diff --git a/docs/model-encyclopedia/benchmarks/2026-05-11T17-10-53-211043_llm_reasoning_ministral-14b-reasoning.json b/docs/model-encyclopedia/benchmarks/2026-05-11T17-10-53-211043_llm_reasoning_ministral-14b-reasoning.json new file mode 100644 index 0000000..32db5d6 --- /dev/null +++ b/docs/model-encyclopedia/benchmarks/2026-05-11T17-10-53-211043_llm_reasoning_ministral-14b-reasoning.json @@ -0,0 +1,1589 @@ +{ + "model_id": "ministral-14b-reasoning", + "suite_name": "llm_reasoning", + "timestamp": "2026-05-11T17:10:53.211043+00:00", + "samples": 98, + "overall_accuracy": 0.5918367346938775, + "per_gate_accuracy": { + "gsm8k": 0.86, + "mmlu_pro:math": 0.25, + "mmlu_pro:physics": 0.5, + "mmlu_pro:law": 0.16666666666666666, + "mmlu_pro:philosophy": 0.3333333333333333 + }, + "avg_inference_time_s": 34.82062127455096, + "sample_results": [ + { + "sample_id": "gsm8k-0", + "predictions": { + "gsm8k": "18" + }, + "ground_truth": { + "gsm8k": "18" + }, + "correct": 1, + "total": 1, + "inference_time_s": 5.349177418000181, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, Janet's ducks lay 16 eggs per day. That's the total number of eggs she starts with each day.\n\nNext, she eats three eggs for breakfast every morning. So, she uses 3 eggs for herself.\n\nThen, she bakes muffins for her friends every day with four eggs. So, she uses another 4 eggs for baking muffins.\n\nNow, we need to find out how many eggs are left after she uses some for herself and for baking muffins. That would be the remainder that she sells at the farmers' market.\n\nLet's calculate the total number of eggs used:\n- Eggs eaten for breakfast: 3\n- Eggs used for baking muffins: 4\nTotal eggs used = 3 + 4 = 7 eggs\n\nNow, subtract the total eggs used from the total eggs laid to find the remainder:\nTotal eggs laid = 16\nTotal eggs used = 7\nRemainder = 16 - 7 = 9 eggs\n\nShe sells the remainder at the farmers' market for $2 per egg. So, the amount she makes is:\n9 eggs * $2 per egg = $18\n\nLet me double-check this to make sure I didn't make any mistakes" + } + }, + { + "sample_id": "gsm8k-1", + "predictions": { + "gsm8k": "3" + }, + "ground_truth": { + "gsm8k": "3" + }, + "correct": 1, + "total": 1, + "inference_time_s": 6.839234463001048, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem about a robe made from blue and white fiber. Let me break it down step by step.\n\nFirst, the problem says: \"A robe takes 2 bolts of blue fiber and half that much white fiber.\" So, I need to find out how many bolts of blue and white fiber are used in total for one robe.\n\nLet's start with the blue fiber. It says it takes 2 bolts of blue fiber. That part is straightforward.\n\nNow, the tricky part is the white fiber. It says it takes \"half that much white fiber.\" The phrase \"that much\" refers to the amount of blue fiber, which is 2 bolts. So, half of 2 bolts is 1 bolt of white fiber.\n\nNow, to find the total number of bolts, I need to add the blue and white fiber together. That would be 2 bolts (blue) + 1 bolt (white) = 3 bolts in total.\n\nLet me double-check to make sure I didn't miss anything. The problem is about the total bolts used for one robe. It mentions blue fiber first, which is 2 bolts, and then white fiber, which is half of the blue fiber, so 1 bo" + } + }, + { + "sample_id": "gsm8k-2", + "predictions": { + "gsm8k": "0" + }, + "ground_truth": { + "gsm8k": "70000" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.35667665599976, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem about Josh flipping a house. Let me break it down step by step.\n\nFirst, let's understand what's given:\n1. Josh buys a house for $80,000.\n2. He spends $50,000 on repairs.\n3. The repairs increase the value of the house by 150%.\n\nI need to find out how much profit he made.\n\nFirst, I need to understand what \"increased the value of the house by 150%\" means. Does it mean the value increased by 150% of the original value, or 150% of the value after repairs? I think it's the former, i.e., the value increased by 150% of the original value before repairs.\n\nBut, I'm not sure. Let me think about it. If the value increased by 150%, it means the new value is the original value plus 150% of the original value. That would be 250% of the original value, because 100% + 150% = 250%.\n\nBut, the repairs cost is $50,000, and it's not clear if this is included in the increased value or not. I think the increased value is the difference between the new value and the original " + } + }, + { + "sample_id": "gsm8k-3", + "predictions": { + "gsm8k": "540" + }, + "ground_truth": { + "gsm8k": "540" + }, + "correct": 1, + "total": 1, + "inference_time_s": 11.144161436001013, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down. James is running 3 sprints, 3 times a week. Each sprint is 60 meters. I need to find out how many total meters he runs in a week.\n\nFirst, I need to figure out how many sprints he does in total per week. He runs 3 sprints, 3 times a week. So, that's 3 sprints per session, and he does this 3 times a week. To find the total number of sprints in a week, I multiply the number of sprints per session by the number of sessions per week: 3 sprints/session * 3 sessions/week = 9 sprints/week.\n\nNext, each sprint is 60 meters. So, to find the total distance, I multiply the total number of sprints by the distance per sprint: 9 sprints * 60 meters/sprint = 540 meters.\n\nLet me double-check that. If he runs 3 sprints (each 60 meters) once, that's 3 * 60 = 180 meters. He does this 3 times a week, so 180 meters * 3 = 540 meters. That matches my previous calculation. So, the total distance he runs in a week is 540 meters.\n\nNow, the problem asks for the answer to be a single in" + } + }, + { + "sample_id": "gsm8k-4", + "predictions": { + "gsm8k": "1" + }, + "ground_truth": { + "gsm8k": "20" + }, + "correct": 0, + "total": 1, + "inference_time_s": 66.04351693500212, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, the problem says that Wendi feeds each chicken 3 cups of mixed chicken feed per day, divided into three separate meals. So, per chicken, the total daily feed is 3 cups.\n\nNow, the problem gives us information about the feed given in the morning and afternoon, and asks for the feed needed in the final meal of the day, given that the flock size is 20 chickens.\n\nLet's start by calculating the total daily feed required for all chickens. Since each chicken gets 3 cups per day, and there are 20 chickens, the total daily feed is:\nTotal daily feed = 3 cups/chicken * 20 chickens = 60 cups.\n\nNow, we know that in the morning, she gives 15 cups, and in the afternoon, she gives 25 cups. The question is asking for the amount of feed needed in the final meal of the day.\n\nLet's denote the feed in the final meal as F. So, the total daily feed is the sum of the morning, afternoon, and final meal feeds:\nTotal daily feed = Morning feed + Afternoon feed + Fi" + } + }, + { + "sample_id": "gsm8k-5", + "predictions": { + "gsm8k": "64" + }, + "ground_truth": { + "gsm8k": "64" + }, + "correct": 1, + "total": 1, + "inference_time_s": 52.150508167000226, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem about Kylar buying glasses. Let me break it down step by step.\n\nFirst, the problem says that one glass costs $5, but every second glass costs only 60% of the price. Kylar wants to buy 16 glasses. I need to calculate the total cost for 16 glasses under this pricing scheme.\n\nLet me understand the pricing:\n- The first glass costs $5.\n- The second glass costs 60% of $5, which is 0.6 * 5 = $3.\n- The third glass would then cost $5 again, since it's the first in a new pair (odd-numbered glass).\n- The fourth glass would cost $3, since it's the second in the pair (even-numbered glass).\n- And so on, alternating between $5 and $3 for each pair of glasses.\n\nSo, the pattern is: $5, $3, $5, $3, ..., up to 16 glasses.\n\nNow, since the pattern repeats every two glasses, I can think of this in terms of pairs of glasses. For every two glasses, the cost is $5 + $3 = $8.\n\nKylar wants to buy 16 glasses. How many such pairs are there in 16 glasses?\n\nWell, 16 divided by 2 is" + } + }, + { + "sample_id": "gsm8k-6", + "predictions": { + "gsm8k": "260" + }, + "ground_truth": { + "gsm8k": "260" + }, + "correct": 1, + "total": 1, + "inference_time_s": 30.08266057899891, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem step by step. Let's break it down.\n\nFirst, the problem states that Seattle has 20 sheep. That's our starting point.