question stringclasses 3
values | metadata stringclasses 3
values | task_source stringclasses 1
value | formatted_prompt listlengths 2 2 | responses_by_sample listlengths 1 1 | tokens_by_sample listlengths 1 1 | num_rounds_by_sample listlengths 1 1 | continuation_prompts_by_sample listlengths 1 1 | continuation_text_by_sample listlengths 1 1 | strategy_type stringclasses 1
value | termination_reason_by_sample listlengths 1 1 | correct_round_by_sample listlengths 1 1 | smart_termination_enabled bool 1
class | answers_by_sample listlengths 1 1 | evals_by_sample listlengths 1 1 | eval_metadata_by_sample listlengths 1 1 | annotations_by_sample listlengths 1 1 | reasoning_action_spans_by_sample listlengths 1 1 | action_metadata_by_sample listlengths 1 1 | action_self_similarity_by_sample listlengths 1 1 | has_reasoning_actions bool 2
classes | arithmetic_attempts_by_sample listlengths 1 1 | expression_attempts_by_sample listlengths 1 1 | subgoals_by_sample listlengths 1 1 | failure_markers_by_sample listlengths 1 1 | subgoal_windows_by_sample listlengths 1 1 | branches_by_sample listlengths 1 1 | extraction_stats_by_sample listlengths 1 1 | llm_supplement_stats_by_sample listlengths 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
"Using ALL of the numbers 12, 4, 7, 1, 2, 5, 21, 88, create an expression that equals 109. You must (...TRUNCATED) | "{\"numbers\": [12, 4, 7, 1, 2, 5, 21, 88], \"target\": 109, \"operators_used\": [\"/\", \"+\", \"/\(...TRUNCATED) | countdown | [{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED) | [["We are given the numbers: \n**12, 4, 7, 1, 2, 5, 21, 88** \nWe must use **each number exactly o(...TRUNCATED) | [
33767
] | [
19
] | [["Continue exploring alternative solution strategies.","Continue exploring alternative solution str(...TRUNCATED) | [["We are given the numbers: \n**12, 4, 7, 1, 2, 5, 21, 88** \nWe must use **each number exactly o(...TRUNCATED) | iterative | [
"budget_reached"
] | [
null
] | false | [[["88 + 12 + 7 + 2 + (21 × (5 - 4 - 1))"],["88 + 12 + 7 + 2 + (21 × (5 - 4 - 1))"],["88 + 12 + 7 (...TRUNCATED) | [[[true],[true],[true],[true],[true],[true,true],[true,true],[true,true],[true,true],[true,true],[tr(...TRUNCATED) | [[[{"answer_block":"88 + 12 + 7 + 2 + (21 * (5 - 4 - 1))","error":null,"final_answer":109.0,"is_corr(...TRUNCATED) | [[{"class_label":"X-X","created_at":"2025-12-25T05:18:08.814928","description":"","end_word_idx":235(...TRUNCATED) | [[{"action_type":"restate_constraints","chunk_idx":0,"confidence":0.9,"end_char":92,"end_char_in_rou(...TRUNCATED) | [{"action_type_counts":{"add_all":33,"add_multiple":142,"add_two_numbers":579,"backtrack":5,"divide_(...TRUNCATED) | [{"action_ngrams":{"add_all -> add_all":2,"add_all -> add_all -> restate_constraints":1,"add_all -> (...TRUNCATED) | true | [[{"all_operands":[109.0,88.0],"all_operators":["-"],"branch_id":1,"canonical_form":"109 - 88 = 21",(...TRUNCATED) | [[{"branch_id":1,"canonical_key":"expr:109-88<109","end_char":367,"end_char_in_round":367,"eval_valu(...TRUNCATED) | [[{"canonical_key":"subgoal:109","confidence":0.9,"end_char":354,"end_char_in_round":354,"goal_value(...TRUNCATED) | [[{"end_char":2720,"end_char_in_round":2720,"marker_type":"not_helpful","round_idx":0,"span_text":"n(...TRUNCATED) | [[{"branch_id":1,"end_char":816,"end_char_in_round":816,"evidence_kind":"goal","evidence_text":"get (...TRUNCATED) | [[{"branch_id":0,"end_char":190,"end_char_in_round":190,"round_idx":0,"start_char":0,"start_char_in_(...TRUNCATED) | [{"attempts_by_match_type":{"infix":587,"latex_frac":115,"multi_op_chain":53,"nested_paren":null,"pa(...TRUNCATED) | [{"candidates_proposed":765,"candidates_validated":597,"duplicates":564,"new_finds":33,"total_attemp(...TRUNCATED) |
"Using ALL of the numbers 25, 69, 58, 14, 55, 24, 36, 60, create an expression that equals 176. You (...TRUNCATED) | "{\"numbers\": [25, 69, 58, 14, 55, 24, 36, 60], \"target\": 176, \"operators_used\": [\"-\", \"+\",(...TRUNCATED) | countdown | [{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED) | [["We are given the numbers: \n**25, 69, 58, 14, 55, 24, 36, 60** \nWe must use **each number exac(...TRUNCATED) | [
55243
] | [
1
] | [
[]
] | [["We are given the numbers: \n**25, 69, 58, 14, 55, 24, 36, 60** \nWe must use **each number exac(...TRUNCATED) | iterative | [
"budget_reached"
] | [
null
] | false | [[["25 + 69 + 58 + 24 = 176","(69 + 58 + 55) - (60 + 24) / 14 = 176","25 + 69 + 58 + 24 + (60 - 60) (...TRUNCATED) | [[[false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,f(...TRUNCATED) | [[[{"answer_block":"25 + 69 + 58 + 24 = 176","error":"Expression must use ALL available numbers. Unu(...TRUNCATED) | [
[]
] | [
[]
] | [{"action_type_counts":null,"chunks_processed":null,"chunks_with_actions":null,"status":"not_process(...TRUNCATED) | [{"action_ngrams":null,"action_sequence":null,"action_type_counts":null,"repetition_rate":null,"tota(...TRUNCATED) | false | [[{"all_operands":[25.0,69.0],"all_operators":["+"],"branch_id":1,"canonical_form":"25 + 69 = 94","c(...TRUNCATED) | [[{"branch_id":1,"canonical_key":"expr:25+69+58+14+55+24+36+60=(25+69)","end_char":468,"end_char_in_(...TRUNCATED) | [[{"canonical_key":"subgoal:100","confidence":0.85,"end_char":1028,"end_char_in_round":1028,"goal_va(...TRUNCATED) | [[{"end_char":1876,"end_char_in_round":1876,"marker_type":"not_helpful","round_idx":0,"span_text":"n(...TRUNCATED) | [[{"branch_id":2,"end_char":1840,"end_char_in_round":1840,"evidence_kind":"intermediate","evidence_t(...TRUNCATED) | [[{"branch_id":0,"end_char":198,"end_char_in_round":198,"round_idx":0,"start_char":0,"start_char_in_(...TRUNCATED) | [{"attempts_by_match_type":{"infix":157,"latex_frac":null,"multi_op_chain":17,"nested_paren":2,"pare(...TRUNCATED) | [{"candidates_proposed":460,"candidates_validated":245,"duplicates":242,"new_finds":3,"total_attempt(...TRUNCATED) |
"Using ALL of the numbers 55, 36, 6, 3, 14, 99, 17, 82, create an expression that equals 245. You mu(...TRUNCATED) | "{\"numbers\": [55, 36, 6, 3, 14, 99, 17, 82], \"target\": 245, \"operators_used\": [\"*\", \"-\", \(...TRUNCATED) | countdown | [{"content":"You are a helpful assistant that solves math problems by reasoning step-by-step. Show y(...TRUNCATED) | [["We are given the numbers: \n**55, 36, 6, 3, 14, 99, 17, 82** \nWe must use **each number exactl(...TRUNCATED) | [
57057
] | [
1
] | [
[]
] | [["We are given the numbers: \n**55, 36, 6, 3, 14, 99, 17, 82** \nWe must use **each number exactl(...TRUNCATED) | iterative | [
"budget_reached"
] | [
null
] | false | [[["99 + 82 + 55 + 6 + 3 = 245","99 + 82 + 55 + 36 - 14 - 17 + 6 + 3 = 245","99 + 82 + 55 + 6 + 3 = (...TRUNCATED) | [[[false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,false,f(...TRUNCATED) | [[[{"answer_block":"99 + 82 + 55 + 6 + 3 = 245","error":"Expression must use ALL available numbers. (...TRUNCATED) | [
[]
] | [
[]
] | [{"action_type_counts":null,"chunks_processed":null,"chunks_with_actions":null,"status":"not_process(...TRUNCATED) | [{"action_ngrams":null,"action_sequence":null,"action_type_counts":null,"repetition_rate":null,"tota(...TRUNCATED) | false | [[{"all_operands":[55.0,36.0],"all_operators":["+"],"branch_id":1,"canonical_form":"55 + 36 = 91","c(...TRUNCATED) | [[{"branch_id":1,"canonical_key":"expr:55+36=91","end_char":402,"end_char_in_round":402,"eval_value"(...TRUNCATED) | [[{"canonical_key":"subgoal:245","confidence":0.85,"end_char":4037,"end_char_in_round":4037,"goal_va(...TRUNCATED) | [[{"end_char":1097,"end_char_in_round":1097,"marker_type":"too_big","round_idx":0,"span_text":"too b(...TRUNCATED) | [[{"branch_id":3,"end_char":4506,"end_char_in_round":4506,"evidence_kind":"need","evidence_text":"ne(...TRUNCATED) | [[{"branch_id":0,"end_char":192,"end_char_in_round":192,"round_idx":0,"start_char":0,"start_char_in_(...TRUNCATED) | [{"attempts_by_match_type":{"infix":369,"latex_frac":null,"multi_op_chain":350,"nested_paren":1,"par(...TRUNCATED) | [{"candidates_proposed":636,"candidates_validated":609,"duplicates":602,"new_finds":7,"total_attempt(...TRUNCATED) |
EAS-qwen3-4B-Instruct-2507-cd8arg-iterative-stage02b-stage02a
Deterministic extraction of arithmetic attempts, expressions, subgoals, branches, and failure markers from Countdown reasoning traces
Dataset Info
- Rows: 3
- Columns: 29
Columns
| Column | Type | Description |
|---|---|---|
| question | Value('string') | No description provided |
| metadata | Value('string') | No description provided |
| task_source | Value('string') | No description provided |
| formatted_prompt | List({'content': Value('string'), 'role': Value('string')}) | No description provided |
| responses_by_sample | List(List(Value('string'))) | No description provided |
| tokens_by_sample | List(Value('int64')) | No description provided |
| num_rounds_by_sample | List(Value('int64')) | No description provided |
| continuation_prompts_by_sample | List(List(Value('string'))) | No description provided |
| continuation_text_by_sample | List(List(Value('string'))) | No description provided |
| strategy_type | Value('string') | No description provided |
| termination_reason_by_sample | List(Value('string')) | No description provided |
| correct_round_by_sample | List(Value('null')) | No description provided |
| smart_termination_enabled | Value('bool') | No description provided |
| answers_by_sample | List(List(List(Value('string')))) | No description provided |
| evals_by_sample | List(List(List(Value('bool')))) | No description provided |
| eval_metadata_by_sample | List(List(List({'answer_block': Value('string'), 'error': Value('string'), 'final_answer': Value('float64'), 'is_correct': Value('bool')}))) | No description provided |
| annotations_by_sample | List(List({'class_label': Value('string'), 'created_at': Value('string'), 'description': Value('string'), 'end_word_idx': Value('int64'), 'id': Value('string'), 'modified_at': Value('string'), 'round_idx': Value('int64'), 'start_word_idx': Value('int64'), 'tags': List(Value('string'))})) | No description provided |
| reasoning_action_spans_by_sample | List(List({'action_type': Value('string'), 'chunk_idx': Value('int64'), 'confidence': Value('float64'), 'end_char': Value('int64'), 'end_char_in_round': Value('int64'), 'metadata': {'notes': Value('string'), 'numbers_involved': List(Value('string')), 'operations': List(Value('string')), 'result': Value('string')}, 'offset_validated': Value('bool'), 'round_idx': Value('int64'), 'span_text': Value('string'), 'start_char': Value('int64'), 'start_char_in_round': Value('int64')})) | No description provided |
| action_metadata_by_sample | List({'action_type_counts': {'add_all': Value('int64'), 'add_multiple': Value('int64'), 'add_two_numbers': Value('int64'), 'backtrack': Value('int64'), 'divide_for_factor': Value('int64'), 'exhaustive_enumeration': Value('int64'), 'find_difference_pair': Value('int64'), 'find_product_pair': Value('int64'), 'find_sum_pair': Value('int64'), 'intermediate_goal': Value('int64'), 'meta_reasoning': Value('int64'), 'multiply_all': Value('int64'), 'multiply_multiple': Value('int64'), 'multiply_two': Value('int64'), 'realize_error': Value('int64'), 'repeat_failed': Value('int64'), 'restate_constraints': Value('int64'), 'restated_constraints': Value('int64'), 'restating_constraints': Value('int64'), 'small_adjustment': Value('int64'), 'strategic_decomposition': Value('int64'), 'subtract_all': Value('int64'), 'subtract_different': Value('int64'), 'subtract_multiple': Value('int64'), 'subtract_same': Value('int64'), 'subtract_two_numbers': Value('int64'), 'target_decomposition': Value('int64'), 'use_zero': Value('int64'), 'verify_calculation': Value('int64')}, 'chunks_processed': Value('int64'), 'chunks_with_actions': Value('int64'), 'status': Value('string'), 'total_spans': Value('int64'), 'unique_action_types': List(Value('string'))}) | No description provided |
