question string | solution string | eval_prompt list | eval_internal_cot string | eval_solution string | raw_eval_prompt string | judge_correct bool | judge_reasoning string | eval_steps list | steps_word_count int64 | trace_word_count int64 | word_count_diff int64 | measurement_type string | measurement_prompt string | row_id int64 | measurement_answer_verification_final_count int64 | measurement_answer_verification_reasoning string | measurement_answer_verification_metadata sequence | measurement_answer_verification_raw_response null | measurement_step_verification_final_count int64 | measurement_step_verification_reasoning string | measurement_step_verification_metadata sequence | measurement_step_verification_raw_response null | measurement_reasoning_deliberation_final_count int64 | measurement_reasoning_deliberation_reasoning string | measurement_reasoning_deliberation_metadata sequence | measurement_reasoning_deliberation_raw_response null | metadata_verification_step_needed sequence | metadata_verification_step_needed_judge_data list | metadata_answers_correct sequence | metadata_answers_correct_judge_data list | metadata_reasoning_deliberation_needed sequence | metadata_reasoning_deliberation_needed_judge_data list |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
97511989 x 29677209
Think step by step. | 2893883677558701 | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | ### Understanding the Problem
First, I need to multiply two large numbers: **97,511,989** and **29,677,209**. Directly multiplying these seems complex, so I recall that breaking them down using the **distributive property of multiplication over addition** (also known as the FOIL method) might simplify the process. Thi... | What is the solution to the long multiplication equation below?
97511989 x 29677209
Think step by step. | true | The solution presented calculates the product of the two numbers using detailed breakdowns of the multiplication process and partial products, arriving at the correct final answer. The evaluation of the number and use of verification methods also confirm the result matches the ground truth solution. | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **97,511,989** and **29,677,209**. Directly multiplying these seems complex, so I recall that breaking them down using the **distributive property of multiplication over addition** (al... | 923 | 966 | 43 | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 0 | 3 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. First, the... | [
"2893883677558701",
"2893883677558701",
"2893883677558701"
] | null | 16 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"\\[ 97,511,989 \\times 9 = 97,511,989 \\times (10 - 1) = 975,119,890 - 97,511,989 = 877,607,901\\]",
"1,950,239,780,000,000 + 877,607,901,000,000 = 2,827,847,681,000,000",
"2,827,847,681,000,000 + 58,507,193,400,000 = 2,886,354,874,400,000",
"2,886,354,874,400,000 + 6,825,839,230,000 = 2,893,180,713,630,000"... | null | 3 | To answer your question1how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)1we need to identify all moments in the reasoning trace where:
The model questions its current method or ... | [
"But this seems a bit complex. Maybe a better approach is to use the standard form... However, this might not simplify things. Let's stick to the original approach.",
"Given the complexity, perhaps the standard long multiplication method is more straightforward. Let's break it down:",
"But before diving into th... | null | [
false,
false,
false,
false,
false,
true,
false,
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false,
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] | [
{
"error_explanation": "The calculation in this step is correctly executed and results in the correct partial product for 97,511,989 multiplied by 9. There is no prior value for 97,511,989 * 9 to compare against, thus no correction or fix is happening here.",
"next_step": "Multiply by 9 (units place):\n \... | [
true,
true,
true
] | [
{
"correct": true,
"reasoning": "The solution provided is 2893883677558701 for the multiplication of 97511989 and 29677209. The ground truth solution matches exactly with the provided solution. Since both the calculated solution and the ground truth are identical, the solution is correct."