\n\nNext, it says Charleston has 4 times as many sheep as Seattle. So, if Seattle has 20 sheep, then Charleston would have 4 times that number. Let me calculate that:\nCharleston's sheep = 4 * Seattle's sheep = 4 * 20 = 80 sheep.\n\nNow, the problem also mentions that Toulouse has twice as many sheep as Charleston. We already found out that Charleston has 80 sheep, so Toulouse would have twice that amount:\nToulouse's sheep = 2 * Charleston's sheep = 2 * 80 = 160 sheep.\n\nNow, the question asks for the total number of sheep that Toulouse, Charleston, and Seattle have together. So, we need to add up the sheep from all three cities:\nTotal sheep = Toulouse's sheep + Charleston's sheep + Seattle's sheep = 160 + 80 + 20.\n\nLet me do the addition:\n160 + 80 = 240\n240 + 20 = 260.\n\nSo, the total number of sheep is 260.\n\nBut wait, I need to double-check my" + } + }, + { + "sample_id": "gsm8k-7", + "predictions": { + "gsm8k": "120" + }, + "ground_truth": { + "gsm8k": "160" + }, + "correct": 0, + "total": 1, + "inference_time_s": 56.742353522000485, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem about Carla downloading a file with interruptions. Let me break it down step by step.\n\nFirst, the total size of the file is 200 GB. Normally, Carla downloads at a rate of 2 GB per minute. But there's a catch: 40% of the way through the download, Windows forces a restart that takes 20 minutes, and then she has to restart the download from the beginning.\n\nLet's calculate how much data she downloads before the restart is forced.\n\n40% of 200 GB is 0.40 * 200 = 80 GB. So, she downloads 80 GB before the restart happens.\n\nNow, her download speed is 2 GB per minute. So, the time it takes to download 80 GB is 80 GB / 2 GB per minute = 40 minutes.\n\nBut then, Windows forces a restart that takes 20 minutes. After the restart, she has to start the download from the beginning again. So, she's already downloaded 80 GB, but now she has to download the entire 200 GB again from the start.\n\nWait, that doesn't make sense. If she has to restart from the beginning, does th" + } + }, + { + "sample_id": "gsm8k-8", + "predictions": { + "gsm8k": "45" + }, + "ground_truth": { + "gsm8k": "45" + }, + "correct": 1, + "total": 1, + "inference_time_s": 16.047565737000696, + "error": null, + "extra": { + "raw_response": "Okay, let's break this problem down step by step. First, I need to understand what's happening in each part of John's journey.\n\nFirst part: John drives for 3 hours at 60 mph. So, the distance he covers in this part is speed multiplied by time, which is 60 mph * 3 hours = 180 miles. So, he's 180 miles away from home after the first part.\n\nBut then he turns around because he forgot something. So, he's now driving back home. The problem says he tries to get home in 4 hours, but there are some delays and changes in speed during this 4-hour period.\n\nLet's look at the second part: He spends the first 2 hours in standstill traffic. That means he's not moving during these 2 hours. So, in the first 2 hours of the 4-hour period, he doesn't cover any distance.\n\nNext, he spends the next half-hour (which is 0.5 hours) driving at 30 mph. So, the distance covered in this part is 30 mph * 0.5 hours = 15 miles.\n\nThen, he has the remaining time of the 4 hours to drive at 80 mph. Let's calculate the rema" + } + }, + { + "sample_id": "gsm8k-9", + "predictions": { + "gsm8k": "460" + }, + "ground_truth": { + "gsm8k": "460" + }, + "correct": 1, + "total": 1, + "inference_time_s": 8.191478197000833, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, I need to understand the problem. Eliza has a regular hourly rate of $10 for the first 40 hours she works. For any hours worked beyond 40, she gets overtime pay, which is 1.2 times her regular rate. This week, she worked 45 hours. I need to calculate her total earnings for this week.\n\nSo, the first part is straightforward: for the first 40 hours, she earns $10 per hour. That's her regular pay.\n\nThen, for the overtime hours, which would be any hours over 40. Since she worked 45 hours, the overtime hours are 45 - 40 = 5 hours.\n\nHer overtime rate is 1.2 times her regular rate. So, her regular rate is $10, so overtime rate is 1.2 * $10 = $12 per hour.\n\nNow, let's calculate her regular pay: 40 hours * $10/hour = $400.\n\nThen, her overtime pay: 5 hours * $12/hour = $60.\n\nTotal earnings would be regular pay plus overtime pay: $400 + $60 = $460.\n\nLet me double-check that.\n\nRegular hours: 40 hours at $10/hour = $400.\n\nOvertime hours: 5 hours at $" + } + }, + { + "sample_id": "gsm8k-10", + "predictions": { + "gsm8k": "366" + }, + "ground_truth": { + "gsm8k": "366" + }, + "correct": 1, + "total": 1, + "inference_time_s": 6.259860119000223, + "error": null, + "extra": { + "raw_response": "Okay, let's break this problem down step by step.\n\nFirst, the problem states that the program had 60 downloads in the first month. That's straightforward.\n\nNext, it says the number of downloads in the second month was three times as many as the first month. So, for the second month, we need to calculate 3 times the first month's downloads. That would be 3 * 60. Let me do that calculation: 3 * 60 = 180. So, 180 downloads in the second month.\n\nNow, the third month is a bit more complex. It says the downloads reduced by 30% compared to the second month. So, we need to find 30% of the second month's downloads and subtract that from the second month's total to get the third month's downloads.\n\nFirst, calculate 30% of 180. 30% is the same as 0.3 in decimal form. So, 0.3 * 180 = 54. Now, subtract that from the second month's downloads: 180 - 54 = 126. So, 126 downloads in the third month.\n\nNow, to find the total downloads over the three months, we add the downloads from each month together: f" + } + }, + { + "sample_id": "gsm8k-11", + "predictions": { + "gsm8k": "694" + }, + "ground_truth": { + "gsm8k": "694" + }, + "correct": 1, + "total": 1, + "inference_time_s": 15.893421022999974, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem about Toula's bakery purchases. Let me break it down step by step.\n\nFirst, I need to understand what's being asked. Toula bought three types of pastries: donuts, mini cupcakes, and mini cheesecakes. The problem gives quantities in dozens and prices per dozen for each type. The goal is to find the total cost.\n\nLet's list out the information:\n\n1. Donuts:\n - Quantity: 3 dozen\n - Cost per dozen: $68\n\n2. Mini cupcakes:\n - Quantity: 2 dozen\n - Cost per dozen: $80\n\n3. Mini cheesecakes:\n - Quantity: 6 dozen\n - Cost per dozen: $55\n\nI need to calculate the cost for each type separately and then add them up to get the total cost.\n\n**Step 1: Calculate the cost of donuts.**\n- Quantity: 3 dozen\n- Cost per dozen: $68\n- So, cost of donuts = 3 * $68\n\nLet me calculate that:\n3 * 68 = 3 * 70 - 3 * 2 = 210 - 6 = 204\nSo, the cost of donuts is $204.\n\n**Step 2: Calculate the cost of mini cupcakes.**\n- Quantity: 2 dozen\n- Cost per dozen: $80\n- So, cost of mini cup" + } + }, + { + "sample_id": "gsm8k-12", + "predictions": { + "gsm8k": "1" + }, + "ground_truth": { + "gsm8k": "13" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.1376494569995, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out how many years it will take for Carlos to start earning money from his lemon tree. Let's break this down step by step.\n\nFirst, let's understand the costs and earnings involved:\n\n1. **Initial Cost**: The tree costs $90 to plant. This is a one-time cost.\n2. **Annual Growth**: Each year, the tree grows 7 lemons.\n3. **Selling Price**: Each lemon sells for $1.5.\n4. **Annual Maintenance Cost**: It costs $3 per year to water and feed the tree.\n\nFirst, I need to calculate the annual net income from the lemon tree after accounting for the maintenance cost.\n\n**Annual Revenue from Lemons**:\n- Number of lemons per year: 7\n- Price per lemon: $1.5\n- Total revenue per year: 7 * $1.5 = $10.5\n\n**Annual Cost**:\n- Maintenance cost per year: $3\n\n**Annual Net Income**:\n- Net income per year = Total revenue - Annual cost\n- Net income per year = $10.5 - $3 = $7.5\n\nNow, the initial cost is $90. We need to find out after how many years the cumulative net income will cover the initial" + } + }, + { + "sample_id": "gsm8k-13", + "predictions": { + "gsm8k": "18" + }, + "ground_truth": { + "gsm8k": "18" + }, + "correct": 1, + "total": 1, + "inference_time_s": 23.572274058002222, + "error": null, + "extra": { + "raw_response": "Okay, let's try to figure out this problem step by step. So, Melanie is a saleswoman who starts with some number of vacuum cleaners. Let's call that number \\( x \\). The problem says she sold a third of her vacuum cleaners at the green house, then 2 more to the red house, and then half of what was left at the orange house. After all that, she has 5 left. We need to find out how many she started with, so we need to solve for \\( x \\).