question string | solution string | eval_prompt string | eval_internal_cot string | eval_solution string | raw_eval_prompt string | judge_correct bool | judge_reasoning string | 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?
468474295138 x 549622370782
Think step by step. | 257483952744173935857916 | What is the solution to the long multiplication equation below?
468474295138 x 549622370782
Think step by step. | Okay, so I need to solve this multiplication problem: 468,474,295,138 multiplied by 549,622,370,782. Wow, those are really big numbers! I remember that multiplying large numbers can be done using the standard algorithm, breaking them down into smaller parts. But doing this manually would take a lot of steps and time. L... | The solution to the long multiplication equation 468,474,295,138 × 549,622,370,782 is calculated by breaking down each number into manageable parts, multiplying them individually, and summing the results. After careful computation and verification, the exact product is:
**257,483,952,853,496,361,857,916**
**Step-by-S... | What is the solution to the long multiplication equation below?
468474295138 x 549622370782
Think step by step. | false | The provided solution claims that the product of the two numbers is 257,483,952,853,496,361,857,916, but the ground truth solution indicates it is actually 257,483,952,744,173,935,857,916. This discrepancy shows the computed value is incorrect. | 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 | 2 | 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.
The model goes ... | [
"257366221257473433812916",
"257483952853496361857916"
] | null | 7 | 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 c... | [
"Calculating 468 * 550: Let's do 468 * 500 = 234,000 and 468 * 50 = 23,400. Adding those gives 234,000 + 23,400 = 257,400.",
"Let's compute 4.68474295138 x 5.49622370782. Let's approximate this: 4.6847 * 5.4962 ≈ ? ... Adding all together: 20 + 1.9848 + 3.4235 + 0.33975 ≈ 25.748.",
"Let's subtract digit by digi... | null | 19 | 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 o... | [
"\"But doing this by hand would be tedious. Maybe there's a pattern or a way to simplify this?\"",
"\"But with such large numbers, even breaking them into parts might not help much unless there's a specific structure.\"",
"\"Alternatively, maybe I can use estimation to check if my final answer is reasonable.\""... | null | [
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{
"error_explanation": "There was no error in the previous calculation of 468 * 550; the breakdown into 468*500 and 468*50 was correctly done, and their sum of 257,400 is accurate. Hence, no correction or verification was necessary.",
"next_step": "Calculating 468 * 550: Let's do 468 * 500 = 234,000 and 468... | [
false,
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] | [
{
"correct": false,
"reasoning": "The provided solution is 257366221257473433812916, whereas the ground truth solution is 257483952744173935857916. Comparing both numbers digit by digit shows that the provided solution differs significantly from the ground truth. Therefore, the provided solution to the long... | [
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"change_in_direction_explanation": "The deliberation led the model to explicitly consider alternative calculation methods and algebraic identities that go beyond the initial consideration of standard manual multiplication and estimation. This shifted the approach from just estimating or considering standard m... |
"What is the solution to the long multiplication equation below?\n\n606369443979 x 932406292495\n\nT(...TRUNCATED) | 565382685142713990637605 | "What is the solution to the long multiplication equation below?\n\n606369443979 x 932406292495\n\nT(...TRUNCATED) | "Okay, so I need to multiply these two huge numbers: 606,369,443,979 and 932,406,292,495. Wow, that'(...TRUNCATED) | "To solve the long multiplication equation \\(606369443979 \\times 932406292495\\), we can break dow(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n606369443979 x 932406292495\n\nT(...TRUNCATED) | false | "The computed answer of 565382685142713990636605 does not match the ground truth solution of 5653826(...TRUNCATED) | 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) | [
"565382685142713990636605"
] | null | 5 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["Let's do that division.","Now sum all four parts: 540,000,000,000 + 19,443,600,000 = 559,443,600,0(...TRUNCATED) | null | 11 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["But honestly, with numbers this big, even breaking them down might be tedious. Let me think.","But(...TRUNCATED) | null | [
true,
false,
true,
true,
true
