{"id":1,"expression_no_base_symbol":"($1048$∲⫓$1039$)⫥∨⫟$3289$+⇶⊼$1220$","expression":"(⫏≰1102211∲⫓⫏≰1102111)⫥∨⫟⫏≰11111211+⇶⊼⫏≰1200012","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":157,"operation_count":3,"complexity_ratio":52.333333333333336,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":1048,"base":3},"right_expr":{"type":"numeric_atoms","value":1039,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":3289,"base":3},"right_expr":{"type":"numeric_atoms","value":1220,"base":3}}},"used_operators":["KYD54nUTWz","i8ToyICDmI","TpPTUOHfaN"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1048","layer":2},{"info":"number node, value=1039","layer":2},{"info":"compute binary expreesion, left_input=1048, right_input=1039, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=3289","layer":2},{"info":"number node, value=1220","layer":2},{"info":"compute binary expreesion, left_input=3289, right_input=1220, 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":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1102211∲⫓⫏≰1102111)⫥∨⫟⫏≰11111211+⇶⊼⫏≰1200012=NaN","reverse_text":"NaN=(⫏≰1102211∲⫓⫏≰1102111)⫥∨⫟⫏≰11111211+⇶⊼⫏≰1200012","cot":[{"info":"⫏≰1102211∲⫓⫏≰1102111=⫏≰0","layer":1},{"info":"⫏≰11111211+⇶⊼⫏≰1200012=NaN","layer":1},{"info":"⫏≰0⫥∨⫟NaN=NaN","layer":0}]}
{"id":2,"expression_no_base_symbol":"(⫓⪴$3633$)⩚⊴⇥($2651$⫡⨏$2242$)","expression":"(⫓⪴⫏≰11222120)⩚⊴⇥(⫏≰10122012⫡⨏⫏≰10002001)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3643,"operation_count":3,"complexity_ratio":1214.3333333333333,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":3633,"base":3}},"right_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":2651,"base":3},"right_expr":{"type":"numeric_atoms","value":2242,"base":3}}},"used_operators":["NTOWxs364D","eLxqMNBOBk","QMFrweE19q"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","9HNa5Wba9A","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-220212111202211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3633","layer":2},{"info":"compute unary expreesion, input=3633, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=13198689","layer":1},{"info":"number node, value=2651","layer":2},{"info":"number node, value=2242","layer":2},{"info":"compute binary expreesion, left_input=2651, right_input=2242, 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=18522","layer":1},{"info":"compute binary expreesion, left_input=13198689, right_input=18522, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-13217332","layer":0}],"base":3,"result_base":3,"text":"(⫓⪴⫏≰11222120)⩚⊴⇥(⫏≰10122012⫡⨏⫏≰10002001)=⫏≰-220212111202211","reverse_text":"⫏≰-220212111202211=(⫓⪴⫏≰11222120)⩚⊴⇥(⫏≰10122012⫡⨏⫏≰10002001)","cot":[{"info":"⫓⪴⫏≰11222120=⫏≰220211120012100","layer":1},{"info":"⫏≰10122012⫡⨏⫏≰10002001=⫏≰221102000","layer":1},{"info":"⫏≰220211120012100⩚⊴⇥⫏≰221102000=⫏≰-220212111202211","layer":0}]}
{"id":3,"expression_no_base_symbol":"↥($3494$⪒$1242$)","expression":"↥(⫏≰11210102⪒⫏≰1201000)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":95,"operation_count":2,"complexity_ratio":47.5,"tree":{"type":"unary","operator":"↥","unary_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":3494,"base":3},"right_expr":{"type":"numeric_atoms","value":1242,"base":3}}},"used_operators":["A8NUZmVepG","f6k1SAg4EE"],"dependent_operators":["k8jYdgA6NY","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3494","layer":2},{"info":"number node, value=1242","layer":2},{"info":"compute binary expreesion, left_input=3494, right_input=1242, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-4736","layer":1},{"info":"compute unary expreesion, input=-4736, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=7","layer":0}],"base":3,"result_base":3,"text":"↥(⫏≰11210102⪒⫏≰1201000)=⫏≰21","reverse_text":"⫏≰21=↥(⫏≰11210102⪒⫏≰1201000)","cot":[{"info":"⫏≰11210102⪒⫏≰1201000=⫏≰-20111102","layer":1},{"info":"↥⫏≰-20111102=⫏≰21","layer":0}]}
{"id":4,"expression_no_base_symbol":"(∥⊫$7279$)∼($2353$⩨$1025$)","expression":"(∥⊫⫏≰100222121)∼(⫏≰10020011⩨⫏≰1101222)","highest_n_order":4,"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":7279,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":2353,"base":3},"right_expr":{"type":"numeric_atoms","value":1025,"base":3}}},"used_operators":["DyGG3AbaNP","P8v4zCKN1o","2DlMacCsIx"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰202","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7279","layer":2},{"info":"compute unary expreesion, input=7279, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=8147","layer":1},{"info":"number node, value=2353","layer":2},{"info":"number node, value=1025","layer":2},{"info":"compute binary expreesion, left_input=2353, right_input=1025, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=8147, right_input=0, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=20","layer":0}],"base":3,"result_base":3,"text":"(∥⊫⫏≰100222121)∼(⫏≰10020011⩨⫏≰1101222)=⫏≰202","reverse_text":"⫏≰202=(∥⊫⫏≰100222121)∼(⫏≰10020011⩨⫏≰1101222)","cot":[{"info":"∥⊫⫏≰100222121=⫏≰102011202","layer":1},{"info":"⫏≰10020011⩨⫏≰1101222=⫏≰0","layer":1},{"info":"⫏≰102011202∼⫏≰0=⫏≰202","layer":0}]}
{"id":5,"expression_no_base_symbol":"($1672$⫩⊇)/(⩦⩻⨪$2096$)","expression":"(⫏≰2021221⫩⊇)/(⩦⩻⨪⫏≰2212122)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"/","left_expr":{"type":"unary","operator":"⫩⊇","unary_expr":{"type":"numeric_atoms","value":1672,"base":3}},"right_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":2096,"base":3}}},"used_operators":["XhwjNDsVaA","BjRHVeLaeN","2td37pGCOC"],"dependent_operators":["rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1672","layer":2},{"info":"compute unary expreesion, input=1672, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=-1630","layer":1},{"info":"number node, value=2096","layer":2},{"info":"compute unary expreesion, input=2096, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=2096","layer":1},{"info":"compute binary expreesion, left_input=-1630, right_input=2096, op_id = XhwjNDsVaA binary_op_definition= 'None', output=-1","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2021221⫩⊇)/(⩦⩻⨪⫏≰2212122)=⫏≰-1","reverse_text":"⫏≰-1=(⫏≰2021221⫩⊇)/(⩦⩻⨪⫏≰2212122)","cot":[{"info":"⫏≰2021221⫩⊇=⫏≰-2020101","layer":1},{"info":"⩦⩻⨪⫏≰2212122=⫏≰2212122","layer":1},{"info":"⫏≰-2020101/⫏≰2212122=⫏≰-1","layer":0}]}
{"id":6,"expression_no_base_symbol":"$1255$⋝⋈⪟$2668$↪⪝","expression":"⫏≰1201111⋝⋈⪟⫏≰10122211↪⪝","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":703,"operation_count":2,"complexity_ratio":351.5,"tree":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":1255,"base":3},"right_expr":{"type":"numeric_atoms","value":2668,"base":3}}},"used_operators":["l07mrZUIn9","2DDjHMKMc0"],"dependent_operators":["9HNa5Wba9A","2DDjHMKMc0","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰12100111000001000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1255","layer":2},{"info":"number node, value=2668","layer":2},{"info":"compute binary expreesion, left_input=1255, right_input=2668, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=1255","layer":1},{"info":"compute unary expreesion, input=1255, op_id = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=76783410","layer":0}],"base":3,"result_base":3,"text":"⫏≰1201111⋝⋈⪟⫏≰10122211↪⪝=⫏≰12100111000001000","reverse_text":"⫏≰12100111000001000=⫏≰1201111⋝⋈⪟⫏≰10122211↪⪝","cot":[{"info":"⫏≰1201111⋝⋈⪟⫏≰10122211=⫏≰1201111","layer":1},{"info":"⫏≰1201111↪⪝=⫏≰12100111000001000","layer":0}]}
{"id":7,"expression_no_base_symbol":"$3181$⊭↱$6001$+($1138$⪠⩆⊳)","expression":"⫏≰11100211⊭↱⫏≰22020021+(⫏≰1120011⪠⩆⊳)","highest_n_order":1,"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":3181,"base":3},"right_expr":{"type":"numeric_atoms","value":6001,"base":3}},"right_expr":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"numeric_atoms","value":1138,"base":3}}},"used_operators":["W4YGzv6Whe","COABgblf1C","JLbD19bQDL"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21202002","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3181","layer":2},{"info":"number node, value=6001","layer":2},{"info":"compute binary expreesion, left_input=3181, right_input=6001, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=5645","layer":1},{"info":"number node, value=1138","layer":2},{"info":"compute unary expreesion, input=1138, 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":"compute binary expreesion, left_input=5645, right_input=0, op_id = W4YGzv6Whe binary_op_definition= 'None', output=5645","layer":0}],"base":3,"result_base":3,"text":"⫏≰11100211⊭↱⫏≰22020021+(⫏≰1120011⪠⩆⊳)=⫏≰21202002","reverse_text":"⫏≰21202002=⫏≰11100211⊭↱⫏≰22020021+(⫏≰1120011⪠⩆⊳)","cot":[{"info":"⫏≰11100211⊭↱⫏≰22020021=⫏≰21202002","layer":1},{"info":"⫏≰1120011⪠⩆⊳=⫏≰0","layer":1},{"info":"⫏≰21202002+⫏≰0=⫏≰21202002","layer":0}]}
{"id":8,"expression_no_base_symbol":"$1043$⩷∴$8581$⋳⪒$2751$⊴$1400$","expression":"⫏≰1102122⩷∴⫏≰102202211⋳⪒⫏≰10202220⊴⫏≰1220212","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1867,"operation_count":3,"complexity_ratio":622.3333333333334,"tree":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":1043,"base":3},"right_expr":{"type":"numeric_atoms","value":8581,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":2751,"base":3},"right_expr":{"type":"numeric_atoms","value":1400,"base":3}}},"used_operators":["12rbrZMWeM","9FxExcQeMw","Nsiff2A1zJ"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1043","layer":2},{"info":"number node, value=8581","layer":2},{"info":"compute binary expreesion, left_input=1043, right_input=8581, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-15108","layer":1},{"info":"number node, value=2751","layer":2},{"info":"number node, value=1400","layer":2},{"info":"compute binary expreesion, left_input=2751, right_input=1400, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-15108, right_input=nan, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1102122⩷∴⫏≰102202211⋳⪒⫏≰10202220⊴⫏≰1220212=NaN","reverse_text":"NaN=⫏≰1102122⩷∴⫏≰102202211⋳⪒⫏≰10202220⊴⫏≰1220212","cot":[{"info":"⫏≰1102122⩷∴⫏≰102202211=⫏≰-202201120","layer":1},{"info":"⫏≰10202220⊴⫏≰1220212=NaN","layer":1},{"info":"⫏≰-202201120⋳⪒NaN=NaN","layer":0}]}
{"id":9,"expression_no_base_symbol":"$3319$≹⇙⪍$2331$⋳⪒$2040$⋓$1123$","expression":"⫏≰11112221≹⇙⪍⫏≰10012100⋳⪒⫏≰2210120⋓⫏≰1112121","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":3319,"base":3},"right_expr":{"type":"numeric_atoms","value":2331,"base":3}},"right_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":2040,"base":3},"right_expr":{"type":"numeric_atoms","value":1123,"base":3}}},"used_operators":["12rbrZMWeM","AHs5Up7iyr","T2fj7uvVaJ"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3319","layer":2},{"info":"number node, value=2331","layer":2},{"info":"compute binary expreesion, left_input=3319, right_input=2331, 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":"number node, value=2040","layer":2},{"info":"number node, value=1123","layer":2},{"info":"compute binary expreesion, left_input=2040, right_input=1123, 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=nan, right_input=0, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11112221≹⇙⪍⫏≰10012100⋳⪒⫏≰2210120⋓⫏≰1112121=NaN","reverse_text":"NaN=⫏≰11112221≹⇙⪍⫏≰10012100⋳⪒⫏≰2210120⋓⫏≰1112121","cot":[{"info":"⫏≰11112221≹⇙⪍⫏≰10012100=NaN","layer":1},{"info":"⫏≰2210120⋓⫏≰1112121=⫏≰0","layer":1},{"info":"NaN⋳⪒⫏≰0=NaN","layer":0}]}
{"id":10,"expression_no_base_symbol":"⊥(+⊝⨔$3794$)","expression":"⊥(+⊝⨔⫏≰12012112)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":41,"operation_count":2,"complexity_ratio":20.5,"tree":{"type":"unary","operator":"⊥","unary_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":3794,"base":3}}},"used_operators":["Q3PJZHRvZv","DhbWaqg5eL"],"dependent_operators":["fu6greOZ01","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3794","layer":2},{"info":"compute unary expreesion, input=3794, 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 = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊥(+⊝⨔⫏≰12012112)=NaN","reverse_text":"NaN=⊥(+⊝⨔⫏≰12012112)","cot":[{"info":"+⊝⨔⫏≰12012112=⫏≰2002101","layer":1},{"info":"⊥⫏≰2002101=NaN","layer":0}]}
{"id":11,"expression_no_base_symbol":"$1248$⪮%⊝$1490$↬($1523$+$2129$)","expression":"⫏≰1201020⪮%⊝⫏≰2001012↬(⫏≰2002102+⫏≰2220212)","highest_n_order":5,"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":1248,"base":3},"right_expr":{"type":"numeric_atoms","value":1490,"base":3}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":1523,"base":3},"right_expr":{"type":"numeric_atoms","value":2129,"base":3}}},"used_operators":["B5M0gjZbta","IWmyXbctLI","W4YGzv6Whe"],"dependent_operators":["rGHVDoGpnC","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1248","layer":2},{"info":"number node, value=1490","layer":2},{"info":"compute binary expreesion, left_input=1248, right_input=1490, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=2812","layer":1},{"info":"number node, value=1523","layer":2},{"info":"number node, value=2129","layer":2},{"info":"compute binary expreesion, left_input=1523, right_input=2129, op_id = W4YGzv6Whe binary_op_definition= 'None', output=3652","layer":1},{"info":"compute binary expreesion, left_input=2812, right_input=3652, 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":3,"result_base":3,"text":"⫏≰1201020⪮%⊝⫏≰2001012↬(⫏≰2002102+⫏≰2220212)=NaN","reverse_text":"NaN=⫏≰1201020⪮%⊝⫏≰2001012↬(⫏≰2002102+⫏≰2220212)","cot":[{"info":"⫏≰1201020⪮%⊝⫏≰2001012=⫏≰10212011","layer":1},{"info":"⫏≰2002102+⫏≰2220212=⫏≰12000021","layer":1},{"info":"⫏≰10212011↬⫏≰12000021=NaN","layer":0}]}
{"id":12,"expression_no_base_symbol":"$3346$↬$1781$⩨(⪝⪂⫅$5201$)","expression":"⫏≰11120221↬⫏≰2102222⩨(⪝⪂⫅⫏≰21010122)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":155,"operation_count":3,"complexity_ratio":51.666666666666664,"tree":{"type":"binary","operator":"⩨","left_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":3346,"base":3},"right_expr":{"type":"numeric_atoms","value":1781,"base":3}},"right_expr":{"type":"unary","operator":"⪝⪂⫅","unary_expr":{"type":"numeric_atoms","value":5201,"base":3}}},"used_operators":["2DlMacCsIx","B5M0gjZbta","XTarYq4gQB"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","rGHVDoGpnC","9HNa5Wba9A","8w2t5hMYqp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3346","layer":2},{"info":"number node, value=1781","layer":2},{"info":"compute binary expreesion, left_input=3346, right_input=1781, 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=5201","layer":2},{"info":"compute unary expreesion, input=5201, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=-764547","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-764547, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11120221↬⫏≰2102222⩨(⪝⪂⫅⫏≰21010122)=NaN","reverse_text":"NaN=⫏≰11120221↬⫏≰2102222⩨(⪝⪂⫅⫏≰21010122)","cot":[{"info":"⫏≰11120221↬⫏≰2102222=NaN","layer":1},{"info":"⪝⪂⫅⫏≰21010122=⫏≰-1102211202120","layer":1},{"info":"NaN⩨⫏≰-1102211202120=NaN","layer":0}]}
{"id":13,"expression_no_base_symbol":"($5987$⨁⊸⫻)⇼⇔∾($3483$⊉≛↸$2134$)","expression":"(⫏≰22012202⨁⊸⫻)⇼⇔∾(⫏≰11210000⊉≛↸⫏≰2221001)","highest_n_order":1,"priority_hierarchical_complexity":2,"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":5987,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":3483,"base":3},"right_expr":{"type":"numeric_atoms","value":2134,"base":3}}},"used_operators":["tifHPKVTfV","glklzrTFfD","DZ8iAZOCBD"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1100021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5987","layer":2},{"info":"compute unary expreesion, input=5987, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=5987","layer":1},{"info":"number node, value=3483","layer":2},{"info":"number node, value=2134","layer":2},{"info":"compute binary expreesion, left_input=3483, right_input=2134, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=6966","layer":1},{"info":"compute binary expreesion, left_input=5987, right_input=6966, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=979","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22012202⨁⊸⫻)⇼⇔∾(⫏≰11210000⊉≛↸⫏≰2221001)=⫏≰1100021","reverse_text":"⫏≰1100021=(⫏≰22012202⨁⊸⫻)⇼⇔∾(⫏≰11210000⊉≛↸⫏≰2221001)","cot":[{"info":"⫏≰22012202⨁⊸⫻=⫏≰22012202","layer":1},{"info":"⫏≰11210000⊉≛↸⫏≰2221001=⫏≰100120000","layer":1},{"info":"⫏≰22012202⇼⇔∾⫏≰100120000=⫏≰1100021","layer":0}]}
{"id":14,"expression_no_base_symbol":"≦∁$1452$⊉≛↸$2226$","expression":"≦∁⫏≰1222210⊉≛↸⫏≰10001110","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":1452,"base":3},"right_expr":{"type":"numeric_atoms","value":2226,"base":3}}},"used_operators":["9ICcGScMcE","DZ8iAZOCBD"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰10222120","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1452","layer":2},{"info":"number node, value=2226","layer":2},{"info":"compute binary expreesion, left_input=1452, right_input=2226, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=2904","layer":1},{"info":"compute unary expreesion, input=2904, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=2904","layer":0}],"base":3,"result_base":3,"text":"≦∁⫏≰1222210⊉≛↸⫏≰10001110=⫏≰10222120","reverse_text":"⫏≰10222120=≦∁⫏≰1222210⊉≛↸⫏≰10001110","cot":[{"info":"⫏≰1222210⊉≛↸⫏≰10001110=⫏≰10222120","layer":1},{"info":"≦∁⫏≰10222120=⫏≰10222120","layer":0}]}
{"id":15,"expression_no_base_symbol":"$7493$↬$1399$-(⊄⩳↩$4171$)","expression":"⫏≰101021112↬⫏≰1220211-(⊄⩳↩⫏≰12201111)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5,"operation_count":3,"complexity_ratio":1.6666666666666667,"tree":{"type":"binary","operator":"-","left_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":7493,"base":3},"right_expr":{"type":"numeric_atoms","value":1399,"base":3}},"right_expr":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":4171,"base":3}}},"used_operators":["rysDP5nf3Z","B5M0gjZbta","8w2t5hMYqp"],"dependent_operators":["rGHVDoGpnC","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7493","layer":2},{"info":"number node, value=1399","layer":2},{"info":"compute binary expreesion, left_input=7493, right_input=1399, 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=4171","layer":2},{"info":"compute unary expreesion, input=4171, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-12513","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-12513, op_id = rysDP5nf3Z binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰101021112↬⫏≰1220211-(⊄⩳↩⫏≰12201111)=NaN","reverse_text":"NaN=⫏≰101021112↬⫏≰1220211-(⊄⩳↩⫏≰12201111)","cot":[{"info":"⫏≰101021112↬⫏≰1220211=NaN","layer":1},{"info":"⊄⩳↩⫏≰12201111=⫏≰-122011110","layer":1},{"info":"NaN-⫏≰-122011110=NaN","layer":0}]}
{"id":16,"expression_no_base_symbol":"(⊥$1177$)⨪↰⇹(≦∁$2615$)","expression":"(⊥⫏≰1121121)⨪↰⇹(≦∁⫏≰10120212)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3,"operation_count":3,"complexity_ratio":1.0,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":1177,"base":3}},"right_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":2615,"base":3}}},"used_operators":["tmPS8pqC7x","Q3PJZHRvZv","9ICcGScMcE"],"dependent_operators":["rJVOvQCfKK","fu6greOZ01","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1177","layer":2},{"info":"compute unary expreesion, input=1177, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"number node, value=2615","layer":2},{"info":"compute unary expreesion, input=2615, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=2615","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2615, 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=nan","layer":0}],"base":3,"result_base":3,"text":"(⊥⫏≰1121121)⨪↰⇹(≦∁⫏≰10120212)=NaN","reverse_text":"NaN=(⊥⫏≰1121121)⨪↰⇹(≦∁⫏≰10120212)","cot":[{"info":"⊥⫏≰1121121=NaN","layer":1},{"info":"≦∁⫏≰10120212=⫏≰10120212","layer":1},{"info":"NaN⨪↰⇹⫏≰10120212=NaN","layer":0}]}
{"id":17,"expression_no_base_symbol":"↩(⨞⊢$7796$)","expression":"↩(⨞⊢⫏≰101200202)","highest_n_order":2,"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":7796,"base":3}}},"used_operators":["jLgFTUHLKL","xUOZtlo3hN"],"dependent_operators":["sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1202022210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7796","layer":2},{"info":"compute unary expreesion, input=7796, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-7970","layer":1},{"info":"compute unary expreesion, input=-7970, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=34500","layer":0}],"base":3,"result_base":3,"text":"↩(⨞⊢⫏≰101200202)=⫏≰1202022210","reverse_text":"⫏≰1202022210=↩(⨞⊢⫏≰101200202)","cot":[{"info":"⨞⊢⫏≰101200202=⫏≰-101221012","layer":1},{"info":"↩⫏≰-101221012=⫏≰1202022210","layer":0}]}
{"id":18,"expression_no_base_symbol":"(⫓⪴$1135$)%($1676$⪠⩆⊳)","expression":"(⫓⪴⫏≰1120001)%(⫏≰2022002⪠⩆⊳)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1142,"operation_count":3,"complexity_ratio":380.6666666666667,"tree":{"type":"binary","operator":"%","left_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":1135,"base":3}},"right_expr":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"numeric_atoms","value":1676,"base":3}}},"used_operators":["k8jYdgA6NY","eLxqMNBOBk","JLbD19bQDL"],"dependent_operators":["rysDP5nf3Z","9HNa5Wba9A","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1135","layer":2},{"info":"compute unary expreesion, input=1135, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=1288225","layer":1},{"info":"number node, value=1676","layer":2},{"info":"compute unary expreesion, input=1676, 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":"compute binary expreesion, left_input=1288225, right_input=0, op_id = k8jYdgA6NY binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫓⪴⫏≰1120001)%(⫏≰2022002⪠⩆⊳)=NaN","reverse_text":"NaN=(⫓⪴⫏≰1120001)%(⫏≰2022002⪠⩆⊳)","cot":[{"info":"⫓⪴⫏≰1120001=⫏≰2102110010001","layer":1},{"info":"⫏≰2022002⪠⩆⊳=⫏≰0","layer":1},{"info":"⫏≰2102110010001%⫏≰0=NaN","layer":0}]}
{"id":19,"expression_no_base_symbol":"⨞⊢($4005$*$6090$)","expression":"⨞⊢(⫏≰12111100*⫏≰22100120)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4007,"operation_count":2,"complexity_ratio":2003.5,"tree":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":4005,"base":3},"right_expr":{"type":"numeric_atoms","value":6090,"base":3}}},"used_operators":["xUOZtlo3hN","9HNa5Wba9A"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-1200220011122110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4005","layer":2},{"info":"number node, value=6090","layer":2},{"info":"compute binary expreesion, left_input=4005, right_input=6090, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=24390450","layer":1},{"info":"compute unary expreesion, input=24390450, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-24390624","layer":0}],"base":3,"result_base":3,"text":"⨞⊢(⫏≰12111100*⫏≰22100120)=⫏≰-1200220011122110","reverse_text":"⫏≰-1200220011122110=⨞⊢(⫏≰12111100*⫏≰22100120)","cot":[{"info":"⫏≰12111100*⫏≰22100120=⫏≰1200220011102000","layer":1},{"info":"⨞⊢⫏≰1200220011102000=⫏≰-1200220011122110","layer":0}]}
{"id":20,"expression_no_base_symbol":"(⊥$4883$)⇷($3148$≋⫹)","expression":"(⊥⫏≰20200212)⇷(⫏≰11022121≋⫹)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13,"operation_count":3,"complexity_ratio":4.333333333333333,"tree":{"type":"binary","operator":"⇷","left_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":4883,"base":3}},"right_expr":{"type":"unary","operator":"≋⫹","unary_expr":{"type":"numeric_atoms","value":3148,"base":3}}},"used_operators":["mp7IySMOzn","Q3PJZHRvZv","N41Kp7NANJ"],"dependent_operators":["DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","fu6greOZ01","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4883","layer":2},{"info":"compute unary expreesion, input=4883, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"number node, value=3148","layer":2},{"info":"compute unary expreesion, input=3148, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-6296","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-6296, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⊥⫏≰20200212)⇷(⫏≰11022121≋⫹)=NaN","reverse_text":"NaN=(⊥⫏≰20200212)⇷(⫏≰11022121≋⫹)","cot":[{"info":"⊥⫏≰20200212=NaN","layer":1},{"info":"⫏≰11022121≋⫹=⫏≰-22122012","layer":1},{"info":"NaN⇷⫏≰-22122012=NaN","layer":0}]}
{"id":21,"expression_no_base_symbol":"(≦∁$1934$)⨵⪆(↣≠⋷$5347$)","expression":"(≦∁⫏≰2122122)⨵⪆(↣≠⋷⫏≰21100001)","highest_n_order":4,"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":1934,"base":3}},"right_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":5347,"base":3}}},"used_operators":["2DQ55sFlQl","9ICcGScMcE","Asc51vEJeQ"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","XhwjNDsVaA","AHs5Up7iyr"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1934","layer":2},{"info":"compute unary expreesion, input=1934, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=1934","layer":1},{"info":"number node, value=5347","layer":2},{"info":"compute unary expreesion, input=5347, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1934, right_input=nan, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"(≦∁⫏≰2122122)⨵⪆(↣≠⋷⫏≰21100001)=⫏≰12221","reverse_text":"⫏≰12221=(≦∁⫏≰2122122)⨵⪆(↣≠⋷⫏≰21100001)","cot":[{"info":"≦∁⫏≰2122122=⫏≰2122122","layer":1},{"info":"↣≠⋷⫏≰21100001=NaN","layer":1},{"info":"⫏≰2122122⨵⪆NaN=⫏≰12221","layer":0}]}
{"id":22,"expression_no_base_symbol":"($2964$⨐⩸⫘$3152$)⋥≓≎$2311$⪘⫢$1462$","expression":"(⫏≰11001210⨐⩸⫘⫏≰11022202)⋥≓≎⫏≰10011121⪘⫢⫏≰2000011","highest_n_order":4,"priority_hierarchical_complexity":2,"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":2964,"base":3},"right_expr":{"type":"numeric_atoms","value":3152,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":2311,"base":3},"right_expr":{"type":"numeric_atoms","value":1462,"base":3}}},"used_operators":["Qy55tPpLXF","fu6greOZ01","oacrs7FA3X"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","3ViojmjbAp","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2964","layer":2},{"info":"number node, value=3152","layer":2},{"info":"compute binary expreesion, left_input=2964, right_input=3152, 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=2311","layer":2},{"info":"number node, value=1462","layer":2},{"info":"compute binary expreesion, left_input=2311, right_input=1462, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=4498","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=4498, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=67","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11001210⨐⩸⫘⫏≰11022202)⋥≓≎⫏≰10011121⪘⫢⫏≰2000011=⫏≰2111","reverse_text":"⫏≰2111=(⫏≰11001210⨐⩸⫘⫏≰11022202)⋥≓≎⫏≰10011121⪘⫢⫏≰2000011","cot":[{"info":"⫏≰11001210⨐⩸⫘⫏≰11022202=NaN","layer":1},{"info":"⫏≰10011121⪘⫢⫏≰2000011=⫏≰20011121","layer":1},{"info":"NaN⋥≓≎⫏≰20011121=⫏≰2111","layer":0}]}
{"id":23,"expression_no_base_symbol":"($4149$⨐⩸⫘$5804$)⋓$1300$⪮%⊝$1041$","expression":"(⫏≰12200200⨐⩸⫘⫏≰21221222)⋓⫏≰1210011⪮%⊝⫏≰1102120","highest_n_order":4,"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":4149,"base":3},"right_expr":{"type":"numeric_atoms","value":5804,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1300,"base":3},"right_expr":{"type":"numeric_atoms","value":1041,"base":3}}},"used_operators":["T2fj7uvVaJ","fu6greOZ01","IWmyXbctLI"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","3ViojmjbAp","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4149","layer":2},{"info":"number node, value=5804","layer":2},{"info":"compute binary expreesion, left_input=4149, right_input=5804, 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=1300","layer":2},{"info":"number node, value=1041","layer":2},{"info":"compute binary expreesion, left_input=1300, right_input=1041, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=2916","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2916, 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":3,"result_base":3,"text":"(⫏≰12200200⨐⩸⫘⫏≰21221222)⋓⫏≰1210011⪮%⊝⫏≰1102120=⫏≰0","reverse_text":"⫏≰0=(⫏≰12200200⨐⩸⫘⫏≰21221222)⋓⫏≰1210011⪮%⊝⫏≰1102120","cot":[{"info":"⫏≰12200200⨐⩸⫘⫏≰21221222=NaN","layer":1},{"info":"⫏≰1210011⪮%⊝⫏≰1102120=⫏≰11000000","layer":1},{"info":"NaN⋓⫏≰11000000=⫏≰0","layer":0}]}
{"id":24,"expression_no_base_symbol":"(↔$1201$)*($1235$⋷$3607$)","expression":"(↔⫏≰1122111)*(⫏≰1200202⋷⫏≰11221121)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":938,"operation_count":3,"complexity_ratio":312.6666666666667,"tree":{"type":"binary","operator":"*","left_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":1201,"base":3}},"right_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":1235,"base":3},"right_expr":{"type":"numeric_atoms","value":3607,"base":3}}},"used_operators":["9HNa5Wba9A","ruOEQAzv1W","23Mk6UjR3U"],"dependent_operators":["W4YGzv6Whe","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-101102220010110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1201","layer":2},{"info":"compute unary expreesion, input=1201, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-928","layer":1},{"info":"number node, value=1235","layer":2},{"info":"number node, value=3607","layer":2},{"info":"compute binary expreesion, left_input=1235, right_input=3607, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=5979","layer":1},{"info":"compute binary expreesion, left_input=-928, right_input=5979, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=-5548512","layer":0}],"base":3,"result_base":3,"text":"(↔⫏≰1122111)*(⫏≰1200202⋷⫏≰11221121)=⫏≰-101102220010110","reverse_text":"⫏≰-101102220010110=(↔⫏≰1122111)*(⫏≰1200202⋷⫏≰11221121)","cot":[{"info":"↔⫏≰1122111=⫏≰-1021101","layer":1},{"info":"⫏≰1200202⋷⫏≰11221121=⫏≰22012110","layer":1},{"info":"⫏≰-1021101*⫏≰22012110=⫏≰-101102220010110","layer":0}]}
{"id":25,"expression_no_base_symbol":"($1165$⨎$6974$)≭($4572$⫥∨⫟$4011$)","expression":"(⫏≰1121011⨎⫏≰100120022)≭(⫏≰20021100⫥∨⫟⫏≰12111120)","highest_n_order":5,"priority_hierarchical_complexity":2,"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":1165,"base":3},"right_expr":{"type":"numeric_atoms","value":6974,"base":3}},"right_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":4572,"base":3},"right_expr":{"type":"numeric_atoms","value":4011,"base":3}}},"used_operators":["rxpJgHHUmx","rJVOvQCfKK","KYD54nUTWz"],"dependent_operators":["AHs5Up7iyr","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1165","layer":2},{"info":"number node, value=6974","layer":2},{"info":"compute binary expreesion, left_input=1165, right_input=6974, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=6974","layer":1},{"info":"number node, value=4572","layer":2},{"info":"number node, value=4011","layer":2},{"info":"compute binary expreesion, left_input=4572, right_input=4011, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=6974, right_input=nan, 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":3,"result_base":3,"text":"(⫏≰1121011⨎⫏≰100120022)≭(⫏≰20021100⫥∨⫟⫏≰12111120)=NaN","reverse_text":"NaN=(⫏≰1121011⨎⫏≰100120022)≭(⫏≰20021100⫥∨⫟⫏≰12111120)","cot":[{"info":"⫏≰1121011⨎⫏≰100120022=⫏≰100120022","layer":1},{"info":"⫏≰20021100⫥∨⫟⫏≰12111120=NaN","layer":1},{"info":"⫏≰100120022≭NaN=NaN","layer":0}]}
{"id":26,"expression_no_base_symbol":"$4087$⨰$4629$⫡⨏$2535$⪘⫢$5707$","expression":"⫏≰12121101⨰⫏≰20100110⫡⨏⫏≰10110220⪘⫢⫏≰21211101","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":4087,"base":3},"right_expr":{"type":"numeric_atoms","value":4629,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":2535,"base":3},"right_expr":{"type":"numeric_atoms","value":5707,"base":3}}},"used_operators":["QMFrweE19q","eewbuw0ToL","oacrs7FA3X"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⫏≰101222212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4087","layer":2},{"info":"number node, value=4629","layer":2},{"info":"compute binary expreesion, left_input=4087, right_input=4629, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-532","layer":1},{"info":"number node, value=2535","layer":2},{"info":"number node, value=5707","layer":2},{"info":"compute binary expreesion, left_input=2535, right_input=5707, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=4946","layer":1},{"info":"compute binary expreesion, left_input=-532, right_input=4946, 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=8015","layer":0}],"base":3,"result_base":3,"text":"⫏≰12121101⨰⫏≰20100110⫡⨏⫏≰10110220⪘⫢⫏≰21211101=⫏≰101222212","reverse_text":"⫏≰101222212=⫏≰12121101⨰⫏≰20100110⫡⨏⫏≰10110220⪘⫢⫏≰21211101","cot":[{"info":"⫏≰12121101⨰⫏≰20100110=⫏≰-201201","layer":1},{"info":"⫏≰10110220⪘⫢⫏≰21211101=⫏≰20210012","layer":1},{"info":"⫏≰-201201⫡⨏⫏≰20210012=⫏≰101222212","layer":0}]}
{"id":27,"expression_no_base_symbol":"(≤/$1025$)⪮%⊝($1646$≭$7311$)","expression":"(≤/⫏≰1101222)⪮%⊝(⫏≰2020222≭⫏≰101000210)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11,"operation_count":3,"complexity_ratio":3.6666666666666665,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"unary","operator":"≤/","unary_expr":{"type":"numeric_atoms","value":1025,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":1646,"base":3},"right_expr":{"type":"numeric_atoms","value":7311,"base":3}}},"used_operators":["IWmyXbctLI","eLAdDNolq6","rxpJgHHUmx"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","rysDP5nf3Z","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1025","layer":2},{"info":"compute unary expreesion, input=1025, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-541","layer":1},{"info":"number node, value=1646","layer":2},{"info":"number node, value=7311","layer":2},{"info":"compute binary expreesion, left_input=1646, right_input=7311, 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=-541, right_input=nan, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(≤/⫏≰1101222)⪮%⊝(⫏≰2020222≭⫏≰101000210)=NaN","reverse_text":"NaN=(≤/⫏≰1101222)⪮%⊝(⫏≰2020222≭⫏≰101000210)","cot":[{"info":"≤/⫏≰1101222=⫏≰-202001","layer":1},{"info":"⫏≰2020222≭⫏≰101000210=NaN","layer":1},{"info":"⫏≰-202001⪮%⊝NaN=NaN","layer":0}]}
{"id":28,"expression_no_base_symbol":"($7305$⋥≓≎$1251$)≭($3007$≎⊠⪸$3406$)","expression":"(⫏≰101000120⋥≓≎⫏≰1201100)≭(⫏≰11010101≎⊠⪸⫏≰11200011)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":275,"operation_count":3,"complexity_ratio":91.66666666666667,"tree":{"type":"binary","operator":"≭","left_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":7305,"base":3},"right_expr":{"type":"numeric_atoms","value":1251,"base":3}},"right_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":3007,"base":3},"right_expr":{"type":"numeric_atoms","value":3406,"base":3}}},"used_operators":["rxpJgHHUmx","Qy55tPpLXF","bJkvcejdHO"],"dependent_operators":["AHs5Up7iyr","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7305","layer":2},{"info":"number node, value=1251","layer":2},{"info":"compute binary expreesion, left_input=7305, right_input=1251, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-4770","layer":1},{"info":"number node, value=3007","layer":2},{"info":"number node, value=3406","layer":2},{"info":"compute binary expreesion, left_input=3007, right_input=3406, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=778340","layer":1},{"info":"compute binary expreesion, left_input=-4770, right_input=778340, 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":3,"result_base":3,"text":"(⫏≰101000120⋥≓≎⫏≰1201100)≭(⫏≰11010101≎⊠⪸⫏≰11200011)=NaN","reverse_text":"NaN=(⫏≰101000120⋥≓≎⫏≰1201100)≭(⫏≰11010101≎⊠⪸⫏≰11200011)","cot":[{"info":"⫏≰101000120⋥≓≎⫏≰1201100=⫏≰-20112200","layer":1},{"info":"⫏≰11010101≎⊠⪸⫏≰11200011=⫏≰1110112200102","layer":1},{"info":"⫏≰-20112200≭⫏≰1110112200102=NaN","layer":0}]}
{"id":29,"expression_no_base_symbol":"$1808$⪢$1027$⨳⩥⨓($7811$⪄$1560$)","expression":"⫏≰2110222⪢⫏≰1102001⨳⩥⨓(⫏≰101201022⪄⫏≰2010210)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2055,"operation_count":3,"complexity_ratio":685.0,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1808,"base":3},"right_expr":{"type":"numeric_atoms","value":1027,"base":3}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":7811,"base":3},"right_expr":{"type":"numeric_atoms","value":1560,"base":3}}},"used_operators":["nCS4ZIUYfx","dWAJyo7jo9","SUmda5xLS4"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","k8jYdgA6NY","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1808","layer":2},{"info":"number node, value=1027","layer":2},{"info":"compute binary expreesion, left_input=1808, right_input=1027, 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=7811","layer":2},{"info":"number node, value=1560","layer":2},{"info":"compute binary expreesion, left_input=7811, right_input=1560, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-1158357","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-1158357, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2110222⪢⫏≰1102001⨳⩥⨓(⫏≰101201022⪄⫏≰2010210)=NaN","reverse_text":"NaN=⫏≰2110222⪢⫏≰1102001⨳⩥⨓(⫏≰101201022⪄⫏≰2010210)","cot":[{"info":"⫏≰2110222⪢⫏≰1102001=NaN","layer":1},{"info":"⫏≰101201022⪄⫏≰2010210=⫏≰-2011211222010","layer":1},{"info":"NaN⨳⩥⨓⫏≰-2011211222010=NaN","layer":0}]}
{"id":30,"expression_no_base_symbol":"$4135$⋝⋈⪟$5015$⇋≉","expression":"⫏≰12200011⋝⋈⪟⫏≰20212202⇋≉","highest_n_order":1,"priority_hierarchical_complexity":1,"normalized_expansion_degree":6,"operation_count":2,"complexity_ratio":3.0,"tree":{"type":"unary","operator":"⇋≉","unary_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":4135,"base":3},"right_expr":{"type":"numeric_atoms","value":5015,"base":3}}},"used_operators":["XIabStNQrY","2DDjHMKMc0"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰102012200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4135","layer":2},{"info":"number node, value=5015","layer":2},{"info":"compute binary expreesion, left_input=4135, right_input=5015, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=4135","layer":1},{"info":"compute unary expreesion, input=4135, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=8172","layer":0}],"base":3,"result_base":3,"text":"⫏≰12200011⋝⋈⪟⫏≰20212202⇋≉=⫏≰102012200","reverse_text":"⫏≰102012200=⫏≰12200011⋝⋈⪟⫏≰20212202⇋≉","cot":[{"info":"⫏≰12200011⋝⋈⪟⫏≰20212202=⫏≰12200011","layer":1},{"info":"⫏≰12200011⇋≉=⫏≰102012200","layer":0}]}
{"id":31,"expression_no_base_symbol":"$4998$≹⇙⪍$6054$⋓($1276$≋⫹)","expression":"⫏≰20212010≹⇙⪍⫏≰22022020⋓(⫏≰1202021≋⫹)","highest_n_order":4,"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":4998,"base":3},"right_expr":{"type":"numeric_atoms","value":6054,"base":3}},"right_expr":{"type":"unary","operator":"≋⫹","unary_expr":{"type":"numeric_atoms","value":1276,"base":3}}},"used_operators":["T2fj7uvVaJ","AHs5Up7iyr","N41Kp7NANJ"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","dWAJyo7jo9","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4998","layer":2},{"info":"number node, value=6054","layer":2},{"info":"compute binary expreesion, left_input=4998, right_input=6054, 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":"number node, value=1276","layer":2},{"info":"compute unary expreesion, input=1276, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-2552","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-2552, 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":3,"result_base":3,"text":"⫏≰20212010≹⇙⪍⫏≰22022020⋓(⫏≰1202021≋⫹)=⫏≰0","reverse_text":"⫏≰0=⫏≰20212010≹⇙⪍⫏≰22022020⋓(⫏≰1202021≋⫹)","cot":[{"info":"⫏≰20212010≹⇙⪍⫏≰22022020=NaN","layer":1},{"info":"⫏≰1202021≋⫹=⫏≰-10111112","layer":1},{"info":"NaN⋓⫏≰-10111112=⫏≰0","layer":0}]}
{"id":32,"expression_no_base_symbol":"⊙↵-($1185$⨳⩥⨓$3131$)","expression":"⊙↵-(⫏≰1121220⨳⩥⨓⫏≰11021222)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1995,"operation_count":2,"complexity_ratio":997.5,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":1185,"base":3},"right_expr":{"type":"numeric_atoms","value":3131,"base":3}}},"used_operators":["oWn0xqSxBt","nCS4ZIUYfx"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1185","layer":2},{"info":"number node, value=3131","layer":2},{"info":"compute binary expreesion, left_input=1185, right_input=3131, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=1946","layer":1},{"info":"compute unary expreesion, input=1946, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⫏≰1121220⨳⩥⨓⫏≰11021222)=⫏≰-1","reverse_text":"⫏≰-1=⊙↵-(⫏≰1121220⨳⩥⨓⫏≰11021222)","cot":[{"info":"⫏≰1121220⨳⩥⨓⫏≰11021222=⫏≰2200002","layer":1},{"info":"⊙↵-⫏≰2200002=⫏≰-1","layer":0}]}
{"id":33,"expression_no_base_symbol":"($5418$⫩⊇)⨵⪆(↥$1524$)","expression":"(⫏≰21102200⫩⊇)⨵⪆(↥⫏≰2002110)","highest_n_order":2,"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":5418,"base":3}},"right_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":1524,"base":3}}},"used_operators":["2DQ55sFlQl","BjRHVeLaeN","A8NUZmVepG"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","k8jYdgA6NY"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5418","layer":2},{"info":"compute unary expreesion, input=5418, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=-5376","layer":1},{"info":"number node, value=1524","layer":2},{"info":"compute unary expreesion, input=1524, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=45","layer":1},{"info":"compute binary expreesion, left_input=-5376, right_input=45, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"(⫏≰21102200⫩⊇)⨵⪆(↥⫏≰2002110)=⫏≰12221","reverse_text":"⫏≰12221=(⫏≰21102200⫩⊇)⨵⪆(↥⫏≰2002110)","cot":[{"info":"⫏≰21102200⫩⊇=⫏≰-21101010","layer":1},{"info":"↥⫏≰2002110=⫏≰1200","layer":1},{"info":"⫏≰-21101010⨵⪆⫏≰1200=⫏≰12221","layer":0}]}
{"id":34,"expression_no_base_symbol":"(↔$2173$)⪐","expression":"(↔⫏≰2222111)⪐","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9,"operation_count":2,"complexity_ratio":4.5,"tree":{"type":"unary","operator":"⪐","unary_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":2173,"base":3}}},"used_operators":["eH2TOUuTDT","ruOEQAzv1W"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp"],"result":"⫏≰-12012202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2173","layer":2},{"info":"compute unary expreesion, input=2173, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-1900","layer":1},{"info":"compute unary expreesion, input=-1900, op_id = eH2TOUuTDT, unary_op_definition = 'a⪐ = { (a+a) , if (-a)!=532 or a<368 ; (-a) , else }', output=-3800","layer":0}],"base":3,"result_base":3,"text":"(↔⫏≰2222111)⪐=⫏≰-12012202","reverse_text":"⫏≰-12012202=(↔⫏≰2222111)⪐","cot":[{"info":"↔⫏≰2222111=⫏≰-2121101","layer":1},{"info":"⫏≰-2121101⪐=⫏≰-12012202","layer":0}]}
{"id":35,"expression_no_base_symbol":"⨞⊢(⪲⇎$5729$)","expression":"⨞⊢(⪲⇎⫏≰21212012)","highest_n_order":1,"priority_hierarchical_complexity":1,"normalized_expansion_degree":4,"operation_count":2,"complexity_ratio":2.0,"tree":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":5729,"base":3}}},"used_operators":["xUOZtlo3hN","XPYlsWDdGa"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-120221211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5729","layer":2},{"info":"compute unary expreesion, input=5729, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=11458","layer":1},{"info":"compute unary expreesion, input=11458, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-11632","layer":0}],"base":3,"result_base":3,"text":"⨞⊢(⪲⇎⫏≰21212012)=⫏≰-120221211","reverse_text":"⫏≰-120221211=⨞⊢(⪲⇎⫏≰21212012)","cot":[{"info":"⪲⇎⫏≰21212012=⫏≰120201101","layer":1},{"info":"⨞⊢⫏≰120201101=⫏≰-120221211","layer":0}]}
{"id":36,"expression_no_base_symbol":"↥(-$1618$)","expression":"↥(-⫏≰2012221)","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":1618,"base":3}}},"used_operators":["A8NUZmVepG","t8gj7n24qd"],"dependent_operators":["k8jYdgA6NY"],"result":"⫏≰112","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1618","layer":2},{"info":"compute unary expreesion, input=1618, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1618","layer":1},{"info":"compute unary expreesion, input=-1618, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=14","layer":0}],"base":3,"result_base":3,"text":"↥(-⫏≰2012221)=⫏≰112","reverse_text":"⫏≰112=↥(-⫏≰2012221)","cot":[{"info":"-⫏≰2012221=⫏≰-2012221","layer":1},{"info":"↥⫏≰-2012221=⫏≰112","layer":0}]}
{"id":37,"expression_no_base_symbol":"$3425$↙$1302$∲⫓(⨈⫕$1128$)","expression":"⫏≰11200212↙⫏≰1210020∲⫓(⨈⫕⫏≰1112210)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1692,"operation_count":3,"complexity_ratio":564.0,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":3425,"base":3},"right_expr":{"type":"numeric_atoms","value":1302,"base":3}},"right_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":1128,"base":3}}},"used_operators":["i8ToyICDmI","yyfyN0ffXY","megm06wKyl"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","tmPS8pqC7x","DpFCA1CohY","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q"],"result":"⫏≰-12100200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3425","layer":2},{"info":"number node, value=1302","layer":2},{"info":"compute binary expreesion, left_input=3425, right_input=1302, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-3906","layer":1},{"info":"number node, value=1128","layer":2},{"info":"compute unary expreesion, input=1128, 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=-3906, right_input=-21, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=-3906","layer":0}],"base":3,"result_base":3,"text":"⫏≰11200212↙⫏≰1210020∲⫓(⨈⫕⫏≰1112210)=⫏≰-12100200","reverse_text":"⫏≰-12100200=⫏≰11200212↙⫏≰1210020∲⫓(⨈⫕⫏≰1112210)","cot":[{"info":"⫏≰11200212↙⫏≰1210020=⫏≰-12100200","layer":1},{"info":"⨈⫕⫏≰1112210=⫏≰-210","layer":1},{"info":"⫏≰-12100200∲⫓⫏≰-210=⫏≰-12100200","layer":0}]}
{"id":38,"expression_no_base_symbol":"$1771$⨰$2296$⊭↱$1811$⊴$1287$","expression":"⫏≰2102121⨰⫏≰10011001⊭↱⫏≰2111002⊴⫏≰1202200","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4344,"operation_count":3,"complexity_ratio":1448.0,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":1771,"base":3},"right_expr":{"type":"numeric_atoms","value":2296,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1811,"base":3},"right_expr":{"type":"numeric_atoms","value":1287,"base":3}}},"used_operators":["COABgblf1C","eewbuw0ToL","Nsiff2A1zJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1771","layer":2},{"info":"number node, value=2296","layer":2},{"info":"compute binary expreesion, left_input=1771, right_input=2296, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-515","layer":1},{"info":"number node, value=1811","layer":2},{"info":"number node, value=1287","layer":2},{"info":"compute binary expreesion, left_input=1811, right_input=1287, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-515, right_input=nan, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2102121⨰⫏≰10011001⊭↱⫏≰2111002⊴⫏≰1202200=NaN","reverse_text":"NaN=⫏≰2102121⨰⫏≰10011001⊭↱⫏≰2111002⊴⫏≰1202200","cot":[{"info":"⫏≰2102121⨰⫏≰10011001=⫏≰-201002","layer":1},{"info":"⫏≰2111002⊴⫏≰1202200=NaN","layer":1},{"info":"⫏≰-201002⊭↱NaN=NaN","layer":0}]}
{"id":39,"expression_no_base_symbol":"(≦∁$4092$)⨵⪆$2060$⪢$2167$","expression":"(≦∁⫏≰12121120)⨵⪆⫏≰2211022⪢⫏≰2222021","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2169,"operation_count":3,"complexity_ratio":723.0,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":4092,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":2060,"base":3},"right_expr":{"type":"numeric_atoms","value":2167,"base":3}}},"used_operators":["2DQ55sFlQl","9ICcGScMcE","dWAJyo7jo9"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","k8jYdgA6NY"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4092","layer":2},{"info":"compute unary expreesion, input=4092, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=4092","layer":1},{"info":"number node, value=2060","layer":2},{"info":"number node, value=2167","layer":2},{"info":"compute binary expreesion, left_input=2060, right_input=2167, 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=4092, right_input=nan, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"(≦∁⫏≰12121120)⨵⪆⫏≰2211022⪢⫏≰2222021=⫏≰12221","reverse_text":"⫏≰12221=(≦∁⫏≰12121120)⨵⪆⫏≰2211022⪢⫏≰2222021","cot":[{"info":"≦∁⫏≰12121120=⫏≰12121120","layer":1},{"info":"⫏≰2211022⪢⫏≰2222021=NaN","layer":1},{"info":"⫏≰12121120⨵⪆NaN=⫏≰12221","layer":0}]}
{"id":40,"expression_no_base_symbol":"⫓⪴($3798$≭$1101$)","expression":"⫓⪴(⫏≰12012200≭⫏≰1111210)","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":3798,"base":3},"right_expr":{"type":"numeric_atoms","value":1101,"base":3}}},"used_operators":["eLxqMNBOBk","rxpJgHHUmx"],"dependent_operators":["9HNa5Wba9A","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3798","layer":2},{"info":"number node, value=1101","layer":2},{"info":"compute binary expreesion, left_input=3798, right_input=1101, 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 = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫓⪴(⫏≰12012200≭⫏≰1111210)=NaN","reverse_text":"NaN=⫓⪴(⫏≰12012200≭⫏≰1111210)","cot":[{"info":"⫏≰12012200≭⫏≰1111210=NaN","layer":1},{"info":"⫓⪴NaN=NaN","layer":0}]}
{"id":41,"expression_no_base_symbol":"$1260$⋓$8307$⩷∴(⪲⇎$3166$)","expression":"⫏≰1201200⋓⫏≰102101200⩷∴(⪲⇎⫏≰11100021)","highest_n_order":3,"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":1260,"base":3},"right_expr":{"type":"numeric_atoms","value":8307,"base":3}},"right_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":3166,"base":3}}},"used_operators":["9FxExcQeMw","T2fj7uvVaJ","XPYlsWDdGa"],"dependent_operators":["rysDP5nf3Z","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-122102020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1260","layer":2},{"info":"number node, value=8307","layer":2},{"info":"compute binary expreesion, left_input=1260, right_input=8307, 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=3166","layer":2},{"info":"compute unary expreesion, input=3166, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=6332","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=6332, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-12696","layer":0}],"base":3,"result_base":3,"text":"⫏≰1201200⋓⫏≰102101200⩷∴(⪲⇎⫏≰11100021)=⫏≰-122102020","reverse_text":"⫏≰-122102020=⫏≰1201200⋓⫏≰102101200⩷∴(⪲⇎⫏≰11100021)","cot":[{"info":"⫏≰1201200⋓⫏≰102101200=⫏≰0","layer":1},{"info":"⪲⇎⫏≰11100021=⫏≰22200112","layer":1},{"info":"⫏≰0⩷∴⫏≰22200112=⫏≰-122102020","layer":0}]}
{"id":42,"expression_no_base_symbol":"($2217$⇼⇔∾$2388$)⇋≉","expression":"(⫏≰10001010⇼⇔∾⫏≰10021110)⇋≉","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":2217,"base":3},"right_expr":{"type":"numeric_atoms","value":2388,"base":3}}},"used_operators":["XIabStNQrY","tifHPKVTfV"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰100001","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2217","layer":2},{"info":"number node, value=2388","layer":2},{"info":"compute binary expreesion, left_input=2217, right_input=2388, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=171","layer":1},{"info":"compute unary expreesion, input=171, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=244","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10001010⇼⇔∾⫏≰10021110)⇋≉=⫏≰100001","reverse_text":"⫏≰100001=(⫏≰10001010⇼⇔∾⫏≰10021110)⇋≉","cot":[{"info":"⫏≰10001010⇼⇔∾⫏≰10021110=⫏≰20100","layer":1},{"info":"⫏≰20100⇋≉=⫏≰100001","layer":0}]}
{"id":43,"expression_no_base_symbol":"($4615$⋷$2620$)↙$3810$∑⇟⊟$4912$","expression":"(⫏≰20022221⋷⫏≰10121001)↙⫏≰12020010∑⇟⊟⫏≰20201221","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"↙","left_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":4615,"base":3},"right_expr":{"type":"numeric_atoms","value":2620,"base":3}},"right_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":3810,"base":3},"right_expr":{"type":"numeric_atoms","value":4912,"base":3}}},"used_operators":["yyfyN0ffXY","23Mk6UjR3U","U7g4x0WXJJ"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4615","layer":2},{"info":"number node, value=2620","layer":2},{"info":"compute binary expreesion, left_input=4615, right_input=2620, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=625","layer":1},{"info":"number node, value=3810","layer":2},{"info":"number node, value=4912","layer":2},{"info":"compute binary expreesion, left_input=3810, right_input=4912, 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=625, right_input=nan, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20022221⋷⫏≰10121001)↙⫏≰12020010∑⇟⊟⫏≰20201221=NaN","reverse_text":"NaN=(⫏≰20022221⋷⫏≰10121001)↙⫏≰12020010∑⇟⊟⫏≰20201221","cot":[{"info":"⫏≰20022221⋷⫏≰10121001=⫏≰212011","layer":1},{"info":"⫏≰12020010∑⇟⊟⫏≰20201221=NaN","layer":1},{"info":"⫏≰212011↙NaN=NaN","layer":0}]}
{"id":44,"expression_no_base_symbol":"(+⊝⨔$1070$)⊭↱$2205$+⇶⊼$6187$","expression":"(+⊝⨔⫏≰1110122)⊭↱⫏≰10000200+⇶⊼⫏≰22111011","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":47,"operation_count":3,"complexity_ratio":15.666666666666666,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":1070,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":2205,"base":3},"right_expr":{"type":"numeric_atoms","value":6187,"base":3}}},"used_operators":["COABgblf1C","DhbWaqg5eL","TpPTUOHfaN"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1070","layer":2},{"info":"compute unary expreesion, input=1070, 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=2205","layer":2},{"info":"number node, value=6187","layer":2},{"info":"compute binary expreesion, left_input=2205, right_input=6187, 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":1},{"info":"compute binary expreesion, left_input=1522, right_input=nan, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(+⊝⨔⫏≰1110122)⊭↱⫏≰10000200+⇶⊼⫏≰22111011=NaN","reverse_text":"NaN=(+⊝⨔⫏≰1110122)⊭↱⫏≰10000200+⇶⊼⫏≰22111011","cot":[{"info":"+⊝⨔⫏≰1110122=⫏≰2002101","layer":1},{"info":"⫏≰10000200+⇶⊼⫏≰22111011=NaN","layer":1},{"info":"⫏≰2002101⊭↱NaN=NaN","layer":0}]}
{"id":45,"expression_no_base_symbol":"↥(⇁⨣⪵$1601$)","expression":"↥(⇁⨣⪵⫏≰2012022)","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":1601,"base":3}}},"used_operators":["A8NUZmVepG","inkyxCbjAn"],"dependent_operators":["k8jYdgA6NY","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1601","layer":2},{"info":"compute unary expreesion, input=1601, 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":3,"result_base":3,"text":"↥(⇁⨣⪵⫏≰2012022)=NaN","reverse_text":"NaN=↥(⇁⨣⪵⫏≰2012022)","cot":[{"info":"⇁⨣⪵⫏≰2012022=NaN","layer":1},{"info":"↥NaN=NaN","layer":0}]}
{"id":46,"expression_no_base_symbol":"($6893$-$9453$)⋝⋈⪟($2210$≎⊠⪸$8568$)","expression":"(⫏≰100110022-⫏≰110222010)⋝⋈⪟(⫏≰10000212≎⊠⪸⫏≰102202100)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":274,"operation_count":3,"complexity_ratio":91.33333333333333,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":6893,"base":3},"right_expr":{"type":"numeric_atoms","value":9453,"base":3}},"right_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":2210,"base":3},"right_expr":{"type":"numeric_atoms","value":8568,"base":3}}},"used_operators":["2DDjHMKMc0","rysDP5nf3Z","bJkvcejdHO"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"⫏≰-10111211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6893","layer":2},{"info":"number node, value=9453","layer":2},{"info":"compute binary expreesion, left_input=6893, right_input=9453, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-2560","layer":1},{"info":"number node, value=2210","layer":2},{"info":"number node, value=8568","layer":2},{"info":"compute binary expreesion, left_input=2210, right_input=8568, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=571917","layer":1},{"info":"compute binary expreesion, left_input=-2560, right_input=571917, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=-2560","layer":0}],"base":3,"result_base":3,"text":"(⫏≰100110022-⫏≰110222010)⋝⋈⪟(⫏≰10000212≎⊠⪸⫏≰102202100)=⫏≰-10111211","reverse_text":"⫏≰-10111211=(⫏≰100110022-⫏≰110222010)⋝⋈⪟(⫏≰10000212≎⊠⪸⫏≰102202100)","cot":[{"info":"⫏≰100110022-⫏≰110222010=⫏≰-10111211","layer":1},{"info":"⫏≰10000212≎⊠⪸⫏≰102202100=⫏≰1002001112010","layer":1},{"info":"⫏≰-10111211⋝⋈⪟⫏≰1002001112010=⫏≰-10111211","layer":0}]}
{"id":47,"expression_no_base_symbol":"∂($2519$↺$3720$)","expression":"∂(⫏≰10110022↺⫏≰12002210)","highest_n_order":5,"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":2519,"base":3},"right_expr":{"type":"numeric_atoms","value":3720,"base":3}}},"used_operators":["Uaa54Peajs","7j4O788W3g"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2519","layer":2},{"info":"number node, value=3720","layer":2},{"info":"compute binary expreesion, left_input=2519, right_input=3720, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=3720","layer":1},{"info":"compute unary expreesion, input=3720, 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":3,"result_base":3,"text":"∂(⫏≰10110022↺⫏≰12002210)=NaN","reverse_text":"NaN=∂(⫏≰10110022↺⫏≰12002210)","cot":[{"info":"⫏≰10110022↺⫏≰12002210=⫏≰12002210","layer":1},{"info":"∂⫏≰12002210=NaN","layer":0}]}
{"id":48,"expression_no_base_symbol":"($1823$%$9084$)≣⋋","expression":"(⫏≰2111112%⫏≰110110110)≣⋋","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":515,"operation_count":2,"complexity_ratio":257.5,"tree":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":1823,"base":3},"right_expr":{"type":"numeric_atoms","value":9084,"base":3}}},"used_operators":["Tcnh7f0tEr","k8jYdgA6NY"],"dependent_operators":["dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A","rysDP5nf3Z"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1823","layer":2},{"info":"number node, value=9084","layer":2},{"info":"compute binary expreesion, left_input=1823, right_input=9084, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1823","layer":1},{"info":"compute unary expreesion, input=1823, op_id = Tcnh7f0tEr, unary_op_definition = 'a≣⋋ = { ((a/a)⋥≓≎(a⨪↰⇹248)) , if (a⪢148)<38 ; ((511*a)⊠≄⫣) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2111112%⫏≰110110110)≣⋋=⫏≰0","reverse_text":"⫏≰0=(⫏≰2111112%⫏≰110110110)≣⋋","cot":[{"info":"⫏≰2111112%⫏≰110110110=⫏≰2111112","layer":1},{"info":"⫏≰2111112≣⋋=⫏≰0","layer":0}]}
{"id":49,"expression_no_base_symbol":"($3491$⪠⩆⊳)⪒$2249$⩷∴$5523$","expression":"(⫏≰11210022⪠⩆⊳)⪒⫏≰10002022⩷∴⫏≰21120120","highest_n_order":1,"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":3491,"base":3}},"right_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":2249,"base":3},"right_expr":{"type":"numeric_atoms","value":5523,"base":3}}},"used_operators":["f6k1SAg4EE","JLbD19bQDL","9FxExcQeMw"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰100000201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3491","layer":2},{"info":"compute unary expreesion, input=3491, 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=2249","layer":2},{"info":"number node, value=5523","layer":2},{"info":"compute binary expreesion, left_input=2249, right_input=5523, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-6580","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-6580, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=6580","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11210022⪠⩆⊳)⪒⫏≰10002022⩷∴⫏≰21120120=⫏≰100000201","reverse_text":"⫏≰100000201=(⫏≰11210022⪠⩆⊳)⪒⫏≰10002022⩷∴⫏≰21120120","cot":[{"info":"⫏≰11210022⪠⩆⊳=⫏≰0","layer":1},{"info":"⫏≰10002022⩷∴⫏≰21120120=⫏≰-100000201","layer":1},{"info":"⫏≰0⪒⫏≰-100000201=⫏≰100000201","layer":0}]}
{"id":50,"expression_no_base_symbol":"↽≂$1325$⨰$2590$","expression":"↽≂⫏≰1211002⨰⫏≰10112221","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":1325,"base":3},"right_expr":{"type":"numeric_atoms","value":2590,"base":3}}},"used_operators":["u6S6b8DprG","eewbuw0ToL"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰10102222","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1325","layer":2},{"info":"number node, value=2590","layer":2},{"info":"compute binary expreesion, left_input=1325, right_input=2590, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-1255","layer":1},{"info":"compute unary expreesion, input=-1255, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=2510","layer":0}],"base":3,"result_base":3,"text":"↽≂⫏≰1211002⨰⫏≰10112221=⫏≰10102222","reverse_text":"⫏≰10102222=↽≂⫏≰1211002⨰⫏≰10112221","cot":[{"info":"⫏≰1211002⨰⫏≰10112221=⫏≰-1201111","layer":1},{"info":"↽≂⫏≰-1201111=⫏≰10102222","layer":0}]}
{"id":51,"expression_no_base_symbol":"(∥⊫$4279$)⨽(⊥$6813$)","expression":"(∥⊫⫏≰12212111)⨽(⊥⫏≰100100100)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5161,"operation_count":3,"complexity_ratio":1720.3333333333333,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":4279,"base":3}},"right_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":6813,"base":3}}},"used_operators":["8HhzD0ZcuI","P8v4zCKN1o","Q3PJZHRvZv"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","W4YGzv6Whe","t8gj7n24qd","fu6greOZ01"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4279","layer":2},{"info":"compute unary expreesion, input=4279, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=5147","layer":1},{"info":"number node, value=6813","layer":2},{"info":"compute unary expreesion, input=6813, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=5147, right_input=nan, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(∥⊫⫏≰12212111)⨽(⊥⫏≰100100100)=NaN","reverse_text":"NaN=(∥⊫⫏≰12212111)⨽(⊥⫏≰100100100)","cot":[{"info":"∥⊫⫏≰12212111=⫏≰21001122","layer":1},{"info":"⊥⫏≰100100100=NaN","layer":1},{"info":"⫏≰21001122⨽NaN=NaN","layer":0}]}
{"id":52,"expression_no_base_symbol":"($3425$⊭∹↮)↬($1585$⨎$3481$)","expression":"(⫏≰11200212⊭∹↮)↬(⫏≰2011201⨎⫏≰11202221)","highest_n_order":5,"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":3425,"base":3}},"right_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":1585,"base":3},"right_expr":{"type":"numeric_atoms","value":3481,"base":3}}},"used_operators":["B5M0gjZbta","xNBdhnnwKq","rJVOvQCfKK"],"dependent_operators":["rGHVDoGpnC","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3425","layer":2},{"info":"compute unary expreesion, input=3425, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=6850","layer":1},{"info":"number node, value=1585","layer":2},{"info":"number node, value=3481","layer":2},{"info":"compute binary expreesion, left_input=1585, right_input=3481, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=3481","layer":1},{"info":"compute binary expreesion, left_input=6850, right_input=3481, 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":3,"result_base":3,"text":"(⫏≰11200212⊭∹↮)↬(⫏≰2011201⨎⫏≰11202221)=NaN","reverse_text":"NaN=(⫏≰11200212⊭∹↮)↬(⫏≰2011201⨎⫏≰11202221)","cot":[{"info":"⫏≰11200212⊭∹↮=⫏≰100101201","layer":1},{"info":"⫏≰2011201⨎⫏≰11202221=⫏≰11202221","layer":1},{"info":"⫏≰100101201↬⫏≰11202221=NaN","layer":0}]}
{"id":53,"expression_no_base_symbol":"($1643$⋫)↪⪝","expression":"(⫏≰2020212⋫)↪⪝","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":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":1643,"base":3}}},"used_operators":["l07mrZUIn9","JL8yIekQnl"],"dependent_operators":["9HNa5Wba9A","2DDjHMKMc0","tmPS8pqC7x"],"result":"⫏≰21000011001022000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1643","layer":2},{"info":"compute unary expreesion, input=1643, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=1643","layer":1},{"info":"compute unary expreesion, input=1643, op_id = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=100522026","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2020212⋫)↪⪝=⫏≰21000011001022000","reverse_text":"⫏≰21000011001022000=(⫏≰2020212⋫)↪⪝","cot":[{"info":"⫏≰2020212⋫=⫏≰2020212","layer":1},{"info":"⫏≰2020212↪⪝=⫏≰21000011001022000","layer":0}]}
{"id":54,"expression_no_base_symbol":"(-$1325$)⩠","expression":"(-⫏≰1211002)⩠","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":18,"operation_count":2,"complexity_ratio":9.0,"tree":{"type":"unary","operator":"⩠","unary_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":1325,"base":3}}},"used_operators":["sJAwomhLZr","t8gj7n24qd"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","k8jYdgA6NY","eH2TOUuTDT","W4YGzv6Whe","Z2TMIBDE3Q","COABgblf1C"],"result":"⫏≰21120001","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1325","layer":2},{"info":"compute unary expreesion, input=1325, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1325","layer":1},{"info":"compute unary expreesion, input=-1325, op_id = sJAwomhLZr, unary_op_definition = 'a⩠ = { (((a+a)⊭↱(a⪨≂a))∲⫓((a⩤)%(a⪐))) }', output=5509","layer":0}],"base":3,"result_base":3,"text":"(-⫏≰1211002)⩠=⫏≰21120001","reverse_text":"⫏≰21120001=(-⫏≰1211002)⩠","cot":[{"info":"-⫏≰1211002=⫏≰-1211002","layer":1},{"info":"⫏≰-1211002⩠=⫏≰21120001","layer":0}]}
{"id":55,"expression_no_base_symbol":"≉($5188$⊠≄⫣)","expression":"≉(⫏≰21010011⊠≄⫣)","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":"unary","operator":"⊠≄⫣","unary_expr":{"type":"numeric_atoms","value":5188,"base":3}}},"used_operators":["e1ybzncUwg","DIvbN7qnHd"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰201200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5188","layer":2},{"info":"compute unary expreesion, input=5188, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=531","layer":0}],"base":3,"result_base":3,"text":"≉(⫏≰21010011⊠≄⫣)=⫏≰201200","reverse_text":"⫏≰201200=≉(⫏≰21010011⊠≄⫣)","cot":[{"info":"⫏≰21010011⊠≄⫣=⫏≰0","layer":1},{"info":"≉⫏≰0=⫏≰201200","layer":0}]}
{"id":56,"expression_no_base_symbol":"≉($2383$⊘)","expression":"≉(⫏≰10021021⊘)","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":2383,"base":3}}},"used_operators":["e1ybzncUwg","gu96TGCTMs"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D"],"result":"⫏≰201200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2383","layer":2},{"info":"compute unary expreesion, input=2383, 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":"compute unary expreesion, input=0, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=531","layer":0}],"base":3,"result_base":3,"text":"≉(⫏≰10021021⊘)=⫏≰201200","reverse_text":"⫏≰201200=≉(⫏≰10021021⊘)","cot":[{"info":"⫏≰10021021⊘=⫏≰0","layer":1},{"info":"≉⫏≰0=⫏≰201200","layer":0}]}
{"id":57,"expression_no_base_symbol":"$4291$≹⇙⪍$5389$⨐⩸⫘($1794$∧)","expression":"⫏≰12212221≹⇙⪍⫏≰21101121⨐⩸⫘(⫏≰2110110∧)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":4291,"base":3},"right_expr":{"type":"numeric_atoms","value":5389,"base":3}},"right_expr":{"type":"unary","operator":"∧","unary_expr":{"type":"numeric_atoms","value":1794,"base":3}}},"used_operators":["fu6greOZ01","AHs5Up7iyr","z63VuFQld9"],"dependent_operators":["3ViojmjbAp","dWAJyo7jo9","B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4291","layer":2},{"info":"number node, value=5389","layer":2},{"info":"compute binary expreesion, left_input=4291, right_input=5389, 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":"number node, value=1794","layer":2},{"info":"compute unary expreesion, input=1794, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , 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":3,"result_base":3,"text":"⫏≰12212221≹⇙⪍⫏≰21101121⨐⩸⫘(⫏≰2110110∧)=NaN","reverse_text":"NaN=⫏≰12212221≹⇙⪍⫏≰21101121⨐⩸⫘(⫏≰2110110∧)","cot":[{"info":"⫏≰12212221≹⇙⪍⫏≰21101121=NaN","layer":1},{"info":"⫏≰2110110∧=NaN","layer":1},{"info":"NaN⨐⩸⫘NaN=NaN","layer":0}]}
{"id":58,"expression_no_base_symbol":"↔($1833$≫≃)","expression":"↔(⫏≰2111220≫≃)","highest_n_order":2,"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":1833,"base":3}}},"used_operators":["ruOEQAzv1W","X99M06cbEe"],"dependent_operators":["XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A"],"result":"⫏≰-20120120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1833","layer":2},{"info":"compute unary expreesion, input=1833, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=5067","layer":1},{"info":"compute unary expreesion, input=5067, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-4794","layer":0}],"base":3,"result_base":3,"text":"↔(⫏≰2111220≫≃)=⫏≰-20120120","reverse_text":"⫏≰-20120120=↔(⫏≰2111220≫≃)","cot":[{"info":"⫏≰2111220≫≃=⫏≰20221200","layer":1},{"info":"↔⫏≰20221200=⫏≰-20120120","layer":0}]}
{"id":59,"expression_no_base_symbol":"($1536$≎⊠⪸$1055$)≧⫂∧($1296$⇼⇔∾$8542$)","expression":"(⫏≰2002220≎⊠⪸⫏≰1110002)≧⫂∧(⫏≰1210000⇼⇔∾⫏≰102201101)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":273,"operation_count":3,"complexity_ratio":91.0,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1536,"base":3},"right_expr":{"type":"numeric_atoms","value":1055,"base":3}},"right_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":1296,"base":3},"right_expr":{"type":"numeric_atoms","value":8542,"base":3}}},"used_operators":["Ph9nP6C5qx","bJkvcejdHO","tifHPKVTfV"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰100021212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1536","layer":2},{"info":"number node, value=1055","layer":2},{"info":"compute binary expreesion, left_input=1536, right_input=1055, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=397351","layer":1},{"info":"number node, value=1296","layer":2},{"info":"number node, value=8542","layer":2},{"info":"compute binary expreesion, left_input=1296, right_input=8542, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=7246","layer":1},{"info":"compute binary expreesion, left_input=397351, right_input=7246, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=6773","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2002220≎⊠⪸⫏≰1110002)≧⫂∧(⫏≰1210000⇼⇔∾⫏≰102201101)=⫏≰100021212","reverse_text":"⫏≰100021212=(⫏≰2002220≎⊠⪸⫏≰1110002)≧⫂∧(⫏≰1210000⇼⇔∾⫏≰102201101)","cot":[{"info":"⫏≰2002220≎⊠⪸⫏≰1110002=⫏≰202012001201","layer":1},{"info":"⫏≰1210000⇼⇔∾⫏≰102201101=⫏≰100221101","layer":1},{"info":"⫏≰202012001201≧⫂∧⫏≰100221101=⫏≰100021212","layer":0}]}
{"id":60,"expression_no_base_symbol":"$7439$↺$1845$⨳⩥⨓$9785$⪮%⊝$3208$","expression":"⫏≰101012112↺⫏≰2112100⨳⩥⨓⫏≰111102102⪮%⊝⫏≰11101211","highest_n_order":2,"priority_hierarchical_complexity":2,"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":7439,"base":3},"right_expr":{"type":"numeric_atoms","value":1845,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":9785,"base":3},"right_expr":{"type":"numeric_atoms","value":3208,"base":3}}},"used_operators":["nCS4ZIUYfx","7j4O788W3g","IWmyXbctLI"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰220202012","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7439","layer":2},{"info":"number node, value=1845","layer":2},{"info":"compute binary expreesion, left_input=7439, right_input=1845, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1845","layer":1},{"info":"number node, value=9785","layer":2},{"info":"number node, value=3208","layer":2},{"info":"compute binary expreesion, left_input=9785, right_input=3208, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=19886","layer":1},{"info":"compute binary expreesion, left_input=1845, right_input=19886, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=18041","layer":0}],"base":3,"result_base":3,"text":"⫏≰101012112↺⫏≰2112100⨳⩥⨓⫏≰111102102⪮%⊝⫏≰11101211=⫏≰220202012","reverse_text":"⫏≰220202012=⫏≰101012112↺⫏≰2112100⨳⩥⨓⫏≰111102102⪮%⊝⫏≰11101211","cot":[{"info":"⫏≰101012112↺⫏≰2112100=⫏≰2112100","layer":1},{"info":"⫏≰111102102⪮%⊝⫏≰11101211=⫏≰1000021112","layer":1},{"info":"⫏≰2112100⨳⩥⨓⫏≰1000021112=⫏≰220202012","layer":0}]}
{"id":61,"expression_no_base_symbol":"($7447$⪛$4999$)≹⇙⪍($1229$⋥≓≎$6246$)","expression":"(⫏≰101012211⪛⫏≰20212011)≹⇙⪍(⫏≰1200112⋥≓≎⫏≰22120100)","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":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":7447,"base":3},"right_expr":{"type":"numeric_atoms","value":4999,"base":3}},"right_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":1229,"base":3},"right_expr":{"type":"numeric_atoms","value":6246,"base":3}}},"used_operators":["AHs5Up7iyr","uFcxV4UQCh","Qy55tPpLXF"],"dependent_operators":["dWAJyo7jo9","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7447","layer":2},{"info":"number node, value=4999","layer":2},{"info":"compute binary expreesion, left_input=7447, right_input=4999, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=2448","layer":1},{"info":"number node, value=1229","layer":2},{"info":"number node, value=6246","layer":2},{"info":"compute binary expreesion, left_input=1229, right_input=6246, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=11296","layer":1},{"info":"compute binary expreesion, left_input=2448, right_input=11296, 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":3,"result_base":3,"text":"(⫏≰101012211⪛⫏≰20212011)≹⇙⪍(⫏≰1200112⋥≓≎⫏≰22120100)=NaN","reverse_text":"NaN=(⫏≰101012211⪛⫏≰20212011)≹⇙⪍(⫏≰1200112⋥≓≎⫏≰22120100)","cot":[{"info":"⫏≰101012211⪛⫏≰20212011=⫏≰10100200","layer":1},{"info":"⫏≰1200112⋥≓≎⫏≰22120100=⫏≰120111101","layer":1},{"info":"⫏≰10100200≹⇙⪍⫏≰120111101=NaN","layer":0}]}
{"id":62,"expression_no_base_symbol":"$4303$⨓$2186$+⇶⊼($3781$⪄$1064$)","expression":"⫏≰12220101⨓⫏≰2222222+⇶⊼(⫏≰12012001⪄⫏≰1110102)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2288,"operation_count":3,"complexity_ratio":762.6666666666666,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":4303,"base":3},"right_expr":{"type":"numeric_atoms","value":2186,"base":3}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":3781,"base":3},"right_expr":{"type":"numeric_atoms","value":1064,"base":3}}},"used_operators":["TpPTUOHfaN","3ViojmjbAp","SUmda5xLS4"],"dependent_operators":["AHs5Up7iyr","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4303","layer":2},{"info":"number node, value=2186","layer":2},{"info":"compute binary expreesion, left_input=4303, right_input=2186, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-2189","layer":1},{"info":"number node, value=3781","layer":2},{"info":"number node, value=1064","layer":2},{"info":"compute binary expreesion, left_input=3781, right_input=1064, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-559933","layer":1},{"info":"compute binary expreesion, left_input=-2189, right_input=-559933, 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":3,"result_base":3,"text":"⫏≰12220101⨓⫏≰2222222+⇶⊼(⫏≰12012001⪄⫏≰1110102)=NaN","reverse_text":"NaN=⫏≰12220101⨓⫏≰2222222+⇶⊼(⫏≰12012001⪄⫏≰1110102)","cot":[{"info":"⫏≰12220101⨓⫏≰2222222=⫏≰-10000002","layer":1},{"info":"⫏≰12012001⪄⫏≰1110102=⫏≰-1001110002021","layer":1},{"info":"⫏≰-10000002+⇶⊼⫏≰-1001110002021=NaN","layer":0}]}
{"id":63,"expression_no_base_symbol":"($1119$⨵⪆$6721$)⪘⫢($7534$⨳⩥⨓$1612$)","expression":"(⫏≰1112110⨵⪆⫏≰100012221)⪘⫢(⫏≰101100001⨳⩥⨓⫏≰2012201)","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":1119,"base":3},"right_expr":{"type":"numeric_atoms","value":6721,"base":3}},"right_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":7534,"base":3},"right_expr":{"type":"numeric_atoms","value":1612,"base":3}}},"used_operators":["oacrs7FA3X","2DQ55sFlQl","nCS4ZIUYfx"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1119","layer":2},{"info":"number node, value=6721","layer":2},{"info":"compute binary expreesion, left_input=1119, right_input=6721, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=7534","layer":2},{"info":"number node, value=1612","layer":2},{"info":"compute binary expreesion, left_input=7534, right_input=1612, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-5922","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=-5922, 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":3,"result_base":3,"text":"(⫏≰1112110⨵⪆⫏≰100012221)⪘⫢(⫏≰101100001⨳⩥⨓⫏≰2012201)=⫏≰-1","reverse_text":"⫏≰-1=(⫏≰1112110⨵⪆⫏≰100012221)⪘⫢(⫏≰101100001⨳⩥⨓⫏≰2012201)","cot":[{"info":"⫏≰1112110⨵⪆⫏≰100012221=⫏≰12221","layer":1},{"info":"⫏≰101100001⨳⩥⨓⫏≰2012201=⫏≰-22010100","layer":1},{"info":"⫏≰12221⪘⫢⫏≰-22010100=⫏≰-1","layer":0}]}
{"id":64,"expression_no_base_symbol":"(↯⪼$2015$)⪒$1458$⋓$4937$","expression":"(↯⪼⫏≰2202122)⪒⫏≰2000000⋓⫏≰20202212","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":47,"operation_count":3,"complexity_ratio":15.666666666666666,"tree":{"type":"binary","operator":"⪒","left_expr":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"numeric_atoms","value":2015,"base":3}},"right_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":1458,"base":3},"right_expr":{"type":"numeric_atoms","value":4937,"base":3}}},"used_operators":["f6k1SAg4EE","8jW3W4yZS5","T2fj7uvVaJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⫏≰210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2015","layer":2},{"info":"compute unary expreesion, input=2015, 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=1458","layer":2},{"info":"number node, value=4937","layer":2},{"info":"compute binary expreesion, left_input=1458, right_input=4937, 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=-21, right_input=0, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=21","layer":0}],"base":3,"result_base":3,"text":"(↯⪼⫏≰2202122)⪒⫏≰2000000⋓⫏≰20202212=⫏≰210","reverse_text":"⫏≰210=(↯⪼⫏≰2202122)⪒⫏≰2000000⋓⫏≰20202212","cot":[{"info":"↯⪼⫏≰2202122=⫏≰-210","layer":1},{"info":"⫏≰2000000⋓⫏≰20202212=⫏≰0","layer":1},{"info":"⫏≰-210⪒⫏≰0=⫏≰210","layer":0}]}
{"id":65,"expression_no_base_symbol":"($4743$⨽$1680$)≧⫂∧(↽≂$7266$)","expression":"(⫏≰20111200⨽⫏≰2022020)≧⫂∧(↽≂⫏≰100222010)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4757,"operation_count":3,"complexity_ratio":1585.6666666666667,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":4743,"base":3},"right_expr":{"type":"numeric_atoms","value":1680,"base":3}},"right_expr":{"type":"unary","operator":"↽≂","unary_expr":{"type":"numeric_atoms","value":7266,"base":3}}},"used_operators":["Ph9nP6C5qx","8HhzD0ZcuI","u6S6b8DprG"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-11200222012111210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4743","layer":2},{"info":"number node, value=1680","layer":2},{"info":"compute binary expreesion, left_input=4743, right_input=1680, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-67491873","layer":1},{"info":"number node, value=7266","layer":2},{"info":"compute unary expreesion, input=7266, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-14532","layer":1},{"info":"compute binary expreesion, left_input=-67491873, right_input=-14532, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=-67477341","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20111200⨽⫏≰2022020)≧⫂∧(↽≂⫏≰100222010)=⫏≰-11200222012111210","reverse_text":"⫏≰-11200222012111210=(⫏≰20111200⨽⫏≰2022020)≧⫂∧(↽≂⫏≰100222010)","cot":[{"info":"⫏≰20111200⨽⫏≰2022020=⫏≰-11200222221110000","layer":1},{"info":"↽≂⫏≰100222010=⫏≰-201221020","layer":1},{"info":"⫏≰-11200222221110000≧⫂∧⫏≰-201221020=⫏≰-11200222012111210","layer":0}]}
{"id":66,"expression_no_base_symbol":"($1845$/$5907$)⇼⇔∾($3810$⪒$6121$)","expression":"(⫏≰2112100/⫏≰22002210)⇼⇔∾(⫏≰12020010⪒⫏≰22101201)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":1845,"base":3},"right_expr":{"type":"numeric_atoms","value":5907,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":3810,"base":3},"right_expr":{"type":"numeric_atoms","value":6121,"base":3}}},"used_operators":["tifHPKVTfV","XhwjNDsVaA","f6k1SAg4EE"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-111121211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1845","layer":2},{"info":"number node, value=5907","layer":2},{"info":"compute binary expreesion, left_input=1845, right_input=5907, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"number node, value=3810","layer":2},{"info":"number node, value=6121","layer":2},{"info":"compute binary expreesion, left_input=3810, right_input=6121, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-9931","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-9931, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-9931","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2112100/⫏≰22002210)⇼⇔∾(⫏≰12020010⪒⫏≰22101201)=⫏≰-111121211","reverse_text":"⫏≰-111121211=(⫏≰2112100/⫏≰22002210)⇼⇔∾(⫏≰12020010⪒⫏≰22101201)","cot":[{"info":"⫏≰2112100/⫏≰22002210=⫏≰0","layer":1},{"info":"⫏≰12020010⪒⫏≰22101201=⫏≰-111121211","layer":1},{"info":"⫏≰0⇼⇔∾⫏≰-111121211=⫏≰-111121211","layer":0}]}
{"id":67,"expression_no_base_symbol":"($2479$/$4401$)-(↔$1139$)","expression":"(⫏≰10101211/⫏≰20001000)-(↔⫏≰1120012)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"-","left_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":2479,"base":3},"right_expr":{"type":"numeric_atoms","value":4401,"base":3}},"right_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":1139,"base":3}}},"used_operators":["rysDP5nf3Z","XhwjNDsVaA","ruOEQAzv1W"],"dependent_operators":["rysDP5nf3Z","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp"],"result":"⫏≰1012002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2479","layer":2},{"info":"number node, value=4401","layer":2},{"info":"compute binary expreesion, left_input=2479, right_input=4401, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"number node, value=1139","layer":2},{"info":"compute unary expreesion, input=1139, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-866","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-866, op_id = rysDP5nf3Z binary_op_definition= 'None', output=866","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10101211/⫏≰20001000)-(↔⫏≰1120012)=⫏≰1012002","reverse_text":"⫏≰1012002=(⫏≰10101211/⫏≰20001000)-(↔⫏≰1120012)","cot":[{"info":"⫏≰10101211/⫏≰20001000=⫏≰0","layer":1},{"info":"↔⫏≰1120012=⫏≰-1012002","layer":1},{"info":"⫏≰0-⫏≰-1012002=⫏≰1012002","layer":0}]}
{"id":68,"expression_no_base_symbol":"$1128$∼$3667$⩚⊴⇥$4886$⨓$2166$","expression":"⫏≰1112210∼⫏≰12000211⩚⊴⇥⫏≰20200222⨓⫏≰2222020","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2199,"operation_count":3,"complexity_ratio":733.0,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":1128,"base":3},"right_expr":{"type":"numeric_atoms","value":3667,"base":3}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":4886,"base":3},"right_expr":{"type":"numeric_atoms","value":2166,"base":3}}},"used_operators":["NTOWxs364D","DyGG3AbaNP","3ViojmjbAp"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1128","layer":2},{"info":"number node, value=3667","layer":2},{"info":"compute binary expreesion, left_input=1128, right_input=3667, 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=4886","layer":2},{"info":"number node, value=2166","layer":2},{"info":"compute binary expreesion, left_input=4886, right_input=2166, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-2169","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-2169, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1112210∼⫏≰12000211⩚⊴⇥⫏≰20200222⨓⫏≰2222020=NaN","reverse_text":"NaN=⫏≰1112210∼⫏≰12000211⩚⊴⇥⫏≰20200222⨓⫏≰2222020","cot":[{"info":"⫏≰1112210∼⫏≰12000211=NaN","layer":1},{"info":"⫏≰20200222⨓⫏≰2222020=⫏≰-2222100","layer":1},{"info":"NaN⩚⊴⇥⫏≰-2222100=NaN","layer":0}]}
{"id":69,"expression_no_base_symbol":"≉($1941$⊭↱$1825$)","expression":"≉(⫏≰2122220⊭↱⫏≰2111121)","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":1941,"base":3},"right_expr":{"type":"numeric_atoms","value":1825,"base":3}}},"used_operators":["e1ybzncUwg","COABgblf1C"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-22102","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1941","layer":2},{"info":"number node, value=1825","layer":2},{"info":"compute binary expreesion, left_input=1941, right_input=1825, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-227","layer":1},{"info":"compute unary expreesion, input=-227, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=-227","layer":0}],"base":3,"result_base":3,"text":"≉(⫏≰2122220⊭↱⫏≰2111121)=⫏≰-22102","reverse_text":"⫏≰-22102=≉(⫏≰2122220⊭↱⫏≰2111121)","cot":[{"info":"⫏≰2122220⊭↱⫏≰2111121=⫏≰-22102","layer":1},{"info":"≉⫏≰-22102=⫏≰-22102","layer":0}]}
{"id":70,"expression_no_base_symbol":"($1248$⪒$2014$)⨽($8227$⩨$3247$)","expression":"(⫏≰1201020⪒⫏≰2202121)⨽(⫏≰102021201⩨⫏≰11110021)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3278,"operation_count":3,"complexity_ratio":1092.6666666666667,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":1248,"base":3},"right_expr":{"type":"numeric_atoms","value":2014,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":8227,"base":3},"right_expr":{"type":"numeric_atoms","value":3247,"base":3}}},"used_operators":["8HhzD0ZcuI","f6k1SAg4EE","2DlMacCsIx"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","W4YGzv6Whe","t8gj7n24qd","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰-2020001201212010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1248","layer":2},{"info":"number node, value=2014","layer":2},{"info":"compute binary expreesion, left_input=1248, right_input=2014, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-3262","layer":1},{"info":"number node, value=8227","layer":2},{"info":"number node, value=3247","layer":2},{"info":"compute binary expreesion, left_input=8227, right_input=3247, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-3262, right_input=0, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-31920618","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1201020⪒⫏≰2202121)⨽(⫏≰102021201⩨⫏≰11110021)=⫏≰-2020001201212010","reverse_text":"⫏≰-2020001201212010=(⫏≰1201020⪒⫏≰2202121)⨽(⫏≰102021201⩨⫏≰11110021)","cot":[{"info":"⫏≰1201020⪒⫏≰2202121=⫏≰-11110211","layer":1},{"info":"⫏≰102021201⩨⫏≰11110021=⫏≰0","layer":1},{"info":"⫏≰-11110211⨽⫏≰0=⫏≰-2020001201212010","layer":0}]}
{"id":71,"expression_no_base_symbol":"⨞⊢($1360$⋷$2999$)","expression":"⨞⊢(⫏≰1212101⋷⫏≰11010002)","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":1360,"base":3},"right_expr":{"type":"numeric_atoms","value":2999,"base":3}}},"used_operators":["xUOZtlo3hN","23Mk6UjR3U"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-20121020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1360","layer":2},{"info":"number node, value=2999","layer":2},{"info":"compute binary expreesion, left_input=1360, right_input=2999, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=4638","layer":1},{"info":"compute unary expreesion, input=4638, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-4812","layer":0}],"base":3,"result_base":3,"text":"⨞⊢(⫏≰1212101⋷⫏≰11010002)=⫏≰-20121020","reverse_text":"⫏≰-20121020=⨞⊢(⫏≰1212101⋷⫏≰11010002)","cot":[{"info":"⫏≰1212101⋷⫏≰11010002=⫏≰20100210","layer":1},{"info":"⨞⊢⫏≰20100210=⫏≰-20121020","layer":0}]}
{"id":72,"expression_no_base_symbol":"($2305$⇼⇔∾$1387$)≫≃","expression":"(⫏≰10011101⇼⇔∾⫏≰1220101)≫≃","highest_n_order":2,"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":2305,"base":3},"right_expr":{"type":"numeric_atoms","value":1387,"base":3}}},"used_operators":["X99M06cbEe","tifHPKVTfV"],"dependent_operators":["2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-121010","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2305","layer":2},{"info":"number node, value=1387","layer":2},{"info":"compute binary expreesion, left_input=2305, right_input=1387, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-918","layer":1},{"info":"compute unary expreesion, input=-918, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=-435","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10011101⇼⇔∾⫏≰1220101)≫≃=⫏≰-121010","reverse_text":"⫏≰-121010=(⫏≰10011101⇼⇔∾⫏≰1220101)≫≃","cot":[{"info":"⫏≰10011101⇼⇔∾⫏≰1220101=⫏≰-1021000","layer":1},{"info":"⫏≰-1021000≫≃=⫏≰-121010","layer":0}]}
{"id":73,"expression_no_base_symbol":"$7189$⪛$1336$%($1632$≫≃)","expression":"⫏≰100212021⪛⫏≰1211111%(⫏≰2020110≫≃)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16,"operation_count":3,"complexity_ratio":5.333333333333333,"tree":{"type":"binary","operator":"%","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":7189,"base":3},"right_expr":{"type":"numeric_atoms","value":1336,"base":3}},"right_expr":{"type":"unary","operator":"≫≃","unary_expr":{"type":"numeric_atoms","value":1632,"base":3}}},"used_operators":["k8jYdgA6NY","uFcxV4UQCh","X99M06cbEe"],"dependent_operators":["rysDP5nf3Z","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A"],"result":"⫏≰200212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7189","layer":2},{"info":"number node, value=1336","layer":2},{"info":"compute binary expreesion, left_input=7189, right_input=1336, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=509","layer":1},{"info":"number node, value=1632","layer":2},{"info":"compute unary expreesion, input=1632, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=4665","layer":1},{"info":"compute binary expreesion, left_input=509, right_input=4665, op_id = k8jYdgA6NY binary_op_definition= 'None', output=509","layer":0}],"base":3,"result_base":3,"text":"⫏≰100212021⪛⫏≰1211111%(⫏≰2020110≫≃)=⫏≰200212","reverse_text":"⫏≰200212=⫏≰100212021⪛⫏≰1211111%(⫏≰2020110≫≃)","cot":[{"info":"⫏≰100212021⪛⫏≰1211111=⫏≰200212","layer":1},{"info":"⫏≰2020110≫≃=⫏≰20101210","layer":1},{"info":"⫏≰200212%⫏≰20101210=⫏≰200212","layer":0}]}
{"id":74,"expression_no_base_symbol":"($2259$↺$1697$)⋳⪒($4120$⋷$1966$)","expression":"(⫏≰10002200↺⫏≰2022212)⋳⪒(⫏≰12122121⋷⫏≰2200211)","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":2259,"base":3},"right_expr":{"type":"numeric_atoms","value":1697,"base":3}},"right_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":4120,"base":3},"right_expr":{"type":"numeric_atoms","value":1966,"base":3}}},"used_operators":["12rbrZMWeM","7j4O788W3g","23Mk6UjR3U"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰11112001","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2259","layer":2},{"info":"number node, value=1697","layer":2},{"info":"compute binary expreesion, left_input=2259, right_input=1697, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1697","layer":1},{"info":"number node, value=4120","layer":2},{"info":"number node, value=1966","layer":2},{"info":"compute binary expreesion, left_input=4120, right_input=1966, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-188","layer":1},{"info":"compute binary expreesion, left_input=1697, right_input=-188, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=3295","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10002200↺⫏≰2022212)⋳⪒(⫏≰12122121⋷⫏≰2200211)=⫏≰11112001","reverse_text":"⫏≰11112001=(⫏≰10002200↺⫏≰2022212)⋳⪒(⫏≰12122121⋷⫏≰2200211)","cot":[{"info":"⫏≰10002200↺⫏≰2022212=⫏≰2022212","layer":1},{"info":"⫏≰12122121⋷⫏≰2200211=⫏≰-20222","layer":1},{"info":"⫏≰2022212⋳⪒⫏≰-20222=⫏≰11112001","layer":0}]}
{"id":75,"expression_no_base_symbol":"($1151$+⇶⊼$7425$)⨓$4350$⪢$3422$","expression":"(⫏≰1120122+⇶⊼⫏≰101012000)⨓⫏≰12222010⪢⫏≰11200202","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3469,"operation_count":3,"complexity_ratio":1156.3333333333333,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":1151,"base":3},"right_expr":{"type":"numeric_atoms","value":7425,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":4350,"base":3},"right_expr":{"type":"numeric_atoms","value":3422,"base":3}}},"used_operators":["3ViojmjbAp","TpPTUOHfaN","dWAJyo7jo9"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","AHs5Up7iyr","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1151","layer":2},{"info":"number node, value=7425","layer":2},{"info":"compute binary expreesion, left_input=1151, right_input=7425, 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":1},{"info":"number node, value=4350","layer":2},{"info":"number node, value=3422","layer":2},{"info":"compute binary expreesion, left_input=4350, right_input=3422, 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 = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1120122+⇶⊼⫏≰101012000)⨓⫏≰12222010⪢⫏≰11200202=NaN","reverse_text":"NaN=(⫏≰1120122+⇶⊼⫏≰101012000)⨓⫏≰12222010⪢⫏≰11200202","cot":[{"info":"⫏≰1120122+⇶⊼⫏≰101012000=NaN","layer":1},{"info":"⫏≰12222010⪢⫏≰11200202=NaN","layer":1},{"info":"NaN⨓NaN=NaN","layer":0}]}
{"id":76,"expression_no_base_symbol":"$2856$≧⫂∧$1109$⨰($1328$⪐)","expression":"⫏≰10220210≧⫂∧⫏≰1112002⨰(⫏≰1211012⪐)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⨰","left_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":2856,"base":3},"right_expr":{"type":"numeric_atoms","value":1109,"base":3}},"right_expr":{"type":"unary","operator":"⪐","unary_expr":{"type":"numeric_atoms","value":1328,"base":3}}},"used_operators":["eewbuw0ToL","Ph9nP6C5qx","eH2TOUuTDT"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-2202110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2856","layer":2},{"info":"number node, value=1109","layer":2},{"info":"compute binary expreesion, left_input=2856, right_input=1109, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=636","layer":1},{"info":"number node, value=1328","layer":2},{"info":"compute unary expreesion, input=1328, op_id = eH2TOUuTDT, unary_op_definition = 'a⪐ = { (a+a) , if (-a)!=532 or a<368 ; (-a) , else }', output=2656","layer":1},{"info":"compute binary expreesion, left_input=636, right_input=2656, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-2010","layer":0}],"base":3,"result_base":3,"text":"⫏≰10220210≧⫂∧⫏≰1112002⨰(⫏≰1211012⪐)=⫏≰-2202110","reverse_text":"⫏≰-2202110=⫏≰10220210≧⫂∧⫏≰1112002⨰(⫏≰1211012⪐)","cot":[{"info":"⫏≰10220210≧⫂∧⫏≰1112002=⫏≰212120","layer":1},{"info":"⫏≰1211012⪐=⫏≰10122101","layer":1},{"info":"⫏≰212120⨰⫏≰10122101=⫏≰-2202110","layer":0}]}
{"id":77,"expression_no_base_symbol":"($1930$⊦⊿)⊴(⊙↵-$1202$)","expression":"(⫏≰2122111⊦⊿)⊴(⊙↵-⫏≰1122112)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7129,"operation_count":3,"complexity_ratio":2376.3333333333335,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":1930,"base":3}},"right_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":1202,"base":3}}},"used_operators":["Nsiff2A1zJ","14qkJME0vr","oWn0xqSxBt"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"⫏≰-2221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1930","layer":2},{"info":"compute unary expreesion, input=1930, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-5869","layer":1},{"info":"number node, value=1202","layer":2},{"info":"compute unary expreesion, input=1202, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute binary expreesion, left_input=-5869, right_input=-1, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=-79","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2122111⊦⊿)⊴(⊙↵-⫏≰1122112)=⫏≰-2221","reverse_text":"⫏≰-2221=(⫏≰2122111⊦⊿)⊴(⊙↵-⫏≰1122112)","cot":[{"info":"⫏≰2122111⊦⊿=⫏≰-22001101","layer":1},{"info":"⊙↵-⫏≰1122112=⫏≰-1","layer":1},{"info":"⫏≰-22001101⊴⫏≰-1=⫏≰-2221","layer":0}]}
{"id":78,"expression_no_base_symbol":"$2273$⪛$2260$∲⫓($1174$≦≮≮)","expression":"⫏≰10010012⪛⫏≰10002201∲⫓(⫏≰1121111≦≮≮)","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":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":2273,"base":3},"right_expr":{"type":"numeric_atoms","value":2260,"base":3}},"right_expr":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":1174,"base":3}}},"used_operators":["i8ToyICDmI","uFcxV4UQCh","D4vGDi5EA2"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2273","layer":2},{"info":"number node, value=2260","layer":2},{"info":"compute binary expreesion, left_input=2273, right_input=2260, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=13","layer":1},{"info":"number node, value=1174","layer":2},{"info":"compute unary expreesion, input=1174, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-3522","layer":1},{"info":"compute binary expreesion, left_input=13, right_input=-3522, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=13","layer":0}],"base":3,"result_base":3,"text":"⫏≰10010012⪛⫏≰10002201∲⫓(⫏≰1121111≦≮≮)=⫏≰111","reverse_text":"⫏≰111=⫏≰10010012⪛⫏≰10002201∲⫓(⫏≰1121111≦≮≮)","cot":[{"info":"⫏≰10010012⪛⫏≰10002201=⫏≰111","layer":1},{"info":"⫏≰1121111≦≮≮=⫏≰-11211110","layer":1},{"info":"⫏≰111∲⫓⫏≰-11211110=⫏≰111","layer":0}]}
{"id":79,"expression_no_base_symbol":"≦∁$2982$⋳⪒$3568$","expression":"≦∁⫏≰11002110⋳⪒⫏≰11220011","highest_n_order":2,"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":2982,"base":3},"right_expr":{"type":"numeric_atoms","value":3568,"base":3}}},"used_operators":["9ICcGScMcE","12rbrZMWeM"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰2220010","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2982","layer":2},{"info":"number node, value=3568","layer":2},{"info":"compute binary expreesion, left_input=2982, right_input=3568, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=2109","layer":1},{"info":"compute unary expreesion, input=2109, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=2109","layer":0}],"base":3,"result_base":3,"text":"≦∁⫏≰11002110⋳⪒⫏≰11220011=⫏≰2220010","reverse_text":"⫏≰2220010=≦∁⫏≰11002110⋳⪒⫏≰11220011","cot":[{"info":"⫏≰11002110⋳⪒⫏≰11220011=⫏≰2220010","layer":1},{"info":"≦∁⫏≰2220010=⫏≰2220010","layer":0}]}
{"id":80,"expression_no_base_symbol":"⊙↵-($1094$⫡⨏$2251$)","expression":"⊙↵-(⫏≰1111112⫡⨏⫏≰10002101)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":10808,"operation_count":2,"complexity_ratio":5404.0,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":1094,"base":3},"right_expr":{"type":"numeric_atoms","value":2251,"base":3}}},"used_operators":["oWn0xqSxBt","QMFrweE19q"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1094","layer":2},{"info":"number node, value=2251","layer":2},{"info":"compute binary expreesion, left_input=1094, right_input=2251, 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=10755","layer":1},{"info":"compute unary expreesion, input=10755, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⫏≰1111112⫡⨏⫏≰10002101)=⫏≰-1","reverse_text":"⫏≰-1=⊙↵-(⫏≰1111112⫡⨏⫏≰10002101)","cot":[{"info":"⫏≰1111112⫡⨏⫏≰10002101=⫏≰112202100","layer":1},{"info":"⊙↵-⫏≰112202100=⫏≰-1","layer":0}]}
{"id":81,"expression_no_base_symbol":"$5778$⋥≓≎$4624$*(⨑⩽⪐$3045$)","expression":"⫏≰21221000⋥≓≎⫏≰20100021*(⨑⩽⪐⫏≰11011210)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2780,"operation_count":3,"complexity_ratio":926.6666666666666,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":5778,"base":3},"right_expr":{"type":"numeric_atoms","value":4624,"base":3}},"right_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":3045,"base":3}}},"used_operators":["9HNa5Wba9A","Qy55tPpLXF","AF7qkfDlqP"],"dependent_operators":["W4YGzv6Whe","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-200021100001100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5778","layer":2},{"info":"number node, value=4624","layer":2},{"info":"compute binary expreesion, left_input=5778, right_input=4624, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=3503","layer":1},{"info":"number node, value=3045","layer":2},{"info":"compute unary expreesion, input=3045, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-2772","layer":1},{"info":"compute binary expreesion, left_input=3503, right_input=-2772, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=-9710316","layer":0}],"base":3,"result_base":3,"text":"⫏≰21221000⋥≓≎⫏≰20100021*(⨑⩽⪐⫏≰11011210)=⫏≰-200021100001100","reverse_text":"⫏≰-200021100001100=⫏≰21221000⋥≓≎⫏≰20100021*(⨑⩽⪐⫏≰11011210)","cot":[{"info":"⫏≰21221000⋥≓≎⫏≰20100021=⫏≰11210202","layer":1},{"info":"⨑⩽⪐⫏≰11011210=⫏≰-10210200","layer":1},{"info":"⫏≰11210202*⫏≰-10210200=⫏≰-200021100001100","layer":0}]}
{"id":82,"expression_no_base_symbol":"(⨵≀≌$1644$)∲⫓$4494$⨪↰⇹$6132$","expression":"(⨵≀≌⫏≰2020220)∲⫓⫏≰20011110⨪↰⇹⫏≰22102010","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4499,"operation_count":3,"complexity_ratio":1499.6666666666667,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":1644,"base":3}},"right_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":4494,"base":3},"right_expr":{"type":"numeric_atoms","value":6132,"base":3}}},"used_operators":["i8ToyICDmI","srAu1WTS94","tmPS8pqC7x"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","rJVOvQCfKK"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1644","layer":2},{"info":"compute unary expreesion, input=1644, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-4932","layer":1},{"info":"number node, value=4494","layer":2},{"info":"number node, value=6132","layer":2},{"info":"compute binary expreesion, left_input=4494, right_input=6132, 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=4494","layer":1},{"info":"compute binary expreesion, left_input=-4932, right_input=4494, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⨵≀≌⫏≰2020220)∲⫓⫏≰20011110⨪↰⇹⫏≰22102010=⫏≰0","reverse_text":"⫏≰0=(⨵≀≌⫏≰2020220)∲⫓⫏≰20011110⨪↰⇹⫏≰22102010","cot":[{"info":"⨵≀≌⫏≰2020220=⫏≰-20202200","layer":1},{"info":"⫏≰20011110⨪↰⇹⫏≰22102010=⫏≰20011110","layer":1},{"info":"⫏≰-20202200∲⫓⫏≰20011110=⫏≰0","layer":0}]}
{"id":83,"expression_no_base_symbol":"$1196$⩷∴$2472$⋓($3788$⪒$4337$)","expression":"⫏≰1122022⩷∴⫏≰10101120⋓(⫏≰12012022⪒⫏≰12221122)","highest_n_order":3,"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":1196,"base":3},"right_expr":{"type":"numeric_atoms","value":2472,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":3788,"base":3},"right_expr":{"type":"numeric_atoms","value":4337,"base":3}}},"used_operators":["T2fj7uvVaJ","9FxExcQeMw","f6k1SAg4EE"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1196","layer":2},{"info":"number node, value=2472","layer":2},{"info":"compute binary expreesion, left_input=1196, right_input=2472, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-2584","layer":1},{"info":"number node, value=3788","layer":2},{"info":"number node, value=4337","layer":2},{"info":"compute binary expreesion, left_input=3788, right_input=4337, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-8125","layer":1},{"info":"compute binary expreesion, left_input=-2584, right_input=-8125, 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":3,"result_base":3,"text":"⫏≰1122022⩷∴⫏≰10101120⋓(⫏≰12012022⪒⫏≰12221122)=⫏≰0","reverse_text":"⫏≰0=⫏≰1122022⩷∴⫏≰10101120⋓(⫏≰12012022⪒⫏≰12221122)","cot":[{"info":"⫏≰1122022⩷∴⫏≰10101120=⫏≰-10112201","layer":1},{"info":"⫏≰12012022⪒⫏≰12221122=⫏≰-102010221","layer":1},{"info":"⫏≰-10112201⋓⫏≰-102010221=⫏≰0","layer":0}]}
{"id":84,"expression_no_base_symbol":"$2353$⋥≓≎$1132$⫡⨏(⨑⩽⪐$4527$)","expression":"⫏≰10020011⋥≓≎⫏≰1112221⫡⨏(⨑⩽⪐⫏≰20012200)","highest_n_order":1,"priority_hierarchical_complexity":2,"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":2353,"base":3},"right_expr":{"type":"numeric_atoms","value":1132,"base":3}},"right_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":4527,"base":3}}},"used_operators":["QMFrweE19q","Qy55tPpLXF","AF7qkfDlqP"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-101222111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2353","layer":2},{"info":"number node, value=1132","layer":2},{"info":"compute binary expreesion, left_input=2353, right_input=1132, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-56","layer":1},{"info":"number node, value=4527","layer":2},{"info":"compute unary expreesion, input=4527, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-4254","layer":1},{"info":"compute binary expreesion, left_input=-56, right_input=-4254, 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=-8005","layer":0}],"base":3,"result_base":3,"text":"⫏≰10020011⋥≓≎⫏≰1112221⫡⨏(⨑⩽⪐⫏≰20012200)=⫏≰-101222111","reverse_text":"⫏≰-101222111=⫏≰10020011⋥≓≎⫏≰1112221⫡⨏(⨑⩽⪐⫏≰20012200)","cot":[{"info":"⫏≰10020011⋥≓≎⫏≰1112221=⫏≰-2002","layer":1},{"info":"⨑⩽⪐⫏≰20012200=⫏≰-12211120","layer":1},{"info":"⫏≰-2002⫡⨏⫏≰-12211120=⫏≰-101222111","layer":0}]}
{"id":85,"expression_no_base_symbol":"$2635$⨎$2201$⨎(⇁⨣⪵$2816$)","expression":"⫏≰10121121⨎⫏≰10000112⨎(⇁⨣⪵⫏≰10212022)","highest_n_order":5,"priority_hierarchical_complexity":2,"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":2635,"base":3},"right_expr":{"type":"numeric_atoms","value":2201,"base":3}},"right_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":2816,"base":3}}},"used_operators":["rJVOvQCfKK","inkyxCbjAn"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2635","layer":2},{"info":"number node, value=2201","layer":2},{"info":"compute binary expreesion, left_input=2635, right_input=2201, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=2201","layer":1},{"info":"number node, value=2816","layer":2},{"info":"compute unary expreesion, input=2816, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=2201, 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":3,"result_base":3,"text":"⫏≰10121121⨎⫏≰10000112⨎(⇁⨣⪵⫏≰10212022)=NaN","reverse_text":"NaN=⫏≰10121121⨎⫏≰10000112⨎(⇁⨣⪵⫏≰10212022)","cot":[{"info":"⫏≰10121121⨎⫏≰10000112=⫏≰10000112","layer":1},{"info":"⇁⨣⪵⫏≰10212022=NaN","layer":1},{"info":"⫏≰10000112⨎NaN=NaN","layer":0}]}
{"id":86,"expression_no_base_symbol":"(↔$2514$)⪛$8570$⨟⋌⩍$7085$","expression":"(↔⫏≰10110010)⪛⫏≰102202102⨟⋌⩍⫏≰100201102","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":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":2514,"base":3}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":8570,"base":3},"right_expr":{"type":"numeric_atoms","value":7085,"base":3}}},"used_operators":["uFcxV4UQCh","ruOEQAzv1W","rGHVDoGpnC"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2514","layer":2},{"info":"compute unary expreesion, input=2514, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-2241","layer":1},{"info":"number node, value=8570","layer":2},{"info":"number node, value=7085","layer":2},{"info":"compute binary expreesion, left_input=8570, right_input=7085, 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=-2241, right_input=nan, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(↔⫏≰10110010)⪛⫏≰102202102⨟⋌⩍⫏≰100201102=NaN","reverse_text":"NaN=(↔⫏≰10110010)⪛⫏≰102202102⨟⋌⩍⫏≰100201102","cot":[{"info":"↔⫏≰10110010=⫏≰-10002000","layer":1},{"info":"⫏≰102202102⨟⋌⩍⫏≰100201102=NaN","layer":1},{"info":"⫏≰-10002000⪛NaN=NaN","layer":0}]}
{"id":87,"expression_no_base_symbol":"$1440$⨟⋌⩍$2037$↛⩡⫤","expression":"⫏≰1222100⨟⋌⩍⫏≰2210110↛⩡⫤","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":1440,"base":3},"right_expr":{"type":"numeric_atoms","value":2037,"base":3}}},"used_operators":["FU0Cs4j7VP","rGHVDoGpnC"],"dependent_operators":["8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1440","layer":2},{"info":"number node, value=2037","layer":2},{"info":"compute binary expreesion, left_input=1440, right_input=2037, 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 unary expreesion, input=nan, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1222100⨟⋌⩍⫏≰2210110↛⩡⫤=NaN","reverse_text":"NaN=⫏≰1222100⨟⋌⩍⫏≰2210110↛⩡⫤","cot":[{"info":"⫏≰1222100⨟⋌⩍⫏≰2210110=NaN","layer":1},{"info":"NaN↛⩡⫤=NaN","layer":0}]}
{"id":88,"expression_no_base_symbol":"⇁⨣⪵($1042$/$1059$)","expression":"⇁⨣⪵(⫏≰1102121/⫏≰1110020)","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":1042,"base":3},"right_expr":{"type":"numeric_atoms","value":1059,"base":3}}},"used_operators":["inkyxCbjAn","XhwjNDsVaA"],"dependent_operators":["B5M0gjZbta","rysDP5nf3Z"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1042","layer":2},{"info":"number node, value=1059","layer":2},{"info":"compute binary expreesion, left_input=1042, right_input=1059, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵(⫏≰1102121/⫏≰1110020)=⫏≰0","reverse_text":"⫏≰0=⇁⨣⪵(⫏≰1102121/⫏≰1110020)","cot":[{"info":"⫏≰1102121/⫏≰1110020=⫏≰0","layer":1},{"info":"⇁⨣⪵⫏≰0=⫏≰0","layer":0}]}
{"id":89,"expression_no_base_symbol":"(⩦⩻⨪$1596$)⩚⊴⇥$1700$⪢$1454$","expression":"(⩦⩻⨪⫏≰2012010)⩚⊴⇥⫏≰2022222⪢⫏≰1222212","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1659,"operation_count":3,"complexity_ratio":553.0,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":1596,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1700,"base":3},"right_expr":{"type":"numeric_atoms","value":1454,"base":3}}},"used_operators":["NTOWxs364D","2td37pGCOC","dWAJyo7jo9"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1596","layer":2},{"info":"compute unary expreesion, input=1596, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=1596","layer":1},{"info":"number node, value=1700","layer":2},{"info":"number node, value=1454","layer":2},{"info":"compute binary expreesion, left_input=1700, right_input=1454, 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=1596, right_input=nan, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⩦⩻⨪⫏≰2012010)⩚⊴⇥⫏≰2022222⪢⫏≰1222212=NaN","reverse_text":"NaN=(⩦⩻⨪⫏≰2012010)⩚⊴⇥⫏≰2022222⪢⫏≰1222212","cot":[{"info":"⩦⩻⨪⫏≰2012010=⫏≰2012010","layer":1},{"info":"⫏≰2022222⪢⫏≰1222212=NaN","layer":1},{"info":"⫏≰2012010⩚⊴⇥NaN=NaN","layer":0}]}
{"id":90,"expression_no_base_symbol":"$6196$≧⫂∧$1235$⫸⊐$2607$⨳⩥⨓$3713$","expression":"⫏≰22111111≧⫂∧⫏≰1200202⫸⊐⫏≰10120120⨳⩥⨓⫏≰12002112","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":6196,"base":3},"right_expr":{"type":"numeric_atoms","value":1235,"base":3}},"right_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":2607,"base":3},"right_expr":{"type":"numeric_atoms","value":3713,"base":3}}},"used_operators":["mqXw5SEYmG","Ph9nP6C5qx","nCS4ZIUYfx"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰12220020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6196","layer":2},{"info":"number node, value=1235","layer":2},{"info":"compute binary expreesion, left_input=6196, right_input=1235, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=762","layer":1},{"info":"number node, value=2607","layer":2},{"info":"number node, value=3713","layer":2},{"info":"compute binary expreesion, left_input=2607, right_input=3713, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=1106","layer":1},{"info":"compute binary expreesion, left_input=762, right_input=1106, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=4299","layer":0}],"base":3,"result_base":3,"text":"⫏≰22111111≧⫂∧⫏≰1200202⫸⊐⫏≰10120120⨳⩥⨓⫏≰12002112=⫏≰12220020","reverse_text":"⫏≰12220020=⫏≰22111111≧⫂∧⫏≰1200202⫸⊐⫏≰10120120⨳⩥⨓⫏≰12002112","cot":[{"info":"⫏≰22111111≧⫂∧⫏≰1200202=⫏≰1001020","layer":1},{"info":"⫏≰10120120⨳⩥⨓⫏≰12002112=⫏≰1111222","layer":1},{"info":"⫏≰1001020⫸⊐⫏≰1111222=⫏≰12220020","layer":0}]}
{"id":91,"expression_no_base_symbol":"($3534$⊉≛↸$4068$)↺($1813$⨸⪁$4336$)","expression":"(⫏≰11211220⊉≛↸⫏≰12120200)↺(⫏≰2111011⨸⪁⫏≰12221121)","highest_n_order":1,"priority_hierarchical_complexity":2,"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":3534,"base":3},"right_expr":{"type":"numeric_atoms","value":4068,"base":3}},"right_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":1813,"base":3},"right_expr":{"type":"numeric_atoms","value":4336,"base":3}}},"used_operators":["7j4O788W3g","DZ8iAZOCBD","g55IO6H4Gj"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰121212111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3534","layer":2},{"info":"number node, value=4068","layer":2},{"info":"compute binary expreesion, left_input=3534, right_input=4068, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=7068","layer":1},{"info":"number node, value=1813","layer":2},{"info":"number node, value=4336","layer":2},{"info":"compute binary expreesion, left_input=1813, right_input=4336, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=12298","layer":1},{"info":"compute binary expreesion, left_input=7068, right_input=12298, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=12298","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11211220⊉≛↸⫏≰12120200)↺(⫏≰2111011⨸⪁⫏≰12221121)=⫏≰121212111","reverse_text":"⫏≰121212111=(⫏≰11211220⊉≛↸⫏≰12120200)↺(⫏≰2111011⨸⪁⫏≰12221121)","cot":[{"info":"⫏≰11211220⊉≛↸⫏≰12120200=⫏≰100200210","layer":1},{"info":"⫏≰2111011⨸⪁⫏≰12221121=⫏≰121212111","layer":1},{"info":"⫏≰100200210↺⫏≰121212111=⫏≰121212111","layer":0}]}
{"id":92,"expression_no_base_symbol":"$1320$⪢$1221$↺($1712$⇋≉)","expression":"⫏≰1210220⪢⫏≰1200020↺(⫏≰2100102⇋≉)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1277,"operation_count":3,"complexity_ratio":425.6666666666667,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1320,"base":3},"right_expr":{"type":"numeric_atoms","value":1221,"base":3}},"right_expr":{"type":"unary","operator":"⇋≉","unary_expr":{"type":"numeric_atoms","value":1712,"base":3}}},"used_operators":["7j4O788W3g","dWAJyo7jo9","XIabStNQrY"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","k8jYdgA6NY","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰11120012","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1320","layer":2},{"info":"number node, value=1221","layer":2},{"info":"compute binary expreesion, left_input=1320, right_input=1221, 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=1712","layer":2},{"info":"compute unary expreesion, input=1712, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=3326","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=3326, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=3326","layer":0}],"base":3,"result_base":3,"text":"⫏≰1210220⪢⫏≰1200020↺(⫏≰2100102⇋≉)=⫏≰11120012","reverse_text":"⫏≰11120012=⫏≰1210220⪢⫏≰1200020↺(⫏≰2100102⇋≉)","cot":[{"info":"⫏≰1210220⪢⫏≰1200020=NaN","layer":1},{"info":"⫏≰2100102⇋≉=⫏≰11120012","layer":1},{"info":"NaN↺⫏≰11120012=⫏≰11120012","layer":0}]}
{"id":93,"expression_no_base_symbol":"($5203$*$2244$)⊘","expression":"(⫏≰21010201*⫏≰10002010)⊘","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2263,"operation_count":2,"complexity_ratio":1131.5,"tree":{"type":"unary","operator":"⊘","unary_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":5203,"base":3},"right_expr":{"type":"numeric_atoms","value":2244,"base":3}}},"used_operators":["gu96TGCTMs","9HNa5Wba9A"],"dependent_operators":["XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","W4YGzv6Whe"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5203","layer":2},{"info":"number node, value=2244","layer":2},{"info":"compute binary expreesion, left_input=5203, right_input=2244, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=11675532","layer":1},{"info":"compute unary expreesion, input=11675532, 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":3,"result_base":3,"text":"(⫏≰21010201*⫏≰10002010)⊘=⫏≰0","reverse_text":"⫏≰0=(⫏≰21010201*⫏≰10002010)⊘","cot":[{"info":"⫏≰21010201*⫏≰10002010=⫏≰210222011211010","layer":1},{"info":"⫏≰210222011211010⊘=⫏≰0","layer":0}]}
{"id":94,"expression_no_base_symbol":"$1045$↬$1326$/($4774$≫≃)","expression":"⫏≰1102201↬⫏≰1211010/(⫏≰20112211≫≃)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"/","left_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":1045,"base":3},"right_expr":{"type":"numeric_atoms","value":1326,"base":3}},"right_expr":{"type":"unary","operator":"≫≃","unary_expr":{"type":"numeric_atoms","value":4774,"base":3}}},"used_operators":["XhwjNDsVaA","B5M0gjZbta","X99M06cbEe"],"dependent_operators":["rysDP5nf3Z","rGHVDoGpnC","2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1045","layer":2},{"info":"number node, value=1326","layer":2},{"info":"compute binary expreesion, left_input=1045, right_input=1326, 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=4774","layer":2},{"info":"compute unary expreesion, input=4774, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=10949","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=10949, op_id = XhwjNDsVaA binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1102201↬⫏≰1211010/(⫏≰20112211≫≃)=NaN","reverse_text":"NaN=⫏≰1102201↬⫏≰1211010/(⫏≰20112211≫≃)","cot":[{"info":"⫏≰1102201↬⫏≰1211010=NaN","layer":1},{"info":"⫏≰20112211≫≃=⫏≰120000112","layer":1},{"info":"NaN/⫏≰120000112=NaN","layer":0}]}
{"id":95,"expression_no_base_symbol":"⊙↵-($3527$∑⇟⊟$2920$)","expression":"⊙↵-(⫏≰11211122∑⇟⊟⫏≰11000011)","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":3527,"base":3},"right_expr":{"type":"numeric_atoms","value":2920,"base":3}}},"used_operators":["oWn0xqSxBt","U7g4x0WXJJ"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3527","layer":2},{"info":"number node, value=2920","layer":2},{"info":"compute binary expreesion, left_input=3527, right_input=2920, 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 = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⫏≰11211122∑⇟⊟⫏≰11000011)=NaN","reverse_text":"NaN=⊙↵-(⫏≰11211122∑⇟⊟⫏≰11000011)","cot":[{"info":"⫏≰11211122∑⇟⊟⫏≰11000011=NaN","layer":1},{"info":"⊙↵-NaN=NaN","layer":0}]}
{"id":96,"expression_no_base_symbol":"($1060$⫸⊐$3638$)≭(⋗⩬⋾$2202$)","expression":"(⫏≰1110021⫸⊐⫏≰11222202)≭(⋗⩬⋾⫏≰10000120)","highest_n_order":5,"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":1060,"base":3},"right_expr":{"type":"numeric_atoms","value":3638,"base":3}},"right_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":2202,"base":3}}},"used_operators":["rxpJgHHUmx","mqXw5SEYmG","DpFCA1CohY"],"dependent_operators":["AHs5Up7iyr","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1060","layer":2},{"info":"number node, value=3638","layer":2},{"info":"compute binary expreesion, left_input=1060, right_input=3638, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=14427","layer":1},{"info":"number node, value=2202","layer":2},{"info":"compute unary expreesion, input=2202, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-6606","layer":1},{"info":"compute binary expreesion, left_input=14427, right_input=-6606, 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":3,"result_base":3,"text":"(⫏≰1110021⫸⊐⫏≰11222202)≭(⋗⩬⋾⫏≰10000120)=NaN","reverse_text":"NaN=(⫏≰1110021⫸⊐⫏≰11222202)≭(⋗⩬⋾⫏≰10000120)","cot":[{"info":"⫏≰1110021⫸⊐⫏≰11222202=⫏≰201210100","layer":1},{"info":"⋗⩬⋾⫏≰10000120=⫏≰-100001200","layer":1},{"info":"⫏≰201210100≭⫏≰-100001200=NaN","layer":0}]}
{"id":97,"expression_no_base_symbol":"($1068$≎⊠⪸$6799$)⪮%⊝($1080$∑⇟⊟$1849$)","expression":"(⫏≰1110120≎⊠⪸⫏≰100022211)⪮%⊝(⫏≰1111000∑⇟⊟⫏≰2112111)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":280,"operation_count":3,"complexity_ratio":93.33333333333333,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1068,"base":3},"right_expr":{"type":"numeric_atoms","value":6799,"base":3}},"right_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":1080,"base":3},"right_expr":{"type":"numeric_atoms","value":1849,"base":3}}},"used_operators":["IWmyXbctLI","bJkvcejdHO","U7g4x0WXJJ"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1068","layer":2},{"info":"number node, value=6799","layer":2},{"info":"compute binary expreesion, left_input=1068, right_input=6799, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=276139","layer":1},{"info":"number node, value=1080","layer":2},{"info":"number node, value=1849","layer":2},{"info":"compute binary expreesion, left_input=1080, right_input=1849, 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=276139, right_input=nan, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1110120≎⊠⪸⫏≰100022211)⪮%⊝(⫏≰1111000∑⇟⊟⫏≰2112111)=NaN","reverse_text":"NaN=(⫏≰1110120≎⊠⪸⫏≰100022211)⪮%⊝(⫏≰1111000∑⇟⊟⫏≰2112111)","cot":[{"info":"⫏≰1110120≎⊠⪸⫏≰100022211=⫏≰112000210101","layer":1},{"info":"⫏≰1111000∑⇟⊟⫏≰2112111=NaN","layer":1},{"info":"⫏≰112000210101⪮%⊝NaN=NaN","layer":0}]}
{"id":98,"expression_no_base_symbol":"(⇁⨣⪵$6467$)⨎$1242$⊴$1282$","expression":"(⇁⨣⪵⫏≰22212112)⨎⫏≰1201000⊴⫏≰1202111","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1290,"operation_count":3,"complexity_ratio":430.0,"tree":{"type":"binary","operator":"⨎","left_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":6467,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1242,"base":3},"right_expr":{"type":"numeric_atoms","value":1282,"base":3}}},"used_operators":["rJVOvQCfKK","inkyxCbjAn","Nsiff2A1zJ"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","B5M0gjZbta","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6467","layer":2},{"info":"compute unary expreesion, input=6467, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"number node, value=1242","layer":2},{"info":"number node, value=1282","layer":2},{"info":"compute binary expreesion, left_input=1242, right_input=1282, 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 = 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":3,"result_base":3,"text":"(⇁⨣⪵⫏≰22212112)⨎⫏≰1201000⊴⫏≰1202111=NaN","reverse_text":"NaN=(⇁⨣⪵⫏≰22212112)⨎⫏≰1201000⊴⫏≰1202111","cot":[{"info":"⇁⨣⪵⫏≰22212112=NaN","layer":1},{"info":"⫏≰1201000⊴⫏≰1202111=NaN","layer":1},{"info":"NaN⨎NaN=NaN","layer":0}]}
{"id":99,"expression_no_base_symbol":"($3062$/$5860$)⋳⪒$3645$⩚⊴⇥$1789$","expression":"(⫏≰11012102/⫏≰22001001)⋳⪒⫏≰12000000⩚⊴⇥⫏≰2110021","highest_n_order":2,"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":3062,"base":3},"right_expr":{"type":"numeric_atoms","value":5860,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":3645,"base":3},"right_expr":{"type":"numeric_atoms","value":1789,"base":3}}},"used_operators":["12rbrZMWeM","XhwjNDsVaA","NTOWxs364D"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰21020010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3062","layer":2},{"info":"number node, value=5860","layer":2},{"info":"compute binary expreesion, left_input=3062, right_input=5860, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"number node, value=3645","layer":2},{"info":"number node, value=1789","layer":2},{"info":"compute binary expreesion, left_input=3645, right_input=1789, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-5555","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-5555, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=5268","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11012102/⫏≰22001001)⋳⪒⫏≰12000000⩚⊴⇥⫏≰2110021=⫏≰21020010","reverse_text":"⫏≰21020010=(⫏≰11012102/⫏≰22001001)⋳⪒⫏≰12000000⩚⊴⇥⫏≰2110021","cot":[{"info":"⫏≰11012102/⫏≰22001001=⫏≰0","layer":1},{"info":"⫏≰12000000⩚⊴⇥⫏≰2110021=⫏≰-21121202","layer":1},{"info":"⫏≰0⋳⪒⫏≰-21121202=⫏≰21020010","layer":0}]}
{"id":100,"expression_no_base_symbol":"$3551$∑⇟⊟$1328$⩨$1071$⨟⋌⩍$6178$","expression":"⫏≰11212112∑⇟⊟⫏≰1211012⩨⫏≰1110200⨟⋌⩍⫏≰22110211","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"⩨","left_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":3551,"base":3},"right_expr":{"type":"numeric_atoms","value":1328,"base":3}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":1071,"base":3},"right_expr":{"type":"numeric_atoms","value":6178,"base":3}}},"used_operators":["2DlMacCsIx","U7g4x0WXJJ","rGHVDoGpnC"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3551","layer":2},{"info":"number node, value=1328","layer":2},{"info":"compute binary expreesion, left_input=3551, right_input=1328, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"number node, value=1071","layer":2},{"info":"number node, value=6178","layer":2},{"info":"compute binary expreesion, left_input=1071, right_input=6178, 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=nan, right_input=nan, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11212112∑⇟⊟⫏≰1211012⩨⫏≰1110200⨟⋌⩍⫏≰22110211=NaN","reverse_text":"NaN=⫏≰11212112∑⇟⊟⫏≰1211012⩨⫏≰1110200⨟⋌⩍⫏≰22110211","cot":[{"info":"⫏≰11212112∑⇟⊟⫏≰1211012=NaN","layer":1},{"info":"⫏≰1110200⨟⋌⩍⫏≰22110211=NaN","layer":1},{"info":"NaN⩨NaN=NaN","layer":0}]}
{"id":101,"expression_no_base_symbol":"(⨰⫟⨤$5095$)∲⫓(⊙↵-$2847$)","expression":"(⨰⫟⨤⫏≰20222201)∲⫓(⊙↵-⫏≰10220110)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":22434,"operation_count":3,"complexity_ratio":7478.0,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":5095,"base":3}},"right_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":2847,"base":3}}},"used_operators":["i8ToyICDmI","Tw270M8GLb","oWn0xqSxBt"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5095","layer":2},{"info":"compute unary expreesion, input=5095, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":1},{"info":"number node, value=2847","layer":2},{"info":"compute unary expreesion, input=2847, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-1, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⨰⫟⨤⫏≰20222201)∲⫓(⊙↵-⫏≰10220110)=NaN","reverse_text":"NaN=(⨰⫟⨤⫏≰20222201)∲⫓(⊙↵-⫏≰10220110)","cot":[{"info":"⨰⫟⨤⫏≰20222201=NaN","layer":1},{"info":"⊙↵-⫏≰10220110=⫏≰-1","layer":1},{"info":"NaN∲⫓⫏≰-1=NaN","layer":0}]}
{"id":102,"expression_no_base_symbol":"⩦⩻⨪$2282$⪛$2098$","expression":"⩦⩻⨪⫏≰10010112⪛⫏≰2212201","highest_n_order":2,"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":2282,"base":3},"right_expr":{"type":"numeric_atoms","value":2098,"base":3}}},"used_operators":["2td37pGCOC","uFcxV4UQCh"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⫏≰20211","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2282","layer":2},{"info":"number node, value=2098","layer":2},{"info":"compute binary expreesion, left_input=2282, right_input=2098, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=184","layer":1},{"info":"compute unary expreesion, input=184, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=184","layer":0}],"base":3,"result_base":3,"text":"⩦⩻⨪⫏≰10010112⪛⫏≰2212201=⫏≰20211","reverse_text":"⫏≰20211=⩦⩻⨪⫏≰10010112⪛⫏≰2212201","cot":[{"info":"⫏≰10010112⪛⫏≰2212201=⫏≰20211","layer":1},{"info":"⩦⩻⨪⫏≰20211=⫏≰20211","layer":0}]}
{"id":103,"expression_no_base_symbol":"$2227$≭$1903$⋳⪒$1123$⪢$1175$","expression":"⫏≰10001111≭⫏≰2121111⋳⪒⫏≰1112121⪢⫏≰1121112","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1183,"operation_count":3,"complexity_ratio":394.3333333333333,"tree":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":2227,"base":3},"right_expr":{"type":"numeric_atoms","value":1903,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1123,"base":3},"right_expr":{"type":"numeric_atoms","value":1175,"base":3}}},"used_operators":["12rbrZMWeM","rxpJgHHUmx","dWAJyo7jo9"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","AHs5Up7iyr","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2227","layer":2},{"info":"number node, value=1903","layer":2},{"info":"compute binary expreesion, left_input=2227, right_input=1903, 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=1123","layer":2},{"info":"number node, value=1175","layer":2},{"info":"compute binary expreesion, left_input=1123, right_input=1175, 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 = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰10001111≭⫏≰2121111⋳⪒⫏≰1112121⪢⫏≰1121112=NaN","reverse_text":"NaN=⫏≰10001111≭⫏≰2121111⋳⪒⫏≰1112121⪢⫏≰1121112","cot":[{"info":"⫏≰10001111≭⫏≰2121111=NaN","layer":1},{"info":"⫏≰1112121⪢⫏≰1121112=NaN","layer":1},{"info":"NaN⋳⪒NaN=NaN","layer":0}]}
{"id":104,"expression_no_base_symbol":"($4316$⨵⪆$2987$)*($4447$⩨$2813$)","expression":"(⫏≰12220212⨵⪆⫏≰11002122)*(⫏≰20002201⩨⫏≰10212012)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":4316,"base":3},"right_expr":{"type":"numeric_atoms","value":2987,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":4447,"base":3},"right_expr":{"type":"numeric_atoms","value":2813,"base":3}}},"used_operators":["9HNa5Wba9A","2DQ55sFlQl","2DlMacCsIx"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4316","layer":2},{"info":"number node, value=2987","layer":2},{"info":"compute binary expreesion, left_input=4316, right_input=2987, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=4447","layer":2},{"info":"number node, value=2813","layer":2},{"info":"compute binary expreesion, left_input=4447, right_input=2813, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=0, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12220212⨵⪆⫏≰11002122)*(⫏≰20002201⩨⫏≰10212012)=⫏≰0","reverse_text":"⫏≰0=(⫏≰12220212⨵⪆⫏≰11002122)*(⫏≰20002201⩨⫏≰10212012)","cot":[{"info":"⫏≰12220212⨵⪆⫏≰11002122=⫏≰12221","layer":1},{"info":"⫏≰20002201⩨⫏≰10212012=⫏≰0","layer":1},{"info":"⫏≰12221*⫏≰0=⫏≰0","layer":0}]}
{"id":105,"expression_no_base_symbol":"(⨑⩽⪐$1303$)*$6354$⨳⩥⨓$3221$","expression":"(⨑⩽⪐⫏≰1210021)*⫏≰22201100⨳⩥⨓⫏≰11102022","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1037,"operation_count":3,"complexity_ratio":345.6666666666667,"tree":{"type":"binary","operator":"*","left_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":1303,"base":3}},"right_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":6354,"base":3},"right_expr":{"type":"numeric_atoms","value":3221,"base":3}}},"used_operators":["9HNa5Wba9A","AF7qkfDlqP","nCS4ZIUYfx"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰20001221121011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1303","layer":2},{"info":"compute unary expreesion, input=1303, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-1030","layer":1},{"info":"number node, value=6354","layer":2},{"info":"number node, value=3221","layer":2},{"info":"compute binary expreesion, left_input=6354, right_input=3221, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-3133","layer":1},{"info":"compute binary expreesion, left_input=-1030, right_input=-3133, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=3226990","layer":0}],"base":3,"result_base":3,"text":"(⨑⩽⪐⫏≰1210021)*⫏≰22201100⨳⩥⨓⫏≰11102022=⫏≰20001221121011","reverse_text":"⫏≰20001221121011=(⨑⩽⪐⫏≰1210021)*⫏≰22201100⨳⩥⨓⫏≰11102022","cot":[{"info":"⨑⩽⪐⫏≰1210021=⫏≰-1102011","layer":1},{"info":"⫏≰22201100⨳⩥⨓⫏≰11102022=⫏≰-11022001","layer":1},{"info":"⫏≰-1102011*⫏≰-11022001=⫏≰20001221121011","layer":0}]}
{"id":106,"expression_no_base_symbol":"≉$4346$⨟⋌⩍$1585$","expression":"≉⫏≰12221222⨟⋌⩍⫏≰2011201","highest_n_order":4,"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":4346,"base":3},"right_expr":{"type":"numeric_atoms","value":1585,"base":3}}},"used_operators":["e1ybzncUwg","rGHVDoGpnC"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4346","layer":2},{"info":"number node, value=1585","layer":2},{"info":"compute binary expreesion, left_input=4346, right_input=1585, 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 unary expreesion, input=nan, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"≉⫏≰12221222⨟⋌⩍⫏≰2011201=NaN","reverse_text":"NaN=≉⫏≰12221222⨟⋌⩍⫏≰2011201","cot":[{"info":"⫏≰12221222⨟⋌⩍⫏≰2011201=NaN","layer":1},{"info":"≉NaN=NaN","layer":0}]}
{"id":107,"expression_no_base_symbol":"⨈⫕($1064$⇼⇔∾$1696$)","expression":"⨈⫕(⫏≰1110102⇼⇔∾⫏≰2022211)","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":1064,"base":3},"right_expr":{"type":"numeric_atoms","value":1696,"base":3}}},"used_operators":["megm06wKyl","tifHPKVTfV"],"dependent_operators":["8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1064","layer":2},{"info":"number node, value=1696","layer":2},{"info":"compute binary expreesion, left_input=1064, right_input=1696, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=632","layer":1},{"info":"compute unary expreesion, input=632, 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":3,"result_base":3,"text":"⨈⫕(⫏≰1110102⇼⇔∾⫏≰2022211)=⫏≰-210","reverse_text":"⫏≰-210=⨈⫕(⫏≰1110102⇼⇔∾⫏≰2022211)","cot":[{"info":"⫏≰1110102⇼⇔∾⫏≰2022211=⫏≰212102","layer":1},{"info":"⨈⫕⫏≰212102=⫏≰-210","layer":0}]}
{"id":108,"expression_no_base_symbol":"↽≂($5357$⋷$1240$)","expression":"↽≂(⫏≰21100102⋷⫏≰1200221)","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":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":5357,"base":3},"right_expr":{"type":"numeric_atoms","value":1240,"base":3}}},"used_operators":["u6S6b8DprG","23Mk6UjR3U"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21220010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5357","layer":2},{"info":"number node, value=1240","layer":2},{"info":"compute binary expreesion, left_input=5357, right_input=1240, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-2877","layer":1},{"info":"compute unary expreesion, input=-2877, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=5754","layer":0}],"base":3,"result_base":3,"text":"↽≂(⫏≰21100102⋷⫏≰1200221)=⫏≰21220010","reverse_text":"⫏≰21220010=↽≂(⫏≰21100102⋷⫏≰1200221)","cot":[{"info":"⫏≰21100102⋷⫏≰1200221=⫏≰-10221120","layer":1},{"info":"↽≂⫏≰-10221120=⫏≰21220010","layer":0}]}
{"id":109,"expression_no_base_symbol":"$3218$⨟⋌⩍$1171$⩚⊴⇥(⊙↵-$4265$)","expression":"⫏≰11102012⨟⋌⩍⫏≰1121101⩚⊴⇥(⊙↵-⫏≰12211222)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4315,"operation_count":3,"complexity_ratio":1438.3333333333333,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":3218,"base":3},"right_expr":{"type":"numeric_atoms","value":1171,"base":3}},"right_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":4265,"base":3}}},"used_operators":["NTOWxs364D","rGHVDoGpnC","oWn0xqSxBt"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","Tcnh7f0tEr","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3218","layer":2},{"info":"number node, value=1171","layer":2},{"info":"compute binary expreesion, left_input=3218, right_input=1171, 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=4265","layer":2},{"info":"compute unary expreesion, input=4265, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-1, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11102012⨟⋌⩍⫏≰1121101⩚⊴⇥(⊙↵-⫏≰12211222)=NaN","reverse_text":"NaN=⫏≰11102012⨟⋌⩍⫏≰1121101⩚⊴⇥(⊙↵-⫏≰12211222)","cot":[{"info":"⫏≰11102012⨟⋌⩍⫏≰1121101=NaN","layer":1},{"info":"⊙↵-⫏≰12211222=⫏≰-1","layer":1},{"info":"NaN⩚⊴⇥⫏≰-1=NaN","layer":0}]}
{"id":110,"expression_no_base_symbol":"⋗⩬⋾$2030$⨰$1895$","expression":"⋗⩬⋾⫏≰2210012⨰⫏≰2121012","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":2030,"base":3},"right_expr":{"type":"numeric_atoms","value":1895,"base":3}}},"used_operators":["DpFCA1CohY","eewbuw0ToL"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-121010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2030","layer":2},{"info":"number node, value=1895","layer":2},{"info":"compute binary expreesion, left_input=2030, right_input=1895, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=145","layer":1},{"info":"compute unary expreesion, input=145, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-435","layer":0}],"base":3,"result_base":3,"text":"⋗⩬⋾⫏≰2210012⨰⫏≰2121012=⫏≰-121010","reverse_text":"⫏≰-121010=⋗⩬⋾⫏≰2210012⨰⫏≰2121012","cot":[{"info":"⫏≰2210012⨰⫏≰2121012=⫏≰12101","layer":1},{"info":"⋗⩬⋾⫏≰12101=⫏≰-121010","layer":0}]}
{"id":111,"expression_no_base_symbol":"($2397$⊉≛↸$1226$)⋝⋈⪟$7230$⪮%⊝$4641$","expression":"(⫏≰10021210⊉≛↸⫏≰1200102)⋝⋈⪟⫏≰100220210⪮%⊝⫏≰20100220","highest_n_order":2,"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":2397,"base":3},"right_expr":{"type":"numeric_atoms","value":1226,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":7230,"base":3},"right_expr":{"type":"numeric_atoms","value":4641,"base":3}}},"used_operators":["2DDjHMKMc0","DZ8iAZOCBD","IWmyXbctLI"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰20120120","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2397","layer":2},{"info":"number node, value=1226","layer":2},{"info":"compute binary expreesion, left_input=2397, right_input=1226, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=4794","layer":1},{"info":"number node, value=7230","layer":2},{"info":"number node, value=4641","layer":2},{"info":"compute binary expreesion, left_input=7230, right_input=4641, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=14776","layer":1},{"info":"compute binary expreesion, left_input=4794, right_input=14776, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=4794","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10021210⊉≛↸⫏≰1200102)⋝⋈⪟⫏≰100220210⪮%⊝⫏≰20100220=⫏≰20120120","reverse_text":"⫏≰20120120=(⫏≰10021210⊉≛↸⫏≰1200102)⋝⋈⪟⫏≰100220210⪮%⊝⫏≰20100220","cot":[{"info":"⫏≰10021210⊉≛↸⫏≰1200102=⫏≰20120120","layer":1},{"info":"⫏≰100220210⪮%⊝⫏≰20100220=⫏≰202021021","layer":1},{"info":"⫏≰20120120⋝⋈⪟⫏≰202021021=⫏≰20120120","layer":0}]}
{"id":112,"expression_no_base_symbol":"($6061$∸)⇼⇔∾$3975$⨓$3749$","expression":"(⫏≰22022111∸)⇼⇔∾⫏≰12110020⨓⫏≰12010212","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3934,"operation_count":3,"complexity_ratio":1311.3333333333333,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":6061,"base":3}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":3975,"base":3},"right_expr":{"type":"numeric_atoms","value":3749,"base":3}}},"used_operators":["tifHPKVTfV","o20kRiQErp","3ViojmjbAp"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","tmPS8pqC7x","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⫏≰-12101112","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6061","layer":2},{"info":"compute unary expreesion, input=6061, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"number node, value=3975","layer":2},{"info":"number node, value=3749","layer":2},{"info":"compute binary expreesion, left_input=3975, right_input=3749, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-3752","layer":1},{"info":"compute binary expreesion, left_input=177, right_input=-3752, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-3929","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22022111∸)⇼⇔∾⫏≰12110020⨓⫏≰12010212=⫏≰-12101112","reverse_text":"⫏≰-12101112=(⫏≰22022111∸)⇼⇔∾⫏≰12110020⨓⫏≰12010212","cot":[{"info":"⫏≰22022111∸=⫏≰20120","layer":1},{"info":"⫏≰12110020⨓⫏≰12010212=⫏≰-12010222","layer":1},{"info":"⫏≰20120⇼⇔∾⫏≰-12010222=⫏≰-12101112","layer":0}]}
{"id":113,"expression_no_base_symbol":"(∂$6044$)⪐","expression":"(∂⫏≰22021212)⪐","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3,"operation_count":2,"complexity_ratio":1.5,"tree":{"type":"unary","operator":"⪐","unary_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":6044,"base":3}}},"used_operators":["eH2TOUuTDT","Uaa54Peajs"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6044","layer":2},{"info":"compute unary expreesion, input=6044, 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 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":3,"result_base":3,"text":"(∂⫏≰22021212)⪐=NaN","reverse_text":"NaN=(∂⫏≰22021212)⪐","cot":[{"info":"∂⫏≰22021212=NaN","layer":1},{"info":"NaN⪐=NaN","layer":0}]}
{"id":114,"expression_no_base_symbol":"($5574$≎⊠⪸$2995$)⊴(⫓⪴$2562$)","expression":"(⫏≰21122110≎⊠⪸⫏≰11002221)⊴(⫓⪴⫏≰10111220)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2839,"operation_count":3,"complexity_ratio":946.3333333333334,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":5574,"base":3},"right_expr":{"type":"numeric_atoms","value":2995,"base":3}},"right_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":2562,"base":3}}},"used_operators":["Nsiff2A1zJ","bJkvcejdHO","eLxqMNBOBk"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5574","layer":2},{"info":"number node, value=2995","layer":2},{"info":"compute binary expreesion, left_input=5574, right_input=2995, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=1443193","layer":1},{"info":"number node, value=2562","layer":2},{"info":"compute unary expreesion, input=2562, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=6563844","layer":1},{"info":"compute binary expreesion, left_input=1443193, right_input=6563844, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰21122110≎⊠⪸⫏≰11002221)⊴(⫓⪴⫏≰10111220)=NaN","reverse_text":"NaN=(⫏≰21122110≎⊠⪸⫏≰11002221)⊴(⫓⪴⫏≰10111220)","cot":[{"info":"⫏≰21122110≎⊠⪸⫏≰11002221=⫏≰2201022200121","layer":1},{"info":"⫓⪴⫏≰10111220=⫏≰110100110220100","layer":1},{"info":"⫏≰2201022200121⊴⫏≰110100110220100=NaN","layer":0}]}
{"id":115,"expression_no_base_symbol":"$3434$⫸⊐$3097$⊉≛↸$1477$⨽$6043$","expression":"⫏≰11201012⫸⊐⫏≰11020201⊉≛↸⫏≰2000201⨽⫏≰22021211","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1512,"operation_count":3,"complexity_ratio":504.0,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":3434,"base":3},"right_expr":{"type":"numeric_atoms","value":3097,"base":3}},"right_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1477,"base":3},"right_expr":{"type":"numeric_atoms","value":6043,"base":3}}},"used_operators":["DZ8iAZOCBD","mqXw5SEYmG","8HhzD0ZcuI"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"⫏≰1020122101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3434","layer":2},{"info":"number node, value=3097","layer":2},{"info":"compute binary expreesion, left_input=3434, right_input=3097, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=12263","layer":1},{"info":"number node, value=1477","layer":2},{"info":"number node, value=6043","layer":2},{"info":"compute binary expreesion, left_input=1477, right_input=6043, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-6561402","layer":1},{"info":"compute binary expreesion, left_input=12263, right_input=-6561402, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=24526","layer":0}],"base":3,"result_base":3,"text":"⫏≰11201012⫸⊐⫏≰11020201⊉≛↸⫏≰2000201⨽⫏≰22021211=⫏≰1020122101","reverse_text":"⫏≰1020122101=⫏≰11201012⫸⊐⫏≰11020201⊉≛↸⫏≰2000201⨽⫏≰22021211","cot":[{"info":"⫏≰11201012⫸⊐⫏≰11020201=⫏≰121211012","layer":1},{"info":"⫏≰2000201⨽⫏≰22021211=⫏≰-110100100112220","layer":1},{"info":"⫏≰121211012⊉≛↸⫏≰-110100100112220=⫏≰1020122101","layer":0}]}
{"id":116,"expression_no_base_symbol":"(↥$1003$)⨽($3427$≋⫹)","expression":"(↥⫏≰1101011)⨽(⫏≰11200221≋⫹)","highest_n_order":2,"priority_hierarchical_complexity":2,"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":1003,"base":3}},"right_expr":{"type":"unary","operator":"≋⫹","unary_expr":{"type":"numeric_atoms","value":3427,"base":3}}},"used_operators":["8HhzD0ZcuI","A8NUZmVepG","N41Kp7NANJ"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","k8jYdgA6NY","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰221020210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1003","layer":2},{"info":"compute unary expreesion, input=1003, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=34","layer":1},{"info":"number node, value=3427","layer":2},{"info":"compute unary expreesion, input=3427, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-6854","layer":1},{"info":"compute binary expreesion, left_input=34, right_input=-6854, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=18408","layer":0}],"base":3,"result_base":3,"text":"(↥⫏≰1101011)⨽(⫏≰11200221≋⫹)=⫏≰221020210","reverse_text":"⫏≰221020210=(↥⫏≰1101011)⨽(⫏≰11200221≋⫹)","cot":[{"info":"↥⫏≰1101011=⫏≰1021","layer":1},{"info":"⫏≰11200221≋⫹=⫏≰-100101212","layer":1},{"info":"⫏≰1021⨽⫏≰-100101212=⫏≰221020210","layer":0}]}
{"id":117,"expression_no_base_symbol":"(↔$1143$)⪘⫢(⪲⇎$2640$)","expression":"(↔⫏≰1120100)⪘⫢(⪲⇎⫏≰10121210)","highest_n_order":2,"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":1143,"base":3}},"right_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":2640,"base":3}}},"used_operators":["oacrs7FA3X","ruOEQAzv1W","XPYlsWDdGa"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1143","layer":2},{"info":"compute unary expreesion, input=1143, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-870","layer":1},{"info":"number node, value=2640","layer":2},{"info":"compute unary expreesion, input=2640, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=5280","layer":1},{"info":"compute binary expreesion, left_input=-870, right_input=5280, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(↔⫏≰1120100)⪘⫢(⪲⇎⫏≰10121210)=⫏≰0","reverse_text":"⫏≰0=(↔⫏≰1120100)⪘⫢(⪲⇎⫏≰10121210)","cot":[{"info":"↔⫏≰1120100=⫏≰-1012020","layer":1},{"info":"⪲⇎⫏≰10121210=⫏≰21020120","layer":1},{"info":"⫏≰-1012020⪘⫢⫏≰21020120=⫏≰0","layer":0}]}
{"id":118,"expression_no_base_symbol":"($1874$⋷$6567$)⨸⪁(⋗⩬⋾$2011$)","expression":"(⫏≰2120102⋷⫏≰100000020)⨸⪁(⋗⩬⋾⫏≰2202111)","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":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":1874,"base":3},"right_expr":{"type":"numeric_atoms","value":6567,"base":3}},"right_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":2011,"base":3}}},"used_operators":["g55IO6H4Gj","23Mk6UjR3U","DpFCA1CohY"],"dependent_operators":["W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰112100012","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1874","layer":2},{"info":"number node, value=6567","layer":2},{"info":"compute binary expreesion, left_input=1874, right_input=6567, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=11260","layer":1},{"info":"number node, value=2011","layer":2},{"info":"compute unary expreesion, input=2011, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-6033","layer":1},{"info":"compute binary expreesion, left_input=11260, right_input=-6033, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=10454","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2120102⋷⫏≰100000020)⨸⪁(⋗⩬⋾⫏≰2202111)=⫏≰112100012","reverse_text":"⫏≰112100012=(⫏≰2120102⋷⫏≰100000020)⨸⪁(⋗⩬⋾⫏≰2202111)","cot":[{"info":"⫏≰2120102⋷⫏≰100000020=⫏≰120110001","layer":1},{"info":"⋗⩬⋾⫏≰2202111=⫏≰-22021110","layer":1},{"info":"⫏≰120110001⨸⪁⫏≰-22021110=⫏≰112100012","layer":0}]}
{"id":119,"expression_no_base_symbol":"($2243$∧)⫥∨⫟($2081$+$7792$)","expression":"(⫏≰10002002∧)⫥∨⫟(⫏≰2212002+⫏≰101200121)","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":"unary","operator":"∧","unary_expr":{"type":"numeric_atoms","value":2243,"base":3}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":2081,"base":3},"right_expr":{"type":"numeric_atoms","value":7792,"base":3}}},"used_operators":["KYD54nUTWz","z63VuFQld9","W4YGzv6Whe"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2243","layer":2},{"info":"compute unary expreesion, input=2243, 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=2081","layer":2},{"info":"number node, value=7792","layer":2},{"info":"compute binary expreesion, left_input=2081, right_input=7792, op_id = W4YGzv6Whe binary_op_definition= 'None', output=9873","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=9873, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10002002∧)⫥∨⫟(⫏≰2212002+⫏≰101200121)=NaN","reverse_text":"NaN=(⫏≰10002002∧)⫥∨⫟(⫏≰2212002+⫏≰101200121)","cot":[{"info":"⫏≰10002002∧=NaN","layer":1},{"info":"⫏≰2212002+⫏≰101200121=⫏≰111112200","layer":1},{"info":"NaN⫥∨⫟⫏≰111112200=NaN","layer":0}]}
{"id":120,"expression_no_base_symbol":"$1802$⪘⫢$1582$%$1144$∼$2845$","expression":"⫏≰2110202⪘⫢⫏≰2011121%⫏≰1120101∼⫏≰10220101","highest_n_order":4,"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":1802,"base":3},"right_expr":{"type":"numeric_atoms","value":1582,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":1144,"base":3},"right_expr":{"type":"numeric_atoms","value":2845,"base":3}}},"used_operators":["k8jYdgA6NY","oacrs7FA3X","DyGG3AbaNP"],"dependent_operators":["rysDP5nf3Z","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1802","layer":2},{"info":"number node, value=1582","layer":2},{"info":"compute binary expreesion, left_input=1802, right_input=1582, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=3480","layer":1},{"info":"number node, value=1144","layer":2},{"info":"number node, value=2845","layer":2},{"info":"compute binary expreesion, left_input=1144, right_input=2845, 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=3480, right_input=nan, op_id = k8jYdgA6NY binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2110202⪘⫢⫏≰2011121%⫏≰1120101∼⫏≰10220101=NaN","reverse_text":"NaN=⫏≰2110202⪘⫢⫏≰2011121%⫏≰1120101∼⫏≰10220101","cot":[{"info":"⫏≰2110202⪘⫢⫏≰2011121=⫏≰11202220","layer":1},{"info":"⫏≰1120101∼⫏≰10220101=NaN","layer":1},{"info":"⫏≰11202220%NaN=NaN","layer":0}]}
{"id":121,"expression_no_base_symbol":"$1970$⪢$1635$⊭∹↮","expression":"⫏≰2200222⪢⫏≰2020120⊭∹↮","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1909,"operation_count":2,"complexity_ratio":954.5,"tree":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1970,"base":3},"right_expr":{"type":"numeric_atoms","value":1635,"base":3}}},"used_operators":["xNBdhnnwKq","dWAJyo7jo9"],"dependent_operators":["2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1970","layer":2},{"info":"number node, value=1635","layer":2},{"info":"compute binary expreesion, left_input=1970, right_input=1635, 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 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":3,"result_base":3,"text":"⫏≰2200222⪢⫏≰2020120⊭∹↮=NaN","reverse_text":"NaN=⫏≰2200222⪢⫏≰2020120⊭∹↮","cot":[{"info":"⫏≰2200222⪢⫏≰2020120=NaN","layer":1},{"info":"NaN⊭∹↮=NaN","layer":0}]}
{"id":122,"expression_no_base_symbol":"$6717$⪮%⊝$3036$≧⫂∧(⨰⫟⨤$2527$)","expression":"⫏≰100012210⪮%⊝⫏≰11011110≧⫂∧(⨰⫟⨤⫏≰10110121)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9278,"operation_count":3,"complexity_ratio":3092.6666666666665,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":6717,"base":3},"right_expr":{"type":"numeric_atoms","value":3036,"base":3}},"right_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":2527,"base":3}}},"used_operators":["Ph9nP6C5qx","IWmyXbctLI","Tw270M8GLb"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6717","layer":2},{"info":"number node, value=3036","layer":2},{"info":"compute binary expreesion, left_input=6717, right_input=3036, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=13750","layer":1},{"info":"number node, value=2527","layer":2},{"info":"compute unary expreesion, input=2527, 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=13750, right_input=nan, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰100012210⪮%⊝⫏≰11011110≧⫂∧(⨰⫟⨤⫏≰10110121)=NaN","reverse_text":"NaN=⫏≰100012210⪮%⊝⫏≰11011110≧⫂∧(⨰⫟⨤⫏≰10110121)","cot":[{"info":"⫏≰100012210⪮%⊝⫏≰11011110=⫏≰200212021","layer":1},{"info":"⨰⫟⨤⫏≰10110121=NaN","layer":1},{"info":"⫏≰200212021≧⫂∧NaN=NaN","layer":0}]}
{"id":123,"expression_no_base_symbol":"(⊄⩳↩$7973$)∼($1617$⪛$1641$)","expression":"(⊄⩳↩⫏≰101221022)∼(⫏≰2012220⪛⫏≰2020210)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":478,"operation_count":3,"complexity_ratio":159.33333333333334,"tree":{"type":"binary","operator":"∼","left_expr":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":7973,"base":3}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":1617,"base":3},"right_expr":{"type":"numeric_atoms","value":1641,"base":3}}},"used_operators":["DyGG3AbaNP","8w2t5hMYqp","uFcxV4UQCh"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7973","layer":2},{"info":"compute unary expreesion, input=7973, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-23919","layer":1},{"info":"number node, value=1617","layer":2},{"info":"number node, value=1641","layer":2},{"info":"compute binary expreesion, left_input=1617, right_input=1641, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1617","layer":1},{"info":"compute binary expreesion, left_input=-23919, right_input=1617, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⊄⩳↩⫏≰101221022)∼(⫏≰2012220⪛⫏≰2020210)=NaN","reverse_text":"NaN=(⊄⩳↩⫏≰101221022)∼(⫏≰2012220⪛⫏≰2020210)","cot":[{"info":"⊄⩳↩⫏≰101221022=⫏≰-1012210220","layer":1},{"info":"⫏≰2012220⪛⫏≰2020210=⫏≰2012220","layer":1},{"info":"⫏≰-1012210220∼⫏≰2012220=NaN","layer":0}]}
{"id":124,"expression_no_base_symbol":"$3747$+⇶⊼$3748$*($2565$⊭↱$1177$)","expression":"⫏≰12010210+⇶⊼⫏≰12010211*(⫏≰10112000⊭↱⫏≰1121121)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":3747,"base":3},"right_expr":{"type":"numeric_atoms","value":3748,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":2565,"base":3},"right_expr":{"type":"numeric_atoms","value":1177,"base":3}}},"used_operators":["9HNa5Wba9A","TpPTUOHfaN","COABgblf1C"],"dependent_operators":["W4YGzv6Whe","AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3747","layer":2},{"info":"number node, value=3748","layer":2},{"info":"compute binary expreesion, left_input=3747, right_input=3748, 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":1},{"info":"number node, value=2565","layer":2},{"info":"number node, value=1177","layer":2},{"info":"compute binary expreesion, left_input=2565, right_input=1177, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-2771","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-2771, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰12010210+⇶⊼⫏≰12010211*(⫏≰10112000⊭↱⫏≰1121121)=NaN","reverse_text":"NaN=⫏≰12010210+⇶⊼⫏≰12010211*(⫏≰10112000⊭↱⫏≰1121121)","cot":[{"info":"⫏≰12010210+⇶⊼⫏≰12010211=NaN","layer":1},{"info":"⫏≰10112000⊭↱⫏≰1121121=⫏≰-10210122","layer":1},{"info":"NaN*⫏≰-10210122=NaN","layer":0}]}
{"id":125,"expression_no_base_symbol":"($3864$⩚⊴⇥$2147$)⨪↰⇹($1344$*$6723$)","expression":"(⫏≰12022010⩚⊴⇥⫏≰2221112)⨪↰⇹(⫏≰1211210*⫏≰100020000)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7479,"operation_count":3,"complexity_ratio":2493.0,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":3864,"base":3},"right_expr":{"type":"numeric_atoms","value":2147,"base":3}},"right_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1344,"base":3},"right_expr":{"type":"numeric_atoms","value":6723,"base":3}}},"used_operators":["tmPS8pqC7x","NTOWxs364D","9HNa5Wba9A"],"dependent_operators":["rJVOvQCfKK","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe"],"result":"⫏≰-22102010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3864","layer":2},{"info":"number node, value=2147","layer":2},{"info":"compute binary expreesion, left_input=3864, right_input=2147, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-6132","layer":1},{"info":"number node, value=1344","layer":2},{"info":"number node, value=6723","layer":2},{"info":"compute binary expreesion, left_input=1344, right_input=6723, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=9035712","layer":1},{"info":"compute binary expreesion, left_input=-6132, right_input=9035712, 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=-6132","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12022010⩚⊴⇥⫏≰2221112)⨪↰⇹(⫏≰1211210*⫏≰100020000)=⫏≰-22102010","reverse_text":"⫏≰-22102010=(⫏≰12022010⩚⊴⇥⫏≰2221112)⨪↰⇹(⫏≰1211210*⫏≰100020000)","cot":[{"info":"⫏≰12022010⩚⊴⇥⫏≰2221112=⫏≰-22102010","layer":1},{"info":"⫏≰1211210*⫏≰100020000=⫏≰122000001200000","layer":1},{"info":"⫏≰-22102010⨪↰⇹⫏≰122000001200000=⫏≰-22102010","layer":0}]}
{"id":126,"expression_no_base_symbol":"↩$7679$≧⫂∧$1940$","expression":"↩⫏≰101112102≧⫂∧⫏≰2122212","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":7679,"base":3},"right_expr":{"type":"numeric_atoms","value":1940,"base":3}}},"used_operators":["jLgFTUHLKL","Ph9nP6C5qx"],"dependent_operators":["sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-110021201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7679","layer":2},{"info":"number node, value=1940","layer":2},{"info":"compute binary expreesion, left_input=7679, right_input=1940, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=1467","layer":1},{"info":"compute unary expreesion, input=1467, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-8956","layer":0}],"base":3,"result_base":3,"text":"↩⫏≰101112102≧⫂∧⫏≰2122212=⫏≰-110021201","reverse_text":"⫏≰-110021201=↩⫏≰101112102≧⫂∧⫏≰2122212","cot":[{"info":"⫏≰101112102≧⫂∧⫏≰2122212=⫏≰2000100","layer":1},{"info":"↩⫏≰2000100=⫏≰-110021201","layer":0}]}
{"id":127,"expression_no_base_symbol":"($1372$⋫)⊉≛↸(⫛⫱⨽$2206$)","expression":"(⫏≰1212211⋫)⊉≛↸(⫛⫱⨽⫏≰10000201)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2796,"operation_count":3,"complexity_ratio":932.0,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":1372,"base":3}},"right_expr":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"numeric_atoms","value":2206,"base":3}}},"used_operators":["DZ8iAZOCBD","JL8yIekQnl","DlLNRPXxWL"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","tmPS8pqC7x","rGHVDoGpnC"],"result":"⫏≰10202122","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1372","layer":2},{"info":"compute unary expreesion, input=1372, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=1372","layer":1},{"info":"number node, value=2206","layer":2},{"info":"compute unary expreesion, input=2206, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=1372, right_input=0, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=2744","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1212211⋫)⊉≛↸(⫛⫱⨽⫏≰10000201)=⫏≰10202122","reverse_text":"⫏≰10202122=(⫏≰1212211⋫)⊉≛↸(⫛⫱⨽⫏≰10000201)","cot":[{"info":"⫏≰1212211⋫=⫏≰1212211","layer":1},{"info":"⫛⫱⨽⫏≰10000201=⫏≰0","layer":1},{"info":"⫏≰1212211⊉≛↸⫏≰0=⫏≰10202122","layer":0}]}
{"id":128,"expression_no_base_symbol":"$1221$⇷$4182$⫩⊇","expression":"⫏≰1200020⇷⫏≰12201220⫩⊇","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":17102,"operation_count":2,"complexity_ratio":8551.0,"tree":{"type":"unary","operator":"⫩⊇","unary_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":1221,"base":3},"right_expr":{"type":"numeric_atoms","value":4182,"base":3}}},"used_operators":["BjRHVeLaeN","mp7IySMOzn"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"⫏≰-102102020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1221","layer":2},{"info":"number node, value=4182","layer":2},{"info":"compute binary expreesion, left_input=1221, right_input=4182, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=8364","layer":1},{"info":"compute unary expreesion, input=8364, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=-8322","layer":0}],"base":3,"result_base":3,"text":"⫏≰1200020⇷⫏≰12201220⫩⊇=⫏≰-102102020","reverse_text":"⫏≰-102102020=⫏≰1200020⇷⫏≰12201220⫩⊇","cot":[{"info":"⫏≰1200020⇷⫏≰12201220=⫏≰102110210","layer":1},{"info":"⫏≰102110210⫩⊇=⫏≰-102102020","layer":0}]}