\n\nFirst, let's break down the problem:\n\n1. She starts with \\( x \\) vacuum cleaners.\n2. She sells a third of them at the green house. So, she sells \\( \\frac{x}{3} \\) vacuum cleaners there. That means she has \\( x - \\frac{x}{3} = \\frac{2x}{3} \\) left after the green house.\n3. Then, she sells 2 more to the red house. So, she subtracts 2 from what she had left, which is \\( \\frac{2x}{3} - 2 \\).\n4. Next, she sells half of what was left at the orange house. So, she sells half of \\( \\frac{2x}{3} - 2 \\), which is \\( \\frac{1}{2} \\left( \\frac{2x}{3} - 2 \\right) \\). Afte" + } + }, + { + "sample_id": "gsm8k-14", + "predictions": { + "gsm8k": "60" + }, + "ground_truth": { + "gsm8k": "60" + }, + "correct": 1, + "total": 1, + "inference_time_s": 14.463132394997956, + "error": null, + "extra": { + "raw_response": "Okay, let's tackle this problem step by step. I need to find out what percentage of the entire class is enrolled in hip-hop dance. The problem gives me some percentages and I need to break it down carefully.\n\nFirst, the total number of students is 20. But since we're dealing with percentages, the actual number might not be necessary if I can work with percentages directly. Let's see.\n\nThe problem says 20% enrolled in contemporary dance. So, 20% of the total students are in contemporary dance. That means 80% are remaining students who didn't choose contemporary dance. Let me write that down:\n\n- Contemporary dance: 20% of total students\n- Remaining students: 100% - 20% = 80%\n\nNext, it says 25% of the remaining students enrolled in jazz dance. So, 25% of the 80% remaining students are in jazz dance. Let's calculate that:\n\nJazz dance: 25% of 80% = 0.25 * 80% = 20%\n\nNow, the rest of the students enrolled in hip-hop dance. The \"rest\" here would be the remaining students after contemporary an" + } + }, + { + "sample_id": "gsm8k-15", + "predictions": { + "gsm8k": "125" + }, + "ground_truth": { + "gsm8k": "125" + }, + "correct": 1, + "total": 1, + "inference_time_s": 52.98705040599816, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem where a merchant has to choose between buying jewelry worth $5,000 or electronic gadgets worth $8,000. The goal is to maximize profit at the end of the month, considering the expected market growth rates for each item.\n\nFirst, let's understand the problem:\n- There are two options:\n 1. Jewelry: initial cost is $5,000, expected to increase by 2.5% in a month.\n 2. Electronic gadgets: initial cost is $8,000, expected to increase by 1.2% in a month.\n\nThe merchant wants to maximize profit at the end of the month. So, I need to calculate the final value of each option after one month and then see which one gives a higher profit.\n\nBut wait, the problem says \"how much profit would this be?\" So, it's asking for the profit amount, not which option to choose. But to find the profit, I need to know the initial investment and the final value.\n\nBut the problem doesn't specify if the merchant is buying the items at their current price or if the prices given are the" + } + }, + { + "sample_id": "gsm8k-16", + "predictions": { + "gsm8k": "230" + }, + "ground_truth": { + "gsm8k": "230" + }, + "correct": 1, + "total": 1, + "inference_time_s": 53.39978736299963, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down. The problem says two trains leave San Rafael at the same time. They both travel westward for 80 miles on the first day. Then, the next day, they travel northwards for 150 miles. We need to find the total distance covered by each train over the two days.\n\nFirst, I need to understand the directions. Westward and northward are perpendicular to each other. So, the first day they go west, and the second day they go north. The question is asking for the total distance covered, not the displacement or the straight-line distance from the starting point.\n\nDistance covered is the sum of all the distances traveled, regardless of direction. So, on the first day, each train travels 80 miles westward. On the second day, each travels 150 miles northward. So, the total distance for each train would be the sum of these two distances.\n\nLet me calculate that: 80 miles (west) + 150 miles (north) = 230 miles.\n\nWait, the problem says \"the distance covered by each train in the tw" + } + }, + { + "sample_id": "gsm8k-17", + "predictions": { + "gsm8k": "57500" + }, + "ground_truth": { + "gsm8k": "57500" + }, + "correct": 1, + "total": 1, + "inference_time_s": 10.527626112001599, + "error": null, + "extra": { + "raw_response": "Okay, I need to calculate Jill's annual salary based on her hourly wages for teaching and cheerleading coaching, along with her weekly hours and the number of weeks she works in a year.\n\nFirst, let's break down the problem:\n\n1. **Hourly Wages:**\n - Teaching: $20 per hour\n - Cheerleading coaching: $30 per hour\n\n2. **Weekly Hours:**\n - Teaching: 35 hours per week\n - Cheerleading coaching: 15 hours per week\n\n3. **Annual Weeks:**\n - She works 50 weeks a year.\n\nNow, I need to calculate her weekly earnings from both jobs and then multiply by the number of weeks she works in a year to get her annual salary.\n\n**Step 1: Calculate Weekly Earnings from Teaching**\n- Teaching hours per week: 35 hours\n- Teaching wage per hour: $20\n- Weekly earnings from teaching = 35 hours * $20/hour = $700\n\n**Step 2: Calculate Weekly Earnings from Cheerleading Coaching**\n- Cheerleading coaching hours per week: 15 hours\n- Cheerleading coaching wage per hour: $30\n- Weekly earnings from coaching = 15 hours *" + } + }, + { + "sample_id": "gsm8k-18", + "predictions": { + "gsm8k": "7" + }, + "ground_truth": { + "gsm8k": "7" + }, + "correct": 1, + "total": 1, + "inference_time_s": 9.166824435000308, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem step by step. The problem is about Claire making a 3-egg omelet every morning for breakfast and I need to find out how many dozens of eggs she will eat in 4 weeks.\n\nFirst, I need to break this down into smaller, more manageable parts.\n\n1. **Understand the time frame**: The problem mentions 4 weeks. I know that a week has 7 days, so 4 weeks would be 4 * 7 = 28 days.\n\n2. **Daily egg consumption**: Claire makes a 3-egg omelet every morning. So, she uses 3 eggs per day.\n\n3. **Total eggs in 4 weeks**: To find out how many eggs she uses in 4 weeks, I need to multiply the number of days by the number of eggs per day. That would be 28 days * 3 eggs/day = 84 eggs.\n\n4. **Convert eggs to dozens**: The problem asks for the number of dozens of eggs. I know that 1 dozen equals 12 eggs. So, to find out how many dozens are in 84 eggs, I divide 84 by 12. That would be 84 / 12 = 7 dozens.\n\nLet me double-check my calculations to make sure I didn't make any mistakes.\n\n- " + } + }, + { + "sample_id": "gsm8k-19", + "predictions": { + "gsm8k": "1" + }, + "ground_truth": { + "gsm8k": "6" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.014877460002026, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, let's understand what's given:\n- Total distance of the trail: 12 miles.\n- Marissa has already walked 4 miles in 1 hour and then another 2 miles in another hour. So, she's walked 4 + 2 = 6 miles in 1 + 1 = 2 hours.\n- The remaining distance is 12 - 6 = 6 miles.\n- She wants her average speed for the entire 12-mile trail to be 4 miles per hour.\n\nAverage speed is calculated as total distance divided by total time. So, if her average speed is to be 4 mph, then the total time she can take for the entire 12 miles is 12 miles / 4 mph = 3 hours.\n\nShe's already taken 2 hours to walk the first 6 miles. So, the time she has left to walk the remaining 6 miles is 3 hours (total time) - 2 hours (time already taken) = 1 hour.\n\nWait, but if she walks the remaining 6 miles in 1 hour, her speed would be 6 miles / 1 hour = 6 mph. But let's double-check this because it seems a bit counterintuitive that she needs to walk faster than her initial speeds to achi" + } + }, + { + "sample_id": "gsm8k-20", + "predictions": { + "gsm8k": "15" + }, + "ground_truth": { + "gsm8k": "15" + }, + "correct": 1, + "total": 1, + "inference_time_s": 54.950030497002444, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem step by step. Let's break it down.