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. | ### Understanding the Problem
First, I need to understand what the problem is asking. We have two very large numbers:
- **Multiplicand (M):** 468,474,295,138
- **Multiplier (N):** 549,622,370,782
The goal is to find the product of these two numbers, i.e., M Ă— N.
### Breaking Down the Problem
Multiplying two 12-dig... | What is the solution to the long multiplication equation below?
468474295138 x 549622370782
Think step by step. | true | The solution performed the multiplication correctly using the distributive property, and the final answer matches the ground truth solution exactly. Thus, it is accurate. | 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 | 1 | <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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
Ste... | [
"257,483,952,744,173,935,857,916"
] | <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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
Ste... | 0 | <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 look for any step where the model computes a sub-result, doubts it, redoes it, or explicitly verifies by repea... | [] | <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 look for any step where the model computes a sub-result, doubts it, redoes it, or explicitly verifies by repea... | 3 | <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?
606369443979 x 932406292495
Think step by step. | 565382685142713990637605 | What is the solution to the long multiplication equation below?
606369443979 x 932406292495
Think step by step. | ### Understanding the Problem
First, I need to understand what's being asked. The problem presents a long multiplication equation:
**606369443979 Ă— 932406292495**
At first glance, both numbers are enormous—12-digit numbers. Multiplying them directly seems daunting, but perhaps breaking them down using the distributi... | What is the solution to the long multiplication equation below?
606369443979 x 932406292495
Think step by step. | false | The provided solution includes approximations and incorrect steps in multiplying the components. The calculations ultimately do not yield the exact ground truth result of 565,382,685,142,713,990,637,605. The final result quoted in the solution does not match the provided ground truth solution. | 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... | 1 | 2 | <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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
The... | [
"5.6530213 Ă— 10^{23}",
"565,382,093,814,591,328,713,990,637,605"
] | <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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
The... | 0 | <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-p... | [] | <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-p... | 5 | <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?
655201995859 x 961112225959
Think step by step. | 629722648692822990303781 | What is the solution to the long multiplication equation below?
655201995859 x 961112225959
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two very large numbers:
- **Multiplicand (M):** 655,201,995,859
- **Multiplier (N):** 961,112,225,959
The goal is to find the product \( M \times N \).
### Breaking It Down
Directly multiplying these two ... | What is the solution to the long multiplication equation below?
655201995859 x 961112225959
Think step by step. | false | The proposed solution inaccurately used a series of assumptions and calculations that do not align with correct arithmetic operations. The correct final product of multiplying the two large numbers is significantly different from the proposed result in the solution. | 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... | 2 | 2 | <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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. ... | [
"897,103,692,822,990,303,781",
"897,103,692,822,990,303,781"
] | <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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. ... | 0 | <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-p... | [] | <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-p... | 4 | <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?
851533585653 x 598003545713
Think step by step. | 509220103514198586455589 | What is the solution to the long multiplication equation below?
851533585653 x 598003545713
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. We have two very large numbers:
- **Multiplicand (M):** 851,533,585,653
- **Multiplier (N):** 598,003,545,713
The goal is to find the product of these two numbers, i.e., M Ă— N.
### Breaking Down the Problem
Multiplying two 12-dig... | What is the solution to the long multiplication equation below?
851533585653 x 598003545713
Think step by step. | false | The calculated product is 5,097,148,663,156,528,355,589, but the ground truth solution is 509220103514198586455589. The two results do not match, indicating that the solution provided 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... | 3 | 2 | <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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. ... | [
"5,097,148,663,156,528,355,589",
"5,097,148,663,156,528,355,589"
] | <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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. ... | 1 | <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-p... | [
"Verification of intermediate large addition step",
"Double checking addition of 5,096,428,510,133,205,000,000 + 255,460,075,695,900,000"
] | <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-p... | 4 | <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\n845276163170 x 658995925941\n\nT(...TRUNCATED) | 557033547824069951792970 | "What is the solution to the long multiplication equation below?\n\n845276163170 x 658995925941\n\nT(...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\n845276163170 x 658995925941\n\nT(...TRUNCATED) | true | "The provided solution correctly implements the steps for long multiplication and arrives at the fin(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 4 | 4 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | ["557,033,547,824,068,951,792,970","557,033,547,824,069,951,792,970","557,033,547,824,069,951,792,97(...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) | ["verification of 45,276,163,170 × 1,004,074,059 = 45,460,620,930,048,207,030 = 45,460,620,930,048,(...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\n593655419598 x 130312704899\n\nT(...TRUNCATED) | 77360843505766195210602 | "What is the solution to the long multiplication equation below?\n\n593655419598 x 130312704899\n\nT(...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\n593655419598 x 130312704899\n\nT(...TRUNCATED) | true | "The solution obtained is 77,363,748,915,348,905,210,602, which matches 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) | 5 | 2 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"77,363,748,915,348,905,210,602",
"77,363,748,915,348,905,210,602"
] | "<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) | ["Double check of Term 0 multiplication: 593,655,419,598 × 9 recalculated","Verification of additio(...TRUNCATED) | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | 4 | "<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) | "### Understanding the Problem\n\nThe task is to find the product of two very large numbers:\n\n- **(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n312512318448 x 599289404802\n\nT(...TRUNCATED) | false | "The provided solution contains an error in the calculations, leading to an incorrect final product (...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 6 | 2 | "<thinking>\nTo determine how many times the model proposed a final answer, we look for each point i(...TRUNCATED) | [
"187,285,321,940,994,620,700,000",
"187,285,321,940,994,620,700,000"
] | "<thinking>\nTo determine how many times the model proposed a final answer, we look for each point i(...TRUNCATED) | 0 | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | [] | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | 4 | "<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) | "### 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\n873656183224 x 428521035204\n\nT(...TRUNCATED) | false | "The provided solution calculates the product of 873,656,183,224 and 428,521,035,204 correctly, but (...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 7 | 4 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | ["374,380,052,044,032,848,109,696","374,380,052,047,363,978,217,696","374,380,052,044,032,848,109,69(...TRUNCATED) | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 13 | "<thinking>Let's step through the reasoning trace to count how many times the model verifies an inte(...TRUNCATED) | ["Verification of multiplication M x 4e11","Verification of multiplication M x 2e10","Verification o(...TRUNCATED) | "<thinking>Let's step through the reasoning trace to count how many times the model verifies an inte(...TRUNCATED) | 5 | "<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) | "### 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\n219832752637 x 171887431938\n\nT(...TRUNCATED) | false | "The provided solution calculates a value of 37,786,262,984,224,647,402,955,520,506 for the product (...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 8 | 3 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | ["37,786,262,984,224,647,402,955,520,506","37,786,487,306,694,945,906","37,786,262,984,224,647,402,9(...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) | [
"219,832 Ă— 171,887 = 37,786,262,984 = 219,832Ă—100,000 + 219,832Ă—70,000 + ... + 219,832Ă—7"
] | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | 3 | "<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) | "### 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\n883158551821 x 522556187928\n\nT(...TRUNCATED) | false | "The SOLUTION calculated the product as 461,499,966,175,610,802,616,888, but the GROUND TRUTH SOLUTI(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 9 | 2 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"4.614999661756108 Ă— 10^23",
"461,499,966,175,610,802,616,888"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 2 | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | ["883,158,551,821 × 500,000,000,000 = 441,579,275,910,500,000,000,000","883,158,551,821 × 22,000,0(...TRUNCATED) | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | 3 | "<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) |
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