| action_self_similarity_by_sample | List({'action_ngrams': {'add_all -> add_all': Value('int64'), 'add_all -> add_all -> restate_constraints': Value('int64'), 'add_all -> add_all -> verify_calculation': Value('int64'), 'add_all -> add_multiple': Value('int64'), 'add_all -> add_multiple -> add_multiple': Value('int64'), 'add_all -> add_two_numbers': Value('int64'), 'add_all -> add_two_numbers -> subtract_different': Value('int64'), 'add_all -> find_sum_pair': Value('int64'), 'add_all -> find_sum_pair -> find_difference_pair': Value('int64'), 'add_all -> find_sum_pair -> subtract_same': Value('int64'), 'add_all -> restate_constraints': Value('int64'), 'add_all -> restate_constraints -> find_difference_pair': Value('int64'), 'add_all -> restate_constraints -> find_sum_pair': Value('int64'), 'add_all -> restate_constraints -> intermediate_goal': Value('int64'), 'add_all -> restate_constraints -> meta_reasoning': Value('int64'), 'add_all -> restate_constraints -> restate_constraints': Value('int64'), 'add_all -> restating_constraints': Value('int64'), 'add_all -> restating_constraints -> find_sum_pair': Value('int64'), 'add_all -> subtract_different': Value('int64'), 'add_all -> subtract_different -> subtract_same': Value('int64'), 'add_all -> subtract_two_numbers': Value('int64'), 'add_all -> subtract_two_numbers -> find_difference_pair': Value('int64'), 'add_all -> verify_calculation': Value('int64'), 'add_all -> verify_calculation -> restate_constraints': Value('int64'), 'add_multiple -> add_all': Value('int64'), 'add_multiple -> add_all -> find_sum_pair': Value('int64'), 'add_multiple -> add_multiple': Value('int64'), 'add_multiple -> add_multiple -> add_all': Value('int64'), 'add_multiple -> add_multiple -> add_multiple': Value('int64'), 'add_multiple -> add_multiple -> add_two_numbers': Value('int64'), 'add_multiple -> add_multiple -> find_sum_pair': Value('int64'), 'add_multiple -> add_multiple -> intermediate_goal': Value('int64'), 'add_multiple -> add_multiple -> restate_constraints': Value('int64'), 'add_multiple -> add_multiple -> strategic_decomposition': Value('int64'), 'add_multiple -> add_multiple -> subtract_different': Value('int64'), 'add_multiple -> add_two_numbers': Value('int64'), 'add_multiple -> add_two_numbers -> add_multiple': Value('int64'), 'add_multiple -> add_two_numbers -> add_two_numbers': Value('int64'), 'add_multiple -> add_two_numbers -> intermediate_goal': Value('int64'), 'add_multiple -> add_two_numbers -> multiply_two': Value('int64'), 'add_multiple -> add_two_numbers -> restate_constraints': Value('int64'), 'add_multiple -> add_two_numbers -> subtract_different': Value('int64'), 'add_multiple -> divide_for_factor': Value('int64'), 'add_multiple -> divide_for_factor -> add_multiple': Value('int64'), 'add_multiple -> divide_for_factor -> divide_for_factor': Value('int64'), 'add_multiple -> divide_for_factor -> subtract_different': Value('int64'), 'add_multiple -> find_sum_pair': Value('int64'), 'add_multiple -> find_sum_pair -> find_difference_pair': Value('int64'), 'add_multiple -> find_sum_pair -> target_decomposition': Value('int64'), 'add_multiple -> intermediate_goal': Value('int64'), 'add_multiple -> intermediate_goal -> use_zero': Value('int64'), 'add_multiple -> intermediate_goal -> verify_calculation': Value('int64'), 'add_multiple -> multiply_two': Value('int64'), 'add_multiple -> multiply_two -> add_multiple': Value('int64'), 'add_multiple -> multiply_two -> divide_for_factor': Value('int64'), 'add_multiple -> multiply_two -> multiply_two': Value('int64'), 'add_multiple -> multiply_two -> subtract_different': Value('int64'), 'add_multiple -> multiply_two -> subtract_multiple': Value('int64'), 'add_multiple -> realize_error': Value('int64'), 'add_multiple -> realize_error -> restate_constraints': Value('int64'), 'add_multiple -> restate_constraints': Value('int64'), 'add_multiple -> restate_constraints -> add_multiple': Value('int64'), 'add_multiple -> restate_constraints -> intermediate_goal': Value('int64'), 'add_multiple -> restate_constraints -> restate_constraints': Value('int64'), 'add_multiple -> restate_constraints -> restating_constraints': Value('int64'), 'add_multiple -> restate_constraints -> use_zero': Value('int64'), 'add_multiple -> restated_constraints': Value('int64'), 'add_multiple -> restated_constraints -> restate_constraints': Value('int64'), 'add_multiple -> restated_constraints -> restated_constraints': Value('int64'), 'add_multiple -> restating_constraints': Value('int64'), 'add_multiple -> restating_constraints -> restating_constraints': Value('int64'), 'add_multiple -> restating_constraints -> subtract_same': Value('int64'), 'add_multiple -> small_adjustment': Value('int64'), 'add_multiple -> small_adjustment -> add_two_numbers': Value('int64'), 'add_multiple -> small_adjustment -> realize_error': Value('int64'), 'add_multiple -> small_adjustment -> restate_constraints': Value('int64'), 'add_multiple -> strategic_decomposition': Value('int64'), 'add_multiple -> strategic_decomposition -> restate_constraints': Value('int64'), 'add_multiple -> subtract_different': Value('int64'), 'add_multiple -> subtract_different -> add_two_numbers': Value('int64'), 'add_multiple -> subtract_different -> find_difference_pair': Value('int64'), 'add_multiple -> subtract_different -> intermediate_goal': Value('int64'), 'add_multiple -> subtract_different -> restate_constraints': Value('int64'), 'add_multiple -> subtract_different -> subtract_different': Value('int64'), 'add_multiple -> subtract_different -> use_zero': Value('int64'), 'add_multiple -> subtract_different -> verify_calculation': Value('int64'), 'add_multiple -> subtract_multiple': Value('int64'), 'add_multiple -> subtract_multiple -> subtract_multiple': Value('int64'), 'add_multiple -> subtract_same': Value('int64'), 'add_multiple -> subtract_same -> add_multiple': Value('int64'), 'add_multiple -> subtract_same -> restate_constraints': Value('int64'), 'add_multiple -> subtract_same -> subtract_same': Value('int64'), 'add_multiple -> verify_calculation': Value('int64'), 'add_multiple -> verify_calculation -> restate_constraints': Value('int64'), 'add_multiple -> verify_calculation -> target_decomposition': Value('int64'), 'add_two_numbers -> add_all': Value('int64'), 'add_two_numbers -> add_all -> add_two_numbers': Value('int64'), 'add_two_numbers -> add_all -> find_sum_pair': Value('int64'), 'add_two_numbers -> add_all -> restate_constraints': Value('int64'), 'add_two_numbers -> add_all -> restating_constraints': Value('int64'), 'add_two_numbers -> add_multiple': Value('int64'), 'add_two_numbers -> add_multiple -> add_multiple': Value('int64'), 'add_two_numbers -> add_multiple -> add_two_numbers': Value('int64'), 'add_two_numbers -> add_multiple -> divide_for_factor': Value('int64'), 'add_two_numbers -> add_multiple -> multiply_two': Value('int64'), 'add_two_numbers -> add_multiple -> restate_constraints': Value('int64'), 'add_two_numbers -> add_multiple -> restated_constraints': Value('int64'), 'add_two_numbers -> add_multiple -> subtract_same': Value('int64'), 'add_two_numbers -> add_multiple -> verify_calculation': Value('int64'), 'add_two_numbers -> add_two_numbers': Value('int64'), 'add_two_numbers -> add_two_numbers -> add_multiple': Value('int64'), 'add_two_numbers -> add_two_numbers -> add_two_numbers': Value('int64'), 'add_two_numbers -> add_two_numbers -> divide_for_factor': Value('int64'), 'add_two_numbers -> add_two_numbers -> intermediate_goal': Value('int64'), 'add_two_numbers -> add_two_numbers -> multiply_two': Value('int64'), 'add_two_numbers -> add_two_numbers -> realize_error': Value('int64'), 'add_two_numbers -> add_two_numbers -> restate_constraints': Value('int64'), 'add_two_numbers -> add_two_numbers -> restating_constraints': Value('int64'), 'add_two_numbers -> add_two_numbers -> small_adjustment': Value('int64'), 'add_two_numbers -> add_two_numbers -> subtract_different': Value('int64'), 'add_two_numbers -> add_two_numbers -> subtract_multiple': Value('int64'), 'add_two_numbers -> add_two_numbers -> subtract_same': Value('int64'), 'add_two_numbers -> add_two_numbers -> subtract_two_numbers': Value('int64'), 'add_two_numbers -> add_two_numbers -> use_zero': Value('int64'), 'add_two_numbers -> add_two_numbers -> verify_calculation': Value('int64'), 'add_two_numbers -> backtrack': Value('int64'), 'add_two_numbers -> backtrack -> add_multiple': Value('int64'), 'add_two_numbers -> divide_for_factor': Value('int64'), 'add_two_numbers -> divide_for_factor -> add_two_numbers': Value('int64'), 'add_two_numbers -> divide_for_factor -> divide_for_factor': Value('int64'), 'add_two_numbers -> divide_for_factor -> multiply_two': Value('int64'), 'add_two_numbers -> divide_for_factor -> restate_constraints': Value('int64'), 'add_two_numbers -> divide_for_factor -> subtract_different': Value('int64'), 'add_two_numbers -> exhaustive_enumeration': Value('int64'), 'add_two_numbers -> exhaustive_enumeration -> divide_for_factor': Value('int64'), 'add_two_numbers -> exhaustive_enumeration -> exhaustive_enumeration': Value('int64'), 'add_two_numbers -> exhaustive_enumeration -> multiply_two': Value('int64'), 'add_two_numbers -> find_difference_pair': Value('int64'), 'add_two_numbers -> find_difference_pair -> add_two_numbers': Value('int64'), 'add_two_numbers -> find_sum_pair': Value('int64'), 'add_two_numbers -> find_sum_pair -> add_multiple': Value('int64'), 'add_two_numbers -> find_sum_pair -> exhaustive_enumeration': Value('int64'), 'add_two_numbers -> find_sum_pair -> find_difference_pair': Value('int64'), 'add_two_numbers -> find_sum_pair -> intermediate_goal': Value('int64'), 'add_two_numbers -> find_sum_pair -> restate_constraints': Value('int64'), 'add_two_numbers -> find_sum_pair -> verify_calculation': Value('int64'), 'add_two_numbers -> intermediate_goal': Value('int64'), 'add_two_numbers -> intermediate_goal -> add_multiple': Value('int64'), 'add_two_numbers -> intermediate_goal -> add_two_numbers': Value('int64'), 'add_two_numbers -> intermediate_goal -> exhaustive_enumeration': Value('int64'), 'add_two_numbers -> intermediate_goal -> find_sum_pair': Value('int64'), 'add_two_numbers -> intermediate_goal -> intermediate_goal': Value('int64'), 'add_two_numbers -> intermediate_goal -> multiply_two': Value('int64'), 'add_two_numbers -> intermediate_goal -> restate_constraints': Value('int64'), 'add_two_numbers -> intermediate_goal -> subtract_same': Value('int64'), 'add_two_numbers -> intermediate_goal -> use_zero': Value('int64'), 'add_two_numbers -> intermediate_goal -> verify_calculation': Value('int64'), 'add_two_numbers -> multiply_two': Value('int64'), 'add_two_numbers -> multiply_two -> add_two_numbers': Value('int64'), 'add_two_numbers -> multiply_two -> multiply_two': Value('int64'), 'add_two_numbers -> multiply_two -> restate_constraints': Value('int64'), 'add_two_numbers -> realize_error': Value('int64'), 'add_two_numbers -> realize_error -> add_multiple': Value('int64'), 'add_two_numbers -> realize_error -> realize_error': Value('int64'), 'add_two_numbers -> realize_error -> restate_constraints': Value('int64'), 'add_two_numbers -> repeat_failed': Value('int64'), 'add_two_numbers -> repeat_failed -> use_zero': Value('int64'), 'add_two_numbers -> restate_constraints': Value('int64'), 'add_two_numbers -> restate_constraints -> add_all': Value('int64'), 'add_two_numbers -> restate_constraints -> find_difference_pair': Value('int64'), 'add_two_numbers -> restate_constraints -> find_sum_pair': Value('int64'), 'add_two_numbers -> restate_constraints -> intermediate_goal': Value('int64'), 'add_two_numbers -> restate_constraints -> repeat_failed': Value('int64'), 'add_two_numbers -> restate_constraints -> restate_constraints': Value('int64'), 'add_two_numbers -> restate_constraints -> target_decomposition': Value('int64'), 'add_two_numbers -> restate_constraints -> use_zero': Value('int64'), 'add_two_numbers -> restating_constraints': Value('int64'), 'add_two_numbers -> restating_constraints -> restating_constraints': Value('int64'), 'add_two_numbers -> restating_constraints -> target_decomposition': Value('int64'), 'add_two_numbers -> small_adjustment': Value('int64'), 'add_two_numbers -> small_adjustment -> add_two_numbers': Value('int64'), 'add_two_numbers -> small_adjustment -> realize_error': Value('int64'), 'add_two_numbers -> small_adjustment -> restate_constraints': Value('int64'), 'add_two_numbers -> subtract_different': Value('int64'), 'add_two_numbers -> subtract_different -> add_two_numbers': Value('int64'), 'add_two_numbers -> subtract_different -> exhaustive_enumeration': Value('int64'), 'add_two_numbers -> subtract_different -> find_sum_pair': Value('int64'), 'add_two_numbers -> subtract_different -> multiply_two': Value('int64'), 'add_two_numbers -> subtract_different -> realize_error': Value('int64'), 'add_two_numbers -> subtract_different -> restate_constraints': Value('int64'), 'add_two_numbers -> subtract_different -> subtract_different': Value('int64'), 'add_two_numbers -> subtract_different -> subtract_same': Value('int64'), 'add_two_numbers -> subtract_multiple': Value('int64'), 'add_two_numbers -> subtract_multiple -> add_two_numbers': Value('int64'), 'add_two_numbers -> subtract_same': Value('int64'), 'add_two_numbers -> subtract_same -> add_multiple': Value('int64'), 'add_two_numbers -> subtract_same -> multiply_two': Value('int64'), 'add_two_numbers -> subtract_same -> restate_constraints': Value('int64'), 'add_two_numbers -> subtract_same -> subtract_same': Value('int64'), 'add_two_numbers -> subtract_same -> use_zero': Value('int64'), 'add_two_numbers -> subtract_two_numbers': Value('int64'), 'add_two_numbers -> subtract_two_numbers -> intermediate_goal': Value('int64'), 'add_two_numbers -> subtract_two_numbers -> subtract_two_numbers': Value('int64'), 'add_two_numbers -> use_zero': Value('int64'), 'add_two_numbers -> use_zero -> add_multiple': Value('int64'), 'add_two_numbers -> use_zero -> add_two_numbers': Value('int64'), 'add_two_numbers -> use_zero -> find_sum_pair': Value('int64'), 'add_two_numbers -> use_zero -> intermediate_goal': Value('int64'), 'add_two_numbers -> use_zero -> restate_constraints': Value('int64'), 'add_two_numbers -> use_zero -> subtract_same': Value('int64'), 'add_two_numbers -> use_zero -> target_decomposition': Value('int64'), 'add_two_numbers -> use_zero -> use_zero': Value('int64'), 'add_two_numbers -> verify_calculation': Value('int64'), 'add_two_numbers -> verify_calculation -> add_two_numbers': Value('int64'), 'add_two_numbers -> verify_calculation -> restate_constraints': Value('int64'), 'backtrack -> add_multiple': Value('int64'), 'backtrack -> add_multiple -> multiply_two': Value('int64'), 'backtrack -> find_sum_pair': Value('int64'), 'backtrack -> find_sum_pair -> find_difference_pair': Value('int64'), 'backtrack -> multiply_two': Value('int64'), 'backtrack -> multiply_two -> subtract_different': Value('int64'), 'backtrack -> restate_constraints': Value('int64'), 'backtrack -> restate_constraints -> restate_constraints': Value('int64'), 'backtrack -> restating_constraints': Value('int64'), 'backtrack -> restating_constraints -> find_difference_pair': Value('int64'), 'divide_for_factor -> add_multiple': Value('int64'), 'divide_for_factor -> add_multiple -> add_two_numbers': Value('int64'), 'divide_for_factor -> add_multiple -> restating_constraints': Value('int64'), 'divide_for_factor -> add_multiple -> subtract_different': Value('int64'), 'divide_for_factor -> add_two_numbers': Value('int64'), 'divide_for_factor -> add_two_numbers -> add_multiple': Value('int64'), 'divide_for_factor -> add_two_numbers -> add_two_numbers': Value('int64'), 'divide_for_factor -> add_two_numbers -> intermediate_goal': Value('int64'), 'divide_for_factor -> add_two_numbers -> multiply_two': Value('int64'), 'divide_for_factor -> add_two_numbers -> realize_error': Value('int64'), 'divide_for_factor -> add_two_numbers -> restate_constraints': Value('int64'), 'divide_for_factor -> add_two_numbers -> subtract_same': Value('int64'), 'divide_for_factor -> divide_for_factor': Value('int64'), 'divide_for_factor -> divide_for_factor -> add_multiple': Value('int64'), 'divide_for_factor -> divide_for_factor -> add_two_numbers': Value('int64'), 'divide_for_factor -> divide_for_factor -> divide_for_factor': Value('int64'), 'divide_for_factor -> divide_for_factor -> multiply_two': Value('int64'), 'divide_for_factor -> divide_for_factor -> realize_error': Value('int64'), 'divide_for_factor -> divide_for_factor -> restate_constraints': Value('int64'), 'divide_for_factor -> divide_for_factor -> small_adjustment': Value('int64'), 'divide_for_factor -> divide_for_factor -> subtract_different': Value('int64'), 'divide_for_factor -> divide_for_factor -> target_decomposition': Value('int64'), 'divide_for_factor -> divide_for_factor -> verify_calculation': Value('int64'), 'divide_for_factor -> exhaustive_enumeration': Value('int64'), 'divide_for_factor -> exhaustive_enumeration -> exhaustive_enumeration': Value('int64'), 'divide_for_factor -> find_sum_pair': Value('int64'), 'divide_for_factor -> find_sum_pair -> find_difference_pair': Value('int64'), 'divide_for_factor -> intermediate_goal': Value('int64'), 'divide_for_factor -> intermediate_goal -> divide_for_factor': Value('int64'), 'divide_for_factor -> intermediate_goal -> restate_constraints': Value('int64'), 'divide_for_factor -> multiply_two': Value('int64'), 'divide_for_factor -> multiply_two -> add_two_numbers': Value('int64'), 'divide_for_factor -> multiply_two -> divide_for_factor': Value('int64'), 'divide_for_factor -> multiply_two -> multiply_two': Value('int64'), 'divide_for_factor -> multiply_two -> subtract_different': Value('int64'), 'divide_for_factor -> realize_error': Value('int64'), 'divide_for_factor -> realize_error -> restate_constraints': Value('int64'), 'divide_for_factor -> restate_constraints': Value('int64'), 'divide_for_factor -> restate_constraints -> divide_for_factor': Value('int64'), 'divide_for_factor -> restate_constraints -> find_sum_pair': Value('int64'), 'divide_for_factor -> restate_constraints -> restate_constraints': Value('int64'), 'divide_for_factor -> small_adjustment': Value('int64'), 'divide_for_factor -> small_adjustment -> restate_constraints': Value('int64'), 'divide_for_factor -> subtract_different': Value('int64'), 'divide_for_factor -> subtract_different -> add_two_numbers': Value('int64'), 'divide_for_factor -> subtract_different -> restate_constraints': Value('int64'), 'divide_for_factor -> subtract_different -> subtract_different': Value('int64'), 'divide_for_factor -> target_decomposition': Value('int64'), 'divide_for_factor -> target_decomposition -> add_two_numbers': Value('int64'), 'divide_for_factor -> verify_calculation': Value('int64'), 'divide_for_factor -> verify_calculation -> add_two_numbers': Value('int64'), 'divide_for_factor -> verify_calculation -> verify_calculation': Value('int64'), 'exhaustive_enumeration -> add_two_numbers': Value('int64'), 'exhaustive_enumeration -> add_two_numbers -> add_multiple': Value('int64'), 'exhaustive_enumeration -> add_two_numbers -> add_two_numbers': Value('int64'), 'exhaustive_enumeration -> divide_for_factor': Value('int64'), 'exhaustive_enumeration -> divide_for_factor -> exhaustive_enumeration': Value('int64'), 'exhaustive_enumeration -> exhaustive_enumeration': Value('int64'), 'exhaustive_enumeration -> exhaustive_enumeration -> exhaustive_enumeration': Value('int64'), 'exhaustive_enumeration -> exhaustive_enumeration -> restate_constraints': Value('int64'), 'exhaustive_enumeration -> exhaustive_enumeration -> target_decomposition': Value('int64'), 'exhaustive_enumeration -> multiply_two': Value('int64'), 'exhaustive_enumeration -> multiply_two -> add_two_numbers': Value('int64'), 'exhaustive_enumeration -> restate_constraints': Value('int64'), 'exhaustive_enumeration -> restate_constraints -> restate_constraints': Value('int64'), 'exhaustive_enumeration -> target_decomposition': Value('int64'), 'exhaustive_enumeration -> target_decomposition -> restate_constraints': Value('int64'), 'exhaustive_enumeration -> target_decomposition -> target_decomposition': Value('int64'), 'find_difference_pair -> add_all': Value('int64'), 'find_difference_pair -> add_all -> restate_constraints': Value('int64'), 'find_difference_pair -> add_multiple': Value('int64'), 'find_difference_pair -> add_multiple -> multiply_two': Value('int64'), 'find_difference_pair -> add_multiple -> restate_constraints': Value('int64'), 'find_difference_pair -> add_two_numbers': Value('int64'), 'find_difference_pair -> add_two_numbers -> add_all': Value('int64'), 'find_difference_pair -> add_two_numbers -> add_multiple': Value('int64'), 'find_difference_pair -> add_two_numbers -> add_two_numbers': Value('int64'), 'find_difference_pair -> add_two_numbers -> divide_for_factor': Value('int64'), 'find_difference_pair -> add_two_numbers -> exhaustive_enumeration': Value('int64'), 'find_difference_pair -> add_two_numbers -> find_sum_pair': Value('int64'), 'find_difference_pair -> add_two_numbers -> intermediate_goal': Value('int64'), 'find_difference_pair -> add_two_numbers -> multiply_two': Value('int64'), 'find_difference_pair -> add_two_numbers -> restate_constraints': Value('int64'), 'find_difference_pair -> add_two_numbers -> restating_constraints': Value('int64'), 'find_difference_pair -> add_two_numbers -> subtract_different': Value('int64'), 'find_difference_pair -> add_two_numbers -> subtract_same': Value('int64'), 'find_difference_pair -> add_two_numbers -> use_zero': Value('int64'), 'find_difference_pair -> backtrack': Value('int64'), 'find_difference_pair -> backtrack -> restate_constraints': Value('int64'), 'find_difference_pair -> divide_for_factor': Value('int64'), 'find_difference_pair -> divide_for_factor -> divide_for_factor': Value('int64'), 'find_difference_pair -> divide_for_factor -> intermediate_goal': Value('int64'), 'find_difference_pair -> exhaustive_enumeration': Value('int64'), 'find_difference_pair -> exhaustive_enumeration -> exhaustive_enumeration': Value('int64'), 'find_difference_pair -> find_difference_pair': Value('int64'), 'find_difference_pair -> find_difference_pair -> find_difference_pair': Value('int64'), 'find_difference_pair -> find_difference_pair -> subtract_multiple': Value('int64'), 