\n\nFirst, I have 10 liters of orange drink that is two-thirds water. I need to find out how much water is in the orange drink initially.\n\nSo, the amount of water in the orange drink is (2/3) * 10 liters. Let me calculate that:\n(2/3) * 10 = 20/3 \u2248 6.666... liters of water.\n\nBut I spill one liter of the orange drink. The problem is, when I spill one liter, I don't know if it's proportional or not. But since the drink is homogeneous, the spilled liter should have the same proportion of water as the rest. So, the spilled liter would have (2/3) * 1 liter of water, which is 2/3 liters of water.\n\nSo, the remaining orange drink is 10 liters - 1 liter = 9 liters. But I need to find out how much water is in these 9 liters.\n\nThe initial water in orange drink was 20/3 liters. If I spill 2/3 liters of water, then the remaining water in the orange drink is 20/3 - 2/3 = 18/3 = 6 liters.\n\nWait, let me double-check that. The total oran" + } + }, + { + "sample_id": "gsm8k-21", + "predictions": { + "gsm8k": "14" + }, + "ground_truth": { + "gsm8k": "14" + }, + "correct": 1, + "total": 1, + "inference_time_s": 18.491663471999345, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, we know that Samantha is currently 31 years old. Raymond is her cousin and was born 6 years before her. So, Raymond's current age would be Samantha's age plus 6 years. That means Raymond is 31 + 6 = 37 years old now.\n\nNext, the problem states that Raymond had a son at the age of 23. That means when Raymond was 23 years old, his son was born. Now, Raymond is 37 years old. To find out how many years ago that was, we subtract the age at which he had his son from his current age: 37 - 23 = 14.\n\nSo, Raymond's son was born 14 years ago.\n\nLet me double-check this to make sure I didn't miss anything.\n\n- Samantha's current age: 31\n- Raymond's current age: 31 + 6 = 37\n- Age when Raymond had his son: 23\n- Years since the son was born: 37 - 23 = 14\n\nEverything checks out. I don't see any mistakes in this reasoning.\n\nNow, the problem asks for the number of years ago that Raymond's son was born, which we've calculated as 14.\n\nSo, the final answer sho" + } + }, + { + "sample_id": "gsm8k-22", + "predictions": { + "gsm8k": "7" + }, + "ground_truth": { + "gsm8k": "7" + }, + "correct": 1, + "total": 1, + "inference_time_s": 4.304143085999385, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, Billy has 8 customers on Tuesday. The problem is about how many DVDs he sold, so we need to focus on the customers who actually bought DVDs.\n\nThe problem says:\n- His first 3 customers buy one DVD each.\n- His next 2 customers buy 2 DVDs each.\n- His last 3 customers don't buy any DVDs.\n\nSo, let's calculate the DVDs sold from each group:\n\n1. First 3 customers: 3 customers * 1 DVD each = 3 DVDs.\n2. Next 2 customers: 2 customers * 2 DVDs each = 4 DVDs.\n3. Last 3 customers: 3 customers * 0 DVDs each = 0 DVDs.\n\nNow, add them up: 3 (from first group) + 4 (from second group) + 0 (from third group) = 7 DVDs.\n\nWait, let me double-check that. First 3 customers buy 1 each, so 3 * 1 = 3. Next 2 buy 2 each, so 2 * 2 = 4. Last 3 buy none, so 0. Total is 3 + 4 = 7. That seems right.\n\nIs there any chance I missed something? Let's see: total customers are 3 + 2 + 3 = 8, which matches the problem statement. So, the calculation seems correct.\n\nSo, the total" + } + }, + { + "sample_id": "gsm8k-23", + "predictions": { + "gsm8k": "8" + }, + "ground_truth": { + "gsm8k": "8" + }, + "correct": 1, + "total": 1, + "inference_time_s": 5.699006845999975, + "error": null, + "extra": { + "raw_response": "Okay, the problem is about a candle that melts at a rate of 2 centimeters per hour. We need to find out how much shorter the candle will be after burning from 1:00 PM to 5:00 PM.\n\nFirst, I need to figure out how long the candle burns. The time given is from 1:00 PM to 5:00 PM. Let's calculate the duration:\n\n- From 1:00 PM to 2:00 PM is 1 hour.\n- From 2:00 PM to 3:00 PM is another hour, so that's 2 hours total.\n- From 3:00 PM to 4:00 PM is another hour, so that's 3 hours total.\n- From 4:00 PM to 5:00 PM is another hour, so that's 4 hours total.\n\nSo, the candle burns for 4 hours.\n\nNow, the candle melts at a rate of 2 centimeters per hour. To find the total amount it melts, we multiply the rate by the time it burns:\n\nTotal melt = rate \u00d7 time\nTotal melt = 2 cm/hour \u00d7 4 hours = 8 cm\n\nSo, the candle will be 8 centimeters shorter after burning from 1:00 PM to 5:00 PM.\n\nLet me double-check the time calculation to make sure I didn't make a mistake. From 1:00 PM to 5:00 PM is indeed 4 hours (1 t" + } + }, + { + "sample_id": "gsm8k-24", + "predictions": { + "gsm8k": "19.5" + }, + "ground_truth": { + "gsm8k": "26" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.082357416002196, + "error": null, + "extra": { + "raw_response": "Okay, I need to find the original price of the book before the 25% discount was applied. Kyle paid $19.50 after the discount, and I need to figure out what the price was before the discount.\n\nFirst, I recall that a 25% discount means that Kyle paid 75% of the original price because 100% - 25% = 75%. So, $19.50 is 75% of the original price.\n\nLet me denote the original price as \\( P \\). According to the problem, 75% of \\( P \\) is $19.50. Mathematically, that can be written as:\n\\[ 0.75 \\times P = 19.50 \\]\n\nTo find \\( P \\), I need to divide both sides of the equation by 0.75:\n\\[ P = \\frac{19.50}{0.75} \\]\n\nNow, let's do the calculation:\n\\[ P = \\frac{19.50}{0.75} \\]\n\nI know that dividing by 0.75 is the same as multiplying by 4/3 (since 0.75 is 3/4, and dividing by 3/4 is the same as multiplying by 4/3). So:\n\\[ P = 19.50 \\times \\frac{4}{3} \\]\n\nLet's calculate that:\nFirst, multiply 19.50 by 4:\n\\[ 19.50 \\times 4 = 78.00 \\]\n\nNow, divide that by 3:\n\\[ 78.00 \\div 3 = 26.00 \\]\n\nSo, the original pri" + } + }, + { + "sample_id": "gsm8k-25", + "predictions": { + "gsm8k": "2" + }, + "ground_truth": { + "gsm8k": "2" + }, + "correct": 1, + "total": 1, + "inference_time_s": 8.545514659999753, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step. First, I need to figure out how much Marie spent on everything except the pizza, and then see how much was left for the pizza. That way, I can find out how many pizza boxes she ordered.\n\nFirst, let's list out all the items and their costs:\n\n1. Chicken meal: 1 meal at $12 each.\n2. Milk: 5 packs at $3 each.\n3. Apples: 4 apples at $1.50 each.\n4. Pizza: some boxes at $8.50 each. We need to find out how many boxes this is.\n\nMarie paid a total of $50. So, the total cost of chicken meal, milk, and apples plus the cost of pizza boxes equals $50.\n\nLet's calculate the cost of each non-pizza item:\n\n1. Chicken meal: 1 * $12 = $12\n2. Milk: 5 * $3 = $15\n3. Apples: 4 * $1.50 = $6\n\nNow, let's add these up to find out how much Marie spent on non-pizza items:\n\n$12 (chicken) + $15 (milk) + $6 (apples) = $33\n\nNow, subtract this from the total amount she paid to find out how much was spent on pizza:\n\n$50 (total) - $33 (non-pizza) = $17\n\nNow, we know that each pizza" + } + }, + { + "sample_id": "gsm8k-26", + "predictions": { + "gsm8k": "243" + }, + "ground_truth": { + "gsm8k": "243" + }, + "correct": 1, + "total": 1, + "inference_time_s": 8.312229333998403, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down. Mishka bought three types of clothing: shorts, pants, and shoes. He bought 3 pairs of each. We need to calculate the total cost for all these items.\n\nFirst, let's list out the quantities and prices:\n- Shorts: 3 pairs at $16.50 each\n- Pants: 3 pairs at $22.50 each\n- Shoes: 3 pairs at $42 each\n\nNow, let's calculate the cost for each type separately.\n\nFor shorts:\nNumber of pairs = 3\nPrice per pair = $16.50\nTotal cost for shorts = 3 * $16.50\nLet me calculate that: 3 * 16.50 = 49.50\nSo, shorts cost $49.50 in total.\n\nFor pants:\nNumber of pairs = 3\nPrice per pair = $22.50\nTotal cost for pants = 3 * $22.50\nCalculating that: 3 * 22.50 = 67.50\nSo, pants cost $67.50 in total.\n\nFor shoes:\nNumber of pairs = 3\nPrice per pair = $42\nTotal cost for shoes = 3 * $42\nCalculating that: 3 * 42 = 126\nSo, shoes cost $126 in total.