] | [{"error_explanation":"The previous step only stated that the number is divisible by 3 but did not p(...TRUNCATED) | [
false
] | [{"correct":false,"reasoning":"The given solution is 565382685142713990636605, while the ground trut(...TRUNCATED) | [
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] | [{"change_in_direction_explanation":"The deliberation prompted the model to reconsider the initial p(...TRUNCATED) |
"What is the solution to the long multiplication equation below?\n\n655201995859 x 961112225959\n\nT(...TRUNCATED) | 629722648692822990303781 | "What is the solution to the long multiplication equation below?\n\n655201995859 x 961112225959\n\nT(...TRUNCATED) | "Okay, so I need to multiply these two huge numbers: 655,201,995,859 and 961,112,225,959. Wow, that'(...TRUNCATED) | "The solution to the long multiplication equation 655,201,995,859 × 961,112,225,959 is calculated b(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n655201995859 x 961112225959\n\nT(...TRUNCATED) | true | "The provided solution matches the ground truth solution exactly. The long multiplication and verifi(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 2 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"629722648692822990303781",
"629722648692822990303781"
] | null | 8 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["Sum of digits for 3-divisibility: Adding digits 6+5+5+2+0+1+9+9+5+8+5+9 equals 64, which is not di(...TRUNCATED) | null | 15 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"Maybe there's a pattern or a trick to simplify it? Let me check if there's any relationship betw(...TRUNCATED) | null | [
false,
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true,
true,
false,
false,
true,
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] | [{"error_explanation":"There is no error in the previous step because it did not produce any digit s(...TRUNCATED) | [
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] | [{"correct":true,"reasoning":"The solution given is 629722648692822990303781. The ground truth solut(...TRUNCATED) | [
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"What is the solution to the long multiplication equation below?\n\n851533585653 x 598003545713\n\nT(...TRUNCATED) | 509220103514198586455589 | "What is the solution to the long multiplication equation below?\n\n851533585653 x 598003545713\n\nT(...TRUNCATED) | "Okay, so I need to multiply these two huge numbers: 851,533,585,653 and 598,003,545,713. Wow, that'(...TRUNCATED) | "To solve the long multiplication equation \\(851,533,585,653 \\times 598,003,545,713\\), we can bre(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n851533585653 x 598003545713\n\nT(...TRUNCATED) | false | "The computed product in the solution is incorrect as it did not match the ground truth solution of (...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 3 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"509219288599814914878988319598455589"
] | null | 10 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["Let me check if the first number is divisible by 3. ... sum is 57, which is divisible by 3.","Wait(...TRUNCATED) | null | 9 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"Maybe there's a smarter way or some pattern I can exploit?\"","\"I wonder if there's a way to br(...TRUNCATED) | null | [
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] | [{"error_explanation":"","next_step":"Let's try dividing 851,533,585,653 by 3 to find the quotient a(...TRUNCATED) | [
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] | [{"correct":false,"reasoning":"The solution provided is 509219288599814914878988319598455589, which (...TRUNCATED) | [
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] | [{"change_in_direction_explanation":"The model changed its initial direction from directly using the(...TRUNCATED) |
"What is the solution to the long multiplication equation below?\n\n845276163170 x 658995925941\n\nT(...TRUNCATED) | 557033547824069951792970 | "What is the solution to the long multiplication equation below?\n\n845276163170 x 658995925941\n\nT(...TRUNCATED) | "Okay, so I need to multiply these two huge numbers: 845,276,163,170 and 658,995,925,941. Wow, that'(...TRUNCATED) | "The solution to the long multiplication equation 845,276,163,170 × 658,995,925,941 is calculated b(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n845276163170 x 658995925941\n\nT(...TRUNCATED) | false | "The calculated answer differs from the ground truth solution. The calculations performed in the sol(...TRUNCATED) | 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) | [
"557036988085325039951792970",
"557036988085325039951792970"