{"id":129,"expression_no_base_symbol":"↥(⪲⇎$1768$)","expression":"↥(⪲⇎⫏≰2102111)","highest_n_order":2,"priority_hierarchical_complexity":1,"normalized_expansion_degree":71,"operation_count":2,"complexity_ratio":35.5,"tree":{"type":"unary","operator":"↥","unary_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":1768,"base":3}}},"used_operators":["A8NUZmVepG","XPYlsWDdGa"],"dependent_operators":["k8jYdgA6NY","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰122","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1768","layer":2},{"info":"compute unary expreesion, input=1768, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=3536","layer":1},{"info":"compute unary expreesion, input=3536, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=17","layer":0}],"base":3,"result_base":3,"text":"↥(⪲⇎⫏≰2102111)=⫏≰122","reverse_text":"⫏≰122=↥(⪲⇎⫏≰2102111)","cot":[{"info":"⪲⇎⫏≰2102111=⫏≰11211222","layer":1},{"info":"↥⫏≰11211222=⫏≰122","layer":0}]}
{"id":130,"expression_no_base_symbol":"$1172$⨓$7718$⨵⪆$2997$⪄$3997$","expression":"⫏≰1121102⨓⫏≰101120212⨵⪆⫏≰11010000⪄⫏≰12111001","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7820,"operation_count":3,"complexity_ratio":2606.6666666666665,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":1172,"base":3},"right_expr":{"type":"numeric_atoms","value":7718,"base":3}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2997,"base":3},"right_expr":{"type":"numeric_atoms","value":3997,"base":3}}},"used_operators":["2DQ55sFlQl","3ViojmjbAp","SUmda5xLS4"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1172","layer":2},{"info":"number node, value=7718","layer":2},{"info":"compute binary expreesion, left_input=1172, right_input=7718, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-7721","layer":1},{"info":"number node, value=2997","layer":2},{"info":"number node, value=3997","layer":2},{"info":"compute binary expreesion, left_input=2997, right_input=3997, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-455633","layer":1},{"info":"compute binary expreesion, left_input=-7721, right_input=-455633, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰1121102⨓⫏≰101120212⨵⪆⫏≰11010000⪄⫏≰12111001=⫏≰12221","reverse_text":"⫏≰12221=⫏≰1121102⨓⫏≰101120212⨵⪆⫏≰11010000⪄⫏≰12111001","cot":[{"info":"⫏≰1121102⨓⫏≰101120212=⫏≰-101120222","layer":1},{"info":"⫏≰11010000⪄⫏≰12111001=⫏≰-212011000022","layer":1},{"info":"⫏≰-101120222⨵⪆⫏≰-212011000022=⫏≰12221","layer":0}]}
{"id":131,"expression_no_base_symbol":"$1805$⨎$1435$⩨$5284$↬$1582$","expression":"⫏≰2110212⨎⫏≰1222011⩨⫏≰21020201↬⫏≰2011121","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"⩨","left_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":1805,"base":3},"right_expr":{"type":"numeric_atoms","value":1435,"base":3}},"right_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":5284,"base":3},"right_expr":{"type":"numeric_atoms","value":1582,"base":3}}},"used_operators":["2DlMacCsIx","rJVOvQCfKK","B5M0gjZbta"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1805","layer":2},{"info":"number node, value=1435","layer":2},{"info":"compute binary expreesion, left_input=1805, right_input=1435, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=1435","layer":1},{"info":"number node, value=5284","layer":2},{"info":"number node, value=1582","layer":2},{"info":"compute binary expreesion, left_input=5284, right_input=1582, 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=1435, right_input=nan, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2110212⨎⫏≰1222011⩨⫏≰21020201↬⫏≰2011121=NaN","reverse_text":"NaN=⫏≰2110212⨎⫏≰1222011⩨⫏≰21020201↬⫏≰2011121","cot":[{"info":"⫏≰2110212⨎⫏≰1222011=⫏≰1222011","layer":1},{"info":"⫏≰21020201↬⫏≰2011121=NaN","layer":1},{"info":"⫏≰1222011⩨NaN=NaN","layer":0}]}
{"id":132,"expression_no_base_symbol":"(⨈⫕$1238$)⨓(↔$2967$)","expression":"(⨈⫕⫏≰1200212)⨓(↔⫏≰11001220)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3093,"operation_count":3,"complexity_ratio":1031.0,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":1238,"base":3}},"right_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":2967,"base":3}}},"used_operators":["3ViojmjbAp","megm06wKyl","ruOEQAzv1W"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp"],"result":"⫏≰10200200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1238","layer":2},{"info":"compute unary expreesion, input=1238, 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":"number node, value=2967","layer":2},{"info":"compute unary expreesion, input=2967, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-2694","layer":1},{"info":"compute binary expreesion, left_input=-21, right_input=-2694, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=2691","layer":0}],"base":3,"result_base":3,"text":"(⨈⫕⫏≰1200212)⨓(↔⫏≰11001220)=⫏≰10200200","reverse_text":"⫏≰10200200=(⨈⫕⫏≰1200212)⨓(↔⫏≰11001220)","cot":[{"info":"⨈⫕⫏≰1200212=⫏≰-210","layer":1},{"info":"↔⫏≰11001220=⫏≰-10200210","layer":1},{"info":"⫏≰-210⨓⫏≰-10200210=⫏≰10200200","layer":0}]}
{"id":133,"expression_no_base_symbol":"($1372$≭$3855$)⨟⋌⩍($1043$⊭∹↮)","expression":"(⫏≰1212211≭⫏≰12021210)⨟⋌⩍(⫏≰1102122⊭∹↮)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":1372,"base":3},"right_expr":{"type":"numeric_atoms","value":3855,"base":3}},"right_expr":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"numeric_atoms","value":1043,"base":3}}},"used_operators":["rGHVDoGpnC","rxpJgHHUmx","xNBdhnnwKq"],"dependent_operators":["Tcnh7f0tEr","AHs5Up7iyr","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1372","layer":2},{"info":"number node, value=3855","layer":2},{"info":"compute binary expreesion, left_input=1372, right_input=3855, 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=1043","layer":2},{"info":"compute unary expreesion, input=1043, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=2086","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2086, 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":0}],"base":3,"result_base":3,"text":"(⫏≰1212211≭⫏≰12021210)⨟⋌⩍(⫏≰1102122⊭∹↮)=NaN","reverse_text":"NaN=(⫏≰1212211≭⫏≰12021210)⨟⋌⩍(⫏≰1102122⊭∹↮)","cot":[{"info":"⫏≰1212211≭⫏≰12021210=NaN","layer":1},{"info":"⫏≰1102122⊭∹↮=⫏≰2212021","layer":1},{"info":"NaN⨟⋌⩍⫏≰2212021=NaN","layer":0}]}
{"id":134,"expression_no_base_symbol":"($1950$⩠)∀⇚≩($3424$⋫)","expression":"(⫏≰2200020⩠)∀⇚≩(⫏≰11200211⋫)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3443,"operation_count":3,"complexity_ratio":1147.6666666666667,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"unary","operator":"⩠","unary_expr":{"type":"numeric_atoms","value":1950,"base":3}},"right_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":3424,"base":3}}},"used_operators":["LRNGc0VcxI","sJAwomhLZr","JL8yIekQnl"],"dependent_operators":["X99M06cbEe","sdazOOVcIp","i8ToyICDmI","k8jYdgA6NY","eH2TOUuTDT","W4YGzv6Whe","Z2TMIBDE3Q","COABgblf1C","tmPS8pqC7x"],"result":"⫏≰11200211","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1950","layer":2},{"info":"compute unary expreesion, input=1950, op_id = sJAwomhLZr, unary_op_definition = 'a⩠ = { (((a+a)⊭↱(a⪨≂a))∲⫓((a⩤)%(a⪐))) }', output=0","layer":1},{"info":"number node, value=3424","layer":2},{"info":"compute unary expreesion, input=3424, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=3424","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=3424, 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=3424","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2200020⩠)∀⇚≩(⫏≰11200211⋫)=⫏≰11200211","reverse_text":"⫏≰11200211=(⫏≰2200020⩠)∀⇚≩(⫏≰11200211⋫)","cot":[{"info":"⫏≰2200020⩠=⫏≰0","layer":1},{"info":"⫏≰11200211⋫=⫏≰11200211","layer":1},{"info":"⫏≰0∀⇚≩⫏≰11200211=⫏≰11200211","layer":0}]}
{"id":135,"expression_no_base_symbol":"⨈⫕(≉$1023$)","expression":"⨈⫕(≉⫏≰1101220)","highest_n_order":5,"priority_hierarchical_complexity":1,"normalized_expansion_degree":388,"operation_count":2,"complexity_ratio":194.0,"tree":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"unary","operator":"≉","unary_expr":{"type":"numeric_atoms","value":1023,"base":3}}},"used_operators":["megm06wKyl","e1ybzncUwg"],"dependent_operators":["8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1023","layer":2},{"info":"compute unary expreesion, input=1023, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=1554","layer":1},{"info":"compute unary expreesion, input=1554, 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":3,"result_base":3,"text":"⨈⫕(≉⫏≰1101220)=⫏≰-210","reverse_text":"⫏≰-210=⨈⫕(≉⫏≰1101220)","cot":[{"info":"≉⫏≰1101220=⫏≰2010120","layer":1},{"info":"⨈⫕⫏≰2010120=⫏≰-210","layer":0}]}
{"id":136,"expression_no_base_symbol":"($3651$⨰$6899$)↬($2723$⪠⩆⊳)","expression":"(⫏≰12000020⨰⫏≰100110112)↬(⫏≰10201212⪠⩆⊳)","highest_n_order":5,"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":3651,"base":3},"right_expr":{"type":"numeric_atoms","value":6899,"base":3}},"right_expr":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"numeric_atoms","value":2723,"base":3}}},"used_operators":["B5M0gjZbta","eewbuw0ToL","JLbD19bQDL"],"dependent_operators":["rGHVDoGpnC","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3651","layer":2},{"info":"number node, value=6899","layer":2},{"info":"compute binary expreesion, left_input=3651, right_input=6899, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-3238","layer":1},{"info":"number node, value=2723","layer":2},{"info":"compute unary expreesion, input=2723, 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":"compute binary expreesion, left_input=-3238, right_input=0, 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":3,"result_base":3,"text":"(⫏≰12000020⨰⫏≰100110112)↬(⫏≰10201212⪠⩆⊳)=NaN","reverse_text":"NaN=(⫏≰12000020⨰⫏≰100110112)↬(⫏≰10201212⪠⩆⊳)","cot":[{"info":"⫏≰12000020⨰⫏≰100110112=⫏≰-11102221","layer":1},{"info":"⫏≰10201212⪠⩆⊳=⫏≰0","layer":1},{"info":"⫏≰-11102221↬⫏≰0=NaN","layer":0}]}
{"id":137,"expression_no_base_symbol":"⫛⫱⨽($4206$⩚⊴⇥$2573$)","expression":"⫛⫱⨽(⫏≰12202210⩚⊴⇥⫏≰10112022)","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":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":4206,"base":3},"right_expr":{"type":"numeric_atoms","value":2573,"base":3}}},"used_operators":["DlLNRPXxWL","NTOWxs364D"],"dependent_operators":["rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4206","layer":2},{"info":"number node, value=2573","layer":2},{"info":"compute binary expreesion, left_input=4206, right_input=2573, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-6900","layer":1},{"info":"compute unary expreesion, input=-6900, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫛⫱⨽(⫏≰12202210⩚⊴⇥⫏≰10112022)=⫏≰0","reverse_text":"⫏≰0=⫛⫱⨽(⫏≰12202210⩚⊴⇥⫏≰10112022)","cot":[{"info":"⫏≰12202210⩚⊴⇥⫏≰10112022=⫏≰-100110120","layer":1},{"info":"⫛⫱⨽⫏≰-100110120=⫏≰0","layer":0}]}
{"id":138,"expression_no_base_symbol":"(⋗⩬⋾$3979$)⩚⊴⇥$7003$∀⇚≩$3534$","expression":"(⋗⩬⋾⫏≰12110101)⩚⊴⇥⫏≰100121101∀⇚≩⫏≰11211220","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":49027,"operation_count":3,"complexity_ratio":16342.333333333334,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":3979,"base":3}},"right_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":7003,"base":3},"right_expr":{"type":"numeric_atoms","value":3534,"base":3}}},"used_operators":["NTOWxs364D","DpFCA1CohY","LRNGc0VcxI"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3979","layer":2},{"info":"compute unary expreesion, input=3979, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-11937","layer":1},{"info":"number node, value=7003","layer":2},{"info":"number node, value=3534","layer":2},{"info":"compute binary expreesion, left_input=7003, right_input=3534, 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=-11937, right_input=nan, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⋗⩬⋾⫏≰12110101)⩚⊴⇥⫏≰100121101∀⇚≩⫏≰11211220=NaN","reverse_text":"NaN=(⋗⩬⋾⫏≰12110101)⩚⊴⇥⫏≰100121101∀⇚≩⫏≰11211220","cot":[{"info":"⋗⩬⋾⫏≰12110101=⫏≰-121101010","layer":1},{"info":"⫏≰100121101∀⇚≩⫏≰11211220=NaN","layer":1},{"info":"⫏≰-121101010⩚⊴⇥NaN=NaN","layer":0}]}
{"id":139,"expression_no_base_symbol":"$2197$⊴$1818$⨟⋌⩍$5191$⪢$2978$","expression":"⫏≰10000101⊴⫏≰2111100⨟⋌⩍⫏≰21010021⪢⫏≰11002022","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":14767,"operation_count":3,"complexity_ratio":4922.333333333333,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":2197,"base":3},"right_expr":{"type":"numeric_atoms","value":1818,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":5191,"base":3},"right_expr":{"type":"numeric_atoms","value":2978,"base":3}}},"used_operators":["rGHVDoGpnC","Nsiff2A1zJ","dWAJyo7jo9"],"dependent_operators":["Tcnh7f0tEr","dWAJyo7jo9","14qkJME0vr","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2197","layer":2},{"info":"number node, value=1818","layer":2},{"info":"compute binary expreesion, left_input=2197, right_input=1818, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=5191","layer":2},{"info":"number node, value=2978","layer":2},{"info":"compute binary expreesion, left_input=5191, right_input=2978, 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 = 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":0}],"base":3,"result_base":3,"text":"⫏≰10000101⊴⫏≰2111100⨟⋌⩍⫏≰21010021⪢⫏≰11002022=NaN","reverse_text":"NaN=⫏≰10000101⊴⫏≰2111100⨟⋌⩍⫏≰21010021⪢⫏≰11002022","cot":[{"info":"⫏≰10000101⊴⫏≰2111100=NaN","layer":1},{"info":"⫏≰21010021⪢⫏≰11002022=NaN","layer":1},{"info":"NaN⨟⋌⩍NaN=NaN","layer":0}]}
{"id":140,"expression_no_base_symbol":"↽≂$3688$⨰$2089$","expression":"↽≂⫏≰12001121⨰⫏≰2212101","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":3688,"base":3},"right_expr":{"type":"numeric_atoms","value":2089,"base":3}}},"used_operators":["u6S6b8DprG","eewbuw0ToL"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-11102012","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3688","layer":2},{"info":"number node, value=2089","layer":2},{"info":"compute binary expreesion, left_input=3688, right_input=2089, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=1609","layer":1},{"info":"compute unary expreesion, input=1609, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-3218","layer":0}],"base":3,"result_base":3,"text":"↽≂⫏≰12001121⨰⫏≰2212101=⫏≰-11102012","reverse_text":"⫏≰-11102012=↽≂⫏≰12001121⨰⫏≰2212101","cot":[{"info":"⫏≰12001121⨰⫏≰2212101=⫏≰2012121","layer":1},{"info":"↽≂⫏≰2012121=⫏≰-11102012","layer":0}]}
{"id":141,"expression_no_base_symbol":"(↯⪼$2123$)∲⫓(≦∁$2995$)","expression":"(↯⪼⫏≰2220122)∲⫓(≦∁⫏≰11002221)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34,"operation_count":3,"complexity_ratio":11.333333333333334,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"numeric_atoms","value":2123,"base":3}},"right_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":2995,"base":3}}},"used_operators":["i8ToyICDmI","8jW3W4yZS5","9ICcGScMcE"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2123","layer":2},{"info":"compute unary expreesion, input=2123, 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=2995","layer":2},{"info":"compute unary expreesion, input=2995, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=2995","layer":1},{"info":"compute binary expreesion, left_input=-21, right_input=2995, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(↯⪼⫏≰2220122)∲⫓(≦∁⫏≰11002221)=⫏≰0","reverse_text":"⫏≰0=(↯⪼⫏≰2220122)∲⫓(≦∁⫏≰11002221)","cot":[{"info":"↯⪼⫏≰2220122=⫏≰-210","layer":1},{"info":"≦∁⫏≰11002221=⫏≰11002221","layer":1},{"info":"⫏≰-210∲⫓⫏≰11002221=⫏≰0","layer":0}]}
{"id":142,"expression_no_base_symbol":"$1848$⩚⊴⇥$3125$⩚⊴⇥$5224$∀⇚≩$2114$","expression":"⫏≰2112110⩚⊴⇥⫏≰11021202⩚⊴⇥⫏≰21011111∀⇚≩⫏≰2220022","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":36574,"operation_count":3,"complexity_ratio":12191.333333333334,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":1848,"base":3},"right_expr":{"type":"numeric_atoms","value":3125,"base":3}},"right_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":5224,"base":3},"right_expr":{"type":"numeric_atoms","value":2114,"base":3}}},"used_operators":["NTOWxs364D","LRNGc0VcxI"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1848","layer":2},{"info":"number node, value=3125","layer":2},{"info":"compute binary expreesion, left_input=1848, right_input=3125, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-5094","layer":1},{"info":"number node, value=5224","layer":2},{"info":"number node, value=2114","layer":2},{"info":"compute binary expreesion, left_input=5224, right_input=2114, 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=-5094, right_input=nan, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2112110⩚⊴⇥⫏≰11021202⩚⊴⇥⫏≰21011111∀⇚≩⫏≰2220022=NaN","reverse_text":"NaN=⫏≰2112110⩚⊴⇥⫏≰11021202⩚⊴⇥⫏≰21011111∀⇚≩⫏≰2220022","cot":[{"info":"⫏≰2112110⩚⊴⇥⫏≰11021202=⫏≰-20222200","layer":1},{"info":"⫏≰21011111∀⇚≩⫏≰2220022=NaN","layer":1},{"info":"⫏≰-20222200⩚⊴⇥NaN=NaN","layer":0}]}
{"id":143,"expression_no_base_symbol":"$1001$≭$1961$≭($1881$⫸⊐$1171$)","expression":"⫏≰1101002≭⫏≰2200122≭(⫏≰2120200⫸⊐⫏≰1121101)","highest_n_order":5,"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":1001,"base":3},"right_expr":{"type":"numeric_atoms","value":1961,"base":3}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":1881,"base":3},"right_expr":{"type":"numeric_atoms","value":1171,"base":3}}},"used_operators":["rxpJgHHUmx","mqXw5SEYmG"],"dependent_operators":["AHs5Up7iyr","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1001","layer":2},{"info":"number node, value=1961","layer":2},{"info":"compute binary expreesion, left_input=1001, right_input=1961, 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=1881","layer":2},{"info":"number node, value=1171","layer":2},{"info":"compute binary expreesion, left_input=1881, right_input=1171, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=4559","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=4559, 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":3,"result_base":3,"text":"⫏≰1101002≭⫏≰2200122≭(⫏≰2120200⫸⊐⫏≰1121101)=NaN","reverse_text":"NaN=⫏≰1101002≭⫏≰2200122≭(⫏≰2120200⫸⊐⫏≰1121101)","cot":[{"info":"⫏≰1101002≭⫏≰2200122=NaN","layer":1},{"info":"⫏≰2120200⫸⊐⫏≰1121101=⫏≰20020212","layer":1},{"info":"NaN≭⫏≰20020212=NaN","layer":0}]}
{"id":144,"expression_no_base_symbol":"⊥(↯⪼$3971$)","expression":"⊥(↯⪼⫏≰12110002)","highest_n_order":4,"priority_hierarchical_complexity":1,"normalized_expansion_degree":598,"operation_count":2,"complexity_ratio":299.0,"tree":{"type":"unary","operator":"⊥","unary_expr":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"numeric_atoms","value":3971,"base":3}}},"used_operators":["Q3PJZHRvZv","8jW3W4yZS5"],"dependent_operators":["fu6greOZ01","eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp"],"result":"⫏≰220","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3971","layer":2},{"info":"compute unary expreesion, input=3971, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":1},{"info":"compute unary expreesion, input=-21, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=24","layer":0}],"base":3,"result_base":3,"text":"⊥(↯⪼⫏≰12110002)=⫏≰220","reverse_text":"⫏≰220=⊥(↯⪼⫏≰12110002)","cot":[{"info":"↯⪼⫏≰12110002=⫏≰-210","layer":1},{"info":"⊥⫏≰-210=⫏≰220","layer":0}]}
{"id":145,"expression_no_base_symbol":"($7592$⇼⇔∾$1018$)⋝⋈⪟($6957$⇼⇔∾$1646$)","expression":"(⫏≰101102012⇼⇔∾⫏≰1101201)⋝⋈⪟(⫏≰100112200⇼⇔∾⫏≰2020222)","highest_n_order":1,"priority_hierarchical_complexity":2,"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":7592,"base":3},"right_expr":{"type":"numeric_atoms","value":1018,"base":3}},"right_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":6957,"base":3},"right_expr":{"type":"numeric_atoms","value":1646,"base":3}}},"used_operators":["2DDjHMKMc0","tifHPKVTfV"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-100000111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7592","layer":2},{"info":"number node, value=1018","layer":2},{"info":"compute binary expreesion, left_input=7592, right_input=1018, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-6574","layer":1},{"info":"number node, value=6957","layer":2},{"info":"number node, value=1646","layer":2},{"info":"compute binary expreesion, left_input=6957, right_input=1646, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-5311","layer":1},{"info":"compute binary expreesion, left_input=-6574, right_input=-5311, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=-6574","layer":0}],"base":3,"result_base":3,"text":"(⫏≰101102012⇼⇔∾⫏≰1101201)⋝⋈⪟(⫏≰100112200⇼⇔∾⫏≰2020222)=⫏≰-100000111","reverse_text":"⫏≰-100000111=(⫏≰101102012⇼⇔∾⫏≰1101201)⋝⋈⪟(⫏≰100112200⇼⇔∾⫏≰2020222)","cot":[{"info":"⫏≰101102012⇼⇔∾⫏≰1101201=⫏≰-100000111","layer":1},{"info":"⫏≰100112200⇼⇔∾⫏≰2020222=⫏≰-21021201","layer":1},{"info":"⫏≰-100000111⋝⋈⪟⫏≰-21021201=⫏≰-100000111","layer":0}]}
{"id":146,"expression_no_base_symbol":"($1587$⊉≛↸$7229$)≎⊠⪸($8117$∲⫓$2282$)","expression":"(⫏≰2011210⊉≛↸⫏≰100220202)≎⊠⪸(⫏≰102010122∲⫓⫏≰10010112)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":274,"operation_count":3,"complexity_ratio":91.33333333333333,"tree":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":1587,"base":3},"right_expr":{"type":"numeric_atoms","value":7229,"base":3}},"right_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":8117,"base":3},"right_expr":{"type":"numeric_atoms","value":2282,"base":3}}},"used_operators":["bJkvcejdHO","DZ8iAZOCBD","i8ToyICDmI"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1112202000101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1587","layer":2},{"info":"number node, value=7229","layer":2},{"info":"compute binary expreesion, left_input=1587, right_input=7229, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=3174","layer":1},{"info":"number node, value=8117","layer":2},{"info":"number node, value=2282","layer":2},{"info":"compute binary expreesion, left_input=8117, right_input=2282, 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=3174, right_input=0, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=821593","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2011210⊉≛↸⫏≰100220202)≎⊠⪸(⫏≰102010122∲⫓⫏≰10010112)=⫏≰1112202000101","reverse_text":"⫏≰1112202000101=(⫏≰2011210⊉≛↸⫏≰100220202)≎⊠⪸(⫏≰102010122∲⫓⫏≰10010112)","cot":[{"info":"⫏≰2011210⊉≛↸⫏≰100220202=⫏≰11100120","layer":1},{"info":"⫏≰102010122∲⫓⫏≰10010112=⫏≰0","layer":1},{"info":"⫏≰11100120≎⊠⪸⫏≰0=⫏≰1112202000101","layer":0}]}
{"id":147,"expression_no_base_symbol":"($1658$∲⫓$6909$)*$4019$⨓$1887$","expression":"(⫏≰2021102∲⫓⫏≰100110220)*⫏≰12111212⨓⫏≰2120220","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1896,"operation_count":3,"complexity_ratio":632.0,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":1658,"base":3},"right_expr":{"type":"numeric_atoms","value":6909,"base":3}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":4019,"base":3},"right_expr":{"type":"numeric_atoms","value":1887,"base":3}}},"used_operators":["9HNa5Wba9A","i8ToyICDmI","3ViojmjbAp"],"dependent_operators":["W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1658","layer":2},{"info":"number node, value=6909","layer":2},{"info":"compute binary expreesion, left_input=1658, right_input=6909, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=4019","layer":2},{"info":"number node, value=1887","layer":2},{"info":"compute binary expreesion, left_input=4019, right_input=1887, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1890","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-1890, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2021102∲⫓⫏≰100110220)*⫏≰12111212⨓⫏≰2120220=⫏≰0","reverse_text":"⫏≰0=(⫏≰2021102∲⫓⫏≰100110220)*⫏≰12111212⨓⫏≰2120220","cot":[{"info":"⫏≰2021102∲⫓⫏≰100110220=⫏≰0","layer":1},{"info":"⫏≰12111212⨓⫏≰2120220=⫏≰-2121000","layer":1},{"info":"⫏≰0*⫏≰-2121000=⫏≰0","layer":0}]}
{"id":148,"expression_no_base_symbol":"$5094$∼$1265$⪨≂$6776$*$1060$","expression":"⫏≰20222200∼⫏≰1201212⪨≂⫏≰100021222*⫏≰1110021","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1166,"operation_count":3,"complexity_ratio":388.6666666666667,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":5094,"base":3},"right_expr":{"type":"numeric_atoms","value":1265,"base":3}},"right_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":6776,"base":3},"right_expr":{"type":"numeric_atoms","value":1060,"base":3}}},"used_operators":["sdazOOVcIp","DyGG3AbaNP","9HNa5Wba9A"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5094","layer":2},{"info":"number node, value=1265","layer":2},{"info":"compute binary expreesion, left_input=5094, right_input=1265, 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=6776","layer":2},{"info":"number node, value=1060","layer":2},{"info":"compute binary expreesion, left_input=6776, right_input=1060, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=7182560","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=7182560, 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":3,"result_base":3,"text":"⫏≰20222200∼⫏≰1201212⪨≂⫏≰100021222*⫏≰1110021=NaN","reverse_text":"NaN=⫏≰20222200∼⫏≰1201212⪨≂⫏≰100021222*⫏≰1110021","cot":[{"info":"⫏≰20222200∼⫏≰1201212=NaN","layer":1},{"info":"⫏≰100021222*⫏≰1110021=⫏≰111111220121202","layer":1},{"info":"NaN⪨≂⫏≰111111220121202=NaN","layer":0}]}
{"id":149,"expression_no_base_symbol":"($1401$⨽$3285$)⨎($7210$⋫)","expression":"(⫏≰1220220⨽⫏≰11111200)⨎(⫏≰100220001⋫)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8621,"operation_count":3,"complexity_ratio":2873.6666666666665,"tree":{"type":"binary","operator":"⨎","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1401,"base":3},"right_expr":{"type":"numeric_atoms","value":3285,"base":3}},"right_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":7210,"base":3}}},"used_operators":["rJVOvQCfKK","8HhzD0ZcuI","JL8yIekQnl"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","tmPS8pqC7x"],"result":"⫏≰100220001","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1401","layer":2},{"info":"number node, value=3285","layer":2},{"info":"compute binary expreesion, left_input=1401, right_input=3285, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-5896944","layer":1},{"info":"number node, value=7210","layer":2},{"info":"compute unary expreesion, input=7210, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=7210","layer":1},{"info":"compute binary expreesion, left_input=-5896944, right_input=7210, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=7210","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1220220⨽⫏≰11111200)⨎(⫏≰100220001⋫)=⫏≰100220001","reverse_text":"⫏≰100220001=(⫏≰1220220⨽⫏≰11111200)⨎(⫏≰100220001⋫)","cot":[{"info":"⫏≰1220220⨽⫏≰11111200=⫏≰-102002121002100","layer":1},{"info":"⫏≰100220001⋫=⫏≰100220001","layer":1},{"info":"⫏≰-102002121002100⨎⫏≰100220001=⫏≰100220001","layer":0}]}
{"id":150,"expression_no_base_symbol":"⨑⩽⪐$2547$⨽$1847$","expression":"⨑⩽⪐⫏≰10111100⨽⫏≰2112102","highest_n_order":2,"priority_hierarchical_complexity":1,"normalized_expansion_degree":2563,"operation_count":2,"complexity_ratio":1281.5,"tree":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":2547,"base":3},"right_expr":{"type":"numeric_atoms","value":1847,"base":3}}},"used_operators":["AF7qkfDlqP","8HhzD0ZcuI"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"⫏≰2201020222100100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2547","layer":2},{"info":"number node, value=1847","layer":2},{"info":"compute binary expreesion, left_input=2547, right_input=1847, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-19465854","layer":1},{"info":"compute unary expreesion, input=-19465854, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=38932497","layer":0}],"base":3,"result_base":3,"text":"⨑⩽⪐⫏≰10111100⨽⫏≰2112102=⫏≰2201020222100100","reverse_text":"⫏≰2201020222100100=⨑⩽⪐⫏≰10111100⨽⫏≰2112102","cot":[{"info":"⫏≰10111100⨽⫏≰2112102=⫏≰-1100121222010120","layer":1},{"info":"⨑⩽⪐⫏≰-1100121222010120=⫏≰2201020222100100","layer":0}]}
{"id":151,"expression_no_base_symbol":"↯⪼(-$1832$)","expression":"↯⪼(-⫏≰2111212)","highest_n_order":2,"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":1832,"base":3}}},"used_operators":["8jW3W4yZS5","t8gj7n24qd"],"dependent_operators":["eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp"],"result":"⫏≰10202202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1832","layer":2},{"info":"compute unary expreesion, input=1832, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1832","layer":1},{"info":"compute unary expreesion, input=-1832, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=2747","layer":0}],"base":3,"result_base":3,"text":"↯⪼(-⫏≰2111212)=⫏≰10202202","reverse_text":"⫏≰10202202=↯⪼(-⫏≰2111212)","cot":[{"info":"-⫏≰2111212=⫏≰-2111212","layer":1},{"info":"↯⪼⫏≰-2111212=⫏≰10202202","layer":0}]}
{"id":152,"expression_no_base_symbol":"(⩦⩻⨪$1979$)∑⇟⊟$2050$⪘⫢$5974$","expression":"(⩦⩻⨪⫏≰2201022)∑⇟⊟⫏≰2210221⪘⫢⫏≰22012021","highest_n_order":4,"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":1979,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":2050,"base":3},"right_expr":{"type":"numeric_atoms","value":5974,"base":3}}},"used_operators":["U7g4x0WXJJ","2td37pGCOC","oacrs7FA3X"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","rysDP5nf3Z","t8gj7n24qd","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1979","layer":2},{"info":"compute unary expreesion, input=1979, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=1979","layer":1},{"info":"number node, value=2050","layer":2},{"info":"number node, value=5974","layer":2},{"info":"compute binary expreesion, left_input=2050, right_input=5974, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=3976","layer":1},{"info":"compute binary expreesion, left_input=1979, right_input=3976, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⩦⩻⨪⫏≰2201022)∑⇟⊟⫏≰2210221⪘⫢⫏≰22012021=NaN","reverse_text":"NaN=(⩦⩻⨪⫏≰2201022)∑⇟⊟⫏≰2210221⪘⫢⫏≰22012021","cot":[{"info":"⩦⩻⨪⫏≰2201022=⫏≰2201022","layer":1},{"info":"⫏≰2210221⪘⫢⫏≰22012021=⫏≰12110021","layer":1},{"info":"⫏≰2201022∑⇟⊟⫏≰12110021=NaN","layer":0}]}
{"id":153,"expression_no_base_symbol":"$2863$∑⇟⊟$5543$⨐⩸⫘($1198$⊪)","expression":"⫏≰10221001∑⇟⊟⫏≰21121022⨐⩸⫘(⫏≰1122101⊪)","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":2863,"base":3},"right_expr":{"type":"numeric_atoms","value":5543,"base":3}},"right_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":1198,"base":3}}},"used_operators":["fu6greOZ01","U7g4x0WXJJ","zVYPLywUTj"],"dependent_operators":["3ViojmjbAp","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2863","layer":2},{"info":"number node, value=5543","layer":2},{"info":"compute binary expreesion, left_input=2863, right_input=5543, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"number node, value=1198","layer":2},{"info":"compute unary expreesion, input=1198, 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=nan, right_input=0, 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":3,"result_base":3,"text":"⫏≰10221001∑⇟⊟⫏≰21121022⨐⩸⫘(⫏≰1122101⊪)=NaN","reverse_text":"NaN=⫏≰10221001∑⇟⊟⫏≰21121022⨐⩸⫘(⫏≰1122101⊪)","cot":[{"info":"⫏≰10221001∑⇟⊟⫏≰21121022=NaN","layer":1},{"info":"⫏≰1122101⊪=⫏≰0","layer":1},{"info":"NaN⨐⩸⫘⫏≰0=NaN","layer":0}]}
{"id":154,"expression_no_base_symbol":"$2174$⇷$4626$⫸⊐$2279$⋳⪒$1178$","expression":"⫏≰2222112⇷⫏≰20100100⫸⊐⫏≰10010102⋳⪒⫏≰1121122","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":30473,"operation_count":3,"complexity_ratio":10157.666666666666,"tree":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":2174,"base":3},"right_expr":{"type":"numeric_atoms","value":4626,"base":3}},"right_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":2279,"base":3},"right_expr":{"type":"numeric_atoms","value":1178,"base":3}}},"used_operators":["mqXw5SEYmG","mp7IySMOzn","12rbrZMWeM"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰121210121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2174","layer":2},{"info":"number node, value=4626","layer":2},{"info":"compute binary expreesion, left_input=2174, right_input=4626, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=9252","layer":1},{"info":"number node, value=2279","layer":2},{"info":"number node, value=1178","layer":2},{"info":"compute binary expreesion, left_input=2279, right_input=1178, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=3093","layer":1},{"info":"compute binary expreesion, left_input=9252, right_input=3093, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=12247","layer":0}],"base":3,"result_base":3,"text":"⫏≰2222112⇷⫏≰20100100⫸⊐⫏≰10010102⋳⪒⫏≰1121122=⫏≰121210121","reverse_text":"⫏≰121210121=⫏≰2222112⇷⫏≰20100100⫸⊐⫏≰10010102⋳⪒⫏≰1121122","cot":[{"info":"⫏≰2222112⇷⫏≰20100100=⫏≰110200200","layer":1},{"info":"⫏≰10010102⋳⪒⫏≰1121122=⫏≰11020120","layer":1},{"info":"⫏≰110200200⫸⊐⫏≰11020120=⫏≰121210121","layer":0}]}
{"id":155,"expression_no_base_symbol":"(⨑⩽⪐$3952$)⫌⩹⨱","expression":"(⨑⩽⪐⫏≰12102101)⫌⩹⨱","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":3952,"base":3}}},"used_operators":["EBcxylXtPf","AF7qkfDlqP"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-22011122","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3952","layer":2},{"info":"compute unary expreesion, input=3952, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-3679","layer":1},{"info":"compute unary expreesion, input=-3679, op_id = EBcxylXtPf, unary_op_definition = 'a⫌⩹⨱ = { (((80+a)+(750-a))+((149+422)+(a+a))) }', output=-5957","layer":0}],"base":3,"result_base":3,"text":"(⨑⩽⪐⫏≰12102101)⫌⩹⨱=⫏≰-22011122","reverse_text":"⫏≰-22011122=(⨑⩽⪐⫏≰12102101)⫌⩹⨱","cot":[{"info":"⨑⩽⪐⫏≰12102101=⫏≰-12001021","layer":1},{"info":"⫏≰-12001021⫌⩹⨱=⫏≰-22011122","layer":0}]}
{"id":156,"expression_no_base_symbol":"$1006$⨳⩥⨓$2435$-$2964$⪢$1225$","expression":"⫏≰1101021⨳⩥⨓⫏≰10100012-⫏≰11001210⪢⫏≰1200101","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2029,"operation_count":3,"complexity_ratio":676.3333333333334,"tree":{"type":"binary","operator":"-","left_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":1006,"base":3},"right_expr":{"type":"numeric_atoms","value":2435,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":2964,"base":3},"right_expr":{"type":"numeric_atoms","value":1225,"base":3}}},"used_operators":["rysDP5nf3Z","nCS4ZIUYfx","dWAJyo7jo9"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1006","layer":2},{"info":"number node, value=2435","layer":2},{"info":"compute binary expreesion, left_input=1006, right_input=2435, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=1429","layer":1},{"info":"number node, value=2964","layer":2},{"info":"number node, value=1225","layer":2},{"info":"compute binary expreesion, left_input=2964, right_input=1225, 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=1429, right_input=nan, op_id = rysDP5nf3Z binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1101021⨳⩥⨓⫏≰10100012-⫏≰11001210⪢⫏≰1200101=NaN","reverse_text":"NaN=⫏≰1101021⨳⩥⨓⫏≰10100012-⫏≰11001210⪢⫏≰1200101","cot":[{"info":"⫏≰1101021⨳⩥⨓⫏≰10100012=⫏≰1221221","layer":1},{"info":"⫏≰11001210⪢⫏≰1200101=NaN","layer":1},{"info":"⫏≰1221221-NaN=NaN","layer":0}]}
{"id":157,"expression_no_base_symbol":"(≉$2866$)⪄$2557$⨓$4390$","expression":"(≉⫏≰10221011)⪄⫏≰10111201⨓⫏≰20000121","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4492,"operation_count":3,"complexity_ratio":1497.3333333333333,"tree":{"type":"binary","operator":"⪄","left_expr":{"type":"unary","operator":"≉","unary_expr":{"type":"numeric_atoms","value":2866,"base":3}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":2557,"base":3},"right_expr":{"type":"numeric_atoms","value":4390,"base":3}}},"used_operators":["SUmda5xLS4","e1ybzncUwg","3ViojmjbAp"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","W4YGzv6Whe","t8gj7n24qd","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⫏≰-220110011221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2866","layer":2},{"info":"compute unary expreesion, input=2866, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=3397","layer":1},{"info":"number node, value=2557","layer":2},{"info":"number node, value=4390","layer":2},{"info":"compute binary expreesion, left_input=2557, right_input=4390, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-4393","layer":1},{"info":"compute binary expreesion, left_input=3397, right_input=-4393, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-481273","layer":0}],"base":3,"result_base":3,"text":"(≉⫏≰10221011)⪄⫏≰10111201⨓⫏≰20000121=⫏≰-220110011221","reverse_text":"⫏≰-220110011221=(≉⫏≰10221011)⪄⫏≰10111201⨓⫏≰20000121","cot":[{"info":"≉⫏≰10221011=⫏≰11122211","layer":1},{"info":"⫏≰10111201⨓⫏≰20000121=⫏≰-20000201","layer":1},{"info":"⫏≰11122211⪄⫏≰-20000201=⫏≰-220110011221","layer":0}]}
{"id":158,"expression_no_base_symbol":"⨑⩽⪐$2425$∀⇚≩$1806$","expression":"⨑⩽⪐⫏≰10022211∀⇚≩⫏≰2110220","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16982,"operation_count":2,"complexity_ratio":8491.0,"tree":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":2425,"base":3},"right_expr":{"type":"numeric_atoms","value":1806,"base":3}}},"used_operators":["AF7qkfDlqP","LRNGc0VcxI"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2425","layer":2},{"info":"number node, value=1806","layer":2},{"info":"compute binary expreesion, left_input=2425, right_input=1806, 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 = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⨑⩽⪐⫏≰10022211∀⇚≩⫏≰2110220=NaN","reverse_text":"NaN=⨑⩽⪐⫏≰10022211∀⇚≩⫏≰2110220","cot":[{"info":"⫏≰10022211∀⇚≩⫏≰2110220=NaN","layer":1},{"info":"⨑⩽⪐NaN=NaN","layer":0}]}
{"id":159,"expression_no_base_symbol":"$4165$⋓$3372$⪠⩆⊳","expression":"⫏≰12201021⋓⫏≰11121220⪠⩆⊳","highest_n_order":3,"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":4165,"base":3},"right_expr":{"type":"numeric_atoms","value":3372,"base":3}}},"used_operators":["JLbD19bQDL","T2fj7uvVaJ"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4165","layer":2},{"info":"number node, value=3372","layer":2},{"info":"compute binary expreesion, left_input=4165, right_input=3372, 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 = 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":0}],"base":3,"result_base":3,"text":"⫏≰12201021⋓⫏≰11121220⪠⩆⊳=⫏≰0","reverse_text":"⫏≰0=⫏≰12201021⋓⫏≰11121220⪠⩆⊳","cot":[{"info":"⫏≰12201021⋓⫏≰11121220=⫏≰0","layer":1},{"info":"⫏≰0⪠⩆⊳=⫏≰0","layer":0}]}
{"id":160,"expression_no_base_symbol":"⫓⪴$4950$⇷$3992$","expression":"⫓⪴⫏≰20210100⇷⫏≰12110212","highest_n_order":3,"priority_hierarchical_complexity":1,"normalized_expansion_degree":77290,"operation_count":2,"complexity_ratio":38645.0,"tree":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":4950,"base":3},"right_expr":{"type":"numeric_atoms","value":3992,"base":3}}},"used_operators":["eLxqMNBOBk","mp7IySMOzn"],"dependent_operators":["9HNa5Wba9A","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"⫏≰11102221112200101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4950","layer":2},{"info":"number node, value=3992","layer":2},{"info":"compute binary expreesion, left_input=4950, right_input=3992, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=7984","layer":1},{"info":"compute unary expreesion, input=7984, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=63744256","layer":0}],"base":3,"result_base":3,"text":"⫓⪴⫏≰20210100⇷⫏≰12110212=⫏≰11102221112200101","reverse_text":"⫏≰11102221112200101=⫓⪴⫏≰20210100⇷⫏≰12110212","cot":[{"info":"⫏≰20210100⇷⫏≰12110212=⫏≰101221201","layer":1},{"info":"⫓⪴⫏≰101221201=⫏≰11102221112200101","layer":0}]}
{"id":161,"expression_no_base_symbol":"≤/$4275$⨳⩥⨓$1286$","expression":"≤/⫏≰12212100⨳⩥⨓⫏≰1202122","highest_n_order":1,"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":4275,"base":3},"right_expr":{"type":"numeric_atoms","value":1286,"base":3}}},"used_operators":["eLAdDNolq6","nCS4ZIUYfx"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰11202122","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4275","layer":2},{"info":"number node, value=1286","layer":2},{"info":"compute binary expreesion, left_input=4275, right_input=1286, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-2989","layer":1},{"info":"compute unary expreesion, input=-2989, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=3473","layer":0}],"base":3,"result_base":3,"text":"≤/⫏≰12212100⨳⩥⨓⫏≰1202122=⫏≰11202122","reverse_text":"⫏≰11202122=≤/⫏≰12212100⨳⩥⨓⫏≰1202122","cot":[{"info":"⫏≰12212100⨳⩥⨓⫏≰1202122=⫏≰-11002201","layer":1},{"info":"≤/⫏≰-11002201=⫏≰11202122","layer":0}]}
{"id":162,"expression_no_base_symbol":"⊥($4018$≧⫂∧$2817$)","expression":"⊥(⫏≰12111211≧⫂∧⫏≰10212100)","highest_n_order":4,"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":4018,"base":3},"right_expr":{"type":"numeric_atoms","value":2817,"base":3}}},"used_operators":["Q3PJZHRvZv","Ph9nP6C5qx"],"dependent_operators":["fu6greOZ01","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4018","layer":2},{"info":"number node, value=2817","layer":2},{"info":"compute binary expreesion, left_input=4018, right_input=2817, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=2344","layer":1},{"info":"compute unary expreesion, input=2344, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊥(⫏≰12111211≧⫂∧⫏≰10212100)=NaN","reverse_text":"NaN=⊥(⫏≰12111211≧⫂∧⫏≰10212100)","cot":[{"info":"⫏≰12111211≧⫂∧⫏≰10212100=⫏≰10012211","layer":1},{"info":"⊥⫏≰10012211=NaN","layer":0}]}
{"id":163,"expression_no_base_symbol":"$3298$⫥∨⫟$2151$⪨≂(⫓⪴$2922$)","expression":"⫏≰11112011⫥∨⫟⫏≰2221200⪨≂(⫓⪴⫏≰11000020)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3081,"operation_count":3,"complexity_ratio":1027.0,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":3298,"base":3},"right_expr":{"type":"numeric_atoms","value":2151,"base":3}},"right_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":2922,"base":3}}},"used_operators":["sdazOOVcIp","KYD54nUTWz","eLxqMNBOBk"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","8HhzD0ZcuI","rGHVDoGpnC","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3298","layer":2},{"info":"number node, value=2151","layer":2},{"info":"compute binary expreesion, left_input=3298, right_input=2151, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=2922","layer":2},{"info":"compute unary expreesion, input=2922, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=8538084","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=8538084, 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":3,"result_base":3,"text":"⫏≰11112011⫥∨⫟⫏≰2221200⪨≂(⫓⪴⫏≰11000020)=NaN","reverse_text":"NaN=⫏≰11112011⫥∨⫟⫏≰2221200⪨≂(⫓⪴⫏≰11000020)","cot":[{"info":"⫏≰11112011⫥∨⫟⫏≰2221200=NaN","layer":1},{"info":"⫓⪴⫏≰11000020=⫏≰121001210001100","layer":1},{"info":"NaN⪨≂⫏≰121001210001100=NaN","layer":0}]}
{"id":164,"expression_no_base_symbol":"($3848$⩷∴$2118$)∑⇟⊟(-$1748$)","expression":"(⫏≰12021112⩷∴⫏≰2220110)∑⇟⊟(-⫏≰2101202)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":3848,"base":3},"right_expr":{"type":"numeric_atoms","value":2118,"base":3}},"right_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":1748,"base":3}}},"used_operators":["U7g4x0WXJJ","9FxExcQeMw","t8gj7n24qd"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3848","layer":2},{"info":"number node, value=2118","layer":2},{"info":"compute binary expreesion, left_input=3848, right_input=2118, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=3428","layer":1},{"info":"number node, value=1748","layer":2},{"info":"compute unary expreesion, input=1748, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1748","layer":1},{"info":"compute binary expreesion, left_input=3428, right_input=-1748, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12021112⩷∴⫏≰2220110)∑⇟⊟(-⫏≰2101202)=NaN","reverse_text":"NaN=(⫏≰12021112⩷∴⫏≰2220110)∑⇟⊟(-⫏≰2101202)","cot":[{"info":"⫏≰12021112⩷∴⫏≰2220110=⫏≰11200222","layer":1},{"info":"-⫏≰2101202=⫏≰-2101202","layer":1},{"info":"⫏≰11200222∑⇟⊟⫏≰-2101202=NaN","layer":0}]}
{"id":165,"expression_no_base_symbol":"↯⪼(⨈⫕$1134$)","expression":"↯⪼(⨈⫕⫏≰1120000)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":417,"operation_count":2,"complexity_ratio":208.5,"tree":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":1134,"base":3}}},"used_operators":["8jW3W4yZS5","megm06wKyl"],"dependent_operators":["eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q"],"result":"⫏≰-210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1134","layer":2},{"info":"compute unary expreesion, input=1134, 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 unary expreesion, input=-21, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":0}],"base":3,"result_base":3,"text":"↯⪼(⨈⫕⫏≰1120000)=⫏≰-210","reverse_text":"⫏≰-210=↯⪼(⨈⫕⫏≰1120000)","cot":[{"info":"⨈⫕⫏≰1120000=⫏≰-210","layer":1},{"info":"↯⪼⫏≰-210=⫏≰-210","layer":0}]}
{"id":166,"expression_no_base_symbol":"$5542$⪛$5357$⪠⩆⊳","expression":"⫏≰21121021⪛⫏≰21100102⪠⩆⊳","highest_n_order":2,"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":5542,"base":3},"right_expr":{"type":"numeric_atoms","value":5357,"base":3}}},"used_operators":["JLbD19bQDL","uFcxV4UQCh"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5542","layer":2},{"info":"number node, value=5357","layer":2},{"info":"compute binary expreesion, left_input=5542, right_input=5357, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=185","layer":1},{"info":"compute unary expreesion, input=185, 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":0}],"base":3,"result_base":3,"text":"⫏≰21121021⪛⫏≰21100102⪠⩆⊳=⫏≰0","reverse_text":"⫏≰0=⫏≰21121021⪛⫏≰21100102⪠⩆⊳","cot":[{"info":"⫏≰21121021⪛⫏≰21100102=⫏≰20212","layer":1},{"info":"⫏≰20212⪠⩆⊳=⫏≰0","layer":0}]}
{"id":167,"expression_no_base_symbol":"$1168$⪢$2181$⨳⩥⨓($1436$∲⫓$5713$)","expression":"⫏≰1121021⪢⫏≰2222210⨳⩥⨓(⫏≰1222012∲⫓⫏≰21211121)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2186,"operation_count":3,"complexity_ratio":728.6666666666666,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1168,"base":3},"right_expr":{"type":"numeric_atoms","value":2181,"base":3}},"right_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":1436,"base":3},"right_expr":{"type":"numeric_atoms","value":5713,"base":3}}},"used_operators":["nCS4ZIUYfx","dWAJyo7jo9","i8ToyICDmI"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","k8jYdgA6NY","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1168","layer":2},{"info":"number node, value=2181","layer":2},{"info":"compute binary expreesion, left_input=1168, right_input=2181, 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=1436","layer":2},{"info":"number node, value=5713","layer":2},{"info":"compute binary expreesion, left_input=1436, right_input=5713, 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=nan, right_input=0, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1121021⪢⫏≰2222210⨳⩥⨓(⫏≰1222012∲⫓⫏≰21211121)=NaN","reverse_text":"NaN=⫏≰1121021⪢⫏≰2222210⨳⩥⨓(⫏≰1222012∲⫓⫏≰21211121)","cot":[{"info":"⫏≰1121021⪢⫏≰2222210=NaN","layer":1},{"info":"⫏≰1222012∲⫓⫏≰21211121=⫏≰0","layer":1},{"info":"NaN⨳⩥⨓⫏≰0=NaN","layer":0}]}
{"id":168,"expression_no_base_symbol":"$3487$∼$6712$∲⫓(⨵≀≌$8996$)","expression":"⫏≰11210011∼⫏≰100012121∲⫓(⨵≀≌⫏≰110100012)","highest_n_order":4,"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":3487,"base":3},"right_expr":{"type":"numeric_atoms","value":6712,"base":3}},"right_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":8996,"base":3}}},"used_operators":["i8ToyICDmI","DyGG3AbaNP","srAu1WTS94"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3487","layer":2},{"info":"number node, value=6712","layer":2},{"info":"compute binary expreesion, left_input=3487, right_input=6712, 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=8996","layer":2},{"info":"compute unary expreesion, input=8996, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-26988","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-26988, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11210011∼⫏≰100012121∲⫓(⨵≀≌⫏≰110100012)=NaN","reverse_text":"NaN=⫏≰11210011∼⫏≰100012121∲⫓(⨵≀≌⫏≰110100012)","cot":[{"info":"⫏≰11210011∼⫏≰100012121=NaN","layer":1},{"info":"⨵≀≌⫏≰110100012=⫏≰-1101000120","layer":1},{"info":"NaN∲⫓⫏≰-1101000120=NaN","layer":0}]}
{"id":169,"expression_no_base_symbol":"↩(⫛⫱⨽$2007$)","expression":"↩(⫛⫱⨽⫏≰2202100)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1441,"operation_count":2,"complexity_ratio":720.5,"tree":{"type":"unary","operator":"↩","unary_expr":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"numeric_atoms","value":2007,"base":3}}},"used_operators":["jLgFTUHLKL","DlLNRPXxWL"],"dependent_operators":["sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D","rGHVDoGpnC"],"result":"⫏≰20122102","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2007","layer":2},{"info":"compute unary expreesion, input=2007, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=4844","layer":0}],"base":3,"result_base":3,"text":"↩(⫛⫱⨽⫏≰2202100)=⫏≰20122102","reverse_text":"⫏≰20122102=↩(⫛⫱⨽⫏≰2202100)","cot":[{"info":"⫛⫱⨽⫏≰2202100=⫏≰0","layer":1},{"info":"↩⫏≰0=⫏≰20122102","layer":0}]}
{"id":170,"expression_no_base_symbol":"≦∁$1229$≎⊠⪸$1103$","expression":"≦∁⫏≰1200112≎⊠⪸⫏≰1111212","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":271,"operation_count":2,"complexity_ratio":135.5,"tree":{"type":"unary","operator":"≦∁","unary_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1229,"base":3},"right_expr":{"type":"numeric_atoms","value":1103,"base":3}}},"used_operators":["9ICcGScMcE","bJkvcejdHO"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"⫏≰121010222210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1229","layer":2},{"info":"number node, value=1103","layer":2},{"info":"compute binary expreesion, left_input=1229, right_input=1103, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=317838","layer":1},{"info":"compute unary expreesion, input=317838, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=317838","layer":0}],"base":3,"result_base":3,"text":"≦∁⫏≰1200112≎⊠⪸⫏≰1111212=⫏≰121010222210","reverse_text":"⫏≰121010222210=≦∁⫏≰1200112≎⊠⪸⫏≰1111212","cot":[{"info":"⫏≰1200112≎⊠⪸⫏≰1111212=⫏≰121010222210","layer":1},{"info":"≦∁⫏≰121010222210=⫏≰121010222210","layer":0}]}
{"id":171,"expression_no_base_symbol":"↔($2533$⇷$1012$)","expression":"↔(⫏≰10110211⇷⫏≰1101111)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":35475,"operation_count":2,"complexity_ratio":17737.5,"tree":{"type":"unary","operator":"↔","unary_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":2533,"base":3},"right_expr":{"type":"numeric_atoms","value":1012,"base":3}}},"used_operators":["ruOEQAzv1W","mp7IySMOzn"],"dependent_operators":["XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"⫏≰-2101212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2533","layer":2},{"info":"number node, value=1012","layer":2},{"info":"compute binary expreesion, left_input=2533, right_input=1012, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=2024","layer":1},{"info":"compute unary expreesion, input=2024, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-1751","layer":0}],"base":3,"result_base":3,"text":"↔(⫏≰10110211⇷⫏≰1101111)=⫏≰-2101212","reverse_text":"⫏≰-2101212=↔(⫏≰10110211⇷⫏≰1101111)","cot":[{"info":"⫏≰10110211⇷⫏≰1101111=⫏≰2202222","layer":1},{"info":"↔⫏≰2202222=⫏≰-2101212","layer":0}]}
{"id":172,"expression_no_base_symbol":"⫛⫱⨽($2994$⩷∴$1374$)","expression":"⫛⫱⨽(⫏≰11002220⩷∴⫏≰1212220)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1428,"operation_count":2,"complexity_ratio":714.0,"tree":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":2994,"base":3},"right_expr":{"type":"numeric_atoms","value":1374,"base":3}}},"used_operators":["DlLNRPXxWL","9FxExcQeMw"],"dependent_operators":["rGHVDoGpnC","rysDP5nf3Z"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2994","layer":2},{"info":"number node, value=1374","layer":2},{"info":"compute binary expreesion, left_input=2994, right_input=1374, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=3208","layer":1},{"info":"compute unary expreesion, input=3208, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫛⫱⨽(⫏≰11002220⩷∴⫏≰1212220)=⫏≰0","reverse_text":"⫏≰0=⫛⫱⨽(⫏≰11002220⩷∴⫏≰1212220)","cot":[{"info":"⫏≰11002220⩷∴⫏≰1212220=⫏≰11101211","layer":1},{"info":"⫛⫱⨽⫏≰11101211=⫏≰0","layer":0}]}
{"id":173,"expression_no_base_symbol":"$4747$-$2238$⫡⨏$1429$⋥≓≎$2770$","expression":"⫏≰20111211-⫏≰10001220⫡⨏⫏≰1221221⋥≓≎⫏≰10210121","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":4747,"base":3},"right_expr":{"type":"numeric_atoms","value":2238,"base":3}},"right_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":1429,"base":3},"right_expr":{"type":"numeric_atoms","value":2770,"base":3}}},"used_operators":["QMFrweE19q","rysDP5nf3Z","Qy55tPpLXF"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰1002122121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4747","layer":2},{"info":"number node, value=2238","layer":2},{"info":"compute binary expreesion, left_input=4747, right_input=2238, op_id = rysDP5nf3Z binary_op_definition= 'None', output=2509","layer":1},{"info":"number node, value=1429","layer":2},{"info":"number node, value=2770","layer":2},{"info":"compute binary expreesion, left_input=1429, right_input=2770, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=4144","layer":1},{"info":"compute binary expreesion, left_input=2509, right_input=4144, 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=21616","layer":0}],"base":3,"result_base":3,"text":"⫏≰20111211-⫏≰10001220⫡⨏⫏≰1221221⋥≓≎⫏≰10210121=⫏≰1002122121","reverse_text":"⫏≰1002122121=⫏≰20111211-⫏≰10001220⫡⨏⫏≰1221221⋥≓≎⫏≰10210121","cot":[{"info":"⫏≰20111211-⫏≰10001220=⫏≰10102221","layer":1},{"info":"⫏≰1221221⋥≓≎⫏≰10210121=⫏≰12200111","layer":1},{"info":"⫏≰10102221⫡⨏⫏≰12200111=⫏≰1002122121","layer":0}]}
{"id":174,"expression_no_base_symbol":"($1039$⋷$1880$)⪒$1532$⩨$4927$","expression":"(⫏≰1102111⋷⫏≰2120122)⪒⫏≰2002202⩨⫏≰20202111","highest_n_order":2,"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":1039,"base":3},"right_expr":{"type":"numeric_atoms","value":1880,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":1532,"base":3},"right_expr":{"type":"numeric_atoms","value":4927,"base":3}}},"used_operators":["f6k1SAg4EE","23Mk6UjR3U","2DlMacCsIx"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰-10201110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1039","layer":2},{"info":"number node, value=1880","layer":2},{"info":"compute binary expreesion, left_input=1039, right_input=1880, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=2721","layer":1},{"info":"number node, value=1532","layer":2},{"info":"number node, value=4927","layer":2},{"info":"compute binary expreesion, left_input=1532, right_input=4927, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-9","layer":1},{"info":"compute binary expreesion, left_input=2721, right_input=-9, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-2712","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1102111⋷⫏≰2120122)⪒⫏≰2002202⩨⫏≰20202111=⫏≰-10201110","reverse_text":"⫏≰-10201110=(⫏≰1102111⋷⫏≰2120122)⪒⫏≰2002202⩨⫏≰20202111","cot":[{"info":"⫏≰1102111⋷⫏≰2120122=⫏≰10201210","layer":1},{"info":"⫏≰2002202⩨⫏≰20202111=⫏≰-100","layer":1},{"info":"⫏≰10201210⪒⫏≰-100=⫏≰-10201110","layer":0}]}
{"id":175,"expression_no_base_symbol":"(↣≠⋷$9527$)+$1388$⨪↰⇹$1089$","expression":"(↣≠⋷⫏≰111001212)+⫏≰1220102⨪↰⇹⫏≰1111100","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1392,"operation_count":3,"complexity_ratio":464.0,"tree":{"type":"binary","operator":"+","left_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":9527,"base":3}},"right_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":1388,"base":3},"right_expr":{"type":"numeric_atoms","value":1089,"base":3}}},"used_operators":["W4YGzv6Whe","Asc51vEJeQ","tmPS8pqC7x"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","rJVOvQCfKK"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=9527","layer":2},{"info":"compute unary expreesion, input=9527, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"number node, value=1388","layer":2},{"info":"number node, value=1089","layer":2},{"info":"compute binary expreesion, left_input=1388, right_input=1089, 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=1388","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1388, op_id = W4YGzv6Whe binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"(↣≠⋷⫏≰111001212)+⫏≰1220102⨪↰⇹⫏≰1111100=NaN","reverse_text":"NaN=(↣≠⋷⫏≰111001212)+⫏≰1220102⨪↰⇹⫏≰1111100","cot":[{"info":"↣≠⋷⫏≰111001212=NaN","layer":1},{"info":"⫏≰1220102⨪↰⇹⫏≰1111100=⫏≰1220102","layer":1},{"info":"NaN+⫏≰1220102=NaN","layer":0}]}
{"id":176,"expression_no_base_symbol":"($1653$⨐⩸⫘$1311$)≭($4809$≭$1935$)","expression":"(⫏≰2021020⨐⩸⫘⫏≰1210120)≭(⫏≰20121010≭⫏≰2122200)","highest_n_order":5,"priority_hierarchical_complexity":2,"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":1653,"base":3},"right_expr":{"type":"numeric_atoms","value":1311,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":4809,"base":3},"right_expr":{"type":"numeric_atoms","value":1935,"base":3}}},"used_operators":["rxpJgHHUmx","fu6greOZ01"],"dependent_operators":["AHs5Up7iyr","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1653","layer":2},{"info":"number node, value=1311","layer":2},{"info":"compute binary expreesion, left_input=1653, right_input=1311, 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=4809","layer":2},{"info":"number node, value=1935","layer":2},{"info":"compute binary expreesion, left_input=4809, right_input=1935, 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=nan, right_input=nan, 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":3,"result_base":3,"text":"(⫏≰2021020⨐⩸⫘⫏≰1210120)≭(⫏≰20121010≭⫏≰2122200)=NaN","reverse_text":"NaN=(⫏≰2021020⨐⩸⫘⫏≰1210120)≭(⫏≰20121010≭⫏≰2122200)","cot":[{"info":"⫏≰2021020⨐⩸⫘⫏≰1210120=NaN","layer":1},{"info":"⫏≰20121010≭⫏≰2122200=NaN","layer":1},{"info":"NaN≭NaN=NaN","layer":0}]}
{"id":177,"expression_no_base_symbol":"($2262$⨐⩸⫘$4057$)⊪","expression":"(⫏≰10002210⨐⩸⫘⫏≰12120021)⊪","highest_n_order":4,"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":2262,"base":3},"right_expr":{"type":"numeric_atoms","value":4057,"base":3}}},"used_operators":["zVYPLywUTj","fu6greOZ01"],"dependent_operators":["sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2262","layer":2},{"info":"number node, value=4057","layer":2},{"info":"compute binary expreesion, left_input=2262, right_input=4057, 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 unary expreesion, input=nan, 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=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10002210⨐⩸⫘⫏≰12120021)⊪=NaN","reverse_text":"NaN=(⫏≰10002210⨐⩸⫘⫏≰12120021)⊪","cot":[{"info":"⫏≰10002210⨐⩸⫘⫏≰12120021=NaN","layer":1},{"info":"NaN⊪=NaN","layer":0}]}
{"id":178,"expression_no_base_symbol":"(↔$3120$)⪢($2606$%$1243$)","expression":"(↔⫏≰11021120)⪢(⫏≰10120112%⫏≰1201001)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2089,"operation_count":3,"complexity_ratio":696.3333333333334,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":3120,"base":3}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":2606,"base":3},"right_expr":{"type":"numeric_atoms","value":1243,"base":3}}},"used_operators":["dWAJyo7jo9","ruOEQAzv1W","k8jYdgA6NY"],"dependent_operators":["k8jYdgA6NY","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3120","layer":2},{"info":"compute unary expreesion, input=3120, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-2847","layer":1},{"info":"number node, value=2606","layer":2},{"info":"number node, value=1243","layer":2},{"info":"compute binary expreesion, left_input=2606, right_input=1243, op_id = k8jYdgA6NY binary_op_definition= 'None', output=120","layer":1},{"info":"compute binary expreesion, left_input=-2847, right_input=120, 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":3,"result_base":3,"text":"(↔⫏≰11021120)⪢(⫏≰10120112%⫏≰1201001)=NaN","reverse_text":"NaN=(↔⫏≰11021120)⪢(⫏≰10120112%⫏≰1201001)","cot":[{"info":"↔⫏≰11021120=⫏≰-10220110","layer":1},{"info":"⫏≰10120112%⫏≰1201001=⫏≰11110","layer":1},{"info":"⫏≰-10220110⪢⫏≰11110=NaN","layer":0}]}
{"id":179,"expression_no_base_symbol":"$2000$⨟⋌⩍$1111$⋳⪒$4930$⩚⊴⇥$2775$","expression":"⫏≰2202002⨟⋌⩍⫏≰1112011⋳⪒⫏≰20202121⩚⊴⇥⫏≰10210210","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":2000,"base":3},"right_expr":{"type":"numeric_atoms","value":1111,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":4930,"base":3},"right_expr":{"type":"numeric_atoms","value":2775,"base":3}}},"used_operators":["12rbrZMWeM","rGHVDoGpnC","NTOWxs364D"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","Tcnh7f0tEr","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2000","layer":2},{"info":"number node, value=1111","layer":2},{"info":"compute binary expreesion, left_input=2000, right_input=1111, 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=4930","layer":2},{"info":"number node, value=2775","layer":2},{"info":"compute binary expreesion, left_input=4930, right_input=2775, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-7826","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-7826, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2202002⨟⋌⩍⫏≰1112011⋳⪒⫏≰20202121⩚⊴⇥⫏≰10210210=NaN","reverse_text":"NaN=⫏≰2202002⨟⋌⩍⫏≰1112011⋳⪒⫏≰20202121⩚⊴⇥⫏≰10210210","cot":[{"info":"⫏≰2202002⨟⋌⩍⫏≰1112011=NaN","layer":1},{"info":"⫏≰20202121⩚⊴⇥⫏≰10210210=⫏≰-101201212","layer":1},{"info":"NaN⋳⪒⫏≰-101201212=NaN","layer":0}]}
{"id":180,"expression_no_base_symbol":"(≦∁$3900$)⊉≛↸$3173$⇷$5751$","expression":"(≦∁⫏≰12100110)⊉≛↸⫏≰11100112⇷⫏≰21220000","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":44431,"operation_count":3,"complexity_ratio":14810.333333333334,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":3900,"base":3}},"right_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":3173,"base":3},"right_expr":{"type":"numeric_atoms","value":5751,"base":3}}},"used_operators":["DZ8iAZOCBD","9ICcGScMcE","mp7IySMOzn"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"⫏≰101200220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3900","layer":2},{"info":"compute unary expreesion, input=3900, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=3900","layer":1},{"info":"number node, value=3173","layer":2},{"info":"number node, value=5751","layer":2},{"info":"compute binary expreesion, left_input=3173, right_input=5751, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=11502","layer":1},{"info":"compute binary expreesion, left_input=3900, right_input=11502, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=7800","layer":0}],"base":3,"result_base":3,"text":"(≦∁⫏≰12100110)⊉≛↸⫏≰11100112⇷⫏≰21220000=⫏≰101200220","reverse_text":"⫏≰101200220=(≦∁⫏≰12100110)⊉≛↸⫏≰11100112⇷⫏≰21220000","cot":[{"info":"≦∁⫏≰12100110=⫏≰12100110","layer":1},{"info":"⫏≰11100112⇷⫏≰21220000=⫏≰120210000","layer":1},{"info":"⫏≰12100110⊉≛↸⫏≰120210000=⫏≰101200220","layer":0}]}
{"id":181,"expression_no_base_symbol":"($2500$-$4511$)⩚⊴⇥$4101$⊴$4181$","expression":"(⫏≰10102121-⫏≰20012002)⩚⊴⇥⫏≰12121220⊴⫏≰12201212","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4191,"operation_count":3,"complexity_ratio":1397.0,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":2500,"base":3},"right_expr":{"type":"numeric_atoms","value":4511,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":4101,"base":3},"right_expr":{"type":"numeric_atoms","value":4181,"base":3}}},"used_operators":["NTOWxs364D","rysDP5nf3Z","Nsiff2A1zJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2500","layer":2},{"info":"number node, value=4511","layer":2},{"info":"compute binary expreesion, left_input=2500, right_input=4511, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-2011","layer":1},{"info":"number node, value=4101","layer":2},{"info":"number node, value=4181","layer":2},{"info":"compute binary expreesion, left_input=4101, right_input=4181, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-2011, right_input=nan, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10102121-⫏≰20012002)⩚⊴⇥⫏≰12121220⊴⫏≰12201212=NaN","reverse_text":"NaN=(⫏≰10102121-⫏≰20012002)⩚⊴⇥⫏≰12121220⊴⫏≰12201212","cot":[{"info":"⫏≰10102121-⫏≰20012002=⫏≰-2202111","layer":1},{"info":"⫏≰12121220⊴⫏≰12201212=NaN","layer":1},{"info":"⫏≰-2202111⩚⊴⇥NaN=NaN","layer":0}]}
{"id":182,"expression_no_base_symbol":"($2228$⪒$1621$)⋳⪒($1018$⨐⩸⫘$6057$)","expression":"(⫏≰10001112⪒⫏≰2020001)⋳⪒(⫏≰1101201⨐⩸⫘⫏≰22022100)","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":2228,"base":3},"right_expr":{"type":"numeric_atoms","value":1621,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":1018,"base":3},"right_expr":{"type":"numeric_atoms","value":6057,"base":3}}},"used_operators":["12rbrZMWeM","f6k1SAg4EE","fu6greOZ01"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2228","layer":2},{"info":"number node, value=1621","layer":2},{"info":"compute binary expreesion, left_input=2228, right_input=1621, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-3849","layer":1},{"info":"number node, value=1018","layer":2},{"info":"number node, value=6057","layer":2},{"info":"compute binary expreesion, left_input=1018, right_input=6057, 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=-3849, right_input=nan, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10001112⪒⫏≰2020001)⋳⪒(⫏≰1101201⨐⩸⫘⫏≰22022100)=NaN","reverse_text":"NaN=(⫏≰10001112⪒⫏≰2020001)⋳⪒(⫏≰1101201⨐⩸⫘⫏≰22022100)","cot":[{"info":"⫏≰10001112⪒⫏≰2020001=⫏≰-12021120","layer":1},{"info":"⫏≰1101201⨐⩸⫘⫏≰22022100=NaN","layer":1},{"info":"⫏≰-12021120⋳⪒NaN=NaN","layer":0}]}
{"id":183,"expression_no_base_symbol":"⊥($5183$⇷$1548$)","expression":"⊥(⫏≰21002222⇷⫏≰2010100)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":72569,"operation_count":2,"complexity_ratio":36284.5,"tree":{"type":"unary","operator":"⊥","unary_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":5183,"base":3},"right_expr":{"type":"numeric_atoms","value":1548,"base":3}}},"used_operators":["Q3PJZHRvZv","mp7IySMOzn"],"dependent_operators":["fu6greOZ01","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5183","layer":2},{"info":"number node, value=1548","layer":2},{"info":"compute binary expreesion, left_input=5183, right_input=1548, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=3096","layer":1},{"info":"compute unary expreesion, input=3096, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊥(⫏≰21002222⇷⫏≰2010100)=NaN","reverse_text":"NaN=⊥(⫏≰21002222⇷⫏≰2010100)","cot":[{"info":"⫏≰21002222⇷⫏≰2010100=⫏≰11020200","layer":1},{"info":"⊥⫏≰11020200=NaN","layer":0}]}
{"id":184,"expression_no_base_symbol":"($4471$⩷∴$3036$)⇷($3807$⋝⋈⪟$1383$)","expression":"(⫏≰20010121⩷∴⫏≰11011110)⇷(⫏≰12020000⋝⋈⪟⫏≰1220020)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":39747,"operation_count":3,"complexity_ratio":13249.0,"tree":{"type":"binary","operator":"⇷","left_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":4471,"base":3},"right_expr":{"type":"numeric_atoms","value":3036,"base":3}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":3807,"base":3},"right_expr":{"type":"numeric_atoms","value":1383,"base":3}}},"used_operators":["mp7IySMOzn","9FxExcQeMw","2DDjHMKMc0"],"dependent_operators":["DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰101110000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4471","layer":2},{"info":"number node, value=3036","layer":2},{"info":"compute binary expreesion, left_input=4471, right_input=3036, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=2838","layer":1},{"info":"number node, value=3807","layer":2},{"info":"number node, value=1383","layer":2},{"info":"compute binary expreesion, left_input=3807, right_input=1383, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=3807","layer":1},{"info":"compute binary expreesion, left_input=2838, right_input=3807, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=7614","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20010121⩷∴⫏≰11011110)⇷(⫏≰12020000⋝⋈⪟⫏≰1220020)=⫏≰101110000","reverse_text":"⫏≰101110000=(⫏≰20010121⩷∴⫏≰11011110)⇷(⫏≰12020000⋝⋈⪟⫏≰1220020)","cot":[{"info":"⫏≰20010121⩷∴⫏≰11011110=⫏≰10220010","layer":1},{"info":"⫏≰12020000⋝⋈⪟⫏≰1220020=⫏≰12020000","layer":1},{"info":"⫏≰10220010⇷⫏≰12020000=⫏≰101110000","layer":0}]}
{"id":185,"expression_no_base_symbol":"(⨰⫟⨤$6640$)/$1489$⪮%⊝$3817$","expression":"(⨰⫟⨤⫏≰100002221)/⫏≰2001011⪮%⊝⫏≰12020101","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":25730,"operation_count":3,"complexity_ratio":8576.666666666666,"tree":{"type":"binary","operator":"/","left_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":6640,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1489,"base":3},"right_expr":{"type":"numeric_atoms","value":3817,"base":3}}},"used_operators":["XhwjNDsVaA","Tw270M8GLb","IWmyXbctLI"],"dependent_operators":["rysDP5nf3Z","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6640","layer":2},{"info":"compute unary expreesion, input=6640, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":1},{"info":"number node, value=1489","layer":2},{"info":"number node, value=3817","layer":2},{"info":"compute binary expreesion, left_input=1489, right_input=3817, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=3294","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=3294, op_id = XhwjNDsVaA binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⨰⫟⨤⫏≰100002221)/⫏≰2001011⪮%⊝⫏≰12020101=NaN","reverse_text":"NaN=(⨰⫟⨤⫏≰100002221)/⫏≰2001011⪮%⊝⫏≰12020101","cot":[{"info":"⨰⫟⨤⫏≰100002221=NaN","layer":1},{"info":"⫏≰2001011⪮%⊝⫏≰12020101=⫏≰11112000","layer":1},{"info":"NaN/⫏≰11112000=NaN","layer":0}]}
{"id":186,"expression_no_base_symbol":"($2799$/$2473$)⨳⩥⨓$1051$≭$2509$","expression":"(⫏≰10211200/⫏≰10101121)⨳⩥⨓⫏≰1102221≭⫏≰10102221","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5,"operation_count":3,"complexity_ratio":1.6666666666666667,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":2799,"base":3},"right_expr":{"type":"numeric_atoms","value":2473,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":1051,"base":3},"right_expr":{"type":"numeric_atoms","value":2509,"base":3}}},"used_operators":["nCS4ZIUYfx","XhwjNDsVaA","rxpJgHHUmx"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2799","layer":2},{"info":"number node, value=2473","layer":2},{"info":"compute binary expreesion, left_input=2799, right_input=2473, op_id = XhwjNDsVaA binary_op_definition= 'None', output=1","layer":1},{"info":"number node, value=1051","layer":2},{"info":"number node, value=2509","layer":2},{"info":"compute binary expreesion, left_input=1051, right_input=2509, 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=1, right_input=nan, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10211200/⫏≰10101121)⨳⩥⨓⫏≰1102221≭⫏≰10102221=NaN","reverse_text":"NaN=(⫏≰10211200/⫏≰10101121)⨳⩥⨓⫏≰1102221≭⫏≰10102221","cot":[{"info":"⫏≰10211200/⫏≰10101121=⫏≰1","layer":1},{"info":"⫏≰1102221≭⫏≰10102221=NaN","layer":1},{"info":"⫏≰1⨳⩥⨓NaN=NaN","layer":0}]}
{"id":187,"expression_no_base_symbol":"($3817$≎⊠⪸$2458$)↬($2200$⊉≛↸$3645$)","expression":"(⫏≰12020101≎⊠⪸⫏≰10101001)↬(⫏≰10000111⊉≛↸⫏≰12000000)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":273,"operation_count":3,"complexity_ratio":91.0,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":3817,"base":3},"right_expr":{"type":"numeric_atoms","value":2458,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":2200,"base":3},"right_expr":{"type":"numeric_atoms","value":3645,"base":3}}},"used_operators":["B5M0gjZbta","bJkvcejdHO","DZ8iAZOCBD"],"dependent_operators":["rGHVDoGpnC","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3817","layer":2},{"info":"number node, value=2458","layer":2},{"info":"compute binary expreesion, left_input=3817, right_input=2458, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=988130","layer":1},{"info":"number node, value=2200","layer":2},{"info":"number node, value=3645","layer":2},{"info":"compute binary expreesion, left_input=2200, right_input=3645, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=4400","layer":1},{"info":"compute binary expreesion, left_input=988130, right_input=4400, 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":3,"result_base":3,"text":"(⫏≰12020101≎⊠⪸⫏≰10101001)↬(⫏≰10000111⊉≛↸⫏≰12000000)=NaN","reverse_text":"NaN=(⫏≰12020101≎⊠⪸⫏≰10101001)↬(⫏≰10000111⊉≛↸⫏≰12000000)","cot":[{"info":"⫏≰12020101≎⊠⪸⫏≰10101001=⫏≰1212012110102","layer":1},{"info":"⫏≰10000111⊉≛↸⫏≰12000000=⫏≰20000222","layer":1},{"info":"⫏≰1212012110102↬⫏≰20000222=NaN","layer":0}]}
{"id":188,"expression_no_base_symbol":"⪲⇎($3081$/$1576$)","expression":"⪲⇎(⫏≰11020010/⫏≰2011101)","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":3081,"base":3},"right_expr":{"type":"numeric_atoms","value":1576,"base":3}}},"used_operators":["XPYlsWDdGa","XhwjNDsVaA"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰2","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3081","layer":2},{"info":"number node, value=1576","layer":2},{"info":"compute binary expreesion, left_input=3081, right_input=1576, op_id = XhwjNDsVaA binary_op_definition= 'None', output=1","layer":1},{"info":"compute unary expreesion, input=1, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=2","layer":0}],"base":3,"result_base":3,"text":"⪲⇎(⫏≰11020010/⫏≰2011101)=⫏≰2","reverse_text":"⫏≰2=⪲⇎(⫏≰11020010/⫏≰2011101)","cot":[{"info":"⫏≰11020010/⫏≰2011101=⫏≰1","layer":1},{"info":"⪲⇎⫏≰1=⫏≰2","layer":0}]}
{"id":189,"expression_no_base_symbol":"($1148$⊭↱$3563$)∀⇚≩$4286$⇷$5928$","expression":"(⫏≰1120112⊭↱⫏≰11212222)∀⇚≩⫏≰12212202⇷⫏≰22010120","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":93861,"operation_count":3,"complexity_ratio":31287.0,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":1148,"base":3},"right_expr":{"type":"numeric_atoms","value":3563,"base":3}},"right_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":4286,"base":3},"right_expr":{"type":"numeric_atoms","value":5928,"base":3}}},"used_operators":["LRNGc0VcxI","COABgblf1C","mp7IySMOzn"],"dependent_operators":["X99M06cbEe","W4YGzv6Whe","t8gj7n24qd","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1148","layer":2},{"info":"number node, value=3563","layer":2},{"info":"compute binary expreesion, left_input=1148, right_input=3563, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=4835","layer":1},{"info":"number node, value=4286","layer":2},{"info":"number node, value=5928","layer":2},{"info":"compute binary expreesion, left_input=4286, right_input=5928, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=11856","layer":1},{"info":"compute binary expreesion, left_input=4835, right_input=11856, 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":3,"result_base":3,"text":"(⫏≰1120112⊭↱⫏≰11212222)∀⇚≩⫏≰12212202⇷⫏≰22010120=NaN","reverse_text":"NaN=(⫏≰1120112⊭↱⫏≰11212222)∀⇚≩⫏≰12212202⇷⫏≰22010120","cot":[{"info":"⫏≰1120112⊭↱⫏≰11212222=⫏≰20122002","layer":1},{"info":"⫏≰12212202⇷⫏≰22010120=⫏≰121021010","layer":1},{"info":"⫏≰20122002∀⇚≩⫏≰121021010=NaN","layer":0}]}
{"id":190,"expression_no_base_symbol":"$4916$∼$4640$⨓($1153$⪄$1535$)","expression":"⫏≰20202002∼⫏≰20100212⨓(⫏≰1120201⪄⫏≰2002212)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":173072,"operation_count":3,"complexity_ratio":57690.666666666664,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":4916,"base":3},"right_expr":{"type":"numeric_atoms","value":4640,"base":3}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":1153,"base":3},"right_expr":{"type":"numeric_atoms","value":1535,"base":3}}},"used_operators":["3ViojmjbAp","DyGG3AbaNP","SUmda5xLS4"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⫏≰-22210010211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4916","layer":2},{"info":"number node, value=4640","layer":2},{"info":"compute binary expreesion, left_input=4916, right_input=4640, 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=1153","layer":2},{"info":"number node, value=1535","layer":2},{"info":"compute binary expreesion, left_input=1153, right_input=1535, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-172873","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-172873, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-172876","layer":0}],"base":3,"result_base":3,"text":"⫏≰20202002∼⫏≰20100212⨓(⫏≰1120201⪄⫏≰2002212)=⫏≰-22210010211","reverse_text":"⫏≰-22210010211=⫏≰20202002∼⫏≰20100212⨓(⫏≰1120201⪄⫏≰2002212)","cot":[{"info":"⫏≰20202002∼⫏≰20100212=NaN","layer":1},{"info":"⫏≰1120201⪄⫏≰2002212=⫏≰-22210010201","layer":1},{"info":"NaN⨓⫏≰-22210010201=⫏≰-22210010211","layer":0}]}
{"id":191,"expression_no_base_symbol":"($3274$⫡⨏$1232$)↙($4428$⩨$1838$)","expression":"(⫏≰11111021⫡⨏⫏≰1200122)↙(⫏≰20002000⩨⫏≰2112002)","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":3274,"base":3},"right_expr":{"type":"numeric_atoms","value":1232,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":4428,"base":3},"right_expr":{"type":"numeric_atoms","value":1838,"base":3}}},"used_operators":["yyfyN0ffXY","QMFrweE19q","2DlMacCsIx"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","W4YGzv6Whe","t8gj7n24qd","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3274","layer":2},{"info":"number node, value=1232","layer":2},{"info":"compute binary expreesion, left_input=3274, right_input=1232, 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=19617","layer":1},{"info":"number node, value=4428","layer":2},{"info":"number node, value=1838","layer":2},{"info":"compute binary expreesion, left_input=4428, right_input=1838, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=19617, right_input=0, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11111021⫡⨏⫏≰1200122)↙(⫏≰20002000⩨⫏≰2112002)=⫏≰0","reverse_text":"⫏≰0=(⫏≰11111021⫡⨏⫏≰1200122)↙(⫏≰20002000⩨⫏≰2112002)","cot":[{"info":"⫏≰11111021⫡⨏⫏≰1200122=⫏≰222220120","layer":1},{"info":"⫏≰20002000⩨⫏≰2112002=⫏≰0","layer":1},{"info":"⫏≰222220120↙⫏≰0=⫏≰0","layer":0}]}
{"id":192,"expression_no_base_symbol":"$5144$⋳⪒$1842$⊉≛↸($3527$⨸⪁$3819$)","expression":"⫏≰21001112⋳⪒⫏≰2112020⊉≛↸(⫏≰11211122⨸⪁⫏≰12020110)","highest_n_order":1,"priority_hierarchical_complexity":2,"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":5144,"base":3},"right_expr":{"type":"numeric_atoms","value":1842,"base":3}},"right_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":3527,"base":3},"right_expr":{"type":"numeric_atoms","value":3819,"base":3}}},"used_operators":["DZ8iAZOCBD","12rbrZMWeM","g55IO6H4Gj"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰211101101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5144","layer":2},{"info":"number node, value=1842","layer":2},{"info":"compute binary expreesion, left_input=5144, right_input=1842, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=8159","layer":1},{"info":"number node, value=3527","layer":2},{"info":"number node, value=3819","layer":2},{"info":"compute binary expreesion, left_input=3527, right_input=3819, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=14692","layer":1},{"info":"compute binary expreesion, left_input=8159, right_input=14692, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=16318","layer":0}],"base":3,"result_base":3,"text":"⫏≰21001112⋳⪒⫏≰2112020⊉≛↸(⫏≰11211122⨸⪁⫏≰12020110)=⫏≰211101101","reverse_text":"⫏≰211101101=⫏≰21001112⋳⪒⫏≰2112020⊉≛↸(⫏≰11211122⨸⪁⫏≰12020110)","cot":[{"info":"⫏≰21001112⋳⪒⫏≰2112020=⫏≰102012012","layer":1},{"info":"⫏≰11211122⨸⪁⫏≰12020110=⫏≰202011011","layer":1},{"info":"⫏≰102012012⊉≛↸⫏≰202011011=⫏≰211101101","layer":0}]}
{"id":193,"expression_no_base_symbol":"($1618$⋓$1932$)⨟⋌⩍($4585$⨽$3872$)","expression":"(⫏≰2012221⋓⫏≰2122120)⨟⋌⩍(⫏≰20021211⨽⫏≰12022102)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4608,"operation_count":3,"complexity_ratio":1536.0,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":1618,"base":3},"right_expr":{"type":"numeric_atoms","value":1932,"base":3}},"right_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":4585,"base":3},"right_expr":{"type":"numeric_atoms","value":3872,"base":3}}},"used_operators":["rGHVDoGpnC","T2fj7uvVaJ","8HhzD0ZcuI"],"dependent_operators":["Tcnh7f0tEr","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1618","layer":2},{"info":"number node, value=1932","layer":2},{"info":"compute binary expreesion, left_input=1618, right_input=1932, 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=4585","layer":2},{"info":"number node, value=3872","layer":2},{"info":"compute binary expreesion, left_input=4585, right_input=3872, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-63076977","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-63076977, 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":0}],"base":3,"result_base":3,"text":"(⫏≰2012221⋓⫏≰2122120)⨟⋌⩍(⫏≰20021211⨽⫏≰12022102)=NaN","reverse_text":"NaN=(⫏≰2012221⋓⫏≰2122120)⨟⋌⩍(⫏≰20021211⨽⫏≰12022102)","cot":[{"info":"⫏≰2012221⋓⫏≰2122120=⫏≰0","layer":1},{"info":"⫏≰20021211⨽⫏≰12022102=⫏≰-11101200122100100","layer":1},{"info":"⫏≰0⨟⋌⩍⫏≰-11101200122100100=NaN","layer":0}]}
{"id":194,"expression_no_base_symbol":"∥⊫$3040$⨟⋌⩍$2570$","expression":"∥⊫⫏≰11011121⨟⋌⩍⫏≰10112012","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":3040,"base":3},"right_expr":{"type":"numeric_atoms","value":2570,"base":3}}},"used_operators":["P8v4zCKN1o","rGHVDoGpnC"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3040","layer":2},{"info":"number node, value=2570","layer":2},{"info":"compute binary expreesion, left_input=3040, right_input=2570, 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 unary expreesion, input=nan, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"∥⊫⫏≰11011121⨟⋌⩍⫏≰10112012=NaN","reverse_text":"NaN=∥⊫⫏≰11011121⨟⋌⩍⫏≰10112012","cot":[{"info":"⫏≰11011121⨟⋌⩍⫏≰10112012=NaN","layer":1},{"info":"∥⊫NaN=NaN","layer":0}]}
{"id":195,"expression_no_base_symbol":"$2869$+⇶⊼$6349$↙(∂$5085$)","expression":"⫏≰10221021+⇶⊼⫏≰22201011↙(∂⫏≰20222100)","highest_n_order":5,"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":2869,"base":3},"right_expr":{"type":"numeric_atoms","value":6349,"base":3}},"right_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":5085,"base":3}}},"used_operators":["yyfyN0ffXY","TpPTUOHfaN","Uaa54Peajs"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","AHs5Up7iyr","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2869","layer":2},{"info":"number node, value=6349","layer":2},{"info":"compute binary expreesion, left_input=2869, right_input=6349, 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":1},{"info":"number node, value=5085","layer":2},{"info":"compute unary expreesion, input=5085, 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=nan, right_input=nan, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰10221021+⇶⊼⫏≰22201011↙(∂⫏≰20222100)=NaN","reverse_text":"NaN=⫏≰10221021+⇶⊼⫏≰22201011↙(∂⫏≰20222100)","cot":[{"info":"⫏≰10221021+⇶⊼⫏≰22201011=NaN","layer":1},{"info":"∂⫏≰20222100=NaN","layer":1},{"info":"NaN↙NaN=NaN","layer":0}]}
{"id":196,"expression_no_base_symbol":"($1301$∲⫓$3487$)⨳⩥⨓$3624$⨰$9456$","expression":"(⫏≰1210012∲⫓⫏≰11210011)⨳⩥⨓⫏≰11222020⨰⫏≰110222020","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":1301,"base":3},"right_expr":{"type":"numeric_atoms","value":3487,"base":3}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":3624,"base":3},"right_expr":{"type":"numeric_atoms","value":9456,"base":3}}},"used_operators":["nCS4ZIUYfx","i8ToyICDmI","eewbuw0ToL"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-21222122","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1301","layer":2},{"info":"number node, value=3487","layer":2},{"info":"compute binary expreesion, left_input=1301, right_input=3487, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=3624","layer":2},{"info":"number node, value=9456","layer":2},{"info":"compute binary expreesion, left_input=3624, right_input=9456, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-5822","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-5822, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-5822","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1210012∲⫓⫏≰11210011)⨳⩥⨓⫏≰11222020⨰⫏≰110222020=⫏≰-21222122","reverse_text":"⫏≰-21222122=(⫏≰1210012∲⫓⫏≰11210011)⨳⩥⨓⫏≰11222020⨰⫏≰110222020","cot":[{"info":"⫏≰1210012∲⫓⫏≰11210011=⫏≰0","layer":1},{"info":"⫏≰11222020⨰⫏≰110222020=⫏≰-21222122","layer":1},{"info":"⫏≰0⨳⩥⨓⫏≰-21222122=⫏≰-21222122","layer":0}]}
{"id":197,"expression_no_base_symbol":"($2184$⨳⩥⨓$8064$)⊴($4444$+$8985$)","expression":"(⫏≰2222220⨳⩥⨓⫏≰102001200)⊴(⫏≰20002121+⫏≰110022210)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13439,"operation_count":3,"complexity_ratio":4479.666666666667,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":2184,"base":3},"right_expr":{"type":"numeric_atoms","value":8064,"base":3}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":4444,"base":3},"right_expr":{"type":"numeric_atoms","value":8985,"base":3}}},"used_operators":["Nsiff2A1zJ","nCS4ZIUYfx","W4YGzv6Whe"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","W4YGzv6Whe","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2184","layer":2},{"info":"number node, value=8064","layer":2},{"info":"compute binary expreesion, left_input=2184, right_input=8064, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=5880","layer":1},{"info":"number node, value=4444","layer":2},{"info":"number node, value=8985","layer":2},{"info":"compute binary expreesion, left_input=4444, right_input=8985, op_id = W4YGzv6Whe binary_op_definition= 'None', output=13429","layer":1},{"info":"compute binary expreesion, left_input=5880, right_input=13429, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2222220⨳⩥⨓⫏≰102001200)⊴(⫏≰20002121+⫏≰110022210)=NaN","reverse_text":"NaN=(⫏≰2222220⨳⩥⨓⫏≰102001200)⊴(⫏≰20002121+⫏≰110022210)","cot":[{"info":"⫏≰2222220⨳⩥⨓⫏≰102001200=⫏≰22001210","layer":1},{"info":"⫏≰20002121+⫏≰110022210=⫏≰200102101","layer":1},{"info":"⫏≰22001210⊴⫏≰200102101=NaN","layer":0}]}
{"id":198,"expression_no_base_symbol":"($7264$⨵⪆$1948$)⊭↱(⫛⫱⨽$2895$)","expression":"(⫏≰100222001⨵⪆⫏≰2200011)⊭↱(⫛⫱⨽⫏≰10222020)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1429,"operation_count":3,"complexity_ratio":476.3333333333333,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":7264,"base":3},"right_expr":{"type":"numeric_atoms","value":1948,"base":3}},"right_expr":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"numeric_atoms","value":2895,"base":3}}},"used_operators":["COABgblf1C","2DQ55sFlQl","DlLNRPXxWL"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","rGHVDoGpnC"],"result":"⫏≰-102200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7264","layer":2},{"info":"number node, value=1948","layer":2},{"info":"compute binary expreesion, left_input=7264, right_input=1948, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=2895","layer":2},{"info":"compute unary expreesion, input=2895, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=0, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-315","layer":0}],"base":3,"result_base":3,"text":"(⫏≰100222001⨵⪆⫏≰2200011)⊭↱(⫛⫱⨽⫏≰10222020)=⫏≰-102200","reverse_text":"⫏≰-102200=(⫏≰100222001⨵⪆⫏≰2200011)⊭↱(⫛⫱⨽⫏≰10222020)","cot":[{"info":"⫏≰100222001⨵⪆⫏≰2200011=⫏≰12221","layer":1},{"info":"⫛⫱⨽⫏≰10222020=⫏≰0","layer":1},{"info":"⫏≰12221⊭↱⫏≰0=⫏≰-102200","layer":0}]}
{"id":199,"expression_no_base_symbol":"↔($8122$⪮%⊝$2698$)","expression":"↔(⫏≰102010211⪮%⊝⫏≰10200221)","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":8122,"base":3},"right_expr":{"type":"numeric_atoms","value":2698,"base":3}}},"used_operators":["ruOEQAzv1W","IWmyXbctLI"],"dependent_operators":["XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰-211100020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=8122","layer":2},{"info":"number node, value=2698","layer":2},{"info":"compute binary expreesion, left_input=8122, right_input=2698, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=16560","layer":1},{"info":"compute unary expreesion, input=16560, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-16287","layer":0}],"base":3,"result_base":3,"text":"↔(⫏≰102010211⪮%⊝⫏≰10200221)=⫏≰-211100020","reverse_text":"⫏≰-211100020=↔(⫏≰102010211⪮%⊝⫏≰10200221)","cot":[{"info":"⫏≰102010211⪮%⊝⫏≰10200221=⫏≰211201100","layer":1},{"info":"↔⫏≰211201100=⫏≰-211100020","layer":0}]}
{"id":200,"expression_no_base_symbol":"(⊙↵-$4631$)⊠≄⫣","expression":"(⊙↵-⫏≰20100112)⊠≄⫣","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4680,"operation_count":2,"complexity_ratio":2340.0,"tree":{"type":"unary","operator":"⊠≄⫣","unary_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":4631,"base":3}}},"used_operators":["DIvbN7qnHd","oWn0xqSxBt"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4631","layer":2},{"info":"compute unary expreesion, input=4631, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute unary expreesion, input=-1, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⊙↵-⫏≰20100112)⊠≄⫣=⫏≰0","reverse_text":"⫏≰0=(⊙↵-⫏≰20100112)⊠≄⫣","cot":[{"info":"⊙↵-⫏≰20100112=⫏≰-1","layer":1},{"info":"⫏≰-1⊠≄⫣=⫏≰0","layer":0}]}
{"id":201,"expression_no_base_symbol":"(⨑⩽⪐$3618$)↙($2667$⪠⩆⊳)","expression":"(⨑⩽⪐⫏≰11222000)↙(⫏≰10122210⪠⩆⊳)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11,"operation_count":3,"complexity_ratio":3.6666666666666665,"tree":{"type":"binary","operator":"↙","left_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":3618,"base":3}},"right_expr":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"numeric_atoms","value":2667,"base":3}}},"used_operators":["yyfyN0ffXY","AF7qkfDlqP","JLbD19bQDL"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-11120220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3618","layer":2},{"info":"compute unary expreesion, input=3618, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-3345","layer":1},{"info":"number node, value=2667","layer":2},{"info":"compute unary expreesion, input=2667, 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":"compute binary expreesion, left_input=-3345, right_input=0, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-3345","layer":0}],"base":3,"result_base":3,"text":"(⨑⩽⪐⫏≰11222000)↙(⫏≰10122210⪠⩆⊳)=⫏≰-11120220","reverse_text":"⫏≰-11120220=(⨑⩽⪐⫏≰11222000)↙(⫏≰10122210⪠⩆⊳)","cot":[{"info":"⨑⩽⪐⫏≰11222000=⫏≰-11120220","layer":1},{"info":"⫏≰10122210⪠⩆⊳=⫏≰0","layer":1},{"info":"⫏≰-11120220↙⫏≰0=⫏≰-11120220","layer":0}]}
{"id":202,"expression_no_base_symbol":"($1606$⨁⊸⫻)∀⇚≩($1372$↪⪝)","expression":"(⫏≰2012111⨁⊸⫻)∀⇚≩(⫏≰1212211↪⪝)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11943,"operation_count":3,"complexity_ratio":3981.0,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"unary","operator":"⨁⊸⫻","unary_expr":{"type":"numeric_atoms","value":1606,"base":3}},"right_expr":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"numeric_atoms","value":1372,"base":3}}},"used_operators":["LRNGc0VcxI","glklzrTFfD","l07mrZUIn9"],"dependent_operators":["X99M06cbEe","W4YGzv6Whe","rysDP5nf3Z","9HNa5Wba9A","2DDjHMKMc0"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1606","layer":2},{"info":"compute unary expreesion, input=1606, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=1606","layer":1},{"info":"number node, value=1372","layer":2},{"info":"compute unary expreesion, input=1372, op_id = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=83941704","layer":1},{"info":"compute binary expreesion, left_input=1606, right_input=83941704, 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":3,"result_base":3,"text":"(⫏≰2012111⨁⊸⫻)∀⇚≩(⫏≰1212211↪⪝)=NaN","reverse_text":"NaN=(⫏≰2012111⨁⊸⫻)∀⇚≩(⫏≰1212211↪⪝)","cot":[{"info":"⫏≰2012111⨁⊸⫻=⫏≰2012111","layer":1},{"info":"⫏≰1212211↪⪝=⫏≰12211221200101000","layer":1},{"info":"⫏≰2012111∀⇚≩⫏≰12211221200101000=NaN","layer":0}]}
{"id":203,"expression_no_base_symbol":"⨞⊢(⨵≀≌$2351$)","expression":"⨞⊢(⨵≀≌⫏≰10020002)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5,"operation_count":2,"complexity_ratio":2.5,"tree":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":2351,"base":3}}},"used_operators":["xUOZtlo3hN","srAu1WTS94"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A"],"result":"⫏≰100102210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2351","layer":2},{"info":"compute unary expreesion, input=2351, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-7053","layer":1},{"info":"compute unary expreesion, input=-7053, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=6879","layer":0}],"base":3,"result_base":3,"text":"⨞⊢(⨵≀≌⫏≰10020002)=⫏≰100102210","reverse_text":"⫏≰100102210=⨞⊢(⨵≀≌⫏≰10020002)","cot":[{"info":"⨵≀≌⫏≰10020002=⫏≰-100200020","layer":1},{"info":"⨞⊢⫏≰-100200020=⫏≰100102210","layer":0}]}
{"id":204,"expression_no_base_symbol":"(≉$6433$)⩠","expression":"(≉⫏≰22211021)⩠","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":20,"operation_count":2,"complexity_ratio":10.0,"tree":{"type":"unary","operator":"⩠","unary_expr":{"type":"unary","operator":"≉","unary_expr":{"type":"numeric_atoms","value":6433,"base":3}}},"used_operators":["sJAwomhLZr","e1ybzncUwg"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","k8jYdgA6NY","eH2TOUuTDT","W4YGzv6Whe","Z2TMIBDE3Q","COABgblf1C","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6433","layer":2},{"info":"compute unary expreesion, input=6433, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=6964","layer":1},{"info":"compute unary expreesion, input=6964, op_id = sJAwomhLZr, unary_op_definition = 'a⩠ = { (((a+a)⊭↱(a⪨≂a))∲⫓((a⩤)%(a⪐))) }', output=0","layer":0}],"base":3,"result_base":3,"text":"(≉⫏≰22211021)⩠=⫏≰0","reverse_text":"⫏≰0=(≉⫏≰22211021)⩠","cot":[{"info":"≉⫏≰22211021=⫏≰100112221","layer":1},{"info":"⫏≰100112221⩠=⫏≰0","layer":0}]}
{"id":205,"expression_no_base_symbol":"($5760$⇼⇔∾$1929$)⋓(≤/$1517$)","expression":"(⫏≰21220100⇼⇔∾⫏≰2122110)⋓(≤/⫏≰2002012)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16,"operation_count":3,"complexity_ratio":5.333333333333333,"tree":{"type":"binary","operator":"⋓","left_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":5760,"base":3},"right_expr":{"type":"numeric_atoms","value":1929,"base":3}},"right_expr":{"type":"unary","operator":"≤/","unary_expr":{"type":"numeric_atoms","value":1517,"base":3}}},"used_operators":["T2fj7uvVaJ","tifHPKVTfV","eLAdDNolq6"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5760","layer":2},{"info":"number node, value=1929","layer":2},{"info":"compute binary expreesion, left_input=5760, right_input=1929, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-3831","layer":1},{"info":"number node, value=1517","layer":2},{"info":"compute unary expreesion, input=1517, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-1033","layer":1},{"info":"compute binary expreesion, left_input=-3831, right_input=-1033, 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":3,"result_base":3,"text":"(⫏≰21220100⇼⇔∾⫏≰2122110)⋓(≤/⫏≰2002012)=⫏≰0","reverse_text":"⫏≰0=(⫏≰21220100⇼⇔∾⫏≰2122110)⋓(≤/⫏≰2002012)","cot":[{"info":"⫏≰21220100⇼⇔∾⫏≰2122110=⫏≰-12020220","layer":1},{"info":"≤/⫏≰2002012=⫏≰-1102021","layer":1},{"info":"⫏≰-12020220⋓⫏≰-1102021=⫏≰0","layer":0}]}
{"id":206,"expression_no_base_symbol":"(⊙↵-$1049$)⪢($2067$⨽$3956$)","expression":"(⊙↵-⫏≰1102212)⪢(⫏≰2211120⨽⫏≰12102112)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3172,"operation_count":3,"complexity_ratio":1057.3333333333333,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":1049,"base":3}},"right_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":2067,"base":3},"right_expr":{"type":"numeric_atoms","value":3956,"base":3}}},"used_operators":["dWAJyo7jo9","oWn0xqSxBt","8HhzD0ZcuI"],"dependent_operators":["k8jYdgA6NY","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1049","layer":2},{"info":"compute unary expreesion, input=1049, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"number node, value=2067","layer":2},{"info":"number node, value=3956","layer":2},{"info":"compute binary expreesion, left_input=2067, right_input=3956, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-12828021","layer":1},{"info":"compute binary expreesion, left_input=-1, right_input=-12828021, 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":3,"result_base":3,"text":"(⊙↵-⫏≰1102212)⪢(⫏≰2211120⨽⫏≰12102112)=NaN","reverse_text":"NaN=(⊙↵-⫏≰1102212)⪢(⫏≰2211120⨽⫏≰12102112)","cot":[{"info":"⊙↵-⫏≰1102212=⫏≰-1","layer":1},{"info":"⫏≰2211120⨽⫏≰12102112=⫏≰-220010201201220","layer":1},{"info":"⫏≰-1⪢⫏≰-220010201201220=NaN","layer":0}]}
{"id":207,"expression_no_base_symbol":"$5362$≹⇙⪍$3585$⋝⋈⪟($1457$⊉≛↸$1062$)","expression":"⫏≰21100121≹⇙⪍⫏≰11220210⋝⋈⪟(⫏≰1222222⊉≛↸⫏≰1110100)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":5362,"base":3},"right_expr":{"type":"numeric_atoms","value":3585,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":1457,"base":3},"right_expr":{"type":"numeric_atoms","value":1062,"base":3}}},"used_operators":["2DDjHMKMc0","AHs5Up7iyr","DZ8iAZOCBD"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5362","layer":2},{"info":"number node, value=3585","layer":2},{"info":"compute binary expreesion, left_input=5362, right_input=3585, 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":"number node, value=1457","layer":2},{"info":"number node, value=1062","layer":2},{"info":"compute binary expreesion, left_input=1457, right_input=1062, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=2914","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2914, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰21100121≹⇙⪍⫏≰11220210⋝⋈⪟(⫏≰1222222⊉≛↸⫏≰1110100)=NaN","reverse_text":"NaN=⫏≰21100121≹⇙⪍⫏≰11220210⋝⋈⪟(⫏≰1222222⊉≛↸⫏≰1110100)","cot":[{"info":"⫏≰21100121≹⇙⪍⫏≰11220210=NaN","layer":1},{"info":"⫏≰1222222⊉≛↸⫏≰1110100=⫏≰10222221","layer":1},{"info":"NaN⋝⋈⪟⫏≰10222221=NaN","layer":0}]}
{"id":208,"expression_no_base_symbol":"⨞⊢(⩦⩻⨪$4902$)","expression":"⨞⊢(⩦⩻⨪⫏≰20201120)","highest_n_order":1,"priority_hierarchical_complexity":1,"normalized_expansion_degree":5,"operation_count":2,"complexity_ratio":2.5,"tree":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":4902,"base":3}}},"used_operators":["xUOZtlo3hN","2td37pGCOC"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-20222000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4902","layer":2},{"info":"compute unary expreesion, input=4902, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=4902","layer":1},{"info":"compute unary expreesion, input=4902, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-5076","layer":0}],"base":3,"result_base":3,"text":"⨞⊢(⩦⩻⨪⫏≰20201120)=⫏≰-20222000","reverse_text":"⫏≰-20222000=⨞⊢(⩦⩻⨪⫏≰20201120)","cot":[{"info":"⩦⩻⨪⫏≰20201120=⫏≰20201120","layer":1},{"info":"⨞⊢⫏≰20201120=⫏≰-20222000","layer":0}]}
{"id":209,"expression_no_base_symbol":"≉$8800$↙$2656$","expression":"≉⫏≰110001221↙⫏≰10122101","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2660,"operation_count":2,"complexity_ratio":1330.0,"tree":{"type":"unary","operator":"≉","unary_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":8800,"base":3},"right_expr":{"type":"numeric_atoms","value":2656,"base":3}}},"used_operators":["e1ybzncUwg","yyfyN0ffXY"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰-101221010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=8800","layer":2},{"info":"number node, value=2656","layer":2},{"info":"compute binary expreesion, left_input=8800, right_input=2656, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-7968","layer":1},{"info":"compute unary expreesion, input=-7968, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=-7968","layer":0}],"base":3,"result_base":3,"text":"≉⫏≰110001221↙⫏≰10122101=⫏≰-101221010","reverse_text":"⫏≰-101221010=≉⫏≰110001221↙⫏≰10122101","cot":[{"info":"⫏≰110001221↙⫏≰10122101=⫏≰-101221010","layer":1},{"info":"≉⫏≰-101221010=⫏≰-101221010","layer":0}]}
{"id":210,"expression_no_base_symbol":"($1301$*$6181$)⪐","expression":"(⫏≰1210012*⫏≰22110221)⪐","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1303,"operation_count":2,"complexity_ratio":651.5,"tree":{"type":"unary","operator":"⪐","unary_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1301,"base":3},"right_expr":{"type":"numeric_atoms","value":6181,"base":3}}},"used_operators":["eH2TOUuTDT","9HNa5Wba9A"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰1010021002200021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1301","layer":2},{"info":"number node, value=6181","layer":2},{"info":"compute binary expreesion, left_input=1301, right_input=6181, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=8041481","layer":1},{"info":"compute unary expreesion, input=8041481, op_id = eH2TOUuTDT, unary_op_definition = 'a⪐ = { (a+a) , if (-a)!=532 or a<368 ; (-a) , else }', output=16082962","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1210012*⫏≰22110221)⪐=⫏≰1010021002200021","reverse_text":"⫏≰1010021002200021=(⫏≰1210012*⫏≰22110221)⪐","cot":[{"info":"⫏≰1210012*⫏≰22110221=⫏≰120010112211122","layer":1},{"info":"⫏≰120010112211122⪐=⫏≰1010021002200021","layer":0}]}
{"id":211,"expression_no_base_symbol":"$1660$⩚⊴⇥$1536$↙($1414$≣⋋)","expression":"⫏≰2021111⩚⊴⇥⫏≰2002220↙(⫏≰1221101≣⋋)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":518,"operation_count":3,"complexity_ratio":172.66666666666666,"tree":{"type":"binary","operator":"↙","left_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":1660,"base":3},"right_expr":{"type":"numeric_atoms","value":1536,"base":3}},"right_expr":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"numeric_atoms","value":1414,"base":3}}},"used_operators":["yyfyN0ffXY","NTOWxs364D","Tcnh7f0tEr"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A"],"result":"⫏≰-11112212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1660","layer":2},{"info":"number node, value=1536","layer":2},{"info":"compute binary expreesion, left_input=1660, right_input=1536, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-3317","layer":1},{"info":"number node, value=1414","layer":2},{"info":"compute unary expreesion, input=1414, 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=-3317, right_input=0, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-3317","layer":0}],"base":3,"result_base":3,"text":"⫏≰2021111⩚⊴⇥⫏≰2002220↙(⫏≰1221101≣⋋)=⫏≰-11112212","reverse_text":"⫏≰-11112212=⫏≰2021111⩚⊴⇥⫏≰2002220↙(⫏≰1221101≣⋋)","cot":[{"info":"⫏≰2021111⩚⊴⇥⫏≰2002220=⫏≰-11112212","layer":1},{"info":"⫏≰1221101≣⋋=⫏≰0","layer":1},{"info":"⫏≰-11112212↙⫏≰0=⫏≰-11112212","layer":0}]}
{"id":212,"expression_no_base_symbol":"($4254$⪒$1048$)⨰$3464$⪛$2215$","expression":"(⫏≰12211120⪒⫏≰1102211)⨰⫏≰11202022⪛⫏≰10001001","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":4254,"base":3},"right_expr":{"type":"numeric_atoms","value":1048,"base":3}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":3464,"base":3},"right_expr":{"type":"numeric_atoms","value":2215,"base":3}}},"used_operators":["eewbuw0ToL","f6k1SAg4EE","uFcxV4UQCh"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⫏≰-22222021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4254","layer":2},{"info":"number node, value=1048","layer":2},{"info":"compute binary expreesion, left_input=4254, right_input=1048, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-5302","layer":1},{"info":"number node, value=3464","layer":2},{"info":"number node, value=2215","layer":2},{"info":"compute binary expreesion, left_input=3464, right_input=2215, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1249","layer":1},{"info":"compute binary expreesion, left_input=-5302, right_input=1249, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-6541","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12211120⪒⫏≰1102211)⨰⫏≰11202022⪛⫏≰10001001=⫏≰-22222021","reverse_text":"⫏≰-22222021=(⫏≰12211120⪒⫏≰1102211)⨰⫏≰11202022⪛⫏≰10001001","cot":[{"info":"⫏≰12211120⪒⫏≰1102211=⫏≰-21021101","layer":1},{"info":"⫏≰11202022⪛⫏≰10001001=⫏≰1201021","layer":1},{"info":"⫏≰-21021101⨰⫏≰1201021=⫏≰-22222021","layer":0}]}
{"id":213,"expression_no_base_symbol":"$1551$⇷$5958$≧⫂∧($3877$≦≮≮)","expression":"⫏≰2010110⇷⫏≰22011200≧⫂∧(⫏≰12022121≦≮≮)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":21725,"operation_count":3,"complexity_ratio":7241.666666666667,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":1551,"base":3},"right_expr":{"type":"numeric_atoms","value":5958,"base":3}},"right_expr":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":3877,"base":3}}},"used_operators":["Ph9nP6C5qx","mp7IySMOzn","D4vGDi5EA2"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1012022010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1551","layer":2},{"info":"number node, value=5958","layer":2},{"info":"compute binary expreesion, left_input=1551, right_input=5958, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=11916","layer":1},{"info":"number node, value=3877","layer":2},{"info":"compute unary expreesion, input=3877, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-11631","layer":1},{"info":"compute binary expreesion, left_input=11916, right_input=-11631, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=23547","layer":0}],"base":3,"result_base":3,"text":"⫏≰2010110⇷⫏≰22011200≧⫂∧(⫏≰12022121≦≮≮)=⫏≰1012022010","reverse_text":"⫏≰1012022010=⫏≰2010110⇷⫏≰22011200≧⫂∧(⫏≰12022121≦≮≮)","cot":[{"info":"⫏≰2010110⇷⫏≰22011200=⫏≰121100100","layer":1},{"info":"⫏≰12022121≦≮≮=⫏≰-120221210","layer":1},{"info":"⫏≰121100100≧⫂∧⫏≰-120221210=⫏≰1012022010","layer":0}]}
{"id":214,"expression_no_base_symbol":"($1571$⫥∨⫟$5145$)⪮%⊝($2895$⨓$3593$)","expression":"(⫏≰2011012⫥∨⫟⫏≰21001120)⪮%⊝(⫏≰10222020⨓⫏≰11221002)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3762,"operation_count":3,"complexity_ratio":1254.0,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1571,"base":3},"right_expr":{"type":"numeric_atoms","value":5145,"base":3}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":2895,"base":3},"right_expr":{"type":"numeric_atoms","value":3593,"base":3}}},"used_operators":["IWmyXbctLI","KYD54nUTWz","3ViojmjbAp"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","8HhzD0ZcuI","rGHVDoGpnC","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1571","layer":2},{"info":"number node, value=5145","layer":2},{"info":"compute binary expreesion, left_input=1571, right_input=5145, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=2895","layer":2},{"info":"number node, value=3593","layer":2},{"info":"compute binary expreesion, left_input=2895, right_input=3593, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-3596","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-3596, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2011012⫥∨⫟⫏≰21001120)⪮%⊝(⫏≰10222020⨓⫏≰11221002)=NaN","reverse_text":"NaN=(⫏≰2011012⫥∨⫟⫏≰21001120)⪮%⊝(⫏≰10222020⨓⫏≰11221002)","cot":[{"info":"⫏≰2011012⫥∨⫟⫏≰21001120=NaN","layer":1},{"info":"⫏≰10222020⨓⫏≰11221002=⫏≰-11221012","layer":1},{"info":"NaN⪮%⊝⫏≰-11221012=NaN","layer":0}]}
{"id":215,"expression_no_base_symbol":"$6055$≧⫂∧$3286$⋓($4207$≭$1690$)","expression":"⫏≰22022021≧⫂∧⫏≰11111201⋓(⫏≰12202211≭⫏≰2022121)","highest_n_order":5,"priority_hierarchical_complexity":2,"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":6055,"base":3},"right_expr":{"type":"numeric_atoms","value":3286,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":4207,"base":3},"right_expr":{"type":"numeric_atoms","value":1690,"base":3}}},"used_operators":["T2fj7uvVaJ","Ph9nP6C5qx","rxpJgHHUmx"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rysDP5nf3Z","t8gj7n24qd","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6055","layer":2},{"info":"number node, value=3286","layer":2},{"info":"compute binary expreesion, left_input=6055, right_input=3286, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=2813","layer":1},{"info":"number node, value=4207","layer":2},{"info":"number node, value=1690","layer":2},{"info":"compute binary expreesion, left_input=4207, right_input=1690, 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=2813, 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":3,"result_base":3,"text":"⫏≰22022021≧⫂∧⫏≰11111201⋓(⫏≰12202211≭⫏≰2022121)=NaN","reverse_text":"NaN=⫏≰22022021≧⫂∧⫏≰11111201⋓(⫏≰12202211≭⫏≰2022121)","cot":[{"info":"⫏≰22022021≧⫂∧⫏≰11111201=⫏≰10212012","layer":1},{"info":"⫏≰12202211≭⫏≰2022121=NaN","layer":1},{"info":"⫏≰10212012⋓NaN=NaN","layer":0}]}
{"id":216,"expression_no_base_symbol":"$4553$⪄$1089$⪨≂$7825$⊭↱$5965$","expression":"⫏≰20020122⪄⫏≰1111100⪨≂⫏≰101201211⊭↱⫏≰22011221","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":106,"operation_count":3,"complexity_ratio":35.333333333333336,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":4553,"base":3},"right_expr":{"type":"numeric_atoms","value":1089,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":7825,"base":3},"right_expr":{"type":"numeric_atoms","value":5965,"base":3}}},"used_operators":["sdazOOVcIp","SUmda5xLS4","COABgblf1C"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-2112010120101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4553","layer":2},{"info":"number node, value=1089","layer":2},{"info":"compute binary expreesion, left_input=4553, right_input=1089, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-674289","layer":1},{"info":"number node, value=7825","layer":2},{"info":"number node, value=5965","layer":2},{"info":"compute binary expreesion, left_input=7825, right_input=5965, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-3715","layer":1},{"info":"compute binary expreesion, left_input=-674289, right_input=-3715, 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=-1341046","layer":0}],"base":3,"result_base":3,"text":"⫏≰20020122⪄⫏≰1111100⪨≂⫏≰101201211⊭↱⫏≰22011221=⫏≰-2112010120101","reverse_text":"⫏≰-2112010120101=⫏≰20020122⪄⫏≰1111100⪨≂⫏≰101201211⊭↱⫏≰22011221","cot":[{"info":"⫏≰20020122⪄⫏≰1111100=⫏≰-1021020221200","layer":1},{"info":"⫏≰101201211⊭↱⫏≰22011221=⫏≰-12002121","layer":1},{"info":"⫏≰-1021020221200⪨≂⫏≰-12002121=⫏≰-2112010120101","layer":0}]}
{"id":217,"expression_no_base_symbol":"$4431$⪮%⊝$1925$⊉≛↸$1341$∑⇟⊟$2113$","expression":"⫏≰20002010⪮%⊝⫏≰2122022⊉≛↸⫏≰1211200∑⇟⊟⫏≰2220021","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":4431,"base":3},"right_expr":{"type":"numeric_atoms","value":1925,"base":3}},"right_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":1341,"base":3},"right_expr":{"type":"numeric_atoms","value":2113,"base":3}}},"used_operators":["DZ8iAZOCBD","IWmyXbctLI","U7g4x0WXJJ"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"⫏≰221011212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4431","layer":2},{"info":"number node, value=1925","layer":2},{"info":"compute binary expreesion, left_input=4431, right_input=1925, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=9178","layer":1},{"info":"number node, value=1341","layer":2},{"info":"number node, value=2113","layer":2},{"info":"compute binary expreesion, left_input=1341, right_input=2113, 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=9178, right_input=nan, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=18356","layer":0}],"base":3,"result_base":3,"text":"⫏≰20002010⪮%⊝⫏≰2122022⊉≛↸⫏≰1211200∑⇟⊟⫏≰2220021=⫏≰221011212","reverse_text":"⫏≰221011212=⫏≰20002010⪮%⊝⫏≰2122022⊉≛↸⫏≰1211200∑⇟⊟⫏≰2220021","cot":[{"info":"⫏≰20002010⪮%⊝⫏≰2122022=⫏≰110120221","layer":1},{"info":"⫏≰1211200∑⇟⊟⫏≰2220021=NaN","layer":1},{"info":"⫏≰110120221⊉≛↸NaN=⫏≰221011212","layer":0}]}
{"id":218,"expression_no_base_symbol":"($3039$⇋≉)⪒$4796$⫸⊐$4119$","expression":"(⫏≰11011120⇋≉)⪒⫏≰20120122⫸⊐⫏≰12122120","highest_n_order":2,"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":3039,"base":3}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":4796,"base":3},"right_expr":{"type":"numeric_atoms","value":4119,"base":3}}},"used_operators":["f6k1SAg4EE","XIabStNQrY","mqXw5SEYmG"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"⫏≰-1010122002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3039","layer":2},{"info":"compute unary expreesion, input=3039, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=5980","layer":1},{"info":"number node, value=4796","layer":2},{"info":"number node, value=4119","layer":2},{"info":"compute binary expreesion, left_input=4796, right_input=4119, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=16351","layer":1},{"info":"compute binary expreesion, left_input=5980, right_input=16351, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-22331","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11011120⇋≉)⪒⫏≰20120122⫸⊐⫏≰12122120=⫏≰-1010122002","reverse_text":"⫏≰-1010122002=(⫏≰11011120⇋≉)⪒⫏≰20120122⫸⊐⫏≰12122120","cot":[{"info":"⫏≰11011120⇋≉=⫏≰22012111","layer":1},{"info":"⫏≰20120122⫸⊐⫏≰12122120=⫏≰211102121","layer":1},{"info":"⫏≰22012111⪒⫏≰211102121=⫏≰-1010122002","layer":0}]}
{"id":219,"expression_no_base_symbol":"(⇁⨣⪵$2436$)⊭∹↮","expression":"(⇁⨣⪵⫏≰10100020)⊭∹↮","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7,"operation_count":2,"complexity_ratio":3.5,"tree":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":2436,"base":3}}},"used_operators":["xNBdhnnwKq","inkyxCbjAn"],"dependent_operators":["2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2436","layer":2},{"info":"compute unary expreesion, input=2436, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', 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":3,"result_base":3,"text":"(⇁⨣⪵⫏≰10100020)⊭∹↮=NaN","reverse_text":"NaN=(⇁⨣⪵⫏≰10100020)⊭∹↮","cot":[{"info":"⇁⨣⪵⫏≰10100020=NaN","layer":1},{"info":"NaN⊭∹↮=NaN","layer":0}]}
{"id":220,"expression_no_base_symbol":"$6532$⩷∴$1785$↺($2563$⊭↱$1660$)","expression":"⫏≰22221221⩷∴⫏≰2110010↺(⫏≰10111221⊭↱⫏≰2021111)","highest_n_order":1,"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":6532,"base":3},"right_expr":{"type":"numeric_atoms","value":1785,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":2563,"base":3},"right_expr":{"type":"numeric_atoms","value":1660,"base":3}}},"used_operators":["7j4O788W3g","9FxExcQeMw","COABgblf1C"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-2110201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6532","layer":2},{"info":"number node, value=1785","layer":2},{"info":"compute binary expreesion, left_input=6532, right_input=1785, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=9462","layer":1},{"info":"number node, value=2563","layer":2},{"info":"number node, value=1660","layer":2},{"info":"compute binary expreesion, left_input=2563, right_input=1660, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-1801","layer":1},{"info":"compute binary expreesion, left_input=9462, right_input=-1801, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=-1801","layer":0}],"base":3,"result_base":3,"text":"⫏≰22221221⩷∴⫏≰2110010↺(⫏≰10111221⊭↱⫏≰2021111)=⫏≰-2110201","reverse_text":"⫏≰-2110201=⫏≰22221221⩷∴⫏≰2110010↺(⫏≰10111221⊭↱⫏≰2021111)","cot":[{"info":"⫏≰22221221⩷∴⫏≰2110010=⫏≰110222110","layer":1},{"info":"⫏≰10111221⊭↱⫏≰2021111=⫏≰-2110201","layer":1},{"info":"⫏≰110222110↺⫏≰-2110201=⫏≰-2110201","layer":0}]}
{"id":221,"expression_no_base_symbol":"⨑⩽⪐(↯⪼$2139$)","expression":"⨑⩽⪐(↯⪼⫏≰2221020)","highest_n_order":2,"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":2139,"base":3}}},"used_operators":["AF7qkfDlqP","8jW3W4yZS5"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp"],"result":"⫏≰1010210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2139","layer":2},{"info":"compute unary expreesion, input=2139, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":1},{"info":"compute unary expreesion, input=-21, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=831","layer":0}],"base":3,"result_base":3,"text":"⨑⩽⪐(↯⪼⫏≰2221020)=⫏≰1010210","reverse_text":"⫏≰1010210=⨑⩽⪐(↯⪼⫏≰2221020)","cot":[{"info":"↯⪼⫏≰2221020=⫏≰-210","layer":1},{"info":"⨑⩽⪐⫏≰-210=⫏≰1010210","layer":0}]}
{"id":222,"expression_no_base_symbol":"($2405$≧⫂∧$3059$)↬(⨈⫕$1852$)","expression":"(⫏≰10022002≧⫂∧⫏≰11012022)↬(⨈⫕⫏≰2112121)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":388,"operation_count":3,"complexity_ratio":129.33333333333334,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":2405,"base":3},"right_expr":{"type":"numeric_atoms","value":3059,"base":3}},"right_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":1852,"base":3}}},"used_operators":["B5M0gjZbta","Ph9nP6C5qx","megm06wKyl"],"dependent_operators":["rGHVDoGpnC","rysDP5nf3Z","t8gj7n24qd","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2405","layer":2},{"info":"number node, value=3059","layer":2},{"info":"compute binary expreesion, left_input=2405, right_input=3059, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=2586","layer":1},{"info":"number node, value=1852","layer":2},{"info":"compute unary expreesion, input=1852, 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=2586, right_input=-21, 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":3,"result_base":3,"text":"(⫏≰10022002≧⫂∧⫏≰11012022)↬(⨈⫕⫏≰2112121)=NaN","reverse_text":"NaN=(⫏≰10022002≧⫂∧⫏≰11012022)↬(⨈⫕⫏≰2112121)","cot":[{"info":"⫏≰10022002≧⫂∧⫏≰11012022=⫏≰10112210","layer":1},{"info":"⨈⫕⫏≰2112121=⫏≰-210","layer":1},{"info":"⫏≰10112210↬⫏≰-210=NaN","layer":0}]}
{"id":223,"expression_no_base_symbol":"($1029$-$1836$)⊭↱($1466$⊉≛↸$1241$)","expression":"(⫏≰1102010-⫏≰2112000)⊭↱(⫏≰2000022⊉≛↸⫏≰1200222)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1029,"base":3},"right_expr":{"type":"numeric_atoms","value":1836,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":1466,"base":3},"right_expr":{"type":"numeric_atoms","value":1241,"base":3}}},"used_operators":["COABgblf1C","rysDP5nf3Z","DZ8iAZOCBD"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰101021011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1029","layer":2},{"info":"number node, value=1836","layer":2},{"info":"compute binary expreesion, left_input=1029, right_input=1836, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-807","layer":1},{"info":"number node, value=1466","layer":2},{"info":"number node, value=1241","layer":2},{"info":"compute binary expreesion, left_input=1466, right_input=1241, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=2932","layer":1},{"info":"compute binary expreesion, left_input=-807, right_input=2932, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=7483","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1102010-⫏≰2112000)⊭↱(⫏≰2000022⊉≛↸⫏≰1200222)=⫏≰101021011","reverse_text":"⫏≰101021011=(⫏≰1102010-⫏≰2112000)⊭↱(⫏≰2000022⊉≛↸⫏≰1200222)","cot":[{"info":"⫏≰1102010-⫏≰2112000=⫏≰-1002220","layer":1},{"info":"⫏≰2000022⊉≛↸⫏≰1200222=⫏≰11000121","layer":1},{"info":"⫏≰-1002220⊭↱⫏≰11000121=⫏≰101021011","layer":0}]}
{"id":224,"expression_no_base_symbol":"↥$1418$∀⇚≩$9140$","expression":"↥⫏≰1221112∀⇚≩⫏≰110112112","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9927,"operation_count":2,"complexity_ratio":4963.5,"tree":{"type":"unary","operator":"↥","unary_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":1418,"base":3},"right_expr":{"type":"numeric_atoms","value":9140,"base":3}}},"used_operators":["A8NUZmVepG","LRNGc0VcxI"],"dependent_operators":["k8jYdgA6NY","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1418","layer":2},{"info":"number node, value=9140","layer":2},{"info":"compute binary expreesion, left_input=1418, right_input=9140, 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 = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↥⫏≰1221112∀⇚≩⫏≰110112112=NaN","reverse_text":"NaN=↥⫏≰1221112∀⇚≩⫏≰110112112","cot":[{"info":"⫏≰1221112∀⇚≩⫏≰110112112=NaN","layer":1},{"info":"↥NaN=NaN","layer":0}]}
{"id":225,"expression_no_base_symbol":"$3735$⊴$4778$⋷$1663$⊴$1122$","expression":"⫏≰12010100⊴⫏≰20112222⋷⫏≰2021121⊴⫏≰1112120","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8892,"operation_count":3,"complexity_ratio":2964.0,"tree":{"type":"binary","operator":"⋷","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":3735,"base":3},"right_expr":{"type":"numeric_atoms","value":4778,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1663,"base":3},"right_expr":{"type":"numeric_atoms","value":1122,"base":3}}},"used_operators":["23Mk6UjR3U","Nsiff2A1zJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3735","layer":2},{"info":"number node, value=4778","layer":2},{"info":"compute binary expreesion, left_input=3735, right_input=4778, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=1663","layer":2},{"info":"number node, value=1122","layer":2},{"info":"compute binary expreesion, left_input=1663, right_input=1122, 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 = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰12010100⊴⫏≰20112222⋷⫏≰2021121⊴⫏≰1112120=NaN","reverse_text":"NaN=⫏≰12010100⊴⫏≰20112222⋷⫏≰2021121⊴⫏≰1112120","cot":[{"info":"⫏≰12010100⊴⫏≰20112222=NaN","layer":1},{"info":"⫏≰2021121⊴⫏≰1112120=NaN","layer":1},{"info":"NaN⋷NaN=NaN","layer":0}]}
{"id":226,"expression_no_base_symbol":"$2254$≧⫂∧$1430$⋷($3972$⋷$4855$)","expression":"⫏≰10002111≧⫂∧⫏≰1221222⋷(⫏≰12110010⋷⫏≰20122211)","highest_n_order":1,"priority_hierarchical_complexity":2,"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":2254,"base":3},"right_expr":{"type":"numeric_atoms","value":1430,"base":3}},"right_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":3972,"base":3},"right_expr":{"type":"numeric_atoms","value":4855,"base":3}}},"used_operators":["23Mk6UjR3U","Ph9nP6C5qx"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰112102121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2254","layer":2},{"info":"number node, value=1430","layer":2},{"info":"compute binary expreesion, left_input=2254, right_input=1430, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=957","layer":1},{"info":"number node, value=3972","layer":2},{"info":"number node, value=4855","layer":2},{"info":"compute binary expreesion, left_input=3972, right_input=4855, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=5738","layer":1},{"info":"compute binary expreesion, left_input=957, right_input=5738, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=10519","layer":0}],"base":3,"result_base":3,"text":"⫏≰10002111≧⫂∧⫏≰1221222⋷(⫏≰12110010⋷⫏≰20122211)=⫏≰112102121","reverse_text":"⫏≰112102121=⫏≰10002111≧⫂∧⫏≰1221222⋷(⫏≰12110010⋷⫏≰20122211)","cot":[{"info":"⫏≰10002111≧⫂∧⫏≰1221222=⫏≰1022110","layer":1},{"info":"⫏≰12110010⋷⫏≰20122211=⫏≰21212112","layer":1},{"info":"⫏≰1022110⋷⫏≰21212112=⫏≰112102121","layer":0}]}
{"id":227,"expression_no_base_symbol":"$6134$⨎$1553$↛⩡⫤","expression":"⫏≰22102012⨎⫏≰2010112↛⩡⫤","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4794,"operation_count":2,"complexity_ratio":2397.0,"tree":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":6134,"base":3},"right_expr":{"type":"numeric_atoms","value":1553,"base":3}}},"used_operators":["FU0Cs4j7VP","rJVOvQCfKK"],"dependent_operators":["8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"⫏≰-102201022110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6134","layer":2},{"info":"number node, value=1553","layer":2},{"info":"compute binary expreesion, left_input=6134, right_input=1553, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=1553","layer":1},{"info":"compute unary expreesion, input=1553, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-230592","layer":0}],"base":3,"result_base":3,"text":"⫏≰22102012⨎⫏≰2010112↛⩡⫤=⫏≰-102201022110","reverse_text":"⫏≰-102201022110=⫏≰22102012⨎⫏≰2010112↛⩡⫤","cot":[{"info":"⫏≰22102012⨎⫏≰2010112=⫏≰2010112","layer":1},{"info":"⫏≰2010112↛⩡⫤=⫏≰-102201022110","layer":0}]}
{"id":228,"expression_no_base_symbol":"(⨰⫟⨤$2423$)⨓(⨵≀≌$1865$)","expression":"(⨰⫟⨤⫏≰10022202)⨓(⨵≀≌⫏≰2120002)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":14456,"operation_count":3,"complexity_ratio":4818.666666666667,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":2423,"base":3}},"right_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":1865,"base":3}}},"used_operators":["3ViojmjbAp","Tw270M8GLb","srAu1WTS94"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A"],"result":"⫏≰-21200100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2423","layer":2},{"info":"compute unary expreesion, input=2423, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":1},{"info":"number node, value=1865","layer":2},{"info":"compute unary expreesion, input=1865, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-5595","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-5595, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-5598","layer":0}],"base":3,"result_base":3,"text":"(⨰⫟⨤⫏≰10022202)⨓(⨵≀≌⫏≰2120002)=⫏≰-21200100","reverse_text":"⫏≰-21200100=(⨰⫟⨤⫏≰10022202)⨓(⨵≀≌⫏≰2120002)","cot":[{"info":"⨰⫟⨤⫏≰10022202=NaN","layer":1},{"info":"⨵≀≌⫏≰2120002=⫏≰-21200020","layer":1},{"info":"NaN⨓⫏≰-21200020=⫏≰-21200100","layer":0}]}
{"id":229,"expression_no_base_symbol":"($2667$⋷$5104$)⩨($1023$⊠≄⫣)","expression":"(⫏≰10122210⋷⫏≰21000001)⩨(⫏≰1101220⊠≄⫣)","highest_n_order":2,"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":2667,"base":3},"right_expr":{"type":"numeric_atoms","value":5104,"base":3}},"right_expr":{"type":"unary","operator":"⊠≄⫣","unary_expr":{"type":"numeric_atoms","value":1023,"base":3}}},"used_operators":["2DlMacCsIx","23Mk6UjR3U","DIvbN7qnHd"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2667","layer":2},{"info":"number node, value=5104","layer":2},{"info":"compute binary expreesion, left_input=2667, right_input=5104, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=7541","layer":1},{"info":"number node, value=1023","layer":2},{"info":"compute unary expreesion, input=1023, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=7541, right_input=0, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10122210⋷⫏≰21000001)⩨(⫏≰1101220⊠≄⫣)=⫏≰0","reverse_text":"⫏≰0=(⫏≰10122210⋷⫏≰21000001)⩨(⫏≰1101220⊠≄⫣)","cot":[{"info":"⫏≰10122210⋷⫏≰21000001=⫏≰101100022","layer":1},{"info":"⫏≰1101220⊠≄⫣=⫏≰0","layer":1},{"info":"⫏≰101100022⩨⫏≰0=⫏≰0","layer":0}]}
{"id":230,"expression_no_base_symbol":"$1050$⪒$1517$⪨≂$2649$⊉≛↸$2139$","expression":"⫏≰1102220⪒⫏≰2002012⪨≂⫏≰10122010⊉≛↸⫏≰2221020","highest_n_order":1,"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":1050,"base":3},"right_expr":{"type":"numeric_atoms","value":1517,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":2649,"base":3},"right_expr":{"type":"numeric_atoms","value":2139,"base":3}}},"used_operators":["sdazOOVcIp","f6k1SAg4EE","DZ8iAZOCBD"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-210102211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1050","layer":2},{"info":"number node, value=1517","layer":2},{"info":"compute binary expreesion, left_input=1050, right_input=1517, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-2567","layer":1},{"info":"number node, value=2649","layer":2},{"info":"number node, value=2139","layer":2},{"info":"compute binary expreesion, left_input=2649, right_input=2139, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=5298","layer":1},{"info":"compute binary expreesion, left_input=-2567, right_input=5298, 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=-15628","layer":0}],"base":3,"result_base":3,"text":"⫏≰1102220⪒⫏≰2002012⪨≂⫏≰10122010⊉≛↸⫏≰2221020=⫏≰-210102211","reverse_text":"⫏≰-210102211=⫏≰1102220⪒⫏≰2002012⪨≂⫏≰10122010⊉≛↸⫏≰2221020","cot":[{"info":"⫏≰1102220⪒⫏≰2002012=⫏≰-10112002","layer":1},{"info":"⫏≰10122010⊉≛↸⫏≰2221020=⫏≰21021020","layer":1},{"info":"⫏≰-10112002⪨≂⫏≰21021020=⫏≰-210102211","layer":0}]}
{"id":231,"expression_no_base_symbol":"↥($7229$⫡⨏$5617$)","expression":"↥(⫏≰100220202⫡⨏⫏≰21201001)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":951,"operation_count":2,"complexity_ratio":475.5,"tree":{"type":"unary","operator":"↥","unary_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":7229,"base":3},"right_expr":{"type":"numeric_atoms","value":5617,"base":3}}},"used_operators":["A8NUZmVepG","QMFrweE19q"],"dependent_operators":["k8jYdgA6NY","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7229","layer":2},{"info":"number node, value=5617","layer":2},{"info":"compute binary expreesion, left_input=7229, right_input=5617, 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=48162","layer":1},{"info":"compute unary expreesion, input=48162, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=18","layer":0}],"base":3,"result_base":3,"text":"↥(⫏≰100220202⫡⨏⫏≰21201001)=⫏≰200","reverse_text":"⫏≰200=↥(⫏≰100220202⫡⨏⫏≰21201001)","cot":[{"info":"⫏≰100220202⫡⨏⫏≰21201001=⫏≰2110001210","layer":1},{"info":"↥⫏≰2110001210=⫏≰200","layer":0}]}
{"id":232,"expression_no_base_symbol":"($6312$⋫)⫩⊇","expression":"(⫏≰22122210⋫)⫩⊇","highest_n_order":3,"priority_hierarchical_complexity":1,"normalized_expansion_degree":6314,"operation_count":2,"complexity_ratio":3157.0,"tree":{"type":"unary","operator":"⫩⊇","unary_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":6312,"base":3}}},"used_operators":["BjRHVeLaeN","JL8yIekQnl"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","tmPS8pqC7x"],"result":"⫏≰-22121020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6312","layer":2},{"info":"compute unary expreesion, input=6312, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=6312","layer":1},{"info":"compute unary expreesion, input=6312, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=-6270","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22122210⋫)⫩⊇=⫏≰-22121020","reverse_text":"⫏≰-22121020=(⫏≰22122210⋫)⫩⊇","cot":[{"info":"⫏≰22122210⋫=⫏≰22122210","layer":1},{"info":"⫏≰22122210⫩⊇=⫏≰-22121020","layer":0}]}
{"id":233,"expression_no_base_symbol":"(≤/$1487$)⨸⪁$4489$⪘⫢$2381$","expression":"(≤/⫏≰2001002)⨸⪁⫏≰20011021⪘⫢⫏≰10021012","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":1487,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":4489,"base":3},"right_expr":{"type":"numeric_atoms","value":2381,"base":3}}},"used_operators":["g55IO6H4Gj","eLAdDNolq6","oacrs7FA3X"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⫏≰210112120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1487","layer":2},{"info":"compute unary expreesion, input=1487, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-1003","layer":1},{"info":"number node, value=4489","layer":2},{"info":"number node, value=2381","layer":2},{"info":"compute binary expreesion, left_input=4489, right_input=2381, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=8854","layer":1},{"info":"compute binary expreesion, left_input=-1003, right_input=8854, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=15702","layer":0}],"base":3,"result_base":3,"text":"(≤/⫏≰2001002)⨸⪁⫏≰20011021⪘⫢⫏≰10021012=⫏≰210112120","reverse_text":"⫏≰210112120=(≤/⫏≰2001002)⨸⪁⫏≰20011021⪘⫢⫏≰10021012","cot":[{"info":"≤/⫏≰2001002=⫏≰-1101011","layer":1},{"info":"⫏≰20011021⪘⫢⫏≰10021012=⫏≰110010221","layer":1},{"info":"⫏≰-1101011⨸⪁⫏≰110010221=⫏≰210112120","layer":0}]}
{"id":234,"expression_no_base_symbol":"⊙↵-($1404$⊭↱$1108$)","expression":"⊙↵-(⫏≰1221000⊭↱⫏≰1112001)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":625,"operation_count":2,"complexity_ratio":312.5,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":1404,"base":3},"right_expr":{"type":"numeric_atoms","value":1108,"base":3}}},"used_operators":["oWn0xqSxBt","COABgblf1C"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21021","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1404","layer":2},{"info":"number node, value=1108","layer":2},{"info":"compute binary expreesion, left_input=1404, right_input=1108, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-587","layer":1},{"info":"compute unary expreesion, input=-587, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=196","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⫏≰1221000⊭↱⫏≰1112001)=⫏≰21021","reverse_text":"⫏≰21021=⊙↵-(⫏≰1221000⊭↱⫏≰1112001)","cot":[{"info":"⫏≰1221000⊭↱⫏≰1112001=⫏≰-210202","layer":1},{"info":"⊙↵-⫏≰-210202=⫏≰21021","layer":0}]}
{"id":235,"expression_no_base_symbol":"⨵≀≌($8159$⩨$1067$)","expression":"⨵≀≌(⫏≰102012012⩨⫏≰1110112)","highest_n_order":2,"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":8159,"base":3},"right_expr":{"type":"numeric_atoms","value":1067,"base":3}}},"used_operators":["srAu1WTS94","2DlMacCsIx"],"dependent_operators":["glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=8159","layer":2},{"info":"number node, value=1067","layer":2},{"info":"compute binary expreesion, left_input=8159, right_input=1067, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"⨵≀≌(⫏≰102012012⩨⫏≰1110112)=⫏≰0","reverse_text":"⫏≰0=⨵≀≌(⫏≰102012012⩨⫏≰1110112)","cot":[{"info":"⫏≰102012012⩨⫏≰1110112=⫏≰0","layer":1},{"info":"⨵≀≌⫏≰0=⫏≰0","layer":0}]}
{"id":236,"expression_no_base_symbol":"↥($2894$⋷$3015$)","expression":"↥(⫏≰10222012⋷⫏≰11010200)","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":2894,"base":3},"right_expr":{"type":"numeric_atoms","value":3015,"base":3}}},"used_operators":["A8NUZmVepG","23Mk6UjR3U"],"dependent_operators":["k8jYdgA6NY","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2894","layer":2},{"info":"number node, value=3015","layer":2},{"info":"compute binary expreesion, left_input=2894, right_input=3015, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=3136","layer":1},{"info":"compute unary expreesion, input=3136, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=25","layer":0}],"base":3,"result_base":3,"text":"↥(⫏≰10222012⋷⫏≰11010200)=⫏≰221","reverse_text":"⫏≰221=↥(⫏≰10222012⋷⫏≰11010200)","cot":[{"info":"⫏≰10222012⋷⫏≰11010200=⫏≰11022011","layer":1},{"info":"↥⫏≰11022011=⫏≰221","layer":0}]}
{"id":237,"expression_no_base_symbol":"$7994$⨪↰⇹$2608$⪄$4535$↬$3748$","expression":"⫏≰101222002⨪↰⇹⫏≰10120121⪄⫏≰20012222↬⫏≰12010211","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8089,"operation_count":3,"complexity_ratio":2696.3333333333335,"tree":{"type":"binary","operator":"⪄","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":7994,"base":3},"right_expr":{"type":"numeric_atoms","value":2608,"base":3}},"right_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":4535,"base":3},"right_expr":{"type":"numeric_atoms","value":3748,"base":3}}},"used_operators":["SUmda5xLS4","tmPS8pqC7x","B5M0gjZbta"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","rJVOvQCfKK","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7994","layer":2},{"info":"number node, value=2608","layer":2},{"info":"compute binary expreesion, left_input=7994, right_input=2608, 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=7994","layer":1},{"info":"number node, value=4535","layer":2},{"info":"number node, value=3748","layer":2},{"info":"compute binary expreesion, left_input=4535, right_input=3748, 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=7994, right_input=nan, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰101222002⨪↰⇹⫏≰10120121⪄⫏≰20012222↬⫏≰12010211=NaN","reverse_text":"NaN=⫏≰101222002⨪↰⇹⫏≰10120121⪄⫏≰20012222↬⫏≰12010211","cot":[{"info":"⫏≰101222002⨪↰⇹⫏≰10120121=⫏≰101222002","layer":1},{"info":"⫏≰20012222↬⫏≰12010211=NaN","layer":1},{"info":"⫏≰101222002⪄NaN=NaN","layer":0}]}
{"id":238,"expression_no_base_symbol":"($1189$⨸⪁$1118$)⩷∴$1385$⪮%⊝$1687$","expression":"(⫏≰1122001⨸⪁⫏≰1112102)⩷∴⫏≰1220022⪮%⊝⫏≰2022111","highest_n_order":2,"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":1189,"base":3},"right_expr":{"type":"numeric_atoms","value":1118,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1385,"base":3},"right_expr":{"type":"numeric_atoms","value":1687,"base":3}}},"used_operators":["9FxExcQeMw","g55IO6H4Gj","IWmyXbctLI"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰11011000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1189","layer":2},{"info":"number node, value=1118","layer":2},{"info":"compute binary expreesion, left_input=1189, right_input=1118, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=4614","layer":1},{"info":"number node, value=1385","layer":2},{"info":"number node, value=1687","layer":2},{"info":"compute binary expreesion, left_input=1385, right_input=1687, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=3086","layer":1},{"info":"compute binary expreesion, left_input=4614, right_input=3086, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=3024","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1122001⨸⪁⫏≰1112102)⩷∴⫏≰1220022⪮%⊝⫏≰2022111=⫏≰11011000","reverse_text":"⫏≰11011000=(⫏≰1122001⨸⪁⫏≰1112102)⩷∴⫏≰1220022⪮%⊝⫏≰2022111","cot":[{"info":"⫏≰1122001⨸⪁⫏≰1112102=⫏≰20022220","layer":1},{"info":"⫏≰1220022⪮%⊝⫏≰2022111=⫏≰11020022","layer":1},{"info":"⫏≰20022220⩷∴⫏≰11020022=⫏≰11011000","layer":0}]}
{"id":239,"expression_no_base_symbol":"$1219$⇼⇔∾$6701$∲⫓$2197$≧⫂∧$1201$","expression":"⫏≰1200011⇼⇔∾⫏≰100012012∲⫓⫏≰10000101≧⫂∧⫏≰1122111","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5,"operation_count":3,"complexity_ratio":1.6666666666666667,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":1219,"base":3},"right_expr":{"type":"numeric_atoms","value":6701,"base":3}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":2197,"base":3},"right_expr":{"type":"numeric_atoms","value":1201,"base":3}}},"used_operators":["i8ToyICDmI","tifHPKVTfV","Ph9nP6C5qx"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1219","layer":2},{"info":"number node, value=6701","layer":2},{"info":"compute binary expreesion, left_input=1219, right_input=6701, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=5482","layer":1},{"info":"number node, value=2197","layer":2},{"info":"number node, value=1201","layer":2},{"info":"compute binary expreesion, left_input=2197, right_input=1201, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=728","layer":1},{"info":"compute binary expreesion, left_input=5482, right_input=728, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫏≰1200011⇼⇔∾⫏≰100012012∲⫓⫏≰10000101≧⫂∧⫏≰1122111=⫏≰0","reverse_text":"⫏≰0=⫏≰1200011⇼⇔∾⫏≰100012012∲⫓⫏≰10000101≧⫂∧⫏≰1122111","cot":[{"info":"⫏≰1200011⇼⇔∾⫏≰100012012=⫏≰21112001","layer":1},{"info":"⫏≰10000101≧⫂∧⫏≰1122111=⫏≰222222","layer":1},{"info":"⫏≰21112001∲⫓⫏≰222222=⫏≰0","layer":0}]}
{"id":240,"expression_no_base_symbol":"⊙↵-($4398$∧)","expression":"⊙↵-(⫏≰20000220∧)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":33,"operation_count":2,"complexity_ratio":16.5,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"unary","operator":"∧","unary_expr":{"type":"numeric_atoms","value":4398,"base":3}}},"used_operators":["oWn0xqSxBt","z63VuFQld9"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4398","layer":2},{"info":"compute unary expreesion, input=4398, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⫏≰20000220∧)=NaN","reverse_text":"NaN=⊙↵-(⫏≰20000220∧)","cot":[{"info":"⫏≰20000220∧=NaN","layer":1},{"info":"⊙↵-NaN=NaN","layer":0}]}
{"id":241,"expression_no_base_symbol":"($3203$⫸⊐$3312$)⨐⩸⫘(↯⪼$1011$)","expression":"(⫏≰11101122⫸⊐⫏≰11112200)⨐⩸⫘(↯⪼⫏≰1101110)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":622,"operation_count":3,"complexity_ratio":207.33333333333334,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":3203,"base":3},"right_expr":{"type":"numeric_atoms","value":3312,"base":3}},"right_expr":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"numeric_atoms","value":1011,"base":3}}},"used_operators":["fu6greOZ01","mqXw5SEYmG","8jW3W4yZS5"],"dependent_operators":["3ViojmjbAp","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp"],"result":"⫏≰220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3203","layer":2},{"info":"number node, value=3312","layer":2},{"info":"compute binary expreesion, left_input=3203, right_input=3312, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=13123","layer":1},{"info":"number node, value=1011","layer":2},{"info":"compute unary expreesion, input=1011, 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=13123, right_input=-21, 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=24","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11101122⫸⊐⫏≰11112200)⨐⩸⫘(↯⪼⫏≰1101110)=⫏≰220","reverse_text":"⫏≰220=(⫏≰11101122⫸⊐⫏≰11112200)⨐⩸⫘(↯⪼⫏≰1101110)","cot":[{"info":"⫏≰11101122⫸⊐⫏≰11112200=⫏≰200000001","layer":1},{"info":"↯⪼⫏≰1101110=⫏≰-210","layer":1},{"info":"⫏≰200000001⨐⩸⫘⫏≰-210=⫏≰220","layer":0}]}
{"id":242,"expression_no_base_symbol":"($2719$⇋≉)⋓(-$2383$)","expression":"(⫏≰10201201⇋≉)⋓(-⫏≰10021021)","highest_n_order":3,"priority_hierarchical_complexity":2,"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":2719,"base":3}},"right_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":2383,"base":3}}},"used_operators":["T2fj7uvVaJ","XIabStNQrY","t8gj7n24qd"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2719","layer":2},{"info":"compute unary expreesion, input=2719, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=5340","layer":1},{"info":"number node, value=2383","layer":2},{"info":"compute unary expreesion, input=2383, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-2383","layer":1},{"info":"compute binary expreesion, left_input=5340, right_input=-2383, 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":3,"result_base":3,"text":"(⫏≰10201201⇋≉)⋓(-⫏≰10021021)=⫏≰0","reverse_text":"⫏≰0=(⫏≰10201201⇋≉)⋓(-⫏≰10021021)","cot":[{"info":"⫏≰10201201⇋≉=⫏≰21022210","layer":1},{"info":"-⫏≰10021021=⫏≰-10021021","layer":1},{"info":"⫏≰21022210⋓⫏≰-10021021=⫏≰0","layer":0}]}
{"id":243,"expression_no_base_symbol":"(⨞⊢$1977$)↙(≦∁$5070$)","expression":"(⨞⊢⫏≰2201020)↙(≦∁⫏≰20221210)","highest_n_order":3,"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":1977,"base":3}},"right_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":5070,"base":3}}},"used_operators":["yyfyN0ffXY","xUOZtlo3hN","9ICcGScMcE"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"⫏≰-2221200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1977","layer":2},{"info":"compute unary expreesion, input=1977, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-2151","layer":1},{"info":"number node, value=5070","layer":2},{"info":"compute unary expreesion, input=5070, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=5070","layer":1},{"info":"compute binary expreesion, left_input=-2151, right_input=5070, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-2151","layer":0}],"base":3,"result_base":3,"text":"(⨞⊢⫏≰2201020)↙(≦∁⫏≰20221210)=⫏≰-2221200","reverse_text":"⫏≰-2221200=(⨞⊢⫏≰2201020)↙(≦∁⫏≰20221210)","cot":[{"info":"⨞⊢⫏≰2201020=⫏≰-2221200","layer":1},{"info":"≦∁⫏≰20221210=⫏≰20221210","layer":1},{"info":"⫏≰-2221200↙⫏≰20221210=⫏≰-2221200","layer":0}]}
{"id":244,"expression_no_base_symbol":"↯⪼($8034$⨵⪆$1402$)","expression":"↯⪼(⫏≰102000120⨵⪆⫏≰1220221)","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":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":8034,"base":3},"right_expr":{"type":"numeric_atoms","value":1402,"base":3}}},"used_operators":["8jW3W4yZS5","2DQ55sFlQl"],"dependent_operators":["eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=8034","layer":2},{"info":"number node, value=1402","layer":2},{"info":"compute binary expreesion, left_input=8034, right_input=1402, 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 = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":0}],"base":3,"result_base":3,"text":"↯⪼(⫏≰102000120⨵⪆⫏≰1220221)=⫏≰-210","reverse_text":"⫏≰-210=↯⪼(⫏≰102000120⨵⪆⫏≰1220221)","cot":[{"info":"⫏≰102000120⨵⪆⫏≰1220221=⫏≰12221","layer":1},{"info":"↯⪼⫏≰12221=⫏≰-210","layer":0}]}
{"id":245,"expression_no_base_symbol":"(⪲⇎$1588$)∑⇟⊟($3138$≎⊠⪸$2432$)","expression":"(⪲⇎⫏≰2011211)∑⇟⊟(⫏≰11022020≎⊠⪸⫏≰10100002)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":273,"operation_count":3,"complexity_ratio":91.0,"tree":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":1588,"base":3}},"right_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":3138,"base":3},"right_expr":{"type":"numeric_atoms","value":2432,"base":3}}},"used_operators":["U7g4x0WXJJ","XPYlsWDdGa","bJkvcejdHO"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1588","layer":2},{"info":"compute unary expreesion, input=1588, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=3176","layer":1},{"info":"number node, value=3138","layer":2},{"info":"number node, value=2432","layer":2},{"info":"compute binary expreesion, left_input=3138, right_input=2432, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=812269","layer":1},{"info":"compute binary expreesion, left_input=3176, right_input=812269, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⪲⇎⫏≰2011211)∑⇟⊟(⫏≰11022020≎⊠⪸⫏≰10100002)=NaN","reverse_text":"NaN=(⪲⇎⫏≰2011211)∑⇟⊟(⫏≰11022020≎⊠⪸⫏≰10100002)","cot":[{"info":"⪲⇎⫏≰2011211=⫏≰11100122","layer":1},{"info":"⫏≰11022020≎⊠⪸⫏≰10100002=⫏≰1112021020001","layer":1},{"info":"⫏≰11100122∑⇟⊟⫏≰1112021020001=NaN","layer":0}]}
{"id":246,"expression_no_base_symbol":"⪲⇎($3378$⫌⩹⨱)","expression":"⪲⇎(⫏≰11122010⫌⩹⨱)","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":"unary","operator":"⫌⩹⨱","unary_expr":{"type":"numeric_atoms","value":3378,"base":3}}},"used_operators":["XPYlsWDdGa","EBcxylXtPf"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰211101020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3378","layer":2},{"info":"compute unary expreesion, input=3378, op_id = EBcxylXtPf, unary_op_definition = 'a⫌⩹⨱ = { (((80+a)+(750-a))+((149+422)+(a+a))) }', output=8157","layer":1},{"info":"compute unary expreesion, input=8157, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=16314","layer":0}],"base":3,"result_base":3,"text":"⪲⇎(⫏≰11122010⫌⩹⨱)=⫏≰211101020","reverse_text":"⫏≰211101020=⪲⇎(⫏≰11122010⫌⩹⨱)","cot":[{"info":"⫏≰11122010⫌⩹⨱=⫏≰102012010","layer":1},{"info":"⪲⇎⫏≰102012010=⫏≰211101020","layer":0}]}
{"id":247,"expression_no_base_symbol":"($2115$↬$1314$)∼($7098$⨰$2294$)","expression":"(⫏≰2220100↬⫏≰1210200)∼(⫏≰100201220⨰⫏≰10010222)","highest_n_order":5,"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":2115,"base":3},"right_expr":{"type":"numeric_atoms","value":1314,"base":3}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":7098,"base":3},"right_expr":{"type":"numeric_atoms","value":2294,"base":3}}},"used_operators":["DyGG3AbaNP","B5M0gjZbta","eewbuw0ToL"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","rGHVDoGpnC","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2115","layer":2},{"info":"number node, value=1314","layer":2},{"info":"compute binary expreesion, left_input=2115, right_input=1314, 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=7098","layer":2},{"info":"number node, value=2294","layer":2},{"info":"compute binary expreesion, left_input=7098, right_input=2294, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=4814","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=4814, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2220100↬⫏≰1210200)∼(⫏≰100201220⨰⫏≰10010222)=NaN","reverse_text":"NaN=(⫏≰2220100↬⫏≰1210200)∼(⫏≰100201220⨰⫏≰10010222)","cot":[{"info":"⫏≰2220100↬⫏≰1210200=NaN","layer":1},{"info":"⫏≰100201220⨰⫏≰10010222=⫏≰20121022","layer":1},{"info":"NaN∼⫏≰20121022=NaN","layer":0}]}
{"id":248,"expression_no_base_symbol":"($5087$⪠⩆⊳)⋝⋈⪟($1310$⋳⪒$8318$)","expression":"(⫏≰20222102⪠⩆⊳)⋝⋈⪟(⫏≰1210112⋳⪒⫏≰102102002)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16,"operation_count":3,"complexity_ratio":5.333333333333333,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"numeric_atoms","value":5087,"base":3}},"right_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":1310,"base":3},"right_expr":{"type":"numeric_atoms","value":8318,"base":3}}},"used_operators":["2DDjHMKMc0","JLbD19bQDL","12rbrZMWeM"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5087","layer":2},{"info":"compute unary expreesion, input=5087, 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=1310","layer":2},{"info":"number node, value=8318","layer":2},{"info":"compute binary expreesion, left_input=1310, right_input=8318, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=-5985","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-5985, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20222102⪠⩆⊳)⋝⋈⪟(⫏≰1210112⋳⪒⫏≰102102002)=⫏≰0","reverse_text":"⫏≰0=(⫏≰20222102⪠⩆⊳)⋝⋈⪟(⫏≰1210112⋳⪒⫏≰102102002)","cot":[{"info":"⫏≰20222102⪠⩆⊳=⫏≰0","layer":1},{"info":"⫏≰1210112⋳⪒⫏≰102102002=⫏≰-22012200","layer":1},{"info":"⫏≰0⋝⋈⪟⫏≰-22012200=⫏≰0","layer":0}]}
{"id":249,"expression_no_base_symbol":"≦∁($5123$≦≮≮)","expression":"≦∁(⫏≰21000202≦≮≮)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":80,"operation_count":2,"complexity_ratio":40.0,"tree":{"type":"unary","operator":"≦∁","unary_expr":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":5123,"base":3}}},"used_operators":["9ICcGScMcE","D4vGDi5EA2"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5123","layer":2},{"info":"compute unary expreesion, input=5123, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-15369","layer":1},{"info":"compute unary expreesion, input=-15369, 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":3,"result_base":3,"text":"≦∁(⫏≰21000202≦≮≮)=⫏≰2111","reverse_text":"⫏≰2111=≦∁(⫏≰21000202≦≮≮)","cot":[{"info":"⫏≰21000202≦≮≮=⫏≰-210002020","layer":1},{"info":"≦∁⫏≰-210002020=⫏≰2111","layer":0}]}
{"id":250,"expression_no_base_symbol":"($2154$≦≮≮)⪘⫢($4466$⫌⩹⨱)","expression":"(⫏≰2221210≦≮≮)⪘⫢(⫏≰20010102⫌⩹⨱)","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":2154,"base":3}},"right_expr":{"type":"unary","operator":"⫌⩹⨱","unary_expr":{"type":"numeric_atoms","value":4466,"base":3}}},"used_operators":["oacrs7FA3X","D4vGDi5EA2","EBcxylXtPf"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2154","layer":2},{"info":"compute unary expreesion, input=2154, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-6462","layer":1},{"info":"number node, value=4466","layer":2},{"info":"compute unary expreesion, input=4466, op_id = EBcxylXtPf, unary_op_definition = 'a⫌⩹⨱ = { (((80+a)+(750-a))+((149+422)+(a+a))) }', output=10333","layer":1},{"info":"compute binary expreesion, left_input=-6462, right_input=10333, 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":3,"result_base":3,"text":"(⫏≰2221210≦≮≮)⪘⫢(⫏≰20010102⫌⩹⨱)=⫏≰-1","reverse_text":"⫏≰-1=(⫏≰2221210≦≮≮)⪘⫢(⫏≰20010102⫌⩹⨱)","cot":[{"info":"⫏≰2221210≦≮≮=⫏≰-22212100","layer":1},{"info":"⫏≰20010102⫌⩹⨱=⫏≰112011201","layer":1},{"info":"⫏≰-22212100⪘⫢⫏≰112011201=⫏≰-1","layer":0}]}
{"id":251,"expression_no_base_symbol":"($2215$/$1443$)∧","expression":"(⫏≰10001001/⫏≰1222110)∧","highest_n_order":5,"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":2215,"base":3},"right_expr":{"type":"numeric_atoms","value":1443,"base":3}}},"used_operators":["z63VuFQld9","XhwjNDsVaA"],"dependent_operators":["B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","rysDP5nf3Z"],"result":"⫏≰-2","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2215","layer":2},{"info":"number node, value=1443","layer":2},{"info":"compute binary expreesion, left_input=2215, right_input=1443, op_id = XhwjNDsVaA binary_op_definition= 'None', output=1","layer":1},{"info":"compute unary expreesion, input=1, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=-2","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10001001/⫏≰1222110)∧=⫏≰-2","reverse_text":"⫏≰-2=(⫏≰10001001/⫏≰1222110)∧","cot":[{"info":"⫏≰10001001/⫏≰1222110=⫏≰1","layer":1},{"info":"⫏≰1∧=⫏≰-2","layer":0}]}
{"id":252,"expression_no_base_symbol":"(∥⊫$1538$)⨪↰⇹($4962$⨵⪆$3013$)","expression":"(∥⊫⫏≰2002222)⨪↰⇹(⫏≰20210210⨵⪆⫏≰11010121)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2411,"operation_count":3,"complexity_ratio":803.6666666666666,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":1538,"base":3}},"right_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":4962,"base":3},"right_expr":{"type":"numeric_atoms","value":3013,"base":3}}},"used_operators":["tmPS8pqC7x","P8v4zCKN1o","2DQ55sFlQl"],"dependent_operators":["rJVOvQCfKK","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰10022010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1538","layer":2},{"info":"compute unary expreesion, input=1538, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=2406","layer":1},{"info":"number node, value=4962","layer":2},{"info":"number node, value=3013","layer":2},{"info":"compute binary expreesion, left_input=4962, right_input=3013, 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=2406, right_input=160, 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=2406","layer":0}],"base":3,"result_base":3,"text":"(∥⊫⫏≰2002222)⨪↰⇹(⫏≰20210210⨵⪆⫏≰11010121)=⫏≰10022010","reverse_text":"⫏≰10022010=(∥⊫⫏≰2002222)⨪↰⇹(⫏≰20210210⨵⪆⫏≰11010121)","cot":[{"info":"∥⊫⫏≰2002222=⫏≰10022010","layer":1},{"info":"⫏≰20210210⨵⪆⫏≰11010121=⫏≰12221","layer":1},{"info":"⫏≰10022010⨪↰⇹⫏≰12221=⫏≰10022010","layer":0}]}
{"id":253,"expression_no_base_symbol":"($1703$↪⪝)↺($3823$⪠⩆⊳)","expression":"(⫏≰2100002↪⪝)↺(⫏≰12020121⪠⩆⊳)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":708,"operation_count":3,"complexity_ratio":236.0,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"numeric_atoms","value":1703,"base":3}},"right_expr":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"numeric_atoms","value":3823,"base":3}}},"used_operators":["7j4O788W3g","l07mrZUIn9","JLbD19bQDL"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","9HNa5Wba9A","2DDjHMKMc0","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1703","layer":2},{"info":"compute unary expreesion, input=1703, op_id = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=104192946","layer":1},{"info":"number node, value=3823","layer":2},{"info":"compute unary expreesion, input=3823, 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":"compute binary expreesion, left_input=104192946, 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":3,"result_base":3,"text":"(⫏≰2100002↪⪝)↺(⫏≰12020121⪠⩆⊳)=⫏≰0","reverse_text":"⫏≰0=(⫏≰2100002↪⪝)↺(⫏≰12020121⪠⩆⊳)","cot":[{"info":"⫏≰2100002↪⪝=⫏≰21021001112212000","layer":1},{"info":"⫏≰12020121⪠⩆⊳=⫏≰0","layer":1},{"info":"⫏≰21021001112212000↺⫏≰0=⫏≰0","layer":0}]}
{"id":254,"expression_no_base_symbol":"($1747$⋝⋈⪟$1763$)⨓(↣≠⋷$1901$)","expression":"(⫏≰2101201⋝⋈⪟⫏≰2102022)⨓(↣≠⋷⫏≰2121102)","highest_n_order":4,"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":1747,"base":3},"right_expr":{"type":"numeric_atoms","value":1763,"base":3}},"right_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":1901,"base":3}}},"used_operators":["3ViojmjbAp","2DDjHMKMc0","Asc51vEJeQ"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1747","layer":2},{"info":"number node, value=1763","layer":2},{"info":"compute binary expreesion, left_input=1747, right_input=1763, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=1747","layer":1},{"info":"number node, value=1901","layer":2},{"info":"compute unary expreesion, input=1901, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1747, right_input=nan, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2101201⋝⋈⪟⫏≰2102022)⨓(↣≠⋷⫏≰2121102)=NaN","reverse_text":"NaN=(⫏≰2101201⋝⋈⪟⫏≰2102022)⨓(↣≠⋷⫏≰2121102)","cot":[{"info":"⫏≰2101201⋝⋈⪟⫏≰2102022=⫏≰2101201","layer":1},{"info":"↣≠⋷⫏≰2121102=NaN","layer":1},{"info":"⫏≰2101201⨓NaN=NaN","layer":0}]}
{"id":255,"expression_no_base_symbol":"($2436$%$1689$)≧⫂∧($1367$⩚⊴⇥$2726$)","expression":"(⫏≰10100020%⫏≰2022120)≧⫂∧(⫏≰1212122⩚⊴⇥⫏≰10201222)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":2436,"base":3},"right_expr":{"type":"numeric_atoms","value":1689,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":1367,"base":3},"right_expr":{"type":"numeric_atoms","value":2726,"base":3}}},"used_operators":["Ph9nP6C5qx","k8jYdgA6NY","NTOWxs364D"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰20210202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2436","layer":2},{"info":"number node, value=1689","layer":2},{"info":"compute binary expreesion, left_input=2436, right_input=1689, op_id = k8jYdgA6NY binary_op_definition= 'None', output=747","layer":1},{"info":"number node, value=1367","layer":2},{"info":"number node, value=2726","layer":2},{"info":"compute binary expreesion, left_input=1367, right_input=2726, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-4214","layer":1},{"info":"compute binary expreesion, left_input=747, right_input=-4214, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=4961","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10100020%⫏≰2022120)≧⫂∧(⫏≰1212122⩚⊴⇥⫏≰10201222)=⫏≰20210202","reverse_text":"⫏≰20210202=(⫏≰10100020%⫏≰2022120)≧⫂∧(⫏≰1212122⩚⊴⇥⫏≰10201222)","cot":[{"info":"⫏≰10100020%⫏≰2022120=⫏≰1000200","layer":1},{"info":"⫏≰1212122⩚⊴⇥⫏≰10201222=⫏≰-12210002","layer":1},{"info":"⫏≰1000200≧⫂∧⫏≰-12210002=⫏≰20210202","layer":0}]}