'find_difference_pair -> find_product_pair': Value('int64'), 'find_difference_pair -> find_product_pair -> restate_constraints': Value('int64'), 'find_difference_pair -> find_sum_pair': Value('int64'), 'find_difference_pair -> find_sum_pair -> add_multiple': Value('int64'), 'find_difference_pair -> find_sum_pair -> add_two_numbers': Value('int64'), 'find_difference_pair -> find_sum_pair -> exhaustive_enumeration': Value('int64'), 'find_difference_pair -> find_sum_pair -> find_difference_pair': Value('int64'), 'find_difference_pair -> find_sum_pair -> find_sum_pair': Value('int64'), 'find_difference_pair -> intermediate_goal': Value('int64'), 'find_difference_pair -> intermediate_goal -> add_two_numbers': Value('int64'), 'find_difference_pair -> realize_error': Value('int64'), 'find_difference_pair -> realize_error -> add_two_numbers': Value('int64'), 'find_difference_pair -> restate_constraints': Value('int64'), 'find_difference_pair -> restate_constraints -> find_difference_pair': Value('int64'), 'find_difference_pair -> restate_constraints -> intermediate_goal': Value('int64'), 'find_difference_pair -> restate_constraints -> restate_constraints': Value('int64'), 'find_difference_pair -> restating_constraints': Value('int64'), 'find_difference_pair -> restating_constraints -> restating_constraints': Value('int64'), 'find_difference_pair -> subtract_different': Value('int64'), 'find_difference_pair -> subtract_different -> add_two_numbers': Value('int64'), 'find_difference_pair -> subtract_different -> use_zero': Value('int64'), 'find_difference_pair -> subtract_multiple': Value('int64'), 'find_difference_pair -> subtract_multiple -> add_two_numbers': Value('int64'), 'find_difference_pair -> subtract_multiple -> subtract_different': Value('int64'), 'find_difference_pair -> use_zero': Value('int64'), 'find_difference_pair -> use_zero -> restate_constraints': Value('int64'), 'find_product_pair -> restate_constraints': Value('int64'), 'find_product_pair -> restate_constraints -> restate_constraints': Value('int64'), 'find_sum_pair -> add_multiple': Value('int64'), 'find_sum_pair -> add_multiple -> add_two_numbers': Value('int64'), 'find_sum_pair -> add_multiple -> multiply_two': Value('int64'), 'find_sum_pair -> add_multiple -> restate_constraints': Value('int64'), 'find_sum_pair -> add_multiple -> restated_constraints': Value('int64'), 'find_sum_pair -> add_multiple -> restating_constraints': Value('int64'), 'find_sum_pair -> add_two_numbers': Value('int64'), 'find_sum_pair -> add_two_numbers -> add_multiple': Value('int64'), 'find_sum_pair -> add_two_numbers -> add_two_numbers': Value('int64'), 'find_sum_pair -> add_two_numbers -> intermediate_goal': Value('int64'), 'find_sum_pair -> divide_for_factor': Value('int64'), 'find_sum_pair -> divide_for_factor -> add_two_numbers': Value('int64'), 'find_sum_pair -> divide_for_factor -> multiply_two': Value('int64'), 'find_sum_pair -> exhaustive_enumeration': Value('int64'), 'find_sum_pair -> exhaustive_enumeration -> exhaustive_enumeration': Value('int64'), 'find_sum_pair -> exhaustive_enumeration -> restate_constraints': Value('int64'), 'find_sum_pair -> find_difference_pair': Value('int64'), 'find_sum_pair -> find_difference_pair -> add_all': Value('int64'), 'find_sum_pair -> find_difference_pair -> add_multiple': Value('int64'), 'find_sum_pair -> find_difference_pair -> add_two_numbers': Value('int64'), 'find_sum_pair -> find_difference_pair -> divide_for_factor': Value('int64'), 'find_sum_pair -> find_difference_pair -> exhaustive_enumeration': Value('int64'), 'find_sum_pair -> find_difference_pair -> find_product_pair': Value('int64'), 'find_sum_pair -> find_difference_pair -> find_sum_pair': Value('int64'), 'find_sum_pair -> find_difference_pair -> restate_constraints': Value('int64'), 'find_sum_pair -> find_difference_pair -> restating_constraints': Value('int64'), 'find_sum_pair -> find_difference_pair -> subtract_different': Value('int64'), 'find_sum_pair -> find_difference_pair -> use_zero': Value('int64'), 'find_sum_pair -> find_sum_pair': Value('int64'), 'find_sum_pair -> find_sum_pair -> find_difference_pair': Value('int64'), 'find_sum_pair -> find_sum_pair -> multiply_two': Value('int64'), 'find_sum_pair -> intermediate_goal': Value('int64'), 'find_sum_pair -> intermediate_goal -> add_two_numbers': Value('int64'), 'find_sum_pair -> intermediate_goal -> find_difference_pair': Value('int64'), 'find_sum_pair -> intermediate_goal -> find_sum_pair': Value('int64'), 'find_sum_pair -> multiply_two': Value('int64'), 'find_sum_pair -> multiply_two -> add_two_numbers': Value('int64'), 'find_sum_pair -> restate_constraints': Value('int64'), 'find_sum_pair -> restate_constraints -> add_multiple': Value('int64'), 'find_sum_pair -> restate_constraints -> find_difference_pair': Value('int64'), 'find_sum_pair -> restate_constraints -> intermediate_goal': Value('int64'), 'find_sum_pair -> restate_constraints -> restate_constraints': Value('int64'), 'find_sum_pair -> restate_constraints -> target_decomposition': Value('int64'), 'find_sum_pair -> subtract_same': Value('int64'), 'find_sum_pair -> subtract_same -> subtract_multiple': Value('int64'), 'find_sum_pair -> target_decomposition': Value('int64'), 'find_sum_pair -> target_decomposition -> restate_constraints': Value('int64'), 'find_sum_pair -> target_decomposition -> subtract_different': Value('int64'), 'find_sum_pair -> verify_calculation': Value('int64'), 'find_sum_pair -> verify_calculation -> add_multiple': Value('int64'), 'find_sum_pair -> verify_calculation -> verify_calculation': Value('int64'), 'intermediate_goal -> add_all': Value('int64'), 'intermediate_goal -> add_all -> add_all': Value('int64'), 'intermediate_goal -> add_all -> add_multiple': Value('int64'), 'intermediate_goal -> add_multiple': Value('int64'), 'intermediate_goal -> add_multiple -> add_multiple': Value('int64'), 'intermediate_goal -> add_multiple -> find_sum_pair': Value('int64'), 'intermediate_goal -> add_multiple -> multiply_two': Value('int64'), 'intermediate_goal -> add_multiple -> restate_constraints': Value('int64'), 'intermediate_goal -> add_multiple -> subtract_different': Value('int64'), 'intermediate_goal -> add_multiple -> verify_calculation': Value('int64'), 'intermediate_goal -> add_two_numbers': Value('int64'), 'intermediate_goal -> add_two_numbers -> add_multiple': Value('int64'), 'intermediate_goal -> add_two_numbers -> add_two_numbers': Value('int64'), 'intermediate_goal -> add_two_numbers -> multiply_two': Value('int64'), 'intermediate_goal -> add_two_numbers -> subtract_different': Value('int64'), 'intermediate_goal -> add_two_numbers -> subtract_same': Value('int64'), 'intermediate_goal -> add_two_numbers -> use_zero': Value('int64'), 'intermediate_goal -> divide_for_factor': Value('int64'), 'intermediate_goal -> divide_for_factor -> add_multiple': Value('int64'), 'intermediate_goal -> divide_for_factor -> add_two_numbers': Value('int64'), 'intermediate_goal -> divide_for_factor -> divide_for_factor': Value('int64'), 'intermediate_goal -> divide_for_factor -> multiply_two': Value('int64'), 'intermediate_goal -> divide_for_factor -> subtract_different': Value('int64'), 'intermediate_goal -> exhaustive_enumeration': Value('int64'), 'intermediate_goal -> exhaustive_enumeration -> add_two_numbers': Value('int64'), 'intermediate_goal -> find_difference_pair': Value('int64'), 'intermediate_goal -> find_difference_pair -> add_two_numbers': Value('int64'), 'intermediate_goal -> find_difference_pair -> realize_error': Value('int64'), 'intermediate_goal -> find_sum_pair': Value('int64'), 'intermediate_goal -> find_sum_pair -> add_multiple': Value('int64'), 'intermediate_goal -> find_sum_pair -> add_two_numbers': Value('int64'), 'intermediate_goal -> find_sum_pair -> restate_constraints': Value('int64'), 'intermediate_goal -> intermediate_goal': Value('int64'), 'intermediate_goal -> intermediate_goal -> multiply_two': Value('int64'), 'intermediate_goal -> intermediate_goal -> restate_constraints': Value('int64'), 'intermediate_goal -> multiply_multiple': Value('int64'), 'intermediate_goal -> multiply_multiple -> divide_for_factor': Value('int64'), 'intermediate_goal -> multiply_two': Value('int64'), 'intermediate_goal -> multiply_two -> add_two_numbers': Value('int64'), 'intermediate_goal -> multiply_two -> divide_for_factor': Value('int64'), 'intermediate_goal -> multiply_two -> multiply_two': Value('int64'), 'intermediate_goal -> multiply_two -> restate_constraints': Value('int64'), 'intermediate_goal -> multiply_two -> subtract_different': Value('int64'), 'intermediate_goal -> restate_constraints': Value('int64'), 'intermediate_goal -> restate_constraints -> find_sum_pair': Value('int64'), 'intermediate_goal -> restate_constraints -> restate_constraints': Value('int64'), 'intermediate_goal -> restate_constraints -> verify_calculation': Value('int64'), 'intermediate_goal -> subtract_different': Value('int64'), 'intermediate_goal -> subtract_different -> subtract_different': Value('int64'), 'intermediate_goal -> subtract_same': Value('int64'), 'intermediate_goal -> subtract_same -> add_multiple': Value('int64'), 'intermediate_goal -> subtract_same -> find_sum_pair': Value('int64'), 'intermediate_goal -> subtract_same -> multiply_two': Value('int64'), 'intermediate_goal -> subtract_two_numbers': Value('int64'), 'intermediate_goal -> subtract_two_numbers -> add_multiple': Value('int64'), 'intermediate_goal -> use_zero': Value('int64'), 'intermediate_goal -> use_zero -> subtract_different': Value('int64'), 'intermediate_goal -> use_zero -> subtract_same': Value('int64'), 'intermediate_goal -> use_zero -> use_zero': Value('int64'), 'intermediate_goal -> verify_calculation': Value('int64'), 'intermediate_goal -> verify_calculation -> add_multiple': Value('int64'), 'intermediate_goal -> verify_calculation -> realize_error': Value('int64'), 'intermediate_goal -> verify_calculation -> verify_calculation': Value('int64'), 'meta_reasoning -> restate_constraints': Value('int64'), 'meta_reasoning -> restate_constraints -> restate_constraints': Value('int64'), 'multiply_all -> divide_for_factor': Value('int64'), 'multiply_all -> divide_for_factor -> subtract_different': Value('int64'), 'multiply_multiple -> divide_for_factor': Value('int64'), 'multiply_multiple -> divide_for_factor -> subtract_different': Value('int64'), 'multiply_two -> add_multiple': Value('int64'), 'multiply_two -> add_multiple -> intermediate_goal': Value('int64'), 'multiply_two -> add_two_numbers': Value('int64'), 'multiply_two -> add_two_numbers -> add_multiple': Value('int64'), 'multiply_two -> add_two_numbers -> add_two_numbers': Value('int64'), 'multiply_two -> add_two_numbers -> backtrack': Value('int64'), 'multiply_two -> add_two_numbers -> divide_for_factor': Value('int64'), 'multiply_two -> add_two_numbers -> intermediate_goal': Value('int64'), 'multiply_two -> add_two_numbers -> multiply_two': Value('int64'), 'multiply_two -> add_two_numbers -> restate_constraints': Value('int64'), 'multiply_two -> add_two_numbers -> subtract_different': Value('int64'), 'multiply_two -> divide_for_factor': Value('int64'), 'multiply_two -> divide_for_factor -> add_two_numbers': Value('int64'), 'multiply_two -> divide_for_factor -> divide_for_factor': Value('int64'), 'multiply_two -> divide_for_factor -> multiply_two': Value('int64'), 'multiply_two -> divide_for_factor -> subtract_different': Value('int64'), 'multiply_two -> intermediate_goal': Value('int64'), 'multiply_two -> intermediate_goal -> subtract_same': Value('int64'), 'multiply_two -> multiply_two': Value('int64'), 'multiply_two -> multiply_two -> add_two_numbers': Value('int64'), 'multiply_two -> restate_constraints': Value('int64'), 'multiply_two -> restate_constraints -> restate_constraints': Value('int64'), 'multiply_two -> subtract_different': Value('int64'), 'multiply_two -> subtract_different -> add_two_numbers': Value('int64'), 'multiply_two -> subtract_different -> restate_constraints': Value('int64'), 'multiply_two -> subtract_different -> subtract_different': Value('int64'), 'multiply_two -> subtract_multiple': Value('int64'), 'multiply_two -> subtract_multiple -> intermediate_goal': Value('int64'), 'multiply_two -> subtract_multiple -> multiply_two': Value('int64'), 'multiply_two -> subtract_same': Value('int64'), 'multiply_two -> subtract_same -> use_zero': Value('int64'), 'multiply_two -> use_zero': Value('int64'), 'multiply_two -> use_zero -> find_sum_pair': Value('int64'), 'multiply_two -> use_zero -> subtract_same': Value('int64'), 'realize_error -> add_multiple': Value('int64'), 'realize_error -> add_multiple -> add_two_numbers': Value('int64'), 'realize_error -> add_multiple -> subtract_different': Value('int64'), 'realize_error -> add_two_numbers': Value('int64'), 'realize_error -> add_two_numbers -> restate_constraints': Value('int64'), 'realize_error -> divide_for_factor': Value('int64'), 'realize_error -> divide_for_factor -> divide_for_factor': Value('int64'), 'realize_error -> divide_for_factor -> restate_constraints': Value('int64'), 'realize_error -> find_sum_pair': Value('int64'), 'realize_error -> find_sum_pair -> find_difference_pair': Value('int64'), 'realize_error -> multiply_two': Value('int64'), 'realize_error -> multiply_two -> add_two_numbers': Value('int64'), 'realize_error -> realize_error': Value('int64'), 'realize_error -> realize_error -> divide_for_factor': Value('int64'), 'realize_error -> realize_error -> find_sum_pair': Value('int64'), 'realize_error -> realize_error -> realize_error': Value('int64'), 'realize_error -> realize_error -> restate_constraints': Value('int64'), 'realize_error -> restate_constraints': Value('int64'), 'realize_error -> restate_constraints -> find_sum_pair': Value('int64'), 'realize_error -> restate_constraints -> realize_error': Value('int64'), 'realize_error -> restate_constraints -> restate_constraints': Value('int64'), 'realize_error -> subtract_multiple': Value('int64'), 'realize_error -> subtract_multiple -> subtract_same': Value('int64'), 'realize_error -> subtract_same': Value('int64'), 'realize_error -> subtract_same -> restate_constraints': Value('int64'), 'realize_error -> subtract_same -> subtract_same': Value('int64'), 'realize_error -> subtract_same -> use_zero': Value('int64'), 'realize_error -> subtract_same -> verify_calculation': Value('int64'), 'realize_error -> use_zero': Value('int64'), 'realize_error -> use_zero -> restate_constraints': Value('int64'), 'realize_error -> use_zero -> subtract_different': Value('int64'), 'realize_error -> verify_calculation': Value('int64'), 'realize_error -> verify_calculation -> add_two_numbers': Value('int64'), 'realize_error -> verify_calculation -> use_zero': Value('int64'), 'repeat_failed -> find_sum_pair': Value('int64'), 'repeat_failed -> find_sum_pair -> find_difference_pair': Value('int64'), 'repeat_failed -> repeat_failed': Value('int64'), 'repeat_failed -> repeat_failed -> find_sum_pair': Value('int64'), 'repeat_failed -> repeat_failed -> repeat_failed': Value('int64'), 'repeat_failed -> subtract_different': Value('int64'), 'repeat_failed -> subtract_different -> add_two_numbers': Value('int64'), 'repeat_failed -> use_zero': Value('int64'), 'repeat_failed -> use_zero -> subtract_same': Value('int64'), 'restate_constraints -> add_all': Value('int64'), 'restate_constraints -> add_all -> add_all': Value('int64'), 'restate_constraints -> add_all -> add_two_numbers': Value('int64'), 'restate_constraints -> add_all -> find_sum_pair': Value('int64'), 'restate_constraints -> add_all -> restate_constraints': Value('int64'), 'restate_constraints -> add_all -> subtract_different': Value('int64'), 'restate_constraints -> add_multiple': Value('int64'), 'restate_constraints -> add_multiple -> add_multiple': Value('int64'), 'restate_constraints -> add_multiple -> add_two_numbers': Value('int64'), 'restate_constraints -> add_multiple -> divide_for_factor': Value('int64'), 'restate_constraints -> add_multiple -> multiply_two': Value('int64'), 'restate_constraints -> add_multiple -> realize_error': Value('int64'), 'restate_constraints -> add_multiple -> restate_constraints': Value('int64'), 'restate_constraints -> add_multiple -> small_adjustment': Value('int64'), 'restate_constraints -> add_multiple -> subtract_different': Value('int64'), 'restate_constraints -> add_multiple -> subtract_multiple': Value('int64'), 'restate_constraints -> add_multiple -> subtract_same': Value('int64'), 'restate_constraints -> add_two_numbers': Value('int64'), 'restate_constraints -> add_two_numbers -> add_two_numbers': Value('int64'), 'restate_constraints -> add_two_numbers -> divide_for_factor': Value('int64'), 'restate_constraints -> add_two_numbers -> find_sum_pair': Value('int64'), 'restate_constraints -> add_two_numbers -> intermediate_goal': Value('int64'), 'restate_constraints -> add_two_numbers -> multiply_two': Value('int64'), 'restate_constraints -> add_two_numbers -> repeat_failed': Value('int64'), 'restate_constraints -> add_two_numbers -> subtract_different': Value('int64'), 'restate_constraints -> add_two_numbers -> subtract_same': Value('int64'), 'restate_constraints -> add_two_numbers -> use_zero': Value('int64'), 'restate_constraints -> divide_for_factor': Value('int64'), 'restate_constraints -> divide_for_factor -> add_multiple': Value('int64'), 'restate_constraints -> divide_for_factor -> add_two_numbers': Value('int64'), 'restate_constraints -> divide_for_factor -> divide_for_factor': Value('int64'), 'restate_constraints -> divide_for_factor -> intermediate_goal': Value('int64'), 'restate_constraints -> divide_for_factor -> multiply_two': Value('int64'), 'restate_constraints -> divide_for_factor -> restate_constraints': Value('int64'), 'restate_constraints -> exhaustive_enumeration': Value('int64'), 'restate_constraints -> exhaustive_enumeration -> target_decomposition': Value('int64'), 'restate_constraints -> find_difference_pair': Value('int64'), 'restate_constraints -> find_difference_pair -> add_two_numbers': Value('int64'), 'restate_constraints -> find_difference_pair -> find_sum_pair': Value('int64'), 'restate_constraints -> find_difference_pair -> intermediate_goal': Value('int64'), 'restate_constraints -> find_sum_pair': Value('int64'), 'restate_constraints -> find_sum_pair -> divide_for_factor': Value('int64'), 'restate_constraints -> find_sum_pair -> find_difference_pair': Value('int64'), 'restate_constraints -> find_sum_pair -> find_sum_pair': Value('int64'), 'restate_constraints -> find_sum_pair -> intermediate_goal': Value('int64'), 'restate_constraints -> find_sum_pair -> restate_constraints': Value('int64'), 'restate_constraints -> find_sum_pair -> target_decomposition': Value('int64'), 'restate_constraints -> find_sum_pair -> verify_calculation': Value('int64'), 'restate_constraints -> intermediate_goal': Value('int64'), 'restate_constraints -> intermediate_goal -> add_all': Value('int64'), 'restate_constraints -> intermediate_goal -> add_multiple': Value('int64'), 'restate_constraints -> intermediate_goal -> add_two_numbers': Value('int64'), 'restate_constraints -> intermediate_goal -> divide_for_factor': Value('int64'), 'restate_constraints -> intermediate_goal -> multiply_multiple': Value('int64'), 'restate_constraints -> intermediate_goal -> multiply_two': Value('int64'), 'restate_constraints -> intermediate_goal -> use_zero': Value('int64'), 'restate_constraints -> intermediate_goal -> verify_calculation': Value('int64'), 'restate_constraints -> meta_reasoning': Value('int64'), 'restate_constraints -> meta_reasoning -> restate_constraints': Value('int64'), 'restate_constraints -> multiply_two': Value('int64'), 'restate_constraints -> multiply_two -> add_two_numbers': Value('int64'), 'restate_constraints -> multiply_two -> divide_for_factor': Value('int64'), 'restate_constraints -> multiply_two -> multiply_two': Value('int64'), 'restate_constraints -> multiply_two -> subtract_different': Value('int64'), 'restate_constraints -> realize_error': Value('int64'), 'restate_constraints -> realize_error -> realize_error': Value('int64'), 'restate_constraints -> realize_error -> restate_constraints': Value('int64'), 'restate_constraints -> repeat_failed': Value('int64'), 'restate_constraints -> repeat_failed -> repeat_failed': Value('int64'), 'restate_constraints -> repeat_failed -> subtract_different': Value('int64'), 'restate_constraints -> restate_constraints': Value('int64'), 'restate_constraints -> restate_constraints -> add_all': Value('int64'), 'restate_constraints -> restate_constraints -> add_multiple': Value('int64'), 'restate_constraints -> restate_constraints -> add_two_numbers': Value('int64'), 'restate_constraints -> restate_constraints -> divide_for_factor': Value('int64'), 'restate_constraints -> restate_constraints -> exhaustive_enumeration': Value('int64'), 'restate_constraints -> restate_constraints -> find_difference_pair': Value('int64'), 'restate_constraints -> restate_constraints -> find_sum_pair': Value('int64'), 'restate_constraints -> restate_constraints -> intermediate_goal': Value('int64'), 'restate_constraints -> restate_constraints -> multiply_two': Value('int64'), 'restate_constraints -> restate_constraints -> realize_error': Value('int64'), 'restate_constraints -> restate_constraints -> repeat_failed': Value('int64'), 'restate_constraints -> restate_constraints -> restate_constraints': Value('int64'), 'restate_constraints -> restate_constraints -> restating_constraints': Value('int64'), 'restate_constraints -> restate_constraints -> subtract_different': Value('int64'), 'restate_constraints -> restate_constraints -> subtract_multiple': Value('int64'), 'restate_constraints -> restate_constraints -> subtract_same': Value('int64'), 'restate_constraints -> restate_constraints -> subtract_two_numbers': Value('int64'), 'restate_constraints -> restate_constraints -> target_decomposition': Value('int64'), 'restate_constraints -> restate_constraints -> use_zero': Value('int64'), 'restate_constraints -> restate_constraints -> verify_calculation': Value('int64'), 'restate_constraints -> restating_constraints': Value('int64'), 'restate_constraints -> restating_constraints -> add_multiple': Value('int64'), 'restate_constraints -> restating_constraints -> find_sum_pair': Value('int64'), 'restate_constraints -> restating_constraints -> restating_constraints': Value('int64'), 'restate_constraints -> restating_constraints -> subtract_different': Value('int64'), 'restate_constraints -> restating_constraints -> subtract_same': Value('int64'), 'restate_constraints -> subtract_different': Value('int64'), 'restate_constraints -> subtract_different -> divide_for_factor': Value('int64'), 'restate_constraints -> subtract_different -> restate_constraints': Value('int64'), 