc0","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx","QMFrweE19q","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-22333103","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7653","layer":2},{"info":"compute unary expreesion, input=7653, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=15306","layer":1},{"info":"compute unary expreesion, input=15306, op_id = z4E1FaHLuy, unary_op_definition = '⫟a = { (((-a)⪨≂(a⨸⪁a))≧⫂∧((a⩷∴a)⨰(a⫡⨏a))) , if (a⫌⩹⨱)>=11 ; (((a+263)⋝⋈⪟(a⨳⩥⨓a))⪒((a⋥≓≎a)⫩⊇)) , else }', output=-45011","layer":0}],"base":4,"result_base":4,"text":"⫟(⪲⇎⪩⨒∯1313211)=⪩⨒∯-22333103","reverse_text":"⪩⨒∯-22333103=⫟(⪲⇎⪩⨒∯1313211)","cot":[{"info":"⪲⇎⪩⨒∯1313211=⪩⨒∯3233022","layer":1},{"info":"⫟⪩⨒∯3233022=⪩⨒∯-22333103","layer":0}]}
{"id":742,"expression_no_base_symbol":"($6256$∙∹∝$1590$)≧⫂∧($9283$⨔≚≋$1016$)","expression":"(⪩⨒∯1201300∙∹∝⪩⨒∯120312)≧⫂∧(⪩⨒∯2101003⨔≚≋⪩⨒∯33320)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":58,"operation_count":3,"complexity_ratio":19.333333333333332,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"numeric_atoms","value":6256,"base":4},"right_expr":{"type":"numeric_atoms","value":1590,"base":4}},"right_expr":{"type":"binary","operator":"⨔≚≋","left_expr":{"type":"numeric_atoms","value":9283,"base":4},"right_expr":{"type":"numeric_atoms","value":1016,"base":4}}},"used_operators":["Ph9nP6C5qx","HmxsFra2vL","Z57zeUYC9z"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","zR4jO40bMj","QvoQhV0rrE","RHru8klgy8","3tVxb0NHM4","f6k1SAg4EE","IWmyXbctLI"],"result":"⪩⨒∯2102313","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6256","layer":2},{"info":"number node, value=1590","layer":2},{"info":"compute binary expreesion, left_input=6256, right_input=1590, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":1},{"info":"number node, value=9283","layer":2},{"info":"number node, value=1016","layer":2},{"info":"compute binary expreesion, left_input=9283, right_input=1016, op_id = Z57zeUYC9z binary_op_definition= 'a⨔≚≋b = { ((⊈(b⪎↠b))⪶≀⋏((29⪒b)∠⫱(a⪮%⊝521))) }', output=9872","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=9872, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=9399","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1201300∙∹∝⪩⨒∯120312)≧⫂∧(⪩⨒∯2101003⨔≚≋⪩⨒∯33320)=⪩⨒∯2102313","reverse_text":"⪩⨒∯2102313=(⪩⨒∯1201300∙∹∝⪩⨒∯120312)≧⫂∧(⪩⨒∯2101003⨔≚≋⪩⨒∯33320)","cot":[{"info":"⪩⨒∯1201300∙∹∝⪩⨒∯120312=⪩⨒∯0","layer":1},{"info":"⪩⨒∯2101003⨔≚≋⪩⨒∯33320=⪩⨒∯2122100","layer":1},{"info":"⪩⨒∯0≧⫂∧⪩⨒∯2122100=⪩⨒∯2102313","layer":0}]}
{"id":743,"expression_no_base_symbol":"$1569$∘$2873$⊹∫⫚(↴⪽⋼$3025$)","expression":"⪩⨒∯120201∘⪩⨒∯230321⊹∫⫚(↴⪽⋼⪩⨒∯233101)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":41,"operation_count":3,"complexity_ratio":13.666666666666666,"tree":{"type":"binary","operator":"⊹∫⫚","left_expr":{"type":"binary","operator":"∘","left_expr":{"type":"numeric_atoms","value":1569,"base":4},"right_expr":{"type":"numeric_atoms","value":2873,"base":4}},"right_expr":{"type":"unary","operator":"↴⪽⋼","unary_expr":{"type":"numeric_atoms","value":3025,"base":4}}},"used_operators":["uWAJUKEvyW","Z5m6OM72h2","5TUYCnJO6w"],"dependent_operators":["BiWNJpBvwn","w2P8NbNXyL","vg4gO5BX6G","k8jYdgA6NY","g55IO6H4Gj","2td37pGCOC","jLgFTUHLKL","eH2TOUuTDT","rysDP5nf3Z","MGuIdZPyUC","UqFzSgLMvQ","k7HXdKtiEU","yyfyN0ffXY","pRsWfj4Fpp","diKm42VcIt"],"result":"⪩⨒∯-2300","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1569","layer":2},{"info":"number node, value=2873","layer":2},{"info":"compute binary expreesion, left_input=1569, right_input=2873, op_id = Z5m6OM72h2 binary_op_definition= 'a∘b = { (380-a) , if b<=483 ; (a⪐) , else }', output=3138","layer":1},{"info":"number node, value=3025","layer":2},{"info":"compute unary expreesion, input=3025, op_id = 5TUYCnJO6w, unary_op_definition = '↴⪽⋼a = { a , if ((∡a)<5 or (⇘a)>=19 or (⊲⪭a)==199) ; (((a↙a)⇡)⇉⇉) , else }', output=3025","layer":1},{"info":"compute binary expreesion, left_input=3138, right_input=3025, op_id = uWAJUKEvyW binary_op_definition= 'a⊹∫⫚b = { (↩(a⊨b)) , if (⩦⩻⨪a)==479 or (b⊉↱≁467)==779 ; ((b⨸⪁b)%(b⩍⋽⫝̸187)) , else }', output=-176","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯120201∘⪩⨒∯230321⊹∫⫚(↴⪽⋼⪩⨒∯233101)=⪩⨒∯-2300","reverse_text":"⪩⨒∯-2300=⪩⨒∯120201∘⪩⨒∯230321⊹∫⫚(↴⪽⋼⪩⨒∯233101)","cot":[{"info":"⪩⨒∯120201∘⪩⨒∯230321=⪩⨒∯301002","layer":1},{"info":"↴⪽⋼⪩⨒∯233101=⪩⨒∯233101","layer":1},{"info":"⪩⨒∯301002⊹∫⫚⪩⨒∯233101=⪩⨒∯-2300","layer":0}]}
{"id":744,"expression_no_base_symbol":"(+⊝⨔$2045$)∴($1093$∠↢$2044$)","expression":"(+⊝⨔⪩⨒∯133331)∴(⪩⨒∯101011∠↢⪩⨒∯133330)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":62,"operation_count":3,"complexity_ratio":20.666666666666668,"tree":{"type":"binary","operator":"∴","left_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":2045,"base":4}},"right_expr":{"type":"binary","operator":"∠↢","left_expr":{"type":"numeric_atoms","value":1093,"base":4},"right_expr":{"type":"numeric_atoms","value":2044,"base":4}}},"used_operators":["hrf7POJlIJ","DhbWaqg5eL","KbjG8mgYpV"],"dependent_operators":["g55IO6H4Gj","P8v4zCKN1o","23Mk6UjR3U","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","rysDP5nf3Z","NTOWxs364D","XPYlsWDdGa","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","nCS4ZIUYfx","COABgblf1C"],"result":"⪩⨒∯1021110","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2045","layer":2},{"info":"compute unary expreesion, input=2045, op_id = DhbWaqg5eL, unary_op_definition = '+⊝⨔a = { ((⪲⇎(⨑⩽⪐14))⨁⊸⫻) , if (a⫸⊐100)!=276 or (a⩷∴98)>390 ; (((a⪐)⪢(a⫸⊐221))+((a⩨a)⪘⫢(-370))) , else }', output=1522","layer":1},{"info":"number node, value=1093","layer":2},{"info":"number node, value=2044","layer":2},{"info":"compute binary expreesion, left_input=1093, right_input=2044, op_id = KbjG8mgYpV binary_op_definition= 'a∠↢b = { (a⊭↱((159⨳⩥⨓16)-(b⨸⪁a))) , if (b==488 or (⨞⊢a)==254) ; (⪲⇎((-b)⫡⨏(b⩚⊴⇥a))) , else }', output=-31906","layer":1},{"info":"compute binary expreesion, left_input=1522, right_input=-31906, op_id = hrf7POJlIJ binary_op_definition= 'a∴b = { ((∥⊫(22⋷b))⨸⪁a) }', output=4692","layer":0}],"base":4,"result_base":4,"text":"(+⊝⨔⪩⨒∯133331)∴(⪩⨒∯101011∠↢⪩⨒∯133330)=⪩⨒∯1021110","reverse_text":"⪩⨒∯1021110=(+⊝⨔⪩⨒∯133331)∴(⪩⨒∯101011∠↢⪩⨒∯133330)","cot":[{"info":"+⊝⨔⪩⨒∯133331=⪩⨒∯113302","layer":1},{"info":"⪩⨒∯101011∠↢⪩⨒∯133330=⪩⨒∯-13302202","layer":1},{"info":"⪩⨒∯113302∴⪩⨒∯-13302202=⪩⨒∯1021110","layer":0}]}
{"id":745,"expression_no_base_symbol":"$3396$⇂≾⫗$1235$⪎↠($3454$⫦⪉$2287$)","expression":"⪩⨒∯311010⇂≾⫗⪩⨒∯103103⪎↠(⪩⨒∯311332⫦⪉⪩⨒∯203233)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":86,"operation_count":3,"complexity_ratio":28.666666666666668,"tree":{"type":"binary","operator":"⪎↠","left_expr":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"numeric_atoms","value":3396,"base":4},"right_expr":{"type":"numeric_atoms","value":1235,"base":4}},"right_expr":{"type":"binary","operator":"⫦⪉","left_expr":{"type":"numeric_atoms","value":3454,"base":4},"right_expr":{"type":"numeric_atoms","value":2287,"base":4}}},"used_operators":["3tVxb0NHM4","aBQ6xLxuTc","wscyQdcy20"],"dependent_operators":["P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM","g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U","W4YGzv6Whe","B3sABdIn96","9HNa5Wba9A","g7Hmc5v1ko","nREPSIbpBE","D3AQDKkPcf"],"result":"⪩⨒∯-313","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3396","layer":2},{"info":"number node, value=1235","layer":2},{"info":"compute binary expreesion, left_input=3396, right_input=1235, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-676","layer":1},{"info":"number node, value=3454","layer":2},{"info":"number node, value=2287","layer":2},{"info":"compute binary expreesion, left_input=3454, right_input=2287, op_id = wscyQdcy20 binary_op_definition= 'a⫦⪉b = { ((a⩌⋺206)⪹) , if (a∷677)>=23 ; ((b+a)*(b⨚b)) , else }', output=-2008","layer":1},{"info":"compute binary expreesion, left_input=-676, right_input=-2008, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=-55","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯311010⇂≾⫗⪩⨒∯103103⪎↠(⪩⨒∯311332⫦⪉⪩⨒∯203233)=⪩⨒∯-313","reverse_text":"⪩⨒∯-313=⪩⨒∯311010⇂≾⫗⪩⨒∯103103⪎↠(⪩⨒∯311332⫦⪉⪩⨒∯203233)","cot":[{"info":"⪩⨒∯311010⇂≾⫗⪩⨒∯103103=⪩⨒∯-22210","layer":1},{"info":"⪩⨒∯311332⫦⪉⪩⨒∯203233=⪩⨒∯-133120","layer":1},{"info":"⪩⨒∯-22210⪎↠⪩⨒∯-133120=⪩⨒∯-313","layer":0}]}
{"id":746,"expression_no_base_symbol":"↸⊣$2129$⊕∕$2109$","expression":"↸⊣⪩⨒∯201101⊕∕⪩⨒∯200331","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":15,"operation_count":2,"complexity_ratio":7.5,"tree":{"type":"unary","operator":"↸⊣","unary_expr":{"type":"binary","operator":"⊕∕","left_expr":{"type":"numeric_atoms","value":2129,"base":4},"right_expr":{"type":"numeric_atoms","value":2109,"base":4}}},"used_operators":["wztAlM01eG","9cloC0Ngie"],"dependent_operators":["N41Kp7NANJ","XPYlsWDdGa","7j4O788W3g","DZ8iAZOCBD","8w2t5hMYqp","12rbrZMWeM","f6k1SAg4EE","Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf"],"result":"⪩⨒∯-130302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2129","layer":2},{"info":"number node, value=2109","layer":2},{"info":"compute binary expreesion, left_input=2129, right_input=2109, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=2129","layer":1},{"info":"compute unary expreesion, input=2129, op_id = wztAlM01eG, unary_op_definition = '↸⊣a = { ((⊄⩳↩a)↺(a≋⫹)) , if (⪲⇎a)<33 ; ((a⪒a)⊉≛↸(a⋳⪒a)) , else }', output=-1842","layer":0}],"base":4,"result_base":4,"text":"↸⊣⪩⨒∯201101⊕∕⪩⨒∯200331=⪩⨒∯-130302","reverse_text":"⪩⨒∯-130302=↸⊣⪩⨒∯201101⊕∕⪩⨒∯200331","cot":[{"info":"⪩⨒∯201101⊕∕⪩⨒∯200331=⪩⨒∯201101","layer":1},{"info":"↸⊣⪩⨒∯201101=⪩⨒∯-130302","layer":0}]}
{"id":747,"expression_no_base_symbol":"($1443$⪛⫼$1704$)∛≔","expression":"(⪩⨒∯112203⪛⫼⪩⨒∯122220)∛≔","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1471,"operation_count":2,"complexity_ratio":735.5,"tree":{"type":"unary","operator":"∛≔","unary_expr":{"type":"binary","operator":"⪛⫼","left_expr":{"type":"numeric_atoms","value":1443,"base":4},"right_expr":{"type":"numeric_atoms","value":1704,"base":4}}},"used_operators":["mGnSCrte3L","hyuBjUqXlG"],"dependent_operators":["d7ASUq0ydm","OKKcZfAt5B","212REbPD9h","gx7XJ7hdpj","nEsXyWgiOK","oWn0xqSxBt","HJ9erzHUuu","9ICcGScMcE","DO4fhlbJSI","BX1lVwlMe0","Noe24qw2ks","uFcxV4UQCh","A8NUZmVepG","vg4gO5BX6G","dfKe02y8D2","hrf7POJlIJ","mqXw5SEYmG","QMFrweE19q","wztAlM01eG"],"result":"⪩⨒∯-1022202013","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1443","layer":2},{"info":"number node, value=1704","layer":2},{"info":"compute binary expreesion, left_input=1443, right_input=1704, op_id = hyuBjUqXlG binary_op_definition= 'a⪛⫼b = { (((↸⊣b)⫡⨏(⊿b))⫸⊐(≦∁(↥a))) , if (a⇟⨁⪰)!=192 ; (((b⊨a)⪛b)⨐((37⪔⊥b)∴(11⫚↹⊑395))) , else }', output=968","layer":1},{"info":"compute unary expreesion, input=968, op_id = mGnSCrte3L, unary_op_definition = 'a∛≔ = { (((⊙↵-a)⋾⨃∁(a⨻⩈⩔a))≝⊿(a⫸⇳(a⫯⪬∳a))) }', output=-305287","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯112203⪛⫼⪩⨒∯122220)∛≔=⪩⨒∯-1022202013","reverse_text":"⪩⨒∯-1022202013=(⪩⨒∯112203⪛⫼⪩⨒∯122220)∛≔","cot":[{"info":"⪩⨒∯112203⪛⫼⪩⨒∯122220=⪩⨒∯33020","layer":1},{"info":"⪩⨒∯33020∛≔=⪩⨒∯-1022202013","layer":0}]}
{"id":748,"expression_no_base_symbol":"$1373$⩦$5735$⨹","expression":"⪩⨒∯111131⩦⪩⨒∯1121213⨹","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3227,"operation_count":2,"complexity_ratio":1613.5,"tree":{"type":"unary","operator":"⨹","unary_expr":{"type":"binary","operator":"⩦","left_expr":{"type":"numeric_atoms","value":1373,"base":4},"right_expr":{"type":"numeric_atoms","value":5735,"base":4}}},"used_operators":["UnCoSGIALn","0kmYd0q39Y"],"dependent_operators":["mp7IySMOzn","N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q"],"result":"⪩⨒∯1111310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1373","layer":2},{"info":"number node, value=5735","layer":2},{"info":"compute binary expreesion, left_input=1373, right_input=5735, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=2746","layer":1},{"info":"compute unary expreesion, input=2746, op_id = UnCoSGIALn, unary_op_definition = 'a⨹ = { (229⇷a) }', output=5492","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯111131⩦⪩⨒∯1121213⨹=⪩⨒∯1111310","reverse_text":"⪩⨒∯1111310=⪩⨒∯111131⩦⪩⨒∯1121213⨹","cot":[{"info":"⪩⨒∯111131⩦⪩⨒∯1121213=⪩⨒∯222322","layer":1},{"info":"⪩⨒∯222322⨹=⪩⨒∯1111310","layer":0}]}
{"id":749,"expression_no_base_symbol":"($1111$⋛$9850$)⊱⇼⊻($1384$⨐⩸⫘$7608$)","expression":"(⪩⨒∯101113⋛⪩⨒∯2121322)⊱⇼⊻(⪩⨒∯111220⨐⩸⫘⪩⨒∯1312320)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":272,"operation_count":3,"complexity_ratio":90.66666666666667,"tree":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"binary","operator":"⋛","left_expr":{"type":"numeric_atoms","value":1111,"base":4},"right_expr":{"type":"numeric_atoms","value":9850,"base":4}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":1384,"base":4},"right_expr":{"type":"numeric_atoms","value":7608,"base":4}}},"used_operators":["FyVja0WsTP","YbUVn0Rbpy","fu6greOZ01"],"dependent_operators":["W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA","3ViojmjbAp"],"result":"⪩⨒∯1313120100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1111","layer":2},{"info":"number node, value=9850","layer":2},{"info":"compute binary expreesion, left_input=1111, right_input=9850, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-122193","layer":1},{"info":"number node, value=1384","layer":2},{"info":"number node, value=7608","layer":2},{"info":"compute binary expreesion, left_input=1384, right_input=7608, op_id = fu6greOZ01 binary_op_definition= 'a⨐⩸⫘b = {a, if b == 0; (a⨐⩸⫘(b-1))⨓(b), if b > 0 and abs(b) < 1000; -(a⨐⩸⫘(b+1))⨓(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-122193, right_input=nan, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=488976","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101113⋛⪩⨒∯2121322)⊱⇼⊻(⪩⨒∯111220⨐⩸⫘⪩⨒∯1312320)=⪩⨒∯1313120100","reverse_text":"⪩⨒∯1313120100=(⪩⨒∯101113⋛⪩⨒∯2121322)⊱⇼⊻(⪩⨒∯111220⨐⩸⫘⪩⨒∯1312320)","cot":[{"info":"⪩⨒∯101113⋛⪩⨒∯2121322=⪩⨒∯-131311101","layer":1},{"info":"⪩⨒∯111220⨐⩸⫘⪩⨒∯1312320=NaN","layer":1},{"info":"⪩⨒∯-131311101⊱⇼⊻NaN=⪩⨒∯1313120100","layer":0}]}
{"id":750,"expression_no_base_symbol":"⨞⊢(⊁⨺$1609$)","expression":"⨞⊢(⊁⨺⪩⨒∯121021)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":14,"operation_count":2,"complexity_ratio":7.0,"tree":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"unary","operator":"⊁⨺","unary_expr":{"type":"numeric_atoms","value":1609,"base":4}}},"used_operators":["xUOZtlo3hN","PxiHyQbrIp"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","e1ybzncUwg","XPYlsWDdGa","23Mk6UjR3U","7j4O788W3g","2td37pGCOC","2DQ55sFlQl","xUOZtlo3hN","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"⪩⨒∯-11032","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1609","layer":2},{"info":"compute unary expreesion, input=1609, op_id = PxiHyQbrIp, unary_op_definition = '⊁⨺a = { (((⨞⊢a)⋷(3↺a))⨵⪆((⪲⇎a)-(≉a))) , if a>5 ; (((a↺a)⨳⩥⨓(⩦⩻⨪a))⨳⩥⨓((a∲⫓a)⫡⨏(≉a))) , else }', output=160","layer":1},{"info":"compute unary expreesion, input=160, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-334","layer":0}],"base":4,"result_base":4,"text":"⨞⊢(⊁⨺⪩⨒∯121021)=⪩⨒∯-11032","reverse_text":"⪩⨒∯-11032=⨞⊢(⊁⨺⪩⨒∯121021)","cot":[{"info":"⊁⨺⪩⨒∯121021=⪩⨒∯2200","layer":1},{"info":"⨞⊢⪩⨒∯2200=⪩⨒∯-11032","layer":0}]}
{"id":751,"expression_no_base_symbol":"$3249$↓$1063$⫏⊷","expression":"⪩⨒∯302301↓⪩⨒∯100213⫏⊷","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":15774,"operation_count":2,"complexity_ratio":7887.0,"tree":{"type":"unary","operator":"⫏⊷","unary_expr":{"type":"binary","operator":"↓","left_expr":{"type":"numeric_atoms","value":3249,"base":4},"right_expr":{"type":"numeric_atoms","value":1063,"base":4}}},"used_operators":["dcShxvzhyw","Af076pWI7l"],"dependent_operators":["FU0Cs4j7VP","7YooWSwCyH","HK0tfVPux8","nhYeJWJD5X","mp7IySMOzn","Noe24qw2ks","lvlrscuwVU","T2fj7uvVaJ","PoHhknlbAi"],"result":"⪩⨒∯1301200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3249","layer":2},{"info":"number node, value=1063","layer":2},{"info":"compute binary expreesion, left_input=3249, right_input=1063, op_id = Af076pWI7l binary_op_definition= 'a↓b = { (((b⇷b)∓⋝b)⨐((462≴⪞⇿a)∇⊂⋱(a⋓a))) }', output=-134","layer":1},{"info":"compute unary expreesion, input=-134, op_id = dcShxvzhyw, unary_op_definition = 'a⫏⊷ = { ((224∪⫐a)⊾⪯⋞(a↛⩡⫤)) }', output=7264","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯302301↓⪩⨒∯100213⫏⊷=⪩⨒∯1301200","reverse_text":"⪩⨒∯1301200=⪩⨒∯302301↓⪩⨒∯100213⫏⊷","cot":[{"info":"⪩⨒∯302301↓⪩⨒∯100213=⪩⨒∯-2012","layer":1},{"info":"⪩⨒∯-2012⫏⊷=⪩⨒∯1301200","layer":0}]}
{"id":752,"expression_no_base_symbol":"($3238$∐⫣)⨸(⊽$2230$)","expression":"(⪩⨒∯302212∐⫣)⨸(⊽⪩⨒∯202312)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":681,"operation_count":3,"complexity_ratio":227.0,"tree":{"type":"binary","operator":"⨸","left_expr":{"type":"unary","operator":"∐⫣","unary_expr":{"type":"numeric_atoms","value":3238,"base":4}},"right_expr":{"type":"unary","operator":"⊽","unary_expr":{"type":"numeric_atoms","value":2230,"base":4}}},"used_operators":["KmoU8R5UQR","4CyGpkTkEk","QxG7OkqoLX"],"dependent_operators":["ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl","XPYlsWDdGa","eewbuw0ToL","e1ybzncUwg","g55IO6H4Gj","VJ330n2nnx","z63VuFQld9"],"result":"⪩⨒∯101032","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3238","layer":2},{"info":"compute unary expreesion, input=3238, op_id = 4CyGpkTkEk, unary_op_definition = 'a∐⫣ = { (≉(⪲⇎(a⨰a))) }', output=551","layer":1},{"info":"number node, value=2230","layer":2},{"info":"compute unary expreesion, input=2230, op_id = QxG7OkqoLX, unary_op_definition = '⊽a = { (a⨸⪁761) , if (a↬⩅∪)<402 ; (a∧) , else }', output=5982","layer":1},{"info":"compute binary expreesion, left_input=551, right_input=5982, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=1102","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯302212∐⫣)⨸(⊽⪩⨒∯202312)=⪩⨒∯101032","reverse_text":"⪩⨒∯101032=(⪩⨒∯302212∐⫣)⨸(⊽⪩⨒∯202312)","cot":[{"info":"⪩⨒∯302212∐⫣=⪩⨒∯20213","layer":1},{"info":"⊽⪩⨒∯202312=⪩⨒∯1131132","layer":1},{"info":"⪩⨒∯20213⨸⪩⨒∯1131132=⪩⨒∯101032","layer":0}]}
{"id":753,"expression_no_base_symbol":"$1277$⨽∌$1246$∺≝⩲($3395$≝⊿$2360$)","expression":"⪩⨒∯103331⨽∌⪩⨒∯103132∺≝⩲(⪩⨒∯311003≝⊿⪩⨒∯210320)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":80,"operation_count":3,"complexity_ratio":26.666666666666668,"tree":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"binary","operator":"⨽∌","left_expr":{"type":"numeric_atoms","value":1277,"base":4},"right_expr":{"type":"numeric_atoms","value":1246,"base":4}},"right_expr":{"type":"binary","operator":"≝⊿","left_expr":{"type":"numeric_atoms","value":3395,"base":4},"right_expr":{"type":"numeric_atoms","value":2360,"base":4}}},"used_operators":["KPf6cnQVty","9samAPKr6k","OKKcZfAt5B"],"dependent_operators":["BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl","YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu","12rbrZMWeM"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1277","layer":2},{"info":"number node, value=1246","layer":2},{"info":"compute binary expreesion, left_input=1277, right_input=1246, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":1},{"info":"number node, value=3395","layer":2},{"info":"number node, value=2360","layer":2},{"info":"compute binary expreesion, left_input=3395, right_input=2360, op_id = OKKcZfAt5B binary_op_definition= 'a≝⊿b = { ((82⋳⪒b)⋳⪒a) }', output=-8648","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-8648, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯103331⨽∌⪩⨒∯103132∺≝⩲(⪩⨒∯311003≝⊿⪩⨒∯210320)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⪩⨒∯103331⨽∌⪩⨒∯103132∺≝⩲(⪩⨒∯311003≝⊿⪩⨒∯210320)","cot":[{"info":"⪩⨒∯103331⨽∌⪩⨒∯103132=⪩⨒∯0","layer":1},{"info":"⪩⨒∯311003≝⊿⪩⨒∯210320=⪩⨒∯-2013020","layer":1},{"info":"⪩⨒∯0∺≝⩲⪩⨒∯-2013020=⪩⨒∯2200","layer":0}]}
{"id":754,"expression_no_base_symbol":"($1858$⋝⋈⪟$3233$)≹⇙⪍($1037$≒∊$3149$)","expression":"(⪩⨒∯131002⋝⋈⪟⪩⨒∯302201)≹⇙⪍(⪩⨒∯100031≒∊⪩⨒∯301031)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":306880,"operation_count":3,"complexity_ratio":102293.33333333333,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":1858,"base":4},"right_expr":{"type":"numeric_atoms","value":3233,"base":4}},"right_expr":{"type":"binary","operator":"≒∊","left_expr":{"type":"numeric_atoms","value":1037,"base":4},"right_expr":{"type":"numeric_atoms","value":3149,"base":4}}},"used_operators":["AHs5Up7iyr","2DDjHMKMc0","5KTvxBwnZo"],"dependent_operators":["dWAJyo7jo9","W4YGzv6Whe","t8gj7n24qd","3EYGwJThht","dWAJyo7jo9","Z2TMIBDE3Q","bjFbhXSADs","3DZMoQKiUl"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1858","layer":2},{"info":"number node, value=3233","layer":2},{"info":"compute binary expreesion, left_input=1858, right_input=3233, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=1858","layer":1},{"info":"number node, value=1037","layer":2},{"info":"number node, value=3149","layer":2},{"info":"compute binary expreesion, left_input=1037, right_input=3149, op_id = 5KTvxBwnZo binary_op_definition= 'a≒∊b = { (≱⇩⩕(a⪢a)) , if (a⩤)==117 ; ((b⪊≅)⇄a) , else }', output=-553","layer":1},{"info":"compute binary expreesion, left_input=1858, right_input=-553, op_id = AHs5Up7iyr binary_op_definition= 'a≹⇙⪍b = {a, if b == 0; (a≹⇙⪍(b-1))⪢(b), if b > 0 and abs(b) < 1000; -(a≹⇙⪍(b+1))⪢(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯131002⋝⋈⪟⪩⨒∯302201)≹⇙⪍(⪩⨒∯100031≒∊⪩⨒∯301031)=NaN","reverse_text":"NaN=(⪩⨒∯131002⋝⋈⪟⪩⨒∯302201)≹⇙⪍(⪩⨒∯100031≒∊⪩⨒∯301031)","cot":[{"info":"⪩⨒∯131002⋝⋈⪟⪩⨒∯302201=⪩⨒∯131002","layer":1},{"info":"⪩⨒∯100031≒∊⪩⨒∯301031=⪩⨒∯-20221","layer":1},{"info":"⪩⨒∯131002≹⇙⪍⪩⨒∯-20221=NaN","layer":0}]}
{"id":755,"expression_no_base_symbol":"⨙⪌($1033$⋛$3485$)","expression":"⨙⪌(⪩⨒∯100021⋛⪩⨒∯312131)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1166,"operation_count":2,"complexity_ratio":583.0,"tree":{"type":"unary","operator":"⨙⪌","unary_expr":{"type":"binary","operator":"⋛","left_expr":{"type":"numeric_atoms","value":1033,"base":4},"right_expr":{"type":"numeric_atoms","value":3485,"base":4}}},"used_operators":["vEGLkm4Z2k","YbUVn0Rbpy"],"dependent_operators":["tmPS8pqC7x","kbkesczE7y","D3AQDKkPcf","cTDWOvIxvz","2MzE1hQ0cz","oacrs7FA3X","d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA"],"result":"⪩⨒∯31210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1033","layer":2},{"info":"number node, value=3485","layer":2},{"info":"compute binary expreesion, left_input=1033, right_input=3485, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-122895","layer":1},{"info":"compute unary expreesion, input=-122895, op_id = vEGLkm4Z2k, unary_op_definition = '⨙⪌a = { (((a⪘⫢a)∷(a≬⋮a))⨪↰⇹(a∝(a∩⋅))) }', output=868","layer":0}],"base":4,"result_base":4,"text":"⨙⪌(⪩⨒∯100021⋛⪩⨒∯312131)=⪩⨒∯31210","reverse_text":"⪩⨒∯31210=⨙⪌(⪩⨒∯100021⋛⪩⨒∯312131)","cot":[{"info":"⪩⨒∯100021⋛⪩⨒∯312131=⪩⨒∯-132000033","layer":1},{"info":"⨙⪌⪩⨒∯-132000033=⪩⨒∯31210","layer":0}]}
{"id":756,"expression_no_base_symbol":"≛($5821$⫡⨏$2150$)","expression":"≛(⪩⨒∯1122331⫡⨏⪩⨒∯201212)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":30,"operation_count":2,"complexity_ratio":15.0,"tree":{"type":"unary","operator":"≛","unary_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":5821,"base":4},"right_expr":{"type":"numeric_atoms","value":2150,"base":4}}},"used_operators":["W7eaUhjymW","QMFrweE19q"],"dependent_operators":["W4YGzv6Whe","NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","DZ8iAZOCBD","JLbD19bQDL","sdazOOVcIp","2DDjHMKMc0","f6k1SAg4EE","eewbuw0ToL","COABgblf1C","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-22","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5821","layer":2},{"info":"number node, value=2150","layer":2},{"info":"compute binary expreesion, left_input=5821, right_input=2150, op_id = QMFrweE19q binary_op_definition= 'a⫡⨏b = { 497 , if (-b)==408 and (-a)>=56 ; (((a+783)+(a+a))+((b+a)+(a+b))) , else }', output=34188","layer":1},{"info":"compute unary expreesion, input=34188, op_id = W7eaUhjymW, unary_op_definition = '≛a = { (((a+a)⊉≛↸(a⪠⩆⊳))⊭↱((a⪒a)⩚⊴⇥(a⋝⋈⪟a))) , if (a⫩⊇)>7 or a==273 ; (((a-a)⪒(a⪨≂a))⊉≛↸((a⨰a)⋝⋈⪟(a+a))) , else }', output=-10","layer":0}],"base":4,"result_base":4,"text":"≛(⪩⨒∯1122331⫡⨏⪩⨒∯201212)=⪩⨒∯-22","reverse_text":"⪩⨒∯-22=≛(⪩⨒∯1122331⫡⨏⪩⨒∯201212)","cot":[{"info":"⪩⨒∯1122331⫡⨏⪩⨒∯201212=⪩⨒∯20112030","layer":1},{"info":"≛⪩⨒∯20112030=⪩⨒∯-22","layer":0}]}
{"id":757,"expression_no_base_symbol":"⫎≠⋺$3131$⪎↠$2821$","expression":"⫎≠⋺⪩⨒∯300323⪎↠⪩⨒∯230011","highest_n_order":1,"priority_hierarchical_complexity":1,"normalized_expansion_degree":24,"operation_count":2,"complexity_ratio":12.0,"tree":{"type":"unary","operator":"⫎≠⋺","unary_expr":{"type":"binary","operator":"⪎↠","left_expr":{"type":"numeric_atoms","value":3131,"base":4},"right_expr":{"type":"numeric_atoms","value":2821,"base":4}}},"used_operators":["LYeZOJ0nQG","3tVxb0NHM4"],"dependent_operators":["9FxExcQeMw","NTOWxs364D","P8v4zCKN1o","tifHPKVTfV","i8ToyICDmI","COABgblf1C","P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM"],"result":"⪩⨒∯-23011","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3131","layer":2},{"info":"number node, value=2821","layer":2},{"info":"compute binary expreesion, left_input=3131, right_input=2821, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=160","layer":1},{"info":"compute unary expreesion, input=160, op_id = LYeZOJ0nQG, unary_op_definition = '⫎≠⋺a = { ((655⩚⊴⇥a)∲⫓(∥⊫86)) , if (a⩷∴509)>=9 ; ((1⊭↱337)⇼⇔∾(a⩷∴a)) , else }', output=-709","layer":0}],"base":4,"result_base":4,"text":"⫎≠⋺⪩⨒∯300323⪎↠⪩⨒∯230011=⪩⨒∯-23011","reverse_text":"⪩⨒∯-23011=⫎≠⋺⪩⨒∯300323⪎↠⪩⨒∯230011","cot":[{"info":"⪩⨒∯300323⪎↠⪩⨒∯230011=⪩⨒∯2200","layer":1},{"info":"⫎≠⋺⪩⨒∯2200=⪩⨒∯-23011","layer":0}]}
{"id":758,"expression_no_base_symbol":"⪸($3867$⪄$6115$)","expression":"⪸(⪩⨒∯330123⪄⪩⨒∯1133203)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":123,"operation_count":2,"complexity_ratio":61.5,"tree":{"type":"unary","operator":"⪸","unary_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":3867,"base":4},"right_expr":{"type":"numeric_atoms","value":6115,"base":4}}},"used_operators":["86A5ENbKR9","SUmda5xLS4"],"dependent_operators":["Qy55tPpLXF","23Mk6UjR3U","tifHPKVTfV","sdazOOVcIp","g55IO6H4Gj","AF7qkfDlqP","QMFrweE19q","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⪩⨒∯112212331200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3867","layer":2},{"info":"number node, value=6115","layer":2},{"info":"compute binary expreesion, left_input=3867, right_input=6115, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-592865","layer":1},{"info":"compute unary expreesion, input=-592865, op_id = 86A5ENbKR9, unary_op_definition = '⪸a = { (((220⪨≂51)⇼⇔∾(a⫡⨏303))⋷((a⨸⪁a)⋥≓≎(⨑⩽⪐a))) }', output=5926752","layer":0}],"base":4,"result_base":4,"text":"⪸(⪩⨒∯330123⪄⪩⨒∯1133203)=⪩⨒∯112212331200","reverse_text":"⪩⨒∯112212331200=⪸(⪩⨒∯330123⪄⪩⨒∯1133203)","cot":[{"info":"⪩⨒∯330123⪄⪩⨒∯1133203=⪩⨒∯-2100233201","layer":1},{"info":"⪸⪩⨒∯-2100233201=⪩⨒∯112212331200","layer":0}]}
{"id":759,"expression_no_base_symbol":"($1376$⪭$6439$)⩅⪻⪻","expression":"(⪩⨒∯111200⪭⪩⨒∯1210213)⩅⪻⪻","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":83,"operation_count":2,"complexity_ratio":41.5,"tree":{"type":"unary","operator":"⩅⪻⪻","unary_expr":{"type":"binary","operator":"⪭","left_expr":{"type":"numeric_atoms","value":1376,"base":4},"right_expr":{"type":"numeric_atoms","value":6439,"base":4}}},"used_operators":["kHoXpA7yos","j9kHMeSvPp"],"dependent_operators":["SUmda5xLS4","KPf6cnQVty","8HhzD0ZcuI","9Isq31Ruls","COABgblf1C","xUOZtlo3hN"],"result":"⪩⨒∯213213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1376","layer":2},{"info":"number node, value=6439","layer":2},{"info":"compute binary expreesion, left_input=1376, right_input=6439, op_id = j9kHMeSvPp binary_op_definition= 'a⪭b = { (⨞⊢a) , if a<649 ; (b⊭↱b) , else }', output=5","layer":1},{"info":"compute unary expreesion, input=5, op_id = kHoXpA7yos, unary_op_definition = 'a⩅⪻⪻ = { (a⪄((a∌↝a)⨽(a∺≝⩲a))) }', output=2535","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯111200⪭⪩⨒∯1210213)⩅⪻⪻=⪩⨒∯213213","reverse_text":"⪩⨒∯213213=(⪩⨒∯111200⪭⪩⨒∯1210213)⩅⪻⪻","cot":[{"info":"⪩⨒∯111200⪭⪩⨒∯1210213=⪩⨒∯11","layer":1},{"info":"⪩⨒∯11⩅⪻⪻=⪩⨒∯213213","layer":0}]}
{"id":760,"expression_no_base_symbol":"⨝⨆(⩩$6506$)","expression":"⨝⨆(⩩⪩⨒∯1211222)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7444,"operation_count":2,"complexity_ratio":3722.0,"tree":{"type":"unary","operator":"⨝⨆","unary_expr":{"type":"unary","operator":"⩩","unary_expr":{"type":"numeric_atoms","value":6506,"base":4}}},"used_operators":["bQ67fsrMVf","kMhfGuqI2H"],"dependent_operators":["tifHPKVTfV","6aG7x05OhS","z63VuFQld9","lFBm8KRb8F","f6k1SAg4EE","ZGCBLdVRRX"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6506","layer":2},{"info":"compute unary expreesion, input=6506, op_id = kMhfGuqI2H, unary_op_definition = '⩩a = { (⇜(a⫩)) , if (⇵⪽a)!=444 ; ((a⪒a)∧) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = bQ67fsrMVf, unary_op_definition = '⨝⨆a = { (209⇼⇔∾a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⨝⨆(⩩⪩⨒∯1211222)=NaN","reverse_text":"NaN=⨝⨆(⩩⪩⨒∯1211222)","cot":[{"info":"⩩⪩⨒∯1211222=NaN","layer":1},{"info":"⨝⨆NaN=NaN","layer":0}]}
{"id":761,"expression_no_base_symbol":"(⊿$7763$)≳⇉$1072$∴$1849$","expression":"(⊿⪩⨒∯1321103)≳⇉⪩⨒∯100300∴⪩⨒∯130321","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":239983033,"operation_count":3,"complexity_ratio":79994344.33333333,"tree":{"type":"binary","operator":"≳⇉","left_expr":{"type":"unary","operator":"⊿","unary_expr":{"type":"numeric_atoms","value":7763,"base":4}},"right_expr":{"type":"binary","operator":"∴","left_expr":{"type":"numeric_atoms","value":1072,"base":4},"right_expr":{"type":"numeric_atoms","value":1849,"base":4}}},"used_operators":["V0kx6qeWkN","DO4fhlbJSI","hrf7POJlIJ"],"dependent_operators":["KbjG8mgYpV","48vC8HMD2b","fu6greOZ01","I7sXao9hZE","D3AQDKkPcf","KipPnG1M2J","9Isq31Ruls","9FxExcQeMw","e1ybzncUwg","XPYlsWDdGa","sdazOOVcIp","2DQ55sFlQl","12rbrZMWeM","g55IO6H4Gj","P8v4zCKN1o","23Mk6UjR3U"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7763","layer":2},{"info":"compute unary expreesion, input=7763, op_id = DO4fhlbJSI, unary_op_definition = '⊿a = { ((⪲⇎(a⨵⪆a))⩷∴((≉a)⋳⪒(a⪨≂a))) }', output=-31790","layer":1},{"info":"number node, value=1072","layer":2},{"info":"number node, value=1849","layer":2},{"info":"compute binary expreesion, left_input=1072, right_input=1849, op_id = hrf7POJlIJ binary_op_definition= 'a∴b = { ((∥⊫(22⋷b))⨸⪁a) }', output=3792","layer":1},{"info":"compute binary expreesion, left_input=-31790, right_input=3792, op_id = V0kx6qeWkN binary_op_definition= 'a≳⇉b = { ((b⪁b)∌↝(a∷b)) , if (a∀⋜↑)<109 ; ((b⫘a)∠↢(a⨐⩸⫘a)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⊿⪩⨒∯1321103)≳⇉⪩⨒∯100300∴⪩⨒∯130321=NaN","reverse_text":"NaN=(⊿⪩⨒∯1321103)≳⇉⪩⨒∯100300∴⪩⨒∯130321","cot":[{"info":"⊿⪩⨒∯1321103=⪩⨒∯-13300232","layer":1},{"info":"⪩⨒∯100300∴⪩⨒∯130321=⪩⨒∯323100","layer":1},{"info":"⪩⨒∯-13300232≳⇉⪩⨒∯323100=NaN","layer":0}]}
{"id":762,"expression_no_base_symbol":"($5684$↫)⨽∌($3083$∺≝⩲$2224$)","expression":"(⪩⨒∯1120310↫)⨽∌(⪩⨒∯300023∺≝⩲⪩⨒∯202300)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":65,"operation_count":3,"complexity_ratio":21.666666666666668,"tree":{"type":"binary","operator":"⨽∌","left_expr":{"type":"unary","operator":"↫","unary_expr":{"type":"numeric_atoms","value":5684,"base":4}},"right_expr":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"numeric_atoms","value":3083,"base":4},"right_expr":{"type":"numeric_atoms","value":2224,"base":4}}},"used_operators":["9samAPKr6k","uPb5QRN0te","KPf6cnQVty"],"dependent_operators":["YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu","i8ToyICDmI","2DQ55sFlQl","t8gj7n24qd","BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5684","layer":2},{"info":"compute unary expreesion, input=5684, op_id = uPb5QRN0te, unary_op_definition = 'a↫ = { (a∲⫓a) , if (-a)>=333 ; (a⨵⪆a) , else }', output=160","layer":1},{"info":"number node, value=3083","layer":2},{"info":"number node, value=2224","layer":2},{"info":"compute binary expreesion, left_input=3083, right_input=2224, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=160, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1120310↫)⨽∌(⪩⨒∯300023∺≝⩲⪩⨒∯202300)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯1120310↫)⨽∌(⪩⨒∯300023∺≝⩲⪩⨒∯202300)","cot":[{"info":"⪩⨒∯1120310↫=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯300023∺≝⩲⪩⨒∯202300=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯2200⨽∌⪩⨒∯2200=⪩⨒∯0","layer":0}]}
{"id":763,"expression_no_base_symbol":"($3765$⨚$6254$)⨚(≦∁$7035$)","expression":"(⪩⨒∯322311⨚⪩⨒∯1201232)⨚(≦∁⪩⨒∯1231323)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":33,"operation_count":3,"complexity_ratio":11.0,"tree":{"type":"binary","operator":"⨚","left_expr":{"type":"binary","operator":"⨚","left_expr":{"type":"numeric_atoms","value":3765,"base":4},"right_expr":{"type":"numeric_atoms","value":6254,"base":4}},"right_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":7035,"base":4}}},"used_operators":["nREPSIbpBE","9ICcGScMcE"],"dependent_operators":["BjRHVeLaeN","12rbrZMWeM","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"⪩⨒∯-32232112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3765","layer":2},{"info":"number node, value=6254","layer":2},{"info":"compute binary expreesion, left_input=3765, right_input=6254, op_id = nREPSIbpBE binary_op_definition= 'a⨚b = { (((b⋳⪒a)⋳⪒31)⫩⊇) }', output=-16552","layer":1},{"info":"number node, value=7035","layer":2},{"info":"compute unary expreesion, input=7035, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=7035","layer":1},{"info":"compute binary expreesion, left_input=-16552, right_input=7035, op_id = nREPSIbpBE binary_op_definition= 'a⨚b = { (((b⋳⪒a)⋳⪒31)⫩⊇) }', output=-60310","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯322311⨚⪩⨒∯1201232)⨚(≦∁⪩⨒∯1231323)=⪩⨒∯-32232112","reverse_text":"⪩⨒∯-32232112=(⪩⨒∯322311⨚⪩⨒∯1201232)⨚(≦∁⪩⨒∯1231323)","cot":[{"info":"⪩⨒∯322311⨚⪩⨒∯1201232=⪩⨒∯-10002220","layer":1},{"info":"≦∁⪩⨒∯1231323=⪩⨒∯1231323","layer":1},{"info":"⪩⨒∯-10002220⨚⪩⨒∯1231323=⪩⨒∯-32232112","layer":0}]}
{"id":764,"expression_no_base_symbol":"$6770$↢$1127$⋛$3373$≎⪠$3765$","expression":"⪩⨒∯1221302↢⪩⨒∯101213⋛⪩⨒∯310231≎⪠⪩⨒∯322311","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19381,"operation_count":3,"complexity_ratio":6460.333333333333,"tree":{"type":"binary","operator":"⋛","left_expr":{"type":"binary","operator":"↢","left_expr":{"type":"numeric_atoms","value":6770,"base":4},"right_expr":{"type":"numeric_atoms","value":1127,"base":4}},"right_expr":{"type":"binary","operator":"≎⪠","left_expr":{"type":"numeric_atoms","value":3373,"base":4},"right_expr":{"type":"numeric_atoms","value":3765,"base":4}}},"used_operators":["YbUVn0Rbpy","WR6HLWljOP","aNhz54LH3e"],"dependent_operators":["d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA","eLAdDNolq6","g55IO6H4Gj","7j4O788W3g","12rbrZMWeM","f6k1SAg4EE","i8ToyICDmI","COABgblf1C","bl5wxAcryP","RygbFNSyEJ","SLLxy00UIr","AcOhelriW5","ctOc4cKSDt","cHh1gJQ2o6","KYD54nUTWz","kbkesczE7y","BUOGQAYlQx","PPChnnnBFF"],"result":"⪩⨒∯-102131202","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6770","layer":2},{"info":"number node, value=1127","layer":2},{"info":"compute binary expreesion, left_input=6770, right_input=1127, op_id = WR6HLWljOP binary_op_definition= 'a↢b = { ((a∲⫓a)⪒(≤/a)) , if (a⊭↱114)<=535 ; ((a⋳⪒749)↺(b⨸⪁a)) , else }', output=6286","layer":1},{"info":"number node, value=3373","layer":2},{"info":"number node, value=3765","layer":2},{"info":"compute binary expreesion, left_input=3373, right_input=3765, op_id = aNhz54LH3e binary_op_definition= 'a≎⪠b = { (((a⫥∨⫟11)≦↸(657∣a))⩘((⇈a)≬⋮(a↰))) , if a==21 ; (∟⋨(⋂(⨣⨃⇪b))) , else }', output=19558","layer":1},{"info":"compute binary expreesion, left_input=6286, right_input=19558, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-75618","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1221302↢⪩⨒∯101213⋛⪩⨒∯310231≎⪠⪩⨒∯322311=⪩⨒∯-102131202","reverse_text":"⪩⨒∯-102131202=⪩⨒∯1221302↢⪩⨒∯101213⋛⪩⨒∯310231≎⪠⪩⨒∯322311","cot":[{"info":"⪩⨒∯1221302↢⪩⨒∯101213=⪩⨒∯1202032","layer":1},{"info":"⪩⨒∯310231≎⪠⪩⨒∯322311=⪩⨒∯10301212","layer":1},{"info":"⪩⨒∯1202032⋛⪩⨒∯10301212=⪩⨒∯-102131202","layer":0}]}
{"id":765,"expression_no_base_symbol":"⩏⊷≩$4011$≌$2020$","expression":"⩏⊷≩⪩⨒∯332223≌⪩⨒∯133210","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2167,"operation_count":2,"complexity_ratio":1083.5,"tree":{"type":"unary","operator":"⩏⊷≩","unary_expr":{"type":"binary","operator":"≌","left_expr":{"type":"numeric_atoms","value":4011,"base":4},"right_expr":{"type":"numeric_atoms","value":2020,"base":4}}},"used_operators":["uOZ1tnYMDE","lyWz822IDG"],"dependent_operators":["23Mk6UjR3U","12rbrZMWeM","B5M0gjZbta","W7eaUhjymW","CpSg5vQTgA","w2P8NbNXyL","0kmYd0q39Y","3sJ7IOPOlU","Bmrmz2XGnR","WkeUrDK8WX","03sUfWo75k","5twsqlHp2o","oacrs7FA3X","aMUSaJuDRU"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4011","layer":2},{"info":"number node, value=2020","layer":2},{"info":"compute binary expreesion, left_input=4011, right_input=2020, op_id = lyWz822IDG binary_op_definition= 'a≌b = { (≛((132⩦9)⊉↱≁(a⪇≇⋚a))) , if (a⪘⫢419)==234 ; (((⩰124)≚⊃≕(b⨴∎))⊢((16⨉)↬(a⊟⇱))) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = uOZ1tnYMDE, unary_op_definition = '⩏⊷≩a = { ((a⋳⪒20)⋷(a⋳⪒17)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⩏⊷≩⪩⨒∯332223≌⪩⨒∯133210=NaN","reverse_text":"NaN=⩏⊷≩⪩⨒∯332223≌⪩⨒∯133210","cot":[{"info":"⪩⨒∯332223≌⪩⨒∯133210=NaN","layer":1},{"info":"⩏⊷≩NaN=NaN","layer":0}]}
{"id":766,"expression_no_base_symbol":"($5008$⩌⋺$3365$)≝⊿($3196$⋥≓≎$1603$)","expression":"(⪩⨒∯1032100⩌⋺⪩⨒∯310211)≝⊿(⪩⨒∯301330⋥≓≎⪩⨒∯121003)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":25,"operation_count":3,"complexity_ratio":8.333333333333334,"tree":{"type":"binary","operator":"≝⊿","left_expr":{"type":"binary","operator":"⩌⋺","left_expr":{"type":"numeric_atoms","value":5008,"base":4},"right_expr":{"type":"numeric_atoms","value":3365,"base":4}},"right_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":3196,"base":4},"right_expr":{"type":"numeric_atoms","value":1603,"base":4}}},"used_operators":["OKKcZfAt5B","g7Hmc5v1ko","Qy55tPpLXF"],"dependent_operators":["12rbrZMWeM","9FxExcQeMw","W4YGzv6Whe","NTOWxs364D","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","i8ToyICDmI","QMFrweE19q","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯1323003","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5008","layer":2},{"info":"number node, value=3365","layer":2},{"info":"compute binary expreesion, left_input=5008, right_input=3365, op_id = g7Hmc5v1ko binary_op_definition= 'a⩌⋺b = { ((⨞⊢(b⨵⪆b))∲⫓((a⪨≂b)⪨≂(b⩷∴919))) , if (b⫡⨏102)>364 and (-b)==524 ; (b⇼⇔∾((a+a)⩚⊴⇥(-a))) , else }', output=-8494","layer":1},{"info":"number node, value=3196","layer":2},{"info":"number node, value=1603","layer":2},{"info":"compute binary expreesion, left_input=3196, right_input=1603, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=43","layer":1},{"info":"compute binary expreesion, left_input=-8494, right_input=43, op_id = OKKcZfAt5B binary_op_definition= 'a≝⊿b = { ((82⋳⪒b)⋳⪒a) }', output=7875","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1032100⩌⋺⪩⨒∯310211)≝⊿(⪩⨒∯301330⋥≓≎⪩⨒∯121003)=⪩⨒∯1323003","reverse_text":"⪩⨒∯1323003=(⪩⨒∯1032100⩌⋺⪩⨒∯310211)≝⊿(⪩⨒∯301330⋥≓≎⪩⨒∯121003)","cot":[{"info":"⪩⨒∯1032100⩌⋺⪩⨒∯310211=⪩⨒∯-2010232","layer":1},{"info":"⪩⨒∯301330⋥≓≎⪩⨒∯121003=⪩⨒∯223","layer":1},{"info":"⪩⨒∯-2010232≝⊿⪩⨒∯223=⪩⨒∯1323003","layer":0}]}
{"id":767,"expression_no_base_symbol":"($1792$⩺⪪$1946$)⩦($1402$≹⇙⪍$3448$)","expression":"(⪩⨒∯130000⩺⪪⪩⨒∯132122)⩦(⪩⨒∯111322≹⇙⪍⪩⨒∯311320)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":132,"operation_count":3,"complexity_ratio":44.0,"tree":{"type":"binary","operator":"⩦","left_expr":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"numeric_atoms","value":1792,"base":4},"right_expr":{"type":"numeric_atoms","value":1946,"base":4}},"right_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":1402,"base":4},"right_expr":{"type":"numeric_atoms","value":3448,"base":4}}},"used_operators":["0kmYd0q39Y","uvdQJvN4PV","AHs5Up7iyr"],"dependent_operators":["N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q","Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U","dWAJyo7jo9"],"result":"⪩⨒∯323310","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1792","layer":2},{"info":"number node, value=1946","layer":2},{"info":"compute binary expreesion, left_input=1792, right_input=1946, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=1914","layer":1},{"info":"number node, value=1402","layer":2},{"info":"number node, value=3448","layer":2},{"info":"compute binary expreesion, left_input=1402, right_input=3448, op_id = AHs5Up7iyr binary_op_definition= 'a≹⇙⪍b = {a, if b == 0; (a≹⇙⪍(b-1))⪢(b), if b > 0 and abs(b) < 1000; -(a≹⇙⪍(b+1))⪢(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1914, right_input=nan, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=3828","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯130000⩺⪪⪩⨒∯132122)⩦(⪩⨒∯111322≹⇙⪍⪩⨒∯311320)=⪩⨒∯323310","reverse_text":"⪩⨒∯323310=(⪩⨒∯130000⩺⪪⪩⨒∯132122)⩦(⪩⨒∯111322≹⇙⪍⪩⨒∯311320)","cot":[{"info":"⪩⨒∯130000⩺⪪⪩⨒∯132122=⪩⨒∯131322","layer":1},{"info":"⪩⨒∯111322≹⇙⪍⪩⨒∯311320=NaN","layer":1},{"info":"⪩⨒∯131322⩦NaN=⪩⨒∯323310","layer":0}]}
{"id":768,"expression_no_base_symbol":"⪭⩑⪱($4886$⋣⋖$3289$)","expression":"⪭⩑⪱(⪩⨒∯1030112⋣⋖⪩⨒∯303121)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":40452,"operation_count":2,"complexity_ratio":20226.0,"tree":{"type":"unary","operator":"⪭⩑⪱","unary_expr":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"numeric_atoms","value":4886,"base":4},"right_expr":{"type":"numeric_atoms","value":3289,"base":4}}},"used_operators":["SIgE0bArFf","J0M6qkBnIM"],"dependent_operators":["FU0Cs4j7VP","ZvLB05nZmT","E64sFOc4tB","dWAJyo7jo9","VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2"],"result":"⪩⨒∯133233123300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4886","layer":2},{"info":"number node, value=3289","layer":2},{"info":"compute binary expreesion, left_input=4886, right_input=3289, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=4886","layer":1},{"info":"compute unary expreesion, input=4886, op_id = SIgE0bArFf, unary_op_definition = '⪭⩑⪱a = { (⋎⨆((a↛⩡⫤)⪢(a⫳≱↱715))) }', output=8320752","layer":0}],"base":4,"result_base":4,"text":"⪭⩑⪱(⪩⨒∯1030112⋣⋖⪩⨒∯303121)=⪩⨒∯133233123300","reverse_text":"⪩⨒∯133233123300=⪭⩑⪱(⪩⨒∯1030112⋣⋖⪩⨒∯303121)","cot":[{"info":"⪩⨒∯1030112⋣⋖⪩⨒∯303121=⪩⨒∯1030112","layer":1},{"info":"⪭⩑⪱⪩⨒∯1030112=⪩⨒∯133233123300","layer":0}]}
{"id":769,"expression_no_base_symbol":"⇺⋃($3802$⩌⋺$1059$)","expression":"⇺⋃(⪩⨒∯323122⩌⋺⪩⨒∯100203)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":62,"operation_count":2,"complexity_ratio":31.0,"tree":{"type":"unary","operator":"⇺⋃","unary_expr":{"type":"binary","operator":"⩌⋺","left_expr":{"type":"numeric_atoms","value":3802,"base":4},"right_expr":{"type":"numeric_atoms","value":1059,"base":4}}},"used_operators":["E5v5B3UAjG","g7Hmc5v1ko"],"dependent_operators":["bl5wxAcryP","Q3PJZHRvZv","gub5Cegaqo","8INZBEW696","kuIXHzHcAH","7YooWSwCyH","9FxExcQeMw","W4YGzv6Whe","NTOWxs364D","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","i8ToyICDmI","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3802","layer":2},{"info":"number node, value=1059","layer":2},{"info":"compute binary expreesion, left_input=3802, right_input=1059, op_id = g7Hmc5v1ko binary_op_definition= 'a⩌⋺b = { ((⨞⊢(b⨵⪆b))∲⫓((a⪨≂b)⪨≂(b⩷∴919))) , if (b⫡⨏102)>364 and (-b)==524 ; (b⇼⇔∾((a+a)⩚⊴⇥(-a))) , else }', output=-4982","layer":1},{"info":"compute unary expreesion, input=-4982, op_id = E5v5B3UAjG, unary_op_definition = '⇺⋃a = { (((a≀⩗∶a)∪⫐(a⩁⩘229))⪨⊡(⊥(a↰))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇺⋃(⪩⨒∯323122⩌⋺⪩⨒∯100203)=NaN","reverse_text":"NaN=⇺⋃(⪩⨒∯323122⩌⋺⪩⨒∯100203)","cot":[{"info":"⪩⨒∯323122⩌⋺⪩⨒∯100203=⪩⨒∯-1031312","layer":1},{"info":"⇺⋃⪩⨒∯-1031312=NaN","layer":0}]}
{"id":770,"expression_no_base_symbol":"⫇($1090$⩘$6068$)","expression":"⫇(⪩⨒∯101002⩘⪩⨒∯1132310)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":112,"operation_count":2,"complexity_ratio":56.0,"tree":{"type":"unary","operator":"⫇","unary_expr":{"type":"binary","operator":"⩘","left_expr":{"type":"numeric_atoms","value":1090,"base":4},"right_expr":{"type":"numeric_atoms","value":6068,"base":4}}},"used_operators":["YjI8oCXuph","cHh1gJQ2o6"],"dependent_operators":["rysDP5nf3Z","Qy55tPpLXF","N41Kp7NANJ","23Mk6UjR3U","2DQ55sFlQl","12rbrZMWeM","f6k1SAg4EE","i8ToyICDmI","23Mk6UjR3U","eRqsBgTDFp","zVYPLywUTj","bPywburJMS","KPf6cnQVty","YbVcJGFEVW","5twsqlHp2o"],"result":"⪩⨒∯30010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1090","layer":2},{"info":"number node, value=6068","layer":2},{"info":"compute binary expreesion, left_input=1090, right_input=6068, op_id = cHh1gJQ2o6 binary_op_definition= 'a⩘b = { (((b⋷b)↼⊘⨖(a⊢6))∺≝⩲((a⪒⊣⊆619)≃(a⊪))) }', output=160","layer":1},{"info":"compute unary expreesion, input=160, op_id = YjI8oCXuph, unary_op_definition = '⫇a = { (((a⋥≓≎a)⋷(a⋳⪒a))≋⫹) , if a>62 ; (a-((a⨵⪆101)⪒(786∲⫓a))) , else }', output=772","layer":0}],"base":4,"result_base":4,"text":"⫇(⪩⨒∯101002⩘⪩⨒∯1132310)=⪩⨒∯30010","reverse_text":"⪩⨒∯30010=⫇(⪩⨒∯101002⩘⪩⨒∯1132310)","cot":[{"info":"⪩⨒∯101002⩘⪩⨒∯1132310=⪩⨒∯2200","layer":1},{"info":"⫇⪩⨒∯2200=⪩⨒∯30010","layer":0}]}
{"id":771,"expression_no_base_symbol":"$6695$∴$1558$⨔≚≋$2556$⇴$5541$","expression":"⪩⨒∯1220213∴⪩⨒∯120112⨔≚≋⪩⨒∯213330⇴⪩⨒∯1112211","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":73,"operation_count":3,"complexity_ratio":24.333333333333332,"tree":{"type":"binary","operator":"⨔≚≋","left_expr":{"type":"binary","operator":"∴","left_expr":{"type":"numeric_atoms","value":6695,"base":4},"right_expr":{"type":"numeric_atoms","value":1558,"base":4}},"right_expr":{"type":"binary","operator":"⇴","left_expr":{"type":"numeric_atoms","value":2556,"base":4},"right_expr":{"type":"numeric_atoms","value":5541,"base":4}}},"used_operators":["Z57zeUYC9z","hrf7POJlIJ","4JB6nKBMSY"],"dependent_operators":["zR4jO40bMj","QvoQhV0rrE","RHru8klgy8","3tVxb0NHM4","f6k1SAg4EE","IWmyXbctLI","g55IO6H4Gj","P8v4zCKN1o","23Mk6UjR3U","sdazOOVcIp","NTOWxs364D","COABgblf1C"],"result":"⪩⨒∯2122100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6695","layer":2},{"info":"number node, value=1558","layer":2},{"info":"compute binary expreesion, left_input=6695, right_input=1558, op_id = hrf7POJlIJ binary_op_definition= 'a∴b = { ((∥⊫(22⋷b))⨸⪁a) }', output=15038","layer":1},{"info":"number node, value=2556","layer":2},{"info":"number node, value=5541","layer":2},{"info":"compute binary expreesion, left_input=2556, right_input=5541, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=26032","layer":1},{"info":"compute binary expreesion, left_input=15038, right_input=26032, op_id = Z57zeUYC9z binary_op_definition= 'a⨔≚≋b = { ((⊈(b⪎↠b))⪶≀⋏((29⪒b)∠⫱(a⪮%⊝521))) }', output=9872","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1220213∴⪩⨒∯120112⨔≚≋⪩⨒∯213330⇴⪩⨒∯1112211=⪩⨒∯2122100","reverse_text":"⪩⨒∯2122100=⪩⨒∯1220213∴⪩⨒∯120112⨔≚≋⪩⨒∯213330⇴⪩⨒∯1112211","cot":[{"info":"⪩⨒∯1220213∴⪩⨒∯120112=⪩⨒∯3222332","layer":1},{"info":"⪩⨒∯213330⇴⪩⨒∯1112211=⪩⨒∯12112300","layer":1},{"info":"⪩⨒∯3222332⨔≚≋⪩⨒∯12112300=⪩⨒∯2122100","layer":0}]}
{"id":772,"expression_no_base_symbol":"$1595$≁$2780$⨐⩸⫘(⋗⩴⪓$1175$)","expression":"⪩⨒∯120323≁⪩⨒∯223130⨐⩸⫘(⋗⩴⪓⪩⨒∯102113)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":71503,"operation_count":3,"complexity_ratio":23834.333333333332,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"≁","left_expr":{"type":"numeric_atoms","value":1595,"base":4},"right_expr":{"type":"numeric_atoms","value":2780,"base":4}},"right_expr":{"type":"unary","operator":"⋗⩴⪓","unary_expr":{"type":"numeric_atoms","value":1175,"base":4}}},"used_operators":["fu6greOZ01","8N2wDY1A35","nOKPl9n5zu"],"dependent_operators":["3ViojmjbAp","B5M0gjZbta","6Ko8hGgeMq","3tVxb0NHM4","G9tJMlZ94a","R5aXW34M0v","Qtd6bqUJcN","tifHPKVTfV","tmPS8pqC7x","jLgFTUHLKL","wztAlM01eG"],"result":"⪩⨒∯-10003","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1595","layer":2},{"info":"number node, value=2780","layer":2},{"info":"compute binary expreesion, left_input=1595, right_input=2780, op_id = 8N2wDY1A35 binary_op_definition= 'a≁b = { (∨∊⋏b) , if (⇨a)<365 ; ((a⪎↠b)↬(b⫒⫫b)) , else }', output=53519","layer":1},{"info":"number node, value=1175","layer":2},{"info":"compute unary expreesion, input=1175, op_id = nOKPl9n5zu, unary_op_definition = '⋗⩴⪓a = { (↩a) , if (↸⊣a)>=41 ; (a⇼⇔∾(≪(a⨪↰⇹a))) , else }', output=-262","layer":1},{"info":"compute binary expreesion, left_input=53519, right_input=-262, op_id = fu6greOZ01 binary_op_definition= 'a⨐⩸⫘b = {a, if b == 0; (a⨐⩸⫘(b-1))⨓(b), if b > 0 and abs(b) < 1000; -(a⨐⩸⫘(b+1))⨓(b), if b < 0 and abs(b) < 1000; NaN, else}', output=-259","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯120323≁⪩⨒∯223130⨐⩸⫘(⋗⩴⪓⪩⨒∯102113)=⪩⨒∯-10003","reverse_text":"⪩⨒∯-10003=⪩⨒∯120323≁⪩⨒∯223130⨐⩸⫘(⋗⩴⪓⪩⨒∯102113)","cot":[{"info":"⪩⨒∯120323≁⪩⨒∯223130=⪩⨒∯31010033","layer":1},{"info":"⋗⩴⪓⪩⨒∯102113=⪩⨒∯-10012","layer":1},{"info":"⪩⨒∯31010033⨐⩸⫘⪩⨒∯-10012=⪩⨒∯-10003","layer":0}]}
{"id":773,"expression_no_base_symbol":"⨴⫝$3301$∠⫱$2457$","expression":"⨴⫝⪩⨒∯303211∠⫱⪩⨒∯212121","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1828,"operation_count":2,"complexity_ratio":914.0,"tree":{"type":"unary","operator":"⨴⫝","unary_expr":{"type":"binary","operator":"∠⫱","left_expr":{"type":"numeric_atoms","value":3301,"base":4},"right_expr":{"type":"numeric_atoms","value":2457,"base":4}}},"used_operators":["SVb2v531z1","QvoQhV0rrE"],"dependent_operators":["oDCm7WA9JY","XnXgA4xnOs","ocnLzx9CaJ","3sJ7IOPOlU","9cloC0Ngie","SWo3A1KBJH","jWTQ2TZYIH","pRsWfj4Fpp","DyGG3AbaNP","5obUd6DV38","8HhzD0ZcuI","YbUVn0Rbpy","AdZkA7nFnk","SIgE0bArFf","eLAdDNolq6","DZ8iAZOCBD","7j4O788W3g","tifHPKVTfV","AF7qkfDlqP"],"result":"⪩⨒∯22302132212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3301","layer":2},{"info":"number node, value=2457","layer":2},{"info":"compute binary expreesion, left_input=3301, right_input=2457, op_id = QvoQhV0rrE binary_op_definition= 'a∠⫱b = { ((⨑⩽⪐a)↺(617⊉≛↸a)) , if (≤/b)<=3 ; (b⇼⇔∾a) , else }', output=1234","layer":1},{"info":"compute unary expreesion, input=1234, op_id = SVb2v531z1, unary_op_definition = '⨴⫝a = { ((⪨⨬(⇋↷a))≬⇓((a⋅⇍a)⨑≵⋬(∡178))) , if (a⪇≇⋚963)!=62 ; (((541⋛107)⩼⇪↪(⪭⩑⪱a))⋻⩜⩜((a⊕∕a)∼(459⨽6))) , else }', output=2828198","layer":0}],"base":4,"result_base":4,"text":"⨴⫝⪩⨒∯303211∠⫱⪩⨒∯212121=⪩⨒∯22302132212","reverse_text":"⪩⨒∯22302132212=⨴⫝⪩⨒∯303211∠⫱⪩⨒∯212121","cot":[{"info":"⪩⨒∯303211∠⫱⪩⨒∯212121=⪩⨒∯103102","layer":1},{"info":"⨴⫝⪩⨒∯103102=⪩⨒∯22302132212","layer":0}]}
{"id":774,"expression_no_base_symbol":"$5525$⊉↱≁$4443$⫩","expression":"⪩⨒∯1112111⊉↱≁⪩⨒∯1011123⫩","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":28565,"operation_count":2,"complexity_ratio":14282.5,"tree":{"type":"unary","operator":"⫩","unary_expr":{"type":"binary","operator":"⊉↱≁","left_expr":{"type":"numeric_atoms","value":5525,"base":4},"right_expr":{"type":"numeric_atoms","value":4443,"base":4}}},"used_operators":["6aG7x05OhS","w2P8NbNXyL"],"dependent_operators":["dWAJyo7jo9","9FxExcQeMw","e1ybzncUwg","sdazOOVcIp","t8gj7n24qd","eewbuw0ToL"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5525","layer":2},{"info":"number node, value=4443","layer":2},{"info":"compute binary expreesion, left_input=5525, right_input=4443, op_id = w2P8NbNXyL binary_op_definition= 'a⊉↱≁b = { ((≉(a⨰b))⪨≂((145⩷∴a)⪨≂(-b))) }', output=28540","layer":1},{"info":"compute unary expreesion, input=28540, op_id = 6aG7x05OhS, unary_op_definition = 'a⫩ = { (a⪢a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1112111⊉↱≁⪩⨒∯1011123⫩=NaN","reverse_text":"NaN=⪩⨒∯1112111⊉↱≁⪩⨒∯1011123⫩","cot":[{"info":"⪩⨒∯1112111⊉↱≁⪩⨒∯1011123=⪩⨒∯12331330","layer":1},{"info":"⪩⨒∯12331330⫩=NaN","layer":0}]}