\n\nNow, to find the total amount Mishka spent on all clothing items, we add up the costs of shorts, pants, and shoes:\nTotal cost = cost of shorts + cost o" + } + }, + { + "sample_id": "gsm8k-27", + "predictions": { + "gsm8k": "16" + }, + "ground_truth": { + "gsm8k": "16" + }, + "correct": 1, + "total": 1, + "inference_time_s": 6.518710001000727, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, Cynthia eats one serving of ice cream every night. That means she eats 1 serving per day. The problem mentions 60 days, so we need to figure out how many servings she'll consume in 60 days.\n\nSince she eats 1 serving per day, in 60 days she'll eat 60 servings.\n\nNext, the ice cream comes in cartons with 15 servings per carton. So, we need to determine how many cartons she'll need to buy to have enough servings for 60 days.\n\nTo find out how many cartons she needs, we divide the total number of servings by the number of servings per carton:\n60 servings \u00f7 15 servings per carton = 4 cartons.\n\nNow, each carton costs $4.00. So, the total cost will be the number of cartons multiplied by the cost per carton:\n4 cartons \u00d7 $4.00 per carton = $16.00.\n\nLet me double-check this to make sure I didn't miss anything.\n\n- Servings per day: 1\n- Number of days: 60\n- Total servings needed: 60 \u00d7 1 = 60 servings\n- Servings per carton: 15\n- Number of cartons need" + } + }, + { + "sample_id": "gsm8k-28", + "predictions": { + "gsm8k": "25" + }, + "ground_truth": { + "gsm8k": "25" + }, + "correct": 1, + "total": 1, + "inference_time_s": 9.450474833000044, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down. Henry is biking a total of 60 miles. He makes two stops: the first one after 20 miles, and the second one 15 miles before the end of the trip. We need to find out how many miles he traveled between the first and second stops.\n\nFirst, let's visualize the trip. The total distance is 60 miles. The first stop is at 20 miles. So, from the start to the first stop is 20 miles.\n\nNow, the second stop is 15 miles before the end. The end is at 60 miles, so 15 miles before that would be 60 - 15 = 45 miles. So, the second stop is at 45 miles.\n\nNow, we need to find the distance between the first stop (20 miles) and the second stop (45 miles). That would be the difference between these two points: 45 - 20 = 25 miles.\n\nLet me double-check that. If he starts at 0, first stop at 20, then travels some distance to the second stop, and then 15 miles to the end (60 miles). So, from the second stop to the end is 15 miles, so the second stop must be at 60 - 15 = 45 miles. Then, th" + } + }, + { + "sample_id": "gsm8k-29", + "predictions": { + "gsm8k": "104" + }, + "ground_truth": { + "gsm8k": "104" + }, + "correct": 1, + "total": 1, + "inference_time_s": 4.564926712999295, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, the problem says Gloria is choosing between boots and two pairs of high heels. The two pairs of heels together cost five dollars less than the boots. So, if the boots cost B dollars, then the two pairs of heels cost B - 5 dollars.\n\nNext, it says one pair of heels costs $33, and the other costs twice as much. So, the second pair of heels costs 2 * $33 = $66.\n\nNow, the total cost of the two pairs of heels is the sum of the two pairs. So, that would be $33 + $66 = $99.\n\nBut we also know that the two pairs of heels together cost five dollars less than the boots. So, the total cost of the heels ($99) is equal to the cost of the boots minus five dollars. Let's write that as an equation:\n\nCost of heels = Cost of boots - 5\n$99 = B - $5\n\nNow, to find the cost of the boots (B), we can solve for B:\n\nB = $99 + $5\nB = $104\n\nLet me double-check that. If the boots cost $104, then the heels should cost $104 - $5 = $99. And indeed, $33 + $66 = $99. That" + } + }, + { + "sample_id": "gsm8k-30", + "predictions": { + "gsm8k": "109" + }, + "ground_truth": { + "gsm8k": "109" + }, + "correct": 1, + "total": 1, + "inference_time_s": 4.4248353710027, + "error": null, + "extra": { + "raw_response": "Okay, let's see. The problem says Darrell and Allen's ages are in the ratio of 7:11. Their total age now is 162. We need to find Allen's age 10 years from now.\n\nFirst, I need to figure out their current ages. Since the ratio is 7:11, that means for every 7 parts Darrell's age, Allen's age is 11 parts. The total parts would be 7 + 11 = 18 parts.\n\nNow, the total age is 162, which corresponds to 18 parts. So, each part is 162 divided by 18. Let me calculate that: 162 \u00f7 18 = 9. So, each part is 9 years.\n\nNow, Allen's current age is 11 parts. So, 11 \u00d7 9 = 99. So, Allen is currently 99 years old.\n\nThe question asks for Allen's age 10 years from now. So, we add 10 to his current age: 99 + 10 = 109.\n\nLet me double-check to make sure I didn't make a mistake. If Darrell is 7 parts, that's 7 \u00d7 9 = 63 years old. Allen is 99, so total is 63 + 99 = 162, which matches the given total age. So, that checks out.\n\nTherefore, Allen's age 10 years from now will be 109.\n#### 109" + } + }, + { + "sample_id": "gsm8k-31", + "predictions": { + "gsm8k": "80" + }, + "ground_truth": { + "gsm8k": "80" + }, + "correct": 1, + "total": 1, + "inference_time_s": 52.86681378799767, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem about Gunter and his friends guessing the number of jelly beans in a jar. The problem gives three guesses and asks for the average of these guesses. Let me break it down step by step.\n\nFirst, the first guess is straightforward: one friend says 80 jelly beans. So, the first guess is 80.\n\nNext, the second friend says \"20 more than half the first one.\" The first guess is 80, so half of that is 80 / 2 = 40. Then, 20 more than that would be 40 + 20 = 60. So, the second guess is 60.\n\nThe third friend says \"25% more than the first one.\" The first guess is 80, so 25% of 80 is 0.25 * 80 = 20. Adding that to the first guess gives 80 + 20 = 100. So, the third guess is 100.\n\nNow, to find the average of these three guesses, I need to add them together and then divide by 3.\n\nLet's add them up: 80 (first guess) + 60 (second guess) + 100 (third guess) = 240.\n\nNow, divide the total by 3 to get the average: 240 / 3 = 80.\n\nWait, that seems interesting. The average is 80" + } + }, + { + "sample_id": "gsm8k-32", + "predictions": { + "gsm8k": "35" + }, + "ground_truth": { + "gsm8k": "35" + }, + "correct": 1, + "total": 1, + "inference_time_s": 7.719036755999696, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem about John taking care of 10 dogs. The question is asking how many hours a week John spends taking care of dogs.\n\nFirst, let's break down the information given:\n- Number of dogs: 10\n- Time per dog per day: 0.5 hours\n- We need to find the time per week.\n\nFirst, I need to find out how many hours John spends per day taking care of all the dogs. Since each dog takes 0.5 hours per day, for 10 dogs, it would be:\n10 dogs * 0.5 hours/dog/day = 5 hours/day\n\nNow, the question asks for the time per week. There are 7 days in a week, so I need to multiply the daily time by 7:\n5 hours/day * 7 days/week = 35 hours/week\n\nLet me double-check my calculations to make sure I didn't make any mistakes:\n- 10 dogs * 0.5 hours = 5 hours per day is correct.\n- 5 hours per day * 7 days = 35 hours per week is also correct.\n\nSo, the final answer should be 35 hours per week.\n\nBut wait, the problem says to write only the answer on the final line in the format:\n#### \n\nAnd the" + } + }, + { + "sample_id": "gsm8k-33", + "predictions": { + "gsm8k": "70" + }, + "ground_truth": { + "gsm8k": "70" + }, + "correct": 1, + "total": 1, + "inference_time_s": 5.154724522999459, + "error": null, + "extra": { + "raw_response": "Okay, let's see. Gretchen has 110 coins in total. Some are gold and some are silver. The problem says there are 30 more gold coins than silver coins. I need to find out how many gold coins she has.\n\nFirst, I need to define variables to represent the unknowns. Let's say the number of silver coins is S. Then, since there are 30 more gold coins than silver coins, the number of gold coins would be S + 30.\n\nNow, the total number of coins is the sum of gold and silver coins, which is given as 110. So, I can write the equation:\n\nS (silver coins) + (S + 30) (gold coins) = 110\n\nLet me simplify that. Combining like terms:\n\nS + S + 30 = 110\n2S + 30 = 110\n\nNow, I need to solve for S. Subtract 30 from both sides:\n\n2S = 110 - 30\n2S = 80\n\nThen, divide both sides by 2:\n\nS = 80 / 2\nS = 40\n\nSo, there are 40 silver coins. Now, the number of gold coins is S + 30, which is 40 + 30 = 70.