{"id":256,"expression_no_base_symbol":"($4336$⩠)⪘⫢($1774$⩷∴$2306$)","expression":"(⫏≰12221121⩠)⪘⫢(⫏≰2102201⩷∴⫏≰10011102)","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":4336,"base":3}},"right_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":1774,"base":3},"right_expr":{"type":"numeric_atoms","value":2306,"base":3}}},"used_operators":["oacrs7FA3X","sJAwomhLZr","9FxExcQeMw"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","sdazOOVcIp","i8ToyICDmI","k8jYdgA6NY","eH2TOUuTDT","W4YGzv6Whe","Z2TMIBDE3Q","COABgblf1C","rysDP5nf3Z"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4336","layer":2},{"info":"compute unary expreesion, input=4336, op_id = sJAwomhLZr, unary_op_definition = 'a⩠ = { (((a+a)⊭↱(a⪨≂a))∲⫓((a⩤)%(a⪐))) }', output=0","layer":1},{"info":"number node, value=1774","layer":2},{"info":"number node, value=2306","layer":2},{"info":"compute binary expreesion, left_input=1774, right_input=2306, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-1096","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-1096, 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":3,"result_base":3,"text":"(⫏≰12221121⩠)⪘⫢(⫏≰2102201⩷∴⫏≰10011102)=⫏≰-1","reverse_text":"⫏≰-1=(⫏≰12221121⩠)⪘⫢(⫏≰2102201⩷∴⫏≰10011102)","cot":[{"info":"⫏≰12221121⩠=⫏≰0","layer":1},{"info":"⫏≰2102201⩷∴⫏≰10011102=⫏≰-1111121","layer":1},{"info":"⫏≰0⪘⫢⫏≰-1111121=⫏≰-1","layer":0}]}
{"id":257,"expression_no_base_symbol":"($4142$⨸⪁$2760$)⪛($5149$⋷$3648$)","expression":"(⫏≰12200102⨸⪁⫏≰10210020)⪛(⫏≰21001201⋷⫏≰12000010)","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":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":4142,"base":3},"right_expr":{"type":"numeric_atoms","value":2760,"base":3}},"right_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":5149,"base":3},"right_expr":{"type":"numeric_atoms","value":3648,"base":3}}},"used_operators":["uFcxV4UQCh","g55IO6H4Gj","23Mk6UjR3U"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1021011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4142","layer":2},{"info":"number node, value=2760","layer":2},{"info":"compute binary expreesion, left_input=4142, right_input=2760, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=13804","layer":1},{"info":"number node, value=5149","layer":2},{"info":"number node, value=3648","layer":2},{"info":"compute binary expreesion, left_input=5149, right_input=3648, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=2147","layer":1},{"info":"compute binary expreesion, left_input=13804, right_input=2147, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=922","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12200102⨸⪁⫏≰10210020)⪛(⫏≰21001201⋷⫏≰12000010)=⫏≰1021011","reverse_text":"⫏≰1021011=(⫏≰12200102⨸⪁⫏≰10210020)⪛(⫏≰21001201⋷⫏≰12000010)","cot":[{"info":"⫏≰12200102⨸⪁⫏≰10210020=⫏≰200221021","layer":1},{"info":"⫏≰21001201⋷⫏≰12000010=⫏≰2221112","layer":1},{"info":"⫏≰200221021⪛⫏≰2221112=⫏≰1021011","layer":0}]}
{"id":258,"expression_no_base_symbol":"(⫓⪴$1272$)≫≃","expression":"(⫓⪴⫏≰1202010)≫≃","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1279,"operation_count":2,"complexity_ratio":639.5,"tree":{"type":"unary","operator":"≫≃","unary_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":1272,"base":3}}},"used_operators":["X99M06cbEe","eLxqMNBOBk"],"dependent_operators":["2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A","9HNa5Wba9A"],"result":"⫏≰20002110211120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1272","layer":2},{"info":"compute unary expreesion, input=1272, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=1617984","layer":1},{"info":"compute unary expreesion, input=1617984, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=3237369","layer":0}],"base":3,"result_base":3,"text":"(⫓⪴⫏≰1202010)≫≃=⫏≰20002110211120","reverse_text":"⫏≰20002110211120=(⫓⪴⫏≰1202010)≫≃","cot":[{"info":"⫓⪴⫏≰1202010=⫏≰10001012110100","layer":1},{"info":"⫏≰10001012110100≫≃=⫏≰20002110211120","layer":0}]}
{"id":259,"expression_no_base_symbol":"($1172$∧)+⇶⊼($1757$⨎$2184$)","expression":"(⫏≰1121102∧)+⇶⊼(⫏≰2102002⨎⫏≰2222220)","highest_n_order":5,"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":1172,"base":3}},"right_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":1757,"base":3},"right_expr":{"type":"numeric_atoms","value":2184,"base":3}}},"used_operators":["TpPTUOHfaN","z63VuFQld9","rJVOvQCfKK"],"dependent_operators":["AHs5Up7iyr","B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1172","layer":2},{"info":"compute unary expreesion, input=1172, 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=1757","layer":2},{"info":"number node, value=2184","layer":2},{"info":"compute binary expreesion, left_input=1757, right_input=2184, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=2184","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2184, 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":3,"result_base":3,"text":"(⫏≰1121102∧)+⇶⊼(⫏≰2102002⨎⫏≰2222220)=NaN","reverse_text":"NaN=(⫏≰1121102∧)+⇶⊼(⫏≰2102002⨎⫏≰2222220)","cot":[{"info":"⫏≰1121102∧=NaN","layer":1},{"info":"⫏≰2102002⨎⫏≰2222220=⫏≰2222220","layer":1},{"info":"NaN+⇶⊼⫏≰2222220=NaN","layer":0}]}
{"id":260,"expression_no_base_symbol":"↔($1380$⨽$3946$)","expression":"↔(⫏≰1220010⨽⫏≰12102011)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1411,"operation_count":2,"complexity_ratio":705.5,"tree":{"type":"unary","operator":"↔","unary_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1380,"base":3},"right_expr":{"type":"numeric_atoms","value":3946,"base":3}}},"used_operators":["ruOEQAzv1W","8HhzD0ZcuI"],"dependent_operators":["XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"⫏≰-11222","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1380","layer":2},{"info":"number node, value=3946","layer":2},{"info":"compute binary expreesion, left_input=1380, right_input=3946, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-5723724","layer":1},{"info":"compute unary expreesion, input=-5723724, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-134","layer":0}],"base":3,"result_base":3,"text":"↔(⫏≰1220010⨽⫏≰12102011)=⫏≰-11222","reverse_text":"⫏≰-11222=↔(⫏≰1220010⨽⫏≰12102011)","cot":[{"info":"⫏≰1220010⨽⫏≰12102011=⫏≰-101202210110210","layer":1},{"info":"↔⫏≰-101202210110210=⫏≰-11222","layer":0}]}
{"id":261,"expression_no_base_symbol":"($2603$⊭↱$2908$)≹⇙⪍($1547$⊦⊿)","expression":"(⫏≰10120102⊭↱⫏≰10222201)≹⇙⪍(⫏≰2010022⊦⊿)","highest_n_order":4,"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":2603,"base":3},"right_expr":{"type":"numeric_atoms","value":2908,"base":3}},"right_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":1547,"base":3}}},"used_operators":["AHs5Up7iyr","COABgblf1C","14qkJME0vr"],"dependent_operators":["dWAJyo7jo9","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2603","layer":2},{"info":"number node, value=2908","layer":2},{"info":"compute binary expreesion, left_input=2603, right_input=2908, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=615","layer":1},{"info":"number node, value=1547","layer":2},{"info":"compute unary expreesion, input=1547, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-4720","layer":1},{"info":"compute binary expreesion, left_input=615, right_input=-4720, 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":3,"result_base":3,"text":"(⫏≰10120102⊭↱⫏≰10222201)≹⇙⪍(⫏≰2010022⊦⊿)=NaN","reverse_text":"NaN=(⫏≰10120102⊭↱⫏≰10222201)≹⇙⪍(⫏≰2010022⊦⊿)","cot":[{"info":"⫏≰10120102⊭↱⫏≰10222201=⫏≰211210","layer":1},{"info":"⫏≰2010022⊦⊿=⫏≰-20110211","layer":1},{"info":"⫏≰211210≹⇙⪍⫏≰-20110211=NaN","layer":0}]}
{"id":262,"expression_no_base_symbol":"($1075$*$1847$)⨓$1569$⇷$3609$","expression":"(⫏≰1110211*⫏≰2112102)⨓⫏≰2011010⇷⫏≰11221200","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":30271,"operation_count":3,"complexity_ratio":10090.333333333334,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1075,"base":3},"right_expr":{"type":"numeric_atoms","value":1847,"base":3}},"right_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":1569,"base":3},"right_expr":{"type":"numeric_atoms","value":3609,"base":3}}},"used_operators":["3ViojmjbAp","9HNa5Wba9A","mp7IySMOzn"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"⫏≰-100220110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1075","layer":2},{"info":"number node, value=1847","layer":2},{"info":"compute binary expreesion, left_input=1075, right_input=1847, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=1985525","layer":1},{"info":"number node, value=1569","layer":2},{"info":"number node, value=3609","layer":2},{"info":"compute binary expreesion, left_input=1569, right_input=3609, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=7218","layer":1},{"info":"compute binary expreesion, left_input=1985525, right_input=7218, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-7221","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1110211*⫏≰2112102)⨓⫏≰2011010⇷⫏≰11221200=⫏≰-100220110","reverse_text":"⫏≰-100220110=(⫏≰1110211*⫏≰2112102)⨓⫏≰2011010⇷⫏≰11221200","cot":[{"info":"⫏≰1110211*⫏≰2112102=⫏≰10201212121222","layer":1},{"info":"⫏≰2011010⇷⫏≰11221200=⫏≰100220100","layer":1},{"info":"⫏≰10201212121222⨓⫏≰100220100=⫏≰-100220110","layer":0}]}
{"id":263,"expression_no_base_symbol":"$1899$⨓$2656$⨳⩥⨓(↣≠⋷$4100$)","expression":"⫏≰2121100⨓⫏≰10122101⨳⩥⨓(↣≠⋷⫏≰12121212)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2668,"operation_count":3,"complexity_ratio":889.3333333333334,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":1899,"base":3},"right_expr":{"type":"numeric_atoms","value":2656,"base":3}},"right_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":4100,"base":3}}},"used_operators":["nCS4ZIUYfx","3ViojmjbAp","Asc51vEJeQ"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","XhwjNDsVaA","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1899","layer":2},{"info":"number node, value=2656","layer":2},{"info":"compute binary expreesion, left_input=1899, right_input=2656, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-2659","layer":1},{"info":"number node, value=4100","layer":2},{"info":"compute unary expreesion, input=4100, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-2659, right_input=nan, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2121100⨓⫏≰10122101⨳⩥⨓(↣≠⋷⫏≰12121212)=NaN","reverse_text":"NaN=⫏≰2121100⨓⫏≰10122101⨳⩥⨓(↣≠⋷⫏≰12121212)","cot":[{"info":"⫏≰2121100⨓⫏≰10122101=⫏≰-10122111","layer":1},{"info":"↣≠⋷⫏≰12121212=NaN","layer":1},{"info":"⫏≰-10122111⨳⩥⨓NaN=NaN","layer":0}]}
{"id":264,"expression_no_base_symbol":"(⨞⊢$4686$)⫡⨏(⊄⩳↩$1987$)","expression":"(⨞⊢⫏≰20102120)⫡⨏(⊄⩳↩⫏≰2201121)","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":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":4686,"base":3}},"right_expr":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":1987,"base":3}}},"used_operators":["QMFrweE19q","xUOZtlo3hN","8w2t5hMYqp"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-1210121120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4686","layer":2},{"info":"compute unary expreesion, input=4686, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-4860","layer":1},{"info":"number node, value=1987","layer":2},{"info":"compute unary expreesion, input=1987, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-5961","layer":1},{"info":"compute binary expreesion, left_input=-4860, right_input=-5961, 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=-35439","layer":0}],"base":3,"result_base":3,"text":"(⨞⊢⫏≰20102120)⫡⨏(⊄⩳↩⫏≰2201121)=⫏≰-1210121120","reverse_text":"⫏≰-1210121120=(⨞⊢⫏≰20102120)⫡⨏(⊄⩳↩⫏≰2201121)","cot":[{"info":"⨞⊢⫏≰20102120=⫏≰-20200000","layer":1},{"info":"⊄⩳↩⫏≰2201121=⫏≰-22011210","layer":1},{"info":"⫏≰-20200000⫡⨏⫏≰-22011210=⫏≰-1210121120","layer":0}]}
{"id":265,"expression_no_base_symbol":"($1646$+$2398$)⊘","expression":"(⫏≰2020222+⫏≰10021211)⊘","highest_n_order":2,"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":1646,"base":3},"right_expr":{"type":"numeric_atoms","value":2398,"base":3}}},"used_operators":["gu96TGCTMs","W4YGzv6Whe"],"dependent_operators":["XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1646","layer":2},{"info":"number node, value=2398","layer":2},{"info":"compute binary expreesion, left_input=1646, right_input=2398, op_id = W4YGzv6Whe binary_op_definition= 'None', output=4044","layer":1},{"info":"compute unary expreesion, input=4044, 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":3,"result_base":3,"text":"(⫏≰2020222+⫏≰10021211)⊘=⫏≰0","reverse_text":"⫏≰0=(⫏≰2020222+⫏≰10021211)⊘","cot":[{"info":"⫏≰2020222+⫏≰10021211=⫏≰12112210","layer":1},{"info":"⫏≰12112210⊘=⫏≰0","layer":0}]}
{"id":266,"expression_no_base_symbol":"($7108$/$1585$)⪛($2913$/$4096$)","expression":"(⫏≰100202021/⫏≰2011201)⪛(⫏≰10222220/⫏≰12121201)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⪛","left_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":7108,"base":3},"right_expr":{"type":"numeric_atoms","value":1585,"base":3}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":2913,"base":3},"right_expr":{"type":"numeric_atoms","value":4096,"base":3}}},"used_operators":["uFcxV4UQCh","XhwjNDsVaA"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7108","layer":2},{"info":"number node, value=1585","layer":2},{"info":"compute binary expreesion, left_input=7108, right_input=1585, op_id = XhwjNDsVaA binary_op_definition= 'None', output=4","layer":1},{"info":"number node, value=2913","layer":2},{"info":"number node, value=4096","layer":2},{"info":"compute binary expreesion, left_input=2913, right_input=4096, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute binary expreesion, left_input=4, right_input=0, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰100202021/⫏≰2011201)⪛(⫏≰10222220/⫏≰12121201)=NaN","reverse_text":"NaN=(⫏≰100202021/⫏≰2011201)⪛(⫏≰10222220/⫏≰12121201)","cot":[{"info":"⫏≰100202021/⫏≰2011201=⫏≰11","layer":1},{"info":"⫏≰10222220/⫏≰12121201=⫏≰0","layer":1},{"info":"⫏≰11⪛⫏≰0=NaN","layer":0}]}
{"id":267,"expression_no_base_symbol":"$1915$≭$5389$⨳⩥⨓($1358$⩨$1013$)","expression":"⫏≰2121221≭⫏≰21101121⨳⩥⨓(⫏≰1212022⩨⫏≰1101112)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":1915,"base":3},"right_expr":{"type":"numeric_atoms","value":5389,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":1358,"base":3},"right_expr":{"type":"numeric_atoms","value":1013,"base":3}}},"used_operators":["nCS4ZIUYfx","rxpJgHHUmx","2DlMacCsIx"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","AHs5Up7iyr","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1915","layer":2},{"info":"number node, value=5389","layer":2},{"info":"compute binary expreesion, left_input=1915, right_input=5389, 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=1358","layer":2},{"info":"number node, value=1013","layer":2},{"info":"compute binary expreesion, left_input=1358, right_input=1013, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=0, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2121221≭⫏≰21101121⨳⩥⨓(⫏≰1212022⩨⫏≰1101112)=NaN","reverse_text":"NaN=⫏≰2121221≭⫏≰21101121⨳⩥⨓(⫏≰1212022⩨⫏≰1101112)","cot":[{"info":"⫏≰2121221≭⫏≰21101121=NaN","layer":1},{"info":"⫏≰1212022⩨⫏≰1101112=⫏≰0","layer":1},{"info":"NaN⨳⩥⨓⫏≰0=NaN","layer":0}]}
{"id":268,"expression_no_base_symbol":"∂(⋗⩬⋾$4052$)","expression":"∂(⋗⩬⋾⫏≰12120002)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":420,"operation_count":2,"complexity_ratio":210.0,"tree":{"type":"unary","operator":"∂","unary_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":4052,"base":3}}},"used_operators":["Uaa54Peajs","DpFCA1CohY"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰121022110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4052","layer":2},{"info":"compute unary expreesion, input=4052, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-12156","layer":1},{"info":"compute unary expreesion, input=-12156, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=11892","layer":0}],"base":3,"result_base":3,"text":"∂(⋗⩬⋾⫏≰12120002)=⫏≰121022110","reverse_text":"⫏≰121022110=∂(⋗⩬⋾⫏≰12120002)","cot":[{"info":"⋗⩬⋾⫏≰12120002=⫏≰-121200020","layer":1},{"info":"∂⫏≰-121200020=⫏≰121022110","layer":0}]}
{"id":269,"expression_no_base_symbol":"(⊙↵-$5208$)⨎(⨑⩽⪐$1363$)","expression":"(⊙↵-⫏≰21010220)⨎(⨑⩽⪐⫏≰1212111)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5259,"operation_count":3,"complexity_ratio":1753.0,"tree":{"type":"binary","operator":"⨎","left_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":5208,"base":3}},"right_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":1363,"base":3}}},"used_operators":["rJVOvQCfKK","oWn0xqSxBt","AF7qkfDlqP"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-1111101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5208","layer":2},{"info":"compute unary expreesion, input=5208, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"number node, value=1363","layer":2},{"info":"compute unary expreesion, input=1363, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-1090","layer":1},{"info":"compute binary expreesion, left_input=-1, right_input=-1090, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=-1090","layer":0}],"base":3,"result_base":3,"text":"(⊙↵-⫏≰21010220)⨎(⨑⩽⪐⫏≰1212111)=⫏≰-1111101","reverse_text":"⫏≰-1111101=(⊙↵-⫏≰21010220)⨎(⨑⩽⪐⫏≰1212111)","cot":[{"info":"⊙↵-⫏≰21010220=⫏≰-1","layer":1},{"info":"⨑⩽⪐⫏≰1212111=⫏≰-1111101","layer":1},{"info":"⫏≰-1⨎⫏≰-1111101=⫏≰-1111101","layer":0}]}
{"id":270,"expression_no_base_symbol":"($1971$⩷∴$5607$)∧","expression":"(⫏≰2201000⩷∴⫏≰21200200)∧","highest_n_order":5,"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":1971,"base":3},"right_expr":{"type":"numeric_atoms","value":5607,"base":3}}},"used_operators":["z63VuFQld9","9FxExcQeMw"],"dependent_operators":["B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","rysDP5nf3Z"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1971","layer":2},{"info":"number node, value=5607","layer":2},{"info":"compute binary expreesion, left_input=1971, right_input=5607, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-7304","layer":1},{"info":"compute unary expreesion, input=-7304, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2201000⩷∴⫏≰21200200)∧=⫏≰0","reverse_text":"⫏≰0=(⫏≰2201000⩷∴⫏≰21200200)∧","cot":[{"info":"⫏≰2201000⩷∴⫏≰21200200=⫏≰-101000112","layer":1},{"info":"⫏≰-101000112∧=⫏≰0","layer":0}]}
{"id":271,"expression_no_base_symbol":"(⫓⪴$1149$)⊪","expression":"(⫓⪴⫏≰1120120)⊪","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1182,"operation_count":2,"complexity_ratio":591.0,"tree":{"type":"unary","operator":"⊪","unary_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":1149,"base":3}}},"used_operators":["zVYPLywUTj","eLxqMNBOBk"],"dependent_operators":["sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL","9HNa5Wba9A"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1149","layer":2},{"info":"compute unary expreesion, input=1149, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=1320201","layer":1},{"info":"compute unary expreesion, input=1320201, 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":3,"result_base":3,"text":"(⫓⪴⫏≰1120120)⊪=⫏≰0","reverse_text":"⫏≰0=(⫓⪴⫏≰1120120)⊪","cot":[{"info":"⫓⪴⫏≰1120120=⫏≰2111001222100","layer":1},{"info":"⫏≰2111001222100⊪=⫏≰0","layer":0}]}
{"id":272,"expression_no_base_symbol":"(⪲⇎$7259$)⪢($1031$⊭∹↮)","expression":"(⪲⇎⫏≰100221212)⪢(⫏≰1102012⊭∹↮)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4006,"operation_count":3,"complexity_ratio":1335.3333333333333,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":7259,"base":3}},"right_expr":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"numeric_atoms","value":1031,"base":3}}},"used_operators":["dWAJyo7jo9","XPYlsWDdGa","xNBdhnnwKq"],"dependent_operators":["k8jYdgA6NY","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7259","layer":2},{"info":"compute unary expreesion, input=7259, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=14518","layer":1},{"info":"number node, value=1031","layer":2},{"info":"compute unary expreesion, input=1031, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=2062","layer":1},{"info":"compute binary expreesion, left_input=14518, right_input=2062, 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":3,"result_base":3,"text":"(⪲⇎⫏≰100221212)⪢(⫏≰1102012⊭∹↮)=NaN","reverse_text":"NaN=(⪲⇎⫏≰100221212)⪢(⫏≰1102012⊭∹↮)","cot":[{"info":"⪲⇎⫏≰100221212=⫏≰201220201","layer":1},{"info":"⫏≰1102012⊭∹↮=⫏≰2211101","layer":1},{"info":"⫏≰201220201⪢⫏≰2211101=NaN","layer":0}]}
{"id":273,"expression_no_base_symbol":"⨞⊢($1762$⊉≛↸$3628$)","expression":"⨞⊢(⫏≰2102021⊉≛↸⫏≰11222101)","highest_n_order":1,"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":1762,"base":3},"right_expr":{"type":"numeric_atoms","value":3628,"base":3}}},"used_operators":["xUOZtlo3hN","DZ8iAZOCBD"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-12001222","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1762","layer":2},{"info":"number node, value=3628","layer":2},{"info":"compute binary expreesion, left_input=1762, right_input=3628, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=3524","layer":1},{"info":"compute unary expreesion, input=3524, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-3698","layer":0}],"base":3,"result_base":3,"text":"⨞⊢(⫏≰2102021⊉≛↸⫏≰11222101)=⫏≰-12001222","reverse_text":"⫏≰-12001222=⨞⊢(⫏≰2102021⊉≛↸⫏≰11222101)","cot":[{"info":"⫏≰2102021⊉≛↸⫏≰11222101=⫏≰11211112","layer":1},{"info":"⨞⊢⫏≰11211112=⫏≰-12001222","layer":0}]}
{"id":274,"expression_no_base_symbol":"(-$1635$)-$1311$⩷∴$1248$","expression":"(-⫏≰2020120)-⫏≰1210120⩷∴⫏≰1201020","highest_n_order":1,"priority_hierarchical_complexity":2,"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":1635,"base":3}},"right_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":1311,"base":3},"right_expr":{"type":"numeric_atoms","value":1248,"base":3}}},"used_operators":["rysDP5nf3Z","t8gj7n24qd","9FxExcQeMw"],"dependent_operators":["rysDP5nf3Z"],"result":"⫏≰-2101001","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1635","layer":2},{"info":"compute unary expreesion, input=1635, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1635","layer":1},{"info":"number node, value=1311","layer":2},{"info":"number node, value=1248","layer":2},{"info":"compute binary expreesion, left_input=1311, right_input=1248, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=94","layer":1},{"info":"compute binary expreesion, left_input=-1635, right_input=94, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-1729","layer":0}],"base":3,"result_base":3,"text":"(-⫏≰2020120)-⫏≰1210120⩷∴⫏≰1201020=⫏≰-2101001","reverse_text":"⫏≰-2101001=(-⫏≰2020120)-⫏≰1210120⩷∴⫏≰1201020","cot":[{"info":"-⫏≰2020120=⫏≰-2020120","layer":1},{"info":"⫏≰1210120⩷∴⫏≰1201020=⫏≰10111","layer":1},{"info":"⫏≰-2020120-⫏≰10111=⫏≰-2101001","layer":0}]}
{"id":275,"expression_no_base_symbol":"($2330$⨵⪆$2410$)⪢($6496$⪛$5348$)","expression":"(⫏≰10012022⨵⪆⫏≰10022021)⪢(⫏≰22220121⪛⫏≰21100002)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1153,"operation_count":3,"complexity_ratio":384.3333333333333,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":2330,"base":3},"right_expr":{"type":"numeric_atoms","value":2410,"base":3}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":6496,"base":3},"right_expr":{"type":"numeric_atoms","value":5348,"base":3}}},"used_operators":["dWAJyo7jo9","2DQ55sFlQl","uFcxV4UQCh"],"dependent_operators":["k8jYdgA6NY","rysDP5nf3Z","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2330","layer":2},{"info":"number node, value=2410","layer":2},{"info":"compute binary expreesion, left_input=2330, right_input=2410, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=6496","layer":2},{"info":"number node, value=5348","layer":2},{"info":"compute binary expreesion, left_input=6496, right_input=5348, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1148","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=1148, 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":3,"result_base":3,"text":"(⫏≰10012022⨵⪆⫏≰10022021)⪢(⫏≰22220121⪛⫏≰21100002)=NaN","reverse_text":"NaN=(⫏≰10012022⨵⪆⫏≰10022021)⪢(⫏≰22220121⪛⫏≰21100002)","cot":[{"info":"⫏≰10012022⨵⪆⫏≰10022021=⫏≰12221","layer":1},{"info":"⫏≰22220121⪛⫏≰21100002=⫏≰1120112","layer":1},{"info":"⫏≰12221⪢⫏≰1120112=NaN","layer":0}]}
{"id":276,"expression_no_base_symbol":"(↩$7155$)-$2181$⩚⊴⇥$4803$","expression":"(↩⫏≰100211000)-⫏≰2222210⩚⊴⇥⫏≰20120220","highest_n_order":2,"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":7155,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":2181,"base":3},"right_expr":{"type":"numeric_atoms","value":4803,"base":3}}},"used_operators":["rysDP5nf3Z","jLgFTUHLKL","NTOWxs364D"],"dependent_operators":["sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰-2101221220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7155","layer":2},{"info":"compute unary expreesion, input=7155, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-54460","layer":1},{"info":"number node, value=2181","layer":2},{"info":"number node, value=4803","layer":2},{"info":"compute binary expreesion, left_input=2181, right_input=4803, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-7105","layer":1},{"info":"compute binary expreesion, left_input=-54460, right_input=-7105, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-47355","layer":0}],"base":3,"result_base":3,"text":"(↩⫏≰100211000)-⫏≰2222210⩚⊴⇥⫏≰20120220=⫏≰-2101221220","reverse_text":"⫏≰-2101221220=(↩⫏≰100211000)-⫏≰2222210⩚⊴⇥⫏≰20120220","cot":[{"info":"↩⫏≰100211000=⫏≰-2202201001","layer":1},{"info":"⫏≰2222210⩚⊴⇥⫏≰20120220=⫏≰-100202011","layer":1},{"info":"⫏≰-2202201001-⫏≰-100202011=⫏≰-2101221220","layer":0}]}
{"id":277,"expression_no_base_symbol":"$2857$⨸⪁$1947$⫡⨏$2765$⨐⩸⫘$2411$","expression":"⫏≰10220211⨸⪁⫏≰2200010⫡⨏⫏≰10210102⨐⩸⫘⫏≰10022022","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":2857,"base":3},"right_expr":{"type":"numeric_atoms","value":1947,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":2765,"base":3},"right_expr":{"type":"numeric_atoms","value":2411,"base":3}}},"used_operators":["QMFrweE19q","g55IO6H4Gj","fu6greOZ01"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2857","layer":2},{"info":"number node, value=1947","layer":2},{"info":"compute binary expreesion, left_input=2857, right_input=1947, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=9608","layer":1},{"info":"number node, value=2765","layer":2},{"info":"number node, value=2411","layer":2},{"info":"compute binary expreesion, left_input=2765, right_input=2411, 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=9608, 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":3,"result_base":3,"text":"⫏≰10220211⨸⪁⫏≰2200010⫡⨏⫏≰10210102⨐⩸⫘⫏≰10022022=NaN","reverse_text":"NaN=⫏≰10220211⨸⪁⫏≰2200010⫡⨏⫏≰10210102⨐⩸⫘⫏≰10022022","cot":[{"info":"⫏≰10220211⨸⪁⫏≰2200010=⫏≰111011212","layer":1},{"info":"⫏≰10210102⨐⩸⫘⫏≰10022022=NaN","layer":1},{"info":"⫏≰111011212⫡⨏NaN=NaN","layer":0}]}
{"id":278,"expression_no_base_symbol":"($1333$⋝⋈⪟$2435$)∑⇟⊟(⨰⫟⨤$5775$)","expression":"(⫏≰1211101⋝⋈⪟⫏≰10100012)∑⇟⊟(⨰⫟⨤⫏≰21220220)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":22264,"operation_count":3,"complexity_ratio":7421.333333333333,"tree":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":1333,"base":3},"right_expr":{"type":"numeric_atoms","value":2435,"base":3}},"right_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":5775,"base":3}}},"used_operators":["U7g4x0WXJJ","2DDjHMKMc0","Tw270M8GLb"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1333","layer":2},{"info":"number node, value=2435","layer":2},{"info":"compute binary expreesion, left_input=1333, right_input=2435, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=1333","layer":1},{"info":"number node, value=5775","layer":2},{"info":"compute unary expreesion, input=5775, 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=1333, right_input=nan, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1211101⋝⋈⪟⫏≰10100012)∑⇟⊟(⨰⫟⨤⫏≰21220220)=NaN","reverse_text":"NaN=(⫏≰1211101⋝⋈⪟⫏≰10100012)∑⇟⊟(⨰⫟⨤⫏≰21220220)","cot":[{"info":"⫏≰1211101⋝⋈⪟⫏≰10100012=⫏≰1211101","layer":1},{"info":"⨰⫟⨤⫏≰21220220=NaN","layer":1},{"info":"⫏≰1211101∑⇟⊟NaN=NaN","layer":0}]}
{"id":279,"expression_no_base_symbol":"($1281$⨓$1315$)∧","expression":"(⫏≰1202110⨓⫏≰1210201)∧","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1329,"operation_count":2,"complexity_ratio":664.5,"tree":{"type":"unary","operator":"∧","unary_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":1281,"base":3},"right_expr":{"type":"numeric_atoms","value":1315,"base":3}}},"used_operators":["z63VuFQld9","3ViojmjbAp"],"dependent_operators":["B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1281","layer":2},{"info":"number node, value=1315","layer":2},{"info":"compute binary expreesion, left_input=1281, right_input=1315, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1318","layer":1},{"info":"compute unary expreesion, input=-1318, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1202110⨓⫏≰1210201)∧=⫏≰0","reverse_text":"⫏≰0=(⫏≰1202110⨓⫏≰1210201)∧","cot":[{"info":"⫏≰1202110⨓⫏≰1210201=⫏≰-1210211","layer":1},{"info":"⫏≰-1210211∧=⫏≰0","layer":0}]}
{"id":280,"expression_no_base_symbol":"($1467$%$3242$)≭$1356$≹⇙⪍$1370$","expression":"(⫏≰2000100%⫏≰11110002)≭⫏≰1212020≹⇙⪍⫏≰1212202","highest_n_order":5,"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":1467,"base":3},"right_expr":{"type":"numeric_atoms","value":3242,"base":3}},"right_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":1356,"base":3},"right_expr":{"type":"numeric_atoms","value":1370,"base":3}}},"used_operators":["rxpJgHHUmx","k8jYdgA6NY","AHs5Up7iyr"],"dependent_operators":["AHs5Up7iyr","rysDP5nf3Z","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1467","layer":2},{"info":"number node, value=3242","layer":2},{"info":"compute binary expreesion, left_input=1467, right_input=3242, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1467","layer":1},{"info":"number node, value=1356","layer":2},{"info":"number node, value=1370","layer":2},{"info":"compute binary expreesion, left_input=1356, right_input=1370, 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=1467, right_input=nan, 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":3,"result_base":3,"text":"(⫏≰2000100%⫏≰11110002)≭⫏≰1212020≹⇙⪍⫏≰1212202=NaN","reverse_text":"NaN=(⫏≰2000100%⫏≰11110002)≭⫏≰1212020≹⇙⪍⫏≰1212202","cot":[{"info":"⫏≰2000100%⫏≰11110002=⫏≰2000100","layer":1},{"info":"⫏≰1212020≹⇙⪍⫏≰1212202=NaN","layer":1},{"info":"⫏≰2000100≭NaN=NaN","layer":0}]}
{"id":281,"expression_no_base_symbol":"($4760$⊪)⪄(⨰⫟⨤$1274$)","expression":"(⫏≰20112022⊪)⪄(⨰⫟⨤⫏≰1202012)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4312,"operation_count":3,"complexity_ratio":1437.3333333333333,"tree":{"type":"binary","operator":"⪄","left_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":4760,"base":3}},"right_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":1274,"base":3}}},"used_operators":["SUmda5xLS4","zVYPLywUTj","Tw270M8GLb"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4760","layer":2},{"info":"compute unary expreesion, input=4760, 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":"number node, value=1274","layer":2},{"info":"compute unary expreesion, input=1274, 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=0, right_input=nan, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20112022⊪)⪄(⨰⫟⨤⫏≰1202012)=NaN","reverse_text":"NaN=(⫏≰20112022⊪)⪄(⨰⫟⨤⫏≰1202012)","cot":[{"info":"⫏≰20112022⊪=⫏≰0","layer":1},{"info":"⨰⫟⨤⫏≰1202012=NaN","layer":1},{"info":"⫏≰0⪄NaN=NaN","layer":0}]}
{"id":282,"expression_no_base_symbol":"$2310$↬$9073$⫥∨⫟$6316$⩚⊴⇥$1860$","expression":"⫏≰10011120↬⫏≰110110001⫥∨⫟⫏≰22122221⩚⊴⇥⫏≰2112220","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":158,"operation_count":3,"complexity_ratio":52.666666666666664,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":2310,"base":3},"right_expr":{"type":"numeric_atoms","value":9073,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":6316,"base":3},"right_expr":{"type":"numeric_atoms","value":1860,"base":3}}},"used_operators":["KYD54nUTWz","B5M0gjZbta","NTOWxs364D"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2310","layer":2},{"info":"number node, value=9073","layer":2},{"info":"compute binary expreesion, left_input=2310, right_input=9073, 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=6316","layer":2},{"info":"number node, value=1860","layer":2},{"info":"compute binary expreesion, left_input=6316, right_input=1860, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-8297","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-8297, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰10011120↬⫏≰110110001⫥∨⫟⫏≰22122221⩚⊴⇥⫏≰2112220=NaN","reverse_text":"NaN=⫏≰10011120↬⫏≰110110001⫥∨⫟⫏≰22122221⩚⊴⇥⫏≰2112220","cot":[{"info":"⫏≰10011120↬⫏≰110110001=NaN","layer":1},{"info":"⫏≰22122221⩚⊴⇥⫏≰2112220=⫏≰-102101022","layer":1},{"info":"NaN⫥∨⫟⫏≰-102101022=NaN","layer":0}]}
{"id":283,"expression_no_base_symbol":"⫛⫱⨽($1033$⫡⨏$3784$)","expression":"⫛⫱⨽(⫏≰1102021⫡⨏⫏≰12012011)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1429,"operation_count":2,"complexity_ratio":714.5,"tree":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":1033,"base":3},"right_expr":{"type":"numeric_atoms","value":3784,"base":3}}},"used_operators":["DlLNRPXxWL","QMFrweE19q"],"dependent_operators":["rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1033","layer":2},{"info":"number node, value=3784","layer":2},{"info":"compute binary expreesion, left_input=1033, right_input=3784, 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=13516","layer":1},{"info":"compute unary expreesion, input=13516, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫛⫱⨽(⫏≰1102021⫡⨏⫏≰12012011)=⫏≰0","reverse_text":"⫏≰0=⫛⫱⨽(⫏≰1102021⫡⨏⫏≰12012011)","cot":[{"info":"⫏≰1102021⫡⨏⫏≰12012011=⫏≰200112121","layer":1},{"info":"⫛⫱⨽⫏≰200112121=⫏≰0","layer":0}]}
{"id":284,"expression_no_base_symbol":"$3122$⊴$1644$+⇶⊼(⩦⩻⨪$3449$)","expression":"⫏≰11021122⊴⫏≰2020220+⇶⊼(⩦⩻⨪⫏≰11201202)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3331,"operation_count":3,"complexity_ratio":1110.3333333333333,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":3122,"base":3},"right_expr":{"type":"numeric_atoms","value":1644,"base":3}},"right_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":3449,"base":3}}},"used_operators":["TpPTUOHfaN","Nsiff2A1zJ","2td37pGCOC"],"dependent_operators":["AHs5Up7iyr","dWAJyo7jo9","14qkJME0vr","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3122","layer":2},{"info":"number node, value=1644","layer":2},{"info":"compute binary expreesion, left_input=3122, right_input=1644, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=3449","layer":2},{"info":"compute unary expreesion, input=3449, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=3449","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=3449, 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":3,"result_base":3,"text":"⫏≰11021122⊴⫏≰2020220+⇶⊼(⩦⩻⨪⫏≰11201202)=NaN","reverse_text":"NaN=⫏≰11021122⊴⫏≰2020220+⇶⊼(⩦⩻⨪⫏≰11201202)","cot":[{"info":"⫏≰11021122⊴⫏≰2020220=NaN","layer":1},{"info":"⩦⩻⨪⫏≰11201202=⫏≰11201202","layer":1},{"info":"NaN+⇶⊼⫏≰11201202=NaN","layer":0}]}
{"id":285,"expression_no_base_symbol":"($4704$+$1494$)⨸⪁$6232$⋳⪒$2961$","expression":"(⫏≰20110020+⫏≰2001100)⨸⪁⫏≰22112211⋳⪒⫏≰11001200","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":4704,"base":3},"right_expr":{"type":"numeric_atoms","value":1494,"base":3}},"right_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":6232,"base":3},"right_expr":{"type":"numeric_atoms","value":2961,"base":3}}},"used_operators":["g55IO6H4Gj","W4YGzv6Whe","12rbrZMWeM"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰1120021210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4704","layer":2},{"info":"number node, value=1494","layer":2},{"info":"compute binary expreesion, left_input=4704, right_input=1494, op_id = W4YGzv6Whe binary_op_definition= 'None', output=6198","layer":1},{"info":"number node, value=6232","layer":2},{"info":"number node, value=2961","layer":2},{"info":"compute binary expreesion, left_input=6232, right_input=2961, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=9216","layer":1},{"info":"compute binary expreesion, left_input=6198, right_input=9216, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=30828","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20110020+⫏≰2001100)⨸⪁⫏≰22112211⋳⪒⫏≰11001200=⫏≰1120021210","reverse_text":"⫏≰1120021210=(⫏≰20110020+⫏≰2001100)⨸⪁⫏≰22112211⋳⪒⫏≰11001200","cot":[{"info":"⫏≰20110020+⫏≰2001100=⫏≰22111120","layer":1},{"info":"⫏≰22112211⋳⪒⫏≰11001200=⫏≰110122100","layer":1},{"info":"⫏≰22111120⨸⪁⫏≰110122100=⫏≰1120021210","layer":0}]}
{"id":286,"expression_no_base_symbol":"$2466$⊭↱$4616$⨵⪆(∥⊫$2896$)","expression":"⫏≰10101100⊭↱⫏≰20022222⨵⪆(∥⊫⫏≰10222021)","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":2466,"base":3},"right_expr":{"type":"numeric_atoms","value":4616,"base":3}},"right_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":2896,"base":3}}},"used_operators":["2DQ55sFlQl","COABgblf1C","P8v4zCKN1o"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2466","layer":2},{"info":"number node, value=4616","layer":2},{"info":"compute binary expreesion, left_input=2466, right_input=4616, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=4305","layer":1},{"info":"number node, value=2896","layer":2},{"info":"compute unary expreesion, input=2896, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=3764","layer":1},{"info":"compute binary expreesion, left_input=4305, right_input=3764, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰10101100⊭↱⫏≰20022222⨵⪆(∥⊫⫏≰10222021)=⫏≰12221","reverse_text":"⫏≰12221=⫏≰10101100⊭↱⫏≰20022222⨵⪆(∥⊫⫏≰10222021)","cot":[{"info":"⫏≰10101100⊭↱⫏≰20022222=⫏≰12220110","layer":1},{"info":"∥⊫⫏≰10222021=⫏≰12011102","layer":1},{"info":"⫏≰12220110⨵⪆⫏≰12011102=⫏≰12221","layer":0}]}
{"id":287,"expression_no_base_symbol":"($2834$/$5820$)↺$2351$⪮%⊝$1076$","expression":"(⫏≰10212222/⫏≰21222120)↺⫏≰10020002⪮%⊝⫏≰1110212","highest_n_order":2,"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":2834,"base":3},"right_expr":{"type":"numeric_atoms","value":5820,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":2351,"base":3},"right_expr":{"type":"numeric_atoms","value":1076,"base":3}}},"used_operators":["7j4O788W3g","XhwjNDsVaA","IWmyXbctLI"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰20212212","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2834","layer":2},{"info":"number node, value=5820","layer":2},{"info":"compute binary expreesion, left_input=2834, right_input=5820, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"number node, value=2351","layer":2},{"info":"number node, value=1076","layer":2},{"info":"compute binary expreesion, left_input=2351, right_input=1076, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=5018","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=5018, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=5018","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10212222/⫏≰21222120)↺⫏≰10020002⪮%⊝⫏≰1110212=⫏≰20212212","reverse_text":"⫏≰20212212=(⫏≰10212222/⫏≰21222120)↺⫏≰10020002⪮%⊝⫏≰1110212","cot":[{"info":"⫏≰10212222/⫏≰21222120=⫏≰0","layer":1},{"info":"⫏≰10020002⪮%⊝⫏≰1110212=⫏≰20212212","layer":1},{"info":"⫏≰0↺⫏≰20212212=⫏≰20212212","layer":0}]}
{"id":288,"expression_no_base_symbol":"($1442$⫡⨏$2172$)≎⊠⪸(⨞⊢$3263$)","expression":"(⫏≰1222102⫡⨏⫏≰2222110)≎⊠⪸(⨞⊢⫏≰11110212)","highest_n_order":2,"priority_hierarchical_complexity":3,"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":1442,"base":3},"right_expr":{"type":"numeric_atoms","value":2172,"base":3}},"right_expr":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":3263,"base":3}}},"used_operators":["bJkvcejdHO","QMFrweE19q","xUOZtlo3hN"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1442","layer":2},{"info":"number node, value=2172","layer":2},{"info":"compute binary expreesion, left_input=1442, right_input=2172, 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=12337","layer":1},{"info":"number node, value=3263","layer":2},{"info":"compute unary expreesion, input=3263, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-3437","layer":1},{"info":"compute binary expreesion, left_input=12337, right_input=-3437, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=67","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1222102⫡⨏⫏≰2222110)≎⊠⪸(⨞⊢⫏≰11110212)=⫏≰2111","reverse_text":"⫏≰2111=(⫏≰1222102⫡⨏⫏≰2222110)≎⊠⪸(⨞⊢⫏≰11110212)","cot":[{"info":"⫏≰1222102⫡⨏⫏≰2222110=⫏≰121220221","layer":1},{"info":"⨞⊢⫏≰11110212=⫏≰-11201022","layer":1},{"info":"⫏≰121220221≎⊠⪸⫏≰-11201022=⫏≰2111","layer":0}]}
{"id":289,"expression_no_base_symbol":"$2824$≹⇙⪍$1348$⨟⋌⩍($1197$+$4126$)","expression":"⫏≰10212121≹⇙⪍⫏≰1211221⨟⋌⩍(⫏≰1122100+⫏≰12122211)","highest_n_order":4,"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":2824,"base":3},"right_expr":{"type":"numeric_atoms","value":1348,"base":3}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":1197,"base":3},"right_expr":{"type":"numeric_atoms","value":4126,"base":3}}},"used_operators":["rGHVDoGpnC","AHs5Up7iyr","W4YGzv6Whe"],"dependent_operators":["Tcnh7f0tEr","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2824","layer":2},{"info":"number node, value=1348","layer":2},{"info":"compute binary expreesion, left_input=2824, right_input=1348, 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":"number node, value=1197","layer":2},{"info":"number node, value=4126","layer":2},{"info":"compute binary expreesion, left_input=1197, right_input=4126, op_id = W4YGzv6Whe binary_op_definition= 'None', output=5323","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=5323, 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":0}],"base":3,"result_base":3,"text":"⫏≰10212121≹⇙⪍⫏≰1211221⨟⋌⩍(⫏≰1122100+⫏≰12122211)=NaN","reverse_text":"NaN=⫏≰10212121≹⇙⪍⫏≰1211221⨟⋌⩍(⫏≰1122100+⫏≰12122211)","cot":[{"info":"⫏≰10212121≹⇙⪍⫏≰1211221=NaN","layer":1},{"info":"⫏≰1122100+⫏≰12122211=⫏≰21022011","layer":1},{"info":"NaN⨟⋌⩍⫏≰21022011=NaN","layer":0}]}
{"id":290,"expression_no_base_symbol":"⫛⫱⨽(∥⊫$1036$)","expression":"⫛⫱⨽(∥⊫⫏≰1102101)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1426,"operation_count":2,"complexity_ratio":713.0,"tree":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":1036,"base":3}}},"used_operators":["DlLNRPXxWL","P8v4zCKN1o"],"dependent_operators":["rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1036","layer":2},{"info":"compute unary expreesion, input=1036, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=1904","layer":1},{"info":"compute unary expreesion, input=1904, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫛⫱⨽(∥⊫⫏≰1102101)=⫏≰0","reverse_text":"⫏≰0=⫛⫱⨽(∥⊫⫏≰1102101)","cot":[{"info":"∥⊫⫏≰1102101=⫏≰2121112","layer":1},{"info":"⫛⫱⨽⫏≰2121112=⫏≰0","layer":0}]}
{"id":291,"expression_no_base_symbol":"≦∁$5397$⩚⊴⇥$4310$","expression":"≦∁⫏≰21101220⩚⊴⇥⫏≰12220122","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":5397,"base":3},"right_expr":{"type":"numeric_atoms","value":4310,"base":3}}},"used_operators":["9ICcGScMcE","NTOWxs364D"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5397","layer":2},{"info":"number node, value=4310","layer":2},{"info":"compute binary expreesion, left_input=5397, right_input=4310, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-9828","layer":1},{"info":"compute unary expreesion, input=-9828, 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":3,"result_base":3,"text":"≦∁⫏≰21101220⩚⊴⇥⫏≰12220122=⫏≰2111","reverse_text":"⫏≰2111=≦∁⫏≰21101220⩚⊴⇥⫏≰12220122","cot":[{"info":"⫏≰21101220⩚⊴⇥⫏≰12220122=⫏≰-111111000","layer":1},{"info":"≦∁⫏≰-111111000=⫏≰2111","layer":0}]}
{"id":292,"expression_no_base_symbol":"($2868$⫥∨⫟$2895$)≹⇙⪍($4990$⫸⊐$1042$)","expression":"(⫏≰10221020⫥∨⫟⫏≰10222020)≹⇙⪍(⫏≰20211211⫸⊐⫏≰1102121)","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":2868,"base":3},"right_expr":{"type":"numeric_atoms","value":2895,"base":3}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":4990,"base":3},"right_expr":{"type":"numeric_atoms","value":1042,"base":3}}},"used_operators":["AHs5Up7iyr","KYD54nUTWz","mqXw5SEYmG"],"dependent_operators":["dWAJyo7jo9","8HhzD0ZcuI","rGHVDoGpnC","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2868","layer":2},{"info":"number node, value=2895","layer":2},{"info":"compute binary expreesion, left_input=2868, right_input=2895, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=4990","layer":2},{"info":"number node, value=1042","layer":2},{"info":"compute binary expreesion, left_input=4990, right_input=1042, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=4043","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=4043, 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":3,"result_base":3,"text":"(⫏≰10221020⫥∨⫟⫏≰10222020)≹⇙⪍(⫏≰20211211⫸⊐⫏≰1102121)=NaN","reverse_text":"NaN=(⫏≰10221020⫥∨⫟⫏≰10222020)≹⇙⪍(⫏≰20211211⫸⊐⫏≰1102121)","cot":[{"info":"⫏≰10221020⫥∨⫟⫏≰10222020=NaN","layer":1},{"info":"⫏≰20211211⫸⊐⫏≰1102121=⫏≰12112202","layer":1},{"info":"NaN≹⇙⪍⫏≰12112202=NaN","layer":0}]}
{"id":293,"expression_no_base_symbol":"($5725$⊉≛↸$2402$)⨟⋌⩍($3102$⩤)","expression":"(⫏≰21212001⊉≛↸⫏≰10021222)⨟⋌⩍(⫏≰11020220⩤)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4,"operation_count":3,"complexity_ratio":1.3333333333333333,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":5725,"base":3},"right_expr":{"type":"numeric_atoms","value":2402,"base":3}},"right_expr":{"type":"unary","operator":"⩤","unary_expr":{"type":"numeric_atoms","value":3102,"base":3}}},"used_operators":["rGHVDoGpnC","DZ8iAZOCBD","Z2TMIBDE3Q"],"dependent_operators":["Tcnh7f0tEr","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5725","layer":2},{"info":"number node, value=2402","layer":2},{"info":"compute binary expreesion, left_input=5725, right_input=2402, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=11450","layer":1},{"info":"number node, value=3102","layer":2},{"info":"compute unary expreesion, input=3102, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-3102","layer":1},{"info":"compute binary expreesion, left_input=11450, right_input=-3102, 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":0}],"base":3,"result_base":3,"text":"(⫏≰21212001⊉≛↸⫏≰10021222)⨟⋌⩍(⫏≰11020220⩤)=NaN","reverse_text":"NaN=(⫏≰21212001⊉≛↸⫏≰10021222)⨟⋌⩍(⫏≰11020220⩤)","cot":[{"info":"⫏≰21212001⊉≛↸⫏≰10021222=⫏≰120201002","layer":1},{"info":"⫏≰11020220⩤=⫏≰-11020220","layer":1},{"info":"⫏≰120201002⨟⋌⩍⫏≰-11020220=NaN","layer":0}]}
{"id":294,"expression_no_base_symbol":"(⪲⇎$6897$)⪮%⊝($3178$⪨≂$5717$)","expression":"(⪲⇎⫏≰100110110)⪮%⊝(⫏≰11100201⪨≂⫏≰21211202)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16,"operation_count":3,"complexity_ratio":5.333333333333333,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":6897,"base":3}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":3178,"base":3},"right_expr":{"type":"numeric_atoms","value":5717,"base":3}}},"used_operators":["IWmyXbctLI","XPYlsWDdGa","sdazOOVcIp"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰1102021111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6897","layer":2},{"info":"compute unary expreesion, input=6897, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=13794","layer":1},{"info":"number node, value=3178","layer":2},{"info":"number node, value=5717","layer":2},{"info":"compute binary expreesion, left_input=3178, right_input=5717, 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=-4976","layer":1},{"info":"compute binary expreesion, left_input=13794, right_input=-4976, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=27904","layer":0}],"base":3,"result_base":3,"text":"(⪲⇎⫏≰100110110)⪮%⊝(⫏≰11100201⪨≂⫏≰21211202)=⫏≰1102021111","reverse_text":"⫏≰1102021111=(⪲⇎⫏≰100110110)⪮%⊝(⫏≰11100201⪨≂⫏≰21211202)","cot":[{"info":"⪲⇎⫏≰100110110=⫏≰200220220","layer":1},{"info":"⫏≰11100201⪨≂⫏≰21211202=⫏≰-20211022","layer":1},{"info":"⫏≰200220220⪮%⊝⫏≰-20211022=⫏≰1102021111","layer":0}]}
{"id":295,"expression_no_base_symbol":"(⪝⪂⫅$2441$)↬($1042$↺$1379$)","expression":"(⪝⪂⫅⫏≰10100102)↬(⫏≰1102121↺⫏≰1220002)","highest_n_order":5,"priority_hierarchical_complexity":2,"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":2441,"base":3}},"right_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":1042,"base":3},"right_expr":{"type":"numeric_atoms","value":1379,"base":3}}},"used_operators":["B5M0gjZbta","XTarYq4gQB","7j4O788W3g"],"dependent_operators":["rGHVDoGpnC","9HNa5Wba9A","8w2t5hMYqp","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2441","layer":2},{"info":"compute unary expreesion, input=2441, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=-358827","layer":1},{"info":"number node, value=1042","layer":2},{"info":"number node, value=1379","layer":2},{"info":"compute binary expreesion, left_input=1042, right_input=1379, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1379","layer":1},{"info":"compute binary expreesion, left_input=-358827, right_input=1379, 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":3,"result_base":3,"text":"(⪝⪂⫅⫏≰10100102)↬(⫏≰1102121↺⫏≰1220002)=NaN","reverse_text":"NaN=(⪝⪂⫅⫏≰10100102)↬(⫏≰1102121↺⫏≰1220002)","cot":[{"info":"⪝⪂⫅⫏≰10100102=⫏≰-200020012220","layer":1},{"info":"⫏≰1102121↺⫏≰1220002=⫏≰1220002","layer":1},{"info":"⫏≰-200020012220↬⫏≰1220002=NaN","layer":0}]}
{"id":296,"expression_no_base_symbol":"($1998$⨳⩥⨓$1368$)≦≮≮","expression":"(⫏≰2202000⨳⩥⨓⫏≰1212200)≦≮≮","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":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":1998,"base":3},"right_expr":{"type":"numeric_atoms","value":1368,"base":3}}},"used_operators":["D4vGDi5EA2","nCS4ZIUYfx"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰2121000","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1998","layer":2},{"info":"number node, value=1368","layer":2},{"info":"compute binary expreesion, left_input=1998, right_input=1368, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-630","layer":1},{"info":"compute unary expreesion, input=-630, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=1890","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2202000⨳⩥⨓⫏≰1212200)≦≮≮=⫏≰2121000","reverse_text":"⫏≰2121000=(⫏≰2202000⨳⩥⨓⫏≰1212200)≦≮≮","cot":[{"info":"⫏≰2202000⨳⩥⨓⫏≰1212200=⫏≰-212100","layer":1},{"info":"⫏≰-212100≦≮≮=⫏≰2121000","layer":0}]}
{"id":297,"expression_no_base_symbol":"$1442$⨪↰⇹$7464$≧⫂∧($2552$⩨$1624$)","expression":"⫏≰1222102⨪↰⇹⫏≰101020110≧⫂∧(⫏≰10111112⩨⫏≰2020011)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1447,"operation_count":3,"complexity_ratio":482.3333333333333,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":1442,"base":3},"right_expr":{"type":"numeric_atoms","value":7464,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":2552,"base":3},"right_expr":{"type":"numeric_atoms","value":1624,"base":3}}},"used_operators":["Ph9nP6C5qx","tmPS8pqC7x","2DlMacCsIx"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rJVOvQCfKK","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰-122112","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1442","layer":2},{"info":"number node, value=7464","layer":2},{"info":"compute binary expreesion, left_input=1442, right_input=7464, 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=1442","layer":1},{"info":"number node, value=2552","layer":2},{"info":"number node, value=1624","layer":2},{"info":"compute binary expreesion, left_input=2552, right_input=1624, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=1442, right_input=0, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=-473","layer":0}],"base":3,"result_base":3,"text":"⫏≰1222102⨪↰⇹⫏≰101020110≧⫂∧(⫏≰10111112⩨⫏≰2020011)=⫏≰-122112","reverse_text":"⫏≰-122112=⫏≰1222102⨪↰⇹⫏≰101020110≧⫂∧(⫏≰10111112⩨⫏≰2020011)","cot":[{"info":"⫏≰1222102⨪↰⇹⫏≰101020110=⫏≰1222102","layer":1},{"info":"⫏≰10111112⩨⫏≰2020011=⫏≰0","layer":1},{"info":"⫏≰1222102≧⫂∧⫏≰0=⫏≰-122112","layer":0}]}
{"id":298,"expression_no_base_symbol":"⪲⇎(+⊝⨔$5147$)","expression":"⪲⇎(+⊝⨔⫏≰21001122)","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":5147,"base":3}}},"used_operators":["XPYlsWDdGa","DhbWaqg5eL"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe"],"result":"⫏≰11011202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5147","layer":2},{"info":"compute unary expreesion, input=5147, 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 = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=3044","layer":0}],"base":3,"result_base":3,"text":"⪲⇎(+⊝⨔⫏≰21001122)=⫏≰11011202","reverse_text":"⫏≰11011202=⪲⇎(+⊝⨔⫏≰21001122)","cot":[{"info":"+⊝⨔⫏≰21001122=⫏≰2002101","layer":1},{"info":"⪲⇎⫏≰2002101=⫏≰11011202","layer":0}]}
{"id":299,"expression_no_base_symbol":"$1181$∑⇟⊟$1682$⊭↱$2237$⪄$1023$","expression":"⫏≰1121202∑⇟⊟⫏≰2022022⊭↱⫏≰10001212⪄⫏≰1101220","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":102,"operation_count":3,"complexity_ratio":34.0,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":1181,"base":3},"right_expr":{"type":"numeric_atoms","value":1682,"base":3}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2237,"base":3},"right_expr":{"type":"numeric_atoms","value":1023,"base":3}}},"used_operators":["COABgblf1C","U7g4x0WXJJ","SUmda5xLS4"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1181","layer":2},{"info":"number node, value=1682","layer":2},{"info":"compute binary expreesion, left_input=1181, right_input=1682, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"number node, value=2237","layer":2},{"info":"number node, value=1023","layer":2},{"info":"compute binary expreesion, left_input=2237, right_input=1023, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-331257","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-331257, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1121202∑⇟⊟⫏≰2022022⊭↱⫏≰10001212⪄⫏≰1101220=NaN","reverse_text":"NaN=⫏≰1121202∑⇟⊟⫏≰2022022⊭↱⫏≰10001212⪄⫏≰1101220","cot":[{"info":"⫏≰1121202∑⇟⊟⫏≰2022022=NaN","layer":1},{"info":"⫏≰10001212⪄⫏≰1101220=⫏≰-121211101210","layer":1},{"info":"NaN⊭↱⫏≰-121211101210=NaN","layer":0}]}
{"id":300,"expression_no_base_symbol":"$6015$⨰$4610$⩤","expression":"⫏≰22020210⨰⫏≰20022202⩤","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":6015,"base":3},"right_expr":{"type":"numeric_atoms","value":4610,"base":3}}},"used_operators":["Z2TMIBDE3Q","eewbuw0ToL"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-1221102","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6015","layer":2},{"info":"number node, value=4610","layer":2},{"info":"compute binary expreesion, left_input=6015, right_input=4610, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=1415","layer":1},{"info":"compute unary expreesion, input=1415, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-1415","layer":0}],"base":3,"result_base":3,"text":"⫏≰22020210⨰⫏≰20022202⩤=⫏≰-1221102","reverse_text":"⫏≰-1221102=⫏≰22020210⨰⫏≰20022202⩤","cot":[{"info":"⫏≰22020210⨰⫏≰20022202=⫏≰1221102","layer":1},{"info":"⫏≰1221102⩤=⫏≰-1221102","layer":0}]}
{"id":301,"expression_no_base_symbol":"($4686$⊉≛↸$3470$)⨳⩥⨓(≤/$3249$)","expression":"(⫏≰20102120⊉≛↸⫏≰11202112)⨳⩥⨓(≤/⫏≰11110100)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":4686,"base":3},"right_expr":{"type":"numeric_atoms","value":3470,"base":3}},"right_expr":{"type":"unary","operator":"≤/","unary_expr":{"type":"numeric_atoms","value":3249,"base":3}}},"used_operators":["nCS4ZIUYfx","DZ8iAZOCBD","eLAdDNolq6"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰-121122112","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4686","layer":2},{"info":"number node, value=3470","layer":2},{"info":"compute binary expreesion, left_input=4686, right_input=3470, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=9372","layer":1},{"info":"number node, value=3249","layer":2},{"info":"compute unary expreesion, input=3249, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-2765","layer":1},{"info":"compute binary expreesion, left_input=9372, right_input=-2765, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-12137","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20102120⊉≛↸⫏≰11202112)⨳⩥⨓(≤/⫏≰11110100)=⫏≰-121122112","reverse_text":"⫏≰-121122112=(⫏≰20102120⊉≛↸⫏≰11202112)⨳⩥⨓(≤/⫏≰11110100)","cot":[{"info":"⫏≰20102120⊉≛↸⫏≰11202112=⫏≰110212010","layer":1},{"info":"≤/⫏≰11110100=⫏≰-10210102","layer":1},{"info":"⫏≰110212010⨳⩥⨓⫏≰-10210102=⫏≰-121122112","layer":0}]}
{"id":302,"expression_no_base_symbol":"↯⪼($1725$⊭↱$2685$)","expression":"↯⪼(⫏≰2100220⊭↱⫏≰10200110)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":37,"operation_count":2,"complexity_ratio":18.5,"tree":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":1725,"base":3},"right_expr":{"type":"numeric_atoms","value":2685,"base":3}}},"used_operators":["8jW3W4yZS5","COABgblf1C"],"dependent_operators":["eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1725","layer":2},{"info":"number node, value=2685","layer":2},{"info":"compute binary expreesion, left_input=1725, right_input=2685, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=1925","layer":1},{"info":"compute unary expreesion, input=1925, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":0}],"base":3,"result_base":3,"text":"↯⪼(⫏≰2100220⊭↱⫏≰10200110)=⫏≰-210","reverse_text":"⫏≰-210=↯⪼(⫏≰2100220⊭↱⫏≰10200110)","cot":[{"info":"⫏≰2100220⊭↱⫏≰10200110=⫏≰2122022","layer":1},{"info":"↯⪼⫏≰2122022=⫏≰-210","layer":0}]}
{"id":303,"expression_no_base_symbol":"($1037$∀⇚≩$5823$)⪘⫢(↔$2629$)","expression":"(⫏≰1102102∀⇚≩⫏≰21222200)⪘⫢(↔⫏≰10121101)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7275,"operation_count":3,"complexity_ratio":2425.0,"tree":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":1037,"base":3},"right_expr":{"type":"numeric_atoms","value":5823,"base":3}},"right_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":2629,"base":3}}},"used_operators":["oacrs7FA3X","LRNGc0VcxI","ruOEQAzv1W"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","X99M06cbEe","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1037","layer":2},{"info":"number node, value=5823","layer":2},{"info":"compute binary expreesion, left_input=1037, right_input=5823, 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=2629","layer":2},{"info":"compute unary expreesion, input=2629, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-2356","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-2356, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1102102∀⇚≩⫏≰21222200)⪘⫢(↔⫏≰10121101)=NaN","reverse_text":"NaN=(⫏≰1102102∀⇚≩⫏≰21222200)⪘⫢(↔⫏≰10121101)","cot":[{"info":"⫏≰1102102∀⇚≩⫏≰21222200=NaN","layer":1},{"info":"↔⫏≰10121101=⫏≰-10020021","layer":1},{"info":"NaN⪘⫢⫏≰-10020021=NaN","layer":0}]}
{"id":304,"expression_no_base_symbol":"↣≠⋷(⫓⪴$1234$)","expression":"↣≠⋷(⫓⪴⫏≰1200201)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1237,"operation_count":2,"complexity_ratio":618.5,"tree":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":1234,"base":3}}},"used_operators":["Asc51vEJeQ","eLxqMNBOBk"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1234","layer":2},{"info":"compute unary expreesion, input=1234, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=1522756","layer":1},{"info":"compute unary expreesion, input=1522756, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(⫓⪴⫏≰1200201)=NaN","reverse_text":"NaN=↣≠⋷(⫓⪴⫏≰1200201)","cot":[{"info":"⫓⪴⫏≰1200201=⫏≰2212100211101","layer":1},{"info":"↣≠⋷⫏≰2212100211101=NaN","layer":0}]}
{"id":305,"expression_no_base_symbol":"($1132$≦≮≮)⨳⩥⨓$3256$⨰$1252$","expression":"(⫏≰1112221≦≮≮)⨳⩥⨓⫏≰11110121⨰⫏≰1201101","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":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":1132,"base":3}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":3256,"base":3},"right_expr":{"type":"numeric_atoms","value":1252,"base":3}}},"used_operators":["nCS4ZIUYfx","D4vGDi5EA2","eewbuw0ToL"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21102101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1132","layer":2},{"info":"compute unary expreesion, input=1132, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-3396","layer":1},{"info":"number node, value=3256","layer":2},{"info":"number node, value=1252","layer":2},{"info":"compute binary expreesion, left_input=3256, right_input=1252, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=2014","layer":1},{"info":"compute binary expreesion, left_input=-3396, right_input=2014, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=5410","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1112221≦≮≮)⨳⩥⨓⫏≰11110121⨰⫏≰1201101=⫏≰21102101","reverse_text":"⫏≰21102101=(⫏≰1112221≦≮≮)⨳⩥⨓⫏≰11110121⨰⫏≰1201101","cot":[{"info":"⫏≰1112221≦≮≮=⫏≰-11122210","layer":1},{"info":"⫏≰11110121⨰⫏≰1201101=⫏≰2202121","layer":1},{"info":"⫏≰-11122210⨳⩥⨓⫏≰2202121=⫏≰21102101","layer":0}]}
{"id":306,"expression_no_base_symbol":"(⋗⩬⋾$1305$)⨸⪁(⪲⇎$1885$)","expression":"(⋗⩬⋾⫏≰1210100)⨸⪁(⪲⇎⫏≰2120211)","highest_n_order":1,"priority_hierarchical_complexity":2,"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":1305,"base":3}},"right_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":1885,"base":3}}},"used_operators":["g55IO6H4Gj","DpFCA1CohY","XPYlsWDdGa"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-101202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1305","layer":2},{"info":"compute unary expreesion, input=1305, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-3915","layer":1},{"info":"number node, value=1885","layer":2},{"info":"compute unary expreesion, input=1885, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=3770","layer":1},{"info":"compute binary expreesion, left_input=-3915, right_input=3770, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=-290","layer":0}],"base":3,"result_base":3,"text":"(⋗⩬⋾⫏≰1210100)⨸⪁(⪲⇎⫏≰2120211)=⫏≰-101202","reverse_text":"⫏≰-101202=(⋗⩬⋾⫏≰1210100)⨸⪁(⪲⇎⫏≰2120211)","cot":[{"info":"⋗⩬⋾⫏≰1210100=⫏≰-12101000","layer":1},{"info":"⪲⇎⫏≰2120211=⫏≰12011122","layer":1},{"info":"⫏≰-12101000⨸⪁⫏≰12011122=⫏≰-101202","layer":0}]}
{"id":307,"expression_no_base_symbol":"$2862$⋳⪒$1126$⩨(≤/$1686$)","expression":"⫏≰10221000⋳⪒⫏≰1112201⩨(≤/⫏≰2022110)","highest_n_order":2,"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":2862,"base":3},"right_expr":{"type":"numeric_atoms","value":1126,"base":3}},"right_expr":{"type":"unary","operator":"≤/","unary_expr":{"type":"numeric_atoms","value":1686,"base":3}}},"used_operators":["2DlMacCsIx","12rbrZMWeM","eLAdDNolq6"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰10","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2862","layer":2},{"info":"number node, value=1126","layer":2},{"info":"compute binary expreesion, left_input=2862, right_input=1126, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=4311","layer":1},{"info":"number node, value=1686","layer":2},{"info":"compute unary expreesion, input=1686, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-1202","layer":1},{"info":"compute binary expreesion, left_input=4311, right_input=-1202, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=3","layer":0}],"base":3,"result_base":3,"text":"⫏≰10221000⋳⪒⫏≰1112201⩨(≤/⫏≰2022110)=⫏≰10","reverse_text":"⫏≰10=⫏≰10221000⋳⪒⫏≰1112201⩨(≤/⫏≰2022110)","cot":[{"info":"⫏≰10221000⋳⪒⫏≰1112201=⫏≰12220200","layer":1},{"info":"≤/⫏≰2022110=⫏≰-1122112","layer":1},{"info":"⫏≰12220200⩨⫏≰-1122112=⫏≰10","layer":0}]}
{"id":308,"expression_no_base_symbol":"⨵≀≌($4267$⇼⇔∾$1692$)","expression":"⨵≀≌(⫏≰12212001⇼⇔∾⫏≰2022200)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2582,"operation_count":2,"complexity_ratio":1291.0,"tree":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":4267,"base":3},"right_expr":{"type":"numeric_atoms","value":1692,"base":3}}},"used_operators":["srAu1WTS94","tifHPKVTfV"],"dependent_operators":["glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰110110212111201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4267","layer":2},{"info":"number node, value=1692","layer":2},{"info":"compute binary expreesion, left_input=4267, right_input=1692, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-2575","layer":1},{"info":"compute unary expreesion, input=-2575, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=6630625","layer":0}],"base":3,"result_base":3,"text":"⨵≀≌(⫏≰12212001⇼⇔∾⫏≰2022200)=⫏≰110110212111201","reverse_text":"⫏≰110110212111201=⨵≀≌(⫏≰12212001⇼⇔∾⫏≰2022200)","cot":[{"info":"⫏≰12212001⇼⇔∾⫏≰2022200=⫏≰-10112101","layer":1},{"info":"⨵≀≌⫏≰-10112101=⫏≰110110212111201","layer":0}]}
{"id":309,"expression_no_base_symbol":"($6866$⨳⩥⨓$1829$)⨐⩸⫘(⪝⪂⫅$1385$)","expression":"(⫏≰100102022⨳⩥⨓⫏≰2111202)⨐⩸⫘(⪝⪂⫅⫏≰1220022)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":154,"operation_count":3,"complexity_ratio":51.333333333333336,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":6866,"base":3},"right_expr":{"type":"numeric_atoms","value":1829,"base":3}},"right_expr":{"type":"unary","operator":"⪝⪂⫅","unary_expr":{"type":"numeric_atoms","value":1385,"base":3}}},"used_operators":["fu6greOZ01","nCS4ZIUYfx","XTarYq4gQB"],"dependent_operators":["3ViojmjbAp","W4YGzv6Whe","rysDP5nf3Z","9HNa5Wba9A","8w2t5hMYqp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6866","layer":2},{"info":"number node, value=1829","layer":2},{"info":"compute binary expreesion, left_input=6866, right_input=1829, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-5037","layer":1},{"info":"number node, value=1385","layer":2},{"info":"compute unary expreesion, input=1385, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=-203595","layer":1},{"info":"compute binary expreesion, left_input=-5037, right_input=-203595, 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":3,"result_base":3,"text":"(⫏≰100102022⨳⩥⨓⫏≰2111202)⨐⩸⫘(⪝⪂⫅⫏≰1220022)=NaN","reverse_text":"NaN=(⫏≰100102022⨳⩥⨓⫏≰2111202)⨐⩸⫘(⪝⪂⫅⫏≰1220022)","cot":[{"info":"⫏≰100102022⨳⩥⨓⫏≰2111202=⫏≰-20220120","layer":1},{"info":"⪝⪂⫅⫏≰1220022=⫏≰-101100021120","layer":1},{"info":"⫏≰-20220120⨐⩸⫘⫏≰-101100021120=NaN","layer":0}]}
{"id":310,"expression_no_base_symbol":"($4878$⇼⇔∾$1229$)⫌⩹⨱","expression":"(⫏≰20200200⇼⇔∾⫏≰1200112)⫌⩹⨱","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":4878,"base":3},"right_expr":{"type":"numeric_atoms","value":1229,"base":3}}},"used_operators":["EBcxylXtPf","tifHPKVTfV"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-22002102","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4878","layer":2},{"info":"number node, value=1229","layer":2},{"info":"compute binary expreesion, left_input=4878, right_input=1229, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-3649","layer":1},{"info":"compute unary expreesion, input=-3649, op_id = EBcxylXtPf, unary_op_definition = 'a⫌⩹⨱ = { (((80+a)+(750-a))+((149+422)+(a+a))) }', output=-5897","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20200200⇼⇔∾⫏≰1200112)⫌⩹⨱=⫏≰-22002102","reverse_text":"⫏≰-22002102=(⫏≰20200200⇼⇔∾⫏≰1200112)⫌⩹⨱","cot":[{"info":"⫏≰20200200⇼⇔∾⫏≰1200112=⫏≰-12000011","layer":1},{"info":"⫏≰-12000011⫌⩹⨱=⫏≰-22002102","layer":0}]}
{"id":311,"expression_no_base_symbol":"⨰⫟⨤(⩦⩻⨪$1299$)","expression":"⨰⫟⨤(⩦⩻⨪⫏≰1210010)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4359,"operation_count":2,"complexity_ratio":2179.5,"tree":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":1299,"base":3}}},"used_operators":["Tw270M8GLb","2td37pGCOC"],"dependent_operators":["sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1299","layer":2},{"info":"compute unary expreesion, input=1299, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=1299","layer":1},{"info":"compute unary expreesion, input=1299, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⨰⫟⨤(⩦⩻⨪⫏≰1210010)=NaN","reverse_text":"NaN=⨰⫟⨤(⩦⩻⨪⫏≰1210010)","cot":[{"info":"⩦⩻⨪⫏≰1210010=⫏≰1210010","layer":1},{"info":"⨰⫟⨤⫏≰1210010=NaN","layer":0}]}
{"id":312,"expression_no_base_symbol":"($1246$⇷$6179$)≹⇙⪍($7638$≹⇙⪍$1142$)","expression":"(⫏≰1201011⇷⫏≰22110212)≹⇙⪍(⫏≰101110220≹⇙⪍⫏≰1120022)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":17452,"operation_count":3,"complexity_ratio":5817.333333333333,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":1246,"base":3},"right_expr":{"type":"numeric_atoms","value":6179,"base":3}},"right_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":7638,"base":3},"right_expr":{"type":"numeric_atoms","value":1142,"base":3}}},"used_operators":["AHs5Up7iyr","mp7IySMOzn"],"dependent_operators":["dWAJyo7jo9","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1246","layer":2},{"info":"number node, value=6179","layer":2},{"info":"compute binary expreesion, left_input=1246, right_input=6179, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=12358","layer":1},{"info":"number node, value=7638","layer":2},{"info":"number node, value=1142","layer":2},{"info":"compute binary expreesion, left_input=7638, right_input=1142, 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=12358, 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":3,"result_base":3,"text":"(⫏≰1201011⇷⫏≰22110212)≹⇙⪍(⫏≰101110220≹⇙⪍⫏≰1120022)=NaN","reverse_text":"NaN=(⫏≰1201011⇷⫏≰22110212)≹⇙⪍(⫏≰101110220≹⇙⪍⫏≰1120022)","cot":[{"info":"⫏≰1201011⇷⫏≰22110212=⫏≰121221201","layer":1},{"info":"⫏≰101110220≹⇙⪍⫏≰1120022=NaN","layer":1},{"info":"⫏≰121221201≹⇙⪍NaN=NaN","layer":0}]}
{"id":313,"expression_no_base_symbol":"$3742$↬$3857$∑⇟⊟($4019$⨐⩸⫘$1142$)","expression":"⫏≰12010121↬⫏≰12021212∑⇟⊟(⫏≰12111212⨐⩸⫘⫏≰1120022)","highest_n_order":5,"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":3742,"base":3},"right_expr":{"type":"numeric_atoms","value":3857,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":4019,"base":3},"right_expr":{"type":"numeric_atoms","value":1142,"base":3}}},"used_operators":["U7g4x0WXJJ","B5M0gjZbta","fu6greOZ01"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","rGHVDoGpnC","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3742","layer":2},{"info":"number node, value=3857","layer":2},{"info":"compute binary expreesion, left_input=3742, right_input=3857, 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=4019","layer":2},{"info":"number node, value=1142","layer":2},{"info":"compute binary expreesion, left_input=4019, right_input=1142, 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=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":3,"result_base":3,"text":"⫏≰12010121↬⫏≰12021212∑⇟⊟(⫏≰12111212⨐⩸⫘⫏≰1120022)=NaN","reverse_text":"NaN=⫏≰12010121↬⫏≰12021212∑⇟⊟(⫏≰12111212⨐⩸⫘⫏≰1120022)","cot":[{"info":"⫏≰12010121↬⫏≰12021212=NaN","layer":1},{"info":"⫏≰12111212⨐⩸⫘⫏≰1120022=NaN","layer":1},{"info":"NaN∑⇟⊟NaN=NaN","layer":0}]}
{"id":314,"expression_no_base_symbol":"($3003$⩚⊴⇥$1232$)∼($2819$+⇶⊼$2279$)","expression":"(⫏≰11010020⩚⊴⇥⫏≰1200122)∼(⫏≰10212102+⇶⊼⫏≰10010102)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":91,"operation_count":3,"complexity_ratio":30.333333333333332,"tree":{"type":"binary","operator":"∼","left_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":3003,"base":3},"right_expr":{"type":"numeric_atoms","value":1232,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":2819,"base":3},"right_expr":{"type":"numeric_atoms","value":2279,"base":3}}},"used_operators":["DyGG3AbaNP","NTOWxs364D","TpPTUOHfaN"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3003","layer":2},{"info":"number node, value=1232","layer":2},{"info":"compute binary expreesion, left_input=3003, right_input=1232, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-4356","layer":1},{"info":"number node, value=2819","layer":2},{"info":"number node, value=2279","layer":2},{"info":"compute binary expreesion, left_input=2819, right_input=2279, 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":1},{"info":"compute binary expreesion, left_input=-4356, 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":3,"result_base":3,"text":"(⫏≰11010020⩚⊴⇥⫏≰1200122)∼(⫏≰10212102+⇶⊼⫏≰10010102)=NaN","reverse_text":"NaN=(⫏≰11010020⩚⊴⇥⫏≰1200122)∼(⫏≰10212102+⇶⊼⫏≰10010102)","cot":[{"info":"⫏≰11010020⩚⊴⇥⫏≰1200122=⫏≰-12222100","layer":1},{"info":"⫏≰10212102+⇶⊼⫏≰10010102=NaN","layer":1},{"info":"⫏≰-12222100∼NaN=NaN","layer":0}]}
{"id":315,"expression_no_base_symbol":"(⋗⩬⋾$1131$)⪘⫢($2755$⨎$4811$)","expression":"(⋗⩬⋾⫏≰1112220)⪘⫢(⫏≰10210001⨎⫏≰20121012)","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":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":1131,"base":3}},"right_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":2755,"base":3},"right_expr":{"type":"numeric_atoms","value":4811,"base":3}}},"used_operators":["oacrs7FA3X","DpFCA1CohY","rJVOvQCfKK"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1131","layer":2},{"info":"compute unary expreesion, input=1131, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-3393","layer":1},{"info":"number node, value=2755","layer":2},{"info":"number node, value=4811","layer":2},{"info":"compute binary expreesion, left_input=2755, right_input=4811, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=4811","layer":1},{"info":"compute binary expreesion, left_input=-3393, right_input=4811, 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":3,"result_base":3,"text":"(⋗⩬⋾⫏≰1112220)⪘⫢(⫏≰10210001⨎⫏≰20121012)=⫏≰-1","reverse_text":"⫏≰-1=(⋗⩬⋾⫏≰1112220)⪘⫢(⫏≰10210001⨎⫏≰20121012)","cot":[{"info":"⋗⩬⋾⫏≰1112220=⫏≰-11122200","layer":1},{"info":"⫏≰10210001⨎⫏≰20121012=⫏≰20121012","layer":1},{"info":"⫏≰-11122200⪘⫢⫏≰20121012=⫏≰-1","layer":0}]}
{"id":316,"expression_no_base_symbol":"≤/(⩦⩻⨪$2233$)","expression":"≤/(⩦⩻⨪⫏≰10001201)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4,"operation_count":2,"complexity_ratio":2.0,"tree":{"type":"unary","operator":"≤/","unary_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":2233,"base":3}}},"used_operators":["eLAdDNolq6","2td37pGCOC"],"dependent_operators":["rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-2101210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2233","layer":2},{"info":"compute unary expreesion, input=2233, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=2233","layer":1},{"info":"compute unary expreesion, input=2233, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-1749","layer":0}],"base":3,"result_base":3,"text":"≤/(⩦⩻⨪⫏≰10001201)=⫏≰-2101210","reverse_text":"⫏≰-2101210=≤/(⩦⩻⨪⫏≰10001201)","cot":[{"info":"⩦⩻⨪⫏≰10001201=⫏≰10001201","layer":1},{"info":"≤/⫏≰10001201=⫏≰-2101210","layer":0}]}
{"id":317,"expression_no_base_symbol":"($4138$⊭↱$1927$)≹⇙⪍($2637$/$8447$)","expression":"(⫏≰12200021⊭↱⫏≰2122101)≹⇙⪍(⫏≰10121200/⫏≰102120212)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":4138,"base":3},"right_expr":{"type":"numeric_atoms","value":1927,"base":3}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":2637,"base":3},"right_expr":{"type":"numeric_atoms","value":8447,"base":3}}},"used_operators":["AHs5Up7iyr","COABgblf1C","XhwjNDsVaA"],"dependent_operators":["dWAJyo7jo9","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰-20001121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4138","layer":2},{"info":"number node, value=1927","layer":2},{"info":"compute binary expreesion, left_input=4138, right_input=1927, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-4417","layer":1},{"info":"number node, value=2637","layer":2},{"info":"number node, value=8447","layer":2},{"info":"compute binary expreesion, left_input=2637, right_input=8447, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute binary expreesion, left_input=-4417, right_input=0, 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=-4417","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12200021⊭↱⫏≰2122101)≹⇙⪍(⫏≰10121200/⫏≰102120212)=⫏≰-20001121","reverse_text":"⫏≰-20001121=(⫏≰12200021⊭↱⫏≰2122101)≹⇙⪍(⫏≰10121200/⫏≰102120212)","cot":[{"info":"⫏≰12200021⊭↱⫏≰2122101=⫏≰-20001121","layer":1},{"info":"⫏≰10121200/⫏≰102120212=⫏≰0","layer":1},{"info":"⫏≰-20001121≹⇙⪍⫏≰0=⫏≰-20001121","layer":0}]}
{"id":318,"expression_no_base_symbol":"$1995$⨸⪁$2451$⊭↱($1505$≦≮≮)","expression":"⫏≰2201220⨸⪁⫏≰10100210⊭↱(⫏≰2001202≦≮≮)","highest_n_order":1,"priority_hierarchical_complexity":2,"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":1995,"base":3},"right_expr":{"type":"numeric_atoms","value":2451,"base":3}},"right_expr":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":1505,"base":3}}},"used_operators":["COABgblf1C","g55IO6H4Gj","D4vGDi5EA2"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-1100202221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1995","layer":2},{"info":"number node, value=2451","layer":2},{"info":"compute binary expreesion, left_input=1995, right_input=2451, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=8892","layer":1},{"info":"number node, value=1505","layer":2},{"info":"compute unary expreesion, input=1505, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-4515","layer":1},{"info":"compute binary expreesion, left_input=8892, right_input=-4515, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-26809","layer":0}],"base":3,"result_base":3,"text":"⫏≰2201220⨸⪁⫏≰10100210⊭↱(⫏≰2001202≦≮≮)=⫏≰-1100202221","reverse_text":"⫏≰-1100202221=⫏≰2201220⨸⪁⫏≰10100210⊭↱(⫏≰2001202≦≮≮)","cot":[{"info":"⫏≰2201220⨸⪁⫏≰10100210=⫏≰110012100","layer":1},{"info":"⫏≰2001202≦≮≮=⫏≰-20012020","layer":1},{"info":"⫏≰110012100⊭↱⫏≰-20012020=⫏≰-1100202221","layer":0}]}
{"id":319,"expression_no_base_symbol":"$3219$⫸⊐$4177$∲⫓$6823$⨟⋌⩍$2653$","expression":"⫏≰11102020⫸⊐⫏≰12201201∲⫓⫏≰100100201⨟⋌⩍⫏≰10122021","highest_n_order":4,"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":3219,"base":3},"right_expr":{"type":"numeric_atoms","value":4177,"base":3}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":6823,"base":3},"right_expr":{"type":"numeric_atoms","value":2653,"base":3}}},"used_operators":["i8ToyICDmI","mqXw5SEYmG","rGHVDoGpnC"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3219","layer":2},{"info":"number node, value=4177","layer":2},{"info":"compute binary expreesion, left_input=3219, right_input=4177, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=16583","layer":1},{"info":"number node, value=6823","layer":2},{"info":"number node, value=2653","layer":2},{"info":"compute binary expreesion, left_input=6823, right_input=2653, 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=16583, right_input=nan, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11102020⫸⊐⫏≰12201201∲⫓⫏≰100100201⨟⋌⩍⫏≰10122021=NaN","reverse_text":"NaN=⫏≰11102020⫸⊐⫏≰12201201∲⫓⫏≰100100201⨟⋌⩍⫏≰10122021","cot":[{"info":"⫏≰11102020⫸⊐⫏≰12201201=⫏≰211202012","layer":1},{"info":"⫏≰100100201⨟⋌⩍⫏≰10122021=NaN","layer":1},{"info":"⫏≰211202012∲⫓NaN=NaN","layer":0}]}
{"id":320,"expression_no_base_symbol":"∥⊫$4596$∼$4604$","expression":"∥⊫⫏≰20022020∼⫏≰20022112","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":95,"operation_count":2,"complexity_ratio":47.5,"tree":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":4596,"base":3},"right_expr":{"type":"numeric_atoms","value":4604,"base":3}}},"used_operators":["P8v4zCKN1o","DyGG3AbaNP"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4596","layer":2},{"info":"number node, value=4604","layer":2},{"info":"compute binary expreesion, left_input=4596, right_input=4604, 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 = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"∥⊫⫏≰20022020∼⫏≰20022112=NaN","reverse_text":"NaN=∥⊫⫏≰20022020∼⫏≰20022112","cot":[{"info":"⫏≰20022020∼⫏≰20022112=NaN","layer":1},{"info":"∥⊫NaN=NaN","layer":0}]}
{"id":321,"expression_no_base_symbol":"↥(⋗⩬⋾$2452$)","expression":"↥(⋗⩬⋾⫏≰10100211)","highest_n_order":2,"priority_hierarchical_complexity":1,"normalized_expansion_degree":147,"operation_count":2,"complexity_ratio":73.5,"tree":{"type":"unary","operator":"↥","unary_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":2452,"base":3}}},"used_operators":["A8NUZmVepG","DpFCA1CohY"],"dependent_operators":["k8jYdgA6NY","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2452","layer":2},{"info":"compute unary expreesion, input=2452, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-7356","layer":1},{"info":"compute unary expreesion, input=-7356, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=39","layer":0}],"base":3,"result_base":3,"text":"↥(⋗⩬⋾⫏≰10100211)=⫏≰1110","reverse_text":"⫏≰1110=↥(⋗⩬⋾⫏≰10100211)","cot":[{"info":"⋗⩬⋾⫏≰10100211=⫏≰-101002110","layer":1},{"info":"↥⫏≰-101002110=⫏≰1110","layer":0}]}
{"id":322,"expression_no_base_symbol":"$5471$⋳⪒$3441$⨵⪆($2948$⨵⪆$2762$)","expression":"⫏≰21111122⋳⪒⫏≰11201110⨵⪆(⫏≰11001012⨵⪆⫏≰10210022)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":5471,"base":3},"right_expr":{"type":"numeric_atoms","value":3441,"base":3}},"right_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":2948,"base":3},"right_expr":{"type":"numeric_atoms","value":2762,"base":3}}},"used_operators":["2DQ55sFlQl","12rbrZMWeM"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5471","layer":2},{"info":"number node, value=3441","layer":2},{"info":"compute binary expreesion, left_input=5471, right_input=3441, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=7214","layer":1},{"info":"number node, value=2948","layer":2},{"info":"number node, value=2762","layer":2},{"info":"compute binary expreesion, left_input=2948, right_input=2762, 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=7214, right_input=160, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰21111122⋳⪒⫏≰11201110⨵⪆(⫏≰11001012⨵⪆⫏≰10210022)=⫏≰12221","reverse_text":"⫏≰12221=⫏≰21111122⋳⪒⫏≰11201110⨵⪆(⫏≰11001012⨵⪆⫏≰10210022)","cot":[{"info":"⫏≰21111122⋳⪒⫏≰11201110=⫏≰100220012","layer":1},{"info":"⫏≰11001012⨵⪆⫏≰10210022=⫏≰12221","layer":1},{"info":"⫏≰100220012⨵⪆⫏≰12221=⫏≰12221","layer":0}]}
{"id":323,"expression_no_base_symbol":"($1086$%$4863$)⪢($3802$⊉≛↸$5180$)","expression":"(⫏≰1111020%⫏≰20200010)⪢(⫏≰12012211⊉≛↸⫏≰21002212)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7607,"operation_count":3,"complexity_ratio":2535.6666666666665,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":1086,"base":3},"right_expr":{"type":"numeric_atoms","value":4863,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":3802,"base":3},"right_expr":{"type":"numeric_atoms","value":5180,"base":3}}},"used_operators":["dWAJyo7jo9","k8jYdgA6NY","DZ8iAZOCBD"],"dependent_operators":["k8jYdgA6NY","rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1086","layer":2},{"info":"number node, value=4863","layer":2},{"info":"compute binary expreesion, left_input=1086, right_input=4863, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1086","layer":1},{"info":"number node, value=3802","layer":2},{"info":"number node, value=5180","layer":2},{"info":"compute binary expreesion, left_input=3802, right_input=5180, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=7604","layer":1},{"info":"compute binary expreesion, left_input=1086, right_input=7604, 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":3,"result_base":3,"text":"(⫏≰1111020%⫏≰20200010)⪢(⫏≰12012211⊉≛↸⫏≰21002212)=NaN","reverse_text":"NaN=(⫏≰1111020%⫏≰20200010)⪢(⫏≰12012211⊉≛↸⫏≰21002212)","cot":[{"info":"⫏≰1111020%⫏≰20200010=⫏≰1111020","layer":1},{"info":"⫏≰12012211⊉≛↸⫏≰21002212=⫏≰101102122","layer":1},{"info":"⫏≰1111020⪢⫏≰101102122=NaN","layer":0}]}
{"id":324,"expression_no_base_symbol":"($2182$≦≮≮)⋳⪒($2585$⨐⩸⫘$3920$)","expression":"(⫏≰2222211≦≮≮)⋳⪒(⫏≰10112202⨐⩸⫘⫏≰12101012)","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":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":2182,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":2585,"base":3},"right_expr":{"type":"numeric_atoms","value":3920,"base":3}}},"used_operators":["12rbrZMWeM","D4vGDi5EA2","fu6greOZ01"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2182","layer":2},{"info":"compute unary expreesion, input=2182, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-6546","layer":1},{"info":"number node, value=2585","layer":2},{"info":"number node, value=3920","layer":2},{"info":"compute binary expreesion, left_input=2585, right_input=3920, 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=-6546, right_input=nan, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2222211≦≮≮)⋳⪒(⫏≰10112202⨐⩸⫘⫏≰12101012)=NaN","reverse_text":"NaN=(⫏≰2222211≦≮≮)⋳⪒(⫏≰10112202⨐⩸⫘⫏≰12101012)","cot":[{"info":"⫏≰2222211≦≮≮=⫏≰-22222110","layer":1},{"info":"⫏≰10112202⨐⩸⫘⫏≰12101012=NaN","layer":1},{"info":"⫏≰-22222110⋳⪒NaN=NaN","layer":0}]}
{"id":325,"expression_no_base_symbol":"$6669$≹⇙⪍$2893$⨐⩸⫘$1127$⪘⫢$1271$","expression":"⫏≰100011000≹⇙⪍⫏≰10222011⨐⩸⫘⫏≰1112202⪘⫢⫏≰1202002","highest_n_order":4,"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":6669,"base":3},"right_expr":{"type":"numeric_atoms","value":2893,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1127,"base":3},"right_expr":{"type":"numeric_atoms","value":1271,"base":3}}},"used_operators":["fu6greOZ01","AHs5Up7iyr","oacrs7FA3X"],"dependent_operators":["3ViojmjbAp","dWAJyo7jo9","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6669","layer":2},{"info":"number node, value=2893","layer":2},{"info":"compute binary expreesion, left_input=6669, right_input=2893, 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":"number node, value=1127","layer":2},{"info":"number node, value=1271","layer":2},{"info":"compute binary expreesion, left_input=1127, right_input=1271, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=2130","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2130, 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":3,"result_base":3,"text":"⫏≰100011000≹⇙⪍⫏≰10222011⨐⩸⫘⫏≰1112202⪘⫢⫏≰1202002=NaN","reverse_text":"NaN=⫏≰100011000≹⇙⪍⫏≰10222011⨐⩸⫘⫏≰1112202⪘⫢⫏≰1202002","cot":[{"info":"⫏≰100011000≹⇙⪍⫏≰10222011=NaN","layer":1},{"info":"⫏≰1112202⪘⫢⫏≰1202002=⫏≰2220220","layer":1},{"info":"NaN⨐⩸⫘⫏≰2220220=NaN","layer":0}]}
{"id":326,"expression_no_base_symbol":"(⨵≀≌$3709$)-($2006$⇋≉)","expression":"(⨵≀≌⫏≰12002101)-(⫏≰2202022⇋≉)","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":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":3709,"base":3}},"right_expr":{"type":"unary","operator":"⇋≉","unary_expr":{"type":"numeric_atoms","value":2006,"base":3}}},"used_operators":["rysDP5nf3Z","srAu1WTS94","XIabStNQrY"],"dependent_operators":["glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-202122002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3709","layer":2},{"info":"compute unary expreesion, input=3709, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-11127","layer":1},{"info":"number node, value=2006","layer":2},{"info":"compute unary expreesion, input=2006, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=3914","layer":1},{"info":"compute binary expreesion, left_input=-11127, right_input=3914, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-15041","layer":0}],"base":3,"result_base":3,"text":"(⨵≀≌⫏≰12002101)-(⫏≰2202022⇋≉)=⫏≰-202122002","reverse_text":"⫏≰-202122002=(⨵≀≌⫏≰12002101)-(⫏≰2202022⇋≉)","cot":[{"info":"⨵≀≌⫏≰12002101=⫏≰-120021010","layer":1},{"info":"⫏≰2202022⇋≉=⫏≰12100222","layer":1},{"info":"⫏≰-120021010-⫏≰12100222=⫏≰-202122002","layer":0}]}
{"id":327,"expression_no_base_symbol":"$1269$⊉≛↸$5988$⨸⪁$2716$∼$6910$","expression":"⫏≰1202000⊉≛↸⫏≰22012210⨸⪁⫏≰10201121∼⫏≰100110221","highest_n_order":4,"priority_hierarchical_complexity":2,"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":1269,"base":3},"right_expr":{"type":"numeric_atoms","value":5988,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":2716,"base":3},"right_expr":{"type":"numeric_atoms","value":6910,"base":3}}},"used_operators":["g55IO6H4Gj","DZ8iAZOCBD","DyGG3AbaNP"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1269","layer":2},{"info":"number node, value=5988","layer":2},{"info":"compute binary expreesion, left_input=1269, right_input=5988, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=2538","layer":1},{"info":"number node, value=2716","layer":2},{"info":"number node, value=6910","layer":2},{"info":"compute binary expreesion, left_input=2716, right_input=6910, 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=2538, right_input=nan, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1202000⊉≛↸⫏≰22012210⨸⪁⫏≰10201121∼⫏≰100110221=NaN","reverse_text":"NaN=⫏≰1202000⊉≛↸⫏≰22012210⨸⪁⫏≰10201121∼⫏≰100110221","cot":[{"info":"⫏≰1202000⊉≛↸⫏≰22012210=⫏≰10111000","layer":1},{"info":"⫏≰10201121∼⫏≰100110221=NaN","layer":1},{"info":"⫏≰10111000⨸⪁NaN=NaN","layer":0}]}
{"id":328,"expression_no_base_symbol":"↥$1045$⨰$1361$","expression":"↥⫏≰1102201⨰⫏≰1212102","highest_n_order":2,"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":1045,"base":3},"right_expr":{"type":"numeric_atoms","value":1361,"base":3}}},"used_operators":["A8NUZmVepG","eewbuw0ToL"],"dependent_operators":["k8jYdgA6NY","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1045","layer":2},{"info":"number node, value=1361","layer":2},{"info":"compute binary expreesion, left_input=1045, right_input=1361, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-306","layer":1},{"info":"compute unary expreesion, input=-306, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=0","layer":0}],"base":3,"result_base":3,"text":"↥⫏≰1102201⨰⫏≰1212102=⫏≰0","reverse_text":"⫏≰0=↥⫏≰1102201⨰⫏≰1212102","cot":[{"info":"⫏≰1102201⨰⫏≰1212102=⫏≰-102100","layer":1},{"info":"↥⫏≰-102100=⫏≰0","layer":0}]}
{"id":329,"expression_no_base_symbol":"(⨵≀≌$1141$)%$1129$⋝⋈⪟$1508$","expression":"(⨵≀≌⫏≰1120021)%⫏≰1112211⋝⋈⪟⫏≰2001212","highest_n_order":2,"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":1141,"base":3}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":1129,"base":3},"right_expr":{"type":"numeric_atoms","value":1508,"base":3}}},"used_operators":["k8jYdgA6NY","srAu1WTS94","2DDjHMKMc0"],"dependent_operators":["rysDP5nf3Z","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1111111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1141","layer":2},{"info":"compute unary expreesion, input=1141, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-3423","layer":1},{"info":"number node, value=1129","layer":2},{"info":"number node, value=1508","layer":2},{"info":"compute binary expreesion, left_input=1129, right_input=1508, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=1129","layer":1},{"info":"compute binary expreesion, left_input=-3423, right_input=1129, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1093","layer":0}],"base":3,"result_base":3,"text":"(⨵≀≌⫏≰1120021)%⫏≰1112211⋝⋈⪟⫏≰2001212=⫏≰1111111","reverse_text":"⫏≰1111111=(⨵≀≌⫏≰1120021)%⫏≰1112211⋝⋈⪟⫏≰2001212","cot":[{"info":"⨵≀≌⫏≰1120021=⫏≰-11200210","layer":1},{"info":"⫏≰1112211⋝⋈⪟⫏≰2001212=⫏≰1112211","layer":1},{"info":"⫏≰-11200210%⫏≰1112211=⫏≰1111111","layer":0}]}
{"id":330,"expression_no_base_symbol":"↣≠⋷($7154$⋝⋈⪟$1129$)","expression":"↣≠⋷(⫏≰100210222⋝⋈⪟⫏≰1112211)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":2,"complexity_ratio":3.0,"tree":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":7154,"base":3},"right_expr":{"type":"numeric_atoms","value":1129,"base":3}}},"used_operators":["Asc51vEJeQ","2DDjHMKMc0"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7154","layer":2},{"info":"number node, value=1129","layer":2},{"info":"compute binary expreesion, left_input=7154, right_input=1129, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=7154","layer":1},{"info":"compute unary expreesion, input=7154, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(⫏≰100210222⋝⋈⪟⫏≰1112211)=NaN","reverse_text":"NaN=↣≠⋷(⫏≰100210222⋝⋈⪟⫏≰1112211)","cot":[{"info":"⫏≰100210222⋝⋈⪟⫏≰1112211=⫏≰100210222","layer":1},{"info":"↣≠⋷⫏≰100210222=NaN","layer":0}]}
{"id":331,"expression_no_base_symbol":"$2971$⪘⫢$6543$%(⋗⩬⋾$2094$)","expression":"⫏≰11002001⪘⫢⫏≰22222100%(⋗⩬⋾⫏≰2212120)","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":2971,"base":3},"right_expr":{"type":"numeric_atoms","value":6543,"base":3}},"right_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":2094,"base":3}}},"used_operators":["k8jYdgA6NY","oacrs7FA3X","DpFCA1CohY"],"dependent_operators":["rysDP5nf3Z","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-122012","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2971","layer":2},{"info":"number node, value=6543","layer":2},{"info":"compute binary expreesion, left_input=2971, right_input=6543, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=5818","layer":1},{"info":"number node, value=2094","layer":2},{"info":"compute unary expreesion, input=2094, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-6282","layer":1},{"info":"compute binary expreesion, left_input=5818, right_input=-6282, op_id = k8jYdgA6NY binary_op_definition= 'None', output=-464","layer":0}],"base":3,"result_base":3,"text":"⫏≰11002001⪘⫢⫏≰22222100%(⋗⩬⋾⫏≰2212120)=⫏≰-122012","reverse_text":"⫏≰-122012=⫏≰11002001⪘⫢⫏≰22222100%(⋗⩬⋾⫏≰2212120)","cot":[{"info":"⫏≰11002001⪘⫢⫏≰22222100=⫏≰21222111","layer":1},{"info":"⋗⩬⋾⫏≰2212120=⫏≰-22121200","layer":1},{"info":"⫏≰21222111%⫏≰-22121200=⫏≰-122012","layer":0}]}
{"id":332,"expression_no_base_symbol":"$2461$≹⇙⪍$2803$⫡⨏(⨈⫕$2374$)","expression":"⫏≰10101011≹⇙⪍⫏≰10211211⫡⨏(⨈⫕⫏≰10020221)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":394,"operation_count":3,"complexity_ratio":131.33333333333334,"tree":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":2461,"base":3},"right_expr":{"type":"numeric_atoms","value":2803,"base":3}},"right_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":2374,"base":3}}},"used_operators":["QMFrweE19q","AHs5Up7iyr","megm06wKyl"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2461","layer":2},{"info":"number node, value=2803","layer":2},{"info":"compute binary expreesion, left_input=2461, right_input=2803, 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":"number node, value=2374","layer":2},{"info":"compute unary expreesion, input=2374, 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=nan, right_input=-21, 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":3,"result_base":3,"text":"⫏≰10101011≹⇙⪍⫏≰10211211⫡⨏(⨈⫕⫏≰10020221)=NaN","reverse_text":"NaN=⫏≰10101011≹⇙⪍⫏≰10211211⫡⨏(⨈⫕⫏≰10020221)","cot":[{"info":"⫏≰10101011≹⇙⪍⫏≰10211211=NaN","layer":1},{"info":"⨈⫕⫏≰10020221=⫏≰-210","layer":1},{"info":"NaN⫡⨏⫏≰-210=NaN","layer":0}]}
{"id":333,"expression_no_base_symbol":"($4187$⫸⊐$1943$)+⇶⊼$1271$∀⇚≩$1510$","expression":"(⫏≰12202002⫸⊐⫏≰2122222)+⇶⊼⫏≰1202002∀⇚≩⫏≰2001221","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8922,"operation_count":3,"complexity_ratio":2974.0,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":4187,"base":3},"right_expr":{"type":"numeric_atoms","value":1943,"base":3}},"right_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":1271,"base":3},"right_expr":{"type":"numeric_atoms","value":1510,"base":3}}},"used_operators":["TpPTUOHfaN","mqXw5SEYmG","LRNGc0VcxI"],"dependent_operators":["AHs5Up7iyr","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4187","layer":2},{"info":"number node, value=1943","layer":2},{"info":"compute binary expreesion, left_input=4187, right_input=1943, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=7647","layer":1},{"info":"number node, value=1271","layer":2},{"info":"number node, value=1510","layer":2},{"info":"compute binary expreesion, left_input=1271, right_input=1510, 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=7647, right_input=nan, 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":3,"result_base":3,"text":"(⫏≰12202002⫸⊐⫏≰2122222)+⇶⊼⫏≰1202002∀⇚≩⫏≰2001221=NaN","reverse_text":"NaN=(⫏≰12202002⫸⊐⫏≰2122222)+⇶⊼⫏≰1202002∀⇚≩⫏≰2001221","cot":[{"info":"⫏≰12202002⫸⊐⫏≰2122222=⫏≰101111020","layer":1},{"info":"⫏≰1202002∀⇚≩⫏≰2001221=NaN","layer":1},{"info":"⫏≰101111020+⇶⊼NaN=NaN","layer":0}]}
{"id":334,"expression_no_base_symbol":"$3152$⪨≂$3635$↪⪝","expression":"⫏≰11022202⪨≂⫏≰11222122↪⪝","highest_n_order":2,"priority_hierarchical_complexity":1,"normalized_expansion_degree":705,"operation_count":2,"complexity_ratio":352.5,"tree":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":3152,"base":3},"right_expr":{"type":"numeric_atoms","value":3635,"base":3}}},"used_operators":["l07mrZUIn9","sdazOOVcIp"],"dependent_operators":["9HNa5Wba9A","2DDjHMKMc0","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-10200110122000000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3152","layer":2},{"info":"number node, value=3635","layer":2},{"info":"compute binary expreesion, left_input=3152, right_input=3635, 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=-864","layer":1},{"info":"compute unary expreesion, input=-864, op_id = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=-52861248","layer":0}],"base":3,"result_base":3,"text":"⫏≰11022202⪨≂⫏≰11222122↪⪝=⫏≰-10200110122000000","reverse_text":"⫏≰-10200110122000000=⫏≰11022202⪨≂⫏≰11222122↪⪝","cot":[{"info":"⫏≰11022202⪨≂⫏≰11222122=⫏≰-1012000","layer":1},{"info":"⫏≰-1012000↪⪝=⫏≰-10200110122000000","layer":0}]}
{"id":335,"expression_no_base_symbol":"($1465$⪨≂$3969$)⨎($1775$⨁⊸⫻)","expression":"(⫏≰2000021⪨≂⫏≰12110000)⨎(⫏≰2102202⨁⊸⫻)","highest_n_order":2,"priority_hierarchical_complexity":2,"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":1465,"base":3},"right_expr":{"type":"numeric_atoms","value":3969,"base":3}},"right_expr":{"type":"unary","operator":"⨁⊸⫻","unary_expr":{"type":"numeric_atoms","value":1775,"base":3}}},"used_operators":["rJVOvQCfKK","sdazOOVcIp","glklzrTFfD"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰2102202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1465","layer":2},{"info":"number node, value=3969","layer":2},{"info":"compute binary expreesion, left_input=1465, right_input=3969, 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=-4906","layer":1},{"info":"number node, value=1775","layer":2},{"info":"compute unary expreesion, input=1775, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=1775","layer":1},{"info":"compute binary expreesion, left_input=-4906, right_input=1775, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=1775","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2000021⪨≂⫏≰12110000)⨎(⫏≰2102202⨁⊸⫻)=⫏≰2102202","reverse_text":"⫏≰2102202=(⫏≰2000021⪨≂⫏≰12110000)⨎(⫏≰2102202⨁⊸⫻)","cot":[{"info":"⫏≰2000021⪨≂⫏≰12110000=⫏≰-20201201","layer":1},{"info":"⫏≰2102202⨁⊸⫻=⫏≰2102202","layer":1},{"info":"⫏≰-20201201⨎⫏≰2102202=⫏≰2102202","layer":0}]}
{"id":336,"expression_no_base_symbol":"$4086$≧⫂∧$4010$↺($2999$↙$1170$)","expression":"⫏≰12121100≧⫂∧⫏≰12111112↺(⫏≰11010002↙⫏≰1121100)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1176,"operation_count":3,"complexity_ratio":392.0,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":4086,"base":3},"right_expr":{"type":"numeric_atoms","value":4010,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":2999,"base":3},"right_expr":{"type":"numeric_atoms","value":1170,"base":3}}},"used_operators":["7j4O788W3g","Ph9nP6C5qx","yyfyN0ffXY"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰-11211000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4086","layer":2},{"info":"number node, value=4010","layer":2},{"info":"compute binary expreesion, left_input=4086, right_input=4010, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=3537","layer":1},{"info":"number node, value=2999","layer":2},{"info":"number node, value=1170","layer":2},{"info":"compute binary expreesion, left_input=2999, right_input=1170, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-3510","layer":1},{"info":"compute binary expreesion, left_input=3537, right_input=-3510, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=-3510","layer":0}],"base":3,"result_base":3,"text":"⫏≰12121100≧⫂∧⫏≰12111112↺(⫏≰11010002↙⫏≰1121100)=⫏≰-11211000","reverse_text":"⫏≰-11211000=⫏≰12121100≧⫂∧⫏≰12111112↺(⫏≰11010002↙⫏≰1121100)","cot":[{"info":"⫏≰12121100≧⫂∧⫏≰12111112=⫏≰11212000","layer":1},{"info":"⫏≰11010002↙⫏≰1121100=⫏≰-11211000","layer":1},{"info":"⫏≰11212000↺⫏≰-11211000=⫏≰-11211000","layer":0}]}
{"id":337,"expression_no_base_symbol":"($6421$⪠⩆⊳)⊘","expression":"(⫏≰22210211⪠⩆⊳)⊘","highest_n_order":2,"priority_hierarchical_complexity":1,"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":6421,"base":3}}},"used_operators":["gu96TGCTMs","JLbD19bQDL"],"dependent_operators":["XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6421","layer":2},{"info":"compute unary expreesion, input=6421, 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":"compute unary expreesion, input=0, 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":3,"result_base":3,"text":"(⫏≰22210211⪠⩆⊳)⊘=⫏≰0","reverse_text":"⫏≰0=(⫏≰22210211⪠⩆⊳)⊘","cot":[{"info":"⫏≰22210211⪠⩆⊳=⫏≰0","layer":1},{"info":"⫏≰0⊘=⫏≰0","layer":0}]}
{"id":338,"expression_no_base_symbol":"$1405$⨐⩸⫘$2673$⨵⪆($4283$+$7794$)","expression":"⫏≰1221001⨐⩸⫘⫏≰10200000⨵⪆(⫏≰12212122+⫏≰101200200)","highest_n_order":4,"priority_hierarchical_complexity":2,"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":1405,"base":3},"right_expr":{"type":"numeric_atoms","value":2673,"base":3}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":4283,"base":3},"right_expr":{"type":"numeric_atoms","value":7794,"base":3}}},"used_operators":["2DQ55sFlQl","fu6greOZ01","W4YGzv6Whe"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","3ViojmjbAp"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1405","layer":2},{"info":"number node, value=2673","layer":2},{"info":"compute binary expreesion, left_input=1405, right_input=2673, 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=4283","layer":2},{"info":"number node, value=7794","layer":2},{"info":"compute binary expreesion, left_input=4283, right_input=7794, op_id = W4YGzv6Whe binary_op_definition= 'None', output=12077","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=12077, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰1221001⨐⩸⫘⫏≰10200000⨵⪆(⫏≰12212122+⫏≰101200200)=⫏≰12221","reverse_text":"⫏≰12221=⫏≰1221001⨐⩸⫘⫏≰10200000⨵⪆(⫏≰12212122+⫏≰101200200)","cot":[{"info":"⫏≰1221001⨐⩸⫘⫏≰10200000=NaN","layer":1},{"info":"⫏≰12212122+⫏≰101200200=⫏≰121120022","layer":1},{"info":"NaN⨵⪆⫏≰121120022=⫏≰12221","layer":0}]}
{"id":339,"expression_no_base_symbol":"$2863$⨟⋌⩍$3113$⨓(⨞⊢$2363$)","expression":"⫏≰10221001⨟⋌⩍⫏≰11021022⨓(⨞⊢⫏≰10020112)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2546,"operation_count":3,"complexity_ratio":848.6666666666666,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":2863,"base":3},"right_expr":{"type":"numeric_atoms","value":3113,"base":3}},"right_expr":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":2363,"base":3}}},"used_operators":["3ViojmjbAp","rGHVDoGpnC","xUOZtlo3hN"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","Tcnh7f0tEr","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-10111002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2863","layer":2},{"info":"number node, value=3113","layer":2},{"info":"compute binary expreesion, left_input=2863, right_input=3113, 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=2363","layer":2},{"info":"compute unary expreesion, input=2363, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-2537","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-2537, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-2540","layer":0}],"base":3,"result_base":3,"text":"⫏≰10221001⨟⋌⩍⫏≰11021022⨓(⨞⊢⫏≰10020112)=⫏≰-10111002","reverse_text":"⫏≰-10111002=⫏≰10221001⨟⋌⩍⫏≰11021022⨓(⨞⊢⫏≰10020112)","cot":[{"info":"⫏≰10221001⨟⋌⩍⫏≰11021022=NaN","layer":1},{"info":"⨞⊢⫏≰10020112=⫏≰-10110222","layer":1},{"info":"NaN⨓⫏≰-10110222=⫏≰-10111002","layer":0}]}
{"id":340,"expression_no_base_symbol":"↣≠⋷(⊥$5079$)","expression":"↣≠⋷(⊥⫏≰20222010)","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":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":5079,"base":3}}},"used_operators":["Asc51vEJeQ","Q3PJZHRvZv"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","fu6greOZ01"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5079","layer":2},{"info":"compute unary expreesion, input=5079, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(⊥⫏≰20222010)=NaN","reverse_text":"NaN=↣≠⋷(⊥⫏≰20222010)","cot":[{"info":"⊥⫏≰20222010=NaN","layer":1},{"info":"↣≠⋷NaN=NaN","layer":0}]}
{"id":341,"expression_no_base_symbol":"($3101$+⇶⊼$5907$)⨰(⊥$2100$)","expression":"(⫏≰11020212+⇶⊼⫏≰22002210)⨰(⊥⫏≰2212210)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⨰","left_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":3101,"base":3},"right_expr":{"type":"numeric_atoms","value":5907,"base":3}},"right_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":2100,"base":3}}},"used_operators":["eewbuw0ToL","TpPTUOHfaN","Q3PJZHRvZv"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr","fu6greOZ01"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3101","layer":2},{"info":"number node, value=5907","layer":2},{"info":"compute binary expreesion, left_input=3101, right_input=5907, 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":1},{"info":"number node, value=2100","layer":2},{"info":"compute unary expreesion, input=2100, 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 = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11020212+⇶⊼⫏≰22002210)⨰(⊥⫏≰2212210)=NaN","reverse_text":"NaN=(⫏≰11020212+⇶⊼⫏≰22002210)⨰(⊥⫏≰2212210)","cot":[{"info":"⫏≰11020212+⇶⊼⫏≰22002210=NaN","layer":1},{"info":"⊥⫏≰2212210=NaN","layer":1},{"info":"NaN⨰NaN=NaN","layer":0}]}
{"id":342,"expression_no_base_symbol":"(↔$3837$)/$5561$⪛$4196$","expression":"(↔⫏≰12021010)/⫏≰21121222⪛⫏≰12202102","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":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":3837,"base":3}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":5561,"base":3},"right_expr":{"type":"numeric_atoms","value":4196,"base":3}}},"used_operators":["XhwjNDsVaA","ruOEQAzv1W","uFcxV4UQCh"],"dependent_operators":["rysDP5nf3Z","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⫏≰-10","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3837","layer":2},{"info":"compute unary expreesion, input=3837, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-3564","layer":1},{"info":"number node, value=5561","layer":2},{"info":"number node, value=4196","layer":2},{"info":"compute binary expreesion, left_input=5561, right_input=4196, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1365","layer":1},{"info":"compute binary expreesion, left_input=-3564, right_input=1365, op_id = XhwjNDsVaA binary_op_definition= 'None', output=-3","layer":0}],"base":3,"result_base":3,"text":"(↔⫏≰12021010)/⫏≰21121222⪛⫏≰12202102=⫏≰-10","reverse_text":"⫏≰-10=(↔⫏≰12021010)/⫏≰21121222⪛⫏≰12202102","cot":[{"info":"↔⫏≰12021010=⫏≰-11220000","layer":1},{"info":"⫏≰21121222⪛⫏≰12202102=⫏≰1212120","layer":1},{"info":"⫏≰-11220000/⫏≰1212120=⫏≰-10","layer":0}]}
{"id":343,"expression_no_base_symbol":"($1110$⨽$7266$)⊦⊿","expression":"(⫏≰1112010⨽⫏≰100222010)⊦⊿","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1125,"operation_count":2,"complexity_ratio":562.5,"tree":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1110,"base":3},"right_expr":{"type":"numeric_atoms","value":7266,"base":3}}},"used_operators":["14qkJME0vr","8HhzD0ZcuI"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"⫏≰202222111022002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1110","layer":2},{"info":"number node, value=7266","layer":2},{"info":"compute binary expreesion, left_input=1110, right_input=7266, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-3716784","layer":1},{"info":"compute unary expreesion, input=-3716784, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=11150273","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1112010⨽⫏≰100222010)⊦⊿=⫏≰202222111022002","reverse_text":"⫏≰202222111022002=(⫏≰1112010⨽⫏≰100222010)⊦⊿","cot":[{"info":"⫏≰1112010⨽⫏≰100222010=⫏≰-20222211110200","layer":1},{"info":"⫏≰-20222211110200⊦⊿=⫏≰202222111022002","layer":0}]}
{"id":344,"expression_no_base_symbol":"$2332$⨪↰⇹$6184$≎⊠⪸($1982$↙$6489$)","expression":"⫏≰10012101⨪↰⇹⫏≰22111001≎⊠⪸(⫏≰2201102↙⫏≰22220100)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8835,"operation_count":3,"complexity_ratio":2945.0,"tree":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":2332,"base":3},"right_expr":{"type":"numeric_atoms","value":6184,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":1982,"base":3},"right_expr":{"type":"numeric_atoms","value":6489,"base":3}}},"used_operators":["bJkvcejdHO","tmPS8pqC7x","yyfyN0ffXY"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","rJVOvQCfKK","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2332","layer":2},{"info":"number node, value=6184","layer":2},{"info":"compute binary expreesion, left_input=2332, right_input=6184, 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=2332","layer":1},{"info":"number node, value=1982","layer":2},{"info":"number node, value=6489","layer":2},{"info":"compute binary expreesion, left_input=1982, right_input=6489, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-19467","layer":1},{"info":"compute binary expreesion, left_input=2332, right_input=-19467, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=67","layer":0}],"base":3,"result_base":3,"text":"⫏≰10012101⨪↰⇹⫏≰22111001≎⊠⪸(⫏≰2201102↙⫏≰22220100)=⫏≰2111","reverse_text":"⫏≰2111=⫏≰10012101⨪↰⇹⫏≰22111001≎⊠⪸(⫏≰2201102↙⫏≰22220100)","cot":[{"info":"⫏≰10012101⨪↰⇹⫏≰22111001=⫏≰10012101","layer":1},{"info":"⫏≰2201102↙⫏≰22220100=⫏≰-222201000","layer":1},{"info":"⫏≰10012101≎⊠⪸⫏≰-222201000=⫏≰2111","layer":0}]}
{"id":345,"expression_no_base_symbol":"($2539$⪄$3271$)⨟⋌⩍($1009$⊦⊿)","expression":"(⫏≰10111001⪄⫏≰11111011)⨟⋌⩍(⫏≰1101101⊦⊿)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":102,"operation_count":3,"complexity_ratio":34.0,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2539,"base":3},"right_expr":{"type":"numeric_atoms","value":3271,"base":3}},"right_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":1009,"base":3}}},"used_operators":["rGHVDoGpnC","SUmda5xLS4","14qkJME0vr"],"dependent_operators":["Tcnh7f0tEr","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2539","layer":2},{"info":"number node, value=3271","layer":2},{"info":"compute binary expreesion, left_input=2539, right_input=3271, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-384945","layer":1},{"info":"number node, value=1009","layer":2},{"info":"compute unary expreesion, input=1009, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-3106","layer":1},{"info":"compute binary expreesion, left_input=-384945, right_input=-3106, 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":0}],"base":3,"result_base":3,"text":"(⫏≰10111001⪄⫏≰11111011)⨟⋌⩍(⫏≰1101101⊦⊿)=NaN","reverse_text":"NaN=(⫏≰10111001⪄⫏≰11111011)⨟⋌⩍(⫏≰1101101⊦⊿)","cot":[{"info":"⫏≰10111001⪄⫏≰11111011=⫏≰-201120001020","layer":1},{"info":"⫏≰1101101⊦⊿=⫏≰-11021001","layer":1},{"info":"⫏≰-201120001020⨟⋌⩍⫏≰-11021001=NaN","layer":0}]}
{"id":346,"expression_no_base_symbol":"$2332$⨐⩸⫘$3257$⇼⇔∾(⇁⨣⪵$2076$)","expression":"⫏≰10012101⨐⩸⫘⫏≰11110122⇼⇔∾(⇁⨣⪵⫏≰2211220)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4,"operation_count":3,"complexity_ratio":1.3333333333333333,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":2332,"base":3},"right_expr":{"type":"numeric_atoms","value":3257,"base":3}},"right_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":2076,"base":3}}},"used_operators":["tifHPKVTfV","fu6greOZ01","inkyxCbjAn"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","3ViojmjbAp","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2332","layer":2},{"info":"number node, value=3257","layer":2},{"info":"compute binary expreesion, left_input=2332, right_input=3257, 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=2076","layer":2},{"info":"compute unary expreesion, input=2076, 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 = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰10012101⨐⩸⫘⫏≰11110122⇼⇔∾(⇁⨣⪵⫏≰2211220)=NaN","reverse_text":"NaN=⫏≰10012101⨐⩸⫘⫏≰11110122⇼⇔∾(⇁⨣⪵⫏≰2211220)","cot":[{"info":"⫏≰10012101⨐⩸⫘⫏≰11110122=NaN","layer":1},{"info":"⇁⨣⪵⫏≰2211220=NaN","layer":1},{"info":"NaN⇼⇔∾NaN=NaN","layer":0}]}
{"id":347,"expression_no_base_symbol":"(⨑⩽⪐$1871$)⇼⇔∾$2408$∑⇟⊟$1030$","expression":"(⨑⩽⪐⫏≰2120022)⇼⇔∾⫏≰10022012∑⇟⊟⫏≰1102011","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":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":1871,"base":3}},"right_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":2408,"base":3},"right_expr":{"type":"numeric_atoms","value":1030,"base":3}}},"used_operators":["tifHPKVTfV","AF7qkfDlqP","U7g4x0WXJJ"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1871","layer":2},{"info":"compute unary expreesion, input=1871, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-1598","layer":1},{"info":"number node, value=2408","layer":2},{"info":"number node, value=1030","layer":2},{"info":"compute binary expreesion, left_input=2408, right_input=1030, 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=-1598, right_input=nan, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⨑⩽⪐⫏≰2120022)⇼⇔∾⫏≰10022012∑⇟⊟⫏≰1102011=NaN","reverse_text":"NaN=(⨑⩽⪐⫏≰2120022)⇼⇔∾⫏≰10022012∑⇟⊟⫏≰1102011","cot":[{"info":"⨑⩽⪐⫏≰2120022=⫏≰-2012012","layer":1},{"info":"⫏≰10022012∑⇟⊟⫏≰1102011=NaN","layer":1},{"info":"⫏≰-2012012⇼⇔∾NaN=NaN","layer":0}]}
{"id":348,"expression_no_base_symbol":"$6475$⪛$3614$∼$3470$⪮%⊝$6471$","expression":"⫏≰22212211⪛⫏≰11221212∼⫏≰11202112⪮%⊝⫏≰22212200","highest_n_order":4,"priority_hierarchical_complexity":2,"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":6475,"base":3},"right_expr":{"type":"numeric_atoms","value":3614,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":3470,"base":3},"right_expr":{"type":"numeric_atoms","value":6471,"base":3}}},"used_operators":["DyGG3AbaNP","uFcxV4UQCh","IWmyXbctLI"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6475","layer":2},{"info":"number node, value=3614","layer":2},{"info":"compute binary expreesion, left_input=6475, right_input=3614, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=2861","layer":1},{"info":"number node, value=3470","layer":2},{"info":"number node, value=6471","layer":2},{"info":"compute binary expreesion, left_input=3470, right_input=6471, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=7256","layer":1},{"info":"compute binary expreesion, left_input=2861, right_input=7256, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰22212211⪛⫏≰11221212∼⫏≰11202112⪮%⊝⫏≰22212200=NaN","reverse_text":"NaN=⫏≰22212211⪛⫏≰11221212∼⫏≰11202112⪮%⊝⫏≰22212200","cot":[{"info":"⫏≰22212211⪛⫏≰11221212=⫏≰10220222","layer":1},{"info":"⫏≰11202112⪮%⊝⫏≰22212200=⫏≰100221202","layer":1},{"info":"⫏≰10220222∼⫏≰100221202=NaN","layer":0}]}
{"id":349,"expression_no_base_symbol":"$4005$⨰$6344$⨳⩥⨓$3826$⋝⋈⪟$2771$","expression":"⫏≰12111100⨰⫏≰22200222⨳⩥⨓⫏≰12020201⋝⋈⪟⫏≰10210122","highest_n_order":1,"priority_hierarchical_complexity":2,"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":4005,"base":3},"right_expr":{"type":"numeric_atoms","value":6344,"base":3}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":3826,"base":3},"right_expr":{"type":"numeric_atoms","value":2771,"base":3}}},"used_operators":["nCS4ZIUYfx","eewbuw0ToL","2DDjHMKMc0"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰22102222","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4005","layer":2},{"info":"number node, value=6344","layer":2},{"info":"compute binary expreesion, left_input=4005, right_input=6344, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-2329","layer":1},{"info":"number node, value=3826","layer":2},{"info":"number node, value=2771","layer":2},{"info":"compute binary expreesion, left_input=3826, right_input=2771, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=3826","layer":1},{"info":"compute binary expreesion, left_input=-2329, right_input=3826, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=6155","layer":0}],"base":3,"result_base":3,"text":"⫏≰12111100⨰⫏≰22200222⨳⩥⨓⫏≰12020201⋝⋈⪟⫏≰10210122=⫏≰22102222","reverse_text":"⫏≰22102222=⫏≰12111100⨰⫏≰22200222⨳⩥⨓⫏≰12020201⋝⋈⪟⫏≰10210122","cot":[{"info":"⫏≰12111100⨰⫏≰22200222=⫏≰-10012021","layer":1},{"info":"⫏≰12020201⋝⋈⪟⫏≰10210122=⫏≰12020201","layer":1},{"info":"⫏≰-10012021⨳⩥⨓⫏≰12020201=⫏≰22102222","layer":0}]}
{"id":350,"expression_no_base_symbol":"(↣≠⋷$2862$)⨪↰⇹$6425$⪢$4447$","expression":"(↣≠⋷⫏≰10221000)⨪↰⇹⫏≰22210222⪢⫏≰20002201","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13329,"operation_count":3,"complexity_ratio":4443.0,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":2862,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":6425,"base":3},"right_expr":{"type":"numeric_atoms","value":4447,"base":3}}},"used_operators":["tmPS8pqC7x","Asc51vEJeQ","dWAJyo7jo9"],"dependent_operators":["rJVOvQCfKK","XhwjNDsVaA","AHs5Up7iyr","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2862","layer":2},{"info":"compute unary expreesion, input=2862, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"number node, value=6425","layer":2},{"info":"number node, value=4447","layer":2},{"info":"compute binary expreesion, left_input=6425, right_input=4447, 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 = 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=nan","layer":0}],"base":3,"result_base":3,"text":"(↣≠⋷⫏≰10221000)⨪↰⇹⫏≰22210222⪢⫏≰20002201=NaN","reverse_text":"NaN=(↣≠⋷⫏≰10221000)⨪↰⇹⫏≰22210222⪢⫏≰20002201","cot":[{"info":"↣≠⋷⫏≰10221000=NaN","layer":1},{"info":"⫏≰22210222⪢⫏≰20002201=NaN","layer":1},{"info":"NaN⨪↰⇹NaN=NaN","layer":0}]}
{"id":351,"expression_no_base_symbol":"$3705$⪮%⊝$5769$≋⫹","expression":"⫏≰12002020⪮%⊝⫏≰21220200≋⫹","highest_n_order":2,"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":3705,"base":3},"right_expr":{"type":"numeric_atoms","value":5769,"base":3}}},"used_operators":["N41Kp7NANJ","IWmyXbctLI"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰-210012022","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3705","layer":2},{"info":"number node, value=5769","layer":2},{"info":"compute binary expreesion, left_input=3705, right_input=5769, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=7726","layer":1},{"info":"compute unary expreesion, input=7726, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-15452","layer":0}],"base":3,"result_base":3,"text":"⫏≰12002020⪮%⊝⫏≰21220200≋⫹=⫏≰-210012022","reverse_text":"⫏≰-210012022=⫏≰12002020⪮%⊝⫏≰21220200≋⫹","cot":[{"info":"⫏≰12002020⪮%⊝⫏≰21220200=⫏≰101121011","layer":1},{"info":"⫏≰101121011≋⫹=⫏≰-210012022","layer":0}]}
{"id":352,"expression_no_base_symbol":"($4938$↺$5497$)⨪↰⇹$1317$∼$5532$","expression":"(⫏≰20202220↺⫏≰21112121)⨪↰⇹⫏≰1210210∼⫏≰21120220","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5526,"operation_count":3,"complexity_ratio":1842.0,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":4938,"base":3},"right_expr":{"type":"numeric_atoms","value":5497,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":1317,"base":3},"right_expr":{"type":"numeric_atoms","value":5532,"base":3}}},"used_operators":["tmPS8pqC7x","7j4O788W3g","DyGG3AbaNP"],"dependent_operators":["rJVOvQCfKK","rysDP5nf3Z","t8gj7n24qd","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"⫏≰21112121","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4938","layer":2},{"info":"number node, value=5497","layer":2},{"info":"compute binary expreesion, left_input=4938, right_input=5497, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=5497","layer":1},{"info":"number node, value=1317","layer":2},{"info":"number node, value=5532","layer":2},{"info":"compute binary expreesion, left_input=1317, right_input=5532, 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=5497, right_input=nan, 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=5497","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20202220↺⫏≰21112121)⨪↰⇹⫏≰1210210∼⫏≰21120220=⫏≰21112121","reverse_text":"⫏≰21112121=(⫏≰20202220↺⫏≰21112121)⨪↰⇹⫏≰1210210∼⫏≰21120220","cot":[{"info":"⫏≰20202220↺⫏≰21112121=⫏≰21112121","layer":1},{"info":"⫏≰1210210∼⫏≰21120220=NaN","layer":1},{"info":"⫏≰21112121⨪↰⇹NaN=⫏≰21112121","layer":0}]}
{"id":353,"expression_no_base_symbol":"($6019$⋳⪒$1474$)≹⇙⪍($1037$⊴$3293$)","expression":"(⫏≰22020221⋳⪒⫏≰2000121)≹⇙⪍(⫏≰1102102⊴⫏≰11111222)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3307,"operation_count":3,"complexity_ratio":1102.3333333333333,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":6019,"base":3},"right_expr":{"type":"numeric_atoms","value":1474,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1037,"base":3},"right_expr":{"type":"numeric_atoms","value":3293,"base":3}}},"used_operators":["AHs5Up7iyr","12rbrZMWeM","Nsiff2A1zJ"],"dependent_operators":["dWAJyo7jo9","rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6019","layer":2},{"info":"number node, value=1474","layer":2},{"info":"compute binary expreesion, left_input=6019, right_input=1474, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=10277","layer":1},{"info":"number node, value=1037","layer":2},{"info":"number node, value=3293","layer":2},{"info":"compute binary expreesion, left_input=1037, right_input=3293, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=10277, 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":3,"result_base":3,"text":"(⫏≰22020221⋳⪒⫏≰2000121)≹⇙⪍(⫏≰1102102⊴⫏≰11111222)=NaN","reverse_text":"NaN=(⫏≰22020221⋳⪒⫏≰2000121)≹⇙⪍(⫏≰1102102⊴⫏≰11111222)","cot":[{"info":"⫏≰22020221⋳⪒⫏≰2000121=⫏≰112002122","layer":1},{"info":"⫏≰1102102⊴⫏≰11111222=NaN","layer":1},{"info":"⫏≰112002122≹⇙⪍NaN=NaN","layer":0}]}
{"id":354,"expression_no_base_symbol":"≉($2156$⇼⇔∾$4697$)","expression":"≉(⫏≰2221212⇼⇔∾⫏≰20102222)","highest_n_order":1,"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":2156,"base":3},"right_expr":{"type":"numeric_atoms","value":4697,"base":3}}},"used_operators":["e1ybzncUwg","tifHPKVTfV"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰11012210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2156","layer":2},{"info":"number node, value=4697","layer":2},{"info":"compute binary expreesion, left_input=2156, right_input=4697, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=2541","layer":1},{"info":"compute unary expreesion, input=2541, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=3072","layer":0}],"base":3,"result_base":3,"text":"≉(⫏≰2221212⇼⇔∾⫏≰20102222)=⫏≰11012210","reverse_text":"⫏≰11012210=≉(⫏≰2221212⇼⇔∾⫏≰20102222)","cot":[{"info":"⫏≰2221212⇼⇔∾⫏≰20102222=⫏≰10111010","layer":1},{"info":"≉⫏≰10111010=⫏≰11012210","layer":0}]}
{"id":355,"expression_no_base_symbol":"-$1032$-$4631$","expression":"-⫏≰1102020-⫏≰20100112","highest_n_order":1,"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":1032,"base":3},"right_expr":{"type":"numeric_atoms","value":4631,"base":3}}},"used_operators":["t8gj7n24qd","rysDP5nf3Z"],"dependent_operators":[],"result":"⫏≰11221022","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1032","layer":2},{"info":"number node, value=4631","layer":2},{"info":"compute binary expreesion, left_input=1032, right_input=4631, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-3599","layer":1},{"info":"compute unary expreesion, input=-3599, op_id = t8gj7n24qd, unary_op_definition = 'None', output=3599","layer":0}],"base":3,"result_base":3,"text":"-⫏≰1102020-⫏≰20100112=⫏≰11221022","reverse_text":"⫏≰11221022=-⫏≰1102020-⫏≰20100112","cot":[{"info":"⫏≰1102020-⫏≰20100112=⫏≰-11221022","layer":1},{"info":"-⫏≰-11221022=⫏≰11221022","layer":0}]}
{"id":356,"expression_no_base_symbol":"⇁⨣⪵($2615$⊪)","expression":"⇁⨣⪵(⫏≰10120212⊪)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34,"operation_count":2,"complexity_ratio":17.0,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":2615,"base":3}}},"used_operators":["inkyxCbjAn","zVYPLywUTj"],"dependent_operators":["B5M0gjZbta","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2615","layer":2},{"info":"compute unary expreesion, input=2615, 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 unary expreesion, input=0, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵(⫏≰10120212⊪)=⫏≰0","reverse_text":"⫏≰0=⇁⨣⪵(⫏≰10120212⊪)","cot":[{"info":"⫏≰10120212⊪=⫏≰0","layer":1},{"info":"⇁⨣⪵⫏≰0=⫏≰0","layer":0}]}
{"id":357,"expression_no_base_symbol":"-($1655$↛⩡⫤)","expression":"-(⫏≰2021022↛⩡⫤)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5100,"operation_count":2,"complexity_ratio":2550.0,"tree":{"type":"unary","operator":"-","unary_expr":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"numeric_atoms","value":1655,"base":3}}},"used_operators":["t8gj7n24qd","FU0Cs4j7VP"],"dependent_operators":["8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X"],"result":"⫏≰110111102220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1655","layer":2},{"info":"compute unary expreesion, input=1655, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-245994","layer":1},{"info":"compute unary expreesion, input=-245994, op_id = t8gj7n24qd, unary_op_definition = 'None', output=245994","layer":0}],"base":3,"result_base":3,"text":"-(⫏≰2021022↛⩡⫤)=⫏≰110111102220","reverse_text":"⫏≰110111102220=-(⫏≰2021022↛⩡⫤)","cot":[{"info":"⫏≰2021022↛⩡⫤=⫏≰-110111102220","layer":1},{"info":"-⫏≰-110111102220=⫏≰110111102220","layer":0}]}
{"id":358,"expression_no_base_symbol":"(-$2827$)⨳⩥⨓($1027$↛⩡⫤)","expression":"(-⫏≰10212201)⨳⩥⨓(⫏≰1102001↛⩡⫤)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3219,"operation_count":3,"complexity_ratio":1073.0,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":2827,"base":3}},"right_expr":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"numeric_atoms","value":1027,"base":3}}},"used_operators":["nCS4ZIUYfx","t8gj7n24qd","FU0Cs4j7VP"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X"],"result":"⫏≰-21112111001","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2827","layer":2},{"info":"compute unary expreesion, input=2827, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-2827","layer":1},{"info":"number node, value=1027","layer":2},{"info":"compute unary expreesion, input=1027, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-151166","layer":1},{"info":"compute binary expreesion, left_input=-2827, right_input=-151166, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-148339","layer":0}],"base":3,"result_base":3,"text":"(-⫏≰10212201)⨳⩥⨓(⫏≰1102001↛⩡⫤)=⫏≰-21112111001","reverse_text":"⫏≰-21112111001=(-⫏≰10212201)⨳⩥⨓(⫏≰1102001↛⩡⫤)","cot":[{"info":"-⫏≰10212201=⫏≰-10212201","layer":1},{"info":"⫏≰1102001↛⩡⫤=⫏≰-21200100202","layer":1},{"info":"⫏≰-10212201⨳⩥⨓⫏≰-21200100202=⫏≰-21112111001","layer":0}]}
{"id":359,"expression_no_base_symbol":"($1879$⨽$3987$)⨰($1713$≧⫂∧$3611$)","expression":"(⫏≰2120121⨽⫏≰12110200)⨰(⫏≰2100110≧⫂∧⫏≰11221202)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1895,"operation_count":3,"complexity_ratio":631.6666666666666,"tree":{"type":"binary","operator":"⨰","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1879,"base":3},"right_expr":{"type":"numeric_atoms","value":3987,"base":3}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":1713,"base":3},"right_expr":{"type":"numeric_atoms","value":3611,"base":3}}},"used_operators":["eewbuw0ToL","8HhzD0ZcuI","Ph9nP6C5qx"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-201221211021122","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1879","layer":2},{"info":"number node, value=3987","layer":2},{"info":"compute binary expreesion, left_input=1879, right_input=3987, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-10602570","layer":1},{"info":"number node, value=1713","layer":2},{"info":"number node, value=3611","layer":2},{"info":"compute binary expreesion, left_input=1713, right_input=3611, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=3138","layer":1},{"info":"compute binary expreesion, left_input=-10602570, right_input=3138, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-10605698","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2120121⨽⫏≰12110200)⨰(⫏≰2100110≧⫂∧⫏≰11221202)=⫏≰-201221211021122","reverse_text":"⫏≰-201221211021122=(⫏≰2120121⨽⫏≰12110200)⨰(⫏≰2100110≧⫂∧⫏≰11221202)","cot":[{"info":"⫏≰2120121⨽⫏≰12110200=⫏≰-201221122222210","layer":1},{"info":"⫏≰2100110≧⫂∧⫏≰11221202=⫏≰11022020","layer":1},{"info":"⫏≰-201221122222210⨰⫏≰11022020=⫏≰-201221211021122","layer":0}]}
{"id":360,"expression_no_base_symbol":"$1473$∑⇟⊟$1415$⨵⪆$2014$⨰$7440$","expression":"⫏≰2000120∑⇟⊟⫏≰1221102⨵⪆⫏≰2202121⨰⫏≰101012120","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":1473,"base":3},"right_expr":{"type":"numeric_atoms","value":1415,"base":3}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":2014,"base":3},"right_expr":{"type":"numeric_atoms","value":7440,"base":3}}},"used_operators":["2DQ55sFlQl","U7g4x0WXJJ","eewbuw0ToL"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1473","layer":2},{"info":"number node, value=1415","layer":2},{"info":"compute binary expreesion, left_input=1473, right_input=1415, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"number node, value=2014","layer":2},{"info":"number node, value=7440","layer":2},{"info":"compute binary expreesion, left_input=2014, right_input=7440, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-5416","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-5416, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰2000120∑⇟⊟⫏≰1221102⨵⪆⫏≰2202121⨰⫏≰101012120=⫏≰12221","reverse_text":"⫏≰12221=⫏≰2000120∑⇟⊟⫏≰1221102⨵⪆⫏≰2202121⨰⫏≰101012120","cot":[{"info":"⫏≰2000120∑⇟⊟⫏≰1221102=NaN","layer":1},{"info":"⫏≰2202121⨰⫏≰101012120=⫏≰-21102121","layer":1},{"info":"NaN⨵⪆⫏≰-21102121=⫏≰12221","layer":0}]}
{"id":361,"expression_no_base_symbol":"$2882$∼$6174$↬($3400$⋥≓≎$1591$)","expression":"⫏≰10221202∼⫏≰22110200↬(⫏≰11122221⋥≓≎⫏≰2011221)","highest_n_order":5,"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":2882,"base":3},"right_expr":{"type":"numeric_atoms","value":6174,"base":3}},"right_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":3400,"base":3},"right_expr":{"type":"numeric_atoms","value":1591,"base":3}}},"used_operators":["B5M0gjZbta","DyGG3AbaNP","Qy55tPpLXF"],"dependent_operators":["rGHVDoGpnC","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2882","layer":2},{"info":"number node, value=6174","layer":2},{"info":"compute binary expreesion, left_input=2882, right_input=6174, 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=3400","layer":2},{"info":"number node, value=1591","layer":2},{"info":"compute binary expreesion, left_input=3400, right_input=1591, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-185","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-185, 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":3,"result_base":3,"text":"⫏≰10221202∼⫏≰22110200↬(⫏≰11122221⋥≓≎⫏≰2011221)=NaN","reverse_text":"NaN=⫏≰10221202∼⫏≰22110200↬(⫏≰11122221⋥≓≎⫏≰2011221)","cot":[{"info":"⫏≰10221202∼⫏≰22110200=NaN","layer":1},{"info":"⫏≰11122221⋥≓≎⫏≰2011221=⫏≰-20212","layer":1},{"info":"NaN↬⫏≰-20212=NaN","layer":0}]}
{"id":362,"expression_no_base_symbol":"($3019$≧⫂∧$1142$)⊴($5059$≦≮≮)","expression":"(⫏≰11010211≧⫂∧⫏≰1120022)⊴(⫏≰20221101≦≮≮)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15187,"operation_count":3,"complexity_ratio":5062.333333333333,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":3019,"base":3},"right_expr":{"type":"numeric_atoms","value":1142,"base":3}},"right_expr":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":5059,"base":3}}},"used_operators":["Nsiff2A1zJ","Ph9nP6C5qx","D4vGDi5EA2"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3019","layer":2},{"info":"number node, value=1142","layer":2},{"info":"compute binary expreesion, left_input=3019, right_input=1142, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=669","layer":1},{"info":"number node, value=5059","layer":2},{"info":"compute unary expreesion, input=5059, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-15177","layer":1},{"info":"compute binary expreesion, left_input=669, right_input=-15177, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11010211≧⫂∧⫏≰1120022)⊴(⫏≰20221101≦≮≮)=NaN","reverse_text":"NaN=(⫏≰11010211≧⫂∧⫏≰1120022)⊴(⫏≰20221101≦≮≮)","cot":[{"info":"⫏≰11010211≧⫂∧⫏≰1120022=⫏≰220210","layer":1},{"info":"⫏≰20221101≦≮≮=⫏≰-202211010","layer":1},{"info":"⫏≰220210⊴⫏≰-202211010=NaN","layer":0}]}
{"id":363,"expression_no_base_symbol":"$5425$↺$7113$∲⫓$6307$⨽$2138$","expression":"⫏≰21102221↺⫏≰100202110∲⫓⫏≰22122121⨽⫏≰2221012","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6319,"operation_count":3,"complexity_ratio":2106.3333333333335,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":5425,"base":3},"right_expr":{"type":"numeric_atoms","value":7113,"base":3}},"right_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":6307,"base":3},"right_expr":{"type":"numeric_atoms","value":2138,"base":3}}},"used_operators":["i8ToyICDmI","7j4O788W3g","8HhzD0ZcuI"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"⫏≰100202110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5425","layer":2},{"info":"number node, value=7113","layer":2},{"info":"compute binary expreesion, left_input=5425, right_input=7113, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=7113","layer":1},{"info":"number node, value=6307","layer":2},{"info":"number node, value=2138","layer":2},{"info":"compute binary expreesion, left_input=6307, right_input=2138, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-119339847","layer":1},{"info":"compute binary expreesion, left_input=7113, right_input=-119339847, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=7113","layer":0}],"base":3,"result_base":3,"text":"⫏≰21102221↺⫏≰100202110∲⫓⫏≰22122121⨽⫏≰2221012=⫏≰100202110","reverse_text":"⫏≰100202110=⫏≰21102221↺⫏≰100202110∲⫓⫏≰22122121⨽⫏≰2221012","cot":[{"info":"⫏≰21102221↺⫏≰100202110=⫏≰100202110","layer":1},{"info":"⫏≰22122121⨽⫏≰2221012=⫏≰-22022120002111100","layer":1},{"info":"⫏≰100202110∲⫓⫏≰-22022120002111100=⫏≰100202110","layer":0}]}
{"id":364,"expression_no_base_symbol":"⫛⫱⨽($6367$≋⫹)","expression":"⫛⫱⨽(⫏≰22201211≋⫹)","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":6367,"base":3}}},"used_operators":["DlLNRPXxWL","N41Kp7NANJ"],"dependent_operators":["rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6367","layer":2},{"info":"compute unary expreesion, input=6367, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-12734","layer":1},{"info":"compute unary expreesion, input=-12734, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫛⫱⨽(⫏≰22201211≋⫹)=⫏≰0","reverse_text":"⫏≰0=⫛⫱⨽(⫏≰22201211≋⫹)","cot":[{"info":"⫏≰22201211≋⫹=⫏≰-122110122","layer":1},{"info":"⫛⫱⨽⫏≰-122110122=⫏≰0","layer":0}]}
{"id":365,"expression_no_base_symbol":"$1935$↬$2635$⋳⪒$1219$+⇶⊼$1034$","expression":"⫏≰2122200↬⫏≰10121121⋳⪒⫏≰1200011+⇶⊼⫏≰1102022","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":1935,"base":3},"right_expr":{"type":"numeric_atoms","value":2635,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":1219,"base":3},"right_expr":{"type":"numeric_atoms","value":1034,"base":3}}},"used_operators":["12rbrZMWeM","B5M0gjZbta","TpPTUOHfaN"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rGHVDoGpnC","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1935","layer":2},{"info":"number node, value=2635","layer":2},{"info":"compute binary expreesion, left_input=1935, right_input=2635, 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=1219","layer":2},{"info":"number node, value=1034","layer":2},{"info":"compute binary expreesion, left_input=1219, right_input=1034, 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":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2122200↬⫏≰10121121⋳⪒⫏≰1200011+⇶⊼⫏≰1102022=NaN","reverse_text":"NaN=⫏≰2122200↬⫏≰10121121⋳⪒⫏≰1200011+⇶⊼⫏≰1102022","cot":[{"info":"⫏≰2122200↬⫏≰10121121=NaN","layer":1},{"info":"⫏≰1200011+⇶⊼⫏≰1102022=NaN","layer":1},{"info":"NaN⋳⪒NaN=NaN","layer":0}]}
{"id":366,"expression_no_base_symbol":"(⨰⫟⨤$2973$)⇷($2658$⩨$1534$)","expression":"(⨰⫟⨤⫏≰11002010)⇷(⫏≰10122110⩨⫏≰2002211)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":11063,"operation_count":3,"complexity_ratio":3687.6666666666665,"tree":{"type":"binary","operator":"⇷","left_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":2973,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":2658,"base":3},"right_expr":{"type":"numeric_atoms","value":1534,"base":3}}},"used_operators":["mp7IySMOzn","Tw270M8GLb","2DlMacCsIx"],"dependent_operators":["DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2973","layer":2},{"info":"compute unary expreesion, input=2973, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":1},{"info":"number node, value=2658","layer":2},{"info":"number node, value=1534","layer":2},{"info":"compute binary expreesion, left_input=2658, right_input=1534, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=0, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⨰⫟⨤⫏≰11002010)⇷(⫏≰10122110⩨⫏≰2002211)=⫏≰0","reverse_text":"⫏≰0=(⨰⫟⨤⫏≰11002010)⇷(⫏≰10122110⩨⫏≰2002211)","cot":[{"info":"⨰⫟⨤⫏≰11002010=NaN","layer":1},{"info":"⫏≰10122110⩨⫏≰2002211=⫏≰0","layer":1},{"info":"NaN⇷⫏≰0=⫏≰0","layer":0}]}
{"id":367,"expression_no_base_symbol":"($1540$%$2652$)⊭↱$2746$⋳⪒$4855$","expression":"(⫏≰2010001%⫏≰10122020)⊭↱⫏≰10202201⋳⪒⫏≰20122211","highest_n_order":2,"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":1540,"base":3},"right_expr":{"type":"numeric_atoms","value":2652,"base":3}},"right_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":2746,"base":3},"right_expr":{"type":"numeric_atoms","value":4855,"base":3}}},"used_operators":["COABgblf1C","k8jYdgA6NY","12rbrZMWeM"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-10020222","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1540","layer":2},{"info":"number node, value=2652","layer":2},{"info":"compute binary expreesion, left_input=1540, right_input=2652, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1540","layer":1},{"info":"number node, value=2746","layer":2},{"info":"number node, value=4855","layer":2},{"info":"compute binary expreesion, left_input=2746, right_input=4855, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=350","layer":1},{"info":"compute binary expreesion, left_input=1540, right_input=350, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-2375","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2010001%⫏≰10122020)⊭↱⫏≰10202201⋳⪒⫏≰20122211=⫏≰-10020222","reverse_text":"⫏≰-10020222=(⫏≰2010001%⫏≰10122020)⊭↱⫏≰10202201⋳⪒⫏≰20122211","cot":[{"info":"⫏≰2010001%⫏≰10122020=⫏≰2010001","layer":1},{"info":"⫏≰10202201⋳⪒⫏≰20122211=⫏≰110222","layer":1},{"info":"⫏≰2010001⊭↱⫏≰110222=⫏≰-10020222","layer":0}]}
{"id":368,"expression_no_base_symbol":"($1222$⋷$8655$)⪠⩆⊳","expression":"(⫏≰1200021⋷⫏≰102212120)⪠⩆⊳","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":1222,"base":3},"right_expr":{"type":"numeric_atoms","value":8655,"base":3}}},"used_operators":["JLbD19bQDL","23Mk6UjR3U"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1222","layer":2},{"info":"number node, value=8655","layer":2},{"info":"compute binary expreesion, left_input=1222, right_input=8655, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=16088","layer":1},{"info":"compute unary expreesion, input=16088, 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":0}],"base":3,"result_base":3,"text":"(⫏≰1200021⋷⫏≰102212120)⪠⩆⊳=⫏≰0","reverse_text":"⫏≰0=(⫏≰1200021⋷⫏≰102212120)⪠⩆⊳","cot":[{"info":"⫏≰1200021⋷⫏≰102212120=⫏≰211001212","layer":1},{"info":"⫏≰211001212⪠⩆⊳=⫏≰0","layer":0}]}
{"id":369,"expression_no_base_symbol":"$2894$⪘⫢$1730$↛⩡⫤","expression":"⫏≰10222012⪘⫢⫏≰2101002↛⩡⫤","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":17141,"operation_count":2,"complexity_ratio":8570.5,"tree":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":2894,"base":3},"right_expr":{"type":"numeric_atoms","value":1730,"base":3}}},"used_operators":["FU0Cs4j7VP","oacrs7FA3X"],"dependent_operators":["8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⫏≰-1121020211121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2894","layer":2},{"info":"number node, value=1730","layer":2},{"info":"compute binary expreesion, left_input=2894, right_input=1730, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=5664","layer":1},{"info":"compute unary expreesion, input=5664, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-851353","layer":0}],"base":3,"result_base":3,"text":"⫏≰10222012⪘⫢⫏≰2101002↛⩡⫤=⫏≰-1121020211121","reverse_text":"⫏≰-1121020211121=⫏≰10222012⪘⫢⫏≰2101002↛⩡⫤","cot":[{"info":"⫏≰10222012⪘⫢⫏≰2101002=⫏≰21202210","layer":1},{"info":"⫏≰21202210↛⩡⫤=⫏≰-1121020211121","layer":0}]}
{"id":370,"expression_no_base_symbol":"($2462$⋫)∧","expression":"(⫏≰10101012⋫)∧","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2468,"operation_count":2,"complexity_ratio":1234.0,"tree":{"type":"unary","operator":"∧","unary_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":2462,"base":3}}},"used_operators":["z63VuFQld9","JL8yIekQnl"],"dependent_operators":["B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","tmPS8pqC7x"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2462","layer":2},{"info":"compute unary expreesion, input=2462, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=2462","layer":1},{"info":"compute unary expreesion, input=2462, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10101012⋫)∧=NaN","reverse_text":"NaN=(⫏≰10101012⋫)∧","cot":[{"info":"⫏≰10101012⋫=⫏≰10101012","layer":1},{"info":"⫏≰10101012∧=NaN","layer":0}]}
{"id":371,"expression_no_base_symbol":"(-$8618$)⫥∨⫟$1484$≧⫂∧$3548$","expression":"(-⫏≰102211012)⫥∨⫟⫏≰2000222≧⫂∧⫏≰11212102","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":156,"operation_count":3,"complexity_ratio":52.0,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":8618,"base":3}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":1484,"base":3},"right_expr":{"type":"numeric_atoms","value":3548,"base":3}}},"used_operators":["KYD54nUTWz","t8gj7n24qd","Ph9nP6C5qx"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=8618","layer":2},{"info":"compute unary expreesion, input=8618, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-8618","layer":1},{"info":"number node, value=1484","layer":2},{"info":"number node, value=3548","layer":2},{"info":"compute binary expreesion, left_input=1484, right_input=3548, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=3075","layer":1},{"info":"compute binary expreesion, left_input=-8618, right_input=3075, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(-⫏≰102211012)⫥∨⫟⫏≰2000222≧⫂∧⫏≰11212102=NaN","reverse_text":"NaN=(-⫏≰102211012)⫥∨⫟⫏≰2000222≧⫂∧⫏≰11212102","cot":[{"info":"-⫏≰102211012=⫏≰-102211012","layer":1},{"info":"⫏≰2000222≧⫂∧⫏≰11212102=⫏≰11012220","layer":1},{"info":"⫏≰-102211012⫥∨⫟⫏≰11012220=NaN","layer":0}]}
{"id":372,"expression_no_base_symbol":"⊄⩳↩($2343$↺$1226$)","expression":"⊄⩳↩(⫏≰10012210↺⫏≰1200102)","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":2343,"base":3},"right_expr":{"type":"numeric_atoms","value":1226,"base":3}}},"used_operators":["8w2t5hMYqp","7j4O788W3g"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-12001020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2343","layer":2},{"info":"number node, value=1226","layer":2},{"info":"compute binary expreesion, left_input=2343, right_input=1226, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1226","layer":1},{"info":"compute unary expreesion, input=1226, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-3678","layer":0}],"base":3,"result_base":3,"text":"⊄⩳↩(⫏≰10012210↺⫏≰1200102)=⫏≰-12001020","reverse_text":"⫏≰-12001020=⊄⩳↩(⫏≰10012210↺⫏≰1200102)","cot":[{"info":"⫏≰10012210↺⫏≰1200102=⫏≰1200102","layer":1},{"info":"⊄⩳↩⫏≰1200102=⫏≰-12001020","layer":0}]}
{"id":373,"expression_no_base_symbol":"(∂$1610$)∀⇚≩($1561$+⇶⊼$6000$)","expression":"(∂⫏≰2012122)∀⇚≩(⫏≰2010211+⇶⊼⫏≰22020020)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3,"operation_count":3,"complexity_ratio":1.0,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":1610,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":1561,"base":3},"right_expr":{"type":"numeric_atoms","value":6000,"base":3}}},"used_operators":["LRNGc0VcxI","Uaa54Peajs","TpPTUOHfaN"],"dependent_operators":["X99M06cbEe","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1610","layer":2},{"info":"compute unary expreesion, input=1610, 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":"number node, value=1561","layer":2},{"info":"number node, value=6000","layer":2},{"info":"compute binary expreesion, left_input=1561, right_input=6000, 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":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, 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":3,"result_base":3,"text":"(∂⫏≰2012122)∀⇚≩(⫏≰2010211+⇶⊼⫏≰22020020)=NaN","reverse_text":"NaN=(∂⫏≰2012122)∀⇚≩(⫏≰2010211+⇶⊼⫏≰22020020)","cot":[{"info":"∂⫏≰2012122=NaN","layer":1},{"info":"⫏≰2010211+⇶⊼⫏≰22020020=NaN","layer":1},{"info":"NaN∀⇚≩NaN=NaN","layer":0}]}
{"id":374,"expression_no_base_symbol":"($1515$⇼⇔∾$7473$)↺$3573$⋝⋈⪟$3966$","expression":"(⫏≰2002010⇼⇔∾⫏≰101020210)↺⫏≰11220100⋝⋈⪟⫏≰12102220","highest_n_order":1,"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":1515,"base":3},"right_expr":{"type":"numeric_atoms","value":7473,"base":3}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":3573,"base":3},"right_expr":{"type":"numeric_atoms","value":3966,"base":3}}},"used_operators":["7j4O788W3g","tifHPKVTfV","2DDjHMKMc0"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰11220100","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1515","layer":2},{"info":"number node, value=7473","layer":2},{"info":"compute binary expreesion, left_input=1515, right_input=7473, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=5958","layer":1},{"info":"number node, value=3573","layer":2},{"info":"number node, value=3966","layer":2},{"info":"compute binary expreesion, left_input=3573, right_input=3966, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=3573","layer":1},{"info":"compute binary expreesion, left_input=5958, right_input=3573, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=3573","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2002010⇼⇔∾⫏≰101020210)↺⫏≰11220100⋝⋈⪟⫏≰12102220=⫏≰11220100","reverse_text":"⫏≰11220100=(⫏≰2002010⇼⇔∾⫏≰101020210)↺⫏≰11220100⋝⋈⪟⫏≰12102220","cot":[{"info":"⫏≰2002010⇼⇔∾⫏≰101020210=⫏≰22011200","layer":1},{"info":"⫏≰11220100⋝⋈⪟⫏≰12102220=⫏≰11220100","layer":1},{"info":"⫏≰22011200↺⫏≰11220100=⫏≰11220100","layer":0}]}
{"id":375,"expression_no_base_symbol":"$8555$⨪↰⇹$1549$⋓($2017$+⇶⊼$1348$)","expression":"⫏≰102201212⨪↰⇹⫏≰2010101⋓(⫏≰2202201+⇶⊼⫏≰1211221)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8569,"operation_count":3,"complexity_ratio":2856.3333333333335,"tree":{"type":"binary","operator":"⋓","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":8555,"base":3},"right_expr":{"type":"numeric_atoms","value":1549,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":2017,"base":3},"right_expr":{"type":"numeric_atoms","value":1348,"base":3}}},"used_operators":["T2fj7uvVaJ","tmPS8pqC7x","TpPTUOHfaN"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rJVOvQCfKK","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=8555","layer":2},{"info":"number node, value=1549","layer":2},{"info":"compute binary expreesion, left_input=8555, right_input=1549, 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=8555","layer":1},{"info":"number node, value=2017","layer":2},{"info":"number node, value=1348","layer":2},{"info":"compute binary expreesion, left_input=2017, right_input=1348, 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":1},{"info":"compute binary expreesion, left_input=8555, 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":3,"result_base":3,"text":"⫏≰102201212⨪↰⇹⫏≰2010101⋓(⫏≰2202201+⇶⊼⫏≰1211221)=NaN","reverse_text":"NaN=⫏≰102201212⨪↰⇹⫏≰2010101⋓(⫏≰2202201+⇶⊼⫏≰1211221)","cot":[{"info":"⫏≰102201212⨪↰⇹⫏≰2010101=⫏≰102201212","layer":1},{"info":"⫏≰2202201+⇶⊼⫏≰1211221=NaN","layer":1},{"info":"⫏≰102201212⋓NaN=NaN","layer":0}]}
{"id":376,"expression_no_base_symbol":"($6957$⪨≂$1269$)⪒($4111$⫩⊇)","expression":"(⫏≰100112200⪨≂⫏≰1202000)⪒(⫏≰12122021⫩⊇)","highest_n_order":1,"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":6957,"base":3},"right_expr":{"type":"numeric_atoms","value":1269,"base":3}},"right_expr":{"type":"unary","operator":"⫩⊇","unary_expr":{"type":"numeric_atoms","value":4111,"base":3}}},"used_operators":["f6k1SAg4EE","sdazOOVcIp","BjRHVeLaeN"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-101011102","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6957","layer":2},{"info":"number node, value=1269","layer":2},{"info":"compute binary expreesion, left_input=6957, right_input=1269, 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=11478","layer":1},{"info":"number node, value=4111","layer":2},{"info":"compute unary expreesion, input=4111, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=-4069","layer":1},{"info":"compute binary expreesion, left_input=11478, right_input=-4069, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-7409","layer":0}],"base":3,"result_base":3,"text":"(⫏≰100112200⪨≂⫏≰1202000)⪒(⫏≰12122021⫩⊇)=⫏≰-101011102","reverse_text":"⫏≰-101011102=(⫏≰100112200⪨≂⫏≰1202000)⪒(⫏≰12122021⫩⊇)","cot":[{"info":"⫏≰100112200⪨≂⫏≰1202000=⫏≰120202010","layer":1},{"info":"⫏≰12122021⫩⊇=⫏≰-12120201","layer":1},{"info":"⫏≰120202010⪒⫏≰-12120201=⫏≰-101011102","layer":0}]}
{"id":377,"expression_no_base_symbol":"$1246$⪘⫢$1675$↙$6195$⨪↰⇹$3436$","expression":"⫏≰1201011⪘⫢⫏≰2022001↙⫏≰22111110⨪↰⇹⫏≰11201021","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":12408,"operation_count":3,"complexity_ratio":4136.0,"tree":{"type":"binary","operator":"↙","left_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1246,"base":3},"right_expr":{"type":"numeric_atoms","value":1675,"base":3}},"right_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":6195,"base":3},"right_expr":{"type":"numeric_atoms","value":3436,"base":3}}},"used_operators":["yyfyN0ffXY","oacrs7FA3X","tmPS8pqC7x"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rJVOvQCfKK"],"result":"⫏≰-221111100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1246","layer":2},{"info":"number node, value=1675","layer":2},{"info":"compute binary expreesion, left_input=1246, right_input=1675, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=2368","layer":1},{"info":"number node, value=6195","layer":2},{"info":"number node, value=3436","layer":2},{"info":"compute binary expreesion, left_input=6195, right_input=3436, 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=6195","layer":1},{"info":"compute binary expreesion, left_input=2368, right_input=6195, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-18585","layer":0}],"base":3,"result_base":3,"text":"⫏≰1201011⪘⫢⫏≰2022001↙⫏≰22111110⨪↰⇹⫏≰11201021=⫏≰-221111100","reverse_text":"⫏≰-221111100=⫏≰1201011⪘⫢⫏≰2022001↙⫏≰22111110⨪↰⇹⫏≰11201021","cot":[{"info":"⫏≰1201011⪘⫢⫏≰2022001=⫏≰10020201","layer":1},{"info":"⫏≰22111110⨪↰⇹⫏≰11201021=⫏≰22111110","layer":1},{"info":"⫏≰10020201↙⫏≰22111110=⫏≰-221111100","layer":0}]}
{"id":378,"expression_no_base_symbol":"(⨞⊢$1167$)⋳⪒(↩$1056$)","expression":"(⨞⊢⫏≰1121020)⋳⪒(↩⫏≰1110010)","highest_n_order":2,"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":1167,"base":3}},"right_expr":{"type":"unary","operator":"↩","unary_expr":{"type":"numeric_atoms","value":1056,"base":3}}},"used_operators":["12rbrZMWeM","xUOZtlo3hN","jLgFTUHLKL"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D"],"result":"⫏≰10200222","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1167","layer":2},{"info":"compute unary expreesion, input=1167, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-1341","layer":1},{"info":"number node, value=1056","layer":2},{"info":"compute unary expreesion, input=1056, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-5668","layer":1},{"info":"compute binary expreesion, left_input=-1341, right_input=-5668, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=2699","layer":0}],"base":3,"result_base":3,"text":"(⨞⊢⫏≰1121020)⋳⪒(↩⫏≰1110010)=⫏≰10200222","reverse_text":"⫏≰10200222=(⨞⊢⫏≰1121020)⋳⪒(↩⫏≰1110010)","cot":[{"info":"⨞⊢⫏≰1121020=⫏≰-1211200","layer":1},{"info":"↩⫏≰1110010=⫏≰-21202221","layer":1},{"info":"⫏≰-1211200⋳⪒⫏≰-21202221=⫏≰10200222","layer":0}]}
{"id":379,"expression_no_base_symbol":"≦∁$1022$⨰$1031$","expression":"≦∁⫏≰1101212⨰⫏≰1102012","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":1022,"base":3},"right_expr":{"type":"numeric_atoms","value":1031,"base":3}}},"used_operators":["9ICcGScMcE","eewbuw0ToL"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-110022","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1022","layer":2},{"info":"number node, value=1031","layer":2},{"info":"compute binary expreesion, left_input=1022, right_input=1031, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=1","layer":1},{"info":"compute unary expreesion, input=1, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=-332","layer":0}],"base":3,"result_base":3,"text":"≦∁⫏≰1101212⨰⫏≰1102012=⫏≰-110022","reverse_text":"⫏≰-110022=≦∁⫏≰1101212⨰⫏≰1102012","cot":[{"info":"⫏≰1101212⨰⫏≰1102012=⫏≰1","layer":1},{"info":"≦∁⫏≰1=⫏≰-110022","layer":0}]}
{"id":380,"expression_no_base_symbol":"⊙↵-($1009$⨪↰⇹$5512$)","expression":"⊙↵-(⫏≰1101101⨪↰⇹⫏≰21120011)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2064,"operation_count":2,"complexity_ratio":1032.0,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":1009,"base":3},"right_expr":{"type":"numeric_atoms","value":5512,"base":3}}},"used_operators":["oWn0xqSxBt","tmPS8pqC7x"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","rJVOvQCfKK"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1009","layer":2},{"info":"number node, value=5512","layer":2},{"info":"compute binary expreesion, left_input=1009, right_input=5512, 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=1009","layer":1},{"info":"compute unary expreesion, input=1009, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⫏≰1101101⨪↰⇹⫏≰21120011)=⫏≰-1","reverse_text":"⫏≰-1=⊙↵-(⫏≰1101101⨪↰⇹⫏≰21120011)","cot":[{"info":"⫏≰1101101⨪↰⇹⫏≰21120011=⫏≰1101101","layer":1},{"info":"⊙↵-⫏≰1101101=⫏≰-1","layer":0}]}
{"id":381,"expression_no_base_symbol":"($3083$∸)-$6689$⩨$7726$","expression":"(⫏≰11020012∸)-⫏≰100011202⩨⫏≰101121011","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":182,"operation_count":3,"complexity_ratio":60.666666666666664,"tree":{"type":"binary","operator":"-","left_expr":{"type":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":3083,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":6689,"base":3},"right_expr":{"type":"numeric_atoms","value":7726,"base":3}}},"used_operators":["rysDP5nf3Z","o20kRiQErp","2DlMacCsIx"],"dependent_operators":["tmPS8pqC7x","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰20200","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3083","layer":2},{"info":"compute unary expreesion, input=3083, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"number node, value=6689","layer":2},{"info":"number node, value=7726","layer":2},{"info":"compute binary expreesion, left_input=6689, right_input=7726, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-3","layer":1},{"info":"compute binary expreesion, left_input=177, right_input=-3, op_id = rysDP5nf3Z binary_op_definition= 'None', output=180","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11020012∸)-⫏≰100011202⩨⫏≰101121011=⫏≰20200","reverse_text":"⫏≰20200=(⫏≰11020012∸)-⫏≰100011202⩨⫏≰101121011","cot":[{"info":"⫏≰11020012∸=⫏≰20120","layer":1},{"info":"⫏≰100011202⩨⫏≰101121011=⫏≰-10","layer":1},{"info":"⫏≰20120-⫏≰-10=⫏≰20200","layer":0}]}
{"id":382,"expression_no_base_symbol":"+⊝⨔($1796$⋥≓≎$1100$)","expression":"+⊝⨔(⫏≰2110112⋥≓≎⫏≰1111202)","highest_n_order":3,"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":1796,"base":3},"right_expr":{"type":"numeric_atoms","value":1100,"base":3}}},"used_operators":["DhbWaqg5eL","Qy55tPpLXF"],"dependent_operators":["dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰2002101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1796","layer":2},{"info":"number node, value=1100","layer":2},{"info":"compute binary expreesion, left_input=1796, right_input=1100, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=437","layer":1},{"info":"compute unary expreesion, input=437, 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":3,"result_base":3,"text":"+⊝⨔(⫏≰2110112⋥≓≎⫏≰1111202)=⫏≰2002101","reverse_text":"⫏≰2002101=+⊝⨔(⫏≰2110112⋥≓≎⫏≰1111202)","cot":[{"info":"⫏≰2110112⋥≓≎⫏≰1111202=⫏≰121012","layer":1},{"info":"+⊝⨔⫏≰121012=⫏≰2002101","layer":0}]}