{"id":775,"expression_no_base_symbol":"$5158$⊮⊟↴$6360$∙∹∝$1547$∼$8189$","expression":"⪩⨒∯1100212⊮⊟↴⪩⨒∯1203120∙∹∝⪩⨒∯120023∼⪩⨒∯1333331","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":83,"operation_count":3,"complexity_ratio":27.666666666666668,"tree":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"binary","operator":"⊮⊟↴","left_expr":{"type":"numeric_atoms","value":5158,"base":4},"right_expr":{"type":"numeric_atoms","value":6360,"base":4}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":1547,"base":4},"right_expr":{"type":"numeric_atoms","value":8189,"base":4}}},"used_operators":["HmxsFra2vL","QDVgd2eftb","DyGG3AbaNP"],"dependent_operators":["BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","XhwjNDsVaA","C6VvDP6HwP","WkeUrDK8WX","kuIXHzHcAH","3Oe9XWJUTD","rJVOvQCfKK","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5158","layer":2},{"info":"number node, value=6360","layer":2},{"info":"compute binary expreesion, left_input=5158, right_input=6360, op_id = QDVgd2eftb binary_op_definition= 'a⊮⊟↴b = { ((⩰267)⪨⊡(b⊝⪿⪼a)) , if a!=19 ; ((b⨎372)/(b⪑⩈)) , else }', output=0","layer":1},{"info":"number node, value=1547","layer":2},{"info":"number node, value=8189","layer":2},{"info":"compute binary expreesion, left_input=1547, right_input=8189, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1100212⊮⊟↴⪩⨒∯1203120∙∹∝⪩⨒∯120023∼⪩⨒∯1333331=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯1100212⊮⊟↴⪩⨒∯1203120∙∹∝⪩⨒∯120023∼⪩⨒∯1333331","cot":[{"info":"⪩⨒∯1100212⊮⊟↴⪩⨒∯1203120=⪩⨒∯0","layer":1},{"info":"⪩⨒∯120023∼⪩⨒∯1333331=NaN","layer":1},{"info":"⪩⨒∯0∙∹∝NaN=⪩⨒∯0","layer":0}]}
{"id":776,"expression_no_base_symbol":"⪡⇡≛($1996$⇤$3966$)","expression":"⪡⇡≛(⪩⨒∯133030⇤⪩⨒∯331332)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":50,"operation_count":2,"complexity_ratio":25.0,"tree":{"type":"unary","operator":"⪡⇡≛","unary_expr":{"type":"binary","operator":"⇤","left_expr":{"type":"numeric_atoms","value":1996,"base":4},"right_expr":{"type":"numeric_atoms","value":3966,"base":4}}},"used_operators":["qL4PrbW1Dq","YSKBFp38Pu"],"dependent_operators":["oacrs7FA3X","apS25hmuAe","iuk5sVOGFA","8cLx32lpNA","X99M06cbEe","rysDP5nf3Z","XPYlsWDdGa","tifHPKVTfV","2DQ55sFlQl","2DDjHMKMc0","xUOZtlo3hN","QMFrweE19q"],"result":"⪩⨒∯-12211102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1996","layer":2},{"info":"number node, value=3966","layer":2},{"info":"compute binary expreesion, left_input=1996, right_input=3966, op_id = YSKBFp38Pu binary_op_definition= 'a⇤b = { (((b-523)⇼⇔∾(⨞⊢a))⫡⨏((⪲⇎a)⨵⪆(336⋝⋈⪟a))) }', output=-26962","layer":1},{"info":"compute unary expreesion, input=-26962, op_id = qL4PrbW1Dq, unary_op_definition = '⪡⇡≛a = { (a∌a) , if (a⪘⫢111)>=396 or (≅≯⇸a)!=229 or (a⪣⫩)<228 ; (a≫≃) , else }', output=-26962","layer":0}],"base":4,"result_base":4,"text":"⪡⇡≛(⪩⨒∯133030⇤⪩⨒∯331332)=⪩⨒∯-12211102","reverse_text":"⪩⨒∯-12211102=⪡⇡≛(⪩⨒∯133030⇤⪩⨒∯331332)","cot":[{"info":"⪩⨒∯133030⇤⪩⨒∯331332=⪩⨒∯-12211102","layer":1},{"info":"⪡⇡≛⪩⨒∯-12211102=⪩⨒∯-12211102","layer":0}]}
{"id":777,"expression_no_base_symbol":"≇⪴($1143$⊋≦⊧$2390$)","expression":"≇⪴(⪩⨒∯101313⊋≦⊧⪩⨒∯211112)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":33,"operation_count":2,"complexity_ratio":16.5,"tree":{"type":"unary","operator":"≇⪴","unary_expr":{"type":"binary","operator":"⊋≦⊧","left_expr":{"type":"numeric_atoms","value":1143,"base":4},"right_expr":{"type":"numeric_atoms","value":2390,"base":4}}},"used_operators":["zoVPnxeHJ3","oRDoc9rAEX"],"dependent_operators":["7j4O788W3g","Ph9nP6C5qx","f6k1SAg4EE","14qkJME0vr","g55IO6H4Gj","COABgblf1C","DZ8iAZOCBD","tifHPKVTfV","sdazOOVcIp","glklzrTFfD","DIvbN7qnHd","12rbrZMWeM","Ph9nP6C5qx","eewbuw0ToL","2td37pGCOC"],"result":"⪩⨒∯-3031310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1143","layer":2},{"info":"number node, value=2390","layer":2},{"info":"compute binary expreesion, left_input=1143, right_input=2390, op_id = oRDoc9rAEX binary_op_definition= 'a⊋≦⊧b = { (((24⊉≛↸a)⊉≛↸(⩦⩻⨪b))⊉≛↸((a⊠≄⫣)⪨≂(b⇼⇔∾a))) , if a<=128 ; (((a⇼⇔∾b)⨁⊸⫻)⇼⇔∾((22⋳⪒a)⨰(a≧⫂∧a))) , else }', output=-3293","layer":1},{"info":"compute unary expreesion, input=-3293, op_id = zoVPnxeHJ3, unary_op_definition = '≇⪴a = { ((a⪒a)↺(a⨸⪁a)) , if (a⊭↱741)>=792 ; ((a≧⫂∧a)⊦⊿) , else }', output=-13172","layer":0}],"base":4,"result_base":4,"text":"≇⪴(⪩⨒∯101313⊋≦⊧⪩⨒∯211112)=⪩⨒∯-3031310","reverse_text":"⪩⨒∯-3031310=≇⪴(⪩⨒∯101313⊋≦⊧⪩⨒∯211112)","cot":[{"info":"⪩⨒∯101313⊋≦⊧⪩⨒∯211112=⪩⨒∯-303131","layer":1},{"info":"≇⪴⪩⨒∯-303131=⪩⨒∯-3031310","layer":0}]}
{"id":778,"expression_no_base_symbol":"(⊬↢$1238$)∠⫱($1533$≬⋮$1167$)","expression":"(⊬↢⪩⨒∯103112)∠⫱(⪩⨒∯113331≬⋮⪩⨒∯102033)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1312,"operation_count":3,"complexity_ratio":437.3333333333333,"tree":{"type":"binary","operator":"∠⫱","left_expr":{"type":"unary","operator":"⊬↢","unary_expr":{"type":"numeric_atoms","value":1238,"base":4}},"right_expr":{"type":"binary","operator":"≬⋮","left_expr":{"type":"numeric_atoms","value":1533,"base":4},"right_expr":{"type":"numeric_atoms","value":1167,"base":4}}},"used_operators":["QvoQhV0rrE","WPoGxAaPR1","kbkesczE7y"],"dependent_operators":["eLAdDNolq6","DZ8iAZOCBD","7j4O788W3g","tifHPKVTfV","AF7qkfDlqP","XGcMNugi78","d7ASUq0ydm","OwUj7dcsQK","FyVja0WsTP","1eCjFl0mb9","j6NVkjMzuk","SL6IHkK8vl","MRPaB8lBjK","yyfyN0ffXY","3Oe9XWJUTD","3tVxb0NHM4","8cLx32lpNA","P8v4zCKN1o","rysDP5nf3Z","7j4O788W3g","XIabStNQrY","t8gj7n24qd","i8ToyICDmI"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1238","layer":2},{"info":"compute unary expreesion, input=1238, op_id = WPoGxAaPR1, unary_op_definition = '⊬↢a = { (((a⫞⩸⩒a)⊝⪿⪼(a⫯⪬∳a))⪎↠((a⨀⨒)↸(∐⩳⋚a))) , if (∓a)>278 ; (((a↙a)⊱⇼⊻(a∌480))⇉⇱⇎) , else }', output=218","layer":1},{"info":"number node, value=1533","layer":2},{"info":"number node, value=1167","layer":2},{"info":"compute binary expreesion, left_input=1533, right_input=1167, op_id = kbkesczE7y binary_op_definition= 'a≬⋮b = { (((-a)∲⫓(b⇋≉))↺(∥⊫(b-b))) }', output=868","layer":1},{"info":"compute binary expreesion, left_input=218, right_input=868, op_id = QvoQhV0rrE binary_op_definition= 'a∠⫱b = { ((⨑⩽⪐a)↺(617⊉≛↸a)) , if (≤/b)<=3 ; (b⇼⇔∾a) , else }', output=1234","layer":0}],"base":4,"result_base":4,"text":"(⊬↢⪩⨒∯103112)∠⫱(⪩⨒∯113331≬⋮⪩⨒∯102033)=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=(⊬↢⪩⨒∯103112)∠⫱(⪩⨒∯113331≬⋮⪩⨒∯102033)","cot":[{"info":"⊬↢⪩⨒∯103112=⪩⨒∯3122","layer":1},{"info":"⪩⨒∯113331≬⋮⪩⨒∯102033=⪩⨒∯31210","layer":1},{"info":"⪩⨒∯3122∠⫱⪩⨒∯31210=⪩⨒∯103102","layer":0}]}
{"id":779,"expression_no_base_symbol":"$3486$∘$4669$⇌⫙⪟$3408$∴$4263$","expression":"⪩⨒∯312132∘⪩⨒∯1020331⇌⫙⪟⪩⨒∯311100∴⪩⨒∯1002213","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":24,"operation_count":3,"complexity_ratio":8.0,"tree":{"type":"binary","operator":"⇌⫙⪟","left_expr":{"type":"binary","operator":"∘","left_expr":{"type":"numeric_atoms","value":3486,"base":4},"right_expr":{"type":"numeric_atoms","value":4669,"base":4}},"right_expr":{"type":"binary","operator":"∴","left_expr":{"type":"numeric_atoms","value":3408,"base":4},"right_expr":{"type":"numeric_atoms","value":4263,"base":4}}},"used_operators":["AFVx7xoS7T","Z5m6OM72h2","hrf7POJlIJ"],"dependent_operators":["DpFCA1CohY","DZ8iAZOCBD","tifHPKVTfV","2DQ55sFlQl","12rbrZMWeM","xUOZtlo3hN","eewbuw0ToL","eH2TOUuTDT","rysDP5nf3Z","g55IO6H4Gj","P8v4zCKN1o","23Mk6UjR3U"],"result":"⪩⨒∯1301","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3486","layer":2},{"info":"number node, value=4669","layer":2},{"info":"compute binary expreesion, left_input=3486, right_input=4669, op_id = Z5m6OM72h2 binary_op_definition= 'a∘b = { (380-a) , if b<=483 ; (a⪐) , else }', output=6972","layer":1},{"info":"number node, value=3408","layer":2},{"info":"number node, value=4263","layer":2},{"info":"compute binary expreesion, left_input=3408, right_input=4263, op_id = hrf7POJlIJ binary_op_definition= 'a∴b = { ((∥⊫(22⋷b))⨸⪁a) }', output=8464","layer":1},{"info":"compute binary expreesion, left_input=6972, right_input=8464, op_id = AFVx7xoS7T binary_op_definition= 'a⇌⫙⪟b = { (⨞⊢(a⇼⇔∾(a⋳⪒a))) , if (⨞⊢b)<133 ; ((a⋳⪒(b⨰261))⇼⇔∾((⋗⩬⋾b)⊉≛↸(a⨵⪆75))) , else }', output=113","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯312132∘⪩⨒∯1020331⇌⫙⪟⪩⨒∯311100∴⪩⨒∯1002213=⪩⨒∯1301","reverse_text":"⪩⨒∯1301=⪩⨒∯312132∘⪩⨒∯1020331⇌⫙⪟⪩⨒∯311100∴⪩⨒∯1002213","cot":[{"info":"⪩⨒∯312132∘⪩⨒∯1020331=⪩⨒∯1230330","layer":1},{"info":"⪩⨒∯311100∴⪩⨒∯1002213=⪩⨒∯2010100","layer":1},{"info":"⪩⨒∯1230330⇌⫙⪟⪩⨒∯2010100=⪩⨒∯1301","layer":0}]}
{"id":780,"expression_no_base_symbol":"(↩$1612$)⊾⪯⋞$2676$⫁⪎$3757$","expression":"(↩⪩⨒∯121030)⊾⪯⋞⪩⨒∯221310⫁⪎⪩⨒∯322231","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":79,"operation_count":3,"complexity_ratio":26.333333333333332,"tree":{"type":"binary","operator":"⊾⪯⋞","left_expr":{"type":"unary","operator":"↩","unary_expr":{"type":"numeric_atoms","value":1612,"base":4}},"right_expr":{"type":"binary","operator":"⫁⪎","left_expr":{"type":"numeric_atoms","value":2676,"base":4},"right_expr":{"type":"numeric_atoms","value":3757,"base":4}}},"used_operators":["HK0tfVPux8","jLgFTUHLKL","xRrnTEsQ6j"],"dependent_operators":["s3Fd5m9Dh2","KFSx94NKJn","MmTdOpaElr","XnXgA4xnOs","fOIeswaMU4","YSKBFp38Pu","oacrs7FA3X","xNBdhnnwKq","sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D","P8v4zCKN1o","Qy55tPpLXF","tifHPKVTfV","sdazOOVcIp","2DDjHMKMc0","i8ToyICDmI"],"result":"⪩⨒∯-30310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1612","layer":2},{"info":"compute unary expreesion, input=1612, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-10116","layer":1},{"info":"number node, value=2676","layer":2},{"info":"number node, value=3757","layer":2},{"info":"compute binary expreesion, left_input=2676, right_input=3757, op_id = xRrnTEsQ6j binary_op_definition= 'a⫁⪎b = { ((b⋝⋈⪟a)⇼⇔∾a) , if (∥⊫b)!=57 ; ((191∲⫓a)⋥≓≎(a⪨≂368)) , else }', output=-1081","layer":1},{"info":"compute binary expreesion, left_input=-10116, right_input=-1081, op_id = HK0tfVPux8 binary_op_definition= 'a⊾⪯⋞b = { ((121⊭∹↮)⊬⨰(a⨑≵⋬b)) , if (a⩟)==395 or (a⨱∎)>94 ; ((b⪘⫢b)⩒⫫(a⇤b)) , else }', output=-820","layer":0}],"base":4,"result_base":4,"text":"(↩⪩⨒∯121030)⊾⪯⋞⪩⨒∯221310⫁⪎⪩⨒∯322231=⪩⨒∯-30310","reverse_text":"⪩⨒∯-30310=(↩⪩⨒∯121030)⊾⪯⋞⪩⨒∯221310⫁⪎⪩⨒∯322231","cot":[{"info":"↩⪩⨒∯121030=⪩⨒∯-2132010","layer":1},{"info":"⪩⨒∯221310⫁⪎⪩⨒∯322231=⪩⨒∯-100321","layer":1},{"info":"⪩⨒∯-2132010⊾⪯⋞⪩⨒∯-100321=⪩⨒∯-30310","layer":0}]}
{"id":781,"expression_no_base_symbol":"($1089$⨫⇇↔$7021$)⊬⨰($1751$⩍⋽⫝̸$6992$)","expression":"(⪩⨒∯101001⨫⇇↔⪩⨒∯1231231)⊬⨰(⪩⨒∯123113⩍⋽⫝̸⪩⨒∯1231100)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":26,"operation_count":3,"complexity_ratio":8.666666666666666,"tree":{"type":"binary","operator":"⊬⨰","left_expr":{"type":"binary","operator":"⨫⇇↔","left_expr":{"type":"numeric_atoms","value":1089,"base":4},"right_expr":{"type":"numeric_atoms","value":7021,"base":4}},"right_expr":{"type":"binary","operator":"⩍⋽⫝̸","left_expr":{"type":"numeric_atoms","value":1751,"base":4},"right_expr":{"type":"numeric_atoms","value":6992,"base":4}}},"used_operators":["s3Fd5m9Dh2","LXhwmt4mBO","BiWNJpBvwn"],"dependent_operators":["23Mk6UjR3U","g55IO6H4Gj","nCS4ZIUYfx","d7ASUq0ydm","DZ8iAZOCBD","rJVOvQCfKK","Ph9nP6C5qx","xUOZtlo3hN"],"result":"⪩⨒∯11221122","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1089","layer":2},{"info":"number node, value=7021","layer":2},{"info":"compute binary expreesion, left_input=1089, right_input=7021, op_id = LXhwmt4mBO binary_op_definition= 'a⨫⇇↔b = { ((9⊉≛↸b)⫯⪬∳(a⨎a)) }', output=-527","layer":1},{"info":"number node, value=1751","layer":2},{"info":"number node, value=6992","layer":2},{"info":"compute binary expreesion, left_input=1751, right_input=6992, op_id = BiWNJpBvwn binary_op_definition= 'a⩍⋽⫝̸b = { ((⨞⊢508)≧⫂∧(a≧⫂∧b)) }', output=6046","layer":1},{"info":"compute binary expreesion, left_input=-527, right_input=6046, op_id = s3Fd5m9Dh2 binary_op_definition= 'a⊬⨰b = { ((a⋷528)⨳⩥⨓(b⨸⪁b)) }', output=23130","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101001⨫⇇↔⪩⨒∯1231231)⊬⨰(⪩⨒∯123113⩍⋽⫝̸⪩⨒∯1231100)=⪩⨒∯11221122","reverse_text":"⪩⨒∯11221122=(⪩⨒∯101001⨫⇇↔⪩⨒∯1231231)⊬⨰(⪩⨒∯123113⩍⋽⫝̸⪩⨒∯1231100)","cot":[{"info":"⪩⨒∯101001⨫⇇↔⪩⨒∯1231231=⪩⨒∯-20033","layer":1},{"info":"⪩⨒∯123113⩍⋽⫝̸⪩⨒∯1231100=⪩⨒∯1132132","layer":1},{"info":"⪩⨒∯-20033⊬⨰⪩⨒∯1132132=⪩⨒∯11221122","layer":0}]}
{"id":782,"expression_no_base_symbol":"($1617$⫻⋑⊟)⩚⊴⇥($1773$⨳⩥⨓$2051$)","expression":"(⪩⨒∯121101⫻⋑⊟)⩚⊴⇥(⪩⨒∯123231⨳⩥⨓⪩⨒∯200003)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":26,"operation_count":3,"complexity_ratio":8.666666666666666,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"unary","operator":"⫻⋑⊟","unary_expr":{"type":"numeric_atoms","value":1617,"base":4}},"right_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":1773,"base":4},"right_expr":{"type":"numeric_atoms","value":2051,"base":4}}},"used_operators":["NTOWxs364D","o575Zjdmzy","nCS4ZIUYfx"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rysDP5nf3Z","sdazOOVcIp","12rbrZMWeM","xUOZtlo3hN","g55IO6H4Gj","i8ToyICDmI","W4YGzv6Whe","rysDP5nf3Z"],"result":"⪩⨒∯210111","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1617","layer":2},{"info":"compute unary expreesion, input=1617, op_id = o575Zjdmzy, unary_op_definition = 'a⫻⋑⊟ = { ((a⨸⪁(⨞⊢a))⪨≂((a∲⫓a)⋳⪒(265-a))) }', output=-2724","layer":1},{"info":"number node, value=1773","layer":2},{"info":"number node, value=2051","layer":2},{"info":"compute binary expreesion, left_input=1773, right_input=2051, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=278","layer":1},{"info":"compute binary expreesion, left_input=-2724, right_input=278, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=2325","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯121101⫻⋑⊟)⩚⊴⇥(⪩⨒∯123231⨳⩥⨓⪩⨒∯200003)=⪩⨒∯210111","reverse_text":"⪩⨒∯210111=(⪩⨒∯121101⫻⋑⊟)⩚⊴⇥(⪩⨒∯123231⨳⩥⨓⪩⨒∯200003)","cot":[{"info":"⪩⨒∯121101⫻⋑⊟=⪩⨒∯-222210","layer":1},{"info":"⪩⨒∯123231⨳⩥⨓⪩⨒∯200003=⪩⨒∯10112","layer":1},{"info":"⪩⨒∯-222210⩚⊴⇥⪩⨒∯10112=⪩⨒∯210111","layer":0}]}
{"id":783,"expression_no_base_symbol":"($1962$⪁$1866$)≓∲($4121$⩁)","expression":"(⪩⨒∯132222⪁⪩⨒∯131022)≓∲(⪩⨒∯1000121⩁)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":53528800,"operation_count":3,"complexity_ratio":17842933.333333332,"tree":{"type":"binary","operator":"≓∲","left_expr":{"type":"binary","operator":"⪁","left_expr":{"type":"numeric_atoms","value":1962,"base":4},"right_expr":{"type":"numeric_atoms","value":1866,"base":4}},"right_expr":{"type":"unary","operator":"⩁","unary_expr":{"type":"numeric_atoms","value":4121,"base":4}}},"used_operators":["s1XTVnmDOJ","I7sXao9hZE","5GqDbVmqXU"],"dependent_operators":["HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu","dWAJyo7jo9","wxb3vTeyAj","nlCqmYiOvY","7j4O788W3g","jLgFTUHLKL","8cLx32lpNA"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1962","layer":2},{"info":"number node, value=1866","layer":2},{"info":"compute binary expreesion, left_input=1962, right_input=1866, op_id = I7sXao9hZE binary_op_definition= 'a⪁b = { (((⫶⊄≣b)⨽⪊≇)⪢a) }', output=nan","layer":1},{"info":"number node, value=4121","layer":2},{"info":"compute unary expreesion, input=4121, op_id = 5GqDbVmqXU, unary_op_definition = 'a⩁ = { ((↩a)∌(a↺a)) }', output=-30188","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-30188, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯132222⪁⪩⨒∯131022)≓∲(⪩⨒∯1000121⩁)=NaN","reverse_text":"NaN=(⪩⨒∯132222⪁⪩⨒∯131022)≓∲(⪩⨒∯1000121⩁)","cot":[{"info":"⪩⨒∯132222⪁⪩⨒∯131022=NaN","layer":1},{"info":"⪩⨒∯1000121⩁=⪩⨒∯-13113230","layer":1},{"info":"NaN≓∲⪩⨒∯-13113230=NaN","layer":0}]}
{"id":784,"expression_no_base_symbol":"($5895$⪢$3907$)↳∿⪆($1560$⪔$1221$)","expression":"(⪩⨒∯1130013⪢⪩⨒∯331003)↳∿⪆(⪩⨒∯120120⪔⪩⨒∯103011)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8460,"operation_count":3,"complexity_ratio":2820.0,"tree":{"type":"binary","operator":"↳∿⪆","left_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":5895,"base":4},"right_expr":{"type":"numeric_atoms","value":3907,"base":4}},"right_expr":{"type":"binary","operator":"⪔","left_expr":{"type":"numeric_atoms","value":1560,"base":4},"right_expr":{"type":"numeric_atoms","value":1221,"base":4}}},"used_operators":["Cw4SuJJGHO","dWAJyo7jo9","GjBEYRfMaF"],"dependent_operators":["hyuBjUqXlG","bF6eod5Gvf","nEsXyWgiOK","ruOEQAzv1W","Tw270M8GLb","QMFrweE19q","k8jYdgA6NY","YjI8oCXuph","8INZBEW696","dWAJyo7jo9","nREPSIbpBE","2DDjHMKMc0","IWmyXbctLI","PoHhknlbAi"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5895","layer":2},{"info":"number node, value=3907","layer":2},{"info":"compute binary expreesion, left_input=5895, right_input=3907, op_id = dWAJyo7jo9 binary_op_definition= 'a⪢b = {b, if b == 0; (a)%(a⪢(b-1)), if b > 0 and abs(b) < 1000000; -(a)%(a⪢(b+1)), if b < 0 and abs(b) < 1000000; NaN, else}', output=nan","layer":1},{"info":"number node, value=1560","layer":2},{"info":"number node, value=1221","layer":2},{"info":"compute binary expreesion, left_input=1560, right_input=1221, op_id = GjBEYRfMaF binary_op_definition= 'a⪔b = { (((⫇a)∓⋝(61⪢b))⪮%⊝((b⋝⋈⪟b)⨚(a≀⩗∶a))) }', output=450","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=450, op_id = Cw4SuJJGHO binary_op_definition= 'a↳∿⪆b = { ((⨰⫟⨤(↔15))⨻⩈⩔((b⪛⫼133)⫡⨏(b→⨶⪴a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1130013⪢⪩⨒∯331003)↳∿⪆(⪩⨒∯120120⪔⪩⨒∯103011)=NaN","reverse_text":"NaN=(⪩⨒∯1130013⪢⪩⨒∯331003)↳∿⪆(⪩⨒∯120120⪔⪩⨒∯103011)","cot":[{"info":"⪩⨒∯1130013⪢⪩⨒∯331003=NaN","layer":1},{"info":"⪩⨒∯120120⪔⪩⨒∯103011=⪩⨒∯13002","layer":1},{"info":"NaN↳∿⪆⪩⨒∯13002=NaN","layer":0}]}
{"id":785,"expression_no_base_symbol":"$1089$⨚⇆$4802$⊭∹↮","expression":"⪩⨒∯101001⨚⇆⪩⨒∯1023002⊭∹↮","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7660,"operation_count":2,"complexity_ratio":3830.0,"tree":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"numeric_atoms","value":1089,"base":4},"right_expr":{"type":"numeric_atoms","value":4802,"base":4}}},"used_operators":["xNBdhnnwKq","lwHaAYXP2r"],"dependent_operators":["2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1089","layer":2},{"info":"number node, value=4802","layer":2},{"info":"compute binary expreesion, left_input=1089, right_input=4802, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯101001⨚⇆⪩⨒∯1023002⊭∹↮=NaN","reverse_text":"NaN=⪩⨒∯101001⨚⇆⪩⨒∯1023002⊭∹↮","cot":[{"info":"⪩⨒∯101001⨚⇆⪩⨒∯1023002=NaN","layer":1},{"info":"NaN⊭∹↮=NaN","layer":0}]}
{"id":786,"expression_no_base_symbol":"($2924$≬⋮$1625$)⩦($4414$⩼⇪↪$5577$)","expression":"(⪩⨒∯231230≬⋮⪩⨒∯121121)⩦(⪩⨒∯1010332⩼⇪↪⪩⨒∯1113021)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":40,"operation_count":3,"complexity_ratio":13.333333333333334,"tree":{"type":"binary","operator":"⩦","left_expr":{"type":"binary","operator":"≬⋮","left_expr":{"type":"numeric_atoms","value":2924,"base":4},"right_expr":{"type":"numeric_atoms","value":1625,"base":4}},"right_expr":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"numeric_atoms","value":4414,"base":4},"right_expr":{"type":"numeric_atoms","value":5577,"base":4}}},"used_operators":["0kmYd0q39Y","kbkesczE7y","ocnLzx9CaJ"],"dependent_operators":["N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q","P8v4zCKN1o","rysDP5nf3Z","7j4O788W3g","XIabStNQrY","t8gj7n24qd","i8ToyICDmI","9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q"],"result":"⪩⨒∯123020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2924","layer":2},{"info":"number node, value=1625","layer":2},{"info":"compute binary expreesion, left_input=2924, right_input=1625, op_id = kbkesczE7y binary_op_definition= 'a≬⋮b = { (((-a)∲⫓(b⇋≉))↺(∥⊫(b-b))) }', output=868","layer":1},{"info":"number node, value=4414","layer":2},{"info":"number node, value=5577","layer":2},{"info":"compute binary expreesion, left_input=4414, right_input=5577, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=-30994","layer":1},{"info":"compute binary expreesion, left_input=868, right_input=-30994, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=1736","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯231230≬⋮⪩⨒∯121121)⩦(⪩⨒∯1010332⩼⇪↪⪩⨒∯1113021)=⪩⨒∯123020","reverse_text":"⪩⨒∯123020=(⪩⨒∯231230≬⋮⪩⨒∯121121)⩦(⪩⨒∯1010332⩼⇪↪⪩⨒∯1113021)","cot":[{"info":"⪩⨒∯231230≬⋮⪩⨒∯121121=⪩⨒∯31210","layer":1},{"info":"⪩⨒∯1010332⩼⇪↪⪩⨒∯1113021=⪩⨒∯-13210102","layer":1},{"info":"⪩⨒∯31210⩦⪩⨒∯-13210102=⪩⨒∯123020","layer":0}]}
{"id":787,"expression_no_base_symbol":"$1156$⇴$1375$⇋≉","expression":"⪩⨒∯102010⇴⪩⨒∯111133⇋≉","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":17,"operation_count":2,"complexity_ratio":8.5,"tree":{"type":"unary","operator":"⇋≉","unary_expr":{"type":"binary","operator":"⇴","left_expr":{"type":"numeric_atoms","value":1156,"base":4},"right_expr":{"type":"numeric_atoms","value":1375,"base":4}}},"used_operators":["XIabStNQrY","4JB6nKBMSY"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","sdazOOVcIp","NTOWxs364D","COABgblf1C"],"result":"⪩⨒∯10201012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1156","layer":2},{"info":"number node, value=1375","layer":2},{"info":"compute binary expreesion, left_input=1156, right_input=1375, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=9300","layer":1},{"info":"compute unary expreesion, input=9300, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=18502","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102010⇴⪩⨒∯111133⇋≉=⪩⨒∯10201012","reverse_text":"⪩⨒∯10201012=⪩⨒∯102010⇴⪩⨒∯111133⇋≉","cot":[{"info":"⪩⨒∯102010⇴⪩⨒∯111133=⪩⨒∯2101110","layer":1},{"info":"⪩⨒∯2101110⇋≉=⪩⨒∯10201012","layer":0}]}
{"id":788,"expression_no_base_symbol":"$1109$⫉⨲⊜$3694$⪡($2891$⊟⇱)","expression":"⪩⨒∯101111⫉⨲⊜⪩⨒∯321232⪡(⪩⨒∯231023⊟⇱)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":47,"operation_count":3,"complexity_ratio":15.666666666666666,"tree":{"type":"binary","operator":"⪡","left_expr":{"type":"binary","operator":"⫉⨲⊜","left_expr":{"type":"numeric_atoms","value":1109,"base":4},"right_expr":{"type":"numeric_atoms","value":3694,"base":4}},"right_expr":{"type":"unary","operator":"⊟⇱","unary_expr":{"type":"numeric_atoms","value":2891,"base":4}}},"used_operators":["oraRL2iQuh","WhqkvtTD3t","03sUfWo75k"],"dependent_operators":["2Wsdkap16l","ljTHtUsqzn","k8jYdgA6NY","8WDwsbhb0R","eewbuw0ToL","zVYPLywUTj","IWmyXbctLI"],"result":"⪩⨒∯-132100","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1109","layer":2},{"info":"number node, value=3694","layer":2},{"info":"compute binary expreesion, left_input=1109, right_input=3694, op_id = WhqkvtTD3t binary_op_definition= 'a⫉⨲⊜b = { (b⨰120) , if b<=7 ; (a⊪) , else }', output=0","layer":1},{"info":"number node, value=2891","layer":2},{"info":"compute unary expreesion, input=2891, op_id = 03sUfWo75k, unary_op_definition = 'a⊟⇱ = { (a⪮%⊝a) }', output=6098","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=6098, op_id = oraRL2iQuh binary_op_definition= 'a⪡b = { (107%(a⩹b)) , if a>=49 ; (≀↧⇸(∂⩏⊆a)) , else }', output=-1936","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯101111⫉⨲⊜⪩⨒∯321232⪡(⪩⨒∯231023⊟⇱)=⪩⨒∯-132100","reverse_text":"⪩⨒∯-132100=⪩⨒∯101111⫉⨲⊜⪩⨒∯321232⪡(⪩⨒∯231023⊟⇱)","cot":[{"info":"⪩⨒∯101111⫉⨲⊜⪩⨒∯321232=⪩⨒∯0","layer":1},{"info":"⪩⨒∯231023⊟⇱=⪩⨒∯1133102","layer":1},{"info":"⪩⨒∯0⪡⪩⨒∯1133102=⪩⨒∯-132100","layer":0}]}
{"id":789,"expression_no_base_symbol":"⩷⨜⫀($1226$≀⩗∶$1940$)","expression":"⩷⨜⫀(⪩⨒∯103022≀⩗∶⪩⨒∯132110)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16,"operation_count":2,"complexity_ratio":8.0,"tree":{"type":"unary","operator":"⩷⨜⫀","unary_expr":{"type":"binary","operator":"≀⩗∶","left_expr":{"type":"numeric_atoms","value":1226,"base":4},"right_expr":{"type":"numeric_atoms","value":1940,"base":4}}},"used_operators":["CDi0ktkjQ4","8INZBEW696"],"dependent_operators":["ruOEQAzv1W","nhYeJWJD5X","KPf6cnQVty","2DlMacCsIx","l07mrZUIn9"],"result":"⪩⨒∯-23332","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1226","layer":2},{"info":"number node, value=1940","layer":2},{"info":"compute binary expreesion, left_input=1226, right_input=1940, op_id = 8INZBEW696 binary_op_definition= 'a≀⩗∶b = { (a⩨b) , if (a∺≝⩲555)<251 ; (306↪⪝) , else }', output=-3","layer":1},{"info":"compute unary expreesion, input=-3, op_id = CDi0ktkjQ4, unary_op_definition = '⩷⨜⫀a = { (a∇⊂⋱383) , if a<1 ; (↔a) , else }', output=-766","layer":0}],"base":4,"result_base":4,"text":"⩷⨜⫀(⪩⨒∯103022≀⩗∶⪩⨒∯132110)=⪩⨒∯-23332","reverse_text":"⪩⨒∯-23332=⩷⨜⫀(⪩⨒∯103022≀⩗∶⪩⨒∯132110)","cot":[{"info":"⪩⨒∯103022≀⩗∶⪩⨒∯132110=⪩⨒∯-3","layer":1},{"info":"⩷⨜⫀⪩⨒∯-3=⪩⨒∯-23332","layer":0}]}
{"id":790,"expression_no_base_symbol":"∨∊⋏($4500$⨳⩥⨓$1507$)","expression":"∨∊⋏(⪩⨒∯1012110⨳⩥⨓⪩⨒∯113203)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":92,"operation_count":2,"complexity_ratio":46.0,"tree":{"type":"unary","operator":"∨∊⋏","unary_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":4500,"base":4},"right_expr":{"type":"numeric_atoms","value":1507,"base":4}}},"used_operators":["R5aXW34M0v","nCS4ZIUYfx"],"dependent_operators":["L05ObWFQCd","YjI8oCXuph","9ICcGScMcE","g7Hmc5v1ko","ocnLzx9CaJ","2DDjHMKMc0","hrf7POJlIJ","W4YGzv6Whe","rysDP5nf3Z"],"result":"⪩⨒∯-113001111","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4500","layer":2},{"info":"number node, value=1507","layer":2},{"info":"compute binary expreesion, left_input=4500, right_input=1507, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-2993","layer":1},{"info":"compute unary expreesion, input=-2993, op_id = R5aXW34M0v, unary_op_definition = '∨∊⋏a = { (((101⋝⋈⪟206)⪍↜⋙(≦∁a))⩼⇪↪((a⩌⋺a)∴(⫇a))) }', output=-94293","layer":0}],"base":4,"result_base":4,"text":"∨∊⋏(⪩⨒∯1012110⨳⩥⨓⪩⨒∯113203)=⪩⨒∯-113001111","reverse_text":"⪩⨒∯-113001111=∨∊⋏(⪩⨒∯1012110⨳⩥⨓⪩⨒∯113203)","cot":[{"info":"⪩⨒∯1012110⨳⩥⨓⪩⨒∯113203=⪩⨒∯-232301","layer":1},{"info":"∨∊⋏⪩⨒∯-232301=⪩⨒∯-113001111","layer":0}]}
{"id":791,"expression_no_base_symbol":"(≅≯⇸$1932$)↳∿⪆(⨆≐≲$1231$)","expression":"(≅≯⇸⪩⨒∯132030)↳∿⪆(⨆≐≲⪩⨒∯103033)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":260114,"operation_count":3,"complexity_ratio":86704.66666666667,"tree":{"type":"binary","operator":"↳∿⪆","left_expr":{"type":"unary","operator":"≅≯⇸","unary_expr":{"type":"numeric_atoms","value":1932,"base":4}},"right_expr":{"type":"unary","operator":"⨆≐≲","unary_expr":{"type":"numeric_atoms","value":1231,"base":4}}},"used_operators":["Cw4SuJJGHO","apS25hmuAe","Bi9z9uYZqW"],"dependent_operators":["hyuBjUqXlG","bF6eod5Gvf","nEsXyWgiOK","ruOEQAzv1W","Tw270M8GLb","QMFrweE19q","EBcxylXtPf","QMFrweE19q","SWo3A1KBJH","SUmda5xLS4","bx9Z9DAK5y"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1932","layer":2},{"info":"compute unary expreesion, input=1932, op_id = apS25hmuAe, unary_op_definition = '≅≯⇸a = { ((471⫡⨏a)⫌⩹⨱) }', output=15405","layer":1},{"info":"number node, value=1231","layer":2},{"info":"compute unary expreesion, input=1231, op_id = Bi9z9uYZqW, unary_op_definition = '⨆≐≲a = { (⇋↷(⇾⩊⇾(a⪄a))) }', output=13138584","layer":1},{"info":"compute binary expreesion, left_input=15405, right_input=13138584, op_id = Cw4SuJJGHO binary_op_definition= 'a↳∿⪆b = { ((⨰⫟⨤(↔15))⨻⩈⩔((b⪛⫼133)⫡⨏(b→⨶⪴a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(≅≯⇸⪩⨒∯132030)↳∿⪆(⨆≐≲⪩⨒∯103033)=NaN","reverse_text":"NaN=(≅≯⇸⪩⨒∯132030)↳∿⪆(⨆≐≲⪩⨒∯103033)","cot":[{"info":"≅≯⇸⪩⨒∯132030=⪩⨒∯3300231","layer":1},{"info":"⨆≐≲⪩⨒∯103033=⪩⨒∯302013222120","layer":1},{"info":"⪩⨒∯3300231↳∿⪆⪩⨒∯302013222120=NaN","layer":0}]}
{"id":792,"expression_no_base_symbol":"(≦∁$7703$)⫉⨲⊜($1111$⫃⨇$1001$)","expression":"(≦∁⪩⨒∯1320113)⫉⨲⊜(⪩⨒∯101113⫃⨇⪩⨒∯33221)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19,"operation_count":3,"complexity_ratio":6.333333333333333,"tree":{"type":"binary","operator":"⫉⨲⊜","left_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":7703,"base":4}},"right_expr":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"numeric_atoms","value":1111,"base":4},"right_expr":{"type":"numeric_atoms","value":1001,"base":4}}},"used_operators":["WhqkvtTD3t","9ICcGScMcE","09Ly4LVMIf"],"dependent_operators":["eewbuw0ToL","zVYPLywUTj","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG"],"result":"⪩⨒∯-1000302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7703","layer":2},{"info":"compute unary expreesion, input=7703, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=7703","layer":1},{"info":"number node, value=1111","layer":2},{"info":"number node, value=1001","layer":2},{"info":"compute binary expreesion, left_input=1111, right_input=1001, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=-4036","layer":1},{"info":"compute binary expreesion, left_input=7703, right_input=-4036, op_id = WhqkvtTD3t binary_op_definition= 'a⫉⨲⊜b = { (b⨰120) , if b<=7 ; (a⊪) , else }', output=-4146","layer":0}],"base":4,"result_base":4,"text":"(≦∁⪩⨒∯1320113)⫉⨲⊜(⪩⨒∯101113⫃⨇⪩⨒∯33221)=⪩⨒∯-1000302","reverse_text":"⪩⨒∯-1000302=(≦∁⪩⨒∯1320113)⫉⨲⊜(⪩⨒∯101113⫃⨇⪩⨒∯33221)","cot":[{"info":"≦∁⪩⨒∯1320113=⪩⨒∯1320113","layer":1},{"info":"⪩⨒∯101113⫃⨇⪩⨒∯33221=⪩⨒∯-333010","layer":1},{"info":"⪩⨒∯1320113⫉⨲⊜⪩⨒∯-333010=⪩⨒∯-1000302","layer":0}]}
{"id":793,"expression_no_base_symbol":"($7781$∋$6323$)⇡⇂($1127$/$1868$)","expression":"(⪩⨒∯1321211∋⪩⨒∯1202303)⇡⇂(⪩⨒∯101213/⪩⨒∯131030)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1384,"operation_count":3,"complexity_ratio":461.3333333333333,"tree":{"type":"binary","operator":"⇡⇂","left_expr":{"type":"binary","operator":"∋","left_expr":{"type":"numeric_atoms","value":7781,"base":4},"right_expr":{"type":"numeric_atoms","value":6323,"base":4}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":1127,"base":4},"right_expr":{"type":"numeric_atoms","value":1868,"base":4}}},"used_operators":["UMwdvZNt44","ukq6epAj5P","XhwjNDsVaA"],"dependent_operators":["9FxExcQeMw","23Mk6UjR3U","z4E1FaHLuy","3tj9sqzovi","fu6greOZ01","AHs5Up7iyr","lvlrscuwVU","KPf6cnQVty","uBihLCJcMX","12rbrZMWeM","WPoGxAaPR1","SUmda5xLS4","61wBmkZwlr","KbjG8mgYpV","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7781","layer":2},{"info":"number node, value=6323","layer":2},{"info":"compute binary expreesion, left_input=7781, right_input=6323, op_id = ukq6epAj5P binary_op_definition= 'a∋b = { ((≋a)∠↢(b⪄a)) }', output=13452196","layer":1},{"info":"number node, value=1127","layer":2},{"info":"number node, value=1868","layer":2},{"info":"compute binary expreesion, left_input=1127, right_input=1868, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute binary expreesion, left_input=13452196, right_input=0, op_id = UMwdvZNt44 binary_op_definition= 'a⇡⇂b = { (((b≹⇙⪍b)⋳⪒(b⋷a))∺≝⩲(⫟(a⩷∴43))) , if (⊬↢a)==727 or (a⇔⨋)<18 ; ((604≴⪞⇿(≻⋜b))⨐⩸⫘a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1321211∋⪩⨒∯1202303)⇡⇂(⪩⨒∯101213/⪩⨒∯131030)=NaN","reverse_text":"NaN=(⪩⨒∯1321211∋⪩⨒∯1202303)⇡⇂(⪩⨒∯101213/⪩⨒∯131030)","cot":[{"info":"⪩⨒∯1321211∋⪩⨒∯1202303=⪩⨒∯303110032210","layer":1},{"info":"⪩⨒∯101213/⪩⨒∯131030=⪩⨒∯0","layer":1},{"info":"⪩⨒∯303110032210⇡⇂⪩⨒∯0=NaN","layer":0}]}
{"id":794,"expression_no_base_symbol":"($4871$⨪↰⇹$2039$)⇂≾⫗($5361$⇮⋭$1484$)","expression":"(⪩⨒∯1030013⨪↰⇹⪩⨒∯133313)⇂≾⫗(⪩⨒∯1103301⇮⋭⪩⨒∯113030)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4991,"operation_count":3,"complexity_ratio":1663.6666666666667,"tree":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":4871,"base":4},"right_expr":{"type":"numeric_atoms","value":2039,"base":4}},"right_expr":{"type":"binary","operator":"⇮⋭","left_expr":{"type":"numeric_atoms","value":5361,"base":4},"right_expr":{"type":"numeric_atoms","value":1484,"base":4}}},"used_operators":["aBQ6xLxuTc","tmPS8pqC7x","vkpjKywKVM"],"dependent_operators":["g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U","rJVOvQCfKK","nhYeJWJD5X","U6pG0PXrV3","tifHPKVTfV","bJkvcejdHO","40aOVDgCDB","YbVcJGFEVW"],"result":"⪩⨒∯-22210","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4871","layer":2},{"info":"number node, value=2039","layer":2},{"info":"compute binary expreesion, left_input=4871, right_input=2039, op_id = tmPS8pqC7x binary_op_definition= 'a⨪↰⇹b = {a, if a == 0; (b)⨎((a-1)⨪↰⇹b), if a > 0 and abs(a) < 1000000; -(b)⨎((a+1)⨪↰⇹b), if a < 0 and abs(a) < 1000000; NaN, else}', output=4871","layer":1},{"info":"number node, value=5361","layer":2},{"info":"number node, value=1484","layer":2},{"info":"compute binary expreesion, left_input=5361, right_input=1484, op_id = vkpjKywKVM binary_op_definition= 'a⇮⋭b = { (((⊖b)⊢)≎⊠⪸((a≃b)⇼⇔∾(47∇⊂⋱106))) }', output=-473","layer":1},{"info":"compute binary expreesion, left_input=4871, right_input=-473, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-676","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1030013⨪↰⇹⪩⨒∯133313)⇂≾⫗(⪩⨒∯1103301⇮⋭⪩⨒∯113030)=⪩⨒∯-22210","reverse_text":"⪩⨒∯-22210=(⪩⨒∯1030013⨪↰⇹⪩⨒∯133313)⇂≾⫗(⪩⨒∯1103301⇮⋭⪩⨒∯113030)","cot":[{"info":"⪩⨒∯1030013⨪↰⇹⪩⨒∯133313=⪩⨒∯1030013","layer":1},{"info":"⪩⨒∯1103301⇮⋭⪩⨒∯113030=⪩⨒∯-13121","layer":1},{"info":"⪩⨒∯1030013⇂≾⫗⪩⨒∯-13121=⪩⨒∯-22210","layer":0}]}
{"id":795,"expression_no_base_symbol":"$4225$⋥⋵⩄$2929$⪒(⩷⨜⫀$1625$)","expression":"⪩⨒∯1002001⋥⋵⩄⪩⨒∯231301⪒(⩷⨜⫀⪩⨒∯121121)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":35,"operation_count":3,"complexity_ratio":11.666666666666666,"tree":{"type":"binary","operator":"⪒","left_expr":{"type":"binary","operator":"⋥⋵⩄","left_expr":{"type":"numeric_atoms","value":4225,"base":4},"right_expr":{"type":"numeric_atoms","value":2929,"base":4}},"right_expr":{"type":"unary","operator":"⩷⨜⫀","unary_expr":{"type":"numeric_atoms","value":1625,"base":4}}},"used_operators":["f6k1SAg4EE","7t3wd0Fuz7","CDi0ktkjQ4"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","IWmyXbctLI","2td37pGCOC","AFVx7xoS7T","ruOEQAzv1W","nhYeJWJD5X"],"result":"⪩⨒∯103113","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4225","layer":2},{"info":"number node, value=2929","layer":2},{"info":"compute binary expreesion, left_input=4225, right_input=2929, op_id = 7t3wd0Fuz7 binary_op_definition= 'a⋥⋵⩄b = { ((⩦⩻⨪a)⇌⫙⪟(b⪮%⊝b)) }', output=113","layer":1},{"info":"number node, value=1625","layer":2},{"info":"compute unary expreesion, input=1625, op_id = CDi0ktkjQ4, unary_op_definition = '⩷⨜⫀a = { (a∇⊂⋱383) , if a<1 ; (↔a) , else }', output=-1352","layer":1},{"info":"compute binary expreesion, left_input=113, right_input=-1352, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=1239","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1002001⋥⋵⩄⪩⨒∯231301⪒(⩷⨜⫀⪩⨒∯121121)=⪩⨒∯103113","reverse_text":"⪩⨒∯103113=⪩⨒∯1002001⋥⋵⩄⪩⨒∯231301⪒(⩷⨜⫀⪩⨒∯121121)","cot":[{"info":"⪩⨒∯1002001⋥⋵⩄⪩⨒∯231301=⪩⨒∯1301","layer":1},{"info":"⩷⨜⫀⪩⨒∯121121=⪩⨒∯-111020","layer":1},{"info":"⪩⨒∯1301⪒⪩⨒∯-111020=⪩⨒∯103113","layer":0}]}
{"id":796,"expression_no_base_symbol":"$1449$∷$2113$⩢≌","expression":"⪩⨒∯112221∷⪩⨒∯201001⩢≌","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":234,"operation_count":2,"complexity_ratio":117.0,"tree":{"type":"unary","operator":"⩢≌","unary_expr":{"type":"binary","operator":"∷","left_expr":{"type":"numeric_atoms","value":1449,"base":4},"right_expr":{"type":"numeric_atoms","value":2113,"base":4}}},"used_operators":["D617RFjZIq","D3AQDKkPcf"],"dependent_operators":["hTbEZDJLEm","o20kRiQErp","9FxExcQeMw","NTOWxs364D","7j4O788W3g"],"result":"⪩⨒∯1301","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1449","layer":2},{"info":"number node, value=2113","layer":2},{"info":"compute binary expreesion, left_input=1449, right_input=2113, op_id = D3AQDKkPcf binary_op_definition= 'a∷b = { (a⩚⊴⇥673) , if (b⩷∴24)<=112 ; (a↺b) , else }', output=2113","layer":1},{"info":"compute unary expreesion, input=2113, op_id = D617RFjZIq, unary_op_definition = 'a⩢≌ = { ((a∸)∟) }', output=113","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯112221∷⪩⨒∯201001⩢≌=⪩⨒∯1301","reverse_text":"⪩⨒∯1301=⪩⨒∯112221∷⪩⨒∯201001⩢≌","cot":[{"info":"⪩⨒∯112221∷⪩⨒∯201001=⪩⨒∯201001","layer":1},{"info":"⪩⨒∯201001⩢≌=⪩⨒∯1301","layer":0}]}
{"id":797,"expression_no_base_symbol":"(⩎⋉$6000$)⫳≱↱$2225$≚⊃≕$6233$","expression":"(⩎⋉⪩⨒∯1131300)⫳≱↱⪩⨒∯202301≚⊃≕⪩⨒∯1201121","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":405,"operation_count":3,"complexity_ratio":135.0,"tree":{"type":"binary","operator":"⫳≱↱","left_expr":{"type":"unary","operator":"⩎⋉","unary_expr":{"type":"numeric_atoms","value":6000,"base":4}},"right_expr":{"type":"binary","operator":"≚⊃≕","left_expr":{"type":"numeric_atoms","value":2225,"base":4},"right_expr":{"type":"numeric_atoms","value":6233,"base":4}}},"used_operators":["ZvLB05nZmT","FlXk3pOYe8","Bmrmz2XGnR"],"dependent_operators":["2Wsdkap16l","FyVja0WsTP","wEfv7U73WA","bJkvcejdHO","HmxsFra2vL","8cLx32lpNA","KbjG8mgYpV","wztAlM01eG","JclMnS0uGI","XhwjNDsVaA","W7eaUhjymW","9ICcGScMcE","fG6uBQFnGz","8w2t5hMYqp","Bmrmz2XGnR","Noe24qw2ks","1aApVXNlOP","i8ToyICDmI","nCS4ZIUYfx","2DlMacCsIx","hrf7POJlIJ","9FxExcQeMw","Qy55tPpLXF","7j4O788W3g","sdazOOVcIp","8w2t5hMYqp","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q"],"result":"⪩⨒∯-3030","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6000","layer":2},{"info":"compute unary expreesion, input=6000, op_id = FlXk3pOYe8, unary_op_definition = '⩎⋉a = { (((a/a)∲⫓(≛a))∴((a⩨a)⨳⩥⨓(⊄⩳↩a))) , if (a⩇∃⫛268)<=24 or a==244 or (↩⪖a)>=4 ; (((a⨔⇊a)∠↢(↸⊣a))≚⊃≕((≦∁a)⨐461)) , else }', output=1650","layer":1},{"info":"number node, value=2225","layer":2},{"info":"number node, value=6233","layer":2},{"info":"compute binary expreesion, left_input=2225, right_input=6233, op_id = Bmrmz2XGnR binary_op_definition= 'a≚⊃≕b = { (-((⊄⩳↩b)⪨≂(a⩷∴b))) , if ((b⫡⨏524)<690 or (⨞⊢a)>=395) ; ((⊄⩳↩(b⋥≓≎a))⋥≓≎((a↺a)⪨≂(479⨸⪁a))) , else }', output=-17745","layer":1},{"info":"compute binary expreesion, left_input=1650, right_input=-17745, op_id = ZvLB05nZmT binary_op_definition= 'a⫳≱↱b = { (((a⩹b)⇐≅)∌((a∙∹∝345)⊱⇼⊻(b≎⊠⪸a))) }', output=-204","layer":0}],"base":4,"result_base":4,"text":"(⩎⋉⪩⨒∯1131300)⫳≱↱⪩⨒∯202301≚⊃≕⪩⨒∯1201121=⪩⨒∯-3030","reverse_text":"⪩⨒∯-3030=(⩎⋉⪩⨒∯1131300)⫳≱↱⪩⨒∯202301≚⊃≕⪩⨒∯1201121","cot":[{"info":"⩎⋉⪩⨒∯1131300=⪩⨒∯121302","layer":1},{"info":"⪩⨒∯202301≚⊃≕⪩⨒∯1201121=⪩⨒∯-10111101","layer":1},{"info":"⪩⨒∯121302⫳≱↱⪩⨒∯-10111101=⪩⨒∯-3030","layer":0}]}
{"id":798,"expression_no_base_symbol":"⋃(⇘$1271$)","expression":"⋃(⇘⪩⨒∯103313)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2591,"operation_count":2,"complexity_ratio":1295.5,"tree":{"type":"unary","operator":"⋃","unary_expr":{"type":"unary","operator":"⇘","unary_expr":{"type":"numeric_atoms","value":1271,"base":4}}},"used_operators":["3mBM5G4a3l","MGuIdZPyUC"],"dependent_operators":["g55IO6H4Gj","eLxqMNBOBk","86A5ENbKR9","9HNa5Wba9A","E4l6HwMY31","40aOVDgCDB","bF6eod5Gvf","AFVx7xoS7T","f6k1SAg4EE","5twsqlHp2o","oacrs7FA3X"],"result":"⪩⨒∯202201022","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1271","layer":2},{"info":"compute unary expreesion, input=1271, op_id = MGuIdZPyUC, unary_op_definition = '⇘a = { (⪸((⫓⪴a)→⨶⪴(a⪘⫢a))) , if (⫓⪴a)>35 ; (((a*a)⊢)⊔((a⊢a)⇌⫙⪟(193⪒a))) , else }', output=70642","layer":1},{"info":"compute unary expreesion, input=70642, op_id = 3mBM5G4a3l, unary_op_definition = '⋃a = { (51⨸⪁a) }', output=141386","layer":0}],"base":4,"result_base":4,"text":"⋃(⇘⪩⨒∯103313)=⪩⨒∯202201022","reverse_text":"⪩⨒∯202201022=⋃(⇘⪩⨒∯103313)","cot":[{"info":"⇘⪩⨒∯103313=⪩⨒∯101033302","layer":1},{"info":"⋃⪩⨒∯101033302=⪩⨒∯202201022","layer":0}]}
{"id":799,"expression_no_base_symbol":"⇐($3794$⪨≂$1489$)","expression":"⇐(⪩⨒∯323102⪨≂⪩⨒∯113101)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":52,"operation_count":2,"complexity_ratio":26.0,"tree":{"type":"unary","operator":"⇐","unary_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":3794,"base":4},"right_expr":{"type":"numeric_atoms","value":1489,"base":4}}},"used_operators":["nmZMaaE0Q9","sdazOOVcIp"],"dependent_operators":["23Mk6UjR3U","ocnLzx9CaJ","SWo3A1KBJH","nREPSIbpBE","k8jYdgA6NY","u6S6b8DprG","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯3302022","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3794","layer":2},{"info":"number node, value=1489","layer":2},{"info":"compute binary expreesion, left_input=3794, right_input=1489, op_id = sdazOOVcIp binary_op_definition= 'a⪨≂b = { (((a-117)-b)-((145-b)-(a-a))) , if (-b)==187 ; ((-(b-102))-((b-a)-a)) , else }', output=4712","layer":1},{"info":"compute unary expreesion, input=4712, op_id = nmZMaaE0Q9, unary_op_definition = '⇐a = { (((⇋↷a)⋷(a⩼⇪↪a))%(↽≂(a⨚a))) }', output=15498","layer":0}],"base":4,"result_base":4,"text":"⇐(⪩⨒∯323102⪨≂⪩⨒∯113101)=⪩⨒∯3302022","reverse_text":"⪩⨒∯3302022=⇐(⪩⨒∯323102⪨≂⪩⨒∯113101)","cot":[{"info":"⪩⨒∯323102⪨≂⪩⨒∯113101=⪩⨒∯1021220","layer":1},{"info":"⇐⪩⨒∯1021220=⪩⨒∯3302022","layer":0}]}
{"id":800,"expression_no_base_symbol":"∡$1395$⩍⋽⫝̸$6103$","expression":"∡⪩⨒∯111303⩍⋽⫝̸⪩⨒∯1133113","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":14,"operation_count":2,"complexity_ratio":7.0,"tree":{"type":"unary","operator":"∡","unary_expr":{"type":"binary","operator":"⩍⋽⫝̸","left_expr":{"type":"numeric_atoms","value":1395,"base":4},"right_expr":{"type":"numeric_atoms","value":6103,"base":4}}},"used_operators":["pRsWfj4Fpp","BiWNJpBvwn"],"dependent_operators":["D4vGDi5EA2","DZ8iAZOCBD","2DDjHMKMc0","Ph9nP6C5qx","xUOZtlo3hN"],"result":"⪩⨒∯-1100211","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1395","layer":2},{"info":"number node, value=6103","layer":2},{"info":"compute binary expreesion, left_input=1395, right_input=6103, op_id = BiWNJpBvwn binary_op_definition= 'a⩍⋽⫝̸b = { ((⨞⊢508)≧⫂∧(a≧⫂∧b)) }', output=5157","layer":1},{"info":"compute unary expreesion, input=5157, op_id = pRsWfj4Fpp, unary_op_definition = '∡a = { ((a≦≮≮)⊉≛↸(a⋝⋈⪟a)) }', output=-5157","layer":0}],"base":4,"result_base":4,"text":"∡⪩⨒∯111303⩍⋽⫝̸⪩⨒∯1133113=⪩⨒∯-1100211","reverse_text":"⪩⨒∯-1100211=∡⪩⨒∯111303⩍⋽⫝̸⪩⨒∯1133113","cot":[{"info":"⪩⨒∯111303⩍⋽⫝̸⪩⨒∯1133113=⪩⨒∯1100211","layer":1},{"info":"∡⪩⨒∯1100211=⪩⨒∯-1100211","layer":0}]}
{"id":801,"expression_no_base_symbol":"≛$6596$⋅⇍$1677$","expression":"≛⪩⨒∯1213010⋅⇍⪩⨒∯122031","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":30,"operation_count":2,"complexity_ratio":15.0,"tree":{"type":"unary","operator":"≛","unary_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":6596,"base":4},"right_expr":{"type":"numeric_atoms","value":1677,"base":4}}},"used_operators":["W7eaUhjymW","AdZkA7nFnk"],"dependent_operators":["W4YGzv6Whe","NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","DZ8iAZOCBD","JLbD19bQDL","sdazOOVcIp","2DDjHMKMc0","f6k1SAg4EE","eewbuw0ToL","COABgblf1C","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6"],"result":"⪩⨒∯-1221","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6596","layer":2},{"info":"number node, value=1677","layer":2},{"info":"compute binary expreesion, left_input=6596, right_input=1677, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"compute unary expreesion, input=-22, op_id = W7eaUhjymW, unary_op_definition = '≛a = { (((a+a)⊉≛↸(a⪠⩆⊳))⊭↱((a⪒a)⩚⊴⇥(a⋝⋈⪟a))) , if (a⫩⊇)>7 or a==273 ; (((a-a)⪒(a⪨≂a))⊉≛↸((a⨰a)⋝⋈⪟(a+a))) , else }', output=-105","layer":0}],"base":4,"result_base":4,"text":"≛⪩⨒∯1213010⋅⇍⪩⨒∯122031=⪩⨒∯-1221","reverse_text":"⪩⨒∯-1221=≛⪩⨒∯1213010⋅⇍⪩⨒∯122031","cot":[{"info":"⪩⨒∯1213010⋅⇍⪩⨒∯122031=⪩⨒∯-112","layer":1},{"info":"≛⪩⨒∯-112=⪩⨒∯-1221","layer":0}]}
{"id":802,"expression_no_base_symbol":"(≀↧⇸$1531$)⋳⪒$1033$↹⊜$2257$","expression":"(≀↧⇸⪩⨒∯113323)⋳⪒⪩⨒∯100021↹⊜⪩⨒∯203101","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":35,"operation_count":3,"complexity_ratio":11.666666666666666,"tree":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"unary","operator":"≀↧⇸","unary_expr":{"type":"numeric_atoms","value":1531,"base":4}},"right_expr":{"type":"binary","operator":"↹⊜","left_expr":{"type":"numeric_atoms","value":1033,"base":4},"right_expr":{"type":"numeric_atoms","value":2257,"base":4}}},"used_operators":["12rbrZMWeM","ljTHtUsqzn","9bazX3JMtO"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","XPYlsWDdGa","23Mk6UjR3U","9FxExcQeMw","rysDP5nf3Z","23Mk6UjR3U","tifHPKVTfV","eH2TOUuTDT","DIvbN7qnHd"],"result":"⪩⨒∯3021133","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1531","layer":2},{"info":"compute unary expreesion, input=1531, op_id = ljTHtUsqzn, unary_op_definition = '≀↧⇸a = { (⪲⇎(a⋷a)) }', output=3062","layer":1},{"info":"number node, value=1033","layer":2},{"info":"number node, value=2257","layer":2},{"info":"compute binary expreesion, left_input=1033, right_input=2257, op_id = 9bazX3JMtO binary_op_definition= 'a↹⊜b = { (((a⊠≄⫣)⩷∴(b-a))⩷∴((a⋷b)⇼⇔∾(b⪐))) }', output=-7058","layer":1},{"info":"compute binary expreesion, left_input=3062, right_input=-7058, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=12895","layer":0}],"base":4,"result_base":4,"text":"(≀↧⇸⪩⨒∯113323)⋳⪒⪩⨒∯100021↹⊜⪩⨒∯203101=⪩⨒∯3021133","reverse_text":"⪩⨒∯3021133=(≀↧⇸⪩⨒∯113323)⋳⪒⪩⨒∯100021↹⊜⪩⨒∯203101","cot":[{"info":"≀↧⇸⪩⨒∯113323=⪩⨒∯233312","layer":1},{"info":"⪩⨒∯100021↹⊜⪩⨒∯203101=⪩⨒∯-1232102","layer":1},{"info":"⪩⨒∯233312⋳⪒⪩⨒∯-1232102=⪩⨒∯3021133","layer":0}]}
{"id":803,"expression_no_base_symbol":"$9093$↤⩊$8809$∷$2625$↞⋁$1210$","expression":"⪩⨒∯2032011↤⩊⪩⨒∯2021221∷⪩⨒∯221001↞⋁⪩⨒∯102322","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":349,"operation_count":3,"complexity_ratio":116.33333333333333,"tree":{"type":"binary","operator":"∷","left_expr":{"type":"binary","operator":"↤⩊","left_expr":{"type":"numeric_atoms","value":9093,"base":4},"right_expr":{"type":"numeric_atoms","value":8809,"base":4}},"right_expr":{"type":"binary","operator":"↞⋁","left_expr":{"type":"numeric_atoms","value":2625,"base":4},"right_expr":{"type":"numeric_atoms","value":1210,"base":4}}},"used_operators":["D3AQDKkPcf","13rbtpv6ld","RqrPlJkxDo"],"dependent_operators":["9FxExcQeMw","NTOWxs364D","7j4O788W3g","s1XTVnmDOJ","wEfv7U73WA","9cloC0Ngie","KPf6cnQVty","KYD54nUTWz","k8jYdgA6NY","Uaa54Peajs","CArV6hThFE","13rbtpv6ld"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=9093","layer":2},{"info":"number node, value=8809","layer":2},{"info":"compute binary expreesion, left_input=9093, right_input=8809, op_id = 13rbtpv6ld binary_op_definition= 'a↤⩊b = { ((a⫥∨⫟63)⇐≅) , if (a∺≝⩲71)<727 ; ((b%b)⊕∕(b≓∲14)) , else }', output=nan","layer":1},{"info":"number node, value=2625","layer":2},{"info":"number node, value=1210","layer":2},{"info":"compute binary expreesion, left_input=2625, right_input=1210, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = D3AQDKkPcf binary_op_definition= 'a∷b = { (a⩚⊴⇥673) , if (b⩷∴24)<=112 ; (a↺b) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯2032011↤⩊⪩⨒∯2021221∷⪩⨒∯221001↞⋁⪩⨒∯102322=NaN","reverse_text":"NaN=⪩⨒∯2032011↤⩊⪩⨒∯2021221∷⪩⨒∯221001↞⋁⪩⨒∯102322","cot":[{"info":"⪩⨒∯2032011↤⩊⪩⨒∯2021221=NaN","layer":1},{"info":"⪩⨒∯221001↞⋁⪩⨒∯102322=NaN","layer":1},{"info":"NaN∷NaN=NaN","layer":0}]}
{"id":804,"expression_no_base_symbol":"($4990$⪪$6863$)⪬($4752$⊕∕$5257$)","expression":"(⪩⨒∯1031332⪪⪩⨒∯1223033)⪬(⪩⨒∯1022100⊕∕⪩⨒∯1102021)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15674,"operation_count":3,"complexity_ratio":5224.666666666667,"tree":{"type":"binary","operator":"⪬","left_expr":{"type":"binary","operator":"⪪","left_expr":{"type":"numeric_atoms","value":4990,"base":4},"right_expr":{"type":"numeric_atoms","value":6863,"base":4}},"right_expr":{"type":"binary","operator":"⊕∕","left_expr":{"type":"numeric_atoms","value":4752,"base":4},"right_expr":{"type":"numeric_atoms","value":5257,"base":4}}},"used_operators":["Ez1Nq5fNfI","xD69zh8xqp","9cloC0Ngie"],"dependent_operators":["eRqsBgTDFp","mp7IySMOzn","JL8yIekQnl","QvoQhV0rrE","kbkesczE7y","FU0Cs4j7VP","JclMnS0uGI","Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4990","layer":2},{"info":"number node, value=6863","layer":2},{"info":"compute binary expreesion, left_input=4990, right_input=6863, op_id = xD69zh8xqp binary_op_definition= 'a⪪b = { ((b⨔⇊a)↛⩡⫤) }', output=-749579","layer":1},{"info":"number node, value=4752","layer":2},{"info":"number node, value=5257","layer":2},{"info":"compute binary expreesion, left_input=4752, right_input=5257, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=4752","layer":1},{"info":"compute binary expreesion, left_input=-749579, right_input=4752, op_id = Ez1Nq5fNfI binary_op_definition= 'a⪬b = { (((514⋫)⪒⊣⊆(b≬⋮a))∠⫱(1⇷(b≬⋮32))) }', output=1234","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1031332⪪⪩⨒∯1223033)⪬(⪩⨒∯1022100⊕∕⪩⨒∯1102021)=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=(⪩⨒∯1031332⪪⪩⨒∯1223033)⪬(⪩⨒∯1022100⊕∕⪩⨒∯1102021)","cot":[{"info":"⪩⨒∯1031332⪪⪩⨒∯1223033=⪩⨒∯-2313000023","layer":1},{"info":"⪩⨒∯1022100⊕∕⪩⨒∯1102021=⪩⨒∯1022100","layer":1},{"info":"⪩⨒∯-2313000023⪬⪩⨒∯1022100=⪩⨒∯103102","layer":0}]}
{"id":805,"expression_no_base_symbol":"(≇⪴$6407$)⫉⨲⊜(⇁⨣⪵$2667$)","expression":"(≇⪴⪩⨒∯1210013)⫉⨲⊜(⇁⨣⪵⪩⨒∯221223)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":53668,"operation_count":3,"complexity_ratio":17889.333333333332,"tree":{"type":"binary","operator":"⫉⨲⊜","left_expr":{"type":"unary","operator":"≇⪴","unary_expr":{"type":"numeric_atoms","value":6407,"base":4}},"right_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":2667,"base":4}}},"used_operators":["WhqkvtTD3t","zoVPnxeHJ3","inkyxCbjAn"],"dependent_operators":["eewbuw0ToL","zVYPLywUTj","7j4O788W3g","Ph9nP6C5qx","f6k1SAg4EE","14qkJME0vr","g55IO6H4Gj","COABgblf1C","B5M0gjZbta"],"result":"Inf","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6407","layer":2},{"info":"compute unary expreesion, input=6407, op_id = zoVPnxeHJ3, unary_op_definition = '≇⪴a = { ((a⪒a)↺(a⨸⪁a)) , if (a⊭↱741)>=792 ; ((a≧⫂∧a)⊦⊿) , else }', output=-17881","layer":1},{"info":"number node, value=2667","layer":2},{"info":"compute unary expreesion, input=2667, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-17881, right_input=nan, op_id = WhqkvtTD3t binary_op_definition= 'a⫉⨲⊜b = { (b⨰120) , if b<=7 ; (a⊪) , else }', output=inf","layer":0}],"base":4,"result_base":4,"text":"(≇⪴⪩⨒∯1210013)⫉⨲⊜(⇁⨣⪵⪩⨒∯221223)=Inf","reverse_text":"Inf=(≇⪴⪩⨒∯1210013)⫉⨲⊜(⇁⨣⪵⪩⨒∯221223)","cot":[{"info":"≇⪴⪩⨒∯1210013=⪩⨒∯-10113121","layer":1},{"info":"⇁⨣⪵⪩⨒∯221223=NaN","layer":1},{"info":"⪩⨒∯-10113121⫉⨲⊜NaN=Inf","layer":0}]}
{"id":806,"expression_no_base_symbol":"$2498$⊮⊟↴$4980$⩇∃⫛($1506$⫭)","expression":"⪩⨒∯213002⊮⊟↴⪩⨒∯1031310⩇∃⫛(⪩⨒∯113202⫭)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":67,"operation_count":3,"complexity_ratio":22.333333333333332,"tree":{"type":"binary","operator":"⩇∃⫛","left_expr":{"type":"binary","operator":"⊮⊟↴","left_expr":{"type":"numeric_atoms","value":2498,"base":4},"right_expr":{"type":"numeric_atoms","value":4980,"base":4}},"right_expr":{"type":"unary","operator":"⫭","unary_expr":{"type":"numeric_atoms","value":1506,"base":4}}},"used_operators":["1aApVXNlOP","QDVgd2eftb","t4WUHVGj7f"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","e1ybzncUwg","Qy55tPpLXF","DZ8iAZOCBD","2DQ55sFlQl","t8gj7n24qd","2DDjHMKMc0","Z2TMIBDE3Q","14qkJME0vr","f6k1SAg4EE","Ph9nP6C5qx","eewbuw0ToL","u6S6b8DprG","XhwjNDsVaA","C6VvDP6HwP","WkeUrDK8WX","kuIXHzHcAH","3Oe9XWJUTD","rJVOvQCfKK","NTOWxs364D","2DDjHMKMc0","xUOZtlo3hN","g55IO6H4Gj"],"result":"⪩⨒∯1101300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2498","layer":2},{"info":"number node, value=4980","layer":2},{"info":"compute binary expreesion, left_input=2498, right_input=4980, op_id = QDVgd2eftb binary_op_definition= 'a⊮⊟↴b = { ((⩰267)⪨⊡(b⊝⪿⪼a)) , if a!=19 ; ((b⨎372)/(b⪑⩈)) , else }', output=0","layer":1},{"info":"number node, value=1506","layer":2},{"info":"compute unary expreesion, input=1506, op_id = t4WUHVGj7f, unary_op_definition = 'a⫭ = { (⨞⊢((a⨸⪁147)⩚⊴⇥(a⋝⋈⪟a))) }', output=4759","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=4759, op_id = 1aApVXNlOP binary_op_definition= 'a⩇∃⫛b = { (((b⊉≛↸a)⩤)⨰((362⩷∴b)⋥≓≎(↽≂a))) , if (a⊦⊿)>7 and b<=506 and (-a)==737 ; (((b⩤)⪒(b≧⫂∧a))⋝⋈⪟((a⨵⪆a)-(≉a))) , else }', output=5232","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯213002⊮⊟↴⪩⨒∯1031310⩇∃⫛(⪩⨒∯113202⫭)=⪩⨒∯1101300","reverse_text":"⪩⨒∯1101300=⪩⨒∯213002⊮⊟↴⪩⨒∯1031310⩇∃⫛(⪩⨒∯113202⫭)","cot":[{"info":"⪩⨒∯213002⊮⊟↴⪩⨒∯1031310=⪩⨒∯0","layer":1},{"info":"⪩⨒∯113202⫭=⪩⨒∯1022113","layer":1},{"info":"⪩⨒∯0⩇∃⫛⪩⨒∯1022113=⪩⨒∯1101300","layer":0}]}
{"id":807,"expression_no_base_symbol":"(≸$5425$)⇉⇱⇎","expression":"(≸⪩⨒∯1110301)⇉⇱⇎","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":100,"operation_count":2,"complexity_ratio":50.0,"tree":{"type":"unary","operator":"⇉⇱⇎","unary_expr":{"type":"unary","operator":"≸","unary_expr":{"type":"numeric_atoms","value":5425,"base":4}}},"used_operators":["MRPaB8lBjK","eOf03JbCpp"],"dependent_operators":["XhwjNDsVaA","QiR2Oyf5Xj","uFcxV4UQCh","EWw2JM7wp4","t8gj7n24qd","keWfFq85dY","WmT3o8z6ya","l07mrZUIn9","NTOWxs364D","RygbFNSyEJ","tifHPKVTfV","oRDoc9rAEX","IwW236VD4Y","1aApVXNlOP","Z5m6OM72h2","mqXw5SEYmG","IWmyXbctLI"],"result":"⪩⨒∯-32","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5425","layer":2},{"info":"compute unary expreesion, input=5425, op_id = eOf03JbCpp, unary_op_definition = '≸a = { (29∘((630⊋≦⊧a)⩚⊴⇥(a≦↸a))) , if (a⋘⨑⨽)>2 ; (((a⪮%⊝a)⇼⇔∾(a↪⪝))⫸⊐((a⪮%⊝a)≠≀(3⩇∃⫛a))) , else }', output=58","layer":1},{"info":"compute unary expreesion, input=58, op_id = MRPaB8lBjK, unary_op_definition = 'a⇉⇱⇎ = { (((a/a)⪉⨛(≯757))⪛(∷≠(-a))) }', output=-14","layer":0}],"base":4,"result_base":4,"text":"(≸⪩⨒∯1110301)⇉⇱⇎=⪩⨒∯-32","reverse_text":"⪩⨒∯-32=(≸⪩⨒∯1110301)⇉⇱⇎","cot":[{"info":"≸⪩⨒∯1110301=⪩⨒∯322","layer":1},{"info":"⪩⨒∯322⇉⇱⇎=⪩⨒∯-32","layer":0}]}
