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?
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. | Okay, so I need to multiply 97,511,989 by 29,677,209. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts can make the multiplication easier. Maybe using the distributive property, like splitting each number i... | To solve the long multiplication equation \(97,511,989 \times 29,677,209\), we can break down each number into smaller parts and use the distributive property. Here are the key steps:
1. **Break down the numbers:**
- \(97,511,989 = 97,000,000 + 511,989\)
- \(29,677,209 = 29,000,000 + 677,209\)
2. **Use the dist... | What is the solution to the long multiplication equation below?
97511989 x 29677209
Think step by step. | true | The solution provided correctly follows the steps of multiplication using the distributive property, and the final 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 | 4 | 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. Initially, t... | [
"2893883677558701",
"2893883677558701",
"346723558701",
"2893883677558701"
] | 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 ... | [
"Wait, 97,000,000 is 97 million, which is 97 x 10^6, and 29,000,000 is 29 x 10^6. So multiplying them gives (97 x 29) x 10^12. Which is 2,813 x 10^12, so 2,813,000,000,000,000. That seems right.",
"Wait, let me check that again. If 97,000,000 is 97 x 10^6, then multiplying by 677,209 gives (97 x 677,209) x 10^6. ... | null | 7 | 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 method or ap... | [
"\"Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts can make the multiplication easier. Maybe using the distributive property, like splitting each number into parts that are easier to handle. Let me try... | null | [
false,
false,
false,
false,
false,
false
] | [
{
"error_explanation": "There was no error in the previous step's calculation of 97,000,000 x 29,000,000; the multiplication and powers of ten application were correct.",
"next_step": "Wait, 97,000,000 is 97 million, which is 97 x 10^6, and 29,000,000 is 29 x 10^6. So multiplying them gives (97 x 29) x 10^1... | [
true,
true,
false,
true
] | [
{
"correct": true,
"reasoning": "The question asks for the solution to the multiplication of 97511989 by 29677209. The provided solution is 2893883677558701. The ground truth solution given is also 2893883677558701. Since the solution exactly matches the ground truth, and no intermediate calculation errors ... | [
true,
true,
false,
false,
false,
true,
false
] | [
{
"change_in_direction_explanation": "The model shifted from considering a straightforward multiplication approach to deliberately choosing to break down the numbers using the distributive property for easier computation. This is a meaningful change in problem-solving strategy informed by the deliberation.",
... |
"What is the solution to the long multiplication equation below?\n\n39634656 x 65995812\n\nThink ste(...TRUNCATED) | 2615721306060672 | "What is the solution to the long multiplication equation below?\n\n39634656 x 65995812\n\nThink ste(...TRUNCATED) | "Okay, so I need to multiply these two big numbers: 39,634,656 and 65,995,812. Hmm, that's a huge mu(...TRUNCATED) | "To solve the long multiplication equation \\(39,634,656 \\times 65,995,812\\), we can break down th(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n39634656 x 65995812\n\nThink ste(...TRUNCATED) | true | "The solution provided accurately follows the steps for long multiplication using the distributive p(...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) | [
"2615721306060672"
] | null | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, let me check that subtraction again. Maybe I made a mistake here.\"","\"Wait, let me check(...TRUNCATED) | null | 6 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Hmm, that's a huge multiplication problem. Let me think about how to approach this. I remember tha(...TRUNCATED) | null | [
true,
true,
true,
true
] | [{"error_explanation":"The previous step made an arithmetic mistake in large number subtraction duri(...TRUNCATED) | [
true
] | [{"correct":true,"reasoning":"The solution given for the multiplication 39634656 x 65995812 is 26157(...TRUNCATED) | [
true,
true,
true,
false,
true,
true
] | [{"change_in_direction_explanation":"The deliberation recognized the difficulty of the initial appro(...TRUNCATED) |
"What is the solution to the long multiplication equation below?\n\n24755057 x 57601784\n\nThink ste(...TRUNCATED) | 1425935446221688 | "What is the solution to the long multiplication equation below?\n\n24755057 x 57601784\n\nThink ste(...TRUNCATED) | "Okay, so I need to multiply 24,755,057 by 57,601,784. Hmm, that's a pretty big multiplication probl(...TRUNCATED) | "To solve the long multiplication equation \\(24755057 \\times 57601784\\), we can break down each n(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n24755057 x 57601784\n\nThink ste(...TRUNCATED) | true | "The provided solution accurately follows the steps of long multiplication, correctly applying the d(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 2 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"1425935446221688",
"1425935446221688",
"1425935446221688"
] | null | 3 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, hold on. Wait, 24,000,000 is 24 * 1,000,000, and 57,000,000 is 57 * 1,000,000. So multiply(...TRUNCATED) | null | 4 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I rememb(...TRUNCATED) | null | [
false,
true,
false
] | [{"error_explanation":"There was no error in the previous step about setting up the multiplication o(...TRUNCATED) | [