] | null | 9 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, let me verify that subtraction:\\n\\n659,000,000,000 \\n- 658,995,925,941 \\n= 4,074,059(...TRUNCATED) | null | 5 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["\"Let me think about how to approach this. I remember that multiplying large numbers can be done u(...TRUNCATED) | null | [
true,
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false,
true,
true,
false,
true,
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] | [{"error_explanation":"No error was present in the previous step's decomposition; however, the subtr(...TRUNCATED) | [
false,
false
] | [{"correct":false,"reasoning":"The provided solution is 557036988085325039951792970, whereas the gro(...TRUNCATED) | [
true,
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] | [{"change_in_direction_explanation":"The model changed from initially considering the standard multi(...TRUNCATED) |
"What is the solution to the long multiplication equation below?\n\n593655419598 x 130312704899\n\nT(...TRUNCATED) | 77360843505766195210602 | "What is the solution to the long multiplication equation below?\n\n593655419598 x 130312704899\n\nT(...TRUNCATED) | "Okay, so I need to solve this multiplication problem: 593,655,419,598 multiplied by 130,312,704,899(...TRUNCATED) | "The solution to the long multiplication equation \\(593,\\!655,\\!419,\\!598 \\times 130,\\!312,\\!(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n593655419598 x 130312704899\n\nT(...TRUNCATED) | true | "The provided solution for the long multiplication of the numbers 593,655,419,598 and 130,312,704,89(...TRUNCATED) | 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) | [
"77,360,843,505,766,195,210,602",
"77,360,843,505,766,195,210,602",
"77,360,843,505,766,195,210,602"
] | null | 10 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, let me check that division again because it's easy to make a mistake here.\"","\"Alternati(...TRUNCATED) | null | 4 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Maybe there's a smarter way or a pattern I can use?","Hmm, not sure if they are close to any parti(...TRUNCATED) | null | [
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] | [{"error_explanation":"No explicit error in the previous division result is identified yet; the step(...TRUNCATED) | [
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] | [{"correct":true,"reasoning":"The given solution is '77,360,843,505,766,195,210,602', which when the(...TRUNCATED) | [
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true,
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] | [{"change_in_direction_explanation":"The deliberation led the reasoning to shift from the standard b(...TRUNCATED) |
"What is the solution to the long multiplication equation below?\n\n312512318448 x 599289404802\n\nT(...TRUNCATED) | 187285321315995004387296 | "What is the solution to the long multiplication equation below?\n\n312512318448 x 599289404802\n\nT(...TRUNCATED) | "Okay, so I need to solve this multiplication problem: 312,512,318,448 multiplied by 599,289,404,802(...TRUNCATED) | "The solution to the long multiplication equation \\(312,\\!512,\\!318,\\!448 \\times 599,\\!289,\\!(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n312512318448 x 599289404802\n\nT(...TRUNCATED) | false | "The calculated product of the multiplication does not match the ground truth solution. The provided(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 6 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"187343736728273612419296",
"187343736728273612419296"
] | null | 5 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Let me compute that. 19,532,019,903 ÷ 3... Wait, maybe this is too time-consuming. Alternativel(...TRUNCATED) | null | 8 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Hmm, both numbers are in the hundreds of billions. Multiplying them directly would result in a num(...TRUNCATED) | null | [
false,
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true,
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] | [{"error_explanation":"No error occurred in the previous step; the divisibility by 3 was correctly i(...TRUNCATED) | [
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] | [{"correct":false,"reasoning":"The given solution is 187343736728273612419296, whereas the ground tr(...TRUNCATED) | [
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] | [{"change_in_direction_explanation":"The deliberation caused the model to reconsider the initial dir(...TRUNCATED) |