{"id":808,"expression_no_base_symbol":"≦∁$6709$⩧⪆$4258$","expression":"≦∁⪩⨒∯1220311⩧⪆⪩⨒∯1002202","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":41,"operation_count":2,"complexity_ratio":20.5,"tree":{"type":"unary","operator":"≦∁","unary_expr":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"numeric_atoms","value":6709,"base":4},"right_expr":{"type":"numeric_atoms","value":4258,"base":4}}},"used_operators":["9ICcGScMcE","Ikt5ks8PT7"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","eewbuw0ToL","t8gj7n24qd"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6709","layer":2},{"info":"number node, value=4258","layer":2},{"info":"compute binary expreesion, left_input=6709, right_input=4258, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-4258","layer":1},{"info":"compute unary expreesion, input=-4258, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=67","layer":0}],"base":4,"result_base":4,"text":"≦∁⪩⨒∯1220311⩧⪆⪩⨒∯1002202=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=≦∁⪩⨒∯1220311⩧⪆⪩⨒∯1002202","cot":[{"info":"⪩⨒∯1220311⩧⪆⪩⨒∯1002202=⪩⨒∯-1002202","layer":1},{"info":"≦∁⪩⨒∯-1002202=⪩⨒∯1003","layer":0}]}
{"id":809,"expression_no_base_symbol":"($1037$≝⊿$1049$)≴⪞⇿($1378$⨓$6090$)","expression":"(⪩⨒∯100031≝⊿⪩⨒∯100121)≴⪞⇿(⪩⨒∯111202⨓⪩⨒∯1133022)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6151,"operation_count":3,"complexity_ratio":2050.3333333333335,"tree":{"type":"binary","operator":"≴⪞⇿","left_expr":{"type":"binary","operator":"≝⊿","left_expr":{"type":"numeric_atoms","value":1037,"base":4},"right_expr":{"type":"numeric_atoms","value":1049,"base":4}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":1378,"base":4},"right_expr":{"type":"numeric_atoms","value":6090,"base":4}}},"used_operators":["lvlrscuwVU","OKKcZfAt5B","3ViojmjbAp"],"dependent_operators":["DpFCA1CohY","Qy55tPpLXF","Bmrmz2XGnR","srAu1WTS94","AF7qkfDlqP","12rbrZMWeM","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⪩⨒∯-131213313","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1037","layer":2},{"info":"number node, value=1049","layer":2},{"info":"compute binary expreesion, left_input=1037, right_input=1049, op_id = OKKcZfAt5B binary_op_definition= 'a≝⊿b = { ((82⋳⪒b)⋳⪒a) }', output=-3668","layer":1},{"info":"number node, value=1378","layer":2},{"info":"number node, value=6090","layer":2},{"info":"compute binary expreesion, left_input=1378, right_input=6090, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-6093","layer":1},{"info":"compute binary expreesion, left_input=-3668, right_input=-6093, op_id = lvlrscuwVU binary_op_definition= 'a≴⪞⇿b = { ((⋗⩬⋾(b≚⊃≕166))⋥≓≎(⨵≀≌(⨑⩽⪐a))) }', output=-121335","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100031≝⊿⪩⨒∯100121)≴⪞⇿(⪩⨒∯111202⨓⪩⨒∯1133022)=⪩⨒∯-131213313","reverse_text":"⪩⨒∯-131213313=(⪩⨒∯100031≝⊿⪩⨒∯100121)≴⪞⇿(⪩⨒∯111202⨓⪩⨒∯1133022)","cot":[{"info":"⪩⨒∯100031≝⊿⪩⨒∯100121=⪩⨒∯-321110","layer":1},{"info":"⪩⨒∯111202⨓⪩⨒∯1133022=⪩⨒∯-1133031","layer":1},{"info":"⪩⨒∯-321110≴⪞⇿⪩⨒∯-1133031=⪩⨒∯-131213313","layer":0}]}
{"id":810,"expression_no_base_symbol":"⇤←$1125$⩍⋽⫝̸$8986$","expression":"⇤←⪩⨒∯101211⩍⋽⫝̸⪩⨒∯2030122","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":52,"operation_count":2,"complexity_ratio":26.0,"tree":{"type":"unary","operator":"⇤←","unary_expr":{"type":"binary","operator":"⩍⋽⫝̸","left_expr":{"type":"numeric_atoms","value":1125,"base":4},"right_expr":{"type":"numeric_atoms","value":8986,"base":4}}},"used_operators":["jfAgQ2OQeM","BiWNJpBvwn"],"dependent_operators":["NTOWxs364D","FyVja0WsTP","zVYPLywUTj","nCS4ZIUYfx","Ph9nP6C5qx","xUOZtlo3hN"],"result":"⪩⨒∯-21132302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1125","layer":2},{"info":"number node, value=8986","layer":2},{"info":"compute binary expreesion, left_input=1125, right_input=8986, op_id = BiWNJpBvwn binary_op_definition= 'a⩍⋽⫝̸b = { ((⨞⊢508)≧⫂∧(a≧⫂∧b)) }', output=8040","layer":1},{"info":"compute unary expreesion, input=8040, op_id = jfAgQ2OQeM, unary_op_definition = '⇤←a = { (a⨳⩥⨓((a⩚⊴⇥238)⊱⇼⊻(a⊪))) }', output=-38834","layer":0}],"base":4,"result_base":4,"text":"⇤←⪩⨒∯101211⩍⋽⫝̸⪩⨒∯2030122=⪩⨒∯-21132302","reverse_text":"⪩⨒∯-21132302=⇤←⪩⨒∯101211⩍⋽⫝̸⪩⨒∯2030122","cot":[{"info":"⪩⨒∯101211⩍⋽⫝̸⪩⨒∯2030122=⪩⨒∯1331220","layer":1},{"info":"⇤←⪩⨒∯1331220=⪩⨒∯-21132302","layer":0}]}
{"id":811,"expression_no_base_symbol":"⪲⇎($4441$⪄$5228$)","expression":"⪲⇎(⪩⨒∯1011121⪄⪩⨒∯1101230)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":97,"operation_count":2,"complexity_ratio":48.5,"tree":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":4441,"base":4},"right_expr":{"type":"numeric_atoms","value":5228,"base":4}}},"used_operators":["XPYlsWDdGa","SUmda5xLS4"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⪩⨒∯-11021032322","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4441","layer":2},{"info":"number node, value=5228","layer":2},{"info":"compute binary expreesion, left_input=4441, right_input=5228, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-674269","layer":1},{"info":"compute unary expreesion, input=-674269, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=-1348538","layer":0}],"base":4,"result_base":4,"text":"⪲⇎(⪩⨒∯1011121⪄⪩⨒∯1101230)=⪩⨒∯-11021032322","reverse_text":"⪩⨒∯-11021032322=⪲⇎(⪩⨒∯1011121⪄⪩⨒∯1101230)","cot":[{"info":"⪩⨒∯1011121⪄⪩⨒∯1101230=⪩⨒∯-2210213131","layer":1},{"info":"⪲⇎⪩⨒∯-2210213131=⪩⨒∯-11021032322","layer":0}]}
{"id":812,"expression_no_base_symbol":"≻⋜($3406$⊊)","expression":"≻⋜(⪩⨒∯311032⊊)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":454982,"operation_count":2,"complexity_ratio":227491.0,"tree":{"type":"unary","operator":"≻⋜","unary_expr":{"type":"unary","operator":"⊊","unary_expr":{"type":"numeric_atoms","value":3406,"base":4}}},"used_operators":["3tj9sqzovi","W9R8I5fN5A"],"dependent_operators":["XGcMNugi78","dWAJyo7jo9","Tw270M8GLb","Y7wcNGrDQJ","DlLNRPXxWL","aBQ6xLxuTc","8n5YIzOsVS","oZj3VtZNQx","MahUMFw56D","hyuBjUqXlG","aA7tF3KVD3","2DDjHMKMc0","QMFrweE19q","SxTAKzQCrw","8cLx32lpNA"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3406","layer":2},{"info":"compute unary expreesion, input=3406, op_id = W9R8I5fN5A, unary_op_definition = 'a⊊ = { (((⫛⫱⨽a)∙⊟a)∌((a⇂≾⫗536)⋝⋈⪟(a⫡⨏a))) , if ((a≚⋢)==7 or (a⪘⨀)==15) ; ((a≀⫉(6⪛⫼a))⫠↝⫳) , else }', output=90927","layer":1},{"info":"compute unary expreesion, input=90927, op_id = 3tj9sqzovi, unary_op_definition = '≻⋜a = { (((a⩵∡a)⫞⩸⩒(⨰⫟⨤a))⪢a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"≻⋜(⪩⨒∯311032⊊)=NaN","reverse_text":"NaN=≻⋜(⪩⨒∯311032⊊)","cot":[{"info":"⪩⨒∯311032⊊=⪩⨒∯112030233","layer":1},{"info":"≻⋜⪩⨒∯112030233=NaN","layer":0}]}
{"id":813,"expression_no_base_symbol":"⨡↴$1481$⩌⋺$6217$","expression":"⨡↴⪩⨒∯113021⩌⋺⪩⨒∯1201021","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":11,"operation_count":2,"complexity_ratio":5.5,"tree":{"type":"unary","operator":"⨡↴","unary_expr":{"type":"binary","operator":"⩌⋺","left_expr":{"type":"numeric_atoms","value":1481,"base":4},"right_expr":{"type":"numeric_atoms","value":6217,"base":4}}},"used_operators":["liw5iZPkLH","g7Hmc5v1ko"],"dependent_operators":["W4YGzv6Whe","P8v4zCKN1o","9FxExcQeMw","W4YGzv6Whe","NTOWxs364D","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","i8ToyICDmI","QMFrweE19q"],"result":"⪩⨒∯-313","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1481","layer":2},{"info":"number node, value=6217","layer":2},{"info":"compute binary expreesion, left_input=1481, right_input=6217, op_id = g7Hmc5v1ko binary_op_definition= 'a⩌⋺b = { ((⨞⊢(b⨵⪆b))∲⫓((a⪨≂b)⪨≂(b⩷∴919))) , if (b⫡⨏102)>364 and (-b)==524 ; (b⇼⇔∾((a+a)⩚⊴⇥(-a))) , else }', output=-7819","layer":1},{"info":"compute unary expreesion, input=-7819, op_id = liw5iZPkLH, unary_op_definition = '⨡↴a = { (∥⊫(a+181)) }', output=-55","layer":0}],"base":4,"result_base":4,"text":"⨡↴⪩⨒∯113021⩌⋺⪩⨒∯1201021=⪩⨒∯-313","reverse_text":"⪩⨒∯-313=⨡↴⪩⨒∯113021⩌⋺⪩⨒∯1201021","cot":[{"info":"⪩⨒∯113021⩌⋺⪩⨒∯1201021=⪩⨒∯-1322023","layer":1},{"info":"⨡↴⪩⨒∯-1322023=⪩⨒∯-313","layer":0}]}
{"id":814,"expression_no_base_symbol":"≸≮($2647$+$3933$)","expression":"≸≮(⪩⨒∯221113+⪩⨒∯331131)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":11035,"operation_count":2,"complexity_ratio":5517.5,"tree":{"type":"unary","operator":"≸≮","unary_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":2647,"base":4},"right_expr":{"type":"numeric_atoms","value":3933,"base":4}}},"used_operators":["AljMvE3RRm","W4YGzv6Whe"],"dependent_operators":["3UMq87Qwqg","QiR2Oyf5Xj","Z57zeUYC9z","6o9Blt3TJ6","kbkesczE7y","oPMjh9089D","Nsiff2A1zJ","7qqUquhhSb"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2647","layer":2},{"info":"number node, value=3933","layer":2},{"info":"compute binary expreesion, left_input=2647, right_input=3933, op_id = W4YGzv6Whe binary_op_definition= 'None', output=6580","layer":1},{"info":"compute unary expreesion, input=6580, op_id = AljMvE3RRm, unary_op_definition = '≸≮a = { (a⊴((a⨔≚≋a)⫰⋱(∤↝a))) , if (a>367 and (a≬⋮702)!=1) ; (⊀((∷≠a)⩉⊫⨁)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"≸≮(⪩⨒∯221113+⪩⨒∯331131)=NaN","reverse_text":"NaN=≸≮(⪩⨒∯221113+⪩⨒∯331131)","cot":[{"info":"⪩⨒∯221113+⪩⨒∯331131=⪩⨒∯1212310","layer":1},{"info":"≸≮⪩⨒∯1212310=NaN","layer":0}]}
{"id":815,"expression_no_base_symbol":"→⩰(⊤⊝$1112$)","expression":"→⩰(⊤⊝⪩⨒∯101120)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1315,"operation_count":2,"complexity_ratio":657.5,"tree":{"type":"unary","operator":"→⩰","unary_expr":{"type":"unary","operator":"⊤⊝","unary_expr":{"type":"numeric_atoms","value":1112,"base":4}}},"used_operators":["o8Pngz0Tml","rXAclfmB4M"],"dependent_operators":["9FxExcQeMw","4X4GscPmMf","YbUVn0Rbpy","Nsiff2A1zJ","l1M9WJ3V7u","eewbuw0ToL","sdazOOVcIp"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1112","layer":2},{"info":"compute unary expreesion, input=1112, op_id = rXAclfmB4M, unary_op_definition = '⊤⊝a = { (a⪨≂700) }', output=926","layer":1},{"info":"compute unary expreesion, input=926, op_id = o8Pngz0Tml, unary_op_definition = '→⩰a = { ((∑⇻≧(a⋛a))⨰((a⊴a)⩷∴(a⨕⋳))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"→⩰(⊤⊝⪩⨒∯101120)=NaN","reverse_text":"NaN=→⩰(⊤⊝⪩⨒∯101120)","cot":[{"info":"⊤⊝⪩⨒∯101120=⪩⨒∯32132","layer":1},{"info":"→⩰⪩⨒∯32132=NaN","layer":0}]}
{"id":816,"expression_no_base_symbol":"$4488$⨑⩅≇$3064$⨶","expression":"⪩⨒∯1012020⨑⩅≇⪩⨒∯233320⨶","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3123,"operation_count":2,"complexity_ratio":1561.5,"tree":{"type":"unary","operator":"⨶","unary_expr":{"type":"binary","operator":"⨑⩅≇","left_expr":{"type":"numeric_atoms","value":4488,"base":4},"right_expr":{"type":"numeric_atoms","value":3064,"base":4}}},"used_operators":["rFxw8gIMmB","h92wMvzauj"],"dependent_operators":["f6k1SAg4EE","Qy55tPpLXF","s3Fd5m9Dh2","3sJ7IOPOlU","nREPSIbpBE","9Isq31Ruls","umQnsF7QlU","8HhzD0ZcuI","u6S6b8DprG","DmTXOeWf9t","AFVx7xoS7T","jLgFTUHLKL","oacrs7FA3X","xNBdhnnwKq"],"result":"⪩⨒∯-2012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4488","layer":2},{"info":"number node, value=3064","layer":2},{"info":"compute binary expreesion, left_input=4488, right_input=3064, op_id = h92wMvzauj binary_op_definition= 'a⨑⩅≇b = { (((a⪇≇⋚b)⊬⨰(b⨽582))∌↝a) , if (↽≂a)<10 or (b⊭∹↮)==22 ; ((a⊲⩕⊾(↩a))⪕((a⨚243)⇌⫙⪟(b⪘⫢b))) , else }', output=-13464","layer":1},{"info":"compute unary expreesion, input=-13464, op_id = rFxw8gIMmB, unary_op_definition = 'a⨶ = { ((a⋥≓≎303)⪒(a⋥≓≎537)) }', output=-134","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1012020⨑⩅≇⪩⨒∯233320⨶=⪩⨒∯-2012","reverse_text":"⪩⨒∯-2012=⪩⨒∯1012020⨑⩅≇⪩⨒∯233320⨶","cot":[{"info":"⪩⨒∯1012020⨑⩅≇⪩⨒∯233320=⪩⨒∯-3102120","layer":1},{"info":"⪩⨒∯-3102120⨶=⪩⨒∯-2012","layer":0}]}
{"id":817,"expression_no_base_symbol":"$4614$⪛$1049$⇄($2856$∝$5078$)","expression":"⪩⨒∯1020012⪛⪩⨒∯100121⇄(⪩⨒∯230220∝⪩⨒∯1033112)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":21,"operation_count":3,"complexity_ratio":7.0,"tree":{"type":"binary","operator":"⇄","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":4614,"base":4},"right_expr":{"type":"numeric_atoms","value":1049,"base":4}},"right_expr":{"type":"binary","operator":"∝","left_expr":{"type":"numeric_atoms","value":2856,"base":4},"right_expr":{"type":"numeric_atoms","value":5078,"base":4}}},"used_operators":["3EYGwJThht","uFcxV4UQCh","cTDWOvIxvz"],"dependent_operators":["eLAdDNolq6","DZ8iAZOCBD","i8ToyICDmI","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","7j4O788W3g","W4YGzv6Whe","COABgblf1C"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4614","layer":2},{"info":"number node, value=1049","layer":2},{"info":"compute binary expreesion, left_input=4614, right_input=1049, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=418","layer":1},{"info":"number node, value=2856","layer":2},{"info":"number node, value=5078","layer":2},{"info":"compute binary expreesion, left_input=2856, right_input=5078, op_id = cTDWOvIxvz binary_op_definition= 'a∝b = { ((b↺a)+(b⊭↱b)) }', output=2861","layer":1},{"info":"compute binary expreesion, left_input=418, right_input=2861, op_id = 3EYGwJThht binary_op_definition= 'a⇄b = { ((≤/b)∲⫓(a⊉≛↸b)) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1020012⪛⪩⨒∯100121⇄(⪩⨒∯230220∝⪩⨒∯1033112)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯1020012⪛⪩⨒∯100121⇄(⪩⨒∯230220∝⪩⨒∯1033112)","cot":[{"info":"⪩⨒∯1020012⪛⪩⨒∯100121=⪩⨒∯12202","layer":1},{"info":"⪩⨒∯230220∝⪩⨒∯1033112=⪩⨒∯230231","layer":1},{"info":"⪩⨒∯12202⇄⪩⨒∯230231=⪩⨒∯0","layer":0}]}
{"id":818,"expression_no_base_symbol":"$4278$⪝$1485$∖$6660$⊉↱≁$1000$","expression":"⪩⨒∯1002312⪝⪩⨒∯113031∖⪩⨒∯1220010⊉↱≁⪩⨒∯33220","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5381,"operation_count":3,"complexity_ratio":1793.6666666666667,"tree":{"type":"binary","operator":"∖","left_expr":{"type":"binary","operator":"⪝","left_expr":{"type":"numeric_atoms","value":4278,"base":4},"right_expr":{"type":"numeric_atoms","value":1485,"base":4}},"right_expr":{"type":"binary","operator":"⊉↱≁","left_expr":{"type":"numeric_atoms","value":6660,"base":4},"right_expr":{"type":"numeric_atoms","value":1000,"base":4}}},"used_operators":["tXD093vOjl","wicAB68Tmb","w2P8NbNXyL"],"dependent_operators":["rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC","L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X","9FxExcQeMw","e1ybzncUwg","sdazOOVcIp","t8gj7n24qd","eewbuw0ToL"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4278","layer":2},{"info":"number node, value=1485","layer":2},{"info":"compute binary expreesion, left_input=4278, right_input=1485, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=-11571","layer":1},{"info":"number node, value=6660","layer":2},{"info":"number node, value=1000","layer":2},{"info":"compute binary expreesion, left_input=6660, right_input=1000, op_id = w2P8NbNXyL binary_op_definition= 'a⊉↱≁b = { ((≉(a⨰b))⪨≂((145⩷∴a)⪨≂(-b))) }', output=60548","layer":1},{"info":"compute binary expreesion, left_input=-11571, right_input=60548, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1002312⪝⪩⨒∯113031∖⪩⨒∯1220010⊉↱≁⪩⨒∯33220=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯1002312⪝⪩⨒∯113031∖⪩⨒∯1220010⊉↱≁⪩⨒∯33220","cot":[{"info":"⪩⨒∯1002312⪝⪩⨒∯113031=⪩⨒∯-2310303","layer":1},{"info":"⪩⨒∯1220010⊉↱≁⪩⨒∯33220=⪩⨒∯32302010","layer":1},{"info":"⪩⨒∯-2310303∖⪩⨒∯32302010=⪩⨒∯0","layer":0}]}
{"id":819,"expression_no_base_symbol":"$3916$⨜⨶$3042$⨳⩥⨓($2341$↺$1323$)","expression":"⪩⨒∯331030⨜⨶⪩⨒∯233202⨳⩥⨓(⪩⨒∯210211↺⪩⨒∯110223)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":30,"operation_count":3,"complexity_ratio":10.0,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":3916,"base":4},"right_expr":{"type":"numeric_atoms","value":3042,"base":4}},"right_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":2341,"base":4},"right_expr":{"type":"numeric_atoms","value":1323,"base":4}}},"used_operators":["nCS4ZIUYfx","HiPekx5b7W","7j4O788W3g"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯1233233","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3916","layer":2},{"info":"number node, value=3042","layer":2},{"info":"compute binary expreesion, left_input=3916, right_input=3042, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-5828","layer":1},{"info":"number node, value=2341","layer":2},{"info":"number node, value=1323","layer":2},{"info":"compute binary expreesion, left_input=2341, right_input=1323, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1323","layer":1},{"info":"compute binary expreesion, left_input=-5828, right_input=1323, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=7151","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯331030⨜⨶⪩⨒∯233202⨳⩥⨓(⪩⨒∯210211↺⪩⨒∯110223)=⪩⨒∯1233233","reverse_text":"⪩⨒∯1233233=⪩⨒∯331030⨜⨶⪩⨒∯233202⨳⩥⨓(⪩⨒∯210211↺⪩⨒∯110223)","cot":[{"info":"⪩⨒∯331030⨜⨶⪩⨒∯233202=⪩⨒∯-1123010","layer":1},{"info":"⪩⨒∯210211↺⪩⨒∯110223=⪩⨒∯110223","layer":1},{"info":"⪩⨒∯-1123010⨳⩥⨓⪩⨒∯110223=⪩⨒∯1233233","layer":0}]}
{"id":820,"expression_no_base_symbol":"($2262$⪇≇⋚$2444$)⊉↱≁(⇜$1528$)","expression":"(⪩⨒∯203112⪇≇⋚⪩⨒∯212030)⊉↱≁(⇜⪩⨒∯113320)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":355,"operation_count":3,"complexity_ratio":118.33333333333333,"tree":{"type":"binary","operator":"⊉↱≁","left_expr":{"type":"binary","operator":"⪇≇⋚","left_expr":{"type":"numeric_atoms","value":2262,"base":4},"right_expr":{"type":"numeric_atoms","value":2444,"base":4}},"right_expr":{"type":"unary","operator":"⇜","unary_expr":{"type":"numeric_atoms","value":1528,"base":4}}},"used_operators":["w2P8NbNXyL","3sJ7IOPOlU","lFBm8KRb8F"],"dependent_operators":["9FxExcQeMw","e1ybzncUwg","sdazOOVcIp","t8gj7n24qd","eewbuw0ToL","DZ8iAZOCBD","JLbD19bQDL","xUOZtlo3hN","s3Fd5m9Dh2","DlLNRPXxWL","ZvLB05nZmT","6o9Blt3TJ6","f6k1SAg4EE","1h0rLqGiFr"],"result":"⪩⨒∯102133130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2262","layer":2},{"info":"number node, value=2444","layer":2},{"info":"compute binary expreesion, left_input=2262, right_input=2444, op_id = 3sJ7IOPOlU binary_op_definition= 'a⪇≇⋚b = { ((⨞⊢(a⊉≛↸b))⪠⩆⊳) }', output=0","layer":1},{"info":"number node, value=1528","layer":2},{"info":"compute unary expreesion, input=1528, op_id = lFBm8KRb8F, unary_op_definition = '⇜a = { ((a⫳≱↱a)⊬⨰(a⪒a)) , if a>51 ; ((⩷10)⫰⋱(⫛⫱⨽a)) , else }', output=-12632","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-12632, op_id = w2P8NbNXyL binary_op_definition= 'a⊉↱≁b = { ((≉(a⨰b))⪨≂((145⩷∴a)⪨≂(-b))) }', output=75740","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯203112⪇≇⋚⪩⨒∯212030)⊉↱≁(⇜⪩⨒∯113320)=⪩⨒∯102133130","reverse_text":"⪩⨒∯102133130=(⪩⨒∯203112⪇≇⋚⪩⨒∯212030)⊉↱≁(⇜⪩⨒∯113320)","cot":[{"info":"⪩⨒∯203112⪇≇⋚⪩⨒∯212030=⪩⨒∯0","layer":1},{"info":"⇜⪩⨒∯113320=⪩⨒∯-3011120","layer":1},{"info":"⪩⨒∯0⊉↱≁⪩⨒∯-3011120=⪩⨒∯102133130","layer":0}]}
{"id":821,"expression_no_base_symbol":"⇾⩊⇾($7141$⨰$2747$)","expression":"⇾⩊⇾(⪩⨒∯1233211⨰⪩⨒∯222323)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":19,"operation_count":2,"complexity_ratio":9.5,"tree":{"type":"unary","operator":"⇾⩊⇾","unary_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":7141,"base":4},"right_expr":{"type":"numeric_atoms","value":2747,"base":4}}},"used_operators":["bx9Z9DAK5y","eewbuw0ToL"],"dependent_operators":["W4YGzv6Whe","BjRHVeLaeN","8w2t5hMYqp","QMFrweE19q","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-23100222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7141","layer":2},{"info":"number node, value=2747","layer":2},{"info":"compute binary expreesion, left_input=7141, right_input=2747, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=4404","layer":1},{"info":"compute unary expreesion, input=4404, op_id = bx9Z9DAK5y, unary_op_definition = '⇾⩊⇾a = { (⊄⩳↩((a+259)⫡⨏(a⫩⊇))) }', output=-46122","layer":0}],"base":4,"result_base":4,"text":"⇾⩊⇾(⪩⨒∯1233211⨰⪩⨒∯222323)=⪩⨒∯-23100222","reverse_text":"⪩⨒∯-23100222=⇾⩊⇾(⪩⨒∯1233211⨰⪩⨒∯222323)","cot":[{"info":"⪩⨒∯1233211⨰⪩⨒∯222323=⪩⨒∯1010310","layer":1},{"info":"⇾⩊⇾⪩⨒∯1010310=⪩⨒∯-23100222","layer":0}]}
{"id":822,"expression_no_base_symbol":"$3722$⨔⇊$1204$⫰⋱($5745$⫠↝⫳)","expression":"⪩⨒∯322022⨔⇊⪩⨒∯102310⫰⋱(⪩⨒∯1121301⫠↝⫳)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":28,"operation_count":3,"complexity_ratio":9.333333333333334,"tree":{"type":"binary","operator":"⫰⋱","left_expr":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"numeric_atoms","value":3722,"base":4},"right_expr":{"type":"numeric_atoms","value":1204,"base":4}},"right_expr":{"type":"unary","operator":"⫠↝⫳","unary_expr":{"type":"numeric_atoms","value":5745,"base":4}}},"used_operators":["6o9Blt3TJ6","JclMnS0uGI","8n5YIzOsVS"],"dependent_operators":["W4YGzv6Whe","nCS4ZIUYfx","Qy55tPpLXF","9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI","9FxExcQeMw","g55IO6H4Gj","2td37pGCOC","QMFrweE19q"],"result":"⪩⨒∯-102103","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3722","layer":2},{"info":"number node, value=1204","layer":2},{"info":"compute binary expreesion, left_input=3722, right_input=1204, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=1204","layer":1},{"info":"number node, value=5745","layer":2},{"info":"compute unary expreesion, input=5745, op_id = 8n5YIzOsVS, unary_op_definition = 'a⫠↝⫳ = { (((a⨸⪁a)⩷∴(⩦⩻⨪a))⫡⨏a) }', output=184463","layer":1},{"info":"compute binary expreesion, left_input=1204, right_input=184463, op_id = 6o9Blt3TJ6 binary_op_definition= 'a⫰⋱b = { ((a+b)⨳⩥⨓(b⋥≓≎b)) }', output=-1171","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯322022⨔⇊⪩⨒∯102310⫰⋱(⪩⨒∯1121301⫠↝⫳)=⪩⨒∯-102103","reverse_text":"⪩⨒∯-102103=⪩⨒∯322022⨔⇊⪩⨒∯102310⫰⋱(⪩⨒∯1121301⫠↝⫳)","cot":[{"info":"⪩⨒∯322022⨔⇊⪩⨒∯102310=⪩⨒∯102310","layer":1},{"info":"⪩⨒∯1121301⫠↝⫳=⪩⨒∯231002033","layer":1},{"info":"⪩⨒∯102310⫰⋱⪩⨒∯231002033=⪩⨒∯-102103","layer":0}]}
{"id":823,"expression_no_base_symbol":"⊄⩳↩($3616$≝⊰⇂)","expression":"⊄⩳↩(⪩⨒∯320200≝⊰⇂)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1425,"operation_count":2,"complexity_ratio":712.5,"tree":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"unary","operator":"≝⊰⇂","unary_expr":{"type":"numeric_atoms","value":3616,"base":4}}},"used_operators":["8w2t5hMYqp","htSmYCowi5"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","9FxExcQeMw","DlLNRPXxWL"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3616","layer":2},{"info":"compute unary expreesion, input=3616, op_id = htSmYCowi5, unary_op_definition = 'a≝⊰⇂ = { (a⩷∴51) , if a<491 ; (⫛⫱⨽a) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⊄⩳↩(⪩⨒∯320200≝⊰⇂)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⊄⩳↩(⪩⨒∯320200≝⊰⇂)","cot":[{"info":"⪩⨒∯320200≝⊰⇂=⪩⨒∯0","layer":1},{"info":"⊄⩳↩⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":824,"expression_no_base_symbol":"⇠($1830$≃$2237$)","expression":"⇠(⪩⨒∯130212≃⪩⨒∯202331)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":29,"operation_count":2,"complexity_ratio":14.5,"tree":{"type":"unary","operator":"⇠","unary_expr":{"type":"binary","operator":"≃","left_expr":{"type":"numeric_atoms","value":1830,"base":4},"right_expr":{"type":"numeric_atoms","value":2237,"base":4}}},"used_operators":["18saOjeKKm","YbVcJGFEVW"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","nCS4ZIUYfx","9FxExcQeMw","Qy55tPpLXF","23Mk6UjR3U","JLbD19bQDL","7j4O788W3g","glklzrTFfD","tifHPKVTfV","t8gj7n24qd","i8ToyICDmI","COABgblf1C"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1830","layer":2},{"info":"number node, value=2237","layer":2},{"info":"compute binary expreesion, left_input=1830, right_input=2237, op_id = YbVcJGFEVW binary_op_definition= 'a≃b = { (((13⋥≓≎b)⋷(a⇼⇔∾b))⨁⊸⫻) , if ((b⨁⊸⫻)>=162 or (b⪠⩆⊳)<=569) ; ((-(17⋷a))↺((a⩷∴a)⊭↱(b∲⫓a))) , else }', output=-7360","layer":1},{"info":"compute unary expreesion, input=-7360, op_id = 18saOjeKKm, unary_op_definition = '⇠a = { ((a⨳⩥⨓242)∲⫓(229⪨≂a)) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⇠(⪩⨒∯130212≃⪩⨒∯202331)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⇠(⪩⨒∯130212≃⪩⨒∯202331)","cot":[{"info":"⪩⨒∯130212≃⪩⨒∯202331=⪩⨒∯-1303000","layer":1},{"info":"⇠⪩⨒∯-1303000=⪩⨒∯0","layer":0}]}
{"id":825,"expression_no_base_symbol":"($5626$⩺⋐⫨)⨸⪁$2376$⪄$1680$","expression":"(⪩⨒∯1113322⩺⋐⫨)⨸⪁⪩⨒∯211020⪄⪩⨒∯122100","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":663,"operation_count":3,"complexity_ratio":221.0,"tree":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"unary","operator":"⩺⋐⫨","unary_expr":{"type":"numeric_atoms","value":5626,"base":4}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2376,"base":4},"right_expr":{"type":"numeric_atoms","value":1680,"base":4}}},"used_operators":["g55IO6H4Gj","yS9ePUuUdn","SUmda5xLS4"],"dependent_operators":["W4YGzv6Whe","9samAPKr6k","j9kHMeSvPp","Tcnh7f0tEr","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⪩⨒∯-2231010302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5626","layer":2},{"info":"compute unary expreesion, input=5626, op_id = yS9ePUuUdn, unary_op_definition = 'a⩺⋐⫨ = { ((a≣⋋)⨽∌(a⪭a)) }', output=0","layer":1},{"info":"number node, value=2376","layer":2},{"info":"number node, value=1680","layer":2},{"info":"compute binary expreesion, left_input=2376, right_input=1680, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-354457","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-354457, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=-708914","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1113322⩺⋐⫨)⨸⪁⪩⨒∯211020⪄⪩⨒∯122100=⪩⨒∯-2231010302","reverse_text":"⪩⨒∯-2231010302=(⪩⨒∯1113322⩺⋐⫨)⨸⪁⪩⨒∯211020⪄⪩⨒∯122100","cot":[{"info":"⪩⨒∯1113322⩺⋐⫨=⪩⨒∯0","layer":1},{"info":"⪩⨒∯211020⪄⪩⨒∯122100=⪩⨒∯-1112202121","layer":1},{"info":"⪩⨒∯0⨸⪁⪩⨒∯-1112202121=⪩⨒∯-2231010302","layer":0}]}
{"id":826,"expression_no_base_symbol":"($1629$⇔⨋)⋓(⇨$2120$)","expression":"(⪩⨒∯121131⇔⨋)⋓(⇨⪩⨒∯201020)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":41,"operation_count":3,"complexity_ratio":13.666666666666666,"tree":{"type":"binary","operator":"⋓","left_expr":{"type":"unary","operator":"⇔⨋","unary_expr":{"type":"numeric_atoms","value":1629,"base":4}},"right_expr":{"type":"unary","operator":"⇨","unary_expr":{"type":"numeric_atoms","value":2120,"base":4}}},"used_operators":["T2fj7uvVaJ","uBihLCJcMX","G9tJMlZ94a"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","N41Kp7NANJ","7j4O788W3g","glklzrTFfD","tifHPKVTfV","12rbrZMWeM","f6k1SAg4EE","D4vGDi5EA2","nCS4ZIUYfx","QMFrweE19q","k8jYdgA6NY"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1629","layer":2},{"info":"compute unary expreesion, input=1629, op_id = uBihLCJcMX, unary_op_definition = 'a⇔⨋ = { (((a⨁⊸⫻)⋳⪒a)⪒((a≦≮≮)⨁⊸⫻)) , if a<217 ; (((a≋⫹)⨳⩥⨓(a↺a))⋳⪒((a⨳⩥⨓a)⫡⨏(a⇼⇔∾a))) , else }', output=8704","layer":1},{"info":"number node, value=2120","layer":2},{"info":"compute unary expreesion, input=2120, op_id = G9tJMlZ94a, unary_op_definition = '⇨a = { (a%a) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=8704, right_input=0, op_id = T2fj7uvVaJ binary_op_definition= 'a⋓b = { (((60⪒b)⊭∹↮)%((a⪘⫢68)⪘⫢(⨵≀≌a))) , if (b>=803 and b<=372 and b<242) ; (16⪢((b⊠≄⫣)⋷(a⫌⩹⨱))) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯121131⇔⨋)⋓(⇨⪩⨒∯201020)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯121131⇔⨋)⋓(⇨⪩⨒∯201020)","cot":[{"info":"⪩⨒∯121131⇔⨋=⪩⨒∯2020000","layer":1},{"info":"⇨⪩⨒∯201020=⪩⨒∯0","layer":1},{"info":"⪩⨒∯2020000⋓⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":827,"expression_no_base_symbol":"($3636$⊋≦⊧$4531$)⪔($5164$⫌⩉⩟$1909$)","expression":"(⪩⨒∯320310⊋≦⊧⪩⨒∯1012303)⪔(⪩⨒∯1100230⫌⩉⩟⪩⨒∯131311)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":10697,"operation_count":3,"complexity_ratio":3565.6666666666665,"tree":{"type":"binary","operator":"⪔","left_expr":{"type":"binary","operator":"⊋≦⊧","left_expr":{"type":"numeric_atoms","value":3636,"base":4},"right_expr":{"type":"numeric_atoms","value":4531,"base":4}},"right_expr":{"type":"binary","operator":"⫌⩉⩟","left_expr":{"type":"numeric_atoms","value":5164,"base":4},"right_expr":{"type":"numeric_atoms","value":1909,"base":4}}},"used_operators":["GjBEYRfMaF","oRDoc9rAEX","XIIwhv8d0m"],"dependent_operators":["YjI8oCXuph","8INZBEW696","dWAJyo7jo9","nREPSIbpBE","2DDjHMKMc0","IWmyXbctLI","PoHhknlbAi","DZ8iAZOCBD","tifHPKVTfV","sdazOOVcIp","glklzrTFfD","DIvbN7qnHd","12rbrZMWeM","Ph9nP6C5qx","eewbuw0ToL","2td37pGCOC","B5M0gjZbta","UMwdvZNt44","MRPaB8lBjK","vkpjKywKVM"],"result":"⪩⨒∯13002","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3636","layer":2},{"info":"number node, value=4531","layer":2},{"info":"compute binary expreesion, left_input=3636, right_input=4531, op_id = oRDoc9rAEX binary_op_definition= 'a⊋≦⊧b = { (((24⊉≛↸a)⊉≛↸(⩦⩻⨪b))⊉≛↸((a⊠≄⫣)⪨≂(b⇼⇔∾a))) , if a<=128 ; (((a⇼⇔∾b)⨁⊸⫻)⇼⇔∾((22⋳⪒a)⨰(a≧⫂∧a))) , else }', output=-7927","layer":1},{"info":"number node, value=5164","layer":2},{"info":"number node, value=1909","layer":2},{"info":"compute binary expreesion, left_input=5164, right_input=1909, op_id = XIIwhv8d0m binary_op_definition= 'a⫌⩉⩟b = { (((a↬179)⇮⋭(b⇡⇂b))⇉⇱⇎) }', output=-50","layer":1},{"info":"compute binary expreesion, left_input=-7927, right_input=-50, op_id = GjBEYRfMaF binary_op_definition= 'a⪔b = { (((⫇a)∓⋝(61⪢b))⪮%⊝((b⋝⋈⪟b)⨚(a≀⩗∶a))) }', output=450","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯320310⊋≦⊧⪩⨒∯1012303)⪔(⪩⨒∯1100230⫌⩉⩟⪩⨒∯131311)=⪩⨒∯13002","reverse_text":"⪩⨒∯13002=(⪩⨒∯320310⊋≦⊧⪩⨒∯1012303)⪔(⪩⨒∯1100230⫌⩉⩟⪩⨒∯131311)","cot":[{"info":"⪩⨒∯320310⊋≦⊧⪩⨒∯1012303=⪩⨒∯-1323313","layer":1},{"info":"⪩⨒∯1100230⫌⩉⩟⪩⨒∯131311=⪩⨒∯-302","layer":1},{"info":"⪩⨒∯-1323313⪔⪩⨒∯-302=⪩⨒∯13002","layer":0}]}
{"id":828,"expression_no_base_symbol":"⨣⨃⇪(⫇$2008$)","expression":"⨣⨃⇪(⫇⪩⨒∯133120)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":31,"operation_count":2,"complexity_ratio":15.5,"tree":{"type":"unary","operator":"⨣⨃⇪","unary_expr":{"type":"unary","operator":"⫇","unary_expr":{"type":"numeric_atoms","value":2008,"base":4}}},"used_operators":["AcOhelriW5","YjI8oCXuph"],"dependent_operators":["s3Fd5m9Dh2","liw5iZPkLH","yyfyN0ffXY","rysDP5nf3Z","Qy55tPpLXF","N41Kp7NANJ","23Mk6UjR3U","2DQ55sFlQl","12rbrZMWeM","f6k1SAg4EE","i8ToyICDmI"],"result":"⪩⨒∯111331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2008","layer":2},{"info":"compute unary expreesion, input=2008, op_id = YjI8oCXuph, unary_op_definition = '⫇a = { (((a⋥≓≎a)⋷(a⋳⪒a))≋⫹) , if a>62 ; (a-((a⨵⪆101)⪒(786∲⫓a))) , else }', output=-2802","layer":1},{"info":"compute unary expreesion, input=-2802, op_id = AcOhelriW5, unary_op_definition = '⨣⨃⇪a = { (⨡↴(172⊬⨰(3↙a))) }', output=1405","layer":0}],"base":4,"result_base":4,"text":"⨣⨃⇪(⫇⪩⨒∯133120)=⪩⨒∯111331","reverse_text":"⪩⨒∯111331=⨣⨃⇪(⫇⪩⨒∯133120)","cot":[{"info":"⫇⪩⨒∯133120=⪩⨒∯-223302","layer":1},{"info":"⨣⨃⇪⪩⨒∯-223302=⪩⨒∯111331","layer":0}]}
{"id":829,"expression_no_base_symbol":"$1065$⨚$3866$⪢($4382$⪹)","expression":"⪩⨒∯100221⨚⪩⨒∯330122⪢(⪩⨒∯1010132⪹)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13421,"operation_count":3,"complexity_ratio":4473.666666666667,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"binary","operator":"⨚","left_expr":{"type":"numeric_atoms","value":1065,"base":4},"right_expr":{"type":"numeric_atoms","value":3866,"base":4}},"right_expr":{"type":"unary","operator":"⪹","unary_expr":{"type":"numeric_atoms","value":4382,"base":4}}},"used_operators":["dWAJyo7jo9","nREPSIbpBE","B3sABdIn96"],"dependent_operators":["k8jYdgA6NY","BjRHVeLaeN","12rbrZMWeM","9FxExcQeMw","e1ybzncUwg","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1065","layer":2},{"info":"number node, value=3866","layer":2},{"info":"compute binary expreesion, left_input=1065, right_input=3866, op_id = nREPSIbpBE binary_op_definition= 'a⨚b = { (((b⋳⪒a)⋳⪒31)⫩⊇) }', output=-12400","layer":1},{"info":"number node, value=4382","layer":2},{"info":"compute unary expreesion, input=4382, op_id = B3sABdIn96, unary_op_definition = 'a⪹ = { ((402⫡⨏a)⩷∴(≉a)) }', output=13256","layer":1},{"info":"compute binary expreesion, left_input=-12400, right_input=13256, op_id = dWAJyo7jo9 binary_op_definition= 'a⪢b = {b, if b == 0; (a)%(a⪢(b-1)), if b > 0 and abs(b) < 1000000; -(a)%(a⪢(b+1)), if b < 0 and abs(b) < 1000000; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯100221⨚⪩⨒∯330122⪢(⪩⨒∯1010132⪹)=NaN","reverse_text":"NaN=⪩⨒∯100221⨚⪩⨒∯330122⪢(⪩⨒∯1010132⪹)","cot":[{"info":"⪩⨒∯100221⨚⪩⨒∯330122=⪩⨒∯-3001300","layer":1},{"info":"⪩⨒∯1010132⪹=⪩⨒∯3033020","layer":1},{"info":"⪩⨒∯-3001300⪢⪩⨒∯3033020=NaN","layer":0}]}
{"id":830,"expression_no_base_symbol":"⇋⊎⋝($6397$⪘⫢$4070$)","expression":"⇋⊎⋝(⪩⨒∯1203331⪘⫢⪩⨒∯333212)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":12685,"operation_count":2,"complexity_ratio":6342.5,"tree":{"type":"unary","operator":"⇋⊎⋝","unary_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":6397,"base":4},"right_expr":{"type":"numeric_atoms","value":4070,"base":4}}},"used_operators":["CzM2PEoXns","oacrs7FA3X"],"dependent_operators":["dWAJyo7jo9","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6397","layer":2},{"info":"number node, value=4070","layer":2},{"info":"compute binary expreesion, left_input=6397, right_input=4070, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=12670","layer":1},{"info":"compute unary expreesion, input=12670, op_id = CzM2PEoXns, unary_op_definition = '⇋⊎⋝a = { (a⪢a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇋⊎⋝(⪩⨒∯1203331⪘⫢⪩⨒∯333212)=NaN","reverse_text":"NaN=⇋⊎⋝(⪩⨒∯1203331⪘⫢⪩⨒∯333212)","cot":[{"info":"⪩⨒∯1203331⪘⫢⪩⨒∯333212=⪩⨒∯3011332","layer":1},{"info":"⇋⊎⋝⪩⨒∯3011332=NaN","layer":0}]}
{"id":831,"expression_no_base_symbol":"$6649$⨔⇊$3339$⪪($1563$⋅⇍$2135$)","expression":"⪩⨒∯1213321⨔⇊⪩⨒∯310023⪪(⪩⨒∯120123⋅⇍⪩⨒∯201113)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":10157,"operation_count":3,"complexity_ratio":3385.6666666666665,"tree":{"type":"binary","operator":"⪪","left_expr":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"numeric_atoms","value":6649,"base":4},"right_expr":{"type":"numeric_atoms","value":3339,"base":4}},"right_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":1563,"base":4},"right_expr":{"type":"numeric_atoms","value":2135,"base":4}}},"used_operators":["xD69zh8xqp","JclMnS0uGI","AdZkA7nFnk"],"dependent_operators":["FU0Cs4j7VP","JclMnS0uGI","9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6"],"result":"⪩⨒∯-1322020312","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6649","layer":2},{"info":"number node, value=3339","layer":2},{"info":"compute binary expreesion, left_input=6649, right_input=3339, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=3339","layer":1},{"info":"number node, value=1563","layer":2},{"info":"number node, value=2135","layer":2},{"info":"compute binary expreesion, left_input=1563, right_input=2135, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"compute binary expreesion, left_input=3339, right_input=-22, op_id = xD69zh8xqp binary_op_definition= 'a⪪b = { ((b⨔⇊a)↛⩡⫤) }', output=-500278","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1213321⨔⇊⪩⨒∯310023⪪(⪩⨒∯120123⋅⇍⪩⨒∯201113)=⪩⨒∯-1322020312","reverse_text":"⪩⨒∯-1322020312=⪩⨒∯1213321⨔⇊⪩⨒∯310023⪪(⪩⨒∯120123⋅⇍⪩⨒∯201113)","cot":[{"info":"⪩⨒∯1213321⨔⇊⪩⨒∯310023=⪩⨒∯310023","layer":1},{"info":"⪩⨒∯120123⋅⇍⪩⨒∯201113=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯310023⪪⪩⨒∯-112=⪩⨒∯-1322020312","layer":0}]}
{"id":832,"expression_no_base_symbol":"($3427$∪⫐$1337$)⊓⋫","expression":"(⪩⨒∯311203∪⫐⪩⨒∯110321)⊓⋫","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":28,"operation_count":2,"complexity_ratio":14.0,"tree":{"type":"unary","operator":"⊓⋫","unary_expr":{"type":"binary","operator":"∪⫐","left_expr":{"type":"numeric_atoms","value":3427,"base":4},"right_expr":{"type":"numeric_atoms","value":1337,"base":4}}},"used_operators":["IqGBaFP0uj","7YooWSwCyH"],"dependent_operators":["2td37pGCOC","sdazOOVcIp","2DDjHMKMc0","f6k1SAg4EE","nCS4ZIUYfx","QMFrweE19q","rJVOvQCfKK","2DDjHMKMc0"],"result":"⪩⨒∯-313203","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3427","layer":2},{"info":"number node, value=1337","layer":2},{"info":"compute binary expreesion, left_input=3427, right_input=1337, op_id = 7YooWSwCyH binary_op_definition= 'a∪⫐b = { ((a⋝⋈⪟b)⨎a) }', output=3427","layer":1},{"info":"compute unary expreesion, input=3427, op_id = IqGBaFP0uj, unary_op_definition = 'a⊓⋫ = { (((a⪨≂a)⨳⩥⨓(⩦⩻⨪230))⪒(a⋝⋈⪟(542⫡⨏384))) }', output=-3555","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯311203∪⫐⪩⨒∯110321)⊓⋫=⪩⨒∯-313203","reverse_text":"⪩⨒∯-313203=(⪩⨒∯311203∪⫐⪩⨒∯110321)⊓⋫","cot":[{"info":"⪩⨒∯311203∪⫐⪩⨒∯110321=⪩⨒∯311203","layer":1},{"info":"⪩⨒∯311203⊓⋫=⪩⨒∯-313203","layer":0}]}
{"id":833,"expression_no_base_symbol":"$1244$⪄$3017$⋷$2637$⊱⇼⊻$1142$","expression":"⪩⨒∯103130⪄⪩⨒∯233021⋷⪩⨒∯221031⊱⇼⊻⪩⨒∯101312","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":105,"operation_count":3,"complexity_ratio":35.0,"tree":{"type":"binary","operator":"⋷","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":1244,"base":4},"right_expr":{"type":"numeric_atoms","value":3017,"base":4}},"right_expr":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"numeric_atoms","value":2637,"base":4},"right_expr":{"type":"numeric_atoms","value":1142,"base":4}}},"used_operators":["23Mk6UjR3U","SUmda5xLS4","FyVja0WsTP"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf"],"result":"⪩⨒∯1131320122","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1244","layer":2},{"info":"number node, value=3017","layer":2},{"info":"compute binary expreesion, left_input=1244, right_input=3017, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-192269","layer":1},{"info":"number node, value=2637","layer":2},{"info":"number node, value=1142","layer":2},{"info":"compute binary expreesion, left_input=2637, right_input=1142, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":1},{"info":"compute binary expreesion, left_input=-192269, right_input=434, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=384538","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯103130⪄⪩⨒∯233021⋷⪩⨒∯221031⊱⇼⊻⪩⨒∯101312=⪩⨒∯1131320122","reverse_text":"⪩⨒∯1131320122=⪩⨒∯103130⪄⪩⨒∯233021⋷⪩⨒∯221031⊱⇼⊻⪩⨒∯101312","cot":[{"info":"⪩⨒∯103130⪄⪩⨒∯233021=⪩⨒∯-232330031","layer":1},{"info":"⪩⨒∯221031⊱⇼⊻⪩⨒∯101312=⪩⨒∯12302","layer":1},{"info":"⪩⨒∯-232330031⋷⪩⨒∯12302=⪩⨒∯1131320122","layer":0}]}
{"id":834,"expression_no_base_symbol":"(⪲⇎$1318$)⊴$4440$+⪬∐$2726$","expression":"(⪲⇎⪩⨒∯110212)⊴⪩⨒∯1011120+⪬∐⪩⨒∯222212","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13331,"operation_count":3,"complexity_ratio":4443.666666666667,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":1318,"base":4}},"right_expr":{"type":"binary","operator":"+⪬∐","left_expr":{"type":"numeric_atoms","value":4440,"base":4},"right_expr":{"type":"numeric_atoms","value":2726,"base":4}}},"used_operators":["Nsiff2A1zJ","XPYlsWDdGa","2GS7woTJqF"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","g55IO6H4Gj","D4vGDi5EA2"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1318","layer":2},{"info":"compute unary expreesion, input=1318, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=2636","layer":1},{"info":"number node, value=4440","layer":2},{"info":"number node, value=2726","layer":2},{"info":"compute binary expreesion, left_input=4440, right_input=2726, op_id = 2GS7woTJqF binary_op_definition= 'a+⪬∐b = { (a≦≮≮) , if b!=63 ; (b⨸⪁575) , else }', output=-13320","layer":1},{"info":"compute binary expreesion, left_input=2636, right_input=-13320, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪲⇎⪩⨒∯110212)⊴⪩⨒∯1011120+⪬∐⪩⨒∯222212=NaN","reverse_text":"NaN=(⪲⇎⪩⨒∯110212)⊴⪩⨒∯1011120+⪬∐⪩⨒∯222212","cot":[{"info":"⪲⇎⪩⨒∯110212=⪩⨒∯221030","layer":1},{"info":"⪩⨒∯1011120+⪬∐⪩⨒∯222212=⪩⨒∯-3100020","layer":1},{"info":"⪩⨒∯221030⊴⪩⨒∯-3100020=NaN","layer":0}]}
{"id":835,"expression_no_base_symbol":"(⨦⪝$2005$)⫉⨲⊜(⩒∊$3138$)","expression":"(⨦⪝⪩⨒∯133111)⫉⨲⊜(⩒∊⪩⨒∯301002)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5708,"operation_count":3,"complexity_ratio":1902.6666666666667,"tree":{"type":"binary","operator":"⫉⨲⊜","left_expr":{"type":"unary","operator":"⨦⪝","unary_expr":{"type":"numeric_atoms","value":2005,"base":4}},"right_expr":{"type":"unary","operator":"⩒∊","unary_expr":{"type":"numeric_atoms","value":3138,"base":4}}},"used_operators":["WhqkvtTD3t","SUjycxNXIR","qazvmhNBbN"],"dependent_operators":["eewbuw0ToL","zVYPLywUTj","V0kx6qeWkN","rJVOvQCfKK","rxpJgHHUmx","AcOhelriW5","SpZWOsLKZJ","LYeZOJ0nQG","HmxsFra2vL","AvED76WdY7","AF7qkfDlqP","f6k1SAg4EE","eLAdDNolq6"],"result":"⪩⨒∯2020033013312","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2005","layer":2},{"info":"compute unary expreesion, input=2005, op_id = SUjycxNXIR, unary_op_definition = '⨦⪝a = { (⫎≠⋺((a≳⇉a)⨎(⊵⊁a))) , if (a∙∹∝10)>301 ; ((⨣⨃⇪(a≭a))⊚⫡⫭) , else }', output=-1884","layer":1},{"info":"number node, value=3138","layer":2},{"info":"compute unary expreesion, input=3138, op_id = qazvmhNBbN, unary_op_definition = '⩒∊a = { ((≤/a)⪒(⨑⩽⪐a)) }', output=5519","layer":1},{"info":"compute binary expreesion, left_input=-1884, right_input=5519, op_id = WhqkvtTD3t binary_op_definition= 'a⫉⨲⊜b = { (b⨰120) , if b<=7 ; (a⊪) , else }', output=35713526","layer":0}],"base":4,"result_base":4,"text":"(⨦⪝⪩⨒∯133111)⫉⨲⊜(⩒∊⪩⨒∯301002)=⪩⨒∯2020033013312","reverse_text":"⪩⨒∯2020033013312=(⨦⪝⪩⨒∯133111)⫉⨲⊜(⩒∊⪩⨒∯301002)","cot":[{"info":"⨦⪝⪩⨒∯133111=⪩⨒∯-131130","layer":1},{"info":"⩒∊⪩⨒∯301002=⪩⨒∯1112033","layer":1},{"info":"⪩⨒∯-131130⫉⨲⊜⪩⨒∯1112033=⪩⨒∯2020033013312","layer":0}]}
{"id":836,"expression_no_base_symbol":"($1972$*$2211$)⨻⩈⩔(↪⫪⫘$6849$)","expression":"(⪩⨒∯132310*⪩⨒∯202203)⨻⩈⩔(↪⫪⫘⪩⨒∯1223001)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2363,"operation_count":3,"complexity_ratio":787.6666666666666,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1972,"base":4},"right_expr":{"type":"numeric_atoms","value":2211,"base":4}},"right_expr":{"type":"unary","operator":"↪⫪⫘","unary_expr":{"type":"numeric_atoms","value":6849,"base":4}}},"used_operators":["nEsXyWgiOK","9HNa5Wba9A","9dWsAM3GFt"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","W4YGzv6Whe","DyGG3AbaNP","nREPSIbpBE","rysDP5nf3Z"],"result":"⪩⨒∯2011001300033","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1972","layer":2},{"info":"number node, value=2211","layer":2},{"info":"compute binary expreesion, left_input=1972, right_input=2211, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=4360092","layer":1},{"info":"number node, value=6849","layer":2},{"info":"compute unary expreesion, input=6849, op_id = 9dWsAM3GFt, unary_op_definition = '↪⫪⫘a = { ((a⨚283)∼(a-a)) }', output=20","layer":1},{"info":"compute binary expreesion, left_input=4360092, right_input=20, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=34872335","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯132310*⪩⨒∯202203)⨻⩈⩔(↪⫪⫘⪩⨒∯1223001)=⪩⨒∯2011001300033","reverse_text":"⪩⨒∯2011001300033=(⪩⨒∯132310*⪩⨒∯202203)⨻⩈⩔(↪⫪⫘⪩⨒∯1223001)","cot":[{"info":"⪩⨒∯132310*⪩⨒∯202203=⪩⨒∯100220132130","layer":1},{"info":"↪⫪⫘⪩⨒∯1223001=⪩⨒∯110","layer":1},{"info":"⪩⨒∯100220132130⨻⩈⩔⪩⨒∯110=⪩⨒∯2011001300033","layer":0}]}
{"id":837,"expression_no_base_symbol":"$4013$⨥⫆$5612$∳⫺($6033$⫘$3280$)","expression":"⪩⨒∯332231⨥⫆⪩⨒∯1113230∳⫺(⪩⨒∯1132101⫘⪩⨒∯303100)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6304,"operation_count":3,"complexity_ratio":2101.3333333333335,"tree":{"type":"binary","operator":"∳⫺","left_expr":{"type":"binary","operator":"⨥⫆","left_expr":{"type":"numeric_atoms","value":4013,"base":4},"right_expr":{"type":"numeric_atoms","value":5612,"base":4}},"right_expr":{"type":"binary","operator":"⫘","left_expr":{"type":"numeric_atoms","value":6033,"base":4},"right_expr":{"type":"numeric_atoms","value":3280,"base":4}}},"used_operators":["AzXXKTstlj","yXekIHxTD4","48vC8HMD2b"],"dependent_operators":["F4yD0voBRQ","Tcnh7f0tEr","ZvLB05nZmT","eRqsBgTDFp","ancx8kZcWl","oacrs7FA3X","OwUj7dcsQK","7j4O788W3g","tfWHHpNKUN","3ViojmjbAp","dfKe02y8D2","tcjXMdvYtA","D4vGDi5EA2","86A5ENbKR9","X99M06cbEe"],"result":"⪩⨒∯-311333203230","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4013","layer":2},{"info":"number node, value=5612","layer":2},{"info":"compute binary expreesion, left_input=4013, right_input=5612, op_id = yXekIHxTD4 binary_op_definition= 'a⨥⫆b = { (b⨝⩣∺) , if (a⪒⊣⊆344)<109 ; (b⪘⫢a) , else }', output=11100","layer":1},{"info":"number node, value=6033","layer":2},{"info":"number node, value=3280","layer":2},{"info":"compute binary expreesion, left_input=6033, right_input=3280, op_id = 48vC8HMD2b binary_op_definition= 'a⫘b = { ((≘(b⨓a))≫≃) , if ((⇖a)!=319 or (a↺926)<190) ; ((∓a)⫚↹⊑(⪸(a≦≮≮))) , else }', output=7099213","layer":1},{"info":"compute binary expreesion, left_input=11100, right_input=7099213, op_id = AzXXKTstlj binary_op_definition= 'a∳⫺b = { (a≣⋋) , if (b⫳≱↱947)==166 ; (a⇣⩺⋵b) , else }', output=-14153964","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯332231⨥⫆⪩⨒∯1113230∳⫺(⪩⨒∯1132101⫘⪩⨒∯303100)=⪩⨒∯-311333203230","reverse_text":"⪩⨒∯-311333203230=⪩⨒∯332231⨥⫆⪩⨒∯1113230∳⫺(⪩⨒∯1132101⫘⪩⨒∯303100)","cot":[{"info":"⪩⨒∯332231⨥⫆⪩⨒∯1113230=⪩⨒∯2231130","layer":1},{"info":"⪩⨒∯1132101⫘⪩⨒∯303100=⪩⨒∯123011031031","layer":1},{"info":"⪩⨒∯2231130∳⫺⪩⨒∯123011031031=⪩⨒∯-311333203230","layer":0}]}
{"id":838,"expression_no_base_symbol":"$1127$⨒$7233$∕⩚(≸≮$1027$)","expression":"⪩⨒∯101213⨒⪩⨒∯1301001∕⩚(≸≮⪩⨒∯100003)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9954,"operation_count":3,"complexity_ratio":3318.0,"tree":{"type":"binary","operator":"∕⩚","left_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":1127,"base":4},"right_expr":{"type":"numeric_atoms","value":7233,"base":4}},"right_expr":{"type":"unary","operator":"≸≮","unary_expr":{"type":"numeric_atoms","value":1027,"base":4}}},"used_operators":["z9ffQ9n5Zr","y75s1iXyHd","AljMvE3RRm"],"dependent_operators":["3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr","srAu1WTS94","oacrs7FA3X","7qqUquhhSb","3UMq87Qwqg","QiR2Oyf5Xj","Z57zeUYC9z","6o9Blt3TJ6","kbkesczE7y","oPMjh9089D","Nsiff2A1zJ","7qqUquhhSb"],"result":"⪩⨒∯-13213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1127","layer":2},{"info":"number node, value=7233","layer":2},{"info":"compute binary expreesion, left_input=1127, right_input=7233, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-6390","layer":1},{"info":"number node, value=1027","layer":2},{"info":"compute unary expreesion, input=1027, op_id = AljMvE3RRm, unary_op_definition = '≸≮a = { (a⊴((a⨔≚≋a)⫰⋱(∤↝a))) , if (a>367 and (a≬⋮702)!=1) ; (⊀((∷≠a)⩉⊫⨁)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-6390, right_input=nan, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-487","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯101213⨒⪩⨒∯1301001∕⩚(≸≮⪩⨒∯100003)=⪩⨒∯-13213","reverse_text":"⪩⨒∯-13213=⪩⨒∯101213⨒⪩⨒∯1301001∕⩚(≸≮⪩⨒∯100003)","cot":[{"info":"⪩⨒∯101213⨒⪩⨒∯1301001=⪩⨒∯-1203312","layer":1},{"info":"≸≮⪩⨒∯100003=NaN","layer":1},{"info":"⪩⨒∯-1203312∕⩚NaN=⪩⨒∯-13213","layer":0}]}
{"id":839,"expression_no_base_symbol":"($3514$⋻⩜⩜$1588$)⪶≀⋏$3218$⊕∕$1284$","expression":"(⪩⨒∯312322⋻⩜⩜⪩⨒∯120310)⪶≀⋏⪩⨒∯302102⊕∕⪩⨒∯110010","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":22251,"operation_count":3,"complexity_ratio":7417.0,"tree":{"type":"binary","operator":"⪶≀⋏","left_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":3514,"base":4},"right_expr":{"type":"numeric_atoms","value":1588,"base":4}},"right_expr":{"type":"binary","operator":"⊕∕","left_expr":{"type":"numeric_atoms","value":3218,"base":4},"right_expr":{"type":"numeric_atoms","value":1284,"base":4}}},"used_operators":["zR4jO40bMj","oDCm7WA9JY","9cloC0Ngie"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","NTOWxs364D","glklzrTFfD","2DDjHMKMc0","g55IO6H4Gj","eewbuw0ToL","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf"],"result":"⪩⨒∯-12301220","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3514","layer":2},{"info":"number node, value=1588","layer":2},{"info":"compute binary expreesion, left_input=3514, right_input=1588, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=7028","layer":1},{"info":"number node, value=3218","layer":2},{"info":"number node, value=1284","layer":2},{"info":"compute binary expreesion, left_input=3218, right_input=1284, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=3218","layer":1},{"info":"compute binary expreesion, left_input=7028, right_input=3218, op_id = zR4jO40bMj binary_op_definition= 'a⪶≀⋏b = { (((b⨸⪁b)⨸⪁(a-a))⋝⋈⪟(b⋝⋈⪟(b+b))) , if a<244 ; (((b⩚⊴⇥a)⨁⊸⫻)⨰a) , else }', output=-27752","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯312322⋻⩜⩜⪩⨒∯120310)⪶≀⋏⪩⨒∯302102⊕∕⪩⨒∯110010=⪩⨒∯-12301220","reverse_text":"⪩⨒∯-12301220=(⪩⨒∯312322⋻⩜⩜⪩⨒∯120310)⪶≀⋏⪩⨒∯302102⊕∕⪩⨒∯110010","cot":[{"info":"⪩⨒∯312322⋻⩜⩜⪩⨒∯120310=⪩⨒∯1231310","layer":1},{"info":"⪩⨒∯302102⊕∕⪩⨒∯110010=⪩⨒∯302102","layer":1},{"info":"⪩⨒∯1231310⪶≀⋏⪩⨒∯302102=⪩⨒∯-12301220","layer":0}]}
{"id":840,"expression_no_base_symbol":"$3951$⩣⫁∢$2247$⪍↜⋙($1375$⫌⩉⩟$7634$)","expression":"⪩⨒∯331233⩣⫁∢⪩⨒∯203013⪍↜⋙(⪩⨒∯111133⫌⩉⩟⪩⨒∯1313102)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":38535,"operation_count":3,"complexity_ratio":12845.0,"tree":{"type":"binary","operator":"⪍↜⋙","left_expr":{"type":"binary","operator":"⩣⫁∢","left_expr":{"type":"numeric_atoms","value":3951,"base":4},"right_expr":{"type":"numeric_atoms","value":2247,"base":4}},"right_expr":{"type":"binary","operator":"⫌⩉⩟","left_expr":{"type":"numeric_atoms","value":1375,"base":4},"right_expr":{"type":"numeric_atoms","value":7634,"base":4}}},"used_operators":["L05ObWFQCd","JDUIKTTSIa","XIIwhv8d0m"],"dependent_operators":["rysDP5nf3Z","DZ8iAZOCBD","tifHPKVTfV","EBcxylXtPf","QMFrweE19q","sdazOOVcIp","eewbuw0ToL","AF7qkfDlqP","u6S6b8DprG","B5M0gjZbta","UMwdvZNt44","MRPaB8lBjK","vkpjKywKVM"],"result":"⪩⨒∯21102012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3951","layer":2},{"info":"number node, value=2247","layer":2},{"info":"compute binary expreesion, left_input=3951, right_input=2247, op_id = JDUIKTTSIa binary_op_definition= 'a⩣⫁∢b = { (⨑⩽⪐((a⪨≂b)⨰(↽≂b))) }', output=-7741","layer":1},{"info":"number node, value=1375","layer":2},{"info":"number node, value=7634","layer":2},{"info":"compute binary expreesion, left_input=1375, right_input=7634, op_id = XIIwhv8d0m binary_op_definition= 'a⫌⩉⩟b = { (((a↬179)⇮⋭(b⇡⇂b))⇉⇱⇎) }', output=-50","layer":1},{"info":"compute binary expreesion, left_input=-7741, right_input=-50, op_id = L05ObWFQCd binary_op_definition= 'a⪍↜⋙b = { ((a-b)⊉≛↸(a⫡⨏b)) , if (a⫌⩹⨱)!=88 ; ((a⫡⨏b)⇼⇔∾(a⫌⩹⨱)) , else }', output=38022","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯331233⩣⫁∢⪩⨒∯203013⪍↜⋙(⪩⨒∯111133⫌⩉⩟⪩⨒∯1313102)=⪩⨒∯21102012","reverse_text":"⪩⨒∯21102012=⪩⨒∯331233⩣⫁∢⪩⨒∯203013⪍↜⋙(⪩⨒∯111133⫌⩉⩟⪩⨒∯1313102)","cot":[{"info":"⪩⨒∯331233⩣⫁∢⪩⨒∯203013=⪩⨒∯-1320331","layer":1},{"info":"⪩⨒∯111133⫌⩉⩟⪩⨒∯1313102=⪩⨒∯-302","layer":1},{"info":"⪩⨒∯-1320331⪍↜⋙⪩⨒∯-302=⪩⨒∯21102012","layer":0}]}
{"id":841,"expression_no_base_symbol":"⇙⪊(∡$1379$)","expression":"⇙⪊(∡⪩⨒∯111203)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":11,"operation_count":2,"complexity_ratio":5.5,"tree":{"type":"unary","operator":"⇙⪊","unary_expr":{"type":"unary","operator":"∡","unary_expr":{"type":"numeric_atoms","value":1379,"base":4}}},"used_operators":["pB6Fcnrjim","pRsWfj4Fpp"],"dependent_operators":["DIvbN7qnHd","2td37pGCOC","rysDP5nf3Z","D4vGDi5EA2","DZ8iAZOCBD","2DDjHMKMc0"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1379","layer":2},{"info":"compute unary expreesion, input=1379, op_id = pRsWfj4Fpp, unary_op_definition = '∡a = { ((a≦≮≮)⊉≛↸(a⋝⋈⪟a)) }', output=-1379","layer":1},{"info":"compute unary expreesion, input=-1379, op_id = pB6Fcnrjim, unary_op_definition = '⇙⪊a = { (633⊠≄⫣) , if (⩦⩻⨪a)>538 ; (a-a) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⇙⪊(∡⪩⨒∯111203)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⇙⪊(∡⪩⨒∯111203)","cot":[{"info":"∡⪩⨒∯111203=⪩⨒∯-111203","layer":1},{"info":"⇙⪊⪩⨒∯-111203=⪩⨒∯0","layer":0}]}
