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?
97511989 x 29677209
Think step by step. | 2893883677558701 | What is the solution to the long multiplication equation below?
97511989 x 29677209
Think step by step. | ### 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. | 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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. ... | [
"2,893,883,677,558,701",
"2,893,883,677,558,701",
"2,893,883,677,558,701"
] | <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 | 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 ... | [
"Verification of 97,511,989 Ă— 9 by rewriting as 97,511,989 Ă— (10 - 1)"
] | 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 ... | 2 | <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?
39634656 x 65995812
Think step by step. | 2615721306060672 | What is the solution to the long multiplication equation below?
39634656 x 65995812
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **39,634,656** and **65,995,812**. 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) can simplify the process. This ... | What is the solution to the long multiplication equation below?
39634656 x 65995812
Think step by step. | false | The final answer provided, '2.615721306060672 \times 10^{15}', is incorrect as it uses scientific notation and has a decimal point that is misplaced. The ground truth solution, '2615721306060672', does not have any decimal point and is not in scientific notation. The correct answer should be '2615721306060672'. | 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 | 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.
1. ... | [
"2.615721306060672 Ă— 10^{15}"
] | <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?
24755057 x 57601784
Think step by step. | 1425935446221688 | What is the solution to the long multiplication equation below?
24755057 x 57601784
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **24,755,057** and **57,601,784**. 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) can simplify the process. This ... | What is the solution to the long multiplication equation below?
24755057 x 57601784
Think step by step. | true | The solution correctly details the multiplication process while verifying each calculation step. The final computed result matches the ground truth solution exactly, confirming that the answer is correct. | 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 | 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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. ... | [
"1,425,935,446,221,688",
"1,425,935,446,221,688",
"1.425935446221688 Ă— 10^{15}"
] | <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. ... | 6 | <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 24,755,057 Ă— 5 = 123,775,285",
"Verification of 123,775,285 Ă— 10,000,000 = 1,237,752,850,000,000",
"Verification of 24,755,057 Ă— 7 = 173,285,399",
"Verification of 173,285,399 Ă— 1,000,000 = 173,285,399,000,000",
"Verification of 24,755,057 Ă— 6 = 148,530,342",
"Verification of 148,530,342 ... | <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?
53563670 x 33752847
Think step by step. | 1807926358268490 | What is the solution to the long multiplication equation below?
53563670 x 33752847
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers:
**53563670 Ă— 33752847**
At first glance, both numbers are in the tens of millions, and multiplying them directly seems daunting. I recall that breaking the problem into sm... | What is the solution to the long multiplication equation below?
53563670 x 33752847
Think step by step. | true | The calculated product of 53563670 and 33752847 has been meticulously verified through step-by-step multiplication and addition, which aligns perfectly with the ground truth solution provided. Both the evaluated solution and ground truth match exactly as 1807926358268490. | 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 | 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,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. T... | [
"1,807,926,358,268,490",
"1,807,926,358,268,490",
"1,807,926,358,268,490"
] | <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. T... | 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 does a sub-calculation, doubts or checks it, and re-pe... | [
"Verified addition steps at the end",
"No double-checking of individual multiplications observed",
"Only one explicit verification phase: addition of partial results",
"Equations verified are the stepwise sums of partial products"
] | <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 does a sub-calculation, doubts or checks it, and re-pe... | 1 | <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 me... | [] | <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 me... | |
What is the solution to the long multiplication equation below?
81471995 x 26159399
Think step by step. | 2131258424531005 | What is the solution to the long multiplication equation below?
81471995 x 26159399
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: **81,471,995** and **26,159,399**. At first glance, multiplying these two numbers seems daunting because of their size. However, breaking it down into simpler, more manageab... | What is the solution to the long multiplication equation below?
81471995 x 26159399
Think step by step. | true | The solution provides a detailed explanation of the multiplication process and arrives at the correct answer, which matches the ground truth solution (2131258424531005). The calculations and methodologies employed are accurate and correctly reach the final result. | 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... | 4 | 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 trac... | [
"2131258424531005",
"2131258424531005"
] | <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 trac... | 3 | <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 multiplication by 9 using subtraction from multiple of ten",
"Verification of 5,697 squared via binomial expansion/difference of squares",
"Verification of 6,298 squared via difference of squares"
] | <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... | 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?\n\n82669731 x 57977955\n\nThink ste(...TRUNCATED) | 4793021943780105 | "What is the solution to the long multiplication equation below?\n\n82669731 x 57977955\n\nThink ste(...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) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 5 | 4 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"663668930280105",
"4793021943780105",
"4793023597174725",
"4793023597174725"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 8 | "<thinking>\nLet's step through the reasoning trace to count how many times the model verifies an in(...TRUNCATED) | ["Verification of 82,669,731 × 7 via partial sums","Verification of 82,669,731 × 9 via partial sum(...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\n60460452 x 59942216\n\nThink ste(...TRUNCATED) | 3624133473241632 | "What is the solution to the long multiplication equation below?\n\n60460452 x 59942216\n\nThink ste(...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) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 6 | 3 | "<thinking>\nTo determine how many times the model proposed a final answer, we look for each point i(...TRUNCATED) | [
"3,624,133,473,241,632",
"3,624,133,473,241,632",
"3,624,133,473,241,632"
] | "<thinking>\nTo determine how many times the model proposed a final answer, we look for each point i(...TRUNCATED) | 2 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | [
"60,460,452 Ă— 9 = 544,144,068 = 544,144,068",
"60,460,452 Ă— 2 = 120,920,904 = 120,920,904"
] | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | 2 | "<thinking> \nTo answer your question—how many times does the model verify its higher-level reaso(...TRUNCATED) | [] | "<thinking> \nTo answer your question—how many times does the model verify its higher-level reaso(...TRUNCATED) | |
"What is the solution to the long multiplication equation below?\n\n78270826 x 89167215\n\nThink ste(...TRUNCATED) | 6979191570169590 | "What is the solution to the long multiplication equation below?\n\n78270826 x 89167215\n\nThink ste(...TRUNCATED) | "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **78,270,826** and **(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n78270826 x 89167215\n\nThink ste(...TRUNCATED) | false | "The provided solution includes a lengthy breakdown and calculation process, but ultimately leads to(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 7 | 1 | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | [
"6,979,191,570,169,590",
"6.97919157016959 Ă— 10^{15}"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...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) | 2 | "<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\n58191452 x 19309974\n\nThink ste(...TRUNCATED) | 1123675425142248 | "What is the solution to the long multiplication equation below?\n\n58191452 x 19309974\n\nThink ste(...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) | 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) | [
"1123675425142248",
"1123675425142248",
"1.123675425142248 Ă— 10^{15}"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 0 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | [] | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...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\n91914600 x 47919466\n\nThink ste(...TRUNCATED) | 4404498549603600 | "What is the solution to the long multiplication equation below?\n\n91914600 x 47919466\n\nThink ste(...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) | 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) | [
"3681624000000000",
"3676584000000000",
"4404498549603600",
"4.4044985496036e+15"
] | "<thinking>To determine how many times the model proposed a final answer, we look for each point in (...TRUNCATED) | 1 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | [
"91914600 Ă— 4 = 368,162,400 = 367,658,400"
] | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | 2 | "<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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