{"id":383,"expression_no_base_symbol":"($4600$%$3040$)⊉≛↸($8501$⊪)","expression":"(⫏≰20022101%⫏≰11011121)⊉≛↸(⫏≰102122212⊪)","highest_n_order":2,"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":4600,"base":3},"right_expr":{"type":"numeric_atoms","value":3040,"base":3}},"right_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":8501,"base":3}}},"used_operators":["DZ8iAZOCBD","k8jYdgA6NY","zVYPLywUTj"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL"],"result":"⫏≰11021120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4600","layer":2},{"info":"number node, value=3040","layer":2},{"info":"compute binary expreesion, left_input=4600, right_input=3040, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1560","layer":1},{"info":"number node, value=8501","layer":2},{"info":"compute unary expreesion, input=8501, 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=1560, right_input=0, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=3120","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20022101%⫏≰11011121)⊉≛↸(⫏≰102122212⊪)=⫏≰11021120","reverse_text":"⫏≰11021120=(⫏≰20022101%⫏≰11011121)⊉≛↸(⫏≰102122212⊪)","cot":[{"info":"⫏≰20022101%⫏≰11011121=⫏≰2010210","layer":1},{"info":"⫏≰102122212⊪=⫏≰0","layer":1},{"info":"⫏≰2010210⊉≛↸⫏≰0=⫏≰11021120","layer":0}]}
{"id":384,"expression_no_base_symbol":"($3633$⨵⪆$2094$)⨪↰⇹(↩$1221$)","expression":"(⫏≰11222120⨵⪆⫏≰2212120)⨪↰⇹(↩⫏≰1200020)","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":3633,"base":3},"right_expr":{"type":"numeric_atoms","value":2094,"base":3}},"right_expr":{"type":"unary","operator":"↩","unary_expr":{"type":"numeric_atoms","value":1221,"base":3}}},"used_operators":["tmPS8pqC7x","2DQ55sFlQl","jLgFTUHLKL"],"dependent_operators":["rJVOvQCfKK","rysDP5nf3Z","t8gj7n24qd","sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3633","layer":2},{"info":"number node, value=2094","layer":2},{"info":"compute binary expreesion, left_input=3633, right_input=2094, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=1221","layer":2},{"info":"compute unary expreesion, input=1221, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-6988","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=-6988, 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=160","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11222120⨵⪆⫏≰2212120)⨪↰⇹(↩⫏≰1200020)=⫏≰12221","reverse_text":"⫏≰12221=(⫏≰11222120⨵⪆⫏≰2212120)⨪↰⇹(↩⫏≰1200020)","cot":[{"info":"⫏≰11222120⨵⪆⫏≰2212120=⫏≰12221","layer":1},{"info":"↩⫏≰1200020=⫏≰-100120211","layer":1},{"info":"⫏≰12221⨪↰⇹⫏≰-100120211=⫏≰12221","layer":0}]}
{"id":385,"expression_no_base_symbol":"$6036$⪢$7369$⨐⩸⫘($1944$⨸⪁$9568$)","expression":"⫏≰22021120⪢⫏≰101002221⨐⩸⫘(⫏≰2200000⨸⪁⫏≰111010101)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7373,"operation_count":3,"complexity_ratio":2457.6666666666665,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":6036,"base":3},"right_expr":{"type":"numeric_atoms","value":7369,"base":3}},"right_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":1944,"base":3},"right_expr":{"type":"numeric_atoms","value":9568,"base":3}}},"used_operators":["fu6greOZ01","dWAJyo7jo9","g55IO6H4Gj"],"dependent_operators":["3ViojmjbAp","k8jYdgA6NY","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6036","layer":2},{"info":"number node, value=7369","layer":2},{"info":"compute binary expreesion, left_input=6036, right_input=7369, 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=1944","layer":2},{"info":"number node, value=9568","layer":2},{"info":"compute binary expreesion, left_input=1944, right_input=9568, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=23024","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=23024, 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":3,"result_base":3,"text":"⫏≰22021120⪢⫏≰101002221⨐⩸⫘(⫏≰2200000⨸⪁⫏≰111010101)=NaN","reverse_text":"NaN=⫏≰22021120⪢⫏≰101002221⨐⩸⫘(⫏≰2200000⨸⪁⫏≰111010101)","cot":[{"info":"⫏≰22021120⪢⫏≰101002221=NaN","layer":1},{"info":"⫏≰2200000⨸⪁⫏≰111010101=⫏≰1011120202","layer":1},{"info":"NaN⨐⩸⫘⫏≰1011120202=NaN","layer":0}]}
{"id":386,"expression_no_base_symbol":"$9399$⨰$2333$⨵⪆$1812$∼$3403$","expression":"⫏≰110220010⨰⫏≰10012102⨵⪆⫏≰2111010∼⫏≰11200001","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":9399,"base":3},"right_expr":{"type":"numeric_atoms","value":2333,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":1812,"base":3},"right_expr":{"type":"numeric_atoms","value":3403,"base":3}}},"used_operators":["2DQ55sFlQl","eewbuw0ToL","DyGG3AbaNP"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=9399","layer":2},{"info":"number node, value=2333","layer":2},{"info":"compute binary expreesion, left_input=9399, right_input=2333, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=7076","layer":1},{"info":"number node, value=1812","layer":2},{"info":"number node, value=3403","layer":2},{"info":"compute binary expreesion, left_input=1812, right_input=3403, 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=7076, right_input=nan, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰110220010⨰⫏≰10012102⨵⪆⫏≰2111010∼⫏≰11200001=⫏≰12221","reverse_text":"⫏≰12221=⫏≰110220010⨰⫏≰10012102⨵⪆⫏≰2111010∼⫏≰11200001","cot":[{"info":"⫏≰110220010⨰⫏≰10012102=⫏≰100201002","layer":1},{"info":"⫏≰2111010∼⫏≰11200001=NaN","layer":1},{"info":"⫏≰100201002⨵⪆NaN=⫏≰12221","layer":0}]}
{"id":387,"expression_no_base_symbol":"($1048$⊭∹↮)⨪↰⇹($1060$⇼⇔∾$3153$)","expression":"(⫏≰1102211⊭∹↮)⨪↰⇹(⫏≰1110021⇼⇔∾⫏≰11022210)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2104,"operation_count":3,"complexity_ratio":701.3333333333334,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"numeric_atoms","value":1048,"base":3}},"right_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":1060,"base":3},"right_expr":{"type":"numeric_atoms","value":3153,"base":3}}},"used_operators":["tmPS8pqC7x","xNBdhnnwKq","tifHPKVTfV"],"dependent_operators":["rJVOvQCfKK","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰2212122","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1048","layer":2},{"info":"compute unary expreesion, input=1048, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=2096","layer":1},{"info":"number node, value=1060","layer":2},{"info":"number node, value=3153","layer":2},{"info":"compute binary expreesion, left_input=1060, right_input=3153, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=2093","layer":1},{"info":"compute binary expreesion, left_input=2096, right_input=2093, 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=2096","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1102211⊭∹↮)⨪↰⇹(⫏≰1110021⇼⇔∾⫏≰11022210)=⫏≰2212122","reverse_text":"⫏≰2212122=(⫏≰1102211⊭∹↮)⨪↰⇹(⫏≰1110021⇼⇔∾⫏≰11022210)","cot":[{"info":"⫏≰1102211⊭∹↮=⫏≰2212122","layer":1},{"info":"⫏≰1110021⇼⇔∾⫏≰11022210=⫏≰2212112","layer":1},{"info":"⫏≰2212122⨪↰⇹⫏≰2212112=⫏≰2212122","layer":0}]}
{"id":388,"expression_no_base_symbol":"(⨑⩽⪐$1093$)⊘","expression":"(⨑⩽⪐⫏≰1111111)⊘","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":1093,"base":3}}},"used_operators":["gu96TGCTMs","AF7qkfDlqP"],"dependent_operators":["XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1093","layer":2},{"info":"compute unary expreesion, input=1093, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-820","layer":1},{"info":"compute unary expreesion, input=-820, op_id = gu96TGCTMs, unary_op_definition = 'a⊘ = { ((a⨰a)/(∥⊫a)) , if (⨑⩽⪐a)!=520 or (a≧⫂∧486)>62 or (⊄⩳↩a)>=602 ; ((-240)⩚⊴⇥a) , else }', output=-1","layer":0}],"base":3,"result_base":3,"text":"(⨑⩽⪐⫏≰1111111)⊘=⫏≰-1","reverse_text":"⫏≰-1=(⨑⩽⪐⫏≰1111111)⊘","cot":[{"info":"⨑⩽⪐⫏≰1111111=⫏≰-1010101","layer":1},{"info":"⫏≰-1010101⊘=⫏≰-1","layer":0}]}
{"id":389,"expression_no_base_symbol":"($1456$%$1521$)⪒(⪲⇎$1046$)","expression":"(⫏≰1222221%⫏≰2002100)⪒(⪲⇎⫏≰1102202)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"⪒","left_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":1456,"base":3},"right_expr":{"type":"numeric_atoms","value":1521,"base":3}},"right_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":1046,"base":3}}},"used_operators":["f6k1SAg4EE","k8jYdgA6NY","XPYlsWDdGa"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-11212102","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1456","layer":2},{"info":"number node, value=1521","layer":2},{"info":"compute binary expreesion, left_input=1456, right_input=1521, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1456","layer":1},{"info":"number node, value=1046","layer":2},{"info":"compute unary expreesion, input=1046, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=2092","layer":1},{"info":"compute binary expreesion, left_input=1456, right_input=2092, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-3548","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1222221%⫏≰2002100)⪒(⪲⇎⫏≰1102202)=⫏≰-11212102","reverse_text":"⫏≰-11212102=(⫏≰1222221%⫏≰2002100)⪒(⪲⇎⫏≰1102202)","cot":[{"info":"⫏≰1222221%⫏≰2002100=⫏≰1222221","layer":1},{"info":"⪲⇎⫏≰1102202=⫏≰2212111","layer":1},{"info":"⫏≰1222221⪒⫏≰2212111=⫏≰-11212102","layer":0}]}
{"id":390,"expression_no_base_symbol":"($9280$⨳⩥⨓$5755$)⨰($2113$+⇶⊼$1127$)","expression":"(⫏≰110201201⨳⩥⨓⫏≰21220011)⨰(⫏≰2220021+⇶⊼⫏≰1112202)","highest_n_order":5,"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":9280,"base":3},"right_expr":{"type":"numeric_atoms","value":5755,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":2113,"base":3},"right_expr":{"type":"numeric_atoms","value":1127,"base":3}}},"used_operators":["eewbuw0ToL","nCS4ZIUYfx","TpPTUOHfaN"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=9280","layer":2},{"info":"number node, value=5755","layer":2},{"info":"compute binary expreesion, left_input=9280, right_input=5755, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-3525","layer":1},{"info":"number node, value=2113","layer":2},{"info":"number node, value=1127","layer":2},{"info":"compute binary expreesion, left_input=2113, right_input=1127, 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":1},{"info":"compute binary expreesion, left_input=-3525, right_input=nan, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰110201201⨳⩥⨓⫏≰21220011)⨰(⫏≰2220021+⇶⊼⫏≰1112202)=NaN","reverse_text":"NaN=(⫏≰110201201⨳⩥⨓⫏≰21220011)⨰(⫏≰2220021+⇶⊼⫏≰1112202)","cot":[{"info":"⫏≰110201201⨳⩥⨓⫏≰21220011=⫏≰-11211120","layer":1},{"info":"⫏≰2220021+⇶⊼⫏≰1112202=NaN","layer":1},{"info":"⫏≰-11211120⨰NaN=NaN","layer":0}]}
{"id":391,"expression_no_base_symbol":"↽≂(⪝⪂⫅$2333$)","expression":"↽≂(⪝⪂⫅⫏≰10012102)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":153,"operation_count":2,"complexity_ratio":76.5,"tree":{"type":"unary","operator":"↽≂","unary_expr":{"type":"unary","operator":"⪝⪂⫅","unary_expr":{"type":"numeric_atoms","value":2333,"base":3}}},"used_operators":["u6S6b8DprG","XTarYq4gQB"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","9HNa5Wba9A","8w2t5hMYqp"],"result":"⫏≰1021211212210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2333","layer":2},{"info":"compute unary expreesion, input=2333, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=-342951","layer":1},{"info":"compute unary expreesion, input=-342951, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=685902","layer":0}],"base":3,"result_base":3,"text":"↽≂(⪝⪂⫅⫏≰10012102)=⫏≰1021211212210","reverse_text":"⫏≰1021211212210=↽≂(⪝⪂⫅⫏≰10012102)","cot":[{"info":"⪝⪂⫅⫏≰10012102=⫏≰-122102102220","layer":1},{"info":"↽≂⫏≰-122102102220=⫏≰1021211212210","layer":0}]}
{"id":392,"expression_no_base_symbol":"$3607$∲⫓$7258$↪⪝","expression":"⫏≰11221121∲⫓⫏≰100221211↪⪝","highest_n_order":2,"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":3607,"base":3},"right_expr":{"type":"numeric_atoms","value":7258,"base":3}}},"used_operators":["l07mrZUIn9","i8ToyICDmI"],"dependent_operators":["9HNa5Wba9A","2DDjHMKMc0","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3607","layer":2},{"info":"number node, value=7258","layer":2},{"info":"compute binary expreesion, left_input=3607, right_input=7258, 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 = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫏≰11221121∲⫓⫏≰100221211↪⪝=⫏≰0","reverse_text":"⫏≰0=⫏≰11221121∲⫓⫏≰100221211↪⪝","cot":[{"info":"⫏≰11221121∲⫓⫏≰100221211=⫏≰0","layer":1},{"info":"⫏≰0↪⪝=⫏≰0","layer":0}]}
{"id":393,"expression_no_base_symbol":"($2193$⇷$3551$)⨟⋌⩍($9232$%$2045$)","expression":"(⫏≰10000020⇷⫏≰11212112)⨟⋌⩍(⫏≰110122221%⫏≰2210202)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":30713,"operation_count":3,"complexity_ratio":10237.666666666666,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":2193,"base":3},"right_expr":{"type":"numeric_atoms","value":3551,"base":3}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":9232,"base":3},"right_expr":{"type":"numeric_atoms","value":2045,"base":3}}},"used_operators":["rGHVDoGpnC","mp7IySMOzn","k8jYdgA6NY"],"dependent_operators":["Tcnh7f0tEr","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2193","layer":2},{"info":"number node, value=3551","layer":2},{"info":"compute binary expreesion, left_input=2193, right_input=3551, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=7102","layer":1},{"info":"number node, value=9232","layer":2},{"info":"number node, value=2045","layer":2},{"info":"compute binary expreesion, left_input=9232, right_input=2045, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1052","layer":1},{"info":"compute binary expreesion, left_input=7102, right_input=1052, 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":0}],"base":3,"result_base":3,"text":"(⫏≰10000020⇷⫏≰11212112)⨟⋌⩍(⫏≰110122221%⫏≰2210202)=NaN","reverse_text":"NaN=(⫏≰10000020⇷⫏≰11212112)⨟⋌⩍(⫏≰110122221%⫏≰2210202)","cot":[{"info":"⫏≰10000020⇷⫏≰11212112=⫏≰100202001","layer":1},{"info":"⫏≰110122221%⫏≰2210202=⫏≰1102222","layer":1},{"info":"⫏≰100202001⨟⋌⩍⫏≰1102222=NaN","layer":0}]}
{"id":394,"expression_no_base_symbol":"($2662$⊉≛↸$5493$)∼($3019$⋓$1876$)","expression":"(⫏≰10122121⊉≛↸⫏≰21112110)∼(⫏≰11010211⋓⫏≰2120111)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":140,"operation_count":3,"complexity_ratio":46.666666666666664,"tree":{"type":"binary","operator":"∼","left_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":2662,"base":3},"right_expr":{"type":"numeric_atoms","value":5493,"base":3}},"right_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":3019,"base":3},"right_expr":{"type":"numeric_atoms","value":1876,"base":3}}},"used_operators":["DyGG3AbaNP","DZ8iAZOCBD","T2fj7uvVaJ"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⫏≰202","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2662","layer":2},{"info":"number node, value=5493","layer":2},{"info":"compute binary expreesion, left_input=2662, right_input=5493, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=5324","layer":1},{"info":"number node, value=3019","layer":2},{"info":"number node, value=1876","layer":2},{"info":"compute binary expreesion, left_input=3019, right_input=1876, 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=5324, right_input=0, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=20","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10122121⊉≛↸⫏≰21112110)∼(⫏≰11010211⋓⫏≰2120111)=⫏≰202","reverse_text":"⫏≰202=(⫏≰10122121⊉≛↸⫏≰21112110)∼(⫏≰11010211⋓⫏≰2120111)","cot":[{"info":"⫏≰10122121⊉≛↸⫏≰21112110=⫏≰21022012","layer":1},{"info":"⫏≰11010211⋓⫏≰2120111=⫏≰0","layer":1},{"info":"⫏≰21022012∼⫏≰0=⫏≰202","layer":0}]}
{"id":395,"expression_no_base_symbol":"($2143$⫸⊐$1040$)≭($6077$⩨$2912$)","expression":"(⫏≰2221101⫸⊐⫏≰1102112)≭(⫏≰22100002⩨⫏≰10222212)","highest_n_order":5,"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":2143,"base":3},"right_expr":{"type":"numeric_atoms","value":1040,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":6077,"base":3},"right_expr":{"type":"numeric_atoms","value":2912,"base":3}}},"used_operators":["rxpJgHHUmx","mqXw5SEYmG","2DlMacCsIx"],"dependent_operators":["AHs5Up7iyr","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰-211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2143","layer":2},{"info":"number node, value=1040","layer":2},{"info":"compute binary expreesion, left_input=2143, right_input=1040, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=4035","layer":1},{"info":"number node, value=6077","layer":2},{"info":"number node, value=2912","layer":2},{"info":"compute binary expreesion, left_input=6077, right_input=2912, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=4035, right_input=0, 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=-22","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2221101⫸⊐⫏≰1102112)≭(⫏≰22100002⩨⫏≰10222212)=⫏≰-211","reverse_text":"⫏≰-211=(⫏≰2221101⫸⊐⫏≰1102112)≭(⫏≰22100002⩨⫏≰10222212)","cot":[{"info":"⫏≰2221101⫸⊐⫏≰1102112=⫏≰12112110","layer":1},{"info":"⫏≰22100002⩨⫏≰10222212=⫏≰0","layer":1},{"info":"⫏≰12112110≭⫏≰0=⫏≰-211","layer":0}]}
{"id":396,"expression_no_base_symbol":"($2261$∀⇚≩$1582$)∼($3084$⋥≓≎$2686$)","expression":"(⫏≰10002202∀⇚≩⫏≰2011121)∼(⫏≰11020020⋥≓≎⫏≰10200111)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15834,"operation_count":3,"complexity_ratio":5278.0,"tree":{"type":"binary","operator":"∼","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":2261,"base":3},"right_expr":{"type":"numeric_atoms","value":1582,"base":3}},"right_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":3084,"base":3},"right_expr":{"type":"numeric_atoms","value":2686,"base":3}}},"used_operators":["DyGG3AbaNP","LRNGc0VcxI","Qy55tPpLXF"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","X99M06cbEe","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2261","layer":2},{"info":"number node, value=1582","layer":2},{"info":"compute binary expreesion, left_input=2261, right_input=1582, 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=3084","layer":2},{"info":"number node, value=2686","layer":2},{"info":"compute binary expreesion, left_input=3084, right_input=2686, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=2321","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2321, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10002202∀⇚≩⫏≰2011121)∼(⫏≰11020020⋥≓≎⫏≰10200111)=NaN","reverse_text":"NaN=(⫏≰10002202∀⇚≩⫏≰2011121)∼(⫏≰11020020⋥≓≎⫏≰10200111)","cot":[{"info":"⫏≰10002202∀⇚≩⫏≰2011121=NaN","layer":1},{"info":"⫏≰11020020⋥≓≎⫏≰10200111=⫏≰10011222","layer":1},{"info":"NaN∼⫏≰10011222=NaN","layer":0}]}
{"id":397,"expression_no_base_symbol":"⫓⪴($3034$⩨$4142$)","expression":"⫓⪴(⫏≰11011101⩨⫏≰12200102)","highest_n_order":2,"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":3034,"base":3},"right_expr":{"type":"numeric_atoms","value":4142,"base":3}}},"used_operators":["eLxqMNBOBk","2DlMacCsIx"],"dependent_operators":["9HNa5Wba9A","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰100","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3034","layer":2},{"info":"number node, value=4142","layer":2},{"info":"compute binary expreesion, left_input=3034, right_input=4142, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-3","layer":1},{"info":"compute unary expreesion, input=-3, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=9","layer":0}],"base":3,"result_base":3,"text":"⫓⪴(⫏≰11011101⩨⫏≰12200102)=⫏≰100","reverse_text":"⫏≰100=⫓⪴(⫏≰11011101⩨⫏≰12200102)","cot":[{"info":"⫏≰11011101⩨⫏≰12200102=⫏≰-10","layer":1},{"info":"⫓⪴⫏≰-10=⫏≰100","layer":0}]}
{"id":398,"expression_no_base_symbol":"$4398$⋝⋈⪟$1483$⨳⩥⨓($2358$⊪)","expression":"⫏≰20000220⋝⋈⪟⫏≰2000221⨳⩥⨓(⫏≰10020100⊪)","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":4398,"base":3},"right_expr":{"type":"numeric_atoms","value":1483,"base":3}},"right_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":2358,"base":3}}},"used_operators":["nCS4ZIUYfx","2DDjHMKMc0","zVYPLywUTj"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL"],"result":"⫏≰-20000220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4398","layer":2},{"info":"number node, value=1483","layer":2},{"info":"compute binary expreesion, left_input=4398, right_input=1483, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=4398","layer":1},{"info":"number node, value=2358","layer":2},{"info":"compute unary expreesion, input=2358, 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=4398, right_input=0, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-4398","layer":0}],"base":3,"result_base":3,"text":"⫏≰20000220⋝⋈⪟⫏≰2000221⨳⩥⨓(⫏≰10020100⊪)=⫏≰-20000220","reverse_text":"⫏≰-20000220=⫏≰20000220⋝⋈⪟⫏≰2000221⨳⩥⨓(⫏≰10020100⊪)","cot":[{"info":"⫏≰20000220⋝⋈⪟⫏≰2000221=⫏≰20000220","layer":1},{"info":"⫏≰10020100⊪=⫏≰0","layer":1},{"info":"⫏≰20000220⨳⩥⨓⫏≰0=⫏≰-20000220","layer":0}]}
{"id":399,"expression_no_base_symbol":"($1212$⪨≂$5464$)⪒(⪲⇎$1754$)","expression":"(⫏≰1122220⪨≂⫏≰21111101)⪒(⪲⇎⫏≰2101222)","highest_n_order":1,"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":1212,"base":3},"right_expr":{"type":"numeric_atoms","value":5464,"base":3}},"right_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":1754,"base":3}}},"used_operators":["f6k1SAg4EE","sdazOOVcIp","XPYlsWDdGa"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰20201021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1212","layer":2},{"info":"number node, value=5464","layer":2},{"info":"compute binary expreesion, left_input=1212, right_input=5464, 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=-8402","layer":1},{"info":"number node, value=1754","layer":2},{"info":"compute unary expreesion, input=1754, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=3508","layer":1},{"info":"compute binary expreesion, left_input=-8402, right_input=3508, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=4894","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1122220⪨≂⫏≰21111101)⪒(⪲⇎⫏≰2101222)=⫏≰20201021","reverse_text":"⫏≰20201021=(⫏≰1122220⪨≂⫏≰21111101)⪒(⪲⇎⫏≰2101222)","cot":[{"info":"⫏≰1122220⪨≂⫏≰21111101=⫏≰-102112012","layer":1},{"info":"⪲⇎⫏≰2101222=⫏≰11210221","layer":1},{"info":"⫏≰-102112012⪒⫏≰11210221=⫏≰20201021","layer":0}]}
{"id":400,"expression_no_base_symbol":"($1185$⨽$4309$)⨟⋌⩍($4481$-$1112$)","expression":"(⫏≰1121220⨽⫏≰12220121)⨟⋌⩍(⫏≰20010222-⫏≰1112012)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1196,"operation_count":3,"complexity_ratio":398.6666666666667,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1185,"base":3},"right_expr":{"type":"numeric_atoms","value":4309,"base":3}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":4481,"base":3},"right_expr":{"type":"numeric_atoms","value":1112,"base":3}}},"used_operators":["rGHVDoGpnC","8HhzD0ZcuI","rysDP5nf3Z"],"dependent_operators":["Tcnh7f0tEr","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1185","layer":2},{"info":"number node, value=4309","layer":2},{"info":"compute binary expreesion, left_input=1185, right_input=4309, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-4224288","layer":1},{"info":"number node, value=4481","layer":2},{"info":"number node, value=1112","layer":2},{"info":"compute binary expreesion, left_input=4481, right_input=1112, op_id = rysDP5nf3Z binary_op_definition= 'None', output=3369","layer":1},{"info":"compute binary expreesion, left_input=-4224288, right_input=3369, 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":0}],"base":3,"result_base":3,"text":"(⫏≰1121220⨽⫏≰12220121)⨟⋌⩍(⫏≰20010222-⫏≰1112012)=NaN","reverse_text":"NaN=(⫏≰1121220⨽⫏≰12220121)⨟⋌⩍(⫏≰20010222-⫏≰1112012)","cot":[{"info":"⫏≰1121220⨽⫏≰12220121=⫏≰-21221121122010","layer":1},{"info":"⫏≰20010222-⫏≰1112012=⫏≰11121210","layer":1},{"info":"⫏≰-21221121122010⨟⋌⩍⫏≰11121210=NaN","layer":0}]}
{"id":401,"expression_no_base_symbol":"↯⪼($3796$⩷∴$4924$)","expression":"↯⪼(⫏≰12012121⩷∴⫏≰20202101)","highest_n_order":2,"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":3796,"base":3},"right_expr":{"type":"numeric_atoms","value":4924,"base":3}}},"used_operators":["8jW3W4yZS5","9FxExcQeMw"],"dependent_operators":["eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","rysDP5nf3Z"],"result":"⫏≰12000112","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3796","layer":2},{"info":"number node, value=4924","layer":2},{"info":"compute binary expreesion, left_input=3796, right_input=4924, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-2288","layer":1},{"info":"compute unary expreesion, input=-2288, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=3659","layer":0}],"base":3,"result_base":3,"text":"↯⪼(⫏≰12012121⩷∴⫏≰20202101)=⫏≰12000112","reverse_text":"⫏≰12000112=↯⪼(⫏≰12012121⩷∴⫏≰20202101)","cot":[{"info":"⫏≰12012121⩷∴⫏≰20202101=⫏≰-10010202","layer":1},{"info":"↯⪼⫏≰-10010202=⫏≰12000112","layer":0}]}
{"id":402,"expression_no_base_symbol":"$7180$≎⊠⪸$1802$⋷(⨞⊢$1333$)","expression":"⫏≰100211221≎⊠⪸⫏≰2110202⋷(⨞⊢⫏≰1211101)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":275,"operation_count":3,"complexity_ratio":91.66666666666667,"tree":{"type":"binary","operator":"⋷","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":7180,"base":3},"right_expr":{"type":"numeric_atoms","value":1802,"base":3}},"right_expr":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":1333,"base":3}}},"used_operators":["23Mk6UjR3U","bJkvcejdHO","xUOZtlo3hN"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-10111121101221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7180","layer":2},{"info":"number node, value=1802","layer":2},{"info":"compute binary expreesion, left_input=7180, right_input=1802, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=1859147","layer":1},{"info":"number node, value=1333","layer":2},{"info":"compute unary expreesion, input=1333, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-1507","layer":1},{"info":"compute binary expreesion, left_input=1859147, right_input=-1507, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-1862161","layer":0}],"base":3,"result_base":3,"text":"⫏≰100211221≎⊠⪸⫏≰2110202⋷(⨞⊢⫏≰1211101)=⫏≰-10111121101221","reverse_text":"⫏≰-10111121101221=⫏≰100211221≎⊠⪸⫏≰2110202⋷(⨞⊢⫏≰1211101)","cot":[{"info":"⫏≰100211221≎⊠⪸⫏≰2110202=⫏≰10111110021022","layer":1},{"info":"⨞⊢⫏≰1211101=⫏≰-2001211","layer":1},{"info":"⫏≰10111110021022⋷⫏≰-2001211=⫏≰-10111121101221","layer":0}]}
{"id":403,"expression_no_base_symbol":"$1941$⨰$3760$⋝⋈⪟($3048$⫌⩹⨱)","expression":"⫏≰2122220⨰⫏≰12011021⋝⋈⪟(⫏≰11011220⫌⩹⨱)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16,"operation_count":3,"complexity_ratio":5.333333333333333,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":1941,"base":3},"right_expr":{"type":"numeric_atoms","value":3760,"base":3}},"right_expr":{"type":"unary","operator":"⫌⩹⨱","unary_expr":{"type":"numeric_atoms","value":3048,"base":3}}},"used_operators":["2DDjHMKMc0","eewbuw0ToL","EBcxylXtPf"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰-2111000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1941","layer":2},{"info":"number node, value=3760","layer":2},{"info":"compute binary expreesion, left_input=1941, right_input=3760, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-1809","layer":1},{"info":"number node, value=3048","layer":2},{"info":"compute unary expreesion, input=3048, op_id = EBcxylXtPf, unary_op_definition = 'a⫌⩹⨱ = { (((80+a)+(750-a))+((149+422)+(a+a))) }', output=7497","layer":1},{"info":"compute binary expreesion, left_input=-1809, right_input=7497, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=-1809","layer":0}],"base":3,"result_base":3,"text":"⫏≰2122220⨰⫏≰12011021⋝⋈⪟(⫏≰11011220⫌⩹⨱)=⫏≰-2111000","reverse_text":"⫏≰-2111000=⫏≰2122220⨰⫏≰12011021⋝⋈⪟(⫏≰11011220⫌⩹⨱)","cot":[{"info":"⫏≰2122220⨰⫏≰12011021=⫏≰-2111000","layer":1},{"info":"⫏≰11011220⫌⩹⨱=⫏≰101021200","layer":1},{"info":"⫏≰-2111000⋝⋈⪟⫏≰101021200=⫏≰-2111000","layer":0}]}
{"id":404,"expression_no_base_symbol":"⇁⨣⪵($1240$⊉≛↸$1115$)","expression":"⇁⨣⪵(⫏≰1200221⊉≛↸⫏≰1112022)","highest_n_order":5,"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":1240,"base":3},"right_expr":{"type":"numeric_atoms","value":1115,"base":3}}},"used_operators":["inkyxCbjAn","DZ8iAZOCBD"],"dependent_operators":["B5M0gjZbta","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1240","layer":2},{"info":"number node, value=1115","layer":2},{"info":"compute binary expreesion, left_input=1240, right_input=1115, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=2480","layer":1},{"info":"compute unary expreesion, input=2480, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵(⫏≰1200221⊉≛↸⫏≰1112022)=NaN","reverse_text":"NaN=⇁⨣⪵(⫏≰1200221⊉≛↸⫏≰1112022)","cot":[{"info":"⫏≰1200221⊉≛↸⫏≰1112022=⫏≰10101212","layer":1},{"info":"⇁⨣⪵⫏≰10101212=NaN","layer":0}]}
{"id":405,"expression_no_base_symbol":"⩦⩻⨪$1652$⨰$2294$","expression":"⩦⩻⨪⫏≰2021012⨰⫏≰10010222","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":1652,"base":3},"right_expr":{"type":"numeric_atoms","value":2294,"base":3}}},"used_operators":["2td37pGCOC","eewbuw0ToL"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-212102","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1652","layer":2},{"info":"number node, value=2294","layer":2},{"info":"compute binary expreesion, left_input=1652, right_input=2294, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-632","layer":1},{"info":"compute unary expreesion, input=-632, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=-632","layer":0}],"base":3,"result_base":3,"text":"⩦⩻⨪⫏≰2021012⨰⫏≰10010222=⫏≰-212102","reverse_text":"⫏≰-212102=⩦⩻⨪⫏≰2021012⨰⫏≰10010222","cot":[{"info":"⫏≰2021012⨰⫏≰10010222=⫏≰-212102","layer":1},{"info":"⩦⩻⨪⫏≰-212102=⫏≰-212102","layer":0}]}
{"id":406,"expression_no_base_symbol":"⨑⩽⪐($1274$⩨$1470$)","expression":"⨑⩽⪐(⫏≰1202012⩨⫏≰2000110)","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":1274,"base":3},"right_expr":{"type":"numeric_atoms","value":1470,"base":3}}},"used_operators":["AF7qkfDlqP","2DlMacCsIx"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰1002110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1274","layer":2},{"info":"number node, value=1470","layer":2},{"info":"compute binary expreesion, left_input=1274, right_input=1470, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-3","layer":1},{"info":"compute unary expreesion, input=-3, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=795","layer":0}],"base":3,"result_base":3,"text":"⨑⩽⪐(⫏≰1202012⩨⫏≰2000110)=⫏≰1002110","reverse_text":"⫏≰1002110=⨑⩽⪐(⫏≰1202012⩨⫏≰2000110)","cot":[{"info":"⫏≰1202012⩨⫏≰2000110=⫏≰-10","layer":1},{"info":"⨑⩽⪐⫏≰-10=⫏≰1002110","layer":0}]}
{"id":407,"expression_no_base_symbol":"⊙↵-(⨞⊢$6453$)","expression":"⊙↵-(⨞⊢⫏≰22212000)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6661,"operation_count":2,"complexity_ratio":3330.5,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":6453,"base":3}}},"used_operators":["oWn0xqSxBt","xUOZtlo3hN"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6453","layer":2},{"info":"compute unary expreesion, input=6453, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-6627","layer":1},{"info":"compute unary expreesion, input=-6627, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=196","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⨞⊢⫏≰22212000)=⫏≰21021","reverse_text":"⫏≰21021=⊙↵-(⨞⊢⫏≰22212000)","cot":[{"info":"⨞⊢⫏≰22212000=⫏≰-100002110","layer":1},{"info":"⊙↵-⫏≰-100002110=⫏≰21021","layer":0}]}
{"id":408,"expression_no_base_symbol":"($2583$⫡⨏$1758$)*($1515$⫩⊇)","expression":"(⫏≰10112200⫡⨏⫏≰2102010)*(⫏≰2002010⫩⊇)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1482,"operation_count":3,"complexity_ratio":494.0,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":2583,"base":3},"right_expr":{"type":"numeric_atoms","value":1758,"base":3}},"right_expr":{"type":"unary","operator":"⫩⊇","unary_expr":{"type":"numeric_atoms","value":1515,"base":3}}},"used_operators":["9HNa5Wba9A","QMFrweE19q","BjRHVeLaeN"],"dependent_operators":["W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-1202201020012100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2583","layer":2},{"info":"number node, value=1758","layer":2},{"info":"compute binary expreesion, left_input=2583, right_input=1758, 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=17214","layer":1},{"info":"number node, value=1515","layer":2},{"info":"compute unary expreesion, input=1515, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=-1473","layer":1},{"info":"compute binary expreesion, left_input=17214, right_input=-1473, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=-25356222","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10112200⫡⨏⫏≰2102010)*(⫏≰2002010⫩⊇)=⫏≰-1202201020012100","reverse_text":"⫏≰-1202201020012100=(⫏≰10112200⫡⨏⫏≰2102010)*(⫏≰2002010⫩⊇)","cot":[{"info":"⫏≰10112200⫡⨏⫏≰2102010=⫏≰212121120","layer":1},{"info":"⫏≰2002010⫩⊇=⫏≰-2000120","layer":1},{"info":"⫏≰212121120*⫏≰-2000120=⫏≰-1202201020012100","layer":0}]}
{"id":409,"expression_no_base_symbol":"⨵≀≌$2525$≎⊠⪸$2284$","expression":"⨵≀≌⫏≰10110112≎⊠⪸⫏≰10010121","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":273,"operation_count":2,"complexity_ratio":136.5,"tree":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":2525,"base":3},"right_expr":{"type":"numeric_atoms","value":2284,"base":3}}},"used_operators":["srAu1WTS94","bJkvcejdHO"],"dependent_operators":["glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"⫏≰-10200121022100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2525","layer":2},{"info":"number node, value=2284","layer":2},{"info":"compute binary expreesion, left_input=2525, right_input=2284, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=653502","layer":1},{"info":"compute unary expreesion, input=653502, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-1960506","layer":0}],"base":3,"result_base":3,"text":"⨵≀≌⫏≰10110112≎⊠⪸⫏≰10010121=⫏≰-10200121022100","reverse_text":"⫏≰-10200121022100=⨵≀≌⫏≰10110112≎⊠⪸⫏≰10010121","cot":[{"info":"⫏≰10110112≎⊠⪸⫏≰10010121=⫏≰1020012102210","layer":1},{"info":"⨵≀≌⫏≰1020012102210=⫏≰-10200121022100","layer":0}]}
{"id":410,"expression_no_base_symbol":"($8658$⨐⩸⫘$3506$)⪢($4161$⋳⪒$1101$)","expression":"(⫏≰102212200⨐⩸⫘⫏≰11210212)⪢(⫏≰12201010⋳⪒⫏≰1111210)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6942,"operation_count":3,"complexity_ratio":2314.0,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":8658,"base":3},"right_expr":{"type":"numeric_atoms","value":3506,"base":3}},"right_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":4161,"base":3},"right_expr":{"type":"numeric_atoms","value":1101,"base":3}}},"used_operators":["dWAJyo7jo9","fu6greOZ01","12rbrZMWeM"],"dependent_operators":["k8jYdgA6NY","3ViojmjbAp","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=8658","layer":2},{"info":"number node, value=3506","layer":2},{"info":"compute binary expreesion, left_input=8658, right_input=3506, 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=4161","layer":2},{"info":"number node, value=1101","layer":2},{"info":"compute binary expreesion, left_input=4161, right_input=1101, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=6934","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=6934, 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":3,"result_base":3,"text":"(⫏≰102212200⨐⩸⫘⫏≰11210212)⪢(⫏≰12201010⋳⪒⫏≰1111210)=NaN","reverse_text":"NaN=(⫏≰102212200⨐⩸⫘⫏≰11210212)⪢(⫏≰12201010⋳⪒⫏≰1111210)","cot":[{"info":"⫏≰102212200⨐⩸⫘⫏≰11210212=NaN","layer":1},{"info":"⫏≰12201010⋳⪒⫏≰1111210=⫏≰100111211","layer":1},{"info":"NaN⪢⫏≰100111211=NaN","layer":0}]}
{"id":411,"expression_no_base_symbol":"$6663$⨵⪆$1578$⋷$3631$⨐⩸⫘$6221$","expression":"⫏≰100010210⨵⪆⫏≰2011110⋷⫏≰11222111⨐⩸⫘⫏≰22112102","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4,"operation_count":3,"complexity_ratio":1.3333333333333333,"tree":{"type":"binary","operator":"⋷","left_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":6663,"base":3},"right_expr":{"type":"numeric_atoms","value":1578,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":3631,"base":3},"right_expr":{"type":"numeric_atoms","value":6221,"base":3}}},"used_operators":["23Mk6UjR3U","2DQ55sFlQl","fu6greOZ01"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","3ViojmjbAp"],"result":"⫏≰-102212","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6663","layer":2},{"info":"number node, value=1578","layer":2},{"info":"compute binary expreesion, left_input=6663, right_input=1578, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=3631","layer":2},{"info":"number node, value=6221","layer":2},{"info":"compute binary expreesion, left_input=3631, right_input=6221, 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=160, right_input=nan, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-320","layer":0}],"base":3,"result_base":3,"text":"⫏≰100010210⨵⪆⫏≰2011110⋷⫏≰11222111⨐⩸⫘⫏≰22112102=⫏≰-102212","reverse_text":"⫏≰-102212=⫏≰100010210⨵⪆⫏≰2011110⋷⫏≰11222111⨐⩸⫘⫏≰22112102","cot":[{"info":"⫏≰100010210⨵⪆⫏≰2011110=⫏≰12221","layer":1},{"info":"⫏≰11222111⨐⩸⫘⫏≰22112102=NaN","layer":1},{"info":"⫏≰12221⋷NaN=⫏≰-102212","layer":0}]}
{"id":412,"expression_no_base_symbol":"-($1271$⋷$2960$)","expression":"-(⫏≰1202002⋷⫏≰11001122)","highest_n_order":1,"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":1271,"base":3},"right_expr":{"type":"numeric_atoms","value":2960,"base":3}}},"used_operators":["t8gj7n24qd","23Mk6UjR3U"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-20101012","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1271","layer":2},{"info":"number node, value=2960","layer":2},{"info":"compute binary expreesion, left_input=1271, right_input=2960, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=4649","layer":1},{"info":"compute unary expreesion, input=4649, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-4649","layer":0}],"base":3,"result_base":3,"text":"-(⫏≰1202002⋷⫏≰11001122)=⫏≰-20101012","reverse_text":"⫏≰-20101012=-(⫏≰1202002⋷⫏≰11001122)","cot":[{"info":"⫏≰1202002⋷⫏≰11001122=⫏≰20101012","layer":1},{"info":"-⫏≰20101012=⫏≰-20101012","layer":0}]}
{"id":413,"expression_no_base_symbol":"($1167$⨎$7005$)⋓(⪝⪂⫅$2573$)","expression":"(⫏≰1121020⨎⫏≰100121110)⋓(⪝⪂⫅⫏≰10112022)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":164,"operation_count":3,"complexity_ratio":54.666666666666664,"tree":{"type":"binary","operator":"⋓","left_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":1167,"base":3},"right_expr":{"type":"numeric_atoms","value":7005,"base":3}},"right_expr":{"type":"unary","operator":"⪝⪂⫅","unary_expr":{"type":"numeric_atoms","value":2573,"base":3}}},"used_operators":["T2fj7uvVaJ","rJVOvQCfKK","XTarYq4gQB"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","9HNa5Wba9A","8w2t5hMYqp"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1167","layer":2},{"info":"number node, value=7005","layer":2},{"info":"compute binary expreesion, left_input=1167, right_input=7005, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=7005","layer":1},{"info":"number node, value=2573","layer":2},{"info":"compute unary expreesion, input=2573, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=-378231","layer":1},{"info":"compute binary expreesion, left_input=7005, right_input=-378231, 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":3,"result_base":3,"text":"(⫏≰1121020⨎⫏≰100121110)⋓(⪝⪂⫅⫏≰10112022)=⫏≰0","reverse_text":"⫏≰0=(⫏≰1121020⨎⫏≰100121110)⋓(⪝⪂⫅⫏≰10112022)","cot":[{"info":"⫏≰1121020⨎⫏≰100121110=⫏≰100121110","layer":1},{"info":"⪝⪂⫅⫏≰10112022=⫏≰-201012211120","layer":1},{"info":"⫏≰100121110⋓⫏≰-201012211120=⫏≰0","layer":0}]}
{"id":414,"expression_no_base_symbol":"$5203$⪘⫢$2504$⨰($1032$⨽$1345$)","expression":"⫏≰21010201⪘⫢⫏≰10102202⨰(⫏≰1102020⨽⫏≰1211211)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1062,"operation_count":3,"complexity_ratio":354.0,"tree":{"type":"binary","operator":"⨰","left_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":5203,"base":3},"right_expr":{"type":"numeric_atoms","value":2504,"base":3}},"right_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1032,"base":3},"right_expr":{"type":"numeric_atoms","value":1345,"base":3}}},"used_operators":["eewbuw0ToL","oacrs7FA3X","8HhzD0ZcuI"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"⫏≰20000222122222","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5203","layer":2},{"info":"number node, value=2504","layer":2},{"info":"compute binary expreesion, left_input=5203, right_input=2504, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=10282","layer":1},{"info":"number node, value=1032","layer":2},{"info":"number node, value=1345","layer":2},{"info":"compute binary expreesion, left_input=1032, right_input=1345, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-3197793","layer":1},{"info":"compute binary expreesion, left_input=10282, right_input=-3197793, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=3208085","layer":0}],"base":3,"result_base":3,"text":"⫏≰21010201⪘⫢⫏≰10102202⨰(⫏≰1102020⨽⫏≰1211211)=⫏≰20000222122222","reverse_text":"⫏≰20000222122222=⫏≰21010201⪘⫢⫏≰10102202⨰(⫏≰1102020⨽⫏≰1211211)","cot":[{"info":"⫏≰21010201⪘⫢⫏≰10102202=⫏≰112002211","layer":1},{"info":"⫏≰1102020⨽⫏≰1211211=⫏≰-20000110112210","layer":1},{"info":"⫏≰112002211⨰⫏≰-20000110112210=⫏≰20000222122222","layer":0}]}
{"id":415,"expression_no_base_symbol":"$7653$≎⊠⪸$5739$⨵⪆$2944$⇷$4712$","expression":"⫏≰101111110≎⊠⪸⫏≰21212120⨵⪆⫏≰11001001⇷⫏≰20110112","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":41493,"operation_count":3,"complexity_ratio":13831.0,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":7653,"base":3},"right_expr":{"type":"numeric_atoms","value":5739,"base":3}},"right_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":2944,"base":3},"right_expr":{"type":"numeric_atoms","value":4712,"base":3}}},"used_operators":["2DQ55sFlQl","bJkvcejdHO","mp7IySMOzn"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7653","layer":2},{"info":"number node, value=5739","layer":2},{"info":"compute binary expreesion, left_input=7653, right_input=5739, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=1981654","layer":1},{"info":"number node, value=2944","layer":2},{"info":"number node, value=4712","layer":2},{"info":"compute binary expreesion, left_input=2944, right_input=4712, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=9424","layer":1},{"info":"compute binary expreesion, left_input=1981654, right_input=9424, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰101111110≎⊠⪸⫏≰21212120⨵⪆⫏≰11001001⇷⫏≰20110112=⫏≰12221","reverse_text":"⫏≰12221=⫏≰101111110≎⊠⪸⫏≰21212120⨵⪆⫏≰11001001⇷⫏≰20110112","cot":[{"info":"⫏≰101111110≎⊠⪸⫏≰21212120=⫏≰10201200022121","layer":1},{"info":"⫏≰11001001⇷⫏≰20110112=⫏≰110221001","layer":1},{"info":"⫏≰10201200022121⨵⪆⫏≰110221001=⫏≰12221","layer":0}]}
{"id":416,"expression_no_base_symbol":"$3655$⪮%⊝$3033$⇼⇔∾$4003$⨟⋌⩍$3635$","expression":"⫏≰12000101⪮%⊝⫏≰11011100⇼⇔∾⫏≰12111021⨟⋌⩍⫏≰11222122","highest_n_order":4,"priority_hierarchical_complexity":2,"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":3655,"base":3},"right_expr":{"type":"numeric_atoms","value":3033,"base":3}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":4003,"base":3},"right_expr":{"type":"numeric_atoms","value":3635,"base":3}}},"used_operators":["tifHPKVTfV","IWmyXbctLI","rGHVDoGpnC"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3655","layer":2},{"info":"number node, value=3033","layer":2},{"info":"compute binary expreesion, left_input=3655, right_input=3033, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=7626","layer":1},{"info":"number node, value=4003","layer":2},{"info":"number node, value=3635","layer":2},{"info":"compute binary expreesion, left_input=4003, right_input=3635, 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=7626, right_input=nan, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰12000101⪮%⊝⫏≰11011100⇼⇔∾⫏≰12111021⨟⋌⩍⫏≰11222122=NaN","reverse_text":"NaN=⫏≰12000101⪮%⊝⫏≰11011100⇼⇔∾⫏≰12111021⨟⋌⩍⫏≰11222122","cot":[{"info":"⫏≰12000101⪮%⊝⫏≰11011100=⫏≰101110110","layer":1},{"info":"⫏≰12111021⨟⋌⩍⫏≰11222122=NaN","layer":1},{"info":"⫏≰101110110⇼⇔∾NaN=NaN","layer":0}]}
{"id":417,"expression_no_base_symbol":"-$1416$⋳⪒$7023$","expression":"-⫏≰1221110⋳⪒⫏≰100122010","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":1416,"base":3},"right_expr":{"type":"numeric_atoms","value":7023,"base":3}}},"used_operators":["t8gj7n24qd","12rbrZMWeM"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰20010212","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1416","layer":2},{"info":"number node, value=7023","layer":2},{"info":"compute binary expreesion, left_input=1416, right_input=7023, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=-4478","layer":1},{"info":"compute unary expreesion, input=-4478, op_id = t8gj7n24qd, unary_op_definition = 'None', output=4478","layer":0}],"base":3,"result_base":3,"text":"-⫏≰1221110⋳⪒⫏≰100122010=⫏≰20010212","reverse_text":"⫏≰20010212=-⫏≰1221110⋳⪒⫏≰100122010","cot":[{"info":"⫏≰1221110⋳⪒⫏≰100122010=⫏≰-20010212","layer":1},{"info":"-⫏≰-20010212=⫏≰20010212","layer":0}]}
{"id":418,"expression_no_base_symbol":"$3452$↙$1101$↛⩡⫤","expression":"⫏≰11201212↙⫏≰1111210↛⩡⫤","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":11128,"operation_count":2,"complexity_ratio":5564.0,"tree":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":3452,"base":3},"right_expr":{"type":"numeric_atoms","value":1101,"base":3}}},"used_operators":["FU0Cs4j7VP","yyfyN0ffXY"],"dependent_operators":["8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰-212210112211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3452","layer":2},{"info":"number node, value=1101","layer":2},{"info":"compute binary expreesion, left_input=3452, right_input=1101, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-3303","layer":1},{"info":"compute unary expreesion, input=-3303, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-468418","layer":0}],"base":3,"result_base":3,"text":"⫏≰11201212↙⫏≰1111210↛⩡⫤=⫏≰-212210112211","reverse_text":"⫏≰-212210112211=⫏≰11201212↙⫏≰1111210↛⩡⫤","cot":[{"info":"⫏≰11201212↙⫏≰1111210=⫏≰-11112100","layer":1},{"info":"⫏≰-11112100↛⩡⫤=⫏≰-212210112211","layer":0}]}
{"id":419,"expression_no_base_symbol":"$1249$⪛$6101$+⇶⊼($8288$%$2925$)","expression":"⫏≰1201021⪛⫏≰22100222+⇶⊼(⫏≰102100222%⫏≰11000100)","highest_n_order":5,"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":1249,"base":3},"right_expr":{"type":"numeric_atoms","value":6101,"base":3}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":8288,"base":3},"right_expr":{"type":"numeric_atoms","value":2925,"base":3}}},"used_operators":["TpPTUOHfaN","uFcxV4UQCh","k8jYdgA6NY"],"dependent_operators":["AHs5Up7iyr","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1249","layer":2},{"info":"number node, value=6101","layer":2},{"info":"compute binary expreesion, left_input=1249, right_input=6101, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1249","layer":1},{"info":"number node, value=8288","layer":2},{"info":"number node, value=2925","layer":2},{"info":"compute binary expreesion, left_input=8288, right_input=2925, op_id = k8jYdgA6NY binary_op_definition= 'None', output=2438","layer":1},{"info":"compute binary expreesion, left_input=1249, right_input=2438, 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":3,"result_base":3,"text":"⫏≰1201021⪛⫏≰22100222+⇶⊼(⫏≰102100222%⫏≰11000100)=NaN","reverse_text":"NaN=⫏≰1201021⪛⫏≰22100222+⇶⊼(⫏≰102100222%⫏≰11000100)","cot":[{"info":"⫏≰1201021⪛⫏≰22100222=⫏≰1201021","layer":1},{"info":"⫏≰102100222%⫏≰11000100=⫏≰10100022","layer":1},{"info":"⫏≰1201021+⇶⊼⫏≰10100022=NaN","layer":0}]}
{"id":420,"expression_no_base_symbol":"(≉$1559$)⫥∨⫟($1345$⫡⨏$2632$)","expression":"(≉⫏≰2010202)⫥∨⫟(⫏≰1211211⫡⨏⫏≰10121111)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":163,"operation_count":3,"complexity_ratio":54.333333333333336,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"unary","operator":"≉","unary_expr":{"type":"numeric_atoms","value":1559,"base":3}},"right_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":1345,"base":3},"right_expr":{"type":"numeric_atoms","value":2632,"base":3}}},"used_operators":["KYD54nUTWz","e1ybzncUwg","QMFrweE19q"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1559","layer":2},{"info":"compute unary expreesion, input=1559, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=2090","layer":1},{"info":"number node, value=1345","layer":2},{"info":"number node, value=2632","layer":2},{"info":"compute binary expreesion, left_input=1345, right_input=2632, 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=12772","layer":1},{"info":"compute binary expreesion, left_input=2090, right_input=12772, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(≉⫏≰2010202)⫥∨⫟(⫏≰1211211⫡⨏⫏≰10121111)=NaN","reverse_text":"NaN=(≉⫏≰2010202)⫥∨⫟(⫏≰1211211⫡⨏⫏≰10121111)","cot":[{"info":"≉⫏≰2010202=⫏≰2212102","layer":1},{"info":"⫏≰1211211⫡⨏⫏≰10121111=⫏≰122112001","layer":1},{"info":"⫏≰2212102⫥∨⫟⫏≰122112001=NaN","layer":0}]}
{"id":421,"expression_no_base_symbol":"$1032$⪛$4820$+⇶⊼($5890$≭$1174$)","expression":"⫏≰1102020⪛⫏≰20121112+⇶⊼(⫏≰22002011≭⫏≰1121111)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":1032,"base":3},"right_expr":{"type":"numeric_atoms","value":4820,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":5890,"base":3},"right_expr":{"type":"numeric_atoms","value":1174,"base":3}}},"used_operators":["TpPTUOHfaN","uFcxV4UQCh","rxpJgHHUmx"],"dependent_operators":["AHs5Up7iyr","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1032","layer":2},{"info":"number node, value=4820","layer":2},{"info":"compute binary expreesion, left_input=1032, right_input=4820, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1032","layer":1},{"info":"number node, value=5890","layer":2},{"info":"number node, value=1174","layer":2},{"info":"compute binary expreesion, left_input=5890, right_input=1174, 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=1032, right_input=nan, 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":3,"result_base":3,"text":"⫏≰1102020⪛⫏≰20121112+⇶⊼(⫏≰22002011≭⫏≰1121111)=NaN","reverse_text":"NaN=⫏≰1102020⪛⫏≰20121112+⇶⊼(⫏≰22002011≭⫏≰1121111)","cot":[{"info":"⫏≰1102020⪛⫏≰20121112=⫏≰1102020","layer":1},{"info":"⫏≰22002011≭⫏≰1121111=NaN","layer":1},{"info":"⫏≰1102020+⇶⊼NaN=NaN","layer":0}]}
{"id":422,"expression_no_base_symbol":"($3915$⋫)⫥∨⫟(⨈⫕$1554$)","expression":"(⫏≰12101000⋫)⫥∨⫟(⨈⫕⫏≰2010120)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4455,"operation_count":3,"complexity_ratio":1485.0,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":3915,"base":3}},"right_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":1554,"base":3}}},"used_operators":["KYD54nUTWz","JL8yIekQnl","megm06wKyl"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","tmPS8pqC7x","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3915","layer":2},{"info":"compute unary expreesion, input=3915, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=3915","layer":1},{"info":"number node, value=1554","layer":2},{"info":"compute unary expreesion, input=1554, 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=3915, right_input=-21, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12101000⋫)⫥∨⫟(⨈⫕⫏≰2010120)=NaN","reverse_text":"NaN=(⫏≰12101000⋫)⫥∨⫟(⨈⫕⫏≰2010120)","cot":[{"info":"⫏≰12101000⋫=⫏≰12101000","layer":1},{"info":"⨈⫕⫏≰2010120=⫏≰-210","layer":1},{"info":"⫏≰12101000⫥∨⫟⫏≰-210=NaN","layer":0}]}
{"id":423,"expression_no_base_symbol":"$3979$⨸⪁$2995$/$2191$⨰$2037$","expression":"⫏≰12110101⨸⪁⫏≰11002221/⫏≰10000011⨰⫏≰2210110","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":94,"operation_count":3,"complexity_ratio":31.333333333333332,"tree":{"type":"binary","operator":"/","left_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":3979,"base":3},"right_expr":{"type":"numeric_atoms","value":2995,"base":3}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":2191,"base":3},"right_expr":{"type":"numeric_atoms","value":2037,"base":3}}},"used_operators":["XhwjNDsVaA","g55IO6H4Gj","eewbuw0ToL"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰10011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3979","layer":2},{"info":"number node, value=2995","layer":2},{"info":"compute binary expreesion, left_input=3979, right_input=2995, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=13948","layer":1},{"info":"number node, value=2191","layer":2},{"info":"number node, value=2037","layer":2},{"info":"compute binary expreesion, left_input=2191, right_input=2037, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=164","layer":1},{"info":"compute binary expreesion, left_input=13948, right_input=164, op_id = XhwjNDsVaA binary_op_definition= 'None', output=85","layer":0}],"base":3,"result_base":3,"text":"⫏≰12110101⨸⪁⫏≰11002221/⫏≰10000011⨰⫏≰2210110=⫏≰10011","reverse_text":"⫏≰10011=⫏≰12110101⨸⪁⫏≰11002221/⫏≰10000011⨰⫏≰2210110","cot":[{"info":"⫏≰12110101⨸⪁⫏≰11002221=⫏≰201010121","layer":1},{"info":"⫏≰10000011⨰⫏≰2210110=⫏≰20002","layer":1},{"info":"⫏≰201010121/⫏≰20002=⫏≰10011","layer":0}]}
{"id":424,"expression_no_base_symbol":"(⨰⫟⨤$1319$)⋝⋈⪟$5805$⊴$1840$","expression":"(⨰⫟⨤⫏≰1210212)⋝⋈⪟⫏≰21222000⊴⫏≰2112011","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6938,"operation_count":3,"complexity_ratio":2312.6666666666665,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":1319,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":5805,"base":3},"right_expr":{"type":"numeric_atoms","value":1840,"base":3}}},"used_operators":["2DDjHMKMc0","Tw270M8GLb","Nsiff2A1zJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1319","layer":2},{"info":"compute unary expreesion, input=1319, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":1},{"info":"number node, value=5805","layer":2},{"info":"number node, value=1840","layer":2},{"info":"compute binary expreesion, left_input=5805, right_input=1840, 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 = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⨰⫟⨤⫏≰1210212)⋝⋈⪟⫏≰21222000⊴⫏≰2112011=NaN","reverse_text":"NaN=(⨰⫟⨤⫏≰1210212)⋝⋈⪟⫏≰21222000⊴⫏≰2112011","cot":[{"info":"⨰⫟⨤⫏≰1210212=NaN","layer":1},{"info":"⫏≰21222000⊴⫏≰2112011=NaN","layer":1},{"info":"NaN⋝⋈⪟NaN=NaN","layer":0}]}
{"id":425,"expression_no_base_symbol":"($2188$⊦⊿)⫸⊐$8140$⫸⊐$2622$","expression":"(⫏≰10000001⊦⊿)⫸⊐⫏≰102011111⫸⊐⫏≰10121010","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34,"operation_count":3,"complexity_ratio":11.333333333333334,"tree":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":2188,"base":3}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":8140,"base":3},"right_expr":{"type":"numeric_atoms","value":2622,"base":3}}},"used_operators":["mqXw5SEYmG","14qkJME0vr"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰1022212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2188","layer":2},{"info":"compute unary expreesion, input=2188, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-6643","layer":1},{"info":"number node, value=8140","layer":2},{"info":"number node, value=2622","layer":2},{"info":"compute binary expreesion, left_input=8140, right_input=2622, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=10363","layer":1},{"info":"compute binary expreesion, left_input=-6643, right_input=10363, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=968","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10000001⊦⊿)⫸⊐⫏≰102011111⫸⊐⫏≰10121010=⫏≰1022212","reverse_text":"⫏≰1022212=(⫏≰10000001⊦⊿)⫸⊐⫏≰102011111⫸⊐⫏≰10121010","cot":[{"info":"⫏≰10000001⊦⊿=⫏≰-100010001","layer":1},{"info":"⫏≰102011111⫸⊐⫏≰10121010=⫏≰112012211","layer":1},{"info":"⫏≰-100010001⫸⊐⫏≰112012211=⫏≰1022212","layer":0}]}
{"id":426,"expression_no_base_symbol":"$7065$⨪↰⇹$1710$↺$1325$⋝⋈⪟$6984$","expression":"⫏≰100200200⨪↰⇹⫏≰2100100↺⫏≰1211002⋝⋈⪟⫏≰100120200","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7070,"operation_count":3,"complexity_ratio":2356.6666666666665,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":7065,"base":3},"right_expr":{"type":"numeric_atoms","value":1710,"base":3}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":1325,"base":3},"right_expr":{"type":"numeric_atoms","value":6984,"base":3}}},"used_operators":["7j4O788W3g","tmPS8pqC7x","2DDjHMKMc0"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rJVOvQCfKK","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1211002","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7065","layer":2},{"info":"number node, value=1710","layer":2},{"info":"compute binary expreesion, left_input=7065, right_input=1710, 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=7065","layer":1},{"info":"number node, value=1325","layer":2},{"info":"number node, value=6984","layer":2},{"info":"compute binary expreesion, left_input=1325, right_input=6984, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=1325","layer":1},{"info":"compute binary expreesion, left_input=7065, right_input=1325, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1325","layer":0}],"base":3,"result_base":3,"text":"⫏≰100200200⨪↰⇹⫏≰2100100↺⫏≰1211002⋝⋈⪟⫏≰100120200=⫏≰1211002","reverse_text":"⫏≰1211002=⫏≰100200200⨪↰⇹⫏≰2100100↺⫏≰1211002⋝⋈⪟⫏≰100120200","cot":[{"info":"⫏≰100200200⨪↰⇹⫏≰2100100=⫏≰100200200","layer":1},{"info":"⫏≰1211002⋝⋈⪟⫏≰100120200=⫏≰1211002","layer":1},{"info":"⫏≰100200200↺⫏≰1211002=⫏≰1211002","layer":0}]}
{"id":427,"expression_no_base_symbol":"∂($4011$/$1819$)","expression":"∂(⫏≰12111120/⫏≰2111101)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":419,"operation_count":2,"complexity_ratio":209.5,"tree":{"type":"unary","operator":"∂","unary_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":4011,"base":3},"right_expr":{"type":"numeric_atoms","value":1819,"base":3}}},"used_operators":["Uaa54Peajs","XhwjNDsVaA"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","rysDP5nf3Z"],"result":"⫏≰-100212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4011","layer":2},{"info":"number node, value=1819","layer":2},{"info":"compute binary expreesion, left_input=4011, right_input=1819, op_id = XhwjNDsVaA binary_op_definition= 'None', output=2","layer":1},{"info":"compute unary expreesion, input=2, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=-266","layer":0}],"base":3,"result_base":3,"text":"∂(⫏≰12111120/⫏≰2111101)=⫏≰-100212","reverse_text":"⫏≰-100212=∂(⫏≰12111120/⫏≰2111101)","cot":[{"info":"⫏≰12111120/⫏≰2111101=⫏≰2","layer":1},{"info":"∂⫏≰2=⫏≰-100212","layer":0}]}
{"id":428,"expression_no_base_symbol":"⪲⇎(↣≠⋷$1115$)","expression":"⪲⇎(↣≠⋷⫏≰1112022)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5,"operation_count":2,"complexity_ratio":2.5,"tree":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":1115,"base":3}}},"used_operators":["XPYlsWDdGa","Asc51vEJeQ"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1115","layer":2},{"info":"compute unary expreesion, input=1115, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⪲⇎(↣≠⋷⫏≰1112022)=NaN","reverse_text":"NaN=⪲⇎(↣≠⋷⫏≰1112022)","cot":[{"info":"↣≠⋷⫏≰1112022=NaN","layer":1},{"info":"⪲⇎NaN=NaN","layer":0}]}
{"id":429,"expression_no_base_symbol":"↥$4500$⪢$7621$","expression":"↥⫏≰20011200⪢⫏≰101110021","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7622,"operation_count":2,"complexity_ratio":3811.0,"tree":{"type":"unary","operator":"↥","unary_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":4500,"base":3},"right_expr":{"type":"numeric_atoms","value":7621,"base":3}}},"used_operators":["A8NUZmVepG","dWAJyo7jo9"],"dependent_operators":["k8jYdgA6NY","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4500","layer":2},{"info":"number node, value=7621","layer":2},{"info":"compute binary expreesion, left_input=4500, right_input=7621, 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 unary expreesion, input=nan, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↥⫏≰20011200⪢⫏≰101110021=NaN","reverse_text":"NaN=↥⫏≰20011200⪢⫏≰101110021","cot":[{"info":"⫏≰20011200⪢⫏≰101110021=NaN","layer":1},{"info":"↥NaN=NaN","layer":0}]}
{"id":430,"expression_no_base_symbol":"$8610$⇼⇔∾$2302$⨸⪁$9700$+⇶⊼$1085$","expression":"⫏≰102210220⇼⇔∾⫏≰10011021⨸⪁⫏≰111022021+⇶⊼⫏≰1111012","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":8610,"base":3},"right_expr":{"type":"numeric_atoms","value":2302,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":9700,"base":3},"right_expr":{"type":"numeric_atoms","value":1085,"base":3}}},"used_operators":["g55IO6H4Gj","tifHPKVTfV","TpPTUOHfaN"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=8610","layer":2},{"info":"number node, value=2302","layer":2},{"info":"compute binary expreesion, left_input=8610, right_input=2302, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-6308","layer":1},{"info":"number node, value=9700","layer":2},{"info":"number node, value=1085","layer":2},{"info":"compute binary expreesion, left_input=9700, right_input=1085, 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":1},{"info":"compute binary expreesion, left_input=-6308, right_input=nan, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰102210220⇼⇔∾⫏≰10011021⨸⪁⫏≰111022021+⇶⊼⫏≰1111012=NaN","reverse_text":"NaN=⫏≰102210220⇼⇔∾⫏≰10011021⨸⪁⫏≰111022021+⇶⊼⫏≰1111012","cot":[{"info":"⫏≰102210220⇼⇔∾⫏≰10011021=⫏≰-22122122","layer":1},{"info":"⫏≰111022021+⇶⊼⫏≰1111012=NaN","layer":1},{"info":"⫏≰-22122122⨸⪁NaN=NaN","layer":0}]}
{"id":431,"expression_no_base_symbol":"($5339$⪄$1944$)∧","expression":"(⫏≰21022202⪄⫏≰2200000)∧","highest_n_order":5,"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":5339,"base":3},"right_expr":{"type":"numeric_atoms","value":1944,"base":3}}},"used_operators":["z63VuFQld9","SUmda5xLS4"],"dependent_operators":["B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5339","layer":2},{"info":"number node, value=1944","layer":2},{"info":"compute binary expreesion, left_input=5339, right_input=1944, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-794037","layer":1},{"info":"compute unary expreesion, input=-794037, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰21022202⪄⫏≰2200000)∧=⫏≰0","reverse_text":"⫏≰0=(⫏≰21022202⪄⫏≰2200000)∧","cot":[{"info":"⫏≰21022202⪄⫏≰2200000=⫏≰-1111100012210","layer":1},{"info":"⫏≰-1111100012210∧=⫏≰0","layer":0}]}
{"id":432,"expression_no_base_symbol":"≉$7096$≧⫂∧$2012$","expression":"≉⫏≰100201211≧⫂∧⫏≰2202112","highest_n_order":1,"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":7096,"base":3},"right_expr":{"type":"numeric_atoms","value":2012,"base":3}}},"used_operators":["e1ybzncUwg","Ph9nP6C5qx"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰2211200","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7096","layer":2},{"info":"number node, value=2012","layer":2},{"info":"compute binary expreesion, left_input=7096, right_input=2012, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=1539","layer":1},{"info":"compute unary expreesion, input=1539, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=2070","layer":0}],"base":3,"result_base":3,"text":"≉⫏≰100201211≧⫂∧⫏≰2202112=⫏≰2211200","reverse_text":"⫏≰2211200=≉⫏≰100201211≧⫂∧⫏≰2202112","cot":[{"info":"⫏≰100201211≧⫂∧⫏≰2202112=⫏≰2010000","layer":1},{"info":"≉⫏≰2010000=⫏≰2211200","layer":0}]}
{"id":433,"expression_no_base_symbol":"(⊥$3428$)⋳⪒$3153$≎⊠⪸$1012$","expression":"(⊥⫏≰11200222)⋳⪒⫏≰11022210≎⊠⪸⫏≰1101111","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":278,"operation_count":3,"complexity_ratio":92.66666666666667,"tree":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":3428,"base":3}},"right_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":3153,"base":3},"right_expr":{"type":"numeric_atoms","value":1012,"base":3}}},"used_operators":["12rbrZMWeM","Q3PJZHRvZv","bJkvcejdHO"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","fu6greOZ01","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3428","layer":2},{"info":"compute unary expreesion, input=3428, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"number node, value=3153","layer":2},{"info":"number node, value=1012","layer":2},{"info":"compute binary expreesion, left_input=3153, right_input=1012, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=816154","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=816154, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⊥⫏≰11200222)⋳⪒⫏≰11022210≎⊠⪸⫏≰1101111=NaN","reverse_text":"NaN=(⊥⫏≰11200222)⋳⪒⫏≰11022210≎⊠⪸⫏≰1101111","cot":[{"info":"⊥⫏≰11200222=NaN","layer":1},{"info":"⫏≰11022210≎⊠⪸⫏≰1101111=⫏≰1112110112221","layer":1},{"info":"NaN⋳⪒⫏≰1112110112221=NaN","layer":0}]}
{"id":434,"expression_no_base_symbol":"(⫓⪴$2250$)⫸⊐$2818$⋝⋈⪟$3120$","expression":"(⫓⪴⫏≰10002100)⫸⊐⫏≰10212101⋝⋈⪟⫏≰11021120","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2277,"operation_count":3,"complexity_ratio":759.0,"tree":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":2250,"base":3}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":2818,"base":3},"right_expr":{"type":"numeric_atoms","value":3120,"base":3}}},"used_operators":["mqXw5SEYmG","eLxqMNBOBk","2DDjHMKMc0"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","9HNa5Wba9A","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰120021212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2250","layer":2},{"info":"compute unary expreesion, input=2250, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=5062500","layer":1},{"info":"number node, value=2818","layer":2},{"info":"number node, value=3120","layer":2},{"info":"compute binary expreesion, left_input=2818, right_input=3120, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=2818","layer":1},{"info":"compute binary expreesion, left_input=5062500, right_input=2818, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=11147","layer":0}],"base":3,"result_base":3,"text":"(⫓⪴⫏≰10002100)⫸⊐⫏≰10212101⋝⋈⪟⫏≰11021120=⫏≰120021212","reverse_text":"⫏≰120021212=(⫓⪴⫏≰10002100)⫸⊐⫏≰10212101⋝⋈⪟⫏≰11021120","cot":[{"info":"⫓⪴⫏≰10002100=⫏≰100112012110000","layer":1},{"info":"⫏≰10212101⋝⋈⪟⫏≰11021120=⫏≰10212101","layer":1},{"info":"⫏≰100112012110000⫸⊐⫏≰10212101=⫏≰120021212","layer":0}]}
{"id":435,"expression_no_base_symbol":"($3263$∲⫓$1015$)⪛($7063$⩚⊴⇥$5693$)","expression":"(⫏≰11110212∲⫓⫏≰1101121)⪛(⫏≰100200121⩚⊴⇥⫏≰21210212)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⪛","left_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":3263,"base":3},"right_expr":{"type":"numeric_atoms","value":1015,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":7063,"base":3},"right_expr":{"type":"numeric_atoms","value":5693,"base":3}}},"used_operators":["uFcxV4UQCh","i8ToyICDmI","NTOWxs364D"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3263","layer":2},{"info":"number node, value=1015","layer":2},{"info":"compute binary expreesion, left_input=3263, right_input=1015, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=7063","layer":2},{"info":"number node, value=5693","layer":2},{"info":"compute binary expreesion, left_input=7063, right_input=5693, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-12877","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-12877, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11110212∲⫓⫏≰1101121)⪛(⫏≰100200121⩚⊴⇥⫏≰21210212)=⫏≰0","reverse_text":"⫏≰0=(⫏≰11110212∲⫓⫏≰1101121)⪛(⫏≰100200121⩚⊴⇥⫏≰21210212)","cot":[{"info":"⫏≰11110212∲⫓⫏≰1101121=⫏≰0","layer":1},{"info":"⫏≰100200121⩚⊴⇥⫏≰21210212=⫏≰-122122221","layer":1},{"info":"⫏≰0⪛⫏≰-122122221=⫏≰0","layer":0}]}
{"id":436,"expression_no_base_symbol":"$5992$↬$8724$≧⫂∧($1960$↙$1655$)","expression":"⫏≰22012221↬⫏≰102222010≧⫂∧(⫏≰2200121↙⫏≰2021022)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1661,"operation_count":3,"complexity_ratio":553.6666666666666,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":5992,"base":3},"right_expr":{"type":"numeric_atoms","value":8724,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":1960,"base":3},"right_expr":{"type":"numeric_atoms","value":1655,"base":3}}},"used_operators":["Ph9nP6C5qx","B5M0gjZbta","yyfyN0ffXY"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rGHVDoGpnC","tmPS8pqC7x","DpFCA1CohY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5992","layer":2},{"info":"number node, value=8724","layer":2},{"info":"compute binary expreesion, left_input=5992, right_input=8724, 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=1960","layer":2},{"info":"number node, value=1655","layer":2},{"info":"compute binary expreesion, left_input=1960, right_input=1655, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-4965","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-4965, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰22012221↬⫏≰102222010≧⫂∧(⫏≰2200121↙⫏≰2021022)=NaN","reverse_text":"NaN=⫏≰22012221↬⫏≰102222010≧⫂∧(⫏≰2200121↙⫏≰2021022)","cot":[{"info":"⫏≰22012221↬⫏≰102222010=NaN","layer":1},{"info":"⫏≰2200121↙⫏≰2021022=⫏≰-20210220","layer":1},{"info":"NaN≧⫂∧⫏≰-20210220=NaN","layer":0}]}
{"id":437,"expression_no_base_symbol":"($1323$⇼⇔∾$1018$)∧","expression":"(⫏≰1211000⇼⇔∾⫏≰1101201)∧","highest_n_order":5,"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":1323,"base":3},"right_expr":{"type":"numeric_atoms","value":1018,"base":3}}},"used_operators":["z63VuFQld9","tifHPKVTfV"],"dependent_operators":["B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1323","layer":2},{"info":"number node, value=1018","layer":2},{"info":"compute binary expreesion, left_input=1323, right_input=1018, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-305","layer":1},{"info":"compute unary expreesion, input=-305, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1211000⇼⇔∾⫏≰1101201)∧=⫏≰0","reverse_text":"⫏≰0=(⫏≰1211000⇼⇔∾⫏≰1101201)∧","cot":[{"info":"⫏≰1211000⇼⇔∾⫏≰1101201=⫏≰-102022","layer":1},{"info":"⫏≰-102022∧=⫏≰0","layer":0}]}
{"id":438,"expression_no_base_symbol":"↽≂($6090$⪨≂$7316$)","expression":"↽≂(⫏≰22100120⪨≂⫏≰101000222)","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":6090,"base":3},"right_expr":{"type":"numeric_atoms","value":7316,"base":3}}},"used_operators":["u6S6b8DprG","sdazOOVcIp"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰20110002","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6090","layer":2},{"info":"number node, value=7316","layer":2},{"info":"compute binary expreesion, left_input=6090, right_input=7316, 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=-2350","layer":1},{"info":"compute unary expreesion, input=-2350, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=4700","layer":0}],"base":3,"result_base":3,"text":"↽≂(⫏≰22100120⪨≂⫏≰101000222)=⫏≰20110002","reverse_text":"⫏≰20110002=↽≂(⫏≰22100120⪨≂⫏≰101000222)","cot":[{"info":"⫏≰22100120⪨≂⫏≰101000222=⫏≰-10020001","layer":1},{"info":"↽≂⫏≰-10020001=⫏≰20110002","layer":0}]}
{"id":439,"expression_no_base_symbol":"(⊙↵-$1742$)⪐","expression":"(⊙↵-⫏≰2101112)⪐","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1790,"operation_count":2,"complexity_ratio":895.0,"tree":{"type":"unary","operator":"⪐","unary_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":1742,"base":3}}},"used_operators":["eH2TOUuTDT","oWn0xqSxBt"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"⫏≰-2","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1742","layer":2},{"info":"compute unary expreesion, input=1742, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute unary expreesion, input=-1, op_id = eH2TOUuTDT, unary_op_definition = 'a⪐ = { (a+a) , if (-a)!=532 or a<368 ; (-a) , else }', output=-2","layer":0}],"base":3,"result_base":3,"text":"(⊙↵-⫏≰2101112)⪐=⫏≰-2","reverse_text":"⫏≰-2=(⊙↵-⫏≰2101112)⪐","cot":[{"info":"⊙↵-⫏≰2101112=⫏≰-1","layer":1},{"info":"⫏≰-1⪐=⫏≰-2","layer":0}]}
{"id":440,"expression_no_base_symbol":"↥($1858$*$2892$)","expression":"↥(⫏≰2112211*⫏≰10222010)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":107217,"operation_count":2,"complexity_ratio":53608.5,"tree":{"type":"unary","operator":"↥","unary_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1858,"base":3},"right_expr":{"type":"numeric_atoms","value":2892,"base":3}}},"used_operators":["A8NUZmVepG","9HNa5Wba9A"],"dependent_operators":["k8jYdgA6NY","W4YGzv6Whe"],"result":"⫏≰1000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1858","layer":2},{"info":"number node, value=2892","layer":2},{"info":"compute binary expreesion, left_input=1858, right_input=2892, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=5373336","layer":1},{"info":"compute unary expreesion, input=5373336, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=27","layer":0}],"base":3,"result_base":3,"text":"↥(⫏≰2112211*⫏≰10222010)=⫏≰1000","reverse_text":"⫏≰1000=↥(⫏≰2112211*⫏≰10222010)","cot":[{"info":"⫏≰2112211*⫏≰10222010=⫏≰101002222211110","layer":1},{"info":"↥⫏≰101002222211110=⫏≰1000","layer":0}]}
{"id":441,"expression_no_base_symbol":"($5669$↬$2677$)≹⇙⪍($3119$≣⋋)","expression":"(⫏≰21202222↬⫏≰10200011)≹⇙⪍(⫏≰11021112≣⋋)","highest_n_order":5,"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":5669,"base":3},"right_expr":{"type":"numeric_atoms","value":2677,"base":3}},"right_expr":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"numeric_atoms","value":3119,"base":3}}},"used_operators":["AHs5Up7iyr","B5M0gjZbta","Tcnh7f0tEr"],"dependent_operators":["dWAJyo7jo9","rGHVDoGpnC","dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5669","layer":2},{"info":"number node, value=2677","layer":2},{"info":"compute binary expreesion, left_input=5669, right_input=2677, 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=3119","layer":2},{"info":"compute unary expreesion, input=3119, 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=nan, right_input=0, 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":3,"result_base":3,"text":"(⫏≰21202222↬⫏≰10200011)≹⇙⪍(⫏≰11021112≣⋋)=NaN","reverse_text":"NaN=(⫏≰21202222↬⫏≰10200011)≹⇙⪍(⫏≰11021112≣⋋)","cot":[{"info":"⫏≰21202222↬⫏≰10200011=NaN","layer":1},{"info":"⫏≰11021112≣⋋=⫏≰0","layer":1},{"info":"NaN≹⇙⪍⫏≰0=NaN","layer":0}]}
{"id":442,"expression_no_base_symbol":"$2161$≹⇙⪍$5619$⩚⊴⇥($2160$-$2158$)","expression":"⫏≰2222001≹⇙⪍⫏≰21201010⩚⊴⇥(⫏≰2222000-⫏≰2221221)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5,"operation_count":3,"complexity_ratio":1.6666666666666667,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":2161,"base":3},"right_expr":{"type":"numeric_atoms","value":5619,"base":3}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":2160,"base":3},"right_expr":{"type":"numeric_atoms","value":2158,"base":3}}},"used_operators":["NTOWxs364D","AHs5Up7iyr","rysDP5nf3Z"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2161","layer":2},{"info":"number node, value=5619","layer":2},{"info":"compute binary expreesion, left_input=2161, right_input=5619, 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":"number node, value=2160","layer":2},{"info":"number node, value=2158","layer":2},{"info":"compute binary expreesion, left_input=2160, right_input=2158, op_id = rysDP5nf3Z binary_op_definition= 'None', output=2","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2222001≹⇙⪍⫏≰21201010⩚⊴⇥(⫏≰2222000-⫏≰2221221)=NaN","reverse_text":"NaN=⫏≰2222001≹⇙⪍⫏≰21201010⩚⊴⇥(⫏≰2222000-⫏≰2221221)","cot":[{"info":"⫏≰2222001≹⇙⪍⫏≰21201010=NaN","layer":1},{"info":"⫏≰2222000-⫏≰2221221=⫏≰2","layer":1},{"info":"NaN⩚⊴⇥⫏≰2=NaN","layer":0}]}
{"id":443,"expression_no_base_symbol":"$3713$∼$1057$↪⪝","expression":"⫏≰12002112∼⫏≰1110011↪⪝","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":79,"operation_count":2,"complexity_ratio":39.5,"tree":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":3713,"base":3},"right_expr":{"type":"numeric_atoms","value":1057,"base":3}}},"used_operators":["l07mrZUIn9","DyGG3AbaNP"],"dependent_operators":["9HNa5Wba9A","2DDjHMKMc0","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3713","layer":2},{"info":"number node, value=1057","layer":2},{"info":"compute binary expreesion, left_input=3713, right_input=1057, 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 = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰12002112∼⫏≰1110011↪⪝=NaN","reverse_text":"NaN=⫏≰12002112∼⫏≰1110011↪⪝","cot":[{"info":"⫏≰12002112∼⫏≰1110011=NaN","layer":1},{"info":"NaN↪⪝=NaN","layer":0}]}
{"id":444,"expression_no_base_symbol":"(↣≠⋷$1261$)⨟⋌⩍($4981$⪘⫢$1578$)","expression":"(↣≠⋷⫏≰1201201)⨟⋌⩍(⫏≰20211111⪘⫢⫏≰2011110)","highest_n_order":4,"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":1261,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":4981,"base":3},"right_expr":{"type":"numeric_atoms","value":1578,"base":3}}},"used_operators":["rGHVDoGpnC","Asc51vEJeQ","oacrs7FA3X"],"dependent_operators":["Tcnh7f0tEr","XhwjNDsVaA","AHs5Up7iyr","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1261","layer":2},{"info":"compute unary expreesion, input=1261, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"number node, value=4981","layer":2},{"info":"number node, value=1578","layer":2},{"info":"compute binary expreesion, left_input=4981, right_input=1578, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=9838","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=9838, 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":0}],"base":3,"result_base":3,"text":"(↣≠⋷⫏≰1201201)⨟⋌⩍(⫏≰20211111⪘⫢⫏≰2011110)=NaN","reverse_text":"NaN=(↣≠⋷⫏≰1201201)⨟⋌⩍(⫏≰20211111⪘⫢⫏≰2011110)","cot":[{"info":"↣≠⋷⫏≰1201201=NaN","layer":1},{"info":"⫏≰20211111⪘⫢⫏≰2011110=⫏≰111111101","layer":1},{"info":"NaN⨟⋌⩍⫏≰111111101=NaN","layer":0}]}
{"id":445,"expression_no_base_symbol":"∥⊫($1942$≫≃)","expression":"∥⊫(⫏≰2122221≫≃)","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":"unary","operator":"≫≃","unary_expr":{"type":"numeric_atoms","value":1942,"base":3}}},"used_operators":["P8v4zCKN1o","X99M06cbEe"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A"],"result":"⫏≰22102220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1942","layer":2},{"info":"compute unary expreesion, input=1942, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=5285","layer":1},{"info":"compute unary expreesion, input=5285, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=6153","layer":0}],"base":3,"result_base":3,"text":"∥⊫(⫏≰2122221≫≃)=⫏≰22102220","reverse_text":"⫏≰22102220=∥⊫(⫏≰2122221≫≃)","cot":[{"info":"⫏≰2122221≫≃=⫏≰21020202","layer":1},{"info":"∥⊫⫏≰21020202=⫏≰22102220","layer":0}]}
{"id":446,"expression_no_base_symbol":"↣≠⋷(∂$2816$)","expression":"↣≠⋷(∂⫏≰10212022)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4,"operation_count":2,"complexity_ratio":2.0,"tree":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":2816,"base":3}}},"used_operators":["Asc51vEJeQ","Uaa54Peajs"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2816","layer":2},{"info":"compute unary expreesion, input=2816, 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 unary expreesion, input=nan, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(∂⫏≰10212022)=NaN","reverse_text":"NaN=↣≠⋷(∂⫏≰10212022)","cot":[{"info":"∂⫏≰10212022=NaN","layer":1},{"info":"↣≠⋷NaN=NaN","layer":0}]}
{"id":447,"expression_no_base_symbol":"$1274$⊴$6461$∀⇚≩($6585$/$3168$)","expression":"⫏≰1202012⊴⫏≰22212022∀⇚≩(⫏≰100000220/⫏≰11100100)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6470,"operation_count":3,"complexity_ratio":2156.6666666666665,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1274,"base":3},"right_expr":{"type":"numeric_atoms","value":6461,"base":3}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":6585,"base":3},"right_expr":{"type":"numeric_atoms","value":3168,"base":3}}},"used_operators":["LRNGc0VcxI","Nsiff2A1zJ","XhwjNDsVaA"],"dependent_operators":["X99M06cbEe","dWAJyo7jo9","14qkJME0vr","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1274","layer":2},{"info":"number node, value=6461","layer":2},{"info":"compute binary expreesion, left_input=1274, right_input=6461, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=6585","layer":2},{"info":"number node, value=3168","layer":2},{"info":"compute binary expreesion, left_input=6585, right_input=3168, op_id = XhwjNDsVaA binary_op_definition= 'None', output=2","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2, 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":3,"result_base":3,"text":"⫏≰1202012⊴⫏≰22212022∀⇚≩(⫏≰100000220/⫏≰11100100)=NaN","reverse_text":"NaN=⫏≰1202012⊴⫏≰22212022∀⇚≩(⫏≰100000220/⫏≰11100100)","cot":[{"info":"⫏≰1202012⊴⫏≰22212022=NaN","layer":1},{"info":"⫏≰100000220/⫏≰11100100=⫏≰2","layer":1},{"info":"NaN∀⇚≩⫏≰2=NaN","layer":0}]}
{"id":448,"expression_no_base_symbol":"($7950$⪐)⨰$1943$⪘⫢$3602$","expression":"(⫏≰101220110⪐)⨰⫏≰2122222⪘⫢⫏≰11221102","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":"unary","operator":"⪐","unary_expr":{"type":"numeric_atoms","value":7950,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1943,"base":3},"right_expr":{"type":"numeric_atoms","value":3602,"base":3}}},"used_operators":["eewbuw0ToL","eH2TOUuTDT","oacrs7FA3X"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⫏≰121122221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7950","layer":2},{"info":"compute unary expreesion, input=7950, op_id = eH2TOUuTDT, unary_op_definition = 'a⪐ = { (a+a) , if (-a)!=532 or a<368 ; (-a) , else }', output=15900","layer":1},{"info":"number node, value=1943","layer":2},{"info":"number node, value=3602","layer":2},{"info":"compute binary expreesion, left_input=1943, right_input=3602, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=3762","layer":1},{"info":"compute binary expreesion, left_input=15900, right_input=3762, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=12148","layer":0}],"base":3,"result_base":3,"text":"(⫏≰101220110⪐)⨰⫏≰2122222⪘⫢⫏≰11221102=⫏≰121122221","reverse_text":"⫏≰121122221=(⫏≰101220110⪐)⨰⫏≰2122222⪘⫢⫏≰11221102","cot":[{"info":"⫏≰101220110⪐=⫏≰210210220","layer":1},{"info":"⫏≰2122222⪘⫢⫏≰11221102=⫏≰12011100","layer":1},{"info":"⫏≰210210220⨰⫏≰12011100=⫏≰121122221","layer":0}]}
{"id":449,"expression_no_base_symbol":"$4416$+⇶⊼$3488$⩨$1764$⫥∨⫟$3305$","expression":"⫏≰20001120+⇶⊼⫏≰11210012⩨⫏≰2102100⫥∨⫟⫏≰11112102","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":159,"operation_count":3,"complexity_ratio":53.0,"tree":{"type":"binary","operator":"⩨","left_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":4416,"base":3},"right_expr":{"type":"numeric_atoms","value":3488,"base":3}},"right_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1764,"base":3},"right_expr":{"type":"numeric_atoms","value":3305,"base":3}}},"used_operators":["2DlMacCsIx","TpPTUOHfaN","KYD54nUTWz"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","AHs5Up7iyr","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4416","layer":2},{"info":"number node, value=3488","layer":2},{"info":"compute binary expreesion, left_input=4416, right_input=3488, 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":1},{"info":"number node, value=1764","layer":2},{"info":"number node, value=3305","layer":2},{"info":"compute binary expreesion, left_input=1764, right_input=3305, 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 = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰20001120+⇶⊼⫏≰11210012⩨⫏≰2102100⫥∨⫟⫏≰11112102=NaN","reverse_text":"NaN=⫏≰20001120+⇶⊼⫏≰11210012⩨⫏≰2102100⫥∨⫟⫏≰11112102","cot":[{"info":"⫏≰20001120+⇶⊼⫏≰11210012=NaN","layer":1},{"info":"⫏≰2102100⫥∨⫟⫏≰11112102=NaN","layer":1},{"info":"NaN⩨NaN=NaN","layer":0}]}
{"id":450,"expression_no_base_symbol":"(≉$8752$)%$1470$⨪↰⇹$6628$","expression":"(≉⫏≰110000011)%⫏≰2000110⨪↰⇹⫏≰100002111","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1478,"operation_count":3,"complexity_ratio":492.6666666666667,"tree":{"type":"binary","operator":"%","left_expr":{"type":"unary","operator":"≉","unary_expr":{"type":"numeric_atoms","value":8752,"base":3}},"right_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":1470,"base":3},"right_expr":{"type":"numeric_atoms","value":6628,"base":3}}},"used_operators":["k8jYdgA6NY","e1ybzncUwg","tmPS8pqC7x"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rJVOvQCfKK"],"result":"⫏≰122011","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=8752","layer":2},{"info":"compute unary expreesion, input=8752, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=9283","layer":1},{"info":"number node, value=1470","layer":2},{"info":"number node, value=6628","layer":2},{"info":"compute binary expreesion, left_input=1470, right_input=6628, 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=1470","layer":1},{"info":"compute binary expreesion, left_input=9283, right_input=1470, op_id = k8jYdgA6NY binary_op_definition= 'None', output=463","layer":0}],"base":3,"result_base":3,"text":"(≉⫏≰110000011)%⫏≰2000110⨪↰⇹⫏≰100002111=⫏≰122011","reverse_text":"⫏≰122011=(≉⫏≰110000011)%⫏≰2000110⨪↰⇹⫏≰100002111","cot":[{"info":"≉⫏≰110000011=⫏≰110201211","layer":1},{"info":"⫏≰2000110⨪↰⇹⫏≰100002111=⫏≰2000110","layer":1},{"info":"⫏≰110201211%⫏≰2000110=⫏≰122011","layer":0}]}
{"id":451,"expression_no_base_symbol":"$3504$↺$1773$⩨$1094$⪢$1881$","expression":"⫏≰11210210↺⫏≰2102200⩨⫏≰1111112⪢⫏≰2120200","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1887,"operation_count":3,"complexity_ratio":629.0,"tree":{"type":"binary","operator":"⩨","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":3504,"base":3},"right_expr":{"type":"numeric_atoms","value":1773,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1094,"base":3},"right_expr":{"type":"numeric_atoms","value":1881,"base":3}}},"used_operators":["2DlMacCsIx","7j4O788W3g","dWAJyo7jo9"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","rysDP5nf3Z","t8gj7n24qd","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3504","layer":2},{"info":"number node, value=1773","layer":2},{"info":"compute binary expreesion, left_input=3504, right_input=1773, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1773","layer":1},{"info":"number node, value=1094","layer":2},{"info":"number node, value=1881","layer":2},{"info":"compute binary expreesion, left_input=1094, right_input=1881, 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=1773, right_input=nan, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11210210↺⫏≰2102200⩨⫏≰1111112⪢⫏≰2120200=NaN","reverse_text":"NaN=⫏≰11210210↺⫏≰2102200⩨⫏≰1111112⪢⫏≰2120200","cot":[{"info":"⫏≰11210210↺⫏≰2102200=⫏≰2102200","layer":1},{"info":"⫏≰1111112⪢⫏≰2120200=NaN","layer":1},{"info":"⫏≰2102200⩨NaN=NaN","layer":0}]}
{"id":452,"expression_no_base_symbol":"⊄⩳↩(⩦⩻⨪$3373$)","expression":"⊄⩳↩(⩦⩻⨪⫏≰11121221)","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":3373,"base":3}}},"used_operators":["8w2t5hMYqp","2td37pGCOC"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-111212210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3373","layer":2},{"info":"compute unary expreesion, input=3373, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=3373","layer":1},{"info":"compute unary expreesion, input=3373, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-10119","layer":0}],"base":3,"result_base":3,"text":"⊄⩳↩(⩦⩻⨪⫏≰11121221)=⫏≰-111212210","reverse_text":"⫏≰-111212210=⊄⩳↩(⩦⩻⨪⫏≰11121221)","cot":[{"info":"⩦⩻⨪⫏≰11121221=⫏≰11121221","layer":1},{"info":"⊄⩳↩⫏≰11121221=⫏≰-111212210","layer":0}]}
{"id":453,"expression_no_base_symbol":"↯⪼(⨞⊢$1399$)","expression":"↯⪼(⨞⊢⫏≰1220211)","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":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":1399,"base":3}}},"used_operators":["8jW3W4yZS5","xUOZtlo3hN"],"dependent_operators":["eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰10001120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1399","layer":2},{"info":"compute unary expreesion, input=1399, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-1573","layer":1},{"info":"compute unary expreesion, input=-1573, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=2229","layer":0}],"base":3,"result_base":3,"text":"↯⪼(⨞⊢⫏≰1220211)=⫏≰10001120","reverse_text":"⫏≰10001120=↯⪼(⨞⊢⫏≰1220211)","cot":[{"info":"⨞⊢⫏≰1220211=⫏≰-2011021","layer":1},{"info":"↯⪼⫏≰-2011021=⫏≰10001120","layer":0}]}
{"id":454,"expression_no_base_symbol":"(⨰⫟⨤$1054$)⇋≉","expression":"(⨰⫟⨤⫏≰1110001)⇋≉","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3379,"operation_count":2,"complexity_ratio":1689.5,"tree":{"type":"unary","operator":"⇋≉","unary_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":1054,"base":3}}},"used_operators":["XIabStNQrY","Tw270M8GLb"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1054","layer":2},{"info":"compute unary expreesion, input=1054, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⨰⫟⨤⫏≰1110001)⇋≉=NaN","reverse_text":"NaN=(⨰⫟⨤⫏≰1110001)⇋≉","cot":[{"info":"⨰⫟⨤⫏≰1110001=NaN","layer":1},{"info":"NaN⇋≉=NaN","layer":0}]}
{"id":455,"expression_no_base_symbol":"($4075$∀⇚≩$7646$)⪛($1051$⊪)","expression":"(⫏≰12120221∀⇚≩⫏≰101111012)⪛(⫏≰1102221⊪)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":28562,"operation_count":3,"complexity_ratio":9520.666666666666,"tree":{"type":"binary","operator":"⪛","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":4075,"base":3},"right_expr":{"type":"numeric_atoms","value":7646,"base":3}},"right_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":1051,"base":3}}},"used_operators":["uFcxV4UQCh","LRNGc0VcxI","zVYPLywUTj"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","X99M06cbEe","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4075","layer":2},{"info":"number node, value=7646","layer":2},{"info":"compute binary expreesion, left_input=4075, right_input=7646, 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=1051","layer":2},{"info":"compute unary expreesion, input=1051, 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=nan, right_input=0, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12120221∀⇚≩⫏≰101111012)⪛(⫏≰1102221⊪)=NaN","reverse_text":"NaN=(⫏≰12120221∀⇚≩⫏≰101111012)⪛(⫏≰1102221⊪)","cot":[{"info":"⫏≰12120221∀⇚≩⫏≰101111012=NaN","layer":1},{"info":"⫏≰1102221⊪=⫏≰0","layer":1},{"info":"NaN⪛⫏≰0=NaN","layer":0}]}
{"id":456,"expression_no_base_symbol":"↽≂$4901$∀⇚≩$6523$","expression":"↽≂⫏≰20201112∀⇚≩⫏≰22221121","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":34310,"operation_count":2,"complexity_ratio":17155.0,"tree":{"type":"unary","operator":"↽≂","unary_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":4901,"base":3},"right_expr":{"type":"numeric_atoms","value":6523,"base":3}}},"used_operators":["u6S6b8DprG","LRNGc0VcxI"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4901","layer":2},{"info":"number node, value=6523","layer":2},{"info":"compute binary expreesion, left_input=4901, right_input=6523, 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 = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↽≂⫏≰20201112∀⇚≩⫏≰22221121=NaN","reverse_text":"NaN=↽≂⫏≰20201112∀⇚≩⫏≰22221121","cot":[{"info":"⫏≰20201112∀⇚≩⫏≰22221121=NaN","layer":1},{"info":"↽≂NaN=NaN","layer":0}]}
{"id":457,"expression_no_base_symbol":"⨞⊢$3368$≧⫂∧$5280$","expression":"⨞⊢⫏≰11121202≧⫂∧⫏≰21020120","highest_n_order":1,"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":3368,"base":3},"right_expr":{"type":"numeric_atoms","value":5280,"base":3}}},"used_operators":["xUOZtlo3hN","Ph9nP6C5qx"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-20211111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3368","layer":2},{"info":"number node, value=5280","layer":2},{"info":"compute binary expreesion, left_input=3368, right_input=5280, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=4807","layer":1},{"info":"compute unary expreesion, input=4807, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-4981","layer":0}],"base":3,"result_base":3,"text":"⨞⊢⫏≰11121202≧⫂∧⫏≰21020120=⫏≰-20211111","reverse_text":"⫏≰-20211111=⨞⊢⫏≰11121202≧⫂∧⫏≰21020120","cot":[{"info":"⫏≰11121202≧⫂∧⫏≰21020120=⫏≰20121001","layer":1},{"info":"⨞⊢⫏≰20121001=⫏≰-20211111","layer":0}]}
{"id":458,"expression_no_base_symbol":"$1108$∼$6773$⋝⋈⪟($4117$≦≮≮)","expression":"⫏≰1112001∼⫏≰100021212⋝⋈⪟(⫏≰12122111≦≮≮)","highest_n_order":4,"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":1108,"base":3},"right_expr":{"type":"numeric_atoms","value":6773,"base":3}},"right_expr":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":4117,"base":3}}},"used_operators":["2DDjHMKMc0","DyGG3AbaNP","D4vGDi5EA2"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1108","layer":2},{"info":"number node, value=6773","layer":2},{"info":"compute binary expreesion, left_input=1108, right_input=6773, 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=4117","layer":2},{"info":"compute unary expreesion, input=4117, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-12351","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-12351, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1112001∼⫏≰100021212⋝⋈⪟(⫏≰12122111≦≮≮)=NaN","reverse_text":"NaN=⫏≰1112001∼⫏≰100021212⋝⋈⪟(⫏≰12122111≦≮≮)","cot":[{"info":"⫏≰1112001∼⫏≰100021212=NaN","layer":1},{"info":"⫏≰12122111≦≮≮=⫏≰-121221110","layer":1},{"info":"NaN⋝⋈⪟⫏≰-121221110=NaN","layer":0}]}
{"id":459,"expression_no_base_symbol":"⊥($7887$⨸⪁$7550$)","expression":"⊥(⫏≰101211010⨸⪁⫏≰101100122)","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":7887,"base":3},"right_expr":{"type":"numeric_atoms","value":7550,"base":3}}},"used_operators":["Q3PJZHRvZv","g55IO6H4Gj"],"dependent_operators":["fu6greOZ01","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7887","layer":2},{"info":"number node, value=7550","layer":2},{"info":"compute binary expreesion, left_input=7887, right_input=7550, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=30874","layer":1},{"info":"compute unary expreesion, input=30874, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊥(⫏≰101211010⨸⪁⫏≰101100122)=NaN","reverse_text":"NaN=⊥(⫏≰101211010⨸⪁⫏≰101100122)","cot":[{"info":"⫏≰101211010⨸⪁⫏≰101100122=⫏≰1120100111","layer":1},{"info":"⊥⫏≰1120100111=NaN","layer":0}]}
{"id":460,"expression_no_base_symbol":"($4971$⊉≛↸$5080$)↺$1680$⊴$1066$","expression":"(⫏≰20211010⊉≛↸⫏≰20222011)↺⫏≰2022020⊴⫏≰1110111","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1110,"operation_count":3,"complexity_ratio":370.0,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":4971,"base":3},"right_expr":{"type":"numeric_atoms","value":5080,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1680,"base":3},"right_expr":{"type":"numeric_atoms","value":1066,"base":3}}},"used_operators":["7j4O788W3g","DZ8iAZOCBD","Nsiff2A1zJ"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4971","layer":2},{"info":"number node, value=5080","layer":2},{"info":"compute binary expreesion, left_input=4971, right_input=5080, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=9942","layer":1},{"info":"number node, value=1680","layer":2},{"info":"number node, value=1066","layer":2},{"info":"compute binary expreesion, left_input=1680, right_input=1066, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=9942, right_input=nan, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20211010⊉≛↸⫏≰20222011)↺⫏≰2022020⊴⫏≰1110111=NaN","reverse_text":"NaN=(⫏≰20211010⊉≛↸⫏≰20222011)↺⫏≰2022020⊴⫏≰1110111","cot":[{"info":"⫏≰20211010⊉≛↸⫏≰20222011=⫏≰111122020","layer":1},{"info":"⫏≰2022020⊴⫏≰1110111=NaN","layer":1},{"info":"⫏≰111122020↺NaN=NaN","layer":0}]}
{"id":461,"expression_no_base_symbol":"($2897$⊭↱$1018$)⫥∨⫟(⊙↵-$6456$)","expression":"(⫏≰10222022⊭↱⫏≰1101201)⫥∨⫟(⊙↵-⫏≰22212010)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6662,"operation_count":3,"complexity_ratio":2220.6666666666665,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":2897,"base":3},"right_expr":{"type":"numeric_atoms","value":1018,"base":3}},"right_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":6456,"base":3}}},"used_operators":["KYD54nUTWz","COABgblf1C","oWn0xqSxBt"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2897","layer":2},{"info":"number node, value=1018","layer":2},{"info":"compute binary expreesion, left_input=2897, right_input=1018, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-3753","layer":1},{"info":"number node, value=6456","layer":2},{"info":"compute unary expreesion, input=6456, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute binary expreesion, left_input=-3753, right_input=-1, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10222022⊭↱⫏≰1101201)⫥∨⫟(⊙↵-⫏≰22212010)=NaN","reverse_text":"NaN=(⫏≰10222022⊭↱⫏≰1101201)⫥∨⫟(⊙↵-⫏≰22212010)","cot":[{"info":"⫏≰10222022⊭↱⫏≰1101201=⫏≰-12011000","layer":1},{"info":"⊙↵-⫏≰22212010=⫏≰-1","layer":1},{"info":"⫏≰-12011000⫥∨⫟⫏≰-1=NaN","layer":0}]}
{"id":462,"expression_no_base_symbol":"∥⊫($5782$*$5651$)","expression":"∥⊫(⫏≰21221011*⫏≰21202022)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5655,"operation_count":2,"complexity_ratio":2827.5,"tree":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":5782,"base":3},"right_expr":{"type":"numeric_atoms","value":5651,"base":3}}},"used_operators":["P8v4zCKN1o","9HNa5Wba9A"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰2021111001121100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5782","layer":2},{"info":"number node, value=5651","layer":2},{"info":"compute binary expreesion, left_input=5782, right_input=5651, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=32674082","layer":1},{"info":"compute unary expreesion, input=32674082, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=32674950","layer":0}],"base":3,"result_base":3,"text":"∥⊫(⫏≰21221011*⫏≰21202022)=⫏≰2021111001121100","reverse_text":"⫏≰2021111001121100=∥⊫(⫏≰21221011*⫏≰21202022)","cot":[{"info":"⫏≰21221011*⫏≰21202022=⫏≰2021111000102012","layer":1},{"info":"∥⊫⫏≰2021111000102012=⫏≰2021111001121100","layer":0}]}
{"id":463,"expression_no_base_symbol":"⇁⨣⪵$5786$⨓$1001$","expression":"⇁⨣⪵⫏≰21221022⨓⫏≰1101002","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1008,"operation_count":2,"complexity_ratio":504.0,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":5786,"base":3},"right_expr":{"type":"numeric_atoms","value":1001,"base":3}}},"used_operators":["inkyxCbjAn","3ViojmjbAp"],"dependent_operators":["B5M0gjZbta","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5786","layer":2},{"info":"number node, value=1001","layer":2},{"info":"compute binary expreesion, left_input=5786, right_input=1001, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1004","layer":1},{"info":"compute unary expreesion, input=-1004, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵⫏≰21221022⨓⫏≰1101002=NaN","reverse_text":"NaN=⇁⨣⪵⫏≰21221022⨓⫏≰1101002","cot":[{"info":"⫏≰21221022⨓⫏≰1101002=⫏≰-1101012","layer":1},{"info":"⇁⨣⪵⫏≰-1101012=NaN","layer":0}]}
{"id":464,"expression_no_base_symbol":"($3637$≣⋋)≭$2137$⋝⋈⪟$2972$","expression":"(⫏≰11222201≣⋋)≭⫏≰2221011⋝⋈⪟⫏≰11002002","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":518,"operation_count":3,"complexity_ratio":172.66666666666666,"tree":{"type":"binary","operator":"≭","left_expr":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"numeric_atoms","value":3637,"base":3}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":2137,"base":3},"right_expr":{"type":"numeric_atoms","value":2972,"base":3}}},"used_operators":["rxpJgHHUmx","Tcnh7f0tEr","2DDjHMKMc0"],"dependent_operators":["AHs5Up7iyr","dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3637","layer":2},{"info":"compute unary expreesion, input=3637, 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=2137","layer":2},{"info":"number node, value=2972","layer":2},{"info":"compute binary expreesion, left_input=2137, right_input=2972, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=2137","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=2137, 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":3,"result_base":3,"text":"(⫏≰11222201≣⋋)≭⫏≰2221011⋝⋈⪟⫏≰11002002=NaN","reverse_text":"NaN=(⫏≰11222201≣⋋)≭⫏≰2221011⋝⋈⪟⫏≰11002002","cot":[{"info":"⫏≰11222201≣⋋=⫏≰0","layer":1},{"info":"⫏≰2221011⋝⋈⪟⫏≰11002002=⫏≰2221011","layer":1},{"info":"⫏≰0≭⫏≰2221011=NaN","layer":0}]}
{"id":465,"expression_no_base_symbol":"$1181$⨰$1700$+$5992$≭$1603$","expression":"⫏≰1121202⨰⫏≰2022222+⫏≰22012221≭⫏≰2012101","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"+","left_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":1181,"base":3},"right_expr":{"type":"numeric_atoms","value":1700,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":5992,"base":3},"right_expr":{"type":"numeric_atoms","value":1603,"base":3}}},"used_operators":["W4YGzv6Whe","eewbuw0ToL","rxpJgHHUmx"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1181","layer":2},{"info":"number node, value=1700","layer":2},{"info":"compute binary expreesion, left_input=1181, right_input=1700, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-509","layer":1},{"info":"number node, value=5992","layer":2},{"info":"number node, value=1603","layer":2},{"info":"compute binary expreesion, left_input=5992, right_input=1603, 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=-509, right_input=nan, op_id = W4YGzv6Whe binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1121202⨰⫏≰2022222+⫏≰22012221≭⫏≰2012101=NaN","reverse_text":"NaN=⫏≰1121202⨰⫏≰2022222+⫏≰22012221≭⫏≰2012101","cot":[{"info":"⫏≰1121202⨰⫏≰2022222=⫏≰-200212","layer":1},{"info":"⫏≰22012221≭⫏≰2012101=NaN","layer":1},{"info":"⫏≰-200212+NaN=NaN","layer":0}]}
{"id":466,"expression_no_base_symbol":"$1986$⫥∨⫟$2006$∲⫓$2186$⊴$1569$","expression":"⫏≰2201120⫥∨⫟⫏≰2202022∲⫓⫏≰2222222⊴⫏≰2011010","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3005,"operation_count":3,"complexity_ratio":1001.6666666666666,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1986,"base":3},"right_expr":{"type":"numeric_atoms","value":2006,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":2186,"base":3},"right_expr":{"type":"numeric_atoms","value":1569,"base":3}}},"used_operators":["i8ToyICDmI","KYD54nUTWz","Nsiff2A1zJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","8HhzD0ZcuI","rGHVDoGpnC","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1986","layer":2},{"info":"number node, value=2006","layer":2},{"info":"compute binary expreesion, left_input=1986, right_input=2006, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=2186","layer":2},{"info":"number node, value=1569","layer":2},{"info":"compute binary expreesion, left_input=2186, right_input=1569, 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 = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2201120⫥∨⫟⫏≰2202022∲⫓⫏≰2222222⊴⫏≰2011010=NaN","reverse_text":"NaN=⫏≰2201120⫥∨⫟⫏≰2202022∲⫓⫏≰2222222⊴⫏≰2011010","cot":[{"info":"⫏≰2201120⫥∨⫟⫏≰2202022=NaN","layer":1},{"info":"⫏≰2222222⊴⫏≰2011010=NaN","layer":1},{"info":"NaN∲⫓NaN=NaN","layer":0}]}
{"id":467,"expression_no_base_symbol":"($3078$⋓$1669$)∀⇚≩($1490$⊭↱$2084$)","expression":"(⫏≰11020000⋓⫏≰2021211)∀⇚≩(⫏≰2001012⊭↱⫏≰2212012)","highest_n_order":3,"priority_hierarchical_complexity":3,"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":3078,"base":3},"right_expr":{"type":"numeric_atoms","value":1669,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":1490,"base":3},"right_expr":{"type":"numeric_atoms","value":2084,"base":3}}},"used_operators":["LRNGc0VcxI","T2fj7uvVaJ","COABgblf1C"],"dependent_operators":["X99M06cbEe","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1122012","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3078","layer":2},{"info":"number node, value=1669","layer":2},{"info":"compute binary expreesion, left_input=3078, right_input=1669, 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=1490","layer":2},{"info":"number node, value=2084","layer":2},{"info":"compute binary expreesion, left_input=1490, right_input=2084, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=1193","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=1193, 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=1193","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11020000⋓⫏≰2021211)∀⇚≩(⫏≰2001012⊭↱⫏≰2212012)=⫏≰1122012","reverse_text":"⫏≰1122012=(⫏≰11020000⋓⫏≰2021211)∀⇚≩(⫏≰2001012⊭↱⫏≰2212012)","cot":[{"info":"⫏≰11020000⋓⫏≰2021211=⫏≰0","layer":1},{"info":"⫏≰2001012⊭↱⫏≰2212012=⫏≰1122012","layer":1},{"info":"⫏≰0∀⇚≩⫏≰1122012=⫏≰1122012","layer":0}]}
{"id":468,"expression_no_base_symbol":"⇁⨣⪵$1130$⨰$6886$","expression":"⇁⨣⪵⫏≰1112212⨰⫏≰100110001","highest_n_order":5,"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":1130,"base":3},"right_expr":{"type":"numeric_atoms","value":6886,"base":3}}},"used_operators":["inkyxCbjAn","eewbuw0ToL"],"dependent_operators":["B5M0gjZbta","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1130","layer":2},{"info":"number node, value=6886","layer":2},{"info":"compute binary expreesion, left_input=1130, right_input=6886, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-5746","layer":1},{"info":"compute unary expreesion, input=-5746, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵⫏≰1112212⨰⫏≰100110001=NaN","reverse_text":"NaN=⇁⨣⪵⫏≰1112212⨰⫏≰100110001","cot":[{"info":"⫏≰1112212⨰⫏≰100110001=⫏≰-21212211","layer":1},{"info":"⇁⨣⪵⫏≰-21212211=NaN","layer":0}]}
{"id":469,"expression_no_base_symbol":"$1997$⨽$5824$⩨($2910$%$2006$)","expression":"⫏≰2201222⨽⫏≰21222201⩨(⫏≰10222210%⫏≰2202022)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2011,"operation_count":3,"complexity_ratio":670.3333333333334,"tree":{"type":"binary","operator":"⩨","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1997,"base":3},"right_expr":{"type":"numeric_atoms","value":5824,"base":3}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":2910,"base":3},"right_expr":{"type":"numeric_atoms","value":2006,"base":3}}},"used_operators":["2DlMacCsIx","8HhzD0ZcuI","k8jYdgA6NY"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","rysDP5nf3Z"],"result":"⫏≰10","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1997","layer":2},{"info":"number node, value=5824","layer":2},{"info":"compute binary expreesion, left_input=1997, right_input=5824, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-11980185","layer":1},{"info":"number node, value=2910","layer":2},{"info":"number node, value=2006","layer":2},{"info":"compute binary expreesion, left_input=2910, right_input=2006, op_id = k8jYdgA6NY binary_op_definition= 'None', output=904","layer":1},{"info":"compute binary expreesion, left_input=-11980185, right_input=904, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=3","layer":0}],"base":3,"result_base":3,"text":"⫏≰2201222⨽⫏≰21222201⩨(⫏≰10222210%⫏≰2202022)=⫏≰10","reverse_text":"⫏≰10=⫏≰2201222⨽⫏≰21222201⩨(⫏≰10222210%⫏≰2202022)","cot":[{"info":"⫏≰2201222⨽⫏≰21222201=⫏≰-211112122201120","layer":1},{"info":"⫏≰10222210%⫏≰2202022=⫏≰1020111","layer":1},{"info":"⫏≰-211112122201120⩨⫏≰1020111=⫏≰10","layer":0}]}
{"id":470,"expression_no_base_symbol":"($1732$⫥∨⫟$1115$)⪛(↥$3983$)","expression":"(⫏≰2101011⫥∨⫟⫏≰1112022)⪛(↥⫏≰12110112)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":236,"operation_count":3,"complexity_ratio":78.66666666666667,"tree":{"type":"binary","operator":"⪛","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1732,"base":3},"right_expr":{"type":"numeric_atoms","value":1115,"base":3}},"right_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":3983,"base":3}}},"used_operators":["uFcxV4UQCh","KYD54nUTWz","A8NUZmVepG"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","8HhzD0ZcuI","rGHVDoGpnC","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1732","layer":2},{"info":"number node, value=1115","layer":2},{"info":"compute binary expreesion, left_input=1732, right_input=1115, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=3983","layer":2},{"info":"compute unary expreesion, input=3983, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=5","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=5, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2101011⫥∨⫟⫏≰1112022)⪛(↥⫏≰12110112)=NaN","reverse_text":"NaN=(⫏≰2101011⫥∨⫟⫏≰1112022)⪛(↥⫏≰12110112)","cot":[{"info":"⫏≰2101011⫥∨⫟⫏≰1112022=NaN","layer":1},{"info":"↥⫏≰12110112=⫏≰12","layer":1},{"info":"NaN⪛⫏≰12=NaN","layer":0}]}
{"id":471,"expression_no_base_symbol":"($4976$⫸⊐$5669$)≹⇙⪍($1787$-$3522$)","expression":"(⫏≰20211022⫸⊐⫏≰21202222)≹⇙⪍(⫏≰2110012-⫏≰11211110)","highest_n_order":4,"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":4976,"base":3},"right_expr":{"type":"numeric_atoms","value":5669,"base":3}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1787,"base":3},"right_expr":{"type":"numeric_atoms","value":3522,"base":3}}},"used_operators":["AHs5Up7iyr","mqXw5SEYmG","rysDP5nf3Z"],"dependent_operators":["dWAJyo7jo9","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4976","layer":2},{"info":"number node, value=5669","layer":2},{"info":"compute binary expreesion, left_input=4976, right_input=5669, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=22551","layer":1},{"info":"number node, value=1787","layer":2},{"info":"number node, value=3522","layer":2},{"info":"compute binary expreesion, left_input=1787, right_input=3522, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-1735","layer":1},{"info":"compute binary expreesion, left_input=22551, right_input=-1735, 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":3,"result_base":3,"text":"(⫏≰20211022⫸⊐⫏≰21202222)≹⇙⪍(⫏≰2110012-⫏≰11211110)=NaN","reverse_text":"NaN=(⫏≰20211022⫸⊐⫏≰21202222)≹⇙⪍(⫏≰2110012-⫏≰11211110)","cot":[{"info":"⫏≰20211022⫸⊐⫏≰21202222=⫏≰1010221020","layer":1},{"info":"⫏≰2110012-⫏≰11211110=⫏≰-2101021","layer":1},{"info":"⫏≰1010221020≹⇙⪍⫏≰-2101021=NaN","layer":0}]}
{"id":472,"expression_no_base_symbol":"⊥(↯⪼$1758$)","expression":"⊥(↯⪼⫏≰2102010)","highest_n_order":4,"priority_hierarchical_complexity":1,"normalized_expansion_degree":598,"operation_count":2,"complexity_ratio":299.0,"tree":{"type":"unary","operator":"⊥","unary_expr":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"numeric_atoms","value":1758,"base":3}}},"used_operators":["Q3PJZHRvZv","8jW3W4yZS5"],"dependent_operators":["fu6greOZ01","eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp"],"result":"⫏≰220","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1758","layer":2},{"info":"compute unary expreesion, input=1758, op_id = 8jW3W4yZS5, unary_op_definition = '↯⪼a = { (≤/(a⫌⩹⨱)) , if (∥⊫a)<382 and (⪲⇎a)!=21 ; ((⊄⩳↩988)%(109⩤)) , else }', output=-21","layer":1},{"info":"compute unary expreesion, input=-21, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=24","layer":0}],"base":3,"result_base":3,"text":"⊥(↯⪼⫏≰2102010)=⫏≰220","reverse_text":"⫏≰220=⊥(↯⪼⫏≰2102010)","cot":[{"info":"↯⪼⫏≰2102010=⫏≰-210","layer":1},{"info":"⊥⫏≰-210=⫏≰220","layer":0}]}
{"id":473,"expression_no_base_symbol":"(⊥$3044$)⋓($6799$↺$1207$)","expression":"(⊥⫏≰11011202)⋓(⫏≰100022211↺⫏≰1122201)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16,"operation_count":3,"complexity_ratio":5.333333333333333,"tree":{"type":"binary","operator":"⋓","left_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":3044,"base":3}},"right_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":6799,"base":3},"right_expr":{"type":"numeric_atoms","value":1207,"base":3}}},"used_operators":["T2fj7uvVaJ","Q3PJZHRvZv","7j4O788W3g"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","fu6greOZ01","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3044","layer":2},{"info":"compute unary expreesion, input=3044, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"number node, value=6799","layer":2},{"info":"number node, value=1207","layer":2},{"info":"compute binary expreesion, left_input=6799, right_input=1207, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1207","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1207, 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":3,"result_base":3,"text":"(⊥⫏≰11011202)⋓(⫏≰100022211↺⫏≰1122201)=⫏≰0","reverse_text":"⫏≰0=(⊥⫏≰11011202)⋓(⫏≰100022211↺⫏≰1122201)","cot":[{"info":"⊥⫏≰11011202=NaN","layer":1},{"info":"⫏≰100022211↺⫏≰1122201=⫏≰1122201","layer":1},{"info":"NaN⋓⫏≰1122201=⫏≰0","layer":0}]}
{"id":474,"expression_no_base_symbol":"(+⊝⨔$1440$)↺($3822$+$2469$)","expression":"(+⊝⨔⫏≰1222100)↺(⫏≰12020120+⫏≰10101110)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":43,"operation_count":3,"complexity_ratio":14.333333333333334,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":1440,"base":3}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":3822,"base":3},"right_expr":{"type":"numeric_atoms","value":2469,"base":3}}},"used_operators":["7j4O788W3g","DhbWaqg5eL","W4YGzv6Whe"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe"],"result":"⫏≰22122000","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1440","layer":2},{"info":"compute unary expreesion, input=1440, 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=3822","layer":2},{"info":"number node, value=2469","layer":2},{"info":"compute binary expreesion, left_input=3822, right_input=2469, op_id = W4YGzv6Whe binary_op_definition= 'None', output=6291","layer":1},{"info":"compute binary expreesion, left_input=1522, right_input=6291, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=6291","layer":0}],"base":3,"result_base":3,"text":"(+⊝⨔⫏≰1222100)↺(⫏≰12020120+⫏≰10101110)=⫏≰22122000","reverse_text":"⫏≰22122000=(+⊝⨔⫏≰1222100)↺(⫏≰12020120+⫏≰10101110)","cot":[{"info":"+⊝⨔⫏≰1222100=⫏≰2002101","layer":1},{"info":"⫏≰12020120+⫏≰10101110=⫏≰22122000","layer":1},{"info":"⫏≰2002101↺⫏≰22122000=⫏≰22122000","layer":0}]}
{"id":475,"expression_no_base_symbol":"($7242$∲⫓$3646$)-$3138$⩚⊴⇥$1172$","expression":"(⫏≰100221020∲⫓⫏≰12000001)-⫏≰11022020⩚⊴⇥⫏≰1121102","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"-","left_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":7242,"base":3},"right_expr":{"type":"numeric_atoms","value":3646,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":3138,"base":3},"right_expr":{"type":"numeric_atoms","value":1172,"base":3}}},"used_operators":["rysDP5nf3Z","i8ToyICDmI","NTOWxs364D"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰20002010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7242","layer":2},{"info":"number node, value=3646","layer":2},{"info":"compute binary expreesion, left_input=7242, right_input=3646, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=3138","layer":2},{"info":"number node, value=1172","layer":2},{"info":"compute binary expreesion, left_input=3138, right_input=1172, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-4431","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-4431, op_id = rysDP5nf3Z binary_op_definition= 'None', output=4431","layer":0}],"base":3,"result_base":3,"text":"(⫏≰100221020∲⫓⫏≰12000001)-⫏≰11022020⩚⊴⇥⫏≰1121102=⫏≰20002010","reverse_text":"⫏≰20002010=(⫏≰100221020∲⫓⫏≰12000001)-⫏≰11022020⩚⊴⇥⫏≰1121102","cot":[{"info":"⫏≰100221020∲⫓⫏≰12000001=⫏≰0","layer":1},{"info":"⫏≰11022020⩚⊴⇥⫏≰1121102=⫏≰-20002010","layer":1},{"info":"⫏≰0-⫏≰-20002010=⫏≰20002010","layer":0}]}
{"id":476,"expression_no_base_symbol":"⨈⫕(↩$3074$)","expression":"⨈⫕(↩⫏≰11012212)","highest_n_order":5,"priority_hierarchical_complexity":1,"normalized_expansion_degree":402,"operation_count":2,"complexity_ratio":201.0,"tree":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"unary","operator":"↩","unary_expr":{"type":"numeric_atoms","value":3074,"base":3}}},"used_operators":["megm06wKyl","jLgFTUHLKL"],"dependent_operators":["8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q","sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D"],"result":"⫏≰-210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3074","layer":2},{"info":"compute unary expreesion, input=3074, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-21812","layer":1},{"info":"compute unary expreesion, input=-21812, 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":3,"result_base":3,"text":"⨈⫕(↩⫏≰11012212)=⫏≰-210","reverse_text":"⫏≰-210=⨈⫕(↩⫏≰11012212)","cot":[{"info":"↩⫏≰11012212=⫏≰-1002220212","layer":1},{"info":"⨈⫕⫏≰-1002220212=⫏≰-210","layer":0}]}
{"id":477,"expression_no_base_symbol":"(⊙↵-$2987$)⪒(⨰⫟⨤$1681$)","expression":"(⊙↵-⫏≰11002122)⪒(⨰⫟⨤⫏≰2022021)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8920,"operation_count":3,"complexity_ratio":2973.3333333333335,"tree":{"type":"binary","operator":"⪒","left_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":2987,"base":3}},"right_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":1681,"base":3}}},"used_operators":["f6k1SAg4EE","oWn0xqSxBt","Tw270M8GLb"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2987","layer":2},{"info":"compute unary expreesion, input=2987, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"number node, value=1681","layer":2},{"info":"compute unary expreesion, input=1681, 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=-1, right_input=nan, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⊙↵-⫏≰11002122)⪒(⨰⫟⨤⫏≰2022021)=NaN","reverse_text":"NaN=(⊙↵-⫏≰11002122)⪒(⨰⫟⨤⫏≰2022021)","cot":[{"info":"⊙↵-⫏≰11002122=⫏≰-1","layer":1},{"info":"⨰⫟⨤⫏≰2022021=NaN","layer":1},{"info":"⫏≰-1⪒NaN=NaN","layer":0}]}
{"id":478,"expression_no_base_symbol":"⇁⨣⪵($4498$⫡⨏$1011$)","expression":"⇁⨣⪵(⫏≰20011121⫡⨏⫏≰1101110)","highest_n_order":5,"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":4498,"base":3},"right_expr":{"type":"numeric_atoms","value":1011,"base":3}}},"used_operators":["inkyxCbjAn","QMFrweE19q"],"dependent_operators":["B5M0gjZbta","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4498","layer":2},{"info":"number node, value=1011","layer":2},{"info":"compute binary expreesion, left_input=4498, right_input=1011, 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=25295","layer":1},{"info":"compute unary expreesion, input=25295, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵(⫏≰20011121⫡⨏⫏≰1101110)=NaN","reverse_text":"NaN=⇁⨣⪵(⫏≰20011121⫡⨏⫏≰1101110)","cot":[{"info":"⫏≰20011121⫡⨏⫏≰1101110=⫏≰1021200212","layer":1},{"info":"⇁⨣⪵⫏≰1021200212=NaN","layer":0}]}
{"id":479,"expression_no_base_symbol":"($5594$⊭∹↮)⨁⊸⫻","expression":"(⫏≰21200012⊭∹↮)⨁⊸⫻","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7,"operation_count":2,"complexity_ratio":3.5,"tree":{"type":"unary","operator":"⨁⊸⫻","unary_expr":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"numeric_atoms","value":5594,"base":3}}},"used_operators":["glklzrTFfD","xNBdhnnwKq"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C"],"result":"⫏≰120100101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5594","layer":2},{"info":"compute unary expreesion, input=5594, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=11188","layer":1},{"info":"compute unary expreesion, input=11188, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=11188","layer":0}],"base":3,"result_base":3,"text":"(⫏≰21200012⊭∹↮)⨁⊸⫻=⫏≰120100101","reverse_text":"⫏≰120100101=(⫏≰21200012⊭∹↮)⨁⊸⫻","cot":[{"info":"⫏≰21200012⊭∹↮=⫏≰120100101","layer":1},{"info":"⫏≰120100101⨁⊸⫻=⫏≰120100101","layer":0}]}
{"id":480,"expression_no_base_symbol":"(↥$4002$)⪢$5257$⪮%⊝$1127$","expression":"(↥⫏≰12111020)⪢⫏≰21012201⪮%⊝⫏≰1112202","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":10917,"operation_count":3,"complexity_ratio":3639.0,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":4002,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":5257,"base":3},"right_expr":{"type":"numeric_atoms","value":1127,"base":3}}},"used_operators":["dWAJyo7jo9","A8NUZmVepG","IWmyXbctLI"],"dependent_operators":["k8jYdgA6NY","k8jYdgA6NY","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4002","layer":2},{"info":"compute unary expreesion, input=4002, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=24","layer":1},{"info":"number node, value=5257","layer":2},{"info":"number node, value=1127","layer":2},{"info":"compute binary expreesion, left_input=5257, right_input=1127, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=10830","layer":1},{"info":"compute binary expreesion, left_input=24, right_input=10830, 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":3,"result_base":3,"text":"(↥⫏≰12111020)⪢⫏≰21012201⪮%⊝⫏≰1112202=NaN","reverse_text":"NaN=(↥⫏≰12111020)⪢⫏≰21012201⪮%⊝⫏≰1112202","cot":[{"info":"↥⫏≰12111020=⫏≰220","layer":1},{"info":"⫏≰21012201⪮%⊝⫏≰1112202=⫏≰112212010","layer":1},{"info":"⫏≰220⪢⫏≰112212010=NaN","layer":0}]}
{"id":481,"expression_no_base_symbol":"($2771$+$3955$)⫸⊐$2607$⪘⫢$5843$","expression":"(⫏≰10210122+⫏≰12102111)⫸⊐⫏≰10120120⪘⫢⫏≰22000102","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":2771,"base":3},"right_expr":{"type":"numeric_atoms","value":3955,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":2607,"base":3},"right_expr":{"type":"numeric_atoms","value":5843,"base":3}}},"used_operators":["mqXw5SEYmG","W4YGzv6Whe","oacrs7FA3X"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⫏≰1000202110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2771","layer":2},{"info":"number node, value=3955","layer":2},{"info":"compute binary expreesion, left_input=2771, right_input=3955, op_id = W4YGzv6Whe binary_op_definition= 'None', output=6726","layer":1},{"info":"number node, value=2607","layer":2},{"info":"number node, value=5843","layer":2},{"info":"compute binary expreesion, left_input=2607, right_input=5843, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=5090","layer":1},{"info":"compute binary expreesion, left_input=6726, right_input=5090, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=20235","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10210122+⫏≰12102111)⫸⊐⫏≰10120120⪘⫢⫏≰22000102=⫏≰1000202110","reverse_text":"⫏≰1000202110=(⫏≰10210122+⫏≰12102111)⫸⊐⫏≰10120120⪘⫢⫏≰22000102","cot":[{"info":"⫏≰10210122+⫏≰12102111=⫏≰100020010","layer":1},{"info":"⫏≰10120120⪘⫢⫏≰22000102=⫏≰20222112","layer":1},{"info":"⫏≰100020010⫸⊐⫏≰20222112=⫏≰1000202110","layer":0}]}
{"id":482,"expression_no_base_symbol":"($2538$⋷$6213$)≦≮≮","expression":"(⫏≰10111000⋷⫏≰22112010)≦≮≮","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":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":2538,"base":3},"right_expr":{"type":"numeric_atoms","value":6213,"base":3}}},"used_operators":["D4vGDi5EA2","23Mk6UjR3U"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-1111200200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2538","layer":2},{"info":"number node, value=6213","layer":2},{"info":"compute binary expreesion, left_input=2538, right_input=6213, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=9888","layer":1},{"info":"compute unary expreesion, input=9888, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-29664","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10111000⋷⫏≰22112010)≦≮≮=⫏≰-1111200200","reverse_text":"⫏≰-1111200200=(⫏≰10111000⋷⫏≰22112010)≦≮≮","cot":[{"info":"⫏≰10111000⋷⫏≰22112010=⫏≰111120020","layer":1},{"info":"⫏≰111120020≦≮≮=⫏≰-1111200200","layer":0}]}
{"id":483,"expression_no_base_symbol":"($3436$⫥∨⫟$2764$)⨰(↽≂$1982$)","expression":"(⫏≰11201021⫥∨⫟⫏≰10210101)⨰(↽≂⫏≰2201102)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":163,"operation_count":3,"complexity_ratio":54.333333333333336,"tree":{"type":"binary","operator":"⨰","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":3436,"base":3},"right_expr":{"type":"numeric_atoms","value":2764,"base":3}},"right_expr":{"type":"unary","operator":"↽≂","unary_expr":{"type":"numeric_atoms","value":1982,"base":3}}},"used_operators":["eewbuw0ToL","KYD54nUTWz","u6S6b8DprG"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","8HhzD0ZcuI","rGHVDoGpnC","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3436","layer":2},{"info":"number node, value=2764","layer":2},{"info":"compute binary expreesion, left_input=3436, right_input=2764, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=1982","layer":2},{"info":"compute unary expreesion, input=1982, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-3964","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-3964, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11201021⫥∨⫟⫏≰10210101)⨰(↽≂⫏≰2201102)=NaN","reverse_text":"NaN=(⫏≰11201021⫥∨⫟⫏≰10210101)⨰(↽≂⫏≰2201102)","cot":[{"info":"⫏≰11201021⫥∨⫟⫏≰10210101=NaN","layer":1},{"info":"↽≂⫏≰2201102=⫏≰-12102211","layer":1},{"info":"NaN⨰⫏≰-12102211=NaN","layer":0}]}
{"id":484,"expression_no_base_symbol":"⫓⪴($5554$⋫)","expression":"⫓⪴(⫏≰21121201⋫)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":11108,"operation_count":2,"complexity_ratio":5554.0,"tree":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":5554,"base":3}}},"used_operators":["eLxqMNBOBk","JL8yIekQnl"],"dependent_operators":["9HNa5Wba9A","tmPS8pqC7x"],"result":"⫏≰2011001012000101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5554","layer":2},{"info":"compute unary expreesion, input=5554, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=5554","layer":1},{"info":"compute unary expreesion, input=5554, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=30846916","layer":0}],"base":3,"result_base":3,"text":"⫓⪴(⫏≰21121201⋫)=⫏≰2011001012000101","reverse_text":"⫏≰2011001012000101=⫓⪴(⫏≰21121201⋫)","cot":[{"info":"⫏≰21121201⋫=⫏≰21121201","layer":1},{"info":"⫓⪴⫏≰21121201=⫏≰2011001012000101","layer":0}]}
{"id":485,"expression_no_base_symbol":"$2251$⨪↰⇹$5769$≭($5924$⩚⊴⇥$6776$)","expression":"⫏≰10002101⨪↰⇹⫏≰21220200≭(⫏≰22010102⩚⊴⇥⫏≰100021222)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2255,"operation_count":3,"complexity_ratio":751.6666666666666,"tree":{"type":"binary","operator":"≭","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":2251,"base":3},"right_expr":{"type":"numeric_atoms","value":5769,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":5924,"base":3},"right_expr":{"type":"numeric_atoms","value":6776,"base":3}}},"used_operators":["rxpJgHHUmx","tmPS8pqC7x","NTOWxs364D"],"dependent_operators":["AHs5Up7iyr","rJVOvQCfKK","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2251","layer":2},{"info":"number node, value=5769","layer":2},{"info":"compute binary expreesion, left_input=2251, right_input=5769, 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=2251","layer":1},{"info":"number node, value=5924","layer":2},{"info":"number node, value=6776","layer":2},{"info":"compute binary expreesion, left_input=5924, right_input=6776, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-12821","layer":1},{"info":"compute binary expreesion, left_input=2251, right_input=-12821, 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":3,"result_base":3,"text":"⫏≰10002101⨪↰⇹⫏≰21220200≭(⫏≰22010102⩚⊴⇥⫏≰100021222)=NaN","reverse_text":"NaN=⫏≰10002101⨪↰⇹⫏≰21220200≭(⫏≰22010102⩚⊴⇥⫏≰100021222)","cot":[{"info":"⫏≰10002101⨪↰⇹⫏≰21220200=⫏≰10002101","layer":1},{"info":"⫏≰22010102⩚⊴⇥⫏≰100021222=⫏≰-122120212","layer":1},{"info":"⫏≰10002101≭⫏≰-122120212=NaN","layer":0}]}
{"id":486,"expression_no_base_symbol":"($4033$-$1865$)⋝⋈⪟$1272$⪮%⊝$2550$","expression":"(⫏≰12112101-⫏≰2120002)⋝⋈⪟⫏≰1202010⪮%⊝⫏≰10111110","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":4033,"base":3},"right_expr":{"type":"numeric_atoms","value":1865,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1272,"base":3},"right_expr":{"type":"numeric_atoms","value":2550,"base":3}}},"used_operators":["2DDjHMKMc0","rysDP5nf3Z","IWmyXbctLI"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰2222022","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4033","layer":2},{"info":"number node, value=1865","layer":2},{"info":"compute binary expreesion, left_input=4033, right_input=1865, op_id = rysDP5nf3Z binary_op_definition= 'None', output=2168","layer":1},{"info":"number node, value=1272","layer":2},{"info":"number node, value=2550","layer":2},{"info":"compute binary expreesion, left_input=1272, right_input=2550, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=2860","layer":1},{"info":"compute binary expreesion, left_input=2168, right_input=2860, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=2168","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12112101-⫏≰2120002)⋝⋈⪟⫏≰1202010⪮%⊝⫏≰10111110=⫏≰2222022","reverse_text":"⫏≰2222022=(⫏≰12112101-⫏≰2120002)⋝⋈⪟⫏≰1202010⪮%⊝⫏≰10111110","cot":[{"info":"⫏≰12112101-⫏≰2120002=⫏≰2222022","layer":1},{"info":"⫏≰1202010⪮%⊝⫏≰10111110=⫏≰10220221","layer":1},{"info":"⫏≰2222022⋝⋈⪟⫏≰10220221=⫏≰2222022","layer":0}]}
{"id":487,"expression_no_base_symbol":"(⨈⫕$1442$)⊴($1113$⨐⩸⫘$1040$)","expression":"(⨈⫕⫏≰1222102)⊴(⫏≰1112020⨐⩸⫘⫏≰1102112)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":394,"operation_count":3,"complexity_ratio":131.33333333333334,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":1442,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":1113,"base":3},"right_expr":{"type":"numeric_atoms","value":1040,"base":3}}},"used_operators":["Nsiff2A1zJ","megm06wKyl","fu6greOZ01"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1442","layer":2},{"info":"compute unary expreesion, input=1442, 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":"number node, value=1113","layer":2},{"info":"number node, value=1040","layer":2},{"info":"compute binary expreesion, left_input=1113, right_input=1040, 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=-21, right_input=nan, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⨈⫕⫏≰1222102)⊴(⫏≰1112020⨐⩸⫘⫏≰1102112)=NaN","reverse_text":"NaN=(⨈⫕⫏≰1222102)⊴(⫏≰1112020⨐⩸⫘⫏≰1102112)","cot":[{"info":"⨈⫕⫏≰1222102=⫏≰-210","layer":1},{"info":"⫏≰1112020⨐⩸⫘⫏≰1102112=NaN","layer":1},{"info":"⫏≰-210⊴NaN=NaN","layer":0}]}
{"id":488,"expression_no_base_symbol":"($1111$⪠⩆⊳)⪨≂$2302$↬$3321$","expression":"(⫏≰1112011⪠⩆⊳)⪨≂⫏≰10011021↬⫏≰11120000","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":12,"operation_count":3,"complexity_ratio":4.0,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"numeric_atoms","value":1111,"base":3}},"right_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":2302,"base":3},"right_expr":{"type":"numeric_atoms","value":3321,"base":3}}},"used_operators":["sdazOOVcIp","JLbD19bQDL","B5M0gjZbta"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1111","layer":2},{"info":"compute unary expreesion, input=1111, 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=2302","layer":2},{"info":"number node, value=3321","layer":2},{"info":"compute binary expreesion, left_input=2302, right_input=3321, 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=0, 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":3,"result_base":3,"text":"(⫏≰1112011⪠⩆⊳)⪨≂⫏≰10011021↬⫏≰11120000=NaN","reverse_text":"NaN=(⫏≰1112011⪠⩆⊳)⪨≂⫏≰10011021↬⫏≰11120000","cot":[{"info":"⫏≰1112011⪠⩆⊳=⫏≰0","layer":1},{"info":"⫏≰10011021↬⫏≰11120000=NaN","layer":1},{"info":"⫏≰0⪨≂NaN=NaN","layer":0}]}
{"id":489,"expression_no_base_symbol":"⩦⩻⨪($1094$↪⪝)","expression":"⩦⩻⨪(⫏≰1111112↪⪝)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":703,"operation_count":2,"complexity_ratio":351.5,"tree":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"numeric_atoms","value":1094,"base":3}}},"used_operators":["2td37pGCOC","l07mrZUIn9"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","9HNa5Wba9A","2DDjHMKMc0"],"result":"⫏≰11122221112222000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1094","layer":2},{"info":"compute unary expreesion, input=1094, op_id = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=66933108","layer":1},{"info":"compute unary expreesion, input=66933108, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=66933108","layer":0}],"base":3,"result_base":3,"text":"⩦⩻⨪(⫏≰1111112↪⪝)=⫏≰11122221112222000","reverse_text":"⫏≰11122221112222000=⩦⩻⨪(⫏≰1111112↪⪝)","cot":[{"info":"⫏≰1111112↪⪝=⫏≰11122221112222000","layer":1},{"info":"⩦⩻⨪⫏≰11122221112222000=⫏≰11122221112222000","layer":0}]}
{"id":490,"expression_no_base_symbol":"($4107$⪛$1820$)⪮%⊝($1021$⪛$2060$)","expression":"(⫏≰12122010⪛⫏≰2111102)⪮%⊝(⫏≰1101211⪛⫏≰2211022)","highest_n_order":2,"priority_hierarchical_complexity":2,"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":4107,"base":3},"right_expr":{"type":"numeric_atoms","value":1820,"base":3}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":1021,"base":3},"right_expr":{"type":"numeric_atoms","value":2060,"base":3}}},"used_operators":["IWmyXbctLI","uFcxV4UQCh"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⫏≰1201022","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4107","layer":2},{"info":"number node, value=1820","layer":2},{"info":"compute binary expreesion, left_input=4107, right_input=1820, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=467","layer":1},{"info":"number node, value=1021","layer":2},{"info":"number node, value=2060","layer":2},{"info":"compute binary expreesion, left_input=1021, right_input=2060, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1021","layer":1},{"info":"compute binary expreesion, left_input=467, right_input=1021, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=1250","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12122010⪛⫏≰2111102)⪮%⊝(⫏≰1101211⪛⫏≰2211022)=⫏≰1201022","reverse_text":"⫏≰1201022=(⫏≰12122010⪛⫏≰2111102)⪮%⊝(⫏≰1101211⪛⫏≰2211022)","cot":[{"info":"⫏≰12122010⪛⫏≰2111102=⫏≰122022","layer":1},{"info":"⫏≰1101211⪛⫏≰2211022=⫏≰1101211","layer":1},{"info":"⫏≰122022⪮%⊝⫏≰1101211=⫏≰1201022","layer":0}]}
{"id":491,"expression_no_base_symbol":"($2465$⫡⨏$5377$)∸","expression":"(⫏≰10101022⫡⨏⫏≰21101011)∸","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":184,"operation_count":2,"complexity_ratio":92.0,"tree":{"type":"unary","operator":"∸","unary_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":2465,"base":3},"right_expr":{"type":"numeric_atoms","value":5377,"base":3}}},"used_operators":["o20kRiQErp","QMFrweE19q"],"dependent_operators":["tmPS8pqC7x","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰20120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2465","layer":2},{"info":"number node, value=5377","layer":2},{"info":"compute binary expreesion, left_input=2465, right_input=5377, 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=23862","layer":1},{"info":"compute unary expreesion, input=23862, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10101022⫡⨏⫏≰21101011)∸=⫏≰20120","reverse_text":"⫏≰20120=(⫏≰10101022⫡⨏⫏≰21101011)∸","cot":[{"info":"⫏≰10101022⫡⨏⫏≰21101011=⫏≰1012201210","layer":1},{"info":"⫏≰1012201210∸=⫏≰20120","layer":0}]}
{"id":492,"expression_no_base_symbol":"($1144$⊭∹↮)≎⊠⪸($1475$/$2661$)","expression":"(⫏≰1120101⊭∹↮)≎⊠⪸(⫏≰2000122/⫏≰10122120)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":277,"operation_count":3,"complexity_ratio":92.33333333333333,"tree":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"numeric_atoms","value":1144,"base":3}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":1475,"base":3},"right_expr":{"type":"numeric_atoms","value":2661,"base":3}}},"used_operators":["bJkvcejdHO","xNBdhnnwKq","XhwjNDsVaA"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","rysDP5nf3Z"],"result":"⫏≰1010002020100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1144","layer":2},{"info":"compute unary expreesion, input=1144, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=2288","layer":1},{"info":"number node, value=1475","layer":2},{"info":"number node, value=2661","layer":2},{"info":"compute binary expreesion, left_input=1475, right_input=2661, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute binary expreesion, left_input=2288, right_input=0, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=592119","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1120101⊭∹↮)≎⊠⪸(⫏≰2000122/⫏≰10122120)=⫏≰1010002020100","reverse_text":"⫏≰1010002020100=(⫏≰1120101⊭∹↮)≎⊠⪸(⫏≰2000122/⫏≰10122120)","cot":[{"info":"⫏≰1120101⊭∹↮=⫏≰10010202","layer":1},{"info":"⫏≰2000122/⫏≰10122120=⫏≰0","layer":1},{"info":"⫏≰10010202≎⊠⪸⫏≰0=⫏≰1010002020100","layer":0}]}
{"id":493,"expression_no_base_symbol":"($1676$⨸⪁$3917$)⋳⪒(⊄⩳↩$1283$)","expression":"(⫏≰2022002⨸⪁⫏≰12101002)⋳⪒(⊄⩳↩⫏≰1202112)","highest_n_order":1,"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":1676,"base":3},"right_expr":{"type":"numeric_atoms","value":3917,"base":3}},"right_expr":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":1283,"base":3}}},"used_operators":["12rbrZMWeM","g55IO6H4Gj","8w2t5hMYqp"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1022120112","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1676","layer":2},{"info":"number node, value=3917","layer":2},{"info":"compute binary expreesion, left_input=1676, right_input=3917, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=11186","layer":1},{"info":"number node, value=1283","layer":2},{"info":"compute unary expreesion, input=1283, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-3849","layer":1},{"info":"compute binary expreesion, left_input=11186, right_input=-3849, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=25934","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2022002⨸⪁⫏≰12101002)⋳⪒(⊄⩳↩⫏≰1202112)=⫏≰1022120112","reverse_text":"⫏≰1022120112=(⫏≰2022002⨸⪁⫏≰12101002)⋳⪒(⊄⩳↩⫏≰1202112)","cot":[{"info":"⫏≰2022002⨸⪁⫏≰12101002=⫏≰120100022","layer":1},{"info":"⊄⩳↩⫏≰1202112=⫏≰-12021120","layer":1},{"info":"⫏≰120100022⋳⪒⫏≰-12021120=⫏≰1022120112","layer":0}]}
{"id":494,"expression_no_base_symbol":"($4185$⋥≓≎$5210$)≹⇙⪍(↣≠⋷$3060$)","expression":"(⫏≰12202000⋥≓≎⫏≰21010222)≹⇙⪍(↣≠⋷⫏≰11012100)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":4185,"base":3},"right_expr":{"type":"numeric_atoms","value":5210,"base":3}},"right_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":3060,"base":3}}},"used_operators":["AHs5Up7iyr","Qy55tPpLXF","Asc51vEJeQ"],"dependent_operators":["dWAJyo7jo9","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","XhwjNDsVaA","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4185","layer":2},{"info":"number node, value=5210","layer":2},{"info":"compute binary expreesion, left_input=4185, right_input=5210, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=6268","layer":1},{"info":"number node, value=3060","layer":2},{"info":"compute unary expreesion, input=3060, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=6268, 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":3,"result_base":3,"text":"(⫏≰12202000⋥≓≎⫏≰21010222)≹⇙⪍(↣≠⋷⫏≰11012100)=NaN","reverse_text":"NaN=(⫏≰12202000⋥≓≎⫏≰21010222)≹⇙⪍(↣≠⋷⫏≰11012100)","cot":[{"info":"⫏≰12202000⋥≓≎⫏≰21010222=⫏≰22121011","layer":1},{"info":"↣≠⋷⫏≰11012100=NaN","layer":1},{"info":"⫏≰22121011≹⇙⪍NaN=NaN","layer":0}]}
{"id":495,"expression_no_base_symbol":"($1817$⩨$1964$)≎⊠⪸$5495$⋝⋈⪟$1308$","expression":"(⫏≰2111022⩨⫏≰2200202)≎⊠⪸⫏≰21112112⋝⋈⪟⫏≰1210110","highest_n_order":2,"priority_hierarchical_complexity":3,"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":1817,"base":3},"right_expr":{"type":"numeric_atoms","value":1964,"base":3}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":5495,"base":3},"right_expr":{"type":"numeric_atoms","value":1308,"base":3}}},"used_operators":["bJkvcejdHO","2DlMacCsIx","2DDjHMKMc0"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1001210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1817","layer":2},{"info":"number node, value=1964","layer":2},{"info":"compute binary expreesion, left_input=1817, right_input=1964, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-3","layer":1},{"info":"number node, value=5495","layer":2},{"info":"number node, value=1308","layer":2},{"info":"compute binary expreesion, left_input=5495, right_input=1308, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=5495","layer":1},{"info":"compute binary expreesion, left_input=-3, right_input=5495, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=777","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2111022⩨⫏≰2200202)≎⊠⪸⫏≰21112112⋝⋈⪟⫏≰1210110=⫏≰1001210","reverse_text":"⫏≰1001210=(⫏≰2111022⩨⫏≰2200202)≎⊠⪸⫏≰21112112⋝⋈⪟⫏≰1210110","cot":[{"info":"⫏≰2111022⩨⫏≰2200202=⫏≰-10","layer":1},{"info":"⫏≰21112112⋝⋈⪟⫏≰1210110=⫏≰21112112","layer":1},{"info":"⫏≰-10≎⊠⪸⫏≰21112112=⫏≰1001210","layer":0}]}
{"id":496,"expression_no_base_symbol":"⨞⊢$1447$⇷$1521$","expression":"⨞⊢⫏≰1222121⇷⫏≰2002100","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":20266,"operation_count":2,"complexity_ratio":10133.0,"tree":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":1447,"base":3},"right_expr":{"type":"numeric_atoms","value":1521,"base":3}}},"used_operators":["xUOZtlo3hN","mp7IySMOzn"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"⫏≰-11102010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1447","layer":2},{"info":"number node, value=1521","layer":2},{"info":"compute binary expreesion, left_input=1447, right_input=1521, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=3042","layer":1},{"info":"compute unary expreesion, input=3042, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-3216","layer":0}],"base":3,"result_base":3,"text":"⨞⊢⫏≰1222121⇷⫏≰2002100=⫏≰-11102010","reverse_text":"⫏≰-11102010=⨞⊢⫏≰1222121⇷⫏≰2002100","cot":[{"info":"⫏≰1222121⇷⫏≰2002100=⫏≰11011200","layer":1},{"info":"⨞⊢⫏≰11011200=⫏≰-11102010","layer":0}]}
{"id":497,"expression_no_base_symbol":"($3661$⨸⪁$6217$)⩤","expression":"(⫏≰12000121⨸⪁⫏≰22112021)⩤","highest_n_order":1,"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":3661,"base":3},"right_expr":{"type":"numeric_atoms","value":6217,"base":3}}},"used_operators":["Z2TMIBDE3Q","g55IO6H4Gj"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-1000002201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3661","layer":2},{"info":"number node, value=6217","layer":2},{"info":"compute binary expreesion, left_input=3661, right_input=6217, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=19756","layer":1},{"info":"compute unary expreesion, input=19756, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-19756","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12000121⨸⪁⫏≰22112021)⩤=⫏≰-1000002201","reverse_text":"⫏≰-1000002201=(⫏≰12000121⨸⪁⫏≰22112021)⩤","cot":[{"info":"⫏≰12000121⨸⪁⫏≰22112021=⫏≰1000002201","layer":1},{"info":"⫏≰1000002201⩤=⫏≰-1000002201","layer":0}]}
{"id":498,"expression_no_base_symbol":"($6103$⊭↱$2364$)⩚⊴⇥($5807$-$3604$)","expression":"(⫏≰22101001⊭↱⫏≰10020120)⩚⊴⇥(⫏≰21222002-⫏≰11221111)","highest_n_order":1,"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":6103,"base":3},"right_expr":{"type":"numeric_atoms","value":2364,"base":3}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":5807,"base":3},"right_expr":{"type":"numeric_atoms","value":3604,"base":3}}},"used_operators":["NTOWxs364D","COABgblf1C","rysDP5nf3Z"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21001201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6103","layer":2},{"info":"number node, value=2364","layer":2},{"info":"compute binary expreesion, left_input=6103, right_input=2364, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-7473","layer":1},{"info":"number node, value=5807","layer":2},{"info":"number node, value=3604","layer":2},{"info":"compute binary expreesion, left_input=5807, right_input=3604, op_id = rysDP5nf3Z binary_op_definition= 'None', output=2203","layer":1},{"info":"compute binary expreesion, left_input=-7473, right_input=2203, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=5149","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22101001⊭↱⫏≰10020120)⩚⊴⇥(⫏≰21222002-⫏≰11221111)=⫏≰21001201","reverse_text":"⫏≰21001201=(⫏≰22101001⊭↱⫏≰10020120)⩚⊴⇥(⫏≰21222002-⫏≰11221111)","cot":[{"info":"⫏≰22101001⊭↱⫏≰10020120=⫏≰-101020210","layer":1},{"info":"⫏≰21222002-⫏≰11221111=⫏≰10000121","layer":1},{"info":"⫏≰-101020210⩚⊴⇥⫏≰10000121=⫏≰21001201","layer":0}]}
{"id":499,"expression_no_base_symbol":"($1119$⊦⊿)⋝⋈⪟($2862$+$6239$)","expression":"(⫏≰1112110⊦⊿)⋝⋈⪟(⫏≰10221000+⫏≰22120002)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":10,"operation_count":3,"complexity_ratio":3.3333333333333335,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":1119,"base":3}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":2862,"base":3},"right_expr":{"type":"numeric_atoms","value":6239,"base":3}}},"used_operators":["2DDjHMKMc0","14qkJME0vr","W4YGzv6Whe"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-11201021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1119","layer":2},{"info":"compute unary expreesion, input=1119, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-3436","layer":1},{"info":"number node, value=2862","layer":2},{"info":"number node, value=6239","layer":2},{"info":"compute binary expreesion, left_input=2862, right_input=6239, op_id = W4YGzv6Whe binary_op_definition= 'None', output=9101","layer":1},{"info":"compute binary expreesion, left_input=-3436, right_input=9101, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=-3436","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1112110⊦⊿)⋝⋈⪟(⫏≰10221000+⫏≰22120002)=⫏≰-11201021","reverse_text":"⫏≰-11201021=(⫏≰1112110⊦⊿)⋝⋈⪟(⫏≰10221000+⫏≰22120002)","cot":[{"info":"⫏≰1112110⊦⊿=⫏≰-11201021","layer":1},{"info":"⫏≰10221000+⫏≰22120002=⫏≰110111002","layer":1},{"info":"⫏≰-11201021⋝⋈⪟⫏≰110111002=⫏≰-11201021","layer":0}]}
{"id":500,"expression_no_base_symbol":"(⨵≀≌$1291$)⫡⨏($2985$/$2792$)","expression":"(⨵≀≌⫏≰1202211)⫡⨏(⫏≰11002120/⫏≰10211102)","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":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":1291,"base":3}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":2985,"base":3},"right_expr":{"type":"numeric_atoms","value":2792,"base":3}}},"used_operators":["QMFrweE19q","srAu1WTS94","XhwjNDsVaA"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","rysDP5nf3Z"],"result":"⫏≰-221111011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1291","layer":2},{"info":"compute unary expreesion, input=1291, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-3873","layer":1},{"info":"number node, value=2985","layer":2},{"info":"number node, value=2792","layer":2},{"info":"compute binary expreesion, left_input=2985, right_input=2792, op_id = XhwjNDsVaA binary_op_definition= 'None', output=1","layer":1},{"info":"compute binary expreesion, left_input=-3873, right_input=1, 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=-18580","layer":0}],"base":3,"result_base":3,"text":"(⨵≀≌⫏≰1202211)⫡⨏(⫏≰11002120/⫏≰10211102)=⫏≰-221111011","reverse_text":"⫏≰-221111011=(⨵≀≌⫏≰1202211)⫡⨏(⫏≰11002120/⫏≰10211102)","cot":[{"info":"⨵≀≌⫏≰1202211=⫏≰-12022110","layer":1},{"info":"⫏≰11002120/⫏≰10211102=⫏≰1","layer":1},{"info":"⫏≰-12022110⫡⨏⫏≰1=⫏≰-221111011","layer":0}]}
{"id":501,"expression_no_base_symbol":"$2996$*$2764$⊭↱$4733$⩚⊴⇥$1001$","expression":"⫏≰11002222*⫏≰10210101⊭↱⫏≰20111022⩚⊴⇥⫏≰1101002","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2773,"operation_count":3,"complexity_ratio":924.3333333333334,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":2996,"base":3},"right_expr":{"type":"numeric_atoms","value":2764,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":4733,"base":3},"right_expr":{"type":"numeric_atoms","value":1001,"base":3}}},"used_operators":["COABgblf1C","9HNa5Wba9A","NTOWxs364D"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰-1011012000200210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2996","layer":2},{"info":"number node, value=2764","layer":2},{"info":"compute binary expreesion, left_input=2996, right_input=2764, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=8280944","layer":1},{"info":"number node, value=4733","layer":2},{"info":"number node, value=1001","layer":2},{"info":"compute binary expreesion, left_input=4733, right_input=1001, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-5855","layer":1},{"info":"compute binary expreesion, left_input=8280944, right_input=-5855, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-16573593","layer":0}],"base":3,"result_base":3,"text":"⫏≰11002222*⫏≰10210101⊭↱⫏≰20111022⩚⊴⇥⫏≰1101002=⫏≰-1011012000200210","reverse_text":"⫏≰-1011012000200210=⫏≰11002222*⫏≰10210101⊭↱⫏≰20111022⩚⊴⇥⫏≰1101002","cot":[{"info":"⫏≰11002222*⫏≰10210101=⫏≰120120201022122","layer":1},{"info":"⫏≰20111022⩚⊴⇥⫏≰1101002=⫏≰-22000212","layer":1},{"info":"⫏≰120120201022122⊭↱⫏≰-22000212=⫏≰-1011012000200210","layer":0}]}
{"id":502,"expression_no_base_symbol":"($2434$≧⫂∧$1681$)⪮%⊝(-$6073$)","expression":"(⫏≰10100011≧⫂∧⫏≰2022021)⪮%⊝(-⫏≰22022221)","highest_n_order":2,"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":2434,"base":3},"right_expr":{"type":"numeric_atoms","value":1681,"base":3}},"right_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":6073,"base":3}}},"used_operators":["IWmyXbctLI","Ph9nP6C5qx","t8gj7n24qd"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰10202012","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2434","layer":2},{"info":"number node, value=1681","layer":2},{"info":"compute binary expreesion, left_input=2434, right_input=1681, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=1208","layer":1},{"info":"number node, value=6073","layer":2},{"info":"compute unary expreesion, input=6073, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-6073","layer":1},{"info":"compute binary expreesion, left_input=1208, right_input=-6073, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=2732","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10100011≧⫂∧⫏≰2022021)⪮%⊝(-⫏≰22022221)=⫏≰10202012","reverse_text":"⫏≰10202012=(⫏≰10100011≧⫂∧⫏≰2022021)⪮%⊝(-⫏≰22022221)","cot":[{"info":"⫏≰10100011≧⫂∧⫏≰2022021=⫏≰1122202","layer":1},{"info":"-⫏≰22022221=⫏≰-22022221","layer":1},{"info":"⫏≰1122202⪮%⊝⫏≰-22022221=⫏≰10202012","layer":0}]}
{"id":503,"expression_no_base_symbol":"($6676$⊦⊿)⪛($2643$⊘)","expression":"(⫏≰100011021⊦⊿)⪛(⫏≰10121220⊘)","highest_n_order":2,"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":6676,"base":3}},"right_expr":{"type":"unary","operator":"⊘","unary_expr":{"type":"numeric_atoms","value":2643,"base":3}}},"used_operators":["uFcxV4UQCh","14qkJME0vr","gu96TGCTMs"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6676","layer":2},{"info":"compute unary expreesion, input=6676, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-20107","layer":1},{"info":"number node, value=2643","layer":2},{"info":"compute unary expreesion, input=2643, 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":"compute binary expreesion, left_input=-20107, right_input=0, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰100011021⊦⊿)⪛(⫏≰10121220⊘)=NaN","reverse_text":"NaN=(⫏≰100011021⊦⊿)⪛(⫏≰10121220⊘)","cot":[{"info":"⫏≰100011021⊦⊿=⫏≰-1000120201","layer":1},{"info":"⫏≰10121220⊘=⫏≰0","layer":1},{"info":"⫏≰-1000120201⪛⫏≰0=NaN","layer":0}]}
{"id":504,"expression_no_base_symbol":"∂($2619$⨽$1652$)","expression":"∂(⫏≰10121000⨽⫏≰2021012)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3045,"operation_count":2,"complexity_ratio":1522.5,"tree":{"type":"unary","operator":"∂","unary_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":2619,"base":3},"right_expr":{"type":"numeric_atoms","value":1652,"base":3}}},"used_operators":["Uaa54Peajs","8HhzD0ZcuI"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"⫏≰1102201121122010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2619","layer":2},{"info":"number node, value=1652","layer":2},{"info":"compute binary expreesion, left_input=2619, right_input=1652, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-20581125","layer":1},{"info":"compute unary expreesion, input=-20581125, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=20580861","layer":0}],"base":3,"result_base":3,"text":"∂(⫏≰10121000⨽⫏≰2021012)=⫏≰1102201121122010","reverse_text":"⫏≰1102201121122010=∂(⫏≰10121000⨽⫏≰2021012)","cot":[{"info":"⫏≰10121000⨽⫏≰2021012=⫏≰-1102201121222220","layer":1},{"info":"∂⫏≰-1102201121222220=⫏≰1102201121122010","layer":0}]}
{"id":505,"expression_no_base_symbol":"$2231$≹⇙⪍$1886$⊉≛↸$6158$⨐⩸⫘$8876$","expression":"⫏≰10001122≹⇙⪍⫏≰2120212⊉≛↸⫏≰22110002⨐⩸⫘⫏≰110011202","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4,"operation_count":3,"complexity_ratio":1.3333333333333333,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":2231,"base":3},"right_expr":{"type":"numeric_atoms","value":1886,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":6158,"base":3},"right_expr":{"type":"numeric_atoms","value":8876,"base":3}}},"used_operators":["DZ8iAZOCBD","AHs5Up7iyr","fu6greOZ01"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2231","layer":2},{"info":"number node, value=1886","layer":2},{"info":"compute binary expreesion, left_input=2231, right_input=1886, 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":"number node, value=6158","layer":2},{"info":"number node, value=8876","layer":2},{"info":"compute binary expreesion, left_input=6158, right_input=8876, 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=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":3,"result_base":3,"text":"⫏≰10001122≹⇙⪍⫏≰2120212⊉≛↸⫏≰22110002⨐⩸⫘⫏≰110011202=NaN","reverse_text":"NaN=⫏≰10001122≹⇙⪍⫏≰2120212⊉≛↸⫏≰22110002⨐⩸⫘⫏≰110011202","cot":[{"info":"⫏≰10001122≹⇙⪍⫏≰2120212=NaN","layer":1},{"info":"⫏≰22110002⨐⩸⫘⫏≰110011202=NaN","layer":1},{"info":"NaN⊉≛↸NaN=NaN","layer":0}]}
{"id":506,"expression_no_base_symbol":"$4805$⪛$4475$⋷($2895$/$6130$)","expression":"⫏≰20120222⪛⫏≰20010202⋷(⫏≰10222020/⫏≰22102001)","highest_n_order":2,"priority_hierarchical_complexity":2,"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":4805,"base":3},"right_expr":{"type":"numeric_atoms","value":4475,"base":3}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":2895,"base":3},"right_expr":{"type":"numeric_atoms","value":6130,"base":3}}},"used_operators":["23Mk6UjR3U","uFcxV4UQCh","XhwjNDsVaA"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","rysDP5nf3Z"],"result":"⫏≰-220110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4805","layer":2},{"info":"number node, value=4475","layer":2},{"info":"compute binary expreesion, left_input=4805, right_input=4475, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=330","layer":1},{"info":"number node, value=2895","layer":2},{"info":"number node, value=6130","layer":2},{"info":"compute binary expreesion, left_input=2895, right_input=6130, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute binary expreesion, left_input=330, right_input=0, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-660","layer":0}],"base":3,"result_base":3,"text":"⫏≰20120222⪛⫏≰20010202⋷(⫏≰10222020/⫏≰22102001)=⫏≰-220110","reverse_text":"⫏≰-220110=⫏≰20120222⪛⫏≰20010202⋷(⫏≰10222020/⫏≰22102001)","cot":[{"info":"⫏≰20120222⪛⫏≰20010202=⫏≰110020","layer":1},{"info":"⫏≰10222020/⫏≰22102001=⫏≰0","layer":1},{"info":"⫏≰110020⋷⫏≰0=⫏≰-220110","layer":0}]}
{"id":507,"expression_no_base_symbol":"($3855$⨪↰⇹$1229$)⨟⋌⩍($5025$⋳⪒$3815$)","expression":"(⫏≰12021210⨪↰⇹⫏≰1200112)⨟⋌⩍(⫏≰20220010⋳⪒⫏≰12020022)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3863,"operation_count":3,"complexity_ratio":1287.6666666666667,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":3855,"base":3},"right_expr":{"type":"numeric_atoms","value":1229,"base":3}},"right_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":5025,"base":3},"right_expr":{"type":"numeric_atoms","value":3815,"base":3}}},"used_operators":["rGHVDoGpnC","tmPS8pqC7x","12rbrZMWeM"],"dependent_operators":["Tcnh7f0tEr","rJVOvQCfKK","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3855","layer":2},{"info":"number node, value=1229","layer":2},{"info":"compute binary expreesion, left_input=3855, right_input=1229, 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=3855","layer":1},{"info":"number node, value=5025","layer":2},{"info":"number node, value=3815","layer":2},{"info":"compute binary expreesion, left_input=5025, right_input=3815, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=5948","layer":1},{"info":"compute binary expreesion, left_input=3855, right_input=5948, 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":0}],"base":3,"result_base":3,"text":"(⫏≰12021210⨪↰⇹⫏≰1200112)⨟⋌⩍(⫏≰20220010⋳⪒⫏≰12020022)=NaN","reverse_text":"NaN=(⫏≰12021210⨪↰⇹⫏≰1200112)⨟⋌⩍(⫏≰20220010⋳⪒⫏≰12020022)","cot":[{"info":"⫏≰12021210⨪↰⇹⫏≰1200112=⫏≰12021210","layer":1},{"info":"⫏≰20220010⋳⪒⫏≰12020022=⫏≰22011022","layer":1},{"info":"⫏≰12021210⨟⋌⩍⫏≰22011022=NaN","layer":0}]}
{"id":508,"expression_no_base_symbol":"($1340$⪠⩆⊳)⋓(↔$4468$)","expression":"(⫏≰1211122⪠⩆⊳)⋓(↔⫏≰20010111)","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":1340,"base":3}},"right_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":4468,"base":3}}},"used_operators":["T2fj7uvVaJ","JLbD19bQDL","ruOEQAzv1W"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1340","layer":2},{"info":"compute unary expreesion, input=1340, 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=4468","layer":2},{"info":"compute unary expreesion, input=4468, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-4195","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-4195, 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":3,"result_base":3,"text":"(⫏≰1211122⪠⩆⊳)⋓(↔⫏≰20010111)=⫏≰0","reverse_text":"⫏≰0=(⫏≰1211122⪠⩆⊳)⋓(↔⫏≰20010111)","cot":[{"info":"⫏≰1211122⪠⩆⊳=⫏≰0","layer":1},{"info":"↔⫏≰20010111=⫏≰-12202101","layer":1},{"info":"⫏≰0⋓⫏≰-12202101=⫏≰0","layer":0}]}