true,
true,
true
] | [{"correct":true,"reasoning":"The solution provided is 1425935446221688. The ground truth solution i(...TRUNCATED) | [
true,
true,
true,
false
] | [{"change_in_direction_explanation":"The deliberation involved deciding to use the distributive prop(...TRUNCATED) |
"What is the solution to the long multiplication equation below?\n\n53563670 x 33752847\n\nThink ste(...TRUNCATED) | 1807926358268490 | "What is the solution to the long multiplication equation below?\n\n53563670 x 33752847\n\nThink ste(...TRUNCATED) | "Okay, so I need to multiply 53,563,670 by 33,752,847. Hmm, that's a pretty big multiplication probl(...TRUNCATED) | "The solution to the long multiplication equation \\(53,\\!563,\\!670 \\times 33,\\!752,\\!847\\) is(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n53563670 x 33752847\n\nThink ste(...TRUNCATED) | true | "The solution provided correctly follows a detailed breakdown of the long multiplication process, ac(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 3 | 2 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"1807926358268490",
"1807926358268490"
] | null | 3 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"But let's compute it accurately. Let's use the standard multiplication method. ... Alternatively(...TRUNCATED) | null | 5 | "To answer your question\u00151how many times does the model verify its higher-level reasoning (i.e.(...TRUNCATED) | ["Hmm, that's a pretty big multiplication problem. Let me think about how to approach this.","Wait, (...TRUNCATED) | null | [
true,
false,
false
] | [{"error_explanation":"The previous step only gave an approximate product for 5.356367 × 3.3752847 (...TRUNCATED) | [
true,
true
] | [{"correct":true,"reasoning":"The problem is to multiply 53,563,670 by 33,752,847. The provided solu(...TRUNCATED) | [
true,
true,
true,
false,
true
] | [{"change_in_direction_explanation":"The deliberation led to a meaningful change by shifting from co(...TRUNCATED) |
"What is the solution to the long multiplication equation below?\n\n81471995 x 26159399\n\nThink ste(...TRUNCATED) | 2131258424531005 | "What is the solution to the long multiplication equation below?\n\n81471995 x 26159399\n\nThink ste(...TRUNCATED) | "Okay, so I need to multiply 81,471,995 by 26,159,399. Hmm, that's a pretty big multiplication probl(...TRUNCATED) | "The solution to the long multiplication equation \\(81471995 \\times 26159399\\) is calculated by b(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n81471995 x 26159399\n\nThink ste(...TRUNCATED) | true | "The original solution accurately follows the long multiplication process and performs the arithmeti(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 4 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"2,131,258,424,531,005",
"2,131,258,424,531,005",
"2,131,258,424,531,005"
] | null | 10 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, 80 million plus 1,471,995? Let me check: 80,000,000 + 1,471,995 = 81,471,995. Yeah, that w(...TRUNCATED) | null | 3 | "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 for large numbers, breaking them down int(...TRUNCATED) | null | [
false,
false,
true,
false,
false,
true,
true,
false,
false,
false
] | [{"error_explanation":"There was no error in the previous step; the original number was correctly sp(...TRUNCATED) | [
true,
true,
true
] | [{"correct":true,"reasoning":"The given solution '2,131,258,424,531,005' matches the ground truth so(...TRUNCATED) | [
true,
false,
true
] | [{"change_in_direction_explanation":"The model initially was going to multiply the numbers directly (...TRUNCATED) |
"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) | "Okay, so I need to multiply these two big numbers: 82,669,731 and 57,977,955. Hmm, that's a pretty (...TRUNCATED) | "To solve the long multiplication equation \\(82669731 \\times 57977955\\), we can break down the mu(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n82669731 x 57977955\n\nThink ste(...TRUNCATED) | false | "The solution provided for the multiplication of 82669731 by 57977955 is incorrect as it yields a fi(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 5 | 1 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"4845103874310105"
] | null | 15 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, 3 x 27,556,577 = 82,669,731? Let me check: 27,556,577 x 3. 7x3=21, carryover 2... So that (...TRUNCATED) | null | 12 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Hmm, that's a pretty hefty multiplication. Let me think about how to approach this.","I remember t(...TRUNCATED) | null | [
false,
true,
false,
false,
true,
true,
true,
false,
false,
false,
false,
true,
false,
false,
false
] | [{"error_explanation":"There was no error in the previous partial division step; the quotient 27,556(...TRUNCATED) | [
false
] | [{"correct":false,"reasoning":"The provided solution is 4845103874310105, whereas the ground truth s(...TRUNCATED) | [
true,
true,
true,
true,
false,
true,
true,
false,
true,
true,
false,
true
] | [{"change_in_direction_explanation":"The deliberation prompted the model to step back and consider d(...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) | "Okay, so I need to multiply 60,460,452 by 59,942,216. Hmm, that's a pretty big multiplication probl(...TRUNCATED) | "To solve the long multiplication equation \\(60460452 \\times 59942216\\), we can break down the nu(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n60460452 x 59942216\n\nThink ste(...TRUNCATED) | true | "The calculated result of the long multiplication of 60460452 and 59942216 as described matches the (...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 6 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"3624133473241632",