{"id":842,"expression_no_base_symbol":"⋣($6366$↯⫤)","expression":"⋣(⪩⨒∯1203132↯⫤)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":42,"operation_count":2,"complexity_ratio":21.0,"tree":{"type":"unary","operator":"⋣","unary_expr":{"type":"unary","operator":"↯⫤","unary_expr":{"type":"numeric_atoms","value":6366,"base":4}}},"used_operators":["zQWRhDnn8F","VwlE7vj6HS"],"dependent_operators":["vRio1gEz1j","x5lMkHmzsq","3EYGwJThht","DbCuESL50I","XTarYq4gQB","IGFM8TAlm9","sdazOOVcIp","8HhzD0ZcuI","keWfFq85dY","W4YGzv6Whe","23Mk6UjR3U","tifHPKVTfV","glklzrTFfD","eH2TOUuTDT","t8gj7n24qd","2DDjHMKMc0","Ph9nP6C5qx","g55IO6H4Gj","nCS4ZIUYfx"],"result":"⪩⨒∯1133","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6366","layer":2},{"info":"compute unary expreesion, input=6366, op_id = VwlE7vj6HS, unary_op_definition = 'a↯⫤ = { (((-a)⋝⋈⪟(a⨳⩥⨓a))⨸⪁((a⨁⊸⫻)⇼⇔∾(a+a))) , if (a⋷221)!=277 ; (((300⪐)⨁⊸⫻)⇼⇔∾(a≧⫂∧(26≧⫂∧87))) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = zQWRhDnn8F, unary_op_definition = '⋣a = { ((⋼∭⪍203)⇄(≯(a⨽a))) , if (a⇩)==859 ; (↥≼⋛((⪝⪂⫅a)⪨≂(⇉-⫰26))) , else }', output=95","layer":0}],"base":4,"result_base":4,"text":"⋣(⪩⨒∯1203132↯⫤)=⪩⨒∯1133","reverse_text":"⪩⨒∯1133=⋣(⪩⨒∯1203132↯⫤)","cot":[{"info":"⪩⨒∯1203132↯⫤=⪩⨒∯0","layer":1},{"info":"⋣⪩⨒∯0=⪩⨒∯1133","layer":0}]}
{"id":843,"expression_no_base_symbol":"($3620$⪹)⨽($1273$⩹$4678$)","expression":"(⪩⨒∯320210⪹)⨽(⪩⨒∯103321⩹⪩⨒∯1021012)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11769,"operation_count":3,"complexity_ratio":3923.0,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"unary","operator":"⪹","unary_expr":{"type":"numeric_atoms","value":3620,"base":4}},"right_expr":{"type":"binary","operator":"⩹","left_expr":{"type":"numeric_atoms","value":1273,"base":4},"right_expr":{"type":"numeric_atoms","value":4678,"base":4}}},"used_operators":["8HhzD0ZcuI","B3sABdIn96","2Wsdkap16l"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","9FxExcQeMw","e1ybzncUwg","QMFrweE19q","rysDP5nf3Z","NTOWxs364D","23Mk6UjR3U","XIabStNQrY","2DDjHMKMc0","12rbrZMWeM","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","nCS4ZIUYfx"],"result":"⪩⨒∯-120213031201122","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3620","layer":2},{"info":"compute unary expreesion, input=3620, op_id = B3sABdIn96, unary_op_definition = 'a⪹ = { ((402⫡⨏a)⩷∴(≉a)) }', output=11732","layer":1},{"info":"number node, value=1273","layer":2},{"info":"number node, value=4678","layer":2},{"info":"compute binary expreesion, left_input=1273, right_input=4678, op_id = 2Wsdkap16l binary_op_definition= 'a⩹b = { (b-((b⨳⩥⨓b)⨸⪁(1⋝⋈⪟b))) , if (b⇋≉)!=246 ; (((a⇋≉)⨰(a⋷a))⋳⪒((a⩚⊴⇥a)⨳⩥⨓(a≧⫂∧a))) , else }', output=4676","layer":1},{"info":"compute binary expreesion, left_input=11732, right_input=4676, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-412932186","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯320210⪹)⨽(⪩⨒∯103321⩹⪩⨒∯1021012)=⪩⨒∯-120213031201122","reverse_text":"⪩⨒∯-120213031201122=(⪩⨒∯320210⪹)⨽(⪩⨒∯103321⩹⪩⨒∯1021012)","cot":[{"info":"⪩⨒∯320210⪹=⪩⨒∯2313110","layer":1},{"info":"⪩⨒∯103321⩹⪩⨒∯1021012=⪩⨒∯1021010","layer":1},{"info":"⪩⨒∯2313110⨽⪩⨒∯1021010=⪩⨒∯-120213031201122","layer":0}]}
{"id":844,"expression_no_base_symbol":"$3910$⩦$2986$⩍⋽⫝̸($1477$⋅⇍$4543$)","expression":"⪩⨒∯331012⩦⪩⨒∯232222⩍⋽⫝̸(⪩⨒∯113011⋅⇍⪩⨒∯1012333)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":24,"operation_count":3,"complexity_ratio":8.0,"tree":{"type":"binary","operator":"⩍⋽⫝̸","left_expr":{"type":"binary","operator":"⩦","left_expr":{"type":"numeric_atoms","value":3910,"base":4},"right_expr":{"type":"numeric_atoms","value":2986,"base":4}},"right_expr":{"type":"binary","operator":"⋅⇍","left_expr":{"type":"numeric_atoms","value":1477,"base":4},"right_expr":{"type":"numeric_atoms","value":4543,"base":4}}},"used_operators":["BiWNJpBvwn","0kmYd0q39Y","AdZkA7nFnk"],"dependent_operators":["Ph9nP6C5qx","xUOZtlo3hN","N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q","g55IO6H4Gj","NTOWxs364D","eLAdDNolq6"],"result":"⪩⨒∯-2323","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3910","layer":2},{"info":"number node, value=2986","layer":2},{"info":"compute binary expreesion, left_input=3910, right_input=2986, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=7820","layer":1},{"info":"number node, value=1477","layer":2},{"info":"number node, value=4543","layer":2},{"info":"compute binary expreesion, left_input=1477, right_input=4543, op_id = AdZkA7nFnk binary_op_definition= 'a⋅⇍b = { (≤/506) , if (b⨸⪁793)>81 ; (a⩚⊴⇥452) , else }', output=-22","layer":1},{"info":"compute binary expreesion, left_input=7820, right_input=-22, op_id = BiWNJpBvwn binary_op_definition= 'a⩍⋽⫝̸b = { ((⨞⊢508)≧⫂∧(a≧⫂∧b)) }', output=-187","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯331012⩦⪩⨒∯232222⩍⋽⫝̸(⪩⨒∯113011⋅⇍⪩⨒∯1012333)=⪩⨒∯-2323","reverse_text":"⪩⨒∯-2323=⪩⨒∯331012⩦⪩⨒∯232222⩍⋽⫝̸(⪩⨒∯113011⋅⇍⪩⨒∯1012333)","cot":[{"info":"⪩⨒∯331012⩦⪩⨒∯232222=⪩⨒∯1322030","layer":1},{"info":"⪩⨒∯113011⋅⇍⪩⨒∯1012333=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯1322030⩍⋽⫝̸⪩⨒∯-112=⪩⨒∯-2323","layer":0}]}
{"id":845,"expression_no_base_symbol":"($3993$↺$3619$)∠↢$1971$∀⇚≩$7414$","expression":"(⪩⨒∯332121↺⪩⨒∯320203)∠↢⪩⨒∯132303∀⇚≩⪩⨒∯1303312","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13812,"operation_count":3,"complexity_ratio":4604.0,"tree":{"type":"binary","operator":"∠↢","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":3993,"base":4},"right_expr":{"type":"numeric_atoms","value":3619,"base":4}},"right_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":1971,"base":4},"right_expr":{"type":"numeric_atoms","value":7414,"base":4}}},"used_operators":["KbjG8mgYpV","7j4O788W3g","LRNGc0VcxI"],"dependent_operators":["rysDP5nf3Z","NTOWxs364D","XPYlsWDdGa","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","nCS4ZIUYfx","COABgblf1C","rysDP5nf3Z","t8gj7n24qd","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3993","layer":2},{"info":"number node, value=3619","layer":2},{"info":"compute binary expreesion, left_input=3993, right_input=3619, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=3619","layer":1},{"info":"number node, value=1971","layer":2},{"info":"number node, value=7414","layer":2},{"info":"compute binary expreesion, left_input=1971, right_input=7414, op_id = LRNGc0VcxI binary_op_definition= 'a∀⇚≩b = {b, if a == 0; ((a-1)∀⇚≩b)≫≃, if a > 0 and abs(a) < 1000000; -((a+1)∀⇚≩b)≫≃, if a < 0 and abs(a) < 1000000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=3619, right_input=nan, op_id = KbjG8mgYpV binary_op_definition= 'a∠↢b = { (a⊭↱((159⨳⩥⨓16)-(b⨸⪁a))) , if (b==488 or (⨞⊢a)==254) ; (⪲⇎((-b)⫡⨏(b⩚⊴⇥a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯332121↺⪩⨒∯320203)∠↢⪩⨒∯132303∀⇚≩⪩⨒∯1303312=NaN","reverse_text":"NaN=(⪩⨒∯332121↺⪩⨒∯320203)∠↢⪩⨒∯132303∀⇚≩⪩⨒∯1303312","cot":[{"info":"⪩⨒∯332121↺⪩⨒∯320203=⪩⨒∯320203","layer":1},{"info":"⪩⨒∯132303∀⇚≩⪩⨒∯1303312=NaN","layer":1},{"info":"⪩⨒∯320203∠↢NaN=NaN","layer":0}]}
{"id":846,"expression_no_base_symbol":"($4378$↛⩡⫤)≚⊃≕($7288$⨶)","expression":"(⪩⨒∯1010122↛⩡⫤)≚⊃≕(⪩⨒∯1301320⨶)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13303,"operation_count":3,"complexity_ratio":4434.333333333333,"tree":{"type":"binary","operator":"≚⊃≕","left_expr":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"numeric_atoms","value":4378,"base":4}},"right_expr":{"type":"unary","operator":"⨶","unary_expr":{"type":"numeric_atoms","value":7288,"base":4}}},"used_operators":["Bmrmz2XGnR","FU0Cs4j7VP","rFxw8gIMmB"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","7j4O788W3g","sdazOOVcIp","8w2t5hMYqp","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X","f6k1SAg4EE","Qy55tPpLXF"],"result":"⪩⨒∯-21323202212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4378","layer":2},{"info":"compute unary expreesion, input=4378, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-657167","layer":1},{"info":"number node, value=7288","layer":2},{"info":"compute unary expreesion, input=7288, op_id = rFxw8gIMmB, unary_op_definition = 'a⨶ = { ((a⋥≓≎303)⪒(a⋥≓≎537)) }', output=12830","layer":1},{"info":"compute binary expreesion, left_input=-657167, right_input=12830, op_id = Bmrmz2XGnR binary_op_definition= 'a≚⊃≕b = { (-((⊄⩳↩b)⪨≂(a⩷∴b))) , if ((b⫡⨏524)<690 or (⨞⊢a)>=395) ; ((⊄⩳↩(b⋥≓≎a))⋥≓≎((a↺a)⪨≂(479⨸⪁a))) , else }', output=-2603174","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1010122↛⩡⫤)≚⊃≕(⪩⨒∯1301320⨶)=⪩⨒∯-21323202212","reverse_text":"⪩⨒∯-21323202212=(⪩⨒∯1010122↛⩡⫤)≚⊃≕(⪩⨒∯1301320⨶)","cot":[{"info":"⪩⨒∯1010122↛⩡⫤=⪩⨒∯-2200130033","layer":1},{"info":"⪩⨒∯1301320⨶=⪩⨒∯3020132","layer":1},{"info":"⪩⨒∯-2200130033≚⊃≕⪩⨒∯3020132=⪩⨒∯-21323202212","layer":0}]}
{"id":847,"expression_no_base_symbol":"($2783$⨌↪)∖(⨡↴$8155$)","expression":"(⪩⨒∯223133⨌↪)∖(⨡↴⪩⨒∯1333123)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":926,"operation_count":3,"complexity_ratio":308.6666666666667,"tree":{"type":"binary","operator":"∖","left_expr":{"type":"unary","operator":"⨌↪","unary_expr":{"type":"numeric_atoms","value":2783,"base":4}},"right_expr":{"type":"unary","operator":"⨡↴","unary_expr":{"type":"numeric_atoms","value":8155,"base":4}}},"used_operators":["tXD093vOjl","cWQsF5MvuD","liw5iZPkLH"],"dependent_operators":["rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC","8w2t5hMYqp","2DQ55sFlQl","i8ToyICDmI","QMFrweE19q","W4YGzv6Whe","P8v4zCKN1o"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2783","layer":2},{"info":"compute unary expreesion, input=2783, op_id = cWQsF5MvuD, unary_op_definition = 'a⨌↪ = { (⊄⩳↩((a∲⫓a)⨵⪆(a⫡⨏a))) }', output=-480","layer":1},{"info":"number node, value=8155","layer":2},{"info":"compute unary expreesion, input=8155, op_id = liw5iZPkLH, unary_op_definition = '⨡↴a = { (∥⊫(a+181)) }', output=9204","layer":1},{"info":"compute binary expreesion, left_input=-480, right_input=9204, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯223133⨌↪)∖(⨡↴⪩⨒∯1333123)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯223133⨌↪)∖(⨡↴⪩⨒∯1333123)","cot":[{"info":"⪩⨒∯223133⨌↪=⪩⨒∯-13200","layer":1},{"info":"⨡↴⪩⨒∯1333123=⪩⨒∯2033310","layer":1},{"info":"⪩⨒∯-13200∖⪩⨒∯2033310=⪩⨒∯0","layer":0}]}
{"id":848,"expression_no_base_symbol":"∤↝($1821$⫻⋑⊟)","expression":"∤↝(⪩⨒∯130131⫻⋑⊟)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":21,"operation_count":2,"complexity_ratio":10.5,"tree":{"type":"unary","operator":"∤↝","unary_expr":{"type":"unary","operator":"⫻⋑⊟","unary_expr":{"type":"numeric_atoms","value":1821,"base":4}}},"used_operators":["3UMq87Qwqg","o575Zjdmzy"],"dependent_operators":["s3Fd5m9Dh2","YjI8oCXuph","7j4O788W3g","k7HXdKtiEU","ocnLzx9CaJ","Noe24qw2ks","fG6uBQFnGz","cTDWOvIxvz","jLgFTUHLKL","rysDP5nf3Z","sdazOOVcIp","12rbrZMWeM","xUOZtlo3hN","g55IO6H4Gj","i8ToyICDmI"],"result":"⪩⨒∯-300330","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1821","layer":2},{"info":"compute unary expreesion, input=1821, op_id = o575Zjdmzy, unary_op_definition = 'a⫻⋑⊟ = { ((a⨸⪁(⨞⊢a))⪨≂((a∲⫓a)⋳⪒(265-a))) }', output=-3132","layer":1},{"info":"compute unary expreesion, input=-3132, op_id = 3UMq87Qwqg, unary_op_definition = '∤↝a = { a , if ((a⊬⨰244)<=56 or (⫇a)>308 or (a⨐673)<=60) ; (((↩⪖a)⩼⇪↪(57∝206))↺(↩(⊲⪭a))) , else }', output=-3132","layer":0}],"base":4,"result_base":4,"text":"∤↝(⪩⨒∯130131⫻⋑⊟)=⪩⨒∯-300330","reverse_text":"⪩⨒∯-300330=∤↝(⪩⨒∯130131⫻⋑⊟)","cot":[{"info":"⪩⨒∯130131⫻⋑⊟=⪩⨒∯-300330","layer":1},{"info":"∤↝⪩⨒∯-300330=⪩⨒∯-300330","layer":0}]}
{"id":849,"expression_no_base_symbol":"⇖⫷⫕($1615$↰)","expression":"⇖⫷⫕(⪩⨒∯121033↰)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":739,"operation_count":2,"complexity_ratio":369.5,"tree":{"type":"unary","operator":"⇖⫷⫕","unary_expr":{"type":"unary","operator":"↰","unary_expr":{"type":"numeric_atoms","value":1615,"base":4}}},"used_operators":["UHmRx3INFg","bl5wxAcryP"],"dependent_operators":["DE7zCoGJt9","FyVja0WsTP","oZj3VtZNQx","DyGG3AbaNP","nCS4ZIUYfx","Z2TMIBDE3Q"],"result":"⪩⨒∯230012","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1615","layer":2},{"info":"compute unary expreesion, input=1615, op_id = bl5wxAcryP, unary_op_definition = 'a↰ = { ((a⨳⩥⨓101)⩤) }', output=1514","layer":1},{"info":"compute unary expreesion, input=1514, op_id = UHmRx3INFg, unary_op_definition = '⇖⫷⫕a = { ((a∼125)≀⫉(↞≼(a⊱⇼⊻51))) }', output=2822","layer":0}],"base":4,"result_base":4,"text":"⇖⫷⫕(⪩⨒∯121033↰)=⪩⨒∯230012","reverse_text":"⪩⨒∯230012=⇖⫷⫕(⪩⨒∯121033↰)","cot":[{"info":"⪩⨒∯121033↰=⪩⨒∯113222","layer":1},{"info":"⇖⫷⫕⪩⨒∯113222=⪩⨒∯230012","layer":0}]}
{"id":850,"expression_no_base_symbol":"⊿$4953$≭$2096$","expression":"⊿⪩⨒∯1031121≭⪩⨒∯200300","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":23,"operation_count":2,"complexity_ratio":11.5,"tree":{"type":"unary","operator":"⊿","unary_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":4953,"base":4},"right_expr":{"type":"numeric_atoms","value":2096,"base":4}}},"used_operators":["DO4fhlbJSI","rxpJgHHUmx"],"dependent_operators":["9FxExcQeMw","e1ybzncUwg","XPYlsWDdGa","sdazOOVcIp","2DQ55sFlQl","12rbrZMWeM","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4953","layer":2},{"info":"number node, value=2096","layer":2},{"info":"compute binary expreesion, left_input=4953, right_input=2096, op_id = rxpJgHHUmx binary_op_definition= 'a≭b = {-22, if b == 0; (a)≹⇙⪍(a≭(b-1)), if b > 0 and abs(b) < 100; -(a)≹⇙⪍(a≭(b+1)), if b < 0 and abs(b) < 100; NaN, else}', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = DO4fhlbJSI, unary_op_definition = '⊿a = { ((⪲⇎(a⨵⪆a))⩷∴((≉a)⋳⪒(a⪨≂a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⊿⪩⨒∯1031121≭⪩⨒∯200300=NaN","reverse_text":"NaN=⊿⪩⨒∯1031121≭⪩⨒∯200300","cot":[{"info":"⪩⨒∯1031121≭⪩⨒∯200300=NaN","layer":1},{"info":"⊿NaN=NaN","layer":0}]}
{"id":851,"expression_no_base_symbol":"($4817$↸$3808$)⫯⪬∳($6351$⨟⋌⩍$3889$)","expression":"(⪩⨒∯1023101↸⪩⨒∯323200)⫯⪬∳(⪩⨒∯1203033⨟⋌⩍⪩⨒∯330301)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3822,"operation_count":3,"complexity_ratio":1274.0,"tree":{"type":"binary","operator":"⫯⪬∳","left_expr":{"type":"binary","operator":"↸","left_expr":{"type":"numeric_atoms","value":4817,"base":4},"right_expr":{"type":"numeric_atoms","value":3808,"base":4}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":6351,"base":4},"right_expr":{"type":"numeric_atoms","value":3889,"base":4}}},"used_operators":["d7ASUq0ydm","1eCjFl0mb9","rGHVDoGpnC"],"dependent_operators":["Qy55tPpLXF","BjRHVeLaeN","8w2t5hMYqp","Ph9nP6C5qx","eewbuw0ToL","D4vGDi5EA2","9HNa5Wba9A","61wBmkZwlr","rJVOvQCfKK","Tcnh7f0tEr"],"result":"⪩⨒∯3202312","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4817","layer":2},{"info":"number node, value=3808","layer":2},{"info":"compute binary expreesion, left_input=4817, right_input=3808, op_id = 1eCjFl0mb9 binary_op_definition= 'a↸b = { ((b*a)⨎(≋a)) }', output=4817","layer":1},{"info":"number node, value=6351","layer":2},{"info":"number node, value=3889","layer":2},{"info":"compute binary expreesion, left_input=6351, right_input=3889, op_id = rGHVDoGpnC binary_op_definition= 'a⨟⋌⩍b = {a, if b == 0; (a⨟⋌⩍(b-1))≣⋋, if b > 0 and abs(b) < 1000; -(a⨟⋌⩍(b+1))≣⋋, if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=4817, right_input=nan, op_id = d7ASUq0ydm binary_op_definition= 'a⫯⪬∳b = { ((b⋥≓≎a)≧⫂∧(⊄⩳↩a)) , if (a≦≮≮)!=65 ; ((b⫩⊇)⋥≓≎(a⨰b)) , else }', output=14518","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1023101↸⪩⨒∯323200)⫯⪬∳(⪩⨒∯1203033⨟⋌⩍⪩⨒∯330301)=⪩⨒∯3202312","reverse_text":"⪩⨒∯3202312=(⪩⨒∯1023101↸⪩⨒∯323200)⫯⪬∳(⪩⨒∯1203033⨟⋌⩍⪩⨒∯330301)","cot":[{"info":"⪩⨒∯1023101↸⪩⨒∯323200=⪩⨒∯1023101","layer":1},{"info":"⪩⨒∯1203033⨟⋌⩍⪩⨒∯330301=NaN","layer":1},{"info":"⪩⨒∯1023101⫯⪬∳NaN=⪩⨒∯3202312","layer":0}]}
{"id":852,"expression_no_base_symbol":"($1807$%$1050$)∓⋝$3704$⨑⩅≇$2448$","expression":"(⪩⨒∯130033%⪩⨒∯100122)∓⋝⪩⨒∯321320⨑⩅≇⪩⨒∯212100","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2540,"operation_count":3,"complexity_ratio":846.6666666666666,"tree":{"type":"binary","operator":"∓⋝","left_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":1807,"base":4},"right_expr":{"type":"numeric_atoms","value":1050,"base":4}},"right_expr":{"type":"binary","operator":"⨑⩅≇","left_expr":{"type":"numeric_atoms","value":3704,"base":4},"right_expr":{"type":"numeric_atoms","value":2448,"base":4}}},"used_operators":["PoHhknlbAi","k8jYdgA6NY","h92wMvzauj"],"dependent_operators":["DZ8iAZOCBD","DbCuESL50I","mqXw5SEYmG","2MzE1hQ0cz","rysDP5nf3Z","s3Fd5m9Dh2","3sJ7IOPOlU","nREPSIbpBE","9Isq31Ruls","umQnsF7QlU","8HhzD0ZcuI","u6S6b8DprG","DmTXOeWf9t","AFVx7xoS7T","jLgFTUHLKL","oacrs7FA3X","xNBdhnnwKq"],"result":"⪩⨒∯1003","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1807","layer":2},{"info":"number node, value=1050","layer":2},{"info":"compute binary expreesion, left_input=1807, right_input=1050, op_id = k8jYdgA6NY binary_op_definition= 'None', output=757","layer":1},{"info":"number node, value=3704","layer":2},{"info":"number node, value=2448","layer":2},{"info":"compute binary expreesion, left_input=3704, right_input=2448, op_id = h92wMvzauj binary_op_definition= 'a⨑⩅≇b = { (((a⪇≇⋚b)⊬⨰(b⨽582))∌↝a) , if (↽≂a)<10 or (b⊭∹↮)==22 ; ((a⊲⩕⊾(↩a))⪕((a⨚243)⇌⫙⪟(b⪘⫢b))) , else }', output=-11112","layer":1},{"info":"compute binary expreesion, left_input=757, right_input=-11112, op_id = PoHhknlbAi binary_op_definition= 'a∓⋝b = { (((a⊉≛↸a)⫸⊐(⋼∭⪍b))∩⋅) }', output=67","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯130033%⪩⨒∯100122)∓⋝⪩⨒∯321320⨑⩅≇⪩⨒∯212100=⪩⨒∯1003","reverse_text":"⪩⨒∯1003=(⪩⨒∯130033%⪩⨒∯100122)∓⋝⪩⨒∯321320⨑⩅≇⪩⨒∯212100","cot":[{"info":"⪩⨒∯130033%⪩⨒∯100122=⪩⨒∯23311","layer":1},{"info":"⪩⨒∯321320⨑⩅≇⪩⨒∯212100=⪩⨒∯-2231220","layer":1},{"info":"⪩⨒∯23311∓⋝⪩⨒∯-2231220=⪩⨒∯1003","layer":0}]}
{"id":853,"expression_no_base_symbol":"$1799$∣$4554$⋻⩜⩜($1784$⨸⪁$9224$)","expression":"⪩⨒∯130013∣⪩⨒∯1013022⋻⩜⩜(⪩⨒∯123320⨸⪁⪩⨒∯2100020)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":308234,"operation_count":3,"complexity_ratio":102744.66666666667,"tree":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"binary","operator":"∣","left_expr":{"type":"numeric_atoms","value":1799,"base":4},"right_expr":{"type":"numeric_atoms","value":4554,"base":4}},"right_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":1784,"base":4},"right_expr":{"type":"numeric_atoms","value":9224,"base":4}}},"used_operators":["oDCm7WA9JY","PPChnnnBFF","g55IO6H4Gj"],"dependent_operators":["mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","eLAdDNolq6","eH2TOUuTDT","Ph9nP6C5qx","i8ToyICDmI","W4YGzv6Whe"],"result":"⪩⨒∯320032","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1799","layer":2},{"info":"number node, value=4554","layer":2},{"info":"compute binary expreesion, left_input=1799, right_input=4554, op_id = PPChnnnBFF binary_op_definition= 'a∣b = { (≤/((a⪐)≧⫂∧(a∲⫓b))) , if (b⪐)<590 ; a , else }', output=1799","layer":1},{"info":"number node, value=1784","layer":2},{"info":"number node, value=9224","layer":2},{"info":"compute binary expreesion, left_input=1784, right_input=9224, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=22016","layer":1},{"info":"compute binary expreesion, left_input=1799, right_input=22016, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=3598","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯130013∣⪩⨒∯1013022⋻⩜⩜(⪩⨒∯123320⨸⪁⪩⨒∯2100020)=⪩⨒∯320032","reverse_text":"⪩⨒∯320032=⪩⨒∯130013∣⪩⨒∯1013022⋻⩜⩜(⪩⨒∯123320⨸⪁⪩⨒∯2100020)","cot":[{"info":"⪩⨒∯130013∣⪩⨒∯1013022=⪩⨒∯130013","layer":1},{"info":"⪩⨒∯123320⨸⪁⪩⨒∯2100020=⪩⨒∯11120000","layer":1},{"info":"⪩⨒∯130013⋻⩜⩜⪩⨒∯11120000=⪩⨒∯320032","layer":0}]}
{"id":854,"expression_no_base_symbol":"($2420$+$1385$)⫌⩉⩟$2958$⇷$7637$","expression":"(⪩⨒∯211310+⪩⨒∯111221)⫌⩉⩟⪩⨒∯232032⇷⪩⨒∯1313111","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":123780,"operation_count":3,"complexity_ratio":41260.0,"tree":{"type":"binary","operator":"⫌⩉⩟","left_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":2420,"base":4},"right_expr":{"type":"numeric_atoms","value":1385,"base":4}},"right_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":2958,"base":4},"right_expr":{"type":"numeric_atoms","value":7637,"base":4}}},"used_operators":["XIIwhv8d0m","W4YGzv6Whe","mp7IySMOzn"],"dependent_operators":["B5M0gjZbta","UMwdvZNt44","MRPaB8lBjK","vkpjKywKVM","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"⪩⨒∯-302","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2420","layer":2},{"info":"number node, value=1385","layer":2},{"info":"compute binary expreesion, left_input=2420, right_input=1385, op_id = W4YGzv6Whe binary_op_definition= 'None', output=3805","layer":1},{"info":"number node, value=2958","layer":2},{"info":"number node, value=7637","layer":2},{"info":"compute binary expreesion, left_input=2958, right_input=7637, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=15274","layer":1},{"info":"compute binary expreesion, left_input=3805, right_input=15274, op_id = XIIwhv8d0m binary_op_definition= 'a⫌⩉⩟b = { (((a↬179)⇮⋭(b⇡⇂b))⇉⇱⇎) }', output=-50","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯211310+⪩⨒∯111221)⫌⩉⩟⪩⨒∯232032⇷⪩⨒∯1313111=⪩⨒∯-302","reverse_text":"⪩⨒∯-302=(⪩⨒∯211310+⪩⨒∯111221)⫌⩉⩟⪩⨒∯232032⇷⪩⨒∯1313111","cot":[{"info":"⪩⨒∯211310+⪩⨒∯111221=⪩⨒∯323131","layer":1},{"info":"⪩⨒∯232032⇷⪩⨒∯1313111=⪩⨒∯3232222","layer":1},{"info":"⪩⨒∯323131⫌⩉⩟⪩⨒∯3232222=⪩⨒∯-302","layer":0}]}
{"id":855,"expression_no_base_symbol":"$1710$→⨶⪴$4598$⨵⪆$1709$⪮%⊝$1224$","expression":"⪩⨒∯122232→⨶⪴⪩⨒∯1013312⨵⪆⪩⨒∯122231⪮%⊝⪩⨒∯103020","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13,"operation_count":3,"complexity_ratio":4.333333333333333,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"binary","operator":"→⨶⪴","left_expr":{"type":"numeric_atoms","value":1710,"base":4},"right_expr":{"type":"numeric_atoms","value":4598,"base":4}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1709,"base":4},"right_expr":{"type":"numeric_atoms","value":1224,"base":4}}},"used_operators":["2DQ55sFlQl","bF6eod5Gvf","IWmyXbctLI"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","8w2t5hMYqp","9FxExcQeMw","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1710","layer":2},{"info":"number node, value=4598","layer":2},{"info":"compute binary expreesion, left_input=1710, right_input=4598, op_id = bF6eod5Gvf binary_op_definition= 'a→⨶⪴b = { (a⩷∴b) , if b<109 ; (⊄⩳↩b) , else }', output=-13794","layer":1},{"info":"number node, value=1709","layer":2},{"info":"number node, value=1224","layer":2},{"info":"compute binary expreesion, left_input=1709, right_input=1224, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=3734","layer":1},{"info":"compute binary expreesion, left_input=-13794, right_input=3734, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯122232→⨶⪴⪩⨒∯1013312⨵⪆⪩⨒∯122231⪮%⊝⪩⨒∯103020=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⪩⨒∯122232→⨶⪴⪩⨒∯1013312⨵⪆⪩⨒∯122231⪮%⊝⪩⨒∯103020","cot":[{"info":"⪩⨒∯122232→⨶⪴⪩⨒∯1013312=⪩⨒∯-3113202","layer":1},{"info":"⪩⨒∯122231⪮%⊝⪩⨒∯103020=⪩⨒∯322112","layer":1},{"info":"⪩⨒∯-3113202⨵⪆⪩⨒∯322112=⪩⨒∯2200","layer":0}]}
{"id":856,"expression_no_base_symbol":"($4553$⩵∡$1214$)↓($2095$⋭≵$6242$)","expression":"(⪩⨒∯1013021⩵∡⪩⨒∯102332)↓(⪩⨒∯200233⋭≵⪩⨒∯1201202)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1296,"operation_count":3,"complexity_ratio":432.0,"tree":{"type":"binary","operator":"↓","left_expr":{"type":"binary","operator":"⩵∡","left_expr":{"type":"numeric_atoms","value":4553,"base":4},"right_expr":{"type":"numeric_atoms","value":1214,"base":4}},"right_expr":{"type":"binary","operator":"⋭≵","left_expr":{"type":"numeric_atoms","value":2095,"base":4},"right_expr":{"type":"numeric_atoms","value":6242,"base":4}}},"used_operators":["Af076pWI7l","Y7wcNGrDQJ","jBncVCNhdl"],"dependent_operators":["nhYeJWJD5X","mp7IySMOzn","Noe24qw2ks","lvlrscuwVU","T2fj7uvVaJ","PoHhknlbAi","NTOWxs364D","glklzrTFfD","tifHPKVTfV","RygbFNSyEJ","gx7XJ7hdpj","9ICcGScMcE","C6VvDP6HwP","mqXw5SEYmG","7IPrd9c3lf","COABgblf1C"],"result":"⪩⨒∯2100010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4553","layer":2},{"info":"number node, value=1214","layer":2},{"info":"compute binary expreesion, left_input=4553, right_input=1214, op_id = Y7wcNGrDQJ binary_op_definition= 'a⩵∡b = { ((b⇼⇔∾a)⩚⊴⇥(a⨁⊸⫻)) }', output=-8013","layer":1},{"info":"number node, value=2095","layer":2},{"info":"number node, value=6242","layer":2},{"info":"compute binary expreesion, left_input=2095, right_input=6242, op_id = jBncVCNhdl binary_op_definition= 'a⋭≵b = { ((156≦↸a)⊭↱(≦∁b)) , if (b⫸⊐434)<=441 and (a⫸⇳180)>=132 ; ((a⪑⩈)⊵↤) , else }', output=67","layer":1},{"info":"compute binary expreesion, left_input=-8013, right_input=67, op_id = Af076pWI7l binary_op_definition= 'a↓b = { (((b⇷b)∓⋝b)⨐((462≴⪞⇿a)∇⊂⋱(a⋓a))) }', output=9220","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1013021⩵∡⪩⨒∯102332)↓(⪩⨒∯200233⋭≵⪩⨒∯1201202)=⪩⨒∯2100010","reverse_text":"⪩⨒∯2100010=(⪩⨒∯1013021⩵∡⪩⨒∯102332)↓(⪩⨒∯200233⋭≵⪩⨒∯1201202)","cot":[{"info":"⪩⨒∯1013021⩵∡⪩⨒∯102332=⪩⨒∯-1331031","layer":1},{"info":"⪩⨒∯200233⋭≵⪩⨒∯1201202=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯-1331031↓⪩⨒∯1003=⪩⨒∯2100010","layer":0}]}
{"id":857,"expression_no_base_symbol":"$2458$⋻⩜⩜$1264$*($2531$∖$1865$)","expression":"⪩⨒∯212122⋻⩜⩜⪩⨒∯103300*(⪩⨒∯213203∖⪩⨒∯131021)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":18035,"operation_count":3,"complexity_ratio":6011.666666666667,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":2458,"base":4},"right_expr":{"type":"numeric_atoms","value":1264,"base":4}},"right_expr":{"type":"binary","operator":"∖","left_expr":{"type":"numeric_atoms","value":2531,"base":4},"right_expr":{"type":"numeric_atoms","value":1865,"base":4}}},"used_operators":["9HNa5Wba9A","oDCm7WA9JY","tXD093vOjl"],"dependent_operators":["W4YGzv6Whe","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2458","layer":2},{"info":"number node, value=1264","layer":2},{"info":"compute binary expreesion, left_input=2458, right_input=1264, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=4916","layer":1},{"info":"number node, value=2531","layer":2},{"info":"number node, value=1865","layer":2},{"info":"compute binary expreesion, left_input=2531, right_input=1865, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=4916, right_input=0, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯212122⋻⩜⩜⪩⨒∯103300*(⪩⨒∯213203∖⪩⨒∯131021)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯212122⋻⩜⩜⪩⨒∯103300*(⪩⨒∯213203∖⪩⨒∯131021)","cot":[{"info":"⪩⨒∯212122⋻⩜⩜⪩⨒∯103300=⪩⨒∯1030310","layer":1},{"info":"⪩⨒∯213203∖⪩⨒∯131021=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1030310*⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":858,"expression_no_base_symbol":"($3651$⩎⪣⊞)⪎↠(⨴⫝$2185$)","expression":"(⪩⨒∯321003⩎⪣⊞)⪎↠(⨴⫝⪩⨒∯202021)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":52949,"operation_count":3,"complexity_ratio":17649.666666666668,"tree":{"type":"binary","operator":"⪎↠","left_expr":{"type":"unary","operator":"⩎⪣⊞","unary_expr":{"type":"numeric_atoms","value":3651,"base":4}},"right_expr":{"type":"unary","operator":"⨴⫝","unary_expr":{"type":"numeric_atoms","value":2185,"base":4}}},"used_operators":["3tVxb0NHM4","waWucp1uQ4","SVb2v531z1"],"dependent_operators":["P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM","mp7IySMOzn","oDCm7WA9JY","XnXgA4xnOs","ocnLzx9CaJ","3sJ7IOPOlU","9cloC0Ngie","SWo3A1KBJH","jWTQ2TZYIH","pRsWfj4Fpp","DyGG3AbaNP","5obUd6DV38","8HhzD0ZcuI","YbUVn0Rbpy","AdZkA7nFnk","SIgE0bArFf"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3651","layer":2},{"info":"compute unary expreesion, input=3651, op_id = waWucp1uQ4, unary_op_definition = 'a⩎⪣⊞ = { (a⇷a) }', output=7302","layer":1},{"info":"number node, value=2185","layer":2},{"info":"compute unary expreesion, input=2185, op_id = SVb2v531z1, unary_op_definition = '⨴⫝a = { ((⪨⨬(⇋↷a))≬⇓((a⋅⇍a)⨑≵⋬(∡178))) , if (a⪇≇⋚963)!=62 ; (((541⋛107)⩼⇪↪(⪭⩑⪱a))⋻⩜⩜((a⊕∕a)∼(459⨽6))) , else }', output=2828198","layer":1},{"info":"compute binary expreesion, left_input=7302, right_input=2828198, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯321003⩎⪣⊞)⪎↠(⨴⫝⪩⨒∯202021)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(⪩⨒∯321003⩎⪣⊞)⪎↠(⨴⫝⪩⨒∯202021)","cot":[{"info":"⪩⨒∯321003⩎⪣⊞=⪩⨒∯1302012","layer":1},{"info":"⨴⫝⪩⨒∯202021=⪩⨒∯22302132212","layer":1},{"info":"⪩⨒∯1302012⪎↠⪩⨒∯22302132212=⪩⨒∯2200","layer":0}]}
{"id":859,"expression_no_base_symbol":"($2718$⋻⩜⩜$2252$)≒∊($1630$⨐⩸⫘$1162$)","expression":"(⪩⨒∯222132⋻⩜⩜⪩⨒∯203030)≒∊(⪩⨒∯121132⨐⩸⫘⪩⨒∯102022)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":31543,"operation_count":3,"complexity_ratio":10514.333333333334,"tree":{"type":"binary","operator":"≒∊","left_expr":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"numeric_atoms","value":2718,"base":4},"right_expr":{"type":"numeric_atoms","value":2252,"base":4}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":1630,"base":4},"right_expr":{"type":"numeric_atoms","value":1162,"base":4}}},"used_operators":["5KTvxBwnZo","oDCm7WA9JY","fu6greOZ01"],"dependent_operators":["3EYGwJThht","dWAJyo7jo9","Z2TMIBDE3Q","bjFbhXSADs","3DZMoQKiUl","mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2718","layer":2},{"info":"number node, value=2252","layer":2},{"info":"compute binary expreesion, left_input=2718, right_input=2252, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=5436","layer":1},{"info":"number node, value=1630","layer":2},{"info":"number node, value=1162","layer":2},{"info":"compute binary expreesion, left_input=1630, right_input=1162, op_id = fu6greOZ01 binary_op_definition= 'a⨐⩸⫘b = {a, if b == 0; (a⨐⩸⫘(b-1))⨓(b), if b > 0 and abs(b) < 1000; -(a⨐⩸⫘(b+1))⨓(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=5436, right_input=nan, op_id = 5KTvxBwnZo binary_op_definition= 'a≒∊b = { (≱⇩⩕(a⪢a)) , if (a⩤)==117 ; ((b⪊≅)⇄a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯222132⋻⩜⩜⪩⨒∯203030)≒∊(⪩⨒∯121132⨐⩸⫘⪩⨒∯102022)=NaN","reverse_text":"NaN=(⪩⨒∯222132⋻⩜⩜⪩⨒∯203030)≒∊(⪩⨒∯121132⨐⩸⫘⪩⨒∯102022)","cot":[{"info":"⪩⨒∯222132⋻⩜⩜⪩⨒∯203030=⪩⨒∯1110330","layer":1},{"info":"⪩⨒∯121132⨐⩸⫘⪩⨒∯102022=NaN","layer":1},{"info":"⪩⨒∯1110330≒∊NaN=NaN","layer":0}]}
{"id":860,"expression_no_base_symbol":"$5091$↓$2413$↬(⇖$7719$)","expression":"⪩⨒∯1033203↓⪩⨒∯211231↬(⇖⪩⨒∯1320213)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":34081,"operation_count":3,"complexity_ratio":11360.333333333334,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"binary","operator":"↓","left_expr":{"type":"numeric_atoms","value":5091,"base":4},"right_expr":{"type":"numeric_atoms","value":2413,"base":4}},"right_expr":{"type":"unary","operator":"⇖","unary_expr":{"type":"numeric_atoms","value":7719,"base":4}}},"used_operators":["B5M0gjZbta","Af076pWI7l","tfWHHpNKUN"],"dependent_operators":["rGHVDoGpnC","nhYeJWJD5X","mp7IySMOzn","Noe24qw2ks","lvlrscuwVU","T2fj7uvVaJ","PoHhknlbAi","2DQ55sFlQl"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5091","layer":2},{"info":"number node, value=2413","layer":2},{"info":"compute binary expreesion, left_input=5091, right_input=2413, op_id = Af076pWI7l binary_op_definition= 'a↓b = { (((b⇷b)∓⋝b)⨐((462≴⪞⇿a)∇⊂⋱(a⋓a))) }', output=-134","layer":1},{"info":"number node, value=7719","layer":2},{"info":"compute unary expreesion, input=7719, op_id = tfWHHpNKUN, unary_op_definition = '⇖a = { (221⨵⪆a) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=-134, right_input=160, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1033203↓⪩⨒∯211231↬(⇖⪩⨒∯1320213)=NaN","reverse_text":"NaN=⪩⨒∯1033203↓⪩⨒∯211231↬(⇖⪩⨒∯1320213)","cot":[{"info":"⪩⨒∯1033203↓⪩⨒∯211231=⪩⨒∯-2012","layer":1},{"info":"⇖⪩⨒∯1320213=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯-2012↬⪩⨒∯2200=NaN","layer":0}]}
{"id":861,"expression_no_base_symbol":"($4683$∠⫱$2843$)⊋($1805$⪶≀⋏$2294$)","expression":"(⪩⨒∯1021023∠⫱⪩⨒∯230123)⊋(⪩⨒∯130031⪶≀⋏⪩⨒∯203312)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":96,"operation_count":3,"complexity_ratio":32.0,"tree":{"type":"binary","operator":"⊋","left_expr":{"type":"binary","operator":"∠⫱","left_expr":{"type":"numeric_atoms","value":4683,"base":4},"right_expr":{"type":"numeric_atoms","value":2843,"base":4}},"right_expr":{"type":"binary","operator":"⪶≀⋏","left_expr":{"type":"numeric_atoms","value":1805,"base":4},"right_expr":{"type":"numeric_atoms","value":2294,"base":4}}},"used_operators":["W4tP9CfskL","QvoQhV0rrE","zR4jO40bMj"],"dependent_operators":["2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu","eLAdDNolq6","DZ8iAZOCBD","7j4O788W3g","tifHPKVTfV","AF7qkfDlqP","W4YGzv6Whe","rysDP5nf3Z","NTOWxs364D","glklzrTFfD","2DDjHMKMc0","g55IO6H4Gj","eewbuw0ToL"],"result":"⪩⨒∯-303103222","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4683","layer":2},{"info":"number node, value=2843","layer":2},{"info":"compute binary expreesion, left_input=4683, right_input=2843, op_id = QvoQhV0rrE binary_op_definition= 'a∠⫱b = { ((⨑⩽⪐a)↺(617⊉≛↸a)) , if (≤/b)<=3 ; (b⇼⇔∾a) , else }', output=1234","layer":1},{"info":"number node, value=1805","layer":2},{"info":"number node, value=2294","layer":2},{"info":"compute binary expreesion, left_input=1805, right_input=2294, op_id = zR4jO40bMj binary_op_definition= 'a⪶≀⋏b = { (((b⨸⪁b)⨸⪁(a-a))⋝⋈⪟(b⋝⋈⪟(b+b))) , if a<244 ; (((b⩚⊴⇥a)⨁⊸⫻)⨰a) , else }', output=-10235","layer":1},{"info":"compute binary expreesion, left_input=1234, right_input=-10235, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=-210154","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1021023∠⫱⪩⨒∯230123)⊋(⪩⨒∯130031⪶≀⋏⪩⨒∯203312)=⪩⨒∯-303103222","reverse_text":"⪩⨒∯-303103222=(⪩⨒∯1021023∠⫱⪩⨒∯230123)⊋(⪩⨒∯130031⪶≀⋏⪩⨒∯203312)","cot":[{"info":"⪩⨒∯1021023∠⫱⪩⨒∯230123=⪩⨒∯103102","layer":1},{"info":"⪩⨒∯130031⪶≀⋏⪩⨒∯203312=⪩⨒∯-2133323","layer":1},{"info":"⪩⨒∯103102⊋⪩⨒∯-2133323=⪩⨒∯-303103222","layer":0}]}
{"id":862,"expression_no_base_symbol":"(∂⩏⊆$2556$)⨚⇆($5873$↯⫤)","expression":"(∂⩏⊆⪩⨒∯213330)⨚⇆(⪩⨒∯1123301↯⫤)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":54281,"operation_count":3,"complexity_ratio":18093.666666666668,"tree":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"unary","operator":"∂⩏⊆","unary_expr":{"type":"numeric_atoms","value":2556,"base":4}},"right_expr":{"type":"unary","operator":"↯⫤","unary_expr":{"type":"numeric_atoms","value":5873,"base":4}}},"used_operators":["lwHaAYXP2r","8WDwsbhb0R","VwlE7vj6HS"],"dependent_operators":["gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi","14qkJME0vr","eLAdDNolq6","W4YGzv6Whe","23Mk6UjR3U","tifHPKVTfV","glklzrTFfD","eH2TOUuTDT","t8gj7n24qd","2DDjHMKMc0","Ph9nP6C5qx","g55IO6H4Gj","nCS4ZIUYfx"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2556","layer":2},{"info":"compute unary expreesion, input=2556, op_id = 8WDwsbhb0R, unary_op_definition = '∂⩏⊆a = { (≤/a) , if a<=92 ; (a⊦⊿) , else }', output=-7747","layer":1},{"info":"number node, value=5873","layer":2},{"info":"compute unary expreesion, input=5873, op_id = VwlE7vj6HS, unary_op_definition = 'a↯⫤ = { (((-a)⋝⋈⪟(a⨳⩥⨓a))⨸⪁((a⨁⊸⫻)⇼⇔∾(a+a))) , if (a⋷221)!=277 ; (((300⪐)⨁⊸⫻)⇼⇔∾(a≧⫂∧(26≧⫂∧87))) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-7747, right_input=0, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(∂⩏⊆⪩⨒∯213330)⨚⇆(⪩⨒∯1123301↯⫤)=NaN","reverse_text":"NaN=(∂⩏⊆⪩⨒∯213330)⨚⇆(⪩⨒∯1123301↯⫤)","cot":[{"info":"∂⩏⊆⪩⨒∯213330=⪩⨒∯-1321003","layer":1},{"info":"⪩⨒∯1123301↯⫤=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-1321003⨚⇆⪩⨒∯0=NaN","layer":0}]}
{"id":863,"expression_no_base_symbol":"$1550$⫘$1101$↬(∂⩏⊆$3148$)","expression":"⪩⨒∯120032⫘⪩⨒∯101031↬(∂⩏⊆⪩⨒∯301030)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1774,"operation_count":3,"complexity_ratio":591.3333333333334,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"binary","operator":"⫘","left_expr":{"type":"numeric_atoms","value":1550,"base":4},"right_expr":{"type":"numeric_atoms","value":1101,"base":4}},"right_expr":{"type":"unary","operator":"∂⩏⊆","unary_expr":{"type":"numeric_atoms","value":3148,"base":4}}},"used_operators":["B5M0gjZbta","48vC8HMD2b","8WDwsbhb0R"],"dependent_operators":["rGHVDoGpnC","OwUj7dcsQK","7j4O788W3g","tfWHHpNKUN","3ViojmjbAp","dfKe02y8D2","tcjXMdvYtA","D4vGDi5EA2","86A5ENbKR9","X99M06cbEe","14qkJME0vr","eLAdDNolq6"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1550","layer":2},{"info":"number node, value=1101","layer":2},{"info":"compute binary expreesion, left_input=1550, right_input=1101, op_id = 48vC8HMD2b binary_op_definition= 'a⫘b = { ((≘(b⨓a))≫≃) , if ((⇖a)!=319 or (a↺926)<190) ; ((∓a)⫚↹⊑(⪸(a≦≮≮))) , else }', output=1827205","layer":1},{"info":"number node, value=3148","layer":2},{"info":"compute unary expreesion, input=3148, op_id = 8WDwsbhb0R, unary_op_definition = '∂⩏⊆a = { (≤/a) , if a<=92 ; (a⊦⊿) , else }', output=-9523","layer":1},{"info":"compute binary expreesion, left_input=1827205, right_input=-9523, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯120032⫘⪩⨒∯101031↬(∂⩏⊆⪩⨒∯301030)=NaN","reverse_text":"NaN=⪩⨒∯120032⫘⪩⨒∯101031↬(∂⩏⊆⪩⨒∯301030)","cot":[{"info":"⪩⨒∯120032⫘⪩⨒∯101031=⪩⨒∯12332012011","layer":1},{"info":"∂⩏⊆⪩⨒∯301030=⪩⨒∯-2110303","layer":1},{"info":"⪩⨒∯12332012011↬⪩⨒∯-2110303=NaN","layer":0}]}
{"id":864,"expression_no_base_symbol":"($6618$⨁⊸⫻)⪘⨀","expression":"(⪩⨒∯1213122⨁⊸⫻)⪘⨀","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":25,"operation_count":2,"complexity_ratio":12.5,"tree":{"type":"unary","operator":"⪘⨀","unary_expr":{"type":"unary","operator":"⨁⊸⫻","unary_expr":{"type":"numeric_atoms","value":6618,"base":4}}},"used_operators":["aA7tF3KVD3","glklzrTFfD"],"dependent_operators":["bl5wxAcryP","L05ObWFQCd","XhwjNDsVaA","W4YGzv6Whe","rysDP5nf3Z"],"result":"⪩⨒∯-3113321","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6618","layer":2},{"info":"compute unary expreesion, input=6618, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=6618","layer":1},{"info":"compute unary expreesion, input=6618, op_id = aA7tF3KVD3, unary_op_definition = 'a⪘⨀ = { ((104/a)⪍↜⋙(a↰)) }', output=-13817","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1213122⨁⊸⫻)⪘⨀=⪩⨒∯-3113321","reverse_text":"⪩⨒∯-3113321=(⪩⨒∯1213122⨁⊸⫻)⪘⨀","cot":[{"info":"⪩⨒∯1213122⨁⊸⫻=⪩⨒∯1213122","layer":1},{"info":"⪩⨒∯1213122⪘⨀=⪩⨒∯-3113321","layer":0}]}
{"id":865,"expression_no_base_symbol":"($2419$∕⩚$1974$)⨼⩣$2557$↤⩊$1921$","expression":"(⪩⨒∯211303∕⩚⪩⨒∯132312)⨼⩣⪩⨒∯213331↤⩊⪩⨒∯132001","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2956,"operation_count":3,"complexity_ratio":985.3333333333334,"tree":{"type":"binary","operator":"⨼⩣","left_expr":{"type":"binary","operator":"∕⩚","left_expr":{"type":"numeric_atoms","value":2419,"base":4},"right_expr":{"type":"numeric_atoms","value":1974,"base":4}},"right_expr":{"type":"binary","operator":"↤⩊","left_expr":{"type":"numeric_atoms","value":2557,"base":4},"right_expr":{"type":"numeric_atoms","value":1921,"base":4}}},"used_operators":["JxwMv5le6e","z9ffQ9n5Zr","13rbtpv6ld"],"dependent_operators":["uFcxV4UQCh","cHh1gJQ2o6","SL6IHkK8vl","KYD54nUTWz","pRsWfj4Fpp","CArV6hThFE","3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr","s1XTVnmDOJ","wEfv7U73WA","9cloC0Ngie","KPf6cnQVty","KYD54nUTWz","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2419","layer":2},{"info":"number node, value=1974","layer":2},{"info":"compute binary expreesion, left_input=2419, right_input=1974, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-2422","layer":1},{"info":"number node, value=2557","layer":2},{"info":"number node, value=1921","layer":2},{"info":"compute binary expreesion, left_input=2557, right_input=1921, op_id = 13rbtpv6ld binary_op_definition= 'a↤⩊b = { ((a⫥∨⫟63)⇐≅) , if (a∺≝⩲71)<727 ; ((b%b)⊕∕(b≓∲14)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-2422, right_input=nan, op_id = JxwMv5le6e binary_op_definition= 'a⨼⩣b = { ((∐⩳⋚(b⩘a))⪛((∡129)⫥∨⫟(a⫲⨊))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯211303∕⩚⪩⨒∯132312)⨼⩣⪩⨒∯213331↤⩊⪩⨒∯132001=NaN","reverse_text":"NaN=(⪩⨒∯211303∕⩚⪩⨒∯132312)⨼⩣⪩⨒∯213331↤⩊⪩⨒∯132001","cot":[{"info":"⪩⨒∯211303∕⩚⪩⨒∯132312=⪩⨒∯-211312","layer":1},{"info":"⪩⨒∯213331↤⩊⪩⨒∯132001=NaN","layer":1},{"info":"⪩⨒∯-211312⨼⩣NaN=NaN","layer":0}]}
{"id":866,"expression_no_base_symbol":"($2878$⪎↠$1541$)⇻⋧≁($3385$⫲≸⪮$7124$)","expression":"(⪩⨒∯230332⪎↠⪩⨒∯120011)⇻⋧≁(⪩⨒∯310321⫲≸⪮⪩⨒∯1233110)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3568,"operation_count":3,"complexity_ratio":1189.3333333333333,"tree":{"type":"binary","operator":"⇻⋧≁","left_expr":{"type":"binary","operator":"⪎↠","left_expr":{"type":"numeric_atoms","value":2878,"base":4},"right_expr":{"type":"numeric_atoms","value":1541,"base":4}},"right_expr":{"type":"binary","operator":"⫲≸⪮","left_expr":{"type":"numeric_atoms","value":3385,"base":4},"right_expr":{"type":"numeric_atoms","value":7124,"base":4}}},"used_operators":["jCPkEVoL5K","3tVxb0NHM4","P3lXMJvFrc"],"dependent_operators":["eLxqMNBOBk","XnXgA4xnOs","3EYGwJThht","XTarYq4gQB","59igzFyhWz","dfKe02y8D2","X99M06cbEe","P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM","tmPS8pqC7x","oWn0xqSxBt","DbCuESL50I"],"result":"⪩⨒∯-103021","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2878","layer":2},{"info":"number node, value=1541","layer":2},{"info":"compute binary expreesion, left_input=2878, right_input=1541, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=160","layer":1},{"info":"number node, value=3385","layer":2},{"info":"number node, value=7124","layer":2},{"info":"compute binary expreesion, left_input=3385, right_input=7124, op_id = P3lXMJvFrc binary_op_definition= 'a⫲≸⪮b = { (⋼∭⪍a) , if (⊙↵-b)>333 ; (a⨪↰⇹b) , else }', output=3385","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=3385, op_id = jCPkEVoL5K binary_op_definition= 'a⇻⋧≁b = { ((⫓⪴a)⫚↹⊑(54≫≃)) , if (a∵≐)<=35 or a>411 ; ((⪝⪂⫅b)⇄(290⨑≵⋬a)) , else }', output=-1225","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯230332⪎↠⪩⨒∯120011)⇻⋧≁(⪩⨒∯310321⫲≸⪮⪩⨒∯1233110)=⪩⨒∯-103021","reverse_text":"⪩⨒∯-103021=(⪩⨒∯230332⪎↠⪩⨒∯120011)⇻⋧≁(⪩⨒∯310321⫲≸⪮⪩⨒∯1233110)","cot":[{"info":"⪩⨒∯230332⪎↠⪩⨒∯120011=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯310321⫲≸⪮⪩⨒∯1233110=⪩⨒∯310321","layer":1},{"info":"⪩⨒∯2200⇻⋧≁⪩⨒∯310321=⪩⨒∯-103021","layer":0}]}
{"id":867,"expression_no_base_symbol":"⊲⪭($3483$⩺⪪$4605$)","expression":"⊲⪭(⪩⨒∯312123⩺⪪⪩⨒∯1013331)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":129,"operation_count":2,"complexity_ratio":64.5,"tree":{"type":"unary","operator":"⊲⪭","unary_expr":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"numeric_atoms","value":3483,"base":4},"right_expr":{"type":"numeric_atoms","value":4605,"base":4}}},"used_operators":["k7HXdKtiEU","uvdQJvN4PV"],"dependent_operators":["i8ToyICDmI","xUOZtlo3hN","Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U"],"result":"⪩⨒∯121230","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3483","layer":2},{"info":"number node, value=4605","layer":2},{"info":"compute binary expreesion, left_input=3483, right_input=4605, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=-1818","layer":1},{"info":"compute unary expreesion, input=-1818, op_id = k7HXdKtiEU, unary_op_definition = '⊲⪭a = { (⨞⊢(a∲⫓0)) }', output=1644","layer":0}],"base":4,"result_base":4,"text":"⊲⪭(⪩⨒∯312123⩺⪪⪩⨒∯1013331)=⪩⨒∯121230","reverse_text":"⪩⨒∯121230=⊲⪭(⪩⨒∯312123⩺⪪⪩⨒∯1013331)","cot":[{"info":"⪩⨒∯312123⩺⪪⪩⨒∯1013331=⪩⨒∯-130122","layer":1},{"info":"⊲⪭⪩⨒∯-130122=⪩⨒∯121230","layer":0}]}
{"id":868,"expression_no_base_symbol":"$1114$⇂≾⫗$4017$⨔⇊($2650$↬$1485$)","expression":"⪩⨒∯101122⇂≾⫗⪩⨒∯332301⨔⇊(⪩⨒∯221122↬⪩⨒∯113031)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":60,"operation_count":3,"complexity_ratio":20.0,"tree":{"type":"binary","operator":"⨔⇊","left_expr":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"numeric_atoms","value":1114,"base":4},"right_expr":{"type":"numeric_atoms","value":4017,"base":4}},"right_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":2650,"base":4},"right_expr":{"type":"numeric_atoms","value":1485,"base":4}}},"used_operators":["JclMnS0uGI","aBQ6xLxuTc","B5M0gjZbta"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","N41Kp7NANJ","DZ8iAZOCBD","f6k1SAg4EE","14qkJME0vr","i8ToyICDmI","g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1114","layer":2},{"info":"number node, value=4017","layer":2},{"info":"compute binary expreesion, left_input=1114, right_input=4017, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-676","layer":1},{"info":"number node, value=2650","layer":2},{"info":"number node, value=1485","layer":2},{"info":"compute binary expreesion, left_input=2650, right_input=1485, op_id = B5M0gjZbta binary_op_definition= 'a↬b = {b, if a == 0; ((a-1)↬b)⨟⋌⩍((a-1)↬b), if a > 0 and abs(a) < 100; -((a+1)↬b)⨟⋌⩍((a+1)↬b), if a < 0 and abs(a) < 100; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-676, right_input=nan, op_id = JclMnS0uGI binary_op_definition= 'a⨔⇊b = { (((a⊦⊿)⩷∴(b⊉≛↸b))⋥≓≎(b⪒(51∲⫓b))) , if (b≋⫹)>106 ; b , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯101122⇂≾⫗⪩⨒∯332301⨔⇊(⪩⨒∯221122↬⪩⨒∯113031)=NaN","reverse_text":"NaN=⪩⨒∯101122⇂≾⫗⪩⨒∯332301⨔⇊(⪩⨒∯221122↬⪩⨒∯113031)","cot":[{"info":"⪩⨒∯101122⇂≾⫗⪩⨒∯332301=⪩⨒∯-22210","layer":1},{"info":"⪩⨒∯221122↬⪩⨒∯113031=NaN","layer":1},{"info":"⪩⨒∯-22210⨔⇊NaN=NaN","layer":0}]}
{"id":869,"expression_no_base_symbol":"⨣⨃⇪(⇈$2352$)","expression":"⨣⨃⇪(⇈⪩⨒∯210300)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1031,"operation_count":2,"complexity_ratio":515.5,"tree":{"type":"unary","operator":"⨣⨃⇪","unary_expr":{"type":"unary","operator":"⇈","unary_expr":{"type":"numeric_atoms","value":2352,"base":4}}},"used_operators":["AcOhelriW5","SLLxy00UIr"],"dependent_operators":["s3Fd5m9Dh2","liw5iZPkLH","yyfyN0ffXY","Qy55tPpLXF","DZ8iAZOCBD","tifHPKVTfV","Tw270M8GLb","8HhzD0ZcuI","jCPkEVoL5K","ZcwmYACASQ"],"result":"⪩⨒∯111331","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2352","layer":2},{"info":"compute unary expreesion, input=2352, op_id = SLLxy00UIr, unary_op_definition = '⇈a = { (((⨰⫟⨤60)⋥≓≎(a⫍⨯↯))⇻⋧≁((a⇼⇔∾a)⨽(323⊉≛↸a))) }', output=-447","layer":1},{"info":"compute unary expreesion, input=-447, op_id = AcOhelriW5, unary_op_definition = '⨣⨃⇪a = { (⨡↴(172⊬⨰(3↙a))) }', output=1405","layer":0}],"base":4,"result_base":4,"text":"⨣⨃⇪(⇈⪩⨒∯210300)=⪩⨒∯111331","reverse_text":"⪩⨒∯111331=⨣⨃⇪(⇈⪩⨒∯210300)","cot":[{"info":"⇈⪩⨒∯210300=⪩⨒∯-12333","layer":1},{"info":"⨣⨃⇪⪩⨒∯-12333=⪩⨒∯111331","layer":0}]}
{"id":870,"expression_no_base_symbol":"∨∊⋏($2277$∊∟⩊$1903$)","expression":"∨∊⋏(⪩⨒∯203211∊∟⩊⪩⨒∯131233)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":69,"operation_count":2,"complexity_ratio":34.5,"tree":{"type":"unary","operator":"∨∊⋏","unary_expr":{"type":"binary","operator":"∊∟⩊","left_expr":{"type":"numeric_atoms","value":2277,"base":4},"right_expr":{"type":"numeric_atoms","value":1903,"base":4}}},"used_operators":["R5aXW34M0v","ddLRYrp01A"],"dependent_operators":["L05ObWFQCd","YjI8oCXuph","9ICcGScMcE","g7Hmc5v1ko","ocnLzx9CaJ","2DDjHMKMc0","hrf7POJlIJ","59igzFyhWz","A8NUZmVepG","3sJ7IOPOlU"],"result":"⪩⨒∯13323113","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2277","layer":2},{"info":"number node, value=1903","layer":2},{"info":"compute binary expreesion, left_input=2277, right_input=1903, op_id = ddLRYrp01A binary_op_definition= 'a∊∟⩊b = { b , if (b∵≐)>=166 or (a⪇≇⋚4)==505 ; (↥a) , else }', output=1903","layer":1},{"info":"compute unary expreesion, input=1903, op_id = R5aXW34M0v, unary_op_definition = '∨∊⋏a = { (((101⋝⋈⪟206)⪍↜⋙(≦∁a))⩼⇪↪((a⩌⋺a)∴(⫇a))) }', output=32471","layer":0}],"base":4,"result_base":4,"text":"∨∊⋏(⪩⨒∯203211∊∟⩊⪩⨒∯131233)=⪩⨒∯13323113","reverse_text":"⪩⨒∯13323113=∨∊⋏(⪩⨒∯203211∊∟⩊⪩⨒∯131233)","cot":[{"info":"⪩⨒∯203211∊∟⩊⪩⨒∯131233=⪩⨒∯131233","layer":1},{"info":"∨∊⋏⪩⨒∯131233=⪩⨒∯13323113","layer":0}]}
{"id":871,"expression_no_base_symbol":"(⋂$6723$)⇣⩺⋵($5230$⩺⪪$3194$)","expression":"(⋂⪩⨒∯1221003)⇣⩺⋵(⪩⨒∯1101232⩺⪪⪩⨒∯301322)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":180,"operation_count":3,"complexity_ratio":60.0,"tree":{"type":"binary","operator":"⇣⩺⋵","left_expr":{"type":"unary","operator":"⋂","unary_expr":{"type":"numeric_atoms","value":6723,"base":4}},"right_expr":{"type":"binary","operator":"⩺⪪","left_expr":{"type":"numeric_atoms","value":5230,"base":4},"right_expr":{"type":"numeric_atoms","value":3194,"base":4}}},"used_operators":["F4yD0voBRQ","BUOGQAYlQx","uvdQJvN4PV"],"dependent_operators":["NTOWxs364D","KPf6cnQVty","8jW3W4yZS5","12rbrZMWeM","g55IO6H4Gj","2DlMacCsIx","NTOWxs364D","XPYlsWDdGa","QMFrweE19q","COABgblf1C","Tcnh7f0tEr","rysDP5nf3Z","RZ5CV9rWsJ","FyVja0WsTP","WYd1w68Nbz","HrjLwUk87U"],"result":"⪩⨒∯-1022332112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6723","layer":2},{"info":"compute unary expreesion, input=6723, op_id = BUOGQAYlQx, unary_op_definition = '⋂a = { a , if (⪲⇎a)==26 ; ((a⩚⊴⇥a)⫡⨏(a⊭↱102)) , else }', output=-93526","layer":1},{"info":"number node, value=5230","layer":2},{"info":"number node, value=3194","layer":2},{"info":"compute binary expreesion, left_input=5230, right_input=3194, op_id = uvdQJvN4PV binary_op_definition= 'a⩺⪪b = { (((b-a)⊱⇼⊻(a⪚23))⩖⊿((612⋩≍≻)≣⋋)) }', output=-33474","layer":1},{"info":"compute binary expreesion, left_input=-93526, right_input=-33474, op_id = F4yD0voBRQ binary_op_definition= 'a⇣⩺⋵b = { (((a⩨565)∺≝⩲(5⨸⪁a))⩚⊴⇥(↯⪼(a⋳⪒b))) }', output=-307094","layer":0}],"base":4,"result_base":4,"text":"(⋂⪩⨒∯1221003)⇣⩺⋵(⪩⨒∯1101232⩺⪪⪩⨒∯301322)=⪩⨒∯-1022332112","reverse_text":"⪩⨒∯-1022332112=(⋂⪩⨒∯1221003)⇣⩺⋵(⪩⨒∯1101232⩺⪪⪩⨒∯301322)","cot":[{"info":"⋂⪩⨒∯1221003=⪩⨒∯-112311112","layer":1},{"info":"⪩⨒∯1101232⩺⪪⪩⨒∯301322=⪩⨒∯-20023002","layer":1},{"info":"⪩⨒∯-112311112⇣⩺⋵⪩⨒∯-20023002=⪩⨒∯-1022332112","layer":0}]}
{"id":872,"expression_no_base_symbol":"($2821$⊦⊿)⇴∐(⇖$9028$)","expression":"(⪩⨒∯230011⊦⊿)⇴∐(⇖⪩⨒∯2031010)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":25628,"operation_count":3,"complexity_ratio":8542.666666666666,"tree":{"type":"binary","operator":"⇴∐","left_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":2821,"base":4}},"right_expr":{"type":"unary","operator":"⇖","unary_expr":{"type":"numeric_atoms","value":9028,"base":4}}},"used_operators":["HnzytWxmAO","14qkJME0vr","tfWHHpNKUN"],"dependent_operators":["2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","2DQ55sFlQl"],"result":"⪩⨒∯-1310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2821","layer":2},{"info":"compute unary expreesion, input=2821, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-8542","layer":1},{"info":"number node, value=9028","layer":2},{"info":"compute unary expreesion, input=9028, op_id = tfWHHpNKUN, unary_op_definition = '⇖a = { (221⨵⪆a) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=-8542, right_input=160, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=-116","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯230011⊦⊿)⇴∐(⇖⪩⨒∯2031010)=⪩⨒∯-1310","reverse_text":"⪩⨒∯-1310=(⪩⨒∯230011⊦⊿)⇴∐(⇖⪩⨒∯2031010)","cot":[{"info":"⪩⨒∯230011⊦⊿=⪩⨒∯-2011132","layer":1},{"info":"⇖⪩⨒∯2031010=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯-2011132⇴∐⪩⨒∯2200=⪩⨒∯-1310","layer":0}]}
{"id":873,"expression_no_base_symbol":"⇜⊴$3248$∀⇚≩$1491$","expression":"⇜⊴⪩⨒∯302300∀⇚≩⪩⨒∯113103","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":22816,"operation_count":2,"complexity_ratio":11408.0,"tree":{"type":"unary","operator":"⇜⊴","unary_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":3248,"base":4},"right_expr":{"type":"numeric_atoms","value":1491,"base":4}}},"used_operators":["XwDhCwWbUn","LRNGc0VcxI"],"dependent_operators":["WR6HLWljOP","JclMnS0uGI","D309nIvmXG","w2P8NbNXyL","YbVcJGFEVW","DmTXOeWf9t","4CyGpkTkEk","cTDWOvIxvz","jLgFTUHLKL","COABgblf1C","hrf7POJlIJ","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3248","layer":2},{"info":"number node, value=1491","layer":2},{"info":"compute binary expreesion, left_input=3248, right_input=1491, op_id = LRNGc0VcxI binary_op_definition= 'a∀⇚≩b = {b, if a == 0; ((a-1)∀⇚≩b)≫≃, if a > 0 and abs(a) < 1000000; -((a+1)∀⇚≩b)≫≃, if a < 0 and abs(a) < 1000000; NaN, else}', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = XwDhCwWbUn, unary_op_definition = '⇜⊴a = { (↩(∓⪦(a≃a))) , if ((a∐⫣)>271 and (a∴779)<=132) ; ((a↢(a⨔⇊a))⊲⩕⊾((a∝a)⊉↱≁(a⊭↱19))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇜⊴⪩⨒∯302300∀⇚≩⪩⨒∯113103=NaN","reverse_text":"NaN=⇜⊴⪩⨒∯302300∀⇚≩⪩⨒∯113103","cot":[{"info":"⪩⨒∯302300∀⇚≩⪩⨒∯113103=NaN","layer":1},{"info":"⇜⊴NaN=NaN","layer":0}]}
{"id":874,"expression_no_base_symbol":"⪨⨬($1417$⊭↱$4725$)","expression":"⪨⨬(⪩⨒∯112021⊭↱⪩⨒∯1021311)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":28,"operation_count":2,"complexity_ratio":14.0,"tree":{"type":"unary","operator":"⪨⨬","unary_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":1417,"base":4},"right_expr":{"type":"numeric_atoms","value":4725,"base":4}}},"used_operators":["5obUd6DV38","COABgblf1C"],"dependent_operators":["T2fj7uvVaJ","nlCqmYiOvY","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯-20032","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1417","layer":2},{"info":"number node, value=4725","layer":2},{"info":"compute binary expreesion, left_input=1417, right_input=4725, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=6621","layer":1},{"info":"compute unary expreesion, input=6621, op_id = 5obUd6DV38, unary_op_definition = '⪨⨬a = { ((a⋓a)⨽⪊≇) }', output=-526","layer":0}],"base":4,"result_base":4,"text":"⪨⨬(⪩⨒∯112021⊭↱⪩⨒∯1021311)=⪩⨒∯-20032","reverse_text":"⪩⨒∯-20032=⪨⨬(⪩⨒∯112021⊭↱⪩⨒∯1021311)","cot":[{"info":"⪩⨒∯112021⊭↱⪩⨒∯1021311=⪩⨒∯1213131","layer":1},{"info":"⪨⨬⪩⨒∯1213131=⪩⨒∯-20032","layer":0}]}