},
{
"cor... | [
false,
true,
false
] | [
{
"change_in_direction_explanation": "The model initially considered switching to a standard form approach but concluded it might not simplify the problem and decided to continue with the original expanded approach. Thus, the deliberation did not change the problem-solving direction significantly.",
"delibe... | |
"What is the solution to the long multiplication equation below?\n\n39634656 x 65995812\n\nThink ste(...TRUNCATED) | 2615721306060672 | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **39,634,656** and **(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n39634656 x 65995812\n\nThink ste(...TRUNCATED) | false | "The final answer provided, '2.615721306060672 \\times 10^{15}', is incorrect as it uses scientific (...TRUNCATED) | [{"contains_final_answer":false,"content":"### Understanding the Problem\n\nFirst, I need to multipl(...TRUNCATED) | 729 | 729 | 0 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 1 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"2615721306060672"
] | null | 15 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["39,634,656 × 6 = 237,807,936","39,634,656 × 5 = 198,173,280","39,634,656 × 9 = 356,711,904","We(...TRUNCATED) | null | 3 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["However, this would result in 8 × 8 = 64 multiplications, which is tedious. To simplify, I recall(...TRUNCATED) | null | [
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false,
false
] | [{"error_explanation":"No error was present in the previous step; it correctly laid out the method b(...TRUNCATED) | [
true
] | [{"correct":true,"reasoning":"The given solution to the multiplication problem 39634656 x 65995812 i(...TRUNCATED) | [
true,
true,
false
] | [{"change_in_direction_explanation":"The deliberation recognized that the initial plan to use the di(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n24755057 x 57601784\n\nThink ste(...TRUNCATED) | 1425935446221688 | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **24,755,057** and **(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n24755057 x 57601784\n\nThink ste(...TRUNCATED) | true | "The solution correctly details the multiplication process while verifying each calculation step. Th(...TRUNCATED) | [{"contains_final_answer":false,"content":"### Understanding the Problem\n\nFirst, I need to multipl(...TRUNCATED) | 797 | 797 | 0 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 2 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"1425935446221688",
"1425935446221688",
"1.425935446221688 × 10^{15}"
] | null | 3 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["24,755,057 × 5 = 123,775,285 → Correct.","24,755,057 × 7 = 173,285,399 → Correct.","24,755,0(...TRUNCATED) | null | 4 | "To answer your question\t6 how many times does the model verify its higher-level reasoning (i.e., d(...TRUNCATED) | ["But for simplicity, perhaps using standard place values is better:","To make it easier, I'll add t(...TRUNCATED) | null | [
false,
false,
false
] | [{"error_explanation":"There was no error in the previous step; the multiplication and place value a(...TRUNCATED) | [
true,
true,
true
] | [{"correct":true,"reasoning":"The provided solution is to multiply 24,755,057 by 57,601,784. The giv(...TRUNCATED) | [
true,
false,
true,
false
] | [{"change_in_direction_explanation":"The deliberation recognizes a simplification to use standard pl(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n53563670 x 33752847\n\nThink ste(...TRUNCATED) | 1807926358268490 | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a str(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n53563670 x 33752847\n\nThink ste(...TRUNCATED) | true | "The calculated product of 53563670 and 33752847 has been meticulously verified through step-by-step(...TRUNCATED) | [{"contains_final_answer":false,"content":"### Understanding the Problem\n\nFirst, I need to underst(...TRUNCATED) | 1,432 | 1,432 | 0 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 3 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"1,807,926,358,268,490",
"1,807,926,358,268,490"
] | null | 7 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["- Adding the first two: 1,606,910,100,000,000 + 160,691,010,000,000 = 1,767,601,110,000,000 ✔","(...TRUNCATED) | null | 1 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["However, given the complexity, I'll stick with the long multiplication method and double-check the(...TRUNCATED) | null | [
false,
false,
false,
false,
false,
false,
false
] | [{"error_explanation":"No error is present in the previous step's addition. The sum is correctly cal(...TRUNCATED) | [
true,
true