\n\nLet me double-check that. If there are 40 silver coins and 70 gold coins, the total is 40 + 70 = 110, which matches the " + } + }, + { + "sample_id": "gsm8k-34", + "predictions": { + "gsm8k": "23" + }, + "ground_truth": { + "gsm8k": "23" + }, + "correct": 1, + "total": 1, + "inference_time_s": 4.36045007100256, + "error": null, + "extra": { + "raw_response": "Okay, let's break this problem down step by step. First, I need to understand the relationships between the number of jewels each person has.\n\n1. **Raymond's jewels**: The problem states that Raymond has 40 jewels. That's straightforward.\n - Raymond = 40 jewels.\n\n2. **Aaron's jewels**: It says Aaron has 5 more jewels than half of Raymond's jewels. So, I need to find half of Raymond's jewels first.\n - Half of Raymond's jewels = 40 / 2 = 20.\n - Aaron has 5 more than that, so Aaron = 20 + 5 = 25 jewels.\n\n3. **Siobhan's jewels**: The problem states that Siobhan has 2 fewer jewels than Aaron.\n - Aaron has 25 jewels, so Siobhan = 25 - 2 = 23 jewels.\n\nLet me double-check my calculations to make sure I didn't make any mistakes.\n\n- Raymond: 40 jewels (given).\n- Half of Raymond's jewels: 40 / 2 = 20.\n- Aaron: 20 + 5 = 25 jewels.\n- Siobhan: 25 - 2 = 23 jewels.\n\nEverything seems to add up correctly. I don't see any errors in my reasoning.\n\nSo, the final answer should be 23. I'll format it " + } + }, + { + "sample_id": "gsm8k-35", + "predictions": { + "gsm8k": "9" + }, + "ground_truth": { + "gsm8k": "9" + }, + "correct": 1, + "total": 1, + "inference_time_s": 8.725918572999944, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down. Mike plays ping pong for 40 minutes. The problem is divided into two 20-minute intervals. In the first 20 minutes, he scores 4 points. Then, in the second 20 minutes, he scores 25% more points than he did in the first 20 minutes. We need to find the total points he scored over the entire 40 minutes.\n\nFirst, let's handle the first part: the first 20 minutes. It's straightforward\u2014he scores 4 points. So, points in the first 20 minutes = 4.\n\nNow, the second 20 minutes: he scores 25% more points than in the first 20 minutes. To find 25% more, we first calculate 25% of the points he scored in the first 20 minutes, which is 4 points. 25% of 4 is (25/100) * 4 = 0.25 * 4 = 1. So, he scores 1 additional point in the second 20 minutes compared to the first. Therefore, his total points in the second 20 minutes would be the original 4 points plus the additional 1 point, which is 5 points.\n\nWait, let me double-check that. If he scores 25% more, that means he scores 125% " + } + }, + { + "sample_id": "gsm8k-36", + "predictions": { + "gsm8k": "75" + }, + "ground_truth": { + "gsm8k": "75" + }, + "correct": 1, + "total": 1, + "inference_time_s": 9.564347120998718, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem step by step. Let's break it down.\n\nFirst, the problem says Terry eats 2 yogurts a day. That means in one day, he consumes 2 yogurts. The question asks how much he spends on yogurt over 30 days.\n\nNext, the yogurts are on sale at 4 yogurts for $5.00. So, the cost per yogurt isn't directly given, but we can calculate it if needed. However, since Terry eats 2 yogurts a day, it might be more efficient to calculate how many packs of 4 yogurts he would consume in 30 days, rather than calculating the cost per yogurt and then multiplying by the total number of yogurts.\n\nLet's start by calculating the total number of yogurts Terry eats in 30 days. He eats 2 yogurts per day, so over 30 days, that would be:\n2 yogurts/day * 30 days = 60 yogurts.\n\nNow, the yogurts are sold in packs of 4 for $5.00. So, we need to figure out how many packs of 4 yogurts are in 60 yogurts.\n\nTo find out how many packs that is, we divide the total number of yogurts by the number of yogu" + } + }, + { + "sample_id": "gsm8k-37", + "predictions": { + "gsm8k": "2" + }, + "ground_truth": { + "gsm8k": "2" + }, + "correct": 1, + "total": 1, + "inference_time_s": 29.971822421997786, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem step by step. Let's break it down.\n\nFirst, John sells his Lego sets to buy video games. He has 13 Lego sets and sells them for $15 each. So, the total money he gets from selling the Lego sets is 13 times $15.\n\nLet me calculate that:\n13 Lego sets * $15 each = 13 * 15 = $195.\n\nNow, he buys 8 video games for $20 each. So, the total cost for the video games is 8 times $20.\n\nCalculating that:\n8 video games * $20 each = 8 * 20 = $160.\n\nHe also has $5 left after buying the video games. So, the total amount of money he spent and saved is $160 (video games) + $5 (leftover) = $165.\n\nBut wait, he initially had $195 from selling the Lego sets. So, the money he spent on video games and saved should add up to the money he got from selling the Lego sets.\n\nLet me check:\n$160 (video games) + $5 (leftover) = $165.\n\nBut he had $195 from selling the Lego sets. That doesn't add up because $165 is less than $195. Hmm, maybe I misunderstood the problem.\n\nWait, the problem s" + } + }, + { + "sample_id": "gsm8k-38", + "predictions": { + "gsm8k": "10" + }, + "ground_truth": { + "gsm8k": "10" + }, + "correct": 1, + "total": 1, + "inference_time_s": 12.296665833997395, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out how fast John runs. The problem says he runs 60 miles a week, 3 days a week. On the first day, he runs for 3 hours, and on the other two days, he runs half as much time, so that's 1.5 hours each on those days.\n\nFirst, I need to find out the total time he spends running in a week. He runs 3 hours on the first day and 1.5 hours on each of the other two days. So, the total time is 3 + 1.5 + 1.5 = 6 hours per week.\n\nNow, I know he runs 60 miles in a week. To find his speed, I need to divide the total distance by the total time. But speed is usually given in miles per hour (mph), so I'll calculate miles per hour.\n\nTotal distance = 60 miles\nTotal time = 6 hours\n\nSpeed = Total distance / Total time = 60 miles / 6 hours = 10 mph\n\nLet me double-check that. If he runs 10 mph, then in 3 hours on the first day, he would cover 3 * 10 = 30 miles. On the other two days, he runs 1.5 hours each, so 1.5 * 10 = 15 miles per day. So, 15 miles * 2 days = 30 miles. Total distance " + } + }, + { + "sample_id": "gsm8k-39", + "predictions": { + "gsm8k": "18" + }, + "ground_truth": { + "gsm8k": "18" + }, + "correct": 1, + "total": 1, + "inference_time_s": 9.999871119998716, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, the problem says Dana can skip at 3 miles per hour (mph). It also mentions that skipping is half as fast as running. So, if skipping is 3 mph, then running must be twice that speed because running is faster than skipping. Let me check that: \"skip at a rate of speed that is half as fast as she can run.\" So, skipping speed = (1/2) * running speed. Therefore, running speed = 2 * skipping speed. Since skipping speed is 3 mph, running speed = 2 * 3 = 6 mph.\n\nNext, the problem states that Dana can run at a rate four times faster than she can walk. So, running speed = 4 * walking speed. We already found that running speed is 6 mph, so walking speed = running speed / 4 = 6 / 4 = 1.5 mph.\n\nNow, the question is about how many miles she can travel in six hours if she spends one-third of the time running and two-thirds of the time walking.\n\nLet's calculate the time spent running and walking:\n- Total time = 6 hours\n- Time spent running = (1/3) * 6 =" + } + }, + { + "sample_id": "gsm8k-40", + "predictions": { + "gsm8k": "8" + }, + "ground_truth": { + "gsm8k": "8" + }, + "correct": 1, + "total": 1, + "inference_time_s": 58.04454434799845, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, the problem says Suzy's iPhone is 1 year old. That's our starting point.\n\nNext, it says Ben's iPhone is two times older than Suzy's iPhone. I need to be careful here with the wording. \"Two times older than\" can sometimes be ambiguous, but in this context, it likely means Ben's iPhone is twice as old as Suzy's. So if Suzy's is 1 year, then Ben's would be 2 times that, which is 2 years.\n\nNow, the problem also states that Brandon's iPhone is four times as old as Ben's iPhone. Since we've determined Ben's iPhone is 2 years old, then Brandon's would be 4 times that. So 4 times 2 is 8.\n\nLet me double-check to make sure I interpreted the \"two times older than\" part correctly. Sometimes people might interpret \"times older than\" as adding to the original, like if something is 100% older, it's double. So if Suzy's is 1, then Ben's would be 1 (original) + 2 (times older) = 3. But that doesn't seem right in this context because the next part is abo" + } + }, + { + "sample_id": "gsm8k-41", + "predictions": { + "gsm8k": "200" + }, + "ground_truth": { + "gsm8k": "200" + }, + "correct": 1, + "total": 1, + "inference_time_s": 13.442106361002516, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem step by step. Let's break it down.