{"id":875,"expression_no_base_symbol":"($2244$⪮%⊝$6840$)∘($4380$⫌⩉⩟$1060$)","expression":"(⪩⨒∯203010⪮%⊝⪩⨒∯1222320)∘(⪩⨒∯1010130⫌⩉⩟⪩⨒∯100210)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6667,"operation_count":3,"complexity_ratio":2222.3333333333335,"tree":{"type":"binary","operator":"∘","left_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":2244,"base":4},"right_expr":{"type":"numeric_atoms","value":6840,"base":4}},"right_expr":{"type":"binary","operator":"⫌⩉⩟","left_expr":{"type":"numeric_atoms","value":4380,"base":4},"right_expr":{"type":"numeric_atoms","value":1060,"base":4}}},"used_operators":["Z5m6OM72h2","IWmyXbctLI","XIIwhv8d0m"],"dependent_operators":["eH2TOUuTDT","rysDP5nf3Z","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","B5M0gjZbta","UMwdvZNt44","MRPaB8lBjK","vkpjKywKVM"],"result":"⪩⨒∯-1011020","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2244","layer":2},{"info":"number node, value=6840","layer":2},{"info":"compute binary expreesion, left_input=2244, right_input=6840, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=4804","layer":1},{"info":"number node, value=4380","layer":2},{"info":"number node, value=1060","layer":2},{"info":"compute binary expreesion, left_input=4380, right_input=1060, op_id = XIIwhv8d0m binary_op_definition= 'a⫌⩉⩟b = { (((a↬179)⇮⋭(b⇡⇂b))⇉⇱⇎) }', output=-50","layer":1},{"info":"compute binary expreesion, left_input=4804, right_input=-50, op_id = Z5m6OM72h2 binary_op_definition= 'a∘b = { (380-a) , if b<=483 ; (a⪐) , else }', output=-4424","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯203010⪮%⊝⪩⨒∯1222320)∘(⪩⨒∯1010130⫌⩉⩟⪩⨒∯100210)=⪩⨒∯-1011020","reverse_text":"⪩⨒∯-1011020=(⪩⨒∯203010⪮%⊝⪩⨒∯1222320)∘(⪩⨒∯1010130⫌⩉⩟⪩⨒∯100210)","cot":[{"info":"⪩⨒∯203010⪮%⊝⪩⨒∯1222320=⪩⨒∯1023010","layer":1},{"info":"⪩⨒∯1010130⫌⩉⩟⪩⨒∯100210=⪩⨒∯-302","layer":1},{"info":"⪩⨒∯1023010∘⪩⨒∯-302=⪩⨒∯-1011020","layer":0}]}
{"id":876,"expression_no_base_symbol":"$1320$⇼⇔∾$1476$∲⫓$2224$≝⊿$3880$","expression":"⪩⨒∯110220⇼⇔∾⪩⨒∯113010∲⫓⪩⨒∯202300≝⊿⪩⨒∯330220","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":17,"operation_count":3,"complexity_ratio":5.666666666666667,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":1320,"base":4},"right_expr":{"type":"numeric_atoms","value":1476,"base":4}},"right_expr":{"type":"binary","operator":"≝⊿","left_expr":{"type":"numeric_atoms","value":2224,"base":4},"right_expr":{"type":"numeric_atoms","value":3880,"base":4}}},"used_operators":["i8ToyICDmI","tifHPKVTfV","OKKcZfAt5B"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","12rbrZMWeM"],"result":"⪩⨒∯2130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1320","layer":2},{"info":"number node, value=1476","layer":2},{"info":"compute binary expreesion, left_input=1320, right_input=1476, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=156","layer":1},{"info":"number node, value=2224","layer":2},{"info":"number node, value=3880","layer":2},{"info":"compute binary expreesion, left_input=2224, right_input=3880, op_id = OKKcZfAt5B binary_op_definition= 'a≝⊿b = { ((82⋳⪒b)⋳⪒a) }', output=-10517","layer":1},{"info":"compute binary expreesion, left_input=156, right_input=-10517, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=156","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯110220⇼⇔∾⪩⨒∯113010∲⫓⪩⨒∯202300≝⊿⪩⨒∯330220=⪩⨒∯2130","reverse_text":"⪩⨒∯2130=⪩⨒∯110220⇼⇔∾⪩⨒∯113010∲⫓⪩⨒∯202300≝⊿⪩⨒∯330220","cot":[{"info":"⪩⨒∯110220⇼⇔∾⪩⨒∯113010=⪩⨒∯2130","layer":1},{"info":"⪩⨒∯202300≝⊿⪩⨒∯330220=⪩⨒∯-2210111","layer":1},{"info":"⪩⨒∯2130∲⫓⪩⨒∯-2210111=⪩⨒∯2130","layer":0}]}
{"id":877,"expression_no_base_symbol":"($4707$⫁⪎$6308$)⨼⩣($1118$⫡⨏$2509$)","expression":"(⪩⨒∯1021203⫁⪎⪩⨒∯1202210)⨼⩣(⪩⨒∯101132⫡⨏⪩⨒∯213031)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":383,"operation_count":3,"complexity_ratio":127.66666666666667,"tree":{"type":"binary","operator":"⨼⩣","left_expr":{"type":"binary","operator":"⫁⪎","left_expr":{"type":"numeric_atoms","value":4707,"base":4},"right_expr":{"type":"numeric_atoms","value":6308,"base":4}},"right_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":1118,"base":4},"right_expr":{"type":"numeric_atoms","value":2509,"base":4}}},"used_operators":["JxwMv5le6e","xRrnTEsQ6j","QMFrweE19q"],"dependent_operators":["uFcxV4UQCh","cHh1gJQ2o6","SL6IHkK8vl","KYD54nUTWz","pRsWfj4Fpp","CArV6hThFE","P8v4zCKN1o","Qy55tPpLXF","tifHPKVTfV","sdazOOVcIp","2DDjHMKMc0","i8ToyICDmI","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4707","layer":2},{"info":"number node, value=6308","layer":2},{"info":"compute binary expreesion, left_input=4707, right_input=6308, op_id = xRrnTEsQ6j binary_op_definition= 'a⫁⪎b = { ((b⋝⋈⪟a)⇼⇔∾a) , if (∥⊫b)!=57 ; ((191∲⫓a)⋥≓≎(a⪨≂368)) , else }', output=-1601","layer":1},{"info":"number node, value=1118","layer":2},{"info":"number node, value=2509","layer":2},{"info":"compute binary expreesion, left_input=1118, right_input=2509, op_id = QMFrweE19q binary_op_definition= 'a⫡⨏b = { 497 , if (-b)==408 and (-a)>=56 ; (((a+783)+(a+a))+((b+a)+(a+b))) , else }', output=11391","layer":1},{"info":"compute binary expreesion, left_input=-1601, right_input=11391, op_id = JxwMv5le6e binary_op_definition= 'a⨼⩣b = { ((∐⩳⋚(b⩘a))⪛((∡129)⫥∨⫟(a⫲⨊))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1021203⫁⪎⪩⨒∯1202210)⨼⩣(⪩⨒∯101132⫡⨏⪩⨒∯213031)=NaN","reverse_text":"NaN=(⪩⨒∯1021203⫁⪎⪩⨒∯1202210)⨼⩣(⪩⨒∯101132⫡⨏⪩⨒∯213031)","cot":[{"info":"⪩⨒∯1021203⫁⪎⪩⨒∯1202210=⪩⨒∯-121001","layer":1},{"info":"⪩⨒∯101132⫡⨏⪩⨒∯213031=⪩⨒∯2301333","layer":1},{"info":"⪩⨒∯-121001⨼⩣⪩⨒∯2301333=NaN","layer":0}]}
{"id":878,"expression_no_base_symbol":"($2890$⫦⪉$1813$)≚⊃≕($1498$⋣⋖$2806$)","expression":"(⪩⨒∯231022⫦⪉⪩⨒∯130111)≚⊃≕(⪩⨒∯113122⋣⋖⪩⨒∯223312)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":48,"operation_count":3,"complexity_ratio":16.0,"tree":{"type":"binary","operator":"≚⊃≕","left_expr":{"type":"binary","operator":"⫦⪉","left_expr":{"type":"numeric_atoms","value":2890,"base":4},"right_expr":{"type":"numeric_atoms","value":1813,"base":4}},"right_expr":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"numeric_atoms","value":1498,"base":4},"right_expr":{"type":"numeric_atoms","value":2806,"base":4}}},"used_operators":["Bmrmz2XGnR","wscyQdcy20","J0M6qkBnIM"],"dependent_operators":["9FxExcQeMw","Qy55tPpLXF","7j4O788W3g","sdazOOVcIp","8w2t5hMYqp","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","W4YGzv6Whe","B3sABdIn96","9HNa5Wba9A","g7Hmc5v1ko","nREPSIbpBE","D3AQDKkPcf","VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2"],"result":"⪩⨒∯-22302","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2890","layer":2},{"info":"number node, value=1813","layer":2},{"info":"compute binary expreesion, left_input=2890, right_input=1813, op_id = wscyQdcy20 binary_op_definition= 'a⫦⪉b = { ((a⩌⋺206)⪹) , if (a∷677)>=23 ; ((b+a)*(b⨚b)) , else }', output=-880","layer":1},{"info":"number node, value=1498","layer":2},{"info":"number node, value=2806","layer":2},{"info":"compute binary expreesion, left_input=1498, right_input=2806, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=1498","layer":1},{"info":"compute binary expreesion, left_input=-880, right_input=1498, op_id = Bmrmz2XGnR binary_op_definition= 'a≚⊃≕b = { (-((⊄⩳↩b)⪨≂(a⩷∴b))) , if ((b⫡⨏524)<690 or (⨞⊢a)>=395) ; ((⊄⩳↩(b⋥≓≎a))⋥≓≎((a↺a)⪨≂(479⨸⪁a))) , else }', output=-690","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯231022⫦⪉⪩⨒∯130111)≚⊃≕(⪩⨒∯113122⋣⋖⪩⨒∯223312)=⪩⨒∯-22302","reverse_text":"⪩⨒∯-22302=(⪩⨒∯231022⫦⪉⪩⨒∯130111)≚⊃≕(⪩⨒∯113122⋣⋖⪩⨒∯223312)","cot":[{"info":"⪩⨒∯231022⫦⪉⪩⨒∯130111=⪩⨒∯-31300","layer":1},{"info":"⪩⨒∯113122⋣⋖⪩⨒∯223312=⪩⨒∯113122","layer":1},{"info":"⪩⨒∯-31300≚⊃≕⪩⨒∯113122=⪩⨒∯-22302","layer":0}]}
{"id":879,"expression_no_base_symbol":"(↯⪼$2129$)⨰($1862$≃$2817$)","expression":"(↯⪼⪩⨒∯201101)⨰(⪩⨒∯131012≃⪩⨒∯230001)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":56,"operation_count":3,"complexity_ratio":18.666666666666668,"tree":{"type":"binary","operator":"⨰","left_expr":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"numeric_atoms","value":2129,"base":4}},"right_expr":{"type":"binary","operator":"≃","left_expr":{"type":"numeric_atoms","value":1862,"base":4},"right_expr":{"type":"numeric_atoms","value":2817,"base":4}}},"used_operators":["eewbuw0ToL","8jW3W4yZS5","YbVcJGFEVW"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","9FxExcQeMw","Qy55tPpLXF","23Mk6UjR3U","JLbD19bQDL","7j4O788W3g","glklzrTFfD","tifHPKVTfV","t8gj7n24qd","i8ToyICDmI","COABgblf1C"],"result":"⪩⨒∯1310311","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2129","layer":2},{"info":"compute unary expreesion, input=2129, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":1},{"info":"number node, value=1862","layer":2},{"info":"number node, value=2817","layer":2},{"info":"compute binary expreesion, left_input=1862, right_input=2817, op_id = YbVcJGFEVW binary_op_definition= 'a≃b = { (((13⋥≓≎b)⋷(a⇼⇔∾b))⨁⊸⫻) , if ((b⨁⊸⫻)>=162 or (b⪠⩆⊳)<=569) ; ((-(17⋷a))↺((a⩷∴a)⊭↱(b∲⫓a))) , else }', output=-7488","layer":1},{"info":"compute binary expreesion, left_input=-21, right_input=-7488, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=7477","layer":0}],"base":4,"result_base":4,"text":"(↯⪼⪩⨒∯201101)⨰(⪩⨒∯131012≃⪩⨒∯230001)=⪩⨒∯1310311","reverse_text":"⪩⨒∯1310311=(↯⪼⪩⨒∯201101)⨰(⪩⨒∯131012≃⪩⨒∯230001)","cot":[{"info":"↯⪼⪩⨒∯201101=⪩⨒∯-111","layer":1},{"info":"⪩⨒∯131012≃⪩⨒∯230001=⪩⨒∯-1311000","layer":1},{"info":"⪩⨒∯-111⨰⪩⨒∯-1311000=⪩⨒∯1310311","layer":0}]}
{"id":880,"expression_no_base_symbol":"($1271$-$2473$)⫒⫫$6899$⊮⊟↴$3373$","expression":"(⪩⨒∯103313-⪩⨒∯212221)⫒⫫⪩⨒∯1223303⊮⊟↴⪩⨒∯310231","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":64,"operation_count":3,"complexity_ratio":21.333333333333332,"tree":{"type":"binary","operator":"⫒⫫","left_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1271,"base":4},"right_expr":{"type":"numeric_atoms","value":2473,"base":4}},"right_expr":{"type":"binary","operator":"⊮⊟↴","left_expr":{"type":"numeric_atoms","value":6899,"base":4},"right_expr":{"type":"numeric_atoms","value":3373,"base":4}}},"used_operators":["6Ko8hGgeMq","rysDP5nf3Z","QDVgd2eftb"],"dependent_operators":["jdwGQqwJi5","AHs5Up7iyr","AFVx7xoS7T","XhwjNDsVaA","C6VvDP6HwP","WkeUrDK8WX","kuIXHzHcAH","3Oe9XWJUTD","rJVOvQCfKK"],"result":"⪩⨒∯1132132","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1271","layer":2},{"info":"number node, value=2473","layer":2},{"info":"compute binary expreesion, left_input=1271, right_input=2473, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-1202","layer":1},{"info":"number node, value=6899","layer":2},{"info":"number node, value=3373","layer":2},{"info":"compute binary expreesion, left_input=6899, right_input=3373, op_id = QDVgd2eftb binary_op_definition= 'a⊮⊟↴b = { ((⩰267)⪨⊡(b⊝⪿⪼a)) , if a!=19 ; ((b⨎372)/(b⪑⩈)) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-1202, right_input=0, op_id = 6Ko8hGgeMq binary_op_definition= 'a⫒⫫b = { (b≹⇙⪍a) , if (a∁)>135 ; (b⇌⫙⪟a) , else }', output=6046","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯103313-⪩⨒∯212221)⫒⫫⪩⨒∯1223303⊮⊟↴⪩⨒∯310231=⪩⨒∯1132132","reverse_text":"⪩⨒∯1132132=(⪩⨒∯103313-⪩⨒∯212221)⫒⫫⪩⨒∯1223303⊮⊟↴⪩⨒∯310231","cot":[{"info":"⪩⨒∯103313-⪩⨒∯212221=⪩⨒∯-102302","layer":1},{"info":"⪩⨒∯1223303⊮⊟↴⪩⨒∯310231=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-102302⫒⫫⪩⨒∯0=⪩⨒∯1132132","layer":0}]}
{"id":881,"expression_no_base_symbol":"($4574$⇐≅)⇡⇂($1127$⫦⪉$3733$)","expression":"(⪩⨒∯1013132⇐≅)⇡⇂(⪩⨒∯101213⫦⪉⪩⨒∯322111)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":18576,"operation_count":3,"complexity_ratio":6192.0,"tree":{"type":"binary","operator":"⇡⇂","left_expr":{"type":"unary","operator":"⇐≅","unary_expr":{"type":"numeric_atoms","value":4574,"base":4}},"right_expr":{"type":"binary","operator":"⫦⪉","left_expr":{"type":"numeric_atoms","value":1127,"base":4},"right_expr":{"type":"numeric_atoms","value":3733,"base":4}}},"used_operators":["UMwdvZNt44","wEfv7U73WA","wscyQdcy20"],"dependent_operators":["9FxExcQeMw","23Mk6UjR3U","z4E1FaHLuy","3tj9sqzovi","fu6greOZ01","AHs5Up7iyr","lvlrscuwVU","KPf6cnQVty","uBihLCJcMX","12rbrZMWeM","WPoGxAaPR1","9FxExcQeMw","t8gj7n24qd","Ph9nP6C5qx","i8ToyICDmI","W4YGzv6Whe","B3sABdIn96","9HNa5Wba9A","g7Hmc5v1ko","nREPSIbpBE","D3AQDKkPcf"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4574","layer":2},{"info":"compute unary expreesion, input=4574, op_id = wEfv7U73WA, unary_op_definition = 'a⇐≅ = { ((a⩷∴(a∲⫓a))≧⫂∧(-a)) }', output=13690","layer":1},{"info":"number node, value=1127","layer":2},{"info":"number node, value=3733","layer":2},{"info":"compute binary expreesion, left_input=1127, right_input=3733, op_id = wscyQdcy20 binary_op_definition= 'a⫦⪉b = { ((a⩌⋺206)⪹) , if (a∷677)>=23 ; ((b+a)*(b⨚b)) , else }', output=2646","layer":1},{"info":"compute binary expreesion, left_input=13690, right_input=2646, op_id = UMwdvZNt44 binary_op_definition= 'a⇡⇂b = { (((b≹⇙⪍b)⋳⪒(b⋷a))∺≝⩲(⫟(a⩷∴43))) , if (⊬↢a)==727 or (a⇔⨋)<18 ; ((604≴⪞⇿(≻⋜b))⨐⩸⫘a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1013132⇐≅)⇡⇂(⪩⨒∯101213⫦⪉⪩⨒∯322111)=NaN","reverse_text":"NaN=(⪩⨒∯1013132⇐≅)⇡⇂(⪩⨒∯101213⫦⪉⪩⨒∯322111)","cot":[{"info":"⪩⨒∯1013132⇐≅=⪩⨒∯3111322","layer":1},{"info":"⪩⨒∯101213⫦⪉⪩⨒∯322111=⪩⨒∯221112","layer":1},{"info":"⪩⨒∯3111322⇡⇂⪩⨒∯221112=NaN","layer":0}]}
{"id":882,"expression_no_base_symbol":"⊵⊁($1910$⩁⩘$1117$)","expression":"⊵⊁(⪩⨒∯131312⩁⩘⪩⨒∯101131)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":48,"operation_count":2,"complexity_ratio":24.0,"tree":{"type":"unary","operator":"⊵⊁","unary_expr":{"type":"binary","operator":"⩁⩘","left_expr":{"type":"numeric_atoms","value":1910,"base":4},"right_expr":{"type":"numeric_atoms","value":1117,"base":4}}},"used_operators":["AvED76WdY7","gub5Cegaqo"],"dependent_operators":["uBihLCJcMX","k8jYdgA6NY","DpFCA1CohY","IWmyXbctLI"],"result":"⪩⨒∯13223002","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1910","layer":2},{"info":"number node, value=1117","layer":2},{"info":"compute binary expreesion, left_input=1910, right_input=1117, op_id = gub5Cegaqo binary_op_definition= 'a⩁⩘b = { ((b⪮%⊝b)⪮%⊝(⋗⩬⋾a)) }', output=5416","layer":1},{"info":"compute unary expreesion, input=5416, op_id = AvED76WdY7, unary_op_definition = '⊵⊁a = { (a⇔⨋) , if a>58 ; (a%a) , else }', output=31426","layer":0}],"base":4,"result_base":4,"text":"⊵⊁(⪩⨒∯131312⩁⩘⪩⨒∯101131)=⪩⨒∯13223002","reverse_text":"⪩⨒∯13223002=⊵⊁(⪩⨒∯131312⩁⩘⪩⨒∯101131)","cot":[{"info":"⪩⨒∯131312⩁⩘⪩⨒∯101131=⪩⨒∯1110220","layer":1},{"info":"⊵⊁⪩⨒∯1110220=⪩⨒∯13223002","layer":0}]}
{"id":883,"expression_no_base_symbol":"($5031$⪮%⊝$1921$)∇⊂⋱$1696$⩼⇪↪$2829$","expression":"(⪩⨒∯1032213⪮%⊝⪩⨒∯132001)∇⊂⋱⪩⨒∯122200⩼⇪↪⪩⨒∯230031","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":34,"operation_count":3,"complexity_ratio":11.333333333333334,"tree":{"type":"binary","operator":"∇⊂⋱","left_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":5031,"base":4},"right_expr":{"type":"numeric_atoms","value":1921,"base":4}},"right_expr":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"numeric_atoms","value":1696,"base":4},"right_expr":{"type":"numeric_atoms","value":2829,"base":4}}},"used_operators":["nhYeJWJD5X","IWmyXbctLI","ocnLzx9CaJ"],"dependent_operators":["P8v4zCKN1o","23Mk6UjR3U","f6k1SAg4EE","AF7qkfDlqP","nCS4ZIUYfx","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q"],"result":"⪩⨒∯10323302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5031","layer":2},{"info":"number node, value=1921","layer":2},{"info":"compute binary expreesion, left_input=5031, right_input=1921, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=10378","layer":1},{"info":"number node, value=1696","layer":2},{"info":"number node, value=2829","layer":2},{"info":"compute binary expreesion, left_input=1696, right_input=2829, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=-17194","layer":1},{"info":"compute binary expreesion, left_input=10378, right_input=-17194, op_id = nhYeJWJD5X binary_op_definition= 'a∇⊂⋱b = { (b⪒b) , if a<143 ; ((⨑⩽⪐a)⋷(∥⊫(a⨳⩥⨓a))) , else }', output=20210","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1032213⪮%⊝⪩⨒∯132001)∇⊂⋱⪩⨒∯122200⩼⇪↪⪩⨒∯230031=⪩⨒∯10323302","reverse_text":"⪩⨒∯10323302=(⪩⨒∯1032213⪮%⊝⪩⨒∯132001)∇⊂⋱⪩⨒∯122200⩼⇪↪⪩⨒∯230031","cot":[{"info":"⪩⨒∯1032213⪮%⊝⪩⨒∯132001=⪩⨒∯2202022","layer":1},{"info":"⪩⨒∯122200⩼⇪↪⪩⨒∯230031=⪩⨒∯-10030222","layer":1},{"info":"⪩⨒∯2202022∇⊂⋱⪩⨒∯-10030222=⪩⨒∯10323302","layer":0}]}
{"id":884,"expression_no_base_symbol":"≸≮($8240$⩚⊴⇥$2823$)","expression":"≸≮(⪩⨒∯2000300⩚⊴⇥⪩⨒∯230013)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":25,"operation_count":2,"complexity_ratio":12.5,"tree":{"type":"unary","operator":"≸≮","unary_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":8240,"base":4},"right_expr":{"type":"numeric_atoms","value":2823,"base":4}}},"used_operators":["AljMvE3RRm","NTOWxs364D"],"dependent_operators":["3UMq87Qwqg","QiR2Oyf5Xj","Z57zeUYC9z","6o9Blt3TJ6","kbkesczE7y","oPMjh9089D","Nsiff2A1zJ","7qqUquhhSb","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⪩⨒∯221021133","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8240","layer":2},{"info":"number node, value=2823","layer":2},{"info":"compute binary expreesion, left_input=8240, right_input=2823, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-11184","layer":1},{"info":"compute unary expreesion, input=-11184, op_id = AljMvE3RRm, unary_op_definition = '≸≮a = { (a⊴((a⨔≚≋a)⫰⋱(∤↝a))) , if (a>367 and (a≬⋮702)!=1) ; (⊀((∷≠a)⩉⊫⨁)) , else }', output=168543","layer":0}],"base":4,"result_base":4,"text":"≸≮(⪩⨒∯2000300⩚⊴⇥⪩⨒∯230013)=⪩⨒∯221021133","reverse_text":"⪩⨒∯221021133=≸≮(⪩⨒∯2000300⩚⊴⇥⪩⨒∯230013)","cot":[{"info":"⪩⨒∯2000300⩚⊴⇥⪩⨒∯230013=⪩⨒∯-2232300","layer":1},{"info":"≸≮⪩⨒∯-2232300=⪩⨒∯221021133","layer":0}]}
{"id":885,"expression_no_base_symbol":"∂($4005$↡⊰⫅$1770$)","expression":"∂(⪩⨒∯332211↡⊰⫅⪩⨒∯123222)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":24796,"operation_count":2,"complexity_ratio":12398.0,"tree":{"type":"unary","operator":"∂","unary_expr":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"numeric_atoms","value":4005,"base":4},"right_expr":{"type":"numeric_atoms","value":1770,"base":4}}},"used_operators":["Uaa54Peajs","VCtxkLNOzz"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4005","layer":2},{"info":"number node, value=1770","layer":2},{"info":"compute binary expreesion, left_input=4005, right_input=1770, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=3540","layer":1},{"info":"compute unary expreesion, input=3540, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"∂(⪩⨒∯332211↡⊰⫅⪩⨒∯123222)=NaN","reverse_text":"NaN=∂(⪩⨒∯332211↡⊰⫅⪩⨒∯123222)","cot":[{"info":"⪩⨒∯332211↡⊰⫅⪩⨒∯123222=⪩⨒∯313110","layer":1},{"info":"∂⪩⨒∯313110=NaN","layer":0}]}
{"id":886,"expression_no_base_symbol":"($4886$⨪↰⇹$3765$)⨂≜($5390$∕⩚$1341$)","expression":"(⪩⨒∯1030112⨪↰⇹⪩⨒∯322311)⨂≜(⪩⨒∯1110032∕⩚⪩⨒∯110331)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15210,"operation_count":3,"complexity_ratio":5070.0,"tree":{"type":"binary","operator":"⨂≜","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":4886,"base":4},"right_expr":{"type":"numeric_atoms","value":3765,"base":4}},"right_expr":{"type":"binary","operator":"∕⩚","left_expr":{"type":"numeric_atoms","value":5390,"base":4},"right_expr":{"type":"numeric_atoms","value":1341,"base":4}}},"used_operators":["k1SHOSEABc","tmPS8pqC7x","z9ffQ9n5Zr"],"dependent_operators":["9FxExcQeMw","HiPekx5b7W","eLxqMNBOBk","JclMnS0uGI","COABgblf1C","U7g4x0WXJJ","rJVOvQCfKK","3ViojmjbAp","nlCqmYiOvY","1h0rLqGiFr"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4886","layer":2},{"info":"number node, value=3765","layer":2},{"info":"compute binary expreesion, left_input=4886, right_input=3765, op_id = tmPS8pqC7x binary_op_definition= 'a⨪↰⇹b = {a, if a == 0; (b)⨎((a-1)⨪↰⇹b), if a > 0 and abs(a) < 1000000; -(b)⨎((a+1)⨪↰⇹b), if a < 0 and abs(a) < 1000000; NaN, else}', output=4886","layer":1},{"info":"number node, value=5390","layer":2},{"info":"number node, value=1341","layer":2},{"info":"compute binary expreesion, left_input=5390, right_input=1341, op_id = z9ffQ9n5Zr binary_op_definition= 'a∕⩚b = { (b⨓a) , if (b⨽⪊≇)>=161 ; (⩷34) , else }', output=-5393","layer":1},{"info":"compute binary expreesion, left_input=4886, right_input=-5393, op_id = k1SHOSEABc binary_op_definition= 'a⨂≜b = { ((37⊭↱(⫓⪴a))⩷∴((111⨜⨶78)⨔⇊(a∑⇟⊟b))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1030112⨪↰⇹⪩⨒∯322311)⨂≜(⪩⨒∯1110032∕⩚⪩⨒∯110331)=NaN","reverse_text":"NaN=(⪩⨒∯1030112⨪↰⇹⪩⨒∯322311)⨂≜(⪩⨒∯1110032∕⩚⪩⨒∯110331)","cot":[{"info":"⪩⨒∯1030112⨪↰⇹⪩⨒∯322311=⪩⨒∯1030112","layer":1},{"info":"⪩⨒∯1110032∕⩚⪩⨒∯110331=⪩⨒∯-1110101","layer":1},{"info":"⪩⨒∯1030112⨂≜⪩⨒∯-1110101=NaN","layer":0}]}
{"id":887,"expression_no_base_symbol":"$1930$⊢$1951$⋣⋖(↔$1209$)","expression":"⪩⨒∯132022⊢⪩⨒∯132133⋣⋖(↔⪩⨒∯102321)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3447,"operation_count":3,"complexity_ratio":1149.0,"tree":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"binary","operator":"⊢","left_expr":{"type":"numeric_atoms","value":1930,"base":4},"right_expr":{"type":"numeric_atoms","value":1951,"base":4}},"right_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":1209,"base":4}}},"used_operators":["J0M6qkBnIM","5twsqlHp2o","ruOEQAzv1W"],"dependent_operators":["VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2","P8v4zCKN1o","Qy55tPpLXF","BjRHVeLaeN","DZ8iAZOCBD","7j4O788W3g","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","14qkJME0vr","D4vGDi5EA2","2td37pGCOC","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp"],"result":"⪩⨒∯-20033","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1930","layer":2},{"info":"number node, value=1951","layer":2},{"info":"compute binary expreesion, left_input=1930, right_input=1951, op_id = 5twsqlHp2o binary_op_definition= 'a⊢b = { (((225⫩⊇)⊉≛↸(∥⊫a))⨵⪆(25⊉≛↸(b⋥≓≎47))) , if (a≦≮≮)==364 ; (((b⊦⊿)⪨≂(⩦⩻⨪b))↺((⨞⊢a)⪨≂(-1))) , else }', output=-4104","layer":1},{"info":"number node, value=1209","layer":2},{"info":"compute unary expreesion, input=1209, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-936","layer":1},{"info":"compute binary expreesion, left_input=-4104, right_input=-936, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=-527","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯132022⊢⪩⨒∯132133⋣⋖(↔⪩⨒∯102321)=⪩⨒∯-20033","reverse_text":"⪩⨒∯-20033=⪩⨒∯132022⊢⪩⨒∯132133⋣⋖(↔⪩⨒∯102321)","cot":[{"info":"⪩⨒∯132022⊢⪩⨒∯132133=⪩⨒∯-1000020","layer":1},{"info":"↔⪩⨒∯102321=⪩⨒∯-32220","layer":1},{"info":"⪩⨒∯-1000020⋣⋖⪩⨒∯-32220=⪩⨒∯-20033","layer":0}]}
{"id":888,"expression_no_base_symbol":"($5368$⋾⨃∁$6959$)↞⋁$2740$⪃⊛⇣$2412$","expression":"(⪩⨒∯1103320⋾⨃∁⪩⨒∯1230233)↞⋁⪩⨒∯222310⪃⊛⇣⪩⨒∯211230","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7734,"operation_count":3,"complexity_ratio":2578.0,"tree":{"type":"binary","operator":"↞⋁","left_expr":{"type":"binary","operator":"⋾⨃∁","left_expr":{"type":"numeric_atoms","value":5368,"base":4},"right_expr":{"type":"numeric_atoms","value":6959,"base":4}},"right_expr":{"type":"binary","operator":"⪃⊛⇣","left_expr":{"type":"numeric_atoms","value":2740,"base":4},"right_expr":{"type":"numeric_atoms","value":2412,"base":4}}},"used_operators":["RqrPlJkxDo","212REbPD9h","rrgAzCduG9"],"dependent_operators":["Uaa54Peajs","CArV6hThFE","13rbtpv6ld","eLxqMNBOBk","Qy55tPpLXF","w2P8NbNXyL","2DQ55sFlQl","f6k1SAg4EE","Ez1Nq5fNfI","AHs5Up7iyr","2DDjHMKMc0","7IPrd9c3lf","8cLx32lpNA"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5368","layer":2},{"info":"number node, value=6959","layer":2},{"info":"compute binary expreesion, left_input=5368, right_input=6959, op_id = 212REbPD9h binary_op_definition= 'a⋾⨃∁b = { ((430⊉↱≁b)⨵⪆b) , if (a⪒898)>=359 ; ((⫓⪴b)⊉↱≁(26⋥≓≎b)) , else }', output=484193208","layer":1},{"info":"number node, value=2740","layer":2},{"info":"number node, value=2412","layer":2},{"info":"compute binary expreesion, left_input=2740, right_input=2412, op_id = rrgAzCduG9 binary_op_definition= 'a⪃⊛⇣b = { ((b∌b)⊵↤) , if b==348 ; ((a≹⇙⪍a)⪬(a⋝⋈⪟a)) , else }', output=1234","layer":1},{"info":"compute binary expreesion, left_input=484193208, right_input=1234, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1103320⋾⨃∁⪩⨒∯1230233)↞⋁⪩⨒∯222310⪃⊛⇣⪩⨒∯211230=NaN","reverse_text":"NaN=(⪩⨒∯1103320⋾⨃∁⪩⨒∯1230233)↞⋁⪩⨒∯222310⪃⊛⇣⪩⨒∯211230","cot":[{"info":"⪩⨒∯1103320⋾⨃∁⪩⨒∯1230233=⪩⨒∯130313003032320","layer":1},{"info":"⪩⨒∯222310⪃⊛⇣⪩⨒∯211230=⪩⨒∯103102","layer":1},{"info":"⪩⨒∯130313003032320↞⋁⪩⨒∯103102=NaN","layer":0}]}
{"id":889,"expression_no_base_symbol":"($5959$⪚$2647$)⊱⇼⊻($3403$⪨≂$1053$)","expression":"(⪩⨒∯1131013⪚⪩⨒∯221113)⊱⇼⊻(⪩⨒∯311023⪨≂⪩⨒∯100131)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":34,"operation_count":3,"complexity_ratio":11.333333333333334,"tree":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"binary","operator":"⪚","left_expr":{"type":"numeric_atoms","value":5959,"base":4},"right_expr":{"type":"numeric_atoms","value":2647,"base":4}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":3403,"base":4},"right_expr":{"type":"numeric_atoms","value":1053,"base":4}}},"used_operators":["FyVja0WsTP","HrjLwUk87U","sdazOOVcIp"],"dependent_operators":["W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","9FxExcQeMw","rysDP5nf3Z","NTOWxs364D","DZ8iAZOCBD","tifHPKVTfV","eH2TOUuTDT","2DDjHMKMc0","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯12302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5959","layer":2},{"info":"number node, value=2647","layer":2},{"info":"compute binary expreesion, left_input=5959, right_input=2647, op_id = HrjLwUk87U binary_op_definition= 'a⪚b = { (((317⩚⊴⇥a)⋝⋈⪟(518-95))⊉≛↸((97⪐)⩷∴(b⇼⇔∾a))) }', output=6268","layer":1},{"info":"number node, value=3403","layer":2},{"info":"number node, value=1053","layer":2},{"info":"compute binary expreesion, left_input=3403, right_input=1053, op_id = sdazOOVcIp binary_op_definition= 'a⪨≂b = { (((a-117)-b)-((145-b)-(a-a))) , if (-b)==187 ; ((-(b-102))-((b-a)-a)) , else }', output=4802","layer":1},{"info":"compute binary expreesion, left_input=6268, right_input=4802, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1131013⪚⪩⨒∯221113)⊱⇼⊻(⪩⨒∯311023⪨≂⪩⨒∯100131)=⪩⨒∯12302","reverse_text":"⪩⨒∯12302=(⪩⨒∯1131013⪚⪩⨒∯221113)⊱⇼⊻(⪩⨒∯311023⪨≂⪩⨒∯100131)","cot":[{"info":"⪩⨒∯1131013⪚⪩⨒∯221113=⪩⨒∯1201330","layer":1},{"info":"⪩⨒∯311023⪨≂⪩⨒∯100131=⪩⨒∯1023002","layer":1},{"info":"⪩⨒∯1201330⊱⇼⊻⪩⨒∯1023002=⪩⨒∯12302","layer":0}]}
{"id":890,"expression_no_base_symbol":"($3706$⊱⇼⊻$4243$)↳≱(⊗$2096$)","expression":"(⪩⨒∯321322⊱⇼⊻⪩⨒∯1002103)↳≱(⊗⪩⨒∯200300)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":96,"operation_count":3,"complexity_ratio":32.0,"tree":{"type":"binary","operator":"↳≱","left_expr":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"numeric_atoms","value":3706,"base":4},"right_expr":{"type":"numeric_atoms","value":4243,"base":4}},"right_expr":{"type":"unary","operator":"⊗","unary_expr":{"type":"numeric_atoms","value":2096,"base":4}}},"used_operators":["JwTKLfZU96","FyVja0WsTP","RhiyfpczSx"],"dependent_operators":["DhbWaqg5eL","WR6HLWljOP","XhwjNDsVaA","T2fj7uvVaJ","7YooWSwCyH","B3sABdIn96","W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","nhYeJWJD5X","sJAwomhLZr","Z5m6OM72h2","HrjLwUk87U"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3706","layer":2},{"info":"number node, value=4243","layer":2},{"info":"compute binary expreesion, left_input=3706, right_input=4243, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":1},{"info":"number node, value=2096","layer":2},{"info":"compute unary expreesion, input=2096, op_id = RhiyfpczSx, unary_op_definition = '⊗a = { (64∇⊂⋱a) , if (a⪚13)>=164 ; (a∘(a⩠)) , else }', output=-4192","layer":1},{"info":"compute binary expreesion, left_input=434, right_input=-4192, op_id = JwTKLfZU96 binary_op_definition= 'a↳≱b = { (((a∪⫐104)↢(147/b))⋓((+⊝⨔b)⪹)) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯321322⊱⇼⊻⪩⨒∯1002103)↳≱(⊗⪩⨒∯200300)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯321322⊱⇼⊻⪩⨒∯1002103)↳≱(⊗⪩⨒∯200300)","cot":[{"info":"⪩⨒∯321322⊱⇼⊻⪩⨒∯1002103=⪩⨒∯12302","layer":1},{"info":"⊗⪩⨒∯200300=⪩⨒∯-1001200","layer":1},{"info":"⪩⨒∯12302↳≱⪩⨒∯-1001200=⪩⨒∯0","layer":0}]}
{"id":891,"expression_no_base_symbol":"($1001$⊝⪿⪼$3765$)⨐($6541$⫃⨇$2893$)","expression":"(⪩⨒∯33221⊝⪿⪼⪩⨒∯322311)⨐(⪩⨒∯1212031⫃⨇⪩⨒∯231031)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":38,"operation_count":3,"complexity_ratio":12.666666666666666,"tree":{"type":"binary","operator":"⨐","left_expr":{"type":"binary","operator":"⊝⪿⪼","left_expr":{"type":"numeric_atoms","value":1001,"base":4},"right_expr":{"type":"numeric_atoms","value":3765,"base":4}},"right_expr":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"numeric_atoms","value":6541,"base":4},"right_expr":{"type":"numeric_atoms","value":2893,"base":4}}},"used_operators":["Noe24qw2ks","3Oe9XWJUTD","09Ly4LVMIf"],"dependent_operators":["u6S6b8DprG","2DQ55sFlQl","QMFrweE19q","NTOWxs364D","Qy55tPpLXF","8w2t5hMYqp","t8gj7n24qd","eewbuw0ToL","QMFrweE19q","9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG"],"result":"⪩⨒∯-30023212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1001","layer":2},{"info":"number node, value=3765","layer":2},{"info":"compute binary expreesion, left_input=1001, right_input=3765, op_id = 3Oe9XWJUTD binary_op_definition= 'a⊝⪿⪼b = { ((⊄⩳↩(480⩚⊴⇥a))⫡⨏((a⨰b)⋥≓≎(-b))) }', output=24947","layer":1},{"info":"number node, value=6541","layer":2},{"info":"number node, value=2893","layer":2},{"info":"compute binary expreesion, left_input=6541, right_input=2893, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=-11604","layer":1},{"info":"compute binary expreesion, left_input=24947, right_input=-11604, op_id = Noe24qw2ks binary_op_definition= 'a⨐b = { (↽≂a) , if (a⨵⪆301)>43 ; (b⫡⨏a) , else }', output=-49894","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯33221⊝⪿⪼⪩⨒∯322311)⨐(⪩⨒∯1212031⫃⨇⪩⨒∯231031)=⪩⨒∯-30023212","reverse_text":"⪩⨒∯-30023212=(⪩⨒∯33221⊝⪿⪼⪩⨒∯322311)⨐(⪩⨒∯1212031⫃⨇⪩⨒∯231031)","cot":[{"info":"⪩⨒∯33221⊝⪿⪼⪩⨒∯322311=⪩⨒∯12011303","layer":1},{"info":"⪩⨒∯1212031⫃⨇⪩⨒∯231031=⪩⨒∯-2311110","layer":1},{"info":"⪩⨒∯12011303⨐⪩⨒∯-2311110=⪩⨒∯-30023212","layer":0}]}
{"id":892,"expression_no_base_symbol":"($8216$⫒⫫$1039$)⩌⋺($4164$∽$1277$)","expression":"(⪩⨒∯2000120⫒⫫⪩⨒∯100033)⩌⋺(⪩⨒∯1001010∽⪩⨒∯103331)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":21,"operation_count":3,"complexity_ratio":7.0,"tree":{"type":"binary","operator":"⩌⋺","left_expr":{"type":"binary","operator":"⫒⫫","left_expr":{"type":"numeric_atoms","value":8216,"base":4},"right_expr":{"type":"numeric_atoms","value":1039,"base":4}},"right_expr":{"type":"binary","operator":"∽","left_expr":{"type":"numeric_atoms","value":4164,"base":4},"right_expr":{"type":"numeric_atoms","value":1277,"base":4}}},"used_operators":["g7Hmc5v1ko","6Ko8hGgeMq","y4ImoPnbV5"],"dependent_operators":["9FxExcQeMw","W4YGzv6Whe","NTOWxs364D","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","i8ToyICDmI","QMFrweE19q","jdwGQqwJi5","AHs5Up7iyr","AFVx7xoS7T","NTOWxs364D","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8216","layer":2},{"info":"number node, value=1039","layer":2},{"info":"compute binary expreesion, left_input=8216, right_input=1039, op_id = 6Ko8hGgeMq binary_op_definition= 'a⫒⫫b = { (b≹⇙⪍a) , if (a∁)>135 ; (b⇌⫙⪟a) , else }', output=nan","layer":1},{"info":"number node, value=4164","layer":2},{"info":"number node, value=1277","layer":2},{"info":"compute binary expreesion, left_input=4164, right_input=1277, op_id = y4ImoPnbV5 binary_op_definition= 'a∽b = { ((a⩚⊴⇥b)⫡⨏b) }', output=-24473","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-24473, op_id = g7Hmc5v1ko binary_op_definition= 'a⩌⋺b = { ((⨞⊢(b⨵⪆b))∲⫓((a⪨≂b)⪨≂(b⩷∴919))) , if (b⫡⨏102)>364 and (-b)==524 ; (b⇼⇔∾((a+a)⩚⊴⇥(-a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯2000120⫒⫫⪩⨒∯100033)⩌⋺(⪩⨒∯1001010∽⪩⨒∯103331)=NaN","reverse_text":"NaN=(⪩⨒∯2000120⫒⫫⪩⨒∯100033)⩌⋺(⪩⨒∯1001010∽⪩⨒∯103331)","cot":[{"info":"⪩⨒∯2000120⫒⫫⪩⨒∯100033=NaN","layer":1},{"info":"⪩⨒∯1001010∽⪩⨒∯103331=⪩⨒∯-11332121","layer":1},{"info":"NaN⩌⋺⪩⨒∯-11332121=NaN","layer":0}]}
{"id":893,"expression_no_base_symbol":"↨⩢⫨($5613$⫃⨇$4459$)","expression":"↨⩢⫨(⪩⨒∯1113231⫃⨇⪩⨒∯1011223)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":61,"operation_count":2,"complexity_ratio":30.5,"tree":{"type":"unary","operator":"↨⩢⫨","unary_expr":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"numeric_atoms","value":5613,"base":4},"right_expr":{"type":"numeric_atoms","value":4459,"base":4}}},"used_operators":["Z5CJsN7DuW","09Ly4LVMIf"],"dependent_operators":["Noe24qw2ks","gu96TGCTMs","8jW3W4yZS5","AFVx7xoS7T","9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5613","layer":2},{"info":"number node, value=4459","layer":2},{"info":"compute binary expreesion, left_input=5613, right_input=4459, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=-17868","layer":1},{"info":"compute unary expreesion, input=-17868, op_id = Z5CJsN7DuW, unary_op_definition = '↨⩢⫨a = { (((211⨐a)⇌⫙⪟(↯⪼a))⊘) }', output=0","layer":0}],"base":4,"result_base":4,"text":"↨⩢⫨(⪩⨒∯1113231⫃⨇⪩⨒∯1011223)=⪩⨒∯0","reverse_text":"⪩⨒∯0=↨⩢⫨(⪩⨒∯1113231⫃⨇⪩⨒∯1011223)","cot":[{"info":"⪩⨒∯1113231⫃⨇⪩⨒∯1011223=⪩⨒∯-10113030","layer":1},{"info":"↨⩢⫨⪩⨒∯-10113030=⪩⨒∯0","layer":0}]}
{"id":894,"expression_no_base_symbol":"∤$4891$⨸$2684$","expression":"∤⪩⨒∯1030123⨸⪩⨒∯221330","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5010,"operation_count":2,"complexity_ratio":2505.0,"tree":{"type":"unary","operator":"∤","unary_expr":{"type":"binary","operator":"⨸","left_expr":{"type":"numeric_atoms","value":4891,"base":4},"right_expr":{"type":"numeric_atoms","value":2684,"base":4}}},"used_operators":["k2HlF1dBQh","KmoU8R5UQR"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","tifHPKVTfV","8w2t5hMYqp","ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl"],"result":"⪩⨒∯21","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4891","layer":2},{"info":"number node, value=2684","layer":2},{"info":"compute binary expreesion, left_input=4891, right_input=2684, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=9782","layer":1},{"info":"compute unary expreesion, input=9782, op_id = k2HlF1dBQh, unary_op_definition = '∤a = { (((a⇼⇔∾a)+(a-a))-(⊄⩳↩3)) }', output=9","layer":0}],"base":4,"result_base":4,"text":"∤⪩⨒∯1030123⨸⪩⨒∯221330=⪩⨒∯21","reverse_text":"⪩⨒∯21=∤⪩⨒∯1030123⨸⪩⨒∯221330","cot":[{"info":"⪩⨒∯1030123⨸⪩⨒∯221330=⪩⨒∯2120312","layer":1},{"info":"∤⪩⨒∯2120312=⪩⨒∯21","layer":0}]}
{"id":895,"expression_no_base_symbol":"($5035$⇷$1207$)⊔(⊙↵-$2905$)","expression":"(⪩⨒∯1032223⇷⪩⨒∯102313)⊔(⊙↵-⪩⨒∯231121)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":73464,"operation_count":3,"complexity_ratio":24488.0,"tree":{"type":"binary","operator":"⊔","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":5035,"base":4},"right_expr":{"type":"numeric_atoms","value":1207,"base":4}},"right_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":2905,"base":4}}},"used_operators":["E4l6HwMY31","mp7IySMOzn","oWn0xqSxBt"],"dependent_operators":["W4YGzv6Whe","DpFCA1CohY","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","QMFrweE19q","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"⪩⨒∯211313","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5035","layer":2},{"info":"number node, value=1207","layer":2},{"info":"compute binary expreesion, left_input=5035, right_input=1207, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=2414","layer":1},{"info":"number node, value=2905","layer":2},{"info":"compute unary expreesion, input=2905, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute binary expreesion, left_input=2414, right_input=-1, op_id = E4l6HwMY31 binary_op_definition= 'a⊔b = { (((a≧⫂∧b)∲⫓(⋗⩬⋾b))⫡⨏((b⪒a)≧⫂∧(a+64))) }', output=2423","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1032223⇷⪩⨒∯102313)⊔(⊙↵-⪩⨒∯231121)=⪩⨒∯211313","reverse_text":"⪩⨒∯211313=(⪩⨒∯1032223⇷⪩⨒∯102313)⊔(⊙↵-⪩⨒∯231121)","cot":[{"info":"⪩⨒∯1032223⇷⪩⨒∯102313=⪩⨒∯211232","layer":1},{"info":"⊙↵-⪩⨒∯231121=⪩⨒∯-1","layer":1},{"info":"⪩⨒∯211232⊔⪩⨒∯-1=⪩⨒∯211313","layer":0}]}
{"id":896,"expression_no_base_symbol":"$3743$⪮%⊝$7814$⫃⨇(⪡⇡≛$2261$)","expression":"⪩⨒∯322133⪮%⊝⪩⨒∯1322012⫃⨇(⪡⇡≛⪩⨒∯203111)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":53,"operation_count":3,"complexity_ratio":17.666666666666668,"tree":{"type":"binary","operator":"⫃⨇","left_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":3743,"base":4},"right_expr":{"type":"numeric_atoms","value":7814,"base":4}},"right_expr":{"type":"unary","operator":"⪡⇡≛","unary_expr":{"type":"numeric_atoms","value":2261,"base":4}}},"used_operators":["09Ly4LVMIf","IWmyXbctLI","qL4PrbW1Dq"],"dependent_operators":["9FxExcQeMw","DIvbN7qnHd","u6S6b8DprG","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","oacrs7FA3X","apS25hmuAe","iuk5sVOGFA","8cLx32lpNA","X99M06cbEe"],"result":"⪩⨒∯2030310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3743","layer":2},{"info":"number node, value=7814","layer":2},{"info":"compute binary expreesion, left_input=3743, right_input=7814, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=7802","layer":1},{"info":"number node, value=2261","layer":2},{"info":"compute unary expreesion, input=2261, op_id = qL4PrbW1Dq, unary_op_definition = '⪡⇡≛a = { (a∌a) , if (a⪘⫢111)>=396 or (≅≯⇸a)!=229 or (a⪣⫩)<228 ; (a≫≃) , else }', output=-2261","layer":1},{"info":"compute binary expreesion, left_input=7802, right_input=-2261, op_id = 09Ly4LVMIf binary_op_definition= 'a⫃⨇b = { ((↽≂b)⩷∴(a⊠≄⫣)) }', output=9012","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯322133⪮%⊝⪩⨒∯1322012⫃⨇(⪡⇡≛⪩⨒∯203111)=⪩⨒∯2030310","reverse_text":"⪩⨒∯2030310=⪩⨒∯322133⪮%⊝⪩⨒∯1322012⫃⨇(⪡⇡≛⪩⨒∯203111)","cot":[{"info":"⪩⨒∯322133⪮%⊝⪩⨒∯1322012=⪩⨒∯1321322","layer":1},{"info":"⪡⇡≛⪩⨒∯203111=⪩⨒∯-203111","layer":1},{"info":"⪩⨒∯1321322⫃⨇⪩⨒∯-203111=⪩⨒∯2030310","layer":0}]}
{"id":897,"expression_no_base_symbol":"($2944$⫳≱↱$2048$)∴($5206$⪐)","expression":"(⪩⨒∯232000⫳≱↱⪩⨒∯200000)∴(⪩⨒∯1101112⪐)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":320,"operation_count":3,"complexity_ratio":106.66666666666667,"tree":{"type":"binary","operator":"∴","left_expr":{"type":"binary","operator":"⫳≱↱","left_expr":{"type":"numeric_atoms","value":2944,"base":4},"right_expr":{"type":"numeric_atoms","value":2048,"base":4}},"right_expr":{"type":"unary","operator":"⪐","unary_expr":{"type":"numeric_atoms","value":5206,"base":4}}},"used_operators":["hrf7POJlIJ","ZvLB05nZmT","eH2TOUuTDT"],"dependent_operators":["g55IO6H4Gj","P8v4zCKN1o","23Mk6UjR3U","2Wsdkap16l","FyVja0WsTP","wEfv7U73WA","bJkvcejdHO","HmxsFra2vL","8cLx32lpNA","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯103120","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2944","layer":2},{"info":"number node, value=2048","layer":2},{"info":"compute binary expreesion, left_input=2944, right_input=2048, op_id = ZvLB05nZmT binary_op_definition= 'a⫳≱↱b = { (((a⩹b)⇐≅)∌((a∙∹∝345)⊱⇼⊻(b≎⊠⪸a))) }', output=-204","layer":1},{"info":"number node, value=5206","layer":2},{"info":"compute unary expreesion, input=5206, op_id = eH2TOUuTDT, unary_op_definition = 'a⪐ = { (a+a) , if (-a)!=532 or a<368 ; (-a) , else }', output=10412","layer":1},{"info":"compute binary expreesion, left_input=-204, right_input=10412, op_id = hrf7POJlIJ binary_op_definition= 'a∴b = { ((∥⊫(22⋷b))⨸⪁a) }', output=1240","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯232000⫳≱↱⪩⨒∯200000)∴(⪩⨒∯1101112⪐)=⪩⨒∯103120","reverse_text":"⪩⨒∯103120=(⪩⨒∯232000⫳≱↱⪩⨒∯200000)∴(⪩⨒∯1101112⪐)","cot":[{"info":"⪩⨒∯232000⫳≱↱⪩⨒∯200000=⪩⨒∯-3030","layer":1},{"info":"⪩⨒∯1101112⪐=⪩⨒∯2202230","layer":1},{"info":"⪩⨒∯-3030∴⪩⨒∯2202230=⪩⨒∯103120","layer":0}]}
{"id":898,"expression_no_base_symbol":"(∮$2201$)≹⇙⪍($1060$⨴∎)","expression":"(∮⪩⨒∯202121)≹⇙⪍(⪩⨒∯100210⨴∎)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1409,"operation_count":3,"complexity_ratio":469.6666666666667,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"unary","operator":"∮","unary_expr":{"type":"numeric_atoms","value":2201,"base":4}},"right_expr":{"type":"unary","operator":"⨴∎","unary_expr":{"type":"numeric_atoms","value":1060,"base":4}}},"used_operators":["AHs5Up7iyr","CqXKPLVYql","CpSg5vQTgA"],"dependent_operators":["dWAJyo7jo9","2Wsdkap16l","eLxqMNBOBk","KbjG8mgYpV","MmTdOpaElr","JclMnS0uGI","bJkvcejdHO","eewbuw0ToL","Q3PJZHRvZv","s1XTVnmDOJ","VEQNXA0ZBg"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2201","layer":2},{"info":"compute unary expreesion, input=2201, op_id = CqXKPLVYql, unary_op_definition = '∮a = { ((a⩹a)⨰(⫓⪴488)) , if (a<=186 and a<741 and (a⨱∎)<232) ; ((a≎⊠⪸a)⨔⇊(973∠↢a)) , else }', output=67","layer":1},{"info":"number node, value=1060","layer":2},{"info":"compute unary expreesion, input=1060, op_id = CpSg5vQTgA, unary_op_definition = 'a⨴∎ = { (⊥a) , if (a≓∲156)<=233 or (a⪗)>744 ; a , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=67, right_input=nan, op_id = AHs5Up7iyr binary_op_definition= 'a≹⇙⪍b = {a, if b == 0; (a≹⇙⪍(b-1))⪢(b), if b > 0 and abs(b) < 1000; -(a≹⇙⪍(b+1))⪢(b), if b < 0 and abs(b) < 1000; NaN, else}', output=nan","layer":0}],"base":4,"result_base":4,"text":"(∮⪩⨒∯202121)≹⇙⪍(⪩⨒∯100210⨴∎)=NaN","reverse_text":"NaN=(∮⪩⨒∯202121)≹⇙⪍(⪩⨒∯100210⨴∎)","cot":[{"info":"∮⪩⨒∯202121=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯100210⨴∎=NaN","layer":1},{"info":"⪩⨒∯1003≹⇙⪍NaN=NaN","layer":0}]}
{"id":899,"expression_no_base_symbol":"$3708$↡⊰⫅$8558$∽(≅≯⇸$4775$)","expression":"⪩⨒∯321330↡⊰⫅⪩⨒∯2011232∽(≅≯⇸⪩⨒∯1022213)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":119851,"operation_count":3,"complexity_ratio":39950.333333333336,"tree":{"type":"binary","operator":"∽","left_expr":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"numeric_atoms","value":3708,"base":4},"right_expr":{"type":"numeric_atoms","value":8558,"base":4}},"right_expr":{"type":"unary","operator":"≅≯⇸","unary_expr":{"type":"numeric_atoms","value":4775,"base":4}}},"used_operators":["y4ImoPnbV5","VCtxkLNOzz","apS25hmuAe"],"dependent_operators":["NTOWxs364D","QMFrweE19q","Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn","EBcxylXtPf","QMFrweE19q"],"result":"⪩⨒∯-220131211","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3708","layer":2},{"info":"number node, value=8558","layer":2},{"info":"compute binary expreesion, left_input=3708, right_input=8558, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=17116","layer":1},{"info":"number node, value=4775","layer":2},{"info":"compute unary expreesion, input=4775, op_id = apS25hmuAe, unary_op_definition = '≅≯⇸a = { ((471⫡⨏a)⫌⩹⨱) }', output=26777","layer":1},{"info":"compute binary expreesion, left_input=17116, right_input=26777, op_id = y4ImoPnbV5 binary_op_definition= 'a∽b = { ((a⩚⊴⇥b)⫡⨏b) }', output=-165733","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯321330↡⊰⫅⪩⨒∯2011232∽(≅≯⇸⪩⨒∯1022213)=⪩⨒∯-220131211","reverse_text":"⪩⨒∯-220131211=⪩⨒∯321330↡⊰⫅⪩⨒∯2011232∽(≅≯⇸⪩⨒∯1022213)","cot":[{"info":"⪩⨒∯321330↡⊰⫅⪩⨒∯2011232=⪩⨒∯10023130","layer":1},{"info":"≅≯⇸⪩⨒∯1022213=⪩⨒∯12202121","layer":1},{"info":"⪩⨒∯10023130∽⪩⨒∯12202121=⪩⨒∯-220131211","layer":0}]}
{"id":900,"expression_no_base_symbol":"$2768$↼⊘⨖$4965$∸","expression":"⪩⨒∯223100↼⊘⨖⪩⨒∯1031211∸","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":183,"operation_count":2,"complexity_ratio":91.5,"tree":{"type":"unary","operator":"∸","unary_expr":{"type":"binary","operator":"↼⊘⨖","left_expr":{"type":"numeric_atoms","value":2768,"base":4},"right_expr":{"type":"numeric_atoms","value":4965,"base":4}}},"used_operators":["o20kRiQErp","bPywburJMS"],"dependent_operators":["tmPS8pqC7x","9FxExcQeMw","P8v4zCKN1o","t8gj7n24qd"],"result":"⪩⨒∯2301","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2768","layer":2},{"info":"number node, value=4965","layer":2},{"info":"compute binary expreesion, left_input=2768, right_input=4965, op_id = bPywburJMS binary_op_definition= 'a↼⊘⨖b = { (-a) , if (∥⊫b)==149 ; (b⩷∴95) , else }', output=9708","layer":1},{"info":"compute unary expreesion, input=9708, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯223100↼⊘⨖⪩⨒∯1031211∸=⪩⨒∯2301","reverse_text":"⪩⨒∯2301=⪩⨒∯223100↼⊘⨖⪩⨒∯1031211∸","cot":[{"info":"⪩⨒∯223100↼⊘⨖⪩⨒∯1031211=⪩⨒∯2113230","layer":1},{"info":"⪩⨒∯2113230∸=⪩⨒∯2301","layer":0}]}
{"id":901,"expression_no_base_symbol":"⨣⨃⇪($2083$⨒$1046$)","expression":"⨣⨃⇪(⪩⨒∯200203⨒⪩⨒∯100112)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34,"operation_count":2,"complexity_ratio":17.0,"tree":{"type":"unary","operator":"⨣⨃⇪","unary_expr":{"type":"binary","operator":"⨒","left_expr":{"type":"numeric_atoms","value":2083,"base":4},"right_expr":{"type":"numeric_atoms","value":1046,"base":4}}},"used_operators":["AcOhelriW5","y75s1iXyHd"],"dependent_operators":["s3Fd5m9Dh2","liw5iZPkLH","yyfyN0ffXY","srAu1WTS94","oacrs7FA3X","7qqUquhhSb"],"result":"⪩⨒∯111331","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2083","layer":2},{"info":"number node, value=1046","layer":2},{"info":"compute binary expreesion, left_input=2083, right_input=1046, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=-12126","layer":1},{"info":"compute unary expreesion, input=-12126, op_id = AcOhelriW5, unary_op_definition = '⨣⨃⇪a = { (⨡↴(172⊬⨰(3↙a))) }', output=1405","layer":0}],"base":4,"result_base":4,"text":"⨣⨃⇪(⪩⨒∯200203⨒⪩⨒∯100112)=⪩⨒∯111331","reverse_text":"⪩⨒∯111331=⨣⨃⇪(⪩⨒∯200203⨒⪩⨒∯100112)","cot":[{"info":"⪩⨒∯200203⨒⪩⨒∯100112=⪩⨒∯-2331132","layer":1},{"info":"⨣⨃⇪⪩⨒∯-2331132=⪩⨒∯111331","layer":0}]}
{"id":902,"expression_no_base_symbol":"$2276$↓$1306$⪭$3357$⇤$7836$","expression":"⪩⨒∯203210↓⪩⨒∯110122⪭⪩⨒∯310131⇤⪩⨒∯1322130","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":18601,"operation_count":3,"complexity_ratio":6200.333333333333,"tree":{"type":"binary","operator":"⪭","left_expr":{"type":"binary","operator":"↓","left_expr":{"type":"numeric_atoms","value":2276,"base":4},"right_expr":{"type":"numeric_atoms","value":1306,"base":4}},"right_expr":{"type":"binary","operator":"⇤","left_expr":{"type":"numeric_atoms","value":3357,"base":4},"right_expr":{"type":"numeric_atoms","value":7836,"base":4}}},"used_operators":["j9kHMeSvPp","Af076pWI7l","YSKBFp38Pu"],"dependent_operators":["COABgblf1C","xUOZtlo3hN","nhYeJWJD5X","mp7IySMOzn","Noe24qw2ks","lvlrscuwVU","T2fj7uvVaJ","PoHhknlbAi","rysDP5nf3Z","XPYlsWDdGa","tifHPKVTfV","2DQ55sFlQl","2DDjHMKMc0","xUOZtlo3hN","QMFrweE19q"],"result":"⪩⨒∯-220","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2276","layer":2},{"info":"number node, value=1306","layer":2},{"info":"compute binary expreesion, left_input=2276, right_input=1306, op_id = Af076pWI7l binary_op_definition= 'a↓b = { (((b⇷b)∓⋝b)⨐((462≴⪞⇿a)∇⊂⋱(a⋓a))) }', output=-134","layer":1},{"info":"number node, value=3357","layer":2},{"info":"number node, value=7836","layer":2},{"info":"compute binary expreesion, left_input=3357, right_input=7836, op_id = YSKBFp38Pu binary_op_definition= 'a⇤b = { (((b-523)⇼⇔∾(⨞⊢a))⫡⨏((⪲⇎a)⨵⪆(336⋝⋈⪟a))) }', output=-53117","layer":1},{"info":"compute binary expreesion, left_input=-134, right_input=-53117, op_id = j9kHMeSvPp binary_op_definition= 'a⪭b = { (⨞⊢a) , if a<649 ; (b⊭↱b) , else }', output=-40","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯203210↓⪩⨒∯110122⪭⪩⨒∯310131⇤⪩⨒∯1322130=⪩⨒∯-220","reverse_text":"⪩⨒∯-220=⪩⨒∯203210↓⪩⨒∯110122⪭⪩⨒∯310131⇤⪩⨒∯1322130","cot":[{"info":"⪩⨒∯203210↓⪩⨒∯110122=⪩⨒∯-2012","layer":1},{"info":"⪩⨒∯310131⇤⪩⨒∯1322130=⪩⨒∯-30331331","layer":1},{"info":"⪩⨒∯-2012⪭⪩⨒∯-30331331=⪩⨒∯-220","layer":0}]}
{"id":903,"expression_no_base_symbol":"$1614$⫁⪎$1675$⨵⪆$2271$↺$1510$","expression":"⪩⨒∯121032⫁⪎⪩⨒∯122023⨵⪆⪩⨒∯203133↺⪩⨒∯113212","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":12,"operation_count":3,"complexity_ratio":4.0,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"binary","operator":"⫁⪎","left_expr":{"type":"numeric_atoms","value":1614,"base":4},"right_expr":{"type":"numeric_atoms","value":1675,"base":4}},"right_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":2271,"base":4},"right_expr":{"type":"numeric_atoms","value":1510,"base":4}}},"used_operators":["2DQ55sFlQl","xRrnTEsQ6j","7j4O788W3g"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","P8v4zCKN1o","Qy55tPpLXF","tifHPKVTfV","sdazOOVcIp","2DDjHMKMc0","i8ToyICDmI","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1614","layer":2},{"info":"number node, value=1675","layer":2},{"info":"compute binary expreesion, left_input=1614, right_input=1675, op_id = xRrnTEsQ6j binary_op_definition= 'a⫁⪎b = { ((b⋝⋈⪟a)⇼⇔∾a) , if (∥⊫b)!=57 ; ((191∲⫓a)⋥≓≎(a⪨≂368)) , else }', output=-61","layer":1},{"info":"number node, value=2271","layer":2},{"info":"number node, value=1510","layer":2},{"info":"compute binary expreesion, left_input=2271, right_input=1510, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1510","layer":1},{"info":"compute binary expreesion, left_input=-61, right_input=1510, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯121032⫁⪎⪩⨒∯122023⨵⪆⪩⨒∯203133↺⪩⨒∯113212=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⪩⨒∯121032⫁⪎⪩⨒∯122023⨵⪆⪩⨒∯203133↺⪩⨒∯113212","cot":[{"info":"⪩⨒∯121032⫁⪎⪩⨒∯122023=⪩⨒∯-331","layer":1},{"info":"⪩⨒∯203133↺⪩⨒∯113212=⪩⨒∯113212","layer":1},{"info":"⪩⨒∯-331⨵⪆⪩⨒∯113212=⪩⨒∯2200","layer":0}]}
{"id":904,"expression_no_base_symbol":"$3498$≬⇓$2034$≬⋮($5230$⋆⋳)","expression":"⪩⨒∯312222≬⇓⪩⨒∯133302≬⋮(⪩⨒∯1101232⋆⋳)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":27,"operation_count":3,"complexity_ratio":9.0,"tree":{"type":"binary","operator":"≬⋮","left_expr":{"type":"binary","operator":"≬⇓","left_expr":{"type":"numeric_atoms","value":3498,"base":4},"right_expr":{"type":"numeric_atoms","value":2034,"base":4}},"right_expr":{"type":"unary","operator":"⋆⋳","unary_expr":{"type":"numeric_atoms","value":5230,"base":4}}},"used_operators":["kbkesczE7y","jWTQ2TZYIH","6MpZysEj17"],"dependent_operators":["P8v4zCKN1o","rysDP5nf3Z","7j4O788W3g","XIabStNQrY","t8gj7n24qd","i8ToyICDmI","AdZkA7nFnk","zVYPLywUTj","XTarYq4gQB","9FxExcQeMw","7j4O788W3g","DIvbN7qnHd"],"result":"⪩⨒∯31210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3498","layer":2},{"info":"number node, value=2034","layer":2},{"info":"compute binary expreesion, left_input=3498, right_input=2034, op_id = jWTQ2TZYIH binary_op_definition= 'a≬⇓b = { (a⊪) , if a<=154 or (⪝⪂⫅a)>=41 ; (a⋅⇍b) , else }', output=-22","layer":1},{"info":"number node, value=5230","layer":2},{"info":"compute unary expreesion, input=5230, op_id = 6MpZysEj17, unary_op_definition = 'a⋆⋳ = { ((a⊠≄⫣)⩷∴(a↺a)) }', output=-10492","layer":1},{"info":"compute binary expreesion, left_input=-22, right_input=-10492, op_id = kbkesczE7y binary_op_definition= 'a≬⋮b = { (((-a)∲⫓(b⇋≉))↺(∥⊫(b-b))) }', output=868","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯312222≬⇓⪩⨒∯133302≬⋮(⪩⨒∯1101232⋆⋳)=⪩⨒∯31210","reverse_text":"⪩⨒∯31210=⪩⨒∯312222≬⇓⪩⨒∯133302≬⋮(⪩⨒∯1101232⋆⋳)","cot":[{"info":"⪩⨒∯312222≬⇓⪩⨒∯133302=⪩⨒∯-112","layer":1},{"info":"⪩⨒∯1101232⋆⋳=⪩⨒∯-2203330","layer":1},{"info":"⪩⨒∯-112≬⋮⪩⨒∯-2203330=⪩⨒∯31210","layer":0}]}
