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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 |
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. | Okay, so I need to multiply these two big numbers: 39,634,656 and 65,995,812. Hmm, that's a huge multiplication problem. Let me think about how to approach this. I remember that multiplying large numbers can be done by breaking them down into smaller parts, maybe using the distributive property. But doing this manually... | To solve the long multiplication equation \(39,634,656 \times 65,995,812\), we can break down the problem using the distributive property and verify the result through multiple methods.
1. **Approximation and Adjustment**:
- Recognize that \(65,995,812\) is close to \(66,000,000\).
- Express \(65,995,812\) as \... | What is the solution to the long multiplication equation below?
39634656 x 65995812
Think step by step. | true | The solution provided accurately follows the steps for long multiplication using the distributive property, and the final result matches the ground truth solution exactly. | 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 | 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 trace inv... | [
"2615721306060672"
] | null | 4 | 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, let me check that subtraction again. Maybe I made a mistake here.\"",
"\"Wait, let me check with smaller numbers to see if the method works.\"",
"\"Alternatively, use logarithms to estimate the product... So the result seems reasonable.\"",
"\"Let me write both numbers in terms of their digits to per... | null | 6 | 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 ... | [
"Hmm, that's a huge multiplication problem. Let me think about how to approach this. I remember that multiplying large numbers can be done by breaking them down into smaller parts, maybe using the distributive property. But doing this manually would take a lot of steps and there's a high chance of making a mistake.... | null |
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. | Okay, so I need to multiply 24,755,057 by 57,601,784. 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 might help. Maybe using the distributive property? Like, split each number into parts that are easier t... | To solve the long multiplication equation \(24755057 \times 57601784\), we can break down each number into smaller parts and use the distributive property \((a + b)(c + d) = ac + ad + bc + bd\).
1. **Split the numbers:**
- \(24755057 = 24000000 + 755057\)
- \(57601784 = 57000000 + 601784\)
2. **Compute each par... | What is the solution to the long multiplication equation below?
24755057 x 57601784
Think step by step. | true | The provided solution accurately follows the steps of long multiplication, correctly applying the distributive property to break down the numbers into manageable parts. Each calculation of the constituent parts is correct, leading to an accurate final sum that 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... | 2 | 3 | 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 trace start... | [
"1425935446221688",
"1425935446221688",
"1425935446221688"
] | null | 3 | 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, hold on. Wait, 24,000,000 is 24 * 1,000,000, and 57,000,000 is 57 * 1,000,000. So multiplying them gives (24 * 57) * (1,000,000 * 1,000,000) = 1368 * 1,000,000,000,000. So that's 1,368,000,000,000,000. Wait, let me check that again... So ac = 1,368,000,000,000,000.\"",
"\"Wait, let's compute 755,057 * 1,... | null | 4 | 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 might help. Maybe using the distributive property? Like, split each number into parts that are easier to multiply and then add them up. Let me try that.... | null |
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. | Okay, so I need to multiply 53,563,670 by 33,752,847. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that multiplying large numbers can be done by breaking them down into smaller parts, maybe using the distributive property. Let me recall: when you have two numbers,... | The solution to the long multiplication equation \(53,\!563,\!670 \times 33,\!752,\!847\) is calculated by breaking down the numbers into manageable parts, using distributive properties, and verifying through multiple methods. Here's the step-by-step breakdown:
1. **Breakdown and Multiplication**:
- Split \(53,\!56... | What is the solution to the long multiplication equation below?
53563670 x 33752847
Think step by step. | true | The solution provided correctly follows a detailed breakdown of the long multiplication process, accurately computes each component, sums them correctly, and confirms the result through multiple methods. The final computed 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... | 3 | 2 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. The model fi... | [
"1807926358268490",
"1807926358268490"
] | null | 3 | 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.
The trace begins by planning large number multiplication and explores scientific notation and splitting numbers into parts.... | [
"\"But let's compute it accurately. Let's use the standard multiplication method. ... Alternatively, use the standard algorithm for decimal multiplication.\" (The model tries multiple approaches to compute 5.356367 × 3.3752847 precisely.)",
"\"63,670 × 52,847. Let's compute this: ... Adding these: 5,356,367,000 +... | null | 5 | To answer your question1how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)1 we need to identify all moments in the reasoning trace where:
- The model questions its current method ... | [
"Hmm, that's a pretty big multiplication problem. Let me think about how to approach this.",
"Wait, but 3,563,670 is still a big number. Maybe breaking them into more parts? Let me see. Alternatively, perhaps using scientific notation? That might help with the exponents.",
"Hmm, this is going to be tedious. May... | null |
"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 |
"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 |
"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 |
"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 |
"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 |
"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 |
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