{"id":509,"expression_no_base_symbol":"($1962$*$6709$)≭($7359$∲⫓$1020$)","expression":"(⫏≰2200200*⫏≰100012111)≭(⫏≰101002120∲⫓⫏≰1101210)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1965,"operation_count":3,"complexity_ratio":655.0,"tree":{"type":"binary","operator":"≭","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1962,"base":3},"right_expr":{"type":"numeric_atoms","value":6709,"base":3}},"right_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":7359,"base":3},"right_expr":{"type":"numeric_atoms","value":1020,"base":3}}},"used_operators":["rxpJgHHUmx","9HNa5Wba9A","i8ToyICDmI"],"dependent_operators":["AHs5Up7iyr","W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1962","layer":2},{"info":"number node, value=6709","layer":2},{"info":"compute binary expreesion, left_input=1962, right_input=6709, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=13163058","layer":1},{"info":"number node, value=7359","layer":2},{"info":"number node, value=1020","layer":2},{"info":"compute binary expreesion, left_input=7359, right_input=1020, 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=13163058, right_input=0, 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=-22","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2200200*⫏≰100012111)≭(⫏≰101002120∲⫓⫏≰1101210)=⫏≰-211","reverse_text":"⫏≰-211=(⫏≰2200200*⫏≰100012111)≭(⫏≰101002120∲⫓⫏≰1101210)","cot":[{"info":"⫏≰2200200*⫏≰100012111=⫏≰220202202022200","layer":1},{"info":"⫏≰101002120∲⫓⫏≰1101210=⫏≰0","layer":1},{"info":"⫏≰220202202022200≭⫏≰0=⫏≰-211","layer":0}]}
{"id":510,"expression_no_base_symbol":"$2147$⪮%⊝$2410$↺$3191$⨓$3317$","expression":"⫏≰2221112⪮%⊝⫏≰10022021↺⫏≰11101012⨓⫏≰11112212","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3334,"operation_count":3,"complexity_ratio":1111.3333333333333,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":2147,"base":3},"right_expr":{"type":"numeric_atoms","value":2410,"base":3}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":3191,"base":3},"right_expr":{"type":"numeric_atoms","value":3317,"base":3}}},"used_operators":["7j4O788W3g","IWmyXbctLI","3ViojmjbAp"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⫏≰-11112222","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2147","layer":2},{"info":"number node, value=2410","layer":2},{"info":"compute binary expreesion, left_input=2147, right_input=2410, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=4610","layer":1},{"info":"number node, value=3191","layer":2},{"info":"number node, value=3317","layer":2},{"info":"compute binary expreesion, left_input=3191, right_input=3317, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-3320","layer":1},{"info":"compute binary expreesion, left_input=4610, right_input=-3320, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=-3320","layer":0}],"base":3,"result_base":3,"text":"⫏≰2221112⪮%⊝⫏≰10022021↺⫏≰11101012⨓⫏≰11112212=⫏≰-11112222","reverse_text":"⫏≰-11112222=⫏≰2221112⪮%⊝⫏≰10022021↺⫏≰11101012⨓⫏≰11112212","cot":[{"info":"⫏≰2221112⪮%⊝⫏≰10022021=⫏≰20022202","layer":1},{"info":"⫏≰11101012⨓⫏≰11112212=⫏≰-11112222","layer":1},{"info":"⫏≰20022202↺⫏≰-11112222=⫏≰-11112222","layer":0}]}
{"id":511,"expression_no_base_symbol":"$4392$⩷∴$1816$⇼⇔∾($5801$⪨≂$1703$)","expression":"⫏≰20000200⩷∴⫏≰2111021⇼⇔∾(⫏≰21221212⪨≂⫏≰2100002)","highest_n_order":1,"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":4392,"base":3},"right_expr":{"type":"numeric_atoms","value":1816,"base":3}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":5801,"base":3},"right_expr":{"type":"numeric_atoms","value":1703,"base":3}}},"used_operators":["tifHPKVTfV","9FxExcQeMw","sdazOOVcIp"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰11100201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4392","layer":2},{"info":"number node, value=1816","layer":2},{"info":"compute binary expreesion, left_input=4392, right_input=1816, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=5120","layer":1},{"info":"number node, value=5801","layer":2},{"info":"number node, value=1703","layer":2},{"info":"compute binary expreesion, left_input=5801, right_input=1703, 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=8298","layer":1},{"info":"compute binary expreesion, left_input=5120, right_input=8298, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=3178","layer":0}],"base":3,"result_base":3,"text":"⫏≰20000200⩷∴⫏≰2111021⇼⇔∾(⫏≰21221212⪨≂⫏≰2100002)=⫏≰11100201","reverse_text":"⫏≰11100201=⫏≰20000200⩷∴⫏≰2111021⇼⇔∾(⫏≰21221212⪨≂⫏≰2100002)","cot":[{"info":"⫏≰20000200⩷∴⫏≰2111021=⫏≰21000122","layer":1},{"info":"⫏≰21221212⪨≂⫏≰2100002=⫏≰102101100","layer":1},{"info":"⫏≰21000122⇼⇔∾⫏≰102101100=⫏≰11100201","layer":0}]}
{"id":512,"expression_no_base_symbol":"($4585$⨽$1627$)⋝⋈⪟(⨰⫟⨤$3884$)","expression":"(⫏≰20021211⨽⫏≰2020021)⋝⋈⪟(⨰⫟⨤⫏≰12022212)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19293,"operation_count":3,"complexity_ratio":6431.0,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":4585,"base":3},"right_expr":{"type":"numeric_atoms","value":1627,"base":3}},"right_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":3884,"base":3}}},"used_operators":["2DDjHMKMc0","8HhzD0ZcuI","Tw270M8GLb"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4585","layer":2},{"info":"number node, value=1627","layer":2},{"info":"compute binary expreesion, left_input=4585, right_input=1627, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-63070242","layer":1},{"info":"number node, value=3884","layer":2},{"info":"compute unary expreesion, input=3884, 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=-63070242, right_input=nan, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20021211⨽⫏≰2020021)⋝⋈⪟(⨰⫟⨤⫏≰12022212)=NaN","reverse_text":"NaN=(⫏≰20021211⨽⫏≰2020021)⋝⋈⪟(⨰⫟⨤⫏≰12022212)","cot":[{"info":"⫏≰20021211⨽⫏≰2020021=⫏≰-11101200022002220","layer":1},{"info":"⨰⫟⨤⫏≰12022212=NaN","layer":1},{"info":"⫏≰-11101200022002220⋝⋈⪟NaN=NaN","layer":0}]}
{"id":513,"expression_no_base_symbol":"($2545$⊭↱$2152$)⨳⩥⨓($3309$∲⫓$3792$)","expression":"(⫏≰10111021⊭↱⫏≰2221201)⨳⩥⨓(⫏≰11112120∲⫓⫏≰12012110)","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":2545,"base":3},"right_expr":{"type":"numeric_atoms","value":2152,"base":3}},"right_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":3309,"base":3},"right_expr":{"type":"numeric_atoms","value":3792,"base":3}}},"used_operators":["nCS4ZIUYfx","COABgblf1C","i8ToyICDmI"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1001221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2545","layer":2},{"info":"number node, value=2152","layer":2},{"info":"compute binary expreesion, left_input=2545, right_input=2152, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-781","layer":1},{"info":"number node, value=3309","layer":2},{"info":"number node, value=3792","layer":2},{"info":"compute binary expreesion, left_input=3309, right_input=3792, 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=-781, right_input=0, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=781","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10111021⊭↱⫏≰2221201)⨳⩥⨓(⫏≰11112120∲⫓⫏≰12012110)=⫏≰1001221","reverse_text":"⫏≰1001221=(⫏≰10111021⊭↱⫏≰2221201)⨳⩥⨓(⫏≰11112120∲⫓⫏≰12012110)","cot":[{"info":"⫏≰10111021⊭↱⫏≰2221201=⫏≰-1001221","layer":1},{"info":"⫏≰11112120∲⫓⫏≰12012110=⫏≰0","layer":1},{"info":"⫏≰-1001221⨳⩥⨓⫏≰0=⫏≰1001221","layer":0}]}
{"id":514,"expression_no_base_symbol":"$1191$≭$3831$⨽$1327$≎⊠⪸$1401$","expression":"⫏≰1122010≭⫏≰12020220⨽⫏≰1211011≎⊠⪸⫏≰1220220","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":281,"operation_count":3,"complexity_ratio":93.66666666666667,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":1191,"base":3},"right_expr":{"type":"numeric_atoms","value":3831,"base":3}},"right_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1327,"base":3},"right_expr":{"type":"numeric_atoms","value":1401,"base":3}}},"used_operators":["8HhzD0ZcuI","rxpJgHHUmx","bJkvcejdHO"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","AHs5Up7iyr","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1191","layer":2},{"info":"number node, value=3831","layer":2},{"info":"compute binary expreesion, left_input=1191, right_input=3831, 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=1327","layer":2},{"info":"number node, value=1401","layer":2},{"info":"compute binary expreesion, left_input=1327, right_input=1401, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=343220","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=343220, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1122010≭⫏≰12020220⨽⫏≰1211011≎⊠⪸⫏≰1220220=NaN","reverse_text":"NaN=⫏≰1122010≭⫏≰12020220⨽⫏≰1211011≎⊠⪸⫏≰1220220","cot":[{"info":"⫏≰1122010≭⫏≰12020220=NaN","layer":1},{"info":"⫏≰1211011≎⊠⪸⫏≰1220220=⫏≰122102210212","layer":1},{"info":"NaN⨽⫏≰122102210212=NaN","layer":0}]}
{"id":515,"expression_no_base_symbol":"(≦∁$1354$)≦≮≮","expression":"(≦∁⫏≰1212011)≦≮≮","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4,"operation_count":2,"complexity_ratio":2.0,"tree":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":1354,"base":3}}},"used_operators":["D4vGDi5EA2","9ICcGScMcE"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"⫏≰-12120110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1354","layer":2},{"info":"compute unary expreesion, input=1354, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=1354","layer":1},{"info":"compute unary expreesion, input=1354, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-4062","layer":0}],"base":3,"result_base":3,"text":"(≦∁⫏≰1212011)≦≮≮=⫏≰-12120110","reverse_text":"⫏≰-12120110=(≦∁⫏≰1212011)≦≮≮","cot":[{"info":"≦∁⫏≰1212011=⫏≰1212011","layer":1},{"info":"⫏≰1212011≦≮≮=⫏≰-12120110","layer":0}]}
{"id":516,"expression_no_base_symbol":"$5968$≹⇙⪍$2113$⨓(⨑⩽⪐$4877$)","expression":"⫏≰22012001≹⇙⪍⫏≰2220021⨓(⨑⩽⪐⫏≰20200122)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4615,"operation_count":3,"complexity_ratio":1538.3333333333333,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":5968,"base":3},"right_expr":{"type":"numeric_atoms","value":2113,"base":3}},"right_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":4877,"base":3}}},"used_operators":["3ViojmjbAp","AHs5Up7iyr","AF7qkfDlqP"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","dWAJyo7jo9","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰20022102","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5968","layer":2},{"info":"number node, value=2113","layer":2},{"info":"compute binary expreesion, left_input=5968, right_input=2113, 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":"number node, value=4877","layer":2},{"info":"compute unary expreesion, input=4877, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-4604","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-4604, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=4601","layer":0}],"base":3,"result_base":3,"text":"⫏≰22012001≹⇙⪍⫏≰2220021⨓(⨑⩽⪐⫏≰20200122)=⫏≰20022102","reverse_text":"⫏≰20022102=⫏≰22012001≹⇙⪍⫏≰2220021⨓(⨑⩽⪐⫏≰20200122)","cot":[{"info":"⫏≰22012001≹⇙⪍⫏≰2220021=NaN","layer":1},{"info":"⨑⩽⪐⫏≰20200122=⫏≰-20022112","layer":1},{"info":"NaN⨓⫏≰-20022112=⫏≰20022102","layer":0}]}
{"id":517,"expression_no_base_symbol":"($1099$⩷∴$4486$)⨟⋌⩍($2682$∧)","expression":"(⫏≰1111201⩷∴⫏≰20011011)⨟⋌⩍(⫏≰10200100∧)","highest_n_order":5,"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":1099,"base":3},"right_expr":{"type":"numeric_atoms","value":4486,"base":3}},"right_expr":{"type":"unary","operator":"∧","unary_expr":{"type":"numeric_atoms","value":2682,"base":3}}},"used_operators":["rGHVDoGpnC","9FxExcQeMw","z63VuFQld9"],"dependent_operators":["Tcnh7f0tEr","rysDP5nf3Z","B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1099","layer":2},{"info":"number node, value=4486","layer":2},{"info":"compute binary expreesion, left_input=1099, right_input=4486, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-6806","layer":1},{"info":"number node, value=2682","layer":2},{"info":"compute unary expreesion, input=2682, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-6806, right_input=nan, 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":0}],"base":3,"result_base":3,"text":"(⫏≰1111201⩷∴⫏≰20011011)⨟⋌⩍(⫏≰10200100∧)=NaN","reverse_text":"NaN=(⫏≰1111201⩷∴⫏≰20011011)⨟⋌⩍(⫏≰10200100∧)","cot":[{"info":"⫏≰1111201⩷∴⫏≰20011011=⫏≰-100100002","layer":1},{"info":"⫏≰10200100∧=NaN","layer":1},{"info":"⫏≰-100100002⨟⋌⩍NaN=NaN","layer":0}]}
{"id":518,"expression_no_base_symbol":"($1545$⊪)⨽(⫓⪴$2699$)","expression":"(⫏≰2010020⊪)⨽(⫓⪴⫏≰10200222)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2742,"operation_count":3,"complexity_ratio":914.0,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":1545,"base":3}},"right_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":2699,"base":3}}},"used_operators":["8HhzD0ZcuI","zVYPLywUTj","eLxqMNBOBk"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL","9HNa5Wba9A"],"result":"⫏≰-1112010012222110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1545","layer":2},{"info":"compute unary expreesion, input=1545, 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":"number node, value=2699","layer":2},{"info":"compute unary expreesion, input=2699, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=7284601","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=7284601, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-21852489","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2010020⊪)⨽(⫓⪴⫏≰10200222)=⫏≰-1112010012222110","reverse_text":"⫏≰-1112010012222110=(⫏≰2010020⊪)⨽(⫓⪴⫏≰10200222)","cot":[{"info":"⫏≰2010020⊪=⫏≰0","layer":1},{"info":"⫓⪴⫏≰10200222=⫏≰111201002121001","layer":1},{"info":"⫏≰0⨽⫏≰111201002121001=⫏≰-1112010012222110","layer":0}]}
{"id":519,"expression_no_base_symbol":"$3873$+⇶⊼$3630$/$1711$⪘⫢$4301$","expression":"⫏≰12022110+⇶⊼⫏≰11222110/⫏≰2100101⪘⫢⫏≰12220022","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":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":3873,"base":3},"right_expr":{"type":"numeric_atoms","value":3630,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1711,"base":3},"right_expr":{"type":"numeric_atoms","value":4301,"base":3}}},"used_operators":["XhwjNDsVaA","TpPTUOHfaN","oacrs7FA3X"],"dependent_operators":["rysDP5nf3Z","AHs5Up7iyr","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3873","layer":2},{"info":"number node, value=3630","layer":2},{"info":"compute binary expreesion, left_input=3873, right_input=3630, 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":1},{"info":"number node, value=1711","layer":2},{"info":"number node, value=4301","layer":2},{"info":"compute binary expreesion, left_input=1711, right_input=4301, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=3298","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=3298, op_id = XhwjNDsVaA binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰12022110+⇶⊼⫏≰11222110/⫏≰2100101⪘⫢⫏≰12220022=NaN","reverse_text":"NaN=⫏≰12022110+⇶⊼⫏≰11222110/⫏≰2100101⪘⫢⫏≰12220022","cot":[{"info":"⫏≰12022110+⇶⊼⫏≰11222110=NaN","layer":1},{"info":"⫏≰2100101⪘⫢⫏≰12220022=⫏≰11112011","layer":1},{"info":"NaN/⫏≰11112011=NaN","layer":0}]}
{"id":520,"expression_no_base_symbol":"(+⊝⨔$1041$)↺($1275$↙$1035$)","expression":"(+⊝⨔⫏≰1102120)↺(⫏≰1202020↙⫏≰1102100)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1080,"operation_count":3,"complexity_ratio":360.0,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":1041,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":1275,"base":3},"right_expr":{"type":"numeric_atoms","value":1035,"base":3}}},"used_operators":["7j4O788W3g","DhbWaqg5eL","yyfyN0ffXY"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰-11021000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1041","layer":2},{"info":"compute unary expreesion, input=1041, 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=1275","layer":2},{"info":"number node, value=1035","layer":2},{"info":"compute binary expreesion, left_input=1275, right_input=1035, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-3105","layer":1},{"info":"compute binary expreesion, left_input=1522, right_input=-3105, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=-3105","layer":0}],"base":3,"result_base":3,"text":"(+⊝⨔⫏≰1102120)↺(⫏≰1202020↙⫏≰1102100)=⫏≰-11021000","reverse_text":"⫏≰-11021000=(+⊝⨔⫏≰1102120)↺(⫏≰1202020↙⫏≰1102100)","cot":[{"info":"+⊝⨔⫏≰1102120=⫏≰2002101","layer":1},{"info":"⫏≰1202020↙⫏≰1102100=⫏≰-11021000","layer":1},{"info":"⫏≰2002101↺⫏≰-11021000=⫏≰-11021000","layer":0}]}
{"id":521,"expression_no_base_symbol":"$2332$↬$2301$↪⪝","expression":"⫏≰10012101↬⫏≰10011020↪⪝","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":2,"complexity_ratio":3.0,"tree":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":2332,"base":3},"right_expr":{"type":"numeric_atoms","value":2301,"base":3}}},"used_operators":["l07mrZUIn9","B5M0gjZbta"],"dependent_operators":["9HNa5Wba9A","2DDjHMKMc0","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2332","layer":2},{"info":"number node, value=2301","layer":2},{"info":"compute binary expreesion, left_input=2332, right_input=2301, 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 = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰10012101↬⫏≰10011020↪⪝=NaN","reverse_text":"NaN=⫏≰10012101↬⫏≰10011020↪⪝","cot":[{"info":"⫏≰10012101↬⫏≰10011020=NaN","layer":1},{"info":"NaN↪⪝=NaN","layer":0}]}
{"id":522,"expression_no_base_symbol":"⨈⫕$1574$⋳⪒$2538$","expression":"⨈⫕⫏≰2011022⋳⪒⫏≰10111000","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":393,"operation_count":2,"complexity_ratio":196.5,"tree":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":1574,"base":3},"right_expr":{"type":"numeric_atoms","value":2538,"base":3}}},"used_operators":["megm06wKyl","12rbrZMWeM"],"dependent_operators":["8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1574","layer":2},{"info":"number node, value=2538","layer":2},{"info":"compute binary expreesion, left_input=1574, right_input=2538, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=323","layer":1},{"info":"compute unary expreesion, input=323, 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":3,"result_base":3,"text":"⨈⫕⫏≰2011022⋳⪒⫏≰10111000=⫏≰-210","reverse_text":"⫏≰-210=⨈⫕⫏≰2011022⋳⪒⫏≰10111000","cot":[{"info":"⫏≰2011022⋳⪒⫏≰10111000=⫏≰102222","layer":1},{"info":"⨈⫕⫏≰102222=⫏≰-210","layer":0}]}
{"id":523,"expression_no_base_symbol":"(≦∁$3438$)⊴($3163$⪛$2711$)","expression":"(≦∁⫏≰11201100)⊴(⫏≰11100011⪛⫏≰10201102)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":834,"operation_count":3,"complexity_ratio":278.0,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":3438,"base":3}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":3163,"base":3},"right_expr":{"type":"numeric_atoms","value":2711,"base":3}}},"used_operators":["Nsiff2A1zJ","9ICcGScMcE","uFcxV4UQCh"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3438","layer":2},{"info":"compute unary expreesion, input=3438, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=3438","layer":1},{"info":"number node, value=3163","layer":2},{"info":"number node, value=2711","layer":2},{"info":"compute binary expreesion, left_input=3163, right_input=2711, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=452","layer":1},{"info":"compute binary expreesion, left_input=3438, right_input=452, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(≦∁⫏≰11201100)⊴(⫏≰11100011⪛⫏≰10201102)=NaN","reverse_text":"NaN=(≦∁⫏≰11201100)⊴(⫏≰11100011⪛⫏≰10201102)","cot":[{"info":"≦∁⫏≰11201100=⫏≰11201100","layer":1},{"info":"⫏≰11100011⪛⫏≰10201102=⫏≰121202","layer":1},{"info":"⫏≰11201100⊴⫏≰121202=NaN","layer":0}]}
{"id":524,"expression_no_base_symbol":"⨰⫟⨤($1192$-$1892$)","expression":"⨰⫟⨤(⫏≰1122011-⫏≰2121002)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3693,"operation_count":2,"complexity_ratio":1846.5,"tree":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1192,"base":3},"right_expr":{"type":"numeric_atoms","value":1892,"base":3}}},"used_operators":["Tw270M8GLb","rysDP5nf3Z"],"dependent_operators":["sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1192","layer":2},{"info":"number node, value=1892","layer":2},{"info":"compute binary expreesion, left_input=1192, right_input=1892, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-700","layer":1},{"info":"compute unary expreesion, input=-700, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⨰⫟⨤(⫏≰1122011-⫏≰2121002)=NaN","reverse_text":"NaN=⨰⫟⨤(⫏≰1122011-⫏≰2121002)","cot":[{"info":"⫏≰1122011-⫏≰2121002=⫏≰-221221","layer":1},{"info":"⨰⫟⨤⫏≰-221221=NaN","layer":0}]}
{"id":525,"expression_no_base_symbol":"$2979$⋝⋈⪟$2779$∲⫓(⊄⩳↩$1019$)","expression":"⫏≰11002100⋝⋈⪟⫏≰10210221∲⫓(⊄⩳↩⫏≰1101202)","highest_n_order":1,"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":2979,"base":3},"right_expr":{"type":"numeric_atoms","value":2779,"base":3}},"right_expr":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":1019,"base":3}}},"used_operators":["i8ToyICDmI","2DDjHMKMc0","8w2t5hMYqp"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰11002100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2979","layer":2},{"info":"number node, value=2779","layer":2},{"info":"compute binary expreesion, left_input=2979, right_input=2779, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=2979","layer":1},{"info":"number node, value=1019","layer":2},{"info":"compute unary expreesion, input=1019, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-3057","layer":1},{"info":"compute binary expreesion, left_input=2979, right_input=-3057, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=2979","layer":0}],"base":3,"result_base":3,"text":"⫏≰11002100⋝⋈⪟⫏≰10210221∲⫓(⊄⩳↩⫏≰1101202)=⫏≰11002100","reverse_text":"⫏≰11002100=⫏≰11002100⋝⋈⪟⫏≰10210221∲⫓(⊄⩳↩⫏≰1101202)","cot":[{"info":"⫏≰11002100⋝⋈⪟⫏≰10210221=⫏≰11002100","layer":1},{"info":"⊄⩳↩⫏≰1101202=⫏≰-11012020","layer":1},{"info":"⫏≰11002100∲⫓⫏≰-11012020=⫏≰11002100","layer":0}]}
{"id":526,"expression_no_base_symbol":"(≦∁$7696$)∧","expression":"(≦∁⫏≰101120001)∧","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7,"operation_count":2,"complexity_ratio":3.5,"tree":{"type":"unary","operator":"∧","unary_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":7696,"base":3}}},"used_operators":["z63VuFQld9","9ICcGScMcE"],"dependent_operators":["B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7696","layer":2},{"info":"compute unary expreesion, input=7696, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=7696","layer":1},{"info":"compute unary expreesion, input=7696, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(≦∁⫏≰101120001)∧=NaN","reverse_text":"NaN=(≦∁⫏≰101120001)∧","cot":[{"info":"≦∁⫏≰101120001=⫏≰101120001","layer":1},{"info":"⫏≰101120001∧=NaN","layer":0}]}
{"id":527,"expression_no_base_symbol":"(⇁⨣⪵$1833$)⩷∴($2222$≋⫹)","expression":"(⇁⨣⪵⫏≰2111220)⩷∴(⫏≰10001022≋⫹)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":10,"operation_count":3,"complexity_ratio":3.3333333333333335,"tree":{"type":"binary","operator":"⩷∴","left_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":1833,"base":3}},"right_expr":{"type":"unary","operator":"≋⫹","unary_expr":{"type":"numeric_atoms","value":2222,"base":3}}},"used_operators":["9FxExcQeMw","inkyxCbjAn","N41Kp7NANJ"],"dependent_operators":["rysDP5nf3Z","B5M0gjZbta","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1833","layer":2},{"info":"compute unary expreesion, input=1833, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"number node, value=2222","layer":2},{"info":"compute unary expreesion, input=2222, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-4444","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-4444, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⇁⨣⪵⫏≰2111220)⩷∴(⫏≰10001022≋⫹)=NaN","reverse_text":"NaN=(⇁⨣⪵⫏≰2111220)⩷∴(⫏≰10001022≋⫹)","cot":[{"info":"⇁⨣⪵⫏≰2111220=NaN","layer":1},{"info":"⫏≰10001022≋⫹=⫏≰-20002121","layer":1},{"info":"NaN⩷∴⫏≰-20002121=NaN","layer":0}]}
{"id":528,"expression_no_base_symbol":"(⩦⩻⨪$1788$)⨪↰⇹($2177$⋥≓≎$4228$)","expression":"(⩦⩻⨪⫏≰2110020)⨪↰⇹(⫏≰2222122⋥≓≎⫏≰12210121)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1795,"operation_count":3,"complexity_ratio":598.3333333333334,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":1788,"base":3}},"right_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":2177,"base":3},"right_expr":{"type":"numeric_atoms","value":4228,"base":3}}},"used_operators":["tmPS8pqC7x","2td37pGCOC","Qy55tPpLXF"],"dependent_operators":["rJVOvQCfKK","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰2110020","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1788","layer":2},{"info":"compute unary expreesion, input=1788, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=1788","layer":1},{"info":"number node, value=2177","layer":2},{"info":"number node, value=4228","layer":2},{"info":"compute binary expreesion, left_input=2177, right_input=4228, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=6312","layer":1},{"info":"compute binary expreesion, left_input=1788, right_input=6312, 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":0}],"base":3,"result_base":3,"text":"(⩦⩻⨪⫏≰2110020)⨪↰⇹(⫏≰2222122⋥≓≎⫏≰12210121)=⫏≰2110020","reverse_text":"⫏≰2110020=(⩦⩻⨪⫏≰2110020)⨪↰⇹(⫏≰2222122⋥≓≎⫏≰12210121)","cot":[{"info":"⩦⩻⨪⫏≰2110020=⫏≰2110020","layer":1},{"info":"⫏≰2222122⋥≓≎⫏≰12210121=⫏≰22122210","layer":1},{"info":"⫏≰2110020⨪↰⇹⫏≰22122210=⫏≰2110020","layer":0}]}
{"id":529,"expression_no_base_symbol":"∂($1982$⋓$8142$)","expression":"∂(⫏≰2201102⋓⫏≰102011120)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":430,"operation_count":2,"complexity_ratio":215.0,"tree":{"type":"unary","operator":"∂","unary_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":1982,"base":3},"right_expr":{"type":"numeric_atoms","value":8142,"base":3}}},"used_operators":["Uaa54Peajs","T2fj7uvVaJ"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⫏≰-100210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1982","layer":2},{"info":"number node, value=8142","layer":2},{"info":"compute binary expreesion, left_input=1982, right_input=8142, 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 = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=-264","layer":0}],"base":3,"result_base":3,"text":"∂(⫏≰2201102⋓⫏≰102011120)=⫏≰-100210","reverse_text":"⫏≰-100210=∂(⫏≰2201102⋓⫏≰102011120)","cot":[{"info":"⫏≰2201102⋓⫏≰102011120=⫏≰0","layer":1},{"info":"∂⫏≰0=⫏≰-100210","layer":0}]}
{"id":530,"expression_no_base_symbol":"⇁⨣⪵($1939$∲⫓$2288$)","expression":"⇁⨣⪵(⫏≰2122211∲⫓⫏≰10010202)","highest_n_order":5,"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":1939,"base":3},"right_expr":{"type":"numeric_atoms","value":2288,"base":3}}},"used_operators":["inkyxCbjAn","i8ToyICDmI"],"dependent_operators":["B5M0gjZbta","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1939","layer":2},{"info":"number node, value=2288","layer":2},{"info":"compute binary expreesion, left_input=1939, right_input=2288, 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 = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵(⫏≰2122211∲⫓⫏≰10010202)=⫏≰0","reverse_text":"⫏≰0=⇁⨣⪵(⫏≰2122211∲⫓⫏≰10010202)","cot":[{"info":"⫏≰2122211∲⫓⫏≰10010202=⫏≰0","layer":1},{"info":"⇁⨣⪵⫏≰0=⫏≰0","layer":0}]}
{"id":531,"expression_no_base_symbol":"(↥$1279$)⪄(↥$2064$)","expression":"(↥⫏≰1202101)⪄(↥⫏≰2211110)","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":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":1279,"base":3}},"right_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":2064,"base":3}}},"used_operators":["SUmda5xLS4","A8NUZmVepG"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","k8jYdgA6NY"],"result":"⫏≰11102101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1279","layer":2},{"info":"compute unary expreesion, input=1279, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=4","layer":1},{"info":"number node, value=2064","layer":2},{"info":"compute unary expreesion, input=2064, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=24","layer":1},{"info":"compute binary expreesion, left_input=4, right_input=24, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=3223","layer":0}],"base":3,"result_base":3,"text":"(↥⫏≰1202101)⪄(↥⫏≰2211110)=⫏≰11102101","reverse_text":"⫏≰11102101=(↥⫏≰1202101)⪄(↥⫏≰2211110)","cot":[{"info":"↥⫏≰1202101=⫏≰11","layer":1},{"info":"↥⫏≰2211110=⫏≰220","layer":1},{"info":"⫏≰11⪄⫏≰220=⫏≰11102101","layer":0}]}
{"id":532,"expression_no_base_symbol":"(+⊝⨔$2950$)⪒(⫛⫱⨽$7396$)","expression":"(+⊝⨔⫏≰11001021)⪒(⫛⫱⨽⫏≰101010221)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1465,"operation_count":3,"complexity_ratio":488.3333333333333,"tree":{"type":"binary","operator":"⪒","left_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":2950,"base":3}},"right_expr":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"numeric_atoms","value":7396,"base":3}}},"used_operators":["f6k1SAg4EE","DhbWaqg5eL","DlLNRPXxWL"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","rGHVDoGpnC"],"result":"⫏≰-2002101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2950","layer":2},{"info":"compute unary expreesion, input=2950, 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=7396","layer":2},{"info":"compute unary expreesion, input=7396, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=1522, right_input=0, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-1522","layer":0}],"base":3,"result_base":3,"text":"(+⊝⨔⫏≰11001021)⪒(⫛⫱⨽⫏≰101010221)=⫏≰-2002101","reverse_text":"⫏≰-2002101=(+⊝⨔⫏≰11001021)⪒(⫛⫱⨽⫏≰101010221)","cot":[{"info":"+⊝⨔⫏≰11001021=⫏≰2002101","layer":1},{"info":"⫛⫱⨽⫏≰101010221=⫏≰0","layer":1},{"info":"⫏≰2002101⪒⫏≰0=⫏≰-2002101","layer":0}]}
{"id":533,"expression_no_base_symbol":"$1545$⪢$3933$↛⩡⫤","expression":"⫏≰2010020⪢⫏≰12101200↛⩡⫤","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3996,"operation_count":2,"complexity_ratio":1998.0,"tree":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1545,"base":3},"right_expr":{"type":"numeric_atoms","value":3933,"base":3}}},"used_operators":["FU0Cs4j7VP","dWAJyo7jo9"],"dependent_operators":["8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1545","layer":2},{"info":"number node, value=3933","layer":2},{"info":"compute binary expreesion, left_input=1545, right_input=3933, 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 unary expreesion, input=nan, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2010020⪢⫏≰12101200↛⩡⫤=NaN","reverse_text":"NaN=⫏≰2010020⪢⫏≰12101200↛⩡⫤","cot":[{"info":"⫏≰2010020⪢⫏≰12101200=NaN","layer":1},{"info":"NaN↛⩡⫤=NaN","layer":0}]}
{"id":534,"expression_no_base_symbol":"(↥$5657$)⇼⇔∾$1586$⪢$2352$","expression":"(↥⫏≰21202112)⇼⇔∾⫏≰2011202⪢⫏≰10020010","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2464,"operation_count":3,"complexity_ratio":821.3333333333334,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":5657,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1586,"base":3},"right_expr":{"type":"numeric_atoms","value":2352,"base":3}}},"used_operators":["tifHPKVTfV","A8NUZmVepG","dWAJyo7jo9"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","k8jYdgA6NY","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5657","layer":2},{"info":"compute unary expreesion, input=5657, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=47","layer":1},{"info":"number node, value=1586","layer":2},{"info":"number node, value=2352","layer":2},{"info":"compute binary expreesion, left_input=1586, right_input=2352, 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=47, right_input=nan, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(↥⫏≰21202112)⇼⇔∾⫏≰2011202⪢⫏≰10020010=NaN","reverse_text":"NaN=(↥⫏≰21202112)⇼⇔∾⫏≰2011202⪢⫏≰10020010","cot":[{"info":"↥⫏≰21202112=⫏≰1202","layer":1},{"info":"⫏≰2011202⪢⫏≰10020010=NaN","layer":1},{"info":"⫏≰1202⇼⇔∾NaN=NaN","layer":0}]}
{"id":535,"expression_no_base_symbol":"∂($5082$⨳⩥⨓$2152$)","expression":"∂(⫏≰20222020⨳⩥⨓⫏≰2221201)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":420,"operation_count":2,"complexity_ratio":210.0,"tree":{"type":"unary","operator":"∂","unary_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":5082,"base":3},"right_expr":{"type":"numeric_atoms","value":2152,"base":3}}},"used_operators":["Uaa54Peajs","nCS4ZIUYfx"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰10122202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5082","layer":2},{"info":"number node, value=2152","layer":2},{"info":"compute binary expreesion, left_input=5082, right_input=2152, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-2930","layer":1},{"info":"compute unary expreesion, input=-2930, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=2666","layer":0}],"base":3,"result_base":3,"text":"∂(⫏≰20222020⨳⩥⨓⫏≰2221201)=⫏≰10122202","reverse_text":"⫏≰10122202=∂(⫏≰20222020⨳⩥⨓⫏≰2221201)","cot":[{"info":"⫏≰20222020⨳⩥⨓⫏≰2221201=⫏≰-11000112","layer":1},{"info":"∂⫏≰-11000112=⫏≰10122202","layer":0}]}
{"id":536,"expression_no_base_symbol":"(↔$4072$)∲⫓$6681$↙$2944$","expression":"(↔⫏≰12120211)∲⫓⫏≰100011110↙⫏≰11001001","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2955,"operation_count":3,"complexity_ratio":985.0,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":4072,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":6681,"base":3},"right_expr":{"type":"numeric_atoms","value":2944,"base":3}}},"used_operators":["i8ToyICDmI","ruOEQAzv1W","yyfyN0ffXY"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰-12012201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4072","layer":2},{"info":"compute unary expreesion, input=4072, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-3799","layer":1},{"info":"number node, value=6681","layer":2},{"info":"number node, value=2944","layer":2},{"info":"compute binary expreesion, left_input=6681, right_input=2944, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-8832","layer":1},{"info":"compute binary expreesion, left_input=-3799, right_input=-8832, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=-3799","layer":0}],"base":3,"result_base":3,"text":"(↔⫏≰12120211)∲⫓⫏≰100011110↙⫏≰11001001=⫏≰-12012201","reverse_text":"⫏≰-12012201=(↔⫏≰12120211)∲⫓⫏≰100011110↙⫏≰11001001","cot":[{"info":"↔⫏≰12120211=⫏≰-12012201","layer":1},{"info":"⫏≰100011110↙⫏≰11001001=⫏≰-110010010","layer":1},{"info":"⫏≰-12012201∲⫓⫏≰-110010010=⫏≰-12012201","layer":0}]}
{"id":537,"expression_no_base_symbol":"($1007$⨓$2527$)⨟⋌⩍($1921$⫩⊇)","expression":"(⫏≰1101022⨓⫏≰10110121)⨟⋌⩍(⫏≰2122011⫩⊇)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2536,"operation_count":3,"complexity_ratio":845.3333333333334,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":1007,"base":3},"right_expr":{"type":"numeric_atoms","value":2527,"base":3}},"right_expr":{"type":"unary","operator":"⫩⊇","unary_expr":{"type":"numeric_atoms","value":1921,"base":3}}},"used_operators":["rGHVDoGpnC","3ViojmjbAp","BjRHVeLaeN"],"dependent_operators":["Tcnh7f0tEr","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1007","layer":2},{"info":"number node, value=2527","layer":2},{"info":"compute binary expreesion, left_input=1007, right_input=2527, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-2530","layer":1},{"info":"number node, value=1921","layer":2},{"info":"compute unary expreesion, input=1921, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=-1879","layer":1},{"info":"compute binary expreesion, left_input=-2530, right_input=-1879, 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":0}],"base":3,"result_base":3,"text":"(⫏≰1101022⨓⫏≰10110121)⨟⋌⩍(⫏≰2122011⫩⊇)=NaN","reverse_text":"NaN=(⫏≰1101022⨓⫏≰10110121)⨟⋌⩍(⫏≰2122011⫩⊇)","cot":[{"info":"⫏≰1101022⨓⫏≰10110121=⫏≰-10110201","layer":1},{"info":"⫏≰2122011⫩⊇=⫏≰-2120121","layer":1},{"info":"⫏≰-10110201⨟⋌⩍⫏≰-2120121=NaN","layer":0}]}
{"id":538,"expression_no_base_symbol":"($1057$⫥∨⫟$1788$)↬($6747$↪⪝)","expression":"(⫏≰1110011⫥∨⫟⫏≰2110020)↬(⫏≰100020220↪⪝)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":855,"operation_count":3,"complexity_ratio":285.0,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1057,"base":3},"right_expr":{"type":"numeric_atoms","value":1788,"base":3}},"right_expr":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"numeric_atoms","value":6747,"base":3}}},"used_operators":["B5M0gjZbta","KYD54nUTWz","l07mrZUIn9"],"dependent_operators":["rGHVDoGpnC","8HhzD0ZcuI","rGHVDoGpnC","9HNa5Wba9A","2DDjHMKMc0"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1057","layer":2},{"info":"number node, value=1788","layer":2},{"info":"compute binary expreesion, left_input=1057, right_input=1788, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=6747","layer":2},{"info":"compute unary expreesion, input=6747, op_id = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=412794954","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=412794954, 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":3,"result_base":3,"text":"(⫏≰1110011⫥∨⫟⫏≰2110020)↬(⫏≰100020220↪⪝)=NaN","reverse_text":"NaN=(⫏≰1110011⫥∨⫟⫏≰2110020)↬(⫏≰100020220↪⪝)","cot":[{"info":"⫏≰1110011⫥∨⫟⫏≰2110020=NaN","layer":1},{"info":"⫏≰100020220↪⪝=⫏≰1001202202011020000","layer":1},{"info":"NaN↬⫏≰1001202202011020000=NaN","layer":0}]}
{"id":539,"expression_no_base_symbol":"($1585$≫≃)⪄$3112$⨳⩥⨓$3131$","expression":"(⫏≰2011201≫≃)⪄⫏≰11021021⨳⩥⨓⫏≰11021222","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":"unary","operator":"≫≃","unary_expr":{"type":"numeric_atoms","value":1585,"base":3}},"right_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":3112,"base":3},"right_expr":{"type":"numeric_atoms","value":3131,"base":3}}},"used_operators":["SUmda5xLS4","X99M06cbEe","nCS4ZIUYfx"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰-1021011201211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1585","layer":2},{"info":"compute unary expreesion, input=1585, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=4571","layer":1},{"info":"number node, value=3112","layer":2},{"info":"number node, value=3131","layer":2},{"info":"compute binary expreesion, left_input=3112, right_input=3131, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=19","layer":1},{"info":"compute binary expreesion, left_input=4571, right_input=19, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-672673","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2011201≫≃)⪄⫏≰11021021⨳⩥⨓⫏≰11021222=⫏≰-1021011201211","reverse_text":"⫏≰-1021011201211=(⫏≰2011201≫≃)⪄⫏≰11021021⨳⩥⨓⫏≰11021222","cot":[{"info":"⫏≰2011201≫≃=⫏≰20021022","layer":1},{"info":"⫏≰11021021⨳⩥⨓⫏≰11021222=⫏≰201","layer":1},{"info":"⫏≰20021022⪄⫏≰201=⫏≰-1021011201211","layer":0}]}
{"id":540,"expression_no_base_symbol":"↩$8656$⫸⊐$1387$","expression":"↩⫏≰102212121⫸⊐⫏≰1220101","highest_n_order":2,"priority_hierarchical_complexity":1,"normalized_expansion_degree":40,"operation_count":2,"complexity_ratio":20.0,"tree":{"type":"unary","operator":"↩","unary_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":8656,"base":3},"right_expr":{"type":"numeric_atoms","value":1387,"base":3}}},"used_operators":["jLgFTUHLKL","mqXw5SEYmG"],"dependent_operators":["sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"⫏≰-2001200212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=8656","layer":2},{"info":"number node, value=1387","layer":2},{"info":"compute binary expreesion, left_input=8656, right_input=1387, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=5423","layer":1},{"info":"compute unary expreesion, input=5423, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-40604","layer":0}],"base":3,"result_base":3,"text":"↩⫏≰102212121⫸⊐⫏≰1220101=⫏≰-2001200212","reverse_text":"⫏≰-2001200212=↩⫏≰102212121⫸⊐⫏≰1220101","cot":[{"info":"⫏≰102212121⫸⊐⫏≰1220101=⫏≰21102212","layer":1},{"info":"↩⫏≰21102212=⫏≰-2001200212","layer":0}]}
{"id":541,"expression_no_base_symbol":"$5272$⊭↱$4730$+$4793$⋓$1688$","expression":"⫏≰21020021⊭↱⫏≰20111012+⫏≰20120112⋓⫏≰2022112","highest_n_order":3,"priority_hierarchical_complexity":3,"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":5272,"base":3},"right_expr":{"type":"numeric_atoms","value":4730,"base":3}},"right_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":4793,"base":3},"right_expr":{"type":"numeric_atoms","value":1688,"base":3}}},"used_operators":["W4YGzv6Whe","COABgblf1C","T2fj7uvVaJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⫏≰-1110222","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5272","layer":2},{"info":"number node, value=4730","layer":2},{"info":"compute binary expreesion, left_input=5272, right_input=4730, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-1079","layer":1},{"info":"number node, value=4793","layer":2},{"info":"number node, value=1688","layer":2},{"info":"compute binary expreesion, left_input=4793, right_input=1688, 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=-1079, right_input=0, op_id = W4YGzv6Whe binary_op_definition= 'None', output=-1079","layer":0}],"base":3,"result_base":3,"text":"⫏≰21020021⊭↱⫏≰20111012+⫏≰20120112⋓⫏≰2022112=⫏≰-1110222","reverse_text":"⫏≰-1110222=⫏≰21020021⊭↱⫏≰20111012+⫏≰20120112⋓⫏≰2022112","cot":[{"info":"⫏≰21020021⊭↱⫏≰20111012=⫏≰-1110222","layer":1},{"info":"⫏≰20120112⋓⫏≰2022112=⫏≰0","layer":1},{"info":"⫏≰-1110222+⫏≰0=⫏≰-1110222","layer":0}]}
{"id":542,"expression_no_base_symbol":"$6732$⋳⪒$5200$⋥≓≎($3982$/$5235$)","expression":"⫏≰100020100⋳⪒⫏≰21010121⋥≓≎(⫏≰12110111/⫏≰21011220)","highest_n_order":2,"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":6732,"base":3},"right_expr":{"type":"numeric_atoms","value":5200,"base":3}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":3982,"base":3},"right_expr":{"type":"numeric_atoms","value":5235,"base":3}}},"used_operators":["Qy55tPpLXF","12rbrZMWeM","XhwjNDsVaA"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰-101220020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6732","layer":2},{"info":"number node, value=5200","layer":2},{"info":"compute binary expreesion, left_input=6732, right_input=5200, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=7977","layer":1},{"info":"number node, value=3982","layer":2},{"info":"number node, value=5235","layer":2},{"info":"compute binary expreesion, left_input=3982, right_input=5235, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute binary expreesion, left_input=7977, right_input=0, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-7944","layer":0}],"base":3,"result_base":3,"text":"⫏≰100020100⋳⪒⫏≰21010121⋥≓≎(⫏≰12110111/⫏≰21011220)=⫏≰-101220020","reverse_text":"⫏≰-101220020=⫏≰100020100⋳⪒⫏≰21010121⋥≓≎(⫏≰12110111/⫏≰21011220)","cot":[{"info":"⫏≰100020100⋳⪒⫏≰21010121=⫏≰101221110","layer":1},{"info":"⫏≰12110111/⫏≰21011220=⫏≰0","layer":1},{"info":"⫏≰101221110⋥≓≎⫏≰0=⫏≰-101220020","layer":0}]}
{"id":543,"expression_no_base_symbol":"($2746$⨵⪆$1720$)⋓$3522$↬$1408$","expression":"(⫏≰10202201⨵⪆⫏≰2100201)⋓⫏≰11211110↬⫏≰1221011","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":2746,"base":3},"right_expr":{"type":"numeric_atoms","value":1720,"base":3}},"right_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":3522,"base":3},"right_expr":{"type":"numeric_atoms","value":1408,"base":3}}},"used_operators":["T2fj7uvVaJ","2DQ55sFlQl","B5M0gjZbta"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rysDP5nf3Z","t8gj7n24qd","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2746","layer":2},{"info":"number node, value=1720","layer":2},{"info":"compute binary expreesion, left_input=2746, right_input=1720, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=3522","layer":2},{"info":"number node, value=1408","layer":2},{"info":"compute binary expreesion, left_input=3522, right_input=1408, 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=160, 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":3,"result_base":3,"text":"(⫏≰10202201⨵⪆⫏≰2100201)⋓⫏≰11211110↬⫏≰1221011=NaN","reverse_text":"NaN=(⫏≰10202201⨵⪆⫏≰2100201)⋓⫏≰11211110↬⫏≰1221011","cot":[{"info":"⫏≰10202201⨵⪆⫏≰2100201=⫏≰12221","layer":1},{"info":"⫏≰11211110↬⫏≰1221011=NaN","layer":1},{"info":"⫏≰12221⋓NaN=NaN","layer":0}]}
{"id":544,"expression_no_base_symbol":"(⨞⊢$2584$)⨐⩸⫘($3034$∲⫓$6484$)","expression":"(⨞⊢⫏≰10112201)⨐⩸⫘(⫏≰11011101∲⫓⫏≰22220011)","highest_n_order":4,"priority_hierarchical_complexity":2,"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":2584,"base":3}},"right_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":3034,"base":3},"right_expr":{"type":"numeric_atoms","value":6484,"base":3}}},"used_operators":["fu6greOZ01","xUOZtlo3hN","i8ToyICDmI"],"dependent_operators":["3ViojmjbAp","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-10210011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2584","layer":2},{"info":"compute unary expreesion, input=2584, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-2758","layer":1},{"info":"number node, value=3034","layer":2},{"info":"number node, value=6484","layer":2},{"info":"compute binary expreesion, left_input=3034, right_input=6484, 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=-2758, right_input=0, 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=-2758","layer":0}],"base":3,"result_base":3,"text":"(⨞⊢⫏≰10112201)⨐⩸⫘(⫏≰11011101∲⫓⫏≰22220011)=⫏≰-10210011","reverse_text":"⫏≰-10210011=(⨞⊢⫏≰10112201)⨐⩸⫘(⫏≰11011101∲⫓⫏≰22220011)","cot":[{"info":"⨞⊢⫏≰10112201=⫏≰-10210011","layer":1},{"info":"⫏≰11011101∲⫓⫏≰22220011=⫏≰0","layer":1},{"info":"⫏≰-10210011⨐⩸⫘⫏≰0=⫏≰-10210011","layer":0}]}
{"id":545,"expression_no_base_symbol":"⊙↵-($3158$/$1407$)","expression":"⊙↵-(⫏≰11022222/⫏≰1221010)","highest_n_order":3,"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":3158,"base":3},"right_expr":{"type":"numeric_atoms","value":1407,"base":3}}},"used_operators":["oWn0xqSxBt","XhwjNDsVaA"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","rysDP5nf3Z"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3158","layer":2},{"info":"number node, value=1407","layer":2},{"info":"compute binary expreesion, left_input=3158, right_input=1407, op_id = XhwjNDsVaA binary_op_definition= 'None', output=2","layer":1},{"info":"compute unary expreesion, input=2, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⫏≰11022222/⫏≰1221010)=⫏≰0","reverse_text":"⫏≰0=⊙↵-(⫏≰11022222/⫏≰1221010)","cot":[{"info":"⫏≰11022222/⫏≰1221010=⫏≰2","layer":1},{"info":"⊙↵-⫏≰2=⫏≰0","layer":0}]}
{"id":546,"expression_no_base_symbol":"($5145$⋷$3072$)⨸⪁$4058$≭$1474$","expression":"(⫏≰21001120⋷⫏≰11012210)⨸⪁⫏≰12120022≭⫏≰2000121","highest_n_order":5,"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":5145,"base":3},"right_expr":{"type":"numeric_atoms","value":3072,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":4058,"base":3},"right_expr":{"type":"numeric_atoms","value":1474,"base":3}}},"used_operators":["g55IO6H4Gj","23Mk6UjR3U","rxpJgHHUmx"],"dependent_operators":["W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5145","layer":2},{"info":"number node, value=3072","layer":2},{"info":"compute binary expreesion, left_input=5145, right_input=3072, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=999","layer":1},{"info":"number node, value=4058","layer":2},{"info":"number node, value=1474","layer":2},{"info":"compute binary expreesion, left_input=4058, right_input=1474, 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=999, right_input=nan, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰21001120⋷⫏≰11012210)⨸⪁⫏≰12120022≭⫏≰2000121=NaN","reverse_text":"NaN=(⫏≰21001120⋷⫏≰11012210)⨸⪁⫏≰12120022≭⫏≰2000121","cot":[{"info":"⫏≰21001120⋷⫏≰11012210=⫏≰1101000","layer":1},{"info":"⫏≰12120022≭⫏≰2000121=NaN","layer":1},{"info":"⫏≰1101000⨸⪁NaN=NaN","layer":0}]}
{"id":547,"expression_no_base_symbol":"(⊄⩳↩$4139$)≎⊠⪸(⨵≀≌$2059$)","expression":"(⊄⩳↩⫏≰12200022)≎⊠⪸(⨵≀≌⫏≰2211021)","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":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":4139,"base":3}},"right_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":2059,"base":3}}},"used_operators":["bJkvcejdHO","8w2t5hMYqp","srAu1WTS94"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4139","layer":2},{"info":"compute unary expreesion, input=4139, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-12417","layer":1},{"info":"number node, value=2059","layer":2},{"info":"compute unary expreesion, input=2059, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-6177","layer":1},{"info":"compute binary expreesion, left_input=-12417, right_input=-6177, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=67","layer":0}],"base":3,"result_base":3,"text":"(⊄⩳↩⫏≰12200022)≎⊠⪸(⨵≀≌⫏≰2211021)=⫏≰2111","reverse_text":"⫏≰2111=(⊄⩳↩⫏≰12200022)≎⊠⪸(⨵≀≌⫏≰2211021)","cot":[{"info":"⊄⩳↩⫏≰12200022=⫏≰-122000220","layer":1},{"info":"⨵≀≌⫏≰2211021=⫏≰-22110210","layer":1},{"info":"⫏≰-122000220≎⊠⪸⫏≰-22110210=⫏≰2111","layer":0}]}
{"id":548,"expression_no_base_symbol":"$2000$⪛$2848$⨽$2917$∼$6208$","expression":"⫏≰2202002⪛⫏≰10220111⨽⫏≰11000001∼⫏≰22111221","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2072,"operation_count":3,"complexity_ratio":690.6666666666666,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":2000,"base":3},"right_expr":{"type":"numeric_atoms","value":2848,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":2917,"base":3},"right_expr":{"type":"numeric_atoms","value":6208,"base":3}}},"used_operators":["8HhzD0ZcuI","uFcxV4UQCh","DyGG3AbaNP"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2000","layer":2},{"info":"number node, value=2848","layer":2},{"info":"compute binary expreesion, left_input=2000, right_input=2848, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=2000","layer":1},{"info":"number node, value=2917","layer":2},{"info":"number node, value=6208","layer":2},{"info":"compute binary expreesion, left_input=2917, right_input=6208, 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=2000, right_input=nan, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2202002⪛⫏≰10220111⨽⫏≰11000001∼⫏≰22111221=NaN","reverse_text":"NaN=⫏≰2202002⪛⫏≰10220111⨽⫏≰11000001∼⫏≰22111221","cot":[{"info":"⫏≰2202002⪛⫏≰10220111=⫏≰2202002","layer":1},{"info":"⫏≰11000001∼⫏≰22111221=NaN","layer":1},{"info":"⫏≰2202002⨽NaN=NaN","layer":0}]}
{"id":549,"expression_no_base_symbol":"$4392$⋓$1004$⨸⪁($2661$⋷$1579$)","expression":"⫏≰20000200⋓⫏≰1101012⨸⪁(⫏≰10122120⋷⫏≰2011111)","highest_n_order":3,"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":4392,"base":3},"right_expr":{"type":"numeric_atoms","value":1004,"base":3}},"right_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":2661,"base":3},"right_expr":{"type":"numeric_atoms","value":1579,"base":3}}},"used_operators":["g55IO6H4Gj","T2fj7uvVaJ","23Mk6UjR3U"],"dependent_operators":["W4YGzv6Whe","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1100211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4392","layer":2},{"info":"number node, value=1004","layer":2},{"info":"compute binary expreesion, left_input=4392, right_input=1004, 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=2661","layer":2},{"info":"number node, value=1579","layer":2},{"info":"compute binary expreesion, left_input=2661, right_input=1579, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=497","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=497, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=994","layer":0}],"base":3,"result_base":3,"text":"⫏≰20000200⋓⫏≰1101012⨸⪁(⫏≰10122120⋷⫏≰2011111)=⫏≰1100211","reverse_text":"⫏≰1100211=⫏≰20000200⋓⫏≰1101012⨸⪁(⫏≰10122120⋷⫏≰2011111)","cot":[{"info":"⫏≰20000200⋓⫏≰1101012=⫏≰0","layer":1},{"info":"⫏≰10122120⋷⫏≰2011111=⫏≰200102","layer":1},{"info":"⫏≰0⨸⪁⫏≰200102=⫏≰1100211","layer":0}]}
{"id":550,"expression_no_base_symbol":"⨰⫟⨤($4959$⨐⩸⫘$4889$)","expression":"⨰⫟⨤(⫏≰20210200⨐⩸⫘⫏≰20201002)","highest_n_order":4,"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":4959,"base":3},"right_expr":{"type":"numeric_atoms","value":4889,"base":3}}},"used_operators":["Tw270M8GLb","fu6greOZ01"],"dependent_operators":["sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4959","layer":2},{"info":"number node, value=4889","layer":2},{"info":"compute binary expreesion, left_input=4959, right_input=4889, 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 unary expreesion, input=nan, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⨰⫟⨤(⫏≰20210200⨐⩸⫘⫏≰20201002)=NaN","reverse_text":"NaN=⨰⫟⨤(⫏≰20210200⨐⩸⫘⫏≰20201002)","cot":[{"info":"⫏≰20210200⨐⩸⫘⫏≰20201002=NaN","layer":1},{"info":"⨰⫟⨤NaN=NaN","layer":0}]}
{"id":551,"expression_no_base_symbol":"$4975$⨪↰⇹$2431$⩷∴($7504$⇼⇔∾$3645$)","expression":"⫏≰20211021⨪↰⇹⫏≰10100001⩷∴(⫏≰101021221⇼⇔∾⫏≰12000000)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4983,"operation_count":3,"complexity_ratio":1661.0,"tree":{"type":"binary","operator":"⩷∴","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":4975,"base":3},"right_expr":{"type":"numeric_atoms","value":2431,"base":3}},"right_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":7504,"base":3},"right_expr":{"type":"numeric_atoms","value":3645,"base":3}}},"used_operators":["9FxExcQeMw","tmPS8pqC7x","tifHPKVTfV"],"dependent_operators":["rysDP5nf3Z","rJVOvQCfKK","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰220012012","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4975","layer":2},{"info":"number node, value=2431","layer":2},{"info":"compute binary expreesion, left_input=4975, right_input=2431, 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=4975","layer":1},{"info":"number node, value=7504","layer":2},{"info":"number node, value=3645","layer":2},{"info":"compute binary expreesion, left_input=7504, right_input=3645, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-3859","layer":1},{"info":"compute binary expreesion, left_input=4975, right_input=-3859, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=17636","layer":0}],"base":3,"result_base":3,"text":"⫏≰20211021⨪↰⇹⫏≰10100001⩷∴(⫏≰101021221⇼⇔∾⫏≰12000000)=⫏≰220012012","reverse_text":"⫏≰220012012=⫏≰20211021⨪↰⇹⫏≰10100001⩷∴(⫏≰101021221⇼⇔∾⫏≰12000000)","cot":[{"info":"⫏≰20211021⨪↰⇹⫏≰10100001=⫏≰20211021","layer":1},{"info":"⫏≰101021221⇼⇔∾⫏≰12000000=⫏≰-12021221","layer":1},{"info":"⫏≰20211021⩷∴⫏≰-12021221=⫏≰220012012","layer":0}]}
{"id":552,"expression_no_base_symbol":"$2259$↺$4860$⩨$2088$⨳⩥⨓$1843$","expression":"⫏≰10002200↺⫏≰20200000⩨⫏≰2212100⨳⩥⨓⫏≰2112021","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⩨","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":2259,"base":3},"right_expr":{"type":"numeric_atoms","value":4860,"base":3}},"right_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":2088,"base":3},"right_expr":{"type":"numeric_atoms","value":1843,"base":3}}},"used_operators":["2DlMacCsIx","7j4O788W3g","nCS4ZIUYfx"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰10","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2259","layer":2},{"info":"number node, value=4860","layer":2},{"info":"compute binary expreesion, left_input=2259, right_input=4860, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=4860","layer":1},{"info":"number node, value=2088","layer":2},{"info":"number node, value=1843","layer":2},{"info":"compute binary expreesion, left_input=2088, right_input=1843, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-245","layer":1},{"info":"compute binary expreesion, left_input=4860, right_input=-245, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=3","layer":0}],"base":3,"result_base":3,"text":"⫏≰10002200↺⫏≰20200000⩨⫏≰2212100⨳⩥⨓⫏≰2112021=⫏≰10","reverse_text":"⫏≰10=⫏≰10002200↺⫏≰20200000⩨⫏≰2212100⨳⩥⨓⫏≰2112021","cot":[{"info":"⫏≰10002200↺⫏≰20200000=⫏≰20200000","layer":1},{"info":"⫏≰2212100⨳⩥⨓⫏≰2112021=⫏≰-100002","layer":1},{"info":"⫏≰20200000⩨⫏≰-100002=⫏≰10","layer":0}]}
{"id":553,"expression_no_base_symbol":"(⨑⩽⪐$3113$)⋫","expression":"(⨑⩽⪐⫏≰11021022)⋫","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2844,"operation_count":2,"complexity_ratio":1422.0,"tree":{"type":"unary","operator":"⋫","unary_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":3113,"base":3}}},"used_operators":["JL8yIekQnl","AF7qkfDlqP"],"dependent_operators":["tmPS8pqC7x","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-10220012","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3113","layer":2},{"info":"compute unary expreesion, input=3113, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-2840","layer":1},{"info":"compute unary expreesion, input=-2840, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=-2840","layer":0}],"base":3,"result_base":3,"text":"(⨑⩽⪐⫏≰11021022)⋫=⫏≰-10220012","reverse_text":"⫏≰-10220012=(⨑⩽⪐⫏≰11021022)⋫","cot":[{"info":"⨑⩽⪐⫏≰11021022=⫏≰-10220012","layer":1},{"info":"⫏≰-10220012⋫=⫏≰-10220012","layer":0}]}
{"id":554,"expression_no_base_symbol":"⊄⩳↩(⪲⇎$1449$)","expression":"⊄⩳↩(⪲⇎⫏≰1222200)","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":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":1449,"base":3}}},"used_operators":["8w2t5hMYqp","XPYlsWDdGa"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-102221000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1449","layer":2},{"info":"compute unary expreesion, input=1449, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=2898","layer":1},{"info":"compute unary expreesion, input=2898, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-8694","layer":0}],"base":3,"result_base":3,"text":"⊄⩳↩(⪲⇎⫏≰1222200)=⫏≰-102221000","reverse_text":"⫏≰-102221000=⊄⩳↩(⪲⇎⫏≰1222200)","cot":[{"info":"⪲⇎⫏≰1222200=⫏≰10222100","layer":1},{"info":"⊄⩳↩⫏≰10222100=⫏≰-102221000","layer":0}]}
{"id":555,"expression_no_base_symbol":"($1029$⨸⪁$4966$)⨓(⨈⫕$5618$)","expression":"(⫏≰1102010⨸⪁⫏≰20210221)⨓(⨈⫕⫏≰21201002)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":416,"operation_count":3,"complexity_ratio":138.66666666666666,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":1029,"base":3},"right_expr":{"type":"numeric_atoms","value":4966,"base":3}},"right_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":5618,"base":3}}},"used_operators":["3ViojmjbAp","g55IO6H4Gj","megm06wKyl"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q"],"result":"⫏≰-220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1029","layer":2},{"info":"number node, value=4966","layer":2},{"info":"compute binary expreesion, left_input=1029, right_input=4966, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=11990","layer":1},{"info":"number node, value=5618","layer":2},{"info":"compute unary expreesion, input=5618, 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=11990, right_input=-21, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-24","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1102010⨸⪁⫏≰20210221)⨓(⨈⫕⫏≰21201002)=⫏≰-220","reverse_text":"⫏≰-220=(⫏≰1102010⨸⪁⫏≰20210221)⨓(⨈⫕⫏≰21201002)","cot":[{"info":"⫏≰1102010⨸⪁⫏≰20210221=⫏≰121110002","layer":1},{"info":"⨈⫕⫏≰21201002=⫏≰-210","layer":1},{"info":"⫏≰121110002⨓⫏≰-210=⫏≰-220","layer":0}]}
{"id":556,"expression_no_base_symbol":"∂($4021$⨓$3994$)","expression":"∂(⫏≰12111221⨓⫏≰12110221)","highest_n_order":5,"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":4021,"base":3},"right_expr":{"type":"numeric_atoms","value":3994,"base":3}}},"used_operators":["Uaa54Peajs","3ViojmjbAp"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⫏≰12010021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4021","layer":2},{"info":"number node, value=3994","layer":2},{"info":"compute binary expreesion, left_input=4021, right_input=3994, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-3997","layer":1},{"info":"compute unary expreesion, input=-3997, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=3733","layer":0}],"base":3,"result_base":3,"text":"∂(⫏≰12111221⨓⫏≰12110221)=⫏≰12010021","reverse_text":"⫏≰12010021=∂(⫏≰12111221⨓⫏≰12110221)","cot":[{"info":"⫏≰12111221⨓⫏≰12110221=⫏≰-12111001","layer":1},{"info":"∂⫏≰-12111001=⫏≰12010021","layer":0}]}
{"id":557,"expression_no_base_symbol":"∂($1929$⩷∴$5578$)","expression":"∂(⫏≰2122110⩷∴⫏≰21122121)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":423,"operation_count":2,"complexity_ratio":211.5,"tree":{"type":"unary","operator":"∂","unary_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":1929,"base":3},"right_expr":{"type":"numeric_atoms","value":5578,"base":3}}},"used_operators":["Uaa54Peajs","9FxExcQeMw"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","rysDP5nf3Z"],"result":"⫏≰100200201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1929","layer":2},{"info":"number node, value=5578","layer":2},{"info":"compute binary expreesion, left_input=1929, right_input=5578, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-7330","layer":1},{"info":"compute unary expreesion, input=-7330, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=7066","layer":0}],"base":3,"result_base":3,"text":"∂(⫏≰2122110⩷∴⫏≰21122121)=⫏≰100200201","reverse_text":"⫏≰100200201=∂(⫏≰2122110⩷∴⫏≰21122121)","cot":[{"info":"⫏≰2122110⩷∴⫏≰21122121=⫏≰-101001111","layer":1},{"info":"∂⫏≰-101001111=⫏≰100200201","layer":0}]}
{"id":558,"expression_no_base_symbol":"≦∁($1598$+$5843$)","expression":"≦∁(⫏≰2012012+⫏≰22000102)","highest_n_order":2,"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":1598,"base":3},"right_expr":{"type":"numeric_atoms","value":5843,"base":3}}},"used_operators":["9ICcGScMcE","W4YGzv6Whe"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"⫏≰101012121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1598","layer":2},{"info":"number node, value=5843","layer":2},{"info":"compute binary expreesion, left_input=1598, right_input=5843, op_id = W4YGzv6Whe binary_op_definition= 'None', output=7441","layer":1},{"info":"compute unary expreesion, input=7441, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=7441","layer":0}],"base":3,"result_base":3,"text":"≦∁(⫏≰2012012+⫏≰22000102)=⫏≰101012121","reverse_text":"⫏≰101012121=≦∁(⫏≰2012012+⫏≰22000102)","cot":[{"info":"⫏≰2012012+⫏≰22000102=⫏≰101012121","layer":1},{"info":"≦∁⫏≰101012121=⫏≰101012121","layer":0}]}
{"id":559,"expression_no_base_symbol":"($5440$⨵⪆$1610$)⨐⩸⫘$2706$∼$2256$","expression":"(⫏≰21110111⨵⪆⫏≰2012122)⨐⩸⫘⫏≰10201020∼⫏≰10002120","highest_n_order":4,"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":5440,"base":3},"right_expr":{"type":"numeric_atoms","value":1610,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":2706,"base":3},"right_expr":{"type":"numeric_atoms","value":2256,"base":3}}},"used_operators":["fu6greOZ01","2DQ55sFlQl","DyGG3AbaNP"],"dependent_operators":["3ViojmjbAp","rysDP5nf3Z","t8gj7n24qd","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5440","layer":2},{"info":"number node, value=1610","layer":2},{"info":"compute binary expreesion, left_input=5440, right_input=1610, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=2706","layer":2},{"info":"number node, value=2256","layer":2},{"info":"compute binary expreesion, left_input=2706, right_input=2256, 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=160, 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":3,"result_base":3,"text":"(⫏≰21110111⨵⪆⫏≰2012122)⨐⩸⫘⫏≰10201020∼⫏≰10002120=NaN","reverse_text":"NaN=(⫏≰21110111⨵⪆⫏≰2012122)⨐⩸⫘⫏≰10201020∼⫏≰10002120","cot":[{"info":"⫏≰21110111⨵⪆⫏≰2012122=⫏≰12221","layer":1},{"info":"⫏≰10201020∼⫏≰10002120=NaN","layer":1},{"info":"⫏≰12221⨐⩸⫘NaN=NaN","layer":0}]}
{"id":560,"expression_no_base_symbol":"($8449$⋷$1729$)⊉≛↸$3479$≹⇙⪍$5765$","expression":"(⫏≰102120221⋷⫏≰2101001)⊉≛↸⫏≰11202212≹⇙⪍⫏≰21220112","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":8449,"base":3},"right_expr":{"type":"numeric_atoms","value":1729,"base":3}},"right_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":3479,"base":3},"right_expr":{"type":"numeric_atoms","value":5765,"base":3}}},"used_operators":["DZ8iAZOCBD","23Mk6UjR3U","AHs5Up7iyr"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=8449","layer":2},{"info":"number node, value=1729","layer":2},{"info":"compute binary expreesion, left_input=8449, right_input=1729, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-4991","layer":1},{"info":"number node, value=3479","layer":2},{"info":"number node, value=5765","layer":2},{"info":"compute binary expreesion, left_input=3479, right_input=5765, 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=-4991, 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":3,"result_base":3,"text":"(⫏≰102120221⋷⫏≰2101001)⊉≛↸⫏≰11202212≹⇙⪍⫏≰21220112=NaN","reverse_text":"NaN=(⫏≰102120221⋷⫏≰2101001)⊉≛↸⫏≰11202212≹⇙⪍⫏≰21220112","cot":[{"info":"⫏≰102120221⋷⫏≰2101001=⫏≰-20211212","layer":1},{"info":"⫏≰11202212≹⇙⪍⫏≰21220112=NaN","layer":1},{"info":"⫏≰-20211212⊉≛↸NaN=NaN","layer":0}]}
{"id":561,"expression_no_base_symbol":"$1705$⊴$2858$⩷∴($1313$⫩⊇)","expression":"⫏≰2100011⊴⫏≰10220212⩷∴(⫏≰1210122⫩⊇)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2872,"operation_count":3,"complexity_ratio":957.3333333333334,"tree":{"type":"binary","operator":"⩷∴","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1705,"base":3},"right_expr":{"type":"numeric_atoms","value":2858,"base":3}},"right_expr":{"type":"unary","operator":"⫩⊇","unary_expr":{"type":"numeric_atoms","value":1313,"base":3}}},"used_operators":["9FxExcQeMw","Nsiff2A1zJ","BjRHVeLaeN"],"dependent_operators":["rysDP5nf3Z","dWAJyo7jo9","14qkJME0vr","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1705","layer":2},{"info":"number node, value=2858","layer":2},{"info":"compute binary expreesion, left_input=1705, right_input=2858, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=1313","layer":2},{"info":"compute unary expreesion, input=1313, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=-1271","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-1271, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2100011⊴⫏≰10220212⩷∴(⫏≰1210122⫩⊇)=NaN","reverse_text":"NaN=⫏≰2100011⊴⫏≰10220212⩷∴(⫏≰1210122⫩⊇)","cot":[{"info":"⫏≰2100011⊴⫏≰10220212=NaN","layer":1},{"info":"⫏≰1210122⫩⊇=⫏≰-1202002","layer":1},{"info":"NaN⩷∴⫏≰-1202002=NaN","layer":0}]}
{"id":562,"expression_no_base_symbol":"$3079$⇼⇔∾$4272$⪨≂($9448$⊦⊿)","expression":"⫏≰11020001⇼⇔∾⫏≰12212020⪨≂(⫏≰110221221⊦⊿)","highest_n_order":1,"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":3079,"base":3},"right_expr":{"type":"numeric_atoms","value":4272,"base":3}},"right_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":9448,"base":3}}},"used_operators":["sdazOOVcIp","tifHPKVTfV","14qkJME0vr"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰10000101120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3079","layer":2},{"info":"number node, value=4272","layer":2},{"info":"compute binary expreesion, left_input=3079, right_input=4272, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=1193","layer":1},{"info":"number node, value=9448","layer":2},{"info":"compute unary expreesion, input=9448, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-28423","layer":1},{"info":"compute binary expreesion, left_input=1193, right_input=-28423, 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=59334","layer":0}],"base":3,"result_base":3,"text":"⫏≰11020001⇼⇔∾⫏≰12212020⪨≂(⫏≰110221221⊦⊿)=⫏≰10000101120","reverse_text":"⫏≰10000101120=⫏≰11020001⇼⇔∾⫏≰12212020⪨≂(⫏≰110221221⊦⊿)","cot":[{"info":"⫏≰11020001⇼⇔∾⫏≰12212020=⫏≰1122012","layer":1},{"info":"⫏≰110221221⊦⊿=⫏≰-1102222201","layer":1},{"info":"⫏≰1122012⪨≂⫏≰-1102222201=⫏≰10000101120","layer":0}]}
{"id":563,"expression_no_base_symbol":"$4494$⫥∨⫟$4710$⨽(⨰⫟⨤$1631$)","expression":"⫏≰20011110⫥∨⫟⫏≰20110110⨽(⨰⫟⨤⫏≰2020102)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5848,"operation_count":3,"complexity_ratio":1949.3333333333333,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":4494,"base":3},"right_expr":{"type":"numeric_atoms","value":4710,"base":3}},"right_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":1631,"base":3}}},"used_operators":["8HhzD0ZcuI","KYD54nUTWz","Tw270M8GLb"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","8HhzD0ZcuI","rGHVDoGpnC","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4494","layer":2},{"info":"number node, value=4710","layer":2},{"info":"compute binary expreesion, left_input=4494, right_input=4710, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=1631","layer":2},{"info":"compute unary expreesion, input=1631, 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 = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰20011110⫥∨⫟⫏≰20110110⨽(⨰⫟⨤⫏≰2020102)=NaN","reverse_text":"NaN=⫏≰20011110⫥∨⫟⫏≰20110110⨽(⨰⫟⨤⫏≰2020102)","cot":[{"info":"⫏≰20011110⫥∨⫟⫏≰20110110=NaN","layer":1},{"info":"⨰⫟⨤⫏≰2020102=NaN","layer":1},{"info":"NaN⨽NaN=NaN","layer":0}]}
{"id":564,"expression_no_base_symbol":"$2164$≧⫂∧$2380$⨵⪆(⇁⨣⪵$1572$)","expression":"⫏≰2222011≧⫂∧⫏≰10021011⨵⪆(⇁⨣⪵⫏≰2011020)","highest_n_order":5,"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":2164,"base":3},"right_expr":{"type":"numeric_atoms","value":2380,"base":3}},"right_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":1572,"base":3}}},"used_operators":["2DQ55sFlQl","Ph9nP6C5qx","inkyxCbjAn"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","B5M0gjZbta"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2164","layer":2},{"info":"number node, value=2380","layer":2},{"info":"compute binary expreesion, left_input=2164, right_input=2380, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=1907","layer":1},{"info":"number node, value=1572","layer":2},{"info":"compute unary expreesion, input=1572, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1907, right_input=nan, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰2222011≧⫂∧⫏≰10021011⨵⪆(⇁⨣⪵⫏≰2011020)=⫏≰12221","reverse_text":"⫏≰12221=⫏≰2222011≧⫂∧⫏≰10021011⨵⪆(⇁⨣⪵⫏≰2011020)","cot":[{"info":"⫏≰2222011≧⫂∧⫏≰10021011=⫏≰2121122","layer":1},{"info":"⇁⨣⪵⫏≰2011020=NaN","layer":1},{"info":"⫏≰2121122⨵⪆NaN=⫏≰12221","layer":0}]}
{"id":565,"expression_no_base_symbol":"$4648$∼$1855$*(⋗⩬⋾$1393$)","expression":"⫏≰20101011∼⫏≰2112201*(⋗⩬⋾⫏≰1220121)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":97,"operation_count":3,"complexity_ratio":32.333333333333336,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":4648,"base":3},"right_expr":{"type":"numeric_atoms","value":1855,"base":3}},"right_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":1393,"base":3}}},"used_operators":["9HNa5Wba9A","DyGG3AbaNP","DpFCA1CohY"],"dependent_operators":["W4YGzv6Whe","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4648","layer":2},{"info":"number node, value=1855","layer":2},{"info":"compute binary expreesion, left_input=4648, right_input=1855, 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=1393","layer":2},{"info":"compute unary expreesion, input=1393, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-4179","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-4179, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰20101011∼⫏≰2112201*(⋗⩬⋾⫏≰1220121)=NaN","reverse_text":"NaN=⫏≰20101011∼⫏≰2112201*(⋗⩬⋾⫏≰1220121)","cot":[{"info":"⫏≰20101011∼⫏≰2112201=NaN","layer":1},{"info":"⋗⩬⋾⫏≰1220121=⫏≰-12201210","layer":1},{"info":"NaN*⫏≰-12201210=NaN","layer":0}]}
{"id":566,"expression_no_base_symbol":"$1067$⊴$4724$↺($1782$∧)","expression":"⫏≰1110112⊴⫏≰20110222↺(⫏≰2110000∧)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4738,"operation_count":3,"complexity_ratio":1579.3333333333333,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1067,"base":3},"right_expr":{"type":"numeric_atoms","value":4724,"base":3}},"right_expr":{"type":"unary","operator":"∧","unary_expr":{"type":"numeric_atoms","value":1782,"base":3}}},"used_operators":["7j4O788W3g","Nsiff2A1zJ","z63VuFQld9"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","14qkJME0vr","B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1067","layer":2},{"info":"number node, value=4724","layer":2},{"info":"compute binary expreesion, left_input=1067, right_input=4724, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=1782","layer":2},{"info":"compute unary expreesion, input=1782, op_id = z63VuFQld9, unary_op_definition = 'a∧ = { ((a⋷a)≹⇙⪍(a↬a)) , if (-a)<=39 ; ((a%a)⋝⋈⪟(a⫸⊐a)) , else }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1110112⊴⫏≰20110222↺(⫏≰2110000∧)=NaN","reverse_text":"NaN=⫏≰1110112⊴⫏≰20110222↺(⫏≰2110000∧)","cot":[{"info":"⫏≰1110112⊴⫏≰20110222=NaN","layer":1},{"info":"⫏≰2110000∧=NaN","layer":1},{"info":"NaN↺NaN=NaN","layer":0}]}
{"id":567,"expression_no_base_symbol":"⨑⩽⪐$1627$⪮%⊝$4001$","expression":"⨑⩽⪐⫏≰2020021⪮%⊝⫏≰12111012","highest_n_order":2,"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":1627,"base":3},"right_expr":{"type":"numeric_atoms","value":4001,"base":3}}},"used_operators":["AF7qkfDlqP","IWmyXbctLI"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰-11112010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1627","layer":2},{"info":"number node, value=4001","layer":2},{"info":"compute binary expreesion, left_input=1627, right_input=4001, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=3570","layer":1},{"info":"compute unary expreesion, input=3570, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-3297","layer":0}],"base":3,"result_base":3,"text":"⨑⩽⪐⫏≰2020021⪮%⊝⫏≰12111012=⫏≰-11112010","reverse_text":"⫏≰-11112010=⨑⩽⪐⫏≰2020021⪮%⊝⫏≰12111012","cot":[{"info":"⫏≰2020021⪮%⊝⫏≰12111012=⫏≰11220020","layer":1},{"info":"⨑⩽⪐⫏≰11220020=⫏≰-11112010","layer":0}]}
{"id":568,"expression_no_base_symbol":"⩦⩻⨪(⨑⩽⪐$1118$)","expression":"⩦⩻⨪(⨑⩽⪐⫏≰1112102)","highest_n_order":1,"priority_hierarchical_complexity":1,"normalized_expansion_degree":7,"operation_count":2,"complexity_ratio":3.5,"tree":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":1118,"base":3}}},"used_operators":["2td37pGCOC","AF7qkfDlqP"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-1011022","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1118","layer":2},{"info":"compute unary expreesion, input=1118, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-845","layer":1},{"info":"compute unary expreesion, input=-845, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=-845","layer":0}],"base":3,"result_base":3,"text":"⩦⩻⨪(⨑⩽⪐⫏≰1112102)=⫏≰-1011022","reverse_text":"⫏≰-1011022=⩦⩻⨪(⨑⩽⪐⫏≰1112102)","cot":[{"info":"⨑⩽⪐⫏≰1112102=⫏≰-1011022","layer":1},{"info":"⩦⩻⨪⫏≰-1011022=⫏≰-1011022","layer":0}]}
{"id":569,"expression_no_base_symbol":"$2601$⨎$8741$⊉≛↸(⨈⫕$5505$)","expression":"⫏≰10120100⨎⫏≰102222202⊉≛↸(⨈⫕⫏≰21112220)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":389,"operation_count":3,"complexity_ratio":129.66666666666666,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":2601,"base":3},"right_expr":{"type":"numeric_atoms","value":8741,"base":3}},"right_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":5505,"base":3}}},"used_operators":["DZ8iAZOCBD","rJVOvQCfKK","megm06wKyl"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q"],"result":"⫏≰212222111","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2601","layer":2},{"info":"number node, value=8741","layer":2},{"info":"compute binary expreesion, left_input=2601, right_input=8741, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=8741","layer":1},{"info":"number node, value=5505","layer":2},{"info":"compute unary expreesion, input=5505, 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=8741, right_input=-21, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=17482","layer":0}],"base":3,"result_base":3,"text":"⫏≰10120100⨎⫏≰102222202⊉≛↸(⨈⫕⫏≰21112220)=⫏≰212222111","reverse_text":"⫏≰212222111=⫏≰10120100⨎⫏≰102222202⊉≛↸(⨈⫕⫏≰21112220)","cot":[{"info":"⫏≰10120100⨎⫏≰102222202=⫏≰102222202","layer":1},{"info":"⨈⫕⫏≰21112220=⫏≰-210","layer":1},{"info":"⫏≰102222202⊉≛↸⫏≰-210=⫏≰212222111","layer":0}]}
{"id":570,"expression_no_base_symbol":"≦∁$1466$⨐⩸⫘$1100$","expression":"≦∁⫏≰2000022⨐⩸⫘⫏≰1111202","highest_n_order":4,"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":1466,"base":3},"right_expr":{"type":"numeric_atoms","value":1100,"base":3}}},"used_operators":["9ICcGScMcE","fu6greOZ01"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1466","layer":2},{"info":"number node, value=1100","layer":2},{"info":"compute binary expreesion, left_input=1466, right_input=1100, 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 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":3,"result_base":3,"text":"≦∁⫏≰2000022⨐⩸⫘⫏≰1111202=NaN","reverse_text":"NaN=≦∁⫏≰2000022⨐⩸⫘⫏≰1111202","cot":[{"info":"⫏≰2000022⨐⩸⫘⫏≰1111202=NaN","layer":1},{"info":"≦∁NaN=NaN","layer":0}]}
{"id":571,"expression_no_base_symbol":"(↣≠⋷$2311$)↙$2349$⪢$2198$","expression":"(↣≠⋷⫏≰10011121)↙⫏≰10020000⪢⫏≰10000102","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2270,"operation_count":3,"complexity_ratio":756.6666666666666,"tree":{"type":"binary","operator":"↙","left_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":2311,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":2349,"base":3},"right_expr":{"type":"numeric_atoms","value":2198,"base":3}}},"used_operators":["yyfyN0ffXY","Asc51vEJeQ","dWAJyo7jo9"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","XhwjNDsVaA","AHs5Up7iyr","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2311","layer":2},{"info":"compute unary expreesion, input=2311, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"number node, value=2349","layer":2},{"info":"number node, value=2198","layer":2},{"info":"compute binary expreesion, left_input=2349, right_input=2198, 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 = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(↣≠⋷⫏≰10011121)↙⫏≰10020000⪢⫏≰10000102=NaN","reverse_text":"NaN=(↣≠⋷⫏≰10011121)↙⫏≰10020000⪢⫏≰10000102","cot":[{"info":"↣≠⋷⫏≰10011121=NaN","layer":1},{"info":"⫏≰10020000⪢⫏≰10000102=NaN","layer":1},{"info":"NaN↙NaN=NaN","layer":0}]}
{"id":572,"expression_no_base_symbol":"($3905$⨽$3974$)≹⇙⪍($1206$⪨≂$5746$)","expression":"(⫏≰12100122⨽⫏≰12110012)≹⇙⪍(⫏≰1122200⪨≂⫏≰21212211)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3920,"operation_count":3,"complexity_ratio":1306.6666666666667,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":3905,"base":3},"right_expr":{"type":"numeric_atoms","value":3974,"base":3}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":1206,"base":3},"right_expr":{"type":"numeric_atoms","value":5746,"base":3}}},"used_operators":["AHs5Up7iyr","8HhzD0ZcuI","sdazOOVcIp"],"dependent_operators":["dWAJyo7jo9","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3905","layer":2},{"info":"number node, value=3974","layer":2},{"info":"compute binary expreesion, left_input=3905, right_input=3974, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-45757683","layer":1},{"info":"number node, value=1206","layer":2},{"info":"number node, value=5746","layer":2},{"info":"compute binary expreesion, left_input=1206, right_input=5746, 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=-8978","layer":1},{"info":"compute binary expreesion, left_input=-45757683, right_input=-8978, 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":3,"result_base":3,"text":"(⫏≰12100122⨽⫏≰12110012)≹⇙⪍(⫏≰1122200⪨≂⫏≰21212211)=NaN","reverse_text":"NaN=(⫏≰12100122⨽⫏≰12110012)≹⇙⪍(⫏≰1122200⪨≂⫏≰21212211)","cot":[{"info":"⫏≰12100122⨽⫏≰12110012=⫏≰-10012002201202000","layer":1},{"info":"⫏≰1122200⪨≂⫏≰21212211=⫏≰-110022112","layer":1},{"info":"⫏≰-10012002201202000≹⇙⪍⫏≰-110022112=NaN","layer":0}]}
{"id":573,"expression_no_base_symbol":"($2296$⇼⇔∾$1228$)⪘⫢($5007$⊭↱$5049$)","expression":"(⫏≰10011001⇼⇔∾⫏≰1200111)⪘⫢(⫏≰20212110⊭↱⫏≰20221000)","highest_n_order":2,"priority_hierarchical_complexity":2,"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":2296,"base":3},"right_expr":{"type":"numeric_atoms","value":1228,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":5007,"base":3},"right_expr":{"type":"numeric_atoms","value":5049,"base":3}}},"used_operators":["oacrs7FA3X","tifHPKVTfV","COABgblf1C"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2296","layer":2},{"info":"number node, value=1228","layer":2},{"info":"compute binary expreesion, left_input=2296, right_input=1228, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-1068","layer":1},{"info":"number node, value=5007","layer":2},{"info":"number node, value=5049","layer":2},{"info":"compute binary expreesion, left_input=5007, right_input=5049, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=89","layer":1},{"info":"compute binary expreesion, left_input=-1068, right_input=89, 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":3,"result_base":3,"text":"(⫏≰10011001⇼⇔∾⫏≰1200111)⪘⫢(⫏≰20212110⊭↱⫏≰20221000)=⫏≰-1","reverse_text":"⫏≰-1=(⫏≰10011001⇼⇔∾⫏≰1200111)⪘⫢(⫏≰20212110⊭↱⫏≰20221000)","cot":[{"info":"⫏≰10011001⇼⇔∾⫏≰1200111=⫏≰-1110120","layer":1},{"info":"⫏≰20212110⊭↱⫏≰20221000=⫏≰10022","layer":1},{"info":"⫏≰-1110120⪘⫢⫏≰10022=⫏≰-1","layer":0}]}
{"id":574,"expression_no_base_symbol":"($1983$↬$1440$)⊴($1250$-$1437$)","expression":"(⫏≰2201110↬⫏≰1222100)⊴(⫏≰1201022-⫏≰1222020)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":195,"operation_count":3,"complexity_ratio":65.0,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":1983,"base":3},"right_expr":{"type":"numeric_atoms","value":1440,"base":3}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1250,"base":3},"right_expr":{"type":"numeric_atoms","value":1437,"base":3}}},"used_operators":["Nsiff2A1zJ","B5M0gjZbta","rysDP5nf3Z"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1983","layer":2},{"info":"number node, value=1440","layer":2},{"info":"compute binary expreesion, left_input=1983, right_input=1440, 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=1250","layer":2},{"info":"number node, value=1437","layer":2},{"info":"compute binary expreesion, left_input=1250, right_input=1437, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-187","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-187, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2201110↬⫏≰1222100)⊴(⫏≰1201022-⫏≰1222020)=NaN","reverse_text":"NaN=(⫏≰2201110↬⫏≰1222100)⊴(⫏≰1201022-⫏≰1222020)","cot":[{"info":"⫏≰2201110↬⫏≰1222100=NaN","layer":1},{"info":"⫏≰1201022-⫏≰1222020=⫏≰-20221","layer":1},{"info":"NaN⊴⫏≰-20221=NaN","layer":0}]}
{"id":575,"expression_no_base_symbol":"($1075$⪒$1974$)⨳⩥⨓$2378$⊴$3804$","expression":"(⫏≰1110211⪒⫏≰2201010)⨳⩥⨓⫏≰10021002⊴⫏≰12012220","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3816,"operation_count":3,"complexity_ratio":1272.0,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":1075,"base":3},"right_expr":{"type":"numeric_atoms","value":1974,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":2378,"base":3},"right_expr":{"type":"numeric_atoms","value":3804,"base":3}}},"used_operators":["nCS4ZIUYfx","f6k1SAg4EE","Nsiff2A1zJ"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1075","layer":2},{"info":"number node, value=1974","layer":2},{"info":"compute binary expreesion, left_input=1075, right_input=1974, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-3049","layer":1},{"info":"number node, value=2378","layer":2},{"info":"number node, value=3804","layer":2},{"info":"compute binary expreesion, left_input=2378, right_input=3804, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-3049, right_input=nan, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1110211⪒⫏≰2201010)⨳⩥⨓⫏≰10021002⊴⫏≰12012220=NaN","reverse_text":"NaN=(⫏≰1110211⪒⫏≰2201010)⨳⩥⨓⫏≰10021002⊴⫏≰12012220","cot":[{"info":"⫏≰1110211⪒⫏≰2201010=⫏≰-11011221","layer":1},{"info":"⫏≰10021002⊴⫏≰12012220=NaN","layer":1},{"info":"⫏≰-11011221⨳⩥⨓NaN=NaN","layer":0}]}
{"id":576,"expression_no_base_symbol":"$5623$⊭↱$1159$⇼⇔∾(⨵≀≌$1290$)","expression":"⫏≰21201021⊭↱⫏≰1120221⇼⇔∾(⨵≀≌⫏≰1202210)","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":5623,"base":3},"right_expr":{"type":"numeric_atoms","value":1159,"base":3}},"right_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":1290,"base":3}}},"used_operators":["tifHPKVTfV","COABgblf1C","srAu1WTS94"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A"],"result":"⫏≰20221011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5623","layer":2},{"info":"number node, value=1159","layer":2},{"info":"compute binary expreesion, left_input=5623, right_input=1159, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-8923","layer":1},{"info":"number node, value=1290","layer":2},{"info":"compute unary expreesion, input=1290, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-3870","layer":1},{"info":"compute binary expreesion, left_input=-8923, right_input=-3870, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=5053","layer":0}],"base":3,"result_base":3,"text":"⫏≰21201021⊭↱⫏≰1120221⇼⇔∾(⨵≀≌⫏≰1202210)=⫏≰20221011","reverse_text":"⫏≰20221011=⫏≰21201021⊭↱⫏≰1120221⇼⇔∾(⨵≀≌⫏≰1202210)","cot":[{"info":"⫏≰21201021⊭↱⫏≰1120221=⫏≰-110020111","layer":1},{"info":"⨵≀≌⫏≰1202210=⫏≰-12022100","layer":1},{"info":"⫏≰-110020111⇼⇔∾⫏≰-12022100=⫏≰20221011","layer":0}]}
{"id":577,"expression_no_base_symbol":"(⨈⫕$3076$)⫡⨏($4737$⋫)","expression":"(⨈⫕⫏≰11012221)⫡⨏(⫏≰20111110⋫)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5130,"operation_count":3,"complexity_ratio":1710.0,"tree":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":3076,"base":3}},"right_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":4737,"base":3}}},"used_operators":["QMFrweE19q","megm06wKyl","JL8yIekQnl"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q","tmPS8pqC7x"],"result":"⫏≰111221000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3076","layer":2},{"info":"compute unary expreesion, input=3076, 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":"number node, value=4737","layer":2},{"info":"compute unary expreesion, input=4737, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=4737","layer":1},{"info":"compute binary expreesion, left_input=-21, right_input=4737, 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=10152","layer":0}],"base":3,"result_base":3,"text":"(⨈⫕⫏≰11012221)⫡⨏(⫏≰20111110⋫)=⫏≰111221000","reverse_text":"⫏≰111221000=(⨈⫕⫏≰11012221)⫡⨏(⫏≰20111110⋫)","cot":[{"info":"⨈⫕⫏≰11012221=⫏≰-210","layer":1},{"info":"⫏≰20111110⋫=⫏≰20111110","layer":1},{"info":"⫏≰-210⫡⨏⫏≰20111110=⫏≰111221000","layer":0}]}
{"id":578,"expression_no_base_symbol":"($3919$⋳⪒$3192$)∸","expression":"(⫏≰12101011⋳⪒⫏≰11101020)∸","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":184,"operation_count":2,"complexity_ratio":92.0,"tree":{"type":"unary","operator":"∸","unary_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":3919,"base":3},"right_expr":{"type":"numeric_atoms","value":3192,"base":3}}},"used_operators":["o20kRiQErp","12rbrZMWeM"],"dependent_operators":["tmPS8pqC7x","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰20120","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3919","layer":2},{"info":"number node, value=3192","layer":2},{"info":"compute binary expreesion, left_input=3919, right_input=3192, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=4359","layer":1},{"info":"compute unary expreesion, input=4359, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12101011⋳⪒⫏≰11101020)∸=⫏≰20120","reverse_text":"⫏≰20120=(⫏≰12101011⋳⪒⫏≰11101020)∸","cot":[{"info":"⫏≰12101011⋳⪒⫏≰11101020=⫏≰12222110","layer":1},{"info":"⫏≰12222110∸=⫏≰20120","layer":0}]}
{"id":579,"expression_no_base_symbol":"($1237$⫸⊐$4639$)⫸⊐$1127$≎⊠⪸$1228$","expression":"(⫏≰1200211⫸⊐⫏≰20100211)⫸⊐⫏≰1112202≎⊠⪸⫏≰1200111","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":318,"operation_count":3,"complexity_ratio":106.0,"tree":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":1237,"base":3},"right_expr":{"type":"numeric_atoms","value":4639,"base":3}},"right_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1127,"base":3},"right_expr":{"type":"numeric_atoms","value":1228,"base":3}}},"used_operators":["mqXw5SEYmG","bJkvcejdHO"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"⫏≰2012012211201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1237","layer":2},{"info":"number node, value=4639","layer":2},{"info":"compute binary expreesion, left_input=1237, right_input=4639, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=18431","layer":1},{"info":"number node, value=1127","layer":2},{"info":"number node, value=1228","layer":2},{"info":"compute binary expreesion, left_input=1127, right_input=1228, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=291420","layer":1},{"info":"compute binary expreesion, left_input=18431, right_input=291420, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=1165555","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1200211⫸⊐⫏≰20100211)⫸⊐⫏≰1112202≎⊠⪸⫏≰1200111=⫏≰2012012211201","reverse_text":"⫏≰2012012211201=(⫏≰1200211⫸⊐⫏≰20100211)⫸⊐⫏≰1112202≎⊠⪸⫏≰1200111","cot":[{"info":"⫏≰1200211⫸⊐⫏≰20100211=⫏≰221021122","layer":1},{"info":"⫏≰1112202≎⊠⪸⫏≰1200111=⫏≰112210202100","layer":1},{"info":"⫏≰221021122⫸⊐⫏≰112210202100=⫏≰2012012211201","layer":0}]}
{"id":580,"expression_no_base_symbol":"$5982$/$2658$⪨≂$2378$⫸⊐$1335$","expression":"⫏≰22012120/⫏≰10122110⪨≂⫏≰10021002⫸⊐⫏≰1211110","highest_n_order":2,"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":5982,"base":3},"right_expr":{"type":"numeric_atoms","value":2658,"base":3}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":2378,"base":3},"right_expr":{"type":"numeric_atoms","value":1335,"base":3}}},"used_operators":["sdazOOVcIp","XhwjNDsVaA","mqXw5SEYmG"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"⫏≰-112011101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5982","layer":2},{"info":"number node, value=2658","layer":2},{"info":"compute binary expreesion, left_input=5982, right_input=2658, op_id = XhwjNDsVaA binary_op_definition= 'None', output=2","layer":1},{"info":"number node, value=2378","layer":2},{"info":"number node, value=1335","layer":2},{"info":"compute binary expreesion, left_input=2378, right_input=1335, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=5215","layer":1},{"info":"compute binary expreesion, left_input=2, right_input=5215, 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=-10324","layer":0}],"base":3,"result_base":3,"text":"⫏≰22012120/⫏≰10122110⪨≂⫏≰10021002⫸⊐⫏≰1211110=⫏≰-112011101","reverse_text":"⫏≰-112011101=⫏≰22012120/⫏≰10122110⪨≂⫏≰10021002⫸⊐⫏≰1211110","cot":[{"info":"⫏≰22012120/⫏≰10122110=⫏≰2","layer":1},{"info":"⫏≰10021002⫸⊐⫏≰1211110=⫏≰21011011","layer":1},{"info":"⫏≰2⪨≂⫏≰21011011=⫏≰-112011101","layer":0}]}
{"id":581,"expression_no_base_symbol":"(-$1476$)⪨≂$4830$⪒$1219$","expression":"(-⫏≰2000200)⪨≂⫏≰20121220⪒⫏≰1200011","highest_n_order":1,"priority_hierarchical_complexity":2,"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":1476,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":4830,"base":3},"right_expr":{"type":"numeric_atoms","value":1219,"base":3}}},"used_operators":["sdazOOVcIp","t8gj7n24qd","f6k1SAg4EE"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰110200112","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1476","layer":2},{"info":"compute unary expreesion, input=1476, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1476","layer":1},{"info":"number node, value=4830","layer":2},{"info":"number node, value=1219","layer":2},{"info":"compute binary expreesion, left_input=4830, right_input=1219, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-6049","layer":1},{"info":"compute binary expreesion, left_input=-1476, right_input=-6049, 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=9248","layer":0}],"base":3,"result_base":3,"text":"(-⫏≰2000200)⪨≂⫏≰20121220⪒⫏≰1200011=⫏≰110200112","reverse_text":"⫏≰110200112=(-⫏≰2000200)⪨≂⫏≰20121220⪒⫏≰1200011","cot":[{"info":"-⫏≰2000200=⫏≰-2000200","layer":1},{"info":"⫏≰20121220⪒⫏≰1200011=⫏≰-22022001","layer":1},{"info":"⫏≰-2000200⪨≂⫏≰-22022001=⫏≰110200112","layer":0}]}
{"id":582,"expression_no_base_symbol":"($4915$⊭∹↮)⫥∨⫟$1042$⪘⫢$3412$","expression":"(⫏≰20202001⊭∹↮)⫥∨⫟⫏≰1102121⪘⫢⫏≰11200101","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":175,"operation_count":3,"complexity_ratio":58.333333333333336,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"numeric_atoms","value":4915,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1042,"base":3},"right_expr":{"type":"numeric_atoms","value":3412,"base":3}}},"used_operators":["KYD54nUTWz","xNBdhnnwKq","oacrs7FA3X"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4915","layer":2},{"info":"compute unary expreesion, input=4915, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=9830","layer":1},{"info":"number node, value=1042","layer":2},{"info":"number node, value=3412","layer":2},{"info":"compute binary expreesion, left_input=1042, right_input=3412, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=1960","layer":1},{"info":"compute binary expreesion, left_input=9830, right_input=1960, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20202001⊭∹↮)⫥∨⫟⫏≰1102121⪘⫢⫏≰11200101=NaN","reverse_text":"NaN=(⫏≰20202001⊭∹↮)⫥∨⫟⫏≰1102121⪘⫢⫏≰11200101","cot":[{"info":"⫏≰20202001⊭∹↮=⫏≰111111002","layer":1},{"info":"⫏≰1102121⪘⫢⫏≰11200101=⫏≰2200121","layer":1},{"info":"⫏≰111111002⫥∨⫟⫏≰2200121=NaN","layer":0}]}
{"id":583,"expression_no_base_symbol":"($1791$⇼⇔∾$4518$)⪘⫢(+⊝⨔$8315$)","expression":"(⫏≰2110100⇼⇔∾⫏≰20012100)⪘⫢(+⊝⨔⫏≰102101222)","highest_n_order":3,"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":1791,"base":3},"right_expr":{"type":"numeric_atoms","value":4518,"base":3}},"right_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":8315,"base":3}}},"used_operators":["oacrs7FA3X","tifHPKVTfV","DhbWaqg5eL"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe"],"result":"⫏≰21022102","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1791","layer":2},{"info":"number node, value=4518","layer":2},{"info":"compute binary expreesion, left_input=1791, right_input=4518, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=2727","layer":1},{"info":"number node, value=8315","layer":2},{"info":"compute unary expreesion, input=8315, 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 binary expreesion, left_input=2727, right_input=1522, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=5330","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2110100⇼⇔∾⫏≰20012100)⪘⫢(+⊝⨔⫏≰102101222)=⫏≰21022102","reverse_text":"⫏≰21022102=(⫏≰2110100⇼⇔∾⫏≰20012100)⪘⫢(+⊝⨔⫏≰102101222)","cot":[{"info":"⫏≰2110100⇼⇔∾⫏≰20012100=⫏≰10202000","layer":1},{"info":"+⊝⨔⫏≰102101222=⫏≰2002101","layer":1},{"info":"⫏≰10202000⪘⫢⫏≰2002101=⫏≰21022102","layer":0}]}
{"id":584,"expression_no_base_symbol":"+⊝⨔($1716$/$6531$)","expression":"+⊝⨔(⫏≰2100120/⫏≰22221220)","highest_n_order":3,"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":1716,"base":3},"right_expr":{"type":"numeric_atoms","value":6531,"base":3}}},"used_operators":["DhbWaqg5eL","XhwjNDsVaA"],"dependent_operators":["dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰2002101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1716","layer":2},{"info":"number node, value=6531","layer":2},{"info":"compute binary expreesion, left_input=1716, right_input=6531, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute unary expreesion, input=0, 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":3,"result_base":3,"text":"+⊝⨔(⫏≰2100120/⫏≰22221220)=⫏≰2002101","reverse_text":"⫏≰2002101=+⊝⨔(⫏≰2100120/⫏≰22221220)","cot":[{"info":"⫏≰2100120/⫏≰22221220=⫏≰0","layer":1},{"info":"+⊝⨔⫏≰0=⫏≰2002101","layer":0}]}
{"id":585,"expression_no_base_symbol":"$5045$⪄$2496$⊉≛↸$1836$∼$1241$","expression":"⫏≰20220212⪄⫏≰10102110⊉≛↸⫏≰2112000∼⫏≰1200222","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":137,"operation_count":3,"complexity_ratio":45.666666666666664,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":5045,"base":3},"right_expr":{"type":"numeric_atoms","value":2496,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":1836,"base":3},"right_expr":{"type":"numeric_atoms","value":1241,"base":3}}},"used_operators":["DZ8iAZOCBD","SUmda5xLS4","DyGG3AbaNP"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5045","layer":2},{"info":"number node, value=2496","layer":2},{"info":"compute binary expreesion, left_input=5045, right_input=2496, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-752733","layer":1},{"info":"number node, value=1836","layer":2},{"info":"number node, value=1241","layer":2},{"info":"compute binary expreesion, left_input=1836, right_input=1241, 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=-752733, 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":3,"result_base":3,"text":"⫏≰20220212⪄⫏≰10102110⊉≛↸⫏≰2112000∼⫏≰1200222=NaN","reverse_text":"NaN=⫏≰20220212⪄⫏≰10102110⊉≛↸⫏≰2112000∼⫏≰1200222","cot":[{"info":"⫏≰20220212⪄⫏≰10102110=⫏≰-1102020120000","layer":1},{"info":"⫏≰2112000∼⫏≰1200222=NaN","layer":1},{"info":"⫏≰-1102020120000⊉≛↸NaN=NaN","layer":0}]}
{"id":586,"expression_no_base_symbol":"$2828$≭$7559$⨳⩥⨓($6311$⪐)","expression":"⫏≰10212202≭⫏≰101100222⨳⩥⨓(⫏≰22122202⪐)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":2828,"base":3},"right_expr":{"type":"numeric_atoms","value":7559,"base":3}},"right_expr":{"type":"unary","operator":"⪐","unary_expr":{"type":"numeric_atoms","value":6311,"base":3}}},"used_operators":["nCS4ZIUYfx","rxpJgHHUmx","eH2TOUuTDT"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2828","layer":2},{"info":"number node, value=7559","layer":2},{"info":"compute binary expreesion, left_input=2828, right_input=7559, 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=6311","layer":2},{"info":"compute unary expreesion, input=6311, op_id = eH2TOUuTDT, unary_op_definition = 'a⪐ = { (a+a) , if (-a)!=532 or a<368 ; (-a) , else }', output=12622","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=12622, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰10212202≭⫏≰101100222⨳⩥⨓(⫏≰22122202⪐)=NaN","reverse_text":"NaN=⫏≰10212202≭⫏≰101100222⨳⩥⨓(⫏≰22122202⪐)","cot":[{"info":"⫏≰10212202≭⫏≰101100222=NaN","layer":1},{"info":"⫏≰22122202⪐=⫏≰122022111","layer":1},{"info":"NaN⨳⩥⨓⫏≰122022111=NaN","layer":0}]}
{"id":587,"expression_no_base_symbol":"($1314$∑⇟⊟$1002$)⨟⋌⩍($1366$+⇶⊼$2983$)","expression":"(⫏≰1210200∑⇟⊟⫏≰1101010)⨟⋌⩍(⫏≰1212121+⇶⊼⫏≰11002111)","highest_n_order":5,"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":1314,"base":3},"right_expr":{"type":"numeric_atoms","value":1002,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":1366,"base":3},"right_expr":{"type":"numeric_atoms","value":2983,"base":3}}},"used_operators":["rGHVDoGpnC","U7g4x0WXJJ","TpPTUOHfaN"],"dependent_operators":["Tcnh7f0tEr","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1314","layer":2},{"info":"number node, value=1002","layer":2},{"info":"compute binary expreesion, left_input=1314, right_input=1002, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"number node, value=1366","layer":2},{"info":"number node, value=2983","layer":2},{"info":"compute binary expreesion, left_input=1366, right_input=2983, 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":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, 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":0}],"base":3,"result_base":3,"text":"(⫏≰1210200∑⇟⊟⫏≰1101010)⨟⋌⩍(⫏≰1212121+⇶⊼⫏≰11002111)=NaN","reverse_text":"NaN=(⫏≰1210200∑⇟⊟⫏≰1101010)⨟⋌⩍(⫏≰1212121+⇶⊼⫏≰11002111)","cot":[{"info":"⫏≰1210200∑⇟⊟⫏≰1101010=NaN","layer":1},{"info":"⫏≰1212121+⇶⊼⫏≰11002111=NaN","layer":1},{"info":"NaN⨟⋌⩍NaN=NaN","layer":0}]}
{"id":588,"expression_no_base_symbol":"($1499$↪⪝)⋓(↔$8033$)","expression":"(⫏≰2001112↪⪝)⋓(↔⫏≰102000112)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":720,"operation_count":3,"complexity_ratio":240.0,"tree":{"type":"binary","operator":"⋓","left_expr":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"numeric_atoms","value":1499,"base":3}},"right_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":8033,"base":3}}},"used_operators":["T2fj7uvVaJ","l07mrZUIn9","ruOEQAzv1W"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","9HNa5Wba9A","2DDjHMKMc0","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1499","layer":2},{"info":"compute unary expreesion, input=1499, op_id = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=91711818","layer":1},{"info":"number node, value=8033","layer":2},{"info":"compute unary expreesion, input=8033, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-7760","layer":1},{"info":"compute binary expreesion, left_input=91711818, right_input=-7760, 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":3,"result_base":3,"text":"(⫏≰2001112↪⪝)⋓(↔⫏≰102000112)=⫏≰0","reverse_text":"⫏≰0=(⫏≰2001112↪⪝)⋓(↔⫏≰102000112)","cot":[{"info":"⫏≰2001112↪⪝=⫏≰20101120102222000","layer":1},{"info":"↔⫏≰102000112=⫏≰-101122102","layer":1},{"info":"⫏≰20101120102222000⋓⫏≰-101122102=⫏≰0","layer":0}]}
{"id":589,"expression_no_base_symbol":"($2933$⨳⩥⨓$1164$)⪮%⊝$1043$⪢$2675$","expression":"(⫏≰11000122⨳⩥⨓⫏≰1121010)⪮%⊝⫏≰1102122⪢⫏≰10200002","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2687,"operation_count":3,"complexity_ratio":895.6666666666666,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":2933,"base":3},"right_expr":{"type":"numeric_atoms","value":1164,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1043,"base":3},"right_expr":{"type":"numeric_atoms","value":2675,"base":3}}},"used_operators":["IWmyXbctLI","nCS4ZIUYfx","dWAJyo7jo9"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","W4YGzv6Whe","rysDP5nf3Z","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2933","layer":2},{"info":"number node, value=1164","layer":2},{"info":"compute binary expreesion, left_input=2933, right_input=1164, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-1769","layer":1},{"info":"number node, value=1043","layer":2},{"info":"number node, value=2675","layer":2},{"info":"compute binary expreesion, left_input=1043, right_input=2675, 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=-1769, right_input=nan, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11000122⨳⩥⨓⫏≰1121010)⪮%⊝⫏≰1102122⪢⫏≰10200002=NaN","reverse_text":"NaN=(⫏≰11000122⨳⩥⨓⫏≰1121010)⪮%⊝⫏≰1102122⪢⫏≰10200002","cot":[{"info":"⫏≰11000122⨳⩥⨓⫏≰1121010=⫏≰-2102112","layer":1},{"info":"⫏≰1102122⪢⫏≰10200002=NaN","layer":1},{"info":"⫏≰-2102112⪮%⊝NaN=NaN","layer":0}]}
{"id":590,"expression_no_base_symbol":"($3111$↙$1173$)⨐⩸⫘($4822$-$7511$)","expression":"(⫏≰11021020↙⫏≰1121110)⨐⩸⫘(⫏≰20121121-⫏≰101022012)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1178,"operation_count":3,"complexity_ratio":392.6666666666667,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":3111,"base":3},"right_expr":{"type":"numeric_atoms","value":1173,"base":3}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":4822,"base":3},"right_expr":{"type":"numeric_atoms","value":7511,"base":3}}},"used_operators":["fu6greOZ01","yyfyN0ffXY","rysDP5nf3Z"],"dependent_operators":["3ViojmjbAp","tmPS8pqC7x","DpFCA1CohY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3111","layer":2},{"info":"number node, value=1173","layer":2},{"info":"compute binary expreesion, left_input=3111, right_input=1173, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-3519","layer":1},{"info":"number node, value=4822","layer":2},{"info":"number node, value=7511","layer":2},{"info":"compute binary expreesion, left_input=4822, right_input=7511, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-2689","layer":1},{"info":"compute binary expreesion, left_input=-3519, right_input=-2689, 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":3,"result_base":3,"text":"(⫏≰11021020↙⫏≰1121110)⨐⩸⫘(⫏≰20121121-⫏≰101022012)=NaN","reverse_text":"NaN=(⫏≰11021020↙⫏≰1121110)⨐⩸⫘(⫏≰20121121-⫏≰101022012)","cot":[{"info":"⫏≰11021020↙⫏≰1121110=⫏≰-11211100","layer":1},{"info":"⫏≰20121121-⫏≰101022012=⫏≰-10200121","layer":1},{"info":"⫏≰-11211100⨐⩸⫘⫏≰-10200121=NaN","layer":0}]}
{"id":591,"expression_no_base_symbol":"$3725$≧⫂∧$8820$⩨($5553$+$4687$)","expression":"⫏≰12002222≧⫂∧⫏≰110002200⩨(⫏≰21121200+⫏≰20102121)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"⩨","left_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":3725,"base":3},"right_expr":{"type":"numeric_atoms","value":8820,"base":3}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":5553,"base":3},"right_expr":{"type":"numeric_atoms","value":4687,"base":3}}},"used_operators":["2DlMacCsIx","Ph9nP6C5qx","W4YGzv6Whe"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-10","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3725","layer":2},{"info":"number node, value=8820","layer":2},{"info":"compute binary expreesion, left_input=3725, right_input=8820, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=8347","layer":1},{"info":"number node, value=5553","layer":2},{"info":"number node, value=4687","layer":2},{"info":"compute binary expreesion, left_input=5553, right_input=4687, op_id = W4YGzv6Whe binary_op_definition= 'None', output=10240","layer":1},{"info":"compute binary expreesion, left_input=8347, right_input=10240, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-3","layer":0}],"base":3,"result_base":3,"text":"⫏≰12002222≧⫂∧⫏≰110002200⩨(⫏≰21121200+⫏≰20102121)=⫏≰-10","reverse_text":"⫏≰-10=⫏≰12002222≧⫂∧⫏≰110002200⩨(⫏≰21121200+⫏≰20102121)","cot":[{"info":"⫏≰12002222≧⫂∧⫏≰110002200=⫏≰102110011","layer":1},{"info":"⫏≰21121200+⫏≰20102121=⫏≰112001021","layer":1},{"info":"⫏≰102110011⩨⫏≰112001021=⫏≰-10","layer":0}]}
{"id":592,"expression_no_base_symbol":"⊙↵-($9177$⨳⩥⨓$6937$)","expression":"⊙↵-(⫏≰110120220⨳⩥⨓⫏≰100111221)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2275,"operation_count":2,"complexity_ratio":1137.5,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":9177,"base":3},"right_expr":{"type":"numeric_atoms","value":6937,"base":3}}},"used_operators":["oWn0xqSxBt","nCS4ZIUYfx"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰21021","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=9177","layer":2},{"info":"number node, value=6937","layer":2},{"info":"compute binary expreesion, left_input=9177, right_input=6937, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-2240","layer":1},{"info":"compute unary expreesion, input=-2240, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=196","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⫏≰110120220⨳⩥⨓⫏≰100111221)=⫏≰21021","reverse_text":"⫏≰21021=⊙↵-(⫏≰110120220⨳⩥⨓⫏≰100111221)","cot":[{"info":"⫏≰110120220⨳⩥⨓⫏≰100111221=⫏≰-10001222","layer":1},{"info":"⊙↵-⫏≰-10001222=⫏≰21021","layer":0}]}
{"id":593,"expression_no_base_symbol":"+⊝⨔($3317$⨪↰⇹$1306$)","expression":"+⊝⨔(⫏≰11112212⨪↰⇹⫏≰1210101)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3357,"operation_count":2,"complexity_ratio":1678.5,"tree":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":3317,"base":3},"right_expr":{"type":"numeric_atoms","value":1306,"base":3}}},"used_operators":["DhbWaqg5eL","tmPS8pqC7x"],"dependent_operators":["dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","rJVOvQCfKK"],"result":"⫏≰2002101","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3317","layer":2},{"info":"number node, value=1306","layer":2},{"info":"compute binary expreesion, left_input=3317, right_input=1306, 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=3317","layer":1},{"info":"compute unary expreesion, input=3317, 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":3,"result_base":3,"text":"+⊝⨔(⫏≰11112212⨪↰⇹⫏≰1210101)=⫏≰2002101","reverse_text":"⫏≰2002101=+⊝⨔(⫏≰11112212⨪↰⇹⫏≰1210101)","cot":[{"info":"⫏≰11112212⨪↰⇹⫏≰1210101=⫏≰11112212","layer":1},{"info":"+⊝⨔⫏≰11112212=⫏≰2002101","layer":0}]}
{"id":594,"expression_no_base_symbol":"($5737$∲⫓$2238$)⨳⩥⨓($1418$⪨≂$3386$)","expression":"(⫏≰21212111∲⫓⫏≰10001220)⨳⩥⨓(⫏≰1221112⪨≂⫏≰11122102)","highest_n_order":1,"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":5737,"base":3},"right_expr":{"type":"numeric_atoms","value":2238,"base":3}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":1418,"base":3},"right_expr":{"type":"numeric_atoms","value":3386,"base":3}}},"used_operators":["nCS4ZIUYfx","i8ToyICDmI","sdazOOVcIp"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-12021000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5737","layer":2},{"info":"number node, value=2238","layer":2},{"info":"compute binary expreesion, left_input=5737, right_input=2238, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=1418","layer":2},{"info":"number node, value=3386","layer":2},{"info":"compute binary expreesion, left_input=1418, right_input=3386, 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=-3834","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-3834, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-3834","layer":0}],"base":3,"result_base":3,"text":"(⫏≰21212111∲⫓⫏≰10001220)⨳⩥⨓(⫏≰1221112⪨≂⫏≰11122102)=⫏≰-12021000","reverse_text":"⫏≰-12021000=(⫏≰21212111∲⫓⫏≰10001220)⨳⩥⨓(⫏≰1221112⪨≂⫏≰11122102)","cot":[{"info":"⫏≰21212111∲⫓⫏≰10001220=⫏≰0","layer":1},{"info":"⫏≰1221112⪨≂⫏≰11122102=⫏≰-12021000","layer":1},{"info":"⫏≰0⨳⩥⨓⫏≰-12021000=⫏≰-12021000","layer":0}]}
{"id":595,"expression_no_base_symbol":"($1830$+$6231$)*($5251$⇋≉)","expression":"(⫏≰2111210+⫏≰22112210)*(⫏≰21012111⇋≉)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8065,"operation_count":3,"complexity_ratio":2688.3333333333335,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":1830,"base":3},"right_expr":{"type":"numeric_atoms","value":6231,"base":3}},"right_expr":{"type":"unary","operator":"⇋≉","unary_expr":{"type":"numeric_atoms","value":5251,"base":3}}},"used_operators":["9HNa5Wba9A","W4YGzv6Whe","XIabStNQrY"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰12211210212102000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1830","layer":2},{"info":"number node, value=6231","layer":2},{"info":"compute binary expreesion, left_input=1830, right_input=6231, op_id = W4YGzv6Whe binary_op_definition= 'None', output=8061","layer":1},{"info":"number node, value=5251","layer":2},{"info":"compute unary expreesion, input=5251, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=10404","layer":1},{"info":"compute binary expreesion, left_input=8061, right_input=10404, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=83866644","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2111210+⫏≰22112210)*(⫏≰21012111⇋≉)=⫏≰12211210212102000","reverse_text":"⫏≰12211210212102000=(⫏≰2111210+⫏≰22112210)*(⫏≰21012111⇋≉)","cot":[{"info":"⫏≰2111210+⫏≰22112210=⫏≰102001120","layer":1},{"info":"⫏≰21012111⇋≉=⫏≰112021100","layer":1},{"info":"⫏≰102001120*⫏≰112021100=⫏≰12211210212102000","layer":0}]}
{"id":596,"expression_no_base_symbol":"($3658$≋⫹)⨸⪁$3295$⨰$1094$","expression":"(⫏≰12000111≋⫹)⨸⪁⫏≰11112001⨰⫏≰1111112","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":12,"operation_count":3,"complexity_ratio":4.0,"tree":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"unary","operator":"≋⫹","unary_expr":{"type":"numeric_atoms","value":3658,"base":3}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":3295,"base":3},"right_expr":{"type":"numeric_atoms","value":1094,"base":3}}},"used_operators":["g55IO6H4Gj","N41Kp7NANJ","eewbuw0ToL"],"dependent_operators":["W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-112000011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3658","layer":2},{"info":"compute unary expreesion, input=3658, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-7316","layer":1},{"info":"number node, value=3295","layer":2},{"info":"number node, value=1094","layer":2},{"info":"compute binary expreesion, left_input=3295, right_input=1094, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=2211","layer":1},{"info":"compute binary expreesion, left_input=-7316, right_input=2211, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=-10210","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12000111≋⫹)⨸⪁⫏≰11112001⨰⫏≰1111112=⫏≰-112000011","reverse_text":"⫏≰-112000011=(⫏≰12000111≋⫹)⨸⪁⫏≰11112001⨰⫏≰1111112","cot":[{"info":"⫏≰12000111≋⫹=⫏≰-101000222","layer":1},{"info":"⫏≰11112001⨰⫏≰1111112=⫏≰10000220","layer":1},{"info":"⫏≰-101000222⨸⪁⫏≰10000220=⫏≰-112000011","layer":0}]}
{"id":597,"expression_no_base_symbol":"↣≠⋷($4133$⋓$2222$)","expression":"↣≠⋷(⫏≰12200002⋓⫏≰10001022)","highest_n_order":4,"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":4133,"base":3},"right_expr":{"type":"numeric_atoms","value":2222,"base":3}}},"used_operators":["Asc51vEJeQ","T2fj7uvVaJ"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4133","layer":2},{"info":"number node, value=2222","layer":2},{"info":"compute binary expreesion, left_input=4133, right_input=2222, 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 = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(⫏≰12200002⋓⫏≰10001022)=NaN","reverse_text":"NaN=↣≠⋷(⫏≰12200002⋓⫏≰10001022)","cot":[{"info":"⫏≰12200002⋓⫏≰10001022=⫏≰0","layer":1},{"info":"↣≠⋷⫏≰0=NaN","layer":0}]}
{"id":598,"expression_no_base_symbol":"($4314$⊭↱$3993$)⋥≓≎($7703$⊉≛↸$1135$)","expression":"(⫏≰12220210⊭↱⫏≰12110220)⋥≓≎(⫏≰101120022⊉≛↸⫏≰1120001)","highest_n_order":1,"priority_hierarchical_complexity":2,"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":4314,"base":3},"right_expr":{"type":"numeric_atoms","value":3993,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":7703,"base":3},"right_expr":{"type":"numeric_atoms","value":1135,"base":3}}},"used_operators":["Qy55tPpLXF","COABgblf1C","DZ8iAZOCBD"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4314","layer":2},{"info":"number node, value=3993","layer":2},{"info":"compute binary expreesion, left_input=4314, right_input=3993, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-637","layer":1},{"info":"number node, value=7703","layer":2},{"info":"number node, value=1135","layer":2},{"info":"compute binary expreesion, left_input=7703, right_input=1135, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=15406","layer":1},{"info":"compute binary expreesion, left_input=-637, right_input=15406, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=67","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12220210⊭↱⫏≰12110220)⋥≓≎(⫏≰101120022⊉≛↸⫏≰1120001)=⫏≰2111","reverse_text":"⫏≰2111=(⫏≰12220210⊭↱⫏≰12110220)⋥≓≎(⫏≰101120022⊉≛↸⫏≰1120001)","cot":[{"info":"⫏≰12220210⊭↱⫏≰12110220=⫏≰-212121","layer":1},{"info":"⫏≰101120022⊉≛↸⫏≰1120001=⫏≰210010121","layer":1},{"info":"⫏≰-212121⋥≓≎⫏≰210010121=⫏≰2111","layer":0}]}
{"id":599,"expression_no_base_symbol":"⪝⪂⫅(⇁⨣⪵$4820$)","expression":"⪝⪂⫅(⇁⨣⪵⫏≰20121112)","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":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":4820,"base":3}}},"used_operators":["XTarYq4gQB","inkyxCbjAn"],"dependent_operators":["9HNa5Wba9A","8w2t5hMYqp","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4820","layer":2},{"info":"compute unary expreesion, input=4820, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⪝⪂⫅(⇁⨣⪵⫏≰20121112)=NaN","reverse_text":"NaN=⪝⪂⫅(⇁⨣⪵⫏≰20121112)","cot":[{"info":"⇁⨣⪵⫏≰20121112=NaN","layer":1},{"info":"⪝⪂⫅NaN=NaN","layer":0}]}
{"id":600,"expression_no_base_symbol":"$2590$⨎$1652$⩨$7240$⪘⫢$4779$","expression":"⫏≰10112221⨎⫏≰2021012⩨⫏≰100221011⪘⫢⫏≰20120000","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":2590,"base":3},"right_expr":{"type":"numeric_atoms","value":1652,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":7240,"base":3},"right_expr":{"type":"numeric_atoms","value":4779,"base":3}}},"used_operators":["2DlMacCsIx","rJVOvQCfKK","oacrs7FA3X"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⫏≰-220","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2590","layer":2},{"info":"number node, value=1652","layer":2},{"info":"compute binary expreesion, left_input=2590, right_input=1652, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=1652","layer":1},{"info":"number node, value=7240","layer":2},{"info":"number node, value=4779","layer":2},{"info":"compute binary expreesion, left_input=7240, right_input=4779, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=14356","layer":1},{"info":"compute binary expreesion, left_input=1652, right_input=14356, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-24","layer":0}],"base":3,"result_base":3,"text":"⫏≰10112221⨎⫏≰2021012⩨⫏≰100221011⪘⫢⫏≰20120000=⫏≰-220","reverse_text":"⫏≰-220=⫏≰10112221⨎⫏≰2021012⩨⫏≰100221011⪘⫢⫏≰20120000","cot":[{"info":"⫏≰10112221⨎⫏≰2021012=⫏≰2021012","layer":1},{"info":"⫏≰100221011⪘⫢⫏≰20120000=⫏≰201200201","layer":1},{"info":"⫏≰2021012⩨⫏≰201200201=⫏≰-220","layer":0}]}
{"id":601,"expression_no_base_symbol":"$1606$⨎$4060$⫡⨏$3377$⋳⪒$1927$","expression":"⫏≰2012111⨎⫏≰12120101⫡⨏⫏≰11122002⋳⪒⫏≰2122101","highest_n_order":2,"priority_hierarchical_complexity":2,"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":1606,"base":3},"right_expr":{"type":"numeric_atoms","value":4060,"base":3}},"right_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":3377,"base":3},"right_expr":{"type":"numeric_atoms","value":1927,"base":3}}},"used_operators":["QMFrweE19q","rJVOvQCfKK","12rbrZMWeM"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰1112101011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1606","layer":2},{"info":"number node, value=4060","layer":2},{"info":"compute binary expreesion, left_input=1606, right_input=4060, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=4060","layer":1},{"info":"number node, value=3377","layer":2},{"info":"number node, value=1927","layer":2},{"info":"compute binary expreesion, left_input=3377, right_input=1927, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=4540","layer":1},{"info":"compute binary expreesion, left_input=4060, right_input=4540, 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=30163","layer":0}],"base":3,"result_base":3,"text":"⫏≰2012111⨎⫏≰12120101⫡⨏⫏≰11122002⋳⪒⫏≰2122101=⫏≰1112101011","reverse_text":"⫏≰1112101011=⫏≰2012111⨎⫏≰12120101⫡⨏⫏≰11122002⋳⪒⫏≰2122101","cot":[{"info":"⫏≰2012111⨎⫏≰12120101=⫏≰12120101","layer":1},{"info":"⫏≰11122002⋳⪒⫏≰2122101=⫏≰20020011","layer":1},{"info":"⫏≰12120101⫡⨏⫏≰20020011=⫏≰1112101011","layer":0}]}
{"id":602,"expression_no_base_symbol":"($2571$⪄$2263$)≎⊠⪸($1308$⊭↱$1724$)","expression":"(⫏≰10112020⪄⫏≰10002211)≎⊠⪸(⫏≰1210110⊭↱⫏≰2100212)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":372,"operation_count":3,"complexity_ratio":124.0,"tree":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2571,"base":3},"right_expr":{"type":"numeric_atoms","value":2263,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":1308,"base":3},"right_expr":{"type":"numeric_atoms","value":1724,"base":3}}},"used_operators":["bJkvcejdHO","SUmda5xLS4","COABgblf1C"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰20221221120211202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2571","layer":2},{"info":"number node, value=2263","layer":2},{"info":"compute binary expreesion, left_input=2571, right_input=2263, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-385649","layer":1},{"info":"number node, value=1308","layer":2},{"info":"number node, value=1724","layer":2},{"info":"compute binary expreesion, left_input=1308, right_input=1724, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=837","layer":1},{"info":"compute binary expreesion, left_input=-385649, right_input=837, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=99883091","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10112020⪄⫏≰10002211)≎⊠⪸(⫏≰1210110⊭↱⫏≰2100212)=⫏≰20221221120211202","reverse_text":"⫏≰20221221120211202=(⫏≰10112020⪄⫏≰10002211)≎⊠⪸(⫏≰1210110⊭↱⫏≰2100212)","cot":[{"info":"⫏≰10112020⪄⫏≰10002211=⫏≰-201121000022","layer":1},{"info":"⫏≰1210110⊭↱⫏≰2100212=⫏≰1011000","layer":1},{"info":"⫏≰-201121000022≎⊠⪸⫏≰1011000=⫏≰20221221120211202","layer":0}]}
{"id":603,"expression_no_base_symbol":"≤/$2579$⋳⪒$4525$","expression":"≤/⫏≰10112112⋳⪒⫏≰20012121","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":2579,"base":3},"right_expr":{"type":"numeric_atoms","value":4525,"base":3}}},"used_operators":["eLAdDNolq6","12rbrZMWeM"],"dependent_operators":["rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰12010","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2579","layer":2},{"info":"number node, value=4525","layer":2},{"info":"compute binary expreesion, left_input=2579, right_input=4525, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=346","layer":1},{"info":"compute unary expreesion, input=346, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=138","layer":0}],"base":3,"result_base":3,"text":"≤/⫏≰10112112⋳⪒⫏≰20012121=⫏≰12010","reverse_text":"⫏≰12010=≤/⫏≰10112112⋳⪒⫏≰20012121","cot":[{"info":"⫏≰10112112⋳⪒⫏≰20012121=⫏≰110211","layer":1},{"info":"≤/⫏≰110211=⫏≰12010","layer":0}]}
{"id":604,"expression_no_base_symbol":"-$1269$⪛$1132$","expression":"-⫏≰1202000⪛⫏≰1112221","highest_n_order":2,"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":1269,"base":3},"right_expr":{"type":"numeric_atoms","value":1132,"base":3}}},"used_operators":["t8gj7n24qd","uFcxV4UQCh"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⫏≰-12002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1269","layer":2},{"info":"number node, value=1132","layer":2},{"info":"compute binary expreesion, left_input=1269, right_input=1132, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=137","layer":1},{"info":"compute unary expreesion, input=137, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-137","layer":0}],"base":3,"result_base":3,"text":"-⫏≰1202000⪛⫏≰1112221=⫏≰-12002","reverse_text":"⫏≰-12002=-⫏≰1202000⪛⫏≰1112221","cot":[{"info":"⫏≰1202000⪛⫏≰1112221=⫏≰12002","layer":1},{"info":"-⫏≰12002=⫏≰-12002","layer":0}]}
{"id":605,"expression_no_base_symbol":"(⇁⨣⪵$1743$)⨓(∥⊫$3807$)","expression":"(⇁⨣⪵⫏≰2101120)⨓(∥⊫⫏≰12020000)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4686,"operation_count":3,"complexity_ratio":1562.0,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":1743,"base":3}},"right_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":3807,"base":3}}},"used_operators":["3ViojmjbAp","inkyxCbjAn","P8v4zCKN1o"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","B5M0gjZbta","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-20102021","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1743","layer":2},{"info":"compute unary expreesion, input=1743, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"number node, value=3807","layer":2},{"info":"compute unary expreesion, input=3807, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=4675","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=4675, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-4678","layer":0}],"base":3,"result_base":3,"text":"(⇁⨣⪵⫏≰2101120)⨓(∥⊫⫏≰12020000)=⫏≰-20102021","reverse_text":"⫏≰-20102021=(⇁⨣⪵⫏≰2101120)⨓(∥⊫⫏≰12020000)","cot":[{"info":"⇁⨣⪵⫏≰2101120=NaN","layer":1},{"info":"∥⊫⫏≰12020000=⫏≰20102011","layer":1},{"info":"NaN⨓⫏≰20102011=⫏≰-20102021","layer":0}]}
{"id":606,"expression_no_base_symbol":"(↔$2684$)⪒$5790$≹⇙⪍$3973$","expression":"(↔⫏≰10200102)⪒⫏≰21221110≹⇙⪍⫏≰12110011","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":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":2684,"base":3}},"right_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":5790,"base":3},"right_expr":{"type":"numeric_atoms","value":3973,"base":3}}},"used_operators":["f6k1SAg4EE","ruOEQAzv1W","AHs5Up7iyr"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2684","layer":2},{"info":"compute unary expreesion, input=2684, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-2411","layer":1},{"info":"number node, value=5790","layer":2},{"info":"number node, value=3973","layer":2},{"info":"compute binary expreesion, left_input=5790, right_input=3973, 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=-2411, right_input=nan, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(↔⫏≰10200102)⪒⫏≰21221110≹⇙⪍⫏≰12110011=NaN","reverse_text":"NaN=(↔⫏≰10200102)⪒⫏≰21221110≹⇙⪍⫏≰12110011","cot":[{"info":"↔⫏≰10200102=⫏≰-10022022","layer":1},{"info":"⫏≰21221110≹⇙⪍⫏≰12110011=NaN","layer":1},{"info":"⫏≰-10022022⪒NaN=NaN","layer":0}]}
{"id":607,"expression_no_base_symbol":"($2324$⪒$2173$)∲⫓$1679$∑⇟⊟$1590$","expression":"(⫏≰10012002⪒⫏≰2222111)∲⫓⫏≰2022012∑⇟⊟⫏≰2011220","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":2324,"base":3},"right_expr":{"type":"numeric_atoms","value":2173,"base":3}},"right_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":1679,"base":3},"right_expr":{"type":"numeric_atoms","value":1590,"base":3}}},"used_operators":["i8ToyICDmI","f6k1SAg4EE","U7g4x0WXJJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2324","layer":2},{"info":"number node, value=2173","layer":2},{"info":"compute binary expreesion, left_input=2324, right_input=2173, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-4497","layer":1},{"info":"number node, value=1679","layer":2},{"info":"number node, value=1590","layer":2},{"info":"compute binary expreesion, left_input=1679, right_input=1590, 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=-4497, right_input=nan, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10012002⪒⫏≰2222111)∲⫓⫏≰2022012∑⇟⊟⫏≰2011220=NaN","reverse_text":"NaN=(⫏≰10012002⪒⫏≰2222111)∲⫓⫏≰2022012∑⇟⊟⫏≰2011220","cot":[{"info":"⫏≰10012002⪒⫏≰2222111=⫏≰-20011120","layer":1},{"info":"⫏≰2022012∑⇟⊟⫏≰2011220=NaN","layer":1},{"info":"⫏≰-20011120∲⫓NaN=NaN","layer":0}]}
{"id":608,"expression_no_base_symbol":"($6421$⊪)⫸⊐$2523$⨓$7162$","expression":"(⫏≰22210211⊪)⫸⊐⫏≰10110110⨓⫏≰100211021","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7205,"operation_count":3,"complexity_ratio":2401.6666666666665,"tree":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":6421,"base":3}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":2523,"base":3},"right_expr":{"type":"numeric_atoms","value":7162,"base":3}}},"used_operators":["mqXw5SEYmG","zVYPLywUTj","3ViojmjbAp"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6421","layer":2},{"info":"compute unary expreesion, input=6421, 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":"number node, value=2523","layer":2},{"info":"number node, value=7162","layer":2},{"info":"compute binary expreesion, left_input=2523, right_input=7162, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-7165","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-7165, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22210211⊪)⫸⊐⫏≰10110110⨓⫏≰100211021=⫏≰0","reverse_text":"⫏≰0=(⫏≰22210211⊪)⫸⊐⫏≰10110110⨓⫏≰100211021","cot":[{"info":"⫏≰22210211⊪=⫏≰0","layer":1},{"info":"⫏≰10110110⨓⫏≰100211021=⫏≰-100211101","layer":1},{"info":"⫏≰0⫸⊐⫏≰-100211101=⫏≰0","layer":0}]}
{"id":609,"expression_no_base_symbol":"⨈⫕$4898$⋳⪒$2491$","expression":"⨈⫕⫏≰20201102⋳⪒⫏≰10102021","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":393,"operation_count":2,"complexity_ratio":196.5,"tree":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":4898,"base":3},"right_expr":{"type":"numeric_atoms","value":2491,"base":3}}},"used_operators":["megm06wKyl","12rbrZMWeM"],"dependent_operators":["8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4898","layer":2},{"info":"number node, value=2491","layer":2},{"info":"compute binary expreesion, left_input=4898, right_input=2491, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=7018","layer":1},{"info":"compute unary expreesion, input=7018, 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":3,"result_base":3,"text":"⨈⫕⫏≰20201102⋳⪒⫏≰10102021=⫏≰-210","reverse_text":"⫏≰-210=⨈⫕⫏≰20201102⋳⪒⫏≰10102021","cot":[{"info":"⫏≰20201102⋳⪒⫏≰10102021=⫏≰100121221","layer":1},{"info":"⨈⫕⫏≰100121221=⫏≰-210","layer":0}]}
{"id":610,"expression_no_base_symbol":"⩦⩻⨪$1266$≎⊠⪸$1938$","expression":"⩦⩻⨪⫏≰1201220≎⊠⪸⫏≰2122210","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":273,"operation_count":2,"complexity_ratio":136.5,"tree":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1266,"base":3},"right_expr":{"type":"numeric_atoms","value":1938,"base":3}}},"used_operators":["2td37pGCOC","bJkvcejdHO"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"⫏≰121122010201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1266","layer":2},{"info":"number node, value=1938","layer":2},{"info":"compute binary expreesion, left_input=1266, right_input=1938, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=327421","layer":1},{"info":"compute unary expreesion, input=327421, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=327421","layer":0}],"base":3,"result_base":3,"text":"⩦⩻⨪⫏≰1201220≎⊠⪸⫏≰2122210=⫏≰121122010201","reverse_text":"⫏≰121122010201=⩦⩻⨪⫏≰1201220≎⊠⪸⫏≰2122210","cot":[{"info":"⫏≰1201220≎⊠⪸⫏≰2122210=⫏≰121122010201","layer":1},{"info":"⩦⩻⨪⫏≰121122010201=⫏≰121122010201","layer":0}]}
{"id":611,"expression_no_base_symbol":"⨑⩽⪐(⪲⇎$1555$)","expression":"⨑⩽⪐(⪲⇎⫏≰2010121)","highest_n_order":1,"priority_hierarchical_complexity":1,"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":1555,"base":3}}},"used_operators":["AF7qkfDlqP","XPYlsWDdGa"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-10220002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1555","layer":2},{"info":"compute unary expreesion, input=1555, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=3110","layer":1},{"info":"compute unary expreesion, input=3110, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-2837","layer":0}],"base":3,"result_base":3,"text":"⨑⩽⪐(⪲⇎⫏≰2010121)=⫏≰-10220002","reverse_text":"⫏≰-10220002=⨑⩽⪐(⪲⇎⫏≰2010121)","cot":[{"info":"⪲⇎⫏≰2010121=⫏≰11021012","layer":1},{"info":"⨑⩽⪐⫏≰11021012=⫏≰-10220002","layer":0}]}
{"id":612,"expression_no_base_symbol":"$5310$+⇶⊼$1286$⋳⪒($1656$⫸⊐$6440$)","expression":"⫏≰21021200+⇶⊼⫏≰1202122⋳⪒(⫏≰2021100⫸⊐⫏≰22211112)","highest_n_order":5,"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":5310,"base":3},"right_expr":{"type":"numeric_atoms","value":1286,"base":3}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":1656,"base":3},"right_expr":{"type":"numeric_atoms","value":6440,"base":3}}},"used_operators":["12rbrZMWeM","TpPTUOHfaN","mqXw5SEYmG"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","AHs5Up7iyr","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5310","layer":2},{"info":"number node, value=1286","layer":2},{"info":"compute binary expreesion, left_input=5310, right_input=1286, 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":1},{"info":"number node, value=1656","layer":2},{"info":"number node, value=6440","layer":2},{"info":"compute binary expreesion, left_input=1656, right_input=6440, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=25635","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=25635, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰21021200+⇶⊼⫏≰1202122⋳⪒(⫏≰2021100⫸⊐⫏≰22211112)=NaN","reverse_text":"NaN=⫏≰21021200+⇶⊼⫏≰1202122⋳⪒(⫏≰2021100⫸⊐⫏≰22211112)","cot":[{"info":"⫏≰21021200+⇶⊼⫏≰1202122=NaN","layer":1},{"info":"⫏≰2021100⫸⊐⫏≰22211112=⫏≰1022011110","layer":1},{"info":"NaN⋳⪒⫏≰1022011110=NaN","layer":0}]}
{"id":613,"expression_no_base_symbol":"$1308$≹⇙⪍$1038$⩷∴$1526$⪮%⊝$5333$","expression":"⫏≰1210110≹⇙⪍⫏≰1102110⩷∴⫏≰2002112⪮%⊝⫏≰21022112","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16,"operation_count":3,"complexity_ratio":5.333333333333333,"tree":{"type":"binary","operator":"⩷∴","left_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":1308,"base":3},"right_expr":{"type":"numeric_atoms","value":1038,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1526,"base":3},"right_expr":{"type":"numeric_atoms","value":5333,"base":3}}},"used_operators":["9FxExcQeMw","AHs5Up7iyr","IWmyXbctLI"],"dependent_operators":["rysDP5nf3Z","dWAJyo7jo9","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1308","layer":2},{"info":"number node, value=1038","layer":2},{"info":"compute binary expreesion, left_input=1308, right_input=1038, 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":"number node, value=1526","layer":2},{"info":"number node, value=5333","layer":2},{"info":"compute binary expreesion, left_input=1526, right_input=5333, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=3368","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=3368, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1210110≹⇙⪍⫏≰1102110⩷∴⫏≰2002112⪮%⊝⫏≰21022112=NaN","reverse_text":"NaN=⫏≰1210110≹⇙⪍⫏≰1102110⩷∴⫏≰2002112⪮%⊝⫏≰21022112","cot":[{"info":"⫏≰1210110≹⇙⪍⫏≰1102110=NaN","layer":1},{"info":"⫏≰2002112⪮%⊝⫏≰21022112=⫏≰11121202","layer":1},{"info":"NaN⩷∴⫏≰11121202=NaN","layer":0}]}
{"id":614,"expression_no_base_symbol":"($1452$-$3091$)⊉≛↸($1495$⊦⊿)","expression":"(⫏≰1222210-⫏≰11020111)⊉≛↸(⫏≰2001101⊦⊿)","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":1452,"base":3},"right_expr":{"type":"numeric_atoms","value":3091,"base":3}},"right_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":1495,"base":3}}},"used_operators":["DZ8iAZOCBD","rysDP5nf3Z","14qkJME0vr"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰20021001","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1452","layer":2},{"info":"number node, value=3091","layer":2},{"info":"compute binary expreesion, left_input=1452, right_input=3091, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-1639","layer":1},{"info":"number node, value=1495","layer":2},{"info":"compute unary expreesion, input=1495, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-4564","layer":1},{"info":"compute binary expreesion, left_input=-1639, right_input=-4564, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=4564","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1222210-⫏≰11020111)⊉≛↸(⫏≰2001101⊦⊿)=⫏≰20021001","reverse_text":"⫏≰20021001=(⫏≰1222210-⫏≰11020111)⊉≛↸(⫏≰2001101⊦⊿)","cot":[{"info":"⫏≰1222210-⫏≰11020111=⫏≰-2020201","layer":1},{"info":"⫏≰2001101⊦⊿=⫏≰-20021001","layer":1},{"info":"⫏≰-2020201⊉≛↸⫏≰-20021001=⫏≰20021001","layer":0}]}
{"id":615,"expression_no_base_symbol":"$1297$%$1024$⋷(⨑⩽⪐$2155$)","expression":"⫏≰1210001%⫏≰1101221⋷(⨑⩽⪐⫏≰2221211)","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":1297,"base":3},"right_expr":{"type":"numeric_atoms","value":1024,"base":3}},"right_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":2155,"base":3}}},"used_operators":["23Mk6UjR3U","k8jYdgA6NY","AF7qkfDlqP"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-202020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1297","layer":2},{"info":"number node, value=1024","layer":2},{"info":"compute binary expreesion, left_input=1297, right_input=1024, op_id = k8jYdgA6NY binary_op_definition= 'None', output=273","layer":1},{"info":"number node, value=2155","layer":2},{"info":"compute unary expreesion, input=2155, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-1882","layer":1},{"info":"compute binary expreesion, left_input=273, right_input=-1882, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-546","layer":0}],"base":3,"result_base":3,"text":"⫏≰1210001%⫏≰1101221⋷(⨑⩽⪐⫏≰2221211)=⫏≰-202020","reverse_text":"⫏≰-202020=⫏≰1210001%⫏≰1101221⋷(⨑⩽⪐⫏≰2221211)","cot":[{"info":"⫏≰1210001%⫏≰1101221=⫏≰101010","layer":1},{"info":"⨑⩽⪐⫏≰2221211=⫏≰-2120201","layer":1},{"info":"⫏≰101010⋷⫏≰-2120201=⫏≰-202020","layer":0}]}
{"id":616,"expression_no_base_symbol":"$1153$≹⇙⪍$8513$⪨≂(⩦⩻⨪$7735$)","expression":"⫏≰1120201≹⇙⪍⫏≰102200022⪨≂(⩦⩻⨪⫏≰101121111)","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":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":1153,"base":3},"right_expr":{"type":"numeric_atoms","value":8513,"base":3}},"right_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":7735,"base":3}}},"used_operators":["sdazOOVcIp","AHs5Up7iyr","2td37pGCOC"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1153","layer":2},{"info":"number node, value=8513","layer":2},{"info":"compute binary expreesion, left_input=1153, right_input=8513, 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":"number node, value=7735","layer":2},{"info":"compute unary expreesion, input=7735, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=7735","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=7735, 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":3,"result_base":3,"text":"⫏≰1120201≹⇙⪍⫏≰102200022⪨≂(⩦⩻⨪⫏≰101121111)=NaN","reverse_text":"NaN=⫏≰1120201≹⇙⪍⫏≰102200022⪨≂(⩦⩻⨪⫏≰101121111)","cot":[{"info":"⫏≰1120201≹⇙⪍⫏≰102200022=NaN","layer":1},{"info":"⩦⩻⨪⫏≰101121111=⫏≰101121111","layer":1},{"info":"NaN⪨≂⫏≰101121111=NaN","layer":0}]}
{"id":617,"expression_no_base_symbol":"($1055$⋷$1239$)⊭↱$5314$⪘⫢$3664$","expression":"(⫏≰1110002⋷⫏≰1200220)⊭↱⫏≰21021211⪘⫢⫏≰12000201","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":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":1055,"base":3},"right_expr":{"type":"numeric_atoms","value":1239,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":5314,"base":3},"right_expr":{"type":"numeric_atoms","value":3664,"base":3}}},"used_operators":["COABgblf1C","23Mk6UjR3U","oacrs7FA3X"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⫏≰220220212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1055","layer":2},{"info":"number node, value=1239","layer":2},{"info":"compute binary expreesion, left_input=1055, right_input=1239, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=1423","layer":1},{"info":"number node, value=5314","layer":2},{"info":"number node, value=3664","layer":2},{"info":"compute binary expreesion, left_input=5314, right_input=3664, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=10504","layer":1},{"info":"compute binary expreesion, left_input=1423, right_input=10504, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=18167","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1110002⋷⫏≰1200220)⊭↱⫏≰21021211⪘⫢⫏≰12000201=⫏≰220220212","reverse_text":"⫏≰220220212=(⫏≰1110002⋷⫏≰1200220)⊭↱⫏≰21021211⪘⫢⫏≰12000201","cot":[{"info":"⫏≰1110002⋷⫏≰1200220=⫏≰1221201","layer":1},{"info":"⫏≰21021211⪘⫢⫏≰12000201=⫏≰112102001","layer":1},{"info":"⫏≰1221201⊭↱⫏≰112102001=⫏≰220220212","layer":0}]}
{"id":618,"expression_no_base_symbol":"(≤/$9754$)⊦⊿","expression":"(≤/⫏≰111101021)⊦⊿","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":"unary","operator":"≤/","unary_expr":{"type":"numeric_atoms","value":9754,"base":3}}},"used_operators":["14qkJME0vr","eLAdDNolq6"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰1102001002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=9754","layer":2},{"info":"compute unary expreesion, input=9754, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-9270","layer":1},{"info":"compute unary expreesion, input=-9270, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=27731","layer":0}],"base":3,"result_base":3,"text":"(≤/⫏≰111101021)⊦⊿=⫏≰1102001002","reverse_text":"⫏≰1102001002=(≤/⫏≰111101021)⊦⊿","cot":[{"info":"≤/⫏≰111101021=⫏≰-110201100","layer":1},{"info":"⫏≰-110201100⊦⊿=⫏≰1102001002","layer":0}]}
{"id":619,"expression_no_base_symbol":"$3372$⨟⋌⩍$3525$⫥∨⫟($2609$⨎$1417$)","expression":"⫏≰11121220⨟⋌⩍⫏≰11211120⫥∨⫟(⫏≰10120122⨎⫏≰1221111)","highest_n_order":4,"priority_hierarchical_complexity":2,"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":3372,"base":3},"right_expr":{"type":"numeric_atoms","value":3525,"base":3}},"right_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":2609,"base":3},"right_expr":{"type":"numeric_atoms","value":1417,"base":3}}},"used_operators":["KYD54nUTWz","rGHVDoGpnC","rJVOvQCfKK"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","Tcnh7f0tEr","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3372","layer":2},{"info":"number node, value=3525","layer":2},{"info":"compute binary expreesion, left_input=3372, right_input=3525, 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=2609","layer":2},{"info":"number node, value=1417","layer":2},{"info":"compute binary expreesion, left_input=2609, right_input=1417, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=1417","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1417, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11121220⨟⋌⩍⫏≰11211120⫥∨⫟(⫏≰10120122⨎⫏≰1221111)=NaN","reverse_text":"NaN=⫏≰11121220⨟⋌⩍⫏≰11211120⫥∨⫟(⫏≰10120122⨎⫏≰1221111)","cot":[{"info":"⫏≰11121220⨟⋌⩍⫏≰11211120=NaN","layer":1},{"info":"⫏≰10120122⨎⫏≰1221111=⫏≰1221111","layer":1},{"info":"NaN⫥∨⫟⫏≰1221111=NaN","layer":0}]}
{"id":620,"expression_no_base_symbol":"⫛⫱⨽($6860$⪮%⊝$1979$)","expression":"⫛⫱⨽(⫏≰100102002⪮%⊝⫏≰2201022)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1431,"operation_count":2,"complexity_ratio":715.5,"tree":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":6860,"base":3},"right_expr":{"type":"numeric_atoms","value":1979,"base":3}}},"used_operators":["DlLNRPXxWL","IWmyXbctLI"],"dependent_operators":["rGHVDoGpnC","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6860","layer":2},{"info":"number node, value=1979","layer":2},{"info":"compute binary expreesion, left_input=6860, right_input=1979, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=14036","layer":1},{"info":"compute unary expreesion, input=14036, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫛⫱⨽(⫏≰100102002⪮%⊝⫏≰2201022)=⫏≰0","reverse_text":"⫏≰0=⫛⫱⨽(⫏≰100102002⪮%⊝⫏≰2201022)","cot":[{"info":"⫏≰100102002⪮%⊝⫏≰2201022=⫏≰201020212","layer":1},{"info":"⫛⫱⨽⫏≰201020212=⫏≰0","layer":0}]}
{"id":621,"expression_no_base_symbol":"(↣≠⋷$9055$)∼(↽≂$1398$)","expression":"(↣≠⋷⫏≰110102101)∼(↽≂⫏≰1220210)","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":9055,"base":3}},"right_expr":{"type":"unary","operator":"↽≂","unary_expr":{"type":"numeric_atoms","value":1398,"base":3}}},"used_operators":["DyGG3AbaNP","Asc51vEJeQ","u6S6b8DprG"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","XhwjNDsVaA","AHs5Up7iyr","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=9055","layer":2},{"info":"compute unary expreesion, input=9055, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"number node, value=1398","layer":2},{"info":"compute unary expreesion, input=1398, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-2796","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-2796, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(↣≠⋷⫏≰110102101)∼(↽≂⫏≰1220210)=NaN","reverse_text":"NaN=(↣≠⋷⫏≰110102101)∼(↽≂⫏≰1220210)","cot":[{"info":"↣≠⋷⫏≰110102101=NaN","layer":1},{"info":"↽≂⫏≰1220210=⫏≰-10211120","layer":1},{"info":"NaN∼⫏≰-10211120=NaN","layer":0}]}
{"id":622,"expression_no_base_symbol":"($1153$⊪)⪨≂(⊄⩳↩$3968$)","expression":"(⫏≰1120201⊪)⪨≂(⊄⩳↩⫏≰12102222)","highest_n_order":2,"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":1153,"base":3}},"right_expr":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":3968,"base":3}}},"used_operators":["sdazOOVcIp","zVYPLywUTj","8w2t5hMYqp"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰1012210120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1153","layer":2},{"info":"compute unary expreesion, input=1153, 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":"number node, value=3968","layer":2},{"info":"compute unary expreesion, input=3968, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-11904","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-11904, 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=23910","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1120201⊪)⪨≂(⊄⩳↩⫏≰12102222)=⫏≰1012210120","reverse_text":"⫏≰1012210120=(⫏≰1120201⊪)⪨≂(⊄⩳↩⫏≰12102222)","cot":[{"info":"⫏≰1120201⊪=⫏≰0","layer":1},{"info":"⊄⩳↩⫏≰12102222=⫏≰-121022220","layer":1},{"info":"⫏≰0⪨≂⫏≰-121022220=⫏≰1012210120","layer":0}]}
{"id":623,"expression_no_base_symbol":"$5441$⇷$2438$⋝⋈⪟($3320$⨽$2633$)","expression":"⫏≰21110112⇷⫏≰10100022⋝⋈⪟(⫏≰11112222⨽⫏≰10121112)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":79512,"operation_count":3,"complexity_ratio":26504.0,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":5441,"base":3},"right_expr":{"type":"numeric_atoms","value":2438,"base":3}},"right_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":3320,"base":3},"right_expr":{"type":"numeric_atoms","value":2633,"base":3}}},"used_operators":["2DDjHMKMc0","mp7IySMOzn","8HhzD0ZcuI"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"⫏≰20200121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5441","layer":2},{"info":"number node, value=2438","layer":2},{"info":"compute binary expreesion, left_input=5441, right_input=2438, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=4876","layer":1},{"info":"number node, value=3320","layer":2},{"info":"number node, value=2633","layer":2},{"info":"compute binary expreesion, left_input=3320, right_input=2633, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-33073785","layer":1},{"info":"compute binary expreesion, left_input=4876, right_input=-33073785, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=4876","layer":0}],"base":3,"result_base":3,"text":"⫏≰21110112⇷⫏≰10100022⋝⋈⪟(⫏≰11112222⨽⫏≰10121112)=⫏≰20200121","reverse_text":"⫏≰20200121=⫏≰21110112⇷⫏≰10100022⋝⋈⪟(⫏≰11112222⨽⫏≰10121112)","cot":[{"info":"⫏≰21110112⇷⫏≰10100022=⫏≰20200121","layer":1},{"info":"⫏≰11112222⨽⫏≰10121112=⫏≰-2022020022201000","layer":1},{"info":"⫏≰20200121⋝⋈⪟⫏≰-2022020022201000=⫏≰20200121","layer":0}]}
{"id":624,"expression_no_base_symbol":"($6343$⪄$2680$)≦≮≮","expression":"(⫏≰22200221⪄⫏≰10200021)≦≮≮","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":98,"operation_count":2,"complexity_ratio":49.0,"tree":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":6343,"base":3},"right_expr":{"type":"numeric_atoms","value":2680,"base":3}}},"used_operators":["D4vGDi5EA2","SUmda5xLS4"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⫏≰12100010020200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6343","layer":2},{"info":"number node, value=2680","layer":2},{"info":"compute binary expreesion, left_input=6343, right_input=2680, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-945573","layer":1},{"info":"compute unary expreesion, input=-945573, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=2836719","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22200221⪄⫏≰10200021)≦≮≮=⫏≰12100010020200","reverse_text":"⫏≰12100010020200=(⫏≰22200221⪄⫏≰10200021)≦≮≮","cot":[{"info":"⫏≰22200221⪄⫏≰10200021=⫏≰-1210001002020","layer":1},{"info":"⫏≰-1210001002020≦≮≮=⫏≰12100010020200","layer":0}]}
{"id":625,"expression_no_base_symbol":"+⊝⨔(⨑⩽⪐$4827$)","expression":"+⊝⨔(⨑⩽⪐⫏≰20121210)","highest_n_order":3,"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":4827,"base":3}}},"used_operators":["DhbWaqg5eL","AF7qkfDlqP"],"dependent_operators":["dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰2002101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4827","layer":2},{"info":"compute unary expreesion, input=4827, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-4554","layer":1},{"info":"compute unary expreesion, input=-4554, 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":3,"result_base":3,"text":"+⊝⨔(⨑⩽⪐⫏≰20121210)=⫏≰2002101","reverse_text":"⫏≰2002101=+⊝⨔(⨑⩽⪐⫏≰20121210)","cot":[{"info":"⨑⩽⪐⫏≰20121210=⫏≰-20020200","layer":1},{"info":"+⊝⨔⫏≰-20020200=⫏≰2002101","layer":0}]}
{"id":626,"expression_no_base_symbol":"$1300$⨰$2100$⋥≓≎($4190$/$1950$)","expression":"⫏≰1210011⨰⫏≰2212210⋥≓≎(⫏≰12202012/⫏≰2200020)","highest_n_order":2,"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":1300,"base":3},"right_expr":{"type":"numeric_atoms","value":2100,"base":3}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":4190,"base":3},"right_expr":{"type":"numeric_atoms","value":1950,"base":3}}},"used_operators":["Qy55tPpLXF","eewbuw0ToL","XhwjNDsVaA"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1300","layer":2},{"info":"number node, value=2100","layer":2},{"info":"compute binary expreesion, left_input=1300, right_input=2100, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-790","layer":1},{"info":"number node, value=4190","layer":2},{"info":"number node, value=1950","layer":2},{"info":"compute binary expreesion, left_input=4190, right_input=1950, op_id = XhwjNDsVaA binary_op_definition= 'None', output=2","layer":1},{"info":"compute binary expreesion, left_input=-790, right_input=2, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=67","layer":0}],"base":3,"result_base":3,"text":"⫏≰1210011⨰⫏≰2212210⋥≓≎(⫏≰12202012/⫏≰2200020)=⫏≰2111","reverse_text":"⫏≰2111=⫏≰1210011⨰⫏≰2212210⋥≓≎(⫏≰12202012/⫏≰2200020)","cot":[{"info":"⫏≰1210011⨰⫏≰2212210=⫏≰-1002021","layer":1},{"info":"⫏≰12202012/⫏≰2200020=⫏≰2","layer":1},{"info":"⫏≰-1002021⋥≓≎⫏≰2=⫏≰2111","layer":0}]}
{"id":627,"expression_no_base_symbol":"⇁⨣⪵$7961$∀⇚≩$3478$","expression":"⇁⨣⪵⫏≰101220212∀⇚≩⫏≰11202211","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":55728,"operation_count":2,"complexity_ratio":27864.0,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":7961,"base":3},"right_expr":{"type":"numeric_atoms","value":3478,"base":3}}},"used_operators":["inkyxCbjAn","LRNGc0VcxI"],"dependent_operators":["B5M0gjZbta","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7961","layer":2},{"info":"number node, value=3478","layer":2},{"info":"compute binary expreesion, left_input=7961, right_input=3478, 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 = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵⫏≰101220212∀⇚≩⫏≰11202211=NaN","reverse_text":"NaN=⇁⨣⪵⫏≰101220212∀⇚≩⫏≰11202211","cot":[{"info":"⫏≰101220212∀⇚≩⫏≰11202211=NaN","layer":1},{"info":"⇁⨣⪵NaN=NaN","layer":0}]}
{"id":628,"expression_no_base_symbol":"$1483$⊉≛↸$2123$*(⫓⪴$2050$)","expression":"⫏≰2000221⊉≛↸⫏≰2220122*(⫓⪴⫏≰2210221)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5018,"operation_count":3,"complexity_ratio":1672.6666666666667,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":1483,"base":3},"right_expr":{"type":"numeric_atoms","value":2123,"base":3}},"right_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":2050,"base":3}}},"used_operators":["9HNa5Wba9A","DZ8iAZOCBD","eLxqMNBOBk"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","9HNa5Wba9A"],"result":"Inf","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1483","layer":2},{"info":"number node, value=2123","layer":2},{"info":"compute binary expreesion, left_input=1483, right_input=2123, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=2966","layer":1},{"info":"number node, value=2050","layer":2},{"info":"compute unary expreesion, input=2050, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=4202500","layer":1},{"info":"compute binary expreesion, left_input=2966, right_input=4202500, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=inf","layer":0}],"base":3,"result_base":3,"text":"⫏≰2000221⊉≛↸⫏≰2220122*(⫓⪴⫏≰2210221)=Inf","reverse_text":"Inf=⫏≰2000221⊉≛↸⫏≰2220122*(⫓⪴⫏≰2210221)","cot":[{"info":"⫏≰2000221⊉≛↸⫏≰2220122=⫏≰11001212","layer":1},{"info":"⫓⪴⫏≰2210221=⫏≰21220111202011","layer":1},{"info":"⫏≰11001212*⫏≰21220111202011=Inf","layer":0}]}
{"id":629,"expression_no_base_symbol":"⇁⨣⪵$2278$⩷∴$1253$","expression":"⇁⨣⪵⫏≰10010101⩷∴⫏≰1201102","highest_n_order":5,"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":2278,"base":3},"right_expr":{"type":"numeric_atoms","value":1253,"base":3}}},"used_operators":["inkyxCbjAn","9FxExcQeMw"],"dependent_operators":["B5M0gjZbta","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2278","layer":2},{"info":"number node, value=1253","layer":2},{"info":"compute binary expreesion, left_input=2278, right_input=1253, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=2018","layer":1},{"info":"compute unary expreesion, input=2018, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵⫏≰10010101⩷∴⫏≰1201102=NaN","reverse_text":"NaN=⇁⨣⪵⫏≰10010101⩷∴⫏≰1201102","cot":[{"info":"⫏≰10010101⩷∴⫏≰1201102=⫏≰2202202","layer":1},{"info":"⇁⨣⪵⫏≰2202202=NaN","layer":0}]}
{"id":630,"expression_no_base_symbol":"⊄⩳↩(⇁⨣⪵$2708$)","expression":"⊄⩳↩(⇁⨣⪵⫏≰10201022)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4,"operation_count":2,"complexity_ratio":2.0,"tree":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":2708,"base":3}}},"used_operators":["8w2t5hMYqp","inkyxCbjAn"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2708","layer":2},{"info":"compute unary expreesion, input=2708, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊄⩳↩(⇁⨣⪵⫏≰10201022)=NaN","reverse_text":"NaN=⊄⩳↩(⇁⨣⪵⫏≰10201022)","cot":[{"info":"⇁⨣⪵⫏≰10201022=NaN","layer":1},{"info":"⊄⩳↩NaN=NaN","layer":0}]}
{"id":631,"expression_no_base_symbol":"$2621$≎⊠⪸$5429$+⇶⊼(⊙↵-$5079$)","expression":"⫏≰10121002≎⊠⪸⫏≰21110002+⇶⊼(⊙↵-⫏≰20222010)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":683761,"operation_count":3,"complexity_ratio":227920.33333333334,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":2621,"base":3},"right_expr":{"type":"numeric_atoms","value":5429,"base":3}},"right_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":5079,"base":3}}},"used_operators":["TpPTUOHfaN","bJkvcejdHO","oWn0xqSxBt"],"dependent_operators":["AHs5Up7iyr","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2621","layer":2},{"info":"number node, value=5429","layer":2},{"info":"compute binary expreesion, left_input=2621, right_input=5429, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=678366","layer":1},{"info":"number node, value=5079","layer":2},{"info":"compute unary expreesion, input=5079, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute binary expreesion, left_input=678366, right_input=-1, 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=0","layer":0}],"base":3,"result_base":3,"text":"⫏≰10121002≎⊠⪸⫏≰21110002+⇶⊼(⊙↵-⫏≰20222010)=⫏≰0","reverse_text":"⫏≰0=⫏≰10121002≎⊠⪸⫏≰21110002+⇶⊼(⊙↵-⫏≰20222010)","cot":[{"info":"⫏≰10121002≎⊠⪸⫏≰21110002=⫏≰1021110112200","layer":1},{"info":"⊙↵-⫏≰20222010=⫏≰-1","layer":1},{"info":"⫏≰1021110112200+⇶⊼⫏≰-1=⫏≰0","layer":0}]}
{"id":632,"expression_no_base_symbol":"($1086$∑⇟⊟$1624$)⪢($1161$↺$1655$)","expression":"(⫏≰1111020∑⇟⊟⫏≰2020011)⪢(⫏≰1121000↺⫏≰2021022)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1658,"operation_count":3,"complexity_ratio":552.6666666666666,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":1086,"base":3},"right_expr":{"type":"numeric_atoms","value":1624,"base":3}},"right_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":1161,"base":3},"right_expr":{"type":"numeric_atoms","value":1655,"base":3}}},"used_operators":["dWAJyo7jo9","U7g4x0WXJJ","7j4O788W3g"],"dependent_operators":["k8jYdgA6NY","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1086","layer":2},{"info":"number node, value=1624","layer":2},{"info":"compute binary expreesion, left_input=1086, right_input=1624, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":1},{"info":"number node, value=1161","layer":2},{"info":"number node, value=1655","layer":2},{"info":"compute binary expreesion, left_input=1161, right_input=1655, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1655","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1655, 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":3,"result_base":3,"text":"(⫏≰1111020∑⇟⊟⫏≰2020011)⪢(⫏≰1121000↺⫏≰2021022)=NaN","reverse_text":"NaN=(⫏≰1111020∑⇟⊟⫏≰2020011)⪢(⫏≰1121000↺⫏≰2021022)","cot":[{"info":"⫏≰1111020∑⇟⊟⫏≰2020011=NaN","layer":1},{"info":"⫏≰1121000↺⫏≰2021022=⫏≰2021022","layer":1},{"info":"NaN⪢⫏≰2021022=NaN","layer":0}]}
{"id":633,"expression_no_base_symbol":"-$1982$⫥∨⫟$1431$","expression":"-⫏≰2201102⫥∨⫟⫏≰1222000","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":155,"operation_count":2,"complexity_ratio":77.5,"tree":{"type":"unary","operator":"-","unary_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1982,"base":3},"right_expr":{"type":"numeric_atoms","value":1431,"base":3}}},"used_operators":["t8gj7n24qd","KYD54nUTWz"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1982","layer":2},{"info":"number node, value=1431","layer":2},{"info":"compute binary expreesion, left_input=1982, right_input=1431, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = t8gj7n24qd, unary_op_definition = 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"-⫏≰2201102⫥∨⫟⫏≰1222000=NaN","reverse_text":"NaN=-⫏≰2201102⫥∨⫟⫏≰1222000","cot":[{"info":"⫏≰2201102⫥∨⫟⫏≰1222000=NaN","layer":1},{"info":"-NaN=NaN","layer":0}]}
{"id":634,"expression_no_base_symbol":"($1025$∸)*$1368$⨟⋌⩍$7081$","expression":"(⫏≰1101222∸)*⫏≰1212200⨟⋌⩍⫏≰100201021","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":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":1025,"base":3}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":1368,"base":3},"right_expr":{"type":"numeric_atoms","value":7081,"base":3}}},"used_operators":["9HNa5Wba9A","o20kRiQErp","rGHVDoGpnC"],"dependent_operators":["W4YGzv6Whe","tmPS8pqC7x","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1025","layer":2},{"info":"compute unary expreesion, input=1025, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"number node, value=1368","layer":2},{"info":"number node, value=7081","layer":2},{"info":"compute binary expreesion, left_input=1368, right_input=7081, 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=177, right_input=nan, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1101222∸)*⫏≰1212200⨟⋌⩍⫏≰100201021=NaN","reverse_text":"NaN=(⫏≰1101222∸)*⫏≰1212200⨟⋌⩍⫏≰100201021","cot":[{"info":"⫏≰1101222∸=⫏≰20120","layer":1},{"info":"⫏≰1212200⨟⋌⩍⫏≰100201021=NaN","layer":1},{"info":"⫏≰20120*NaN=NaN","layer":0}]}
{"id":635,"expression_no_base_symbol":"⇁⨣⪵($2962$↛⩡⫤)","expression":"⇁⨣⪵(⫏≰11001201↛⩡⫤)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9021,"operation_count":2,"complexity_ratio":4510.5,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"numeric_atoms","value":2962,"base":3}}},"used_operators":["inkyxCbjAn","FU0Cs4j7VP"],"dependent_operators":["B5M0gjZbta","8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2962","layer":2},{"info":"compute unary expreesion, input=2962, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-443351","layer":1},{"info":"compute unary expreesion, input=-443351, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵(⫏≰11001201↛⩡⫤)=NaN","reverse_text":"NaN=⇁⨣⪵(⫏≰11001201↛⩡⫤)","cot":[{"info":"⫏≰11001201↛⩡⫤=⫏≰-211112011102","layer":1},{"info":"⇁⨣⪵⫏≰-211112011102=NaN","layer":0}]}