{"id":905,"expression_no_base_symbol":"$1034$≄⊠$1172$⪉⨛$2336$∺≝⩲$4640$","expression":"⪩⨒∯100022≄⊠⪩⨒∯102110⪉⨛⪩⨒∯210200∺≝⩲⪩⨒∯1020200","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":90,"operation_count":3,"complexity_ratio":30.0,"tree":{"type":"binary","operator":"⪉⨛","left_expr":{"type":"binary","operator":"≄⊠","left_expr":{"type":"numeric_atoms","value":1034,"base":4},"right_expr":{"type":"numeric_atoms","value":1172,"base":4}},"right_expr":{"type":"binary","operator":"∺≝⩲","left_expr":{"type":"numeric_atoms","value":2336,"base":4},"right_expr":{"type":"numeric_atoms","value":4640,"base":4}}},"used_operators":["EWw2JM7wp4","vXNesLlMH1","KPf6cnQVty"],"dependent_operators":["NTOWxs364D","tifHPKVTfV","12rbrZMWeM","i8ToyICDmI","eewbuw0ToL","d7ASUq0ydm","nOKPl9n5zu","RabNbG55vr","DyGG3AbaNP","i8ToyICDmI","BjRHVeLaeN","glklzrTFfD","sdazOOVcIp","2DQ55sFlQl"],"result":"⪩⨒∯101022223","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1034","layer":2},{"info":"number node, value=1172","layer":2},{"info":"compute binary expreesion, left_input=1034, right_input=1172, op_id = vXNesLlMH1 binary_op_definition= 'a≄⊠b = { ((a∼b)⫯⪬∳(b∲⫓138)) , if (a⫣⪄⊒915)>=34 ; (⋗⩴⪓(b⫣⪄⊒b)) , else }', output=23420","layer":1},{"info":"number node, value=2336","layer":2},{"info":"number node, value=4640","layer":2},{"info":"compute binary expreesion, left_input=2336, right_input=4640, op_id = KPf6cnQVty binary_op_definition= 'a∺≝⩲b = { (((b⪨≂b)⨁⊸⫻)⨵⪆(a⫩⊇)) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=23420, right_input=160, op_id = EWw2JM7wp4 binary_op_definition= 'a⪉⨛b = { (((82⇼⇔∾a)⩚⊴⇥a)⩚⊴⇥((b∲⫓a)⋳⪒(a⨰b))) }', output=70315","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯100022≄⊠⪩⨒∯102110⪉⨛⪩⨒∯210200∺≝⩲⪩⨒∯1020200=⪩⨒∯101022223","reverse_text":"⪩⨒∯101022223=⪩⨒∯100022≄⊠⪩⨒∯102110⪉⨛⪩⨒∯210200∺≝⩲⪩⨒∯1020200","cot":[{"info":"⪩⨒∯100022≄⊠⪩⨒∯102110=⪩⨒∯11231330","layer":1},{"info":"⪩⨒∯210200∺≝⩲⪩⨒∯1020200=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯11231330⪉⨛⪩⨒∯2200=⪩⨒∯101022223","layer":0}]}
{"id":906,"expression_no_base_symbol":"⇁⨣⪵($5379$↸$1676$)","expression":"⇁⨣⪵(⪩⨒∯1110003↸⪩⨒∯122030)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1680,"operation_count":2,"complexity_ratio":840.0,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"binary","operator":"↸","left_expr":{"type":"numeric_atoms","value":5379,"base":4},"right_expr":{"type":"numeric_atoms","value":1676,"base":4}}},"used_operators":["inkyxCbjAn","1eCjFl0mb9"],"dependent_operators":["B5M0gjZbta","9HNa5Wba9A","61wBmkZwlr","rJVOvQCfKK"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5379","layer":2},{"info":"number node, value=1676","layer":2},{"info":"compute binary expreesion, left_input=5379, right_input=1676, op_id = 1eCjFl0mb9 binary_op_definition= 'a↸b = { ((b*a)⨎(≋a)) }', output=5379","layer":1},{"info":"compute unary expreesion, input=5379, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇁⨣⪵(⪩⨒∯1110003↸⪩⨒∯122030)=NaN","reverse_text":"NaN=⇁⨣⪵(⪩⨒∯1110003↸⪩⨒∯122030)","cot":[{"info":"⪩⨒∯1110003↸⪩⨒∯122030=⪩⨒∯1110003","layer":1},{"info":"⇁⨣⪵⪩⨒∯1110003=NaN","layer":0}]}
{"id":907,"expression_no_base_symbol":"($2362$∠⫱$6451$)⩇∃⫛(⫎≠⋺$3098$)","expression":"(⪩⨒∯210322∠⫱⪩⨒∯1210303)⩇∃⫛(⫎≠⋺⪩⨒∯300122)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":36,"operation_count":3,"complexity_ratio":12.0,"tree":{"type":"binary","operator":"⩇∃⫛","left_expr":{"type":"binary","operator":"∠⫱","left_expr":{"type":"numeric_atoms","value":2362,"base":4},"right_expr":{"type":"numeric_atoms","value":6451,"base":4}},"right_expr":{"type":"unary","operator":"⫎≠⋺","unary_expr":{"type":"numeric_atoms","value":3098,"base":4}}},"used_operators":["1aApVXNlOP","QvoQhV0rrE","LYeZOJ0nQG"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","e1ybzncUwg","Qy55tPpLXF","DZ8iAZOCBD","2DQ55sFlQl","t8gj7n24qd","2DDjHMKMc0","Z2TMIBDE3Q","14qkJME0vr","f6k1SAg4EE","Ph9nP6C5qx","eewbuw0ToL","u6S6b8DprG","eLAdDNolq6","DZ8iAZOCBD","7j4O788W3g","tifHPKVTfV","AF7qkfDlqP","9FxExcQeMw","NTOWxs364D","P8v4zCKN1o","tifHPKVTfV","i8ToyICDmI","COABgblf1C"],"result":"⪩⨒∯-23321","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2362","layer":2},{"info":"number node, value=6451","layer":2},{"info":"compute binary expreesion, left_input=2362, right_input=6451, op_id = QvoQhV0rrE binary_op_definition= 'a∠⫱b = { ((⨑⩽⪐a)↺(617⊉≛↸a)) , if (≤/b)<=3 ; (b⇼⇔∾a) , else }', output=1234","layer":1},{"info":"number node, value=3098","layer":2},{"info":"compute unary expreesion, input=3098, op_id = LYeZOJ0nQG, unary_op_definition = '⫎≠⋺a = { ((655⩚⊴⇥a)∲⫓(∥⊫86)) , if (a⩷∴509)>=9 ; ((1⊭↱337)⇼⇔∾(a⩷∴a)) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=1234, right_input=0, op_id = 1aApVXNlOP binary_op_definition= 'a⩇∃⫛b = { (((b⊉≛↸a)⩤)⨰((362⩷∴b)⋥≓≎(↽≂a))) , if (a⊦⊿)>7 and b<=506 and (-a)==737 ; (((b⩤)⪒(b≧⫂∧a))⋝⋈⪟((a⨵⪆a)-(≉a))) , else }', output=-761","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯210322∠⫱⪩⨒∯1210303)⩇∃⫛(⫎≠⋺⪩⨒∯300122)=⪩⨒∯-23321","reverse_text":"⪩⨒∯-23321=(⪩⨒∯210322∠⫱⪩⨒∯1210303)⩇∃⫛(⫎≠⋺⪩⨒∯300122)","cot":[{"info":"⪩⨒∯210322∠⫱⪩⨒∯1210303=⪩⨒∯103102","layer":1},{"info":"⫎≠⋺⪩⨒∯300122=⪩⨒∯0","layer":1},{"info":"⪩⨒∯103102⩇∃⫛⪩⨒∯0=⪩⨒∯-23321","layer":0}]}
{"id":908,"expression_no_base_symbol":"$1388$⋛$1813$⩒⫫($4737$≧⫂∧$3391$)","expression":"⪩⨒∯111230⋛⪩⨒∯130111⩒⫫(⪩⨒∯1022001≧⫂∧⪩⨒∯310333)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":291,"operation_count":3,"complexity_ratio":97.0,"tree":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"binary","operator":"⋛","left_expr":{"type":"numeric_atoms","value":1388,"base":4},"right_expr":{"type":"numeric_atoms","value":1813,"base":4}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":4737,"base":4},"right_expr":{"type":"numeric_atoms","value":3391,"base":4}}},"used_operators":["KFSx94NKJn","YbUVn0Rbpy","Ph9nP6C5qx"],"dependent_operators":["NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1388","layer":2},{"info":"number node, value=1813","layer":2},{"info":"compute binary expreesion, left_input=1388, right_input=1813, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-119700","layer":1},{"info":"number node, value=4737","layer":2},{"info":"number node, value=3391","layer":2},{"info":"compute binary expreesion, left_input=4737, right_input=3391, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=2918","layer":1},{"info":"compute binary expreesion, left_input=-119700, right_input=2918, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯111230⋛⪩⨒∯130111⩒⫫(⪩⨒∯1022001≧⫂∧⪩⨒∯310333)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=⪩⨒∯111230⋛⪩⨒∯130111⩒⫫(⪩⨒∯1022001≧⫂∧⪩⨒∯310333)","cot":[{"info":"⪩⨒∯111230⋛⪩⨒∯130111=⪩⨒∯-131032110","layer":1},{"info":"⪩⨒∯1022001≧⫂∧⪩⨒∯310333=⪩⨒∯231212","layer":1},{"info":"⪩⨒∯-131032110⩒⫫⪩⨒∯231212=⪩⨒∯2200","layer":0}]}
{"id":909,"expression_no_base_symbol":"$3561$⊕∕$2286$⪄$3108$≚⊃≕$2626$","expression":"⪩⨒∯313221⊕∕⪩⨒∯203232⪄⪩⨒∯300210≚⊃≕⪩⨒∯221002","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":115,"operation_count":3,"complexity_ratio":38.333333333333336,"tree":{"type":"binary","operator":"⪄","left_expr":{"type":"binary","operator":"⊕∕","left_expr":{"type":"numeric_atoms","value":3561,"base":4},"right_expr":{"type":"numeric_atoms","value":2286,"base":4}},"right_expr":{"type":"binary","operator":"≚⊃≕","left_expr":{"type":"numeric_atoms","value":3108,"base":4},"right_expr":{"type":"numeric_atoms","value":2626,"base":4}}},"used_operators":["SUmda5xLS4","9cloC0Ngie","Bmrmz2XGnR"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf","9FxExcQeMw","Qy55tPpLXF","7j4O788W3g","sdazOOVcIp","8w2t5hMYqp","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q"],"result":"⪩⨒∯-1333301321","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3561","layer":2},{"info":"number node, value=2286","layer":2},{"info":"compute binary expreesion, left_input=3561, right_input=2286, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=3561","layer":1},{"info":"number node, value=3108","layer":2},{"info":"number node, value=2626","layer":2},{"info":"compute binary expreesion, left_input=3108, right_input=2626, op_id = Bmrmz2XGnR binary_op_definition= 'a≚⊃≕b = { (-((⊄⩳↩b)⪨≂(a⩷∴b))) , if ((b⫡⨏524)<690 or (⨞⊢a)>=395) ; ((⊄⩳↩(b⋥≓≎a))⋥≓≎((a↺a)⪨≂(479⨸⪁a))) , else }', output=67","layer":1},{"info":"compute binary expreesion, left_input=3561, right_input=67, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-523385","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯313221⊕∕⪩⨒∯203232⪄⪩⨒∯300210≚⊃≕⪩⨒∯221002=⪩⨒∯-1333301321","reverse_text":"⪩⨒∯-1333301321=⪩⨒∯313221⊕∕⪩⨒∯203232⪄⪩⨒∯300210≚⊃≕⪩⨒∯221002","cot":[{"info":"⪩⨒∯313221⊕∕⪩⨒∯203232=⪩⨒∯313221","layer":1},{"info":"⪩⨒∯300210≚⊃≕⪩⨒∯221002=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯313221⪄⪩⨒∯1003=⪩⨒∯-1333301321","layer":0}]}
{"id":910,"expression_no_base_symbol":"($2239$⩷∴$1757$)⊪","expression":"(⪩⨒∯202333⩷∴⪩⨒∯123131)⊪","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":39,"operation_count":2,"complexity_ratio":19.5,"tree":{"type":"unary","operator":"⊪","unary_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":2239,"base":4},"right_expr":{"type":"numeric_atoms","value":1757,"base":4}}},"used_operators":["zVYPLywUTj","9FxExcQeMw"],"dependent_operators":["sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL","rysDP5nf3Z"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2239","layer":2},{"info":"number node, value=1757","layer":2},{"info":"compute binary expreesion, left_input=2239, right_input=1757, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=932","layer":1},{"info":"compute unary expreesion, input=932, op_id = zVYPLywUTj, unary_op_definition = 'a⊪ = { (((a*a)+(18⨵⪆91))⪨≂((62⋥≓≎a)*(a⪒a))) , if (≉a)<304 or (a⫩⊇)==292 ; ((⊄⩳↩(a⪠⩆⊳))*((a/a)≧⫂∧(21*a))) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯202333⩷∴⪩⨒∯123131)⊪=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯202333⩷∴⪩⨒∯123131)⊪","cot":[{"info":"⪩⨒∯202333⩷∴⪩⨒∯123131=⪩⨒∯32210","layer":1},{"info":"⪩⨒∯32210⊪=⪩⨒∯0","layer":0}]}
{"id":911,"expression_no_base_symbol":"⊥$1749$⪟⇏$3887$","expression":"⊥⪩⨒∯123111⪟⇏⪩⨒∯330233","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34,"operation_count":2,"complexity_ratio":17.0,"tree":{"type":"unary","operator":"⊥","unary_expr":{"type":"binary","operator":"⪟⇏","left_expr":{"type":"numeric_atoms","value":1749,"base":4},"right_expr":{"type":"numeric_atoms","value":3887,"base":4}}},"used_operators":["Q3PJZHRvZv","GODebY97qR"],"dependent_operators":["fu6greOZ01","gx7XJ7hdpj","XnXgA4xnOs","wEfv7U73WA","2DQ55sFlQl","f6k1SAg4EE","oacrs7FA3X"],"result":"⪩⨒∯10","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1749","layer":2},{"info":"number node, value=3887","layer":2},{"info":"compute binary expreesion, left_input=1749, right_input=3887, op_id = GODebY97qR binary_op_definition= 'a⪟⇏b = { ((b⨑≵⋬b)⫸⇳(440⪒a)) , if (b⇐≅)<189 ; ((219⨑≵⋬a)⪘⫢(b⨵⪆b)) , else }', output=-1","layer":1},{"info":"compute unary expreesion, input=-1, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=4","layer":0}],"base":4,"result_base":4,"text":"⊥⪩⨒∯123111⪟⇏⪩⨒∯330233=⪩⨒∯10","reverse_text":"⪩⨒∯10=⊥⪩⨒∯123111⪟⇏⪩⨒∯330233","cot":[{"info":"⪩⨒∯123111⪟⇏⪩⨒∯330233=⪩⨒∯-1","layer":1},{"info":"⊥⪩⨒∯-1=⪩⨒∯10","layer":0}]}
{"id":912,"expression_no_base_symbol":"($3013$⫚↹⊑$1767$)⨰$6294$⇡⇂$1033$","expression":"(⪩⨒∯233011⫚↹⊑⪩⨒∯123213)⨰⪩⨒∯1202112⇡⇂⪩⨒∯100021","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6117,"operation_count":3,"complexity_ratio":2039.0,"tree":{"type":"binary","operator":"⨰","left_expr":{"type":"binary","operator":"⫚↹⊑","left_expr":{"type":"numeric_atoms","value":3013,"base":4},"right_expr":{"type":"numeric_atoms","value":1767,"base":4}},"right_expr":{"type":"binary","operator":"⇡⇂","left_expr":{"type":"numeric_atoms","value":6294,"base":4},"right_expr":{"type":"numeric_atoms","value":1033,"base":4}}},"used_operators":["eewbuw0ToL","dfKe02y8D2","UMwdvZNt44"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","2DQ55sFlQl","DIvbN7qnHd","t8gj7n24qd","12rbrZMWeM","g55IO6H4Gj","9FxExcQeMw","23Mk6UjR3U","z4E1FaHLuy","3tj9sqzovi","fu6greOZ01","AHs5Up7iyr","lvlrscuwVU","KPf6cnQVty","uBihLCJcMX","12rbrZMWeM","WPoGxAaPR1"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=3013","layer":2},{"info":"number node, value=1767","layer":2},{"info":"compute binary expreesion, left_input=3013, right_input=1767, op_id = dfKe02y8D2 binary_op_definition= 'a⫚↹⊑b = { ((126⊠≄⫣)⋳⪒((-b)⨵⪆(a⨸⪁b))) }', output=-447","layer":1},{"info":"number node, value=6294","layer":2},{"info":"number node, value=1033","layer":2},{"info":"compute binary expreesion, left_input=6294, right_input=1033, op_id = UMwdvZNt44 binary_op_definition= 'a⇡⇂b = { (((b≹⇙⪍b)⋳⪒(b⋷a))∺≝⩲(⫟(a⩷∴43))) , if (⊬↢a)==727 or (a⇔⨋)<18 ; ((604≴⪞⇿(≻⋜b))⨐⩸⫘a) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-447, right_input=nan, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯233011⫚↹⊑⪩⨒∯123213)⨰⪩⨒∯1202112⇡⇂⪩⨒∯100021=NaN","reverse_text":"NaN=(⪩⨒∯233011⫚↹⊑⪩⨒∯123213)⨰⪩⨒∯1202112⇡⇂⪩⨒∯100021","cot":[{"info":"⪩⨒∯233011⫚↹⊑⪩⨒∯123213=⪩⨒∯-12333","layer":1},{"info":"⪩⨒∯1202112⇡⇂⪩⨒∯100021=NaN","layer":1},{"info":"⪩⨒∯-12333⨰NaN=NaN","layer":0}]}
{"id":913,"expression_no_base_symbol":"$2659$⪭$1025$⩤","expression":"⪩⨒∯221203⪭⪩⨒∯100001⩤","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7,"operation_count":2,"complexity_ratio":3.5,"tree":{"type":"unary","operator":"⩤","unary_expr":{"type":"binary","operator":"⪭","left_expr":{"type":"numeric_atoms","value":2659,"base":4},"right_expr":{"type":"numeric_atoms","value":1025,"base":4}}},"used_operators":["Z2TMIBDE3Q","j9kHMeSvPp"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","COABgblf1C","xUOZtlo3hN"],"result":"⪩⨒∯-11","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2659","layer":2},{"info":"number node, value=1025","layer":2},{"info":"compute binary expreesion, left_input=2659, right_input=1025, op_id = j9kHMeSvPp binary_op_definition= 'a⪭b = { (⨞⊢a) , if a<649 ; (b⊭↱b) , else }', output=5","layer":1},{"info":"compute unary expreesion, input=5, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-5","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯221203⪭⪩⨒∯100001⩤=⪩⨒∯-11","reverse_text":"⪩⨒∯-11=⪩⨒∯221203⪭⪩⨒∯100001⩤","cot":[{"info":"⪩⨒∯221203⪭⪩⨒∯100001=⪩⨒∯11","layer":1},{"info":"⪩⨒∯11⩤=⪩⨒∯-11","layer":0}]}
{"id":914,"expression_no_base_symbol":"$6721$⨻⩈⩔$1352$⨒($2907$≣⋋)","expression":"⪩⨒∯1221001⨻⩈⩔⪩⨒∯111020⨒(⪩⨒∯231123≣⋋)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":642,"operation_count":3,"complexity_ratio":214.0,"tree":{"type":"binary","operator":"⨒","left_expr":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"numeric_atoms","value":6721,"base":4},"right_expr":{"type":"numeric_atoms","value":1352,"base":4}},"right_expr":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"numeric_atoms","value":2907,"base":4}}},"used_operators":["y75s1iXyHd","nEsXyWgiOK","Tcnh7f0tEr"],"dependent_operators":["srAu1WTS94","oacrs7FA3X","7qqUquhhSb","D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6721","layer":2},{"info":"number node, value=1352","layer":2},{"info":"compute binary expreesion, left_input=6721, right_input=1352, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=45367","layer":1},{"info":"number node, value=2907","layer":2},{"info":"compute unary expreesion, input=2907, op_id = Tcnh7f0tEr, unary_op_definition = 'a≣⋋ = { ((a/a)⋥≓≎(a⨪↰⇹248)) , if (a⪢148)<38 ; ((511*a)⊠≄⫣) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=45367, right_input=0, op_id = y75s1iXyHd binary_op_definition= 'a⨒b = { ((⨵≀≌(a⪘⫢b))⩉⊫⨁) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1221001⨻⩈⩔⪩⨒∯111020⨒(⪩⨒∯231123≣⋋)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯1221001⨻⩈⩔⪩⨒∯111020⨒(⪩⨒∯231123≣⋋)","cot":[{"info":"⪩⨒∯1221001⨻⩈⩔⪩⨒∯111020=⪩⨒∯23010313","layer":1},{"info":"⪩⨒∯231123≣⋋=⪩⨒∯0","layer":1},{"info":"⪩⨒∯23010313⨒⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":915,"expression_no_base_symbol":"($1168$⨚$2350$)⊉↱≁($3828$⨑≵⋬$3724$)","expression":"(⪩⨒∯102100⨚⪩⨒∯210232)⊉↱≁(⪩⨒∯323310⨑≵⋬⪩⨒∯322030)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":57,"operation_count":3,"complexity_ratio":19.0,"tree":{"type":"binary","operator":"⊉↱≁","left_expr":{"type":"binary","operator":"⨚","left_expr":{"type":"numeric_atoms","value":1168,"base":4},"right_expr":{"type":"numeric_atoms","value":2350,"base":4}},"right_expr":{"type":"binary","operator":"⨑≵⋬","left_expr":{"type":"numeric_atoms","value":3828,"base":4},"right_expr":{"type":"numeric_atoms","value":3724,"base":4}}},"used_operators":["w2P8NbNXyL","nREPSIbpBE","XnXgA4xnOs"],"dependent_operators":["9FxExcQeMw","e1ybzncUwg","sdazOOVcIp","t8gj7n24qd","eewbuw0ToL","BjRHVeLaeN","12rbrZMWeM","eewbuw0ToL","AF7qkfDlqP","QMFrweE19q"],"result":"⪩⨒∯-13013000","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1168","layer":2},{"info":"number node, value=2350","layer":2},{"info":"compute binary expreesion, left_input=1168, right_input=2350, op_id = nREPSIbpBE binary_op_definition= 'a⨚b = { (((b⋳⪒a)⋳⪒31)⫩⊇) }', output=-6130","layer":1},{"info":"number node, value=3828","layer":2},{"info":"number node, value=3724","layer":2},{"info":"compute binary expreesion, left_input=3828, right_input=3724, op_id = XnXgA4xnOs binary_op_definition= 'a⨑≵⋬b = { ((a⨰b)⫡⨏(⨑⩽⪐b)) }', output=-5549","layer":1},{"info":"compute binary expreesion, left_input=-6130, right_input=-5549, op_id = w2P8NbNXyL binary_op_definition= 'a⊉↱≁b = { ((≉(a⨰b))⪨≂((145⩷∴a)⪨≂(-b))) }', output=-29120","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯102100⨚⪩⨒∯210232)⊉↱≁(⪩⨒∯323310⨑≵⋬⪩⨒∯322030)=⪩⨒∯-13013000","reverse_text":"⪩⨒∯-13013000=(⪩⨒∯102100⨚⪩⨒∯210232)⊉↱≁(⪩⨒∯323310⨑≵⋬⪩⨒∯322030)","cot":[{"info":"⪩⨒∯102100⨚⪩⨒∯210232=⪩⨒∯-1133302","layer":1},{"info":"⪩⨒∯323310⨑≵⋬⪩⨒∯322030=⪩⨒∯-1112231","layer":1},{"info":"⪩⨒∯-1133302⊉↱≁⪩⨒∯-1112231=⪩⨒∯-13013000","layer":0}]}
{"id":916,"expression_no_base_symbol":"(↽≂$1140$)⩒⫫(⇖$7257$)","expression":"(↽≂⪩⨒∯101310)⩒⫫(⇖⪩⨒∯1301121)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":30,"operation_count":3,"complexity_ratio":10.0,"tree":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"unary","operator":"↽≂","unary_expr":{"type":"numeric_atoms","value":1140,"base":4}},"right_expr":{"type":"unary","operator":"⇖","unary_expr":{"type":"numeric_atoms","value":7257,"base":4}}},"used_operators":["KFSx94NKJn","u6S6b8DprG","tfWHHpNKUN"],"dependent_operators":["NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","2DQ55sFlQl"],"result":"⪩⨒∯2200","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1140","layer":2},{"info":"compute unary expreesion, input=1140, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-2280","layer":1},{"info":"number node, value=7257","layer":2},{"info":"compute unary expreesion, input=7257, op_id = tfWHHpNKUN, unary_op_definition = '⇖a = { (221⨵⪆a) }', output=160","layer":1},{"info":"compute binary expreesion, left_input=-2280, right_input=160, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=160","layer":0}],"base":4,"result_base":4,"text":"(↽≂⪩⨒∯101310)⩒⫫(⇖⪩⨒∯1301121)=⪩⨒∯2200","reverse_text":"⪩⨒∯2200=(↽≂⪩⨒∯101310)⩒⫫(⇖⪩⨒∯1301121)","cot":[{"info":"↽≂⪩⨒∯101310=⪩⨒∯-203220","layer":1},{"info":"⇖⪩⨒∯1301121=⪩⨒∯2200","layer":1},{"info":"⪩⨒∯-203220⩒⫫⪩⨒∯2200=⪩⨒∯2200","layer":0}]}
{"id":917,"expression_no_base_symbol":"($3830$⨚⇆$1252$)↞⋁($3193$∙⊟$2723$)","expression":"(⪩⨒∯323312⨚⇆⪩⨒∯103210)↞⋁(⪩⨒∯301321∙⊟⪩⨒∯222203)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":30279,"operation_count":3,"complexity_ratio":10093.0,"tree":{"type":"binary","operator":"↞⋁","left_expr":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"numeric_atoms","value":3830,"base":4},"right_expr":{"type":"numeric_atoms","value":1252,"base":4}},"right_expr":{"type":"binary","operator":"∙⊟","left_expr":{"type":"numeric_atoms","value":3193,"base":4},"right_expr":{"type":"numeric_atoms","value":2723,"base":4}}},"used_operators":["RqrPlJkxDo","lwHaAYXP2r","SxTAKzQCrw"],"dependent_operators":["Uaa54Peajs","CArV6hThFE","13rbtpv6ld","gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi","6iOiAJX1F8","oWn0xqSxBt","3Oe9XWJUTD","4CyGpkTkEk","CArV6hThFE","PPChnnnBFF"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3830","layer":2},{"info":"number node, value=1252","layer":2},{"info":"compute binary expreesion, left_input=3830, right_input=1252, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":1},{"info":"number node, value=3193","layer":2},{"info":"number node, value=2723","layer":2},{"info":"compute binary expreesion, left_input=3193, right_input=2723, op_id = SxTAKzQCrw binary_op_definition= 'a∙⊟b = { (⩪∧⨌(a⫲⨊)) , if (b∐⫣)<386 ; ((a∣a)⊝⪿⪼(⊙↵-a)) , else }', output=51355","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=51355, op_id = RqrPlJkxDo binary_op_definition= 'a↞⋁b = { a , if (b⫲⨊)<=80 ; (∂(243↤⩊b)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯323312⨚⇆⪩⨒∯103210)↞⋁(⪩⨒∯301321∙⊟⪩⨒∯222203)=NaN","reverse_text":"NaN=(⪩⨒∯323312⨚⇆⪩⨒∯103210)↞⋁(⪩⨒∯301321∙⊟⪩⨒∯222203)","cot":[{"info":"⪩⨒∯323312⨚⇆⪩⨒∯103210=NaN","layer":1},{"info":"⪩⨒∯301321∙⊟⪩⨒∯222203=⪩⨒∯30202123","layer":1},{"info":"NaN↞⋁⪩⨒∯30202123=NaN","layer":0}]}
{"id":918,"expression_no_base_symbol":"($1084$⩧⪆$3086$)⊲⩕⊾(∷≠$1505$)","expression":"(⪩⨒∯100330⩧⪆⪩⨒∯300032)⊲⩕⊾(∷≠⪩⨒∯113201)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":33,"operation_count":3,"complexity_ratio":11.0,"tree":{"type":"binary","operator":"⊲⩕⊾","left_expr":{"type":"binary","operator":"⩧⪆","left_expr":{"type":"numeric_atoms","value":1084,"base":4},"right_expr":{"type":"numeric_atoms","value":3086,"base":4}},"right_expr":{"type":"unary","operator":"∷≠","unary_expr":{"type":"numeric_atoms","value":1505,"base":4}}},"used_operators":["DmTXOeWf9t","Ikt5ks8PT7","QiR2Oyf5Xj"],"dependent_operators":["23Mk6UjR3U","DZ8iAZOCBD","BjRHVeLaeN","QMFrweE19q","AF7qkfDlqP","COABgblf1C","eewbuw0ToL","t8gj7n24qd","7j4O788W3g"],"result":"⪩⨒∯-2020202","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1084","layer":2},{"info":"number node, value=3086","layer":2},{"info":"compute binary expreesion, left_input=1084, right_input=3086, op_id = Ikt5ks8PT7 binary_op_definition= 'a⩧⪆b = { (a⨰b) , if a==228 ; (-b) , else }', output=-3086","layer":1},{"info":"number node, value=1505","layer":2},{"info":"compute unary expreesion, input=1505, op_id = QiR2Oyf5Xj, unary_op_definition = '∷≠a = { (71↺a) }', output=1505","layer":1},{"info":"compute binary expreesion, left_input=-3086, right_input=1505, op_id = DmTXOeWf9t binary_op_definition= 'a⊲⩕⊾b = { (((a⊉≛↸b)⊭↱(⨑⩽⪐b))⫡⨏((a⫩⊇)⋷(a⊉≛↸b))) }', output=-8738","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯100330⩧⪆⪩⨒∯300032)⊲⩕⊾(∷≠⪩⨒∯113201)=⪩⨒∯-2020202","reverse_text":"⪩⨒∯-2020202=(⪩⨒∯100330⩧⪆⪩⨒∯300032)⊲⩕⊾(∷≠⪩⨒∯113201)","cot":[{"info":"⪩⨒∯100330⩧⪆⪩⨒∯300032=⪩⨒∯-300032","layer":1},{"info":"∷≠⪩⨒∯113201=⪩⨒∯113201","layer":1},{"info":"⪩⨒∯-300032⊲⩕⊾⪩⨒∯113201=⪩⨒∯-2020202","layer":0}]}
{"id":919,"expression_no_base_symbol":"$4011$∥⊢⊲$1658$⨳⩥⨓($1548$≀⩗∶$1691$)","expression":"⪩⨒∯332223∥⊢⊲⪩⨒∯121322⨳⩥⨓(⪩⨒∯120030≀⩗∶⪩⨒∯122123)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":24,"operation_count":3,"complexity_ratio":8.0,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"∥⊢⊲","left_expr":{"type":"numeric_atoms","value":4011,"base":4},"right_expr":{"type":"numeric_atoms","value":1658,"base":4}},"right_expr":{"type":"binary","operator":"≀⩗∶","left_expr":{"type":"numeric_atoms","value":1548,"base":4},"right_expr":{"type":"numeric_atoms","value":1691,"base":4}}},"used_operators":["nCS4ZIUYfx","v1UQAVDJRr","8INZBEW696"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","EBcxylXtPf","rGHVDoGpnC","KPf6cnQVty","2DlMacCsIx","l07mrZUIn9"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4011","layer":2},{"info":"number node, value=1658","layer":2},{"info":"compute binary expreesion, left_input=4011, right_input=1658, op_id = v1UQAVDJRr binary_op_definition= 'a∥⊢⊲b = { (a⨟⋌⩍b) , if (a⫌⩹⨱)>=49 ; b , else }', output=nan","layer":1},{"info":"number node, value=1548","layer":2},{"info":"number node, value=1691","layer":2},{"info":"compute binary expreesion, left_input=1548, right_input=1691, op_id = 8INZBEW696 binary_op_definition= 'a≀⩗∶b = { (a⩨b) , if (a∺≝⩲555)<251 ; (306↪⪝) , else }', output=-3","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-3, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯332223∥⊢⊲⪩⨒∯121322⨳⩥⨓(⪩⨒∯120030≀⩗∶⪩⨒∯122123)=NaN","reverse_text":"NaN=⪩⨒∯332223∥⊢⊲⪩⨒∯121322⨳⩥⨓(⪩⨒∯120030≀⩗∶⪩⨒∯122123)","cot":[{"info":"⪩⨒∯332223∥⊢⊲⪩⨒∯121322=NaN","layer":1},{"info":"⪩⨒∯120030≀⩗∶⪩⨒∯122123=⪩⨒∯-3","layer":1},{"info":"NaN⨳⩥⨓⪩⨒∯-3=NaN","layer":0}]}
{"id":920,"expression_no_base_symbol":"($3925$⨻⩈⩔$1963$)⩇∃⫛$3917$⋛$3072$","expression":"(⪩⨒∯331111⨻⩈⩔⪩⨒∯132223)⩇∃⫛⪩⨒∯331031⋛⪩⨒∯300000","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":387,"operation_count":3,"complexity_ratio":129.0,"tree":{"type":"binary","operator":"⩇∃⫛","left_expr":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"numeric_atoms","value":3925,"base":4},"right_expr":{"type":"numeric_atoms","value":1963,"base":4}},"right_expr":{"type":"binary","operator":"⋛","left_expr":{"type":"numeric_atoms","value":3917,"base":4},"right_expr":{"type":"numeric_atoms","value":3072,"base":4}}},"used_operators":["1aApVXNlOP","nEsXyWgiOK","YbUVn0Rbpy"],"dependent_operators":["9FxExcQeMw","rysDP5nf3Z","e1ybzncUwg","Qy55tPpLXF","DZ8iAZOCBD","2DQ55sFlQl","t8gj7n24qd","2DDjHMKMc0","Z2TMIBDE3Q","14qkJME0vr","f6k1SAg4EE","Ph9nP6C5qx","eewbuw0ToL","u6S6b8DprG","D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","d7ASUq0ydm","OKKcZfAt5B","FyVja0WsTP","zVYPLywUTj","tifHPKVTfV","sdazOOVcIp","Ikt5ks8PT7","bF6eod5Gvf","k8jYdgA6NY","D3AQDKkPcf","8HhzD0ZcuI","LkLIoiE525","8cLx32lpNA"],"result":"⪩⨒∯-131022221","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3925","layer":2},{"info":"number node, value=1963","layer":2},{"info":"compute binary expreesion, left_input=3925, right_input=1963, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=22999","layer":1},{"info":"number node, value=3917","layer":2},{"info":"number node, value=3072","layer":2},{"info":"compute binary expreesion, left_input=3917, right_input=3072, op_id = YbUVn0Rbpy binary_op_definition= 'a⋛b = { ((293∌(291⇼⇔∾496))⨽((52⊱⇼⊻262)%(a≝⊿a))) , if (b⇯⋐)>355 ; (((b⪨≂b)→⨶⪴(71⊪))%((197∷178)⩧⪆(b⫯⪬∳256))) , else }', output=-96939","layer":1},{"info":"compute binary expreesion, left_input=22999, right_input=-96939, op_id = 1aApVXNlOP binary_op_definition= 'a⩇∃⫛b = { (((b⊉≛↸a)⩤)⨰((362⩷∴b)⋥≓≎(↽≂a))) , if (a⊦⊿)>7 and b<=506 and (-a)==737 ; (((b⩤)⪒(b≧⫂∧a))⋝⋈⪟((a⨵⪆a)-(≉a))) , else }', output=-119465","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯331111⨻⩈⩔⪩⨒∯132223)⩇∃⫛⪩⨒∯331031⋛⪩⨒∯300000=⪩⨒∯-131022221","reverse_text":"⪩⨒∯-131022221=(⪩⨒∯331111⨻⩈⩔⪩⨒∯132223)⩇∃⫛⪩⨒∯331031⋛⪩⨒∯300000","cot":[{"info":"⪩⨒∯331111⨻⩈⩔⪩⨒∯132223=⪩⨒∯11213113","layer":1},{"info":"⪩⨒∯331031⋛⪩⨒∯300000=⪩⨒∯-113222223","layer":1},{"info":"⪩⨒∯11213113⩇∃⫛⪩⨒∯-113222223=⪩⨒∯-131022221","layer":0}]}
{"id":921,"expression_no_base_symbol":"($4280$⋥≓≎$3825$)⨎(⨝⨆$2202$)","expression":"(⪩⨒∯1002320⋥≓≎⪩⨒∯323301)⨎(⨝⨆⪩⨒∯202122)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7,"operation_count":3,"complexity_ratio":2.3333333333333335,"tree":{"type":"binary","operator":"⨎","left_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":4280,"base":4},"right_expr":{"type":"numeric_atoms","value":3825,"base":4}},"right_expr":{"type":"unary","operator":"⨝⨆","unary_expr":{"type":"numeric_atoms","value":2202,"base":4}}},"used_operators":["rJVOvQCfKK","Qy55tPpLXF","bQ67fsrMVf"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","tifHPKVTfV"],"result":"⪩⨒∯133021","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4280","layer":2},{"info":"number node, value=3825","layer":2},{"info":"compute binary expreesion, left_input=4280, right_input=3825, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=3403","layer":1},{"info":"number node, value=2202","layer":2},{"info":"compute unary expreesion, input=2202, op_id = bQ67fsrMVf, unary_op_definition = '⨝⨆a = { (209⇼⇔∾a) }', output=1993","layer":1},{"info":"compute binary expreesion, left_input=3403, right_input=1993, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=1993","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1002320⋥≓≎⪩⨒∯323301)⨎(⨝⨆⪩⨒∯202122)=⪩⨒∯133021","reverse_text":"⪩⨒∯133021=(⪩⨒∯1002320⋥≓≎⪩⨒∯323301)⨎(⨝⨆⪩⨒∯202122)","cot":[{"info":"⪩⨒∯1002320⋥≓≎⪩⨒∯323301=⪩⨒∯311023","layer":1},{"info":"⨝⨆⪩⨒∯202122=⪩⨒∯133021","layer":1},{"info":"⪩⨒∯311023⨎⪩⨒∯133021=⪩⨒∯133021","layer":0}]}
{"id":922,"expression_no_base_symbol":"(↸⊣$1984$)⩠","expression":"(↸⊣⪩⨒∯133000)⩠","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":31,"operation_count":2,"complexity_ratio":15.5,"tree":{"type":"unary","operator":"⩠","unary_expr":{"type":"unary","operator":"↸⊣","unary_expr":{"type":"numeric_atoms","value":1984,"base":4}}},"used_operators":["sJAwomhLZr","wztAlM01eG"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","k8jYdgA6NY","eH2TOUuTDT","W4YGzv6Whe","Z2TMIBDE3Q","COABgblf1C","N41Kp7NANJ","XPYlsWDdGa","7j4O788W3g","DZ8iAZOCBD","8w2t5hMYqp","12rbrZMWeM","f6k1SAg4EE"],"result":"⪩⨒∯1231111","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1984","layer":2},{"info":"compute unary expreesion, input=1984, op_id = wztAlM01eG, unary_op_definition = '↸⊣a = { ((⊄⩳↩a)↺(a≋⫹)) , if (⪲⇎a)<33 ; ((a⪒a)⊉≛↸(a⋳⪒a)) , else }', output=-1697","layer":1},{"info":"compute unary expreesion, input=-1697, op_id = sJAwomhLZr, unary_op_definition = 'a⩠ = { (((a+a)⊭↱(a⪨≂a))∲⫓((a⩤)%(a⪐))) }', output=6997","layer":0}],"base":4,"result_base":4,"text":"(↸⊣⪩⨒∯133000)⩠=⪩⨒∯1231111","reverse_text":"⪩⨒∯1231111=(↸⊣⪩⨒∯133000)⩠","cot":[{"info":"↸⊣⪩⨒∯133000=⪩⨒∯-122201","layer":1},{"info":"⪩⨒∯-122201⩠=⪩⨒∯1231111","layer":0}]}
{"id":923,"expression_no_base_symbol":"($4604$≃$4721$)⇤($2079$⩼⇪↪$4374$)","expression":"(⪩⨒∯1013330≃⪩⨒∯1021301)⇤(⪩⨒∯200133⩼⇪↪⪩⨒∯1010112)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":49,"operation_count":3,"complexity_ratio":16.333333333333332,"tree":{"type":"binary","operator":"⇤","left_expr":{"type":"binary","operator":"≃","left_expr":{"type":"numeric_atoms","value":4604,"base":4},"right_expr":{"type":"numeric_atoms","value":4721,"base":4}},"right_expr":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"numeric_atoms","value":2079,"base":4},"right_expr":{"type":"numeric_atoms","value":4374,"base":4}}},"used_operators":["YSKBFp38Pu","YbVcJGFEVW","ocnLzx9CaJ"],"dependent_operators":["rysDP5nf3Z","XPYlsWDdGa","tifHPKVTfV","2DQ55sFlQl","2DDjHMKMc0","xUOZtlo3hN","QMFrweE19q","9FxExcQeMw","Qy55tPpLXF","23Mk6UjR3U","JLbD19bQDL","7j4O788W3g","glklzrTFfD","tifHPKVTfV","t8gj7n24qd","i8ToyICDmI","COABgblf1C","9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q"],"result":"⪩⨒∯320132233","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4604","layer":2},{"info":"number node, value=4721","layer":2},{"info":"compute binary expreesion, left_input=4604, right_input=4721, op_id = YbVcJGFEVW binary_op_definition= 'a≃b = { (((13⋥≓≎b)⋷(a⇼⇔∾b))⨁⊸⫻) , if ((b⨁⊸⫻)>=162 or (b⪠⩆⊳)<=569) ; ((-(17⋷a))↺((a⩷∴a)⊭↱(b∲⫓a))) , else }', output=-18456","layer":1},{"info":"number node, value=2079","layer":2},{"info":"number node, value=4374","layer":2},{"info":"compute binary expreesion, left_input=2079, right_input=4374, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=-27243","layer":1},{"info":"compute binary expreesion, left_input=-18456, right_input=-27243, op_id = YSKBFp38Pu binary_op_definition= 'a⇤b = { (((b-523)⇼⇔∾(⨞⊢a))⫡⨏((⪲⇎a)⨵⪆(336⋝⋈⪟a))) }', output=231343","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1013330≃⪩⨒∯1021301)⇤(⪩⨒∯200133⩼⇪↪⪩⨒∯1010112)=⪩⨒∯320132233","reverse_text":"⪩⨒∯320132233=(⪩⨒∯1013330≃⪩⨒∯1021301)⇤(⪩⨒∯200133⩼⇪↪⪩⨒∯1010112)","cot":[{"info":"⪩⨒∯1013330≃⪩⨒∯1021301=⪩⨒∯-10200120","layer":1},{"info":"⪩⨒∯200133⩼⇪↪⪩⨒∯1010112=⪩⨒∯-12221223","layer":1},{"info":"⪩⨒∯-10200120⇤⪩⨒∯-12221223=⪩⨒∯320132233","layer":0}]}
{"id":924,"expression_no_base_symbol":"($2985$⊋$3394$)⊮⊟↴($4291$⇄$1295$)","expression":"(⪩⨒∯232221⊋⪩⨒∯311002)⊮⊟↴(⪩⨒∯1003003⇄⪩⨒∯110033)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":818,"operation_count":3,"complexity_ratio":272.6666666666667,"tree":{"type":"binary","operator":"⊮⊟↴","left_expr":{"type":"binary","operator":"⊋","left_expr":{"type":"numeric_atoms","value":2985,"base":4},"right_expr":{"type":"numeric_atoms","value":3394,"base":4}},"right_expr":{"type":"binary","operator":"⇄","left_expr":{"type":"numeric_atoms","value":4291,"base":4},"right_expr":{"type":"numeric_atoms","value":1295,"base":4}}},"used_operators":["QDVgd2eftb","W4tP9CfskL","3EYGwJThht"],"dependent_operators":["XhwjNDsVaA","C6VvDP6HwP","WkeUrDK8WX","kuIXHzHcAH","3Oe9XWJUTD","rJVOvQCfKK","2GS7woTJqF","18saOjeKKm","XPYlsWDdGa","JDUIKTTSIa","9HNa5Wba9A","XIabStNQrY","0kmYd0q39Y","Ph9nP6C5qx","eewbuw0ToL","7IPrd9c3lf","YSKBFp38Pu","eLAdDNolq6","DZ8iAZOCBD","i8ToyICDmI"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2985","layer":2},{"info":"number node, value=3394","layer":2},{"info":"compute binary expreesion, left_input=2985, right_input=3394, op_id = W4tP9CfskL binary_op_definition= 'a⊋b = { (⇠((b⇤b)⩦(b≧⫂∧a))) , if ((a⊵↤)<=50 or b<=499 or (b+⪬∐218)==39) ; (((b⨰a)⇋≉)*(⪲⇎(b⩣⫁∢b))) , else }', output=-9807960","layer":1},{"info":"number node, value=4291","layer":2},{"info":"number node, value=1295","layer":2},{"info":"compute binary expreesion, left_input=4291, right_input=1295, op_id = 3EYGwJThht binary_op_definition= 'a⇄b = { ((≤/b)∲⫓(a⊉≛↸b)) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-9807960, right_input=0, op_id = QDVgd2eftb binary_op_definition= 'a⊮⊟↴b = { ((⩰267)⪨⊡(b⊝⪿⪼a)) , if a!=19 ; ((b⨎372)/(b⪑⩈)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯232221⊋⪩⨒∯311002)⊮⊟↴(⪩⨒∯1003003⇄⪩⨒∯110033)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯232221⊋⪩⨒∯311002)⊮⊟↴(⪩⨒∯1003003⇄⪩⨒∯110033)","cot":[{"info":"⪩⨒∯232221⊋⪩⨒∯311002=⪩⨒∯-211122201120","layer":1},{"info":"⪩⨒∯1003003⇄⪩⨒∯110033=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-211122201120⊮⊟↴⪩⨒∯0=⪩⨒∯0","layer":0}]}
{"id":925,"expression_no_base_symbol":"(⊙↵-$2314$)⨻⩈⩔$4846$⪝$1883$","expression":"(⊙↵-⪩⨒∯210022)⨻⩈⩔⪩⨒∯1023232⪝⪩⨒∯131123","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2850,"operation_count":3,"complexity_ratio":950.0,"tree":{"type":"binary","operator":"⨻⩈⩔","left_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":2314,"base":4}},"right_expr":{"type":"binary","operator":"⪝","left_expr":{"type":"numeric_atoms","value":4846,"base":4},"right_expr":{"type":"numeric_atoms","value":1883,"base":4}}},"used_operators":["nEsXyWgiOK","oWn0xqSxBt","wicAB68Tmb"],"dependent_operators":["D309nIvmXG","nREPSIbpBE","vg4gO5BX6G","mqXw5SEYmG","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X"],"result":"⪩⨒∯-2232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2314","layer":2},{"info":"compute unary expreesion, input=2314, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"number node, value=4846","layer":2},{"info":"number node, value=1883","layer":2},{"info":"compute binary expreesion, left_input=4846, right_input=1883, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=-12251","layer":1},{"info":"compute binary expreesion, left_input=-1, right_input=-12251, op_id = nEsXyWgiOK binary_op_definition= 'a⨻⩈⩔b = { ((∓⪦(a⨚721))⊨((b⊨b)⫸⊐(a⫸⊐a))) }', output=-174","layer":0}],"base":4,"result_base":4,"text":"(⊙↵-⪩⨒∯210022)⨻⩈⩔⪩⨒∯1023232⪝⪩⨒∯131123=⪩⨒∯-2232","reverse_text":"⪩⨒∯-2232=(⊙↵-⪩⨒∯210022)⨻⩈⩔⪩⨒∯1023232⪝⪩⨒∯131123","cot":[{"info":"⊙↵-⪩⨒∯210022=⪩⨒∯-1","layer":1},{"info":"⪩⨒∯1023232⪝⪩⨒∯131123=⪩⨒∯-2333123","layer":1},{"info":"⪩⨒∯-1⨻⩈⩔⪩⨒∯-2333123=⪩⨒∯-2232","layer":0}]}
{"id":926,"expression_no_base_symbol":"$1244$⩁⩘$4548$↱(↯⪼$1432$)","expression":"⪩⨒∯103130⩁⩘⪩⨒∯1013010↱(↯⪼⪩⨒∯112120)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":99,"operation_count":3,"complexity_ratio":33.0,"tree":{"type":"binary","operator":"↱","left_expr":{"type":"binary","operator":"⩁⩘","left_expr":{"type":"numeric_atoms","value":1244,"base":4},"right_expr":{"type":"numeric_atoms","value":4548,"base":4}},"right_expr":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"numeric_atoms","value":1432,"base":4}}},"used_operators":["SR5kFfdi6N","gub5Cegaqo","8jW3W4yZS5"],"dependent_operators":["k4iM1060OG","eOf03JbCpp","2GS7woTJqF","XnXgA4xnOs","ddLRYrp01A","Noe24qw2ks","bF6eod5Gvf","Nsiff2A1zJ","j9kHMeSvPp","pRsWfj4Fpp","apS25hmuAe","DpFCA1CohY","IWmyXbctLI","eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp"],"result":"⪩⨒∯3312022","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1244","layer":2},{"info":"number node, value=4548","layer":2},{"info":"compute binary expreesion, left_input=1244, right_input=4548, op_id = gub5Cegaqo binary_op_definition= 'a⩁⩘b = { ((b⪮%⊝b)⪮%⊝(⋗⩬⋾a)) }', output=19140","layer":1},{"info":"number node, value=1432","layer":2},{"info":"compute unary expreesion, input=1432, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":1},{"info":"compute binary expreesion, left_input=19140, right_input=-21, op_id = SR5kFfdi6N binary_op_definition= 'a↱b = { ((≸a)⊴((b∊∟⩊b)⨐(a+⪬∐830))) , if (a==35 or (b∀⊥⇻)>46) ; ((≅≯⇸b)→⨶⪴((∡b)⪭(b⨑≵⋬499))) , else }', output=15754","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯103130⩁⩘⪩⨒∯1013010↱(↯⪼⪩⨒∯112120)=⪩⨒∯3312022","reverse_text":"⪩⨒∯3312022=⪩⨒∯103130⩁⩘⪩⨒∯1013010↱(↯⪼⪩⨒∯112120)","cot":[{"info":"⪩⨒∯103130⩁⩘⪩⨒∯1013010=⪩⨒∯10223010","layer":1},{"info":"↯⪼⪩⨒∯112120=⪩⨒∯-111","layer":1},{"info":"⪩⨒∯10223010↱⪩⨒∯-111=⪩⨒∯3312022","layer":0}]}
{"id":927,"expression_no_base_symbol":"($3217$⪒⊣⊆$1949$)⇂≾⫗($1106$⨜⨶$4374$)","expression":"(⪩⨒∯302101⪒⊣⊆⪩⨒∯132131)⇂≾⫗(⪩⨒∯101102⨜⨶⪩⨒∯1010112)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":99,"operation_count":3,"complexity_ratio":33.0,"tree":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"binary","operator":"⪒⊣⊆","left_expr":{"type":"numeric_atoms","value":3217,"base":4},"right_expr":{"type":"numeric_atoms","value":1949,"base":4}},"right_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":1106,"base":4},"right_expr":{"type":"numeric_atoms","value":4374,"base":4}}},"used_operators":["aBQ6xLxuTc","eRqsBgTDFp","HiPekx5b7W"],"dependent_operators":["g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U","sdazOOVcIp","W4YGzv6Whe","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"⪩⨒∯-22132","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3217","layer":2},{"info":"number node, value=1949","layer":2},{"info":"compute binary expreesion, left_input=3217, right_input=1949, op_id = eRqsBgTDFp binary_op_definition= 'a⪒⊣⊆b = { (b⪨≂a) , if a<=17 ; (a+a) , else }', output=6434","layer":1},{"info":"number node, value=1106","layer":2},{"info":"number node, value=4374","layer":2},{"info":"compute binary expreesion, left_input=1106, right_input=4374, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-8492","layer":1},{"info":"compute binary expreesion, left_input=6434, right_input=-8492, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-670","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯302101⪒⊣⊆⪩⨒∯132131)⇂≾⫗(⪩⨒∯101102⨜⨶⪩⨒∯1010112)=⪩⨒∯-22132","reverse_text":"⪩⨒∯-22132=(⪩⨒∯302101⪒⊣⊆⪩⨒∯132131)⇂≾⫗(⪩⨒∯101102⨜⨶⪩⨒∯1010112)","cot":[{"info":"⪩⨒∯302101⪒⊣⊆⪩⨒∯132131=⪩⨒∯1210202","layer":1},{"info":"⪩⨒∯101102⨜⨶⪩⨒∯1010112=⪩⨒∯-2010230","layer":1},{"info":"⪩⨒∯1210202⇂≾⫗⪩⨒∯-2010230=⪩⨒∯-22132","layer":0}]}
{"id":928,"expression_no_base_symbol":"($1652$≑≱⪘)↰","expression":"(⪩⨒∯121310≑≱⪘)↰","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":110,"operation_count":2,"complexity_ratio":55.0,"tree":{"type":"unary","operator":"↰","unary_expr":{"type":"unary","operator":"≑≱⪘","unary_expr":{"type":"numeric_atoms","value":1652,"base":4}}},"used_operators":["bl5wxAcryP","tGSeddj7UK"],"dependent_operators":["nCS4ZIUYfx","Z2TMIBDE3Q","9FxExcQeMw","9bazX3JMtO","RygbFNSyEJ","VwlE7vj6HS","v0DYgG9ikt","eRqsBgTDFp","6MpZysEj17","8w2t5hMYqp","Ph9nP6C5qx","DmTXOeWf9t","8HhzD0ZcuI","BiWNJpBvwn"],"result":"⪩⨒∯21210300","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1652","layer":2},{"info":"compute unary expreesion, input=1652, op_id = tGSeddj7UK, unary_op_definition = 'a≑≱⪘ = { ((⊄⩳↩(6≧⫂∧a))⩍⋽⫝̸((a⊲⩕⊾a)≦↸(a⋆⋳))) , if (a↹⊜255)>=30 or (a↯⫤)>122 ; ((a⩷∴(a⪒⊣⊆a))⨽(a⊬⫿⊭)) , else }', output=39317","layer":1},{"info":"compute unary expreesion, input=39317, op_id = bl5wxAcryP, unary_op_definition = 'a↰ = { ((a⨳⩥⨓101)⩤) }', output=39216","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯121310≑≱⪘)↰=⪩⨒∯21210300","reverse_text":"⪩⨒∯21210300=(⪩⨒∯121310≑≱⪘)↰","cot":[{"info":"⪩⨒∯121310≑≱⪘=⪩⨒∯21212111","layer":1},{"info":"⪩⨒∯21212111↰=⪩⨒∯21210300","layer":0}]}
{"id":929,"expression_no_base_symbol":"($1242$⨳⩥⨓$3759$)↢(⨴⫝$4215$)","expression":"(⪩⨒∯103122⨳⩥⨓⪩⨒∯322233)↢(⨴⫝⪩⨒∯1001313)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1834,"operation_count":3,"complexity_ratio":611.3333333333334,"tree":{"type":"binary","operator":"↢","left_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":1242,"base":4},"right_expr":{"type":"numeric_atoms","value":3759,"base":4}},"right_expr":{"type":"unary","operator":"⨴⫝","unary_expr":{"type":"numeric_atoms","value":4215,"base":4}}},"used_operators":["WR6HLWljOP","nCS4ZIUYfx","SVb2v531z1"],"dependent_operators":["eLAdDNolq6","g55IO6H4Gj","7j4O788W3g","12rbrZMWeM","f6k1SAg4EE","i8ToyICDmI","COABgblf1C","W4YGzv6Whe","rysDP5nf3Z","oDCm7WA9JY","XnXgA4xnOs","ocnLzx9CaJ","3sJ7IOPOlU","9cloC0Ngie","SWo3A1KBJH","jWTQ2TZYIH","pRsWfj4Fpp","DyGG3AbaNP","5obUd6DV38","8HhzD0ZcuI","YbUVn0Rbpy","AdZkA7nFnk","SIgE0bArFf"],"result":"⪩⨒∯133301","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1242","layer":2},{"info":"number node, value=3759","layer":2},{"info":"compute binary expreesion, left_input=1242, right_input=3759, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=2517","layer":1},{"info":"number node, value=4215","layer":2},{"info":"compute unary expreesion, input=4215, op_id = SVb2v531z1, unary_op_definition = '⨴⫝a = { ((⪨⨬(⇋↷a))≬⇓((a⋅⇍a)⨑≵⋬(∡178))) , if (a⪇≇⋚963)!=62 ; (((541⋛107)⩼⇪↪(⪭⩑⪱a))⋻⩜⩜((a⊕∕a)∼(459⨽6))) , else }', output=2828198","layer":1},{"info":"compute binary expreesion, left_input=2517, right_input=2828198, op_id = WR6HLWljOP binary_op_definition= 'a↢b = { ((a∲⫓a)⪒(≤/a)) , if (a⊭↱114)<=535 ; ((a⋳⪒749)↺(b⨸⪁a)) , else }', output=2033","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯103122⨳⩥⨓⪩⨒∯322233)↢(⨴⫝⪩⨒∯1001313)=⪩⨒∯133301","reverse_text":"⪩⨒∯133301=(⪩⨒∯103122⨳⩥⨓⪩⨒∯322233)↢(⨴⫝⪩⨒∯1001313)","cot":[{"info":"⪩⨒∯103122⨳⩥⨓⪩⨒∯322233=⪩⨒∯213111","layer":1},{"info":"⨴⫝⪩⨒∯1001313=⪩⨒∯22302132212","layer":1},{"info":"⪩⨒∯213111↢⪩⨒∯22302132212=⪩⨒∯133301","layer":0}]}
{"id":930,"expression_no_base_symbol":"$2987$⨔≚≋$1899$↺$1458$∊∟⩊$3579$","expression":"⪩⨒∯232223⨔≚≋⪩⨒∯131223↺⪩⨒∯112302∊∟⩊⪩⨒∯313323","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":53,"operation_count":3,"complexity_ratio":17.666666666666668,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"⨔≚≋","left_expr":{"type":"numeric_atoms","value":2987,"base":4},"right_expr":{"type":"numeric_atoms","value":1899,"base":4}},"right_expr":{"type":"binary","operator":"∊∟⩊","left_expr":{"type":"numeric_atoms","value":1458,"base":4},"right_expr":{"type":"numeric_atoms","value":3579,"base":4}}},"used_operators":["7j4O788W3g","Z57zeUYC9z","ddLRYrp01A"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","zR4jO40bMj","QvoQhV0rrE","RHru8klgy8","3tVxb0NHM4","f6k1SAg4EE","IWmyXbctLI","59igzFyhWz","A8NUZmVepG","3sJ7IOPOlU"],"result":"⪩⨒∯313323","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2987","layer":2},{"info":"number node, value=1899","layer":2},{"info":"compute binary expreesion, left_input=2987, right_input=1899, op_id = Z57zeUYC9z binary_op_definition= 'a⨔≚≋b = { ((⊈(b⪎↠b))⪶≀⋏((29⪒b)∠⫱(a⪮%⊝521))) }', output=9872","layer":1},{"info":"number node, value=1458","layer":2},{"info":"number node, value=3579","layer":2},{"info":"compute binary expreesion, left_input=1458, right_input=3579, op_id = ddLRYrp01A binary_op_definition= 'a∊∟⩊b = { b , if (b∵≐)>=166 or (a⪇≇⋚4)==505 ; (↥a) , else }', output=3579","layer":1},{"info":"compute binary expreesion, left_input=9872, right_input=3579, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=3579","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯232223⨔≚≋⪩⨒∯131223↺⪩⨒∯112302∊∟⩊⪩⨒∯313323=⪩⨒∯313323","reverse_text":"⪩⨒∯313323=⪩⨒∯232223⨔≚≋⪩⨒∯131223↺⪩⨒∯112302∊∟⩊⪩⨒∯313323","cot":[{"info":"⪩⨒∯232223⨔≚≋⪩⨒∯131223=⪩⨒∯2122100","layer":1},{"info":"⪩⨒∯112302∊∟⩊⪩⨒∯313323=⪩⨒∯313323","layer":1},{"info":"⪩⨒∯2122100↺⪩⨒∯313323=⪩⨒∯313323","layer":0}]}
{"id":931,"expression_no_base_symbol":"↣≠⋷$4242$⨜⨶$1308$","expression":"↣≠⋷⪩⨒∯1002102⨜⨶⪩⨒∯110130","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":28,"operation_count":2,"complexity_ratio":14.0,"tree":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"binary","operator":"⨜⨶","left_expr":{"type":"numeric_atoms","value":4242,"base":4},"right_expr":{"type":"numeric_atoms","value":1308,"base":4}}},"used_operators":["Asc51vEJeQ","HiPekx5b7W"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","N41Kp7NANJ","BjRHVeLaeN","tifHPKVTfV","12rbrZMWeM","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=4242","layer":2},{"info":"number node, value=1308","layer":2},{"info":"compute binary expreesion, left_input=4242, right_input=1308, op_id = HiPekx5b7W binary_op_definition= 'a⨜⨶b = { (((107⋳⪒a)⨳⩥⨓(b⋳⪒a))⫩⊇) , if (b>512 or (b⊦⊿)==395) ; (((b⨳⩥⨓b)⇼⇔∾(a⨸⪁b))⫡⨏((b∲⫓b)≋⫹)) , else }', output=-2360","layer":1},{"info":"compute unary expreesion, input=-2360, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"↣≠⋷⪩⨒∯1002102⨜⨶⪩⨒∯110130=NaN","reverse_text":"NaN=↣≠⋷⪩⨒∯1002102⨜⨶⪩⨒∯110130","cot":[{"info":"⪩⨒∯1002102⨜⨶⪩⨒∯110130=⪩⨒∯-210320","layer":1},{"info":"↣≠⋷⪩⨒∯-210320=NaN","layer":0}]}
{"id":932,"expression_no_base_symbol":"($1117$↯⫤)⩁⩘($5875$≝⊰⇂)","expression":"(⪩⨒∯101131↯⫤)⩁⩘(⪩⨒∯1123303≝⊰⇂)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1460,"operation_count":3,"complexity_ratio":486.6666666666667,"tree":{"type":"binary","operator":"⩁⩘","left_expr":{"type":"unary","operator":"↯⫤","unary_expr":{"type":"numeric_atoms","value":1117,"base":4}},"right_expr":{"type":"unary","operator":"≝⊰⇂","unary_expr":{"type":"numeric_atoms","value":5875,"base":4}}},"used_operators":["gub5Cegaqo","VwlE7vj6HS","htSmYCowi5"],"dependent_operators":["DpFCA1CohY","IWmyXbctLI","W4YGzv6Whe","23Mk6UjR3U","tifHPKVTfV","glklzrTFfD","eH2TOUuTDT","t8gj7n24qd","2DDjHMKMc0","Ph9nP6C5qx","g55IO6H4Gj","nCS4ZIUYfx","9FxExcQeMw","DlLNRPXxWL"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1117","layer":2},{"info":"compute unary expreesion, input=1117, op_id = VwlE7vj6HS, unary_op_definition = 'a↯⫤ = { (((-a)⋝⋈⪟(a⨳⩥⨓a))⨸⪁((a⨁⊸⫻)⇼⇔∾(a+a))) , if (a⋷221)!=277 ; (((300⪐)⨁⊸⫻)⇼⇔∾(a≧⫂∧(26≧⫂∧87))) , else }', output=0","layer":1},{"info":"number node, value=5875","layer":2},{"info":"compute unary expreesion, input=5875, op_id = htSmYCowi5, unary_op_definition = 'a≝⊰⇂ = { (a⩷∴51) , if a<491 ; (⫛⫱⨽a) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=0, op_id = gub5Cegaqo binary_op_definition= 'a⩁⩘b = { ((b⪮%⊝b)⪮%⊝(⋗⩬⋾a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101131↯⫤)⩁⩘(⪩⨒∯1123303≝⊰⇂)=NaN","reverse_text":"NaN=(⪩⨒∯101131↯⫤)⩁⩘(⪩⨒∯1123303≝⊰⇂)","cot":[{"info":"⪩⨒∯101131↯⫤=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1123303≝⊰⇂=⪩⨒∯0","layer":1},{"info":"⪩⨒∯0⩁⩘⪩⨒∯0=NaN","layer":0}]}
{"id":933,"expression_no_base_symbol":"$2114$⩦$1449$↼⊘⨖($1564$≫≃)","expression":"⪩⨒∯201002⩦⪩⨒∯112221↼⊘⨖(⪩⨒∯120130≫≃)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":28,"operation_count":3,"complexity_ratio":9.333333333333334,"tree":{"type":"binary","operator":"↼⊘⨖","left_expr":{"type":"binary","operator":"⩦","left_expr":{"type":"numeric_atoms","value":2114,"base":4},"right_expr":{"type":"numeric_atoms","value":1449,"base":4}},"right_expr":{"type":"unary","operator":"≫≃","unary_expr":{"type":"numeric_atoms","value":1564,"base":4}}},"used_operators":["bPywburJMS","0kmYd0q39Y","X99M06cbEe"],"dependent_operators":["9FxExcQeMw","P8v4zCKN1o","t8gj7n24qd","N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q","2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A"],"result":"⪩⨒∯2022010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2114","layer":2},{"info":"number node, value=1449","layer":2},{"info":"compute binary expreesion, left_input=2114, right_input=1449, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=4228","layer":1},{"info":"number node, value=1564","layer":2},{"info":"compute unary expreesion, input=1564, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=4529","layer":1},{"info":"compute binary expreesion, left_input=4228, right_input=4529, op_id = bPywburJMS binary_op_definition= 'a↼⊘⨖b = { (-a) , if (∥⊫b)==149 ; (b⩷∴95) , else }', output=8836","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯201002⩦⪩⨒∯112221↼⊘⨖(⪩⨒∯120130≫≃)=⪩⨒∯2022010","reverse_text":"⪩⨒∯2022010=⪩⨒∯201002⩦⪩⨒∯112221↼⊘⨖(⪩⨒∯120130≫≃)","cot":[{"info":"⪩⨒∯201002⩦⪩⨒∯112221=⪩⨒∯1002010","layer":1},{"info":"⪩⨒∯120130≫≃=⪩⨒∯1012301","layer":1},{"info":"⪩⨒∯1002010↼⊘⨖⪩⨒∯1012301=⪩⨒∯2022010","layer":0}]}
{"id":934,"expression_no_base_symbol":"($3015$⊱⇼⊻$1700$)⨽∌(⊗$3392$)","expression":"(⪩⨒∯233013⊱⇼⊻⪩⨒∯122210)⨽∌(⊗⪩⨒∯311000)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":156,"operation_count":3,"complexity_ratio":52.0,"tree":{"type":"binary","operator":"⨽∌","left_expr":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"numeric_atoms","value":3015,"base":4},"right_expr":{"type":"numeric_atoms","value":1700,"base":4}},"right_expr":{"type":"unary","operator":"⊗","unary_expr":{"type":"numeric_atoms","value":3392,"base":4}}},"used_operators":["9samAPKr6k","FyVja0WsTP","RhiyfpczSx"],"dependent_operators":["YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu","W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","nhYeJWJD5X","sJAwomhLZr","Z5m6OM72h2","HrjLwUk87U"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3015","layer":2},{"info":"number node, value=1700","layer":2},{"info":"compute binary expreesion, left_input=3015, right_input=1700, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=434","layer":1},{"info":"number node, value=3392","layer":2},{"info":"compute unary expreesion, input=3392, op_id = RhiyfpczSx, unary_op_definition = '⊗a = { (64∇⊂⋱a) , if (a⪚13)>=164 ; (a∘(a⩠)) , else }', output=-6784","layer":1},{"info":"compute binary expreesion, left_input=434, right_input=-6784, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯233013⊱⇼⊻⪩⨒∯122210)⨽∌(⊗⪩⨒∯311000)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯233013⊱⇼⊻⪩⨒∯122210)⨽∌(⊗⪩⨒∯311000)","cot":[{"info":"⪩⨒∯233013⊱⇼⊻⪩⨒∯122210=⪩⨒∯12302","layer":1},{"info":"⊗⪩⨒∯311000=⪩⨒∯-1222000","layer":1},{"info":"⪩⨒∯12302⨽∌⪩⨒∯-1222000=⪩⨒∯0","layer":0}]}
{"id":935,"expression_no_base_symbol":"∤$1671$⇴$5768$","expression":"∤⪩⨒∯122013⇴⪩⨒∯1122020","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":22,"operation_count":2,"complexity_ratio":11.0,"tree":{"type":"unary","operator":"∤","unary_expr":{"type":"binary","operator":"⇴","left_expr":{"type":"numeric_atoms","value":1671,"base":4},"right_expr":{"type":"numeric_atoms","value":5768,"base":4}}},"used_operators":["k2HlF1dBQh","4JB6nKBMSY"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","tifHPKVTfV","8w2t5hMYqp","sdazOOVcIp","NTOWxs364D","COABgblf1C"],"result":"⪩⨒∯21","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1671","layer":2},{"info":"number node, value=5768","layer":2},{"info":"compute binary expreesion, left_input=1671, right_input=5768, op_id = 4JB6nKBMSY binary_op_definition= 'a⇴b = { ((185⊭↱a)⪨≂(b⩚⊴⇥a)) }', output=21176","layer":1},{"info":"compute unary expreesion, input=21176, op_id = k2HlF1dBQh, unary_op_definition = '∤a = { (((a⇼⇔∾a)+(a-a))-(⊄⩳↩3)) }', output=9","layer":0}],"base":4,"result_base":4,"text":"∤⪩⨒∯122013⇴⪩⨒∯1122020=⪩⨒∯21","reverse_text":"⪩⨒∯21=∤⪩⨒∯122013⇴⪩⨒∯1122020","cot":[{"info":"⪩⨒∯122013⇴⪩⨒∯1122020=⪩⨒∯11022320","layer":1},{"info":"∤⪩⨒∯11022320=⪩⨒∯21","layer":0}]}
{"id":936,"expression_no_base_symbol":"≪$2428$⪟⇏$3631$","expression":"≪⪩⨒∯211330⪟⇏⪩⨒∯320233","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":69,"operation_count":2,"complexity_ratio":34.5,"tree":{"type":"unary","operator":"≪","unary_expr":{"type":"binary","operator":"⪟⇏","left_expr":{"type":"numeric_atoms","value":2428,"base":4},"right_expr":{"type":"numeric_atoms","value":3631,"base":4}}},"used_operators":["Qtd6bqUJcN","GODebY97qR"],"dependent_operators":["3nqY3DE9mg","09Ly4LVMIf","wEfv7U73WA","tifHPKVTfV","ruOEQAzv1W","iuk5sVOGFA","gx7XJ7hdpj","XnXgA4xnOs","wEfv7U73WA","2DQ55sFlQl","f6k1SAg4EE","oacrs7FA3X"],"result":"⪩⨒∯32101","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2428","layer":2},{"info":"number node, value=3631","layer":2},{"info":"compute binary expreesion, left_input=2428, right_input=3631, op_id = GODebY97qR binary_op_definition= 'a⪟⇏b = { ((b⨑≵⋬b)⫸⇳(440⪒a)) , if (b⇐≅)<189 ; ((219⨑≵⋬a)⪘⫢(b⨵⪆b)) , else }', output=-1","layer":1},{"info":"compute unary expreesion, input=-1, op_id = Qtd6bqUJcN, unary_op_definition = '≪a = { ((431⫃⨇a)⪣⫩) , if (a⊍)!=211 or (a⇐≅)==294 ; (↔(a⇼⇔∾a)) , else }', output=913","layer":0}],"base":4,"result_base":4,"text":"≪⪩⨒∯211330⪟⇏⪩⨒∯320233=⪩⨒∯32101","reverse_text":"⪩⨒∯32101=≪⪩⨒∯211330⪟⇏⪩⨒∯320233","cot":[{"info":"⪩⨒∯211330⪟⇏⪩⨒∯320233=⪩⨒∯-1","layer":1},{"info":"≪⪩⨒∯-1=⪩⨒∯32101","layer":0}]}