\n\nFirst, the problem states that the dragon's fire can reach anything within 1000 feet. So, the dragon's range is 1000 feet.\n\nPolly can throw the javelin 400 feet without the gemstone. But when she holds the sapphire gemstone, she can throw the javelin three times farther than usual.\n\nSo, without the gemstone, her throw distance is 400 feet. With the gemstone, it's three times that distance. Let's calculate that:\n\n400 feet * 3 = 1200 feet.\n\nNow, the question is asking how far outside the dragon's reach (which is 1000 feet) can Polly stand and still hit the dragon with the javelin when she's holding the gemstone.\n\nIf Polly is standing at a distance of x feet from the dragon, and she's holding the gemstone, she can throw the javelin 1200 feet. To hit the dragon, the distance x must be less than or equal to her throw distance, which is 1200 feet.\n\nBut the dragon's fire can reach up to 1000 feet. So, if Polly is standing " + } + }, + { + "sample_id": "gsm8k-42", + "predictions": { + "gsm8k": "26" + }, + "ground_truth": { + "gsm8k": "26" + }, + "correct": 1, + "total": 1, + "inference_time_s": 3.484212775998458, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, Grandma Jones baked 5 apple pies. Each pie was cut into 8 pieces. So, the total number of pieces she had initially is 5 pies times 8 pieces per pie. That would be 5 * 8 = 40 pieces.\n\nAt the end of the evening, there were 14 pieces remaining. The question is asking how many pieces were taken by the guests.\n\nSo, the number of pieces taken by the guests would be the total number of pieces minus the remaining pieces. That is, 40 (total pieces) - 14 (remaining pieces) = 26 pieces taken by the guests.\n\nLet me double-check that to make sure I didn't make a mistake.\n\nTotal pieces: 5 pies * 8 slices per pie = 40 slices.\nRemaining pieces: 14 slices.\nPieces taken by guests: 40 - 14 = 26.\n\nYes, that seems correct. I don't see any mistakes in my reasoning. So, the answer should be 26.\n#### \n26" + } + }, + { + "sample_id": "gsm8k-43", + "predictions": { + "gsm8k": "48" + }, + "ground_truth": { + "gsm8k": "48" + }, + "correct": 1, + "total": 1, + "inference_time_s": 37.78431540400197, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem step by step. Let's break it down.\n\nFirst, the problem states that a bag of chips has 250 calories per serving. A 300g bag has 5 servings. The question is asking how many grams of chips I can eat if my daily calorie target is 2000 calories and I've already consumed 1800 calories.\n\nFirst, I need to find out how many calories I have left for the day. My daily target is 2000 calories, and I've already eaten 1800 calories. So, the remaining calories I can consume are:\n2000 - 1800 = 200 calories.\n\nNow, I need to figure out how many grams of chips correspond to 200 calories. The problem says that a 300g bag has 5 servings, and each serving is 250 calories.\n\nFirst, let's find out how many calories are in the entire 300g bag. Since there are 5 servings and each serving is 250 calories, the total calories in the bag would be:\n5 servings * 250 calories/serving = 1250 calories.\n\nBut I only have 200 calories left. So, I need to find out what fraction of the bag c" + } + }, + { + "sample_id": "gsm8k-44", + "predictions": { + "gsm8k": "20" + }, + "ground_truth": { + "gsm8k": "20" + }, + "correct": 1, + "total": 1, + "inference_time_s": 24.72216539299916, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem step by step. Let's break it down.\n\nFirst, the problem says Charlie wants to sell beeswax candles. For every pound of beeswax, he can make 10 tapered candles. That means the number of candles is directly proportional to the amount of beeswax he uses.\n\nNext, it mentions that one pound of beeswax and the wicks cost $10.00 in supplies. So, for every pound of beeswax, his cost is $10.00, regardless of how many candles he makes from that pound (since he can make 10 candles per pound).\n\nHe sells each candle for $2.00. We need to find his net profit if he makes and sells 20 candles.\n\nFirst, I need to figure out how much beeswax he needs to make 20 candles. Since he can make 10 candles per pound, for 20 candles, he would need 20 candles / 10 candles per pound = 2 pounds of beeswax.\n\nNow, the cost for 2 pounds of beeswax would be 2 pounds * $10.00 per pound = $20.00.\n\nNext, calculate the total revenue from selling 20 candles. He sells each candle for $2.00, so" + } + }, + { + "sample_id": "gsm8k-45", + "predictions": { + "gsm8k": "5" + }, + "ground_truth": { + "gsm8k": "104" + }, + "correct": 0, + "total": 1, + "inference_time_s": 62.9089452670014, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem step by step. Let's break it down.\n\nFirst, I need to understand what's being asked. Meredith writes blog articles, and each article takes 4 hours to research and write. I need to find out how many hours she spent writing articles over three days: Monday, Tuesday, and Wednesday.\n\nLet's start with Monday:\n- On Monday, she wrote 5 articles.\n\nNow, Tuesday:\n- The problem says she wrote 2/5 times more articles on Tuesday than on Monday.\n- I need to interpret this carefully. Does \"2/5 times more\" mean she wrote 2/5 times the number of articles on Monday, or that she wrote the number on Monday plus 2/5 of that number?\n\nI think it's the latter, meaning she wrote her Monday's count plus 2/5 of Monday's count. So, it's an increase of 2/5 relative to Monday.\n\nLet's calculate Tuesday's articles:\n- Monday's articles: 5\n- Increase: (2/5) * 5 = 2\n- So, Tuesday's articles: 5 (Monday's) + 2 (increase) = 7\n\nWait, but sometimes \"2/5 times more\" can be ambiguous. It could" + } + }, + { + "sample_id": "gsm8k-46", + "predictions": { + "gsm8k": "163" + }, + "ground_truth": { + "gsm8k": "163" + }, + "correct": 1, + "total": 1, + "inference_time_s": 7.669380147999618, + "error": null, + "extra": { + "raw_response": "Okay, let's try to figure out this problem step by step. So, Candice starts with 80 post-it notes in her purse. Then she buys a package of post-it notes, but we don't know how many are in that package\u2014that's what we need to find. Let's call the number of post-it notes in the package \"x.\"\n\nNext, she uses 220 post-it notes at work, one on each cup of coffee. At the end, she has 23 post-it notes left. \n\nLet's break this down. She starts with 80, adds x (the package), and then subtracts the 220 she used. The result is 23. So, the equation should be:\n\nInitial post-its + Post-its from package - Post-its used = Remaining post-its\n\nPlugging in the numbers we know:\n\n80 + x - 220 = 23\n\nNow, let's solve for x. First, combine the constants on the left side:\n\n(80 - 220) + x = 23 \n-140 + x = 23\n\nNow, add 140 to both sides to isolate x:\n\nx = 23 + 140 \nx = 163\n\nWait, let me double-check that. If she started with 80, bought 163, that's 80 + 163 = 243. Then she used 220, so 243 - 220 = 23. That matche" + } + }, + { + "sample_id": "gsm8k-47", + "predictions": { + "gsm8k": "800" + }, + "ground_truth": { + "gsm8k": "800" + }, + "correct": 1, + "total": 1, + "inference_time_s": 7.344233507999888, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, the problem says John spent $200 on blue ties that cost $40 each. So, I need to find out how many blue ties he bought. If each blue tie costs $40 and he spent $200, then the number of blue ties is $200 divided by $40 per tie. Let me calculate that: 200 / 40 = 5. So, he bought 5 blue ties.\n\nNext, the problem states that John buys twice as many red ties as blue ties. Since he bought 5 blue ties, the number of red ties would be 2 times 5, which is 10 red ties.\n\nNow, the cost of red ties is 50% more than blue ties. The blue ties cost $40 each, so 50% more would be $40 plus 50% of $40. Let's calculate that: 50% of $40 is 0.5 * 40 = $20. So, the cost per red tie is $40 + $20 = $60.\n\nNow, to find out how much he spent on red ties, we multiply the number of red ties by the cost per red tie: 10 red ties * $60 each = $600.\n\nHe spent $200 on blue ties and $600 on red ties, so the total amount spent on ties is $200 + $600 = $800.