{"id":636,"expression_no_base_symbol":"(⨞⊢$2921$)⨓($3324$⨎$7487$)","expression":"(⨞⊢⫏≰11000012)⨓(⫏≰11120010⨎⫏≰101021022)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":7496,"operation_count":3,"complexity_ratio":2498.6666666666665,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":2921,"base":3}},"right_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":3324,"base":3},"right_expr":{"type":"numeric_atoms","value":7487,"base":3}}},"used_operators":["3ViojmjbAp","xUOZtlo3hN","rJVOvQCfKK"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","t8gj7n24qd","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"⫏≰-101021102","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2921","layer":2},{"info":"compute unary expreesion, input=2921, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-3095","layer":1},{"info":"number node, value=3324","layer":2},{"info":"number node, value=7487","layer":2},{"info":"compute binary expreesion, left_input=3324, right_input=7487, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=7487","layer":1},{"info":"compute binary expreesion, left_input=-3095, right_input=7487, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-7490","layer":0}],"base":3,"result_base":3,"text":"(⨞⊢⫏≰11000012)⨓(⫏≰11120010⨎⫏≰101021022)=⫏≰-101021102","reverse_text":"⫏≰-101021102=(⨞⊢⫏≰11000012)⨓(⫏≰11120010⨎⫏≰101021022)","cot":[{"info":"⨞⊢⫏≰11000012=⫏≰-11020122","layer":1},{"info":"⫏≰11120010⨎⫏≰101021022=⫏≰101021022","layer":1},{"info":"⫏≰-11020122⨓⫏≰101021022=⫏≰-101021102","layer":0}]}
{"id":637,"expression_no_base_symbol":"$1342$⨎$3458$⪄$1483$⊴$2805$","expression":"⫏≰1211201⨎⫏≰11202002⪄⫏≰2000221⊴⫏≰10211220","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2906,"operation_count":3,"complexity_ratio":968.6666666666666,"tree":{"type":"binary","operator":"⪄","left_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":1342,"base":3},"right_expr":{"type":"numeric_atoms","value":3458,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1483,"base":3},"right_expr":{"type":"numeric_atoms","value":2805,"base":3}}},"used_operators":["SUmda5xLS4","rJVOvQCfKK","Nsiff2A1zJ"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1342","layer":2},{"info":"number node, value=3458","layer":2},{"info":"compute binary expreesion, left_input=1342, right_input=3458, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=3458","layer":1},{"info":"number node, value=1483","layer":2},{"info":"number node, value=2805","layer":2},{"info":"compute binary expreesion, left_input=1483, right_input=2805, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=3458, right_input=nan, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1211201⨎⫏≰11202002⪄⫏≰2000221⊴⫏≰10211220=NaN","reverse_text":"NaN=⫏≰1211201⨎⫏≰11202002⪄⫏≰2000221⊴⫏≰10211220","cot":[{"info":"⫏≰1211201⨎⫏≰11202002=⫏≰11202002","layer":1},{"info":"⫏≰2000221⊴⫏≰10211220=NaN","layer":1},{"info":"⫏≰11202002⪄NaN=NaN","layer":0}]}
{"id":638,"expression_no_base_symbol":"($1201$⊦⊿)⇼⇔∾$1231$↙$1608$","expression":"(⫏≰1122111⊦⊿)⇼⇔∾⫏≰1200121↙⫏≰2012120","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1619,"operation_count":3,"complexity_ratio":539.6666666666666,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":1201,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":1231,"base":3},"right_expr":{"type":"numeric_atoms","value":1608,"base":3}}},"used_operators":["tifHPKVTfV","14qkJME0vr","yyfyN0ffXY"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰-1120022","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1201","layer":2},{"info":"compute unary expreesion, input=1201, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-3682","layer":1},{"info":"number node, value=1231","layer":2},{"info":"number node, value=1608","layer":2},{"info":"compute binary expreesion, left_input=1231, right_input=1608, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-4824","layer":1},{"info":"compute binary expreesion, left_input=-3682, right_input=-4824, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-1142","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1122111⊦⊿)⇼⇔∾⫏≰1200121↙⫏≰2012120=⫏≰-1120022","reverse_text":"⫏≰-1120022=(⫏≰1122111⊦⊿)⇼⇔∾⫏≰1200121↙⫏≰2012120","cot":[{"info":"⫏≰1122111⊦⊿=⫏≰-12001101","layer":1},{"info":"⫏≰1200121↙⫏≰2012120=⫏≰-20121200","layer":1},{"info":"⫏≰-12001101⇼⇔∾⫏≰-20121200=⫏≰-1120022","layer":0}]}
{"id":639,"expression_no_base_symbol":"$9469$↙$2593$≣⋋","expression":"⫏≰110222201↙⫏≰10120001≣⋋","highest_n_order":3,"priority_hierarchical_complexity":1,"normalized_expansion_degree":3110,"operation_count":2,"complexity_ratio":1555.0,"tree":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":9469,"base":3},"right_expr":{"type":"numeric_atoms","value":2593,"base":3}}},"used_operators":["Tcnh7f0tEr","yyfyN0ffXY"],"dependent_operators":["dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=9469","layer":2},{"info":"number node, value=2593","layer":2},{"info":"compute binary expreesion, left_input=9469, right_input=2593, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-7779","layer":1},{"info":"compute unary expreesion, input=-7779, op_id = Tcnh7f0tEr, unary_op_definition = 'a≣⋋ = { ((a/a)⋥≓≎(a⨪↰⇹248)) , if (a⪢148)<38 ; ((511*a)⊠≄⫣) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫏≰110222201↙⫏≰10120001≣⋋=⫏≰0","reverse_text":"⫏≰0=⫏≰110222201↙⫏≰10120001≣⋋","cot":[{"info":"⫏≰110222201↙⫏≰10120001=⫏≰-101200010","layer":1},{"info":"⫏≰-101200010≣⋋=⫏≰0","layer":0}]}
{"id":640,"expression_no_base_symbol":"(≦∁$3896$)≦≮≮","expression":"(≦∁⫏≰12100022)≦≮≮","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4,"operation_count":2,"complexity_ratio":2.0,"tree":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":3896,"base":3}}},"used_operators":["D4vGDi5EA2","9ICcGScMcE"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"⫏≰-121000220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3896","layer":2},{"info":"compute unary expreesion, input=3896, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=3896","layer":1},{"info":"compute unary expreesion, input=3896, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-11688","layer":0}],"base":3,"result_base":3,"text":"(≦∁⫏≰12100022)≦≮≮=⫏≰-121000220","reverse_text":"⫏≰-121000220=(≦∁⫏≰12100022)≦≮≮","cot":[{"info":"≦∁⫏≰12100022=⫏≰12100022","layer":1},{"info":"⫏≰12100022≦≮≮=⫏≰-121000220","layer":0}]}
{"id":641,"expression_no_base_symbol":"($1398$%$1317$)≹⇙⪍($3061$∲⫓$2468$)","expression":"(⫏≰1220210%⫏≰1210210)≹⇙⪍(⫏≰11012101∲⫓⫏≰10101102)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4,"operation_count":3,"complexity_ratio":1.3333333333333333,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":1398,"base":3},"right_expr":{"type":"numeric_atoms","value":1317,"base":3}},"right_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":3061,"base":3},"right_expr":{"type":"numeric_atoms","value":2468,"base":3}}},"used_operators":["AHs5Up7iyr","k8jYdgA6NY","i8ToyICDmI"],"dependent_operators":["dWAJyo7jo9","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰10000","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1398","layer":2},{"info":"number node, value=1317","layer":2},{"info":"compute binary expreesion, left_input=1398, right_input=1317, op_id = k8jYdgA6NY binary_op_definition= 'None', output=81","layer":1},{"info":"number node, value=3061","layer":2},{"info":"number node, value=2468","layer":2},{"info":"compute binary expreesion, left_input=3061, right_input=2468, 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=81, right_input=0, 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=81","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1220210%⫏≰1210210)≹⇙⪍(⫏≰11012101∲⫓⫏≰10101102)=⫏≰10000","reverse_text":"⫏≰10000=(⫏≰1220210%⫏≰1210210)≹⇙⪍(⫏≰11012101∲⫓⫏≰10101102)","cot":[{"info":"⫏≰1220210%⫏≰1210210=⫏≰10000","layer":1},{"info":"⫏≰11012101∲⫓⫏≰10101102=⫏≰0","layer":1},{"info":"⫏≰10000≹⇙⪍⫏≰0=⫏≰10000","layer":0}]}
{"id":642,"expression_no_base_symbol":"$2629$↬$1088$∑⇟⊟($5894$≭$1284$)","expression":"⫏≰10121101↬⫏≰1111022∑⇟⊟(⫏≰22002022≭⫏≰1202120)","highest_n_order":5,"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":2629,"base":3},"right_expr":{"type":"numeric_atoms","value":1088,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":5894,"base":3},"right_expr":{"type":"numeric_atoms","value":1284,"base":3}}},"used_operators":["U7g4x0WXJJ","B5M0gjZbta","rxpJgHHUmx"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","rGHVDoGpnC","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2629","layer":2},{"info":"number node, value=1088","layer":2},{"info":"compute binary expreesion, left_input=2629, right_input=1088, 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=5894","layer":2},{"info":"number node, value=1284","layer":2},{"info":"compute binary expreesion, left_input=5894, right_input=1284, 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=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":3,"result_base":3,"text":"⫏≰10121101↬⫏≰1111022∑⇟⊟(⫏≰22002022≭⫏≰1202120)=NaN","reverse_text":"NaN=⫏≰10121101↬⫏≰1111022∑⇟⊟(⫏≰22002022≭⫏≰1202120)","cot":[{"info":"⫏≰10121101↬⫏≰1111022=NaN","layer":1},{"info":"⫏≰22002022≭⫏≰1202120=NaN","layer":1},{"info":"NaN∑⇟⊟NaN=NaN","layer":0}]}
{"id":643,"expression_no_base_symbol":"+⊝⨔($1192$⩠)","expression":"+⊝⨔(⫏≰1122011⩠)","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":1192,"base":3}}},"used_operators":["DhbWaqg5eL","sJAwomhLZr"],"dependent_operators":["dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","sdazOOVcIp","i8ToyICDmI","k8jYdgA6NY","eH2TOUuTDT","W4YGzv6Whe","Z2TMIBDE3Q","COABgblf1C"],"result":"⫏≰2002101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1192","layer":2},{"info":"compute unary expreesion, input=1192, op_id = sJAwomhLZr, unary_op_definition = 'a⩠ = { (((a+a)⊭↱(a⪨≂a))∲⫓((a⩤)%(a⪐))) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, 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":3,"result_base":3,"text":"+⊝⨔(⫏≰1122011⩠)=⫏≰2002101","reverse_text":"⫏≰2002101=+⊝⨔(⫏≰1122011⩠)","cot":[{"info":"⫏≰1122011⩠=⫏≰0","layer":1},{"info":"+⊝⨔⫏≰0=⫏≰2002101","layer":0}]}
{"id":644,"expression_no_base_symbol":"$2318$≹⇙⪍$2578$⨐⩸⫘($1991$⊉≛↸$2700$)","expression":"⫏≰10011212≹⇙⪍⫏≰10112111⨐⩸⫘(⫏≰2201202⊉≛↸⫏≰10201000)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4,"operation_count":3,"complexity_ratio":1.3333333333333333,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":2318,"base":3},"right_expr":{"type":"numeric_atoms","value":2578,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":1991,"base":3},"right_expr":{"type":"numeric_atoms","value":2700,"base":3}}},"used_operators":["fu6greOZ01","AHs5Up7iyr","DZ8iAZOCBD"],"dependent_operators":["3ViojmjbAp","dWAJyo7jo9","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2318","layer":2},{"info":"number node, value=2578","layer":2},{"info":"compute binary expreesion, left_input=2318, right_input=2578, 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":"number node, value=1991","layer":2},{"info":"number node, value=2700","layer":2},{"info":"compute binary expreesion, left_input=1991, right_input=2700, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=3982","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=3982, 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":3,"result_base":3,"text":"⫏≰10011212≹⇙⪍⫏≰10112111⨐⩸⫘(⫏≰2201202⊉≛↸⫏≰10201000)=NaN","reverse_text":"NaN=⫏≰10011212≹⇙⪍⫏≰10112111⨐⩸⫘(⫏≰2201202⊉≛↸⫏≰10201000)","cot":[{"info":"⫏≰10011212≹⇙⪍⫏≰10112111=NaN","layer":1},{"info":"⫏≰2201202⊉≛↸⫏≰10201000=⫏≰12110111","layer":1},{"info":"NaN⨐⩸⫘⫏≰12110111=NaN","layer":0}]}
{"id":645,"expression_no_base_symbol":"(≦∁$1093$)⨰($2378$⨐⩸⫘$1415$)","expression":"(≦∁⫏≰1111111)⨰(⫏≰10021002⨐⩸⫘⫏≰1221102)","highest_n_order":4,"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":1093,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":2378,"base":3},"right_expr":{"type":"numeric_atoms","value":1415,"base":3}}},"used_operators":["eewbuw0ToL","9ICcGScMcE","fu6greOZ01"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1093","layer":2},{"info":"compute unary expreesion, input=1093, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=1093","layer":1},{"info":"number node, value=2378","layer":2},{"info":"number node, value=1415","layer":2},{"info":"compute binary expreesion, left_input=2378, right_input=1415, 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=1093, right_input=nan, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(≦∁⫏≰1111111)⨰(⫏≰10021002⨐⩸⫘⫏≰1221102)=NaN","reverse_text":"NaN=(≦∁⫏≰1111111)⨰(⫏≰10021002⨐⩸⫘⫏≰1221102)","cot":[{"info":"≦∁⫏≰1111111=⫏≰1111111","layer":1},{"info":"⫏≰10021002⨐⩸⫘⫏≰1221102=NaN","layer":1},{"info":"⫏≰1111111⨰NaN=NaN","layer":0}]}
{"id":646,"expression_no_base_symbol":"$1401$≹⇙⪍$5132$/$5041$↙$2540$","expression":"⫏≰1220220≹⇙⪍⫏≰21001002/⫏≰20220201↙⫏≰10111002","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2545,"operation_count":3,"complexity_ratio":848.3333333333334,"tree":{"type":"binary","operator":"/","left_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":1401,"base":3},"right_expr":{"type":"numeric_atoms","value":5132,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":5041,"base":3},"right_expr":{"type":"numeric_atoms","value":2540,"base":3}}},"used_operators":["XhwjNDsVaA","AHs5Up7iyr","yyfyN0ffXY"],"dependent_operators":["rysDP5nf3Z","dWAJyo7jo9","tmPS8pqC7x","DpFCA1CohY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1401","layer":2},{"info":"number node, value=5132","layer":2},{"info":"compute binary expreesion, left_input=1401, right_input=5132, 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":"number node, value=5041","layer":2},{"info":"number node, value=2540","layer":2},{"info":"compute binary expreesion, left_input=5041, right_input=2540, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-7620","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-7620, op_id = XhwjNDsVaA binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1220220≹⇙⪍⫏≰21001002/⫏≰20220201↙⫏≰10111002=NaN","reverse_text":"NaN=⫏≰1220220≹⇙⪍⫏≰21001002/⫏≰20220201↙⫏≰10111002","cot":[{"info":"⫏≰1220220≹⇙⪍⫏≰21001002=NaN","layer":1},{"info":"⫏≰20220201↙⫏≰10111002=⫏≰-101110020","layer":1},{"info":"NaN/⫏≰-101110020=NaN","layer":0}]}
{"id":647,"expression_no_base_symbol":"($6072$⋥≓≎$2073$)⨓($4380$⨵⪆$1142$)","expression":"(⫏≰22022220⋥≓≎⫏≰2211210)⨓(⫏≰20000020⨵⪆⫏≰1120022)","highest_n_order":3,"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":6072,"base":3},"right_expr":{"type":"numeric_atoms","value":2073,"base":3}},"right_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":4380,"base":3},"right_expr":{"type":"numeric_atoms","value":1142,"base":3}}},"used_operators":["3ViojmjbAp","Qy55tPpLXF","2DQ55sFlQl"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-20001","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6072","layer":2},{"info":"number node, value=2073","layer":2},{"info":"compute binary expreesion, left_input=6072, right_input=2073, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-1893","layer":1},{"info":"number node, value=4380","layer":2},{"info":"number node, value=1142","layer":2},{"info":"compute binary expreesion, left_input=4380, right_input=1142, 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=-1893, right_input=160, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-163","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22022220⋥≓≎⫏≰2211210)⨓(⫏≰20000020⨵⪆⫏≰1120022)=⫏≰-20001","reverse_text":"⫏≰-20001=(⫏≰22022220⋥≓≎⫏≰2211210)⨓(⫏≰20000020⨵⪆⫏≰1120022)","cot":[{"info":"⫏≰22022220⋥≓≎⫏≰2211210=⫏≰-2121010","layer":1},{"info":"⫏≰20000020⨵⪆⫏≰1120022=⫏≰12221","layer":1},{"info":"⫏≰-2121010⨓⫏≰12221=⫏≰-20001","layer":0}]}
{"id":648,"expression_no_base_symbol":"$4518$*$2445$∲⫓$3527$⪒$4202$","expression":"⫏≰20012100*⫏≰10100120∲⫓⫏≰11211122⪒⫏≰12202122","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2449,"operation_count":3,"complexity_ratio":816.3333333333334,"tree":{"type":"binary","operator":"∲⫓","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":4518,"base":3},"right_expr":{"type":"numeric_atoms","value":2445,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":3527,"base":3},"right_expr":{"type":"numeric_atoms","value":4202,"base":3}}},"used_operators":["i8ToyICDmI","9HNa5Wba9A","f6k1SAg4EE"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰202210012222000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4518","layer":2},{"info":"number node, value=2445","layer":2},{"info":"compute binary expreesion, left_input=4518, right_input=2445, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=11046510","layer":1},{"info":"number node, value=3527","layer":2},{"info":"number node, value=4202","layer":2},{"info":"compute binary expreesion, left_input=3527, right_input=4202, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-7729","layer":1},{"info":"compute binary expreesion, left_input=11046510, right_input=-7729, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=11046510","layer":0}],"base":3,"result_base":3,"text":"⫏≰20012100*⫏≰10100120∲⫓⫏≰11211122⪒⫏≰12202122=⫏≰202210012222000","reverse_text":"⫏≰202210012222000=⫏≰20012100*⫏≰10100120∲⫓⫏≰11211122⪒⫏≰12202122","cot":[{"info":"⫏≰20012100*⫏≰10100120=⫏≰202210012222000","layer":1},{"info":"⫏≰11211122⪒⫏≰12202122=⫏≰-101121021","layer":1},{"info":"⫏≰202210012222000∲⫓⫏≰-101121021=⫏≰202210012222000","layer":0}]}
{"id":649,"expression_no_base_symbol":"⨰⫟⨤(⨵≀≌$1836$)","expression":"⨰⫟⨤(⨵≀≌⫏≰2112000)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":22927,"operation_count":2,"complexity_ratio":11463.5,"tree":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":1836,"base":3}}},"used_operators":["Tw270M8GLb","srAu1WTS94"],"dependent_operators":["sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1836","layer":2},{"info":"compute unary expreesion, input=1836, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-5508","layer":1},{"info":"compute unary expreesion, input=-5508, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⨰⫟⨤(⨵≀≌⫏≰2112000)=NaN","reverse_text":"NaN=⨰⫟⨤(⨵≀≌⫏≰2112000)","cot":[{"info":"⨵≀≌⫏≰2112000=⫏≰-21120000","layer":1},{"info":"⨰⫟⨤⫏≰-21120000=NaN","layer":0}]}
{"id":650,"expression_no_base_symbol":"($2275$⨸⪁$2188$)∑⇟⊟($2803$≎⊠⪸$3102$)","expression":"(⫏≰10010021⨸⪁⫏≰10000001)∑⇟⊟(⫏≰10211211≎⊠⪸⫏≰11020220)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":274,"operation_count":3,"complexity_ratio":91.33333333333333,"tree":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":2275,"base":3},"right_expr":{"type":"numeric_atoms","value":2188,"base":3}},"right_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":2803,"base":3},"right_expr":{"type":"numeric_atoms","value":3102,"base":3}}},"used_operators":["U7g4x0WXJJ","g55IO6H4Gj","bJkvcejdHO"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","W4YGzv6Whe","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2275","layer":2},{"info":"number node, value=2188","layer":2},{"info":"compute binary expreesion, left_input=2275, right_input=2188, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=8926","layer":1},{"info":"number node, value=2803","layer":2},{"info":"number node, value=3102","layer":2},{"info":"compute binary expreesion, left_input=2803, right_input=3102, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=725504","layer":1},{"info":"compute binary expreesion, left_input=8926, right_input=725504, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10010021⨸⪁⫏≰10000001)∑⇟⊟(⫏≰10211211≎⊠⪸⫏≰11020220)=NaN","reverse_text":"NaN=(⫏≰10010021⨸⪁⫏≰10000001)∑⇟⊟(⫏≰10211211≎⊠⪸⫏≰11020220)","cot":[{"info":"⫏≰10010021⨸⪁⫏≰10000001=⫏≰110020121","layer":1},{"info":"⫏≰10211211≎⊠⪸⫏≰11020220=⫏≰1100212012112","layer":1},{"info":"⫏≰110020121∑⇟⊟⫏≰1100212012112=NaN","layer":0}]}
{"id":651,"expression_no_base_symbol":"($1776$-$2697$)∼($1256$⋓$5841$)","expression":"(⫏≰2102210-⫏≰10200220)∼(⫏≰1201112⋓⫏≰22000100)","highest_n_order":4,"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":1776,"base":3},"right_expr":{"type":"numeric_atoms","value":2697,"base":3}},"right_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":1256,"base":3},"right_expr":{"type":"numeric_atoms","value":5841,"base":3}}},"used_operators":["DyGG3AbaNP","rysDP5nf3Z","T2fj7uvVaJ"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⫏≰202","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1776","layer":2},{"info":"number node, value=2697","layer":2},{"info":"compute binary expreesion, left_input=1776, right_input=2697, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-921","layer":1},{"info":"number node, value=1256","layer":2},{"info":"number node, value=5841","layer":2},{"info":"compute binary expreesion, left_input=1256, right_input=5841, 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=-921, right_input=0, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=20","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2102210-⫏≰10200220)∼(⫏≰1201112⋓⫏≰22000100)=⫏≰202","reverse_text":"⫏≰202=(⫏≰2102210-⫏≰10200220)∼(⫏≰1201112⋓⫏≰22000100)","cot":[{"info":"⫏≰2102210-⫏≰10200220=⫏≰-1021010","layer":1},{"info":"⫏≰1201112⋓⫏≰22000100=⫏≰0","layer":1},{"info":"⫏≰-1021010∼⫏≰0=⫏≰202","layer":0}]}
{"id":652,"expression_no_base_symbol":"$2444$⪘⫢$2088$≧⫂∧$4991$⨪↰⇹$5913$","expression":"⫏≰10100112⪘⫢⫏≰2212100≧⫂∧⫏≰20211212⨪↰⇹⫏≰22010000","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5007,"operation_count":3,"complexity_ratio":1669.0,"tree":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":2444,"base":3},"right_expr":{"type":"numeric_atoms","value":2088,"base":3}},"right_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":4991,"base":3},"right_expr":{"type":"numeric_atoms","value":5913,"base":3}}},"used_operators":["Ph9nP6C5qx","oacrs7FA3X","tmPS8pqC7x"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rJVOvQCfKK"],"result":"⫏≰20012100","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2444","layer":2},{"info":"number node, value=2088","layer":2},{"info":"compute binary expreesion, left_input=2444, right_input=2088, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=4764","layer":1},{"info":"number node, value=4991","layer":2},{"info":"number node, value=5913","layer":2},{"info":"compute binary expreesion, left_input=4991, right_input=5913, 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=4991","layer":1},{"info":"compute binary expreesion, left_input=4764, right_input=4991, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=4518","layer":0}],"base":3,"result_base":3,"text":"⫏≰10100112⪘⫢⫏≰2212100≧⫂∧⫏≰20211212⨪↰⇹⫏≰22010000=⫏≰20012100","reverse_text":"⫏≰20012100=⫏≰10100112⪘⫢⫏≰2212100≧⫂∧⫏≰20211212⨪↰⇹⫏≰22010000","cot":[{"info":"⫏≰10100112⪘⫢⫏≰2212100=⫏≰20112110","layer":1},{"info":"⫏≰20211212⨪↰⇹⫏≰22010000=⫏≰20211212","layer":1},{"info":"⫏≰20112110≧⫂∧⫏≰20211212=⫏≰20012100","layer":0}]}
{"id":653,"expression_no_base_symbol":"(-$1526$)⪄($8843$⫡⨏$1038$)","expression":"(-⫏≰2002112)⪄(⫏≰110010112⫡⨏⫏≰1102110)","highest_n_order":2,"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":1526,"base":3}},"right_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":8843,"base":3},"right_expr":{"type":"numeric_atoms","value":1038,"base":3}}},"used_operators":["SUmda5xLS4","t8gj7n24qd","QMFrweE19q"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰12110101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1526","layer":2},{"info":"compute unary expreesion, input=1526, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1526","layer":1},{"info":"number node, value=8843","layer":2},{"info":"number node, value=1038","layer":2},{"info":"compute binary expreesion, left_input=8843, right_input=1038, 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=47074","layer":1},{"info":"compute binary expreesion, left_input=-1526, right_input=47074, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=3979","layer":0}],"base":3,"result_base":3,"text":"(-⫏≰2002112)⪄(⫏≰110010112⫡⨏⫏≰1102110)=⫏≰12110101","reverse_text":"⫏≰12110101=(-⫏≰2002112)⪄(⫏≰110010112⫡⨏⫏≰1102110)","cot":[{"info":"-⫏≰2002112=⫏≰-2002112","layer":1},{"info":"⫏≰110010112⫡⨏⫏≰1102110=⫏≰2101120111","layer":1},{"info":"⫏≰-2002112⪄⫏≰2101120111=⫏≰12110101","layer":0}]}
{"id":654,"expression_no_base_symbol":"($2906$⊉≛↸$2440$)∀⇚≩(⪲⇎$1802$)","expression":"(⫏≰10222122⊉≛↸⫏≰10100101)∀⇚≩(⪲⇎⫏≰2110202)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":40688,"operation_count":3,"complexity_ratio":13562.666666666666,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":2906,"base":3},"right_expr":{"type":"numeric_atoms","value":2440,"base":3}},"right_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":1802,"base":3}}},"used_operators":["LRNGc0VcxI","DZ8iAZOCBD","XPYlsWDdGa"],"dependent_operators":["X99M06cbEe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2906","layer":2},{"info":"number node, value=2440","layer":2},{"info":"compute binary expreesion, left_input=2906, right_input=2440, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=5812","layer":1},{"info":"number node, value=1802","layer":2},{"info":"compute unary expreesion, input=1802, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=3604","layer":1},{"info":"compute binary expreesion, left_input=5812, right_input=3604, 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":3,"result_base":3,"text":"(⫏≰10222122⊉≛↸⫏≰10100101)∀⇚≩(⪲⇎⫏≰2110202)=NaN","reverse_text":"NaN=(⫏≰10222122⊉≛↸⫏≰10100101)∀⇚≩(⪲⇎⫏≰2110202)","cot":[{"info":"⫏≰10222122⊉≛↸⫏≰10100101=⫏≰21222021","layer":1},{"info":"⪲⇎⫏≰2110202=⫏≰11221111","layer":1},{"info":"⫏≰21222021∀⇚≩⫏≰11221111=NaN","layer":0}]}
{"id":655,"expression_no_base_symbol":"≤/($3117$⫡⨏$3398$)","expression":"≤/(⫏≰11021110⫡⨏⫏≰11122212)","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":3117,"base":3},"right_expr":{"type":"numeric_atoms","value":3398,"base":3}}},"used_operators":["eLAdDNolq6","QMFrweE19q"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-1011010000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3117","layer":2},{"info":"number node, value=3398","layer":2},{"info":"compute binary expreesion, left_input=3117, right_input=3398, 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=23164","layer":1},{"info":"compute unary expreesion, input=23164, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=-22680","layer":0}],"base":3,"result_base":3,"text":"≤/(⫏≰11021110⫡⨏⫏≰11122212)=⫏≰-1011010000","reverse_text":"⫏≰-1011010000=≤/(⫏≰11021110⫡⨏⫏≰11122212)","cot":[{"info":"⫏≰11021110⫡⨏⫏≰11122212=⫏≰1011202221","layer":1},{"info":"≤/⫏≰1011202221=⫏≰-1011010000","layer":0}]}
{"id":656,"expression_no_base_symbol":"($2854$⋳⪒$1953$)⩤","expression":"(⫏≰10220201⋳⪒⫏≰2200100)⩤","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":2854,"base":3},"right_expr":{"type":"numeric_atoms","value":1953,"base":3}}},"used_operators":["Z2TMIBDE3Q","12rbrZMWeM"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-11202110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2854","layer":2},{"info":"number node, value=1953","layer":2},{"info":"compute binary expreesion, left_input=2854, right_input=1953, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=3468","layer":1},{"info":"compute unary expreesion, input=3468, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-3468","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10220201⋳⪒⫏≰2200100)⩤=⫏≰-11202110","reverse_text":"⫏≰-11202110=(⫏≰10220201⋳⪒⫏≰2200100)⩤","cot":[{"info":"⫏≰10220201⋳⪒⫏≰2200100=⫏≰11202110","layer":1},{"info":"⫏≰11202110⩤=⫏≰-11202110","layer":0}]}
{"id":657,"expression_no_base_symbol":"($1643$⨪↰⇹$5575$)∼(⊥$7969$)","expression":"(⫏≰2020212⨪↰⇹⫏≰21122111)∼(⊥⫏≰101221011)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1678,"operation_count":3,"complexity_ratio":559.3333333333334,"tree":{"type":"binary","operator":"∼","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":1643,"base":3},"right_expr":{"type":"numeric_atoms","value":5575,"base":3}},"right_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":7969,"base":3}}},"used_operators":["DyGG3AbaNP","tmPS8pqC7x","Q3PJZHRvZv"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","rJVOvQCfKK","fu6greOZ01"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1643","layer":2},{"info":"number node, value=5575","layer":2},{"info":"compute binary expreesion, left_input=1643, right_input=5575, 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=1643","layer":1},{"info":"number node, value=7969","layer":2},{"info":"compute unary expreesion, input=7969, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1643, 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":3,"result_base":3,"text":"(⫏≰2020212⨪↰⇹⫏≰21122111)∼(⊥⫏≰101221011)=NaN","reverse_text":"NaN=(⫏≰2020212⨪↰⇹⫏≰21122111)∼(⊥⫏≰101221011)","cot":[{"info":"⫏≰2020212⨪↰⇹⫏≰21122111=⫏≰2020212","layer":1},{"info":"⊥⫏≰101221011=NaN","layer":1},{"info":"⫏≰2020212∼NaN=NaN","layer":0}]}
{"id":658,"expression_no_base_symbol":"($5285$⪨≂$2463$)⨰($5756$⋷$2499$)","expression":"(⫏≰21020202⪨≂⫏≰10101020)⨰(⫏≰21220012⋷⫏≰10102120)","highest_n_order":1,"priority_hierarchical_complexity":2,"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":5285,"base":3},"right_expr":{"type":"numeric_atoms","value":2463,"base":3}},"right_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":5756,"base":3},"right_expr":{"type":"numeric_atoms","value":2499,"base":3}}},"used_operators":["eewbuw0ToL","sdazOOVcIp","23Mk6UjR3U"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰22221021","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5285","layer":2},{"info":"number node, value=2463","layer":2},{"info":"compute binary expreesion, left_input=5285, right_input=2463, 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=5746","layer":1},{"info":"number node, value=5756","layer":2},{"info":"number node, value=2499","layer":2},{"info":"compute binary expreesion, left_input=5756, right_input=2499, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-758","layer":1},{"info":"compute binary expreesion, left_input=5746, right_input=-758, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=6514","layer":0}],"base":3,"result_base":3,"text":"(⫏≰21020202⪨≂⫏≰10101020)⨰(⫏≰21220012⋷⫏≰10102120)=⫏≰22221021","reverse_text":"⫏≰22221021=(⫏≰21020202⪨≂⫏≰10101020)⨰(⫏≰21220012⋷⫏≰10102120)","cot":[{"info":"⫏≰21020202⪨≂⫏≰10101020=⫏≰21212211","layer":1},{"info":"⫏≰21220012⋷⫏≰10102120=⫏≰-1001002","layer":1},{"info":"⫏≰21212211⨰⫏≰-1001002=⫏≰22221021","layer":0}]}
{"id":659,"expression_no_base_symbol":"↩($1305$*$4154$)","expression":"↩(⫏≰1210100*⫏≰12200212)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1321,"operation_count":2,"complexity_ratio":660.5,"tree":{"type":"unary","operator":"↩","unary_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1305,"base":3},"right_expr":{"type":"numeric_atoms","value":4154,"base":3}}},"used_operators":["jLgFTUHLKL","9HNa5Wba9A"],"dependent_operators":["sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D","W4YGzv6Whe"],"result":"⫏≰-10000121011120101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1305","layer":2},{"info":"number node, value=4154","layer":2},{"info":"compute binary expreesion, left_input=1305, right_input=4154, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=5420970","layer":1},{"info":"compute unary expreesion, input=5420970, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-43364980","layer":0}],"base":3,"result_base":3,"text":"↩(⫏≰1210100*⫏≰12200212)=⫏≰-10000121011120101","reverse_text":"⫏≰-10000121011120101=↩(⫏≰1210100*⫏≰12200212)","cot":[{"info":"⫏≰1210100*⫏≰12200212=⫏≰101012102011200","layer":1},{"info":"↩⫏≰101012102011200=⫏≰-10000121011120101","layer":0}]}
{"id":660,"expression_no_base_symbol":"$1589$≹⇙⪍$4242$⨵⪆$1281$⪘⫢$3314$","expression":"⫏≰2011212≹⇙⪍⫏≰12211010⨵⪆⫏≰1202110⪘⫢⫏≰11112202","highest_n_order":4,"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":1589,"base":3},"right_expr":{"type":"numeric_atoms","value":4242,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1281,"base":3},"right_expr":{"type":"numeric_atoms","value":3314,"base":3}}},"used_operators":["2DQ55sFlQl","AHs5Up7iyr","oacrs7FA3X"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1589","layer":2},{"info":"number node, value=4242","layer":2},{"info":"compute binary expreesion, left_input=1589, right_input=4242, 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":"number node, value=1281","layer":2},{"info":"number node, value=3314","layer":2},{"info":"compute binary expreesion, left_input=1281, right_input=3314, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=2438","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2438, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰2011212≹⇙⪍⫏≰12211010⨵⪆⫏≰1202110⪘⫢⫏≰11112202=⫏≰12221","reverse_text":"⫏≰12221=⫏≰2011212≹⇙⪍⫏≰12211010⨵⪆⫏≰1202110⪘⫢⫏≰11112202","cot":[{"info":"⫏≰2011212≹⇙⪍⫏≰12211010=NaN","layer":1},{"info":"⫏≰1202110⪘⫢⫏≰11112202=⫏≰10100022","layer":1},{"info":"NaN⨵⪆⫏≰10100022=⫏≰12221","layer":0}]}
{"id":661,"expression_no_base_symbol":"⨰⫟⨤(⊄⩳↩$1032$)","expression":"⨰⫟⨤(⊄⩳↩⫏≰1102020)","highest_n_order":3,"priority_hierarchical_complexity":1,"normalized_expansion_degree":13279,"operation_count":2,"complexity_ratio":6639.5,"tree":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":1032,"base":3}}},"used_operators":["Tw270M8GLb","8w2t5hMYqp"],"dependent_operators":["sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1032","layer":2},{"info":"compute unary expreesion, input=1032, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-3096","layer":1},{"info":"compute unary expreesion, input=-3096, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⨰⫟⨤(⊄⩳↩⫏≰1102020)=NaN","reverse_text":"NaN=⨰⫟⨤(⊄⩳↩⫏≰1102020)","cot":[{"info":"⊄⩳↩⫏≰1102020=⫏≰-11020200","layer":1},{"info":"⨰⫟⨤⫏≰-11020200=NaN","layer":0}]}
{"id":662,"expression_no_base_symbol":"(⨵≀≌$3738$)+$1661$⪛$2217$","expression":"(⨵≀≌⫏≰12010110)+⫏≰2021112⪛⫏≰10001010","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":3738,"base":3}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":1661,"base":3},"right_expr":{"type":"numeric_atoms","value":2217,"base":3}}},"used_operators":["W4YGzv6Whe","srAu1WTS94","uFcxV4UQCh"],"dependent_operators":["glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⫏≰-111002211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3738","layer":2},{"info":"compute unary expreesion, input=3738, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-11214","layer":1},{"info":"number node, value=1661","layer":2},{"info":"number node, value=2217","layer":2},{"info":"compute binary expreesion, left_input=1661, right_input=2217, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1661","layer":1},{"info":"compute binary expreesion, left_input=-11214, right_input=1661, op_id = W4YGzv6Whe binary_op_definition= 'None', output=-9553","layer":0}],"base":3,"result_base":3,"text":"(⨵≀≌⫏≰12010110)+⫏≰2021112⪛⫏≰10001010=⫏≰-111002211","reverse_text":"⫏≰-111002211=(⨵≀≌⫏≰12010110)+⫏≰2021112⪛⫏≰10001010","cot":[{"info":"⨵≀≌⫏≰12010110=⫏≰-120101100","layer":1},{"info":"⫏≰2021112⪛⫏≰10001010=⫏≰2021112","layer":1},{"info":"⫏≰-120101100+⫏≰2021112=⫏≰-111002211","layer":0}]}
{"id":663,"expression_no_base_symbol":"$1676$⩷∴$1546$+⇶⊼(⊥$2821$)","expression":"⫏≰2022002⩷∴⫏≰2010021+⇶⊼(⊥⫏≰10212111)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":1676,"base":3},"right_expr":{"type":"numeric_atoms","value":1546,"base":3}},"right_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":2821,"base":3}}},"used_operators":["TpPTUOHfaN","9FxExcQeMw","Q3PJZHRvZv"],"dependent_operators":["AHs5Up7iyr","rysDP5nf3Z","fu6greOZ01"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1676","layer":2},{"info":"number node, value=1546","layer":2},{"info":"compute binary expreesion, left_input=1676, right_input=1546, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=228","layer":1},{"info":"number node, value=2821","layer":2},{"info":"compute unary expreesion, input=2821, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=228, right_input=nan, 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":3,"result_base":3,"text":"⫏≰2022002⩷∴⫏≰2010021+⇶⊼(⊥⫏≰10212111)=NaN","reverse_text":"NaN=⫏≰2022002⩷∴⫏≰2010021+⇶⊼(⊥⫏≰10212111)","cot":[{"info":"⫏≰2022002⩷∴⫏≰2010021=⫏≰22110","layer":1},{"info":"⊥⫏≰10212111=NaN","layer":1},{"info":"⫏≰22110+⇶⊼NaN=NaN","layer":0}]}
{"id":664,"expression_no_base_symbol":"($2017$⨽$5299$)⨪↰⇹($2590$⫥∨⫟$1178$)","expression":"(⫏≰2202201⨽⫏≰21021021)⨪↰⇹(⫏≰10112221⫥∨⫟⫏≰1121122)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2181,"operation_count":3,"complexity_ratio":727.0,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":2017,"base":3},"right_expr":{"type":"numeric_atoms","value":5299,"base":3}},"right_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":2590,"base":3},"right_expr":{"type":"numeric_atoms","value":1178,"base":3}}},"used_operators":["tmPS8pqC7x","8HhzD0ZcuI","KYD54nUTWz"],"dependent_operators":["rJVOvQCfKK","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2017","layer":2},{"info":"number node, value=5299","layer":2},{"info":"compute binary expreesion, left_input=2017, right_input=5299, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-12219450","layer":1},{"info":"number node, value=2590","layer":2},{"info":"number node, value=1178","layer":2},{"info":"compute binary expreesion, left_input=2590, right_input=1178, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-12219450, right_input=nan, 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=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2202201⨽⫏≰21021021)⨪↰⇹(⫏≰10112221⫥∨⫟⫏≰1121122)=NaN","reverse_text":"NaN=(⫏≰2202201⨽⫏≰21021021)⨪↰⇹(⫏≰10112221⫥∨⫟⫏≰1121122)","cot":[{"info":"⫏≰2202201⨽⫏≰21021021=⫏≰-211222210221020","layer":1},{"info":"⫏≰10112221⫥∨⫟⫏≰1121122=NaN","layer":1},{"info":"⫏≰-211222210221020⨪↰⇹NaN=NaN","layer":0}]}
{"id":665,"expression_no_base_symbol":"($1625$⩨$1132$)⪛($3520$+⇶⊼$1197$)","expression":"(⫏≰2020012⩨⫏≰1112221)⪛(⫏≰11211101+⇶⊼⫏≰1122100)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⪛","left_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":1625,"base":3},"right_expr":{"type":"numeric_atoms","value":1132,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":3520,"base":3},"right_expr":{"type":"numeric_atoms","value":1197,"base":3}}},"used_operators":["uFcxV4UQCh","2DlMacCsIx","TpPTUOHfaN"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1625","layer":2},{"info":"number node, value=1132","layer":2},{"info":"compute binary expreesion, left_input=1625, right_input=1132, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"number node, value=3520","layer":2},{"info":"number node, value=1197","layer":2},{"info":"compute binary expreesion, left_input=3520, right_input=1197, 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":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2020012⩨⫏≰1112221)⪛(⫏≰11211101+⇶⊼⫏≰1122100)=NaN","reverse_text":"NaN=(⫏≰2020012⩨⫏≰1112221)⪛(⫏≰11211101+⇶⊼⫏≰1122100)","cot":[{"info":"⫏≰2020012⩨⫏≰1112221=⫏≰0","layer":1},{"info":"⫏≰11211101+⇶⊼⫏≰1122100=NaN","layer":1},{"info":"⫏≰0⪛NaN=NaN","layer":0}]}
{"id":666,"expression_no_base_symbol":"-$1727$∀⇚≩$1381$","expression":"-⫏≰2100222∀⇚≩⫏≰1220011","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":12090,"operation_count":2,"complexity_ratio":6045.0,"tree":{"type":"unary","operator":"-","unary_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":1727,"base":3},"right_expr":{"type":"numeric_atoms","value":1381,"base":3}}},"used_operators":["t8gj7n24qd","LRNGc0VcxI"],"dependent_operators":["X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1727","layer":2},{"info":"number node, value=1381","layer":2},{"info":"compute binary expreesion, left_input=1727, right_input=1381, 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 = t8gj7n24qd, unary_op_definition = 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"-⫏≰2100222∀⇚≩⫏≰1220011=NaN","reverse_text":"NaN=-⫏≰2100222∀⇚≩⫏≰1220011","cot":[{"info":"⫏≰2100222∀⇚≩⫏≰1220011=NaN","layer":1},{"info":"-NaN=NaN","layer":0}]}
{"id":667,"expression_no_base_symbol":"($7245$⫡⨏$1773$)⨓($4388$∸)","expression":"(⫏≰100221100⫡⨏⫏≰2102200)⨓(⫏≰20000112∸)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":367,"operation_count":3,"complexity_ratio":122.33333333333333,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":7245,"base":3},"right_expr":{"type":"numeric_atoms","value":1773,"base":3}},"right_expr":{"type":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":4388,"base":3}}},"used_operators":["3ViojmjbAp","QMFrweE19q","o20kRiQErp"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","t8gj7n24qd","tmPS8pqC7x"],"result":"⫏≰-20200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7245","layer":2},{"info":"number node, value=1773","layer":2},{"info":"compute binary expreesion, left_input=7245, right_input=1773, 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=40554","layer":1},{"info":"number node, value=4388","layer":2},{"info":"compute unary expreesion, input=4388, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"compute binary expreesion, left_input=40554, right_input=177, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-180","layer":0}],"base":3,"result_base":3,"text":"(⫏≰100221100⫡⨏⫏≰2102200)⨓(⫏≰20000112∸)=⫏≰-20200","reverse_text":"⫏≰-20200=(⫏≰100221100⫡⨏⫏≰2102200)⨓(⫏≰20000112∸)","cot":[{"info":"⫏≰100221100⫡⨏⫏≰2102200=⫏≰2001122000","layer":1},{"info":"⫏≰20000112∸=⫏≰20120","layer":1},{"info":"⫏≰2001122000⨓⫏≰20120=⫏≰-20200","layer":0}]}
{"id":668,"expression_no_base_symbol":"$5116$⋓$1206$⩚⊴⇥$1882$⨰$1482$","expression":"⫏≰21000111⋓⫏≰1122200⩚⊴⇥⫏≰2120201⨰⫏≰2000220","highest_n_order":3,"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":5116,"base":3},"right_expr":{"type":"numeric_atoms","value":1206,"base":3}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":1882,"base":3},"right_expr":{"type":"numeric_atoms","value":1482,"base":3}}},"used_operators":["NTOWxs364D","T2fj7uvVaJ","eewbuw0ToL"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-201200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5116","layer":2},{"info":"number node, value=1206","layer":2},{"info":"compute binary expreesion, left_input=5116, right_input=1206, 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=1882","layer":2},{"info":"number node, value=1482","layer":2},{"info":"compute binary expreesion, left_input=1882, right_input=1482, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=410","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=410, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-531","layer":0}],"base":3,"result_base":3,"text":"⫏≰21000111⋓⫏≰1122200⩚⊴⇥⫏≰2120201⨰⫏≰2000220=⫏≰-201200","reverse_text":"⫏≰-201200=⫏≰21000111⋓⫏≰1122200⩚⊴⇥⫏≰2120201⨰⫏≰2000220","cot":[{"info":"⫏≰21000111⋓⫏≰1122200=⫏≰0","layer":1},{"info":"⫏≰2120201⨰⫏≰2000220=⫏≰120012","layer":1},{"info":"⫏≰0⩚⊴⇥⫏≰120012=⫏≰-201200","layer":0}]}
{"id":669,"expression_no_base_symbol":"($1611$∲⫓$5950$)⪮%⊝($2093$≧⫂∧$2755$)","expression":"(⫏≰2012200∲⫓⫏≰22011101)⪮%⊝(⫏≰2212112≧⫂∧⫏≰10210001)","highest_n_order":2,"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":1611,"base":3},"right_expr":{"type":"numeric_atoms","value":5950,"base":3}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":2093,"base":3},"right_expr":{"type":"numeric_atoms","value":2755,"base":3}}},"used_operators":["IWmyXbctLI","i8ToyICDmI","Ph9nP6C5qx"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰102201","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1611","layer":2},{"info":"number node, value=5950","layer":2},{"info":"compute binary expreesion, left_input=1611, right_input=5950, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=2093","layer":2},{"info":"number node, value=2755","layer":2},{"info":"compute binary expreesion, left_input=2093, right_input=2755, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=2282","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=2282, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=316","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2012200∲⫓⫏≰22011101)⪮%⊝(⫏≰2212112≧⫂∧⫏≰10210001)=⫏≰102201","reverse_text":"⫏≰102201=(⫏≰2012200∲⫓⫏≰22011101)⪮%⊝(⫏≰2212112≧⫂∧⫏≰10210001)","cot":[{"info":"⫏≰2012200∲⫓⫏≰22011101=⫏≰0","layer":1},{"info":"⫏≰2212112≧⫂∧⫏≰10210001=⫏≰10010112","layer":1},{"info":"⫏≰0⪮%⊝⫏≰10010112=⫏≰102201","layer":0}]}
{"id":670,"expression_no_base_symbol":"($3635$-$4166$)⪢($1403$⪠⩆⊳)","expression":"(⫏≰11222122-⫏≰12201022)⪢(⫏≰1220222⪠⩆⊳)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":3635,"base":3},"right_expr":{"type":"numeric_atoms","value":4166,"base":3}},"right_expr":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"numeric_atoms","value":1403,"base":3}}},"used_operators":["dWAJyo7jo9","rysDP5nf3Z","JLbD19bQDL"],"dependent_operators":["k8jYdgA6NY","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3635","layer":2},{"info":"number node, value=4166","layer":2},{"info":"compute binary expreesion, left_input=3635, right_input=4166, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-531","layer":1},{"info":"number node, value=1403","layer":2},{"info":"compute unary expreesion, input=1403, 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":"compute binary expreesion, left_input=-531, right_input=0, 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=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11222122-⫏≰12201022)⪢(⫏≰1220222⪠⩆⊳)=⫏≰0","reverse_text":"⫏≰0=(⫏≰11222122-⫏≰12201022)⪢(⫏≰1220222⪠⩆⊳)","cot":[{"info":"⫏≰11222122-⫏≰12201022=⫏≰-201200","layer":1},{"info":"⫏≰1220222⪠⩆⊳=⫏≰0","layer":1},{"info":"⫏≰-201200⪢⫏≰0=⫏≰0","layer":0}]}
{"id":671,"expression_no_base_symbol":"($3104$%$1472$)⨸⪁($1311$⩨$1162$)","expression":"(⫏≰11020222%⫏≰2000112)⨸⪁(⫏≰1210120⩨⫏≰1121001)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":3104,"base":3},"right_expr":{"type":"numeric_atoms","value":1472,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":1311,"base":3},"right_expr":{"type":"numeric_atoms","value":1162,"base":3}}},"used_operators":["g55IO6H4Gj","k8jYdgA6NY","2DlMacCsIx"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰102212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3104","layer":2},{"info":"number node, value=1472","layer":2},{"info":"compute binary expreesion, left_input=3104, right_input=1472, op_id = k8jYdgA6NY binary_op_definition= 'None', output=160","layer":1},{"info":"number node, value=1311","layer":2},{"info":"number node, value=1162","layer":2},{"info":"compute binary expreesion, left_input=1311, right_input=1162, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=0, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=320","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11020222%⫏≰2000112)⨸⪁(⫏≰1210120⩨⫏≰1121001)=⫏≰102212","reverse_text":"⫏≰102212=(⫏≰11020222%⫏≰2000112)⨸⪁(⫏≰1210120⩨⫏≰1121001)","cot":[{"info":"⫏≰11020222%⫏≰2000112=⫏≰12221","layer":1},{"info":"⫏≰1210120⩨⫏≰1121001=⫏≰0","layer":1},{"info":"⫏≰12221⨸⪁⫏≰0=⫏≰102212","layer":0}]}
{"id":672,"expression_no_base_symbol":"$7252$⩷∴$1819$≎⊠⪸(⨰⫟⨤$1711$)","expression":"⫏≰100221121⩷∴⫏≰2111101≎⊠⪸(⨰⫟⨤⫏≰2100101)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6021,"operation_count":3,"complexity_ratio":2007.0,"tree":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":7252,"base":3},"right_expr":{"type":"numeric_atoms","value":1819,"base":3}},"right_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":1711,"base":3}}},"used_operators":["bJkvcejdHO","9FxExcQeMw","Tw270M8GLb"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","rysDP5nf3Z","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7252","layer":2},{"info":"number node, value=1819","layer":2},{"info":"compute binary expreesion, left_input=7252, right_input=1819, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=10834","layer":1},{"info":"number node, value=1711","layer":2},{"info":"compute unary expreesion, input=1711, 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=10834, right_input=nan, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=67","layer":0}],"base":3,"result_base":3,"text":"⫏≰100221121⩷∴⫏≰2111101≎⊠⪸(⨰⫟⨤⫏≰2100101)=⫏≰2111","reverse_text":"⫏≰2111=⫏≰100221121⩷∴⫏≰2111101≎⊠⪸(⨰⫟⨤⫏≰2100101)","cot":[{"info":"⫏≰100221121⩷∴⫏≰2111101=⫏≰112212021","layer":1},{"info":"⨰⫟⨤⫏≰2100101=NaN","layer":1},{"info":"⫏≰112212021≎⊠⪸NaN=⫏≰2111","layer":0}]}
{"id":673,"expression_no_base_symbol":"$6683$+⇶⊼$5603$⨽(≦∁$1272$)","expression":"⫏≰100011112+⇶⊼⫏≰21200112⨽(≦∁⫏≰1202010)","highest_n_order":5,"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":6683,"base":3},"right_expr":{"type":"numeric_atoms","value":5603,"base":3}},"right_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":1272,"base":3}}},"used_operators":["8HhzD0ZcuI","TpPTUOHfaN","9ICcGScMcE"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","AHs5Up7iyr","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6683","layer":2},{"info":"number node, value=5603","layer":2},{"info":"compute binary expreesion, left_input=6683, right_input=5603, 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":1},{"info":"number node, value=1272","layer":2},{"info":"compute unary expreesion, input=1272, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=1272","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1272, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰100011112+⇶⊼⫏≰21200112⨽(≦∁⫏≰1202010)=NaN","reverse_text":"NaN=⫏≰100011112+⇶⊼⫏≰21200112⨽(≦∁⫏≰1202010)","cot":[{"info":"⫏≰100011112+⇶⊼⫏≰21200112=NaN","layer":1},{"info":"≦∁⫏≰1202010=⫏≰1202010","layer":1},{"info":"NaN⨽⫏≰1202010=NaN","layer":0}]}
{"id":674,"expression_no_base_symbol":"($2900$≎⊠⪸$1649$)≹⇙⪍($4731$⋥≓≎$1124$)","expression":"(⫏≰10222102≎⊠⪸⫏≰2021002)≹⇙⪍(⫏≰20111020⋥≓≎⫏≰1112122)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":275,"operation_count":3,"complexity_ratio":91.66666666666667,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":2900,"base":3},"right_expr":{"type":"numeric_atoms","value":1649,"base":3}},"right_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":4731,"base":3},"right_expr":{"type":"numeric_atoms","value":1124,"base":3}}},"used_operators":["AHs5Up7iyr","bJkvcejdHO","Qy55tPpLXF"],"dependent_operators":["dWAJyo7jo9","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2900","layer":2},{"info":"number node, value=1649","layer":2},{"info":"compute binary expreesion, left_input=2900, right_input=1649, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=750627","layer":1},{"info":"number node, value=4731","layer":2},{"info":"number node, value=1124","layer":2},{"info":"compute binary expreesion, left_input=4731, right_input=1124, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-2450","layer":1},{"info":"compute binary expreesion, left_input=750627, right_input=-2450, 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":3,"result_base":3,"text":"(⫏≰10222102≎⊠⪸⫏≰2021002)≹⇙⪍(⫏≰20111020⋥≓≎⫏≰1112122)=NaN","reverse_text":"NaN=(⫏≰10222102≎⊠⪸⫏≰2021002)≹⇙⪍(⫏≰20111020⋥≓≎⫏≰1112122)","cot":[{"info":"⫏≰10222102≎⊠⪸⫏≰2021002=⫏≰1102010200000","layer":1},{"info":"⫏≰20111020⋥≓≎⫏≰1112122=⫏≰-10100202","layer":1},{"info":"⫏≰1102010200000≹⇙⪍⫏≰-10100202=NaN","layer":0}]}
{"id":675,"expression_no_base_symbol":"⇁⨣⪵($3014$⨵⪆$4043$)","expression":"⇁⨣⪵(⫏≰11010122⨵⪆⫏≰12112202)","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":3014,"base":3},"right_expr":{"type":"numeric_atoms","value":4043,"base":3}}},"used_operators":["inkyxCbjAn","2DQ55sFlQl"],"dependent_operators":["B5M0gjZbta","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3014","layer":2},{"info":"number node, value=4043","layer":2},{"info":"compute binary expreesion, left_input=3014, right_input=4043, 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 = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵(⫏≰11010122⨵⪆⫏≰12112202)=NaN","reverse_text":"NaN=⇁⨣⪵(⫏≰11010122⨵⪆⫏≰12112202)","cot":[{"info":"⫏≰11010122⨵⪆⫏≰12112202=⫏≰12221","layer":1},{"info":"⇁⨣⪵⫏≰12221=NaN","layer":0}]}
{"id":676,"expression_no_base_symbol":"($6306$-$5447$)∀⇚≩(⨞⊢$2149$)","expression":"(⫏≰22122120-⫏≰21110202)∀⇚≩(⨞⊢⫏≰2221121)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6016,"operation_count":3,"complexity_ratio":2005.3333333333333,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":6306,"base":3},"right_expr":{"type":"numeric_atoms","value":5447,"base":3}},"right_expr":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":2149,"base":3}}},"used_operators":["LRNGc0VcxI","rysDP5nf3Z","xUOZtlo3hN"],"dependent_operators":["X99M06cbEe","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6306","layer":2},{"info":"number node, value=5447","layer":2},{"info":"compute binary expreesion, left_input=6306, right_input=5447, op_id = rysDP5nf3Z binary_op_definition= 'None', output=859","layer":1},{"info":"number node, value=2149","layer":2},{"info":"compute unary expreesion, input=2149, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-2323","layer":1},{"info":"compute binary expreesion, left_input=859, right_input=-2323, 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":3,"result_base":3,"text":"(⫏≰22122120-⫏≰21110202)∀⇚≩(⨞⊢⫏≰2221121)=NaN","reverse_text":"NaN=(⫏≰22122120-⫏≰21110202)∀⇚≩(⨞⊢⫏≰2221121)","cot":[{"info":"⫏≰22122120-⫏≰21110202=⫏≰1011211","layer":1},{"info":"⨞⊢⫏≰2221121=⫏≰-10012001","layer":1},{"info":"⫏≰1011211∀⇚≩⫏≰-10012001=NaN","layer":0}]}
{"id":677,"expression_no_base_symbol":"⪲⇎(⨰⫟⨤$3205$)","expression":"⪲⇎(⨰⫟⨤⫏≰11101201)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":11982,"operation_count":2,"complexity_ratio":5991.0,"tree":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":3205,"base":3}}},"used_operators":["XPYlsWDdGa","Tw270M8GLb"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3205","layer":2},{"info":"compute unary expreesion, input=3205, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⪲⇎(⨰⫟⨤⫏≰11101201)=NaN","reverse_text":"NaN=⪲⇎(⨰⫟⨤⫏≰11101201)","cot":[{"info":"⨰⫟⨤⫏≰11101201=NaN","layer":1},{"info":"⪲⇎NaN=NaN","layer":0}]}
{"id":678,"expression_no_base_symbol":"+⊝⨔($4550$⩨$1176$)","expression":"+⊝⨔(⫏≰20020112⩨⫏≰1121120)","highest_n_order":3,"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":4550,"base":3},"right_expr":{"type":"numeric_atoms","value":1176,"base":3}}},"used_operators":["DhbWaqg5eL","2DlMacCsIx"],"dependent_operators":["dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰2002101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4550","layer":2},{"info":"number node, value=1176","layer":2},{"info":"compute binary expreesion, left_input=4550, right_input=1176, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute unary expreesion, input=0, 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":3,"result_base":3,"text":"+⊝⨔(⫏≰20020112⩨⫏≰1121120)=⫏≰2002101","reverse_text":"⫏≰2002101=+⊝⨔(⫏≰20020112⩨⫏≰1121120)","cot":[{"info":"⫏≰20020112⩨⫏≰1121120=⫏≰0","layer":1},{"info":"+⊝⨔⫏≰0=⫏≰2002101","layer":0}]}
{"id":679,"expression_no_base_symbol":"-($1062$⋷$9123$)","expression":"-(⫏≰1110100⋷⫏≰110111220)","highest_n_order":1,"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":1062,"base":3},"right_expr":{"type":"numeric_atoms","value":9123,"base":3}}},"used_operators":["t8gj7n24qd","23Mk6UjR3U"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-212120110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1062","layer":2},{"info":"number node, value=9123","layer":2},{"info":"compute binary expreesion, left_input=1062, right_input=9123, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=17184","layer":1},{"info":"compute unary expreesion, input=17184, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-17184","layer":0}],"base":3,"result_base":3,"text":"-(⫏≰1110100⋷⫏≰110111220)=⫏≰-212120110","reverse_text":"⫏≰-212120110=-(⫏≰1110100⋷⫏≰110111220)","cot":[{"info":"⫏≰1110100⋷⫏≰110111220=⫏≰212120110","layer":1},{"info":"-⫏≰212120110=⫏≰-212120110","layer":0}]}
{"id":680,"expression_no_base_symbol":"($1145$⪄$1141$)⨎$5723$⋝⋈⪟$3492$","expression":"(⫏≰1120102⪄⫏≰1120021)⨎⫏≰21211222⋝⋈⪟⫏≰11210100","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":1145,"base":3},"right_expr":{"type":"numeric_atoms","value":1141,"base":3}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":5723,"base":3},"right_expr":{"type":"numeric_atoms","value":3492,"base":3}}},"used_operators":["rJVOvQCfKK","SUmda5xLS4","2DDjHMKMc0"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21211222","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1145","layer":2},{"info":"number node, value=1141","layer":2},{"info":"compute binary expreesion, left_input=1145, right_input=1141, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-170113","layer":1},{"info":"number node, value=5723","layer":2},{"info":"number node, value=3492","layer":2},{"info":"compute binary expreesion, left_input=5723, right_input=3492, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=5723","layer":1},{"info":"compute binary expreesion, left_input=-170113, right_input=5723, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=5723","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1120102⪄⫏≰1120021)⨎⫏≰21211222⋝⋈⪟⫏≰11210100=⫏≰21211222","reverse_text":"⫏≰21211222=(⫏≰1120102⪄⫏≰1120021)⨎⫏≰21211222⋝⋈⪟⫏≰11210100","cot":[{"info":"⫏≰1120102⪄⫏≰1120021=⫏≰-22122100111","layer":1},{"info":"⫏≰21211222⋝⋈⪟⫏≰11210100=⫏≰21211222","layer":1},{"info":"⫏≰-22122100111⨎⫏≰21211222=⫏≰21211222","layer":0}]}
{"id":681,"expression_no_base_symbol":"-$1084$∑⇟⊟$5201$","expression":"-⫏≰1111011∑⇟⊟⫏≰21010122","highest_n_order":4,"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":1084,"base":3},"right_expr":{"type":"numeric_atoms","value":5201,"base":3}}},"used_operators":["t8gj7n24qd","U7g4x0WXJJ"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1084","layer":2},{"info":"number node, value=5201","layer":2},{"info":"compute binary expreesion, left_input=1084, right_input=5201, 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 = t8gj7n24qd, unary_op_definition = 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"-⫏≰1111011∑⇟⊟⫏≰21010122=NaN","reverse_text":"NaN=-⫏≰1111011∑⇟⊟⫏≰21010122","cot":[{"info":"⫏≰1111011∑⇟⊟⫏≰21010122=NaN","layer":1},{"info":"-NaN=NaN","layer":0}]}
{"id":682,"expression_no_base_symbol":"($1042$↙$1649$)∀⇚≩(↥$1132$)","expression":"(⫏≰1102121↙⫏≰2021002)∀⇚≩(↥⫏≰1112221)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":36303,"operation_count":3,"complexity_ratio":12101.0,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":1042,"base":3},"right_expr":{"type":"numeric_atoms","value":1649,"base":3}},"right_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":1132,"base":3}}},"used_operators":["LRNGc0VcxI","yyfyN0ffXY","A8NUZmVepG"],"dependent_operators":["X99M06cbEe","tmPS8pqC7x","DpFCA1CohY","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1042","layer":2},{"info":"number node, value=1649","layer":2},{"info":"compute binary expreesion, left_input=1042, right_input=1649, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-4947","layer":1},{"info":"number node, value=1132","layer":2},{"info":"compute unary expreesion, input=1132, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=10","layer":1},{"info":"compute binary expreesion, left_input=-4947, right_input=10, 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":3,"result_base":3,"text":"(⫏≰1102121↙⫏≰2021002)∀⇚≩(↥⫏≰1112221)=NaN","reverse_text":"NaN=(⫏≰1102121↙⫏≰2021002)∀⇚≩(↥⫏≰1112221)","cot":[{"info":"⫏≰1102121↙⫏≰2021002=⫏≰-20210020","layer":1},{"info":"↥⫏≰1112221=⫏≰101","layer":1},{"info":"⫏≰-20210020∀⇚≩⫏≰101=NaN","layer":0}]}
{"id":683,"expression_no_base_symbol":"$4953$↬$1247$⨽($2770$⪒$2521$)","expression":"⫏≰20210110↬⫏≰1201012⨽(⫏≰10210121⪒⫏≰10110101)","highest_n_order":5,"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":4953,"base":3},"right_expr":{"type":"numeric_atoms","value":1247,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":2770,"base":3},"right_expr":{"type":"numeric_atoms","value":2521,"base":3}}},"used_operators":["8HhzD0ZcuI","B5M0gjZbta","f6k1SAg4EE"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4953","layer":2},{"info":"number node, value=1247","layer":2},{"info":"compute binary expreesion, left_input=4953, right_input=1247, 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=2770","layer":2},{"info":"number node, value=2521","layer":2},{"info":"compute binary expreesion, left_input=2770, right_input=2521, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-5291","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-5291, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰20210110↬⫏≰1201012⨽(⫏≰10210121⪒⫏≰10110101)=NaN","reverse_text":"NaN=⫏≰20210110↬⫏≰1201012⨽(⫏≰10210121⪒⫏≰10110101)","cot":[{"info":"⫏≰20210110↬⫏≰1201012=NaN","layer":1},{"info":"⫏≰10210121⪒⫏≰10110101=⫏≰-21020222","layer":1},{"info":"NaN⨽⫏≰-21020222=NaN","layer":0}]}
{"id":684,"expression_no_base_symbol":"(⨞⊢$3429$)-$2381$⋥≓≎$1716$","expression":"(⨞⊢⫏≰11201000)-⫏≰10021012⋥≓≎⫏≰2100120","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7,"operation_count":3,"complexity_ratio":2.3333333333333335,"tree":{"type":"binary","operator":"-","left_expr":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":3429,"base":3}},"right_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":2381,"base":3},"right_expr":{"type":"numeric_atoms","value":1716,"base":3}}},"used_operators":["rysDP5nf3Z","xUOZtlo3hN","Qy55tPpLXF"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-20102121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3429","layer":2},{"info":"compute unary expreesion, input=3429, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-3603","layer":1},{"info":"number node, value=2381","layer":2},{"info":"number node, value=1716","layer":2},{"info":"compute binary expreesion, left_input=2381, right_input=1716, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=1084","layer":1},{"info":"compute binary expreesion, left_input=-3603, right_input=1084, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-4687","layer":0}],"base":3,"result_base":3,"text":"(⨞⊢⫏≰11201000)-⫏≰10021012⋥≓≎⫏≰2100120=⫏≰-20102121","reverse_text":"⫏≰-20102121=(⨞⊢⫏≰11201000)-⫏≰10021012⋥≓≎⫏≰2100120","cot":[{"info":"⨞⊢⫏≰11201000=⫏≰-11221110","layer":1},{"info":"⫏≰10021012⋥≓≎⫏≰2100120=⫏≰1111011","layer":1},{"info":"⫏≰-11221110-⫏≰1111011=⫏≰-20102121","layer":0}]}
{"id":685,"expression_no_base_symbol":"$2234$⋳⪒$1889$+($1911$≫≃)","expression":"⫏≰10001202⋳⪒⫏≰2120222+(⫏≰2121210≫≃)","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":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":2234,"base":3},"right_expr":{"type":"numeric_atoms","value":1889,"base":3}},"right_expr":{"type":"unary","operator":"≫≃","unary_expr":{"type":"numeric_atoms","value":1911,"base":3}}},"used_operators":["W4YGzv6Whe","12rbrZMWeM","X99M06cbEe"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A"],"result":"⫏≰101022100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2234","layer":2},{"info":"number node, value=1889","layer":2},{"info":"compute binary expreesion, left_input=2234, right_input=1889, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=2292","layer":1},{"info":"number node, value=1911","layer":2},{"info":"compute unary expreesion, input=1911, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=5223","layer":1},{"info":"compute binary expreesion, left_input=2292, right_input=5223, op_id = W4YGzv6Whe binary_op_definition= 'None', output=7515","layer":0}],"base":3,"result_base":3,"text":"⫏≰10001202⋳⪒⫏≰2120222+(⫏≰2121210≫≃)=⫏≰101022100","reverse_text":"⫏≰101022100=⫏≰10001202⋳⪒⫏≰2120222+(⫏≰2121210≫≃)","cot":[{"info":"⫏≰10001202⋳⪒⫏≰2120222=⫏≰10010220","layer":1},{"info":"⫏≰2121210≫≃=⫏≰21011110","layer":1},{"info":"⫏≰10010220+⫏≰21011110=⫏≰101022100","layer":0}]}
{"id":686,"expression_no_base_symbol":"($5288$-$1497$)⨟⋌⩍(∂$4161$)","expression":"(⫏≰21020212-⫏≰2001110)⨟⋌⩍(∂⫏≰12201010)","highest_n_order":5,"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":5288,"base":3},"right_expr":{"type":"numeric_atoms","value":1497,"base":3}},"right_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":4161,"base":3}}},"used_operators":["rGHVDoGpnC","rysDP5nf3Z","Uaa54Peajs"],"dependent_operators":["Tcnh7f0tEr","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5288","layer":2},{"info":"number node, value=1497","layer":2},{"info":"compute binary expreesion, left_input=5288, right_input=1497, op_id = rysDP5nf3Z binary_op_definition= 'None', output=3791","layer":1},{"info":"number node, value=4161","layer":2},{"info":"compute unary expreesion, input=4161, 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=3791, right_input=nan, 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":0}],"base":3,"result_base":3,"text":"(⫏≰21020212-⫏≰2001110)⨟⋌⩍(∂⫏≰12201010)=NaN","reverse_text":"NaN=(⫏≰21020212-⫏≰2001110)⨟⋌⩍(∂⫏≰12201010)","cot":[{"info":"⫏≰21020212-⫏≰2001110=⫏≰12012102","layer":1},{"info":"∂⫏≰12201010=NaN","layer":1},{"info":"⫏≰12012102⨟⋌⩍NaN=NaN","layer":0}]}
{"id":687,"expression_no_base_symbol":"$1217$⨎$1485$⫸⊐($1826$%$1636$)","expression":"⫏≰1200002⨎⫏≰2001000⫸⊐(⫏≰2111122%⫏≰2020121)","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":1217,"base":3},"right_expr":{"type":"numeric_atoms","value":1485,"base":3}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":1826,"base":3},"right_expr":{"type":"numeric_atoms","value":1636,"base":3}}},"used_operators":["mqXw5SEYmG","rJVOvQCfKK","k8jYdgA6NY"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","rysDP5nf3Z"],"result":"⫏≰212112","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1217","layer":2},{"info":"number node, value=1485","layer":2},{"info":"compute binary expreesion, left_input=1217, right_input=1485, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=1485","layer":1},{"info":"number node, value=1826","layer":2},{"info":"number node, value=1636","layer":2},{"info":"compute binary expreesion, left_input=1826, right_input=1636, op_id = k8jYdgA6NY binary_op_definition= 'None', output=190","layer":1},{"info":"compute binary expreesion, left_input=1485, right_input=190, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=635","layer":0}],"base":3,"result_base":3,"text":"⫏≰1200002⨎⫏≰2001000⫸⊐(⫏≰2111122%⫏≰2020121)=⫏≰212112","reverse_text":"⫏≰212112=⫏≰1200002⨎⫏≰2001000⫸⊐(⫏≰2111122%⫏≰2020121)","cot":[{"info":"⫏≰1200002⨎⫏≰2001000=⫏≰2001000","layer":1},{"info":"⫏≰2111122%⫏≰2020121=⫏≰21001","layer":1},{"info":"⫏≰2001000⫸⊐⫏≰21001=⫏≰212112","layer":0}]}
{"id":688,"expression_no_base_symbol":"$4805$⇷$3313$⪄(⫛⫱⨽$1070$)","expression":"⫏≰20120222⇷⫏≰11112201⪄(⫛⫱⨽⫏≰1110122)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":68793,"operation_count":3,"complexity_ratio":22931.0,"tree":{"type":"binary","operator":"⪄","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":4805,"base":3},"right_expr":{"type":"numeric_atoms","value":3313,"base":3}},"right_expr":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"numeric_atoms","value":1070,"base":3}}},"used_operators":["SUmda5xLS4","mp7IySMOzn","DlLNRPXxWL"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","rGHVDoGpnC"],"result":"⫏≰-1211121211110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4805","layer":2},{"info":"number node, value=3313","layer":2},{"info":"compute binary expreesion, left_input=4805, right_input=3313, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=6626","layer":1},{"info":"number node, value=1070","layer":2},{"info":"compute unary expreesion, input=1070, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=6626, right_input=0, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-976737","layer":0}],"base":3,"result_base":3,"text":"⫏≰20120222⇷⫏≰11112201⪄(⫛⫱⨽⫏≰1110122)=⫏≰-1211121211110","reverse_text":"⫏≰-1211121211110=⫏≰20120222⇷⫏≰11112201⪄(⫛⫱⨽⫏≰1110122)","cot":[{"info":"⫏≰20120222⇷⫏≰11112201=⫏≰100002102","layer":1},{"info":"⫛⫱⨽⫏≰1110122=⫏≰0","layer":1},{"info":"⫏≰100002102⪄⫏≰0=⫏≰-1211121211110","layer":0}]}
{"id":689,"expression_no_base_symbol":"(↥$1174$)⨎($1647$↙$4197$)","expression":"(↥⫏≰1121111)⨎(⫏≰2021000↙⫏≰12202110)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4224,"operation_count":3,"complexity_ratio":1408.0,"tree":{"type":"binary","operator":"⨎","left_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":1174,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":1647,"base":3},"right_expr":{"type":"numeric_atoms","value":4197,"base":3}}},"used_operators":["rJVOvQCfKK","A8NUZmVepG","yyfyN0ffXY"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","k8jYdgA6NY","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰-122021100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1174","layer":2},{"info":"compute unary expreesion, input=1174, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=1","layer":1},{"info":"number node, value=1647","layer":2},{"info":"number node, value=4197","layer":2},{"info":"compute binary expreesion, left_input=1647, right_input=4197, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-12591","layer":1},{"info":"compute binary expreesion, left_input=1, right_input=-12591, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=-12591","layer":0}],"base":3,"result_base":3,"text":"(↥⫏≰1121111)⨎(⫏≰2021000↙⫏≰12202110)=⫏≰-122021100","reverse_text":"⫏≰-122021100=(↥⫏≰1121111)⨎(⫏≰2021000↙⫏≰12202110)","cot":[{"info":"↥⫏≰1121111=⫏≰1","layer":1},{"info":"⫏≰2021000↙⫏≰12202110=⫏≰-122021100","layer":1},{"info":"⫏≰1⨎⫏≰-122021100=⫏≰-122021100","layer":0}]}
{"id":690,"expression_no_base_symbol":"($1539$∸)⨽($4846$⪒$1307$)","expression":"(⫏≰2010000∸)⨽(⫏≰20122111⪒⫏≰1210102)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":366,"operation_count":3,"complexity_ratio":122.0,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":1539,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":4846,"base":3},"right_expr":{"type":"numeric_atoms","value":1307,"base":3}}},"used_operators":["8HhzD0ZcuI","o20kRiQErp","f6k1SAg4EE"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","tmPS8pqC7x","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-10202210200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1539","layer":2},{"info":"compute unary expreesion, input=1539, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"number node, value=4846","layer":2},{"info":"number node, value=1307","layer":2},{"info":"compute binary expreesion, left_input=4846, right_input=1307, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-6153","layer":1},{"info":"compute binary expreesion, left_input=177, right_input=-6153, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-74214","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2010000∸)⨽(⫏≰20122111⪒⫏≰1210102)=⫏≰-10202210200","reverse_text":"⫏≰-10202210200=(⫏≰2010000∸)⨽(⫏≰20122111⪒⫏≰1210102)","cot":[{"info":"⫏≰2010000∸=⫏≰20120","layer":1},{"info":"⫏≰20122111⪒⫏≰1210102=⫏≰-22102220","layer":1},{"info":"⫏≰20120⨽⫏≰-22102220=⫏≰-10202210200","layer":0}]}
{"id":691,"expression_no_base_symbol":"($3684$⨵⪆$2750$)⨸⪁$3407$⋝⋈⪟$7552$","expression":"(⫏≰12001110⨵⪆⫏≰10202212)⨸⪁⫏≰11200012⋝⋈⪟⫏≰101100201","highest_n_order":1,"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":3684,"base":3},"right_expr":{"type":"numeric_atoms","value":2750,"base":3}},"right_expr":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"numeric_atoms","value":3407,"base":3},"right_expr":{"type":"numeric_atoms","value":7552,"base":3}}},"used_operators":["g55IO6H4Gj","2DQ55sFlQl","2DDjHMKMc0"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰100210020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3684","layer":2},{"info":"number node, value=2750","layer":2},{"info":"compute binary expreesion, left_input=3684, right_input=2750, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=3407","layer":2},{"info":"number node, value=7552","layer":2},{"info":"compute binary expreesion, left_input=3407, right_input=7552, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=3407","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=3407, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=7134","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12001110⨵⪆⫏≰10202212)⨸⪁⫏≰11200012⋝⋈⪟⫏≰101100201=⫏≰100210020","reverse_text":"⫏≰100210020=(⫏≰12001110⨵⪆⫏≰10202212)⨸⪁⫏≰11200012⋝⋈⪟⫏≰101100201","cot":[{"info":"⫏≰12001110⨵⪆⫏≰10202212=⫏≰12221","layer":1},{"info":"⫏≰11200012⋝⋈⪟⫏≰101100201=⫏≰11200012","layer":1},{"info":"⫏≰12221⨸⪁⫏≰11200012=⫏≰100210020","layer":0}]}
{"id":692,"expression_no_base_symbol":"(⊥$2515$)⋳⪒($8887$∸)","expression":"(⊥⫏≰10110011)⋳⪒(⫏≰110012011∸)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":185,"operation_count":3,"complexity_ratio":61.666666666666664,"tree":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":2515,"base":3}},"right_expr":{"type":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":8887,"base":3}}},"used_operators":["12rbrZMWeM","Q3PJZHRvZv","o20kRiQErp"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","fu6greOZ01","tmPS8pqC7x"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2515","layer":2},{"info":"compute unary expreesion, input=2515, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"number node, value=8887","layer":2},{"info":"compute unary expreesion, input=8887, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=177, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⊥⫏≰10110011)⋳⪒(⫏≰110012011∸)=NaN","reverse_text":"NaN=(⊥⫏≰10110011)⋳⪒(⫏≰110012011∸)","cot":[{"info":"⊥⫏≰10110011=NaN","layer":1},{"info":"⫏≰110012011∸=⫏≰20120","layer":1},{"info":"NaN⋳⪒⫏≰20120=NaN","layer":0}]}
{"id":693,"expression_no_base_symbol":"(⨑⩽⪐$4037$)⩷∴($5360$≋⫹)","expression":"(⨑⩽⪐⫏≰12112112)⩷∴(⫏≰21100112≋⫹)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13,"operation_count":3,"complexity_ratio":4.333333333333333,"tree":{"type":"binary","operator":"⩷∴","left_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":4037,"base":3}},"right_expr":{"type":"unary","operator":"≋⫹","unary_expr":{"type":"numeric_atoms","value":5360,"base":3}}},"used_operators":["9FxExcQeMw","AF7qkfDlqP","N41Kp7NANJ"],"dependent_operators":["rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰201001002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4037","layer":2},{"info":"compute unary expreesion, input=4037, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-3764","layer":1},{"info":"number node, value=5360","layer":2},{"info":"compute unary expreesion, input=5360, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-10720","layer":1},{"info":"compute binary expreesion, left_input=-3764, right_input=-10720, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=13880","layer":0}],"base":3,"result_base":3,"text":"(⨑⩽⪐⫏≰12112112)⩷∴(⫏≰21100112≋⫹)=⫏≰201001002","reverse_text":"⫏≰201001002=(⨑⩽⪐⫏≰12112112)⩷∴(⫏≰21100112≋⫹)","cot":[{"info":"⨑⩽⪐⫏≰12112112=⫏≰-12011102","layer":1},{"info":"⫏≰21100112≋⫹=⫏≰-112201001","layer":1},{"info":"⫏≰-12011102⩷∴⫏≰-112201001=⫏≰201001002","layer":0}]}
{"id":694,"expression_no_base_symbol":"(-$1172$)⋝⋈⪟($2220$⊪)","expression":"(-⫏≰1121102)⋝⋈⪟(⫏≰10001020⊪)","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":1172,"base":3}},"right_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":2220,"base":3}}},"used_operators":["2DDjHMKMc0","t8gj7n24qd","zVYPLywUTj"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL"],"result":"⫏≰-1121102","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1172","layer":2},{"info":"compute unary expreesion, input=1172, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1172","layer":1},{"info":"number node, value=2220","layer":2},{"info":"compute unary expreesion, input=2220, 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=-1172, right_input=0, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=-1172","layer":0}],"base":3,"result_base":3,"text":"(-⫏≰1121102)⋝⋈⪟(⫏≰10001020⊪)=⫏≰-1121102","reverse_text":"⫏≰-1121102=(-⫏≰1121102)⋝⋈⪟(⫏≰10001020⊪)","cot":[{"info":"-⫏≰1121102=⫏≰-1121102","layer":1},{"info":"⫏≰10001020⊪=⫏≰0","layer":1},{"info":"⫏≰-1121102⋝⋈⪟⫏≰0=⫏≰-1121102","layer":0}]}
{"id":695,"expression_no_base_symbol":"↣≠⋷($4741$⨐⩸⫘$7868$)","expression":"↣≠⋷(⫏≰20111121⨐⩸⫘⫏≰101210102)","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":4741,"base":3},"right_expr":{"type":"numeric_atoms","value":7868,"base":3}}},"used_operators":["Asc51vEJeQ","fu6greOZ01"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4741","layer":2},{"info":"number node, value=7868","layer":2},{"info":"compute binary expreesion, left_input=4741, right_input=7868, 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 unary expreesion, input=nan, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(⫏≰20111121⨐⩸⫘⫏≰101210102)=NaN","reverse_text":"NaN=↣≠⋷(⫏≰20111121⨐⩸⫘⫏≰101210102)","cot":[{"info":"⫏≰20111121⨐⩸⫘⫏≰101210102=NaN","layer":1},{"info":"↣≠⋷NaN=NaN","layer":0}]}
{"id":696,"expression_no_base_symbol":"($1493$⩨$2617$)≧⫂∧(⨑⩽⪐$1749$)","expression":"(⫏≰2001022⩨⫏≰10120221)≧⫂∧(⨑⩽⪐⫏≰2101210)","highest_n_order":2,"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":1493,"base":3},"right_expr":{"type":"numeric_atoms","value":2617,"base":3}},"right_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":1749,"base":3}}},"used_operators":["Ph9nP6C5qx","2DlMacCsIx","AF7qkfDlqP"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰2000120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1493","layer":2},{"info":"number node, value=2617","layer":2},{"info":"compute binary expreesion, left_input=1493, right_input=2617, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-3","layer":1},{"info":"number node, value=1749","layer":2},{"info":"compute unary expreesion, input=1749, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-1476","layer":1},{"info":"compute binary expreesion, left_input=-3, right_input=-1476, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=1473","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2001022⩨⫏≰10120221)≧⫂∧(⨑⩽⪐⫏≰2101210)=⫏≰2000120","reverse_text":"⫏≰2000120=(⫏≰2001022⩨⫏≰10120221)≧⫂∧(⨑⩽⪐⫏≰2101210)","cot":[{"info":"⫏≰2001022⩨⫏≰10120221=⫏≰-10","layer":1},{"info":"⨑⩽⪐⫏≰2101210=⫏≰-2000200","layer":1},{"info":"⫏≰-10≧⫂∧⫏≰-2000200=⫏≰2000120","layer":0}]}
{"id":697,"expression_no_base_symbol":"($2842$⊭∹↮)≎⊠⪸($1082$↙$1276$)","expression":"(⫏≰10220021⊭∹↮)≎⊠⪸(⫏≰1111002↙⫏≰1202021)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1296,"operation_count":3,"complexity_ratio":432.0,"tree":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"numeric_atoms","value":2842,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":1082,"base":3},"right_expr":{"type":"numeric_atoms","value":1276,"base":3}}},"used_operators":["bJkvcejdHO","xNBdhnnwKq","yyfyN0ffXY"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2842","layer":2},{"info":"compute unary expreesion, input=2842, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=5684","layer":1},{"info":"number node, value=1082","layer":2},{"info":"number node, value=1276","layer":2},{"info":"compute binary expreesion, left_input=1082, right_input=1276, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-3828","layer":1},{"info":"compute binary expreesion, left_input=5684, right_input=-3828, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=67","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10220021⊭∹↮)≎⊠⪸(⫏≰1111002↙⫏≰1202021)=⫏≰2111","reverse_text":"⫏≰2111=(⫏≰10220021⊭∹↮)≎⊠⪸(⫏≰1111002↙⫏≰1202021)","cot":[{"info":"⫏≰10220021⊭∹↮=⫏≰21210112","layer":1},{"info":"⫏≰1111002↙⫏≰1202021=⫏≰-12020210","layer":1},{"info":"⫏≰21210112≎⊠⪸⫏≰-12020210=⫏≰2111","layer":0}]}
{"id":698,"expression_no_base_symbol":"$9257$⩚⊴⇥$6676$⊉≛↸$1803$⩷∴$3841$","expression":"⫏≰110200212⩚⊴⇥⫏≰100011021⊉≛↸⫏≰2110210⩷∴⫏≰12021021","highest_n_order":1,"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":9257,"base":3},"right_expr":{"type":"numeric_atoms","value":6676,"base":3}},"right_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":1803,"base":3},"right_expr":{"type":"numeric_atoms","value":3841,"base":3}}},"used_operators":["DZ8iAZOCBD","NTOWxs364D","9FxExcQeMw"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rysDP5nf3Z"],"result":"⫏≰12122011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=9257","layer":2},{"info":"number node, value=6676","layer":2},{"info":"compute binary expreesion, left_input=9257, right_input=6676, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-16054","layer":1},{"info":"number node, value=1803","layer":2},{"info":"number node, value=3841","layer":2},{"info":"compute binary expreesion, left_input=1803, right_input=3841, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-4108","layer":1},{"info":"compute binary expreesion, left_input=-16054, right_input=-4108, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=4108","layer":0}],"base":3,"result_base":3,"text":"⫏≰110200212⩚⊴⇥⫏≰100011021⊉≛↸⫏≰2110210⩷∴⫏≰12021021=⫏≰12122011","reverse_text":"⫏≰12122011=⫏≰110200212⩚⊴⇥⫏≰100011021⊉≛↸⫏≰2110210⩷∴⫏≰12021021","cot":[{"info":"⫏≰110200212⩚⊴⇥⫏≰100011021=⫏≰-211000121","layer":1},{"info":"⫏≰2110210⩷∴⫏≰12021021=⫏≰-12122011","layer":1},{"info":"⫏≰-211000121⊉≛↸⫏≰-12122011=⫏≰12122011","layer":0}]}
{"id":699,"expression_no_base_symbol":"(∂$1749$)↙$2548$⨰$1025$","expression":"(∂⫏≰2101210)↙⫏≰10111101⨰⫏≰1101222","highest_n_order":5,"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":1749,"base":3}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":2548,"base":3},"right_expr":{"type":"numeric_atoms","value":1025,"base":3}}},"used_operators":["yyfyN0ffXY","Uaa54Peajs","eewbuw0ToL"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1749","layer":2},{"info":"compute unary expreesion, input=1749, 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":"number node, value=2548","layer":2},{"info":"number node, value=1025","layer":2},{"info":"compute binary expreesion, left_input=2548, right_input=1025, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=1533","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1533, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(∂⫏≰2101210)↙⫏≰10111101⨰⫏≰1101222=NaN","reverse_text":"NaN=(∂⫏≰2101210)↙⫏≰10111101⨰⫏≰1101222","cot":[{"info":"∂⫏≰2101210=NaN","layer":1},{"info":"⫏≰10111101⨰⫏≰1101222=⫏≰2002210","layer":1},{"info":"NaN↙⫏≰2002210=NaN","layer":0}]}
{"id":700,"expression_no_base_symbol":"$3078$⪮%⊝$2993$⫸⊐$2322$+⇶⊼$2421$","expression":"⫏≰11020000⪮%⊝⫏≰11002212⫸⊐⫏≰10012000+⇶⊼⫏≰10022200","highest_n_order":5,"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":3078,"base":3},"right_expr":{"type":"numeric_atoms","value":2993,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":2322,"base":3},"right_expr":{"type":"numeric_atoms","value":2421,"base":3}}},"used_operators":["mqXw5SEYmG","IWmyXbctLI","TpPTUOHfaN"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3078","layer":2},{"info":"number node, value=2993","layer":2},{"info":"compute binary expreesion, left_input=3078, right_input=2993, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=6472","layer":1},{"info":"number node, value=2322","layer":2},{"info":"number node, value=2421","layer":2},{"info":"compute binary expreesion, left_input=2322, right_input=2421, 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":1},{"info":"compute binary expreesion, left_input=6472, right_input=nan, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11020000⪮%⊝⫏≰11002212⫸⊐⫏≰10012000+⇶⊼⫏≰10022200=NaN","reverse_text":"NaN=⫏≰11020000⪮%⊝⫏≰11002212⫸⊐⫏≰10012000+⇶⊼⫏≰10022200","cot":[{"info":"⫏≰11020000⪮%⊝⫏≰11002212=⫏≰22212201","layer":1},{"info":"⫏≰10012000+⇶⊼⫏≰10022200=NaN","layer":1},{"info":"⫏≰22212201⫸⊐NaN=NaN","layer":0}]}
{"id":701,"expression_no_base_symbol":"$4563$≭$4811$⊭↱($1870$%$8168$)","expression":"⫏≰20021000≭⫏≰20121012⊭↱(⫏≰2120021%⫏≰102012112)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":4563,"base":3},"right_expr":{"type":"numeric_atoms","value":4811,"base":3}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":1870,"base":3},"right_expr":{"type":"numeric_atoms","value":8168,"base":3}}},"used_operators":["COABgblf1C","rxpJgHHUmx","k8jYdgA6NY"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4563","layer":2},{"info":"number node, value=4811","layer":2},{"info":"compute binary expreesion, left_input=4563, right_input=4811, 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=1870","layer":2},{"info":"number node, value=8168","layer":2},{"info":"compute binary expreesion, left_input=1870, right_input=8168, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1870","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1870, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰20021000≭⫏≰20121012⊭↱(⫏≰2120021%⫏≰102012112)=NaN","reverse_text":"NaN=⫏≰20021000≭⫏≰20121012⊭↱(⫏≰2120021%⫏≰102012112)","cot":[{"info":"⫏≰20021000≭⫏≰20121012=NaN","layer":1},{"info":"⫏≰2120021%⫏≰102012112=⫏≰2120021","layer":1},{"info":"NaN⊭↱⫏≰2120021=NaN","layer":0}]}
{"id":702,"expression_no_base_symbol":"$1168$⪄$3928$⪨≂($6994$⫩⊇)","expression":"⫏≰1121021⪄⫏≰12101111⪨≂(⫏≰100121001⫩⊇)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":102,"operation_count":3,"complexity_ratio":34.0,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":1168,"base":3},"right_expr":{"type":"numeric_atoms","value":3928,"base":3}},"right_expr":{"type":"unary","operator":"⫩⊇","unary_expr":{"type":"numeric_atoms","value":6994,"base":3}}},"used_operators":["sdazOOVcIp","SUmda5xLS4","BjRHVeLaeN"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-200001102011","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1168","layer":2},{"info":"number node, value=3928","layer":2},{"info":"compute binary expreesion, left_input=1168, right_input=3928, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-184665","layer":1},{"info":"number node, value=6994","layer":2},{"info":"compute unary expreesion, input=6994, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=-6952","layer":1},{"info":"compute binary expreesion, left_input=-184665, right_input=-6952, 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=-355324","layer":0}],"base":3,"result_base":3,"text":"⫏≰1121021⪄⫏≰12101111⪨≂(⫏≰100121001⫩⊇)=⫏≰-200001102011","reverse_text":"⫏≰-200001102011=⫏≰1121021⪄⫏≰12101111⪨≂(⫏≰100121001⫩⊇)","cot":[{"info":"⫏≰1121021⪄⫏≰12101111=⫏≰-100101022110","layer":1},{"info":"⫏≰100121001⫩⊇=⫏≰-100112111","layer":1},{"info":"⫏≰-100101022110⪨≂⫏≰-100112111=⫏≰-200001102011","layer":0}]}
{"id":703,"expression_no_base_symbol":"⊥$5006$⨟⋌⩍$3451$","expression":"⊥⫏≰20212102⨟⋌⩍⫏≰11201211","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":5006,"base":3},"right_expr":{"type":"numeric_atoms","value":3451,"base":3}}},"used_operators":["Q3PJZHRvZv","rGHVDoGpnC"],"dependent_operators":["fu6greOZ01","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5006","layer":2},{"info":"number node, value=3451","layer":2},{"info":"compute binary expreesion, left_input=5006, right_input=3451, 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 unary expreesion, input=nan, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊥⫏≰20212102⨟⋌⩍⫏≰11201211=NaN","reverse_text":"NaN=⊥⫏≰20212102⨟⋌⩍⫏≰11201211","cot":[{"info":"⫏≰20212102⨟⋌⩍⫏≰11201211=NaN","layer":1},{"info":"⊥NaN=NaN","layer":0}]}
{"id":704,"expression_no_base_symbol":"$2682$∼$1959$+⇶⊼($4794$⩚⊴⇥$1276$)","expression":"⫏≰10200100∼⫏≰2200120+⇶⊼(⫏≰20120120⩚⊴⇥⫏≰1202021)","highest_n_order":5,"priority_hierarchical_complexity":2,"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":2682,"base":3},"right_expr":{"type":"numeric_atoms","value":1959,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":4794,"base":3},"right_expr":{"type":"numeric_atoms","value":1276,"base":3}}},"used_operators":["TpPTUOHfaN","DyGG3AbaNP","NTOWxs364D"],"dependent_operators":["AHs5Up7iyr","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2682","layer":2},{"info":"number node, value=1959","layer":2},{"info":"compute binary expreesion, left_input=2682, right_input=1959, 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=4794","layer":2},{"info":"number node, value=1276","layer":2},{"info":"compute binary expreesion, left_input=4794, right_input=1276, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-6191","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-6191, 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":3,"result_base":3,"text":"⫏≰10200100∼⫏≰2200120+⇶⊼(⫏≰20120120⩚⊴⇥⫏≰1202021)=NaN","reverse_text":"NaN=⫏≰10200100∼⫏≰2200120+⇶⊼(⫏≰20120120⩚⊴⇥⫏≰1202021)","cot":[{"info":"⫏≰10200100∼⫏≰2200120=NaN","layer":1},{"info":"⫏≰20120120⩚⊴⇥⫏≰1202021=⫏≰-22111022","layer":1},{"info":"NaN+⇶⊼⫏≰-22111022=NaN","layer":0}]}
{"id":705,"expression_no_base_symbol":"$4233$⫡⨏$1624$⪨≂$2701$∑⇟⊟$6423$","expression":"⫏≰12210210⫡⨏⫏≰2020011⪨≂⫏≰10201001∑⇟⊟⫏≰22210220","highest_n_order":4,"priority_hierarchical_complexity":2,"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":4233,"base":3},"right_expr":{"type":"numeric_atoms","value":1624,"base":3}},"right_expr":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"numeric_atoms","value":2701,"base":3},"right_expr":{"type":"numeric_atoms","value":6423,"base":3}}},"used_operators":["sdazOOVcIp","QMFrweE19q","U7g4x0WXJJ"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4233","layer":2},{"info":"number node, value=1624","layer":2},{"info":"compute binary expreesion, left_input=4233, right_input=1624, 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=25196","layer":1},{"info":"number node, value=2701","layer":2},{"info":"number node, value=6423","layer":2},{"info":"compute binary expreesion, left_input=2701, right_input=6423, 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=25196, 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":3,"result_base":3,"text":"⫏≰12210210⫡⨏⫏≰2020011⪨≂⫏≰10201001∑⇟⊟⫏≰22210220=NaN","reverse_text":"NaN=⫏≰12210210⫡⨏⫏≰2020011⪨≂⫏≰10201001∑⇟⊟⫏≰22210220","cot":[{"info":"⫏≰12210210⫡⨏⫏≰2020011=⫏≰1021120012","layer":1},{"info":"⫏≰10201001∑⇟⊟⫏≰22210220=NaN","layer":1},{"info":"⫏≰1021120012⪨≂NaN=NaN","layer":0}]}
{"id":706,"expression_no_base_symbol":"∂($1136$/$1269$)","expression":"∂(⫏≰1120002/⫏≰1202000)","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":1136,"base":3},"right_expr":{"type":"numeric_atoms","value":1269,"base":3}}},"used_operators":["Uaa54Peajs","XhwjNDsVaA"],"dependent_operators":["B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp","rysDP5nf3Z"],"result":"⫏≰-100210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1136","layer":2},{"info":"number node, value=1269","layer":2},{"info":"compute binary expreesion, left_input=1136, right_input=1269, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = Uaa54Peajs, unary_op_definition = '∂a = { (a⪒264) , if ((a⨓405)<13 and a<=191 and (a⨸⪁774)!=889) ; (a↬a) , else }', output=-264","layer":0}],"base":3,"result_base":3,"text":"∂(⫏≰1120002/⫏≰1202000)=⫏≰-100210","reverse_text":"⫏≰-100210=∂(⫏≰1120002/⫏≰1202000)","cot":[{"info":"⫏≰1120002/⫏≰1202000=⫏≰0","layer":1},{"info":"∂⫏≰0=⫏≰-100210","layer":0}]}
{"id":707,"expression_no_base_symbol":"($1052$⩚⊴⇥$1211$)⋝⋈⪟(⪲⇎$2646$)","expression":"(⫏≰1102222⩚⊴⇥⫏≰1122212)⋝⋈⪟(⪲⇎⫏≰10122000)","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":1052,"base":3},"right_expr":{"type":"numeric_atoms","value":1211,"base":3}},"right_expr":{"type":"unary","operator":"⪲⇎","unary_expr":{"type":"numeric_atoms","value":2646,"base":3}}},"used_operators":["2DDjHMKMc0","NTOWxs364D","XPYlsWDdGa"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-10021022","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1052","layer":2},{"info":"number node, value=1211","layer":2},{"info":"compute binary expreesion, left_input=1052, right_input=1211, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-2384","layer":1},{"info":"number node, value=2646","layer":2},{"info":"compute unary expreesion, input=2646, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=5292","layer":1},{"info":"compute binary expreesion, left_input=-2384, right_input=5292, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=-2384","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1102222⩚⊴⇥⫏≰1122212)⋝⋈⪟(⪲⇎⫏≰10122000)=⫏≰-10021022","reverse_text":"⫏≰-10021022=(⫏≰1102222⩚⊴⇥⫏≰1122212)⋝⋈⪟(⪲⇎⫏≰10122000)","cot":[{"info":"⫏≰1102222⩚⊴⇥⫏≰1122212=⫏≰-10021022","layer":1},{"info":"⪲⇎⫏≰10122000=⫏≰21021000","layer":1},{"info":"⫏≰-10021022⋝⋈⪟⫏≰21021000=⫏≰-10021022","layer":0}]}
{"id":708,"expression_no_base_symbol":"($2350$*$2557$)⨪↰⇹($1570$⨽$2491$)","expression":"(⫏≰10020001*⫏≰10111201)⨪↰⇹(⫏≰2011011⨽⫏≰10102021)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3930,"operation_count":3,"complexity_ratio":1310.0,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":2350,"base":3},"right_expr":{"type":"numeric_atoms","value":2557,"base":3}},"right_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1570,"base":3},"right_expr":{"type":"numeric_atoms","value":2491,"base":3}}},"used_operators":["tmPS8pqC7x","9HNa5Wba9A","8HhzD0ZcuI"],"dependent_operators":["rJVOvQCfKK","W4YGzv6Whe","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2350","layer":2},{"info":"number node, value=2557","layer":2},{"info":"compute binary expreesion, left_input=2350, right_input=2557, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=6008950","layer":1},{"info":"number node, value=1570","layer":2},{"info":"number node, value=2491","layer":2},{"info":"compute binary expreesion, left_input=1570, right_input=2491, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-7400859","layer":1},{"info":"compute binary expreesion, left_input=6008950, right_input=-7400859, 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=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10020001*⫏≰10111201)⨪↰⇹(⫏≰2011011⨽⫏≰10102021)=NaN","reverse_text":"NaN=(⫏≰10020001*⫏≰10111201)⨪↰⇹(⫏≰2011011⨽⫏≰10102021)","cot":[{"info":"⫏≰10020001*⫏≰10111201=⫏≰102022021201201","layer":1},{"info":"⫏≰2011011⨽⫏≰10102021=⫏≰-111221000001220","layer":1},{"info":"⫏≰102022021201201⨪↰⇹⫏≰-111221000001220=NaN","layer":0}]}
{"id":709,"expression_no_base_symbol":"($2852$%$1099$)%$2684$⨸⪁$4482$","expression":"(⫏≰10220122%⫏≰1111201)%⫏≰10200102⨸⪁⫏≰20011000","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"%","left_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":2852,"base":3},"right_expr":{"type":"numeric_atoms","value":1099,"base":3}},"right_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":2684,"base":3},"right_expr":{"type":"numeric_atoms","value":4482,"base":3}}},"used_operators":["k8jYdgA6NY","g55IO6H4Gj"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe"],"result":"⫏≰220020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2852","layer":2},{"info":"number node, value=1099","layer":2},{"info":"compute binary expreesion, left_input=2852, right_input=1099, op_id = k8jYdgA6NY binary_op_definition= 'None', output=654","layer":1},{"info":"number node, value=2684","layer":2},{"info":"number node, value=4482","layer":2},{"info":"compute binary expreesion, left_input=2684, right_input=4482, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=14332","layer":1},{"info":"compute binary expreesion, left_input=654, right_input=14332, op_id = k8jYdgA6NY binary_op_definition= 'None', output=654","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10220122%⫏≰1111201)%⫏≰10200102⨸⪁⫏≰20011000=⫏≰220020","reverse_text":"⫏≰220020=(⫏≰10220122%⫏≰1111201)%⫏≰10200102⨸⪁⫏≰20011000","cot":[{"info":"⫏≰10220122%⫏≰1111201=⫏≰220020","layer":1},{"info":"⫏≰10200102⨸⪁⫏≰20011000=⫏≰201122211","layer":1},{"info":"⫏≰220020%⫏≰201122211=⫏≰220020","layer":0}]}
{"id":710,"expression_no_base_symbol":"($4459$⨵⪆$5082$)∲⫓$6356$⪮%⊝$1887$","expression":"(⫏≰20010011⨵⪆⫏≰20222020)∲⫓⫏≰22201102⪮%⊝⫏≰2120220","highest_n_order":2,"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":4459,"base":3},"right_expr":{"type":"numeric_atoms","value":5082,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":6356,"base":3},"right_expr":{"type":"numeric_atoms","value":1887,"base":3}}},"used_operators":["i8ToyICDmI","2DQ55sFlQl","IWmyXbctLI"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4459","layer":2},{"info":"number node, value=5082","layer":2},{"info":"compute binary expreesion, left_input=4459, right_input=5082, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=6356","layer":2},{"info":"number node, value=1887","layer":2},{"info":"compute binary expreesion, left_input=6356, right_input=1887, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=13028","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=13028, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20010011⨵⪆⫏≰20222020)∲⫓⫏≰22201102⪮%⊝⫏≰2120220=⫏≰0","reverse_text":"⫏≰0=(⫏≰20010011⨵⪆⫏≰20222020)∲⫓⫏≰22201102⪮%⊝⫏≰2120220","cot":[{"info":"⫏≰20010011⨵⪆⫏≰20222020=⫏≰12221","layer":1},{"info":"⫏≰22201102⪮%⊝⫏≰2120220=⫏≰122212112","layer":1},{"info":"⫏≰12221∲⫓⫏≰122212112=⫏≰0","layer":0}]}
{"id":711,"expression_no_base_symbol":"$1964$⩷∴$1085$≋⫹","expression":"⫏≰2200202⩷∴⫏≰1111012≋⫹","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":1964,"base":3},"right_expr":{"type":"numeric_atoms","value":1085,"base":3}}},"used_operators":["N41Kp7NANJ","9FxExcQeMw"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰-11201212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1964","layer":2},{"info":"number node, value=1085","layer":2},{"info":"compute binary expreesion, left_input=1964, right_input=1085, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=1726","layer":1},{"info":"compute unary expreesion, input=1726, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-3452","layer":0}],"base":3,"result_base":3,"text":"⫏≰2200202⩷∴⫏≰1111012≋⫹=⫏≰-11201212","reverse_text":"⫏≰-11201212=⫏≰2200202⩷∴⫏≰1111012≋⫹","cot":[{"info":"⫏≰2200202⩷∴⫏≰1111012=⫏≰2100221","layer":1},{"info":"⫏≰2100221≋⫹=⫏≰-11201212","layer":0}]}
{"id":712,"expression_no_base_symbol":"$8275$∀⇚≩$3192$⪨≂$1536$⨸⪁$3687$","expression":"⫏≰102100111∀⇚≩⫏≰11101020⪨≂⫏≰2002220⨸⪁⫏≰12001120","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":57933,"operation_count":3,"complexity_ratio":19311.0,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":8275,"base":3},"right_expr":{"type":"numeric_atoms","value":3192,"base":3}},"right_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":1536,"base":3},"right_expr":{"type":"numeric_atoms","value":3687,"base":3}}},"used_operators":["sdazOOVcIp","LRNGc0VcxI","g55IO6H4Gj"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","X99M06cbEe","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=8275","layer":2},{"info":"number node, value=3192","layer":2},{"info":"compute binary expreesion, left_input=8275, right_input=3192, 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=1536","layer":2},{"info":"number node, value=3687","layer":2},{"info":"compute binary expreesion, left_input=1536, right_input=3687, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=10446","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=10446, 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":3,"result_base":3,"text":"⫏≰102100111∀⇚≩⫏≰11101020⪨≂⫏≰2002220⨸⪁⫏≰12001120=NaN","reverse_text":"NaN=⫏≰102100111∀⇚≩⫏≰11101020⪨≂⫏≰2002220⨸⪁⫏≰12001120","cot":[{"info":"⫏≰102100111∀⇚≩⫏≰11101020=NaN","layer":1},{"info":"⫏≰2002220⨸⪁⫏≰12001120=⫏≰112022220","layer":1},{"info":"NaN⪨≂⫏≰112022220=NaN","layer":0}]}
{"id":713,"expression_no_base_symbol":"(⋗⩬⋾$6214$)∸","expression":"(⋗⩬⋾⫏≰22112011)∸","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":180,"operation_count":2,"complexity_ratio":90.0,"tree":{"type":"unary","operator":"∸","unary_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":6214,"base":3}}},"used_operators":["o20kRiQErp","DpFCA1CohY"],"dependent_operators":["tmPS8pqC7x","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰20120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6214","layer":2},{"info":"compute unary expreesion, input=6214, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-18642","layer":1},{"info":"compute unary expreesion, input=-18642, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":0}],"base":3,"result_base":3,"text":"(⋗⩬⋾⫏≰22112011)∸=⫏≰20120","reverse_text":"⫏≰20120=(⋗⩬⋾⫏≰22112011)∸","cot":[{"info":"⋗⩬⋾⫏≰22112011=⫏≰-221120110","layer":1},{"info":"⫏≰-221120110∸=⫏≰20120","layer":0}]}
{"id":714,"expression_no_base_symbol":"(⫛⫱⨽$1923$)⊭↱($1805$≫≃)","expression":"(⫛⫱⨽⫏≰2122020)⊭↱(⫏≰2110212≫≃)","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":1923,"base":3}},"right_expr":{"type":"unary","operator":"≫≃","unary_expr":{"type":"numeric_atoms","value":1805,"base":3}}},"used_operators":["COABgblf1C","DlLNRPXxWL","X99M06cbEe"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rGHVDoGpnC","2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A"],"result":"⫏≰111202101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1923","layer":2},{"info":"compute unary expreesion, input=1923, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"number node, value=1805","layer":2},{"info":"compute unary expreesion, input=1805, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=5011","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=5011, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=10027","layer":0}],"base":3,"result_base":3,"text":"(⫛⫱⨽⫏≰2122020)⊭↱(⫏≰2110212≫≃)=⫏≰111202101","reverse_text":"⫏≰111202101=(⫛⫱⨽⫏≰2122020)⊭↱(⫏≰2110212≫≃)","cot":[{"info":"⫛⫱⨽⫏≰2122020=⫏≰0","layer":1},{"info":"⫏≰2110212≫≃=⫏≰20212121","layer":1},{"info":"⫏≰0⊭↱⫏≰20212121=⫏≰111202101","layer":0}]}
{"id":715,"expression_no_base_symbol":"↔($1470$⨁⊸⫻)","expression":"↔(⫏≰2000110⨁⊸⫻)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8,"operation_count":2,"complexity_ratio":4.0,"tree":{"type":"unary","operator":"↔","unary_expr":{"type":"unary","operator":"⨁⊸⫻","unary_expr":{"type":"numeric_atoms","value":1470,"base":3}}},"used_operators":["ruOEQAzv1W","glklzrTFfD"],"dependent_operators":["XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰-1122100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1470","layer":2},{"info":"compute unary expreesion, input=1470, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=1470","layer":1},{"info":"compute unary expreesion, input=1470, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-1197","layer":0}],"base":3,"result_base":3,"text":"↔(⫏≰2000110⨁⊸⫻)=⫏≰-1122100","reverse_text":"⫏≰-1122100=↔(⫏≰2000110⨁⊸⫻)","cot":[{"info":"⫏≰2000110⨁⊸⫻=⫏≰2000110","layer":1},{"info":"↔⫏≰2000110=⫏≰-1122100","layer":0}]}
{"id":716,"expression_no_base_symbol":"($3774$⨓$1061$)≹⇙⪍($9145$/$2963$)","expression":"(⫏≰12011210⨓⫏≰1110022)≹⇙⪍(⫏≰110112201/⫏≰11001202)","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":3774,"base":3},"right_expr":{"type":"numeric_atoms","value":1061,"base":3}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":9145,"base":3},"right_expr":{"type":"numeric_atoms","value":2963,"base":3}}},"used_operators":["AHs5Up7iyr","3ViojmjbAp","XhwjNDsVaA"],"dependent_operators":["dWAJyo7jo9","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3774","layer":2},{"info":"number node, value=1061","layer":2},{"info":"compute binary expreesion, left_input=3774, right_input=1061, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1064","layer":1},{"info":"number node, value=9145","layer":2},{"info":"number node, value=2963","layer":2},{"info":"compute binary expreesion, left_input=9145, right_input=2963, op_id = XhwjNDsVaA binary_op_definition= 'None', output=3","layer":1},{"info":"compute binary expreesion, left_input=-1064, 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":3,"result_base":3,"text":"(⫏≰12011210⨓⫏≰1110022)≹⇙⪍(⫏≰110112201/⫏≰11001202)=NaN","reverse_text":"NaN=(⫏≰12011210⨓⫏≰1110022)≹⇙⪍(⫏≰110112201/⫏≰11001202)","cot":[{"info":"⫏≰12011210⨓⫏≰1110022=⫏≰-1110102","layer":1},{"info":"⫏≰110112201/⫏≰11001202=⫏≰10","layer":1},{"info":"⫏≰-1110102≹⇙⪍⫏≰10=NaN","layer":0}]}
{"id":717,"expression_no_base_symbol":"⨵≀≌$3610$∼$1414$","expression":"⨵≀≌⫏≰11221201∼⫏≰1221101","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":75,"operation_count":2,"complexity_ratio":37.5,"tree":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":3610,"base":3},"right_expr":{"type":"numeric_atoms","value":1414,"base":3}}},"used_operators":["srAu1WTS94","DyGG3AbaNP"],"dependent_operators":["glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3610","layer":2},{"info":"number node, value=1414","layer":2},{"info":"compute binary expreesion, left_input=3610, right_input=1414, 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 = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⨵≀≌⫏≰11221201∼⫏≰1221101=NaN","reverse_text":"NaN=⨵≀≌⫏≰11221201∼⫏≰1221101","cot":[{"info":"⫏≰11221201∼⫏≰1221101=NaN","layer":1},{"info":"⨵≀≌NaN=NaN","layer":0}]}
{"id":718,"expression_no_base_symbol":"($3898$+$4602$)⨎($2846$⪨≂$2657$)","expression":"(⫏≰12100101+⫏≰20022110)⨎(⫏≰10220102⪨≂⫏≰10122102)","highest_n_order":2,"priority_hierarchical_complexity":2,"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":3898,"base":3},"right_expr":{"type":"numeric_atoms","value":4602,"base":3}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":2846,"base":3},"right_expr":{"type":"numeric_atoms","value":2657,"base":3}}},"used_operators":["rJVOvQCfKK","W4YGzv6Whe","sdazOOVcIp"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰122210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3898","layer":2},{"info":"number node, value=4602","layer":2},{"info":"compute binary expreesion, left_input=3898, right_input=4602, op_id = W4YGzv6Whe binary_op_definition= 'None', output=8500","layer":1},{"info":"number node, value=2846","layer":2},{"info":"number node, value=2657","layer":2},{"info":"compute binary expreesion, left_input=2846, right_input=2657, 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=480","layer":1},{"info":"compute binary expreesion, left_input=8500, right_input=480, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=480","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12100101+⫏≰20022110)⨎(⫏≰10220102⪨≂⫏≰10122102)=⫏≰122210","reverse_text":"⫏≰122210=(⫏≰12100101+⫏≰20022110)⨎(⫏≰10220102⪨≂⫏≰10122102)","cot":[{"info":"⫏≰12100101+⫏≰20022110=⫏≰102122211","layer":1},{"info":"⫏≰10220102⪨≂⫏≰10122102=⫏≰122210","layer":1},{"info":"⫏≰102122211⨎⫏≰122210=⫏≰122210","layer":0}]}
{"id":719,"expression_no_base_symbol":"$1507$≭$1618$⨐⩸⫘($1085$⪒$6454$)","expression":"⫏≰2001211≭⫏≰2012221⨐⩸⫘(⫏≰1111012⪒⫏≰22212001)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5,"operation_count":3,"complexity_ratio":1.6666666666666667,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":1507,"base":3},"right_expr":{"type":"numeric_atoms","value":1618,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":1085,"base":3},"right_expr":{"type":"numeric_atoms","value":6454,"base":3}}},"used_operators":["fu6greOZ01","rxpJgHHUmx","f6k1SAg4EE"],"dependent_operators":["3ViojmjbAp","AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1507","layer":2},{"info":"number node, value=1618","layer":2},{"info":"compute binary expreesion, left_input=1507, right_input=1618, 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=1085","layer":2},{"info":"number node, value=6454","layer":2},{"info":"compute binary expreesion, left_input=1085, right_input=6454, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-7539","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-7539, 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":3,"result_base":3,"text":"⫏≰2001211≭⫏≰2012221⨐⩸⫘(⫏≰1111012⪒⫏≰22212001)=NaN","reverse_text":"NaN=⫏≰2001211≭⫏≰2012221⨐⩸⫘(⫏≰1111012⪒⫏≰22212001)","cot":[{"info":"⫏≰2001211≭⫏≰2012221=NaN","layer":1},{"info":"⫏≰1111012⪒⫏≰22212001=⫏≰-101100020","layer":1},{"info":"NaN⨐⩸⫘⫏≰-101100020=NaN","layer":0}]}
{"id":720,"expression_no_base_symbol":"($1254$≣⋋)⨎($4498$⫥∨⫟$1619$)","expression":"(⫏≰1201110≣⋋)⨎(⫏≰20011121⫥∨⫟⫏≰2012222)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":669,"operation_count":3,"complexity_ratio":223.0,"tree":{"type":"binary","operator":"⨎","left_expr":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"numeric_atoms","value":1254,"base":3}},"right_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":4498,"base":3},"right_expr":{"type":"numeric_atoms","value":1619,"base":3}}},"used_operators":["rJVOvQCfKK","Tcnh7f0tEr","KYD54nUTWz"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1254","layer":2},{"info":"compute unary expreesion, input=1254, 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=4498","layer":2},{"info":"number node, value=1619","layer":2},{"info":"compute binary expreesion, left_input=4498, right_input=1619, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, 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":3,"result_base":3,"text":"(⫏≰1201110≣⋋)⨎(⫏≰20011121⫥∨⫟⫏≰2012222)=NaN","reverse_text":"NaN=(⫏≰1201110≣⋋)⨎(⫏≰20011121⫥∨⫟⫏≰2012222)","cot":[{"info":"⫏≰1201110≣⋋=⫏≰0","layer":1},{"info":"⫏≰20011121⫥∨⫟⫏≰2012222=NaN","layer":1},{"info":"⫏≰0⨎NaN=NaN","layer":0}]}
{"id":721,"expression_no_base_symbol":"$3736$+⇶⊼$7974$≎⊠⪸(-$1263$)","expression":"⫏≰12010101+⇶⊼⫏≰101221100≎⊠⪸(-⫏≰1201210)","highest_n_order":5,"priority_hierarchical_complexity":2,"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":3736,"base":3},"right_expr":{"type":"numeric_atoms","value":7974,"base":3}},"right_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":1263,"base":3}}},"used_operators":["bJkvcejdHO","TpPTUOHfaN","t8gj7n24qd"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","AHs5Up7iyr"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3736","layer":2},{"info":"number node, value=7974","layer":2},{"info":"compute binary expreesion, left_input=3736, right_input=7974, 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":1},{"info":"number node, value=1263","layer":2},{"info":"compute unary expreesion, input=1263, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1263","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-1263, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=67","layer":0}],"base":3,"result_base":3,"text":"⫏≰12010101+⇶⊼⫏≰101221100≎⊠⪸(-⫏≰1201210)=⫏≰2111","reverse_text":"⫏≰2111=⫏≰12010101+⇶⊼⫏≰101221100≎⊠⪸(-⫏≰1201210)","cot":[{"info":"⫏≰12010101+⇶⊼⫏≰101221100=NaN","layer":1},{"info":"-⫏≰1201210=⫏≰-1201210","layer":1},{"info":"NaN≎⊠⪸⫏≰-1201210=⫏≰2111","layer":0}]}
{"id":722,"expression_no_base_symbol":"($3669$+$1869$)⩚⊴⇥$2199$∀⇚≩$2124$","expression":"(⫏≰12000220+⫏≰2120020)⩚⊴⇥⫏≰10000110∀⇚≩⫏≰2220200","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":15397,"operation_count":3,"complexity_ratio":5132.333333333333,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":3669,"base":3},"right_expr":{"type":"numeric_atoms","value":1869,"base":3}},"right_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":2199,"base":3},"right_expr":{"type":"numeric_atoms","value":2124,"base":3}}},"used_operators":["NTOWxs364D","W4YGzv6Whe","LRNGc0VcxI"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3669","layer":2},{"info":"number node, value=1869","layer":2},{"info":"compute binary expreesion, left_input=3669, right_input=1869, op_id = W4YGzv6Whe binary_op_definition= 'None', output=5538","layer":1},{"info":"number node, value=2199","layer":2},{"info":"number node, value=2124","layer":2},{"info":"compute binary expreesion, left_input=2199, right_input=2124, 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=5538, right_input=nan, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12000220+⫏≰2120020)⩚⊴⇥⫏≰10000110∀⇚≩⫏≰2220200=NaN","reverse_text":"NaN=(⫏≰12000220+⫏≰2120020)⩚⊴⇥⫏≰10000110∀⇚≩⫏≰2220200","cot":[{"info":"⫏≰12000220+⫏≰2120020=⫏≰21121010","layer":1},{"info":"⫏≰10000110∀⇚≩⫏≰2220200=NaN","layer":1},{"info":"⫏≰21121010⩚⊴⇥NaN=NaN","layer":0}]}
{"id":723,"expression_no_base_symbol":"(⊥$1035$)⨳⩥⨓($1492$⫡⨏$2489$)","expression":"(⊥⫏≰1102100)⨳⩥⨓(⫏≰2001021⫡⨏⫏≰10102012)","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":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":1035,"base":3}},"right_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":1492,"base":3},"right_expr":{"type":"numeric_atoms","value":2489,"base":3}}},"used_operators":["nCS4ZIUYfx","Q3PJZHRvZv","QMFrweE19q"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","fu6greOZ01","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1035","layer":2},{"info":"compute unary expreesion, input=1035, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"number node, value=1492","layer":2},{"info":"number node, value=2489","layer":2},{"info":"compute binary expreesion, left_input=1492, right_input=2489, 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=13221","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=13221, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⊥⫏≰1102100)⨳⩥⨓(⫏≰2001021⫡⨏⫏≰10102012)=NaN","reverse_text":"NaN=(⊥⫏≰1102100)⨳⩥⨓(⫏≰2001021⫡⨏⫏≰10102012)","cot":[{"info":"⊥⫏≰1102100=NaN","layer":1},{"info":"⫏≰2001021⫡⨏⫏≰10102012=⫏≰200010200","layer":1},{"info":"NaN⨳⩥⨓⫏≰200010200=NaN","layer":0}]}
{"id":724,"expression_no_base_symbol":"(⫓⪴$5879$)⨸⪁$1285$≎⊠⪸$3026$","expression":"(⫓⪴⫏≰22001202)⨸⪁⫏≰1202121≎⊠⪸⫏≰11011002","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6152,"operation_count":3,"complexity_ratio":2050.6666666666665,"tree":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":5879,"base":3}},"right_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1285,"base":3},"right_expr":{"type":"numeric_atoms","value":3026,"base":3}}},"used_operators":["g55IO6H4Gj","eLxqMNBOBk","bJkvcejdHO"],"dependent_operators":["W4YGzv6Whe","9HNa5Wba9A","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"⫏≰11212022200211120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5879","layer":2},{"info":"compute unary expreesion, input=5879, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=34562641","layer":1},{"info":"number node, value=1285","layer":2},{"info":"number node, value=3026","layer":2},{"info":"compute binary expreesion, left_input=1285, right_input=3026, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=332342","layer":1},{"info":"compute binary expreesion, left_input=34562641, right_input=332342, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=69789966","layer":0}],"base":3,"result_base":3,"text":"(⫓⪴⫏≰22001202)⨸⪁⫏≰1202121≎⊠⪸⫏≰11011002=⫏≰11212022200211120","reverse_text":"⫏≰11212022200211120=(⫓⪴⫏≰22001202)⨸⪁⫏≰1202121≎⊠⪸⫏≰11011002","cot":[{"info":"⫓⪴⫏≰22001202=⫏≰2102000222000211","layer":1},{"info":"⫏≰1202121≎⊠⪸⫏≰11011002=⫏≰121212212222","layer":1},{"info":"⫏≰2102000222000211⨸⪁⫏≰121212212222=⫏≰11212022200211120","layer":0}]}
{"id":725,"expression_no_base_symbol":"(⊙↵-$3630$)≣⋋","expression":"(⊙↵-⫏≰11222110)≣⋋","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3830,"operation_count":2,"complexity_ratio":1915.0,"tree":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":3630,"base":3}}},"used_operators":["Tcnh7f0tEr","oWn0xqSxBt"],"dependent_operators":["dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"⫏≰1021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3630","layer":2},{"info":"compute unary expreesion, input=3630, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute unary expreesion, input=-1, op_id = Tcnh7f0tEr, unary_op_definition = 'a≣⋋ = { ((a/a)⋥≓≎(a⨪↰⇹248)) , if (a⪢148)<38 ; ((511*a)⊠≄⫣) , else }', output=34","layer":0}],"base":3,"result_base":3,"text":"(⊙↵-⫏≰11222110)≣⋋=⫏≰1021","reverse_text":"⫏≰1021=(⊙↵-⫏≰11222110)≣⋋","cot":[{"info":"⊙↵-⫏≰11222110=⫏≰-1","layer":1},{"info":"⫏≰-1≣⋋=⫏≰1021","layer":0}]}
{"id":726,"expression_no_base_symbol":"⩦⩻⨪(⊄⩳↩$4284$)","expression":"⩦⩻⨪(⊄⩳↩⫏≰12212200)","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":4284,"base":3}}},"used_operators":["2td37pGCOC","8w2t5hMYqp"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-122122000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4284","layer":2},{"info":"compute unary expreesion, input=4284, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-12852","layer":1},{"info":"compute unary expreesion, input=-12852, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=-12852","layer":0}],"base":3,"result_base":3,"text":"⩦⩻⨪(⊄⩳↩⫏≰12212200)=⫏≰-122122000","reverse_text":"⫏≰-122122000=⩦⩻⨪(⊄⩳↩⫏≰12212200)","cot":[{"info":"⊄⩳↩⫏≰12212200=⫏≰-122122000","layer":1},{"info":"⩦⩻⨪⫏≰-122122000=⫏≰-122122000","layer":0}]}
{"id":727,"expression_no_base_symbol":"($8915$⨸⪁$2442$)∼($2428$⨸⪁$1954$)","expression":"(⫏≰110020012⨸⪁⫏≰10100110)∼(⫏≰10022221⨸⪁⫏≰2200101)","highest_n_order":4,"priority_hierarchical_complexity":2,"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":8915,"base":3},"right_expr":{"type":"numeric_atoms","value":2442,"base":3}},"right_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":2428,"base":3},"right_expr":{"type":"numeric_atoms","value":1954,"base":3}}},"used_operators":["DyGG3AbaNP","g55IO6H4Gj"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=8915","layer":2},{"info":"number node, value=2442","layer":2},{"info":"compute binary expreesion, left_input=8915, right_input=2442, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=22714","layer":1},{"info":"number node, value=2428","layer":2},{"info":"number node, value=1954","layer":2},{"info":"compute binary expreesion, left_input=2428, right_input=1954, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=8764","layer":1},{"info":"compute binary expreesion, left_input=22714, right_input=8764, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰110020012⨸⪁⫏≰10100110)∼(⫏≰10022221⨸⪁⫏≰2200101)=NaN","reverse_text":"NaN=(⫏≰110020012⨸⪁⫏≰10100110)∼(⫏≰10022221⨸⪁⫏≰2200101)","cot":[{"info":"⫏≰110020012⨸⪁⫏≰10100110=⫏≰1011011021","layer":1},{"info":"⫏≰10022221⨸⪁⫏≰2200101=⫏≰110000121","layer":1},{"info":"⫏≰1011011021∼⫏≰110000121=NaN","layer":0}]}
{"id":728,"expression_no_base_symbol":"$1164$≧⫂∧$1374$↙$1350$⩚⊴⇥$4298$","expression":"⫏≰1121010≧⫂∧⫏≰1212220↙⫏≰1212000⩚⊴⇥⫏≰12220012","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5776,"operation_count":3,"complexity_ratio":1925.3333333333333,"tree":{"type":"binary","operator":"↙","left_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":1164,"base":3},"right_expr":{"type":"numeric_atoms","value":1374,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":1350,"base":3},"right_expr":{"type":"numeric_atoms","value":4298,"base":3}}},"used_operators":["yyfyN0ffXY","Ph9nP6C5qx","NTOWxs364D"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰-212202000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1164","layer":2},{"info":"number node, value=1374","layer":2},{"info":"compute binary expreesion, left_input=1164, right_input=1374, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=901","layer":1},{"info":"number node, value=1350","layer":2},{"info":"number node, value=4298","layer":2},{"info":"compute binary expreesion, left_input=1350, right_input=4298, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-5769","layer":1},{"info":"compute binary expreesion, left_input=901, right_input=-5769, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-17307","layer":0}],"base":3,"result_base":3,"text":"⫏≰1121010≧⫂∧⫏≰1212220↙⫏≰1212000⩚⊴⇥⫏≰12220012=⫏≰-212202000","reverse_text":"⫏≰-212202000=⫏≰1121010≧⫂∧⫏≰1212220↙⫏≰1212000⩚⊴⇥⫏≰12220012","cot":[{"info":"⫏≰1121010≧⫂∧⫏≰1212220=⫏≰1020101","layer":1},{"info":"⫏≰1212000⩚⊴⇥⫏≰12220012=⫏≰-21220200","layer":1},{"info":"⫏≰1020101↙⫏≰-21220200=⫏≰-212202000","layer":0}]}
{"id":729,"expression_no_base_symbol":"$4532$⪛$1743$⇷(⊄⩳↩$3040$)","expression":"⫏≰20012212⪛⫏≰2101120⇷(⊄⩳↩⫏≰11011121)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":14660,"operation_count":3,"complexity_ratio":4886.666666666667,"tree":{"type":"binary","operator":"⇷","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":4532,"base":3},"right_expr":{"type":"numeric_atoms","value":1743,"base":3}},"right_expr":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":3040,"base":3}}},"used_operators":["mp7IySMOzn","uFcxV4UQCh","8w2t5hMYqp"],"dependent_operators":["DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4532","layer":2},{"info":"number node, value=1743","layer":2},{"info":"compute binary expreesion, left_input=4532, right_input=1743, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1046","layer":1},{"info":"number node, value=3040","layer":2},{"info":"compute unary expreesion, input=3040, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-9120","layer":1},{"info":"compute binary expreesion, left_input=1046, right_input=-9120, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰20012212⪛⫏≰2101120⇷(⊄⩳↩⫏≰11011121)=NaN","reverse_text":"NaN=⫏≰20012212⪛⫏≰2101120⇷(⊄⩳↩⫏≰11011121)","cot":[{"info":"⫏≰20012212⪛⫏≰2101120=⫏≰1102202","layer":1},{"info":"⊄⩳↩⫏≰11011121=⫏≰-110111210","layer":1},{"info":"⫏≰1102202⇷⫏≰-110111210=NaN","layer":0}]}
{"id":730,"expression_no_base_symbol":"($2669$⪄$1029$)⨓($1829$⨳⩥⨓$5465$)","expression":"(⫏≰10122212⪄⫏≰1102010)⨓(⫏≰2111202⨳⩥⨓⫏≰21111102)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3740,"operation_count":3,"complexity_ratio":1246.6666666666667,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2669,"base":3},"right_expr":{"type":"numeric_atoms","value":1029,"base":3}},"right_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":1829,"base":3},"right_expr":{"type":"numeric_atoms","value":5465,"base":3}}},"used_operators":["3ViojmjbAp","SUmda5xLS4","nCS4ZIUYfx"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰-11222210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2669","layer":2},{"info":"number node, value=1029","layer":2},{"info":"compute binary expreesion, left_input=2669, right_input=1029, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-395217","layer":1},{"info":"number node, value=1829","layer":2},{"info":"number node, value=5465","layer":2},{"info":"compute binary expreesion, left_input=1829, right_input=5465, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=3636","layer":1},{"info":"compute binary expreesion, left_input=-395217, right_input=3636, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-3639","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10122212⪄⫏≰1102010)⨓(⫏≰2111202⨳⩥⨓⫏≰21111102)=⫏≰-11222210","reverse_text":"⫏≰-11222210=(⫏≰10122212⪄⫏≰1102010)⨓(⫏≰2111202⨳⩥⨓⫏≰21111102)","cot":[{"info":"⫏≰10122212⪄⫏≰1102010=⫏≰-202002010200","layer":1},{"info":"⫏≰2111202⨳⩥⨓⫏≰21111102=⫏≰11222200","layer":1},{"info":"⫏≰-202002010200⨓⫏≰11222200=⫏≰-11222210","layer":0}]}
{"id":731,"expression_no_base_symbol":"($2515$⩷∴$3169$)∀⇚≩($1928$⋳⪒$1493$)","expression":"(⫏≰10110011⩷∴⫏≰11100101)∀⇚≩(⫏≰2122102⋳⪒⫏≰2001022)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9393,"operation_count":3,"complexity_ratio":3131.0,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":2515,"base":3},"right_expr":{"type":"numeric_atoms","value":3169,"base":3}},"right_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":1928,"base":3},"right_expr":{"type":"numeric_atoms","value":1493,"base":3}}},"used_operators":["LRNGc0VcxI","9FxExcQeMw","12rbrZMWeM"],"dependent_operators":["X99M06cbEe","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2515","layer":2},{"info":"number node, value=3169","layer":2},{"info":"compute binary expreesion, left_input=2515, right_input=3169, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-1340","layer":1},{"info":"number node, value=1928","layer":2},{"info":"number node, value=1493","layer":2},{"info":"compute binary expreesion, left_input=1928, right_input=1493, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=2076","layer":1},{"info":"compute binary expreesion, left_input=-1340, right_input=2076, 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":3,"result_base":3,"text":"(⫏≰10110011⩷∴⫏≰11100101)∀⇚≩(⫏≰2122102⋳⪒⫏≰2001022)=NaN","reverse_text":"NaN=(⫏≰10110011⩷∴⫏≰11100101)∀⇚≩(⫏≰2122102⋳⪒⫏≰2001022)","cot":[{"info":"⫏≰10110011⩷∴⫏≰11100101=⫏≰-1211122","layer":1},{"info":"⫏≰2122102⋳⪒⫏≰2001022=⫏≰2211220","layer":1},{"info":"⫏≰-1211122∀⇚≩⫏≰2211220=NaN","layer":0}]}
{"id":732,"expression_no_base_symbol":"≦∁$1401$⫥∨⫟$3722$","expression":"≦∁⫏≰1220220⫥∨⫟⫏≰12002212","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":155,"operation_count":2,"complexity_ratio":77.5,"tree":{"type":"unary","operator":"≦∁","unary_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1401,"base":3},"right_expr":{"type":"numeric_atoms","value":3722,"base":3}}},"used_operators":["9ICcGScMcE","KYD54nUTWz"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1401","layer":2},{"info":"number node, value=3722","layer":2},{"info":"compute binary expreesion, left_input=1401, right_input=3722, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', 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":3,"result_base":3,"text":"≦∁⫏≰1220220⫥∨⫟⫏≰12002212=NaN","reverse_text":"NaN=≦∁⫏≰1220220⫥∨⫟⫏≰12002212","cot":[{"info":"⫏≰1220220⫥∨⫟⫏≰12002212=NaN","layer":1},{"info":"≦∁NaN=NaN","layer":0}]}
{"id":733,"expression_no_base_symbol":"($3775$⨰$2107$)∑⇟⊟($2565$⨳⩥⨓$1433$)","expression":"(⫏≰12011211⨰⫏≰2220001)∑⇟⊟(⫏≰10112000⨳⩥⨓⫏≰1222002)","highest_n_order":4,"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":3775,"base":3},"right_expr":{"type":"numeric_atoms","value":2107,"base":3}},"right_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":2565,"base":3},"right_expr":{"type":"numeric_atoms","value":1433,"base":3}}},"used_operators":["U7g4x0WXJJ","eewbuw0ToL","nCS4ZIUYfx"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3775","layer":2},{"info":"number node, value=2107","layer":2},{"info":"compute binary expreesion, left_input=3775, right_input=2107, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=1678","layer":1},{"info":"number node, value=2565","layer":2},{"info":"number node, value=1433","layer":2},{"info":"compute binary expreesion, left_input=2565, right_input=1433, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-1132","layer":1},{"info":"compute binary expreesion, left_input=1678, right_input=-1132, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12011211⨰⫏≰2220001)∑⇟⊟(⫏≰10112000⨳⩥⨓⫏≰1222002)=NaN","reverse_text":"NaN=(⫏≰12011211⨰⫏≰2220001)∑⇟⊟(⫏≰10112000⨳⩥⨓⫏≰1222002)","cot":[{"info":"⫏≰12011211⨰⫏≰2220001=⫏≰2022011","layer":1},{"info":"⫏≰10112000⨳⩥⨓⫏≰1222002=⫏≰-1112221","layer":1},{"info":"⫏≰2022011∑⇟⊟⫏≰-1112221=NaN","layer":0}]}
{"id":734,"expression_no_base_symbol":"$8209$+⇶⊼$3160$⪨≂($1599$⊠≄⫣)","expression":"⫏≰102021001+⇶⊼⫏≰11100001⪨≂(⫏≰2012020⊠≄⫣)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":8209,"base":3},"right_expr":{"type":"numeric_atoms","value":3160,"base":3}},"right_expr":{"type":"unary","operator":"⊠≄⫣","unary_expr":{"type":"numeric_atoms","value":1599,"base":3}}},"used_operators":["sdazOOVcIp","TpPTUOHfaN","DIvbN7qnHd"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","AHs5Up7iyr","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=8209","layer":2},{"info":"number node, value=3160","layer":2},{"info":"compute binary expreesion, left_input=8209, right_input=3160, 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":1},{"info":"number node, value=1599","layer":2},{"info":"compute unary expreesion, input=1599, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=0, 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":3,"result_base":3,"text":"⫏≰102021001+⇶⊼⫏≰11100001⪨≂(⫏≰2012020⊠≄⫣)=NaN","reverse_text":"NaN=⫏≰102021001+⇶⊼⫏≰11100001⪨≂(⫏≰2012020⊠≄⫣)","cot":[{"info":"⫏≰102021001+⇶⊼⫏≰11100001=NaN","layer":1},{"info":"⫏≰2012020⊠≄⫣=⫏≰0","layer":1},{"info":"NaN⪨≂⫏≰0=NaN","layer":0}]}
{"id":735,"expression_no_base_symbol":"($4932$⪄$4691$)⨁⊸⫻","expression":"(⫏≰20202200⪄⫏≰20102202)⨁⊸⫻","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":98,"operation_count":2,"complexity_ratio":49.0,"tree":{"type":"unary","operator":"⨁⊸⫻","unary_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":4932,"base":3},"right_expr":{"type":"numeric_atoms","value":4691,"base":3}}},"used_operators":["glklzrTFfD","SUmda5xLS4"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⫏≰-2210200022120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4932","layer":2},{"info":"number node, value=4691","layer":2},{"info":"compute binary expreesion, left_input=4932, right_input=4691, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-744789","layer":1},{"info":"compute unary expreesion, input=-744789, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=-1489578","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20202200⪄⫏≰20102202)⨁⊸⫻=⫏≰-2210200022120","reverse_text":"⫏≰-2210200022120=(⫏≰20202200⪄⫏≰20102202)⨁⊸⫻","cot":[{"info":"⫏≰20202200⪄⫏≰20102202=⫏≰-1101211122210","layer":1},{"info":"⫏≰-1101211122210⨁⊸⫻=⫏≰-2210200022120","layer":0}]}
{"id":736,"expression_no_base_symbol":"($4980$↺$3194$)⪘⫢(∥⊫$8184$)","expression":"(⫏≰20211110↺⫏≰11101022)⪘⫢(∥⊫⫏≰102020010)","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":4980,"base":3},"right_expr":{"type":"numeric_atoms","value":3194,"base":3}},"right_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":8184,"base":3}}},"used_operators":["oacrs7FA3X","7j4O788W3g","P8v4zCKN1o"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰22121000","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4980","layer":2},{"info":"number node, value=3194","layer":2},{"info":"compute binary expreesion, left_input=4980, right_input=3194, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=3194","layer":1},{"info":"number node, value=8184","layer":2},{"info":"compute unary expreesion, input=8184, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=9052","layer":1},{"info":"compute binary expreesion, left_input=3194, right_input=9052, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=6264","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20211110↺⫏≰11101022)⪘⫢(∥⊫⫏≰102020010)=⫏≰22121000","reverse_text":"⫏≰22121000=(⫏≰20211110↺⫏≰11101022)⪘⫢(∥⊫⫏≰102020010)","cot":[{"info":"⫏≰20211110↺⫏≰11101022=⫏≰11101022","layer":1},{"info":"∥⊫⫏≰102020010=⫏≰110102021","layer":1},{"info":"⫏≰11101022⪘⫢⫏≰110102021=⫏≰22121000","layer":0}]}
{"id":737,"expression_no_base_symbol":"$5610$⩷∴$6037$⨸⪁($1290$⊠≄⫣)","expression":"⫏≰21200210⩷∴⫏≰22021121⨸⪁(⫏≰1202210⊠≄⫣)","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":5610,"base":3},"right_expr":{"type":"numeric_atoms","value":6037,"base":3}},"right_expr":{"type":"unary","operator":"⊠≄⫣","unary_expr":{"type":"numeric_atoms","value":1290,"base":3}}},"used_operators":["g55IO6H4Gj","9FxExcQeMw","DIvbN7qnHd"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-2102122","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5610","layer":2},{"info":"number node, value=6037","layer":2},{"info":"compute binary expreesion, left_input=5610, right_input=6037, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-886","layer":1},{"info":"number node, value=1290","layer":2},{"info":"compute unary expreesion, input=1290, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-886, right_input=0, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=-1772","layer":0}],"base":3,"result_base":3,"text":"⫏≰21200210⩷∴⫏≰22021121⨸⪁(⫏≰1202210⊠≄⫣)=⫏≰-2102122","reverse_text":"⫏≰-2102122=⫏≰21200210⩷∴⫏≰22021121⨸⪁(⫏≰1202210⊠≄⫣)","cot":[{"info":"⫏≰21200210⩷∴⫏≰22021121=⫏≰-1012211","layer":1},{"info":"⫏≰1202210⊠≄⫣=⫏≰0","layer":1},{"info":"⫏≰-1012211⨸⪁⫏≰0=⫏≰-2102122","layer":0}]}
{"id":738,"expression_no_base_symbol":"(≉$1668$)⨁⊸⫻","expression":"(≉⫏≰2021210)⨁⊸⫻","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3,"operation_count":2,"complexity_ratio":1.5,"tree":{"type":"unary","operator":"⨁⊸⫻","unary_expr":{"type":"unary","operator":"≉","unary_expr":{"type":"numeric_atoms","value":1668,"base":3}}},"used_operators":["glklzrTFfD","e1ybzncUwg"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰10000110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1668","layer":2},{"info":"compute unary expreesion, input=1668, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=2199","layer":1},{"info":"compute unary expreesion, input=2199, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=2199","layer":0}],"base":3,"result_base":3,"text":"(≉⫏≰2021210)⨁⊸⫻=⫏≰10000110","reverse_text":"⫏≰10000110=(≉⫏≰2021210)⨁⊸⫻","cot":[{"info":"≉⫏≰2021210=⫏≰10000110","layer":1},{"info":"⫏≰10000110⨁⊸⫻=⫏≰10000110","layer":0}]}
{"id":739,"expression_no_base_symbol":"$1101$≧⫂∧$1193$⫡⨏$6676$⋓$1345$","expression":"⫏≰1111210≧⫂∧⫏≰1122012⫡⨏⫏≰100011021⋓⫏≰1211211","highest_n_order":3,"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":1101,"base":3},"right_expr":{"type":"numeric_atoms","value":1193,"base":3}},"right_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":6676,"base":3},"right_expr":{"type":"numeric_atoms","value":1345,"base":3}}},"used_operators":["QMFrweE19q","Ph9nP6C5qx","T2fj7uvVaJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⫏≰20000100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1101","layer":2},{"info":"number node, value=1193","layer":2},{"info":"compute binary expreesion, left_input=1101, right_input=1193, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=720","layer":1},{"info":"number node, value=6676","layer":2},{"info":"number node, value=1345","layer":2},{"info":"compute binary expreesion, left_input=6676, right_input=1345, 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=720, right_input=0, 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=4383","layer":0}],"base":3,"result_base":3,"text":"⫏≰1111210≧⫂∧⫏≰1122012⫡⨏⫏≰100011021⋓⫏≰1211211=⫏≰20000100","reverse_text":"⫏≰20000100=⫏≰1111210≧⫂∧⫏≰1122012⫡⨏⫏≰100011021⋓⫏≰1211211","cot":[{"info":"⫏≰1111210≧⫂∧⫏≰1122012=⫏≰222200","layer":1},{"info":"⫏≰100011021⋓⫏≰1211211=⫏≰0","layer":1},{"info":"⫏≰222200⫡⨏⫏≰0=⫏≰20000100","layer":0}]}
{"id":740,"expression_no_base_symbol":"($4635$+$3348$)⋝⋈⪟($3731$⨐⩸⫘$2712$)","expression":"(⫏≰20100200+⫏≰11121000)⋝⋈⪟(⫏≰12010012⨐⩸⫘⫏≰10201110)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5,"operation_count":3,"complexity_ratio":1.6666666666666667,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":4635,"base":3},"right_expr":{"type":"numeric_atoms","value":3348,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":3731,"base":3},"right_expr":{"type":"numeric_atoms","value":2712,"base":3}}},"used_operators":["2DDjHMKMc0","W4YGzv6Whe","fu6greOZ01"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4635","layer":2},{"info":"number node, value=3348","layer":2},{"info":"compute binary expreesion, left_input=4635, right_input=3348, op_id = W4YGzv6Whe binary_op_definition= 'None', output=7983","layer":1},{"info":"number node, value=3731","layer":2},{"info":"number node, value=2712","layer":2},{"info":"compute binary expreesion, left_input=3731, right_input=2712, 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=7983, right_input=nan, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20100200+⫏≰11121000)⋝⋈⪟(⫏≰12010012⨐⩸⫘⫏≰10201110)=NaN","reverse_text":"NaN=(⫏≰20100200+⫏≰11121000)⋝⋈⪟(⫏≰12010012⨐⩸⫘⫏≰10201110)","cot":[{"info":"⫏≰20100200+⫏≰11121000=⫏≰101221200","layer":1},{"info":"⫏≰12010012⨐⩸⫘⫏≰10201110=NaN","layer":1},{"info":"⫏≰101221200⋝⋈⪟NaN=NaN","layer":0}]}
{"id":741,"expression_no_base_symbol":"(↣≠⋷$4974$)⋫","expression":"(↣≠⋷⫏≰20211020)⋫","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":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":4974,"base":3}}},"used_operators":["JL8yIekQnl","Asc51vEJeQ"],"dependent_operators":["tmPS8pqC7x","XhwjNDsVaA","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4974","layer":2},{"info":"compute unary expreesion, input=4974, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(↣≠⋷⫏≰20211020)⋫=NaN","reverse_text":"NaN=(↣≠⋷⫏≰20211020)⋫","cot":[{"info":"↣≠⋷⫏≰20211020=NaN","layer":1},{"info":"NaN⋫=NaN","layer":0}]}
{"id":742,"expression_no_base_symbol":"$1746$∼$6864$/(⇁⨣⪵$5817$)","expression":"⫏≰2101200∼⫏≰100102020/(⇁⨣⪵⫏≰21222110)","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":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":1746,"base":3},"right_expr":{"type":"numeric_atoms","value":6864,"base":3}},"right_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":5817,"base":3}}},"used_operators":["XhwjNDsVaA","DyGG3AbaNP","inkyxCbjAn"],"dependent_operators":["rysDP5nf3Z","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1746","layer":2},{"info":"number node, value=6864","layer":2},{"info":"compute binary expreesion, left_input=1746, right_input=6864, 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=5817","layer":2},{"info":"compute unary expreesion, input=5817, 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 = XhwjNDsVaA binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2101200∼⫏≰100102020/(⇁⨣⪵⫏≰21222110)=NaN","reverse_text":"NaN=⫏≰2101200∼⫏≰100102020/(⇁⨣⪵⫏≰21222110)","cot":[{"info":"⫏≰2101200∼⫏≰100102020=NaN","layer":1},{"info":"⇁⨣⪵⫏≰21222110=NaN","layer":1},{"info":"NaN/NaN=NaN","layer":0}]}
{"id":743,"expression_no_base_symbol":"$8192$⩚⊴⇥$1659$⨎($1137$⋥≓≎$1055$)","expression":"⫏≰102020102⩚⊴⇥⫏≰2021110⨎(⫏≰1120010⋥≓≎⫏≰1110002)","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":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":8192,"base":3},"right_expr":{"type":"numeric_atoms","value":1659,"base":3}},"right_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":1137,"base":3},"right_expr":{"type":"numeric_atoms","value":1055,"base":3}}},"used_operators":["rJVOvQCfKK","NTOWxs364D","Qy55tPpLXF"],"dependent_operators":["Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰1101021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=8192","layer":2},{"info":"number node, value=1659","layer":2},{"info":"compute binary expreesion, left_input=8192, right_input=1659, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-9972","layer":1},{"info":"number node, value=1137","layer":2},{"info":"number node, value=1055","layer":2},{"info":"compute binary expreesion, left_input=1137, right_input=1055, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=1006","layer":1},{"info":"compute binary expreesion, left_input=-9972, right_input=1006, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=1006","layer":0}],"base":3,"result_base":3,"text":"⫏≰102020102⩚⊴⇥⫏≰2021110⨎(⫏≰1120010⋥≓≎⫏≰1110002)=⫏≰1101021","reverse_text":"⫏≰1101021=⫏≰102020102⩚⊴⇥⫏≰2021110⨎(⫏≰1120010⋥≓≎⫏≰1110002)","cot":[{"info":"⫏≰102020102⩚⊴⇥⫏≰2021110=⫏≰-111200100","layer":1},{"info":"⫏≰1120010⋥≓≎⫏≰1110002=⫏≰1101021","layer":1},{"info":"⫏≰-111200100⨎⫏≰1101021=⫏≰1101021","layer":0}]}
{"id":744,"expression_no_base_symbol":"$2326$⪄$2889$⊉≛↸$5041$⨐⩸⫘$1765$","expression":"⫏≰10012011⪄⫏≰10222000⊉≛↸⫏≰20220201⨐⩸⫘⫏≰2102101","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":100,"operation_count":3,"complexity_ratio":33.333333333333336,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2326,"base":3},"right_expr":{"type":"numeric_atoms","value":2889,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":5041,"base":3},"right_expr":{"type":"numeric_atoms","value":1765,"base":3}}},"used_operators":["DZ8iAZOCBD","SUmda5xLS4","fu6greOZ01"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2326","layer":2},{"info":"number node, value=2889","layer":2},{"info":"compute binary expreesion, left_input=2326, right_input=2889, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-351893","layer":1},{"info":"number node, value=5041","layer":2},{"info":"number node, value=1765","layer":2},{"info":"compute binary expreesion, left_input=5041, right_input=1765, 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=-351893, 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":3,"result_base":3,"text":"⫏≰10012011⪄⫏≰10222000⊉≛↸⫏≰20220201⨐⩸⫘⫏≰2102101=NaN","reverse_text":"NaN=⫏≰10012011⪄⫏≰10222000⊉≛↸⫏≰20220201⨐⩸⫘⫏≰2102101","cot":[{"info":"⫏≰10012011⪄⫏≰10222000=⫏≰-122212201002","layer":1},{"info":"⫏≰20220201⨐⩸⫘⫏≰2102101=NaN","layer":1},{"info":"⫏≰-122212201002⊉≛↸NaN=NaN","layer":0}]}
{"id":745,"expression_no_base_symbol":"($1185$-$1267$)↺$1542$∀⇚≩$3880$","expression":"(⫏≰1121220-⫏≰1201221)↺⫏≰2010010∀⇚≩⫏≰12022201","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":10797,"operation_count":3,"complexity_ratio":3599.0,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1185,"base":3},"right_expr":{"type":"numeric_atoms","value":1267,"base":3}},"right_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":1542,"base":3},"right_expr":{"type":"numeric_atoms","value":3880,"base":3}}},"used_operators":["7j4O788W3g","rysDP5nf3Z","LRNGc0VcxI"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1185","layer":2},{"info":"number node, value=1267","layer":2},{"info":"compute binary expreesion, left_input=1185, right_input=1267, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-82","layer":1},{"info":"number node, value=1542","layer":2},{"info":"number node, value=3880","layer":2},{"info":"compute binary expreesion, left_input=1542, right_input=3880, 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=-82, right_input=nan, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1121220-⫏≰1201221)↺⫏≰2010010∀⇚≩⫏≰12022201=NaN","reverse_text":"NaN=(⫏≰1121220-⫏≰1201221)↺⫏≰2010010∀⇚≩⫏≰12022201","cot":[{"info":"⫏≰1121220-⫏≰1201221=⫏≰-10001","layer":1},{"info":"⫏≰2010010∀⇚≩⫏≰12022201=NaN","layer":1},{"info":"⫏≰-10001↺NaN=NaN","layer":0}]}
{"id":746,"expression_no_base_symbol":"↣≠⋷(↥$3434$)","expression":"↣≠⋷(↥⫏≰11201012)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":358,"operation_count":2,"complexity_ratio":179.0,"tree":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":3434,"base":3}}},"used_operators":["Asc51vEJeQ","A8NUZmVepG"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3434","layer":2},{"info":"compute unary expreesion, input=3434, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=17","layer":1},{"info":"compute unary expreesion, input=17, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(↥⫏≰11201012)=NaN","reverse_text":"NaN=↣≠⋷(↥⫏≰11201012)","cot":[{"info":"↥⫏≰11201012=⫏≰122","layer":1},{"info":"↣≠⋷⫏≰122=NaN","layer":0}]}
{"id":747,"expression_no_base_symbol":"⊄⩳↩$1962$⨪↰⇹$2267$","expression":"⊄⩳↩⫏≰2200200⨪↰⇹⫏≰10002222","highest_n_order":3,"priority_hierarchical_complexity":1,"normalized_expansion_degree":1965,"operation_count":2,"complexity_ratio":982.5,"tree":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":1962,"base":3},"right_expr":{"type":"numeric_atoms","value":2267,"base":3}}},"used_operators":["8w2t5hMYqp","tmPS8pqC7x"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rJVOvQCfKK"],"result":"⫏≰-22002000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1962","layer":2},{"info":"number node, value=2267","layer":2},{"info":"compute binary expreesion, left_input=1962, right_input=2267, 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=1962","layer":1},{"info":"compute unary expreesion, input=1962, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-5886","layer":0}],"base":3,"result_base":3,"text":"⊄⩳↩⫏≰2200200⨪↰⇹⫏≰10002222=⫏≰-22002000","reverse_text":"⫏≰-22002000=⊄⩳↩⫏≰2200200⨪↰⇹⫏≰10002222","cot":[{"info":"⫏≰2200200⨪↰⇹⫏≰10002222=⫏≰2200200","layer":1},{"info":"⊄⩳↩⫏≰2200200=⫏≰-22002000","layer":0}]}
{"id":748,"expression_no_base_symbol":"($3483$⊉≛↸$3683$)⫌⩹⨱","expression":"(⫏≰11210000⊉≛↸⫏≰12001102)⫌⩹⨱","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":3483,"base":3},"right_expr":{"type":"numeric_atoms","value":3683,"base":3}}},"used_operators":["EBcxylXtPf","DZ8iAZOCBD"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰210000220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3483","layer":2},{"info":"number node, value=3683","layer":2},{"info":"compute binary expreesion, left_input=3483, right_input=3683, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=6966","layer":1},{"info":"compute unary expreesion, input=6966, op_id = EBcxylXtPf, unary_op_definition = 'a⫌⩹⨱ = { (((80+a)+(750-a))+((149+422)+(a+a))) }', output=15333","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11210000⊉≛↸⫏≰12001102)⫌⩹⨱=⫏≰210000220","reverse_text":"⫏≰210000220=(⫏≰11210000⊉≛↸⫏≰12001102)⫌⩹⨱","cot":[{"info":"⫏≰11210000⊉≛↸⫏≰12001102=⫏≰100120000","layer":1},{"info":"⫏≰100120000⫌⩹⨱=⫏≰210000220","layer":0}]}
{"id":749,"expression_no_base_symbol":"(≉$1497$)⊘","expression":"(≉⫏≰2001110)⊘","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":1497,"base":3}}},"used_operators":["gu96TGCTMs","e1ybzncUwg"],"dependent_operators":["XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1497","layer":2},{"info":"compute unary expreesion, input=1497, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=2028","layer":1},{"info":"compute unary expreesion, input=2028, 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":3,"result_base":3,"text":"(≉⫏≰2001110)⊘=⫏≰0","reverse_text":"⫏≰0=(≉⫏≰2001110)⊘","cot":[{"info":"≉⫏≰2001110=⫏≰2210010","layer":1},{"info":"⫏≰2210010⊘=⫏≰0","layer":0}]}
{"id":750,"expression_no_base_symbol":"($5992$↺$3559$)⨓($5560$⊭↱$2750$)","expression":"(⫏≰22012221↺⫏≰11212211)⨓(⫏≰21121221⊭↱⫏≰10202212)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5629,"operation_count":3,"complexity_ratio":1876.3333333333333,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":5992,"base":3},"right_expr":{"type":"numeric_atoms","value":3559,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":5560,"base":3},"right_expr":{"type":"numeric_atoms","value":2750,"base":3}}},"used_operators":["3ViojmjbAp","7j4O788W3g","COABgblf1C"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-21201002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5992","layer":2},{"info":"number node, value=3559","layer":2},{"info":"compute binary expreesion, left_input=5992, right_input=3559, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=3559","layer":1},{"info":"number node, value=5560","layer":2},{"info":"number node, value=2750","layer":2},{"info":"compute binary expreesion, left_input=5560, right_input=2750, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-5615","layer":1},{"info":"compute binary expreesion, left_input=3559, right_input=-5615, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-5618","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22012221↺⫏≰11212211)⨓(⫏≰21121221⊭↱⫏≰10202212)=⫏≰-21201002","reverse_text":"⫏≰-21201002=(⫏≰22012221↺⫏≰11212211)⨓(⫏≰21121221⊭↱⫏≰10202212)","cot":[{"info":"⫏≰22012221↺⫏≰11212211=⫏≰11212211","layer":1},{"info":"⫏≰21121221⊭↱⫏≰10202212=⫏≰-21200222","layer":1},{"info":"⫏≰11212211⨓⫏≰-21200222=⫏≰-21201002","layer":0}]}
{"id":751,"expression_no_base_symbol":"$3612$⨓$1662$⨸⪁$1934$⨽$5636$","expression":"⫏≰11221210⨓⫏≰2021120⨸⪁⫏≰2122122⨽⫏≰21201202","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3614,"operation_count":3,"complexity_ratio":1204.6666666666667,"tree":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":3612,"base":3},"right_expr":{"type":"numeric_atoms","value":1662,"base":3}},"right_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1934,"base":3},"right_expr":{"type":"numeric_atoms","value":5636,"base":3}}},"used_operators":["g55IO6H4Gj","3ViojmjbAp","8HhzD0ZcuI"],"dependent_operators":["W4YGzv6Whe","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"⫏≰-1120021221011200","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3612","layer":2},{"info":"number node, value=1662","layer":2},{"info":"compute binary expreesion, left_input=3612, right_input=1662, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1665","layer":1},{"info":"number node, value=1934","layer":2},{"info":"number node, value=5636","layer":2},{"info":"compute binary expreesion, left_input=1934, right_input=5636, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-11236662","layer":1},{"info":"compute binary expreesion, left_input=-1665, right_input=-11236662, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=-22476654","layer":0}],"base":3,"result_base":3,"text":"⫏≰11221210⨓⫏≰2021120⨸⪁⫏≰2122122⨽⫏≰21201202=⫏≰-1120021221011200","reverse_text":"⫏≰-1120021221011200=⫏≰11221210⨓⫏≰2021120⨸⪁⫏≰2122122⨽⫏≰21201202","cot":[{"info":"⫏≰11221210⨓⫏≰2021120=⫏≰-2021200","layer":1},{"info":"⫏≰2122122⨽⫏≰21201202=⫏≰-210010212210200","layer":1},{"info":"⫏≰-2021200⨸⪁⫏≰-210010212210200=⫏≰-1120021221011200","layer":0}]}
{"id":752,"expression_no_base_symbol":"($2178$∧)⨓$5856$∼$8632$","expression":"(⫏≰2222200∧)⨓⫏≰22000220∼⫏≰102211201","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":129,"operation_count":3,"complexity_ratio":43.0,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"unary","operator":"∧","unary_expr":{"type":"numeric_atoms","value":2178,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":5856,"base":3},"right_expr":{"type":"numeric_atoms","value":8632,"base":3}}},"used_operators":["3ViojmjbAp","z63VuFQld9","DyGG3AbaNP"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2178","layer":2},{"info":"compute unary expreesion, input=2178, 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=5856","layer":2},{"info":"number node, value=8632","layer":2},{"info":"compute binary expreesion, left_input=5856, right_input=8632, 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=nan, right_input=nan, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2222200∧)⨓⫏≰22000220∼⫏≰102211201=NaN","reverse_text":"NaN=(⫏≰2222200∧)⨓⫏≰22000220∼⫏≰102211201","cot":[{"info":"⫏≰2222200∧=NaN","layer":1},{"info":"⫏≰22000220∼⫏≰102211201=NaN","layer":1},{"info":"NaN⨓NaN=NaN","layer":0}]}
{"id":753,"expression_no_base_symbol":"(↽≂$4598$)⨸⪁(↥$3658$)","expression":"(↽≂⫏≰20022022)⨸⪁(↥⫏≰12000111)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":77,"operation_count":3,"complexity_ratio":25.666666666666668,"tree":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"unary","operator":"↽≂","unary_expr":{"type":"numeric_atoms","value":4598,"base":3}},"right_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":3658,"base":3}}},"used_operators":["g55IO6H4Gj","u6S6b8DprG","A8NUZmVepG"],"dependent_operators":["W4YGzv6Whe","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","k8jYdgA6NY"],"result":"⫏≰-221010110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4598","layer":2},{"info":"compute unary expreesion, input=4598, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-9196","layer":1},{"info":"number node, value=3658","layer":2},{"info":"compute unary expreesion, input=3658, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=37","layer":1},{"info":"compute binary expreesion, left_input=-9196, right_input=37, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=-18318","layer":0}],"base":3,"result_base":3,"text":"(↽≂⫏≰20022022)⨸⪁(↥⫏≰12000111)=⫏≰-221010110","reverse_text":"⫏≰-221010110=(↽≂⫏≰20022022)⨸⪁(↥⫏≰12000111)","cot":[{"info":"↽≂⫏≰20022022=⫏≰-110121121","layer":1},{"info":"↥⫏≰12000111=⫏≰1101","layer":1},{"info":"⫏≰-110121121⨸⪁⫏≰1101=⫏≰-221010110","layer":0}]}
{"id":754,"expression_no_base_symbol":"($4520$⊪)⇼⇔∾(≦∁$2227$)","expression":"(⫏≰20012102⊪)⇼⇔∾(≦∁⫏≰10001111)","highest_n_order":2,"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":4520,"base":3}},"right_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":2227,"base":3}}},"used_operators":["tifHPKVTfV","zVYPLywUTj","9ICcGScMcE"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"⫏≰10001111","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4520","layer":2},{"info":"compute unary expreesion, input=4520, 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":"number node, value=2227","layer":2},{"info":"compute unary expreesion, input=2227, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=2227","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=2227, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=2227","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20012102⊪)⇼⇔∾(≦∁⫏≰10001111)=⫏≰10001111","reverse_text":"⫏≰10001111=(⫏≰20012102⊪)⇼⇔∾(≦∁⫏≰10001111)","cot":[{"info":"⫏≰20012102⊪=⫏≰0","layer":1},{"info":"≦∁⫏≰10001111=⫏≰10001111","layer":1},{"info":"⫏≰0⇼⇔∾⫏≰10001111=⫏≰10001111","layer":0}]}
{"id":755,"expression_no_base_symbol":"↽≂$2479$∼$2402$","expression":"↽≂⫏≰10101211∼⫏≰10021222","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":53,"operation_count":2,"complexity_ratio":26.5,"tree":{"type":"unary","operator":"↽≂","unary_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":2479,"base":3},"right_expr":{"type":"numeric_atoms","value":2402,"base":3}}},"used_operators":["u6S6b8DprG","DyGG3AbaNP"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2479","layer":2},{"info":"number node, value=2402","layer":2},{"info":"compute binary expreesion, left_input=2479, right_input=2402, 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 = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↽≂⫏≰10101211∼⫏≰10021222=NaN","reverse_text":"NaN=↽≂⫏≰10101211∼⫏≰10021222","cot":[{"info":"⫏≰10101211∼⫏≰10021222=NaN","layer":1},{"info":"↽≂NaN=NaN","layer":0}]}
{"id":756,"expression_no_base_symbol":"$2956$⨸⪁$1700$⋷($3492$∸)","expression":"⫏≰11001111⨸⪁⫏≰2022222⋷(⫏≰11210100∸)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":183,"operation_count":3,"complexity_ratio":61.0,"tree":{"type":"binary","operator":"⋷","left_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":2956,"base":3},"right_expr":{"type":"numeric_atoms","value":1700,"base":3}},"right_expr":{"type":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":3492,"base":3}}},"used_operators":["23Mk6UjR3U","g55IO6H4Gj","o20kRiQErp"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","tmPS8pqC7x"],"result":"⫏≰-110021210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2956","layer":2},{"info":"number node, value=1700","layer":2},{"info":"compute binary expreesion, left_input=2956, right_input=1700, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=9312","layer":1},{"info":"number node, value=3492","layer":2},{"info":"compute unary expreesion, input=3492, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"compute binary expreesion, left_input=9312, right_input=177, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-8958","layer":0}],"base":3,"result_base":3,"text":"⫏≰11001111⨸⪁⫏≰2022222⋷(⫏≰11210100∸)=⫏≰-110021210","reverse_text":"⫏≰-110021210=⫏≰11001111⨸⪁⫏≰2022222⋷(⫏≰11210100∸)","cot":[{"info":"⫏≰11001111⨸⪁⫏≰2022222=⫏≰110202220","layer":1},{"info":"⫏≰11210100∸=⫏≰20120","layer":1},{"info":"⫏≰110202220⋷⫏≰20120=⫏≰-110021210","layer":0}]}
{"id":757,"expression_no_base_symbol":"($7009$↙$3148$)⩚⊴⇥(⇁⨣⪵$3315$)","expression":"(⫏≰100121121↙⫏≰11022121)⩚⊴⇥(⇁⨣⪵⫏≰11112210)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3155,"operation_count":3,"complexity_ratio":1051.6666666666667,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":7009,"base":3},"right_expr":{"type":"numeric_atoms","value":3148,"base":3}},"right_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":3315,"base":3}}},"used_operators":["NTOWxs364D","yyfyN0ffXY","inkyxCbjAn"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","tmPS8pqC7x","DpFCA1CohY","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7009","layer":2},{"info":"number node, value=3148","layer":2},{"info":"compute binary expreesion, left_input=7009, right_input=3148, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-9444","layer":1},{"info":"number node, value=3315","layer":2},{"info":"compute unary expreesion, input=3315, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-9444, right_input=nan, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰100121121↙⫏≰11022121)⩚⊴⇥(⇁⨣⪵⫏≰11112210)=NaN","reverse_text":"NaN=(⫏≰100121121↙⫏≰11022121)⩚⊴⇥(⇁⨣⪵⫏≰11112210)","cot":[{"info":"⫏≰100121121↙⫏≰11022121=⫏≰-110221210","layer":1},{"info":"⇁⨣⪵⫏≰11112210=NaN","layer":1},{"info":"⫏≰-110221210⩚⊴⇥NaN=NaN","layer":0}]}
{"id":758,"expression_no_base_symbol":"($4540$≭$2777$)≧⫂∧($2254$⪄$1963$)","expression":"(⫏≰20020011≭⫏≰10210212)≧⫂∧(⫏≰10002111⪄⫏≰2200201)","highest_n_order":5,"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":4540,"base":3},"right_expr":{"type":"numeric_atoms","value":2777,"base":3}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2254,"base":3},"right_expr":{"type":"numeric_atoms","value":1963,"base":3}}},"used_operators":["Ph9nP6C5qx","rxpJgHHUmx","SUmda5xLS4"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","AHs5Up7iyr","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4540","layer":2},{"info":"number node, value=2777","layer":2},{"info":"compute binary expreesion, left_input=4540, right_input=2777, 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=2254","layer":2},{"info":"number node, value=1963","layer":2},{"info":"compute binary expreesion, left_input=2254, right_input=1963, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-337533","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-337533, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20020011≭⫏≰10210212)≧⫂∧(⫏≰10002111⪄⫏≰2200201)=NaN","reverse_text":"NaN=(⫏≰20020011≭⫏≰10210212)≧⫂∧(⫏≰10002111⪄⫏≰2200201)","cot":[{"info":"⫏≰20020011≭⫏≰10210212=NaN","layer":1},{"info":"⫏≰10002111⪄⫏≰2200201=⫏≰-122011000020","layer":1},{"info":"NaN≧⫂∧⫏≰-122011000020=NaN","layer":0}]}