] | [{"correct":true,"reasoning":"The given solution is 1,807,926,358,268,490, which matches the ground (...TRUNCATED) | [
true
] | [{"change_in_direction_explanation":"The model considered alternative methods (such as FOIL) but dec(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n81471995 x 26159399\n\nThink ste(...TRUNCATED) | 2131258424531005 | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a str(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n81471995 x 26159399\n\nThink ste(...TRUNCATED) | true | "The solution provides a detailed explanation of the multiplication process and arrives at the corre(...TRUNCATED) | [{"contains_final_answer":false,"content":"### Understanding the Problem\n\nFirst, I need to underst(...TRUNCATED) | 1,361 | 1,503 | 142 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 4 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"2131258424531005",
"2131258424531005"
] | null | 11 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Multiply by 9 (units place): 81,471,995 \\times 9 = 81,471,995 \\times (10 - 1) = 814,719,950 - (...TRUNCATED) | null | 4 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"Let's express 26,159,399 as... But this seems a bit messy. Maybe using the standard long multipl(...TRUNCATED) | null | [
false,
false,
false,
true,
true
] | [{"error_explanation":"","next_step":"Multiply by 9 (units place): 81,471,995 \\times 9 = 81,471,995(...TRUNCATED) | [
true,
true
] | [{"correct":true,"reasoning":"The given solution is 2131258424531005 and the ground truth solution i(...TRUNCATED) | [
true,
true,
true,
false
] | [{"change_in_direction_explanation":"The deliberation abandons the initial plan of decomposing the s(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n82669731 x 57977955\n\nThink ste(...TRUNCATED) | 4793021943780105 | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **82,669,731** and **(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n82669731 x 57977955\n\nThink ste(...TRUNCATED) | false | "The computed result of the provided solution (4,793,023,597,174,725) does not match the ground trut(...TRUNCATED) | [{"contains_final_answer":false,"content":"### Understanding the Problem\n\nFirst, I need to multipl(...TRUNCATED) | 1,581 | 1,841 | 260 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 5 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"4793023597174725",
"4793023597174725",
"4793023597174725"
] | null | 6 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["Step 2: 'First, 82,669,731 × 7 = 578,688,117 (I did this by breaking it down: 80,000,000 × 7 = 5(...TRUNCATED) | null | 7 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"Directly multiplying these seems complex, so I recall that breaking them down using the distribu(...TRUNCATED) | null | [
true,
false,
true,
false,
false,
false
] | [{"error_explanation":"","next_step":"Step 2: Multiply 82,669,731 by 7,000,000\n- 82,669,731 × 7,00(...TRUNCATED) | [
false,
false,
false
] | [{"correct":false,"reasoning":"To evaluate the correctness, I compare the given solution and the gro(...TRUNCATED) | [
true,
true,
true,
true,
true,
true,
true,
true
] | [{"change_in_direction_explanation":"The deliberation changed the direction meaningfully by moving f(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n60460452 x 59942216\n\nThink ste(...TRUNCATED) | 3624133473241632 | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. We have tw(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n60460452 x 59942216\n\nThink ste(...TRUNCATED) | true | "The solution accurately details each step of the multiplication process, including the breakdown of(...TRUNCATED) | [{"contains_final_answer":false,"content":"### Understanding the Problem\n\nFirst, I need to underst(...TRUNCATED) | 706 | 722 | 16 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 6 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"3624133473241632",
"3624133473241632",
"3624133473241632"
] | null | 3 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["- 60,460,452 × 9 = 544,144,068 (repeated calculation at multiplier 9,000,000 and 900,000)","Calcu(...TRUNCATED) | null | 1 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["But this seems a bit complex. Maybe a simpler breakdown:\n\n59,942,216 = 60,000,000 - 57,784 (sinc(...TRUNCATED) | null | [
false,
false,
false
] | [{"error_explanation":"There was no error in the previous step's calculation of 60,460,452 × 9 = 54(...TRUNCATED) | [
true,
true,
true
] | [{"correct":true,"reasoning":"The problem is to multiply the two numbers: 60460452 and 59942216. The(...TRUNCATED) | [
false
