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 string | measurement_step_verification_final_count int64 | measurement_step_verification_reasoning string | measurement_step_verification_metadata sequence | measurement_step_verification_raw_response string | measurement_reasoning_deliberation_final_count int64 | measurement_reasoning_deliberation_reasoning string | measurement_reasoning_deliberation_metadata sequence | measurement_reasoning_deliberation_raw_response string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | 3 | <thinking>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 (a stated product),
Restates or confirms that same result (verification),
Attempts to verify it using an alternative method (r... | [
"257366221257473433812916",
"257483952853496361857916",
"257483952853496361857916"
] | <thinking>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 (a stated product),
Restates or confirms that same result (verification),
Attempts to verify it using an alternative method (r... | 10 | <thinking>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-pe... | [
"Approximate decimal multiplication check",
"Digit-wise subtraction verification",
"Partial product multiplication and sum verification",
"Multiplying large number by single digit verification",
"Splitting large multiplication into parts and verifying each",
"Summation corrections and re-verifications",
... | <thinking>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-pe... | 14 | <thinking>To answer your question—how 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)—we need to identify all moments in the reasoning trace where:
- The model questions its current ... | [] | <thinking>To answer your question—how 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)—we need to identify all moments in the reasoning trace where:
- The model questions its current ... |
"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 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"565382685142713990636605"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 3 | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | ["Division 606,369,443,979 ÷ 3 = 202,123,147,993","Initial flawed sum of partial products leading t(...TRUNCATED) | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | 19 | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...TRUNCATED) | [] | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...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 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"629722648692822990303781",
"629722648692822990303781"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 3 | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | ["655,201,995,859 + 961,112,225,959 = 1,616,313,221,818 = 1,616,313,221,818","629,722,626,023,644,00(...TRUNCATED) | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | 9 | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...TRUNCATED) | [] | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...TRUNCATED) |
"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 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"509219288599814914878988319598455589"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 11 | "<thinking>Let's step through the reasoning trace to count how many times the model verifies an inte(...TRUNCATED) | ["Verified 3 * 283844528551 = 851533585653","Verified 7 * 85429077959 = 598003545713","Verified 8515(...TRUNCATED) | "<thinking>Let's step through the reasoning trace to count how many times the model verifies an inte(...TRUNCATED) | 12 | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...TRUNCATED) | [] | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...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 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"557036988085325039951792970",
"5.5703698808532503995179297 x 10^23"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 6 | "<thinking>Let's step through the reasoning trace to count how many times the model verifies an inte(...TRUNCATED) | ["Verified subtraction: 659000000000 - 658995925941 = 4074059","Verified multiplication: 84527616317(...TRUNCATED) | "<thinking>Let's step through the reasoning trace to count how many times the model verifies an inte(...TRUNCATED) | 8 | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...TRUNCATED) | [] | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...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 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...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"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["division verification by multiplication","addition verification last two terms","addition verifica(...TRUNCATED) | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | 9 | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...TRUNCATED) | [] | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...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 | 1 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"187,343,736,728,273,612,419,296"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 11 | "<thinking>Let's step through the reasoning trace to count how many times the model verifies an inte(...TRUNCATED) | ["division by 2 steps","digit sum divisibility checks","square computations and re-computations","co(...TRUNCATED) | "<thinking>Let's step through the reasoning trace to count how many times the model verifies an inte(...TRUNCATED) | 16 | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...TRUNCATED) | [] | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...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 | 3 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"3.7438001758156 x 10^23",
"374489214293534450217696",
"374489214293534450217696"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 13 | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | ["approximate coefficient multiplication verified twice","Karatsuba top-level subproduct x1*y1 verif(...TRUNCATED) | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | 8 | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...TRUNCATED) | [] | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...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 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"37783689175016202246506"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 8 | "<thinking>Let's step through the reasoning trace to count how many times the model verifies an inte(...TRUNCATED) | ["Verification of addition: 219,832,752,637 + 171,887,431,938 = 391,770,689,175","Verification of su(...TRUNCATED) | "<thinking>Let's step through the reasoning trace to count how many times the model verifies an inte(...TRUNCATED) | 12 | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...TRUNCATED) | [] | "<thinking>To answer your question—how many times does the model verify its higher-level reasoning(...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 | 4 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | ["461499877990986088184608802616888","461499877990986088184608802616888","46149987799098608818460880(...TRUNCATED) | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 1 | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | ["Explicit double check on 7 * 126,165,507,403 = 883,158,551,821","No other intermediate double chec(...TRUNCATED) | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | 5 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | [] | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) |
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