{"id":759,"expression_no_base_symbol":"$1382$⪛$2498$⪛($1042$*$1230$)","expression":"⫏≰1220012⪛⫏≰10102112⪛(⫏≰1102121*⫏≰1200120)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1050,"operation_count":3,"complexity_ratio":350.0,"tree":{"type":"binary","operator":"⪛","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":1382,"base":3},"right_expr":{"type":"numeric_atoms","value":2498,"base":3}},"right_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1042,"base":3},"right_expr":{"type":"numeric_atoms","value":1230,"base":3}}},"used_operators":["uFcxV4UQCh","9HNa5Wba9A"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","W4YGzv6Whe"],"result":"⫏≰1220012","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1382","layer":2},{"info":"number node, value=2498","layer":2},{"info":"compute binary expreesion, left_input=1382, right_input=2498, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1382","layer":1},{"info":"number node, value=1042","layer":2},{"info":"number node, value=1230","layer":2},{"info":"compute binary expreesion, left_input=1042, right_input=1230, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=1281660","layer":1},{"info":"compute binary expreesion, left_input=1382, right_input=1281660, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=1382","layer":0}],"base":3,"result_base":3,"text":"⫏≰1220012⪛⫏≰10102112⪛(⫏≰1102121*⫏≰1200120)=⫏≰1220012","reverse_text":"⫏≰1220012=⫏≰1220012⪛⫏≰10102112⪛(⫏≰1102121*⫏≰1200120)","cot":[{"info":"⫏≰1220012⪛⫏≰10102112=⫏≰1220012","layer":1},{"info":"⫏≰1102121*⫏≰1200120=⫏≰2102010002220","layer":1},{"info":"⫏≰1220012⪛⫏≰2102010002220=⫏≰1220012","layer":0}]}
{"id":760,"expression_no_base_symbol":"$1137$/$1821$/$2200$⪒$2934$","expression":"⫏≰1120010/⫏≰2111110/⫏≰10000111⪒⫏≰11000200","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5,"operation_count":3,"complexity_ratio":1.6666666666666667,"tree":{"type":"binary","operator":"/","left_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":1137,"base":3},"right_expr":{"type":"numeric_atoms","value":1821,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":2200,"base":3},"right_expr":{"type":"numeric_atoms","value":2934,"base":3}}},"used_operators":["XhwjNDsVaA","f6k1SAg4EE"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1137","layer":2},{"info":"number node, value=1821","layer":2},{"info":"compute binary expreesion, left_input=1137, right_input=1821, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"number node, value=2200","layer":2},{"info":"number node, value=2934","layer":2},{"info":"compute binary expreesion, left_input=2200, right_input=2934, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-5134","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-5134, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":0}],"base":3,"result_base":3,"text":"⫏≰1120010/⫏≰2111110/⫏≰10000111⪒⫏≰11000200=⫏≰0","reverse_text":"⫏≰0=⫏≰1120010/⫏≰2111110/⫏≰10000111⪒⫏≰11000200","cot":[{"info":"⫏≰1120010/⫏≰2111110=⫏≰0","layer":1},{"info":"⫏≰10000111⪒⫏≰11000200=⫏≰-21001011","layer":1},{"info":"⫏≰0/⫏≰-21001011=⫏≰0","layer":0}]}
{"id":761,"expression_no_base_symbol":"↩(⩦⩻⨪$2879$)","expression":"↩(⩦⩻⨪⫏≰10221122)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":19,"operation_count":2,"complexity_ratio":9.5,"tree":{"type":"unary","operator":"↩","unary_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":2879,"base":3}}},"used_operators":["jLgFTUHLKL","2td37pGCOC"],"dependent_operators":["sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-1000210002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2879","layer":2},{"info":"compute unary expreesion, input=2879, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=2879","layer":1},{"info":"compute unary expreesion, input=2879, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-20252","layer":0}],"base":3,"result_base":3,"text":"↩(⩦⩻⨪⫏≰10221122)=⫏≰-1000210002","reverse_text":"⫏≰-1000210002=↩(⩦⩻⨪⫏≰10221122)","cot":[{"info":"⩦⩻⨪⫏≰10221122=⫏≰10221122","layer":1},{"info":"↩⫏≰10221122=⫏≰-1000210002","layer":0}]}
{"id":762,"expression_no_base_symbol":"($1146$⊘)⨰($1411$⫸⊐$6565$)","expression":"(⫏≰1120110⊘)⨰(⫏≰1221021⫸⊐⫏≰100000011)","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":1146,"base":3}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":1411,"base":3},"right_expr":{"type":"numeric_atoms","value":6565,"base":3}}},"used_operators":["eewbuw0ToL","gu96TGCTMs","mqXw5SEYmG"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"⫏≰-1022211121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1146","layer":2},{"info":"compute unary expreesion, input=1146, 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=1411","layer":2},{"info":"number node, value=6565","layer":2},{"info":"compute binary expreesion, left_input=1411, right_input=6565, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=26135","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=26135, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-26125","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1120110⊘)⨰(⫏≰1221021⫸⊐⫏≰100000011)=⫏≰-1022211121","reverse_text":"⫏≰-1022211121=(⫏≰1120110⊘)⨰(⫏≰1221021⫸⊐⫏≰100000011)","cot":[{"info":"⫏≰1120110⊘=⫏≰0","layer":1},{"info":"⫏≰1221021⫸⊐⫏≰100000011=⫏≰1022211222","layer":1},{"info":"⫏≰0⨰⫏≰1022211222=⫏≰-1022211121","layer":0}]}
{"id":763,"expression_no_base_symbol":"⩦⩻⨪$1528$≧⫂∧$2909$","expression":"⩦⩻⨪⫏≰2002121≧⫂∧⫏≰10222202","highest_n_order":1,"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":1528,"base":3},"right_expr":{"type":"numeric_atoms","value":2909,"base":3}}},"used_operators":["2td37pGCOC","Ph9nP6C5qx"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰10100020","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1528","layer":2},{"info":"number node, value=2909","layer":2},{"info":"compute binary expreesion, left_input=1528, right_input=2909, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=2436","layer":1},{"info":"compute unary expreesion, input=2436, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=2436","layer":0}],"base":3,"result_base":3,"text":"⩦⩻⨪⫏≰2002121≧⫂∧⫏≰10222202=⫏≰10100020","reverse_text":"⫏≰10100020=⩦⩻⨪⫏≰2002121≧⫂∧⫏≰10222202","cot":[{"info":"⫏≰2002121≧⫂∧⫏≰10222202=⫏≰10100020","layer":1},{"info":"⩦⩻⨪⫏≰10100020=⫏≰10100020","layer":0}]}
{"id":764,"expression_no_base_symbol":"⊥(≉$1004$)","expression":"⊥(≉⫏≰1101012)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3,"operation_count":2,"complexity_ratio":1.5,"tree":{"type":"unary","operator":"⊥","unary_expr":{"type":"unary","operator":"≉","unary_expr":{"type":"numeric_atoms","value":1004,"base":3}}},"used_operators":["Q3PJZHRvZv","e1ybzncUwg"],"dependent_operators":["fu6greOZ01","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1004","layer":2},{"info":"compute unary expreesion, input=1004, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=1535","layer":1},{"info":"compute unary expreesion, input=1535, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊥(≉⫏≰1101012)=NaN","reverse_text":"NaN=⊥(≉⫏≰1101012)","cot":[{"info":"≉⫏≰1101012=⫏≰2002212","layer":1},{"info":"⊥⫏≰2002212=NaN","layer":0}]}
{"id":765,"expression_no_base_symbol":"($1004$⪨≂$3150$)∀⇚≩($1596$≎⊠⪸$6090$)","expression":"(⫏≰1101012⪨≂⫏≰11022200)∀⇚≩(⫏≰2012010≎⊠⪸⫏≰22100120)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":29605,"operation_count":3,"complexity_ratio":9868.333333333334,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":1004,"base":3},"right_expr":{"type":"numeric_atoms","value":3150,"base":3}},"right_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1596,"base":3},"right_expr":{"type":"numeric_atoms","value":6090,"base":3}}},"used_operators":["LRNGc0VcxI","sdazOOVcIp","bJkvcejdHO"],"dependent_operators":["X99M06cbEe","rysDP5nf3Z","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1004","layer":2},{"info":"number node, value=3150","layer":2},{"info":"compute binary expreesion, left_input=1004, right_input=3150, 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=-4190","layer":1},{"info":"number node, value=1596","layer":2},{"info":"number node, value=6090","layer":2},{"info":"compute binary expreesion, left_input=1596, right_input=6090, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=412891","layer":1},{"info":"compute binary expreesion, left_input=-4190, right_input=412891, 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":3,"result_base":3,"text":"(⫏≰1101012⪨≂⫏≰11022200)∀⇚≩(⫏≰2012010≎⊠⪸⫏≰22100120)=NaN","reverse_text":"NaN=(⫏≰1101012⪨≂⫏≰11022200)∀⇚≩(⫏≰2012010≎⊠⪸⫏≰22100120)","cot":[{"info":"⫏≰1101012⪨≂⫏≰11022200=⫏≰-12202012","layer":1},{"info":"⫏≰2012010≎⊠⪸⫏≰22100120=⫏≰202222101021","layer":1},{"info":"⫏≰-12202012∀⇚≩⫏≰202222101021=NaN","layer":0}]}
{"id":766,"expression_no_base_symbol":"($4450$∲⫓$2182$)⊉≛↸(+⊝⨔$3164$)","expression":"(⫏≰20002211∲⫓⫏≰2222211)⊉≛↸(+⊝⨔⫏≰11100012)","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":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":4450,"base":3},"right_expr":{"type":"numeric_atoms","value":2182,"base":3}},"right_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":3164,"base":3}}},"used_operators":["DZ8iAZOCBD","i8ToyICDmI","DhbWaqg5eL"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4450","layer":2},{"info":"number node, value=2182","layer":2},{"info":"compute binary expreesion, left_input=4450, right_input=2182, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=3164","layer":2},{"info":"compute unary expreesion, input=3164, 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 binary expreesion, left_input=0, right_input=1522, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20002211∲⫓⫏≰2222211)⊉≛↸(+⊝⨔⫏≰11100012)=⫏≰0","reverse_text":"⫏≰0=(⫏≰20002211∲⫓⫏≰2222211)⊉≛↸(+⊝⨔⫏≰11100012)","cot":[{"info":"⫏≰20002211∲⫓⫏≰2222211=⫏≰0","layer":1},{"info":"+⊝⨔⫏≰11100012=⫏≰2002101","layer":1},{"info":"⫏≰0⊉≛↸⫏≰2002101=⫏≰0","layer":0}]}
{"id":767,"expression_no_base_symbol":"($1918$⪒$1583$)⪄$3478$⨟⋌⩍$9382$","expression":"(⫏≰2122001⪒⫏≰2011122)⪄⫏≰11202211⨟⋌⩍⫏≰110212111","highest_n_order":4,"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":1918,"base":3},"right_expr":{"type":"numeric_atoms","value":1583,"base":3}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":3478,"base":3},"right_expr":{"type":"numeric_atoms","value":9382,"base":3}}},"used_operators":["SUmda5xLS4","f6k1SAg4EE","rGHVDoGpnC"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","W4YGzv6Whe","t8gj7n24qd","Tcnh7f0tEr"],"result":"⫏≰12110101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1918","layer":2},{"info":"number node, value=1583","layer":2},{"info":"compute binary expreesion, left_input=1918, right_input=1583, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-3501","layer":1},{"info":"number node, value=3478","layer":2},{"info":"number node, value=9382","layer":2},{"info":"compute binary expreesion, left_input=3478, right_input=9382, 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=-3501, right_input=nan, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=3979","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2122001⪒⫏≰2011122)⪄⫏≰11202211⨟⋌⩍⫏≰110212111=⫏≰12110101","reverse_text":"⫏≰12110101=(⫏≰2122001⪒⫏≰2011122)⪄⫏≰11202211⨟⋌⩍⫏≰110212111","cot":[{"info":"⫏≰2122001⪒⫏≰2011122=⫏≰-11210200","layer":1},{"info":"⫏≰11202211⨟⋌⩍⫏≰110212111=NaN","layer":1},{"info":"⫏≰-11210200⪄NaN=⫏≰12110101","layer":0}]}
{"id":768,"expression_no_base_symbol":"⋗⩬⋾$2477$∑⇟⊟$3551$","expression":"⋗⩬⋾⫏≰10101202∑⇟⊟⫏≰11212112","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":2477,"base":3},"right_expr":{"type":"numeric_atoms","value":3551,"base":3}}},"used_operators":["DpFCA1CohY","U7g4x0WXJJ"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr","srAu1WTS94","12rbrZMWeM"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2477","layer":2},{"info":"number node, value=3551","layer":2},{"info":"compute binary expreesion, left_input=2477, right_input=3551, 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 = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⋗⩬⋾⫏≰10101202∑⇟⊟⫏≰11212112=NaN","reverse_text":"NaN=⋗⩬⋾⫏≰10101202∑⇟⊟⫏≰11212112","cot":[{"info":"⫏≰10101202∑⇟⊟⫏≰11212112=NaN","layer":1},{"info":"⋗⩬⋾NaN=NaN","layer":0}]}
{"id":769,"expression_no_base_symbol":"($6736$⪘⫢$3142$)⨟⋌⩍($1795$%$6163$)","expression":"(⫏≰100020111⪘⫢⫏≰11022101)⨟⋌⩍(⫏≰2110111%⫏≰22110021)","highest_n_order":4,"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":6736,"base":3},"right_expr":{"type":"numeric_atoms","value":3142,"base":3}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":1795,"base":3},"right_expr":{"type":"numeric_atoms","value":6163,"base":3}}},"used_operators":["rGHVDoGpnC","oacrs7FA3X","k8jYdgA6NY"],"dependent_operators":["Tcnh7f0tEr","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6736","layer":2},{"info":"number node, value=3142","layer":2},{"info":"compute binary expreesion, left_input=6736, right_input=3142, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=13348","layer":1},{"info":"number node, value=1795","layer":2},{"info":"number node, value=6163","layer":2},{"info":"compute binary expreesion, left_input=1795, right_input=6163, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1795","layer":1},{"info":"compute binary expreesion, left_input=13348, right_input=1795, 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":0}],"base":3,"result_base":3,"text":"(⫏≰100020111⪘⫢⫏≰11022101)⨟⋌⩍(⫏≰2110111%⫏≰22110021)=NaN","reverse_text":"NaN=(⫏≰100020111⪘⫢⫏≰11022101)⨟⋌⩍(⫏≰2110111%⫏≰22110021)","cot":[{"info":"⫏≰100020111⪘⫢⫏≰11022101=⫏≰200022101","layer":1},{"info":"⫏≰2110111%⫏≰22110021=⫏≰2110111","layer":1},{"info":"⫏≰200022101⨟⋌⩍⫏≰2110111=NaN","layer":0}]}
{"id":770,"expression_no_base_symbol":"($7824$⊘)↙(⨞⊢$2984$)","expression":"(⫏≰101201210⊘)↙(⨞⊢⫏≰11002112)","highest_n_order":3,"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":7824,"base":3}},"right_expr":{"type":"unary","operator":"⨞⊢","unary_expr":{"type":"numeric_atoms","value":2984,"base":3}}},"used_operators":["yyfyN0ffXY","gu96TGCTMs","xUOZtlo3hN"],"dependent_operators":["tmPS8pqC7x","DpFCA1CohY","XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7824","layer":2},{"info":"compute unary expreesion, input=7824, 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=2984","layer":2},{"info":"compute unary expreesion, input=2984, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-3158","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-3158, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰101201210⊘)↙(⨞⊢⫏≰11002112)=⫏≰0","reverse_text":"⫏≰0=(⫏≰101201210⊘)↙(⨞⊢⫏≰11002112)","cot":[{"info":"⫏≰101201210⊘=⫏≰0","layer":1},{"info":"⨞⊢⫏≰11002112=⫏≰-11022222","layer":1},{"info":"⫏≰0↙⫏≰-11022222=⫏≰0","layer":0}]}
{"id":771,"expression_no_base_symbol":"$5315$⊉≛↸$4068$+($1053$⨵⪆$2027$)","expression":"⫏≰21021212⊉≛↸⫏≰12120200+(⫏≰1110000⨵⪆⫏≰2210002)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4,"operation_count":3,"complexity_ratio":1.3333333333333333,"tree":{"type":"binary","operator":"+","left_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":5315,"base":3},"right_expr":{"type":"numeric_atoms","value":4068,"base":3}},"right_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":1053,"base":3},"right_expr":{"type":"numeric_atoms","value":2027,"base":3}}},"used_operators":["W4YGzv6Whe","DZ8iAZOCBD","2DQ55sFlQl"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰112210122","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5315","layer":2},{"info":"number node, value=4068","layer":2},{"info":"compute binary expreesion, left_input=5315, right_input=4068, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=10630","layer":1},{"info":"number node, value=1053","layer":2},{"info":"number node, value=2027","layer":2},{"info":"compute binary expreesion, left_input=1053, right_input=2027, 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=10630, right_input=160, op_id = W4YGzv6Whe binary_op_definition= 'None', output=10790","layer":0}],"base":3,"result_base":3,"text":"⫏≰21021212⊉≛↸⫏≰12120200+(⫏≰1110000⨵⪆⫏≰2210002)=⫏≰112210122","reverse_text":"⫏≰112210122=⫏≰21021212⊉≛↸⫏≰12120200+(⫏≰1110000⨵⪆⫏≰2210002)","cot":[{"info":"⫏≰21021212⊉≛↸⫏≰12120200=⫏≰112120201","layer":1},{"info":"⫏≰1110000⨵⪆⫏≰2210002=⫏≰12221","layer":1},{"info":"⫏≰112120201+⫏≰12221=⫏≰112210122","layer":0}]}
{"id":772,"expression_no_base_symbol":"↔$7815$≹⇙⪍$3214$","expression":"↔⫏≰101201110≹⇙⪍⫏≰11102001","highest_n_order":4,"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":7815,"base":3},"right_expr":{"type":"numeric_atoms","value":3214,"base":3}}},"used_operators":["ruOEQAzv1W","AHs5Up7iyr"],"dependent_operators":["XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp","dWAJyo7jo9"],"result":"⫏≰-11222","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7815","layer":2},{"info":"number node, value=3214","layer":2},{"info":"compute binary expreesion, left_input=7815, right_input=3214, 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 = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-134","layer":0}],"base":3,"result_base":3,"text":"↔⫏≰101201110≹⇙⪍⫏≰11102001=⫏≰-11222","reverse_text":"⫏≰-11222=↔⫏≰101201110≹⇙⪍⫏≰11102001","cot":[{"info":"⫏≰101201110≹⇙⪍⫏≰11102001=NaN","layer":1},{"info":"↔NaN=⫏≰-11222","layer":0}]}
{"id":773,"expression_no_base_symbol":"⫓⪴($3212$⨓$1867$)","expression":"⫓⪴(⫏≰11101222⨓⫏≰2120011)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3743,"operation_count":2,"complexity_ratio":1871.5,"tree":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":3212,"base":3},"right_expr":{"type":"numeric_atoms","value":1867,"base":3}}},"used_operators":["eLxqMNBOBk","3ViojmjbAp"],"dependent_operators":["9HNa5Wba9A","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⫏≰20120122211211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3212","layer":2},{"info":"number node, value=1867","layer":2},{"info":"compute binary expreesion, left_input=3212, right_input=1867, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1870","layer":1},{"info":"compute unary expreesion, input=-1870, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=3496900","layer":0}],"base":3,"result_base":3,"text":"⫓⪴(⫏≰11101222⨓⫏≰2120011)=⫏≰20120122211211","reverse_text":"⫏≰20120122211211=⫓⪴(⫏≰11101222⨓⫏≰2120011)","cot":[{"info":"⫏≰11101222⨓⫏≰2120011=⫏≰-2120021","layer":1},{"info":"⫓⪴⫏≰-2120021=⫏≰20120122211211","layer":0}]}
{"id":774,"expression_no_base_symbol":"$2242$⋓$2047$⊭↱$6415$⊴$1507$","expression":"⫏≰10002001⋓⫏≰2210211⊭↱⫏≰22210121⊴⫏≰2001211","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4511,"operation_count":3,"complexity_ratio":1503.6666666666667,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":2242,"base":3},"right_expr":{"type":"numeric_atoms","value":2047,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":6415,"base":3},"right_expr":{"type":"numeric_atoms","value":1507,"base":3}}},"used_operators":["COABgblf1C","T2fj7uvVaJ","Nsiff2A1zJ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2242","layer":2},{"info":"number node, value=2047","layer":2},{"info":"compute binary expreesion, left_input=2242, right_input=2047, 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=6415","layer":2},{"info":"number node, value=1507","layer":2},{"info":"compute binary expreesion, left_input=6415, right_input=1507, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰10002001⋓⫏≰2210211⊭↱⫏≰22210121⊴⫏≰2001211=NaN","reverse_text":"NaN=⫏≰10002001⋓⫏≰2210211⊭↱⫏≰22210121⊴⫏≰2001211","cot":[{"info":"⫏≰10002001⋓⫏≰2210211=⫏≰0","layer":1},{"info":"⫏≰22210121⊴⫏≰2001211=NaN","layer":1},{"info":"⫏≰0⊭↱NaN=NaN","layer":0}]}
{"id":775,"expression_no_base_symbol":"($4149$↛⩡⫤)⊦⊿","expression":"(⫏≰12200200↛⩡⫤)⊦⊿","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":12587,"operation_count":2,"complexity_ratio":6293.5,"tree":{"type":"unary","operator":"⊦⊿","unary_expr":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"numeric_atoms","value":4149,"base":3}}},"used_operators":["14qkJME0vr","FU0Cs4j7VP"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X"],"result":"⫏≰10111212222112","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4149","layer":2},{"info":"compute unary expreesion, input=4149, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-622588","layer":1},{"info":"compute unary expreesion, input=-622588, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=1867685","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12200200↛⩡⫤)⊦⊿=⫏≰10111212222112","reverse_text":"⫏≰10111212222112=(⫏≰12200200↛⩡⫤)⊦⊿","cot":[{"info":"⫏≰12200200↛⩡⫤=⫏≰-1011122000211","layer":1},{"info":"⫏≰-1011122000211⊦⊿=⫏≰10111212222112","layer":0}]}
{"id":776,"expression_no_base_symbol":"$4292$⨸⪁$2552$⩨$1541$⊴$2617$","expression":"⫏≰12212222⨸⪁⫏≰10111112⩨⫏≰2010002⊴⫏≰10120221","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2630,"operation_count":3,"complexity_ratio":876.6666666666666,"tree":{"type":"binary","operator":"⩨","left_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":4292,"base":3},"right_expr":{"type":"numeric_atoms","value":2552,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1541,"base":3},"right_expr":{"type":"numeric_atoms","value":2617,"base":3}}},"used_operators":["2DlMacCsIx","g55IO6H4Gj","Nsiff2A1zJ"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","W4YGzv6Whe","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4292","layer":2},{"info":"number node, value=2552","layer":2},{"info":"compute binary expreesion, left_input=4292, right_input=2552, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=13688","layer":1},{"info":"number node, value=1541","layer":2},{"info":"number node, value=2617","layer":2},{"info":"compute binary expreesion, left_input=1541, right_input=2617, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=13688, right_input=nan, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰12212222⨸⪁⫏≰10111112⩨⫏≰2010002⊴⫏≰10120221=NaN","reverse_text":"NaN=⫏≰12212222⨸⪁⫏≰10111112⩨⫏≰2010002⊴⫏≰10120221","cot":[{"info":"⫏≰12212222⨸⪁⫏≰10111112=⫏≰200202222","layer":1},{"info":"⫏≰2010002⊴⫏≰10120221=NaN","layer":1},{"info":"⫏≰200202222⩨NaN=NaN","layer":0}]}
{"id":777,"expression_no_base_symbol":"⊄⩳↩($3275$⋷$1028$)","expression":"⊄⩳↩(⫏≰11111022⋷⫏≰1102002)","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":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":3275,"base":3},"right_expr":{"type":"numeric_atoms","value":1028,"base":3}}},"used_operators":["8w2t5hMYqp","23Mk6UjR3U"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰12000110","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3275","layer":2},{"info":"number node, value=1028","layer":2},{"info":"compute binary expreesion, left_input=3275, right_input=1028, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-1219","layer":1},{"info":"compute unary expreesion, input=-1219, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=3657","layer":0}],"base":3,"result_base":3,"text":"⊄⩳↩(⫏≰11111022⋷⫏≰1102002)=⫏≰12000110","reverse_text":"⫏≰12000110=⊄⩳↩(⫏≰11111022⋷⫏≰1102002)","cot":[{"info":"⫏≰11111022⋷⫏≰1102002=⫏≰-1200011","layer":1},{"info":"⊄⩳↩⫏≰-1200011=⫏≰12000110","layer":0}]}
{"id":778,"expression_no_base_symbol":"($1957$≭$5918$)⋝⋈⪟(⨈⫕$4902$)","expression":"(⫏≰2200111≭⫏≰22010012)⋝⋈⪟(⨈⫕⫏≰20201120)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":390,"operation_count":3,"complexity_ratio":130.0,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":1957,"base":3},"right_expr":{"type":"numeric_atoms","value":5918,"base":3}},"right_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":4902,"base":3}}},"used_operators":["2DDjHMKMc0","rxpJgHHUmx","megm06wKyl"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1957","layer":2},{"info":"number node, value=5918","layer":2},{"info":"compute binary expreesion, left_input=1957, right_input=5918, 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=4902","layer":2},{"info":"compute unary expreesion, input=4902, 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=nan, right_input=-21, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2200111≭⫏≰22010012)⋝⋈⪟(⨈⫕⫏≰20201120)=NaN","reverse_text":"NaN=(⫏≰2200111≭⫏≰22010012)⋝⋈⪟(⨈⫕⫏≰20201120)","cot":[{"info":"⫏≰2200111≭⫏≰22010012=NaN","layer":1},{"info":"⨈⫕⫏≰20201120=⫏≰-210","layer":1},{"info":"NaN⋝⋈⪟⫏≰-210=NaN","layer":0}]}
{"id":779,"expression_no_base_symbol":"≤/($4017$/$2811$)","expression":"≤/(⫏≰12111210/⫏≰10212010)","highest_n_order":2,"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":4017,"base":3},"right_expr":{"type":"numeric_atoms","value":2811,"base":3}}},"used_operators":["eLAdDNolq6","XhwjNDsVaA"],"dependent_operators":["rysDP5nf3Z","rysDP5nf3Z"],"result":"⫏≰122220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4017","layer":2},{"info":"number node, value=2811","layer":2},{"info":"compute binary expreesion, left_input=4017, right_input=2811, op_id = XhwjNDsVaA binary_op_definition= 'None', output=1","layer":1},{"info":"compute unary expreesion, input=1, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=483","layer":0}],"base":3,"result_base":3,"text":"≤/(⫏≰12111210/⫏≰10212010)=⫏≰122220","reverse_text":"⫏≰122220=≤/(⫏≰12111210/⫏≰10212010)","cot":[{"info":"⫏≰12111210/⫏≰10212010=⫏≰1","layer":1},{"info":"≤/⫏≰1=⫏≰122220","layer":0}]}
{"id":780,"expression_no_base_symbol":"≦∁$2735$⋓$1240$","expression":"≦∁⫏≰10202022⋓⫏≰1200221","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":40,"operation_count":2,"complexity_ratio":20.0,"tree":{"type":"unary","operator":"≦∁","unary_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":2735,"base":3},"right_expr":{"type":"numeric_atoms","value":1240,"base":3}}},"used_operators":["9ICcGScMcE","T2fj7uvVaJ"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⫏≰-102212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2735","layer":2},{"info":"number node, value=1240","layer":2},{"info":"compute binary expreesion, left_input=2735, right_input=1240, 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 = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=-320","layer":0}],"base":3,"result_base":3,"text":"≦∁⫏≰10202022⋓⫏≰1200221=⫏≰-102212","reverse_text":"⫏≰-102212=≦∁⫏≰10202022⋓⫏≰1200221","cot":[{"info":"⫏≰10202022⋓⫏≰1200221=⫏≰0","layer":1},{"info":"≦∁⫏≰0=⫏≰-102212","layer":0}]}
{"id":781,"expression_no_base_symbol":"$3420$⨓$1052$⪨≂$1007$-$1183$","expression":"⫏≰11200200⨓⫏≰1102222⪨≂⫏≰1101022-⫏≰1121211","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1064,"operation_count":3,"complexity_ratio":354.6666666666667,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":3420,"base":3},"right_expr":{"type":"numeric_atoms","value":1052,"base":3}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1007,"base":3},"right_expr":{"type":"numeric_atoms","value":1183,"base":3}}},"used_operators":["sdazOOVcIp","3ViojmjbAp","rysDP5nf3Z"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⫏≰-2021100","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3420","layer":2},{"info":"number node, value=1052","layer":2},{"info":"compute binary expreesion, left_input=3420, right_input=1052, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1055","layer":1},{"info":"number node, value=1007","layer":2},{"info":"number node, value=1183","layer":2},{"info":"compute binary expreesion, left_input=1007, right_input=1183, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-176","layer":1},{"info":"compute binary expreesion, left_input=-1055, right_input=-176, 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=-1656","layer":0}],"base":3,"result_base":3,"text":"⫏≰11200200⨓⫏≰1102222⪨≂⫏≰1101022-⫏≰1121211=⫏≰-2021100","reverse_text":"⫏≰-2021100=⫏≰11200200⨓⫏≰1102222⪨≂⫏≰1101022-⫏≰1121211","cot":[{"info":"⫏≰11200200⨓⫏≰1102222=⫏≰-1110002","layer":1},{"info":"⫏≰1101022-⫏≰1121211=⫏≰-20112","layer":1},{"info":"⫏≰-1110002⪨≂⫏≰-20112=⫏≰-2021100","layer":0}]}
{"id":782,"expression_no_base_symbol":"($9523$∀⇚≩$6357$)⨟⋌⩍($2102$⋓$1439$)","expression":"(⫏≰111001201∀⇚≩⫏≰22201110)⨟⋌⩍(⫏≰2212212⋓⫏≰1222022)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":66675,"operation_count":3,"complexity_ratio":22225.0,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":9523,"base":3},"right_expr":{"type":"numeric_atoms","value":6357,"base":3}},"right_expr":{"type":"binary","operator":"⋓","left_expr":{"type":"numeric_atoms","value":2102,"base":3},"right_expr":{"type":"numeric_atoms","value":1439,"base":3}}},"used_operators":["rGHVDoGpnC","LRNGc0VcxI","T2fj7uvVaJ"],"dependent_operators":["Tcnh7f0tEr","X99M06cbEe","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=9523","layer":2},{"info":"number node, value=6357","layer":2},{"info":"compute binary expreesion, left_input=9523, right_input=6357, 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=2102","layer":2},{"info":"number node, value=1439","layer":2},{"info":"compute binary expreesion, left_input=2102, right_input=1439, 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=nan, right_input=0, 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":0}],"base":3,"result_base":3,"text":"(⫏≰111001201∀⇚≩⫏≰22201110)⨟⋌⩍(⫏≰2212212⋓⫏≰1222022)=NaN","reverse_text":"NaN=(⫏≰111001201∀⇚≩⫏≰22201110)⨟⋌⩍(⫏≰2212212⋓⫏≰1222022)","cot":[{"info":"⫏≰111001201∀⇚≩⫏≰22201110=NaN","layer":1},{"info":"⫏≰2212212⋓⫏≰1222022=⫏≰0","layer":1},{"info":"NaN⨟⋌⩍⫏≰0=NaN","layer":0}]}
{"id":783,"expression_no_base_symbol":"($1850$⋓$1787$)⇷(-$1940$)","expression":"(⫏≰2112112⋓⫏≰2110012)⇷(-⫏≰2122212)","highest_n_order":3,"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":1850,"base":3},"right_expr":{"type":"numeric_atoms","value":1787,"base":3}},"right_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":1940,"base":3}}},"used_operators":["mp7IySMOzn","T2fj7uvVaJ","t8gj7n24qd"],"dependent_operators":["DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1850","layer":2},{"info":"number node, value=1787","layer":2},{"info":"compute binary expreesion, left_input=1850, right_input=1787, 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=1940","layer":2},{"info":"compute unary expreesion, input=1940, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1940","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-1940, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2112112⋓⫏≰2110012)⇷(-⫏≰2122212)=⫏≰0","reverse_text":"⫏≰0=(⫏≰2112112⋓⫏≰2110012)⇷(-⫏≰2122212)","cot":[{"info":"⫏≰2112112⋓⫏≰2110012=⫏≰0","layer":1},{"info":"-⫏≰2122212=⫏≰-2122212","layer":1},{"info":"⫏≰0⇷⫏≰-2122212=⫏≰0","layer":0}]}
{"id":784,"expression_no_base_symbol":"$6564$⊉≛↸$2122$⊉≛↸$4254$+⇶⊼$1297$","expression":"⫏≰100000010⊉≛↸⫏≰2220121⊉≛↸⫏≰12211120+⇶⊼⫏≰1210001","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5,"operation_count":3,"complexity_ratio":1.6666666666666667,"tree":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":6564,"base":3},"right_expr":{"type":"numeric_atoms","value":2122,"base":3}},"right_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":4254,"base":3},"right_expr":{"type":"numeric_atoms","value":1297,"base":3}}},"used_operators":["DZ8iAZOCBD","TpPTUOHfaN"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr"],"result":"⫏≰1100000110","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6564","layer":2},{"info":"number node, value=2122","layer":2},{"info":"compute binary expreesion, left_input=6564, right_input=2122, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=13128","layer":1},{"info":"number node, value=4254","layer":2},{"info":"number node, value=1297","layer":2},{"info":"compute binary expreesion, left_input=4254, right_input=1297, 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":1},{"info":"compute binary expreesion, left_input=13128, right_input=nan, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=26256","layer":0}],"base":3,"result_base":3,"text":"⫏≰100000010⊉≛↸⫏≰2220121⊉≛↸⫏≰12211120+⇶⊼⫏≰1210001=⫏≰1100000110","reverse_text":"⫏≰1100000110=⫏≰100000010⊉≛↸⫏≰2220121⊉≛↸⫏≰12211120+⇶⊼⫏≰1210001","cot":[{"info":"⫏≰100000010⊉≛↸⫏≰2220121=⫏≰200000020","layer":1},{"info":"⫏≰12211120+⇶⊼⫏≰1210001=NaN","layer":1},{"info":"⫏≰200000020⊉≛↸NaN=⫏≰1100000110","layer":0}]}
{"id":785,"expression_no_base_symbol":"($3896$⨰$2427$)⨪↰⇹($4003$-$4633$)","expression":"(⫏≰12100022⨰⫏≰10022220)⨪↰⇹(⫏≰12111021-⫏≰20100121)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1486,"operation_count":3,"complexity_ratio":495.3333333333333,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":3896,"base":3},"right_expr":{"type":"numeric_atoms","value":2427,"base":3}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":4003,"base":3},"right_expr":{"type":"numeric_atoms","value":4633,"base":3}}},"used_operators":["tmPS8pqC7x","eewbuw0ToL","rysDP5nf3Z"],"dependent_operators":["rJVOvQCfKK","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰2000210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3896","layer":2},{"info":"number node, value=2427","layer":2},{"info":"compute binary expreesion, left_input=3896, right_input=2427, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=1479","layer":1},{"info":"number node, value=4003","layer":2},{"info":"number node, value=4633","layer":2},{"info":"compute binary expreesion, left_input=4003, right_input=4633, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-630","layer":1},{"info":"compute binary expreesion, left_input=1479, right_input=-630, 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=1479","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12100022⨰⫏≰10022220)⨪↰⇹(⫏≰12111021-⫏≰20100121)=⫏≰2000210","reverse_text":"⫏≰2000210=(⫏≰12100022⨰⫏≰10022220)⨪↰⇹(⫏≰12111021-⫏≰20100121)","cot":[{"info":"⫏≰12100022⨰⫏≰10022220=⫏≰2000210","layer":1},{"info":"⫏≰12111021-⫏≰20100121=⫏≰-212100","layer":1},{"info":"⫏≰2000210⨪↰⇹⫏≰-212100=⫏≰2000210","layer":0}]}
{"id":786,"expression_no_base_symbol":"$2946$⨪↰⇹$3045$≋⫹","expression":"⫏≰11001010⨪↰⇹⫏≰11011210≋⫹","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2949,"operation_count":2,"complexity_ratio":1474.5,"tree":{"type":"unary","operator":"≋⫹","unary_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":2946,"base":3},"right_expr":{"type":"numeric_atoms","value":3045,"base":3}}},"used_operators":["N41Kp7NANJ","tmPS8pqC7x"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rJVOvQCfKK"],"result":"⫏≰-22002020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2946","layer":2},{"info":"number node, value=3045","layer":2},{"info":"compute binary expreesion, left_input=2946, right_input=3045, 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=2946","layer":1},{"info":"compute unary expreesion, input=2946, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-5892","layer":0}],"base":3,"result_base":3,"text":"⫏≰11001010⨪↰⇹⫏≰11011210≋⫹=⫏≰-22002020","reverse_text":"⫏≰-22002020=⫏≰11001010⨪↰⇹⫏≰11011210≋⫹","cot":[{"info":"⫏≰11001010⨪↰⇹⫏≰11011210=⫏≰11001010","layer":1},{"info":"⫏≰11001010≋⫹=⫏≰-22002020","layer":0}]}
{"id":787,"expression_no_base_symbol":"$1576$∀⇚≩$2505$⪄($1574$⊭↱$7318$)","expression":"⫏≰2011101∀⇚≩⫏≰10102210⪄(⫏≰2011022⊭↱⫏≰101001001)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":11060,"operation_count":3,"complexity_ratio":3686.6666666666665,"tree":{"type":"binary","operator":"⪄","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":1576,"base":3},"right_expr":{"type":"numeric_atoms","value":2505,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":1574,"base":3},"right_expr":{"type":"numeric_atoms","value":7318,"base":3}}},"used_operators":["SUmda5xLS4","LRNGc0VcxI","COABgblf1C"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","X99M06cbEe","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰12110101","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1576","layer":2},{"info":"number node, value=2505","layer":2},{"info":"compute binary expreesion, left_input=1576, right_input=2505, 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=1574","layer":2},{"info":"number node, value=7318","layer":2},{"info":"compute binary expreesion, left_input=1574, right_input=7318, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=11493","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=11493, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=3979","layer":0}],"base":3,"result_base":3,"text":"⫏≰2011101∀⇚≩⫏≰10102210⪄(⫏≰2011022⊭↱⫏≰101001001)=⫏≰12110101","reverse_text":"⫏≰12110101=⫏≰2011101∀⇚≩⫏≰10102210⪄(⫏≰2011022⊭↱⫏≰101001001)","cot":[{"info":"⫏≰2011101∀⇚≩⫏≰10102210=NaN","layer":1},{"info":"⫏≰2011022⊭↱⫏≰101001001=⫏≰120202200","layer":1},{"info":"NaN⪄⫏≰120202200=⫏≰12110101","layer":0}]}
{"id":788,"expression_no_base_symbol":"($1013$↙$6188$)∀⇚≩($5214$⨓$1496$)","expression":"(⫏≰1101112↙⫏≰22111012)∀⇚≩(⫏≰21011010⨓⫏≰2001102)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":137641,"operation_count":3,"complexity_ratio":45880.333333333336,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":1013,"base":3},"right_expr":{"type":"numeric_atoms","value":6188,"base":3}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":5214,"base":3},"right_expr":{"type":"numeric_atoms","value":1496,"base":3}}},"used_operators":["LRNGc0VcxI","yyfyN0ffXY","3ViojmjbAp"],"dependent_operators":["X99M06cbEe","tmPS8pqC7x","DpFCA1CohY","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1013","layer":2},{"info":"number node, value=6188","layer":2},{"info":"compute binary expreesion, left_input=1013, right_input=6188, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-18564","layer":1},{"info":"number node, value=5214","layer":2},{"info":"number node, value=1496","layer":2},{"info":"compute binary expreesion, left_input=5214, right_input=1496, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1499","layer":1},{"info":"compute binary expreesion, left_input=-18564, right_input=-1499, 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":3,"result_base":3,"text":"(⫏≰1101112↙⫏≰22111012)∀⇚≩(⫏≰21011010⨓⫏≰2001102)=NaN","reverse_text":"NaN=(⫏≰1101112↙⫏≰22111012)∀⇚≩(⫏≰21011010⨓⫏≰2001102)","cot":[{"info":"⫏≰1101112↙⫏≰22111012=⫏≰-221110120","layer":1},{"info":"⫏≰21011010⨓⫏≰2001102=⫏≰-2001112","layer":1},{"info":"⫏≰-221110120∀⇚≩⫏≰-2001112=NaN","layer":0}]}
{"id":789,"expression_no_base_symbol":"$1564$+⇶⊼$3124$⇼⇔∾$1096$↺$4352$","expression":"⫏≰2010221+⇶⊼⫏≰11021201⇼⇔∾⫏≰1111121↺⫏≰12222012","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5,"operation_count":3,"complexity_ratio":1.6666666666666667,"tree":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":1564,"base":3},"right_expr":{"type":"numeric_atoms","value":3124,"base":3}},"right_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":1096,"base":3},"right_expr":{"type":"numeric_atoms","value":4352,"base":3}}},"used_operators":["tifHPKVTfV","TpPTUOHfaN","7j4O788W3g"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","AHs5Up7iyr","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1564","layer":2},{"info":"number node, value=3124","layer":2},{"info":"compute binary expreesion, left_input=1564, right_input=3124, 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":1},{"info":"number node, value=1096","layer":2},{"info":"number node, value=4352","layer":2},{"info":"compute binary expreesion, left_input=1096, right_input=4352, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=4352","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=4352, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2010221+⇶⊼⫏≰11021201⇼⇔∾⫏≰1111121↺⫏≰12222012=NaN","reverse_text":"NaN=⫏≰2010221+⇶⊼⫏≰11021201⇼⇔∾⫏≰1111121↺⫏≰12222012","cot":[{"info":"⫏≰2010221+⇶⊼⫏≰11021201=NaN","layer":1},{"info":"⫏≰1111121↺⫏≰12222012=⫏≰12222012","layer":1},{"info":"NaN⇼⇔∾⫏≰12222012=NaN","layer":0}]}
{"id":790,"expression_no_base_symbol":"($1059$+$2254$)⩨($4650$+$3307$)","expression":"(⫏≰1110020+⫏≰10002111)⩨(⫏≰20101020+⫏≰11112111)","highest_n_order":2,"priority_hierarchical_complexity":2,"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":1059,"base":3},"right_expr":{"type":"numeric_atoms","value":2254,"base":3}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":4650,"base":3},"right_expr":{"type":"numeric_atoms","value":3307,"base":3}}},"used_operators":["2DlMacCsIx","W4YGzv6Whe"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰-20","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1059","layer":2},{"info":"number node, value=2254","layer":2},{"info":"compute binary expreesion, left_input=1059, right_input=2254, op_id = W4YGzv6Whe binary_op_definition= 'None', output=3313","layer":1},{"info":"number node, value=4650","layer":2},{"info":"number node, value=3307","layer":2},{"info":"compute binary expreesion, left_input=4650, right_input=3307, op_id = W4YGzv6Whe binary_op_definition= 'None', output=7957","layer":1},{"info":"compute binary expreesion, left_input=3313, right_input=7957, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-6","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1110020+⫏≰10002111)⩨(⫏≰20101020+⫏≰11112111)=⫏≰-20","reverse_text":"⫏≰-20=(⫏≰1110020+⫏≰10002111)⩨(⫏≰20101020+⫏≰11112111)","cot":[{"info":"⫏≰1110020+⫏≰10002111=⫏≰11112201","layer":1},{"info":"⫏≰20101020+⫏≰11112111=⫏≰101220201","layer":1},{"info":"⫏≰11112201⩨⫏≰101220201=⫏≰-20","layer":0}]}
{"id":791,"expression_no_base_symbol":"$4541$∼$4181$⫸⊐($3432$-$2316$)","expression":"⫏≰20020012∼⫏≰12201212⫸⊐(⫏≰11201010-⫏≰10011210)","highest_n_order":4,"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":4541,"base":3},"right_expr":{"type":"numeric_atoms","value":4181,"base":3}},"right_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":3432,"base":3},"right_expr":{"type":"numeric_atoms","value":2316,"base":3}}},"used_operators":["mqXw5SEYmG","DyGG3AbaNP","rysDP5nf3Z"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4541","layer":2},{"info":"number node, value=4181","layer":2},{"info":"compute binary expreesion, left_input=4541, right_input=4181, 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=3432","layer":2},{"info":"number node, value=2316","layer":2},{"info":"compute binary expreesion, left_input=3432, right_input=2316, op_id = rysDP5nf3Z binary_op_definition= 'None', output=1116","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1116, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰20020012∼⫏≰12201212⫸⊐(⫏≰11201010-⫏≰10011210)=NaN","reverse_text":"NaN=⫏≰20020012∼⫏≰12201212⫸⊐(⫏≰11201010-⫏≰10011210)","cot":[{"info":"⫏≰20020012∼⫏≰12201212=NaN","layer":1},{"info":"⫏≰11201010-⫏≰10011210=⫏≰1112100","layer":1},{"info":"NaN⫸⊐⫏≰1112100=NaN","layer":0}]}
{"id":792,"expression_no_base_symbol":"($2202$⨎$6047$)∼($2382$≋⫹)","expression":"(⫏≰10000120⨎⫏≰22021222)∼(⫏≰10021020≋⫹)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":124,"operation_count":3,"complexity_ratio":41.333333333333336,"tree":{"type":"binary","operator":"∼","left_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":2202,"base":3},"right_expr":{"type":"numeric_atoms","value":6047,"base":3}},"right_expr":{"type":"unary","operator":"≋⫹","unary_expr":{"type":"numeric_atoms","value":2382,"base":3}}},"used_operators":["DyGG3AbaNP","rJVOvQCfKK","N41Kp7NANJ"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2202","layer":2},{"info":"number node, value=6047","layer":2},{"info":"compute binary expreesion, left_input=2202, right_input=6047, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=6047","layer":1},{"info":"number node, value=2382","layer":2},{"info":"compute unary expreesion, input=2382, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-4764","layer":1},{"info":"compute binary expreesion, left_input=6047, right_input=-4764, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10000120⨎⫏≰22021222)∼(⫏≰10021020≋⫹)=NaN","reverse_text":"NaN=(⫏≰10000120⨎⫏≰22021222)∼(⫏≰10021020≋⫹)","cot":[{"info":"⫏≰10000120⨎⫏≰22021222=⫏≰22021222","layer":1},{"info":"⫏≰10021020≋⫹=⫏≰-20112110","layer":1},{"info":"⫏≰22021222∼⫏≰-20112110=NaN","layer":0}]}
{"id":793,"expression_no_base_symbol":"$2874$⋳⪒$3034$⪄($2265$⊭↱$6794$)","expression":"⫏≰10221110⋳⪒⫏≰11011101⪄(⫏≰10002220⊭↱⫏≰100022122)","highest_n_order":2,"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":2874,"base":3},"right_expr":{"type":"numeric_atoms","value":3034,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":2265,"base":3},"right_expr":{"type":"numeric_atoms","value":6794,"base":3}}},"used_operators":["SUmda5xLS4","12rbrZMWeM","COABgblf1C"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-201220002101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2874","layer":2},{"info":"number node, value=3034","layer":2},{"info":"compute binary expreesion, left_input=2874, right_input=3034, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=2427","layer":1},{"info":"number node, value=2265","layer":2},{"info":"number node, value=6794","layer":2},{"info":"compute binary expreesion, left_input=2265, right_input=6794, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=9063","layer":1},{"info":"compute binary expreesion, left_input=2427, right_input=9063, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-391537","layer":0}],"base":3,"result_base":3,"text":"⫏≰10221110⋳⪒⫏≰11011101⪄(⫏≰10002220⊭↱⫏≰100022122)=⫏≰-201220002101","reverse_text":"⫏≰-201220002101=⫏≰10221110⋳⪒⫏≰11011101⪄(⫏≰10002220⊭↱⫏≰100022122)","cot":[{"info":"⫏≰10221110⋳⪒⫏≰11011101=⫏≰10022220","layer":1},{"info":"⫏≰10002220⊭↱⫏≰100022122=⫏≰110102200","layer":1},{"info":"⫏≰10022220⪄⫏≰110102200=⫏≰-201220002101","layer":0}]}
{"id":794,"expression_no_base_symbol":"($3739$∲⫓$3070$)≹⇙⪍($1247$⩷∴$3002$)","expression":"(⫏≰12010111∲⫓⫏≰11012201)≹⇙⪍(⫏≰1201012⩷∴⫏≰11010012)","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":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":3739,"base":3},"right_expr":{"type":"numeric_atoms","value":3070,"base":3}},"right_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":1247,"base":3},"right_expr":{"type":"numeric_atoms","value":3002,"base":3}}},"used_operators":["AHs5Up7iyr","i8ToyICDmI","9FxExcQeMw"],"dependent_operators":["dWAJyo7jo9","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3739","layer":2},{"info":"number node, value=3070","layer":2},{"info":"compute binary expreesion, left_input=3739, right_input=3070, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=1247","layer":2},{"info":"number node, value=3002","layer":2},{"info":"compute binary expreesion, left_input=1247, right_input=3002, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-3542","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-3542, 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":3,"result_base":3,"text":"(⫏≰12010111∲⫓⫏≰11012201)≹⇙⪍(⫏≰1201012⩷∴⫏≰11010012)=NaN","reverse_text":"NaN=(⫏≰12010111∲⫓⫏≰11012201)≹⇙⪍(⫏≰1201012⩷∴⫏≰11010012)","cot":[{"info":"⫏≰12010111∲⫓⫏≰11012201=⫏≰0","layer":1},{"info":"⫏≰1201012⩷∴⫏≰11010012=⫏≰-11212012","layer":1},{"info":"⫏≰0≹⇙⪍⫏≰-11212012=NaN","layer":0}]}
{"id":795,"expression_no_base_symbol":"⫓⪴($4977$⨽$1290$)","expression":"⫓⪴(⫏≰20211100⨽⫏≰1202210)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":74319129,"operation_count":2,"complexity_ratio":37159564.5,"tree":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":4977,"base":3},"right_expr":{"type":"numeric_atoms","value":1290,"base":3}}},"used_operators":["eLxqMNBOBk","8HhzD0ZcuI"],"dependent_operators":["9HNa5Wba9A","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY"],"result":"Inf","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4977","layer":2},{"info":"number node, value=1290","layer":2},{"info":"compute binary expreesion, left_input=4977, right_input=1290, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-74314143","layer":1},{"info":"compute unary expreesion, input=-74314143, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=inf","layer":0}],"base":3,"result_base":3,"text":"⫓⪴(⫏≰20211100⨽⫏≰1202210)=Inf","reverse_text":"Inf=⫓⪴(⫏≰20211100⨽⫏≰1202210)","cot":[{"info":"⫏≰20211100⨽⫏≰1202210=⫏≰-12011211112211200","layer":1},{"info":"⫓⪴⫏≰-12011211112211200=Inf","layer":0}]}
{"id":796,"expression_no_base_symbol":"($1967$+⇶⊼$1485$)∀⇚≩($1037$*$1204$)","expression":"(⫏≰2200212+⇶⊼⫏≰2001000)∀⇚≩(⫏≰1102102*⫏≰1122121)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1039,"operation_count":3,"complexity_ratio":346.3333333333333,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"numeric_atoms","value":1967,"base":3},"right_expr":{"type":"numeric_atoms","value":1485,"base":3}},"right_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1037,"base":3},"right_expr":{"type":"numeric_atoms","value":1204,"base":3}}},"used_operators":["LRNGc0VcxI","TpPTUOHfaN","9HNa5Wba9A"],"dependent_operators":["X99M06cbEe","AHs5Up7iyr","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1967","layer":2},{"info":"number node, value=1485","layer":2},{"info":"compute binary expreesion, left_input=1967, right_input=1485, 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":1},{"info":"number node, value=1037","layer":2},{"info":"number node, value=1204","layer":2},{"info":"compute binary expreesion, left_input=1037, right_input=1204, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=1248548","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1248548, 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":3,"result_base":3,"text":"(⫏≰2200212+⇶⊼⫏≰2001000)∀⇚≩(⫏≰1102102*⫏≰1122121)=NaN","reverse_text":"NaN=(⫏≰2200212+⇶⊼⫏≰2001000)∀⇚≩(⫏≰1102102*⫏≰1122121)","cot":[{"info":"⫏≰2200212+⇶⊼⫏≰2001000=NaN","layer":1},{"info":"⫏≰1102102*⫏≰1122121=⫏≰2100102200112","layer":1},{"info":"NaN∀⇚≩⫏≰2100102200112=NaN","layer":0}]}
{"id":797,"expression_no_base_symbol":"($2847$⊭∹↮)⫡⨏$4860$⪒$3099$","expression":"(⫏≰10220110⊭∹↮)⫡⨏⫏≰20200000⪒⫏≰11020210","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16,"operation_count":3,"complexity_ratio":5.333333333333333,"tree":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"numeric_atoms","value":2847,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":4860,"base":3},"right_expr":{"type":"numeric_atoms","value":3099,"base":3}}},"used_operators":["QMFrweE19q","xNBdhnnwKq","f6k1SAg4EE"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰200021220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2847","layer":2},{"info":"compute unary expreesion, input=2847, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=5694","layer":1},{"info":"number node, value=4860","layer":2},{"info":"number node, value=3099","layer":2},{"info":"compute binary expreesion, left_input=4860, right_input=3099, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-7959","layer":1},{"info":"compute binary expreesion, left_input=5694, right_input=-7959, 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=13335","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10220110⊭∹↮)⫡⨏⫏≰20200000⪒⫏≰11020210=⫏≰200021220","reverse_text":"⫏≰200021220=(⫏≰10220110⊭∹↮)⫡⨏⫏≰20200000⪒⫏≰11020210","cot":[{"info":"⫏≰10220110⊭∹↮=⫏≰21210220","layer":1},{"info":"⫏≰20200000⪒⫏≰11020210=⫏≰-101220210","layer":1},{"info":"⫏≰21210220⫡⨏⫏≰-101220210=⫏≰200021220","layer":0}]}
{"id":798,"expression_no_base_symbol":"$5135$∼$3163$∀⇚≩(⨰⫟⨤$3768$)","expression":"⫏≰21001012∼⫏≰11100011∀⇚≩(⨰⫟⨤⫏≰12011120)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":14335,"operation_count":3,"complexity_ratio":4778.333333333333,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":5135,"base":3},"right_expr":{"type":"numeric_atoms","value":3163,"base":3}},"right_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":3768,"base":3}}},"used_operators":["LRNGc0VcxI","DyGG3AbaNP","Tw270M8GLb"],"dependent_operators":["X99M06cbEe","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5135","layer":2},{"info":"number node, value=3163","layer":2},{"info":"compute binary expreesion, left_input=5135, right_input=3163, 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=3768","layer":2},{"info":"compute unary expreesion, input=3768, 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 = 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":3,"result_base":3,"text":"⫏≰21001012∼⫏≰11100011∀⇚≩(⨰⫟⨤⫏≰12011120)=NaN","reverse_text":"NaN=⫏≰21001012∼⫏≰11100011∀⇚≩(⨰⫟⨤⫏≰12011120)","cot":[{"info":"⫏≰21001012∼⫏≰11100011=NaN","layer":1},{"info":"⨰⫟⨤⫏≰12011120=NaN","layer":1},{"info":"NaN∀⇚≩NaN=NaN","layer":0}]}
{"id":799,"expression_no_base_symbol":"($1306$∸)⪐","expression":"(⫏≰1210101∸)⪐","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":179,"operation_count":2,"complexity_ratio":89.5,"tree":{"type":"unary","operator":"⪐","unary_expr":{"type":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":1306,"base":3}}},"used_operators":["eH2TOUuTDT","o20kRiQErp"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","tmPS8pqC7x"],"result":"⫏≰111010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1306","layer":2},{"info":"compute unary expreesion, input=1306, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"compute unary expreesion, input=177, op_id = eH2TOUuTDT, unary_op_definition = 'a⪐ = { (a+a) , if (-a)!=532 or a<368 ; (-a) , else }', output=354","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1210101∸)⪐=⫏≰111010","reverse_text":"⫏≰111010=(⫏≰1210101∸)⪐","cot":[{"info":"⫏≰1210101∸=⫏≰20120","layer":1},{"info":"⫏≰20120⪐=⫏≰111010","layer":0}]}
{"id":800,"expression_no_base_symbol":"($3929$⊴$5200$)≹⇙⪍($4718$⪛$8228$)","expression":"(⫏≰12101112⊴⫏≰21010121)≹⇙⪍(⫏≰20110202⪛⫏≰102021202)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5211,"operation_count":3,"complexity_ratio":1737.0,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":3929,"base":3},"right_expr":{"type":"numeric_atoms","value":5200,"base":3}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":4718,"base":3},"right_expr":{"type":"numeric_atoms","value":8228,"base":3}}},"used_operators":["AHs5Up7iyr","Nsiff2A1zJ","uFcxV4UQCh"],"dependent_operators":["dWAJyo7jo9","dWAJyo7jo9","14qkJME0vr","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3929","layer":2},{"info":"number node, value=5200","layer":2},{"info":"compute binary expreesion, left_input=3929, right_input=5200, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=4718","layer":2},{"info":"number node, value=8228","layer":2},{"info":"compute binary expreesion, left_input=4718, right_input=8228, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=4718","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=4718, 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":3,"result_base":3,"text":"(⫏≰12101112⊴⫏≰21010121)≹⇙⪍(⫏≰20110202⪛⫏≰102021202)=NaN","reverse_text":"NaN=(⫏≰12101112⊴⫏≰21010121)≹⇙⪍(⫏≰20110202⪛⫏≰102021202)","cot":[{"info":"⫏≰12101112⊴⫏≰21010121=NaN","layer":1},{"info":"⫏≰20110202⪛⫏≰102021202=⫏≰20110202","layer":1},{"info":"NaN≹⇙⪍⫏≰20110202=NaN","layer":0}]}
{"id":801,"expression_no_base_symbol":"$9226$↺$4327$*$1037$⪢$1963$","expression":"⫏≰110122201↺⫏≰12221021*⫏≰1102102⪢⫏≰2200201","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1966,"operation_count":3,"complexity_ratio":655.3333333333334,"tree":{"type":"binary","operator":"*","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":9226,"base":3},"right_expr":{"type":"numeric_atoms","value":4327,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1037,"base":3},"right_expr":{"type":"numeric_atoms","value":1963,"base":3}}},"used_operators":["9HNa5Wba9A","7j4O788W3g","dWAJyo7jo9"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=9226","layer":2},{"info":"number node, value=4327","layer":2},{"info":"compute binary expreesion, left_input=9226, right_input=4327, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=4327","layer":1},{"info":"number node, value=1037","layer":2},{"info":"number node, value=1963","layer":2},{"info":"compute binary expreesion, left_input=1037, right_input=1963, 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=4327, right_input=nan, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰110122201↺⫏≰12221021*⫏≰1102102⪢⫏≰2200201=NaN","reverse_text":"NaN=⫏≰110122201↺⫏≰12221021*⫏≰1102102⪢⫏≰2200201","cot":[{"info":"⫏≰110122201↺⫏≰12221021=⫏≰12221021","layer":1},{"info":"⫏≰1102102⪢⫏≰2200201=NaN","layer":1},{"info":"⫏≰12221021*NaN=NaN","layer":0}]}
{"id":802,"expression_no_base_symbol":"$2259$⋥≓≎$2307$⪄(∂$3839$)","expression":"⫏≰10002200⋥≓≎⫏≰10011110⪄(∂⫏≰12021012)","highest_n_order":5,"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":2259,"base":3},"right_expr":{"type":"numeric_atoms","value":2307,"base":3}},"right_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":3839,"base":3}}},"used_operators":["SUmda5xLS4","Qy55tPpLXF","Uaa54Peajs"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2259","layer":2},{"info":"number node, value=2307","layer":2},{"info":"compute binary expreesion, left_input=2259, right_input=2307, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=2388","layer":1},{"info":"number node, value=3839","layer":2},{"info":"compute unary expreesion, input=3839, 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=2388, right_input=nan, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰10002200⋥≓≎⫏≰10011110⪄(∂⫏≰12021012)=NaN","reverse_text":"NaN=⫏≰10002200⋥≓≎⫏≰10011110⪄(∂⫏≰12021012)","cot":[{"info":"⫏≰10002200⋥≓≎⫏≰10011110=⫏≰10021110","layer":1},{"info":"∂⫏≰12021012=NaN","layer":1},{"info":"⫏≰10021110⪄NaN=NaN","layer":0}]}
{"id":803,"expression_no_base_symbol":"($4544$∧)⫥∨⫟($1212$⇼⇔∾$1270$)","expression":"(⫏≰20020022∧)⫥∨⫟(⫏≰1122220⇼⇔∾⫏≰1202001)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":162,"operation_count":3,"complexity_ratio":54.0,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"unary","operator":"∧","unary_expr":{"type":"numeric_atoms","value":4544,"base":3}},"right_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":1212,"base":3},"right_expr":{"type":"numeric_atoms","value":1270,"base":3}}},"used_operators":["KYD54nUTWz","z63VuFQld9","tifHPKVTfV"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4544","layer":2},{"info":"compute unary expreesion, input=4544, 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=1212","layer":2},{"info":"number node, value=1270","layer":2},{"info":"compute binary expreesion, left_input=1212, right_input=1270, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=58","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=58, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20020022∧)⫥∨⫟(⫏≰1122220⇼⇔∾⫏≰1202001)=NaN","reverse_text":"NaN=(⫏≰20020022∧)⫥∨⫟(⫏≰1122220⇼⇔∾⫏≰1202001)","cot":[{"info":"⫏≰20020022∧=NaN","layer":1},{"info":"⫏≰1122220⇼⇔∾⫏≰1202001=⫏≰2011","layer":1},{"info":"NaN⫥∨⫟⫏≰2011=NaN","layer":0}]}
{"id":804,"expression_no_base_symbol":"⊙↵-($6842$+⇶⊼$3652$)","expression":"⊙↵-(⫏≰100101102+⇶⊼⫏≰12000021)","highest_n_order":5,"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":6842,"base":3},"right_expr":{"type":"numeric_atoms","value":3652,"base":3}}},"used_operators":["oWn0xqSxBt","TpPTUOHfaN"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6842","layer":2},{"info":"number node, value=3652","layer":2},{"info":"compute binary expreesion, left_input=6842, right_input=3652, 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":1},{"info":"compute unary expreesion, input=nan, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⫏≰100101102+⇶⊼⫏≰12000021)=NaN","reverse_text":"NaN=⊙↵-(⫏≰100101102+⇶⊼⫏≰12000021)","cot":[{"info":"⫏≰100101102+⇶⊼⫏≰12000021=NaN","layer":1},{"info":"⊙↵-NaN=NaN","layer":0}]}
{"id":805,"expression_no_base_symbol":"(⨵≀≌$2269$)⨁⊸⫻","expression":"(⨵≀≌⫏≰10010001)⨁⊸⫻","highest_n_order":2,"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":2269,"base":3}}},"used_operators":["glklzrTFfD","srAu1WTS94"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A"],"result":"⫏≰-200200020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2269","layer":2},{"info":"compute unary expreesion, input=2269, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-6807","layer":1},{"info":"compute unary expreesion, input=-6807, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=-13614","layer":0}],"base":3,"result_base":3,"text":"(⨵≀≌⫏≰10010001)⨁⊸⫻=⫏≰-200200020","reverse_text":"⫏≰-200200020=(⨵≀≌⫏≰10010001)⨁⊸⫻","cot":[{"info":"⨵≀≌⫏≰10010001=⫏≰-100100010","layer":1},{"info":"⫏≰-100100010⨁⊸⫻=⫏≰-200200020","layer":0}]}
{"id":806,"expression_no_base_symbol":"(⪲⇎$4192$)⨰($3764$≭$1759$)","expression":"(⪲⇎⫏≰12202021)⨰(⫏≰12011102≭⫏≰2102011)","highest_n_order":5,"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":4192,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":3764,"base":3},"right_expr":{"type":"numeric_atoms","value":1759,"base":3}}},"used_operators":["eewbuw0ToL","XPYlsWDdGa","rxpJgHHUmx"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4192","layer":2},{"info":"compute unary expreesion, input=4192, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=8384","layer":1},{"info":"number node, value=3764","layer":2},{"info":"number node, value=1759","layer":2},{"info":"compute binary expreesion, left_input=3764, right_input=1759, 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=8384, right_input=nan, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⪲⇎⫏≰12202021)⨰(⫏≰12011102≭⫏≰2102011)=NaN","reverse_text":"NaN=(⪲⇎⫏≰12202021)⨰(⫏≰12011102≭⫏≰2102011)","cot":[{"info":"⪲⇎⫏≰12202021=⫏≰102111112","layer":1},{"info":"⫏≰12011102≭⫏≰2102011=NaN","layer":1},{"info":"⫏≰102111112⨰NaN=NaN","layer":0}]}
{"id":807,"expression_no_base_symbol":"($3934$⊘)⨓($8199$⪒$8189$)","expression":"(⫏≰12101201⊘)⨓(⫏≰102020200⪒⫏≰102020022)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16416,"operation_count":3,"complexity_ratio":5472.0,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"unary","operator":"⊘","unary_expr":{"type":"numeric_atoms","value":3934,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":8199,"base":3},"right_expr":{"type":"numeric_atoms","value":8189,"base":3}}},"used_operators":["3ViojmjbAp","gu96TGCTMs","f6k1SAg4EE"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰211110212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3934","layer":2},{"info":"compute unary expreesion, input=3934, 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=8199","layer":2},{"info":"number node, value=8189","layer":2},{"info":"compute binary expreesion, left_input=8199, right_input=8189, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-16388","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-16388, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=16385","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12101201⊘)⨓(⫏≰102020200⪒⫏≰102020022)=⫏≰211110212","reverse_text":"⫏≰211110212=(⫏≰12101201⊘)⨓(⫏≰102020200⪒⫏≰102020022)","cot":[{"info":"⫏≰12101201⊘=⫏≰0","layer":1},{"info":"⫏≰102020200⪒⫏≰102020022=⫏≰-211110222","layer":1},{"info":"⫏≰0⨓⫏≰-211110222=⫏≰211110212","layer":0}]}
{"id":808,"expression_no_base_symbol":"$2582$⪛$4086$≦≮≮","expression":"⫏≰10112122⪛⫏≰12121100≦≮≮","highest_n_order":2,"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":2582,"base":3},"right_expr":{"type":"numeric_atoms","value":4086,"base":3}}},"used_operators":["D4vGDi5EA2","uFcxV4UQCh"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⫏≰-101121220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2582","layer":2},{"info":"number node, value=4086","layer":2},{"info":"compute binary expreesion, left_input=2582, right_input=4086, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=2582","layer":1},{"info":"compute unary expreesion, input=2582, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-7746","layer":0}],"base":3,"result_base":3,"text":"⫏≰10112122⪛⫏≰12121100≦≮≮=⫏≰-101121220","reverse_text":"⫏≰-101121220=⫏≰10112122⪛⫏≰12121100≦≮≮","cot":[{"info":"⫏≰10112122⪛⫏≰12121100=⫏≰10112122","layer":1},{"info":"⫏≰10112122≦≮≮=⫏≰-101121220","layer":0}]}
{"id":809,"expression_no_base_symbol":"($4488$∲⫓$2094$)-(⨈⫕$1815$)","expression":"(⫏≰20011020∲⫓⫏≰2212120)-(⨈⫕⫏≰2111020)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":389,"operation_count":3,"complexity_ratio":129.66666666666666,"tree":{"type":"binary","operator":"-","left_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":4488,"base":3},"right_expr":{"type":"numeric_atoms","value":2094,"base":3}},"right_expr":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"numeric_atoms","value":1815,"base":3}}},"used_operators":["rysDP5nf3Z","i8ToyICDmI","megm06wKyl"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q"],"result":"⫏≰210","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4488","layer":2},{"info":"number node, value=2094","layer":2},{"info":"compute binary expreesion, left_input=4488, right_input=2094, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=1815","layer":2},{"info":"compute unary expreesion, input=1815, 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=0, right_input=-21, op_id = rysDP5nf3Z binary_op_definition= 'None', output=21","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20011020∲⫓⫏≰2212120)-(⨈⫕⫏≰2111020)=⫏≰210","reverse_text":"⫏≰210=(⫏≰20011020∲⫓⫏≰2212120)-(⨈⫕⫏≰2111020)","cot":[{"info":"⫏≰20011020∲⫓⫏≰2212120=⫏≰0","layer":1},{"info":"⨈⫕⫏≰2111020=⫏≰-210","layer":1},{"info":"⫏≰0-⫏≰-210=⫏≰210","layer":0}]}
{"id":810,"expression_no_base_symbol":"$3996$⫥∨⫟$3230$/$3881$∲⫓$1776$","expression":"⫏≰12111000⫥∨⫟⫏≰11102122/⫏≰12022202∲⫓⫏≰2102210","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":157,"operation_count":3,"complexity_ratio":52.333333333333336,"tree":{"type":"binary","operator":"/","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":3996,"base":3},"right_expr":{"type":"numeric_atoms","value":3230,"base":3}},"right_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":3881,"base":3},"right_expr":{"type":"numeric_atoms","value":1776,"base":3}}},"used_operators":["XhwjNDsVaA","KYD54nUTWz","i8ToyICDmI"],"dependent_operators":["rysDP5nf3Z","8HhzD0ZcuI","rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3996","layer":2},{"info":"number node, value=3230","layer":2},{"info":"compute binary expreesion, left_input=3996, right_input=3230, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=3881","layer":2},{"info":"number node, value=1776","layer":2},{"info":"compute binary expreesion, left_input=3881, right_input=1776, 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=nan, right_input=0, op_id = XhwjNDsVaA binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰12111000⫥∨⫟⫏≰11102122/⫏≰12022202∲⫓⫏≰2102210=NaN","reverse_text":"NaN=⫏≰12111000⫥∨⫟⫏≰11102122/⫏≰12022202∲⫓⫏≰2102210","cot":[{"info":"⫏≰12111000⫥∨⫟⫏≰11102122=NaN","layer":1},{"info":"⫏≰12022202∲⫓⫏≰2102210=⫏≰0","layer":1},{"info":"NaN/⫏≰0=NaN","layer":0}]}
{"id":811,"expression_no_base_symbol":"(⩦⩻⨪$1016$)⪨≂$7760$↺$3223$","expression":"(⩦⩻⨪⫏≰1101122)⪨≂⫏≰101122102↺⫏≰11102101","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":10,"operation_count":3,"complexity_ratio":3.3333333333333335,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":1016,"base":3}},"right_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":7760,"base":3},"right_expr":{"type":"numeric_atoms","value":3223,"base":3}}},"used_operators":["sdazOOVcIp","2td37pGCOC","7j4O788W3g"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-12220201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1016","layer":2},{"info":"compute unary expreesion, input=1016, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=1016","layer":1},{"info":"number node, value=7760","layer":2},{"info":"number node, value=3223","layer":2},{"info":"compute binary expreesion, left_input=7760, right_input=3223, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=3223","layer":1},{"info":"compute binary expreesion, left_input=1016, right_input=3223, 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=-4312","layer":0}],"base":3,"result_base":3,"text":"(⩦⩻⨪⫏≰1101122)⪨≂⫏≰101122102↺⫏≰11102101=⫏≰-12220201","reverse_text":"⫏≰-12220201=(⩦⩻⨪⫏≰1101122)⪨≂⫏≰101122102↺⫏≰11102101","cot":[{"info":"⩦⩻⨪⫏≰1101122=⫏≰1101122","layer":1},{"info":"⫏≰101122102↺⫏≰11102101=⫏≰11102101","layer":1},{"info":"⫏≰1101122⪨≂⫏≰11102101=⫏≰-12220201","layer":0}]}
{"id":812,"expression_no_base_symbol":"($3334$∲⫓$7832$)≹⇙⪍($1357$⨰$1763$)","expression":"(⫏≰11120111∲⫓⫏≰101202002)≹⇙⪍(⫏≰1212021⨰⫏≰2102022)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":156824,"operation_count":3,"complexity_ratio":52274.666666666664,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":3334,"base":3},"right_expr":{"type":"numeric_atoms","value":7832,"base":3}},"right_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":1357,"base":3},"right_expr":{"type":"numeric_atoms","value":1763,"base":3}}},"used_operators":["AHs5Up7iyr","i8ToyICDmI","eewbuw0ToL"],"dependent_operators":["dWAJyo7jo9","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3334","layer":2},{"info":"number node, value=7832","layer":2},{"info":"compute binary expreesion, left_input=3334, right_input=7832, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=1357","layer":2},{"info":"number node, value=1763","layer":2},{"info":"compute binary expreesion, left_input=1357, right_input=1763, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-396","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-396, 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":3,"result_base":3,"text":"(⫏≰11120111∲⫓⫏≰101202002)≹⇙⪍(⫏≰1212021⨰⫏≰2102022)=NaN","reverse_text":"NaN=(⫏≰11120111∲⫓⫏≰101202002)≹⇙⪍(⫏≰1212021⨰⫏≰2102022)","cot":[{"info":"⫏≰11120111∲⫓⫏≰101202002=⫏≰0","layer":1},{"info":"⫏≰1212021⨰⫏≰2102022=⫏≰-112200","layer":1},{"info":"⫏≰0≹⇙⪍⫏≰-112200=NaN","layer":0}]}
{"id":813,"expression_no_base_symbol":"($2460$⪨≂$1229$)⩷∴($2132$⫸⊐$1759$)","expression":"(⫏≰10101010⪨≂⫏≰1200112)⩷∴(⫏≰2220222⫸⊐⫏≰2102011)","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":2460,"base":3},"right_expr":{"type":"numeric_atoms","value":1229,"base":3}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":2132,"base":3},"right_expr":{"type":"numeric_atoms","value":1759,"base":3}}},"used_operators":["9FxExcQeMw","sdazOOVcIp","mqXw5SEYmG"],"dependent_operators":["rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"⫏≰-102222012","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2460","layer":2},{"info":"number node, value=1229","layer":2},{"info":"compute binary expreesion, left_input=2460, right_input=1229, 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=2564","layer":1},{"info":"number node, value=2132","layer":2},{"info":"number node, value=1759","layer":2},{"info":"compute binary expreesion, left_input=2132, right_input=1759, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=6911","layer":1},{"info":"compute binary expreesion, left_input=2564, right_input=6911, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-8726","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10101010⪨≂⫏≰1200112)⩷∴(⫏≰2220222⫸⊐⫏≰2102011)=⫏≰-102222012","reverse_text":"⫏≰-102222012=(⫏≰10101010⪨≂⫏≰1200112)⩷∴(⫏≰2220222⫸⊐⫏≰2102011)","cot":[{"info":"⫏≰10101010⪨≂⫏≰1200112=⫏≰10111222","layer":1},{"info":"⫏≰2220222⫸⊐⫏≰2102011=⫏≰100110222","layer":1},{"info":"⫏≰10111222⩷∴⫏≰100110222=⫏≰-102222012","layer":0}]}
{"id":814,"expression_no_base_symbol":"(≉$2909$)⪨≂$1067$⪮%⊝$1052$","expression":"(≉⫏≰10222202)⪨≂⫏≰1110112⪮%⊝⫏≰1102222","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16,"operation_count":3,"complexity_ratio":5.333333333333333,"tree":{"type":"binary","operator":"⪨≂","left_expr":{"type":"unary","operator":"≉","unary_expr":{"type":"numeric_atoms","value":2909,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1067,"base":3},"right_expr":{"type":"numeric_atoms","value":1052,"base":3}}},"used_operators":["sdazOOVcIp","e1ybzncUwg","IWmyXbctLI"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰2212010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2909","layer":2},{"info":"compute unary expreesion, input=2909, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=3440","layer":1},{"info":"number node, value=1067","layer":2},{"info":"number node, value=1052","layer":2},{"info":"compute binary expreesion, left_input=1067, right_input=1052, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=2450","layer":1},{"info":"compute binary expreesion, left_input=3440, right_input=2450, 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=2082","layer":0}],"base":3,"result_base":3,"text":"(≉⫏≰10222202)⪨≂⫏≰1110112⪮%⊝⫏≰1102222=⫏≰2212010","reverse_text":"⫏≰2212010=(≉⫏≰10222202)⪨≂⫏≰1110112⪮%⊝⫏≰1102222","cot":[{"info":"≉⫏≰10222202=⫏≰11201102","layer":1},{"info":"⫏≰1110112⪮%⊝⫏≰1102222=⫏≰10100202","layer":1},{"info":"⫏≰11201102⪨≂⫏≰10100202=⫏≰2212010","layer":0}]}
{"id":815,"expression_no_base_symbol":"$3829$⊭↱$2287$⪨≂(↯⪼$5022$)","expression":"⫏≰12020211⊭↱⫏≰10010201⪨≂(↯⪼⫏≰20220000)","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":3829,"base":3},"right_expr":{"type":"numeric_atoms","value":2287,"base":3}},"right_expr":{"type":"unary","operator":"↯⪼","unary_expr":{"type":"numeric_atoms","value":5022,"base":3}}},"used_operators":["sdazOOVcIp","COABgblf1C","8jW3W4yZS5"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","eLAdDNolq6","P8v4zCKN1o","k8jYdgA6NY","EBcxylXtPf","XPYlsWDdGa","Z2TMIBDE3Q","8w2t5hMYqp"],"result":"⫏≰-22020202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3829","layer":2},{"info":"number node, value=2287","layer":2},{"info":"compute binary expreesion, left_input=3829, right_input=2287, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-3079","layer":1},{"info":"number node, value=5022","layer":2},{"info":"compute unary expreesion, input=5022, 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=-3079, right_input=-21, 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=-6014","layer":0}],"base":3,"result_base":3,"text":"⫏≰12020211⊭↱⫏≰10010201⪨≂(↯⪼⫏≰20220000)=⫏≰-22020202","reverse_text":"⫏≰-22020202=⫏≰12020211⊭↱⫏≰10010201⪨≂(↯⪼⫏≰20220000)","cot":[{"info":"⫏≰12020211⊭↱⫏≰10010201=⫏≰-11020001","layer":1},{"info":"↯⪼⫏≰20220000=⫏≰-210","layer":1},{"info":"⫏≰-11020001⪨≂⫏≰-210=⫏≰-22020202","layer":0}]}
{"id":816,"expression_no_base_symbol":"$5638$⪛$1298$⨵⪆$1379$≧⫂∧$1923$","expression":"⫏≰21201211⪛⫏≰1210002⨵⪆⫏≰1220002≧⫂∧⫏≰2122020","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":5638,"base":3},"right_expr":{"type":"numeric_atoms","value":1298,"base":3}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":1379,"base":3},"right_expr":{"type":"numeric_atoms","value":1923,"base":3}}},"used_operators":["2DQ55sFlQl","uFcxV4UQCh","Ph9nP6C5qx"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5638","layer":2},{"info":"number node, value=1298","layer":2},{"info":"compute binary expreesion, left_input=5638, right_input=1298, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=446","layer":1},{"info":"number node, value=1379","layer":2},{"info":"number node, value=1923","layer":2},{"info":"compute binary expreesion, left_input=1379, right_input=1923, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=1450","layer":1},{"info":"compute binary expreesion, left_input=446, right_input=1450, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰21201211⪛⫏≰1210002⨵⪆⫏≰1220002≧⫂∧⫏≰2122020=⫏≰12221","reverse_text":"⫏≰12221=⫏≰21201211⪛⫏≰1210002⨵⪆⫏≰1220002≧⫂∧⫏≰2122020","cot":[{"info":"⫏≰21201211⪛⫏≰1210002=⫏≰121112","layer":1},{"info":"⫏≰1220002≧⫂∧⫏≰2122020=⫏≰1222201","layer":1},{"info":"⫏≰121112⨵⪆⫏≰1222201=⫏≰12221","layer":0}]}
{"id":817,"expression_no_base_symbol":"($1357$⊭↱$6354$)⊠≄⫣","expression":"(⫏≰1212021⊭↱⫏≰22201100)⊠≄⫣","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":1357,"base":3},"right_expr":{"type":"numeric_atoms","value":6354,"base":3}}},"used_operators":["DIvbN7qnHd","COABgblf1C"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1357","layer":2},{"info":"number node, value=6354","layer":2},{"info":"compute binary expreesion, left_input=1357, right_input=6354, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=9999","layer":1},{"info":"compute unary expreesion, input=9999, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1212021⊭↱⫏≰22201100)⊠≄⫣=⫏≰0","reverse_text":"⫏≰0=(⫏≰1212021⊭↱⫏≰22201100)⊠≄⫣","cot":[{"info":"⫏≰1212021⊭↱⫏≰22201100=⫏≰111201100","layer":1},{"info":"⫏≰111201100⊠≄⫣=⫏≰0","layer":0}]}
{"id":818,"expression_no_base_symbol":"($1236$⇼⇔∾$2499$)↬($2694$⩨$3193$)","expression":"(⫏≰1200210⇼⇔∾⫏≰10102120)↬(⫏≰10200210⩨⫏≰11101021)","highest_n_order":5,"priority_hierarchical_complexity":2,"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":1236,"base":3},"right_expr":{"type":"numeric_atoms","value":2499,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":2694,"base":3},"right_expr":{"type":"numeric_atoms","value":3193,"base":3}}},"used_operators":["B5M0gjZbta","tifHPKVTfV","2DlMacCsIx"],"dependent_operators":["rGHVDoGpnC","rysDP5nf3Z","t8gj7n24qd","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1236","layer":2},{"info":"number node, value=2499","layer":2},{"info":"compute binary expreesion, left_input=1236, right_input=2499, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=1263","layer":1},{"info":"number node, value=2694","layer":2},{"info":"number node, value=3193","layer":2},{"info":"compute binary expreesion, left_input=2694, right_input=3193, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-3","layer":1},{"info":"compute binary expreesion, left_input=1263, right_input=-3, 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":3,"result_base":3,"text":"(⫏≰1200210⇼⇔∾⫏≰10102120)↬(⫏≰10200210⩨⫏≰11101021)=NaN","reverse_text":"NaN=(⫏≰1200210⇼⇔∾⫏≰10102120)↬(⫏≰10200210⩨⫏≰11101021)","cot":[{"info":"⫏≰1200210⇼⇔∾⫏≰10102120=⫏≰1201210","layer":1},{"info":"⫏≰10200210⩨⫏≰11101021=⫏≰-10","layer":1},{"info":"⫏≰1201210↬⫏≰-10=NaN","layer":0}]}
{"id":819,"expression_no_base_symbol":"⇁⨣⪵(-$1084$)","expression":"⇁⨣⪵(-⫏≰1111011)","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":1084,"base":3}}},"used_operators":["inkyxCbjAn","t8gj7n24qd"],"dependent_operators":["B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1084","layer":2},{"info":"compute unary expreesion, input=1084, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-1084","layer":1},{"info":"compute unary expreesion, input=-1084, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵(-⫏≰1111011)=NaN","reverse_text":"NaN=⇁⨣⪵(-⫏≰1111011)","cot":[{"info":"-⫏≰1111011=⫏≰-1111011","layer":1},{"info":"⇁⨣⪵⫏≰-1111011=NaN","layer":0}]}
{"id":820,"expression_no_base_symbol":"$2098$⋥≓≎$1433$≋⫹","expression":"⫏≰2212201⋥≓≎⫏≰1222002≋⫹","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":2098,"base":3},"right_expr":{"type":"numeric_atoms","value":1433,"base":3}}},"used_operators":["N41Kp7NANJ","Qy55tPpLXF"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-2012100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2098","layer":2},{"info":"number node, value=1433","layer":2},{"info":"compute binary expreesion, left_input=2098, right_input=1433, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=801","layer":1},{"info":"compute unary expreesion, input=801, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-1602","layer":0}],"base":3,"result_base":3,"text":"⫏≰2212201⋥≓≎⫏≰1222002≋⫹=⫏≰-2012100","reverse_text":"⫏≰-2012100=⫏≰2212201⋥≓≎⫏≰1222002≋⫹","cot":[{"info":"⫏≰2212201⋥≓≎⫏≰1222002=⫏≰1002200","layer":1},{"info":"⫏≰1002200≋⫹=⫏≰-2012100","layer":0}]}
{"id":821,"expression_no_base_symbol":"⇁⨣⪵$1112$+⇶⊼$7042$","expression":"⇁⨣⪵⫏≰1112012+⇶⊼⫏≰100122211","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":1112,"base":3},"right_expr":{"type":"numeric_atoms","value":7042,"base":3}}},"used_operators":["inkyxCbjAn","TpPTUOHfaN"],"dependent_operators":["B5M0gjZbta","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1112","layer":2},{"info":"number node, value=7042","layer":2},{"info":"compute binary expreesion, left_input=1112, right_input=7042, 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":1},{"info":"compute unary expreesion, input=nan, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵⫏≰1112012+⇶⊼⫏≰100122211=NaN","reverse_text":"NaN=⇁⨣⪵⫏≰1112012+⇶⊼⫏≰100122211","cot":[{"info":"⫏≰1112012+⇶⊼⫏≰100122211=NaN","layer":1},{"info":"⇁⨣⪵NaN=NaN","layer":0}]}
{"id":822,"expression_no_base_symbol":"⨰⫟⨤($6466$⨳⩥⨓$7839$)","expression":"⨰⫟⨤(⫏≰22212111⨳⩥⨓⫏≰101202100)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4655,"operation_count":2,"complexity_ratio":2327.5,"tree":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":6466,"base":3},"right_expr":{"type":"numeric_atoms","value":7839,"base":3}}},"used_operators":["Tw270M8GLb","nCS4ZIUYfx"],"dependent_operators":["sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","W4YGzv6Whe","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6466","layer":2},{"info":"number node, value=7839","layer":2},{"info":"compute binary expreesion, left_input=6466, right_input=7839, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=1373","layer":1},{"info":"compute unary expreesion, input=1373, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⨰⫟⨤(⫏≰22212111⨳⩥⨓⫏≰101202100)=NaN","reverse_text":"NaN=⨰⫟⨤(⫏≰22212111⨳⩥⨓⫏≰101202100)","cot":[{"info":"⫏≰22212111⨳⩥⨓⫏≰101202100=⫏≰1212212","layer":1},{"info":"⨰⫟⨤⫏≰1212212=NaN","layer":0}]}
{"id":823,"expression_no_base_symbol":"-$1882$⨐⩸⫘$7016$","expression":"-⫏≰2120201⨐⩸⫘⫏≰100121212","highest_n_order":4,"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":1882,"base":3},"right_expr":{"type":"numeric_atoms","value":7016,"base":3}}},"used_operators":["t8gj7n24qd","fu6greOZ01"],"dependent_operators":["3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1882","layer":2},{"info":"number node, value=7016","layer":2},{"info":"compute binary expreesion, left_input=1882, right_input=7016, 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 unary expreesion, input=nan, op_id = t8gj7n24qd, unary_op_definition = 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"-⫏≰2120201⨐⩸⫘⫏≰100121212=NaN","reverse_text":"NaN=-⫏≰2120201⨐⩸⫘⫏≰100121212","cot":[{"info":"⫏≰2120201⨐⩸⫘⫏≰100121212=NaN","layer":1},{"info":"-NaN=NaN","layer":0}]}
{"id":824,"expression_no_base_symbol":"-($1490$⫌⩹⨱)","expression":"-(⫏≰2001012⫌⩹⨱)","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":"unary","operator":"⫌⩹⨱","unary_expr":{"type":"numeric_atoms","value":1490,"base":3}}},"used_operators":["t8gj7n24qd","EBcxylXtPf"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰-20000021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1490","layer":2},{"info":"compute unary expreesion, input=1490, op_id = EBcxylXtPf, unary_op_definition = 'a⫌⩹⨱ = { (((80+a)+(750-a))+((149+422)+(a+a))) }', output=4381","layer":1},{"info":"compute unary expreesion, input=4381, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-4381","layer":0}],"base":3,"result_base":3,"text":"-(⫏≰2001012⫌⩹⨱)=⫏≰-20000021","reverse_text":"⫏≰-20000021=-(⫏≰2001012⫌⩹⨱)","cot":[{"info":"⫏≰2001012⫌⩹⨱=⫏≰20000021","layer":1},{"info":"-⫏≰20000021=⫏≰-20000021","layer":0}]}
{"id":825,"expression_no_base_symbol":"($2068$⪄$1463$)↺$3607$⨪↰⇹$2735$","expression":"(⫏≰2211121⪄⫏≰2000012)↺⫏≰11221121⨪↰⇹⫏≰10202022","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3704,"operation_count":3,"complexity_ratio":1234.6666666666667,"tree":{"type":"binary","operator":"↺","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2068,"base":3},"right_expr":{"type":"numeric_atoms","value":1463,"base":3}},"right_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":3607,"base":3},"right_expr":{"type":"numeric_atoms","value":2735,"base":3}}},"used_operators":["7j4O788W3g","SUmda5xLS4","tmPS8pqC7x"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","rJVOvQCfKK"],"result":"⫏≰11221121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2068","layer":2},{"info":"number node, value=1463","layer":2},{"info":"compute binary expreesion, left_input=2068, right_input=1463, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-308005","layer":1},{"info":"number node, value=3607","layer":2},{"info":"number node, value=2735","layer":2},{"info":"compute binary expreesion, left_input=3607, right_input=2735, 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=3607","layer":1},{"info":"compute binary expreesion, left_input=-308005, right_input=3607, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=3607","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2211121⪄⫏≰2000012)↺⫏≰11221121⨪↰⇹⫏≰10202022=⫏≰11221121","reverse_text":"⫏≰11221121=(⫏≰2211121⪄⫏≰2000012)↺⫏≰11221121⨪↰⇹⫏≰10202022","cot":[{"info":"⫏≰2211121⪄⫏≰2000012=⫏≰-120122111121","layer":1},{"info":"⫏≰11221121⨪↰⇹⫏≰10202022=⫏≰11221121","layer":1},{"info":"⫏≰-120122111121↺⫏≰11221121=⫏≰11221121","layer":0}]}
{"id":826,"expression_no_base_symbol":"($2646$⪄$2943$)⪢(+⊝⨔$3372$)","expression":"(⫏≰10122000⪄⫏≰11001000)⪢(+⊝⨔⫏≰11121220)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":68548,"operation_count":3,"complexity_ratio":22849.333333333332,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":2646,"base":3},"right_expr":{"type":"numeric_atoms","value":2943,"base":3}},"right_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":3372,"base":3}}},"used_operators":["dWAJyo7jo9","SUmda5xLS4","DhbWaqg5eL"],"dependent_operators":["k8jYdgA6NY","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2646","layer":2},{"info":"number node, value=2943","layer":2},{"info":"compute binary expreesion, left_input=2646, right_input=2943, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-399469","layer":1},{"info":"number node, value=3372","layer":2},{"info":"compute unary expreesion, input=3372, 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 binary expreesion, left_input=-399469, right_input=1522, 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":3,"result_base":3,"text":"(⫏≰10122000⪄⫏≰11001000)⪢(+⊝⨔⫏≰11121220)=NaN","reverse_text":"NaN=(⫏≰10122000⪄⫏≰11001000)⪢(+⊝⨔⫏≰11121220)","cot":[{"info":"⫏≰10122000⪄⫏≰11001000=⫏≰-202021222011","layer":1},{"info":"+⊝⨔⫏≰11121220=⫏≰2002101","layer":1},{"info":"⫏≰-202021222011⪢⫏≰2002101=NaN","layer":0}]}
{"id":827,"expression_no_base_symbol":"(+⊝⨔$1000$)⪄$1493$∼$2352$","expression":"(+⊝⨔⫏≰1101001)⪄⫏≰2001022∼⫏≰10020010","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":165,"operation_count":3,"complexity_ratio":55.0,"tree":{"type":"binary","operator":"⪄","left_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":1000,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":1493,"base":3},"right_expr":{"type":"numeric_atoms","value":2352,"base":3}}},"used_operators":["SUmda5xLS4","DhbWaqg5eL","DyGG3AbaNP"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1000","layer":2},{"info":"compute unary expreesion, input=1000, 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=1493","layer":2},{"info":"number node, value=2352","layer":2},{"info":"compute binary expreesion, left_input=1493, right_input=2352, 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=1522, right_input=nan, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(+⊝⨔⫏≰1101001)⪄⫏≰2001022∼⫏≰10020010=NaN","reverse_text":"NaN=(+⊝⨔⫏≰1101001)⪄⫏≰2001022∼⫏≰10020010","cot":[{"info":"+⊝⨔⫏≰1101001=⫏≰2002101","layer":1},{"info":"⫏≰2001022∼⫏≰10020010=NaN","layer":1},{"info":"⫏≰2002101⪄NaN=NaN","layer":0}]}
{"id":828,"expression_no_base_symbol":"≦∁$4862$⩷∴$2072$","expression":"≦∁⫏≰20200002⩷∴⫏≰2211202","highest_n_order":2,"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":4862,"base":3},"right_expr":{"type":"numeric_atoms","value":2072,"base":3}}},"used_operators":["9ICcGScMcE","9FxExcQeMw"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","rysDP5nf3Z"],"result":"⫏≰21121111","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4862","layer":2},{"info":"number node, value=2072","layer":2},{"info":"compute binary expreesion, left_input=4862, right_input=2072, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=5548","layer":1},{"info":"compute unary expreesion, input=5548, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=5548","layer":0}],"base":3,"result_base":3,"text":"≦∁⫏≰20200002⩷∴⫏≰2211202=⫏≰21121111","reverse_text":"⫏≰21121111=≦∁⫏≰20200002⩷∴⫏≰2211202","cot":[{"info":"⫏≰20200002⩷∴⫏≰2211202=⫏≰21121111","layer":1},{"info":"≦∁⫏≰21121111=⫏≰21121111","layer":0}]}
{"id":829,"expression_no_base_symbol":"≦∁($1709$⨵⪆$4532$)","expression":"≦∁(⫏≰2100022⨵⪆⫏≰20012212)","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":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":1709,"base":3},"right_expr":{"type":"numeric_atoms","value":4532,"base":3}}},"used_operators":["9ICcGScMcE","2DQ55sFlQl"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-10001222","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1709","layer":2},{"info":"number node, value=4532","layer":2},{"info":"compute binary expreesion, left_input=1709, right_input=4532, 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 = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=-2240","layer":0}],"base":3,"result_base":3,"text":"≦∁(⫏≰2100022⨵⪆⫏≰20012212)=⫏≰-10001222","reverse_text":"⫏≰-10001222=≦∁(⫏≰2100022⨵⪆⫏≰20012212)","cot":[{"info":"⫏≰2100022⨵⪆⫏≰20012212=⫏≰12221","layer":1},{"info":"≦∁⫏≰12221=⫏≰-10001222","layer":0}]}
{"id":830,"expression_no_base_symbol":"$5379$⨵⪆$1712$⫡⨏$2287$↺$5524$","expression":"⫏≰21101020⨵⪆⫏≰2100102⫡⨏⫏≰10010201↺⫏≰21120121","highest_n_order":1,"priority_hierarchical_complexity":2,"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":5379,"base":3},"right_expr":{"type":"numeric_atoms","value":1712,"base":3}},"right_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":2287,"base":3},"right_expr":{"type":"numeric_atoms","value":5524,"base":3}}},"used_operators":["QMFrweE19q","2DQ55sFlQl","7j4O788W3g"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰122022211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5379","layer":2},{"info":"number node, value=1712","layer":2},{"info":"compute binary expreesion, left_input=5379, right_input=1712, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":1},{"info":"number node, value=2287","layer":2},{"info":"number node, value=5524","layer":2},{"info":"compute binary expreesion, left_input=2287, right_input=5524, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=5524","layer":1},{"info":"compute binary expreesion, left_input=160, right_input=5524, 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=12631","layer":0}],"base":3,"result_base":3,"text":"⫏≰21101020⨵⪆⫏≰2100102⫡⨏⫏≰10010201↺⫏≰21120121=⫏≰122022211","reverse_text":"⫏≰122022211=⫏≰21101020⨵⪆⫏≰2100102⫡⨏⫏≰10010201↺⫏≰21120121","cot":[{"info":"⫏≰21101020⨵⪆⫏≰2100102=⫏≰12221","layer":1},{"info":"⫏≰10010201↺⫏≰21120121=⫏≰21120121","layer":1},{"info":"⫏≰12221⫡⨏⫏≰21120121=⫏≰122022211","layer":0}]}
{"id":831,"expression_no_base_symbol":"(⩦⩻⨪$5228$)⋳⪒$4476$⩚⊴⇥$1710$","expression":"(⩦⩻⨪⫏≰21011122)⋳⪒⫏≰20010210⩚⊴⇥⫏≰2100100","highest_n_order":1,"priority_hierarchical_complexity":3,"normalized_expansion_degree":13,"operation_count":3,"complexity_ratio":4.333333333333333,"tree":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":5228,"base":3}},"right_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":4476,"base":3},"right_expr":{"type":"numeric_atoms","value":1710,"base":3}}},"used_operators":["12rbrZMWeM","2td37pGCOC","NTOWxs364D"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰211121020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5228","layer":2},{"info":"compute unary expreesion, input=5228, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=5228","layer":1},{"info":"number node, value=4476","layer":2},{"info":"number node, value=1710","layer":2},{"info":"compute binary expreesion, left_input=4476, right_input=1710, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-6307","layer":1},{"info":"compute binary expreesion, left_input=5228, right_input=-6307, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=16476","layer":0}],"base":3,"result_base":3,"text":"(⩦⩻⨪⫏≰21011122)⋳⪒⫏≰20010210⩚⊴⇥⫏≰2100100=⫏≰211121020","reverse_text":"⫏≰211121020=(⩦⩻⨪⫏≰21011122)⋳⪒⫏≰20010210⩚⊴⇥⫏≰2100100","cot":[{"info":"⩦⩻⨪⫏≰21011122=⫏≰21011122","layer":1},{"info":"⫏≰20010210⩚⊴⇥⫏≰2100100=⫏≰-22122121","layer":1},{"info":"⫏≰21011122⋳⪒⫏≰-22122121=⫏≰211121020","layer":0}]}
{"id":832,"expression_no_base_symbol":"($4330$⫥∨⫟$4838$)⋫","expression":"(⫏≰12221101⫥∨⫟⫏≰20122012)⋫","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":155,"operation_count":2,"complexity_ratio":77.5,"tree":{"type":"unary","operator":"⋫","unary_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":4330,"base":3},"right_expr":{"type":"numeric_atoms","value":4838,"base":3}}},"used_operators":["JL8yIekQnl","KYD54nUTWz"],"dependent_operators":["tmPS8pqC7x","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4330","layer":2},{"info":"number node, value=4838","layer":2},{"info":"compute binary expreesion, left_input=4330, right_input=4838, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12221101⫥∨⫟⫏≰20122012)⋫=NaN","reverse_text":"NaN=(⫏≰12221101⫥∨⫟⫏≰20122012)⋫","cot":[{"info":"⫏≰12221101⫥∨⫟⫏≰20122012=NaN","layer":1},{"info":"NaN⋫=NaN","layer":0}]}
{"id":833,"expression_no_base_symbol":"$1032$⪢$6990$⇋≉","expression":"⫏≰1102020⪢⫏≰100120220⇋≉","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6993,"operation_count":2,"complexity_ratio":3496.5,"tree":{"type":"unary","operator":"⇋≉","unary_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1032,"base":3},"right_expr":{"type":"numeric_atoms","value":6990,"base":3}}},"used_operators":["XIabStNQrY","dWAJyo7jo9"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1032","layer":2},{"info":"number node, value=6990","layer":2},{"info":"compute binary expreesion, left_input=1032, right_input=6990, 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 unary expreesion, input=nan, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1102020⪢⫏≰100120220⇋≉=NaN","reverse_text":"NaN=⫏≰1102020⪢⫏≰100120220⇋≉","cot":[{"info":"⫏≰1102020⪢⫏≰100120220=NaN","layer":1},{"info":"NaN⇋≉=NaN","layer":0}]}
{"id":834,"expression_no_base_symbol":"($1084$⊭↱$1055$)≣⋋","expression":"(⫏≰1111011⊭↱⫏≰1110002)≣⋋","highest_n_order":3,"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":1084,"base":3},"right_expr":{"type":"numeric_atoms","value":1055,"base":3}}},"used_operators":["Tcnh7f0tEr","COABgblf1C"],"dependent_operators":["dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1084","layer":2},{"info":"number node, value=1055","layer":2},{"info":"compute binary expreesion, left_input=1084, right_input=1055, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-53","layer":1},{"info":"compute unary expreesion, input=-53, op_id = Tcnh7f0tEr, unary_op_definition = 'a≣⋋ = { ((a/a)⋥≓≎(a⨪↰⇹248)) , if (a⪢148)<38 ; ((511*a)⊠≄⫣) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1111011⊭↱⫏≰1110002)≣⋋=⫏≰0","reverse_text":"⫏≰0=(⫏≰1111011⊭↱⫏≰1110002)≣⋋","cot":[{"info":"⫏≰1111011⊭↱⫏≰1110002=⫏≰-1222","layer":1},{"info":"⫏≰-1222≣⋋=⫏≰0","layer":0}]}
{"id":835,"expression_no_base_symbol":"($4199$⫥∨⫟$1510$)⪮%⊝($1277$⩷∴$4284$)","expression":"(⫏≰12202112⫥∨⫟⫏≰2001221)⪮%⊝(⫏≰1202022⩷∴⫏≰12212200)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":169,"operation_count":3,"complexity_ratio":56.333333333333336,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":4199,"base":3},"right_expr":{"type":"numeric_atoms","value":1510,"base":3}},"right_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":1277,"base":3},"right_expr":{"type":"numeric_atoms","value":4284,"base":3}}},"used_operators":["IWmyXbctLI","KYD54nUTWz","9FxExcQeMw"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","8HhzD0ZcuI","rGHVDoGpnC","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4199","layer":2},{"info":"number node, value=1510","layer":2},{"info":"compute binary expreesion, left_input=4199, right_input=1510, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=1277","layer":2},{"info":"number node, value=4284","layer":2},{"info":"compute binary expreesion, left_input=1277, right_input=4284, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-6046","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-6046, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12202112⫥∨⫟⫏≰2001221)⪮%⊝(⫏≰1202022⩷∴⫏≰12212200)=NaN","reverse_text":"NaN=(⫏≰12202112⫥∨⫟⫏≰2001221)⪮%⊝(⫏≰1202022⩷∴⫏≰12212200)","cot":[{"info":"⫏≰12202112⫥∨⫟⫏≰2001221=NaN","layer":1},{"info":"⫏≰1202022⩷∴⫏≰12212200=⫏≰-22021221","layer":1},{"info":"NaN⪮%⊝⫏≰-22021221=NaN","layer":0}]}
{"id":836,"expression_no_base_symbol":"$1035$≎⊠⪸$1023$⫥∨⫟(⫓⪴$3362$)","expression":"⫏≰1102100≎⊠⪸⫏≰1101220⫥∨⫟(⫓⪴⫏≰11121112)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3786,"operation_count":3,"complexity_ratio":1262.0,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1035,"base":3},"right_expr":{"type":"numeric_atoms","value":1023,"base":3}},"right_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":3362,"base":3}}},"used_operators":["KYD54nUTWz","bJkvcejdHO","eLxqMNBOBk"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1035","layer":2},{"info":"number node, value=1023","layer":2},{"info":"compute binary expreesion, left_input=1035, right_input=1023, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=267592","layer":1},{"info":"number node, value=3362","layer":2},{"info":"compute unary expreesion, input=3362, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=11303044","layer":1},{"info":"compute binary expreesion, left_input=267592, right_input=11303044, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1102100≎⊠⪸⫏≰1101220⫥∨⫟(⫓⪴⫏≰11121112)=NaN","reverse_text":"NaN=⫏≰1102100≎⊠⪸⫏≰1101220⫥∨⫟(⫓⪴⫏≰11121112)","cot":[{"info":"⫏≰1102100≎⊠⪸⫏≰1101220=⫏≰111121001211","layer":1},{"info":"⫓⪴⫏≰11121112=⫏≰210021020212021","layer":1},{"info":"⫏≰111121001211⫥∨⫟⫏≰210021020212021=NaN","layer":0}]}
{"id":837,"expression_no_base_symbol":"($4680$⨎$6108$)⊴($4982$⫡⨏$1845$)","expression":"(⫏≰20102100⨎⫏≰22101020)⊴(⫏≰20211112⫡⨏⫏≰2112100)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":29397,"operation_count":3,"complexity_ratio":9799.0,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":4680,"base":3},"right_expr":{"type":"numeric_atoms","value":6108,"base":3}},"right_expr":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":4982,"base":3},"right_expr":{"type":"numeric_atoms","value":1845,"base":3}}},"used_operators":["Nsiff2A1zJ","rJVOvQCfKK","QMFrweE19q"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4680","layer":2},{"info":"number node, value=6108","layer":2},{"info":"compute binary expreesion, left_input=4680, right_input=6108, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=6108","layer":1},{"info":"number node, value=4982","layer":2},{"info":"number node, value=1845","layer":2},{"info":"compute binary expreesion, left_input=4982, right_input=1845, 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=29383","layer":1},{"info":"compute binary expreesion, left_input=6108, right_input=29383, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20102100⨎⫏≰22101020)⊴(⫏≰20211112⫡⨏⫏≰2112100)=NaN","reverse_text":"NaN=(⫏≰20102100⨎⫏≰22101020)⊴(⫏≰20211112⫡⨏⫏≰2112100)","cot":[{"info":"⫏≰20102100⨎⫏≰22101020=⫏≰22101020","layer":1},{"info":"⫏≰20211112⫡⨏⫏≰2112100=⫏≰1111022021","layer":1},{"info":"⫏≰22101020⊴⫏≰1111022021=NaN","layer":0}]}
{"id":838,"expression_no_base_symbol":"(∥⊫$2900$)⋫","expression":"(∥⊫⫏≰10222102)⋫","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3772,"operation_count":2,"complexity_ratio":1886.0,"tree":{"type":"unary","operator":"⋫","unary_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":2900,"base":3}}},"used_operators":["JL8yIekQnl","P8v4zCKN1o"],"dependent_operators":["tmPS8pqC7x","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰12011120","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2900","layer":2},{"info":"compute unary expreesion, input=2900, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=3768","layer":1},{"info":"compute unary expreesion, input=3768, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=3768","layer":0}],"base":3,"result_base":3,"text":"(∥⊫⫏≰10222102)⋫=⫏≰12011120","reverse_text":"⫏≰12011120=(∥⊫⫏≰10222102)⋫","cot":[{"info":"∥⊫⫏≰10222102=⫏≰12011120","layer":1},{"info":"⫏≰12011120⋫=⫏≰12011120","layer":0}]}
{"id":839,"expression_no_base_symbol":"($1948$↙$2210$)⨓($1540$⪨≂$5799$)","expression":"(⫏≰2200011↙⫏≰10000212)⨓(⫏≰2010001⪨≂⫏≰21221210)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":10640,"operation_count":3,"complexity_ratio":3546.6666666666665,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":1948,"base":3},"right_expr":{"type":"numeric_atoms","value":2210,"base":3}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":1540,"base":3},"right_expr":{"type":"numeric_atoms","value":5799,"base":3}}},"used_operators":["3ViojmjbAp","yyfyN0ffXY","sdazOOVcIp"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","tmPS8pqC7x","DpFCA1CohY","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰102112121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1948","layer":2},{"info":"number node, value=2210","layer":2},{"info":"compute binary expreesion, left_input=1948, right_input=2210, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-6630","layer":1},{"info":"number node, value=1540","layer":2},{"info":"number node, value=5799","layer":2},{"info":"compute binary expreesion, left_input=1540, right_input=5799, 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=-8416","layer":1},{"info":"compute binary expreesion, left_input=-6630, right_input=-8416, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=8413","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2200011↙⫏≰10000212)⨓(⫏≰2010001⪨≂⫏≰21221210)=⫏≰102112121","reverse_text":"⫏≰102112121=(⫏≰2200011↙⫏≰10000212)⨓(⫏≰2010001⪨≂⫏≰21221210)","cot":[{"info":"⫏≰2200011↙⫏≰10000212=⫏≰-100002120","layer":1},{"info":"⫏≰2010001⪨≂⫏≰21221210=⫏≰-102112201","layer":1},{"info":"⫏≰-100002120⨓⫏≰-102112201=⫏≰102112121","layer":0}]}
{"id":840,"expression_no_base_symbol":"⪲⇎($1010$+$2319$)","expression":"⪲⇎(⫏≰1101102+⫏≰10011220)","highest_n_order":1,"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":1010,"base":3},"right_expr":{"type":"numeric_atoms","value":2319,"base":3}}},"used_operators":["XPYlsWDdGa","W4YGzv6Whe"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰100010121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1010","layer":2},{"info":"number node, value=2319","layer":2},{"info":"compute binary expreesion, left_input=1010, right_input=2319, op_id = W4YGzv6Whe binary_op_definition= 'None', output=3329","layer":1},{"info":"compute unary expreesion, input=3329, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=6658","layer":0}],"base":3,"result_base":3,"text":"⪲⇎(⫏≰1101102+⫏≰10011220)=⫏≰100010121","reverse_text":"⫏≰100010121=⪲⇎(⫏≰1101102+⫏≰10011220)","cot":[{"info":"⫏≰1101102+⫏≰10011220=⫏≰11120022","layer":1},{"info":"⪲⇎⫏≰11120022=⫏≰100010121","layer":0}]}
{"id":841,"expression_no_base_symbol":"≦∁$2792$↙$3651$","expression":"≦∁⫏≰10211102↙⫏≰12000020","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3716,"operation_count":2,"complexity_ratio":1858.0,"tree":{"type":"unary","operator":"≦∁","unary_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":2792,"base":3},"right_expr":{"type":"numeric_atoms","value":3651,"base":3}}},"used_operators":["9ICcGScMcE","yyfyN0ffXY"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2792","layer":2},{"info":"number node, value=3651","layer":2},{"info":"compute binary expreesion, left_input=2792, right_input=3651, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-10953","layer":1},{"info":"compute unary expreesion, input=-10953, 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":3,"result_base":3,"text":"≦∁⫏≰10211102↙⫏≰12000020=⫏≰2111","reverse_text":"⫏≰2111=≦∁⫏≰10211102↙⫏≰12000020","cot":[{"info":"⫏≰10211102↙⫏≰12000020=⫏≰-120000200","layer":1},{"info":"≦∁⫏≰-120000200=⫏≰2111","layer":0}]}
{"id":842,"expression_no_base_symbol":"(⨰⫟⨤$4352$)⊭↱$2285$≭$1537$","expression":"(⨰⫟⨤⫏≰12222012)⊭↱⫏≰10010122≭⫏≰2002221","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":16575,"operation_count":3,"complexity_ratio":5525.0,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":4352,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":2285,"base":3},"right_expr":{"type":"numeric_atoms","value":1537,"base":3}}},"used_operators":["COABgblf1C","Tw270M8GLb","rxpJgHHUmx"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4352","layer":2},{"info":"compute unary expreesion, input=4352, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":1},{"info":"number node, value=2285","layer":2},{"info":"number node, value=1537","layer":2},{"info":"compute binary expreesion, left_input=2285, right_input=1537, 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=nan, right_input=nan, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⨰⫟⨤⫏≰12222012)⊭↱⫏≰10010122≭⫏≰2002221=NaN","reverse_text":"NaN=(⨰⫟⨤⫏≰12222012)⊭↱⫏≰10010122≭⫏≰2002221","cot":[{"info":"⨰⫟⨤⫏≰12222012=NaN","layer":1},{"info":"⫏≰10010122≭⫏≰2002221=NaN","layer":1},{"info":"NaN⊭↱NaN=NaN","layer":0}]}
{"id":843,"expression_no_base_symbol":"(∥⊫$2350$)⨟⋌⩍($1193$↺$6530$)","expression":"(∥⊫⫏≰10020001)⨟⋌⩍(⫏≰1122012↺⫏≰22221212)","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":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":2350,"base":3}},"right_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":1193,"base":3},"right_expr":{"type":"numeric_atoms","value":6530,"base":3}}},"used_operators":["rGHVDoGpnC","P8v4zCKN1o","7j4O788W3g"],"dependent_operators":["Tcnh7f0tEr","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2350","layer":2},{"info":"compute unary expreesion, input=2350, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=3218","layer":1},{"info":"number node, value=1193","layer":2},{"info":"number node, value=6530","layer":2},{"info":"compute binary expreesion, left_input=1193, right_input=6530, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=6530","layer":1},{"info":"compute binary expreesion, left_input=3218, right_input=6530, 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":0}],"base":3,"result_base":3,"text":"(∥⊫⫏≰10020001)⨟⋌⩍(⫏≰1122012↺⫏≰22221212)=NaN","reverse_text":"NaN=(∥⊫⫏≰10020001)⨟⋌⩍(⫏≰1122012↺⫏≰22221212)","cot":[{"info":"∥⊫⫏≰10020001=⫏≰11102012","layer":1},{"info":"⫏≰1122012↺⫏≰22221212=⫏≰22221212","layer":1},{"info":"⫏≰11102012⨟⋌⩍⫏≰22221212=NaN","layer":0}]}
{"id":844,"expression_no_base_symbol":"($3836$↺$2843$)⨐⩸⫘(⋗⩬⋾$2619$)","expression":"(⫏≰12021002↺⫏≰10220022)⨐⩸⫘(⋗⩬⋾⫏≰10121000)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":3836,"base":3},"right_expr":{"type":"numeric_atoms","value":2843,"base":3}},"right_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":2619,"base":3}}},"used_operators":["fu6greOZ01","7j4O788W3g","DpFCA1CohY"],"dependent_operators":["3ViojmjbAp","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3836","layer":2},{"info":"number node, value=2843","layer":2},{"info":"compute binary expreesion, left_input=3836, right_input=2843, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=2843","layer":1},{"info":"number node, value=2619","layer":2},{"info":"compute unary expreesion, input=2619, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-7857","layer":1},{"info":"compute binary expreesion, left_input=2843, right_input=-7857, 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":3,"result_base":3,"text":"(⫏≰12021002↺⫏≰10220022)⨐⩸⫘(⋗⩬⋾⫏≰10121000)=NaN","reverse_text":"NaN=(⫏≰12021002↺⫏≰10220022)⨐⩸⫘(⋗⩬⋾⫏≰10121000)","cot":[{"info":"⫏≰12021002↺⫏≰10220022=⫏≰10220022","layer":1},{"info":"⋗⩬⋾⫏≰10121000=⫏≰-101210000","layer":1},{"info":"⫏≰10220022⨐⩸⫘⫏≰-101210000=NaN","layer":0}]}
{"id":845,"expression_no_base_symbol":"$1963$≹⇙⪍$2555$⊭↱($8220$⊭↱$2622$)","expression":"⫏≰2200201≹⇙⪍⫏≰10111122⊭↱(⫏≰102021110⊭↱⫏≰10121010)","highest_n_order":4,"priority_hierarchical_complexity":2,"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":1963,"base":3},"right_expr":{"type":"numeric_atoms","value":2555,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":8220,"base":3},"right_expr":{"type":"numeric_atoms","value":2622,"base":3}}},"used_operators":["COABgblf1C","AHs5Up7iyr"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1963","layer":2},{"info":"number node, value=2555","layer":2},{"info":"compute binary expreesion, left_input=1963, right_input=2555, 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":"number node, value=8220","layer":2},{"info":"number node, value=2622","layer":2},{"info":"compute binary expreesion, left_input=8220, right_input=2622, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-11191","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-11191, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2200201≹⇙⪍⫏≰10111122⊭↱(⫏≰102021110⊭↱⫏≰10121010)=NaN","reverse_text":"NaN=⫏≰2200201≹⇙⪍⫏≰10111122⊭↱(⫏≰102021110⊭↱⫏≰10121010)","cot":[{"info":"⫏≰2200201≹⇙⪍⫏≰10111122=NaN","layer":1},{"info":"⫏≰102021110⊭↱⫏≰10121010=⫏≰-120100111","layer":1},{"info":"NaN⊭↱⫏≰-120100111=NaN","layer":0}]}
{"id":846,"expression_no_base_symbol":"($3008$⇼⇔∾$1062$)⊴($4939$⪢$2186$)","expression":"(⫏≰11010102⇼⇔∾⫏≰1110100)⊴(⫏≰20202221⪢⫏≰2222222)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3429,"operation_count":3,"complexity_ratio":1143.0,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":3008,"base":3},"right_expr":{"type":"numeric_atoms","value":1062,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":4939,"base":3},"right_expr":{"type":"numeric_atoms","value":2186,"base":3}}},"used_operators":["Nsiff2A1zJ","tifHPKVTfV","dWAJyo7jo9"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","rysDP5nf3Z","t8gj7n24qd","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3008","layer":2},{"info":"number node, value=1062","layer":2},{"info":"compute binary expreesion, left_input=3008, right_input=1062, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-1946","layer":1},{"info":"number node, value=4939","layer":2},{"info":"number node, value=2186","layer":2},{"info":"compute binary expreesion, left_input=4939, right_input=2186, 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=-1946, right_input=nan, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11010102⇼⇔∾⫏≰1110100)⊴(⫏≰20202221⪢⫏≰2222222)=NaN","reverse_text":"NaN=(⫏≰11010102⇼⇔∾⫏≰1110100)⊴(⫏≰20202221⪢⫏≰2222222)","cot":[{"info":"⫏≰11010102⇼⇔∾⫏≰1110100=⫏≰-2200002","layer":1},{"info":"⫏≰20202221⪢⫏≰2222222=NaN","layer":1},{"info":"⫏≰-2200002⊴NaN=NaN","layer":0}]}
{"id":847,"expression_no_base_symbol":"($7906$⋷$1509$)⊴($3167$⇋≉)","expression":"(⫏≰101211211⋷⫏≰2001220)⊴(⫏≰11100022⇋≉)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6372,"operation_count":3,"complexity_ratio":2124.0,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":7906,"base":3},"right_expr":{"type":"numeric_atoms","value":1509,"base":3}},"right_expr":{"type":"unary","operator":"⇋≉","unary_expr":{"type":"numeric_atoms","value":3167,"base":3}}},"used_operators":["Nsiff2A1zJ","23Mk6UjR3U","XIabStNQrY"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7906","layer":2},{"info":"number node, value=1509","layer":2},{"info":"compute binary expreesion, left_input=7906, right_input=1509, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-4888","layer":1},{"info":"number node, value=3167","layer":2},{"info":"compute unary expreesion, input=3167, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=6236","layer":1},{"info":"compute binary expreesion, left_input=-4888, right_input=6236, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰101211211⋷⫏≰2001220)⊴(⫏≰11100022⇋≉)=NaN","reverse_text":"NaN=(⫏≰101211211⋷⫏≰2001220)⊴(⫏≰11100022⇋≉)","cot":[{"info":"⫏≰101211211⋷⫏≰2001220=⫏≰-20201001","layer":1},{"info":"⫏≰11100022⇋≉=⫏≰22112222","layer":1},{"info":"⫏≰-20201001⊴⫏≰22112222=NaN","layer":0}]}
{"id":848,"expression_no_base_symbol":"($4303$≦≮≮)+⇶⊼$1100$⪢$5746$","expression":"(⫏≰12220101≦≮≮)+⇶⊼⫏≰1111202⪢⫏≰21212211","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5750,"operation_count":3,"complexity_ratio":1916.6666666666667,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":4303,"base":3}},"right_expr":{"type":"binary","operator":"⪢","left_expr":{"type":"numeric_atoms","value":1100,"base":3},"right_expr":{"type":"numeric_atoms","value":5746,"base":3}}},"used_operators":["TpPTUOHfaN","D4vGDi5EA2","dWAJyo7jo9"],"dependent_operators":["AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4303","layer":2},{"info":"compute unary expreesion, input=4303, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-12909","layer":1},{"info":"number node, value=1100","layer":2},{"info":"number node, value=5746","layer":2},{"info":"compute binary expreesion, left_input=1100, right_input=5746, 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=-12909, right_input=nan, 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":3,"result_base":3,"text":"(⫏≰12220101≦≮≮)+⇶⊼⫏≰1111202⪢⫏≰21212211=NaN","reverse_text":"NaN=(⫏≰12220101≦≮≮)+⇶⊼⫏≰1111202⪢⫏≰21212211","cot":[{"info":"⫏≰12220101≦≮≮=⫏≰-122201010","layer":1},{"info":"⫏≰1111202⪢⫏≰21212211=NaN","layer":1},{"info":"⫏≰-122201010+⇶⊼NaN=NaN","layer":0}]}
{"id":849,"expression_no_base_symbol":"$2037$⪛$2718$⊘","expression":"⫏≰2210110⪛⫏≰10201200⊘","highest_n_order":2,"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":2037,"base":3},"right_expr":{"type":"numeric_atoms","value":2718,"base":3}}},"used_operators":["gu96TGCTMs","uFcxV4UQCh"],"dependent_operators":["XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2037","layer":2},{"info":"number node, value=2718","layer":2},{"info":"compute binary expreesion, left_input=2037, right_input=2718, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=2037","layer":1},{"info":"compute unary expreesion, input=2037, 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":3,"result_base":3,"text":"⫏≰2210110⪛⫏≰10201200⊘=⫏≰0","reverse_text":"⫏≰0=⫏≰2210110⪛⫏≰10201200⊘","cot":[{"info":"⫏≰2210110⪛⫏≰10201200=⫏≰2210110","layer":1},{"info":"⫏≰2210110⊘=⫏≰0","layer":0}]}
{"id":850,"expression_no_base_symbol":"⋗⩬⋾$2195$⨓$1599$","expression":"⋗⩬⋾⫏≰10000022⨓⫏≰2012020","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1608,"operation_count":2,"complexity_ratio":804.0,"tree":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":2195,"base":3},"right_expr":{"type":"numeric_atoms","value":1599,"base":3}}},"used_operators":["DpFCA1CohY","3ViojmjbAp"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"⫏≰20121000","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2195","layer":2},{"info":"number node, value=1599","layer":2},{"info":"compute binary expreesion, left_input=2195, right_input=1599, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1602","layer":1},{"info":"compute unary expreesion, input=-1602, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=4806","layer":0}],"base":3,"result_base":3,"text":"⋗⩬⋾⫏≰10000022⨓⫏≰2012020=⫏≰20121000","reverse_text":"⫏≰20121000=⋗⩬⋾⫏≰10000022⨓⫏≰2012020","cot":[{"info":"⫏≰10000022⨓⫏≰2012020=⫏≰-2012100","layer":1},{"info":"⋗⩬⋾⫏≰-2012100=⫏≰20121000","layer":0}]}
{"id":851,"expression_no_base_symbol":"($1447$⨽$7116$)+⇶⊼($1215$↛⩡⫤)","expression":"(⫏≰1222121⨽⫏≰100202120)+⇶⊼(⫏≰1200000↛⩡⫤)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5236,"operation_count":3,"complexity_ratio":1745.3333333333333,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1447,"base":3},"right_expr":{"type":"numeric_atoms","value":7116,"base":3}},"right_expr":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"numeric_atoms","value":1215,"base":3}}},"used_operators":["TpPTUOHfaN","8HhzD0ZcuI","FU0Cs4j7VP"],"dependent_operators":["AHs5Up7iyr","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1447","layer":2},{"info":"number node, value=7116","layer":2},{"info":"compute binary expreesion, left_input=1447, right_input=7116, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-6301461","layer":1},{"info":"number node, value=1215","layer":2},{"info":"compute unary expreesion, input=1215, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-179554","layer":1},{"info":"compute binary expreesion, left_input=-6301461, right_input=-179554, 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":3,"result_base":3,"text":"(⫏≰1222121⨽⫏≰100202120)+⇶⊼(⫏≰1200000↛⩡⫤)=NaN","reverse_text":"NaN=(⫏≰1222121⨽⫏≰100202120)+⇶⊼(⫏≰1200000↛⩡⫤)","cot":[{"info":"⫏≰1222121⨽⫏≰100202120=⫏≰-102212010222110","layer":1},{"info":"⫏≰1200000↛⩡⫤=⫏≰-100010022011","layer":1},{"info":"⫏≰-102212010222110+⇶⊼⫏≰-100010022011=NaN","layer":0}]}
{"id":852,"expression_no_base_symbol":"($1058$⨐⩸⫘$2112$)⪮%⊝($2390$∸)","expression":"(⫏≰1110012⨐⩸⫘⫏≰2220020)⪮%⊝(⫏≰10021112∸)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":187,"operation_count":3,"complexity_ratio":62.333333333333336,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":1058,"base":3},"right_expr":{"type":"numeric_atoms","value":2112,"base":3}},"right_expr":{"type":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":2390,"base":3}}},"used_operators":["IWmyXbctLI","fu6greOZ01","o20kRiQErp"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","3ViojmjbAp","tmPS8pqC7x"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1058","layer":2},{"info":"number node, value=2112","layer":2},{"info":"compute binary expreesion, left_input=1058, right_input=2112, 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=2390","layer":2},{"info":"compute unary expreesion, input=2390, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=177, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1110012⨐⩸⫘⫏≰2220020)⪮%⊝(⫏≰10021112∸)=NaN","reverse_text":"NaN=(⫏≰1110012⨐⩸⫘⫏≰2220020)⪮%⊝(⫏≰10021112∸)","cot":[{"info":"⫏≰1110012⨐⩸⫘⫏≰2220020=NaN","layer":1},{"info":"⫏≰10021112∸=⫏≰20120","layer":1},{"info":"NaN⪮%⊝⫏≰20120=NaN","layer":0}]}
{"id":853,"expression_no_base_symbol":"$1470$⪛$1033$⨓(↽≂$2945$)","expression":"⫏≰2000110⪛⫏≰1102021⨓(↽≂⫏≰11001002)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":5903,"operation_count":3,"complexity_ratio":1967.6666666666667,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":1470,"base":3},"right_expr":{"type":"numeric_atoms","value":1033,"base":3}},"right_expr":{"type":"unary","operator":"↽≂","unary_expr":{"type":"numeric_atoms","value":2945,"base":3}}},"used_operators":["3ViojmjbAp","uFcxV4UQCh","u6S6b8DprG"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰22002001","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1470","layer":2},{"info":"number node, value=1033","layer":2},{"info":"compute binary expreesion, left_input=1470, right_input=1033, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=437","layer":1},{"info":"number node, value=2945","layer":2},{"info":"compute unary expreesion, input=2945, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-5890","layer":1},{"info":"compute binary expreesion, left_input=437, right_input=-5890, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=5887","layer":0}],"base":3,"result_base":3,"text":"⫏≰2000110⪛⫏≰1102021⨓(↽≂⫏≰11001002)=⫏≰22002001","reverse_text":"⫏≰22002001=⫏≰2000110⪛⫏≰1102021⨓(↽≂⫏≰11001002)","cot":[{"info":"⫏≰2000110⪛⫏≰1102021=⫏≰121012","layer":1},{"info":"↽≂⫏≰11001002=⫏≰-22002011","layer":1},{"info":"⫏≰121012⨓⫏≰-22002011=⫏≰22002001","layer":0}]}
{"id":854,"expression_no_base_symbol":"($3211$⋫)↬($7192$⨐⩸⫘$3120$)","expression":"(⫏≰11101221⋫)↬(⫏≰100212101⨐⩸⫘⫏≰11021120)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3213,"operation_count":3,"complexity_ratio":1071.0,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":3211,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":7192,"base":3},"right_expr":{"type":"numeric_atoms","value":3120,"base":3}}},"used_operators":["B5M0gjZbta","JL8yIekQnl","fu6greOZ01"],"dependent_operators":["rGHVDoGpnC","tmPS8pqC7x","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3211","layer":2},{"info":"compute unary expreesion, input=3211, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=3211","layer":1},{"info":"number node, value=7192","layer":2},{"info":"number node, value=3120","layer":2},{"info":"compute binary expreesion, left_input=7192, right_input=3120, 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=3211, right_input=nan, 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":3,"result_base":3,"text":"(⫏≰11101221⋫)↬(⫏≰100212101⨐⩸⫘⫏≰11021120)=NaN","reverse_text":"NaN=(⫏≰11101221⋫)↬(⫏≰100212101⨐⩸⫘⫏≰11021120)","cot":[{"info":"⫏≰11101221⋫=⫏≰11101221","layer":1},{"info":"⫏≰100212101⨐⩸⫘⫏≰11021120=NaN","layer":1},{"info":"⫏≰11101221↬NaN=NaN","layer":0}]}
{"id":855,"expression_no_base_symbol":"$1019$⪨≂$2933$⨵⪆$2757$≎⊠⪸$1987$","expression":"⫏≰1101202⪨≂⫏≰11000122⨵⪆⫏≰10210010≎⊠⪸⫏≰2201121","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":276,"operation_count":3,"complexity_ratio":92.0,"tree":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":1019,"base":3},"right_expr":{"type":"numeric_atoms","value":2933,"base":3}},"right_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":2757,"base":3},"right_expr":{"type":"numeric_atoms","value":1987,"base":3}}},"used_operators":["2DQ55sFlQl","sdazOOVcIp","bJkvcejdHO"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"⫏≰12221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1019","layer":2},{"info":"number node, value=2933","layer":2},{"info":"compute binary expreesion, left_input=1019, right_input=2933, 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=-3726","layer":1},{"info":"number node, value=2757","layer":2},{"info":"number node, value=1987","layer":2},{"info":"compute binary expreesion, left_input=2757, right_input=1987, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=713590","layer":1},{"info":"compute binary expreesion, left_input=-3726, right_input=713590, op_id = 2DQ55sFlQl binary_op_definition= 'a⨵⪆b = { (402-242) , if b!=134 ; (-a) , else }', output=160","layer":0}],"base":3,"result_base":3,"text":"⫏≰1101202⪨≂⫏≰11000122⨵⪆⫏≰10210010≎⊠⪸⫏≰2201121=⫏≰12221","reverse_text":"⫏≰12221=⫏≰1101202⪨≂⫏≰11000122⨵⪆⫏≰10210010≎⊠⪸⫏≰2201121","cot":[{"info":"⫏≰1101202⪨≂⫏≰11000122=⫏≰-12010000","layer":1},{"info":"⫏≰10210010≎⊠⪸⫏≰2201121=⫏≰1100020212021","layer":1},{"info":"⫏≰-12010000⨵⪆⫏≰1100020212021=⫏≰12221","layer":0}]}
{"id":856,"expression_no_base_symbol":"($1574$⪄$1057$)⋓($2830$⋫)","expression":"(⫏≰2011022⪄⫏≰1110011)⋓(⫏≰10212211⋫)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2938,"operation_count":3,"complexity_ratio":979.3333333333334,"tree":{"type":"binary","operator":"⋓","left_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":1574,"base":3},"right_expr":{"type":"numeric_atoms","value":1057,"base":3}},"right_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":2830,"base":3}}},"used_operators":["T2fj7uvVaJ","SUmda5xLS4","JL8yIekQnl"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","tmPS8pqC7x"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1574","layer":2},{"info":"number node, value=1057","layer":2},{"info":"compute binary expreesion, left_input=1574, right_input=1057, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-233269","layer":1},{"info":"number node, value=2830","layer":2},{"info":"compute unary expreesion, input=2830, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=2830","layer":1},{"info":"compute binary expreesion, left_input=-233269, right_input=2830, 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":3,"result_base":3,"text":"(⫏≰2011022⪄⫏≰1110011)⋓(⫏≰10212211⋫)=⫏≰0","reverse_text":"⫏≰0=(⫏≰2011022⪄⫏≰1110011)⋓(⫏≰10212211⋫)","cot":[{"info":"⫏≰2011022⪄⫏≰1110011=⫏≰-102211222121","layer":1},{"info":"⫏≰10212211⋫=⫏≰10212211","layer":1},{"info":"⫏≰-102211222121⋓⫏≰10212211=⫏≰0","layer":0}]}
{"id":857,"expression_no_base_symbol":"$1122$⫸⊐$5913$≋⫹","expression":"⫏≰1112120⫸⊐⫏≰22010000≋⫹","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":1122,"base":3},"right_expr":{"type":"numeric_atoms","value":5913,"base":3}}},"used_operators":["N41Kp7NANJ","mqXw5SEYmG"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"⫏≰-2101112202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1122","layer":2},{"info":"number node, value=5913","layer":2},{"info":"compute binary expreesion, left_input=1122, right_input=5913, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=23527","layer":1},{"info":"compute unary expreesion, input=23527, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-47054","layer":0}],"base":3,"result_base":3,"text":"⫏≰1112120⫸⊐⫏≰22010000≋⫹=⫏≰-2101112202","reverse_text":"⫏≰-2101112202=⫏≰1112120⫸⊐⫏≰22010000≋⫹","cot":[{"info":"⫏≰1112120⫸⊐⫏≰22010000=⫏≰1012021101","layer":1},{"info":"⫏≰1012021101≋⫹=⫏≰-2101112202","layer":0}]}
{"id":858,"expression_no_base_symbol":"⫓⪴$1424$⨪↰⇹$6173$","expression":"⫓⪴⫏≰1221202⨪↰⇹⫏≰22110122","highest_n_order":3,"priority_hierarchical_complexity":1,"normalized_expansion_degree":2848,"operation_count":2,"complexity_ratio":1424.0,"tree":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":1424,"base":3},"right_expr":{"type":"numeric_atoms","value":6173,"base":3}}},"used_operators":["eLxqMNBOBk","tmPS8pqC7x"],"dependent_operators":["9HNa5Wba9A","rJVOvQCfKK"],"result":"⫏≰10211000120211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1424","layer":2},{"info":"number node, value=6173","layer":2},{"info":"compute binary expreesion, left_input=1424, right_input=6173, 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=1424","layer":1},{"info":"compute unary expreesion, input=1424, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=2027776","layer":0}],"base":3,"result_base":3,"text":"⫓⪴⫏≰1221202⨪↰⇹⫏≰22110122=⫏≰10211000120211","reverse_text":"⫏≰10211000120211=⫓⪴⫏≰1221202⨪↰⇹⫏≰22110122","cot":[{"info":"⫏≰1221202⨪↰⇹⫏≰22110122=⫏≰1221202","layer":1},{"info":"⫓⪴⫏≰1221202=⫏≰10211000120211","layer":0}]}
{"id":859,"expression_no_base_symbol":"⫛⫱⨽($2296$⪠⩆⊳)","expression":"⫛⫱⨽(⫏≰10011001⪠⩆⊳)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":918,"operation_count":2,"complexity_ratio":459.0,"tree":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"unary","operator":"⪠⩆⊳","unary_expr":{"type":"numeric_atoms","value":2296,"base":3}}},"used_operators":["DlLNRPXxWL","JLbD19bQDL"],"dependent_operators":["rGHVDoGpnC","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2296","layer":2},{"info":"compute unary expreesion, input=2296, 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":"compute unary expreesion, input=0, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫛⫱⨽(⫏≰10011001⪠⩆⊳)=⫏≰0","reverse_text":"⫏≰0=⫛⫱⨽(⫏≰10011001⪠⩆⊳)","cot":[{"info":"⫏≰10011001⪠⩆⊳=⫏≰0","layer":1},{"info":"⫛⫱⨽⫏≰0=⫏≰0","layer":0}]}
{"id":860,"expression_no_base_symbol":"($2102$⋳⪒$1757$)↬($4268$⪄$1008$)","expression":"(⫏≰2212212⋳⪒⫏≰2102002)↬(⫏≰12212002⪄⫏≰1101100)","highest_n_order":5,"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":2102,"base":3},"right_expr":{"type":"numeric_atoms","value":1757,"base":3}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":4268,"base":3},"right_expr":{"type":"numeric_atoms","value":1008,"base":3}}},"used_operators":["B5M0gjZbta","12rbrZMWeM","SUmda5xLS4"],"dependent_operators":["rGHVDoGpnC","rysDP5nf3Z","t8gj7n24qd","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2102","layer":2},{"info":"number node, value=1757","layer":2},{"info":"compute binary expreesion, left_input=2102, right_input=1757, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=2160","layer":1},{"info":"number node, value=4268","layer":2},{"info":"number node, value=1008","layer":2},{"info":"compute binary expreesion, left_input=4268, right_input=1008, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-631785","layer":1},{"info":"compute binary expreesion, left_input=2160, right_input=-631785, 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":3,"result_base":3,"text":"(⫏≰2212212⋳⪒⫏≰2102002)↬(⫏≰12212002⪄⫏≰1101100)=NaN","reverse_text":"NaN=(⫏≰2212212⋳⪒⫏≰2102002)↬(⫏≰12212002⪄⫏≰1101100)","cot":[{"info":"⫏≰2212212⋳⪒⫏≰2102002=⫏≰2222000","layer":1},{"info":"⫏≰12212002⪄⫏≰1101100=⫏≰-1012002122110","layer":1},{"info":"⫏≰2222000↬⫏≰-1012002122110=NaN","layer":0}]}
{"id":861,"expression_no_base_symbol":"($3763$⊴$1302$)≹⇙⪍(↣≠⋷$4538$)","expression":"(⫏≰12011101⊴⫏≰1210020)≹⇙⪍(↣≠⋷⫏≰20020002)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5645,"operation_count":3,"complexity_ratio":1881.6666666666667,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":3763,"base":3},"right_expr":{"type":"numeric_atoms","value":1302,"base":3}},"right_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":4538,"base":3}}},"used_operators":["AHs5Up7iyr","Nsiff2A1zJ","Asc51vEJeQ"],"dependent_operators":["dWAJyo7jo9","dWAJyo7jo9","14qkJME0vr","XhwjNDsVaA","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3763","layer":2},{"info":"number node, value=1302","layer":2},{"info":"compute binary expreesion, left_input=3763, right_input=1302, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=4538","layer":2},{"info":"compute unary expreesion, input=4538, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, 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":3,"result_base":3,"text":"(⫏≰12011101⊴⫏≰1210020)≹⇙⪍(↣≠⋷⫏≰20020002)=NaN","reverse_text":"NaN=(⫏≰12011101⊴⫏≰1210020)≹⇙⪍(↣≠⋷⫏≰20020002)","cot":[{"info":"⫏≰12011101⊴⫏≰1210020=NaN","layer":1},{"info":"↣≠⋷⫏≰20020002=NaN","layer":1},{"info":"NaN≹⇙⪍NaN=NaN","layer":0}]}
{"id":862,"expression_no_base_symbol":"(∥⊫$1601$)⪘⫢$2110$⨪↰⇹$4391$","expression":"(∥⊫⫏≰2012022)⪘⫢⫏≰2220011⨪↰⇹⫏≰20000122","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2129,"operation_count":3,"complexity_ratio":709.6666666666666,"tree":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"numeric_atoms","value":1601,"base":3}},"right_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":2110,"base":3},"right_expr":{"type":"numeric_atoms","value":4391,"base":3}}},"used_operators":["oacrs7FA3X","P8v4zCKN1o","tmPS8pqC7x"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","W4YGzv6Whe","t8gj7n24qd","rJVOvQCfKK"],"result":"⫏≰20121022","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1601","layer":2},{"info":"compute unary expreesion, input=1601, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=2469","layer":1},{"info":"number node, value=2110","layer":2},{"info":"number node, value=4391","layer":2},{"info":"compute binary expreesion, left_input=2110, right_input=4391, 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=2110","layer":1},{"info":"compute binary expreesion, left_input=2469, right_input=2110, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=4814","layer":0}],"base":3,"result_base":3,"text":"(∥⊫⫏≰2012022)⪘⫢⫏≰2220011⨪↰⇹⫏≰20000122=⫏≰20121022","reverse_text":"⫏≰20121022=(∥⊫⫏≰2012022)⪘⫢⫏≰2220011⨪↰⇹⫏≰20000122","cot":[{"info":"∥⊫⫏≰2012022=⫏≰10101110","layer":1},{"info":"⫏≰2220011⨪↰⇹⫏≰20000122=⫏≰2220011","layer":1},{"info":"⫏≰10101110⪘⫢⫏≰2220011=⫏≰20121022","layer":0}]}
{"id":863,"expression_no_base_symbol":"$3912$≧⫂∧$1098$≭($7877$⫥∨⫟$5373$)","expression":"⫏≰12100220≧⫂∧⫏≰1111200≭(⫏≰101210202⫥∨⫟⫏≰21101000)","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":3912,"base":3},"right_expr":{"type":"numeric_atoms","value":1098,"base":3}},"right_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":7877,"base":3},"right_expr":{"type":"numeric_atoms","value":5373,"base":3}}},"used_operators":["rxpJgHHUmx","Ph9nP6C5qx","KYD54nUTWz"],"dependent_operators":["AHs5Up7iyr","rysDP5nf3Z","t8gj7n24qd","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3912","layer":2},{"info":"number node, value=1098","layer":2},{"info":"compute binary expreesion, left_input=3912, right_input=1098, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=625","layer":1},{"info":"number node, value=7877","layer":2},{"info":"number node, value=5373","layer":2},{"info":"compute binary expreesion, left_input=7877, right_input=5373, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=625, right_input=nan, 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":3,"result_base":3,"text":"⫏≰12100220≧⫂∧⫏≰1111200≭(⫏≰101210202⫥∨⫟⫏≰21101000)=NaN","reverse_text":"NaN=⫏≰12100220≧⫂∧⫏≰1111200≭(⫏≰101210202⫥∨⫟⫏≰21101000)","cot":[{"info":"⫏≰12100220≧⫂∧⫏≰1111200=⫏≰212011","layer":1},{"info":"⫏≰101210202⫥∨⫟⫏≰21101000=NaN","layer":1},{"info":"⫏≰212011≭NaN=NaN","layer":0}]}
{"id":864,"expression_no_base_symbol":"($3237$⊘)⋷(↣≠⋷$3165$)","expression":"(⫏≰11102220⊘)⋷(↣≠⋷⫏≰11100020)","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":"unary","operator":"⊘","unary_expr":{"type":"numeric_atoms","value":3237,"base":3}},"right_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":3165,"base":3}}},"used_operators":["23Mk6UjR3U","gu96TGCTMs","Asc51vEJeQ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D","XhwjNDsVaA","AHs5Up7iyr"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3237","layer":2},{"info":"compute unary expreesion, input=3237, 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=3165","layer":2},{"info":"compute unary expreesion, input=3165, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=nan, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11102220⊘)⋷(↣≠⋷⫏≰11100020)=⫏≰0","reverse_text":"⫏≰0=(⫏≰11102220⊘)⋷(↣≠⋷⫏≰11100020)","cot":[{"info":"⫏≰11102220⊘=⫏≰0","layer":1},{"info":"↣≠⋷⫏≰11100020=NaN","layer":1},{"info":"⫏≰0⋷NaN=⫏≰0","layer":0}]}
{"id":865,"expression_no_base_symbol":"($1933$⨳⩥⨓$1558$)∼($4603$⊠≄⫣)","expression":"(⫏≰2122121⨳⩥⨓⫏≰2010201)∼(⫏≰20022111⊠≄⫣)","highest_n_order":4,"priority_hierarchical_complexity":2,"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":1933,"base":3},"right_expr":{"type":"numeric_atoms","value":1558,"base":3}},"right_expr":{"type":"unary","operator":"⊠≄⫣","unary_expr":{"type":"numeric_atoms","value":4603,"base":3}}},"used_operators":["DyGG3AbaNP","nCS4ZIUYfx","DIvbN7qnHd"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","W4YGzv6Whe","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰202","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1933","layer":2},{"info":"number node, value=1558","layer":2},{"info":"compute binary expreesion, left_input=1933, right_input=1558, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-375","layer":1},{"info":"number node, value=4603","layer":2},{"info":"compute unary expreesion, input=4603, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-375, right_input=0, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=20","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2122121⨳⩥⨓⫏≰2010201)∼(⫏≰20022111⊠≄⫣)=⫏≰202","reverse_text":"⫏≰202=(⫏≰2122121⨳⩥⨓⫏≰2010201)∼(⫏≰20022111⊠≄⫣)","cot":[{"info":"⫏≰2122121⨳⩥⨓⫏≰2010201=⫏≰-111220","layer":1},{"info":"⫏≰20022111⊠≄⫣=⫏≰0","layer":1},{"info":"⫏≰-111220∼⫏≰0=⫏≰202","layer":0}]}
{"id":866,"expression_no_base_symbol":"↽≂($7461$⪨≂$2768$)","expression":"↽≂(⫏≰101020100⪨≂⫏≰10210112)","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":7461,"base":3},"right_expr":{"type":"numeric_atoms","value":2768,"base":3}}},"used_operators":["u6S6b8DprG","sdazOOVcIp"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-222000211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7461","layer":2},{"info":"number node, value=2768","layer":2},{"info":"compute binary expreesion, left_input=7461, right_input=2768, 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=9488","layer":1},{"info":"compute unary expreesion, input=9488, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-18976","layer":0}],"base":3,"result_base":3,"text":"↽≂(⫏≰101020100⪨≂⫏≰10210112)=⫏≰-222000211","reverse_text":"⫏≰-222000211=↽≂(⫏≰101020100⪨≂⫏≰10210112)","cot":[{"info":"⫏≰101020100⪨≂⫏≰10210112=⫏≰111000102","layer":1},{"info":"↽≂⫏≰111000102=⫏≰-222000211","layer":0}]}
{"id":867,"expression_no_base_symbol":"$1242$⊴$3136$⊭↱($3937$*$1554$)","expression":"⫏≰1201000⊴⫏≰11022011⊭↱(⫏≰12101211*⫏≰2010120)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":4702,"operation_count":3,"complexity_ratio":1567.3333333333333,"tree":{"type":"binary","operator":"⊭↱","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1242,"base":3},"right_expr":{"type":"numeric_atoms","value":3136,"base":3}},"right_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":3937,"base":3},"right_expr":{"type":"numeric_atoms","value":1554,"base":3}}},"used_operators":["COABgblf1C","Nsiff2A1zJ","9HNa5Wba9A"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","14qkJME0vr","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1242","layer":2},{"info":"number node, value=3136","layer":2},{"info":"compute binary expreesion, left_input=1242, right_input=3136, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=3937","layer":2},{"info":"number node, value=1554","layer":2},{"info":"compute binary expreesion, left_input=3937, right_input=1554, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=6118098","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=6118098, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰1201000⊴⫏≰11022011⊭↱(⫏≰12101211*⫏≰2010120)=NaN","reverse_text":"NaN=⫏≰1201000⊴⫏≰11022011⊭↱(⫏≰12101211*⫏≰2010120)","cot":[{"info":"⫏≰1201000⊴⫏≰11022011=NaN","layer":1},{"info":"⫏≰12101211*⫏≰2010120=⫏≰102111211110020","layer":1},{"info":"NaN⊭↱⫏≰102111211110020=NaN","layer":0}]}
{"id":868,"expression_no_base_symbol":"$2197$⨟⋌⩍$1477$⨽($6371$↪⪝)","expression":"⫏≰10000101⨟⋌⩍⫏≰2000201⨽(⫏≰22201222↪⪝)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":711,"operation_count":3,"complexity_ratio":237.0,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":2197,"base":3},"right_expr":{"type":"numeric_atoms","value":1477,"base":3}},"right_expr":{"type":"unary","operator":"↪⪝","unary_expr":{"type":"numeric_atoms","value":6371,"base":3}}},"used_operators":["8HhzD0ZcuI","rGHVDoGpnC","l07mrZUIn9"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","Tcnh7f0tEr","9HNa5Wba9A","2DDjHMKMc0"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2197","layer":2},{"info":"number node, value=1477","layer":2},{"info":"compute binary expreesion, left_input=2197, right_input=1477, 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=6371","layer":2},{"info":"compute unary expreesion, input=6371, op_id = l07mrZUIn9, unary_op_definition = 'a↪⪝ = { ((103⋝⋈⪟a)*(594*a)) }', output=389790522","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=389790522, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰10000101⨟⋌⩍⫏≰2000201⨽(⫏≰22201222↪⪝)=NaN","reverse_text":"NaN=⫏≰10000101⨟⋌⩍⫏≰2000201⨽(⫏≰22201222↪⪝)","cot":[{"info":"⫏≰10000101⨟⋌⩍⫏≰2000201=NaN","layer":1},{"info":"⫏≰22201222↪⪝=⫏≰1000011110102002000","layer":1},{"info":"NaN⨽⫏≰1000011110102002000=NaN","layer":0}]}
{"id":869,"expression_no_base_symbol":"$1485$⨸⪁$3817$+(⊙↵-$2819$)","expression":"⫏≰2001000⨸⪁⫏≰12020101+(⊙↵-⫏≰10212102)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2869,"operation_count":3,"complexity_ratio":956.3333333333334,"tree":{"type":"binary","operator":"+","left_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":1485,"base":3},"right_expr":{"type":"numeric_atoms","value":3817,"base":3}},"right_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":2819,"base":3}}},"used_operators":["W4YGzv6Whe","g55IO6H4Gj","oWn0xqSxBt"],"dependent_operators":["W4YGzv6Whe","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"⫏≰112112201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1485","layer":2},{"info":"number node, value=3817","layer":2},{"info":"compute binary expreesion, left_input=1485, right_input=3817, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=10604","layer":1},{"info":"number node, value=2819","layer":2},{"info":"compute unary expreesion, input=2819, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute binary expreesion, left_input=10604, right_input=-1, op_id = W4YGzv6Whe binary_op_definition= 'None', output=10603","layer":0}],"base":3,"result_base":3,"text":"⫏≰2001000⨸⪁⫏≰12020101+(⊙↵-⫏≰10212102)=⫏≰112112201","reverse_text":"⫏≰112112201=⫏≰2001000⨸⪁⫏≰12020101+(⊙↵-⫏≰10212102)","cot":[{"info":"⫏≰2001000⨸⪁⫏≰12020101=⫏≰112112202","layer":1},{"info":"⊙↵-⫏≰10212102=⫏≰-1","layer":1},{"info":"⫏≰112112202+⫏≰-1=⫏≰112112201","layer":0}]}
{"id":870,"expression_no_base_symbol":"($3698$⇼⇔∾$1138$)≎⊠⪸($3990$⫥∨⫟$1029$)","expression":"(⫏≰12001222⇼⇔∾⫏≰1120011)≎⊠⪸(⫏≰12110210⫥∨⫟⫏≰1102010)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":167,"operation_count":3,"complexity_ratio":55.666666666666664,"tree":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":3698,"base":3},"right_expr":{"type":"numeric_atoms","value":1138,"base":3}},"right_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":3990,"base":3},"right_expr":{"type":"numeric_atoms","value":1029,"base":3}}},"used_operators":["bJkvcejdHO","tifHPKVTfV","KYD54nUTWz"],"dependent_operators":["DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","rysDP5nf3Z","t8gj7n24qd","8HhzD0ZcuI","rGHVDoGpnC"],"result":"⫏≰2111","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3698","layer":2},{"info":"number node, value=1138","layer":2},{"info":"compute binary expreesion, left_input=3698, right_input=1138, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-2560","layer":1},{"info":"number node, value=3990","layer":2},{"info":"number node, value=1029","layer":2},{"info":"compute binary expreesion, left_input=3990, right_input=1029, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-2560, right_input=nan, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=67","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12001222⇼⇔∾⫏≰1120011)≎⊠⪸(⫏≰12110210⫥∨⫟⫏≰1102010)=⫏≰2111","reverse_text":"⫏≰2111=(⫏≰12001222⇼⇔∾⫏≰1120011)≎⊠⪸(⫏≰12110210⫥∨⫟⫏≰1102010)","cot":[{"info":"⫏≰12001222⇼⇔∾⫏≰1120011=⫏≰-10111211","layer":1},{"info":"⫏≰12110210⫥∨⫟⫏≰1102010=NaN","layer":1},{"info":"⫏≰-10111211≎⊠⪸NaN=⫏≰2111","layer":0}]}
{"id":871,"expression_no_base_symbol":"($6538$≭$3634$)∑⇟⊟($4204$⊪)","expression":"(⫏≰22222011≭⫏≰11222121)∑⇟⊟(⫏≰12202201⊪)","highest_n_order":5,"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":6538,"base":3},"right_expr":{"type":"numeric_atoms","value":3634,"base":3}},"right_expr":{"type":"unary","operator":"⊪","unary_expr":{"type":"numeric_atoms","value":4204,"base":3}}},"used_operators":["U7g4x0WXJJ","rxpJgHHUmx","zVYPLywUTj"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","AHs5Up7iyr","sdazOOVcIp","XhwjNDsVaA","BjRHVeLaeN","9HNa5Wba9A","Qy55tPpLXF","Ph9nP6C5qx","2DQ55sFlQl","f6k1SAg4EE","e1ybzncUwg","W4YGzv6Whe","8w2t5hMYqp","JLbD19bQDL"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=6538","layer":2},{"info":"number node, value=3634","layer":2},{"info":"compute binary expreesion, left_input=6538, right_input=3634, 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=4204","layer":2},{"info":"compute unary expreesion, input=4204, 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=nan, right_input=0, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22222011≭⫏≰11222121)∑⇟⊟(⫏≰12202201⊪)=NaN","reverse_text":"NaN=(⫏≰22222011≭⫏≰11222121)∑⇟⊟(⫏≰12202201⊪)","cot":[{"info":"⫏≰22222011≭⫏≰11222121=NaN","layer":1},{"info":"⫏≰12202201⊪=⫏≰0","layer":1},{"info":"NaN∑⇟⊟⫏≰0=NaN","layer":0}]}
{"id":872,"expression_no_base_symbol":"⊥($2690$⨳⩥⨓$1056$)","expression":"⊥(⫏≰10200122⨳⩥⨓⫏≰1110010)","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":2690,"base":3},"right_expr":{"type":"numeric_atoms","value":1056,"base":3}}},"used_operators":["Q3PJZHRvZv","nCS4ZIUYfx"],"dependent_operators":["fu6greOZ01","W4YGzv6Whe","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2690","layer":2},{"info":"number node, value=1056","layer":2},{"info":"compute binary expreesion, left_input=2690, right_input=1056, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-1634","layer":1},{"info":"compute unary expreesion, input=-1634, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊥(⫏≰10200122⨳⩥⨓⫏≰1110010)=NaN","reverse_text":"NaN=⊥(⫏≰10200122⨳⩥⨓⫏≰1110010)","cot":[{"info":"⫏≰10200122⨳⩥⨓⫏≰1110010=⫏≰-2020112","layer":1},{"info":"⊥⫏≰-2020112=NaN","layer":0}]}
{"id":873,"expression_no_base_symbol":"($1058$⫸⊐$1191$)≧⫂∧($3054$⊉≛↸$6573$)","expression":"(⫏≰1110012⫸⊐⫏≰1122010)≧⫂∧(⫏≰11012010⊉≛↸⫏≰100000110)","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":1058,"base":3},"right_expr":{"type":"numeric_atoms","value":1191,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":3054,"base":3},"right_expr":{"type":"numeric_atoms","value":6573,"base":3}}},"used_operators":["Ph9nP6C5qx","mqXw5SEYmG","DZ8iAZOCBD"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21201201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1058","layer":2},{"info":"number node, value=1191","layer":2},{"info":"compute binary expreesion, left_input=1058, right_input=1191, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=4639","layer":1},{"info":"number node, value=3054","layer":2},{"info":"number node, value=6573","layer":2},{"info":"compute binary expreesion, left_input=3054, right_input=6573, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=6108","layer":1},{"info":"compute binary expreesion, left_input=4639, right_input=6108, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=5635","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1110012⫸⊐⫏≰1122010)≧⫂∧(⫏≰11012010⊉≛↸⫏≰100000110)=⫏≰21201201","reverse_text":"⫏≰21201201=(⫏≰1110012⫸⊐⫏≰1122010)≧⫂∧(⫏≰11012010⊉≛↸⫏≰100000110)","cot":[{"info":"⫏≰1110012⫸⊐⫏≰1122010=⫏≰20100211","layer":1},{"info":"⫏≰11012010⊉≛↸⫏≰100000110=⫏≰22101020","layer":1},{"info":"⫏≰20100211≧⫂∧⫏≰22101020=⫏≰21201201","layer":0}]}
{"id":874,"expression_no_base_symbol":"($2887$⫡⨏$6263$)%(⨵≀≌$1918$)","expression":"(⫏≰10221221⫡⨏⫏≰22120222)%(⨵≀≌⫏≰2122001)","highest_n_order":2,"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":2887,"base":3},"right_expr":{"type":"numeric_atoms","value":6263,"base":3}},"right_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":1918,"base":3}}},"used_operators":["k8jYdgA6NY","QMFrweE19q","srAu1WTS94"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A"],"result":"⫏≰-1102000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2887","layer":2},{"info":"number node, value=6263","layer":2},{"info":"compute binary expreesion, left_input=2887, right_input=6263, 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=27744","layer":1},{"info":"number node, value=1918","layer":2},{"info":"compute unary expreesion, input=1918, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-5754","layer":1},{"info":"compute binary expreesion, left_input=27744, right_input=-5754, op_id = k8jYdgA6NY binary_op_definition= 'None', output=-1026","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10221221⫡⨏⫏≰22120222)%(⨵≀≌⫏≰2122001)=⫏≰-1102000","reverse_text":"⫏≰-1102000=(⫏≰10221221⫡⨏⫏≰22120222)%(⨵≀≌⫏≰2122001)","cot":[{"info":"⫏≰10221221⫡⨏⫏≰22120222=⫏≰1102001120","layer":1},{"info":"⨵≀≌⫏≰2122001=⫏≰-21220010","layer":1},{"info":"⫏≰1102001120%⫏≰-21220010=⫏≰-1102000","layer":0}]}
{"id":875,"expression_no_base_symbol":"⨈⫕($1859$⩨$4267$)","expression":"⨈⫕(⫏≰2112212⩨⫏≰12212001)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":391,"operation_count":2,"complexity_ratio":195.5,"tree":{"type":"unary","operator":"⨈⫕","unary_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":1859,"base":3},"right_expr":{"type":"numeric_atoms","value":4267,"base":3}}},"used_operators":["megm06wKyl","2DlMacCsIx"],"dependent_operators":["8jW3W4yZS5","TpPTUOHfaN","glklzrTFfD","Q3PJZHRvZv","14qkJME0vr","DhbWaqg5eL","W4YGzv6Whe","Z2TMIBDE3Q","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰-210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1859","layer":2},{"info":"number node, value=4267","layer":2},{"info":"compute binary expreesion, left_input=1859, right_input=4267, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=-6","layer":1},{"info":"compute unary expreesion, input=-6, 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":3,"result_base":3,"text":"⨈⫕(⫏≰2112212⩨⫏≰12212001)=⫏≰-210","reverse_text":"⫏≰-210=⨈⫕(⫏≰2112212⩨⫏≰12212001)","cot":[{"info":"⫏≰2112212⩨⫏≰12212001=⫏≰-20","layer":1},{"info":"⨈⫕⫏≰-20=⫏≰-210","layer":0}]}
{"id":876,"expression_no_base_symbol":"⨞⊢($9350$∲⫓$1550$)","expression":"⨞⊢(⫏≰110211022∲⫓⫏≰2010102)","highest_n_order":1,"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":9350,"base":3},"right_expr":{"type":"numeric_atoms","value":1550,"base":3}}},"used_operators":["xUOZtlo3hN","i8ToyICDmI"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-20110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=9350","layer":2},{"info":"number node, value=1550","layer":2},{"info":"compute binary expreesion, left_input=9350, right_input=1550, 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 = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-174","layer":0}],"base":3,"result_base":3,"text":"⨞⊢(⫏≰110211022∲⫓⫏≰2010102)=⫏≰-20110","reverse_text":"⫏≰-20110=⨞⊢(⫏≰110211022∲⫓⫏≰2010102)","cot":[{"info":"⫏≰110211022∲⫓⫏≰2010102=⫏≰0","layer":1},{"info":"⨞⊢⫏≰0=⫏≰-20110","layer":0}]}
{"id":877,"expression_no_base_symbol":"(≦∁$2888$)⪄($1478$⇼⇔∾$1395$)","expression":"(≦∁⫏≰10221222)⪄(⫏≰2000202⇼⇔∾⫏≰1220200)","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":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":2888,"base":3}},"right_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":1478,"base":3},"right_expr":{"type":"numeric_atoms","value":1395,"base":3}}},"used_operators":["SUmda5xLS4","9ICcGScMcE","tifHPKVTfV"],"dependent_operators":["8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-210111111101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2888","layer":2},{"info":"compute unary expreesion, input=2888, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=2888","layer":1},{"info":"number node, value=1478","layer":2},{"info":"number node, value=1395","layer":2},{"info":"compute binary expreesion, left_input=1478, right_input=1395, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-83","layer":1},{"info":"compute binary expreesion, left_input=2888, right_input=-83, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-423181","layer":0}],"base":3,"result_base":3,"text":"(≦∁⫏≰10221222)⪄(⫏≰2000202⇼⇔∾⫏≰1220200)=⫏≰-210111111101","reverse_text":"⫏≰-210111111101=(≦∁⫏≰10221222)⪄(⫏≰2000202⇼⇔∾⫏≰1220200)","cot":[{"info":"≦∁⫏≰10221222=⫏≰10221222","layer":1},{"info":"⫏≰2000202⇼⇔∾⫏≰1220200=⫏≰-10002","layer":1},{"info":"⫏≰10221222⪄⫏≰-10002=⫏≰-210111111101","layer":0}]}
{"id":878,"expression_no_base_symbol":"($1056$⨰$2928$)⪘⫢($5762$⊭↱$3156$)","expression":"(⫏≰1110010⨰⫏≰11000110)⪘⫢(⫏≰21220102⊭↱⫏≰11022220)","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":1056,"base":3},"right_expr":{"type":"numeric_atoms","value":2928,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":5762,"base":3},"right_expr":{"type":"numeric_atoms","value":3156,"base":3}}},"used_operators":["oacrs7FA3X","eewbuw0ToL","COABgblf1C"],"dependent_operators":["sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-1","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1056","layer":2},{"info":"number node, value=2928","layer":2},{"info":"compute binary expreesion, left_input=1056, right_input=2928, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=-1862","layer":1},{"info":"number node, value=5762","layer":2},{"info":"number node, value=3156","layer":2},{"info":"compute binary expreesion, left_input=5762, right_input=3156, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-5207","layer":1},{"info":"compute binary expreesion, left_input=-1862, right_input=-5207, 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":3,"result_base":3,"text":"(⫏≰1110010⨰⫏≰11000110)⪘⫢(⫏≰21220102⊭↱⫏≰11022220)=⫏≰-1","reverse_text":"⫏≰-1=(⫏≰1110010⨰⫏≰11000110)⪘⫢(⫏≰21220102⊭↱⫏≰11022220)","cot":[{"info":"⫏≰1110010⨰⫏≰11000110=⫏≰-2112222","layer":1},{"info":"⫏≰21220102⊭↱⫏≰11022220=⫏≰-21010212","layer":1},{"info":"⫏≰-2112222⪘⫢⫏≰-21010212=⫏≰-1","layer":0}]}
{"id":879,"expression_no_base_symbol":"↥($1513$⋫)","expression":"↥(⫏≰2002001⋫)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1542,"operation_count":2,"complexity_ratio":771.0,"tree":{"type":"unary","operator":"↥","unary_expr":{"type":"unary","operator":"⋫","unary_expr":{"type":"numeric_atoms","value":1513,"base":3}}},"used_operators":["A8NUZmVepG","JL8yIekQnl"],"dependent_operators":["k8jYdgA6NY","tmPS8pqC7x"],"result":"⫏≰1021","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1513","layer":2},{"info":"compute unary expreesion, input=1513, op_id = JL8yIekQnl, unary_op_definition = 'a⋫ = { (a⨪↰⇹a) }', output=1513","layer":1},{"info":"compute unary expreesion, input=1513, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=34","layer":0}],"base":3,"result_base":3,"text":"↥(⫏≰2002001⋫)=⫏≰1021","reverse_text":"⫏≰1021=↥(⫏≰2002001⋫)","cot":[{"info":"⫏≰2002001⋫=⫏≰2002001","layer":1},{"info":"↥⫏≰2002001=⫏≰1021","layer":0}]}
{"id":880,"expression_no_base_symbol":"↩$1082$⨐⩸⫘$1154$","expression":"↩⫏≰1111002⨐⩸⫘⫏≰1120202","highest_n_order":4,"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":1082,"base":3},"right_expr":{"type":"numeric_atoms","value":1154,"base":3}}},"used_operators":["jLgFTUHLKL","fu6greOZ01"],"dependent_operators":["sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1082","layer":2},{"info":"number node, value=1154","layer":2},{"info":"compute binary expreesion, left_input=1082, right_input=1154, 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 unary expreesion, input=nan, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↩⫏≰1111002⨐⩸⫘⫏≰1120202=NaN","reverse_text":"NaN=↩⫏≰1111002⨐⩸⫘⫏≰1120202","cot":[{"info":"⫏≰1111002⨐⩸⫘⫏≰1120202=NaN","layer":1},{"info":"↩NaN=NaN","layer":0}]}
{"id":881,"expression_no_base_symbol":"($1700$⋷$1480$)⊭↱(⨑⩽⪐$1329$)","expression":"(⫏≰2022222⋷⫏≰2000211)⊭↱(⨑⩽⪐⫏≰1211020)","highest_n_order":1,"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":1700,"base":3},"right_expr":{"type":"numeric_atoms","value":1480,"base":3}},"right_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":1329,"base":3}}},"used_operators":["COABgblf1C","23Mk6UjR3U","AF7qkfDlqP"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰-20100101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1700","layer":2},{"info":"number node, value=1480","layer":2},{"info":"compute binary expreesion, left_input=1700, right_input=1480, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=1260","layer":1},{"info":"number node, value=1329","layer":2},{"info":"compute unary expreesion, input=1329, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-1056","layer":1},{"info":"compute binary expreesion, left_input=1260, right_input=-1056, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=-4627","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2022222⋷⫏≰2000211)⊭↱(⨑⩽⪐⫏≰1211020)=⫏≰-20100101","reverse_text":"⫏≰-20100101=(⫏≰2022222⋷⫏≰2000211)⊭↱(⨑⩽⪐⫏≰1211020)","cot":[{"info":"⫏≰2022222⋷⫏≰2000211=⫏≰1201200","layer":1},{"info":"⨑⩽⪐⫏≰1211020=⫏≰-1110010","layer":1},{"info":"⫏≰1201200⊭↱⫏≰-1110010=⫏≰-20100101","layer":0}]}
{"id":882,"expression_no_base_symbol":"(⪝⪂⫅$1209$)⨽$3243$⨎$1407$","expression":"(⪝⪂⫅⫏≰1122210)⨽⫏≰11110010⨎⫏≰1221010","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":177883,"operation_count":3,"complexity_ratio":59294.333333333336,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"unary","operator":"⪝⪂⫅","unary_expr":{"type":"numeric_atoms","value":1209,"base":3}},"right_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":3243,"base":3},"right_expr":{"type":"numeric_atoms","value":1407,"base":3}}},"used_operators":["8HhzD0ZcuI","XTarYq4gQB","rJVOvQCfKK"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","9HNa5Wba9A","8w2t5hMYqp","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"-Inf","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1209","layer":2},{"info":"compute unary expreesion, input=1209, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=-177723","layer":1},{"info":"number node, value=3243","layer":2},{"info":"number node, value=1407","layer":2},{"info":"compute binary expreesion, left_input=3243, right_input=1407, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=1407","layer":1},{"info":"compute binary expreesion, left_input=-177723, right_input=1407, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-inf","layer":0}],"base":3,"result_base":3,"text":"(⪝⪂⫅⫏≰1122210)⨽⫏≰11110010⨎⫏≰1221010=-Inf","reverse_text":"-Inf=(⪝⪂⫅⫏≰1122210)⨽⫏≰11110010⨎⫏≰1221010","cot":[{"info":"⪝⪂⫅⫏≰1122210=⫏≰-100000210100","layer":1},{"info":"⫏≰11110010⨎⫏≰1221010=⫏≰1221010","layer":1},{"info":"⫏≰-100000210100⨽⫏≰1221010=-Inf","layer":0}]}
{"id":883,"expression_no_base_symbol":"$1612$⋝⋈⪟$6782$⫸⊐(⇁⨣⪵$4298$)","expression":"⫏≰2012201⋝⋈⪟⫏≰100022012⫸⊐(⇁⨣⪵⫏≰12220012)","highest_n_order":5,"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":1612,"base":3},"right_expr":{"type":"numeric_atoms","value":6782,"base":3}},"right_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":4298,"base":3}}},"used_operators":["mqXw5SEYmG","2DDjHMKMc0","inkyxCbjAn"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","W4YGzv6Whe","t8gj7n24qd","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1612","layer":2},{"info":"number node, value=6782","layer":2},{"info":"compute binary expreesion, left_input=1612, right_input=6782, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=1612","layer":1},{"info":"number node, value=4298","layer":2},{"info":"compute unary expreesion, input=4298, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1612, right_input=nan, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2012201⋝⋈⪟⫏≰100022012⫸⊐(⇁⨣⪵⫏≰12220012)=NaN","reverse_text":"NaN=⫏≰2012201⋝⋈⪟⫏≰100022012⫸⊐(⇁⨣⪵⫏≰12220012)","cot":[{"info":"⫏≰2012201⋝⋈⪟⫏≰100022012=⫏≰2012201","layer":1},{"info":"⇁⨣⪵⫏≰12220012=NaN","layer":1},{"info":"⫏≰2012201⫸⊐NaN=NaN","layer":0}]}