] | [{"change_in_direction_explanation":"The deliberation proposed a potential alternative approach—br(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n58191452 x 19309974\n\nThink ste(...TRUNCATED) | 1123675425142248 | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **58,191,452** and **(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n58191452 x 19309974\n\nThink ste(...TRUNCATED) | false | "The computed solution of 1.123675425142248 x 10^{15} is not equivalent to the ground truth solution(...TRUNCATED) | [{"contains_final_answer":false,"content":"### Understanding the Problem\n\nFirst, I need to multipl(...TRUNCATED) | 780 | 815 | 35 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 8 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"1123675425142248",
"1123675425142248"
] | null | 1 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["Break 26 into (20 + 6) and compute 58,191,452 x 20 = 1,163,829,040, then 58,191,452 x 6 = 349,148,(...TRUNCATED) | null | 1 | "To answer your question\u00151 how many times does the model verify its higher-level reasoning (i.e(...TRUNCATED) | ["But before diving into that, perhaps using the **long multiplication** method would be more straig(...TRUNCATED) | null | [
false
] | [{"error_explanation":"There was no error in the previous step's calculation of 58,191,452 x 26. The(...TRUNCATED) | [
true,
true
] | [{"correct":true,"reasoning":"The solution provided for the multiplication of 58191452 by 19309974 i(...TRUNCATED) | [
true
] | [{"change_in_direction_explanation":"The deliberation proposes switching from the initial plan of us(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n91914600 x 47919466\n\nThink ste(...TRUNCATED) | 4404498549603600 | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a mul(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n91914600 x 47919466\n\nThink ste(...TRUNCATED) | true | "The solution correctly applies the distributive property and long multiplication methods to compute(...TRUNCATED) | [{"contains_final_answer":false,"content":"### Understanding the Problem\n\nFirst, I need to underst(...TRUNCATED) | 1,482 | 1,564 | 82 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 9 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"4404498549603600",
"4404498549603600",
"4404498549603600"
] | null | 1 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"### Verification of Step 1\\nTo ensure accuracy, I recall that multiplying by 40,000,000 is the (...TRUNCATED) | null | 2 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"Oops! That's different from my previous result. I must have made a mistake.\"","\"However, this (...TRUNCATED) | null | [
true
] | [{"error_explanation":"The error in the previous step was a misrepresentation of the number 91914600(...TRUNCATED) | [
true,
true,
true
] | [{"correct":true,"reasoning":"The solution given is 4404498549603600 and the ground truth solution i(...TRUNCATED) | [
true,
false
] | [{"change_in_direction_explanation":"The deliberation triggered a significant reevaluation of how th(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n51128930 x 65376699\n\nThink ste(...TRUNCATED) | 3342640666802070 | [{"content":"You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON (...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **51,128,930** and **(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n51128930 x 65376699\n\nThink ste(...TRUNCATED) | true | "The provided solution includes a detailed breakdown of the multiplication process using the distrib(...TRUNCATED) | [{"contains_final_answer":false,"content":"### Understanding the Problem\n\nFirst, I need to multipl(...TRUNCATED) | 774 | 790 | 16 | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 11 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"3342640666802070",
"3342640666802070"
] | null | 6 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["50,000,000 x 60,000,000 = 3,000,000,000,000,000 (3 quadrillion) - 1,128,930 x 60,000,000 = 67,735,(...TRUNCATED) | null | 4 | "To answer your question\t6 how many times does the model verify its higher-level reasoning (i.e., d(...TRUNCATED) | ["Direct multiplication seems complex, so I recall that breaking it down using the distributive prop(...TRUNCATED) | null | [
false,
false,
false,
false,
false,
true
] | [{"error_explanation":"No error was found in the previous step's calculation. The partial products a(...TRUNCATED) | [
true,
true
] | [{"correct":true,"reasoning":"The solution provided is 3342640666802070. The ground truth solution i(...TRUNCATED) | [
true,
false,
false,
true
] | [{"change_in_direction_explanation":"The original direction was to multiply directly, but the model (...TRUNCATED) |
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