{"id":937,"expression_no_base_symbol":"($1148$⪘⫢$1182$)⪘⫢$1395$⫘$5158$","expression":"(⪩⨒∯101330⪘⫢⪩⨒∯102132)⪘⫢⪩⨒∯111303⫘⪩⨒∯1100212","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1642,"operation_count":3,"complexity_ratio":547.3333333333334,"tree":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1148,"base":4},"right_expr":{"type":"numeric_atoms","value":1182,"base":4}},"right_expr":{"type":"binary","operator":"⫘","left_expr":{"type":"numeric_atoms","value":1395,"base":4},"right_expr":{"type":"numeric_atoms","value":5158,"base":4}}},"used_operators":["oacrs7FA3X","48vC8HMD2b"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","OwUj7dcsQK","7j4O788W3g","tfWHHpNKUN","3ViojmjbAp","dfKe02y8D2","tcjXMdvYtA","D4vGDi5EA2","86A5ENbKR9","X99M06cbEe"],"result":"⪩⨒∯1001330","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1148","layer":2},{"info":"number node, value=1182","layer":2},{"info":"compute binary expreesion, left_input=1148, right_input=1182, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=2172","layer":1},{"info":"number node, value=1395","layer":2},{"info":"number node, value=5158","layer":2},{"info":"compute binary expreesion, left_input=1395, right_input=5158, op_id = 48vC8HMD2b binary_op_definition= 'a⫘b = { ((≘(b⨓a))≫≃) , if ((⇖a)!=319 or (a↺926)<190) ; ((∓a)⫚↹⊑(⪸(a≦≮≮))) , else }', output=1644925","layer":1},{"info":"compute binary expreesion, left_input=2172, right_input=1644925, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=4220","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101330⪘⫢⪩⨒∯102132)⪘⫢⪩⨒∯111303⫘⪩⨒∯1100212=⪩⨒∯1001330","reverse_text":"⪩⨒∯1001330=(⪩⨒∯101330⪘⫢⪩⨒∯102132)⪘⫢⪩⨒∯111303⫘⪩⨒∯1100212","cot":[{"info":"⪩⨒∯101330⪘⫢⪩⨒∯102132=⪩⨒∯201330","layer":1},{"info":"⪩⨒∯111303⫘⪩⨒∯1100212=⪩⨒∯12101211331","layer":1},{"info":"⪩⨒∯201330⪘⫢⪩⨒∯12101211331=⪩⨒∯1001330","layer":0}]}
{"id":938,"expression_no_base_symbol":"$1820$⪃⊛⇣$3354$⪮%⊝(⇈$1081$)","expression":"⪩⨒∯130130⪃⊛⇣⪩⨒∯310122⪮%⊝(⇈⪩⨒∯100321)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1598,"operation_count":3,"complexity_ratio":532.6666666666666,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"binary","operator":"⪃⊛⇣","left_expr":{"type":"numeric_atoms","value":1820,"base":4},"right_expr":{"type":"numeric_atoms","value":3354,"base":4}},"right_expr":{"type":"unary","operator":"⇈","unary_expr":{"type":"numeric_atoms","value":1081,"base":4}}},"used_operators":["IWmyXbctLI","rrgAzCduG9","SLLxy00UIr"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","Ez1Nq5fNfI","AHs5Up7iyr","2DDjHMKMc0","7IPrd9c3lf","8cLx32lpNA","Qy55tPpLXF","DZ8iAZOCBD","tifHPKVTfV","Tw270M8GLb","8HhzD0ZcuI","jCPkEVoL5K","ZcwmYACASQ"],"result":"⪩⨒∯223200","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1820","layer":2},{"info":"number node, value=3354","layer":2},{"info":"compute binary expreesion, left_input=1820, right_input=3354, op_id = rrgAzCduG9 binary_op_definition= 'a⪃⊛⇣b = { ((b∌b)⊵↤) , if b==348 ; ((a≹⇙⪍a)⪬(a⋝⋈⪟a)) , else }', output=1234","layer":1},{"info":"number node, value=1081","layer":2},{"info":"compute unary expreesion, input=1081, op_id = SLLxy00UIr, unary_op_definition = '⇈a = { (((⨰⫟⨤60)⋥≓≎(a⫍⨯↯))⇻⋧≁((a⇼⇔∾a)⨽(323⊉≛↸a))) }', output=-447","layer":1},{"info":"compute binary expreesion, left_input=1234, right_input=-447, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=2784","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯130130⪃⊛⇣⪩⨒∯310122⪮%⊝(⇈⪩⨒∯100321)=⪩⨒∯223200","reverse_text":"⪩⨒∯223200=⪩⨒∯130130⪃⊛⇣⪩⨒∯310122⪮%⊝(⇈⪩⨒∯100321)","cot":[{"info":"⪩⨒∯130130⪃⊛⇣⪩⨒∯310122=⪩⨒∯103102","layer":1},{"info":"⇈⪩⨒∯100321=⪩⨒∯-12333","layer":1},{"info":"⪩⨒∯103102⪮%⊝⪩⨒∯-12333=⪩⨒∯223200","layer":0}]}
{"id":939,"expression_no_base_symbol":"⊊≼∋($2496$≓∲$4881$)","expression":"⊊≼∋(⪩⨒∯213000≓∲⪩⨒∯1030101)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":25820,"operation_count":2,"complexity_ratio":12910.0,"tree":{"type":"unary","operator":"⊊≼∋","unary_expr":{"type":"binary","operator":"≓∲","left_expr":{"type":"numeric_atoms","value":2496,"base":4},"right_expr":{"type":"numeric_atoms","value":4881,"base":4}}},"used_operators":["FWz7pXsQhA","s1XTVnmDOJ"],"dependent_operators":["B5M0gjZbta","jCPkEVoL5K","HiPekx5b7W","rysDP5nf3Z","9ICcGScMcE","XhwjNDsVaA","3mBM5G4a3l","5twsqlHp2o","nCS4ZIUYfx","YSKBFp38Pu"],"result":"⪩⨒∯-12333","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2496","layer":2},{"info":"number node, value=4881","layer":2},{"info":"compute binary expreesion, left_input=2496, right_input=4881, op_id = s1XTVnmDOJ binary_op_definition= 'a≓∲b = { (≦∁(a⨜⨶(a⨳⩥⨓a))) , if ((⋃b)>775 or (a⊢476)>56) ; (((a⨜⨶b)⇤(77/135))-a) , else }', output=25743","layer":1},{"info":"compute unary expreesion, input=25743, op_id = FWz7pXsQhA, unary_op_definition = '⊊≼∋a = { (a↬a) , if a<=50 ; (a⇻⋧≁a) , else }', output=-447","layer":0}],"base":4,"result_base":4,"text":"⊊≼∋(⪩⨒∯213000≓∲⪩⨒∯1030101)=⪩⨒∯-12333","reverse_text":"⪩⨒∯-12333=⊊≼∋(⪩⨒∯213000≓∲⪩⨒∯1030101)","cot":[{"info":"⪩⨒∯213000≓∲⪩⨒∯1030101=⪩⨒∯12102033","layer":1},{"info":"⊊≼∋⪩⨒∯12102033=⪩⨒∯-12333","layer":0}]}
{"id":940,"expression_no_base_symbol":"(≔$1961$)⨸($6397$⫸⊐$1484$)","expression":"(≔⪩⨒∯132221)⨸(⪩⨒∯1203331⫸⊐⪩⨒∯113030)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":53789,"operation_count":3,"complexity_ratio":17929.666666666668,"tree":{"type":"binary","operator":"⨸","left_expr":{"type":"unary","operator":"≔","unary_expr":{"type":"numeric_atoms","value":1961,"base":4}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":6397,"base":4},"right_expr":{"type":"numeric_atoms","value":1484,"base":4}}},"used_operators":["KmoU8R5UQR","8FLs4eVsLt","mqXw5SEYmG"],"dependent_operators":["ukq6epAj5P","eRqsBgTDFp","JL8yIekQnl","uPb5QRN0te","VwlE7vj6HS","3mBM5G4a3l","8HhzD0ZcuI","BUOGQAYlQx","AYdpE9sXAk","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"⪩⨒∯10303121022","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1961","layer":2},{"info":"compute unary expreesion, input=1961, op_id = 8FLs4eVsLt, unary_op_definition = '≔a = { (⋃(⋂a)) , if (⨂⪏⇭a)<=427 or (a↫)>=16 ; ((a⨽194)↯⫤) , else }', output=-53614","layer":1},{"info":"number node, value=6397","layer":2},{"info":"number node, value=1484","layer":2},{"info":"compute binary expreesion, left_input=6397, right_input=1484, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=5811","layer":1},{"info":"compute binary expreesion, left_input=-53614, right_input=5811, op_id = KmoU8R5UQR binary_op_definition= 'a⨸b = { ((a⋫)⪒⊣⊆(b∋158)) }', output=1259082","layer":0}],"base":4,"result_base":4,"text":"(≔⪩⨒∯132221)⨸(⪩⨒∯1203331⫸⊐⪩⨒∯113030)=⪩⨒∯10303121022","reverse_text":"⪩⨒∯10303121022=(≔⪩⨒∯132221)⨸(⪩⨒∯1203331⫸⊐⪩⨒∯113030)","cot":[{"info":"≔⪩⨒∯132221=⪩⨒∯-31011232","layer":1},{"info":"⪩⨒∯1203331⫸⊐⪩⨒∯113030=⪩⨒∯1122303","layer":1},{"info":"⪩⨒∯-31011232⨸⪩⨒∯1122303=⪩⨒∯10303121022","layer":0}]}
{"id":941,"expression_no_base_symbol":"(⊖∈$1764$)⇪⋭","expression":"(⊖∈⪩⨒∯123210)⇪⋭","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":77,"operation_count":2,"complexity_ratio":38.5,"tree":{"type":"unary","operator":"⇪⋭","unary_expr":{"type":"unary","operator":"⊖∈","unary_expr":{"type":"numeric_atoms","value":1764,"base":4}}},"used_operators":["Z8Yg6dlDSp","YFxL8Sc2Zy"],"dependent_operators":["T2fj7uvVaJ","5KTvxBwnZo","inkyxCbjAn","zVYPLywUTj","sdazOOVcIp","ancx8kZcWl","YSKBFp38Pu"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1764","layer":2},{"info":"compute unary expreesion, input=1764, op_id = YFxL8Sc2Zy, unary_op_definition = '⊖∈a = { a , if (a⨝⩣∺)>=369 ; ((a⊪)⪨≂(a⇤a)) , else }', output=29686","layer":1},{"info":"compute unary expreesion, input=29686, op_id = Z8Yg6dlDSp, unary_op_definition = 'a⇪⋭ = { ((a≒∊a)⋓(⇁⨣⪵a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⊖∈⪩⨒∯123210)⇪⋭=NaN","reverse_text":"NaN=(⊖∈⪩⨒∯123210)⇪⋭","cot":[{"info":"⊖∈⪩⨒∯123210=⪩⨒∯13033312","layer":1},{"info":"⪩⨒∯13033312⇪⋭=NaN","layer":0}]}
{"id":942,"expression_no_base_symbol":"($1002$↡⊰⫅$4763$)⨿(↞≼$1109$)","expression":"(⪩⨒∯33222↡⊰⫅⪩⨒∯1022123)⨿(↞≼⪩⨒∯101111)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":66934,"operation_count":3,"complexity_ratio":22311.333333333332,"tree":{"type":"binary","operator":"⨿","left_expr":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"numeric_atoms","value":1002,"base":4},"right_expr":{"type":"numeric_atoms","value":4763,"base":4}},"right_expr":{"type":"unary","operator":"↞≼","unary_expr":{"type":"numeric_atoms","value":1109,"base":4}}},"used_operators":["abYXlopdE0","VCtxkLNOzz","DE7zCoGJt9"],"dependent_operators":["gJLn6v0xnP","KFSx94NKJn","jWTQ2TZYIH","yXekIHxTD4","KYD54nUTWz","i8ToyICDmI","PoHhknlbAi","Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn","W4YGzv6Whe","D4vGDi5EA2","23Mk6UjR3U","BjRHVeLaeN","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","u6S6b8DprG"],"result":"⪩⨒∯-10333","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1002","layer":2},{"info":"number node, value=4763","layer":2},{"info":"compute binary expreesion, left_input=1002, right_input=4763, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=9526","layer":1},{"info":"number node, value=1109","layer":2},{"info":"compute unary expreesion, input=1109, op_id = DE7zCoGJt9, unary_op_definition = '↞≼a = { (↽≂(197⨰(a⨸⪁a))) , if (a⨸⪁373)!=224 ; (((591⋷a)≧⫂∧(a+a))⨸⪁((a⫩⊇)≦≮≮)) , else }', output=8458","layer":1},{"info":"compute binary expreesion, left_input=9526, right_input=8458, op_id = abYXlopdE0 binary_op_definition= 'a⨿b = { (((a∲⫓409)≬⇓(a⩒⫫a))∓⋝((146⫥∨⫟b)≥⨤⩑(219⨥⫆b))) }', output=-319","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯33222↡⊰⫅⪩⨒∯1022123)⨿(↞≼⪩⨒∯101111)=⪩⨒∯-10333","reverse_text":"⪩⨒∯-10333=(⪩⨒∯33222↡⊰⫅⪩⨒∯1022123)⨿(↞≼⪩⨒∯101111)","cot":[{"info":"⪩⨒∯33222↡⊰⫅⪩⨒∯1022123=⪩⨒∯2110312","layer":1},{"info":"↞≼⪩⨒∯101111=⪩⨒∯2010022","layer":1},{"info":"⪩⨒∯2110312⨿⪩⨒∯2010022=⪩⨒∯-10333","layer":0}]}
{"id":943,"expression_no_base_symbol":"($6166$⇮⋭$2306$)⊝⪿⪼(⨩∲⋌$2585$)","expression":"(⪩⨒∯1200112⇮⋭⪩⨒∯210002)⊝⪿⪼(⨩∲⋌⪩⨒∯220121)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":75,"operation_count":3,"complexity_ratio":25.0,"tree":{"type":"binary","operator":"⊝⪿⪼","left_expr":{"type":"binary","operator":"⇮⋭","left_expr":{"type":"numeric_atoms","value":6166,"base":4},"right_expr":{"type":"numeric_atoms","value":2306,"base":4}},"right_expr":{"type":"unary","operator":"⨩∲⋌","unary_expr":{"type":"numeric_atoms","value":2585,"base":4}}},"used_operators":["3Oe9XWJUTD","vkpjKywKVM","aSik1wnThz"],"dependent_operators":["NTOWxs364D","Qy55tPpLXF","8w2t5hMYqp","t8gj7n24qd","eewbuw0ToL","QMFrweE19q","nhYeJWJD5X","U6pG0PXrV3","tifHPKVTfV","bJkvcejdHO","40aOVDgCDB","YbVcJGFEVW","rysDP5nf3Z","Ph9nP6C5qx","Z2TMIBDE3Q"],"result":"⪩⨒∯2122313","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=6166","layer":2},{"info":"number node, value=2306","layer":2},{"info":"compute binary expreesion, left_input=6166, right_input=2306, op_id = vkpjKywKVM binary_op_definition= 'a⇮⋭b = { (((⊖b)⊢)≎⊠⪸((a≃b)⇼⇔∾(47∇⊂⋱106))) }', output=-473","layer":1},{"info":"number node, value=2585","layer":2},{"info":"compute unary expreesion, input=2585, op_id = aSik1wnThz, unary_op_definition = '⨩∲⋌a = { ((759≧⫂∧(236-a))⩤) }', output=-3108","layer":1},{"info":"compute binary expreesion, left_input=-473, right_input=-3108, op_id = 3Oe9XWJUTD binary_op_definition= 'a⊝⪿⪼b = { ((⊄⩳↩(480⩚⊴⇥a))⫡⨏((a⨰b)⋥≓≎(-b))) }', output=9911","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1200112⇮⋭⪩⨒∯210002)⊝⪿⪼(⨩∲⋌⪩⨒∯220121)=⪩⨒∯2122313","reverse_text":"⪩⨒∯2122313=(⪩⨒∯1200112⇮⋭⪩⨒∯210002)⊝⪿⪼(⨩∲⋌⪩⨒∯220121)","cot":[{"info":"⪩⨒∯1200112⇮⋭⪩⨒∯210002=⪩⨒∯-13121","layer":1},{"info":"⨩∲⋌⪩⨒∯220121=⪩⨒∯-300210","layer":1},{"info":"⪩⨒∯-13121⊝⪿⪼⪩⨒∯-300210=⪩⨒∯2122313","layer":0}]}
{"id":944,"expression_no_base_symbol":"$4737$⨪↰⇹$4005$⪒($4518$⩠)","expression":"⪩⨒∯1022001⨪↰⇹⪩⨒∯332211⪒(⪩⨒∯1012212⩠)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4758,"operation_count":3,"complexity_ratio":1586.0,"tree":{"type":"binary","operator":"⪒","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":4737,"base":4},"right_expr":{"type":"numeric_atoms","value":4005,"base":4}},"right_expr":{"type":"unary","operator":"⩠","unary_expr":{"type":"numeric_atoms","value":4518,"base":4}}},"used_operators":["f6k1SAg4EE","tmPS8pqC7x","sJAwomhLZr"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rJVOvQCfKK","sdazOOVcIp","i8ToyICDmI","k8jYdgA6NY","eH2TOUuTDT","W4YGzv6Whe","Z2TMIBDE3Q","COABgblf1C"],"result":"⪩⨒∯-1022001","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4737","layer":2},{"info":"number node, value=4005","layer":2},{"info":"compute binary expreesion, left_input=4737, right_input=4005, op_id = tmPS8pqC7x binary_op_definition= 'a⨪↰⇹b = {a, if a == 0; (b)⨎((a-1)⨪↰⇹b), if a > 0 and abs(a) < 1000000; -(b)⨎((a+1)⨪↰⇹b), if a < 0 and abs(a) < 1000000; NaN, else}', output=4737","layer":1},{"info":"number node, value=4518","layer":2},{"info":"compute unary expreesion, input=4518, op_id = sJAwomhLZr, unary_op_definition = 'a⩠ = { (((a+a)⊭↱(a⪨≂a))∲⫓((a⩤)%(a⪐))) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=4737, right_input=0, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-4737","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1022001⨪↰⇹⪩⨒∯332211⪒(⪩⨒∯1012212⩠)=⪩⨒∯-1022001","reverse_text":"⪩⨒∯-1022001=⪩⨒∯1022001⨪↰⇹⪩⨒∯332211⪒(⪩⨒∯1012212⩠)","cot":[{"info":"⪩⨒∯1022001⨪↰⇹⪩⨒∯332211=⪩⨒∯1022001","layer":1},{"info":"⪩⨒∯1012212⩠=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1022001⪒⪩⨒∯0=⪩⨒∯-1022001","layer":0}]}
{"id":945,"expression_no_base_symbol":"($5088$↙$2801$)≦≮≮","expression":"(⪩⨒∯1033200↙⪩⨒∯223301)≦≮≮","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2807,"operation_count":2,"complexity_ratio":1403.5,"tree":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":5088,"base":4},"right_expr":{"type":"numeric_atoms","value":2801,"base":4}}},"used_operators":["D4vGDi5EA2","yyfyN0ffXY"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","tmPS8pqC7x","DpFCA1CohY"],"result":"⪩⨒∯12021321","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=5088","layer":2},{"info":"number node, value=2801","layer":2},{"info":"compute binary expreesion, left_input=5088, right_input=2801, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-8403","layer":1},{"info":"compute unary expreesion, input=-8403, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=25209","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1033200↙⪩⨒∯223301)≦≮≮=⪩⨒∯12021321","reverse_text":"⪩⨒∯12021321=(⪩⨒∯1033200↙⪩⨒∯223301)≦≮≮","cot":[{"info":"⪩⨒∯1033200↙⪩⨒∯223301=⪩⨒∯-2003103","layer":1},{"info":"⪩⨒∯-2003103≦≮≮=⪩⨒∯12021321","layer":0}]}
{"id":946,"expression_no_base_symbol":"⫖→$1006$⩌⋺$3493$","expression":"⫖→⪩⨒∯33232⩌⋺⪩⨒∯312211","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4818,"operation_count":2,"complexity_ratio":2409.0,"tree":{"type":"unary","operator":"⫖→","unary_expr":{"type":"binary","operator":"⩌⋺","left_expr":{"type":"numeric_atoms","value":1006,"base":4},"right_expr":{"type":"numeric_atoms","value":3493,"base":4}}},"used_operators":["U4ylXWHChL","g7Hmc5v1ko"],"dependent_operators":["tmPS8pqC7x","Ikt5ks8PT7","AFVx7xoS7T","o20kRiQErp","9FxExcQeMw","W4YGzv6Whe","NTOWxs364D","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","t8gj7n24qd","xUOZtlo3hN","i8ToyICDmI","QMFrweE19q"],"result":"⪩⨒∯2301","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1006","layer":2},{"info":"number node, value=3493","layer":2},{"info":"compute binary expreesion, left_input=1006, right_input=3493, op_id = g7Hmc5v1ko binary_op_definition= 'a⩌⋺b = { ((⨞⊢(b⨵⪆b))∲⫓((a⪨≂b)⪨≂(b⩷∴919))) , if (b⫡⨏102)>364 and (-b)==524 ; (b⇼⇔∾((a+a)⩚⊴⇥(-a))) , else }', output=-4620","layer":1},{"info":"compute unary expreesion, input=-4620, op_id = U4ylXWHChL, unary_op_definition = '⫖→a = { (((a⨪↰⇹a)⇌⫙⪟(a⩧⪆a))∸) }', output=177","layer":0}],"base":4,"result_base":4,"text":"⫖→⪩⨒∯33232⩌⋺⪩⨒∯312211=⪩⨒∯2301","reverse_text":"⪩⨒∯2301=⫖→⪩⨒∯33232⩌⋺⪩⨒∯312211","cot":[{"info":"⪩⨒∯33232⩌⋺⪩⨒∯312211=⪩⨒∯-1020030","layer":1},{"info":"⫖→⪩⨒∯-1020030=⪩⨒∯2301","layer":0}]}
{"id":947,"expression_no_base_symbol":"(⩪∧⨌$8386$)⪝(≤/$5574$)","expression":"(⩪∧⨌⪩⨒∯2003002)⪝(≤/⪩⨒∯1113012)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":430,"operation_count":3,"complexity_ratio":143.33333333333334,"tree":{"type":"binary","operator":"⪝","left_expr":{"type":"unary","operator":"⩪∧⨌","unary_expr":{"type":"numeric_atoms","value":8386,"base":4}},"right_expr":{"type":"unary","operator":"≤/","unary_expr":{"type":"numeric_atoms","value":5574,"base":4}}},"used_operators":["wicAB68Tmb","6iOiAJX1F8","eLAdDNolq6"],"dependent_operators":["L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X","P8v4zCKN1o","23Mk6UjR3U","7j4O788W3g","f6k1SAg4EE","g55IO6H4Gj","rysDP5nf3Z"],"result":"⪩⨒∯-1112331213","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8386","layer":2},{"info":"compute unary expreesion, input=8386, op_id = 6iOiAJX1F8, unary_op_definition = '⩪∧⨌a = { (∥⊫a) , if ((a⋷517)==285 and (a⪒780)<=108) ; ((a↺a)⨸⪁(a⨸⪁a)) , else }', output=83860","layer":1},{"info":"number node, value=5574","layer":2},{"info":"compute unary expreesion, input=5574, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-5090","layer":1},{"info":"compute binary expreesion, left_input=83860, right_input=-5090, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=-356199","layer":0}],"base":4,"result_base":4,"text":"(⩪∧⨌⪩⨒∯2003002)⪝(≤/⪩⨒∯1113012)=⪩⨒∯-1112331213","reverse_text":"⪩⨒∯-1112331213=(⩪∧⨌⪩⨒∯2003002)⪝(≤/⪩⨒∯1113012)","cot":[{"info":"⩪∧⨌⪩⨒∯2003002=⪩⨒∯110132110","layer":1},{"info":"≤/⪩⨒∯1113012=⪩⨒∯-1033202","layer":1},{"info":"⪩⨒∯110132110⪝⪩⨒∯-1033202=⪩⨒∯-1112331213","layer":0}]}
{"id":948,"expression_no_base_symbol":"$1186$⨰$4466$⇴∐$7631$⨓$1005$","expression":"⪩⨒∯102202⨰⪩⨒∯1011302⇴∐⪩⨒∯1313033⨓⪩⨒∯33231","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1037,"operation_count":3,"complexity_ratio":345.6666666666667,"tree":{"type":"binary","operator":"⇴∐","left_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":1186,"base":4},"right_expr":{"type":"numeric_atoms","value":4466,"base":4}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":7631,"base":4},"right_expr":{"type":"numeric_atoms","value":1005,"base":4}}},"used_operators":["HnzytWxmAO","eewbuw0ToL","3ViojmjbAp"],"dependent_operators":["2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⪩⨒∯-1310","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1186","layer":2},{"info":"number node, value=4466","layer":2},{"info":"compute binary expreesion, left_input=1186, right_input=4466, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-3270","layer":1},{"info":"number node, value=7631","layer":2},{"info":"number node, value=1005","layer":2},{"info":"compute binary expreesion, left_input=7631, right_input=1005, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1008","layer":1},{"info":"compute binary expreesion, left_input=-3270, right_input=-1008, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=-116","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102202⨰⪩⨒∯1011302⇴∐⪩⨒∯1313033⨓⪩⨒∯33231=⪩⨒∯-1310","reverse_text":"⪩⨒∯-1310=⪩⨒∯102202⨰⪩⨒∯1011302⇴∐⪩⨒∯1313033⨓⪩⨒∯33231","cot":[{"info":"⪩⨒∯102202⨰⪩⨒∯1011302=⪩⨒∯-303012","layer":1},{"info":"⪩⨒∯1313033⨓⪩⨒∯33231=⪩⨒∯-33300","layer":1},{"info":"⪩⨒∯-303012⇴∐⪩⨒∯-33300=⪩⨒∯-1310","layer":0}]}
{"id":949,"expression_no_base_symbol":"⊿$1153$⫘$1391$","expression":"⊿⪩⨒∯102001⫘⪩⨒∯111233","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1393,"operation_count":2,"complexity_ratio":696.5,"tree":{"type":"unary","operator":"⊿","unary_expr":{"type":"binary","operator":"⫘","left_expr":{"type":"numeric_atoms","value":1153,"base":4},"right_expr":{"type":"numeric_atoms","value":1391,"base":4}}},"used_operators":["DO4fhlbJSI","48vC8HMD2b"],"dependent_operators":["9FxExcQeMw","e1ybzncUwg","XPYlsWDdGa","sdazOOVcIp","2DQ55sFlQl","12rbrZMWeM","OwUj7dcsQK","7j4O788W3g","tfWHHpNKUN","3ViojmjbAp","dfKe02y8D2","tcjXMdvYtA","D4vGDi5EA2","86A5ENbKR9","X99M06cbEe"],"result":"⪩⨒∯-110300220112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1153","layer":2},{"info":"number node, value=1391","layer":2},{"info":"compute binary expreesion, left_input=1153, right_input=1391, op_id = 48vC8HMD2b binary_op_definition= 'a⫘b = { ((≘(b⨓a))≫≃) , if ((⇖a)!=319 or (a↺926)<190) ; ((∓a)⫚↹⊑(⪸(a≦≮≮))) , else }', output=1360333","layer":1},{"info":"compute unary expreesion, input=1360333, op_id = DO4fhlbJSI, unary_op_definition = '⊿a = { ((⪲⇎(a⨵⪆a))⩷∴((≉a)⋳⪒(a⪨≂a))) }', output=-5442070","layer":0}],"base":4,"result_base":4,"text":"⊿⪩⨒∯102001⫘⪩⨒∯111233=⪩⨒∯-110300220112","reverse_text":"⪩⨒∯-110300220112=⊿⪩⨒∯102001⫘⪩⨒∯111233","cot":[{"info":"⪩⨒∯102001⫘⪩⨒∯111233=⪩⨒∯11030013031","layer":1},{"info":"⊿⪩⨒∯11030013031=⪩⨒∯-110300220112","layer":0}]}
{"id":950,"expression_no_base_symbol":"(⇖⫷⫕$4871$)∌↝(⋗⩬⋾$1798$)","expression":"(⇖⫷⫕⪩⨒∯1030013)∌↝(⋗⩬⋾⪩⨒∯130012)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":815,"operation_count":3,"complexity_ratio":271.6666666666667,"tree":{"type":"binary","operator":"∌↝","left_expr":{"type":"unary","operator":"⇖⫷⫕","unary_expr":{"type":"numeric_atoms","value":4871,"base":4}},"right_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":1798,"base":4}}},"used_operators":["9Isq31Ruls","UHmRx3INFg","DpFCA1CohY"],"dependent_operators":["DpFCA1CohY","NTOWxs364D","Qy55tPpLXF","23Mk6UjR3U","EBcxylXtPf","xUOZtlo3hN","t8gj7n24qd","2DDjHMKMc0","Ph9nP6C5qx","i8ToyICDmI","DE7zCoGJt9","FyVja0WsTP","oZj3VtZNQx","DyGG3AbaNP","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯1120030","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4871","layer":2},{"info":"compute unary expreesion, input=4871, op_id = UHmRx3INFg, unary_op_definition = '⇖⫷⫕a = { ((a∼125)≀⫉(↞≼(a⊱⇼⊻51))) }', output=2822","layer":1},{"info":"number node, value=1798","layer":2},{"info":"compute unary expreesion, input=1798, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-5394","layer":1},{"info":"compute binary expreesion, left_input=2822, right_input=-5394, op_id = 9Isq31Ruls binary_op_definition= 'a∌↝b = { ((⋗⩬⋾b)∲⫓(⨞⊢(a⩚⊴⇥145))) , if (b⫌⩹⨱)>=130 ; ((-a)⋷((a≧⫂∧a)⋝⋈⪟(50⋥≓≎196))) , else }', output=5644","layer":0}],"base":4,"result_base":4,"text":"(⇖⫷⫕⪩⨒∯1030013)∌↝(⋗⩬⋾⪩⨒∯130012)=⪩⨒∯1120030","reverse_text":"⪩⨒∯1120030=(⇖⫷⫕⪩⨒∯1030013)∌↝(⋗⩬⋾⪩⨒∯130012)","cot":[{"info":"⇖⫷⫕⪩⨒∯1030013=⪩⨒∯230012","layer":1},{"info":"⋗⩬⋾⪩⨒∯130012=⪩⨒∯-1110102","layer":1},{"info":"⪩⨒∯230012∌↝⪩⨒∯-1110102=⪩⨒∯1120030","layer":0}]}
{"id":951,"expression_no_base_symbol":"⨭⩧⫛($2533$⨵⪆$4012$)","expression":"⨭⩧⫛(⪩⨒∯213211⨵⪆⪩⨒∯332230)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":25607,"operation_count":2,"complexity_ratio":12803.5,"tree":{"type":"unary","operator":"⨭⩧⫛","unary_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":2533,"base":4},"right_expr":{"type":"numeric_atoms","value":4012,"base":4}}},"used_operators":["g21JL6JxX7","2DQ55sFlQl"],"dependent_operators":["Ikt5ks8PT7","Asc51vEJeQ","A8NUZmVepG","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2533","layer":2},{"info":"number node, value=4012","layer":2},{"info":"compute binary expreesion, left_input=2533, right_input=4012, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"compute unary expreesion, input=160, op_id = g21JL6JxX7, unary_op_definition = '⨭⩧⫛a = { ((↥a)⩧⪆(↣≠⋷a)) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⨭⩧⫛(⪩⨒∯213211⨵⪆⪩⨒∯332230)=NaN","reverse_text":"NaN=⨭⩧⫛(⪩⨒∯213211⨵⪆⪩⨒∯332230)","cot":[{"info":"⪩⨒∯213211⨵⪆⪩⨒∯332230=⪩⨒∯2200","layer":1},{"info":"⨭⩧⫛⪩⨒∯2200=NaN","layer":0}]}
{"id":952,"expression_no_base_symbol":"($7487$⩖⊿$1977$)⋹⋡⊁($1710$⫦⪉$1085$)","expression":"(⪩⨒∯1310333⩖⊿⪩⨒∯132321)⋹⋡⊁(⪩⨒∯122232⫦⪉⪩⨒∯100331)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":62586,"operation_count":3,"complexity_ratio":20862.0,"tree":{"type":"binary","operator":"⋹⋡⊁","left_expr":{"type":"binary","operator":"⩖⊿","left_expr":{"type":"numeric_atoms","value":7487,"base":4},"right_expr":{"type":"numeric_atoms","value":1977,"base":4}},"right_expr":{"type":"binary","operator":"⫦⪉","left_expr":{"type":"numeric_atoms","value":1710,"base":4},"right_expr":{"type":"numeric_atoms","value":1085,"base":4}}},"used_operators":["As8RqfVLgs","RZ5CV9rWsJ","wscyQdcy20"],"dependent_operators":["ljTHtUsqzn","WkeUrDK8WX","fu6greOZ01","xRrnTEsQ6j","oPMjh9089D","ivGwdmUAux","HJ9erzHUuu","IWmyXbctLI","8cLx32lpNA","W4YGzv6Whe","B3sABdIn96","9HNa5Wba9A","g7Hmc5v1ko","nREPSIbpBE","D3AQDKkPcf"],"result":"⪩⨒∯202312","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7487","layer":2},{"info":"number node, value=1977","layer":2},{"info":"compute binary expreesion, left_input=7487, right_input=1977, op_id = RZ5CV9rWsJ binary_op_definition= 'a⩖⊿b = { ((b⪔⊥a)⪮%⊝(a∌125)) }', output=-14214","layer":1},{"info":"number node, value=1710","layer":2},{"info":"number node, value=1085","layer":2},{"info":"compute binary expreesion, left_input=1710, right_input=1085, op_id = wscyQdcy20 binary_op_definition= 'a⫦⪉b = { ((a⩌⋺206)⪹) , if (a∷677)>=23 ; ((b+a)*(b⨚b)) , else }', output=1480","layer":1},{"info":"compute binary expreesion, left_input=-14214, right_input=1480, op_id = As8RqfVLgs binary_op_definition= 'a⋹⋡⊁b = { ((a⨐⩸⫘247)⫁⪎(⩰b)) , if (⫵↿b)==517 or b>135 ; (⊀(≀↧⇸a)) , else }', output=2230","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1310333⩖⊿⪩⨒∯132321)⋹⋡⊁(⪩⨒∯122232⫦⪉⪩⨒∯100331)=⪩⨒∯202312","reverse_text":"⪩⨒∯202312=(⪩⨒∯1310333⩖⊿⪩⨒∯132321)⋹⋡⊁(⪩⨒∯122232⫦⪉⪩⨒∯100331)","cot":[{"info":"⪩⨒∯1310333⩖⊿⪩⨒∯132321=⪩⨒∯-3132012","layer":1},{"info":"⪩⨒∯122232⫦⪉⪩⨒∯100331=⪩⨒∯113020","layer":1},{"info":"⪩⨒∯-3132012⋹⋡⊁⪩⨒∯113020=⪩⨒∯202312","layer":0}]}
{"id":953,"expression_no_base_symbol":"($6540$+$1550$)∠⫱$5377$⩦$6174$","expression":"(⪩⨒∯1212030+⪩⨒∯120032)∠⫱⪩⨒∯1110001⩦⪩⨒∯1200132","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":25,"operation_count":3,"complexity_ratio":8.333333333333334,"tree":{"type":"binary","operator":"∠⫱","left_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":6540,"base":4},"right_expr":{"type":"numeric_atoms","value":1550,"base":4}},"right_expr":{"type":"binary","operator":"⩦","left_expr":{"type":"numeric_atoms","value":5377,"base":4},"right_expr":{"type":"numeric_atoms","value":6174,"base":4}}},"used_operators":["QvoQhV0rrE","W4YGzv6Whe","0kmYd0q39Y"],"dependent_operators":["eLAdDNolq6","DZ8iAZOCBD","7j4O788W3g","tifHPKVTfV","AF7qkfDlqP","N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q"],"result":"⪩⨒∯103102","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6540","layer":2},{"info":"number node, value=1550","layer":2},{"info":"compute binary expreesion, left_input=6540, right_input=1550, op_id = W4YGzv6Whe binary_op_definition= 'None', output=8090","layer":1},{"info":"number node, value=5377","layer":2},{"info":"number node, value=6174","layer":2},{"info":"compute binary expreesion, left_input=5377, right_input=6174, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=10754","layer":1},{"info":"compute binary expreesion, left_input=8090, right_input=10754, op_id = QvoQhV0rrE binary_op_definition= 'a∠⫱b = { ((⨑⩽⪐a)↺(617⊉≛↸a)) , if (≤/b)<=3 ; (b⇼⇔∾a) , else }', output=1234","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1212030+⪩⨒∯120032)∠⫱⪩⨒∯1110001⩦⪩⨒∯1200132=⪩⨒∯103102","reverse_text":"⪩⨒∯103102=(⪩⨒∯1212030+⪩⨒∯120032)∠⫱⪩⨒∯1110001⩦⪩⨒∯1200132","cot":[{"info":"⪩⨒∯1212030+⪩⨒∯120032=⪩⨒∯1332122","layer":1},{"info":"⪩⨒∯1110001⩦⪩⨒∯1200132=⪩⨒∯2220002","layer":1},{"info":"⪩⨒∯1332122∠⫱⪩⨒∯2220002=⪩⨒∯103102","layer":0}]}
{"id":954,"expression_no_base_symbol":"⊥($1203$⩚⊴⇥$4665$)","expression":"⊥(⪩⨒∯102303⩚⊴⇥⪩⨒∯1020321)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4,"operation_count":2,"complexity_ratio":2.0,"tree":{"type":"unary","operator":"⊥","unary_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":1203,"base":4},"right_expr":{"type":"numeric_atoms","value":4665,"base":4}}},"used_operators":["Q3PJZHRvZv","NTOWxs364D"],"dependent_operators":["fu6greOZ01","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1203","layer":2},{"info":"number node, value=4665","layer":2},{"info":"compute binary expreesion, left_input=1203, right_input=4665, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-5989","layer":1},{"info":"compute unary expreesion, input=-5989, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⊥(⪩⨒∯102303⩚⊴⇥⪩⨒∯1020321)=NaN","reverse_text":"NaN=⊥(⪩⨒∯102303⩚⊴⇥⪩⨒∯1020321)","cot":[{"info":"⪩⨒∯102303⩚⊴⇥⪩⨒∯1020321=⪩⨒∯-1131211","layer":1},{"info":"⊥⪩⨒∯-1131211=NaN","layer":0}]}
{"id":955,"expression_no_base_symbol":"$4100$∙∹∝$3571$⋻⩜⩜$2192$⇤$6062$","expression":"⪩⨒∯1000010∙∹∝⪩⨒∯313303⋻⩜⩜⪩⨒∯202100⇤⪩⨒∯1132232","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":537939,"operation_count":3,"complexity_ratio":179313.0,"tree":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"numeric_atoms","value":4100,"base":4},"right_expr":{"type":"numeric_atoms","value":3571,"base":4}},"right_expr":{"type":"binary","operator":"⇤","left_expr":{"type":"numeric_atoms","value":2192,"base":4},"right_expr":{"type":"numeric_atoms","value":6062,"base":4}}},"used_operators":["oDCm7WA9JY","HmxsFra2vL","YSKBFp38Pu"],"dependent_operators":["mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","rysDP5nf3Z","XPYlsWDdGa","tifHPKVTfV","2DQ55sFlQl","2DDjHMKMc0","xUOZtlo3hN","QMFrweE19q"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4100","layer":2},{"info":"number node, value=3571","layer":2},{"info":"compute binary expreesion, left_input=4100, right_input=3571, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":1},{"info":"number node, value=2192","layer":2},{"info":"number node, value=6062","layer":2},{"info":"compute binary expreesion, left_input=2192, right_input=6062, op_id = YSKBFp38Pu binary_op_definition= 'a⇤b = { (((b-523)⇼⇔∾(⨞⊢a))⫡⨏((⪲⇎a)⨵⪆(336⋝⋈⪟a))) }', output=-38422","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-38422, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1000010∙∹∝⪩⨒∯313303⋻⩜⩜⪩⨒∯202100⇤⪩⨒∯1132232=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯1000010∙∹∝⪩⨒∯313303⋻⩜⩜⪩⨒∯202100⇤⪩⨒∯1132232","cot":[{"info":"⪩⨒∯1000010∙∹∝⪩⨒∯313303=⪩⨒∯0","layer":1},{"info":"⪩⨒∯202100⇤⪩⨒∯1132232=⪩⨒∯-21120112","layer":1},{"info":"⪩⨒∯0⋻⩜⩜⪩⨒∯-21120112=⪩⨒∯0","layer":0}]}
{"id":956,"expression_no_base_symbol":"($3561$≠≀$1281$)≀⫉$3599$⩼⇪↪$1121$","expression":"(⪩⨒∯313221≠≀⪩⨒∯110001)≀⫉⪩⨒∯320033⩼⇪↪⪩⨒∯101201","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":172,"operation_count":3,"complexity_ratio":57.333333333333336,"tree":{"type":"binary","operator":"≀⫉","left_expr":{"type":"binary","operator":"≠≀","left_expr":{"type":"numeric_atoms","value":3561,"base":4},"right_expr":{"type":"numeric_atoms","value":1281,"base":4}},"right_expr":{"type":"binary","operator":"⩼⇪↪","left_expr":{"type":"numeric_atoms","value":3599,"base":4},"right_expr":{"type":"numeric_atoms","value":1121,"base":4}}},"used_operators":["oZj3VtZNQx","IwW236VD4Y","ocnLzx9CaJ"],"dependent_operators":["9FxExcQeMw","Tcnh7f0tEr","jBncVCNhdl","FyVja0WsTP","Ikt5ks8PT7","EWw2JM7wp4","cTDWOvIxvz","eLAdDNolq6","NTOWxs364D","sdazOOVcIp","2DDjHMKMc0","2td37pGCOC","9FxExcQeMw","rysDP5nf3Z","BjRHVeLaeN","eH2TOUuTDT","2DQ55sFlQl","QMFrweE19q"],"result":"⪩⨒∯230012","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3561","layer":2},{"info":"number node, value=1281","layer":2},{"info":"compute binary expreesion, left_input=3561, right_input=1281, op_id = IwW236VD4Y binary_op_definition= 'a≠≀b = { (⩦⩻⨪(a⩚⊴⇥b)) , if (≤/b)>10 ; ((a⪨≂a)⪨≂(a⋝⋈⪟356)) , else }', output=-6816","layer":1},{"info":"number node, value=3599","layer":2},{"info":"number node, value=1121","layer":2},{"info":"compute binary expreesion, left_input=3599, right_input=1121, op_id = ocnLzx9CaJ binary_op_definition= 'a⩼⇪↪b = { ((a⪐)-(b⫡⨏b)) , if (a⫩⊇)!=96 ; (148⨵⪆(a⩷∴b)) , else }', output=-1432","layer":1},{"info":"compute binary expreesion, left_input=-6816, right_input=-1432, op_id = oZj3VtZNQx binary_op_definition= 'a≀⫉b = { (((55≣⋋)∝(a⩷∴a))⊱⇼⊻((a⪉⨛b)⩧⪆(b⋭≵475))) }', output=2822","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯313221≠≀⪩⨒∯110001)≀⫉⪩⨒∯320033⩼⇪↪⪩⨒∯101201=⪩⨒∯230012","reverse_text":"⪩⨒∯230012=(⪩⨒∯313221≠≀⪩⨒∯110001)≀⫉⪩⨒∯320033⩼⇪↪⪩⨒∯101201","cot":[{"info":"⪩⨒∯313221≠≀⪩⨒∯110001=⪩⨒∯-1222200","layer":1},{"info":"⪩⨒∯320033⩼⇪↪⪩⨒∯101201=⪩⨒∯-112120","layer":1},{"info":"⪩⨒∯-1222200≀⫉⪩⨒∯-112120=⪩⨒∯230012","layer":0}]}
{"id":957,"expression_no_base_symbol":"$6404$⨚⇆$4050$⩒⫫$4046$⪢$8407$","expression":"⪩⨒∯1210010⨚⇆⪩⨒∯333102⩒⫫⪩⨒∯333032⪢⪩⨒∯2003113","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":53293,"operation_count":3,"complexity_ratio":17764.333333333332,"tree":{"type":"binary","operator":"⩒⫫","left_expr":{"type":"binary","operator":"⨚⇆","left_expr":{"type":"numeric_atoms","value":6404,"base":4},"right_expr":{"type":"numeric_atoms","value":4050,"base":4}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":4046,"base":4},"right_expr":{"type":"numeric_atoms","value":8407,"base":4}}},"used_operators":["KFSx94NKJn","lwHaAYXP2r","dWAJyo7jo9"],"dependent_operators":["NTOWxs364D","rysDP5nf3Z","BjRHVeLaeN","XIabStNQrY","glklzrTFfD","tifHPKVTfV","sdazOOVcIp","2DQ55sFlQl","EBcxylXtPf","nCS4ZIUYfx","eewbuw0ToL","AF7qkfDlqP","gx7XJ7hdpj","LRNGc0VcxI","pB6Fcnrjim","DmTXOeWf9t","PoHhknlbAi","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6404","layer":2},{"info":"number node, value=4050","layer":2},{"info":"compute binary expreesion, left_input=6404, right_input=4050, op_id = lwHaAYXP2r binary_op_definition= 'a⨚⇆b = { (a∀⇚≩(b⊲⩕⊾a)) , if (⇙⪊b)<61 ; ((36∓⋝b)∀⇚≩(a⫸⇳b)) , else }', output=nan","layer":1},{"info":"number node, value=4046","layer":2},{"info":"number node, value=8407","layer":2},{"info":"compute binary expreesion, left_input=4046, right_input=8407, op_id = dWAJyo7jo9 binary_op_definition= 'a⪢b = {b, if b == 0; (a)%(a⪢(b-1)), if b > 0 and abs(b) < 1000000; -(a)%(a⪢(b+1)), if b < 0 and abs(b) < 1000000; NaN, else}', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = KFSx94NKJn binary_op_definition= 'a⩒⫫b = { (((195⪨≂263)⪨≂(b⇋≉))⨵⪆((82⫩⊇)⨁⊸⫻)) , if (a⫌⩹⨱)<47 ; (((b⇼⇔∾a)-(a⪨≂a))⩚⊴⇥((⨑⩽⪐a)⨰(b⨳⩥⨓a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1210010⨚⇆⪩⨒∯333102⩒⫫⪩⨒∯333032⪢⪩⨒∯2003113=NaN","reverse_text":"NaN=⪩⨒∯1210010⨚⇆⪩⨒∯333102⩒⫫⪩⨒∯333032⪢⪩⨒∯2003113","cot":[{"info":"⪩⨒∯1210010⨚⇆⪩⨒∯333102=NaN","layer":1},{"info":"⪩⨒∯333032⪢⪩⨒∯2003113=NaN","layer":1},{"info":"NaN⩒⫫NaN=NaN","layer":0}]}
{"id":958,"expression_no_base_symbol":"($1851$⊊)⋻⩜⩜(↞≼$3409$)","expression":"(⪩⨒∯130323⊊)⋻⩜⩜(↞≼⪩⨒∯311101)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":376267,"operation_count":3,"complexity_ratio":125422.33333333333,"tree":{"type":"binary","operator":"⋻⩜⩜","left_expr":{"type":"unary","operator":"⊊","unary_expr":{"type":"numeric_atoms","value":1851,"base":4}},"right_expr":{"type":"unary","operator":"↞≼","unary_expr":{"type":"numeric_atoms","value":3409,"base":4}}},"used_operators":["oDCm7WA9JY","W9R8I5fN5A","DE7zCoGJt9"],"dependent_operators":["mp7IySMOzn","4X4GscPmMf","nREPSIbpBE","DlLNRPXxWL","aBQ6xLxuTc","8n5YIzOsVS","oZj3VtZNQx","MahUMFw56D","hyuBjUqXlG","aA7tF3KVD3","2DDjHMKMc0","QMFrweE19q","SxTAKzQCrw","8cLx32lpNA","W4YGzv6Whe","D4vGDi5EA2","23Mk6UjR3U","BjRHVeLaeN","Ph9nP6C5qx","g55IO6H4Gj","eewbuw0ToL","u6S6b8DprG"],"result":"⪩⨒∯230121132","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1851","layer":2},{"info":"compute unary expreesion, input=1851, op_id = W9R8I5fN5A, unary_op_definition = 'a⊊ = { (((⫛⫱⨽a)∙⊟a)∌((a⇂≾⫗536)⋝⋈⪟(a⫡⨏a))) , if ((a≚⋢)==7 or (a⪘⨀)==15) ; ((a≀⫉(6⪛⫼a))⫠↝⫳) , else }', output=90927","layer":1},{"info":"number node, value=3409","layer":2},{"info":"compute unary expreesion, input=3409, op_id = DE7zCoGJt9, unary_op_definition = '↞≼a = { (↽≂(197⨰(a⨸⪁a))) , if (a⨸⪁373)!=224 ; (((591⋷a)≧⫂∧(a+a))⨸⪁((a⫩⊇)≦≮≮)) , else }', output=26858","layer":1},{"info":"compute binary expreesion, left_input=90927, right_input=26858, op_id = oDCm7WA9JY binary_op_definition= 'a⋻⩜⩜b = { (495⨚a) , if (a⨕⋳)!=7 and b>=394 and a<693 ; (b⇷a) , else }', output=181854","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯130323⊊)⋻⩜⩜(↞≼⪩⨒∯311101)=⪩⨒∯230121132","reverse_text":"⪩⨒∯230121132=(⪩⨒∯130323⊊)⋻⩜⩜(↞≼⪩⨒∯311101)","cot":[{"info":"⪩⨒∯130323⊊=⪩⨒∯112030233","layer":1},{"info":"↞≼⪩⨒∯311101=⪩⨒∯12203222","layer":1},{"info":"⪩⨒∯112030233⋻⩜⩜⪩⨒∯12203222=⪩⨒∯230121132","layer":0}]}
{"id":959,"expression_no_base_symbol":"$5733$⊕∕$6530$⇴∐$5187$⨫⇇↔$7796$","expression":"⪩⨒∯1121211⊕∕⪩⨒∯1212002⇴∐⪩⨒∯1101003⨫⇇↔⪩⨒∯1321310","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":277771,"operation_count":3,"complexity_ratio":92590.33333333333,"tree":{"type":"binary","operator":"⇴∐","left_expr":{"type":"binary","operator":"⊕∕","left_expr":{"type":"numeric_atoms","value":5733,"base":4},"right_expr":{"type":"numeric_atoms","value":6530,"base":4}},"right_expr":{"type":"binary","operator":"⨫⇇↔","left_expr":{"type":"numeric_atoms","value":5187,"base":4},"right_expr":{"type":"numeric_atoms","value":7796,"base":4}}},"used_operators":["HnzytWxmAO","9cloC0Ngie","LXhwmt4mBO"],"dependent_operators":["2GS7woTJqF","QbnwKVWMIQ","U7g4x0WXJJ","Tcnh7f0tEr","wicAB68Tmb","yyfyN0ffXY","sYcpBQ0cFf","d7ASUq0ydm","DZ8iAZOCBD","rJVOvQCfKK"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5733","layer":2},{"info":"number node, value=6530","layer":2},{"info":"compute binary expreesion, left_input=5733, right_input=6530, op_id = 9cloC0Ngie binary_op_definition= 'a⊕∕b = { ((b⪝9)↙(⨮↦↱b)) , if (b≣⋋)>174 ; a , else }', output=5733","layer":1},{"info":"number node, value=5187","layer":2},{"info":"number node, value=7796","layer":2},{"info":"compute binary expreesion, left_input=5187, right_input=7796, op_id = LXhwmt4mBO binary_op_definition= 'a⨫⇇↔b = { ((9⊉≛↸b)⫯⪬∳(a⨎a)) }', output=-527","layer":1},{"info":"compute binary expreesion, left_input=5733, right_input=-527, op_id = HnzytWxmAO binary_op_definition= 'a⇴∐b = { (((b+⪬∐b)∑⇟⊟b)⪥a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1121211⊕∕⪩⨒∯1212002⇴∐⪩⨒∯1101003⨫⇇↔⪩⨒∯1321310=NaN","reverse_text":"NaN=⪩⨒∯1121211⊕∕⪩⨒∯1212002⇴∐⪩⨒∯1101003⨫⇇↔⪩⨒∯1321310","cot":[{"info":"⪩⨒∯1121211⊕∕⪩⨒∯1212002=⪩⨒∯1121211","layer":1},{"info":"⪩⨒∯1101003⨫⇇↔⪩⨒∯1321310=⪩⨒∯-20033","layer":1},{"info":"⪩⨒∯1121211⇴∐⪩⨒∯-20033=NaN","layer":0}]}
{"id":960,"expression_no_base_symbol":"($1144$⫭)≨$7440$⨽∌$1018$","expression":"(⪩⨒∯101320⫭)≨⪩⨒∯1310100⨽∌⪩⨒∯33322","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":138,"operation_count":3,"complexity_ratio":46.0,"tree":{"type":"binary","operator":"≨","left_expr":{"type":"unary","operator":"⫭","unary_expr":{"type":"numeric_atoms","value":1144,"base":4}},"right_expr":{"type":"binary","operator":"⨽∌","left_expr":{"type":"numeric_atoms","value":7440,"base":4},"right_expr":{"type":"numeric_atoms","value":1018,"base":4}}},"used_operators":["0KMCeP1Jsh","t4WUHVGj7f","9samAPKr6k"],"dependent_operators":["jfAgQ2OQeM","bPywburJMS","T2fj7uvVaJ","2td37pGCOC","NTOWxs364D","2DDjHMKMc0","xUOZtlo3hN","g55IO6H4Gj","YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu"],"result":"⪩⨒∯-20113032","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1144","layer":2},{"info":"compute unary expreesion, input=1144, op_id = t4WUHVGj7f, unary_op_definition = 'a⫭ = { (⨞⊢((a⨸⪁147)⩚⊴⇥(a⋝⋈⪟a))) }', output=3673","layer":1},{"info":"number node, value=7440","layer":2},{"info":"number node, value=1018","layer":2},{"info":"compute binary expreesion, left_input=7440, right_input=1018, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=3673, right_input=0, op_id = 0KMCeP1Jsh binary_op_definition= 'a≨b = { (⇤←((b⋓a)↼⊘⨖(⩦⩻⨪a))) }', output=-34254","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101320⫭)≨⪩⨒∯1310100⨽∌⪩⨒∯33322=⪩⨒∯-20113032","reverse_text":"⪩⨒∯-20113032=(⪩⨒∯101320⫭)≨⪩⨒∯1310100⨽∌⪩⨒∯33322","cot":[{"info":"⪩⨒∯101320⫭=⪩⨒∯321121","layer":1},{"info":"⪩⨒∯1310100⨽∌⪩⨒∯33322=⪩⨒∯0","layer":1},{"info":"⪩⨒∯321121≨⪩⨒∯0=⪩⨒∯-20113032","layer":0}]}
{"id":961,"expression_no_base_symbol":"$1203$⨫⇇↔$4804$∲⫓$2433$⨽∌$4681$","expression":"⪩⨒∯102303⨫⇇↔⪩⨒∯1023010∲⫓⪩⨒∯212001⨽∌⪩⨒∯1021021","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":72,"operation_count":3,"complexity_ratio":24.0,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"⨫⇇↔","left_expr":{"type":"numeric_atoms","value":1203,"base":4},"right_expr":{"type":"numeric_atoms","value":4804,"base":4}},"right_expr":{"type":"binary","operator":"⨽∌","left_expr":{"type":"numeric_atoms","value":2433,"base":4},"right_expr":{"type":"numeric_atoms","value":4681,"base":4}}},"used_operators":["i8ToyICDmI","LXhwmt4mBO","9samAPKr6k"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","d7ASUq0ydm","DZ8iAZOCBD","rJVOvQCfKK","YjI8oCXuph","9ICcGScMcE","3sJ7IOPOlU","Ph9nP6C5qx","IWmyXbctLI","YSKBFp38Pu"],"result":"⪩⨒∯-20033","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1203","layer":2},{"info":"number node, value=4804","layer":2},{"info":"compute binary expreesion, left_input=1203, right_input=4804, op_id = LXhwmt4mBO binary_op_definition= 'a⨫⇇↔b = { ((9⊉≛↸b)⫯⪬∳(a⨎a)) }', output=-527","layer":1},{"info":"number node, value=2433","layer":2},{"info":"number node, value=4681","layer":2},{"info":"compute binary expreesion, left_input=2433, right_input=4681, op_id = 9samAPKr6k binary_op_definition= 'a⨽∌b = { ((≦∁(b⪮%⊝b))⪇≇⋚((b⇤a)≧⫂∧(⫇a))) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-527, right_input=0, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=-527","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯102303⨫⇇↔⪩⨒∯1023010∲⫓⪩⨒∯212001⨽∌⪩⨒∯1021021=⪩⨒∯-20033","reverse_text":"⪩⨒∯-20033=⪩⨒∯102303⨫⇇↔⪩⨒∯1023010∲⫓⪩⨒∯212001⨽∌⪩⨒∯1021021","cot":[{"info":"⪩⨒∯102303⨫⇇↔⪩⨒∯1023010=⪩⨒∯-20033","layer":1},{"info":"⪩⨒∯212001⨽∌⪩⨒∯1021021=⪩⨒∯0","layer":1},{"info":"⪩⨒∯-20033∲⫓⪩⨒∯0=⪩⨒∯-20033","layer":0}]}
{"id":962,"expression_no_base_symbol":"(⨆≐≲$4071$)⇂≾⫗($2431$∛$7527$)","expression":"(⨆≐≲⪩⨒∯333213)⇂≾⫗(⪩⨒∯211333∛⪩⨒∯1311213)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":285,"operation_count":3,"complexity_ratio":95.0,"tree":{"type":"binary","operator":"⇂≾⫗","left_expr":{"type":"unary","operator":"⨆≐≲","unary_expr":{"type":"numeric_atoms","value":4071,"base":4}},"right_expr":{"type":"binary","operator":"∛","left_expr":{"type":"numeric_atoms","value":2431,"base":4},"right_expr":{"type":"numeric_atoms","value":7527,"base":4}}},"used_operators":["aBQ6xLxuTc","Bi9z9uYZqW","w2537kitQq"],"dependent_operators":["g7Hmc5v1ko","KPf6cnQVty","vg4gO5BX6G","ruOEQAzv1W","2DlMacCsIx","HrjLwUk87U","SWo3A1KBJH","SUmda5xLS4","bx9Z9DAK5y","DhbWaqg5eL","7IPrd9c3lf","XnXgA4xnOs","nREPSIbpBE","i8ToyICDmI","aBQ6xLxuTc"],"result":"⪩⨒∯-22210","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4071","layer":2},{"info":"compute unary expreesion, input=4071, op_id = Bi9z9uYZqW, unary_op_definition = '⨆≐≲a = { (⇋↷(⇾⩊⇾(a⪄a))) }', output=44219544","layer":1},{"info":"number node, value=2431","layer":2},{"info":"number node, value=7527","layer":2},{"info":"compute binary expreesion, left_input=2431, right_input=7527, op_id = w2537kitQq binary_op_definition= 'a∛b = { ((b⨑≵⋬38)⇂≾⫗(b∲⫓a)) , if (b⨚996)>=244 and b>=3 ; ((+⊝⨔b)⊵↤) , else }', output=-670","layer":1},{"info":"compute binary expreesion, left_input=44219544, right_input=-670, op_id = aBQ6xLxuTc binary_op_definition= 'a⇂≾⫗b = { (((b⩌⋺a)⩨(↔b))⪚((a⊨b)∺≝⩲b)) }', output=-676","layer":0}],"base":4,"result_base":4,"text":"(⨆≐≲⪩⨒∯333213)⇂≾⫗(⪩⨒∯211333∛⪩⨒∯1311213)=⪩⨒∯-22210","reverse_text":"⪩⨒∯-22210=(⨆≐≲⪩⨒∯333213)⇂≾⫗(⪩⨒∯211333∛⪩⨒∯1311213)","cot":[{"info":"⨆≐≲⪩⨒∯333213=⪩⨒∯2220223302120","layer":1},{"info":"⪩⨒∯211333∛⪩⨒∯1311213=⪩⨒∯-22132","layer":1},{"info":"⪩⨒∯2220223302120⇂≾⫗⪩⨒∯-22132=⪩⨒∯-22210","layer":0}]}
{"id":963,"expression_no_base_symbol":"$1675$⪮%⊝$1171$↡⊰⫅($2639$⫡⨏$5561$)","expression":"⪩⨒∯122023⪮%⊝⪩⨒∯102103↡⊰⫅(⪩⨒∯221033⫡⨏⪩⨒∯1112321)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":351431,"operation_count":3,"complexity_ratio":117143.66666666667,"tree":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1675,"base":4},"right_expr":{"type":"numeric_atoms","value":1171,"base":4}},"right_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":2639,"base":4},"right_expr":{"type":"numeric_atoms","value":5561,"base":4}}},"used_operators":["VCtxkLNOzz","IWmyXbctLI","QMFrweE19q"],"dependent_operators":["Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","W4YGzv6Whe","t8gj7n24qd"],"result":"⪩⨒∯30100120","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1675","layer":2},{"info":"number node, value=1171","layer":2},{"info":"compute binary expreesion, left_input=1675, right_input=1171, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=3666","layer":1},{"info":"number node, value=2639","layer":2},{"info":"number node, value=5561","layer":2},{"info":"compute binary expreesion, left_input=2639, right_input=5561, op_id = QMFrweE19q binary_op_definition= 'a⫡⨏b = { 497 , if (-b)==408 and (-a)>=56 ; (((a+783)+(a+a))+((b+a)+(a+b))) , else }', output=25100","layer":1},{"info":"compute binary expreesion, left_input=3666, right_input=25100, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=50200","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯122023⪮%⊝⪩⨒∯102103↡⊰⫅(⪩⨒∯221033⫡⨏⪩⨒∯1112321)=⪩⨒∯30100120","reverse_text":"⪩⨒∯30100120=⪩⨒∯122023⪮%⊝⪩⨒∯102103↡⊰⫅(⪩⨒∯221033⫡⨏⪩⨒∯1112321)","cot":[{"info":"⪩⨒∯122023⪮%⊝⪩⨒∯102103=⪩⨒∯321102","layer":1},{"info":"⪩⨒∯221033⫡⨏⪩⨒∯1112321=⪩⨒∯12020030","layer":1},{"info":"⪩⨒∯321102↡⊰⫅⪩⨒∯12020030=⪩⨒∯30100120","layer":0}]}
{"id":964,"expression_no_base_symbol":"($1711$∙∹∝$4952$)⨼⩣($4944$⇟⨁⪰)","expression":"(⪩⨒∯122233∙∹∝⪩⨒∯1031120)⨼⩣(⪩⨒∯1031100⇟⨁⪰)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15716,"operation_count":3,"complexity_ratio":5238.666666666667,"tree":{"type":"binary","operator":"⨼⩣","left_expr":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"numeric_atoms","value":1711,"base":4},"right_expr":{"type":"numeric_atoms","value":4952,"base":4}},"right_expr":{"type":"unary","operator":"⇟⨁⪰","unary_expr":{"type":"numeric_atoms","value":4944,"base":4}}},"used_operators":["JxwMv5le6e","HmxsFra2vL","BX1lVwlMe0"],"dependent_operators":["uFcxV4UQCh","cHh1gJQ2o6","SL6IHkK8vl","KYD54nUTWz","pRsWfj4Fpp","CArV6hThFE","BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","2DDjHMKMc0","xUOZtlo3hN"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1711","layer":2},{"info":"number node, value=4952","layer":2},{"info":"compute binary expreesion, left_input=1711, right_input=4952, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":1},{"info":"number node, value=4944","layer":2},{"info":"compute unary expreesion, input=4944, op_id = BX1lVwlMe0, unary_op_definition = 'a⇟⨁⪰ = { (⨞⊢(a⋝⋈⪟a)) }', output=-5118","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-5118, op_id = JxwMv5le6e binary_op_definition= 'a⨼⩣b = { ((∐⩳⋚(b⩘a))⪛((∡129)⫥∨⫟(a⫲⨊))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯122233∙∹∝⪩⨒∯1031120)⨼⩣(⪩⨒∯1031100⇟⨁⪰)=NaN","reverse_text":"NaN=(⪩⨒∯122233∙∹∝⪩⨒∯1031120)⨼⩣(⪩⨒∯1031100⇟⨁⪰)","cot":[{"info":"⪩⨒∯122233∙∹∝⪩⨒∯1031120=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1031100⇟⨁⪰=⪩⨒∯-1033332","layer":1},{"info":"⪩⨒∯0⨼⩣⪩⨒∯-1033332=NaN","layer":0}]}
{"id":965,"expression_no_base_symbol":"($2609$⫸⇳$6920$)∵≐","expression":"(⪩⨒∯220301⫸⇳⪩⨒∯1230020)∵≐","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":20,"operation_count":2,"complexity_ratio":10.0,"tree":{"type":"unary","operator":"∵≐","unary_expr":{"type":"binary","operator":"⫸⇳","left_expr":{"type":"numeric_atoms","value":2609,"base":4},"right_expr":{"type":"numeric_atoms","value":6920,"base":4}}},"used_operators":["59igzFyhWz","gx7XJ7hdpj"],"dependent_operators":["W4YGzv6Whe","DZ8iAZOCBD","8w2t5hMYqp","Ph9nP6C5qx","12rbrZMWeM","DpFCA1CohY","7j4O788W3g","tifHPKVTfV","2DQ55sFlQl","DIvbN7qnHd","12rbrZMWeM","t8gj7n24qd","14qkJME0vr","g55IO6H4Gj","eewbuw0ToL"],"result":"⪩⨒∯-12010","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2609","layer":2},{"info":"number node, value=6920","layer":2},{"info":"compute binary expreesion, left_input=2609, right_input=6920, op_id = gx7XJ7hdpj binary_op_definition= 'a⫸⇳b = { (((494⋳⪒b)⇼⇔∾(⋗⩬⋾a))↺((b⊦⊿)⨸⪁(b⨵⪆b))) , if a==116 ; (-((a⨰a)⊠≄⫣)) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = 59igzFyhWz, unary_op_definition = 'a∵≐ = { ((a⊉≛↸31)⋳⪒(101+a)) , if a<=828 ; ((⊄⩳↩a)≧⫂∧(a≧⫂∧a)) , else }', output=-388","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯220301⫸⇳⪩⨒∯1230020)∵≐=⪩⨒∯-12010","reverse_text":"⪩⨒∯-12010=(⪩⨒∯220301⫸⇳⪩⨒∯1230020)∵≐","cot":[{"info":"⪩⨒∯220301⫸⇳⪩⨒∯1230020=⪩⨒∯0","layer":1},{"info":"⪩⨒∯0∵≐=⪩⨒∯-12010","layer":0}]}
{"id":966,"expression_no_base_symbol":"⊆⋠($1535$⫌⩉⩟$6842$)","expression":"⊆⋠(⪩⨒∯113333⫌⩉⩟⪩⨒∯1222322)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34185,"operation_count":2,"complexity_ratio":17092.5,"tree":{"type":"unary","operator":"⊆⋠","unary_expr":{"type":"binary","operator":"⫌⩉⩟","left_expr":{"type":"numeric_atoms","value":1535,"base":4},"right_expr":{"type":"numeric_atoms","value":6842,"base":4}}},"used_operators":["EBhcHTkKd8","XIIwhv8d0m"],"dependent_operators":["YjI8oCXuph","VwlE7vj6HS","e1ybzncUwg","SUmda5xLS4","vg4gO5BX6G","KipPnG1M2J","B5M0gjZbta","UMwdvZNt44","MRPaB8lBjK","vkpjKywKVM"],"result":"⪩⨒∯11130","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1535","layer":2},{"info":"number node, value=6842","layer":2},{"info":"compute binary expreesion, left_input=1535, right_input=6842, op_id = XIIwhv8d0m binary_op_definition= 'a⫌⩉⩟b = { (((a↬179)⇮⋭(b⇡⇂b))⇉⇱⇎) }', output=-50","layer":1},{"info":"compute unary expreesion, input=-50, op_id = EBhcHTkKd8, unary_op_definition = '⊆⋠a = { ((a⊨a)↯⫤) , if (≉a)>=63 ; ((⫇a)⪄(a∀⋜↑)) , else }', output=348","layer":0}],"base":4,"result_base":4,"text":"⊆⋠(⪩⨒∯113333⫌⩉⩟⪩⨒∯1222322)=⪩⨒∯11130","reverse_text":"⪩⨒∯11130=⊆⋠(⪩⨒∯113333⫌⩉⩟⪩⨒∯1222322)","cot":[{"info":"⪩⨒∯113333⫌⩉⩟⪩⨒∯1222322=⪩⨒∯-302","layer":1},{"info":"⊆⋠⪩⨒∯-302=⪩⨒∯11130","layer":0}]}
{"id":967,"expression_no_base_symbol":"($1145$∈)⨲","expression":"(⪩⨒∯101321∈)⨲","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":417966,"operation_count":2,"complexity_ratio":208983.0,"tree":{"type":"unary","operator":"⨲","unary_expr":{"type":"unary","operator":"∈","unary_expr":{"type":"numeric_atoms","value":1145,"base":4}}},"used_operators":["nLYMGWM7L8","ztP7wcbY7m"],"dependent_operators":["DlLNRPXxWL","WR6HLWljOP","48vC8HMD2b","SUmda5xLS4","wicAB68Tmb","hrf7POJlIJ","rysDP5nf3Z","XPYlsWDdGa","8w2t5hMYqp","f6k1SAg4EE","14qkJME0vr"],"result":"⪩⨒∯131023030320031","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1145","layer":2},{"info":"compute unary expreesion, input=1145, op_id = ztP7wcbY7m, unary_op_definition = 'a∈ = { ((⊄⩳↩250)-(a⊦⊿)) , if ((⪲⇎a)>320 or (a⪒777)>25 or a!=39) ; a , else }', output=2764","layer":1},{"info":"compute unary expreesion, input=2764, op_id = nLYMGWM7L8, unary_op_definition = 'a⨲ = { ((a↢a)∴(118⪝a)) , if a==152 ; ((a⪄a)⫘(⫛⫱⨽a)) , else }', output=489475597","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯101321∈)⨲=⪩⨒∯131023030320031","reverse_text":"⪩⨒∯131023030320031=(⪩⨒∯101321∈)⨲","cot":[{"info":"⪩⨒∯101321∈=⪩⨒∯223030","layer":1},{"info":"⪩⨒∯223030⨲=⪩⨒∯131023030320031","layer":0}]}
{"id":968,"expression_no_base_symbol":"(↑$1199$)⪟⇏($1817$⫔⩽⩺$2285$)","expression":"(↑⪩⨒∯102233)⪟⇏(⪩⨒∯130121⫔⩽⩺⪩⨒∯203231)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":101,"operation_count":3,"complexity_ratio":33.666666666666664,"tree":{"type":"binary","operator":"⪟⇏","left_expr":{"type":"unary","operator":"↑","unary_expr":{"type":"numeric_atoms","value":1199,"base":4}},"right_expr":{"type":"binary","operator":"⫔⩽⩺","left_expr":{"type":"numeric_atoms","value":1817,"base":4},"right_expr":{"type":"numeric_atoms","value":2285,"base":4}}},"used_operators":["GODebY97qR","tR7O2zTn5j","i9eR4S00cU"],"dependent_operators":["gx7XJ7hdpj","XnXgA4xnOs","wEfv7U73WA","2DQ55sFlQl","f6k1SAg4EE","oacrs7FA3X","oRDoc9rAEX","RygbFNSyEJ","2DlMacCsIx","Tw270M8GLb","fu6greOZ01"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1199","layer":2},{"info":"compute unary expreesion, input=1199, op_id = tR7O2zTn5j, unary_op_definition = '↑a = { ((a⩨a)⊋≦⊧(a≦↸a)) }', output=192","layer":1},{"info":"number node, value=1817","layer":2},{"info":"number node, value=2285","layer":2},{"info":"compute binary expreesion, left_input=1817, right_input=2285, op_id = i9eR4S00cU binary_op_definition= 'a⫔⩽⩺b = { (⨰⫟⨤(a⨐⩸⫘b)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=192, right_input=nan, op_id = GODebY97qR binary_op_definition= 'a⪟⇏b = { ((b⨑≵⋬b)⫸⇳(440⪒a)) , if (b⇐≅)<189 ; ((219⨑≵⋬a)⪘⫢(b⨵⪆b)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(↑⪩⨒∯102233)⪟⇏(⪩⨒∯130121⫔⩽⩺⪩⨒∯203231)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(↑⪩⨒∯102233)⪟⇏(⪩⨒∯130121⫔⩽⩺⪩⨒∯203231)","cot":[{"info":"↑⪩⨒∯102233=⪩⨒∯3000","layer":1},{"info":"⪩⨒∯130121⫔⩽⩺⪩⨒∯203231=NaN","layer":1},{"info":"⪩⨒∯3000⪟⇏NaN=⪩⨒∯0","layer":0}]}