'restate_constraints -> subtract_different -> subtract_different': Value('int64'), 'restate_constraints -> subtract_different -> subtract_same': Value('int64'), 'restate_constraints -> subtract_different -> use_zero': Value('int64'), 'restate_constraints -> subtract_multiple': Value('int64'), 'restate_constraints -> subtract_multiple -> add_multiple': Value('int64'), 'restate_constraints -> subtract_multiple -> realize_error': Value('int64'), 'restate_constraints -> subtract_multiple -> subtract_different': Value('int64'), 'restate_constraints -> subtract_multiple -> subtract_same': Value('int64'), 'restate_constraints -> subtract_multiple -> use_zero': Value('int64'), 'restate_constraints -> subtract_same': Value('int64'), 'restate_constraints -> subtract_same -> find_sum_pair': Value('int64'), 'restate_constraints -> subtract_same -> intermediate_goal': Value('int64'), 'restate_constraints -> subtract_same -> restate_constraints': Value('int64'), 'restate_constraints -> subtract_same -> subtract_all': Value('int64'), 'restate_constraints -> subtract_same -> subtract_different': Value('int64'), 'restate_constraints -> subtract_same -> subtract_same': Value('int64'), 'restate_constraints -> subtract_two_numbers': Value('int64'), 'restate_constraints -> subtract_two_numbers -> realize_error': Value('int64'), 'restate_constraints -> target_decomposition': Value('int64'), 'restate_constraints -> target_decomposition -> add_multiple': Value('int64'), 'restate_constraints -> target_decomposition -> add_two_numbers': Value('int64'), 'restate_constraints -> target_decomposition -> divide_for_factor': Value('int64'), 'restate_constraints -> target_decomposition -> multiply_all': Value('int64'), 'restate_constraints -> use_zero': Value('int64'), 'restate_constraints -> use_zero -> restate_constraints': Value('int64'), 'restate_constraints -> use_zero -> subtract_different': Value('int64'), 'restate_constraints -> use_zero -> subtract_same': Value('int64'), 'restate_constraints -> use_zero -> use_zero': Value('int64'), 'restate_constraints -> use_zero -> verify_calculation': Value('int64'), 'restate_constraints -> verify_calculation': Value('int64'), 'restate_constraints -> verify_calculation -> realize_error': Value('int64'), 'restate_constraints -> verify_calculation -> restate_constraints': Value('int64'), 'restate_constraints -> verify_calculation -> verify_calculation': Value('int64'), 'restated_constraints -> add_all': Value('int64'), 'restated_constraints -> add_all -> restate_constraints': Value('int64'), 'restated_constraints -> add_multiple': Value('int64'), 'restated_constraints -> add_multiple -> restate_constraints': Value('int64'), 'restated_constraints -> restate_constraints': Value('int64'), 'restated_constraints -> restate_constraints -> use_zero': Value('int64'), 'restated_constraints -> restated_constraints': Value('int64'), 'restated_constraints -> restated_constraints -> add_all': Value('int64'), 'restated_constraints -> restated_constraints -> add_multiple': Value('int64'), 'restated_constraints -> restated_constraints -> restated_constraints': Value('int64'), 'restating_constraints -> add_multiple': Value('int64'), 'restating_constraints -> add_multiple -> multiply_two': Value('int64'), 'restating_constraints -> add_multiple -> restate_constraints': Value('int64'), 'restating_constraints -> add_multiple -> small_adjustment': Value('int64'), 'restating_constraints -> add_two_numbers': Value('int64'), 'restating_constraints -> add_two_numbers -> small_adjustment': Value('int64'), 'restating_constraints -> divide_for_factor': Value('int64'), 'restating_constraints -> divide_for_factor -> add_two_numbers': Value('int64'), 'restating_constraints -> divide_for_factor -> divide_for_factor': Value('int64'), 'restating_constraints -> divide_for_factor -> multiply_two': Value('int64'), 'restating_constraints -> divide_for_factor -> verify_calculation': Value('int64'), 'restating_constraints -> find_difference_pair': Value('int64'), 'restating_constraints -> find_difference_pair -> intermediate_goal': Value('int64'), 'restating_constraints -> find_sum_pair': Value('int64'), 'restating_constraints -> find_sum_pair -> find_difference_pair': Value('int64'), 'restating_constraints -> find_sum_pair -> restate_constraints': Value('int64'), 'restating_constraints -> intermediate_goal': Value('int64'), 'restating_constraints -> intermediate_goal -> intermediate_goal': Value('int64'), 'restating_constraints -> multiply_two': Value('int64'), 'restating_constraints -> multiply_two -> divide_for_factor': Value('int64'), 'restating_constraints -> restate_constraints': Value('int64'), 'restating_constraints -> restate_constraints -> find_sum_pair': Value('int64'), 'restating_constraints -> restating_constraints': Value('int64'), 'restating_constraints -> restating_constraints -> add_multiple': Value('int64'), 'restating_constraints -> restating_constraints -> add_two_numbers': Value('int64'), 'restating_constraints -> restating_constraints -> divide_for_factor': Value('int64'), 'restating_constraints -> restating_constraints -> find_sum_pair': Value('int64'), 'restating_constraints -> restating_constraints -> intermediate_goal': Value('int64'), 'restating_constraints -> restating_constraints -> multiply_two': Value('int64'), 'restating_constraints -> restating_constraints -> restate_constraints': Value('int64'), 'restating_constraints -> restating_constraints -> restating_constraints': Value('int64'), 'restating_constraints -> restating_constraints -> small_adjustment': Value('int64'), 'restating_constraints -> restating_constraints -> subtract_different': Value('int64'), 'restating_constraints -> small_adjustment': Value('int64'), 'restating_constraints -> small_adjustment -> divide_for_factor': Value('int64'), 'restating_constraints -> subtract_different': Value('int64'), 'restating_constraints -> subtract_different -> realize_error': Value('int64'), 'restating_constraints -> subtract_different -> subtract_same': Value('int64'), 'restating_constraints -> subtract_same': Value('int64'), 'restating_constraints -> subtract_same -> restate_constraints': Value('int64'), 'restating_constraints -> subtract_same -> subtract_different': Value('int64'), 'restating_constraints -> target_decomposition': Value('int64'), 'restating_constraints -> target_decomposition -> add_multiple': Value('int64'), 'small_adjustment -> add_two_numbers': Value('int64'), 'small_adjustment -> add_two_numbers -> add_multiple': Value('int64'), 'small_adjustment -> add_two_numbers -> add_two_numbers': Value('int64'), 'small_adjustment -> divide_for_factor': Value('int64'), 'small_adjustment -> divide_for_factor -> divide_for_factor': Value('int64'), 'small_adjustment -> realize_error': Value('int64'), 'small_adjustment -> realize_error -> add_multiple': Value('int64'), 'small_adjustment -> realize_error -> realize_error': Value('int64'), 'small_adjustment -> realize_error -> restate_constraints': Value('int64'), 'small_adjustment -> restate_constraints': Value('int64'), 'small_adjustment -> restate_constraints -> add_multiple': Value('int64'), 'small_adjustment -> restate_constraints -> add_two_numbers': Value('int64'), 'small_adjustment -> restate_constraints -> restate_constraints': Value('int64'), 'strategic_decomposition -> restate_constraints': Value('int64'), 'strategic_decomposition -> restate_constraints -> intermediate_goal': Value('int64'), 'subtract_all -> subtract_same': Value('int64'), 'subtract_all -> subtract_same -> subtract_same': Value('int64'), 'subtract_different -> add_multiple': Value('int64'), 'subtract_different -> add_multiple -> add_two_numbers': Value('int64'), 'subtract_different -> add_multiple -> subtract_different': Value('int64'), 'subtract_different -> add_two_numbers': Value('int64'), 'subtract_different -> add_two_numbers -> add_all': Value('int64'), 'subtract_different -> add_two_numbers -> add_two_numbers': Value('int64'), 'subtract_different -> add_two_numbers -> find_difference_pair': Value('int64'), 'subtract_different -> add_two_numbers -> intermediate_goal': Value('int64'), 'subtract_different -> add_two_numbers -> multiply_two': Value('int64'), 'subtract_different -> add_two_numbers -> restate_constraints': Value('int64'), 'subtract_different -> add_two_numbers -> subtract_different': Value('int64'), 'subtract_different -> add_two_numbers -> subtract_same': Value('int64'), 'subtract_different -> backtrack': Value('int64'), 'subtract_different -> backtrack -> multiply_two': Value('int64'), 'subtract_different -> divide_for_factor': Value('int64'), 'subtract_different -> divide_for_factor -> add_two_numbers': Value('int64'), 'subtract_different -> divide_for_factor -> realize_error': Value('int64'), 'subtract_different -> divide_for_factor -> restate_constraints': Value('int64'), 'subtract_different -> exhaustive_enumeration': Value('int64'), 'subtract_different -> exhaustive_enumeration -> add_two_numbers': Value('int64'), 'subtract_different -> find_difference_pair': Value('int64'), 'subtract_different -> find_difference_pair -> backtrack': Value('int64'), 'subtract_different -> find_sum_pair': Value('int64'), 'subtract_different -> find_sum_pair -> add_two_numbers': Value('int64'), 'subtract_different -> intermediate_goal': Value('int64'), 'subtract_different -> intermediate_goal -> subtract_different': Value('int64'), 'subtract_different -> multiply_two': Value('int64'), 'subtract_different -> multiply_two -> add_two_numbers': Value('int64'), 'subtract_different -> multiply_two -> intermediate_goal': Value('int64'), 'subtract_different -> multiply_two -> multiply_two': Value('int64'), 'subtract_different -> multiply_two -> restate_constraints': Value('int64'), 'subtract_different -> multiply_two -> subtract_different': Value('int64'), 'subtract_different -> realize_error': Value('int64'), 'subtract_different -> realize_error -> restate_constraints': Value('int64'), 'subtract_different -> realize_error -> subtract_multiple': Value('int64'), 'subtract_different -> realize_error -> subtract_same': Value('int64'), 'subtract_different -> realize_error -> use_zero': Value('int64'), 'subtract_different -> realize_error -> verify_calculation': Value('int64'), 'subtract_different -> restate_constraints': Value('int64'), 'subtract_different -> restate_constraints -> add_two_numbers': Value('int64'), 'subtract_different -> restate_constraints -> find_difference_pair': Value('int64'), 'subtract_different -> restate_constraints -> find_sum_pair': Value('int64'), 'subtract_different -> restate_constraints -> restate_constraints': Value('int64'), 'subtract_different -> small_adjustment': Value('int64'), 'subtract_different -> small_adjustment -> restate_constraints': Value('int64'), 'subtract_different -> subtract_different': Value('int64'), 'subtract_different -> subtract_different -> add_multiple': Value('int64'), 'subtract_different -> subtract_different -> add_two_numbers': Value('int64'), 'subtract_different -> subtract_different -> backtrack': Value('int64'), 'subtract_different -> subtract_different -> multiply_two': Value('int64'), 'subtract_different -> subtract_different -> realize_error': Value('int64'), 'subtract_different -> subtract_different -> restate_constraints': Value('int64'), 'subtract_different -> subtract_different -> small_adjustment': Value('int64'), 'subtract_different -> subtract_different -> subtract_different': Value('int64'), 'subtract_different -> subtract_different -> subtract_multiple': Value('int64'), 'subtract_different -> subtract_different -> subtract_same': Value('int64'), 'subtract_different -> subtract_different -> use_zero': Value('int64'), 'subtract_different -> subtract_multiple': Value('int64'), 'subtract_different -> subtract_multiple -> restate_constraints': Value('int64'), 'subtract_different -> subtract_multiple -> subtract_different': Value('int64'), 'subtract_different -> subtract_multiple -> subtract_multiple': Value('int64'), 'subtract_different -> subtract_same': Value('int64'), 'subtract_different -> subtract_same -> add_two_numbers': Value('int64'), 'subtract_different -> subtract_same -> find_sum_pair': Value('int64'), 'subtract_different -> subtract_same -> intermediate_goal': Value('int64'), 'subtract_different -> subtract_same -> multiply_two': Value('int64'), 'subtract_different -> subtract_same -> restate_constraints': Value('int64'), 'subtract_different -> subtract_same -> subtract_different': Value('int64'), 'subtract_different -> subtract_same -> subtract_multiple': Value('int64'), 'subtract_different -> subtract_same -> subtract_same': Value('int64'), 'subtract_different -> subtract_same -> use_zero': Value('int64'), 'subtract_different -> subtract_same -> verify_calculation': Value('int64'), 'subtract_different -> use_zero': Value('int64'), 'subtract_different -> use_zero -> add_multiple': Value('int64'), 'subtract_different -> use_zero -> find_sum_pair': Value('int64'), 'subtract_different -> use_zero -> restate_constraints': Value('int64'), 'subtract_different -> use_zero -> subtract_different': Value('int64'), 'subtract_different -> verify_calculation': Value('int64'), 'subtract_different -> verify_calculation -> multiply_two': Value('int64'), 'subtract_multiple -> add_multiple': Value('int64'), 'subtract_multiple -> add_multiple -> subtract_same': Value('int64'), 'subtract_multiple -> add_two_numbers': Value('int64'), 'subtract_multiple -> add_two_numbers -> intermediate_goal': Value('int64'), 'subtract_multiple -> add_two_numbers -> restate_constraints': Value('int64'), 'subtract_multiple -> intermediate_goal': Value('int64'), 'subtract_multiple -> intermediate_goal -> add_multiple': Value('int64'), 'subtract_multiple -> multiply_two': Value('int64'), 'subtract_multiple -> multiply_two -> add_two_numbers': Value('int64'), 'subtract_multiple -> realize_error': Value('int64'), 'subtract_multiple -> realize_error -> restate_constraints': Value('int64'), 'subtract_multiple -> restate_constraints': Value('int64'), 'subtract_multiple -> restate_constraints -> restate_constraints': Value('int64'), 'subtract_multiple -> subtract_different': Value('int64'), 'subtract_multiple -> subtract_different -> multiply_two': Value('int64'), 'subtract_multiple -> subtract_different -> realize_error': Value('int64'), 'subtract_multiple -> subtract_different -> subtract_different': Value('int64'), 'subtract_multiple -> subtract_multiple': Value('int64'), 'subtract_multiple -> subtract_multiple -> restate_constraints': Value('int64'), 'subtract_multiple -> subtract_same': Value('int64'), 'subtract_multiple -> subtract_same -> backtrack': Value('int64'), 'subtract_multiple -> subtract_same -> restate_constraints': Value('int64'), 'subtract_multiple -> use_zero': Value('int64'), 'subtract_multiple -> use_zero -> restate_constraints': Value('int64'), 'subtract_multiple -> verify_calculation': Value('int64'), 'subtract_multiple -> verify_calculation -> restate_constraints': Value('int64'), 'subtract_same -> add_multiple': Value('int64'), 'subtract_same -> add_multiple -> realize_error': Value('int64'), 'subtract_same -> add_multiple -> restate_constraints': Value('int64'), 'subtract_same -> add_two_numbers': Value('int64'), 'subtract_same -> add_two_numbers -> restate_constraints': Value('int64'), 'subtract_same -> add_two_numbers -> use_zero': Value('int64'), 'subtract_same -> backtrack': Value('int64'), 'subtract_same -> backtrack -> restating_constraints': Value('int64'), 'subtract_same -> find_difference_pair': Value('int64'), 'subtract_same -> find_difference_pair -> find_difference_pair': Value('int64'), 'subtract_same -> find_difference_pair -> subtract_multiple': Value('int64'), 'subtract_same -> find_sum_pair': Value('int64'), 'subtract_same -> find_sum_pair -> add_two_numbers': Value('int64'), 'subtract_same -> find_sum_pair -> find_difference_pair': Value('int64'), 'subtract_same -> find_sum_pair -> multiply_two': Value('int64'), 'subtract_same -> intermediate_goal': Value('int64'), 'subtract_same -> intermediate_goal -> add_multiple': Value('int64'), 'subtract_same -> intermediate_goal -> restate_constraints': Value('int64'), 'subtract_same -> multiply_two': Value('int64'), 'subtract_same -> multiply_two -> add_two_numbers': Value('int64'), 'subtract_same -> multiply_two -> intermediate_goal': Value('int64'), 'subtract_same -> multiply_two -> subtract_same': Value('int64'), 'subtract_same -> multiply_two -> use_zero': Value('int64'), 'subtract_same -> realize_error': Value('int64'), 'subtract_same -> realize_error -> verify_calculation': Value('int64'), 'subtract_same -> restate_constraints': Value('int64'), 'subtract_same -> restate_constraints -> find_difference_pair': Value('int64'), 'subtract_same -> restate_constraints -> restate_constraints': Value('int64'), 'subtract_same -> restate_constraints -> restating_constraints': Value('int64'), 'subtract_same -> restate_constraints -> subtract_same': Value('int64'), 'subtract_same -> restate_constraints -> use_zero': Value('int64'), 'subtract_same -> subtract_all': Value('int64'), 'subtract_same -> subtract_all -> subtract_same': Value('int64'), 'subtract_same -> subtract_different': Value('int64'), 'subtract_same -> subtract_different -> multiply_two': Value('int64'), 'subtract_same -> subtract_different -> realize_error': Value('int64'), 'subtract_same -> subtract_different -> subtract_different': Value('int64'), 'subtract_same -> subtract_different -> subtract_multiple': Value('int64'), 'subtract_same -> subtract_different -> subtract_same': Value('int64'), 'subtract_same -> subtract_multiple': Value('int64'), 'subtract_same -> subtract_multiple -> subtract_different': Value('int64'), 'subtract_same -> subtract_multiple -> subtract_same': Value('int64'), 'subtract_same -> subtract_multiple -> verify_calculation': Value('int64'), 'subtract_same -> subtract_same': Value('int64'), 'subtract_same -> subtract_same -> find_difference_pair': Value('int64'), 'subtract_same -> subtract_same -> intermediate_goal': Value('int64'), 'subtract_same -> subtract_same -> restate_constraints': Value('int64'), 'subtract_same -> subtract_same -> subtract_different': Value('int64'), 'subtract_same -> subtract_same -> subtract_multiple': Value('int64'), 'subtract_same -> subtract_same -> subtract_same': Value('int64'), 'subtract_same -> subtract_same -> use_zero': Value('int64'), 'subtract_same -> use_zero': Value('int64'), 'subtract_same -> use_zero -> backtrack': Value('int64'), 'subtract_same -> use_zero -> divide_for_factor': Value('int64'), 'subtract_same -> use_zero -> restate_constraints': Value('int64'), 'subtract_same -> use_zero -> subtract_different': Value('int64'), 'subtract_same -> use_zero -> subtract_same': Value('int64'), 'subtract_same -> verify_calculation': Value('int64'), 'subtract_same -> verify_calculation -> use_zero': Value('int64'), 'subtract_same -> verify_calculation -> verify_calculation': Value('int64'), 'subtract_two_numbers -> add_multiple': Value('int64'), 'subtract_two_numbers -> add_multiple -> realize_error': Value('int64'), 'subtract_two_numbers -> find_difference_pair': Value('int64'), 'subtract_two_numbers -> find_difference_pair -> subtract_different': Value('int64'), 'subtract_two_numbers -> intermediate_goal': Value('int64'), 'subtract_two_numbers -> intermediate_goal -> subtract_two_numbers': Value('int64'), 'subtract_two_numbers -> realize_error': Value('int64'), 'subtract_two_numbers -> realize_error -> restate_constraints': Value('int64'), 'subtract_two_numbers -> restate_constraints': Value('int64'), 'subtract_two_numbers -> restate_constraints -> find_sum_pair': Value('int64'), 'subtract_two_numbers -> restate_constraints -> restate_constraints': Value('int64'), 'subtract_two_numbers -> restate_constraints -> verify_calculation': Value('int64'), 'subtract_two_numbers -> subtract_same': Value('int64'), 'subtract_two_numbers -> subtract_same -> add_two_numbers': Value('int64'), 'subtract_two_numbers -> subtract_two_numbers': Value('int64'), 'subtract_two_numbers -> subtract_two_numbers -> restate_constraints': Value('int64'), 'subtract_two_numbers -> subtract_two_numbers -> subtract_same': Value('int64'), 'subtract_two_numbers -> subtract_two_numbers -> subtract_two_numbers': Value('int64'), 'target_decomposition -> add_all': Value('int64'), 'target_decomposition -> add_all -> subtract_two_numbers': Value('int64'), 'target_decomposition -> add_multiple': Value('int64'), 'target_decomposition -> add_multiple -> add_two_numbers': Value('int64'), 'target_decomposition -> add_multiple -> divide_for_factor': Value('int64'), 'target_decomposition -> add_two_numbers': Value('int64'), 'target_decomposition -> add_two_numbers -> add_two_numbers': Value('int64'), 'target_decomposition -> add_two_numbers -> subtract_different': Value('int64'), 'target_decomposition -> divide_for_factor': Value('int64'), 'target_decomposition -> divide_for_factor -> add_multiple': Value('int64'), 'target_decomposition -> divide_for_factor -> add_two_numbers': Value('int64'), 'target_decomposition -> multiply_all': Value('int64'), 'target_decomposition -> multiply_all -> divide_for_factor': Value('int64'), 'target_decomposition -> restate_constraints': Value('int64'), 'target_decomposition -> restate_constraints -> add_multiple': Value('int64'), 'target_decomposition -> restate_constraints -> restate_constraints': Value('int64'), 'target_decomposition -> subtract_different': Value('int64'), 'target_decomposition -> subtract_different -> add_two_numbers': Value('int64'), 'target_decomposition -> target_decomposition': Value('int64'), 'target_decomposition -> target_decomposition -> restate_constraints': Value('int64'), 'target_decomposition -> target_decomposition -> target_decomposition': Value('int64'), 'use_zero -> add_multiple': Value('int64'), 'use_zero -> add_multiple -> add_multiple': Value('int64'), 'use_zero -> add_multiple -> subtract_different': Value('int64'), 'use_zero -> add_two_numbers': Value('int64'), 'use_zero -> add_two_numbers -> use_zero': Value('int64'), 'use_zero -> backtrack': Value('int64'), 'use_zero -> backtrack -> find_sum_pair': Value('int64'), 'use_zero -> divide_for_factor': Value('int64'), 'use_zero -> divide_for_factor -> find_sum_pair': Value('int64'), 'use_zero -> find_sum_pair': Value('int64'), 'use_zero -> find_sum_pair -> add_multiple': Value('int64'), 'use_zero -> find_sum_pair -> find_difference_pair': Value('int64'), 'use_zero -> intermediate_goal': Value('int64'), 'use_zero -> intermediate_goal -> use_zero': Value('int64'), 'use_zero -> realize_error': Value('int64'), 'use_zero -> realize_error -> subtract_same': Value('int64'), 'use_zero -> restate_constraints': Value('int64'), 'use_zero -> restate_constraints -> add_all': Value('int64'), 'use_zero -> restate_constraints -> add_multiple': Value('int64'), 'use_zero -> restate_constraints -> add_two_numbers': Value('int64'), 'use_zero -> restate_constraints -> restate_constraints': Value('int64'), 'use_zero -> restate_constraints -> use_zero': Value('int64'), 'use_zero -> subtract_different': Value('int64'), 'use_zero -> subtract_different -> add_two_numbers': Value('int64'), 'use_zero -> subtract_different -> restate_constraints': Value('int64'), 'use_zero -> subtract_different -> subtract_different': Value('int64'), 'use_zero -> subtract_different -> subtract_multiple': Value('int64'), 'use_zero -> subtract_different -> subtract_same': Value('int64'), 'use_zero -> subtract_same': Value('int64'), 'use_zero -> subtract_same -> multiply_two': Value('int64'), 'use_zero -> subtract_same -> realize_error': Value('int64'), 'use_zero -> subtract_same -> restate_constraints': Value('int64'), 'use_zero -> subtract_same -> subtract_different': Value('int64'), 'use_zero -> subtract_same -> subtract_same': Value('int64'), 'use_zero -> target_decomposition': Value('int64'), 'use_zero -> target_decomposition -> add_all': Value('int64'), 'use_zero -> use_zero': Value('int64'), 'use_zero -> use_zero -> realize_error': Value('int64'), 'use_zero -> use_zero -> subtract_same': Value('int64'), 'use_zero -> use_zero -> use_zero': Value('int64'), 'use_zero -> verify_calculation': Value('int64'), 'use_zero -> verify_calculation -> verify_calculation': Value('int64'), 'verify_calculation -> add_multiple': Value('int64'), 'verify_calculation -> add_multiple -> restate_constraints': Value('int64'), 'verify_calculation -> add_two_numbers': Value('int64'), 'verify_calculation -> add_two_numbers -> add_two_numbers': Value('int64'), 'verify_calculation -> add_two_numbers -> realize_error': Value('int64'), 'verify_calculation -> add_two_numbers -> restate_constraints': Value('int64'), 'verify_calculation -> add_two_numbers -> small_adjustment': Value('int64'), 'verify_calculation -> divide_for_factor': Value('int64'), 'verify_calculation -> divide_for_factor -> restate_constraints': Value('int64'), 'verify_calculation -> find_sum_pair': Value('int64'), 'verify_calculation -> find_sum_pair -> find_difference_pair': Value('int64'), 'verify_calculation -> multiply_two': Value('int64'), 'verify_calculation -> multiply_two -> add_two_numbers': Value('int64'), 'verify_calculation -> realize_error': Value('int64'), 'verify_calculation -> realize_error -> divide_for_factor': Value('int64'), 'verify_calculation -> realize_error -> multiply_two': Value('int64'), 'verify_calculation -> realize_error -> realize_error': Value('int64'), 'verify_calculation -> realize_error -> restate_constraints': Value('int64'), 'verify_calculation -> realize_error -> use_zero': Value('int64'), 'verify_calculation -> restate_constraints': Value('int64'), 'verify_calculation -> restate_constraints -> restate_constraints': Value('int64'), 'verify_calculation -> restate_constraints -> subtract_different': Value('int64'), 'verify_calculation -> restating_constraints': Value('int64'), 'verify_calculation -> restating_constraints -> divide_for_factor': Value('int64'), 'verify_calculation -> target_decomposition': Value('int64'), 'verify_calculation -> target_decomposition -> restate_constraints': Value('int64'), 'verify_calculation -> use_zero': Value('int64'), 'verify_calculation -> use_zero -> restate_constraints': Value('int64'), 'verify_calculation -> use_zero -> subtract_same': Value('int64'), 'verify_calculation -> verify_calculation': Value('int64'), 'verify_calculation -> verify_calculation -> add_two_numbers': Value('int64'), 'verify_calculation -> verify_calculation -> divide_for_factor': Value('int64'), 'verify_calculation -> verify_calculation -> find_sum_pair': Value('int64'), 'verify_calculation -> verify_calculation -> realize_error': Value('int64'), 'verify_calculation -> verify_calculation -> restate_constraints': Value('int64'), 'verify_calculation -> verify_calculation -> restating_constraints': Value('int64'), 'verify_calculation -> verify_calculation -> use_zero': Value('int64'), 'verify_calculation -> verify_calculation -> verify_calculation': Value('int64')}, 'action_sequence': List(Value('string')), 'action_type_counts': {'add_all': Value('int64'), 'add_multiple': Value('int64'), 'add_two_numbers': Value('int64'), 'backtrack': Value('int64'), 'divide_for_factor': Value('int64'), 'exhaustive_enumeration': Value('int64'), 'find_difference_pair': Value('int64'), 'find_product_pair': Value('int64'), 'find_sum_pair': Value('int64'), 'intermediate_goal': Value('int64'), 'meta_reasoning': Value('int64'), 'multiply_all': Value('int64'), 'multiply_multiple': Value('int64'), 'multiply_two': Value('int64'), 'realize_error': Value('int64'), 'repeat_failed': Value('int64'), 'restate_constraints': Value('int64'), 'restated_constraints': Value('int64'), 'restating_constraints': Value('int64'), 'small_adjustment': Value('int64'), 'strategic_decomposition': Value('int64'), 'subtract_all': Value('int64'), 'subtract_different': Value('int64'), 'subtract_multiple': Value('int64'), 'subtract_same': Value('int64'), 'subtract_two_numbers': Value('int64'), 'target_decomposition': Value('int64'), 'use_zero': Value('int64'), 'verify_calculation': Value('int64')}, 'repetition_rate': Value('float64'), 'total_actions': Value('int64'), 'unique_actions': Value('int64')}) | No description provided |
| has_reasoning_actions | Value('bool') | No description provided |
| arithmetic_attempts_by_sample | List(List({'all_operands': List(Value('float64')), 'all_operators': List(Value('string')), 'branch_id': Value('int64'), 'canonical_form': Value('string'), 'canonical_key': Value('string'), 'end_char': Value('int64'), 'end_char_in_round': Value('int64'), 'is_legal': Value('bool'), 'is_multi_operand': Value('bool'), 'is_valid_arithmetic': Value('bool'), 'match_type': Value('string'), 'operand_a': Value('float64'), 'operand_a_str': Value('string'), 'operand_b': Value('float64'), 'operand_b_str': Value('string'), 'operator': Value('string'), 'operator_raw': Value('string'), 'result': Value('float64'), 'result_str': Value('string'), 'round_idx': Value('int64'), 'separator_raw': Value('string'), 'span_text': Value('string'), 'start_char': Value('int64'), 'start_char_in_round': Value('int64'), 'subgoal_id': Value('int64'), 'subgoal_value': Value('int64')})) | List of extracted binary arithmetic operations (A op B = C) per sample with spans and validation |
| expression_attempts_by_sample | List(List({'branch_id': Value('int64'), 'canonical_key': Value('string'), 'end_char': Value('int64'), 'end_char_in_round': Value('int64'), 'eval_value': Value('string'), 'expression': Value('string'), 'is_legal_initial': Value('bool'), 'is_valid_arithmetic': Value('bool'), 'numbers_used': List(Value('int64')), 'ops_used': List(Value('string')), 'relation': Value('string'), 'relation_raw': Value('string'), 'rhs': Value('string'), 'rhs_eval_value': Value('string'), 'round_idx': Value('int64'), 'source_kind': Value('string'), 'span_text': Value('string'), 'start_char': Value('int64'), 'start_char_in_round': Value('int64'), 'subgoal_id': Value('int64'), 'subgoal_value': Value('int64')})) | List of extracted LHS = RHS expressions per sample with evaluation info |
| subgoals_by_sample | List(List({'canonical_key': Value('string'), 'confidence': Value('float64'), 'end_char': Value('int64'), 'end_char_in_round': Value('int64'), 'goal_value': Value('int64'), 'kind': Value('string'), 'round_idx': Value('int64'), 'span_text': Value('string'), 'start_char': Value('int64'), 'start_char_in_round': Value('int64')})) | List of detected subgoal markers (goal, need, intermediate, eval_zero, make_zero) per sample with kind and confidence |
| failure_markers_by_sample | List(List({'end_char': Value('int64'), 'end_char_in_round': Value('int64'), 'marker_type': Value('string'), 'round_idx': Value('int64'), 'span_text': Value('string'), 'start_char': Value('int64'), 'start_char_in_round': Value('int64')})) | List of detected failure/backtrack markers per sample |
| subgoal_windows_by_sample | List(List({'branch_id': Value('int64'), 'end_char': Value('int64'), 'end_char_in_round': Value('int64'), 'evidence_kind': Value('string'), 'evidence_text': Value('string'), 'round_idx': Value('int64'), 'start_char': Value('int64'), 'start_char_in_round': Value('int64'), 'subgoal_id': Value('int64'), 'value': Value('int64')})) | List of subgoal window spans (where a subgoal is active) per sample |
| branches_by_sample | List(List({'branch_id': Value('int64'), 'end_char': Value('int64'), 'end_char_in_round': Value('int64'), 'round_idx': Value('int64'), 'start_char': Value('int64'), 'start_char_in_round': Value('int64'), 'start_kind': Value('string'), 'start_label': Value('string'), 'start_text': Value('string')})) | List of branch segments (strategy/alternative sections) per sample |
| extraction_stats_by_sample | List({'attempts_by_match_type': {'infix': Value('int64'), 'latex_frac': Value('int64'), 'multi_op_chain': Value('int64'), 'nested_paren': Value('int64'), 'paren_expr': Value('int64'), 'reversed': Value('int64')}, 'attempts_with_branch': Value('int64'), 'attempts_with_subgoal': Value('int64'), 'binary_attempts': Value('int64'), 'legal_expression_initial': Value('int64'), 'legal_initial': Value('int64'), 'merged_text_length': Value('int64'), 'multi_operand_attempts': Value('int64'), 'rounds_with_content': Value('int64'), 'subgoals_by_kind': {'eval_zero': Value('int64'), 'goal': Value('int64'), 'intermediate': Value('int64'), 'make_zero': Value('int64'), 'need': Value('int64'), 'need_more': Value('int64'), 'short_by': Value('int64')}, 'total_attempts': Value('int64'), 'total_branches': Value('int64'), 'total_expression_attempts': Value('int64'), 'total_failure_markers': Value('int64'), 'total_subgoal_windows': Value('int64'), 'total_subgoals': Value('int64'), 'unique_canonical_keys': Value('int64'), 'unique_expression_keys': Value('int64'), 'valid_arithmetic': Value('int64'), 'valid_expression_arithmetic': Value('int64')}) | Summary statistics of extraction results per sample including subgoals_by_kind breakdown |
| llm_supplement_stats_by_sample | List({'candidates_proposed': Value('int64'), 'candidates_validated': Value('int64'), 'duplicates': Value('int64'), 'new_finds': Value('int64'), 'total_attempts_after': Value('int64'), 'validation_failure_reasons': {'invalid_arithmetic': Value('int64'), 'no_parse': Value('int64'), 'not_found': Value('int64')}}) | No description provided |
Generation Parameters
{
"script_name": "stage_02a_extract_attempts.py",
"model": "deterministic_parser",
"hyperparameters": {},
"input_datasets": [
"reasoning-degeneration-dev/EAS-qwen3-4B-Instruct-2507-cd8arg-iterative-stage02b"
],
"description": "Deterministic extraction of arithmetic attempts, expressions, subgoals, branches, and failure markers from Countdown reasoning traces"
}
Experiment Documentation
For complete experiment details, see https://github.com/reasoning-degeneration/ReasoningDegeneration/tree/main/experiments/degen_test_1_countdown/documentation
Usage
from datasets import load_dataset
dataset = load_dataset("reasoning-degeneration-dev/EAS-qwen3-4B-Instruct-2507-cd8arg-iterative-stage02b-stage02a", split="train")
print(f"Loaded {len(dataset)} rows")
This dataset is tracked in reasoning-degeneration-dev/PROJECT-MANIFEST
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