"3624133473241632",
"3624133473241632"
] | null | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, is that right? Let me check. 60,000,000 is 6×10^7 and 59,000,000 is 5.9×10^7. Multiplyin(...TRUNCATED) | null | 3 | "To answer your question\u00151 how many times does the model verify its higher-level reasoning (i.e(...TRUNCATED) | ["Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I rememb(...TRUNCATED) | null | [
false,
false,
false,
false
] | [{"error_explanation":"There was no error in the previous step as the multiplication was correctly c(...TRUNCATED) | [
true,
true,
true
] | [{"correct":true,"reasoning":"The solution provided is 3624133473241632. The ground truth solution i(...TRUNCATED) | [
true,
false,
true
] | [{"change_in_direction_explanation":"The deliberation explicitly considers the alternative approach (...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) | "Okay, so I need to multiply 78,270,826 by 89,167,215. Hmm, that's a pretty big multiplication probl(...TRUNCATED) | "The solution to the long multiplication equation \\(78,\\!270,\\!826 \\times 89,\\!167,\\!215\\) is(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n78270826 x 89167215\n\nThink ste(...TRUNCATED) | true | "The solution provided correctly follows the steps of long multiplication using the distributive pro(...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 7 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"6979191570169590",
"6942000000000000",
"6979101000000000"
] | null | 4 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["\"Wait, let me check that again. 78,000,000 is 7.8 x 10^7, and 89,000,000 is 8.9 x 10^7. Multiplyi(...TRUNCATED) | null | 7 | "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 for large numbers, breaking them down int(...TRUNCATED) | null | [
false,
false,
false,
false
] | [{"error_explanation":"There was no error in the previous step; the calculation of 78,000,000 * 89,0(...TRUNCATED) | [
true,
false,
false
] | [{"correct":true,"reasoning":"The solution provided for the long multiplication 78270826 multiplied (...TRUNCATED) | [
true,
false,
false,
true,
true,
true,
true
] | [{"change_in_direction_explanation":"The deliberation explicitly shifts from a straightforward full (...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) | "Okay, so I need to multiply 58,191,452 by 19,309,974. Hmm, that's a pretty big multiplication probl(...TRUNCATED) | "To solve the long multiplication equation \\(58,191,452 \\times 19,309,974\\), we can use the Karat(...TRUNCATED) | "What is the solution to the long multiplication equation below?\n\n58191452 x 19309974\n\nThink ste(...TRUNCATED) | true | "The solution correctly applies the Karatsuba algorithm and correctly calculates the final product, (...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 8 | 4 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"1123675425142248",
"1123675425142248",
"1123675425142248",
"1123675425142248"
] | null | 9 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["Wait, let me check that addition: 58,191,452 x 9,000,000...","Let me verify the addition 1,123,618(...TRUNCATED) | null | 7 | "To answer your question\u00151 how many times does the model verify its higher-level reasoning (i.e(...TRUNCATED) | ["\"Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I reme(...TRUNCATED) | null | [
true,
false,
false,
true,
false,
true,
true,
true,
false
] | [{"error_explanation":"The previous step did not include the actual computed value of 58,191,452 mul(...TRUNCATED) | [
true,
true,
true,
true
] | [{"correct":true,"reasoning":"The solution provided is 1123675425142248 for the multiplication of 58(...TRUNCATED) | [
true,
true,
true,
true,
true,
true,
false
] | [{"change_in_direction_explanation":"The deliberation confirmed and explicitly adopted the distribut(...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) | "Okay, so I need to multiply 91,914,600 by 47,919,466. Hmm, that's a pretty big multiplication probl(...TRUNCATED) | "To solve the long multiplication equation \\(91,914,600 \\times 47,919,466\\), we can break down th(...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 accurately calculates each individual (...TRUNCATED) | answer_verification | "How many times does the following reasoning trace propose a final answer then verify it or double c(...TRUNCATED) | 9 | 3 | "To determine how many times the model proposed a final answer, we look for each point in the reason(...TRUNCATED) | [
"4404498549603600",
"4404498549603600",
"4404498549603600"
] | null | 5 | "Let's step through the reasoning trace to count how many times the model verifies an intermediate c(...TRUNCATED) | ["9.19146 * 4.7919466 ... Adding those: 0.47919466 + 0.431275194 = 0.910469854 + 0.0069972 ≈ 0.917(...TRUNCATED) | null | 6 | "To answer your question—how many times does the model verify its higher-level reasoning (i.e., de(...TRUNCATED) | ["Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I rememb(...TRUNCATED) | null | [
false,
true,
false,
false,
false
] | [{"error_explanation":"There is no error in the previous step's partial multiplication; the arithmet(...TRUNCATED) | [
true,
true,
true
] | [{"correct":true,"reasoning":"The solution provided is 4404498549603600. The ground truth solution i(...TRUNCATED) | [
true,
true,
false,
true,
true,
true
] | [{"change_in_direction_explanation":"The deliberation explicitly considered multiple approaches: dis(...TRUNCATED) |
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