{"id":884,"expression_no_base_symbol":"(↽≂$5723$)⩨($1560$⊉≛↸$1007$)","expression":"(↽≂⫏≰21211222)⩨(⫏≰2010210⊉≛↸⫏≰1101022)","highest_n_order":2,"priority_hierarchical_complexity":2,"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":5723,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":1560,"base":3},"right_expr":{"type":"numeric_atoms","value":1007,"base":3}}},"used_operators":["2DlMacCsIx","u6S6b8DprG","DZ8iAZOCBD"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰10","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5723","layer":2},{"info":"compute unary expreesion, input=5723, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-11446","layer":1},{"info":"number node, value=1560","layer":2},{"info":"number node, value=1007","layer":2},{"info":"compute binary expreesion, left_input=1560, right_input=1007, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=3120","layer":1},{"info":"compute binary expreesion, left_input=-11446, right_input=3120, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=3","layer":0}],"base":3,"result_base":3,"text":"(↽≂⫏≰21211222)⩨(⫏≰2010210⊉≛↸⫏≰1101022)=⫏≰10","reverse_text":"⫏≰10=(↽≂⫏≰21211222)⩨(⫏≰2010210⊉≛↸⫏≰1101022)","cot":[{"info":"↽≂⫏≰21211222=⫏≰-120200221","layer":1},{"info":"⫏≰2010210⊉≛↸⫏≰1101022=⫏≰11021120","layer":1},{"info":"⫏≰-120200221⩨⫏≰11021120=⫏≰10","layer":0}]}
{"id":885,"expression_no_base_symbol":"($2869$⫡⨏$3052$)↬($3188$⊘)","expression":"(⫏≰10221021⫡⨏⫏≰11012001)↬(⫏≰11101002⊘)","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":"binary","operator":"⫡⨏","left_expr":{"type":"numeric_atoms","value":2869,"base":3},"right_expr":{"type":"numeric_atoms","value":3052,"base":3}},"right_expr":{"type":"unary","operator":"⊘","unary_expr":{"type":"numeric_atoms","value":3188,"base":3}}},"used_operators":["B5M0gjZbta","QMFrweE19q","gu96TGCTMs"],"dependent_operators":["rGHVDoGpnC","W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","t8gj7n24qd","Ph9nP6C5qx","P8v4zCKN1o","AF7qkfDlqP","eewbuw0ToL","8w2t5hMYqp","NTOWxs364D"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2869","layer":2},{"info":"number node, value=3052","layer":2},{"info":"compute binary expreesion, left_input=2869, right_input=3052, 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=21232","layer":1},{"info":"number node, value=3188","layer":2},{"info":"compute unary expreesion, input=3188, 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":"compute binary expreesion, left_input=21232, right_input=0, 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":3,"result_base":3,"text":"(⫏≰10221021⫡⨏⫏≰11012001)↬(⫏≰11101002⊘)=NaN","reverse_text":"NaN=(⫏≰10221021⫡⨏⫏≰11012001)↬(⫏≰11101002⊘)","cot":[{"info":"⫏≰10221021⫡⨏⫏≰11012001=⫏≰1002010101","layer":1},{"info":"⫏≰11101002⊘=⫏≰0","layer":1},{"info":"⫏≰1002010101↬⫏≰0=NaN","layer":0}]}
{"id":886,"expression_no_base_symbol":"($1102$⫥∨⫟$6561$)↬($7255$⇼⇔∾$1505$)","expression":"(⫏≰1111211⫥∨⫟⫏≰100000000)↬(⫏≰100221201⇼⇔∾⫏≰2001202)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":157,"operation_count":3,"complexity_ratio":52.333333333333336,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1102,"base":3},"right_expr":{"type":"numeric_atoms","value":6561,"base":3}},"right_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":7255,"base":3},"right_expr":{"type":"numeric_atoms","value":1505,"base":3}}},"used_operators":["B5M0gjZbta","KYD54nUTWz","tifHPKVTfV"],"dependent_operators":["rGHVDoGpnC","8HhzD0ZcuI","rGHVDoGpnC","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1102","layer":2},{"info":"number node, value=6561","layer":2},{"info":"compute binary expreesion, left_input=1102, right_input=6561, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=7255","layer":2},{"info":"number node, value=1505","layer":2},{"info":"compute binary expreesion, left_input=7255, right_input=1505, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=-5750","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-5750, 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":3,"result_base":3,"text":"(⫏≰1111211⫥∨⫟⫏≰100000000)↬(⫏≰100221201⇼⇔∾⫏≰2001202)=NaN","reverse_text":"NaN=(⫏≰1111211⫥∨⫟⫏≰100000000)↬(⫏≰100221201⇼⇔∾⫏≰2001202)","cot":[{"info":"⫏≰1111211⫥∨⫟⫏≰100000000=NaN","layer":1},{"info":"⫏≰100221201⇼⇔∾⫏≰2001202=⫏≰-21212222","layer":1},{"info":"NaN↬⫏≰-21212222=NaN","layer":0}]}
{"id":887,"expression_no_base_symbol":"⊙↵-($5187$⪒$2851$)","expression":"⊙↵-(⫏≰21010010⪒⫏≰10220121)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8073,"operation_count":2,"complexity_ratio":4036.5,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":5187,"base":3},"right_expr":{"type":"numeric_atoms","value":2851,"base":3}}},"used_operators":["oWn0xqSxBt","f6k1SAg4EE"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5187","layer":2},{"info":"number node, value=2851","layer":2},{"info":"compute binary expreesion, left_input=5187, right_input=2851, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-8038","layer":1},{"info":"compute unary expreesion, input=-8038, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=196","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⫏≰21010010⪒⫏≰10220121)=⫏≰21021","reverse_text":"⫏≰21021=⊙↵-(⫏≰21010010⪒⫏≰10220121)","cot":[{"info":"⫏≰21010010⪒⫏≰10220121=⫏≰-102000201","layer":1},{"info":"⊙↵-⫏≰-102000201=⫏≰21021","layer":0}]}
{"id":888,"expression_no_base_symbol":"($3110$↺$1219$)⇷($3222$⋥≓≎$1000$)","expression":"(⫏≰11021012↺⫏≰1200011)⇷(⫏≰11102100⋥≓≎⫏≰1101001)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":17080,"operation_count":3,"complexity_ratio":5693.333333333333,"tree":{"type":"binary","operator":"⇷","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":3110,"base":3},"right_expr":{"type":"numeric_atoms","value":1219,"base":3}},"right_expr":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"numeric_atoms","value":3222,"base":3},"right_expr":{"type":"numeric_atoms","value":1000,"base":3}}},"used_operators":["mp7IySMOzn","7j4O788W3g","Qy55tPpLXF"],"dependent_operators":["DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3110","layer":2},{"info":"number node, value=1219","layer":2},{"info":"compute binary expreesion, left_input=3110, right_input=1219, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1219","layer":1},{"info":"number node, value=3222","layer":2},{"info":"number node, value=1000","layer":2},{"info":"compute binary expreesion, left_input=3222, right_input=1000, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-1189","layer":1},{"info":"compute binary expreesion, left_input=1219, right_input=-1189, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11021012↺⫏≰1200011)⇷(⫏≰11102100⋥≓≎⫏≰1101001)=NaN","reverse_text":"NaN=(⫏≰11021012↺⫏≰1200011)⇷(⫏≰11102100⋥≓≎⫏≰1101001)","cot":[{"info":"⫏≰11021012↺⫏≰1200011=⫏≰1200011","layer":1},{"info":"⫏≰11102100⋥≓≎⫏≰1101001=⫏≰-1122001","layer":1},{"info":"⫏≰1200011⇷⫏≰-1122001=NaN","layer":0}]}
{"id":889,"expression_no_base_symbol":"↣≠⋷($1157$⋓$1010$)","expression":"↣≠⋷(⫏≰1120212⋓⫏≰1101102)","highest_n_order":4,"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":1157,"base":3},"right_expr":{"type":"numeric_atoms","value":1010,"base":3}}},"used_operators":["Asc51vEJeQ","T2fj7uvVaJ"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1157","layer":2},{"info":"number node, value=1010","layer":2},{"info":"compute binary expreesion, left_input=1157, right_input=1010, 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 = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(⫏≰1120212⋓⫏≰1101102)=NaN","reverse_text":"NaN=↣≠⋷(⫏≰1120212⋓⫏≰1101102)","cot":[{"info":"⫏≰1120212⋓⫏≰1101102=⫏≰0","layer":1},{"info":"↣≠⋷⫏≰0=NaN","layer":0}]}
{"id":890,"expression_no_base_symbol":"+⊝⨔($5763$/$1982$)","expression":"+⊝⨔(⫏≰21220110/⫏≰2201102)","highest_n_order":3,"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":5763,"base":3},"right_expr":{"type":"numeric_atoms","value":1982,"base":3}}},"used_operators":["DhbWaqg5eL","XhwjNDsVaA"],"dependent_operators":["dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰2002101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5763","layer":2},{"info":"number node, value=1982","layer":2},{"info":"compute binary expreesion, left_input=5763, right_input=1982, op_id = XhwjNDsVaA binary_op_definition= 'None', output=2","layer":1},{"info":"compute unary expreesion, input=2, 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":3,"result_base":3,"text":"+⊝⨔(⫏≰21220110/⫏≰2201102)=⫏≰2002101","reverse_text":"⫏≰2002101=+⊝⨔(⫏≰21220110/⫏≰2201102)","cot":[{"info":"⫏≰21220110/⫏≰2201102=⫏≰2","layer":1},{"info":"+⊝⨔⫏≰2=⫏≰2002101","layer":0}]}
{"id":891,"expression_no_base_symbol":"(⊄⩳↩$2119$)≋⫹","expression":"(⊄⩳↩⫏≰2220111)≋⫹","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":2119,"base":3}}},"used_operators":["N41Kp7NANJ","8w2t5hMYqp"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰122102220","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2119","layer":2},{"info":"compute unary expreesion, input=2119, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-6357","layer":1},{"info":"compute unary expreesion, input=-6357, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=12714","layer":0}],"base":3,"result_base":3,"text":"(⊄⩳↩⫏≰2220111)≋⫹=⫏≰122102220","reverse_text":"⫏≰122102220=(⊄⩳↩⫏≰2220111)≋⫹","cot":[{"info":"⊄⩳↩⫏≰2220111=⫏≰-22201110","layer":1},{"info":"⫏≰-22201110≋⫹=⫏≰122102220","layer":0}]}
{"id":892,"expression_no_base_symbol":"($2814$⨐⩸⫘$2725$)⪮%⊝($2083$≧⫂∧$1253$)","expression":"(⫏≰10212020⨐⩸⫘⫏≰10201221)⪮%⊝(⫏≰2212011≧⫂∧⫏≰1201102)","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":2814,"base":3},"right_expr":{"type":"numeric_atoms","value":2725,"base":3}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":2083,"base":3},"right_expr":{"type":"numeric_atoms","value":1253,"base":3}}},"used_operators":["IWmyXbctLI","fu6greOZ01","Ph9nP6C5qx"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","3ViojmjbAp","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2814","layer":2},{"info":"number node, value=2725","layer":2},{"info":"compute binary expreesion, left_input=2814, right_input=2725, 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=2083","layer":2},{"info":"number node, value=1253","layer":2},{"info":"compute binary expreesion, left_input=2083, right_input=1253, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=780","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=780, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10212020⨐⩸⫘⫏≰10201221)⪮%⊝(⫏≰2212011≧⫂∧⫏≰1201102)=NaN","reverse_text":"NaN=(⫏≰10212020⨐⩸⫘⫏≰10201221)⪮%⊝(⫏≰2212011≧⫂∧⫏≰1201102)","cot":[{"info":"⫏≰10212020⨐⩸⫘⫏≰10201221=NaN","layer":1},{"info":"⫏≰2212011≧⫂∧⫏≰1201102=⫏≰1001220","layer":1},{"info":"NaN⪮%⊝⫏≰1001220=NaN","layer":0}]}
{"id":893,"expression_no_base_symbol":"$1366$⩷∴$4238$⫸⊐$2498$⨟⋌⩍$3917$","expression":"⫏≰1212121⩷∴⫏≰12210222⫸⊐⫏≰10102112⨟⋌⩍⫏≰12101002","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":1366,"base":3},"right_expr":{"type":"numeric_atoms","value":4238,"base":3}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":2498,"base":3},"right_expr":{"type":"numeric_atoms","value":3917,"base":3}}},"used_operators":["mqXw5SEYmG","9FxExcQeMw","rGHVDoGpnC"],"dependent_operators":["QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","rysDP5nf3Z","Tcnh7f0tEr"],"result":"⫏≰1022212","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1366","layer":2},{"info":"number node, value=4238","layer":2},{"info":"compute binary expreesion, left_input=1366, right_input=4238, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-5776","layer":1},{"info":"number node, value=2498","layer":2},{"info":"number node, value=3917","layer":2},{"info":"compute binary expreesion, left_input=2498, right_input=3917, 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=-5776, right_input=nan, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=968","layer":0}],"base":3,"result_base":3,"text":"⫏≰1212121⩷∴⫏≰12210222⫸⊐⫏≰10102112⨟⋌⩍⫏≰12101002=⫏≰1022212","reverse_text":"⫏≰1022212=⫏≰1212121⩷∴⫏≰12210222⫸⊐⫏≰10102112⨟⋌⩍⫏≰12101002","cot":[{"info":"⫏≰1212121⩷∴⫏≰12210222=⫏≰-21220221","layer":1},{"info":"⫏≰10102112⨟⋌⩍⫏≰12101002=NaN","layer":1},{"info":"⫏≰-21220221⫸⊐NaN=⫏≰1022212","layer":0}]}
{"id":894,"expression_no_base_symbol":"($5185$∧)⨐⩸⫘$1815$⨎$2406$","expression":"(⫏≰21010001∧)⨐⩸⫘⫏≰2111020⨎⫏≰10022010","highest_n_order":5,"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":5185,"base":3}},"right_expr":{"type":"binary","operator":"⨎","left_expr":{"type":"numeric_atoms","value":1815,"base":3},"right_expr":{"type":"numeric_atoms","value":2406,"base":3}}},"used_operators":["fu6greOZ01","z63VuFQld9","rJVOvQCfKK"],"dependent_operators":["3ViojmjbAp","B5M0gjZbta","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","mqXw5SEYmG","23Mk6UjR3U","AHs5Up7iyr","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5185","layer":2},{"info":"compute unary expreesion, input=5185, 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=1815","layer":2},{"info":"number node, value=2406","layer":2},{"info":"compute binary expreesion, left_input=1815, right_input=2406, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=2406","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=2406, 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":3,"result_base":3,"text":"(⫏≰21010001∧)⨐⩸⫘⫏≰2111020⨎⫏≰10022010=NaN","reverse_text":"NaN=(⫏≰21010001∧)⨐⩸⫘⫏≰2111020⨎⫏≰10022010","cot":[{"info":"⫏≰21010001∧=NaN","layer":1},{"info":"⫏≰2111020⨎⫏≰10022010=⫏≰10022010","layer":1},{"info":"NaN⨐⩸⫘⫏≰10022010=NaN","layer":0}]}
{"id":895,"expression_no_base_symbol":"⊥($3261$⨁⊸⫻)","expression":"⊥(⫏≰11110210⨁⊸⫻)","highest_n_order":4,"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":3261,"base":3}}},"used_operators":["Q3PJZHRvZv","glklzrTFfD"],"dependent_operators":["fu6greOZ01","W4YGzv6Whe","rysDP5nf3Z"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3261","layer":2},{"info":"compute unary expreesion, input=3261, op_id = glklzrTFfD, unary_op_definition = 'a⨁⊸⫻ = { ((a-a)+(a+a)) , if a<=24 ; a , else }', output=3261","layer":1},{"info":"compute unary expreesion, input=3261, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊥(⫏≰11110210⨁⊸⫻)=NaN","reverse_text":"NaN=⊥(⫏≰11110210⨁⊸⫻)","cot":[{"info":"⫏≰11110210⨁⊸⫻=⫏≰11110210","layer":1},{"info":"⊥⫏≰11110210=NaN","layer":0}]}
{"id":896,"expression_no_base_symbol":"$3462$⪮%⊝$5168$≧⫂∧($3087$∲⫓$2495$)","expression":"⫏≰11202020⪮%⊝⫏≰21002102≧⫂∧(⫏≰11020100∲⫓⫏≰10102102)","highest_n_order":2,"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":3462,"base":3},"right_expr":{"type":"numeric_atoms","value":5168,"base":3}},"right_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":3087,"base":3},"right_expr":{"type":"numeric_atoms","value":2495,"base":3}}},"used_operators":["Ph9nP6C5qx","IWmyXbctLI","i8ToyICDmI"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-122112","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3462","layer":2},{"info":"number node, value=5168","layer":2},{"info":"compute binary expreesion, left_input=3462, right_input=5168, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=7240","layer":1},{"info":"number node, value=3087","layer":2},{"info":"number node, value=2495","layer":2},{"info":"compute binary expreesion, left_input=3087, right_input=2495, 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=7240, right_input=0, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=-473","layer":0}],"base":3,"result_base":3,"text":"⫏≰11202020⪮%⊝⫏≰21002102≧⫂∧(⫏≰11020100∲⫓⫏≰10102102)=⫏≰-122112","reverse_text":"⫏≰-122112=⫏≰11202020⪮%⊝⫏≰21002102≧⫂∧(⫏≰11020100∲⫓⫏≰10102102)","cot":[{"info":"⫏≰11202020⪮%⊝⫏≰21002102=⫏≰100221011","layer":1},{"info":"⫏≰11020100∲⫓⫏≰10102102=⫏≰0","layer":1},{"info":"⫏≰100221011≧⫂∧⫏≰0=⫏≰-122112","layer":0}]}
{"id":897,"expression_no_base_symbol":"($1070$-$3015$)↬($1732$⩨$1068$)","expression":"(⫏≰1110122-⫏≰11010200)↬(⫏≰2101011⩨⫏≰1110120)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":6,"operation_count":3,"complexity_ratio":2.0,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":1070,"base":3},"right_expr":{"type":"numeric_atoms","value":3015,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":1732,"base":3},"right_expr":{"type":"numeric_atoms","value":1068,"base":3}}},"used_operators":["B5M0gjZbta","rysDP5nf3Z","2DlMacCsIx"],"dependent_operators":["rGHVDoGpnC","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1070","layer":2},{"info":"number node, value=3015","layer":2},{"info":"compute binary expreesion, left_input=1070, right_input=3015, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-1945","layer":1},{"info":"number node, value=1732","layer":2},{"info":"number node, value=1068","layer":2},{"info":"compute binary expreesion, left_input=1732, right_input=1068, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-1945, right_input=0, 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":3,"result_base":3,"text":"(⫏≰1110122-⫏≰11010200)↬(⫏≰2101011⩨⫏≰1110120)=NaN","reverse_text":"NaN=(⫏≰1110122-⫏≰11010200)↬(⫏≰2101011⩨⫏≰1110120)","cot":[{"info":"⫏≰1110122-⫏≰11010200=⫏≰-2200001","layer":1},{"info":"⫏≰2101011⩨⫏≰1110120=⫏≰0","layer":1},{"info":"⫏≰-2200001↬⫏≰0=NaN","layer":0}]}
{"id":898,"expression_no_base_symbol":"≤/($5036$⊦⊿)","expression":"≤/(⫏≰20220112⊦⊿)","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":"unary","operator":"⊦⊿","unary_expr":{"type":"numeric_atoms","value":5036,"base":3}}},"used_operators":["eLAdDNolq6","14qkJME0vr"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰210111102","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5036","layer":2},{"info":"compute unary expreesion, input=5036, op_id = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=-15187","layer":1},{"info":"compute unary expreesion, input=-15187, op_id = eLAdDNolq6, unary_op_definition = '≤/a = { (484-a) }', output=15671","layer":0}],"base":3,"result_base":3,"text":"≤/(⫏≰20220112⊦⊿)=⫏≰210111102","reverse_text":"⫏≰210111102=≤/(⫏≰20220112⊦⊿)","cot":[{"info":"⫏≰20220112⊦⊿=⫏≰-202211111","layer":1},{"info":"≤/⫏≰-202211111=⫏≰210111102","layer":0}]}
{"id":899,"expression_no_base_symbol":"↣≠⋷($2001$⩤)","expression":"↣≠⋷(⫏≰2202010⩤)","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":"unary","operator":"⩤","unary_expr":{"type":"numeric_atoms","value":2001,"base":3}}},"used_operators":["Asc51vEJeQ","Z2TMIBDE3Q"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2001","layer":2},{"info":"compute unary expreesion, input=2001, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-2001","layer":1},{"info":"compute unary expreesion, input=-2001, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(⫏≰2202010⩤)=NaN","reverse_text":"NaN=↣≠⋷(⫏≰2202010⩤)","cot":[{"info":"⫏≰2202010⩤=⫏≰-2202010","layer":1},{"info":"↣≠⋷⫏≰-2202010=NaN","layer":0}]}
{"id":900,"expression_no_base_symbol":"⋗⩬⋾$1026$⪮%⊝$2519$","expression":"⋗⩬⋾⫏≰1102000⪮%⊝⫏≰10110022","highest_n_order":2,"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":1026,"base":3},"right_expr":{"type":"numeric_atoms","value":2519,"base":3}}},"used_operators":["DpFCA1CohY","IWmyXbctLI"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"⫏≰-100202010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1026","layer":2},{"info":"number node, value=2519","layer":2},{"info":"compute binary expreesion, left_input=1026, right_input=2519, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=2368","layer":1},{"info":"compute unary expreesion, input=2368, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-7104","layer":0}],"base":3,"result_base":3,"text":"⋗⩬⋾⫏≰1102000⪮%⊝⫏≰10110022=⫏≰-100202010","reverse_text":"⫏≰-100202010=⋗⩬⋾⫏≰1102000⪮%⊝⫏≰10110022","cot":[{"info":"⫏≰1102000⪮%⊝⫏≰10110022=⫏≰10020201","layer":1},{"info":"⋗⩬⋾⫏≰10020201=⫏≰-100202010","layer":0}]}
{"id":901,"expression_no_base_symbol":"$3842$≹⇙⪍$2069$⨓(≦∁$3436$)","expression":"⫏≰12021022≹⇙⪍⫏≰2211122⨓(≦∁⫏≰11201021)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3444,"operation_count":3,"complexity_ratio":1148.0,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":3842,"base":3},"right_expr":{"type":"numeric_atoms","value":2069,"base":3}},"right_expr":{"type":"unary","operator":"≦∁","unary_expr":{"type":"numeric_atoms","value":3436,"base":3}}},"used_operators":["3ViojmjbAp","AHs5Up7iyr","9ICcGScMcE"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","dWAJyo7jo9","XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C"],"result":"⫏≰-11201101","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3842","layer":2},{"info":"number node, value=2069","layer":2},{"info":"compute binary expreesion, left_input=3842, right_input=2069, 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":"number node, value=3436","layer":2},{"info":"compute unary expreesion, input=3436, op_id = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=3436","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=3436, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-3439","layer":0}],"base":3,"result_base":3,"text":"⫏≰12021022≹⇙⪍⫏≰2211122⨓(≦∁⫏≰11201021)=⫏≰-11201101","reverse_text":"⫏≰-11201101=⫏≰12021022≹⇙⪍⫏≰2211122⨓(≦∁⫏≰11201021)","cot":[{"info":"⫏≰12021022≹⇙⪍⫏≰2211122=NaN","layer":1},{"info":"≦∁⫏≰11201021=⫏≰11201021","layer":1},{"info":"NaN⨓⫏≰11201021=⫏≰-11201101","layer":0}]}
{"id":902,"expression_no_base_symbol":"$2009$⩚⊴⇥$1434$⩚⊴⇥($1755$⫥∨⫟$2339$)","expression":"⫏≰2202102⩚⊴⇥⫏≰1222010⩚⊴⇥(⫏≰2102000⫥∨⫟⫏≰10012122)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":160,"operation_count":3,"complexity_ratio":53.333333333333336,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":2009,"base":3},"right_expr":{"type":"numeric_atoms","value":1434,"base":3}},"right_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1755,"base":3},"right_expr":{"type":"numeric_atoms","value":2339,"base":3}}},"used_operators":["NTOWxs364D","KYD54nUTWz"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2009","layer":2},{"info":"number node, value=1434","layer":2},{"info":"compute binary expreesion, left_input=2009, right_input=1434, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-3564","layer":1},{"info":"number node, value=1755","layer":2},{"info":"number node, value=2339","layer":2},{"info":"compute binary expreesion, left_input=1755, right_input=2339, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-3564, right_input=nan, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2202102⩚⊴⇥⫏≰1222010⩚⊴⇥(⫏≰2102000⫥∨⫟⫏≰10012122)=NaN","reverse_text":"NaN=⫏≰2202102⩚⊴⇥⫏≰1222010⩚⊴⇥(⫏≰2102000⫥∨⫟⫏≰10012122)","cot":[{"info":"⫏≰2202102⩚⊴⇥⫏≰1222010=⫏≰-11220000","layer":1},{"info":"⫏≰2102000⫥∨⫟⫏≰10012122=NaN","layer":1},{"info":"⫏≰-11220000⩚⊴⇥NaN=NaN","layer":0}]}
{"id":903,"expression_no_base_symbol":"(+⊝⨔$1113$)⋷(⊄⩳↩$1881$)","expression":"(+⊝⨔⫏≰1112020)⋷(⊄⩳↩⫏≰2120200)","highest_n_order":3,"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":1113,"base":3}},"right_expr":{"type":"unary","operator":"⊄⩳↩","unary_expr":{"type":"numeric_atoms","value":1881,"base":3}}},"used_operators":["23Mk6UjR3U","DhbWaqg5eL","8w2t5hMYqp"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-122120101","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1113","layer":2},{"info":"compute unary expreesion, input=1113, 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=1881","layer":2},{"info":"compute unary expreesion, input=1881, op_id = 8w2t5hMYqp, unary_op_definition = '⊄⩳↩a = { ((-a)-(a+a)) }', output=-5643","layer":1},{"info":"compute binary expreesion, left_input=1522, right_input=-5643, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-12808","layer":0}],"base":3,"result_base":3,"text":"(+⊝⨔⫏≰1112020)⋷(⊄⩳↩⫏≰2120200)=⫏≰-122120101","reverse_text":"⫏≰-122120101=(+⊝⨔⫏≰1112020)⋷(⊄⩳↩⫏≰2120200)","cot":[{"info":"+⊝⨔⫏≰1112020=⫏≰2002101","layer":1},{"info":"⊄⩳↩⫏≰2120200=⫏≰-21202000","layer":1},{"info":"⫏≰2002101⋷⫏≰-21202000=⫏≰-122120101","layer":0}]}
{"id":904,"expression_no_base_symbol":"$2274$≎⊠⪸$1474$⪒($3819$+$2569$)","expression":"⫏≰10010020≎⊠⪸⫏≰2000121⪒(⫏≰12020110+⫏≰10112011)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":274,"operation_count":3,"complexity_ratio":91.33333333333333,"tree":{"type":"binary","operator":"⪒","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":2274,"base":3},"right_expr":{"type":"numeric_atoms","value":1474,"base":3}},"right_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":3819,"base":3},"right_expr":{"type":"numeric_atoms","value":2569,"base":3}}},"used_operators":["f6k1SAg4EE","bJkvcejdHO","W4YGzv6Whe"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A"],"result":"⫏≰-1010020000122","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2274","layer":2},{"info":"number node, value=1474","layer":2},{"info":"compute binary expreesion, left_input=2274, right_input=1474, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=588493","layer":1},{"info":"number node, value=3819","layer":2},{"info":"number node, value=2569","layer":2},{"info":"compute binary expreesion, left_input=3819, right_input=2569, op_id = W4YGzv6Whe binary_op_definition= 'None', output=6388","layer":1},{"info":"compute binary expreesion, left_input=588493, right_input=6388, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-594881","layer":0}],"base":3,"result_base":3,"text":"⫏≰10010020≎⊠⪸⫏≰2000121⪒(⫏≰12020110+⫏≰10112011)=⫏≰-1010020000122","reverse_text":"⫏≰-1010020000122=⫏≰10010020≎⊠⪸⫏≰2000121⪒(⫏≰12020110+⫏≰10112011)","cot":[{"info":"⫏≰10010020≎⊠⪸⫏≰2000121=⫏≰1002220021001","layer":1},{"info":"⫏≰12020110+⫏≰10112011=⫏≰22202121","layer":1},{"info":"⫏≰1002220021001⪒⫏≰22202121=⫏≰-1010020000122","layer":0}]}
{"id":905,"expression_no_base_symbol":"(⪝⪂⫅$1009$)⩷∴($3299$⩨$2753$)","expression":"(⪝⪂⫅⫏≰1101101)⩷∴(⫏≰11112012⩨⫏≰10202222)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":160,"operation_count":3,"complexity_ratio":53.333333333333336,"tree":{"type":"binary","operator":"⩷∴","left_expr":{"type":"unary","operator":"⪝⪂⫅","unary_expr":{"type":"numeric_atoms","value":1009,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":3299,"base":3},"right_expr":{"type":"numeric_atoms","value":2753,"base":3}}},"used_operators":["9FxExcQeMw","XTarYq4gQB","2DlMacCsIx"],"dependent_operators":["rysDP5nf3Z","9HNa5Wba9A","8w2t5hMYqp","D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL"],"result":"⫏≰-120001222002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1009","layer":2},{"info":"compute unary expreesion, input=1009, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=-148323","layer":1},{"info":"number node, value=3299","layer":2},{"info":"number node, value=2753","layer":2},{"info":"compute binary expreesion, left_input=3299, right_input=2753, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=-148323, right_input=0, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-296678","layer":0}],"base":3,"result_base":3,"text":"(⪝⪂⫅⫏≰1101101)⩷∴(⫏≰11112012⩨⫏≰10202222)=⫏≰-120001222002","reverse_text":"⫏≰-120001222002=(⪝⪂⫅⫏≰1101101)⩷∴(⫏≰11112012⩨⫏≰10202222)","cot":[{"info":"⪝⪂⫅⫏≰1101101=⫏≰-21112110110","layer":1},{"info":"⫏≰11112012⩨⫏≰10202222=⫏≰0","layer":1},{"info":"⫏≰-21112110110⩷∴⫏≰0=⫏≰-120001222002","layer":0}]}
{"id":906,"expression_no_base_symbol":"$1751$⊴$1060$⫡⨏$1697$⫸⊐$6614$","expression":"⫏≰2101212⊴⫏≰1110021⫡⨏⫏≰2022212⫸⊐⫏≰100001222","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1274,"operation_count":3,"complexity_ratio":424.6666666666667,"tree":{"type":"binary","operator":"⫡⨏","left_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":1751,"base":3},"right_expr":{"type":"numeric_atoms","value":1060,"base":3}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":1697,"base":3},"right_expr":{"type":"numeric_atoms","value":6614,"base":3}}},"used_operators":["QMFrweE19q","Nsiff2A1zJ","mqXw5SEYmG"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","dWAJyo7jo9","14qkJME0vr","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1751","layer":2},{"info":"number node, value=1060","layer":2},{"info":"compute binary expreesion, left_input=1751, right_input=1060, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"number node, value=1697","layer":2},{"info":"number node, value=6614","layer":2},{"info":"compute binary expreesion, left_input=1697, right_input=6614, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=26331","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=26331, 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":3,"result_base":3,"text":"⫏≰2101212⊴⫏≰1110021⫡⨏⫏≰2022212⫸⊐⫏≰100001222=NaN","reverse_text":"NaN=⫏≰2101212⊴⫏≰1110021⫡⨏⫏≰2022212⫸⊐⫏≰100001222","cot":[{"info":"⫏≰2101212⊴⫏≰1110021=NaN","layer":1},{"info":"⫏≰2022212⫸⊐⫏≰100001222=⫏≰1100010020","layer":1},{"info":"NaN⫡⨏⫏≰1100010020=NaN","layer":0}]}
{"id":907,"expression_no_base_symbol":"↽≂($1828$⊭∹↮)","expression":"↽≂(⫏≰2111201⊭∹↮)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9,"operation_count":2,"complexity_ratio":4.5,"tree":{"type":"unary","operator":"↽≂","unary_expr":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"numeric_atoms","value":1828,"base":3}}},"used_operators":["u6S6b8DprG","xNBdhnnwKq"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C"],"result":"⫏≰-101000211","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1828","layer":2},{"info":"compute unary expreesion, input=1828, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=3656","layer":1},{"info":"compute unary expreesion, input=3656, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-7312","layer":0}],"base":3,"result_base":3,"text":"↽≂(⫏≰2111201⊭∹↮)=⫏≰-101000211","reverse_text":"⫏≰-101000211=↽≂(⫏≰2111201⊭∹↮)","cot":[{"info":"⫏≰2111201⊭∹↮=⫏≰12000102","layer":1},{"info":"↽≂⫏≰12000102=⫏≰-101000211","layer":0}]}
{"id":908,"expression_no_base_symbol":"⪲⇎$5655$⨰$4257$","expression":"⪲⇎⫏≰21202110⨰⫏≰12211200","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":5655,"base":3},"right_expr":{"type":"numeric_atoms","value":4257,"base":3}}},"used_operators":["XPYlsWDdGa","eewbuw0ToL"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰10212022","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5655","layer":2},{"info":"number node, value=4257","layer":2},{"info":"compute binary expreesion, left_input=5655, right_input=4257, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=1408","layer":1},{"info":"compute unary expreesion, input=1408, op_id = XPYlsWDdGa, unary_op_definition = '⪲⇎a = { (a+a) , if (-a)!=821 ; (a-a) , else }', output=2816","layer":0}],"base":3,"result_base":3,"text":"⪲⇎⫏≰21202110⨰⫏≰12211200=⫏≰10212022","reverse_text":"⫏≰10212022=⪲⇎⫏≰21202110⨰⫏≰12211200","cot":[{"info":"⫏≰21202110⨰⫏≰12211200=⫏≰1221011","layer":1},{"info":"⪲⇎⫏≰1221011=⫏≰10212022","layer":0}]}
{"id":909,"expression_no_base_symbol":"($3183$⊭↱$6137$)∼($1839$⩤)","expression":"(⫏≰11100220⊭↱⫏≰22102022)∼(⫏≰2112010⩤)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":124,"operation_count":3,"complexity_ratio":41.333333333333336,"tree":{"type":"binary","operator":"∼","left_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":3183,"base":3},"right_expr":{"type":"numeric_atoms","value":6137,"base":3}},"right_expr":{"type":"unary","operator":"⩤","unary_expr":{"type":"numeric_atoms","value":1839,"base":3}}},"used_operators":["DyGG3AbaNP","COABgblf1C","Z2TMIBDE3Q"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3183","layer":2},{"info":"number node, value=6137","layer":2},{"info":"compute binary expreesion, left_input=3183, right_input=6137, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=5913","layer":1},{"info":"number node, value=1839","layer":2},{"info":"compute unary expreesion, input=1839, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-1839","layer":1},{"info":"compute binary expreesion, left_input=5913, right_input=-1839, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11100220⊭↱⫏≰22102022)∼(⫏≰2112010⩤)=NaN","reverse_text":"NaN=(⫏≰11100220⊭↱⫏≰22102022)∼(⫏≰2112010⩤)","cot":[{"info":"⫏≰11100220⊭↱⫏≰22102022=⫏≰22010000","layer":1},{"info":"⫏≰2112010⩤=⫏≰-2112010","layer":1},{"info":"⫏≰22010000∼⫏≰-2112010=NaN","layer":0}]}
{"id":910,"expression_no_base_symbol":"($7998$⪨≂$5587$)⨓(∂$7645$)","expression":"(⫏≰101222020⪨≂⫏≰21122221)⨓(∂⫏≰101111011)","highest_n_order":5,"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":7998,"base":3},"right_expr":{"type":"numeric_atoms","value":5587,"base":3}},"right_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":7645,"base":3}}},"used_operators":["3ViojmjbAp","sdazOOVcIp","Uaa54Peajs"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","rysDP5nf3Z","t8gj7n24qd","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7998","layer":2},{"info":"number node, value=5587","layer":2},{"info":"compute binary expreesion, left_input=7998, right_input=5587, 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=4924","layer":1},{"info":"number node, value=7645","layer":2},{"info":"compute unary expreesion, input=7645, 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=4924, right_input=nan, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰101222020⪨≂⫏≰21122221)⨓(∂⫏≰101111011)=NaN","reverse_text":"NaN=(⫏≰101222020⪨≂⫏≰21122221)⨓(∂⫏≰101111011)","cot":[{"info":"⫏≰101222020⪨≂⫏≰21122221=⫏≰20202101","layer":1},{"info":"∂⫏≰101111011=NaN","layer":1},{"info":"⫏≰20202101⨓NaN=NaN","layer":0}]}
{"id":911,"expression_no_base_symbol":"∥⊫(↩$2052$)","expression":"∥⊫(↩⫏≰2211000)","highest_n_order":2,"priority_hierarchical_complexity":1,"normalized_expansion_degree":19,"operation_count":2,"complexity_ratio":9.5,"tree":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"unary","operator":"↩","unary_expr":{"type":"numeric_atoms","value":2052,"base":3}}},"used_operators":["P8v4zCKN1o","jLgFTUHLKL"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D"],"result":"⫏≰-2001","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2052","layer":2},{"info":"compute unary expreesion, input=2052, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-13636","layer":1},{"info":"compute unary expreesion, input=-13636, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=-55","layer":0}],"base":3,"result_base":3,"text":"∥⊫(↩⫏≰2211000)=⫏≰-2001","reverse_text":"⫏≰-2001=∥⊫(↩⫏≰2211000)","cot":[{"info":"↩⫏≰2211000=⫏≰-200201001","layer":1},{"info":"∥⊫⫏≰-200201001=⫏≰-2001","layer":0}]}
{"id":912,"expression_no_base_symbol":"$2656$∀⇚≩$1050$≭($1142$⫸⊐$3011$)","expression":"⫏≰10122101∀⇚≩⫏≰1102220≭(⫏≰1120022⫸⊐⫏≰11010112)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":18617,"operation_count":3,"complexity_ratio":6205.666666666667,"tree":{"type":"binary","operator":"≭","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":2656,"base":3},"right_expr":{"type":"numeric_atoms","value":1050,"base":3}},"right_expr":{"type":"binary","operator":"⫸⊐","left_expr":{"type":"numeric_atoms","value":1142,"base":3},"right_expr":{"type":"numeric_atoms","value":3011,"base":3}}},"used_operators":["rxpJgHHUmx","LRNGc0VcxI","mqXw5SEYmG"],"dependent_operators":["AHs5Up7iyr","X99M06cbEe","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2656","layer":2},{"info":"number node, value=1050","layer":2},{"info":"compute binary expreesion, left_input=2656, right_input=1050, 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=1142","layer":2},{"info":"number node, value=3011","layer":2},{"info":"compute binary expreesion, left_input=1142, right_input=3011, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=11919","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=11919, 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":3,"result_base":3,"text":"⫏≰10122101∀⇚≩⫏≰1102220≭(⫏≰1120022⫸⊐⫏≰11010112)=NaN","reverse_text":"NaN=⫏≰10122101∀⇚≩⫏≰1102220≭(⫏≰1120022⫸⊐⫏≰11010112)","cot":[{"info":"⫏≰10122101∀⇚≩⫏≰1102220=NaN","layer":1},{"info":"⫏≰1120022⫸⊐⫏≰11010112=⫏≰121100110","layer":1},{"info":"NaN≭⫏≰121100110=NaN","layer":0}]}
{"id":913,"expression_no_base_symbol":"($2273$⩚⊴⇥$1265$)∸","expression":"(⫏≰10010012⩚⊴⇥⫏≰1201212)∸","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":180,"operation_count":2,"complexity_ratio":90.0,"tree":{"type":"unary","operator":"∸","unary_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":2273,"base":3},"right_expr":{"type":"numeric_atoms","value":1265,"base":3}}},"used_operators":["o20kRiQErp","NTOWxs364D"],"dependent_operators":["tmPS8pqC7x","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰20120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2273","layer":2},{"info":"number node, value=1265","layer":2},{"info":"compute binary expreesion, left_input=2273, right_input=1265, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-3659","layer":1},{"info":"compute unary expreesion, input=-3659, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10010012⩚⊴⇥⫏≰1201212)∸=⫏≰20120","reverse_text":"⫏≰20120=(⫏≰10010012⩚⊴⇥⫏≰1201212)∸","cot":[{"info":"⫏≰10010012⩚⊴⇥⫏≰1201212=⫏≰-12000112","layer":1},{"info":"⫏≰-12000112∸=⫏≰20120","layer":0}]}
{"id":914,"expression_no_base_symbol":"(⨞⊢$4682$)⇼⇔∾($7983$⪨≂$1062$)","expression":"(⨞⊢⫏≰20102102)⇼⇔∾(⫏≰101221200⪨≂⫏≰1110100)","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":4682,"base":3}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":7983,"base":3},"right_expr":{"type":"numeric_atoms","value":1062,"base":3}}},"used_operators":["tifHPKVTfV","xUOZtlo3hN","sdazOOVcIp"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰221210022","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4682","layer":2},{"info":"compute unary expreesion, input=4682, op_id = xUOZtlo3hN, unary_op_definition = '⨞⊢a = { (-(a+174)) }', output=-4856","layer":1},{"info":"number node, value=7983","layer":2},{"info":"number node, value=1062","layer":2},{"info":"compute binary expreesion, left_input=7983, right_input=1062, 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=13944","layer":1},{"info":"compute binary expreesion, left_input=-4856, right_input=13944, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=18800","layer":0}],"base":3,"result_base":3,"text":"(⨞⊢⫏≰20102102)⇼⇔∾(⫏≰101221200⪨≂⫏≰1110100)=⫏≰221210022","reverse_text":"⫏≰221210022=(⨞⊢⫏≰20102102)⇼⇔∾(⫏≰101221200⪨≂⫏≰1110100)","cot":[{"info":"⨞⊢⫏≰20102102=⫏≰-20122212","layer":1},{"info":"⫏≰101221200⪨≂⫏≰1110100=⫏≰201010110","layer":1},{"info":"⫏≰-20122212⇼⇔∾⫏≰201010110=⫏≰221210022","layer":0}]}
{"id":915,"expression_no_base_symbol":"↥($3709$⨳⩥⨓$1180$)","expression":"↥(⫏≰12002101⨳⩥⨓⫏≰1121201)","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":3709,"base":3},"right_expr":{"type":"numeric_atoms","value":1180,"base":3}}},"used_operators":["A8NUZmVepG","nCS4ZIUYfx"],"dependent_operators":["k8jYdgA6NY","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3709","layer":2},{"info":"number node, value=1180","layer":2},{"info":"compute binary expreesion, left_input=3709, right_input=1180, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-2529","layer":1},{"info":"compute unary expreesion, input=-2529, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=21","layer":0}],"base":3,"result_base":3,"text":"↥(⫏≰12002101⨳⩥⨓⫏≰1121201)=⫏≰210","reverse_text":"⫏≰210=↥(⫏≰12002101⨳⩥⨓⫏≰1121201)","cot":[{"info":"⫏≰12002101⨳⩥⨓⫏≰1121201=⫏≰-10110200","layer":1},{"info":"↥⫏≰-10110200=⫏≰210","layer":0}]}
{"id":916,"expression_no_base_symbol":"($2623$⇷$8599$)↬(⨑⩽⪐$4316$)","expression":"(⫏≰10121011⇷⫏≰102210111)↬(⨑⩽⪐⫏≰12220212)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":36733,"operation_count":3,"complexity_ratio":12244.333333333334,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":2623,"base":3},"right_expr":{"type":"numeric_atoms","value":8599,"base":3}},"right_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":4316,"base":3}}},"used_operators":["B5M0gjZbta","mp7IySMOzn","AF7qkfDlqP"],"dependent_operators":["rGHVDoGpnC","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2623","layer":2},{"info":"number node, value=8599","layer":2},{"info":"compute binary expreesion, left_input=2623, right_input=8599, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=17198","layer":1},{"info":"number node, value=4316","layer":2},{"info":"compute unary expreesion, input=4316, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-4043","layer":1},{"info":"compute binary expreesion, left_input=17198, right_input=-4043, 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":3,"result_base":3,"text":"(⫏≰10121011⇷⫏≰102210111)↬(⨑⩽⪐⫏≰12220212)=NaN","reverse_text":"NaN=(⫏≰10121011⇷⫏≰102210111)↬(⨑⩽⪐⫏≰12220212)","cot":[{"info":"⫏≰10121011⇷⫏≰102210111=⫏≰212120222","layer":1},{"info":"⨑⩽⪐⫏≰12220212=⫏≰-12112202","layer":1},{"info":"⫏≰212120222↬⫏≰-12112202=NaN","layer":0}]}
{"id":917,"expression_no_base_symbol":"(∥⊫$3641$)⋝⋈⪟(↔$1197$)","expression":"(∥⊫⫏≰11222212)⋝⋈⪟(↔⫏≰1122100)","highest_n_order":2,"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":3641,"base":3}},"right_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":1197,"base":3}}},"used_operators":["2DDjHMKMc0","P8v4zCKN1o","ruOEQAzv1W"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp"],"result":"⫏≰20012000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3641","layer":2},{"info":"compute unary expreesion, input=3641, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=4509","layer":1},{"info":"number node, value=1197","layer":2},{"info":"compute unary expreesion, input=1197, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-924","layer":1},{"info":"compute binary expreesion, left_input=4509, right_input=-924, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=4509","layer":0}],"base":3,"result_base":3,"text":"(∥⊫⫏≰11222212)⋝⋈⪟(↔⫏≰1122100)=⫏≰20012000","reverse_text":"⫏≰20012000=(∥⊫⫏≰11222212)⋝⋈⪟(↔⫏≰1122100)","cot":[{"info":"∥⊫⫏≰11222212=⫏≰20012000","layer":1},{"info":"↔⫏≰1122100=⫏≰-1021020","layer":1},{"info":"⫏≰20012000⋝⋈⪟⫏≰-1021020=⫏≰20012000","layer":0}]}
{"id":918,"expression_no_base_symbol":"($4509$↺$6724$)↬(⊙↵-$1017$)","expression":"(⫏≰20012000↺⫏≰100020001)↬(⊙↵-⫏≰1101200)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1066,"operation_count":3,"complexity_ratio":355.3333333333333,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":4509,"base":3},"right_expr":{"type":"numeric_atoms","value":6724,"base":3}},"right_expr":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"numeric_atoms","value":1017,"base":3}}},"used_operators":["B5M0gjZbta","7j4O788W3g","oWn0xqSxBt"],"dependent_operators":["rGHVDoGpnC","rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4509","layer":2},{"info":"number node, value=6724","layer":2},{"info":"compute binary expreesion, left_input=4509, right_input=6724, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=6724","layer":1},{"info":"number node, value=1017","layer":2},{"info":"compute unary expreesion, input=1017, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=-1","layer":1},{"info":"compute binary expreesion, left_input=6724, right_input=-1, 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":3,"result_base":3,"text":"(⫏≰20012000↺⫏≰100020001)↬(⊙↵-⫏≰1101200)=NaN","reverse_text":"NaN=(⫏≰20012000↺⫏≰100020001)↬(⊙↵-⫏≰1101200)","cot":[{"info":"⫏≰20012000↺⫏≰100020001=⫏≰100020001","layer":1},{"info":"⊙↵-⫏≰1101200=⫏≰-1","layer":1},{"info":"⫏≰100020001↬⫏≰-1=NaN","layer":0}]}
{"id":919,"expression_no_base_symbol":"$8670$⋝⋈⪟$3088$⫩⊇","expression":"⫏≰102220010⋝⋈⪟⫏≰11020101⫩⊇","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":8670,"base":3},"right_expr":{"type":"numeric_atoms","value":3088,"base":3}}},"used_operators":["BjRHVeLaeN","2DDjHMKMc0"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-102211120","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=8670","layer":2},{"info":"number node, value=3088","layer":2},{"info":"compute binary expreesion, left_input=8670, right_input=3088, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=8670","layer":1},{"info":"compute unary expreesion, input=8670, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=-8628","layer":0}],"base":3,"result_base":3,"text":"⫏≰102220010⋝⋈⪟⫏≰11020101⫩⊇=⫏≰-102211120","reverse_text":"⫏≰-102211120=⫏≰102220010⋝⋈⪟⫏≰11020101⫩⊇","cot":[{"info":"⫏≰102220010⋝⋈⪟⫏≰11020101=⫏≰102220010","layer":1},{"info":"⫏≰102220010⫩⊇=⫏≰-102211120","layer":0}]}
{"id":920,"expression_no_base_symbol":"$3092$⪨≂$6854$⫡⨏(⇁⨣⪵$5204$)","expression":"⫏≰11020112⪨≂⫏≰100101212⫡⨏(⇁⨣⪵⫏≰21010202)","highest_n_order":5,"priority_hierarchical_complexity":2,"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":3092,"base":3},"right_expr":{"type":"numeric_atoms","value":6854,"base":3}},"right_expr":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"numeric_atoms","value":5204,"base":3}}},"used_operators":["QMFrweE19q","sdazOOVcIp","inkyxCbjAn"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","B5M0gjZbta"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3092","layer":2},{"info":"number node, value=6854","layer":2},{"info":"compute binary expreesion, left_input=3092, right_input=6854, 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=-7422","layer":1},{"info":"number node, value=5204","layer":2},{"info":"compute unary expreesion, input=5204, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=-7422, 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":3,"result_base":3,"text":"⫏≰11020112⪨≂⫏≰100101212⫡⨏(⇁⨣⪵⫏≰21010202)=NaN","reverse_text":"NaN=⫏≰11020112⪨≂⫏≰100101212⫡⨏(⇁⨣⪵⫏≰21010202)","cot":[{"info":"⫏≰11020112⪨≂⫏≰100101212=⫏≰-101011220","layer":1},{"info":"⇁⨣⪵⫏≰21010202=NaN","layer":1},{"info":"⫏≰-101011220⫡⨏NaN=NaN","layer":0}]}
{"id":921,"expression_no_base_symbol":"($1033$%$1767$)*$1845$∼$1341$","expression":"(⫏≰1102021%⫏≰2102110)*⫏≰2112100∼⫏≰1211200","highest_n_order":4,"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":1033,"base":3},"right_expr":{"type":"numeric_atoms","value":1767,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":1845,"base":3},"right_expr":{"type":"numeric_atoms","value":1341,"base":3}}},"used_operators":["9HNa5Wba9A","k8jYdgA6NY","DyGG3AbaNP"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1033","layer":2},{"info":"number node, value=1767","layer":2},{"info":"compute binary expreesion, left_input=1033, right_input=1767, op_id = k8jYdgA6NY binary_op_definition= 'None', output=1033","layer":1},{"info":"number node, value=1845","layer":2},{"info":"number node, value=1341","layer":2},{"info":"compute binary expreesion, left_input=1845, right_input=1341, 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=1033, right_input=nan, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1102021%⫏≰2102110)*⫏≰2112100∼⫏≰1211200=NaN","reverse_text":"NaN=(⫏≰1102021%⫏≰2102110)*⫏≰2112100∼⫏≰1211200","cot":[{"info":"⫏≰1102021%⫏≰2102110=⫏≰1102021","layer":1},{"info":"⫏≰2112100∼⫏≰1211200=NaN","layer":1},{"info":"⫏≰1102021*NaN=NaN","layer":0}]}
{"id":922,"expression_no_base_symbol":"$5345$∀⇚≩$2837$⩷∴($3685$⩷∴$2902$)","expression":"⫏≰21022222∀⇚≩⫏≰10220002⩷∴(⫏≰12001111⩷∴⫏≰10222111)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":37427,"operation_count":3,"complexity_ratio":12475.666666666666,"tree":{"type":"binary","operator":"⩷∴","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":5345,"base":3},"right_expr":{"type":"numeric_atoms","value":2837,"base":3}},"right_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":3685,"base":3},"right_expr":{"type":"numeric_atoms","value":2902,"base":3}}},"used_operators":["9FxExcQeMw","LRNGc0VcxI"],"dependent_operators":["rysDP5nf3Z","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5345","layer":2},{"info":"number node, value=2837","layer":2},{"info":"compute binary expreesion, left_input=5345, right_input=2837, 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=3685","layer":2},{"info":"number node, value=2902","layer":2},{"info":"compute binary expreesion, left_input=3685, right_input=2902, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=1534","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1534, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰21022222∀⇚≩⫏≰10220002⩷∴(⫏≰12001111⩷∴⫏≰10222111)=NaN","reverse_text":"NaN=⫏≰21022222∀⇚≩⫏≰10220002⩷∴(⫏≰12001111⩷∴⫏≰10222111)","cot":[{"info":"⫏≰21022222∀⇚≩⫏≰10220002=NaN","layer":1},{"info":"⫏≰12001111⩷∴⫏≰10222111=⫏≰2002211","layer":1},{"info":"NaN⩷∴⫏≰2002211=NaN","layer":0}]}
{"id":923,"expression_no_base_symbol":"$1401$⨰$1104$%$2819$%$5084$","expression":"⫏≰1220220⨰⫏≰1111220%⫏≰10212102%⫏≰20222022","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"%","left_expr":{"type":"binary","operator":"⨰","left_expr":{"type":"numeric_atoms","value":1401,"base":3},"right_expr":{"type":"numeric_atoms","value":1104,"base":3}},"right_expr":{"type":"binary","operator":"%","left_expr":{"type":"numeric_atoms","value":2819,"base":3},"right_expr":{"type":"numeric_atoms","value":5084,"base":3}}},"used_operators":["k8jYdgA6NY","eewbuw0ToL"],"dependent_operators":["rysDP5nf3Z","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰102101","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1401","layer":2},{"info":"number node, value=1104","layer":2},{"info":"compute binary expreesion, left_input=1401, right_input=1104, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=307","layer":1},{"info":"number node, value=2819","layer":2},{"info":"number node, value=5084","layer":2},{"info":"compute binary expreesion, left_input=2819, right_input=5084, op_id = k8jYdgA6NY binary_op_definition= 'None', output=2819","layer":1},{"info":"compute binary expreesion, left_input=307, right_input=2819, op_id = k8jYdgA6NY binary_op_definition= 'None', output=307","layer":0}],"base":3,"result_base":3,"text":"⫏≰1220220⨰⫏≰1111220%⫏≰10212102%⫏≰20222022=⫏≰102101","reverse_text":"⫏≰102101=⫏≰1220220⨰⫏≰1111220%⫏≰10212102%⫏≰20222022","cot":[{"info":"⫏≰1220220⨰⫏≰1111220=⫏≰102101","layer":1},{"info":"⫏≰10212102%⫏≰20222022=⫏≰10212102","layer":1},{"info":"⫏≰102101%⫏≰10212102=⫏≰102101","layer":0}]}
{"id":924,"expression_no_base_symbol":"($3710$∸)⋥≓≎($1352$↙$3357$)","expression":"(⫏≰12002102∸)⋥≓≎(⫏≰1212002↙⫏≰11121100)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3541,"operation_count":3,"complexity_ratio":1180.3333333333333,"tree":{"type":"binary","operator":"⋥≓≎","left_expr":{"type":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":3710,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":1352,"base":3},"right_expr":{"type":"numeric_atoms","value":3357,"base":3}}},"used_operators":["Qy55tPpLXF","o20kRiQErp","yyfyN0ffXY"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","tmPS8pqC7x","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰-1000211100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3710","layer":2},{"info":"compute unary expreesion, input=3710, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"number node, value=1352","layer":2},{"info":"number node, value=3357","layer":2},{"info":"compute binary expreesion, left_input=1352, right_input=3357, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-10071","layer":1},{"info":"compute binary expreesion, left_input=177, right_input=-10071, op_id = Qy55tPpLXF binary_op_definition= 'a⋥≓≎b = { ((b+b)-(a-33)) , if (a+463)>=40 ; (-(-67)) , else }', output=-20286","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12002102∸)⋥≓≎(⫏≰1212002↙⫏≰11121100)=⫏≰-1000211100","reverse_text":"⫏≰-1000211100=(⫏≰12002102∸)⋥≓≎(⫏≰1212002↙⫏≰11121100)","cot":[{"info":"⫏≰12002102∸=⫏≰20120","layer":1},{"info":"⫏≰1212002↙⫏≰11121100=⫏≰-111211000","layer":1},{"info":"⫏≰20120⋥≓≎⫏≰-111211000=⫏≰-1000211100","layer":0}]}
{"id":925,"expression_no_base_symbol":"($7379$⋳⪒$1288$)∀⇚≩$3705$⪛$2737$","expression":"(⫏≰101010022⋳⪒⫏≰1202201)∀⇚≩⫏≰12002020⪛⫏≰10202101","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":92292,"operation_count":3,"complexity_ratio":30764.0,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":7379,"base":3},"right_expr":{"type":"numeric_atoms","value":1288,"base":3}},"right_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":3705,"base":3},"right_expr":{"type":"numeric_atoms","value":2737,"base":3}}},"used_operators":["LRNGc0VcxI","12rbrZMWeM","uFcxV4UQCh"],"dependent_operators":["X99M06cbEe","rysDP5nf3Z","t8gj7n24qd","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7379","layer":2},{"info":"number node, value=1288","layer":2},{"info":"compute binary expreesion, left_input=7379, right_input=1288, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=13183","layer":1},{"info":"number node, value=3705","layer":2},{"info":"number node, value=2737","layer":2},{"info":"compute binary expreesion, left_input=3705, right_input=2737, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=968","layer":1},{"info":"compute binary expreesion, left_input=13183, right_input=968, 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":3,"result_base":3,"text":"(⫏≰101010022⋳⪒⫏≰1202201)∀⇚≩⫏≰12002020⪛⫏≰10202101=NaN","reverse_text":"NaN=(⫏≰101010022⋳⪒⫏≰1202201)∀⇚≩⫏≰12002020⪛⫏≰10202101","cot":[{"info":"⫏≰101010022⋳⪒⫏≰1202201=⫏≰200002021","layer":1},{"info":"⫏≰12002020⪛⫏≰10202101=⫏≰1022212","layer":1},{"info":"⫏≰200002021∀⇚≩⫏≰1022212=NaN","layer":0}]}
{"id":926,"expression_no_base_symbol":"$2903$⨪↰⇹$7744$⫥∨⫟$4729$≭$1371$","expression":"⫏≰10222112⨪↰⇹⫏≰101121211⫥∨⫟⫏≰20111011≭⫏≰1212210","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3058,"operation_count":3,"complexity_ratio":1019.3333333333334,"tree":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":2903,"base":3},"right_expr":{"type":"numeric_atoms","value":7744,"base":3}},"right_expr":{"type":"binary","operator":"≭","left_expr":{"type":"numeric_atoms","value":4729,"base":3},"right_expr":{"type":"numeric_atoms","value":1371,"base":3}}},"used_operators":["KYD54nUTWz","tmPS8pqC7x","rxpJgHHUmx"],"dependent_operators":["8HhzD0ZcuI","rGHVDoGpnC","rJVOvQCfKK","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2903","layer":2},{"info":"number node, value=7744","layer":2},{"info":"compute binary expreesion, left_input=2903, right_input=7744, 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=2903","layer":1},{"info":"number node, value=4729","layer":2},{"info":"number node, value=1371","layer":2},{"info":"compute binary expreesion, left_input=4729, right_input=1371, 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=2903, right_input=nan, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰10222112⨪↰⇹⫏≰101121211⫥∨⫟⫏≰20111011≭⫏≰1212210=NaN","reverse_text":"NaN=⫏≰10222112⨪↰⇹⫏≰101121211⫥∨⫟⫏≰20111011≭⫏≰1212210","cot":[{"info":"⫏≰10222112⨪↰⇹⫏≰101121211=⫏≰10222112","layer":1},{"info":"⫏≰20111011≭⫏≰1212210=NaN","layer":1},{"info":"⫏≰10222112⫥∨⫟NaN=NaN","layer":0}]}
{"id":927,"expression_no_base_symbol":"$1775$⪮%⊝$1944$∑⇟⊟($1145$⨓$6147$)","expression":"⫏≰2102202⪮%⊝⫏≰2200000∑⇟⊟(⫏≰1120102⨓⫏≰22102200)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":6163,"operation_count":3,"complexity_ratio":2054.3333333333335,"tree":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1775,"base":3},"right_expr":{"type":"numeric_atoms","value":1944,"base":3}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":1145,"base":3},"right_expr":{"type":"numeric_atoms","value":6147,"base":3}}},"used_operators":["U7g4x0WXJJ","IWmyXbctLI","3ViojmjbAp"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1775","layer":2},{"info":"number node, value=1944","layer":2},{"info":"compute binary expreesion, left_input=1775, right_input=1944, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=3866","layer":1},{"info":"number node, value=1145","layer":2},{"info":"number node, value=6147","layer":2},{"info":"compute binary expreesion, left_input=1145, right_input=6147, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-6150","layer":1},{"info":"compute binary expreesion, left_input=3866, right_input=-6150, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2102202⪮%⊝⫏≰2200000∑⇟⊟(⫏≰1120102⨓⫏≰22102200)=NaN","reverse_text":"NaN=⫏≰2102202⪮%⊝⫏≰2200000∑⇟⊟(⫏≰1120102⨓⫏≰22102200)","cot":[{"info":"⫏≰2102202⪮%⊝⫏≰2200000=⫏≰12022012","layer":1},{"info":"⫏≰1120102⨓⫏≰22102200=⫏≰-22102210","layer":1},{"info":"⫏≰12022012∑⇟⊟⫏≰-22102210=NaN","layer":0}]}
{"id":928,"expression_no_base_symbol":"($1759$≦≮≮)⫩⊇","expression":"(⫏≰2102011≦≮≮)⫩⊇","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":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":1759,"base":3}}},"used_operators":["BjRHVeLaeN","D4vGDi5EA2"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰21022000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1759","layer":2},{"info":"compute unary expreesion, input=1759, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-5277","layer":1},{"info":"compute unary expreesion, input=-5277, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=5319","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2102011≦≮≮)⫩⊇=⫏≰21022000","reverse_text":"⫏≰21022000=(⫏≰2102011≦≮≮)⫩⊇","cot":[{"info":"⫏≰2102011≦≮≮=⫏≰-21020110","layer":1},{"info":"⫏≰-21020110⫩⊇=⫏≰21022000","layer":0}]}
{"id":929,"expression_no_base_symbol":"↥$4165$⋳⪒$7668$","expression":"↥⫏≰12201021⋳⪒⫏≰101112000","highest_n_order":2,"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":4165,"base":3},"right_expr":{"type":"numeric_atoms","value":7668,"base":3}}},"used_operators":["A8NUZmVepG","12rbrZMWeM"],"dependent_operators":["k8jYdgA6NY","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰200","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4165","layer":2},{"info":"number node, value=7668","layer":2},{"info":"compute binary expreesion, left_input=4165, right_input=7668, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=375","layer":1},{"info":"compute unary expreesion, input=375, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=18","layer":0}],"base":3,"result_base":3,"text":"↥⫏≰12201021⋳⪒⫏≰101112000=⫏≰200","reverse_text":"⫏≰200=↥⫏≰12201021⋳⪒⫏≰101112000","cot":[{"info":"⫏≰12201021⋳⪒⫏≰101112000=⫏≰111220","layer":1},{"info":"↥⫏≰111220=⫏≰200","layer":0}]}
{"id":930,"expression_no_base_symbol":"($1542$≫≃)⩨($2253$⩨$2141$)","expression":"(⫏≰2010010≫≃)⩨(⫏≰10002110⩨⫏≰2221022)","highest_n_order":2,"priority_hierarchical_complexity":2,"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":1542,"base":3}},"right_expr":{"type":"binary","operator":"⩨","left_expr":{"type":"numeric_atoms","value":2253,"base":3},"right_expr":{"type":"numeric_atoms","value":2141,"base":3}}},"used_operators":["2DlMacCsIx","X99M06cbEe"],"dependent_operators":["D4vGDi5EA2","XhwjNDsVaA","JLbD19bQDL","2td37pGCOC","D4vGDi5EA2","EBcxylXtPf","9HNa5Wba9A"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1542","layer":2},{"info":"compute unary expreesion, input=1542, op_id = X99M06cbEe, unary_op_definition = 'a≫≃ = { (a*315) , if (a≦≮≮)>=13 and (⩦⩻⨪a)!=26 and a>=80 ; (a⫌⩹⨱) , else }', output=4485","layer":1},{"info":"number node, value=2253","layer":2},{"info":"number node, value=2141","layer":2},{"info":"compute binary expreesion, left_input=2253, right_input=2141, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":1},{"info":"compute binary expreesion, left_input=4485, right_input=0, op_id = 2DlMacCsIx binary_op_definition= 'a⩨b = { a , if (a⪠⩆⊳)>43 ; ((b/a)≦≮≮) , else }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2010010≫≃)⩨(⫏≰10002110⩨⫏≰2221022)=⫏≰0","reverse_text":"⫏≰0=(⫏≰2010010≫≃)⩨(⫏≰10002110⩨⫏≰2221022)","cot":[{"info":"⫏≰2010010≫≃=⫏≰20011010","layer":1},{"info":"⫏≰10002110⩨⫏≰2221022=⫏≰0","layer":1},{"info":"⫏≰20011010⩨⫏≰0=⫏≰0","layer":0}]}
{"id":931,"expression_no_base_symbol":"$1744$≎⊠⪸$2907$≭($5838$⪄$1604$)","expression":"⫏≰2101121≎⊠⪸⫏≰10222200≭(⫏≰22000020⪄⫏≰2012102)","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":366,"operation_count":3,"complexity_ratio":122.0,"tree":{"type":"binary","operator":"≭","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1744,"base":3},"right_expr":{"type":"numeric_atoms","value":2907,"base":3}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":5838,"base":3},"right_expr":{"type":"numeric_atoms","value":1604,"base":3}}},"used_operators":["rxpJgHHUmx","bJkvcejdHO","SUmda5xLS4"],"dependent_operators":["AHs5Up7iyr","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1744","layer":2},{"info":"number node, value=2907","layer":2},{"info":"compute binary expreesion, left_input=1744, right_input=2907, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=451223","layer":1},{"info":"number node, value=5838","layer":2},{"info":"number node, value=1604","layer":2},{"info":"compute binary expreesion, left_input=5838, right_input=1604, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-866529","layer":1},{"info":"compute binary expreesion, left_input=451223, right_input=-866529, 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":3,"result_base":3,"text":"⫏≰2101121≎⊠⪸⫏≰10222200≭(⫏≰22000020⪄⫏≰2012102)=NaN","reverse_text":"NaN=⫏≰2101121≎⊠⪸⫏≰10222200≭(⫏≰22000020⪄⫏≰2012102)","cot":[{"info":"⫏≰2101121≎⊠⪸⫏≰10222200=⫏≰211220221222","layer":1},{"info":"⫏≰22000020⪄⫏≰2012102=⫏≰-1122000122200","layer":1},{"info":"⫏≰211220221222≭⫏≰-1122000122200=NaN","layer":0}]}
{"id":932,"expression_no_base_symbol":"($2898$⫌⩹⨱)/(↥$1759$)","expression":"(⫏≰10222100⫌⩹⨱)/(↥⫏≰2102011)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":328,"operation_count":3,"complexity_ratio":109.33333333333333,"tree":{"type":"binary","operator":"/","left_expr":{"type":"unary","operator":"⫌⩹⨱","unary_expr":{"type":"numeric_atoms","value":2898,"base":3}},"right_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":1759,"base":3}}},"used_operators":["XhwjNDsVaA","EBcxylXtPf","A8NUZmVepG"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","rysDP5nf3Z","k8jYdgA6NY"],"result":"⫏≰101122","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2898","layer":2},{"info":"compute unary expreesion, input=2898, op_id = EBcxylXtPf, unary_op_definition = 'a⫌⩹⨱ = { (((80+a)+(750-a))+((149+422)+(a+a))) }', output=7197","layer":1},{"info":"number node, value=1759","layer":2},{"info":"compute unary expreesion, input=1759, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=25","layer":1},{"info":"compute binary expreesion, left_input=7197, right_input=25, op_id = XhwjNDsVaA binary_op_definition= 'None', output=287","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10222100⫌⩹⨱)/(↥⫏≰2102011)=⫏≰101122","reverse_text":"⫏≰101122=(⫏≰10222100⫌⩹⨱)/(↥⫏≰2102011)","cot":[{"info":"⫏≰10222100⫌⩹⨱=⫏≰100212120","layer":1},{"info":"↥⫏≰2102011=⫏≰221","layer":1},{"info":"⫏≰100212120/⫏≰221=⫏≰101122","layer":0}]}
{"id":933,"expression_no_base_symbol":"⇁⨣⪵$2369$⨓$1239$","expression":"⇁⨣⪵⫏≰10020202⨓⫏≰1200220","highest_n_order":5,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1246,"operation_count":2,"complexity_ratio":623.0,"tree":{"type":"unary","operator":"⇁⨣⪵","unary_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":2369,"base":3},"right_expr":{"type":"numeric_atoms","value":1239,"base":3}}},"used_operators":["inkyxCbjAn","3ViojmjbAp"],"dependent_operators":["B5M0gjZbta","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2369","layer":2},{"info":"number node, value=1239","layer":2},{"info":"compute binary expreesion, left_input=2369, right_input=1239, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-1242","layer":1},{"info":"compute unary expreesion, input=-1242, op_id = inkyxCbjAn, unary_op_definition = '⇁⨣⪵a = { (a↬a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⇁⨣⪵⫏≰10020202⨓⫏≰1200220=NaN","reverse_text":"NaN=⇁⨣⪵⫏≰10020202⨓⫏≰1200220","cot":[{"info":"⫏≰10020202⨓⫏≰1200220=⫏≰-1201000","layer":1},{"info":"⇁⨣⪵⫏≰-1201000=NaN","layer":0}]}
{"id":934,"expression_no_base_symbol":"(⨵≀≌$5029$)∀⇚≩$1398$⪮%⊝$4785$","expression":"(⨵≀≌⫏≰20220021)∀⇚≩⫏≰1220210⪮%⊝⫏≰20120020","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":105621,"operation_count":3,"complexity_ratio":35207.0,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":5029,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1398,"base":3},"right_expr":{"type":"numeric_atoms","value":4785,"base":3}}},"used_operators":["LRNGc0VcxI","srAu1WTS94","IWmyXbctLI"],"dependent_operators":["X99M06cbEe","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5029","layer":2},{"info":"compute unary expreesion, input=5029, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-15087","layer":1},{"info":"number node, value=1398","layer":2},{"info":"number node, value=4785","layer":2},{"info":"compute binary expreesion, left_input=1398, right_input=4785, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=3112","layer":1},{"info":"compute binary expreesion, left_input=-15087, right_input=3112, 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":3,"result_base":3,"text":"(⨵≀≌⫏≰20220021)∀⇚≩⫏≰1220210⪮%⊝⫏≰20120020=NaN","reverse_text":"NaN=(⨵≀≌⫏≰20220021)∀⇚≩⫏≰1220210⪮%⊝⫏≰20120020","cot":[{"info":"⨵≀≌⫏≰20220021=⫏≰-202200210","layer":1},{"info":"⫏≰1220210⪮%⊝⫏≰20120020=⫏≰11021021","layer":1},{"info":"⫏≰-202200210∀⇚≩⫏≰11021021=NaN","layer":0}]}
{"id":935,"expression_no_base_symbol":"$3613$⋓$1459$⨳⩥⨓($4656$⪨≂$2326$)","expression":"⫏≰11221211⋓⫏≰2000001⨳⩥⨓(⫏≰20101110⪨≂⫏≰10012011)","highest_n_order":3,"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":3613,"base":3},"right_expr":{"type":"numeric_atoms","value":1459,"base":3}},"right_expr":{"type":"binary","operator":"⪨≂","left_expr":{"type":"numeric_atoms","value":4656,"base":3},"right_expr":{"type":"numeric_atoms","value":2326,"base":3}}},"used_operators":["nCS4ZIUYfx","T2fj7uvVaJ","sdazOOVcIp"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰20112101","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3613","layer":2},{"info":"number node, value=1459","layer":2},{"info":"compute binary expreesion, left_input=3613, right_input=1459, 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=4656","layer":2},{"info":"number node, value=2326","layer":2},{"info":"compute binary expreesion, left_input=4656, right_input=2326, 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=4762","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=4762, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=4762","layer":0}],"base":3,"result_base":3,"text":"⫏≰11221211⋓⫏≰2000001⨳⩥⨓(⫏≰20101110⪨≂⫏≰10012011)=⫏≰20112101","reverse_text":"⫏≰20112101=⫏≰11221211⋓⫏≰2000001⨳⩥⨓(⫏≰20101110⪨≂⫏≰10012011)","cot":[{"info":"⫏≰11221211⋓⫏≰2000001=⫏≰0","layer":1},{"info":"⫏≰20101110⪨≂⫏≰10012011=⫏≰20112101","layer":1},{"info":"⫏≰0⨳⩥⨓⫏≰20112101=⫏≰20112101","layer":0}]}
{"id":936,"expression_no_base_symbol":"⊥($3991$⊉≛↸$4714$)","expression":"⊥(⫏≰12110211⊉≛↸⫏≰20110121)","highest_n_order":4,"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":3991,"base":3},"right_expr":{"type":"numeric_atoms","value":4714,"base":3}}},"used_operators":["Q3PJZHRvZv","DZ8iAZOCBD"],"dependent_operators":["fu6greOZ01","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3991","layer":2},{"info":"number node, value=4714","layer":2},{"info":"compute binary expreesion, left_input=3991, right_input=4714, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=7982","layer":1},{"info":"compute unary expreesion, input=7982, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊥(⫏≰12110211⊉≛↸⫏≰20110121)=NaN","reverse_text":"NaN=⊥(⫏≰12110211⊉≛↸⫏≰20110121)","cot":[{"info":"⫏≰12110211⊉≛↸⫏≰20110121=⫏≰101221122","layer":1},{"info":"⊥⫏≰101221122=NaN","layer":0}]}
{"id":937,"expression_no_base_symbol":"(⫓⪴$2551$)⋷(↔$1354$)","expression":"(⫓⪴⫏≰10111111)⋷(↔⫏≰1212011)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":2561,"operation_count":3,"complexity_ratio":853.6666666666666,"tree":{"type":"binary","operator":"⋷","left_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":2551,"base":3}},"right_expr":{"type":"unary","operator":"↔","unary_expr":{"type":"numeric_atoms","value":1354,"base":3}}},"used_operators":["23Mk6UjR3U","eLxqMNBOBk","ruOEQAzv1W"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","9HNa5Wba9A","XhwjNDsVaA","Qy55tPpLXF","12rbrZMWeM","AF7qkfDlqP","D4vGDi5EA2","EBcxylXtPf","23Mk6UjR3U","8w2t5hMYqp"],"result":"⫏≰-110020201201100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2551","layer":2},{"info":"compute unary expreesion, input=2551, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=6507601","layer":1},{"info":"number node, value=1354","layer":2},{"info":"compute unary expreesion, input=1354, op_id = ruOEQAzv1W, unary_op_definition = '↔a = { (⨑⩽⪐a) , if (a≦≮≮)<69 ; (((a⋳⪒a)⋥≓≎(a/a))⋷(⊄⩳↩(a⫌⩹⨱))) , else }', output=-1081","layer":1},{"info":"compute binary expreesion, left_input=6507601, right_input=-1081, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=-6509763","layer":0}],"base":3,"result_base":3,"text":"(⫓⪴⫏≰10111111)⋷(↔⫏≰1212011)=⫏≰-110020201201100","reverse_text":"⫏≰-110020201201100=(⫓⪴⫏≰10111111)⋷(↔⫏≰1212011)","cot":[{"info":"⫓⪴⫏≰10111111=⫏≰110020121202021","layer":1},{"info":"↔⫏≰1212011=⫏≰-1111001","layer":1},{"info":"⫏≰110020121202021⋷⫏≰-1111001=⫏≰-110020201201100","layer":0}]}
{"id":938,"expression_no_base_symbol":"(⫛⫱⨽$1416$)⊠≄⫣","expression":"(⫛⫱⨽⫏≰1221110)⊠≄⫣","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":1416,"base":3}}},"used_operators":["DIvbN7qnHd","DlLNRPXxWL"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","rGHVDoGpnC"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1416","layer":2},{"info":"compute unary expreesion, input=1416, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":1},{"info":"compute unary expreesion, input=0, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":0}],"base":3,"result_base":3,"text":"(⫛⫱⨽⫏≰1221110)⊠≄⫣=⫏≰0","reverse_text":"⫏≰0=(⫛⫱⨽⫏≰1221110)⊠≄⫣","cot":[{"info":"⫛⫱⨽⫏≰1221110=⫏≰0","layer":1},{"info":"⫏≰0⊠≄⫣=⫏≰0","layer":0}]}
{"id":939,"expression_no_base_symbol":"⫛⫱⨽(-$3584$)","expression":"⫛⫱⨽(-⫏≰11220202)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1423,"operation_count":2,"complexity_ratio":711.5,"tree":{"type":"unary","operator":"⫛⫱⨽","unary_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":3584,"base":3}}},"used_operators":["DlLNRPXxWL","t8gj7n24qd"],"dependent_operators":["rGHVDoGpnC"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3584","layer":2},{"info":"compute unary expreesion, input=3584, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-3584","layer":1},{"info":"compute unary expreesion, input=-3584, op_id = DlLNRPXxWL, unary_op_definition = '⫛⫱⨽a = { (a⨟⋌⩍228) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫛⫱⨽(-⫏≰11220202)=⫏≰0","reverse_text":"⫏≰0=⫛⫱⨽(-⫏≰11220202)","cot":[{"info":"-⫏≰11220202=⫏≰-11220202","layer":1},{"info":"⫛⫱⨽⫏≰-11220202=⫏≰0","layer":0}]}
{"id":940,"expression_no_base_symbol":"($8372$∀⇚≩$2118$)⊴($1879$⪮%⊝$4157$)","expression":"(⫏≰102111002∀⇚≩⫏≰2220110)⊴(⫏≰2120121⪮%⊝⫏≰12200222)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":62693,"operation_count":3,"complexity_ratio":20897.666666666668,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":8372,"base":3},"right_expr":{"type":"numeric_atoms","value":2118,"base":3}},"right_expr":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"numeric_atoms","value":1879,"base":3},"right_expr":{"type":"numeric_atoms","value":4157,"base":3}}},"used_operators":["Nsiff2A1zJ","LRNGc0VcxI","IWmyXbctLI"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","X99M06cbEe","9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=8372","layer":2},{"info":"number node, value=2118","layer":2},{"info":"compute binary expreesion, left_input=8372, right_input=2118, 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=1879","layer":2},{"info":"number node, value=4157","layer":2},{"info":"compute binary expreesion, left_input=1879, right_input=4157, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=4074","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=4074, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰102111002∀⇚≩⫏≰2220110)⊴(⫏≰2120121⪮%⊝⫏≰12200222)=NaN","reverse_text":"NaN=(⫏≰102111002∀⇚≩⫏≰2220110)⊴(⫏≰2120121⪮%⊝⫏≰12200222)","cot":[{"info":"⫏≰102111002∀⇚≩⫏≰2220110=NaN","layer":1},{"info":"⫏≰2120121⪮%⊝⫏≰12200222=⫏≰12120220","layer":1},{"info":"NaN⊴⫏≰12120220=NaN","layer":0}]}
{"id":941,"expression_no_base_symbol":"$1375$⨳⩥⨓$1774$⊠≄⫣","expression":"⫏≰1212221⨳⩥⨓⫏≰2102201⊠≄⫣","highest_n_order":1,"priority_hierarchical_complexity":1,"normalized_expansion_degree":6,"operation_count":2,"complexity_ratio":3.0,"tree":{"type":"unary","operator":"⊠≄⫣","unary_expr":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"numeric_atoms","value":1375,"base":3},"right_expr":{"type":"numeric_atoms","value":1774,"base":3}}},"used_operators":["DIvbN7qnHd","nCS4ZIUYfx"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1375","layer":2},{"info":"number node, value=1774","layer":2},{"info":"compute binary expreesion, left_input=1375, right_input=1774, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=399","layer":1},{"info":"compute unary expreesion, input=399, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":0}],"base":3,"result_base":3,"text":"⫏≰1212221⨳⩥⨓⫏≰2102201⊠≄⫣=⫏≰0","reverse_text":"⫏≰0=⫏≰1212221⨳⩥⨓⫏≰2102201⊠≄⫣","cot":[{"info":"⫏≰1212221⨳⩥⨓⫏≰2102201=⫏≰112210","layer":1},{"info":"⫏≰112210⊠≄⫣=⫏≰0","layer":0}]}
{"id":942,"expression_no_base_symbol":"($3889$+$3416$)+⇶⊼$3437$⇷$1214$","expression":"(⫏≰12100001+⫏≰11200112)+⇶⊼⫏≰11201022⇷⫏≰1122222","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":48126,"operation_count":3,"complexity_ratio":16042.0,"tree":{"type":"binary","operator":"+⇶⊼","left_expr":{"type":"binary","operator":"+","left_expr":{"type":"numeric_atoms","value":3889,"base":3},"right_expr":{"type":"numeric_atoms","value":3416,"base":3}},"right_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":3437,"base":3},"right_expr":{"type":"numeric_atoms","value":1214,"base":3}}},"used_operators":["TpPTUOHfaN","W4YGzv6Whe","mp7IySMOzn"],"dependent_operators":["AHs5Up7iyr","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3889","layer":2},{"info":"number node, value=3416","layer":2},{"info":"compute binary expreesion, left_input=3889, right_input=3416, op_id = W4YGzv6Whe binary_op_definition= 'None', output=7305","layer":1},{"info":"number node, value=3437","layer":2},{"info":"number node, value=1214","layer":2},{"info":"compute binary expreesion, left_input=3437, right_input=1214, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=2428","layer":1},{"info":"compute binary expreesion, left_input=7305, right_input=2428, 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":3,"result_base":3,"text":"(⫏≰12100001+⫏≰11200112)+⇶⊼⫏≰11201022⇷⫏≰1122222=NaN","reverse_text":"NaN=(⫏≰12100001+⫏≰11200112)+⇶⊼⫏≰11201022⇷⫏≰1122222","cot":[{"info":"⫏≰12100001+⫏≰11200112=⫏≰101000120","layer":1},{"info":"⫏≰11201022⇷⫏≰1122222=⫏≰10022221","layer":1},{"info":"⫏≰101000120+⇶⊼⫏≰10022221=NaN","layer":0}]}
{"id":943,"expression_no_base_symbol":"($2632$⨐⩸⫘$1004$)⫩⊇","expression":"(⫏≰10121111⨐⩸⫘⫏≰1101012)⫩⊇","highest_n_order":4,"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":2632,"base":3},"right_expr":{"type":"numeric_atoms","value":1004,"base":3}}},"used_operators":["BjRHVeLaeN","fu6greOZ01"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2632","layer":2},{"info":"number node, value=1004","layer":2},{"info":"compute binary expreesion, left_input=2632, right_input=1004, 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 unary expreesion, input=nan, op_id = BjRHVeLaeN, unary_op_definition = 'a⫩⊇ = { (-(a-42)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰10121111⨐⩸⫘⫏≰1101012)⫩⊇=NaN","reverse_text":"NaN=(⫏≰10121111⨐⩸⫘⫏≰1101012)⫩⊇","cot":[{"info":"⫏≰10121111⨐⩸⫘⫏≰1101012=NaN","layer":1},{"info":"NaN⫩⊇=NaN","layer":0}]}
{"id":944,"expression_no_base_symbol":"$3298$/$1796$/$5204$≹⇙⪍$1522$","expression":"⫏≰11112011/⫏≰2110112/⫏≰21010202≹⇙⪍⫏≰2002101","highest_n_order":4,"priority_hierarchical_complexity":2,"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":3298,"base":3},"right_expr":{"type":"numeric_atoms","value":1796,"base":3}},"right_expr":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"numeric_atoms","value":5204,"base":3},"right_expr":{"type":"numeric_atoms","value":1522,"base":3}}},"used_operators":["XhwjNDsVaA","AHs5Up7iyr"],"dependent_operators":["rysDP5nf3Z","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3298","layer":2},{"info":"number node, value=1796","layer":2},{"info":"compute binary expreesion, left_input=3298, right_input=1796, op_id = XhwjNDsVaA binary_op_definition= 'None', output=1","layer":1},{"info":"number node, value=5204","layer":2},{"info":"number node, value=1522","layer":2},{"info":"compute binary expreesion, left_input=5204, right_input=1522, 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=1, right_input=nan, op_id = XhwjNDsVaA binary_op_definition= 'None', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11112011/⫏≰2110112/⫏≰21010202≹⇙⪍⫏≰2002101=NaN","reverse_text":"NaN=⫏≰11112011/⫏≰2110112/⫏≰21010202≹⇙⪍⫏≰2002101","cot":[{"info":"⫏≰11112011/⫏≰2110112=⫏≰1","layer":1},{"info":"⫏≰21010202≹⇙⪍⫏≰2002101=NaN","layer":1},{"info":"⫏≰1/NaN=NaN","layer":0}]}
{"id":945,"expression_no_base_symbol":"($4392$⨸⪁$5185$)⨓($1604$⪄$1311$)","expression":"(⫏≰20000200⨸⪁⫏≰21010001)⨓(⫏≰2012102⪄⫏≰1210120)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":238829,"operation_count":3,"complexity_ratio":79609.66666666667,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":4392,"base":3},"right_expr":{"type":"numeric_atoms","value":5185,"base":3}},"right_expr":{"type":"binary","operator":"⪄","left_expr":{"type":"numeric_atoms","value":1604,"base":3},"right_expr":{"type":"numeric_atoms","value":1311,"base":3}}},"used_operators":["3ViojmjbAp","g55IO6H4Gj","SUmda5xLS4"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C"],"result":"⫏≰-110010110210","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4392","layer":2},{"info":"number node, value=5185","layer":2},{"info":"compute binary expreesion, left_input=4392, right_input=5185, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=19154","layer":1},{"info":"number node, value=1604","layer":2},{"info":"number node, value=1311","layer":2},{"info":"compute binary expreesion, left_input=1604, right_input=1311, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-238725","layer":1},{"info":"compute binary expreesion, left_input=19154, right_input=-238725, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-238728","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20000200⨸⪁⫏≰21010001)⨓(⫏≰2012102⪄⫏≰1210120)=⫏≰-110010110210","reverse_text":"⫏≰-110010110210=(⫏≰20000200⨸⪁⫏≰21010001)⨓(⫏≰2012102⪄⫏≰1210120)","cot":[{"info":"⫏≰20000200⨸⪁⫏≰21010001=⫏≰222021102","layer":1},{"info":"⫏≰2012102⪄⫏≰1210120=⫏≰-110010110200","layer":1},{"info":"⫏≰222021102⨓⫏≰-110010110200=⫏≰-110010110210","layer":0}]}
{"id":946,"expression_no_base_symbol":"(∥⊫$5543$)⨰($3609$⩠)","expression":"(∥⊫⫏≰21121022)⨰(⫏≰11221200⩠)","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":5543,"base":3}},"right_expr":{"type":"unary","operator":"⩠","unary_expr":{"type":"numeric_atoms","value":3609,"base":3}}},"used_operators":["eewbuw0ToL","P8v4zCKN1o","sJAwomhLZr"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","sdazOOVcIp","i8ToyICDmI","k8jYdgA6NY","eH2TOUuTDT","W4YGzv6Whe","Z2TMIBDE3Q","COABgblf1C"],"result":"⫏≰22210211","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5543","layer":2},{"info":"compute unary expreesion, input=5543, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=6411","layer":1},{"info":"number node, value=3609","layer":2},{"info":"compute unary expreesion, input=3609, op_id = sJAwomhLZr, unary_op_definition = 'a⩠ = { (((a+a)⊭↱(a⪨≂a))∲⫓((a⩤)%(a⪐))) }', output=0","layer":1},{"info":"compute binary expreesion, left_input=6411, right_input=0, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=6421","layer":0}],"base":3,"result_base":3,"text":"(∥⊫⫏≰21121022)⨰(⫏≰11221200⩠)=⫏≰22210211","reverse_text":"⫏≰22210211=(∥⊫⫏≰21121022)⨰(⫏≰11221200⩠)","cot":[{"info":"∥⊫⫏≰21121022=⫏≰22210110","layer":1},{"info":"⫏≰11221200⩠=⫏≰0","layer":1},{"info":"⫏≰22210110⨰⫏≰0=⫏≰22210211","layer":0}]}
{"id":947,"expression_no_base_symbol":"⨰⫟⨤$3666$⨪↰⇹$1936$","expression":"⨰⫟⨤⫏≰12000210⨪↰⇹⫏≰2122201","highest_n_order":3,"priority_hierarchical_complexity":1,"normalized_expansion_degree":17490,"operation_count":2,"complexity_ratio":8745.0,"tree":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":3666,"base":3},"right_expr":{"type":"numeric_atoms","value":1936,"base":3}}},"used_operators":["Tw270M8GLb","tmPS8pqC7x"],"dependent_operators":["sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw","rJVOvQCfKK"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3666","layer":2},{"info":"number node, value=1936","layer":2},{"info":"compute binary expreesion, left_input=3666, right_input=1936, 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=3666","layer":1},{"info":"compute unary expreesion, input=3666, op_id = Tw270M8GLb, unary_op_definition = '⨰⫟⨤a = { (((13⪢a)⨳⩥⨓(a⪢a))⪨≂((a⩷∴417)⨽(758⪒a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⨰⫟⨤⫏≰12000210⨪↰⇹⫏≰2122201=NaN","reverse_text":"NaN=⨰⫟⨤⫏≰12000210⨪↰⇹⫏≰2122201","cot":[{"info":"⫏≰12000210⨪↰⇹⫏≰2122201=⫏≰12000210","layer":1},{"info":"⨰⫟⨤⫏≰12000210=NaN","layer":0}]}
{"id":948,"expression_no_base_symbol":"$2181$⪛$8051$⨳⩥⨓($2551$↙$5054$)","expression":"⫏≰2222210⪛⫏≰102001012⨳⩥⨓(⫏≰10111111↙⫏≰20221012)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":5064,"operation_count":3,"complexity_ratio":1688.0,"tree":{"type":"binary","operator":"⨳⩥⨓","left_expr":{"type":"binary","operator":"⪛","left_expr":{"type":"numeric_atoms","value":2181,"base":3},"right_expr":{"type":"numeric_atoms","value":8051,"base":3}},"right_expr":{"type":"binary","operator":"↙","left_expr":{"type":"numeric_atoms","value":2551,"base":3},"right_expr":{"type":"numeric_atoms","value":5054,"base":3}}},"used_operators":["nCS4ZIUYfx","uFcxV4UQCh","yyfyN0ffXY"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","tmPS8pqC7x","DpFCA1CohY"],"result":"⫏≰-212210100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2181","layer":2},{"info":"number node, value=8051","layer":2},{"info":"compute binary expreesion, left_input=2181, right_input=8051, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=2181","layer":1},{"info":"number node, value=2551","layer":2},{"info":"number node, value=5054","layer":2},{"info":"compute binary expreesion, left_input=2551, right_input=5054, op_id = yyfyN0ffXY binary_op_definition= 'a↙b = { (⋗⩬⋾(b⨪↰⇹a)) , if a>=87 ; a , else }', output=-15162","layer":1},{"info":"compute binary expreesion, left_input=2181, right_input=-15162, op_id = nCS4ZIUYfx binary_op_definition= 'a⨳⩥⨓b = { ((b+a)-(a+a)) }', output=-17343","layer":0}],"base":3,"result_base":3,"text":"⫏≰2222210⪛⫏≰102001012⨳⩥⨓(⫏≰10111111↙⫏≰20221012)=⫏≰-212210100","reverse_text":"⫏≰-212210100=⫏≰2222210⪛⫏≰102001012⨳⩥⨓(⫏≰10111111↙⫏≰20221012)","cot":[{"info":"⫏≰2222210⪛⫏≰102001012=⫏≰2222210","layer":1},{"info":"⫏≰10111111↙⫏≰20221012=⫏≰-202210120","layer":1},{"info":"⫏≰2222210⨳⩥⨓⫏≰-202210120=⫏≰-212210100","layer":0}]}
{"id":949,"expression_no_base_symbol":"↩(⊥$2166$)","expression":"↩(⊥⫏≰2222020)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":20,"operation_count":2,"complexity_ratio":10.0,"tree":{"type":"unary","operator":"↩","unary_expr":{"type":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":2166,"base":3}}},"used_operators":["jLgFTUHLKL","Q3PJZHRvZv"],"dependent_operators":["sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D","fu6greOZ01"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2166","layer":2},{"info":"compute unary expreesion, input=2166, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↩(⊥⫏≰2222020)=NaN","reverse_text":"NaN=↩(⊥⫏≰2222020)","cot":[{"info":"⊥⫏≰2222020=NaN","layer":1},{"info":"↩NaN=NaN","layer":0}]}
{"id":950,"expression_no_base_symbol":"($5184$/$1910$)⪒$1266$⪒$2033$","expression":"(⫏≰21010000/⫏≰2121202)⪒⫏≰1201220⪒⫏≰2210022","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⪒","left_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":5184,"base":3},"right_expr":{"type":"numeric_atoms","value":1910,"base":3}},"right_expr":{"type":"binary","operator":"⪒","left_expr":{"type":"numeric_atoms","value":1266,"base":3},"right_expr":{"type":"numeric_atoms","value":2033,"base":3}}},"used_operators":["f6k1SAg4EE","XhwjNDsVaA"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z"],"result":"⫏≰11112010","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5184","layer":2},{"info":"number node, value=1910","layer":2},{"info":"compute binary expreesion, left_input=5184, right_input=1910, op_id = XhwjNDsVaA binary_op_definition= 'None', output=2","layer":1},{"info":"number node, value=1266","layer":2},{"info":"number node, value=2033","layer":2},{"info":"compute binary expreesion, left_input=1266, right_input=2033, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-3299","layer":1},{"info":"compute binary expreesion, left_input=2, right_input=-3299, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=3297","layer":0}],"base":3,"result_base":3,"text":"(⫏≰21010000/⫏≰2121202)⪒⫏≰1201220⪒⫏≰2210022=⫏≰11112010","reverse_text":"⫏≰11112010=(⫏≰21010000/⫏≰2121202)⪒⫏≰1201220⪒⫏≰2210022","cot":[{"info":"⫏≰21010000/⫏≰2121202=⫏≰2","layer":1},{"info":"⫏≰1201220⪒⫏≰2210022=⫏≰-11112012","layer":1},{"info":"⫏≰2⪒⫏≰-11112012=⫏≰11112010","layer":0}]}
{"id":951,"expression_no_base_symbol":"($1545$∲⫓$1977$)≹⇙⪍($4120$⨵⪆$3119$)","expression":"(⫏≰2010020∲⫓⫏≰2201020)≹⇙⪍(⫏≰12122121⨵⪆⫏≰11021112)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":25603,"operation_count":3,"complexity_ratio":8534.333333333334,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"∲⫓","left_expr":{"type":"numeric_atoms","value":1545,"base":3},"right_expr":{"type":"numeric_atoms","value":1977,"base":3}},"right_expr":{"type":"binary","operator":"⨵⪆","left_expr":{"type":"numeric_atoms","value":4120,"base":3},"right_expr":{"type":"numeric_atoms","value":3119,"base":3}}},"used_operators":["AHs5Up7iyr","i8ToyICDmI","2DQ55sFlQl"],"dependent_operators":["dWAJyo7jo9","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1545","layer":2},{"info":"number node, value=1977","layer":2},{"info":"compute binary expreesion, left_input=1545, right_input=1977, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=4120","layer":2},{"info":"number node, value=3119","layer":2},{"info":"compute binary expreesion, left_input=4120, right_input=3119, 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=0, right_input=160, 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":3,"result_base":3,"text":"(⫏≰2010020∲⫓⫏≰2201020)≹⇙⪍(⫏≰12122121⨵⪆⫏≰11021112)=NaN","reverse_text":"NaN=(⫏≰2010020∲⫓⫏≰2201020)≹⇙⪍(⫏≰12122121⨵⪆⫏≰11021112)","cot":[{"info":"⫏≰2010020∲⫓⫏≰2201020=⫏≰0","layer":1},{"info":"⫏≰12122121⨵⪆⫏≰11021112=⫏≰12221","layer":1},{"info":"⫏≰0≹⇙⪍⫏≰12221=NaN","layer":0}]}
{"id":952,"expression_no_base_symbol":"≉($1002$+$2281$)","expression":"≉(⫏≰1101010+⫏≰10010111)","highest_n_order":1,"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":1002,"base":3},"right_expr":{"type":"numeric_atoms","value":2281,"base":3}}},"used_operators":["e1ybzncUwg","W4YGzv6Whe"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰12020021","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1002","layer":2},{"info":"number node, value=2281","layer":2},{"info":"compute binary expreesion, left_input=1002, right_input=2281, op_id = W4YGzv6Whe binary_op_definition= 'None', output=3283","layer":1},{"info":"compute unary expreesion, input=3283, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=3814","layer":0}],"base":3,"result_base":3,"text":"≉(⫏≰1101010+⫏≰10010111)=⫏≰12020021","reverse_text":"⫏≰12020021=≉(⫏≰1101010+⫏≰10010111)","cot":[{"info":"⫏≰1101010+⫏≰10010111=⫏≰11111121","layer":1},{"info":"≉⫏≰11111121=⫏≰12020021","layer":0}]}
{"id":953,"expression_no_base_symbol":"$1280$≎⊠⪸$5032$⪨≂(↩$1020$)","expression":"⫏≰1202102≎⊠⪸⫏≰20220101⪨≂(↩⫏≰1101210)","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":1280,"base":3},"right_expr":{"type":"numeric_atoms","value":5032,"base":3}},"right_expr":{"type":"unary","operator":"↩","unary_expr":{"type":"numeric_atoms","value":1020,"base":3}}},"used_operators":["sdazOOVcIp","bJkvcejdHO","jLgFTUHLKL"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D"],"result":"⫏≰1021012010022","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1280","layer":2},{"info":"number node, value=5032","layer":2},{"info":"compute binary expreesion, left_input=1280, right_input=5032, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=331047","layer":1},{"info":"number node, value=1020","layer":2},{"info":"compute unary expreesion, input=1020, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-5380","layer":1},{"info":"compute binary expreesion, left_input=331047, right_input=-5380, 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=672956","layer":0}],"base":3,"result_base":3,"text":"⫏≰1202102≎⊠⪸⫏≰20220101⪨≂(↩⫏≰1101210)=⫏≰1021012010022","reverse_text":"⫏≰1021012010022=⫏≰1202102≎⊠⪸⫏≰20220101⪨≂(↩⫏≰1101210)","cot":[{"info":"⫏≰1202102≎⊠⪸⫏≰20220101=⫏≰121211010000","layer":1},{"info":"↩⫏≰1101210=⫏≰-21101021","layer":1},{"info":"⫏≰121211010000⪨≂⫏≰-21101021=⫏≰1021012010022","layer":0}]}
{"id":954,"expression_no_base_symbol":"↽≂$1586$⨎$7377$","expression":"↽≂⫏≰2011202⨎⫏≰101010020","highest_n_order":2,"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":1586,"base":3},"right_expr":{"type":"numeric_atoms","value":7377,"base":3}}},"used_operators":["u6S6b8DprG","rJVOvQCfKK"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","Qy55tPpLXF","t8gj7n24qd","XhwjNDsVaA"],"result":"⫏≰-202020110","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1586","layer":2},{"info":"number node, value=7377","layer":2},{"info":"compute binary expreesion, left_input=1586, right_input=7377, op_id = rJVOvQCfKK binary_op_definition= 'a⨎b = { (-(b/b)) , if (-a)!=278 and a>350 and (b⋥≓≎155)==21 ; b , else }', output=7377","layer":1},{"info":"compute unary expreesion, input=7377, op_id = u6S6b8DprG, unary_op_definition = '↽≂a = { (-(a+a)) , if a<=64 or (-a)>182 or a!=568 ; ((a-a)-(a-a)) , else }', output=-14754","layer":0}],"base":3,"result_base":3,"text":"↽≂⫏≰2011202⨎⫏≰101010020=⫏≰-202020110","reverse_text":"⫏≰-202020110=↽≂⫏≰2011202⨎⫏≰101010020","cot":[{"info":"⫏≰2011202⨎⫏≰101010020=⫏≰101010020","layer":1},{"info":"↽≂⫏≰101010020=⫏≰-202020110","layer":0}]}
{"id":955,"expression_no_base_symbol":"↣≠⋷($1041$⨐⩸⫘$7362$)","expression":"↣≠⋷(⫏≰1102120⨐⩸⫘⫏≰101002200)","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":1041,"base":3},"right_expr":{"type":"numeric_atoms","value":7362,"base":3}}},"used_operators":["Asc51vEJeQ","fu6greOZ01"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1041","layer":2},{"info":"number node, value=7362","layer":2},{"info":"compute binary expreesion, left_input=1041, right_input=7362, 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 unary expreesion, input=nan, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(⫏≰1102120⨐⩸⫘⫏≰101002200)=NaN","reverse_text":"NaN=↣≠⋷(⫏≰1102120⨐⩸⫘⫏≰101002200)","cot":[{"info":"⫏≰1102120⨐⩸⫘⫏≰101002200=NaN","layer":1},{"info":"↣≠⋷NaN=NaN","layer":0}]}
{"id":956,"expression_no_base_symbol":"(+⊝⨔$3207$)⪮%⊝$8145$⊴$2303$","expression":"(+⊝⨔⫏≰11101210)⪮%⊝⫏≰102011200⊴⫏≰10011022","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2717,"operation_count":3,"complexity_ratio":905.6666666666666,"tree":{"type":"binary","operator":"⪮%⊝","left_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":3207,"base":3}},"right_expr":{"type":"binary","operator":"⊴","left_expr":{"type":"numeric_atoms","value":8145,"base":3},"right_expr":{"type":"numeric_atoms","value":2303,"base":3}}},"used_operators":["IWmyXbctLI","DhbWaqg5eL","Nsiff2A1zJ"],"dependent_operators":["9FxExcQeMw","xUOZtlo3hN","k8jYdgA6NY","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","dWAJyo7jo9","14qkJME0vr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3207","layer":2},{"info":"compute unary expreesion, input=3207, 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=8145","layer":2},{"info":"number node, value=2303","layer":2},{"info":"compute binary expreesion, left_input=8145, right_input=2303, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=1522, right_input=nan, op_id = IWmyXbctLI binary_op_definition= 'a⪮%⊝b = { ((b%b)⩷∴(⨞⊢a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(+⊝⨔⫏≰11101210)⪮%⊝⫏≰102011200⊴⫏≰10011022=NaN","reverse_text":"NaN=(+⊝⨔⫏≰11101210)⪮%⊝⫏≰102011200⊴⫏≰10011022","cot":[{"info":"+⊝⨔⫏≰11101210=⫏≰2002101","layer":1},{"info":"⫏≰102011200⊴⫏≰10011022=NaN","layer":1},{"info":"⫏≰2002101⪮%⊝NaN=NaN","layer":0}]}
{"id":957,"expression_no_base_symbol":"$3765$⇷$1081$⪒$1323$⨐⩸⫘$7476$","expression":"⫏≰12011110⇷⫏≰1111001⪒⫏≰1211000⨐⩸⫘⫏≰101020220","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":52720,"operation_count":3,"complexity_ratio":17573.333333333332,"tree":{"type":"binary","operator":"⪒","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":3765,"base":3},"right_expr":{"type":"numeric_atoms","value":1081,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":1323,"base":3},"right_expr":{"type":"numeric_atoms","value":7476,"base":3}}},"used_operators":["f6k1SAg4EE","mp7IySMOzn","fu6greOZ01"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3765","layer":2},{"info":"number node, value=1081","layer":2},{"info":"compute binary expreesion, left_input=3765, right_input=1081, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=2162","layer":1},{"info":"number node, value=1323","layer":2},{"info":"number node, value=7476","layer":2},{"info":"compute binary expreesion, left_input=1323, right_input=7476, 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=2162, right_input=nan, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰12011110⇷⫏≰1111001⪒⫏≰1211000⨐⩸⫘⫏≰101020220=NaN","reverse_text":"NaN=⫏≰12011110⇷⫏≰1111001⪒⫏≰1211000⨐⩸⫘⫏≰101020220","cot":[{"info":"⫏≰12011110⇷⫏≰1111001=⫏≰2222002","layer":1},{"info":"⫏≰1211000⨐⩸⫘⫏≰101020220=NaN","layer":1},{"info":"⫏≰2222002⪒NaN=NaN","layer":0}]}
{"id":958,"expression_no_base_symbol":"($7205$⊠≄⫣)∀⇚≩$3244$⨪↰⇹$8528$","expression":"(⫏≰100212212⊠≄⫣)∀⇚≩⫏≰11110011⨪↰⇹⫏≰102200212","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":3248,"operation_count":3,"complexity_ratio":1082.6666666666667,"tree":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"unary","operator":"⊠≄⫣","unary_expr":{"type":"numeric_atoms","value":7205,"base":3}},"right_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":3244,"base":3},"right_expr":{"type":"numeric_atoms","value":8528,"base":3}}},"used_operators":["LRNGc0VcxI","DIvbN7qnHd","tmPS8pqC7x"],"dependent_operators":["X99M06cbEe","rysDP5nf3Z","t8gj7n24qd","rJVOvQCfKK"],"result":"⫏≰11110011","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7205","layer":2},{"info":"compute unary expreesion, input=7205, op_id = DIvbN7qnHd, unary_op_definition = 'a⊠≄⫣ = { ((-a)-(-a)) }', output=0","layer":1},{"info":"number node, value=3244","layer":2},{"info":"number node, value=8528","layer":2},{"info":"compute binary expreesion, left_input=3244, right_input=8528, 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=3244","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=3244, 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=3244","layer":0}],"base":3,"result_base":3,"text":"(⫏≰100212212⊠≄⫣)∀⇚≩⫏≰11110011⨪↰⇹⫏≰102200212=⫏≰11110011","reverse_text":"⫏≰11110011=(⫏≰100212212⊠≄⫣)∀⇚≩⫏≰11110011⨪↰⇹⫏≰102200212","cot":[{"info":"⫏≰100212212⊠≄⫣=⫏≰0","layer":1},{"info":"⫏≰11110011⨪↰⇹⫏≰102200212=⫏≰11110011","layer":1},{"info":"⫏≰0∀⇚≩⫏≰11110011=⫏≰11110011","layer":0}]}
{"id":959,"expression_no_base_symbol":"⊥($1889$⨪↰⇹$1796$)","expression":"⊥(⫏≰2120222⨪↰⇹⫏≰2110112)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":1890,"operation_count":2,"complexity_ratio":945.0,"tree":{"type":"unary","operator":"⊥","unary_expr":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"numeric_atoms","value":1889,"base":3},"right_expr":{"type":"numeric_atoms","value":1796,"base":3}}},"used_operators":["Q3PJZHRvZv","tmPS8pqC7x"],"dependent_operators":["fu6greOZ01","rJVOvQCfKK"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1889","layer":2},{"info":"number node, value=1796","layer":2},{"info":"compute binary expreesion, left_input=1889, right_input=1796, 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=1889","layer":1},{"info":"compute unary expreesion, input=1889, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⊥(⫏≰2120222⨪↰⇹⫏≰2110112)=NaN","reverse_text":"NaN=⊥(⫏≰2120222⨪↰⇹⫏≰2110112)","cot":[{"info":"⫏≰2120222⨪↰⇹⫏≰2110112=⫏≰2120222","layer":1},{"info":"⊥⫏≰2120222=NaN","layer":0}]}
{"id":960,"expression_no_base_symbol":"($3065$≋⫹)⋷$7813$⊉≛↸$8076$","expression":"(⫏≰11012112≋⫹)⋷⫏≰101201101⊉≛↸⫏≰102002010","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7,"operation_count":3,"complexity_ratio":2.3333333333333335,"tree":{"type":"binary","operator":"⋷","left_expr":{"type":"unary","operator":"≋⫹","unary_expr":{"type":"numeric_atoms","value":3065,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":7813,"base":3},"right_expr":{"type":"numeric_atoms","value":8076,"base":3}}},"used_operators":["23Mk6UjR3U","N41Kp7NANJ","DZ8iAZOCBD"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰121211002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3065","layer":2},{"info":"compute unary expreesion, input=3065, op_id = N41Kp7NANJ, unary_op_definition = 'a≋⫹ = { ((-a)+(-a)) }', output=-6130","layer":1},{"info":"number node, value=7813","layer":2},{"info":"number node, value=8076","layer":2},{"info":"compute binary expreesion, left_input=7813, right_input=8076, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=15626","layer":1},{"info":"compute binary expreesion, left_input=-6130, right_input=15626, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=12260","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11012112≋⫹)⋷⫏≰101201101⊉≛↸⫏≰102002010=⫏≰121211002","reverse_text":"⫏≰121211002=(⫏≰11012112≋⫹)⋷⫏≰101201101⊉≛↸⫏≰102002010","cot":[{"info":"⫏≰11012112≋⫹=⫏≰-22102001","layer":1},{"info":"⫏≰101201101⊉≛↸⫏≰102002010=⫏≰210102202","layer":1},{"info":"⫏≰-22102001⋷⫏≰210102202=⫏≰121211002","layer":0}]}
{"id":961,"expression_no_base_symbol":"$1896$⫥∨⫟$2057$⨸⪁$2386$⨐⩸⫘$2337$","expression":"⫏≰2121020⫥∨⫟⫏≰2211012⨸⪁⫏≰10021101⨐⩸⫘⫏≰10012120","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":158,"operation_count":3,"complexity_ratio":52.666666666666664,"tree":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":1896,"base":3},"right_expr":{"type":"numeric_atoms","value":2057,"base":3}},"right_expr":{"type":"binary","operator":"⨐⩸⫘","left_expr":{"type":"numeric_atoms","value":2386,"base":3},"right_expr":{"type":"numeric_atoms","value":2337,"base":3}}},"used_operators":["g55IO6H4Gj","KYD54nUTWz","fu6greOZ01"],"dependent_operators":["W4YGzv6Whe","8HhzD0ZcuI","rGHVDoGpnC","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1896","layer":2},{"info":"number node, value=2057","layer":2},{"info":"compute binary expreesion, left_input=1896, right_input=2057, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"number node, value=2386","layer":2},{"info":"number node, value=2337","layer":2},{"info":"compute binary expreesion, left_input=2386, right_input=2337, 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=nan, right_input=nan, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰2121020⫥∨⫟⫏≰2211012⨸⪁⫏≰10021101⨐⩸⫘⫏≰10012120=NaN","reverse_text":"NaN=⫏≰2121020⫥∨⫟⫏≰2211012⨸⪁⫏≰10021101⨐⩸⫘⫏≰10012120","cot":[{"info":"⫏≰2121020⫥∨⫟⫏≰2211012=NaN","layer":1},{"info":"⫏≰10021101⨐⩸⫘⫏≰10012120=NaN","layer":1},{"info":"NaN⨸⪁NaN=NaN","layer":0}]}
{"id":962,"expression_no_base_symbol":"≦∁$7032$∀⇚≩$2781$","expression":"≦∁⫏≰100122110∀⇚≩⫏≰10211000","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":49225,"operation_count":2,"complexity_ratio":24612.5,"tree":{"type":"unary","operator":"≦∁","unary_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":7032,"base":3},"right_expr":{"type":"numeric_atoms","value":2781,"base":3}}},"used_operators":["9ICcGScMcE","LRNGc0VcxI"],"dependent_operators":["XhwjNDsVaA","g55IO6H4Gj","xUOZtlo3hN","Qy55tPpLXF","DZ8iAZOCBD","eH2TOUuTDT","AF7qkfDlqP","COABgblf1C","X99M06cbEe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7032","layer":2},{"info":"number node, value=2781","layer":2},{"info":"compute binary expreesion, left_input=7032, right_input=2781, 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 = 9ICcGScMcE, unary_op_definition = '≦∁a = { (((a/301)⊭↱(a⨸⪁a))⋥≓≎(⨞⊢(a⊉≛↸a))) , if ((⨑⩽⪐a)>=427 or (a⪐)<=558) ; a , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"≦∁⫏≰100122110∀⇚≩⫏≰10211000=NaN","reverse_text":"NaN=≦∁⫏≰100122110∀⇚≩⫏≰10211000","cot":[{"info":"⫏≰100122110∀⇚≩⫏≰10211000=NaN","layer":1},{"info":"≦∁NaN=NaN","layer":0}]}
{"id":963,"expression_no_base_symbol":"∥⊫$2584$⫥∨⫟$3814$","expression":"∥⊫⫏≰10112201⫥∨⫟⫏≰12020021","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":157,"operation_count":2,"complexity_ratio":78.5,"tree":{"type":"unary","operator":"∥⊫","unary_expr":{"type":"binary","operator":"⫥∨⫟","left_expr":{"type":"numeric_atoms","value":2584,"base":3},"right_expr":{"type":"numeric_atoms","value":3814,"base":3}}},"used_operators":["P8v4zCKN1o","KYD54nUTWz"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","8HhzD0ZcuI","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2584","layer":2},{"info":"number node, value=3814","layer":2},{"info":"compute binary expreesion, left_input=2584, right_input=3814, op_id = KYD54nUTWz binary_op_definition= 'a⫥∨⫟b = { (b⨟⋌⩍(144⨽a)) }', output=nan","layer":1},{"info":"compute unary expreesion, input=nan, op_id = P8v4zCKN1o, unary_op_definition = '∥⊫a = { (-(-(868+a))) , if (-a)<497 ; ((-(a+55))+a) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"∥⊫⫏≰10112201⫥∨⫟⫏≰12020021=NaN","reverse_text":"NaN=∥⊫⫏≰10112201⫥∨⫟⫏≰12020021","cot":[{"info":"⫏≰10112201⫥∨⫟⫏≰12020021=NaN","layer":1},{"info":"∥⊫NaN=NaN","layer":0}]}
{"id":964,"expression_no_base_symbol":"($1750$⫸⊐$1257$)∼($1001$/$3001$)","expression":"(⫏≰2101211⫸⊐⫏≰1201120)∼(⫏≰1101002/⫏≰11010011)","highest_n_order":4,"priority_hierarchical_complexity":3,"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":1750,"base":3},"right_expr":{"type":"numeric_atoms","value":1257,"base":3}},"right_expr":{"type":"binary","operator":"/","left_expr":{"type":"numeric_atoms","value":1001,"base":3},"right_expr":{"type":"numeric_atoms","value":3001,"base":3}}},"used_operators":["DyGG3AbaNP","mqXw5SEYmG","XhwjNDsVaA"],"dependent_operators":["rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr","QMFrweE19q","2DDjHMKMc0","eLAdDNolq6","Qy55tPpLXF","k8jYdgA6NY","AF7qkfDlqP","XPYlsWDdGa","COABgblf1C","rysDP5nf3Z"],"result":"⫏≰202","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1750","layer":2},{"info":"number node, value=1257","layer":2},{"info":"compute binary expreesion, left_input=1750, right_input=1257, op_id = mqXw5SEYmG binary_op_definition= 'a⫸⊐b = { ((b⋥≓≎16)⊭↱(b⋝⋈⪟43)) , if (a⫡⨏274)>318 and (⨑⩽⪐a)<45 ; ((⪲⇎a)%(≤/a)) , else }', output=4903","layer":1},{"info":"number node, value=1001","layer":2},{"info":"number node, value=3001","layer":2},{"info":"compute binary expreesion, left_input=1001, right_input=3001, op_id = XhwjNDsVaA binary_op_definition= 'None', output=0","layer":1},{"info":"compute binary expreesion, left_input=4903, right_input=0, op_id = DyGG3AbaNP binary_op_definition= 'a∼b = { ((a≹⇙⪍b)⋷(a⨪↰⇹a)) , if (a∸)<63 ; ((20⨟⋌⩍b)⨪↰⇹(↥a)) , else }', output=20","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2101211⫸⊐⫏≰1201120)∼(⫏≰1101002/⫏≰11010011)=⫏≰202","reverse_text":"⫏≰202=(⫏≰2101211⫸⊐⫏≰1201120)∼(⫏≰1101002/⫏≰11010011)","cot":[{"info":"⫏≰2101211⫸⊐⫏≰1201120=⫏≰20201121","layer":1},{"info":"⫏≰1101002/⫏≰11010011=⫏≰0","layer":1},{"info":"⫏≰20201121∼⫏≰0=⫏≰202","layer":0}]}
{"id":965,"expression_no_base_symbol":"($1040$⨽$1527$)⋓$2007$↬$5993$","expression":"(⫏≰1102112⨽⫏≰2002120)⋓⫏≰2202100↬⫏≰22012222","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1063,"operation_count":3,"complexity_ratio":354.3333333333333,"tree":{"type":"binary","operator":"⋓","left_expr":{"type":"binary","operator":"⨽","left_expr":{"type":"numeric_atoms","value":1040,"base":3},"right_expr":{"type":"numeric_atoms","value":1527,"base":3}},"right_expr":{"type":"binary","operator":"↬","left_expr":{"type":"numeric_atoms","value":2007,"base":3},"right_expr":{"type":"numeric_atoms","value":5993,"base":3}}},"used_operators":["T2fj7uvVaJ","8HhzD0ZcuI","B5M0gjZbta"],"dependent_operators":["dWAJyo7jo9","xNBdhnnwKq","DIvbN7qnHd","k8jYdgA6NY","f6k1SAg4EE","23Mk6UjR3U","EBcxylXtPf","oacrs7FA3X","srAu1WTS94","nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","rGHVDoGpnC"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1040","layer":2},{"info":"number node, value=1527","layer":2},{"info":"compute binary expreesion, left_input=1040, right_input=1527, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-3248067","layer":1},{"info":"number node, value=2007","layer":2},{"info":"number node, value=5993","layer":2},{"info":"compute binary expreesion, left_input=2007, right_input=5993, 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=-3248067, 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":3,"result_base":3,"text":"(⫏≰1102112⨽⫏≰2002120)⋓⫏≰2202100↬⫏≰22012222=NaN","reverse_text":"NaN=(⫏≰1102112⨽⫏≰2002120)⋓⫏≰2202100↬⫏≰22012222","cot":[{"info":"⫏≰1102112⨽⫏≰2002120=⫏≰-20010000111210","layer":1},{"info":"⫏≰2202100↬⫏≰22012222=NaN","layer":1},{"info":"⫏≰-20010000111210⋓NaN=NaN","layer":0}]}
{"id":966,"expression_no_base_symbol":"($3686$≦≮≮)⪠⩆⊳","expression":"(⫏≰12001112≦≮≮)⪠⩆⊳","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":"unary","operator":"≦≮≮","unary_expr":{"type":"numeric_atoms","value":3686,"base":3}}},"used_operators":["JLbD19bQDL","D4vGDi5EA2"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3686","layer":2},{"info":"compute unary expreesion, input=3686, op_id = D4vGDi5EA2, unary_op_definition = 'a≦≮≮ = { (-(a+(a+a))) }', output=-11058","layer":1},{"info":"compute unary expreesion, input=-11058, 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":0}],"base":3,"result_base":3,"text":"(⫏≰12001112≦≮≮)⪠⩆⊳=⫏≰0","reverse_text":"⫏≰0=(⫏≰12001112≦≮≮)⪠⩆⊳","cot":[{"info":"⫏≰12001112≦≮≮=⫏≰-120011120","layer":1},{"info":"⫏≰-120011120⪠⩆⊳=⫏≰0","layer":0}]}
{"id":967,"expression_no_base_symbol":"($6507$*$3796$)∑⇟⊟($2149$⋳⪒$4513$)","expression":"(⫏≰22221000*⫏≰12012121)∑⇟⊟(⫏≰2221121⋳⪒⫏≰20012011)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":971848,"operation_count":3,"complexity_ratio":323949.3333333333,"tree":{"type":"binary","operator":"∑⇟⊟","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":6507,"base":3},"right_expr":{"type":"numeric_atoms","value":3796,"base":3}},"right_expr":{"type":"binary","operator":"⋳⪒","left_expr":{"type":"numeric_atoms","value":2149,"base":3},"right_expr":{"type":"numeric_atoms","value":4513,"base":3}}},"used_operators":["U7g4x0WXJJ","9HNa5Wba9A","12rbrZMWeM"],"dependent_operators":["AHs5Up7iyr","srAu1WTS94","12rbrZMWeM","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6507","layer":2},{"info":"number node, value=3796","layer":2},{"info":"compute binary expreesion, left_input=6507, right_input=3796, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=24700572","layer":1},{"info":"number node, value=2149","layer":2},{"info":"number node, value=4513","layer":2},{"info":"compute binary expreesion, left_input=2149, right_input=4513, op_id = 12rbrZMWeM binary_op_definition= 'a⋳⪒b = { (((a-b)-(a-a))-((24-a)-(-263))) }', output=-502","layer":1},{"info":"compute binary expreesion, left_input=24700572, right_input=-502, op_id = U7g4x0WXJJ binary_op_definition= 'a∑⇟⊟b = { (⨵≀≌b) , if (a⋳⪒898)==671 ; (a≹⇙⪍b) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22221000*⫏≰12012121)∑⇟⊟(⫏≰2221121⋳⪒⫏≰20012011)=NaN","reverse_text":"NaN=(⫏≰22221000*⫏≰12012121)∑⇟⊟(⫏≰2221121⋳⪒⫏≰20012011)","cot":[{"info":"⫏≰22221000*⫏≰12012121=⫏≰1201110220211000","layer":1},{"info":"⫏≰2221121⋳⪒⫏≰20012011=⫏≰-200121","layer":1},{"info":"⫏≰1201110220211000∑⇟⊟⫏≰-200121=NaN","layer":0}]}
{"id":968,"expression_no_base_symbol":"$4733$≧⫂∧$5295$⪒(⋗⩬⋾$1182$)","expression":"⫏≰20111022≧⫂∧⫏≰21021010⪒(⋗⩬⋾⫏≰1121210)","highest_n_order":1,"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":4733,"base":3},"right_expr":{"type":"numeric_atoms","value":5295,"base":3}},"right_expr":{"type":"unary","operator":"⋗⩬⋾","unary_expr":{"type":"numeric_atoms","value":1182,"base":3}}},"used_operators":["f6k1SAg4EE","Ph9nP6C5qx","DpFCA1CohY"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-1202021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4733","layer":2},{"info":"number node, value=5295","layer":2},{"info":"compute binary expreesion, left_input=4733, right_input=5295, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=4822","layer":1},{"info":"number node, value=1182","layer":2},{"info":"compute unary expreesion, input=1182, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=-3546","layer":1},{"info":"compute binary expreesion, left_input=4822, right_input=-3546, op_id = f6k1SAg4EE binary_op_definition= 'a⪒b = { ((-a)+(-b)) }', output=-1276","layer":0}],"base":3,"result_base":3,"text":"⫏≰20111022≧⫂∧⫏≰21021010⪒(⋗⩬⋾⫏≰1121210)=⫏≰-1202021","reverse_text":"⫏≰-1202021=⫏≰20111022≧⫂∧⫏≰21021010⪒(⋗⩬⋾⫏≰1121210)","cot":[{"info":"⫏≰20111022≧⫂∧⫏≰21021010=⫏≰20121121","layer":1},{"info":"⋗⩬⋾⫏≰1121210=⫏≰-11212100","layer":1},{"info":"⫏≰20121121⪒⫏≰-11212100=⫏≰-1202021","layer":0}]}
{"id":969,"expression_no_base_symbol":"($5422$*$1830$)⨓(↩$6548$)","expression":"(⫏≰21102211*⫏≰2111210)⨓(↩⫏≰22222112)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":51456,"operation_count":3,"complexity_ratio":17152.0,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":5422,"base":3},"right_expr":{"type":"numeric_atoms","value":1830,"base":3}},"right_expr":{"type":"unary","operator":"↩","unary_expr":{"type":"numeric_atoms","value":6548,"base":3}}},"used_operators":["3ViojmjbAp","9HNa5Wba9A","jLgFTUHLKL"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","sdazOOVcIp","t8gj7n24qd","eLAdDNolq6","BjRHVeLaeN","Ph9nP6C5qx","xUOZtlo3hN","k8jYdgA6NY","AF7qkfDlqP","N41Kp7NANJ","NTOWxs364D"],"result":"⫏≰2112001002","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=5422","layer":2},{"info":"number node, value=1830","layer":2},{"info":"compute binary expreesion, left_input=5422, right_input=1830, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=9922260","layer":1},{"info":"number node, value=6548","layer":2},{"info":"compute unary expreesion, input=6548, op_id = jLgFTUHLKL, unary_op_definition = '↩a = { (((83≧⫂∧a)⪨≂(⨑⩽⪐a))≋⫹) , if ((≤/a)>=675 or (a⫩⊇)!=134) ; (⨞⊢((a%a)⩚⊴⇥(-a))) , else }', output=-49604","layer":1},{"info":"compute binary expreesion, left_input=9922260, right_input=-49604, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=49601","layer":0}],"base":3,"result_base":3,"text":"(⫏≰21102211*⫏≰2111210)⨓(↩⫏≰22222112)=⫏≰2112001002","reverse_text":"⫏≰2112001002=(⫏≰21102211*⫏≰2111210)⨓(↩⫏≰22222112)","cot":[{"info":"⫏≰21102211*⫏≰2111210=⫏≰200200002210010","layer":1},{"info":"↩⫏≰22222112=⫏≰-2112001012","layer":1},{"info":"⫏≰200200002210010⨓⫏≰-2112001012=⫏≰2112001002","layer":0}]}
{"id":970,"expression_no_base_symbol":"⋗⩬⋾$7983$⨟⋌⩍$5152$","expression":"⋗⩬⋾⫏≰101221200⨟⋌⩍⫏≰21001211","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":7983,"base":3},"right_expr":{"type":"numeric_atoms","value":5152,"base":3}}},"used_operators":["DpFCA1CohY","rGHVDoGpnC"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=7983","layer":2},{"info":"number node, value=5152","layer":2},{"info":"compute binary expreesion, left_input=7983, right_input=5152, 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 unary expreesion, input=nan, op_id = DpFCA1CohY, unary_op_definition = '⋗⩬⋾a = { (-(-a)) , if (a<=390 and (-a)==853 and (-a)<3) ; ((-a)-(a+a)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⋗⩬⋾⫏≰101221200⨟⋌⩍⫏≰21001211=NaN","reverse_text":"NaN=⋗⩬⋾⫏≰101221200⨟⋌⩍⫏≰21001211","cot":[{"info":"⫏≰101221200⨟⋌⩍⫏≰21001211=NaN","layer":1},{"info":"⋗⩬⋾NaN=NaN","layer":0}]}
{"id":971,"expression_no_base_symbol":"↣≠⋷($1171$⇷$2333$)","expression":"↣≠⋷(⫏≰1121101⇷⫏≰10012102)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":16403,"operation_count":2,"complexity_ratio":8201.5,"tree":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":1171,"base":3},"right_expr":{"type":"numeric_atoms","value":2333,"base":3}}},"used_operators":["Asc51vEJeQ","mp7IySMOzn"],"dependent_operators":["XhwjNDsVaA","AHs5Up7iyr","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1171","layer":2},{"info":"number node, value=2333","layer":2},{"info":"compute binary expreesion, left_input=1171, right_input=2333, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=4666","layer":1},{"info":"compute unary expreesion, input=4666, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"↣≠⋷(⫏≰1121101⇷⫏≰10012102)=NaN","reverse_text":"NaN=↣≠⋷(⫏≰1121101⇷⫏≰10012102)","cot":[{"info":"⫏≰1121101⇷⫏≰10012102=⫏≰20101211","layer":1},{"info":"↣≠⋷⫏≰20101211=NaN","layer":0}]}
{"id":972,"expression_no_base_symbol":"($1675$∸)⨟⋌⩍($8233$≧⫂∧$1308$)","expression":"(⫏≰2022001∸)⨟⋌⩍(⫏≰102021221≧⫂∧⫏≰1210110)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3694,"operation_count":3,"complexity_ratio":1231.3333333333333,"tree":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"unary","operator":"∸","unary_expr":{"type":"numeric_atoms","value":1675,"base":3}},"right_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":8233,"base":3},"right_expr":{"type":"numeric_atoms","value":1308,"base":3}}},"used_operators":["rGHVDoGpnC","o20kRiQErp","Ph9nP6C5qx"],"dependent_operators":["Tcnh7f0tEr","tmPS8pqC7x","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰0","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1675","layer":2},{"info":"compute unary expreesion, input=1675, op_id = o20kRiQErp, unary_op_definition = 'a∸ = { (177⨪↰⇹a) }', output=177","layer":1},{"info":"number node, value=8233","layer":2},{"info":"number node, value=1308","layer":2},{"info":"compute binary expreesion, left_input=8233, right_input=1308, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=835","layer":1},{"info":"compute binary expreesion, left_input=177, right_input=835, 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":3,"result_base":3,"text":"(⫏≰2022001∸)⨟⋌⩍(⫏≰102021221≧⫂∧⫏≰1210110)=⫏≰0","reverse_text":"⫏≰0=(⫏≰2022001∸)⨟⋌⩍(⫏≰102021221≧⫂∧⫏≰1210110)","cot":[{"info":"⫏≰2022001∸=⫏≰20120","layer":1},{"info":"⫏≰102021221≧⫂∧⫏≰1210110=⫏≰1010221","layer":1},{"info":"⫏≰20120⨟⋌⩍⫏≰1010221=⫏≰0","layer":0}]}
{"id":973,"expression_no_base_symbol":"($1459$⊭∹↮)↬($2393$⨓$4871$)","expression":"(⫏≰2000001⊭∹↮)↬(⫏≰10021122⨓⫏≰20200102)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":4884,"operation_count":3,"complexity_ratio":1628.0,"tree":{"type":"binary","operator":"↬","left_expr":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"numeric_atoms","value":1459,"base":3}},"right_expr":{"type":"binary","operator":"⨓","left_expr":{"type":"numeric_atoms","value":2393,"base":3},"right_expr":{"type":"numeric_atoms","value":4871,"base":3}}},"used_operators":["B5M0gjZbta","xNBdhnnwKq","3ViojmjbAp"],"dependent_operators":["rGHVDoGpnC","2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1459","layer":2},{"info":"compute unary expreesion, input=1459, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=2918","layer":1},{"info":"number node, value=2393","layer":2},{"info":"number node, value=4871","layer":2},{"info":"compute binary expreesion, left_input=2393, right_input=4871, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-4874","layer":1},{"info":"compute binary expreesion, left_input=2918, right_input=-4874, 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":3,"result_base":3,"text":"(⫏≰2000001⊭∹↮)↬(⫏≰10021122⨓⫏≰20200102)=NaN","reverse_text":"NaN=(⫏≰2000001⊭∹↮)↬(⫏≰10021122⨓⫏≰20200102)","cot":[{"info":"⫏≰2000001⊭∹↮=⫏≰11000002","layer":1},{"info":"⫏≰10021122⨓⫏≰20200102=⫏≰-20200112","layer":1},{"info":"⫏≰11000002↬⫏≰-20200112=NaN","layer":0}]}
{"id":974,"expression_no_base_symbol":"(⊥$5500$)⋝⋈⪟(↣≠⋷$6163$)","expression":"(⊥⫏≰21112201)⋝⋈⪟(↣≠⋷⫏≰22110021)","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":"unary","operator":"⊥","unary_expr":{"type":"numeric_atoms","value":5500,"base":3}},"right_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":6163,"base":3}}},"used_operators":["2DDjHMKMc0","Q3PJZHRvZv","Asc51vEJeQ"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","fu6greOZ01","XhwjNDsVaA","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=5500","layer":2},{"info":"compute unary expreesion, input=5500, op_id = Q3PJZHRvZv, unary_op_definition = '⊥a = { (a⨐⩸⫘a) }', output=nan","layer":1},{"info":"number node, value=6163","layer":2},{"info":"compute unary expreesion, input=6163, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=nan, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⊥⫏≰21112201)⋝⋈⪟(↣≠⋷⫏≰22110021)=NaN","reverse_text":"NaN=(⊥⫏≰21112201)⋝⋈⪟(↣≠⋷⫏≰22110021)","cot":[{"info":"⊥⫏≰21112201=NaN","layer":1},{"info":"↣≠⋷⫏≰22110021=NaN","layer":1},{"info":"NaN⋝⋈⪟NaN=NaN","layer":0}]}
{"id":975,"expression_no_base_symbol":"($4043$∲⫓$4280$)⩷∴(⨵≀≌$2272$)","expression":"(⫏≰12112202∲⫓⫏≰12212112)⩷∴(⨵≀≌⫏≰10010011)","highest_n_order":2,"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":4043,"base":3},"right_expr":{"type":"numeric_atoms","value":4280,"base":3}},"right_expr":{"type":"unary","operator":"⨵≀≌","unary_expr":{"type":"numeric_atoms","value":2272,"base":3}}},"used_operators":["9FxExcQeMw","i8ToyICDmI","srAu1WTS94"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","glklzrTFfD","DpFCA1CohY","XPYlsWDdGa","9HNa5Wba9A"],"result":"⫏≰200122201","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4043","layer":2},{"info":"number node, value=4280","layer":2},{"info":"compute binary expreesion, left_input=4043, right_input=4280, op_id = i8ToyICDmI binary_op_definition= 'a∲⫓b = { a , if b<=622 ; ((-b)+b) , else }', output=0","layer":1},{"info":"number node, value=2272","layer":2},{"info":"compute unary expreesion, input=2272, op_id = srAu1WTS94, unary_op_definition = '⨵≀≌a = { (a*a) , if (a⨁⊸⫻)!=892 and (⪲⇎a)<454 ; (⋗⩬⋾a) , else }', output=-6816","layer":1},{"info":"compute binary expreesion, left_input=0, right_input=-6816, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=13600","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12112202∲⫓⫏≰12212112)⩷∴(⨵≀≌⫏≰10010011)=⫏≰200122201","reverse_text":"⫏≰200122201=(⫏≰12112202∲⫓⫏≰12212112)⩷∴(⨵≀≌⫏≰10010011)","cot":[{"info":"⫏≰12112202∲⫓⫏≰12212112=⫏≰0","layer":1},{"info":"⨵≀≌⫏≰10010011=⫏≰-100100110","layer":1},{"info":"⫏≰0⩷∴⫏≰-100100110=⫏≰200122201","layer":0}]}
{"id":976,"expression_no_base_symbol":"⊙↵-(⪝⪂⫅$2325$)","expression":"⊙↵-(⪝⪂⫅⫏≰10012010)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":341957,"operation_count":2,"complexity_ratio":170978.5,"tree":{"type":"unary","operator":"⊙↵-","unary_expr":{"type":"unary","operator":"⪝⪂⫅","unary_expr":{"type":"numeric_atoms","value":2325,"base":3}}},"used_operators":["oWn0xqSxBt","XTarYq4gQB"],"dependent_operators":["dWAJyo7jo9","7j4O788W3g","12rbrZMWeM","2DQ55sFlQl","u6S6b8DprG","mqXw5SEYmG","oacrs7FA3X","9HNa5Wba9A","8w2t5hMYqp"],"result":"⫏≰21021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2325","layer":2},{"info":"compute unary expreesion, input=2325, op_id = XTarYq4gQB, unary_op_definition = '⪝⪂⫅a = { ((⊄⩳↩49)*a) }', output=-341775","layer":1},{"info":"compute unary expreesion, input=-341775, op_id = oWn0xqSxBt, unary_op_definition = '⊙↵-a = { (((a⋳⪒a)⨵⪆(a⪢a))⪘⫢((a⫸⊐a)↺(↽≂a))) }', output=196","layer":0}],"base":3,"result_base":3,"text":"⊙↵-(⪝⪂⫅⫏≰10012010)=⫏≰21021","reverse_text":"⫏≰21021=⊙↵-(⪝⪂⫅⫏≰10012010)","cot":[{"info":"⪝⪂⫅⫏≰10012010=⫏≰-122100211100","layer":1},{"info":"⊙↵-⫏≰-122100211100=⫏≰21021","layer":0}]}
{"id":977,"expression_no_base_symbol":"($4630$↺$2712$)⩷∴($1359$⇼⇔∾$2338$)","expression":"(⫏≰20100111↺⫏≰10201110)⩷∴(⫏≰1212100⇼⇔∾⫏≰10012121)","highest_n_order":1,"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":4630,"base":3},"right_expr":{"type":"numeric_atoms","value":2712,"base":3}},"right_expr":{"type":"binary","operator":"⇼⇔∾","left_expr":{"type":"numeric_atoms","value":1359,"base":3},"right_expr":{"type":"numeric_atoms","value":2338,"base":3}}},"used_operators":["9FxExcQeMw","7j4O788W3g","tifHPKVTfV"],"dependent_operators":["rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰11201012","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4630","layer":2},{"info":"number node, value=2712","layer":2},{"info":"compute binary expreesion, left_input=4630, right_input=2712, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=2712","layer":1},{"info":"number node, value=1359","layer":2},{"info":"number node, value=2338","layer":2},{"info":"compute binary expreesion, left_input=1359, right_input=2338, op_id = tifHPKVTfV binary_op_definition= 'a⇼⇔∾b = { (-(a-b)) }', output=979","layer":1},{"info":"compute binary expreesion, left_input=2712, right_input=979, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=3434","layer":0}],"base":3,"result_base":3,"text":"(⫏≰20100111↺⫏≰10201110)⩷∴(⫏≰1212100⇼⇔∾⫏≰10012121)=⫏≰11201012","reverse_text":"⫏≰11201012=(⫏≰20100111↺⫏≰10201110)⩷∴(⫏≰1212100⇼⇔∾⫏≰10012121)","cot":[{"info":"⫏≰20100111↺⫏≰10201110=⫏≰10201110","layer":1},{"info":"⫏≰1212100⇼⇔∾⫏≰10012121=⫏≰1100021","layer":1},{"info":"⫏≰10201110⩷∴⫏≰1100021=⫏≰11201012","layer":0}]}
{"id":978,"expression_no_base_symbol":"⫓⪴($2913$-$5208$)","expression":"⫓⪴(⫏≰10222220-⫏≰21010220)","highest_n_order":2,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2296,"operation_count":2,"complexity_ratio":1148.0,"tree":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"binary","operator":"-","left_expr":{"type":"numeric_atoms","value":2913,"base":3},"right_expr":{"type":"numeric_atoms","value":5208,"base":3}}},"used_operators":["eLxqMNBOBk","rysDP5nf3Z"],"dependent_operators":["9HNa5Wba9A"],"result":"⫏≰100220121000000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=2913","layer":2},{"info":"number node, value=5208","layer":2},{"info":"compute binary expreesion, left_input=2913, right_input=5208, op_id = rysDP5nf3Z binary_op_definition= 'None', output=-2295","layer":1},{"info":"compute unary expreesion, input=-2295, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=5267025","layer":0}],"base":3,"result_base":3,"text":"⫓⪴(⫏≰10222220-⫏≰21010220)=⫏≰100220121000000","reverse_text":"⫏≰100220121000000=⫓⪴(⫏≰10222220-⫏≰21010220)","cot":[{"info":"⫏≰10222220-⫏≰21010220=⫏≰-10011000","layer":1},{"info":"⫓⪴⫏≰-10011000=⫏≰100220121000000","layer":0}]}
{"id":979,"expression_no_base_symbol":"($1472$⪄$2242$)↺(∂$5046$)","expression":"(⫏≰2000112⪄⫏≰10002001)↺(∂⫏≰20220220)","highest_n_order":5,"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":1472,"base":3},"right_expr":{"type":"numeric_atoms","value":2242,"base":3}},"right_expr":{"type":"unary","operator":"∂","unary_expr":{"type":"numeric_atoms","value":5046,"base":3}}},"used_operators":["7j4O788W3g","SUmda5xLS4","Uaa54Peajs"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","8w2t5hMYqp","glklzrTFfD","Qy55tPpLXF","P8v4zCKN1o","f6k1SAg4EE","9HNa5Wba9A","COABgblf1C","B5M0gjZbta","g55IO6H4Gj","f6k1SAg4EE","3ViojmjbAp"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1472","layer":2},{"info":"number node, value=2242","layer":2},{"info":"compute binary expreesion, left_input=1472, right_input=2242, op_id = SUmda5xLS4 binary_op_definition= 'a⪄b = { (((⊄⩳↩320)⨁⊸⫻)⊭↱((a*72)⋥≓≎(b⪒a))) , if (∥⊫b)!=717 ; b , else }', output=-222913","layer":1},{"info":"number node, value=5046","layer":2},{"info":"compute unary expreesion, input=5046, 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=-222913, right_input=nan, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2000112⪄⫏≰10002001)↺(∂⫏≰20220220)=NaN","reverse_text":"NaN=(⫏≰2000112⪄⫏≰10002001)↺(∂⫏≰20220220)","cot":[{"info":"⫏≰2000112⪄⫏≰10002001=⫏≰-102022210001","layer":1},{"info":"∂⫏≰20220220=NaN","layer":1},{"info":"⫏≰-102022210001↺NaN=NaN","layer":0}]}
{"id":980,"expression_no_base_symbol":"($6007$⇋≉)⋝⋈⪟(-$4622$)","expression":"(⫏≰22020111⇋≉)⋝⋈⪟(-⫏≰20100012)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":7,"operation_count":3,"complexity_ratio":2.3333333333333335,"tree":{"type":"binary","operator":"⋝⋈⪟","left_expr":{"type":"unary","operator":"⇋≉","unary_expr":{"type":"numeric_atoms","value":6007,"base":3}},"right_expr":{"type":"unary","operator":"-","unary_expr":{"type":"numeric_atoms","value":4622,"base":3}}},"used_operators":["2DDjHMKMc0","XIabStNQrY","t8gj7n24qd"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰121100100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=6007","layer":2},{"info":"compute unary expreesion, input=6007, op_id = XIabStNQrY, unary_op_definition = 'a⇋≉ = { ((a-98)-(-a)) }', output=11916","layer":1},{"info":"number node, value=4622","layer":2},{"info":"compute unary expreesion, input=4622, op_id = t8gj7n24qd, unary_op_definition = 'None', output=-4622","layer":1},{"info":"compute binary expreesion, left_input=11916, right_input=-4622, op_id = 2DDjHMKMc0 binary_op_definition= 'a⋝⋈⪟b = { ((b+a)+(-b)) }', output=11916","layer":0}],"base":3,"result_base":3,"text":"(⫏≰22020111⇋≉)⋝⋈⪟(-⫏≰20100012)=⫏≰121100100","reverse_text":"⫏≰121100100=(⫏≰22020111⇋≉)⋝⋈⪟(-⫏≰20100012)","cot":[{"info":"⫏≰22020111⇋≉=⫏≰121100100","layer":1},{"info":"-⫏≰20100012=⫏≰-20100012","layer":1},{"info":"⫏≰121100100⋝⋈⪟⫏≰-20100012=⫏≰121100100","layer":0}]}
{"id":981,"expression_no_base_symbol":"($3310$⩷∴$5554$)⨓($2638$⩷∴$2584$)","expression":"(⫏≰11112121⩷∴⫏≰21121201)⨓(⫏≰10121201⩷∴⫏≰10112201)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":94,"operation_count":3,"complexity_ratio":31.333333333333332,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":3310,"base":3},"right_expr":{"type":"numeric_atoms","value":5554,"base":3}},"right_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":2638,"base":3},"right_expr":{"type":"numeric_atoms","value":2584,"base":3}}},"used_operators":["3ViojmjbAp","9FxExcQeMw"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","rysDP5nf3Z"],"result":"⫏≰-2221","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3310","layer":2},{"info":"number node, value=5554","layer":2},{"info":"compute binary expreesion, left_input=3310, right_input=5554, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=-4520","layer":1},{"info":"number node, value=2638","layer":2},{"info":"number node, value=2584","layer":2},{"info":"compute binary expreesion, left_input=2638, right_input=2584, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=76","layer":1},{"info":"compute binary expreesion, left_input=-4520, right_input=76, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=-79","layer":0}],"base":3,"result_base":3,"text":"(⫏≰11112121⩷∴⫏≰21121201)⨓(⫏≰10121201⩷∴⫏≰10112201)=⫏≰-2221","reverse_text":"⫏≰-2221=(⫏≰11112121⩷∴⫏≰21121201)⨓(⫏≰10121201⩷∴⫏≰10112201)","cot":[{"info":"⫏≰11112121⩷∴⫏≰21121201=⫏≰-20012102","layer":1},{"info":"⫏≰10121201⩷∴⫏≰10112201=⫏≰2211","layer":1},{"info":"⫏≰-20012102⨓⫏≰2211=⫏≰-2221","layer":0}]}
{"id":982,"expression_no_base_symbol":"$7992$⇷$1948$⊭∹↮","expression":"⫏≰101222000⇷⫏≰2200011⊭∹↮","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":111900,"operation_count":2,"complexity_ratio":55950.0,"tree":{"type":"unary","operator":"⊭∹↮","unary_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":7992,"base":3},"right_expr":{"type":"numeric_atoms","value":1948,"base":3}}},"used_operators":["xNBdhnnwKq","mp7IySMOzn"],"dependent_operators":["2DDjHMKMc0","k8jYdgA6NY","XPYlsWDdGa","COABgblf1C","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe"],"result":"⫏≰101200121","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=7992","layer":2},{"info":"number node, value=1948","layer":2},{"info":"compute binary expreesion, left_input=7992, right_input=1948, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=3896","layer":1},{"info":"compute unary expreesion, input=3896, op_id = xNBdhnnwKq, unary_op_definition = 'a⊭∹↮ = { a , if (a⊭↱319)>=17 ; ((⪲⇎a)⋝⋈⪟(a%a)) , else }', output=7792","layer":0}],"base":3,"result_base":3,"text":"⫏≰101222000⇷⫏≰2200011⊭∹↮=⫏≰101200121","reverse_text":"⫏≰101200121=⫏≰101222000⇷⫏≰2200011⊭∹↮","cot":[{"info":"⫏≰101222000⇷⫏≰2200011=⫏≰12100022","layer":1},{"info":"⫏≰12100022⊭∹↮=⫏≰101200121","layer":0}]}
{"id":983,"expression_no_base_symbol":"+⊝⨔(≉$1548$)","expression":"+⊝⨔(≉⫏≰2010100)","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":1548,"base":3}}},"used_operators":["DhbWaqg5eL","e1ybzncUwg"],"dependent_operators":["dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰2002101","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1548","layer":2},{"info":"compute unary expreesion, input=1548, op_id = e1ybzncUwg, unary_op_definition = '≉a = { (a+531) , if (-a)<=225 ; a , else }', output=2079","layer":1},{"info":"compute unary expreesion, input=2079, 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":3,"result_base":3,"text":"+⊝⨔(≉⫏≰2010100)=⫏≰2002101","reverse_text":"⫏≰2002101=+⊝⨔(≉⫏≰2010100)","cot":[{"info":"≉⫏≰2010100=⫏≰2212000","layer":1},{"info":"+⊝⨔⫏≰2212000=⫏≰2002101","layer":0}]}
{"id":984,"expression_no_base_symbol":"$8036$⇷$3138$⨰(⨰⫟⨤$1824$)","expression":"⫏≰102000122⇷⫏≰11022020⨰(⨰⫟⨤⫏≰2111120)","highest_n_order":3,"priority_hierarchical_complexity":2,"normalized_expansion_degree":118972,"operation_count":3,"complexity_ratio":39657.333333333336,"tree":{"type":"binary","operator":"⨰","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":8036,"base":3},"right_expr":{"type":"numeric_atoms","value":3138,"base":3}},"right_expr":{"type":"unary","operator":"⨰⫟⨤","unary_expr":{"type":"numeric_atoms","value":1824,"base":3}}},"used_operators":["eewbuw0ToL","mp7IySMOzn","Tw270M8GLb"],"dependent_operators":["rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","sdazOOVcIp","dWAJyo7jo9","nCS4ZIUYfx","8HhzD0ZcuI","f6k1SAg4EE","9FxExcQeMw"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=8036","layer":2},{"info":"number node, value=3138","layer":2},{"info":"compute binary expreesion, left_input=8036, right_input=3138, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=6276","layer":1},{"info":"number node, value=1824","layer":2},{"info":"compute unary expreesion, input=1824, 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=6276, right_input=nan, op_id = eewbuw0ToL binary_op_definition= 'a⨰b = { (((a-a)+(a+10))-(-(-b))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰102000122⇷⫏≰11022020⨰(⨰⫟⨤⫏≰2111120)=NaN","reverse_text":"NaN=⫏≰102000122⇷⫏≰11022020⨰(⨰⫟⨤⫏≰2111120)","cot":[{"info":"⫏≰102000122⇷⫏≰11022020=⫏≰22121110","layer":1},{"info":"⨰⫟⨤⫏≰2111120=NaN","layer":1},{"info":"⫏≰22121110⨰NaN=NaN","layer":0}]}
{"id":985,"expression_no_base_symbol":"($1037$≎⊠⪸$4536$)⨪↰⇹(⨑⩽⪐$1149$)","expression":"(⫏≰1102102≎⊠⪸⫏≰20020000)⨪↰⇹(⨑⩽⪐⫏≰1120120)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":268384,"operation_count":3,"complexity_ratio":89461.33333333333,"tree":{"type":"binary","operator":"⨪↰⇹","left_expr":{"type":"binary","operator":"≎⊠⪸","left_expr":{"type":"numeric_atoms","value":1037,"base":3},"right_expr":{"type":"numeric_atoms","value":4536,"base":3}},"right_expr":{"type":"unary","operator":"⨑⩽⪐","unary_expr":{"type":"numeric_atoms","value":1149,"base":3}}},"used_operators":["tmPS8pqC7x","bJkvcejdHO","AF7qkfDlqP"],"dependent_operators":["rJVOvQCfKK","DIvbN7qnHd","Ph9nP6C5qx","Qy55tPpLXF","2td37pGCOC","EBcxylXtPf","9FxExcQeMw","9HNa5Wba9A","rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe"],"result":"⫏≰111121210000","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1037","layer":2},{"info":"number node, value=4536","layer":2},{"info":"compute binary expreesion, left_input=1037, right_input=4536, op_id = bJkvcejdHO binary_op_definition= 'a≎⊠⪸b = { ((b⊠≄⫣)≧⫂∧(259*a)) , if (b⫌⩹⨱)>=594 ; ((⩦⩻⨪b)⋥≓≎(a⩷∴b)) , else }', output=268110","layer":1},{"info":"number node, value=1149","layer":2},{"info":"compute unary expreesion, input=1149, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-876","layer":1},{"info":"compute binary expreesion, left_input=268110, right_input=-876, 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=268110","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1102102≎⊠⪸⫏≰20020000)⨪↰⇹(⨑⩽⪐⫏≰1120120)=⫏≰111121210000","reverse_text":"⫏≰111121210000=(⫏≰1102102≎⊠⪸⫏≰20020000)⨪↰⇹(⨑⩽⪐⫏≰1120120)","cot":[{"info":"⫏≰1102102≎⊠⪸⫏≰20020000=⫏≰111121210000","layer":1},{"info":"⨑⩽⪐⫏≰1120120=⫏≰-1012110","layer":1},{"info":"⫏≰111121210000⨪↰⇹⫏≰-1012110=⫏≰111121210000","layer":0}]}
{"id":986,"expression_no_base_symbol":"$3601$≹⇙⪍$1779$⊦⊿","expression":"⫏≰11221101≹⇙⪍⫏≰2102220⊦⊿","highest_n_order":4,"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":3601,"base":3},"right_expr":{"type":"numeric_atoms","value":1779,"base":3}}},"used_operators":["14qkJME0vr","AHs5Up7iyr"],"dependent_operators":["W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd","dWAJyo7jo9"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=3601","layer":2},{"info":"number node, value=1779","layer":2},{"info":"compute binary expreesion, left_input=3601, right_input=1779, 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 = 14qkJME0vr, unary_op_definition = 'a⊦⊿ = { ((-(a+a))-((a+79)-(a-a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"⫏≰11221101≹⇙⪍⫏≰2102220⊦⊿=NaN","reverse_text":"NaN=⫏≰11221101≹⇙⪍⫏≰2102220⊦⊿","cot":[{"info":"⫏≰11221101≹⇙⪍⫏≰2102220=NaN","layer":1},{"info":"NaN⊦⊿=NaN","layer":0}]}
{"id":987,"expression_no_base_symbol":"($1820$⩤)⨽($4304$⊉≛↸$1650$)","expression":"(⫏≰2111102⩤)⨽(⫏≰12220102⊉≛↸⫏≰2021010)","highest_n_order":2,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1832,"operation_count":3,"complexity_ratio":610.6666666666666,"tree":{"type":"binary","operator":"⨽","left_expr":{"type":"unary","operator":"⩤","unary_expr":{"type":"numeric_atoms","value":1820,"base":3}},"right_expr":{"type":"binary","operator":"⊉≛↸","left_expr":{"type":"numeric_atoms","value":4304,"base":3},"right_expr":{"type":"numeric_atoms","value":1650,"base":3}}},"used_operators":["8HhzD0ZcuI","Z2TMIBDE3Q","DZ8iAZOCBD"],"dependent_operators":["nCS4ZIUYfx","9HNa5Wba9A","DpFCA1CohY","rysDP5nf3Z","t8gj7n24qd","rysDP5nf3Z","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰-200202002220020","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1820","layer":2},{"info":"compute unary expreesion, input=1820, op_id = Z2TMIBDE3Q, unary_op_definition = 'a⩤ = { (a-a) , if (-a)==434 ; (-a) , else }', output=-1820","layer":1},{"info":"number node, value=4304","layer":2},{"info":"number node, value=1650","layer":2},{"info":"compute binary expreesion, left_input=4304, right_input=1650, op_id = DZ8iAZOCBD binary_op_definition= 'a⊉≛↸b = { ((-a)+(a-b)) , if (-a)>=60 ; (a-(-a)) , else }', output=8608","layer":1},{"info":"compute binary expreesion, left_input=-1820, right_input=8608, op_id = 8HhzD0ZcuI binary_op_definition= 'a⨽b = { (⋗⩬⋾((b⨳⩥⨓438)⨳⩥⨓(a*a))) }', output=-9961710","layer":0}],"base":3,"result_base":3,"text":"(⫏≰2111102⩤)⨽(⫏≰12220102⊉≛↸⫏≰2021010)=⫏≰-200202002220020","reverse_text":"⫏≰-200202002220020=(⫏≰2111102⩤)⨽(⫏≰12220102⊉≛↸⫏≰2021010)","cot":[{"info":"⫏≰2111102⩤=⫏≰-2111102","layer":1},{"info":"⫏≰12220102⊉≛↸⫏≰2021010=⫏≰102210211","layer":1},{"info":"⫏≰-2111102⨽⫏≰102210211=⫏≰-200202002220020","layer":0}]}
{"id":988,"expression_no_base_symbol":"$2649$≧⫂∧$2379$≭(↥$2097$)","expression":"⫏≰10122010≧⫂∧⫏≰10021010≭(↥⫏≰2212200)","highest_n_order":5,"priority_hierarchical_complexity":3,"normalized_expansion_degree":1805,"operation_count":3,"complexity_ratio":601.6666666666666,"tree":{"type":"binary","operator":"≭","left_expr":{"type":"binary","operator":"≧⫂∧","left_expr":{"type":"numeric_atoms","value":2649,"base":3},"right_expr":{"type":"numeric_atoms","value":2379,"base":3}},"right_expr":{"type":"unary","operator":"↥","unary_expr":{"type":"numeric_atoms","value":2097,"base":3}}},"used_operators":["rxpJgHHUmx","Ph9nP6C5qx","A8NUZmVepG"],"dependent_operators":["AHs5Up7iyr","rysDP5nf3Z","t8gj7n24qd","k8jYdgA6NY"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=2649","layer":2},{"info":"number node, value=2379","layer":2},{"info":"compute binary expreesion, left_input=2649, right_input=2379, op_id = Ph9nP6C5qx binary_op_definition= 'a≧⫂∧b = { (a-b) , if (-b)>136 ; (b-473) , else }', output=1906","layer":1},{"info":"number node, value=2097","layer":2},{"info":"compute unary expreesion, input=2097, op_id = A8NUZmVepG, unary_op_definition = '↥a = { (a%51) }', output=6","layer":1},{"info":"compute binary expreesion, left_input=1906, right_input=6, 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":3,"result_base":3,"text":"⫏≰10122010≧⫂∧⫏≰10021010≭(↥⫏≰2212200)=NaN","reverse_text":"NaN=⫏≰10122010≧⫂∧⫏≰10021010≭(↥⫏≰2212200)","cot":[{"info":"⫏≰10122010≧⫂∧⫏≰10021010=⫏≰2121121","layer":1},{"info":"↥⫏≰2212200=⫏≰20","layer":1},{"info":"⫏≰2121121≭⫏≰20=NaN","layer":0}]}
{"id":989,"expression_no_base_symbol":"($1002$⪘⫢$2319$)≹⇙⪍($1548$⊭↱$1934$)","expression":"(⫏≰1101010⪘⫢⫏≰10011220)≹⇙⪍(⫏≰2010100⊭↱⫏≰2122122)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":603897,"operation_count":3,"complexity_ratio":201299.0,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":1002,"base":3},"right_expr":{"type":"numeric_atoms","value":2319,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":1548,"base":3},"right_expr":{"type":"numeric_atoms","value":1934,"base":3}}},"used_operators":["AHs5Up7iyr","oacrs7FA3X","COABgblf1C"],"dependent_operators":["dWAJyo7jo9","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP","W4YGzv6Whe","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1002","layer":2},{"info":"number node, value=2319","layer":2},{"info":"compute binary expreesion, left_input=1002, right_input=2319, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=1880","layer":1},{"info":"number node, value=1548","layer":2},{"info":"number node, value=1934","layer":2},{"info":"compute binary expreesion, left_input=1548, right_input=1934, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=777","layer":1},{"info":"compute binary expreesion, left_input=1880, right_input=777, 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":3,"result_base":3,"text":"(⫏≰1101010⪘⫢⫏≰10011220)≹⇙⪍(⫏≰2010100⊭↱⫏≰2122122)=NaN","reverse_text":"NaN=(⫏≰1101010⪘⫢⫏≰10011220)≹⇙⪍(⫏≰2010100⊭↱⫏≰2122122)","cot":[{"info":"⫏≰1101010⪘⫢⫏≰10011220=⫏≰2120122","layer":1},{"info":"⫏≰2010100⊭↱⫏≰2122122=⫏≰1001210","layer":1},{"info":"⫏≰2120122≹⇙⪍⫏≰1001210=NaN","layer":0}]}
{"id":990,"expression_no_base_symbol":"($4207$⨸⪁$5254$)⇷$1169$∼$8079$","expression":"(⫏≰12202211⨸⪁⫏≰21012121)⇷⫏≰1121022∼⫏≰102002020","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":264941,"operation_count":3,"complexity_ratio":88313.66666666667,"tree":{"type":"binary","operator":"⇷","left_expr":{"type":"binary","operator":"⨸⪁","left_expr":{"type":"numeric_atoms","value":4207,"base":3},"right_expr":{"type":"numeric_atoms","value":5254,"base":3}},"right_expr":{"type":"binary","operator":"∼","left_expr":{"type":"numeric_atoms","value":1169,"base":3},"right_expr":{"type":"numeric_atoms","value":8079,"base":3}}},"used_operators":["mp7IySMOzn","g55IO6H4Gj","DyGG3AbaNP"],"dependent_operators":["DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","W4YGzv6Whe","rGHVDoGpnC","A8NUZmVepG","tmPS8pqC7x","o20kRiQErp","23Mk6UjR3U","AHs5Up7iyr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4207","layer":2},{"info":"number node, value=5254","layer":2},{"info":"compute binary expreesion, left_input=4207, right_input=5254, op_id = g55IO6H4Gj binary_op_definition= 'a⨸⪁b = { ((a+b)+(b+a)) }', output=18922","layer":1},{"info":"number node, value=1169","layer":2},{"info":"number node, value=8079","layer":2},{"info":"compute binary expreesion, left_input=1169, right_input=8079, 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=18922, right_input=nan, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰12202211⨸⪁⫏≰21012121)⇷⫏≰1121022∼⫏≰102002020=NaN","reverse_text":"NaN=(⫏≰12202211⨸⪁⫏≰21012121)⇷⫏≰1121022∼⫏≰102002020","cot":[{"info":"⫏≰12202211⨸⪁⫏≰21012121=⫏≰221221211","layer":1},{"info":"⫏≰1121022∼⫏≰102002020=NaN","layer":1},{"info":"⫏≰221221211⇷NaN=NaN","layer":0}]}
{"id":991,"expression_no_base_symbol":"($1322$⋷$1574$)⨓(⫓⪴$3420$)","expression":"(⫏≰1210222⋷⫏≰2011022)⨓(⫓⪴⫏≰11200200)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":3430,"operation_count":3,"complexity_ratio":1143.3333333333333,"tree":{"type":"binary","operator":"⨓","left_expr":{"type":"binary","operator":"⋷","left_expr":{"type":"numeric_atoms","value":1322,"base":3},"right_expr":{"type":"numeric_atoms","value":1574,"base":3}},"right_expr":{"type":"unary","operator":"⫓⪴","unary_expr":{"type":"numeric_atoms","value":3420,"base":3}}},"used_operators":["3ViojmjbAp","23Mk6UjR3U","eLxqMNBOBk"],"dependent_operators":["tifHPKVTfV","tmPS8pqC7x","2DlMacCsIx","W4YGzv6Whe","t8gj7n24qd","9HNa5Wba9A"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1322","layer":2},{"info":"number node, value=1574","layer":2},{"info":"compute binary expreesion, left_input=1322, right_input=1574, op_id = 23Mk6UjR3U binary_op_definition= 'a⋷b = { ((-a)+(b+b)) , if a>575 ; (-(a+a)) , else }', output=1826","layer":1},{"info":"number node, value=3420","layer":2},{"info":"compute unary expreesion, input=3420, op_id = eLxqMNBOBk, unary_op_definition = '⫓⪴a = { (a*a) }', output=11696400","layer":1},{"info":"compute binary expreesion, left_input=1826, right_input=11696400, op_id = 3ViojmjbAp binary_op_definition= 'a⨓b = { ((b⨪↰⇹a)⇼⇔∾(b⩨b)) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1210222⋷⫏≰2011022)⨓(⫓⪴⫏≰11200200)=NaN","reverse_text":"NaN=(⫏≰1210222⋷⫏≰2011022)⨓(⫓⪴⫏≰11200200)","cot":[{"info":"⫏≰1210222⋷⫏≰2011022=⫏≰2111122","layer":1},{"info":"⫓⪴⫏≰11200200=⫏≰211000020110000","layer":1},{"info":"⫏≰2111122⨓⫏≰211000020110000=NaN","layer":0}]}
{"id":992,"expression_no_base_symbol":"(+⊝⨔$1906$)⪛($5062$⊭↱$5782$)","expression":"(+⊝⨔⫏≰2121121)⪛(⫏≰20221111⊭↱⫏≰21221011)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":50,"operation_count":3,"complexity_ratio":16.666666666666668,"tree":{"type":"binary","operator":"⪛","left_expr":{"type":"unary","operator":"+⊝⨔","unary_expr":{"type":"numeric_atoms","value":1906,"base":3}},"right_expr":{"type":"binary","operator":"⊭↱","left_expr":{"type":"numeric_atoms","value":5062,"base":3},"right_expr":{"type":"numeric_atoms","value":5782,"base":3}}},"used_operators":["uFcxV4UQCh","DhbWaqg5eL","COABgblf1C"],"dependent_operators":["9HNa5Wba9A","u6S6b8DprG","k8jYdgA6NY","dWAJyo7jo9","t8gj7n24qd","oacrs7FA3X","glklzrTFfD","eH2TOUuTDT","AF7qkfDlqP","2DlMacCsIx","mqXw5SEYmG","9FxExcQeMw","XPYlsWDdGa","W4YGzv6Whe","W4YGzv6Whe","t8gj7n24qd"],"result":"⫏≰2212","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1906","layer":2},{"info":"compute unary expreesion, input=1906, 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=5062","layer":2},{"info":"number node, value=5782","layer":2},{"info":"compute binary expreesion, left_input=5062, right_input=5782, op_id = COABgblf1C binary_op_definition= 'a⊭↱b = { (((b+b)+(-a))+((-a)+5)) }', output=1445","layer":1},{"info":"compute binary expreesion, left_input=1522, right_input=1445, op_id = uFcxV4UQCh binary_op_definition= 'a⪛b = { (a%b) , if (↽≂b)!=229 ; (a*b) , else }', output=77","layer":0}],"base":3,"result_base":3,"text":"(+⊝⨔⫏≰2121121)⪛(⫏≰20221111⊭↱⫏≰21221011)=⫏≰2212","reverse_text":"⫏≰2212=(+⊝⨔⫏≰2121121)⪛(⫏≰20221111⊭↱⫏≰21221011)","cot":[{"info":"+⊝⨔⫏≰2121121=⫏≰2002101","layer":1},{"info":"⫏≰20221111⊭↱⫏≰21221011=⫏≰1222112","layer":1},{"info":"⫏≰2002101⪛⫏≰1222112=⫏≰2212","layer":0}]}
{"id":993,"expression_no_base_symbol":"$3828$≭$3859$⫡⨏$3447$⪘⫢$5024$","expression":"⫏≰12020210≭⫏≰12021221⫡⨏⫏≰11201200⪘⫢⫏≰20220002","highest_n_order":5,"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":3828,"base":3},"right_expr":{"type":"numeric_atoms","value":3859,"base":3}},"right_expr":{"type":"binary","operator":"⪘⫢","left_expr":{"type":"numeric_atoms","value":3447,"base":3},"right_expr":{"type":"numeric_atoms","value":5024,"base":3}}},"used_operators":["QMFrweE19q","rxpJgHHUmx","oacrs7FA3X"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","AHs5Up7iyr","sdazOOVcIp","i8ToyICDmI","QMFrweE19q","XhwjNDsVaA","P8v4zCKN1o","2DQ55sFlQl","AF7qkfDlqP"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3828","layer":2},{"info":"number node, value=3859","layer":2},{"info":"compute binary expreesion, left_input=3828, right_input=3859, 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=3447","layer":2},{"info":"number node, value=5024","layer":2},{"info":"compute binary expreesion, left_input=3447, right_input=5024, op_id = oacrs7FA3X binary_op_definition= 'a⪘⫢b = { ((a⨵⪆345)⪨≂(⨑⩽⪐a)) , if ((b∲⫓242)>=654 and (∥⊫a)>649) ; ((b⨵⪆b)/(a⫡⨏b)) , else }', output=6770","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=6770, 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":3,"result_base":3,"text":"⫏≰12020210≭⫏≰12021221⫡⨏⫏≰11201200⪘⫢⫏≰20220002=NaN","reverse_text":"NaN=⫏≰12020210≭⫏≰12021221⫡⨏⫏≰11201200⪘⫢⫏≰20220002","cot":[{"info":"⫏≰12020210≭⫏≰12021221=NaN","layer":1},{"info":"⫏≰11201200⪘⫢⫏≰20220002=⫏≰100021202","layer":1},{"info":"NaN⫡⨏⫏≰100021202=NaN","layer":0}]}
{"id":994,"expression_no_base_symbol":"($1361$⇷$2428$)≹⇙⪍($2873$≣⋋)","expression":"(⫏≰1212102⇷⫏≰10022221)≹⇙⪍(⫏≰10221102≣⋋)","highest_n_order":4,"priority_hierarchical_complexity":3,"normalized_expansion_degree":19575,"operation_count":3,"complexity_ratio":6525.0,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"⇷","left_expr":{"type":"numeric_atoms","value":1361,"base":3},"right_expr":{"type":"numeric_atoms","value":2428,"base":3}},"right_expr":{"type":"unary","operator":"≣⋋","unary_expr":{"type":"numeric_atoms","value":2873,"base":3}}},"used_operators":["AHs5Up7iyr","mp7IySMOzn","Tcnh7f0tEr"],"dependent_operators":["dWAJyo7jo9","DZ8iAZOCBD","LRNGc0VcxI","DpFCA1CohY","W4YGzv6Whe","dWAJyo7jo9","XhwjNDsVaA","DIvbN7qnHd","Qy55tPpLXF","tmPS8pqC7x","9HNa5Wba9A"],"result":"⫏≰20122212","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1361","layer":2},{"info":"number node, value=2428","layer":2},{"info":"compute binary expreesion, left_input=1361, right_input=2428, op_id = mp7IySMOzn binary_op_definition= 'a⇷b = { (b⊉≛↸((a+a)∀⇚≩(⋗⩬⋾a))) }', output=4856","layer":1},{"info":"number node, value=2873","layer":2},{"info":"compute unary expreesion, input=2873, 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=4856, right_input=0, 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=4856","layer":0}],"base":3,"result_base":3,"text":"(⫏≰1212102⇷⫏≰10022221)≹⇙⪍(⫏≰10221102≣⋋)=⫏≰20122212","reverse_text":"⫏≰20122212=(⫏≰1212102⇷⫏≰10022221)≹⇙⪍(⫏≰10221102≣⋋)","cot":[{"info":"⫏≰1212102⇷⫏≰10022221=⫏≰20122212","layer":1},{"info":"⫏≰10221102≣⋋=⫏≰0","layer":1},{"info":"⫏≰20122212≹⇙⪍⫏≰0=⫏≰20122212","layer":0}]}
{"id":995,"expression_no_base_symbol":"(↣≠⋷$1664$)⊴($3991$↛⩡⫤)","expression":"(↣≠⋷⫏≰2021122)⊴(⫏≰12110211↛⩡⫤)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":610846,"operation_count":3,"complexity_ratio":203615.33333333334,"tree":{"type":"binary","operator":"⊴","left_expr":{"type":"unary","operator":"↣≠⋷","unary_expr":{"type":"numeric_atoms","value":1664,"base":3}},"right_expr":{"type":"unary","operator":"↛⩡⫤","unary_expr":{"type":"numeric_atoms","value":3991,"base":3}}},"used_operators":["Nsiff2A1zJ","Asc51vEJeQ","FU0Cs4j7VP"],"dependent_operators":["dWAJyo7jo9","14qkJME0vr","XhwjNDsVaA","AHs5Up7iyr","8jW3W4yZS5","SUmda5xLS4","rJVOvQCfKK","k8jYdgA6NY","P8v4zCKN1o","tmPS8pqC7x","2DlMacCsIx","eewbuw0ToL","oacrs7FA3X"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1664","layer":2},{"info":"compute unary expreesion, input=1664, op_id = Asc51vEJeQ, unary_op_definition = '↣≠⋷a = { ((a/a)≹⇙⪍(a≹⇙⪍a)) }', output=nan","layer":1},{"info":"number node, value=3991","layer":2},{"info":"compute unary expreesion, input=3991, op_id = FU0Cs4j7VP, unary_op_definition = 'a↛⩡⫤ = { (((a⨪↰⇹a)⨪↰⇹(a⨰a))%((a⨪↰⇹a)⪄(a⨎a))) , if (↯⪼a)!=406 ; ((∥⊫(a⪘⫢44))⩨a) , else }', output=-598730","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=-598730, op_id = Nsiff2A1zJ binary_op_definition= 'a⊴b = { ((a⪢b)⊦⊿) }', output=nan","layer":0}],"base":3,"result_base":3,"text":"(↣≠⋷⫏≰2021122)⊴(⫏≰12110211↛⩡⫤)=NaN","reverse_text":"NaN=(↣≠⋷⫏≰2021122)⊴(⫏≰12110211↛⩡⫤)","cot":[{"info":"↣≠⋷⫏≰2021122=NaN","layer":1},{"info":"⫏≰12110211↛⩡⫤=⫏≰-1010102022012","layer":1},{"info":"NaN⊴⫏≰-1010102022012=NaN","layer":0}]}
{"id":996,"expression_no_base_symbol":"($1880$⩷∴$1062$)⪢$1287$⨟⋌⩍$1838$","expression":"(⫏≰2120122⩷∴⫏≰1110100)⪢⫏≰1202200⨟⋌⩍⫏≰2112002","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":8,"operation_count":3,"complexity_ratio":2.6666666666666665,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"binary","operator":"⩷∴","left_expr":{"type":"numeric_atoms","value":1880,"base":3},"right_expr":{"type":"numeric_atoms","value":1062,"base":3}},"right_expr":{"type":"binary","operator":"⨟⋌⩍","left_expr":{"type":"numeric_atoms","value":1287,"base":3},"right_expr":{"type":"numeric_atoms","value":1838,"base":3}}},"used_operators":["dWAJyo7jo9","9FxExcQeMw","rGHVDoGpnC"],"dependent_operators":["k8jYdgA6NY","rysDP5nf3Z","Tcnh7f0tEr"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=1880","layer":2},{"info":"number node, value=1062","layer":2},{"info":"compute binary expreesion, left_input=1880, right_input=1062, op_id = 9FxExcQeMw binary_op_definition= 'a⩷∴b = { (((a-b)-32)-((b-a)-(a-a))) }', output=1604","layer":1},{"info":"number node, value=1287","layer":2},{"info":"number node, value=1838","layer":2},{"info":"compute binary expreesion, left_input=1287, right_input=1838, 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=1604, right_input=nan, 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":3,"result_base":3,"text":"(⫏≰2120122⩷∴⫏≰1110100)⪢⫏≰1202200⨟⋌⩍⫏≰2112002=NaN","reverse_text":"NaN=(⫏≰2120122⩷∴⫏≰1110100)⪢⫏≰1202200⨟⋌⩍⫏≰2112002","cot":[{"info":"⫏≰2120122⩷∴⫏≰1110100=⫏≰2012102","layer":1},{"info":"⫏≰1202200⨟⋌⩍⫏≰2112002=NaN","layer":1},{"info":"⫏≰2012102⪢NaN=NaN","layer":0}]}
{"id":997,"expression_no_base_symbol":"($1174$*$3462$)≹⇙⪍($1087$*$5518$)","expression":"(⫏≰1121111*⫏≰11202020)≹⇙⪍(⫏≰1111021*⫏≰21120101)","highest_n_order":4,"priority_hierarchical_complexity":2,"normalized_expansion_degree":2262,"operation_count":3,"complexity_ratio":754.0,"tree":{"type":"binary","operator":"≹⇙⪍","left_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1174,"base":3},"right_expr":{"type":"numeric_atoms","value":3462,"base":3}},"right_expr":{"type":"binary","operator":"*","left_expr":{"type":"numeric_atoms","value":1087,"base":3},"right_expr":{"type":"numeric_atoms","value":5518,"base":3}}},"used_operators":["AHs5Up7iyr","9HNa5Wba9A"],"dependent_operators":["dWAJyo7jo9","W4YGzv6Whe"],"result":"NaN","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=1174","layer":2},{"info":"number node, value=3462","layer":2},{"info":"compute binary expreesion, left_input=1174, right_input=3462, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=4064388","layer":1},{"info":"number node, value=1087","layer":2},{"info":"number node, value=5518","layer":2},{"info":"compute binary expreesion, left_input=1087, right_input=5518, op_id = 9HNa5Wba9A binary_op_definition= 'None', output=5998066","layer":1},{"info":"compute binary expreesion, left_input=4064388, right_input=5998066, 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":3,"result_base":3,"text":"(⫏≰1121111*⫏≰11202020)≹⇙⪍(⫏≰1111021*⫏≰21120101)=NaN","reverse_text":"NaN=(⫏≰1121111*⫏≰11202020)≹⇙⪍(⫏≰1111021*⫏≰21120101)","cot":[{"info":"⫏≰1121111*⫏≰11202020=⫏≰21122111021220","layer":1},{"info":"⫏≰1111021*⫏≰21120101=⫏≰102021201210121","layer":1},{"info":"⫏≰21122111021220≹⇙⪍⫏≰102021201210121=NaN","layer":0}]}
{"id":998,"expression_no_base_symbol":"($4017$∀⇚≩$3425$)⪢(⩦⩻⨪$1702$)","expression":"(⫏≰12111210∀⇚≩⫏≰11200212)⪢(⩦⩻⨪⫏≰2100001)","highest_n_order":3,"priority_hierarchical_complexity":3,"normalized_expansion_degree":29824,"operation_count":3,"complexity_ratio":9941.333333333334,"tree":{"type":"binary","operator":"⪢","left_expr":{"type":"binary","operator":"∀⇚≩","left_expr":{"type":"numeric_atoms","value":4017,"base":3},"right_expr":{"type":"numeric_atoms","value":3425,"base":3}},"right_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":1702,"base":3}}},"used_operators":["dWAJyo7jo9","LRNGc0VcxI","2td37pGCOC"],"dependent_operators":["k8jYdgA6NY","X99M06cbEe","rysDP5nf3Z","t8gj7n24qd"],"result":"NaN","longer_result_info":{"target_base":3,"flag":false},"cot_info":[{"info":"number node, value=4017","layer":2},{"info":"number node, value=3425","layer":2},{"info":"compute binary expreesion, left_input=4017, right_input=3425, 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=1702","layer":2},{"info":"compute unary expreesion, input=1702, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=1702","layer":1},{"info":"compute binary expreesion, left_input=nan, right_input=1702, 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":3,"result_base":3,"text":"(⫏≰12111210∀⇚≩⫏≰11200212)⪢(⩦⩻⨪⫏≰2100001)=NaN","reverse_text":"NaN=(⫏≰12111210∀⇚≩⫏≰11200212)⪢(⩦⩻⨪⫏≰2100001)","cot":[{"info":"⫏≰12111210∀⇚≩⫏≰11200212=NaN","layer":1},{"info":"⩦⩻⨪⫏≰2100001=⫏≰2100001","layer":1},{"info":"NaN⪢⫏≰2100001=NaN","layer":0}]}
{"id":999,"expression_no_base_symbol":"$4368$⩚⊴⇥$2985$⩚⊴⇥(⩦⩻⨪$1676$)","expression":"⫏≰12222210⩚⊴⇥⫏≰11002120⩚⊴⇥(⩦⩻⨪⫏≰2022002)","highest_n_order":1,"priority_hierarchical_complexity":2,"normalized_expansion_degree":9,"operation_count":3,"complexity_ratio":3.0,"tree":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"binary","operator":"⩚⊴⇥","left_expr":{"type":"numeric_atoms","value":4368,"base":3},"right_expr":{"type":"numeric_atoms","value":2985,"base":3}},"right_expr":{"type":"unary","operator":"⩦⩻⨪","unary_expr":{"type":"numeric_atoms","value":1676,"base":3}}},"used_operators":["NTOWxs364D","2td37pGCOC"],"dependent_operators":["W4YGzv6Whe","t8gj7n24qd","rysDP5nf3Z","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰21210021","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=4368","layer":2},{"info":"number node, value=2985","layer":2},{"info":"compute binary expreesion, left_input=4368, right_input=2985, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=-7474","layer":1},{"info":"number node, value=1676","layer":2},{"info":"compute unary expreesion, input=1676, op_id = 2td37pGCOC, unary_op_definition = '⩦⩻⨪a = { ((a-a)-(-a)) }', output=1676","layer":1},{"info":"compute binary expreesion, left_input=-7474, right_input=1676, op_id = NTOWxs364D binary_op_definition= 'a⩚⊴⇥b = { ((-b)-(121+a)) }', output=5677","layer":0}],"base":3,"result_base":3,"text":"⫏≰12222210⩚⊴⇥⫏≰11002120⩚⊴⇥(⩦⩻⨪⫏≰2022002)=⫏≰21210021","reverse_text":"⫏≰21210021=⫏≰12222210⩚⊴⇥⫏≰11002120⩚⊴⇥(⩦⩻⨪⫏≰2022002)","cot":[{"info":"⫏≰12222210⩚⊴⇥⫏≰11002120=⫏≰-101020211","layer":1},{"info":"⩦⩻⨪⫏≰2022002=⫏≰2022002","layer":1},{"info":"⫏≰-101020211⩚⊴⇥⫏≰2022002=⫏≰21210021","layer":0}]}
{"id":1000,"expression_no_base_symbol":"⨑⩽⪐($3997$↺$1983$)","expression":"⨑⩽⪐(⫏≰12111001↺⫏≰2201110)","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":"binary","operator":"↺","left_expr":{"type":"numeric_atoms","value":3997,"base":3},"right_expr":{"type":"numeric_atoms","value":1983,"base":3}}},"used_operators":["AF7qkfDlqP","7j4O788W3g"],"dependent_operators":["rysDP5nf3Z","t8gj7n24qd","W4YGzv6Whe","rysDP5nf3Z","t8gj7n24qd"],"result":"⫏≰-2100100","longer_result_info":{"target_base":3,"flag":true},"cot_info":[{"info":"number node, value=3997","layer":2},{"info":"number node, value=1983","layer":2},{"info":"compute binary expreesion, left_input=3997, right_input=1983, op_id = 7j4O788W3g binary_op_definition= 'a↺b = { ((b-a)-(146-b)) , if ((-a)<=494 and (-a)>=758) ; (-(-b)) , else }', output=1983","layer":1},{"info":"compute unary expreesion, input=1983, op_id = AF7qkfDlqP, unary_op_definition = '⨑⩽⪐a = { (-((a-a)-(273-a))) , if a>30 ; (((a-a)-(a-789))+((a-a)+(-a))) , else }', output=-1710","layer":0}],"base":3,"result_base":3,"text":"⨑⩽⪐(⫏≰12111001↺⫏≰2201110)=⫏≰-2100100","reverse_text":"⫏≰-2100100=⨑⩽⪐(⫏≰12111001↺⫏≰2201110)","cot":[{"info":"⫏≰12111001↺⫏≰2201110=⫏≰2201110","layer":1},{"info":"⨑⩽⪐⫏≰2201110=⫏≰-2100100","layer":0}]}