{"id":969,"expression_no_base_symbol":"↩⪖(⪫⨮⊛$1664$)","expression":"↩⪖(⪫⨮⊛⪩⨒∯122000)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":997168,"operation_count":2,"complexity_ratio":498584.0,"tree":{"type":"unary","operator":"↩⪖","unary_expr":{"type":"unary","operator":"⪫⨮⊛","unary_expr":{"type":"numeric_atoms","value":1664,"base":4}}},"used_operators":["fG6uBQFnGz","w5FWba1tyO"],"dependent_operators":["rysDP5nf3Z","DpFCA1CohY","e1ybzncUwg","XIabStNQrY","eH2TOUuTDT","2DQ55sFlQl","Ph9nP6C5qx","Z2TMIBDE3Q","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","s3Fd5m9Dh2","RZ5CV9rWsJ","SUmda5xLS4","kn8WO9XteQ","hTbEZDJLEm","Tw270M8GLb"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1664","layer":2},{"info":"compute unary expreesion, input=1664, op_id = w5FWba1tyO, unary_op_definition = '⪫⨮⊛a = { a , if (a⨭⪣527)<=182 ; ((⨰⫟⨤(a⪄a))⩖⊿((a⊬⨰a)∟)) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = fG6uBQFnGz, unary_op_definition = '↩⪖a = { (((a-a)⨵⪆(a⪐))⫡⨏(a⩤)) , if (a⇋≉)==322 ; (((≉487)⨳⩥⨓(⋗⩬⋾a))⨸⪁((a⊦⊿)≧⫂∧(a∲⫓a))) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"↩⪖(⪫⨮⊛⪩⨒∯122000)=NaN","reverse_text":"NaN=↩⪖(⪫⨮⊛⪩⨒∯122000)","cot":[{"info":"⪫⨮⊛⪩⨒∯122000=NaN","layer":1},{"info":"↩⪖NaN=NaN","layer":0}]}
{"id":970,"expression_no_base_symbol":"(⪛⨧$1335$)⫯⪬∳($1007$⨓$3760$)","expression":"(⪛⨧⪩⨒∯110313)⫯⪬∳(⪩⨒∯33233⨓⪩⨒∯322300)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3783,"operation_count":3,"complexity_ratio":1261.0,"tree":{"type":"binary","operator":"⫯⪬∳","left_expr":{"type":"unary","operator":"⪛⨧","unary_expr":{"type":"numeric_atoms","value":1335,"base":4}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":1007,"base":4},"right_expr":{"type":"numeric_atoms","value":3760,"base":4}}},"used_operators":["d7ASUq0ydm","6NJAcO2OWT","3ViojmjbAp"],"dependent_operators":["Qy55tPpLXF","BjRHVeLaeN","8w2t5hMYqp","Ph9nP6C5qx","eewbuw0ToL","D4vGDi5EA2","JLbD19bQDL","W4YGzv6Whe","X99M06cbEe","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⪩⨒∯2333320","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1335","layer":2},{"info":"compute unary expreesion, input=1335, op_id = 6NJAcO2OWT, unary_op_definition = '⪛⨧a = { (a+a) , if (a⪠⩆⊳)>=98 ; (a≫≃) , else }', output=4071","layer":1},{"info":"number node, value=1007","layer":2},{"info":"number node, value=3760","layer":2},{"info":"compute binary expreesion, left_input=1007, right_input=3760, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-3763","layer":1},{"info":"compute binary expreesion, left_input=4071, right_input=-3763, op_id = d7ASUq0ydm binary_op_definition= 'a⫯⪬∳b = { ((b⋥≓≎a)≧⫂∧(⊄⩳↩a)) , if (a≦≮≮)!=65 ; ((b⫩⊇)⋥≓≎(a⨰b)) , else }', output=12280","layer":0}],"base":4,"result_base":4,"text":"(⪛⨧⪩⨒∯110313)⫯⪬∳(⪩⨒∯33233⨓⪩⨒∯322300)=⪩⨒∯2333320","reverse_text":"⪩⨒∯2333320=(⪛⨧⪩⨒∯110313)⫯⪬∳(⪩⨒∯33233⨓⪩⨒∯322300)","cot":[{"info":"⪛⨧⪩⨒∯110313=⪩⨒∯333213","layer":1},{"info":"⪩⨒∯33233⨓⪩⨒∯322300=⪩⨒∯-322303","layer":1},{"info":"⪩⨒∯333213⫯⪬∳⪩⨒∯-322303=⪩⨒∯2333320","layer":0}]}
{"id":971,"expression_no_base_symbol":"⩷⨜⫀($5571$⪎↠$1048$)","expression":"⩷⨜⫀(⪩⨒∯1113003⪎↠⪩⨒∯100120)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":17,"operation_count":2,"complexity_ratio":8.5,"tree":{"type":"unary","operator":"⩷⨜⫀","unary_expr":{"type":"binary","operator":"⪎↠","left_expr":{"type":"numeric_atoms","value":5571,"base":4},"right_expr":{"type":"numeric_atoms","value":1048,"base":4}}},"used_operators":["CDi0ktkjQ4","3tVxb0NHM4"],"dependent_operators":["ruOEQAzv1W","nhYeJWJD5X","P8v4zCKN1o","7j4O788W3g","2DQ55sFlQl","12rbrZMWeM"],"result":"⪩⨒∯1301","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5571","layer":2},{"info":"number node, value=1048","layer":2},{"info":"compute binary expreesion, left_input=5571, right_input=1048, op_id = 3tVxb0NHM4 binary_op_definition= 'a⪎↠b = { ((77⋳⪒665)⨵⪆(662↺b)) , if a>621 ; (∥⊫(a↺a)) , else }', output=160","layer":1},{"info":"compute unary expreesion, input=160, op_id = CDi0ktkjQ4, unary_op_definition = '⩷⨜⫀a = { (a∇⊂⋱383) , if a<1 ; (↔a) , else }', output=113","layer":0}],"base":4,"result_base":4,"text":"⩷⨜⫀(⪩⨒∯1113003⪎↠⪩⨒∯100120)=⪩⨒∯1301","reverse_text":"⪩⨒∯1301=⩷⨜⫀(⪩⨒∯1113003⪎↠⪩⨒∯100120)","cot":[{"info":"⪩⨒∯1113003⪎↠⪩⨒∯100120=⪩⨒∯2200","layer":1},{"info":"⩷⨜⫀⪩⨒∯2200=⪩⨒∯1301","layer":0}]}
{"id":972,"expression_no_base_symbol":"($4809$⨲)⩣⫁∢($1792$↺$2217$)","expression":"(⪩⨒∯1023021⨲)⩣⫁∢(⪩⨒∯130000↺⪩⨒∯202221)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":728811,"operation_count":3,"complexity_ratio":242937.0,"tree":{"type":"binary","operator":"⩣⫁∢","left_expr":{"type":"unary","operator":"⨲","unary_expr":{"type":"numeric_atoms","value":4809,"base":4}},"right_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":1792,"base":4},"right_expr":{"type":"numeric_atoms","value":2217,"base":4}}},"used_operators":["JDUIKTTSIa","nLYMGWM7L8","7j4O788W3g"],"dependent_operators":["sdazOOVcIp","eewbuw0ToL","AF7qkfDlqP","u6S6b8DprG","DlLNRPXxWL","WR6HLWljOP","48vC8HMD2b","SUmda5xLS4","wicAB68Tmb","hrf7POJlIJ","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯-1211323103313321","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4809","layer":2},{"info":"compute unary expreesion, input=4809, op_id = nLYMGWM7L8, unary_op_definition = 'a⨲ = { ((a↢a)∴(118⪝a)) , if a==152 ; ((a⪄a)⫘(⫛⫱⨽a)) , else }', output=855023437","layer":1},{"info":"number node, value=1792","layer":2},{"info":"number node, value=2217","layer":2},{"info":"compute binary expreesion, left_input=1792, right_input=2217, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=2217","layer":1},{"info":"compute binary expreesion, left_input=855023437, right_input=2217, op_id = JDUIKTTSIa binary_op_definition= 'a⩣⫁∢b = { (⨑⩽⪐((a⪨≂b)⨰(↽≂b))) }', output=-1710046713","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1023021⨲)⩣⫁∢(⪩⨒∯130000↺⪩⨒∯202221)=⪩⨒∯-1211323103313321","reverse_text":"⪩⨒∯-1211323103313321=(⪩⨒∯1023021⨲)⩣⫁∢(⪩⨒∯130000↺⪩⨒∯202221)","cot":[{"info":"⪩⨒∯1023021⨲=⪩⨒∯302331221331031","layer":1},{"info":"⪩⨒∯130000↺⪩⨒∯202221=⪩⨒∯202221","layer":1},{"info":"⪩⨒∯302331221331031⩣⫁∢⪩⨒∯202221=⪩⨒∯-1211323103313321","layer":0}]}
{"id":973,"expression_no_base_symbol":"$2799$⪛⫼$6553$∖(⇁⨣⪵$1574$)","expression":"⪩⨒∯223233⪛⫼⪩⨒∯1212121∖(⇁⨣⪵⪩⨒∯120212)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":302,"operation_count":3,"complexity_ratio":100.66666666666667,"tree":{"type":"binary","operator":"∖","left_expr":{"type":"binary","operator":"⪛⫼","left_expr":{"type":"numeric_atoms","value":2799,"base":4},"right_expr":{"type":"numeric_atoms","value":6553,"base":4}},"right_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":1574,"base":4}}},"used_operators":["tXD093vOjl","hyuBjUqXlG","inkyxCbjAn"],"dependent_operators":["rysDP5nf3Z","fu6greOZ01","8INZBEW696","DyGG3AbaNP","z6LnFrNh4i","mqXw5SEYmG","u7fv1HBiaC","HJ9erzHUuu","9ICcGScMcE","DO4fhlbJSI","BX1lVwlMe0","Noe24qw2ks","uFcxV4UQCh","A8NUZmVepG","vg4gO5BX6G","dfKe02y8D2","hrf7POJlIJ","mqXw5SEYmG","QMFrweE19q","wztAlM01eG","B5M0gjZbta"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2799","layer":2},{"info":"number node, value=6553","layer":2},{"info":"compute binary expreesion, left_input=2799, right_input=6553, op_id = hyuBjUqXlG binary_op_definition= 'a⪛⫼b = { (((↸⊣b)⫡⨏(⊿b))⫸⊐(≦∁(↥a))) , if (a⇟⨁⪰)!=192 ; (((b⊨a)⪛b)⨐((37⪔⊥b)∴(11⫚↹⊑395))) , else }', output=968","layer":1},{"info":"number node, value=1574","layer":2},{"info":"compute unary expreesion, input=1574, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=968, right_input=nan, op_id = tXD093vOjl binary_op_definition= 'a∖b = { ((448⨐⩸⫘a)≀⩗∶(b⋕⪉⪜a)) , if (⩦⊞a)>101 ; ((b⫸⊐b)∼(65-101)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯223233⪛⫼⪩⨒∯1212121∖(⇁⨣⪵⪩⨒∯120212)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯223233⪛⫼⪩⨒∯1212121∖(⇁⨣⪵⪩⨒∯120212)","cot":[{"info":"⪩⨒∯223233⪛⫼⪩⨒∯1212121=⪩⨒∯33020","layer":1},{"info":"⇁⨣⪵⪩⨒∯120212=NaN","layer":1},{"info":"⪩⨒∯33020∖NaN=⪩⨒∯0","layer":0}]}
{"id":974,"expression_no_base_symbol":"($2341$⩎⪣⊞)⊓⋫","expression":"(⪩⨒∯210211⩎⪣⊞)⊓⋫","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":32804,"operation_count":2,"complexity_ratio":16402.0,"tree":{"type":"unary","operator":"⊓⋫","unary_expr":{"type":"unary","operator":"⩎⪣⊞","unary_expr":{"type":"numeric_atoms","value":2341,"base":4}}},"used_operators":["IqGBaFP0uj","waWucp1uQ4"],"dependent_operators":["2td37pGCOC","sdazOOVcIp","2DDjHMKMc0","f6k1SAg4EE","nCS4ZIUYfx","QMFrweE19q","mp7IySMOzn"],"result":"⪩⨒∯-1023022","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2341","layer":2},{"info":"compute unary expreesion, input=2341, op_id = waWucp1uQ4, unary_op_definition = 'a⩎⪣⊞ = { (a⇷a) }', output=4682","layer":1},{"info":"compute unary expreesion, input=4682, op_id = IqGBaFP0uj, unary_op_definition = 'a⊓⋫ = { (((a⪨≂a)⨳⩥⨓(⩦⩻⨪230))⪒(a⋝⋈⪟(542⫡⨏384))) }', output=-4810","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯210211⩎⪣⊞)⊓⋫=⪩⨒∯-1023022","reverse_text":"⪩⨒∯-1023022=(⪩⨒∯210211⩎⪣⊞)⊓⋫","cot":[{"info":"⪩⨒∯210211⩎⪣⊞=⪩⨒∯1021022","layer":1},{"info":"⪩⨒∯1021022⊓⋫=⪩⨒∯-1023022","layer":0}]}
{"id":975,"expression_no_base_symbol":"⇺⋃($1147$⪬∳)","expression":"⇺⋃(⪩⨒∯101323⪬∳)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":664608,"operation_count":2,"complexity_ratio":332304.0,"tree":{"type":"unary","operator":"⇺⋃","unary_expr":{"type":"unary","operator":"⪬∳","unary_expr":{"type":"numeric_atoms","value":1147,"base":4}}},"used_operators":["E5v5B3UAjG","O9U3z1385E"],"dependent_operators":["bl5wxAcryP","Q3PJZHRvZv","gub5Cegaqo","8INZBEW696","kuIXHzHcAH","7YooWSwCyH","FU0Cs4j7VP","ukq6epAj5P","k7HXdKtiEU","zVYPLywUTj","LYeZOJ0nQG","kuIXHzHcAH","tcjXMdvYtA"],"result":"⪩⨒∯332301","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1147","layer":2},{"info":"compute unary expreesion, input=1147, op_id = O9U3z1385E, unary_op_definition = 'a⪬∳ = { ((a∋a)⊪) , if ((a⪨⊡684)!=357 and (≘a)<480 and (⊲⪭a)>=673) ; (⫎≠⋺(a↛⩡⫤)) , else }', output=-709","layer":1},{"info":"compute unary expreesion, input=-709, op_id = E5v5B3UAjG, unary_op_definition = '⇺⋃a = { (((a≀⩗∶a)∪⫐(a⩁⩘229))⪨⊡(⊥(a↰))) }', output=4017","layer":0}],"base":4,"result_base":4,"text":"⇺⋃(⪩⨒∯101323⪬∳)=⪩⨒∯332301","reverse_text":"⪩⨒∯332301=⇺⋃(⪩⨒∯101323⪬∳)","cot":[{"info":"⪩⨒∯101323⪬∳=⪩⨒∯-23011","layer":1},{"info":"⇺⋃⪩⨒∯-23011=⪩⨒∯332301","layer":0}]}
{"id":976,"expression_no_base_symbol":"($1277$⪒$2811$)∙∹∝$1987$↡⊰⫅$7217$","expression":"(⪩⨒∯103331⪒⪩⨒∯223323)∙∹∝⪩⨒∯133003↡⊰⫅⪩⨒∯1300301","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":101063,"operation_count":3,"complexity_ratio":33687.666666666664,"tree":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":1277,"base":4},"right_expr":{"type":"numeric_atoms","value":2811,"base":4}},"right_expr":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"numeric_atoms","value":1987,"base":4},"right_expr":{"type":"numeric_atoms","value":7217,"base":4}}},"used_operators":["HmxsFra2vL","f6k1SAg4EE","VCtxkLNOzz"],"dependent_operators":["BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","W4YGzv6Whe","t8gj7n24qd","Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1277","layer":2},{"info":"number node, value=2811","layer":2},{"info":"compute binary expreesion, left_input=1277, right_input=2811, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-4088","layer":1},{"info":"number node, value=1987","layer":2},{"info":"number node, value=7217","layer":2},{"info":"compute binary expreesion, left_input=1987, right_input=7217, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=14434","layer":1},{"info":"compute binary expreesion, left_input=-4088, right_input=14434, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯103331⪒⪩⨒∯223323)∙∹∝⪩⨒∯133003↡⊰⫅⪩⨒∯1300301=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯103331⪒⪩⨒∯223323)∙∹∝⪩⨒∯133003↡⊰⫅⪩⨒∯1300301","cot":[{"info":"⪩⨒∯103331⪒⪩⨒∯223323=⪩⨒∯-333320","layer":1},{"info":"⪩⨒∯133003↡⊰⫅⪩⨒∯1300301=⪩⨒∯3201202","layer":1},{"info":"⪩⨒∯-333320∙∹∝⪩⨒∯3201202=⪩⨒∯0","layer":0}]}
{"id":977,"expression_no_base_symbol":"$3305$⋥⋵⩄$4003$⊱⇼⊻$1391$≝⊿$7202$","expression":"⪩⨒∯303221⋥⋵⩄⪩⨒∯332203⊱⇼⊻⪩⨒∯111233≝⊿⪩⨒∯1300202","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":48,"operation_count":3,"complexity_ratio":16.0,"tree":{"type":"binary","operator":"⊱⇼⊻","left_expr":{"type":"binary","operator":"⋥⋵⩄","left_expr":{"type":"numeric_atoms","value":3305,"base":4},"right_expr":{"type":"numeric_atoms","value":4003,"base":4}},"right_expr":{"type":"binary","operator":"≝⊿","left_expr":{"type":"numeric_atoms","value":1391,"base":4},"right_expr":{"type":"numeric_atoms","value":7202,"base":4}}},"used_operators":["FyVja0WsTP","7t3wd0Fuz7","OKKcZfAt5B"],"dependent_operators":["W4YGzv6Whe","Qy55tPpLXF","23Mk6UjR3U","eH2TOUuTDT","EBcxylXtPf","IWmyXbctLI","2td37pGCOC","AFVx7xoS7T","12rbrZMWeM"],"result":"⪩⨒∯302312","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3305","layer":2},{"info":"number node, value=4003","layer":2},{"info":"compute binary expreesion, left_input=3305, right_input=4003, op_id = 7t3wd0Fuz7 binary_op_definition= 'a⋥⋵⩄b = { ((⩦⩻⨪a)⇌⫙⪟(b⪮%⊝b)) }', output=113","layer":1},{"info":"number node, value=1391","layer":2},{"info":"number node, value=7202","layer":2},{"info":"compute binary expreesion, left_input=1391, right_input=7202, op_id = OKKcZfAt5B binary_op_definition= 'a≝⊿b = { ((82⋳⪒b)⋳⪒a) }', output=-16328","layer":1},{"info":"compute binary expreesion, left_input=113, right_input=-16328, op_id = FyVja0WsTP binary_op_definition= 'a⊱⇼⊻b = { ((a⫌⩹⨱)⪐) , if b<551 ; ((135⋥≓≎a)⋷(166+a)) , else }', output=3254","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯303221⋥⋵⩄⪩⨒∯332203⊱⇼⊻⪩⨒∯111233≝⊿⪩⨒∯1300202=⪩⨒∯302312","reverse_text":"⪩⨒∯302312=⪩⨒∯303221⋥⋵⩄⪩⨒∯332203⊱⇼⊻⪩⨒∯111233≝⊿⪩⨒∯1300202","cot":[{"info":"⪩⨒∯303221⋥⋵⩄⪩⨒∯332203=⪩⨒∯1301","layer":1},{"info":"⪩⨒∯111233≝⊿⪩⨒∯1300202=⪩⨒∯-3333020","layer":1},{"info":"⪩⨒∯1301⊱⇼⊻⪩⨒∯-3333020=⪩⨒∯302312","layer":0}]}
{"id":978,"expression_no_base_symbol":"(⨝⨆$4203$)≥⨤⩑(⫯$2976$)","expression":"(⨝⨆⪩⨒∯1001223)≥⨤⩑(⫯⪩⨒∯232200)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1542934,"operation_count":3,"complexity_ratio":514311.3333333333,"tree":{"type":"binary","operator":"≥⨤⩑","left_expr":{"type":"unary","operator":"⨝⨆","unary_expr":{"type":"numeric_atoms","value":4203,"base":4}},"right_expr":{"type":"unary","operator":"⫯","unary_expr":{"type":"numeric_atoms","value":2976,"base":4}}},"used_operators":["gJLn6v0xnP","bQ67fsrMVf","H6BK1Evt7c"],"dependent_operators":["mp7IySMOzn","aA7tF3KVD3","QvoQhV0rrE","tifHPKVTfV","2Wsdkap16l","KbjG8mgYpV","sJAwomhLZr","Ph9nP6C5qx","AYdpE9sXAk","X99M06cbEe"],"result":"⪩⨒∯1330310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4203","layer":2},{"info":"compute unary expreesion, input=4203, op_id = bQ67fsrMVf, unary_op_definition = '⨝⨆a = { (209⇼⇔∾a) }', output=3994","layer":1},{"info":"number node, value=2976","layer":2},{"info":"compute unary expreesion, input=2976, op_id = H6BK1Evt7c, unary_op_definition = '⫯a = { ((a⩠)∠↢(⨂⪏⇭a)) , if (a≧⫂∧919)>20 ; ((a⩹a)≫≃) , else }', output=-110204","layer":1},{"info":"compute binary expreesion, left_input=3994, right_input=-110204, op_id = gJLn6v0xnP binary_op_definition= 'a≥⨤⩑b = { (b⇷a) , if (b⪘⨀)>356 ; (702∠⫱488) , else }', output=7988","layer":0}],"base":4,"result_base":4,"text":"(⨝⨆⪩⨒∯1001223)≥⨤⩑(⫯⪩⨒∯232200)=⪩⨒∯1330310","reverse_text":"⪩⨒∯1330310=(⨝⨆⪩⨒∯1001223)≥⨤⩑(⫯⪩⨒∯232200)","cot":[{"info":"⨝⨆⪩⨒∯1001223=⪩⨒∯332122","layer":1},{"info":"⫯⪩⨒∯232200=⪩⨒∯-122321330","layer":1},{"info":"⪩⨒∯332122≥⨤⩑⪩⨒∯-122321330=⪩⨒∯1330310","layer":0}]}
{"id":979,"expression_no_base_symbol":"(↔$1042$)⋣⋖($1310$⋆⋳)","expression":"(↔⪩⨒∯100102)⋣⋖(⪩⨒∯110132⋆⋳)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":599410,"operation_count":3,"complexity_ratio":199803.33333333334,"tree":{"type":"binary","operator":"⋣⋖","left_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":1042,"base":4}},"right_expr":{"type":"unary","operator":"⋆⋳","unary_expr":{"type":"numeric_atoms","value":1310,"base":4}}},"used_operators":["J0M6qkBnIM","ruOEQAzv1W","6MpZysEj17"],"dependent_operators":["VwlE7vj6HS","LXhwmt4mBO","o575Zjdmzy","fu6greOZ01","u0R0Locfp2","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","9FxExcQeMw","7j4O788W3g","DIvbN7qnHd"],"result":"⪩⨒∯-20033","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1042","layer":2},{"info":"compute unary expreesion, input=1042, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-769","layer":1},{"info":"number node, value=1310","layer":2},{"info":"compute unary expreesion, input=1310, op_id = 6MpZysEj17, unary_op_definition = 'a⋆⋳ = { ((a⊠≄⫣)⩷∴(a↺a)) }', output=-2652","layer":1},{"info":"compute binary expreesion, left_input=-769, right_input=-2652, op_id = J0M6qkBnIM binary_op_definition= 'a⋣⋖b = { ((a⨐⩸⫘a)⨫⇇↔(⪓⩚165)) , if ((a↯⫤)>=571 and (b⫻⋑⊟)>=52) ; a , else }', output=-527","layer":0}],"base":4,"result_base":4,"text":"(↔⪩⨒∯100102)⋣⋖(⪩⨒∯110132⋆⋳)=⪩⨒∯-20033","reverse_text":"⪩⨒∯-20033=(↔⪩⨒∯100102)⋣⋖(⪩⨒∯110132⋆⋳)","cot":[{"info":"↔⪩⨒∯100102=⪩⨒∯-30001","layer":1},{"info":"⪩⨒∯110132⋆⋳=⪩⨒∯-221130","layer":1},{"info":"⪩⨒∯-30001⋣⋖⪩⨒∯-221130=⪩⨒∯-20033","layer":0}]}
{"id":980,"expression_no_base_symbol":"($3678$∠↢$3078$)⪭≯($2078$⇼⇔∾$2859$)","expression":"(⪩⨒∯321132∠↢⪩⨒∯300012)⪭≯(⪩⨒∯200132⇼⇔∾⪩⨒∯230223)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8072,"operation_count":3,"complexity_ratio":2690.6666666666665,"tree":{"type":"binary","operator":"⪭≯","left_expr":{"type":"binary","operator":"∠↢","left_expr":{"type":"numeric_atoms","value":3678,"base":4},"right_expr":{"type":"numeric_atoms","value":3078,"base":4}},"right_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":2078,"base":4},"right_expr":{"type":"numeric_atoms","value":2859,"base":4}}},"used_operators":["XAx5wpdLa6","KbjG8mgYpV","tifHPKVTfV"],"dependent_operators":["9samAPKr6k","HJ9erzHUuu","TpPTUOHfaN","DbCuESL50I","s1XTVnmDOJ","61wBmkZwlr","Z5CJsN7DuW","rysDP5nf3Z","NTOWxs364D","XPYlsWDdGa","t8gj7n24qd","xUOZtlo3hN","g55IO6H4Gj","QMFrweE19q","nCS4ZIUYfx","COABgblf1C","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3678","layer":2},{"info":"number node, value=3078","layer":2},{"info":"compute binary expreesion, left_input=3678, right_input=3078, op_id = KbjG8mgYpV binary_op_definition= 'a∠↢b = { (a⊭↱((159⨳⩥⨓16)-(b⨸⪁a))) , if (b==488 or (⨞⊢a)==254) ; (⪲⇎((-b)⫡⨏(b⩚⊴⇥a))) , else }', output=-56722","layer":1},{"info":"number node, value=2078","layer":2},{"info":"number node, value=2859","layer":2},{"info":"compute binary expreesion, left_input=2078, right_input=2859, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=781","layer":1},{"info":"compute binary expreesion, left_input=-56722, right_input=781, op_id = XAx5wpdLa6 binary_op_definition= 'a⪭≯b = { (((b⨽∌374)⪔⊥(⋼∭⪍b))+⇶⊼((≋a)≓∲(↨⩢⫨a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯321132∠↢⪩⨒∯300012)⪭≯(⪩⨒∯200132⇼⇔∾⪩⨒∯230223)=NaN","reverse_text":"NaN=(⪩⨒∯321132∠↢⪩⨒∯300012)⪭≯(⪩⨒∯200132⇼⇔∾⪩⨒∯230223)","cot":[{"info":"⪩⨒∯321132∠↢⪩⨒∯300012=⪩⨒∯-31312102","layer":1},{"info":"⪩⨒∯200132⇼⇔∾⪩⨒∯230223=⪩⨒∯30031","layer":1},{"info":"⪩⨒∯-31312102⪭≯⪩⨒∯30031=NaN","layer":0}]}
{"id":981,"expression_no_base_symbol":"⊙↵-$2839$⫗⊷⫓$1156$","expression":"⊙↵-⪩⨒∯230113⫗⊷⫓⪩⨒∯102010","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":897683,"operation_count":2,"complexity_ratio":448841.5,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"binary","operator":"⫗⊷⫓","left_expr":{"type":"numeric_atoms","value":2839,"base":4},"right_expr":{"type":"numeric_atoms","value":1156,"base":4}}},"used_operators":["oWn0xqSxBt","zashukvMKz"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","xD69zh8xqp","Uaa54Peajs","BjRHVeLaeN","QiR2Oyf5Xj","k1SHOSEABc","Asc51vEJeQ","oRDoc9rAEX","bJkvcejdHO","8INZBEW696","Af076pWI7l"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2839","layer":2},{"info":"number node, value=1156","layer":2},{"info":"compute binary expreesion, left_input=2839, right_input=1156, op_id = zashukvMKz binary_op_definition= 'a⫗⊷⫓b = { ((∂(b⨂≜a))⫩⊇) , if (↣≠⋷b)<=196 ; ((∷≠(a⊋≦⊧b))↓((b≎⊠⪸a)⪪(a≀⩗∶b))) , else }', output=-134","layer":1},{"info":"compute unary expreesion, input=-134, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⊙↵-⪩⨒∯230113⫗⊷⫓⪩⨒∯102010=⪩⨒∯0","reverse_text":"⪩⨒∯0=⊙↵-⪩⨒∯230113⫗⊷⫓⪩⨒∯102010","cot":[{"info":"⪩⨒∯230113⫗⊷⫓⪩⨒∯102010=⪩⨒∯-2012","layer":1},{"info":"⊙↵-⪩⨒∯-2012=⪩⨒∯0","layer":0}]}
{"id":982,"expression_no_base_symbol":"∡($1031$-$1012$)","expression":"∡(⪩⨒∯100013-⪩⨒∯33310)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9,"operation_count":2,"complexity_ratio":4.5,"tree":{"type":"unary","operator":"∡","unary_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1031,"base":4},"right_expr":{"type":"numeric_atoms","value":1012,"base":4}}},"used_operators":["pRsWfj4Fpp","rysDP5nf3Z"],"dependent_operators":["D4vGDi5EA2","DZ8iAZOCBD","2DDjHMKMc0"],"result":"⪩⨒∯-1302","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1031","layer":2},{"info":"number node, value=1012","layer":2},{"info":"compute binary expreesion, left_input=1031, right_input=1012, op_id = rysDP5nf3Z binary_op_definition= 'None', output=19","layer":1},{"info":"compute unary expreesion, input=19, op_id = pRsWfj4Fpp, unary_op_definition = '∡a = { ((a≦≮≮)⊉≛↸(a⋝⋈⪟a)) }', output=-114","layer":0}],"base":4,"result_base":4,"text":"∡(⪩⨒∯100013-⪩⨒∯33310)=⪩⨒∯-1302","reverse_text":"⪩⨒∯-1302=∡(⪩⨒∯100013-⪩⨒∯33310)","cot":[{"info":"⪩⨒∯100013-⪩⨒∯33310=⪩⨒∯103","layer":1},{"info":"∡⪩⨒∯103=⪩⨒∯-1302","layer":0}]}
{"id":983,"expression_no_base_symbol":"$1532$⪚$8945$∼($6791$⩷∴$4470$)","expression":"⪩⨒∯113330⪚⪩⨒∯2023301∼(⪩⨒∯1222013⩷∴⪩⨒∯1011312)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":326,"operation_count":3,"complexity_ratio":108.66666666666667,"tree":{"type":"binary","operator":"∼","left_expr":{"type":"binary","operator":"⪚","left_expr":{"type":"numeric_atoms","value":1532,"base":4},"right_expr":{"type":"numeric_atoms","value":8945,"base":4}},"right_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":6791,"base":4},"right_expr":{"type":"numeric_atoms","value":4470,"base":4}}},"used_operators":["DyGG3AbaNP","HrjLwUk87U","9FxExcQeMw"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","9FxExcQeMw","rysDP5nf3Z","NTOWxs364D","DZ8iAZOCBD","tifHPKVTfV","eH2TOUuTDT","2DDjHMKMc0","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1532","layer":2},{"info":"number node, value=8945","layer":2},{"info":"compute binary expreesion, left_input=1532, right_input=8945, op_id = HrjLwUk87U binary_op_definition= 'a⪚b = { (((317⩚⊴⇥a)⋝⋈⪟(518-95))⊉≛↸((97⪐)⩷∴(b⇼⇔∾a))) }', output=-15182","layer":1},{"info":"number node, value=6791","layer":2},{"info":"number node, value=4470","layer":2},{"info":"compute binary expreesion, left_input=6791, right_input=4470, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=4610","layer":1},{"info":"compute binary expreesion, left_input=-15182, right_input=4610, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯113330⪚⪩⨒∯2023301∼(⪩⨒∯1222013⩷∴⪩⨒∯1011312)=NaN","reverse_text":"NaN=⪩⨒∯113330⪚⪩⨒∯2023301∼(⪩⨒∯1222013⩷∴⪩⨒∯1011312)","cot":[{"info":"⪩⨒∯113330⪚⪩⨒∯2023301=⪩⨒∯-3231032","layer":1},{"info":"⪩⨒∯1222013⩷∴⪩⨒∯1011312=⪩⨒∯1020002","layer":1},{"info":"⪩⨒∯-3231032∼⪩⨒∯1020002=NaN","layer":0}]}
{"id":984,"expression_no_base_symbol":"(↨⩢⫨$2622$)⩦($4565$⪨≂$6113$)","expression":"(↨⩢⫨⪩⨒∯220332)⩦(⪩⨒∯1013111⪨≂⪩⨒∯1133201)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":87,"operation_count":3,"complexity_ratio":29.0,"tree":{"type":"binary","operator":"⩦","left_expr":{"type":"unary","operator":"↨⩢⫨","unary_expr":{"type":"numeric_atoms","value":2622,"base":4}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":4565,"base":4},"right_expr":{"type":"numeric_atoms","value":6113,"base":4}}},"used_operators":["0kmYd0q39Y","Z5CJsN7DuW","sdazOOVcIp"],"dependent_operators":["N41Kp7NANJ","DZ8iAZOCBD","g55IO6H4Gj","QMFrweE19q","Noe24qw2ks","gu96TGCTMs","8jW3W4yZS5","AFVx7xoS7T","rysDP5nf3Z","t8gj7n24qd"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2622","layer":2},{"info":"compute unary expreesion, input=2622, op_id = Z5CJsN7DuW, unary_op_definition = '↨⩢⫨a = { (((211⨐a)⇌⫙⪟(↯⪼a))⊘) }', output=0","layer":1},{"info":"number node, value=4565","layer":2},{"info":"number node, value=6113","layer":2},{"info":"compute binary expreesion, left_input=4565, right_input=6113, op_id = sdazOOVcIp binary_op_definition= 'a⪨≂b = { (((a-117)-b)-((145-b)-(a-a))) , if (-b)==187 ; ((-(b-102))-((b-a)-a)) , else }', output=-2994","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-2994, op_id = 0kmYd0q39Y binary_op_definition= 'a⩦b = { (a⊉≛↸((a≋⫹)⫡⨏(b⨸⪁45))) }', output=0","layer":0}],"base":4,"result_base":4,"text":"(↨⩢⫨⪩⨒∯220332)⩦(⪩⨒∯1013111⪨≂⪩⨒∯1133201)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(↨⩢⫨⪩⨒∯220332)⩦(⪩⨒∯1013111⪨≂⪩⨒∯1133201)","cot":[{"info":"↨⩢⫨⪩⨒∯220332=⪩⨒∯0","layer":1},{"info":"⪩⨒∯1013111⪨≂⪩⨒∯1133201=⪩⨒∯-232302","layer":1},{"info":"⪩⨒∯0⩦⪩⨒∯-232302=⪩⨒∯0","layer":0}]}
{"id":985,"expression_no_base_symbol":"$8709$→⨶⪴$1791$↡⊰⫅$1916$⪄$1093$","expression":"⪩⨒∯2020011→⨶⪴⪩⨒∯123333↡⊰⫅⪩⨒∯131330⪄⪩⨒∯101011","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3976521,"operation_count":3,"complexity_ratio":1325507.0,"tree":{"type":"binary","operator":"↡⊰⫅","left_expr":{"type":"binary","operator":"→⨶⪴","left_expr":{"type":"numeric_atoms","value":8709,"base":4},"right_expr":{"type":"numeric_atoms","value":1791,"base":4}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":1916,"base":4},"right_expr":{"type":"numeric_atoms","value":1093,"base":4}}},"used_operators":["VCtxkLNOzz","bF6eod5Gvf","SUmda5xLS4"],"dependent_operators":["Ph9nP6C5qx","xRrnTEsQ6j","mp7IySMOzn","8w2t5hMYqp","9FxExcQeMw","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=8709","layer":2},{"info":"number node, value=1791","layer":2},{"info":"compute binary expreesion, left_input=8709, right_input=1791, op_id = bF6eod5Gvf binary_op_definition= 'a→⨶⪴b = { (a⩷∴b) , if b<109 ; (⊄⩳↩b) , else }', output=-5373","layer":1},{"info":"number node, value=1916","layer":2},{"info":"number node, value=1093","layer":2},{"info":"compute binary expreesion, left_input=1916, right_input=1093, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-284029","layer":1},{"info":"compute binary expreesion, left_input=-5373, right_input=-284029, op_id = VCtxkLNOzz binary_op_definition= 'a↡⊰⫅b = { (b⇷b) , if ((b⫁⪎966)!=450 or a!=328 or a==643) ; (b≧⫂∧a) , else }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯2020011→⨶⪴⪩⨒∯123333↡⊰⫅⪩⨒∯131330⪄⪩⨒∯101011=NaN","reverse_text":"NaN=⪩⨒∯2020011→⨶⪴⪩⨒∯123333↡⊰⫅⪩⨒∯131330⪄⪩⨒∯101011","cot":[{"info":"⪩⨒∯2020011→⨶⪴⪩⨒∯123333=⪩⨒∯-1103331","layer":1},{"info":"⪩⨒∯131330⪄⪩⨒∯101011=⪩⨒∯-1011111331","layer":1},{"info":"⪩⨒∯-1103331↡⊰⫅⪩⨒∯-1011111331=NaN","layer":0}]}
{"id":986,"expression_no_base_symbol":"↴⪽⋼$9137$⫗⊷⫓$1658$","expression":"↴⪽⋼⪩⨒∯2032301⫗⊷⫓⪩⨒∯121322","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1287708,"operation_count":2,"complexity_ratio":643854.0,"tree":{"type":"unary","operator":"↴⪽⋼","unary_expr":{"type":"binary","operator":"⫗⊷⫓","left_expr":{"type":"numeric_atoms","value":9137,"base":4},"right_expr":{"type":"numeric_atoms","value":1658,"base":4}}},"used_operators":["5TUYCnJO6w","zashukvMKz"],"dependent_operators":["MGuIdZPyUC","UqFzSgLMvQ","k7HXdKtiEU","yyfyN0ffXY","pRsWfj4Fpp","diKm42VcIt","xD69zh8xqp","Uaa54Peajs","BjRHVeLaeN","QiR2Oyf5Xj","k1SHOSEABc","Asc51vEJeQ","oRDoc9rAEX","bJkvcejdHO","8INZBEW696","Af076pWI7l"],"result":"⪩⨒∯20233232","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=9137","layer":2},{"info":"number node, value=1658","layer":2},{"info":"compute binary expreesion, left_input=9137, right_input=1658, op_id = zashukvMKz binary_op_definition= 'a⫗⊷⫓b = { ((∂(b⨂≜a))⫩⊇) , if (↣≠⋷b)<=196 ; ((∷≠(a⊋≦⊧b))↓((b≎⊠⪸a)⪪(a≀⩗∶b))) , else }', output=-134","layer":1},{"info":"compute unary expreesion, input=-134, op_id = 5TUYCnJO6w, unary_op_definition = '↴⪽⋼a = { a , if ((∡a)<5 or (⇘a)>=19 or (⊲⪭a)==199) ; (((a↙a)⇡)⇉⇉) , else }', output=35822","layer":0}],"base":4,"result_base":4,"text":"↴⪽⋼⪩⨒∯2032301⫗⊷⫓⪩⨒∯121322=⪩⨒∯20233232","reverse_text":"⪩⨒∯20233232=↴⪽⋼⪩⨒∯2032301⫗⊷⫓⪩⨒∯121322","cot":[{"info":"⪩⨒∯2032301⫗⊷⫓⪩⨒∯121322=⪩⨒∯-2012","layer":1},{"info":"↴⪽⋼⪩⨒∯-2012=⪩⨒∯20233232","layer":0}]}
{"id":987,"expression_no_base_symbol":"$2915$⪝$5857$⋥⋵⩄$6545$⫗⊷⫓$1840$","expression":"⪩⨒∯231203⪝⪩⨒∯1123201⋥⋵⩄⪩⨒∯1212101⫗⊷⫓⪩⨒∯130300","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1429432,"operation_count":3,"complexity_ratio":476477.3333333333,"tree":{"type":"binary","operator":"⋥⋵⩄","left_expr":{"type":"binary","operator":"⪝","left_expr":{"type":"numeric_atoms","value":2915,"base":4},"right_expr":{"type":"numeric_atoms","value":5857,"base":4}},"right_expr":{"type":"binary","operator":"⫗⊷⫓","left_expr":{"type":"numeric_atoms","value":6545,"base":4},"right_expr":{"type":"numeric_atoms","value":1840,"base":4}}},"used_operators":["7t3wd0Fuz7","wicAB68Tmb","zashukvMKz"],"dependent_operators":["IWmyXbctLI","2td37pGCOC","AFVx7xoS7T","L05ObWFQCd","eLxqMNBOBk","aSik1wnThz","oacrs7FA3X","xD69zh8xqp","Uaa54Peajs","BjRHVeLaeN","QiR2Oyf5Xj","k1SHOSEABc","Asc51vEJeQ","oRDoc9rAEX","bJkvcejdHO","8INZBEW696","Af076pWI7l"],"result":"⪩⨒∯1301","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2915","layer":2},{"info":"number node, value=5857","layer":2},{"info":"compute binary expreesion, left_input=2915, right_input=5857, op_id = wicAB68Tmb binary_op_definition= 'a⪝b = { (⨩∲⋌((a⪍↜⋙b)⪘⫢(⫓⪴385))) }', output=237","layer":1},{"info":"number node, value=6545","layer":2},{"info":"number node, value=1840","layer":2},{"info":"compute binary expreesion, left_input=6545, right_input=1840, op_id = zashukvMKz binary_op_definition= 'a⫗⊷⫓b = { ((∂(b⨂≜a))⫩⊇) , if (↣≠⋷b)<=196 ; ((∷≠(a⊋≦⊧b))↓((b≎⊠⪸a)⪪(a≀⩗∶b))) , else }', output=-134","layer":1},{"info":"compute binary expreesion, left_input=237, right_input=-134, op_id = 7t3wd0Fuz7 binary_op_definition= 'a⋥⋵⩄b = { ((⩦⩻⨪a)⇌⫙⪟(b⪮%⊝b)) }', output=113","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯231203⪝⪩⨒∯1123201⋥⋵⩄⪩⨒∯1212101⫗⊷⫓⪩⨒∯130300=⪩⨒∯1301","reverse_text":"⪩⨒∯1301=⪩⨒∯231203⪝⪩⨒∯1123201⋥⋵⩄⪩⨒∯1212101⫗⊷⫓⪩⨒∯130300","cot":[{"info":"⪩⨒∯231203⪝⪩⨒∯1123201=⪩⨒∯3231","layer":1},{"info":"⪩⨒∯1212101⫗⊷⫓⪩⨒∯130300=⪩⨒∯-2012","layer":1},{"info":"⪩⨒∯3231⋥⋵⩄⪩⨒∯-2012=⪩⨒∯1301","layer":0}]}
{"id":988,"expression_no_base_symbol":"$2559$⫗⊷⫓$2339$⩖⊿(↘$4113$)","expression":"⪩⨒∯213333⫗⊷⫓⪩⨒∯210203⩖⊿(↘⪩⨒∯1000101)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1816747,"operation_count":3,"complexity_ratio":605582.3333333334,"tree":{"type":"binary","operator":"⩖⊿","left_expr":{"type":"binary","operator":"⫗⊷⫓","left_expr":{"type":"numeric_atoms","value":2559,"base":4},"right_expr":{"type":"numeric_atoms","value":2339,"base":4}},"right_expr":{"type":"unary","operator":"↘","unary_expr":{"type":"numeric_atoms","value":4113,"base":4}}},"used_operators":["RZ5CV9rWsJ","zashukvMKz","LdNpr8hQHL"],"dependent_operators":["HJ9erzHUuu","IWmyXbctLI","8cLx32lpNA","xD69zh8xqp","Uaa54Peajs","BjRHVeLaeN","QiR2Oyf5Xj","k1SHOSEABc","Asc51vEJeQ","oRDoc9rAEX","bJkvcejdHO","8INZBEW696","Af076pWI7l","uFcxV4UQCh"],"result":"⪩⨒∯113320","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2559","layer":2},{"info":"number node, value=2339","layer":2},{"info":"compute binary expreesion, left_input=2559, right_input=2339, op_id = zashukvMKz binary_op_definition= 'a⫗⊷⫓b = { ((∂(b⨂≜a))⫩⊇) , if (↣≠⋷b)<=196 ; ((∷≠(a⊋≦⊧b))↓((b≎⊠⪸a)⪪(a≀⩗∶b))) , else }', output=-134","layer":1},{"info":"number node, value=4113","layer":2},{"info":"compute unary expreesion, input=4113, op_id = LdNpr8hQHL, unary_op_definition = '↘a = { (a⪛392) }', output=193","layer":1},{"info":"compute binary expreesion, left_input=-134, right_input=193, op_id = RZ5CV9rWsJ binary_op_definition= 'a⩖⊿b = { ((b⪔⊥a)⪮%⊝(a∌125)) }', output=1528","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯213333⫗⊷⫓⪩⨒∯210203⩖⊿(↘⪩⨒∯1000101)=⪩⨒∯113320","reverse_text":"⪩⨒∯113320=⪩⨒∯213333⫗⊷⫓⪩⨒∯210203⩖⊿(↘⪩⨒∯1000101)","cot":[{"info":"⪩⨒∯213333⫗⊷⫓⪩⨒∯210203=⪩⨒∯-2012","layer":1},{"info":"↘⪩⨒∯1000101=⪩⨒∯3001","layer":1},{"info":"⪩⨒∯-2012⩖⊿⪩⨒∯3001=⪩⨒∯113320","layer":0}]}
{"id":989,"expression_no_base_symbol":"⇋⊎⋝(↸⊣$3899$)","expression":"⇋⊎⋝(↸⊣⪩⨒∯330323)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3626,"operation_count":2,"complexity_ratio":1813.0,"tree":{"type":"unary","operator":"⇋⊎⋝","unary_expr":{"type":"unary","operator":"↸⊣","unary_expr":{"type":"numeric_atoms","value":3899,"base":4}}},"used_operators":["CzM2PEoXns","wztAlM01eG"],"dependent_operators":["dWAJyo7jo9","N41Kp7NANJ","XPYlsWDdGa","7j4O788W3g","DZ8iAZOCBD","8w2t5hMYqp","12rbrZMWeM","f6k1SAg4EE"],"result":"NaN","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=3899","layer":2},{"info":"compute unary expreesion, input=3899, op_id = wztAlM01eG, unary_op_definition = '↸⊣a = { ((⊄⩳↩a)↺(a≋⫹)) , if (⪲⇎a)<33 ; ((a⪒a)⊉≛↸(a⋳⪒a)) , else }', output=-3612","layer":1},{"info":"compute unary expreesion, input=-3612, op_id = CzM2PEoXns, unary_op_definition = '⇋⊎⋝a = { (a⪢a) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⇋⊎⋝(↸⊣⪩⨒∯330323)=NaN","reverse_text":"NaN=⇋⊎⋝(↸⊣⪩⨒∯330323)","cot":[{"info":"↸⊣⪩⨒∯330323=⪩⨒∯-320130","layer":1},{"info":"⇋⊎⋝⪩⨒∯-320130=NaN","layer":0}]}
{"id":990,"expression_no_base_symbol":"⨈⪑($1824$⫥∨⫟$1742$)","expression":"⨈⪑(⪩⨒∯130200⫥∨⫟⪩⨒∯123032)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":224,"operation_count":2,"complexity_ratio":112.0,"tree":{"type":"unary","operator":"⨈⪑","unary_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1824,"base":4},"right_expr":{"type":"numeric_atoms","value":1742,"base":4}}},"used_operators":["mp94q5OcYM","KYD54nUTWz"],"dependent_operators":["YjI8oCXuph","09Ly4LVMIf","Bmrmz2XGnR","kbkesczE7y","i8ToyICDmI","IWmyXbctLI","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1824","layer":2},{"info":"number node, value=1742","layer":2},{"info":"compute binary expreesion, left_input=1824, right_input=1742, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = mp94q5OcYM, unary_op_definition = '⨈⪑a = { (((⫇a)⫃⨇(89⪮%⊝a))≬⋮((a≚⊃≕a)∲⫓(a⪮%⊝117))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⨈⪑(⪩⨒∯130200⫥∨⫟⪩⨒∯123032)=NaN","reverse_text":"NaN=⨈⪑(⪩⨒∯130200⫥∨⫟⪩⨒∯123032)","cot":[{"info":"⪩⨒∯130200⫥∨⫟⪩⨒∯123032=NaN","layer":1},{"info":"⨈⪑NaN=NaN","layer":0}]}
{"id":991,"expression_no_base_symbol":"($2024$⪔$3603$)⊲⩕⊾$1214$⪮%⊝$1649$","expression":"(⪩⨒∯133220⪔⪩⨒∯320103)⊲⩕⊾⪩⨒∯102332⪮%⊝⪩⨒∯121301","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3733,"operation_count":3,"complexity_ratio":1244.3333333333333,"tree":{"type":"binary","operator":"⊲⩕⊾","left_expr":{"type":"binary","operator":"⪔","left_expr":{"type":"numeric_atoms","value":2024,"base":4},"right_expr":{"type":"numeric_atoms","value":3603,"base":4}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1214,"base":4},"right_expr":{"type":"numeric_atoms","value":1649,"base":4}}},"used_operators":["DmTXOeWf9t","GjBEYRfMaF","IWmyXbctLI"],"dependent_operators":["23Mk6UjR3U","DZ8iAZOCBD","BjRHVeLaeN","QMFrweE19q","AF7qkfDlqP","COABgblf1C","YjI8oCXuph","8INZBEW696","dWAJyo7jo9","nREPSIbpBE","2DDjHMKMc0","IWmyXbctLI","PoHhknlbAi","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⪩⨒∯-13220212","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2024","layer":2},{"info":"number node, value=3603","layer":2},{"info":"compute binary expreesion, left_input=2024, right_input=3603, op_id = GjBEYRfMaF binary_op_definition= 'a⪔b = { (((⫇a)∓⋝(61⪢b))⪮%⊝((b⋝⋈⪟b)⨚(a≀⩗∶a))) }', output=450","layer":1},{"info":"number node, value=1214","layer":2},{"info":"number node, value=1649","layer":2},{"info":"compute binary expreesion, left_input=1214, right_input=1649, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=2744","layer":1},{"info":"compute binary expreesion, left_input=450, right_input=2744, op_id = DmTXOeWf9t binary_op_definition= 'a⊲⩕⊾b = { (((a⊉≛↸b)⊭↱(⨑⩽⪐b))⫡⨏((a⫩⊇)⋷(a⊉≛↸b))) }', output=-31270","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯133220⪔⪩⨒∯320103)⊲⩕⊾⪩⨒∯102332⪮%⊝⪩⨒∯121301=⪩⨒∯-13220212","reverse_text":"⪩⨒∯-13220212=(⪩⨒∯133220⪔⪩⨒∯320103)⊲⩕⊾⪩⨒∯102332⪮%⊝⪩⨒∯121301","cot":[{"info":"⪩⨒∯133220⪔⪩⨒∯320103=⪩⨒∯13002","layer":1},{"info":"⪩⨒∯102332⪮%⊝⪩⨒∯121301=⪩⨒∯222320","layer":1},{"info":"⪩⨒∯13002⊲⩕⊾⪩⨒∯222320=⪩⨒∯-13220212","layer":0}]}
{"id":992,"expression_no_base_symbol":"$2513$⫗⊷⫓$2525$↳∿⪆($1906$⪉⨛$5024$)","expression":"⪩⨒∯213101⫗⊷⫓⪩⨒∯213131↳∿⪆(⪩⨒∯131302⪉⨛⪩⨒∯1032200)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1963661,"operation_count":3,"complexity_ratio":654553.6666666666,"tree":{"type":"binary","operator":"↳∿⪆","left_expr":{"type":"binary","operator":"⫗⊷⫓","left_expr":{"type":"numeric_atoms","value":2513,"base":4},"right_expr":{"type":"numeric_atoms","value":2525,"base":4}},"right_expr":{"type":"binary","operator":"⪉⨛","left_expr":{"type":"numeric_atoms","value":1906,"base":4},"right_expr":{"type":"numeric_atoms","value":5024,"base":4}}},"used_operators":["Cw4SuJJGHO","zashukvMKz","EWw2JM7wp4"],"dependent_operators":["hyuBjUqXlG","bF6eod5Gvf","nEsXyWgiOK","ruOEQAzv1W","Tw270M8GLb","QMFrweE19q","xD69zh8xqp","Uaa54Peajs","BjRHVeLaeN","QiR2Oyf5Xj","k1SHOSEABc","Asc51vEJeQ","oRDoc9rAEX","bJkvcejdHO","8INZBEW696","Af076pWI7l","NTOWxs364D","tifHPKVTfV","12rbrZMWeM","i8ToyICDmI","eewbuw0ToL"],"result":"NaN","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=2513","layer":2},{"info":"number node, value=2525","layer":2},{"info":"compute binary expreesion, left_input=2513, right_input=2525, op_id = zashukvMKz binary_op_definition= 'a⫗⊷⫓b = { ((∂(b⨂≜a))⫩⊇) , if (↣≠⋷b)<=196 ; ((∷≠(a⊋≦⊧b))↓((b≎⊠⪸a)⪪(a≀⩗∶b))) , else }', output=-134","layer":1},{"info":"number node, value=1906","layer":2},{"info":"number node, value=5024","layer":2},{"info":"compute binary expreesion, left_input=1906, right_input=5024, op_id = EWw2JM7wp4 binary_op_definition= 'a⪉⨛b = { (((82⇼⇔∾a)⩚⊴⇥a)⩚⊴⇥((b∲⫓a)⋳⪒(a⨰b))) }', output=909","layer":1},{"info":"compute binary expreesion, left_input=-134, right_input=909, op_id = Cw4SuJJGHO binary_op_definition= 'a↳∿⪆b = { ((⨰⫟⨤(↔15))⨻⩈⩔((b⪛⫼133)⫡⨏(b→⨶⪴a))) }', output=nan","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯213101⫗⊷⫓⪩⨒∯213131↳∿⪆(⪩⨒∯131302⪉⨛⪩⨒∯1032200)=NaN","reverse_text":"NaN=⪩⨒∯213101⫗⊷⫓⪩⨒∯213131↳∿⪆(⪩⨒∯131302⪉⨛⪩⨒∯1032200)","cot":[{"info":"⪩⨒∯213101⫗⊷⫓⪩⨒∯213131=⪩⨒∯-2012","layer":1},{"info":"⪩⨒∯131302⪉⨛⪩⨒∯1032200=⪩⨒∯32031","layer":1},{"info":"⪩⨒∯-2012↳∿⪆⪩⨒∯32031=NaN","layer":0}]}
{"id":993,"expression_no_base_symbol":"(↩⪖$1819$)⇍⊗$3777$∴$1582$","expression":"(↩⪖⪩⨒∯130123)⇍⊗⪩⨒∯323001∴⪩⨒∯120232","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":69,"operation_count":3,"complexity_ratio":23.0,"tree":{"type":"binary","operator":"⇍⊗","left_expr":{"type":"unary","operator":"↩⪖","unary_expr":{"type":"numeric_atoms","value":1819,"base":4}},"right_expr":{"type":"binary","operator":"∴","left_expr":{"type":"numeric_atoms","value":3777,"base":4},"right_expr":{"type":"numeric_atoms","value":1582,"base":4}}},"used_operators":["5uvYHDjeKN","fG6uBQFnGz","hrf7POJlIJ"],"dependent_operators":["Uaa54Peajs","DZ8iAZOCBD","ddLRYrp01A","3sJ7IOPOlU","5twsqlHp2o","rysDP5nf3Z","DpFCA1CohY","e1ybzncUwg","XIabStNQrY","eH2TOUuTDT","2DQ55sFlQl","Ph9nP6C5qx","Z2TMIBDE3Q","14qkJME0vr","g55IO6H4Gj","i8ToyICDmI","nCS4ZIUYfx","QMFrweE19q","g55IO6H4Gj","P8v4zCKN1o","23Mk6UjR3U"],"result":"⪩⨒∯-3310","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1819","layer":2},{"info":"compute unary expreesion, input=1819, op_id = fG6uBQFnGz, unary_op_definition = '↩⪖a = { (((a-a)⨵⪆(a⪐))⫡⨏(a⩤)) , if (a⇋≉)==322 ; (((≉487)⨳⩥⨓(⋗⩬⋾a))⨸⪁((a⊦⊿)≧⫂∧(a∲⫓a))) , else }', output=-13896","layer":1},{"info":"number node, value=3777","layer":2},{"info":"number node, value=1582","layer":2},{"info":"compute binary expreesion, left_input=3777, right_input=1582, op_id = hrf7POJlIJ binary_op_definition= 'a∴b = { ((∥⊫(22⋷b))⨸⪁a) }', output=9202","layer":1},{"info":"compute binary expreesion, left_input=-13896, right_input=9202, op_id = 5uvYHDjeKN binary_op_definition= 'a⇍⊗b = { (((b⊉≛↸b)⪇≇⋚(447⊉≛↸a))⊢(∂(b∊∟⩊b))) }', output=-244","layer":0}],"base":4,"result_base":4,"text":"(↩⪖⪩⨒∯130123)⇍⊗⪩⨒∯323001∴⪩⨒∯120232=⪩⨒∯-3310","reverse_text":"⪩⨒∯-3310=(↩⪖⪩⨒∯130123)⇍⊗⪩⨒∯323001∴⪩⨒∯120232","cot":[{"info":"↩⪖⪩⨒∯130123=⪩⨒∯-3121020","layer":1},{"info":"⪩⨒∯323001∴⪩⨒∯120232=⪩⨒∯2033302","layer":1},{"info":"⪩⨒∯-3121020⇍⊗⪩⨒∯2033302=⪩⨒∯-3310","layer":0}]}
{"id":994,"expression_no_base_symbol":"$4200$⫗⊷⫓$2933$⊔$7623$↼⊘⨖$1676$","expression":"⪩⨒∯1001220⫗⊷⫓⪩⨒∯231311⊔⪩⨒∯1313013↼⊘⨖⪩⨒∯122030","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2278275,"operation_count":3,"complexity_ratio":759425.0,"tree":{"type":"binary","operator":"⊔","left_expr":{"type":"binary","operator":"⫗⊷⫓","left_expr":{"type":"numeric_atoms","value":4200,"base":4},"right_expr":{"type":"numeric_atoms","value":2933,"base":4}},"right_expr":{"type":"binary","operator":"↼⊘⨖","left_expr":{"type":"numeric_atoms","value":7623,"base":4},"right_expr":{"type":"numeric_atoms","value":1676,"base":4}}},"used_operators":["E4l6HwMY31","zashukvMKz","bPywburJMS"],"dependent_operators":["W4YGzv6Whe","DpFCA1CohY","Ph9nP6C5qx","f6k1SAg4EE","i8ToyICDmI","QMFrweE19q","xD69zh8xqp","Uaa54Peajs","BjRHVeLaeN","QiR2Oyf5Xj","k1SHOSEABc","Asc51vEJeQ","oRDoc9rAEX","bJkvcejdHO","8INZBEW696","Af076pWI7l","9FxExcQeMw","P8v4zCKN1o","t8gj7n24qd"],"result":"⪩⨒∯3022312","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=4200","layer":2},{"info":"number node, value=2933","layer":2},{"info":"compute binary expreesion, left_input=4200, right_input=2933, op_id = zashukvMKz binary_op_definition= 'a⫗⊷⫓b = { ((∂(b⨂≜a))⫩⊇) , if (↣≠⋷b)<=196 ; ((∷≠(a⊋≦⊧b))↓((b≎⊠⪸a)⪪(a≀⩗∶b))) , else }', output=-134","layer":1},{"info":"number node, value=7623","layer":2},{"info":"number node, value=1676","layer":2},{"info":"compute binary expreesion, left_input=7623, right_input=1676, op_id = bPywburJMS binary_op_definition= 'a↼⊘⨖b = { (-a) , if (∥⊫b)==149 ; (b⩷∴95) , else }', output=3130","layer":1},{"info":"compute binary expreesion, left_input=-134, right_input=3130, op_id = E4l6HwMY31 binary_op_definition= 'a⊔b = { (((a≧⫂∧b)∲⫓(⋗⩬⋾b))⫡⨏((b⪒a)≧⫂∧(a+64))) }', output=12982","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1001220⫗⊷⫓⪩⨒∯231311⊔⪩⨒∯1313013↼⊘⨖⪩⨒∯122030=⪩⨒∯3022312","reverse_text":"⪩⨒∯3022312=⪩⨒∯1001220⫗⊷⫓⪩⨒∯231311⊔⪩⨒∯1313013↼⊘⨖⪩⨒∯122030","cot":[{"info":"⪩⨒∯1001220⫗⊷⫓⪩⨒∯231311=⪩⨒∯-2012","layer":1},{"info":"⪩⨒∯1313013↼⊘⨖⪩⨒∯122030=⪩⨒∯300322","layer":1},{"info":"⪩⨒∯-2012⊔⪩⨒∯300322=⪩⨒∯3022312","layer":0}]}
{"id":995,"expression_no_base_symbol":"($5613$⫲≸⪮$7194$)⊮⊟↴($4295$∐⫣)","expression":"(⪩⨒∯1113231⫲≸⪮⪩⨒∯1300122)⊮⊟↴(⪩⨒∯1003013∐⫣)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5665,"operation_count":3,"complexity_ratio":1888.3333333333333,"tree":{"type":"binary","operator":"⊮⊟↴","left_expr":{"type":"binary","operator":"⫲≸⪮","left_expr":{"type":"numeric_atoms","value":5613,"base":4},"right_expr":{"type":"numeric_atoms","value":7194,"base":4}},"right_expr":{"type":"unary","operator":"∐⫣","unary_expr":{"type":"numeric_atoms","value":4295,"base":4}}},"used_operators":["QDVgd2eftb","P3lXMJvFrc","4CyGpkTkEk"],"dependent_operators":["XhwjNDsVaA","C6VvDP6HwP","WkeUrDK8WX","kuIXHzHcAH","3Oe9XWJUTD","rJVOvQCfKK","tmPS8pqC7x","oWn0xqSxBt","DbCuESL50I","XPYlsWDdGa","eewbuw0ToL","e1ybzncUwg"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=5613","layer":2},{"info":"number node, value=7194","layer":2},{"info":"compute binary expreesion, left_input=5613, right_input=7194, op_id = P3lXMJvFrc binary_op_definition= 'a⫲≸⪮b = { (⋼∭⪍a) , if (⊙↵-b)>333 ; (a⨪↰⇹b) , else }', output=5613","layer":1},{"info":"number node, value=4295","layer":2},{"info":"compute unary expreesion, input=4295, op_id = 4CyGpkTkEk, unary_op_definition = 'a∐⫣ = { (≉(⪲⇎(a⨰a))) }', output=551","layer":1},{"info":"compute binary expreesion, left_input=5613, right_input=551, op_id = QDVgd2eftb binary_op_definition= 'a⊮⊟↴b = { ((⩰267)⪨⊡(b⊝⪿⪼a)) , if a!=19 ; ((b⨎372)/(b⪑⩈)) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"(⪩⨒∯1113231⫲≸⪮⪩⨒∯1300122)⊮⊟↴(⪩⨒∯1003013∐⫣)=⪩⨒∯0","reverse_text":"⪩⨒∯0=(⪩⨒∯1113231⫲≸⪮⪩⨒∯1300122)⊮⊟↴(⪩⨒∯1003013∐⫣)","cot":[{"info":"⪩⨒∯1113231⫲≸⪮⪩⨒∯1300122=⪩⨒∯1113231","layer":1},{"info":"⪩⨒∯1003013∐⫣=⪩⨒∯20213","layer":1},{"info":"⪩⨒∯1113231⊮⊟↴⪩⨒∯20213=⪩⨒∯0","layer":0}]}
{"id":996,"expression_no_base_symbol":"⇾⩊⇾($1580$∙∹∝$1053$)","expression":"⇾⩊⇾(⪩⨒∯120230∙∹∝⪩⨒∯100131)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":20,"operation_count":2,"complexity_ratio":10.0,"tree":{"type":"unary","operator":"⇾⩊⇾","unary_expr":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"numeric_atoms","value":1580,"base":4},"right_expr":{"type":"numeric_atoms","value":1053,"base":4}}},"used_operators":["bx9Z9DAK5y","HmxsFra2vL"],"dependent_operators":["W4YGzv6Whe","BjRHVeLaeN","8w2t5hMYqp","QMFrweE19q","BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI"],"result":"⪩⨒∯-1211112","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=1580","layer":2},{"info":"number node, value=1053","layer":2},{"info":"compute binary expreesion, left_input=1580, right_input=1053, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = bx9Z9DAK5y, unary_op_definition = '⇾⩊⇾a = { (⊄⩳↩((a+259)⫡⨏(a⫩⊇))) }', output=-6486","layer":0}],"base":4,"result_base":4,"text":"⇾⩊⇾(⪩⨒∯120230∙∹∝⪩⨒∯100131)=⪩⨒∯-1211112","reverse_text":"⪩⨒∯-1211112=⇾⩊⇾(⪩⨒∯120230∙∹∝⪩⨒∯100131)","cot":[{"info":"⪩⨒∯120230∙∹∝⪩⨒∯100131=⪩⨒∯0","layer":1},{"info":"⇾⩊⇾⪩⨒∯0=⪩⨒∯-1211112","layer":0}]}
{"id":997,"expression_no_base_symbol":"⇁⨣⪵($6176$⋹)","expression":"⇁⨣⪵(⪩⨒∯1200200⋹)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":186,"operation_count":2,"complexity_ratio":93.0,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"unary","operator":"⋹","unary_expr":{"type":"numeric_atoms","value":6176,"base":4}}},"used_operators":["inkyxCbjAn","opAxDRczMr"],"dependent_operators":["B5M0gjZbta","13rbtpv6ld","mp7IySMOzn","z63VuFQld9","aN9a90urxU","27wFxooxGf","SVb2v531z1","eewbuw0ToL"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=6176","layer":2},{"info":"compute unary expreesion, input=6176, op_id = opAxDRczMr, unary_op_definition = 'a⋹ = { ((⨴⫝a)⇷(a↤⩊a)) , if (a≃⋄)<20 or (⊢≑≆a)<=20 ; ((a⨰a)∧) , else }', output=-20","layer":1},{"info":"compute unary expreesion, input=-20, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=0","layer":0}],"base":4,"result_base":4,"text":"⇁⨣⪵(⪩⨒∯1200200⋹)=⪩⨒∯0","reverse_text":"⪩⨒∯0=⇁⨣⪵(⪩⨒∯1200200⋹)","cot":[{"info":"⪩⨒∯1200200⋹=⪩⨒∯-110","layer":1},{"info":"⇁⨣⪵⪩⨒∯-110=⪩⨒∯0","layer":0}]}
{"id":998,"expression_no_base_symbol":"$7238$⫗⊷⫓$3104$⨫⇇↔($4571$⨑≵⋬$3432$)","expression":"⪩⨒∯1301012⫗⊷⫓⪩⨒∯300200⨫⇇↔(⪩⨒∯1013123⨑≵⋬⪩⨒∯311220)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2411150,"operation_count":3,"complexity_ratio":803716.6666666666,"tree":{"type":"binary","operator":"⨫⇇↔","left_expr":{"type":"binary","operator":"⫗⊷⫓","left_expr":{"type":"numeric_atoms","value":7238,"base":4},"right_expr":{"type":"numeric_atoms","value":3104,"base":4}},"right_expr":{"type":"binary","operator":"⨑≵⋬","left_expr":{"type":"numeric_atoms","value":4571,"base":4},"right_expr":{"type":"numeric_atoms","value":3432,"base":4}}},"used_operators":["LXhwmt4mBO","zashukvMKz","XnXgA4xnOs"],"dependent_operators":["d7ASUq0ydm","DZ8iAZOCBD","rJVOvQCfKK","xD69zh8xqp","Uaa54Peajs","BjRHVeLaeN","QiR2Oyf5Xj","k1SHOSEABc","Asc51vEJeQ","oRDoc9rAEX","bJkvcejdHO","8INZBEW696","Af076pWI7l","eewbuw0ToL","AF7qkfDlqP","QMFrweE19q"],"result":"⪩⨒∯-20033","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=7238","layer":2},{"info":"number node, value=3104","layer":2},{"info":"compute binary expreesion, left_input=7238, right_input=3104, op_id = zashukvMKz binary_op_definition= 'a⫗⊷⫓b = { ((∂(b⨂≜a))⫩⊇) , if (↣≠⋷b)<=196 ; ((∷≠(a⊋≦⊧b))↓((b≎⊠⪸a)⪪(a≀⩗∶b))) , else }', output=-134","layer":1},{"info":"number node, value=4571","layer":2},{"info":"number node, value=3432","layer":2},{"info":"compute binary expreesion, left_input=4571, right_input=3432, op_id = XnXgA4xnOs binary_op_definition= 'a⨑≵⋬b = { ((a⨰b)⫡⨏(⨑⩽⪐b)) }', output=210","layer":1},{"info":"compute binary expreesion, left_input=-134, right_input=210, op_id = LXhwmt4mBO binary_op_definition= 'a⨫⇇↔b = { ((9⊉≛↸b)⫯⪬∳(a⨎a)) }', output=-527","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯1301012⫗⊷⫓⪩⨒∯300200⨫⇇↔(⪩⨒∯1013123⨑≵⋬⪩⨒∯311220)=⪩⨒∯-20033","reverse_text":"⪩⨒∯-20033=⪩⨒∯1301012⫗⊷⫓⪩⨒∯300200⨫⇇↔(⪩⨒∯1013123⨑≵⋬⪩⨒∯311220)","cot":[{"info":"⪩⨒∯1301012⫗⊷⫓⪩⨒∯300200=⪩⨒∯-2012","layer":1},{"info":"⪩⨒∯1013123⨑≵⋬⪩⨒∯311220=⪩⨒∯3102","layer":1},{"info":"⪩⨒∯-2012⨫⇇↔⪩⨒∯3102=⪩⨒∯-20033","layer":0}]}
{"id":999,"expression_no_base_symbol":"$2885$⫁⪎$1062$∙∹∝$1857$⊝⪿⪼$5848$","expression":"⪩⨒∯231011⫁⪎⪩⨒∯100212∙∹∝⪩⨒∯131001⊝⪿⪼⪩⨒∯1123120","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":38,"operation_count":3,"complexity_ratio":12.666666666666666,"tree":{"type":"binary","operator":"∙∹∝","left_expr":{"type":"binary","operator":"⫁⪎","left_expr":{"type":"numeric_atoms","value":2885,"base":4},"right_expr":{"type":"numeric_atoms","value":1062,"base":4}},"right_expr":{"type":"binary","operator":"⊝⪿⪼","left_expr":{"type":"numeric_atoms","value":1857,"base":4},"right_expr":{"type":"numeric_atoms","value":5848,"base":4}}},"used_operators":["HmxsFra2vL","xRrnTEsQ6j","3Oe9XWJUTD"],"dependent_operators":["BjRHVeLaeN","JLbD19bQDL","f6k1SAg4EE","Z2TMIBDE3Q","i8ToyICDmI","P8v4zCKN1o","Qy55tPpLXF","tifHPKVTfV","sdazOOVcIp","2DDjHMKMc0","i8ToyICDmI","NTOWxs364D","Qy55tPpLXF","8w2t5hMYqp","t8gj7n24qd","eewbuw0ToL","QMFrweE19q"],"result":"⪩⨒∯0","longer_result_info":{"target_base":4,"flag":true},"cot_info":[{"info":"number node, value=2885","layer":2},{"info":"number node, value=1062","layer":2},{"info":"compute binary expreesion, left_input=2885, right_input=1062, op_id = xRrnTEsQ6j binary_op_definition= 'a⫁⪎b = { ((b⋝⋈⪟a)⇼⇔∾a) , if (∥⊫b)!=57 ; ((191∲⫓a)⋥≓≎(a⪨≂368)) , else }', output=1823","layer":1},{"info":"number node, value=1857","layer":2},{"info":"number node, value=5848","layer":2},{"info":"compute binary expreesion, left_input=1857, right_input=5848, op_id = 3Oe9XWJUTD binary_op_definition= 'a⊝⪿⪼b = { ((⊄⩳↩(480⩚⊴⇥a))⫡⨏((a⨰b)⋥≓≎(-b))) }', output=37787","layer":1},{"info":"compute binary expreesion, left_input=1823, right_input=37787, op_id = HmxsFra2vL binary_op_definition= 'a∙∹∝b = { ((a⪒408)∲⫓(b⩤)) , if (a⫩⊇)==144 ; ((a⩤)⪠⩆⊳) , else }', output=0","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯231011⫁⪎⪩⨒∯100212∙∹∝⪩⨒∯131001⊝⪿⪼⪩⨒∯1123120=⪩⨒∯0","reverse_text":"⪩⨒∯0=⪩⨒∯231011⫁⪎⪩⨒∯100212∙∹∝⪩⨒∯131001⊝⪿⪼⪩⨒∯1123120","cot":[{"info":"⪩⨒∯231011⫁⪎⪩⨒∯100212=⪩⨒∯130133","layer":1},{"info":"⪩⨒∯131001⊝⪿⪼⪩⨒∯1123120=⪩⨒∯21032123","layer":1},{"info":"⪩⨒∯130133∙∹∝⪩⨒∯21032123=⪩⨒∯0","layer":0}]}
{"id":1000,"expression_no_base_symbol":"$1005$⫗⊷⫓$3490$↸($1840$⩘)","expression":"⪩⨒∯33231⫗⊷⫓⪩⨒∯312202↸(⪩⨒∯130300⩘)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2711153,"operation_count":3,"complexity_ratio":903717.6666666666,"tree":{"type":"binary","operator":"↸","left_expr":{"type":"binary","operator":"⫗⊷⫓","left_expr":{"type":"numeric_atoms","value":1005,"base":4},"right_expr":{"type":"numeric_atoms","value":3490,"base":4}},"right_expr":{"type":"unary","operator":"⩘","unary_expr":{"type":"numeric_atoms","value":1840,"base":4}}},"used_operators":["1eCjFl0mb9","zashukvMKz","wvHyciQT5X"],"dependent_operators":["9HNa5Wba9A","61wBmkZwlr","rJVOvQCfKK","xD69zh8xqp","Uaa54Peajs","BjRHVeLaeN","QiR2Oyf5Xj","k1SHOSEABc","Asc51vEJeQ","oRDoc9rAEX","bJkvcejdHO","8INZBEW696","Af076pWI7l","9ICcGScMcE","dfKe02y8D2"],"result":"⪩⨒∯-2012","longer_result_info":{"target_base":4,"flag":false},"cot_info":[{"info":"number node, value=1005","layer":2},{"info":"number node, value=3490","layer":2},{"info":"compute binary expreesion, left_input=1005, right_input=3490, op_id = zashukvMKz binary_op_definition= 'a⫗⊷⫓b = { ((∂(b⨂≜a))⫩⊇) , if (↣≠⋷b)<=196 ; ((∷≠(a⊋≦⊧b))↓((b≎⊠⪸a)⪪(a≀⩗∶b))) , else }', output=-134","layer":1},{"info":"number node, value=1840","layer":2},{"info":"compute unary expreesion, input=1840, op_id = wvHyciQT5X, unary_op_definition = 'a⩘ = { (≦∁(a⫚↹⊑129)) }', output=67","layer":1},{"info":"compute binary expreesion, left_input=-134, right_input=67, op_id = 1eCjFl0mb9 binary_op_definition= 'a↸b = { ((b*a)⨎(≋a)) }', output=-134","layer":0}],"base":4,"result_base":4,"text":"⪩⨒∯33231⫗⊷⫓⪩⨒∯312202↸(⪩⨒∯130300⩘)=⪩⨒∯-2012","reverse_text":"⪩⨒∯-2012=⪩⨒∯33231⫗⊷⫓⪩⨒∯312202↸(⪩⨒∯130300⩘)","cot":[{"info":"⪩⨒∯33231⫗⊷⫓⪩⨒∯312202=⪩⨒∯-2012","layer":1},{"info":"⪩⨒∯130300⩘=⪩⨒∯1003","layer":1},{"info":"⪩⨒∯-2012↸⪩⨒∯1003=⪩⨒∯-2012","layer":0}]}