"What is the solution to the long multiplication equation below?\n\n873656183224 x 428521035204\n\nT(...TRUNCATED) | 374380052047523978217696 | "What is the solution to the long multiplication equation below?\n\n873656183224 x 428521035204\n\nT(...TRUNCATED) | "Okay, so I need to multiply these two huge numbers: 873,656,183,224 and 428,521,035,204. Wow, that'(...TRUNCATED) | "The solution to the long multiplication equation \\(873,\\!656,\\!183,\\!224 \\times 428,\\!521,\\!(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n873656183224 x 428521035204\n\nT(...TRUNCATED) | false | "The given solution calculates a product of two large numbers using the Karatsuba algorithm but arri(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 7 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"374489214293534450217696"
] | null | 10 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"But this is a rough estimate. The actual product might be slightly different because I approxima(...TRUNCATED) | null | 11 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["But these numbers are so big; even breaking them down might take a while. Let me think.","But brea(...TRUNCATED) | null | [
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] | [{"error_explanation":"The previous step's product of the coefficients was approximate due to roundi(...TRUNCATED) | [
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] | [{"correct":false,"reasoning":"The solution given is 374489214293534450217696, while the ground trut(...TRUNCATED) | [
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] | [{"change_in_direction_explanation":"The deliberation acknowledges the difficulty of breaking down l(...TRUNCATED) |
"What is the solution to the long multiplication equation below?\n\n219832752637 x 171887431938\n\nT(...TRUNCATED) | 37786487306635527520506 | "What is the solution to the long multiplication equation below?\n\n219832752637 x 171887431938\n\nT(...TRUNCATED) | "Okay, so I need to multiply these two huge numbers: 219,832,752,637 and 171,887,431,938. Wow, that'(...TRUNCATED) | "To solve the long multiplication equation \\(219,832,752,637 \\times 171,887,431,938\\), we need to(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n219832752637 x 171887431938\n\nT(...TRUNCATED) | false | "The multiplication result calculated in the solution, 37783689175016202246506, does not match the g(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 8 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"37783689175016202246506"
] | null | 5 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["Adding the two numbers step by step and then rechecking the addition for errors.","Computing the d(...TRUNCATED) | null | 25 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Let me see how to approach this.","But these numbers are so big; even breaking them down might tak(...TRUNCATED) | null | [
true,
true,
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] | [{"error_explanation":"The initial manual addition had multiple inconsistencies and carryover miscal(...TRUNCATED) | [
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] | [{"correct":false,"reasoning":"The problem asks to multiply 219832752637 by 171887431938. The propos(...TRUNCATED) | [true,true,true,false,true,true,true,true,true,true,true,true,true,true,true,true,true,true,true,tru(...TRUNCATED) | [{"change_in_direction_explanation":"The deliberation step explicitly reflects the model pausing to (...TRUNCATED) |
"What is the solution to the long multiplication equation below?\n\n883158551821 x 522556187928\n\nT(...TRUNCATED) | 461499966175594802616888 | "What is the solution to the long multiplication equation below?\n\n883158551821 x 522556187928\n\nT(...TRUNCATED) | "Okay, so I need to multiply these two huge numbers: 883,158,551,821 and 522,556,187,928. Wow, that'(...TRUNCATED) | "The solution to the long multiplication equation \\(883,\\!158,\\!551,\\!821 \\times 522,\\!556,\\!(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n883158551821 x 522556187928\n\nT(...TRUNCATED) | false | "The provided solution shows a different result than the ground truth solution. The formatting of th(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 9 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"461499877990986088184608802616888"
] | null | 2 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["'Adding the digits: ... So 48 is divisible by 3, so yes. 65,319,523,491 ÷ 3 = let's see, 3*21,773(...TRUNCATED) | null | 8 | "To answer your question\t61how many times does the model verify its higher-level reasoning (i.e., d(...TRUNCATED) | ["Let me think about how to approach this. Maybe there's a smarter way or a pattern I can use?","May(...TRUNCATED) | null | [
false,
true
] | [{"error_explanation":"There was no error in the previous step; the digit sum correctly determined d(...TRUNCATED) | [
false
] | [{"correct":false,"reasoning":"The solution provided for the multiplication, 883158551821 x 52255618(...TRUNCATED) | [
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