\n\nLet me double-che" + } + }, + { + "sample_id": "gsm8k-48", + "predictions": { + "gsm8k": "8" + }, + "ground_truth": { + "gsm8k": "8" + }, + "correct": 1, + "total": 1, + "inference_time_s": 5.374421155000164, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem where Tracy uses a 4-foot wire to cut into 6-inch pieces. I need to find out how many 6-inch pieces she can get from a 4-foot wire.\n\nFirst, I need to make sure the units are consistent. The wire is 4 feet long, but the pieces are 6 inches long. I know that 1 foot equals 12 inches. So, I should convert 4 feet to inches to make the units match.\n\nLet me calculate that: 4 feet * 12 inches/foot = 48 inches. So, the wire is 48 inches long in total.\n\nNow, each piece is 6 inches long. To find out how many 6-inch pieces are in 48 inches, I can divide the total length by the length of each piece.\n\nSo, 48 inches \u00f7 6 inches per piece = 8 pieces.\n\nLet me double-check that. If I have 8 pieces, each 6 inches long, the total length would be 8 * 6 = 48 inches, which matches the original length of the wire. So, that seems correct.\n\nI should also consider if there's any remainder, but since 48 is exactly divisible by 6, there's no remainder. So, Tracy gets exactly 8 pie" + } + }, + { + "sample_id": "gsm8k-49", + "predictions": { + "gsm8k": "30" + }, + "ground_truth": { + "gsm8k": "30" + }, + "correct": 1, + "total": 1, + "inference_time_s": 8.75346496000202, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, the building has 15 floors, and each floor has 8 units. So, the total number of units in the building is 15 floors times 8 units per floor. Let me calculate that: 15 * 8 = 120 units. So, there are 120 units in total.\n\nNext, the problem states that 3/4 of the building is occupied. That means 3/4 of the total units are occupied. To find the number of occupied units, I can calculate 3/4 of 120. That would be (3/4) * 120 = 90 units. So, 90 units are occupied.\n\nNow, to find the number of unoccupied units, I subtract the occupied units from the total units. So, 120 total units minus 90 occupied units equals 30 unoccupied units.\n\nLet me double-check my calculations to make sure I didn't make any mistakes.\n\nTotal units: 15 floors * 8 units/floor = 120 units. That seems correct.\n\nOccupied units: 3/4 of 120 = 90 units. That's correct because 120 divided by 4 is 30, and 30 times 3 is 90.\n\nUnoccupied units: 120 - 90 = 30. That checks out.\n\nSo, the " + } + }, + { + "sample_id": "mmlu_pro-law-1", + "predictions": { + "mmlu_pro:law": "A" + }, + "ground_truth": { + "mmlu_pro:law": "D" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.3884648059975, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out the correct answer to this multiple-choice question about criminal offenses under common law. The scenario involves a man stealing a woman's purse on a subway and using force to push her away while escaping. I need to determine which crime he can be properly convicted of.\n\nFirst, let's recall the definitions of the relevant crimes under common law:\n\n1. **Larceny**: This is the unlawful taking and carrying away of someone else's personal property with the intent to permanently deprive the owner of it. It's a crime of trespass against the owner's property. Importantly, larceny typically does not involve force or violence against the person at the time of the taking.\n\n2. **Robbery**: This is larceny plus the use of force or the threat of force to overcome the victim's resistance or to facilitate the taking of the property. So, if force or violence is used during the taking or immediately before or after, it can be considered robbery.\n\n3. **Burglary**: This invol" + } + }, + { + "sample_id": "mmlu_pro-law-2", + "predictions": { + "mmlu_pro:law": "E" + }, + "ground_truth": { + "mmlu_pro:law": "B" + }, + "correct": 0, + "total": 1, + "inference_time_s": 54.62296446799883, + "error": null, + "extra": { + "raw_response": "Okay, I need to answer this multiple-choice question about a federal grand jury's subpoena and a corporation's Fifth Amendment privilege against self-incrimination. Let me break this down.\n\nFirst, the scenario: A federal grand jury is investigating a corporation whose tanker ship spilled crude oil into environmentally sensitive waters. The grand jury issued a subpoena requiring the corporation to produce all emails and internal documents regarding the corporation's knowledge of the risks of an oil spill. The corporation is objecting, citing its Fifth Amendment privilege against self-incrimination. The question is whether the subpoena can be enforced.\n\nNow, the options are A through J, each with different reasoning. I need to figure out which one is correct.\n\nFirst, I recall that the Fifth Amendment privilege against self-incrimination generally protects individuals from being compelled to testify against themselves. But does it apply to corporations? I think corporations are considered" + } + }, + { + "sample_id": "mmlu_pro-law-3", + "predictions": { + "mmlu_pro:law": "A" + }, + "ground_truth": { + "mmlu_pro:law": "F" + }, + "correct": 0, + "total": 1, + "inference_time_s": 61.542806655001186, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out the strongest constitutional argument the candidate could make against the state officials' interpretation of the statute. Let's break this down.\n\nFirst, the scenario involves a state statute that requires write-in candidates to have their names and offices printed in ink on the ballot. The candidate in question is a German-American who believes he needs a large turnout of German voters to win. His campaign manager mails tear-off stickers to every registered German voter, which bear the candidate's name and office. The campaign manager does this because many German voters are not proficient in English and might have trouble writing the candidate's name and office on the ballot. The campaign manager also runs a media campaign to inform voters on how to apply the stickers to the ballot.\n\nFive months before the election, an election official notifies the candidate's campaign committee that the tear-off stickers do not comply with the state statute because the st" + } + }, + { + "sample_id": "mmlu_pro-law-4", + "predictions": { + "mmlu_pro:law": "A" + }, + "ground_truth": { + "mmlu_pro:law": "A" + }, + "correct": 1, + "total": 1, + "inference_time_s": 55.90956623599777, + "error": null, + "extra": { + "raw_response": "Okay, I need to answer this multiple-choice question about the alter ego rule and the use of force in defense. Let me break this down.\n\nFirst, I need to understand the scenario:\n- A defendant sees a woman struggling with a man over a briefcase.\n- The woman had actually stolen the briefcase from the man, but the defendant didn't know that.\n- The defendant thought the woman was a victim and intervened by punching the man until the woman got away with the briefcase.\n- Later, the defendant realized he was wrong and apologized.\n\nThe question is about the alter ego rule and whether the defendant was justified in using force to protect the woman.\n\nNow, what's the alter ego rule? From what I recall, the alter ego rule is a legal concept that allows a person to act on behalf of another person, especially in situations where the other person is unable to act for themselves. It's often used in the context of agency or representation, but in this case, it seems to be about defense.\n\nBut in this sc" + } + }, + { + "sample_id": "mmlu_pro-law-5", + "predictions": { + "mmlu_pro:law": "A" + }, + "ground_truth": { + "mmlu_pro:law": "E" + }, + "correct": 0, + "total": 1, + "inference_time_s": 56.768339758000366, + "error": null, + "extra": { + "raw_response": "Okay, I need to analyze this multiple-choice question carefully. Let's break it down step by step.\n\nFirst, let's summarize the scenario:\n- Two college students, members of the same fraternity, are at a party.\n- The defendant pulls out a gun, points it at the other student, and says, \"Beg for your life, sucker.\"\n- The other student responds, \"Get lost, you jerk,\" implying he doesn't believe the gun is real or that the defendant is serious, likely because the defendant has a reputation as a practical joker.\n- The defendant then pulls the trigger and shoots the student to death.\n\nNow, let's look at the statute provided:\n- **First-degree murder**: Any intentional and premeditated killing with malice aforethought.\n- **Second-degree murder**: Any killing that occurs during the commission or attempted commission of a serious or inherently dangerous felony.\n- **Manslaughter**: All other types of unlawful homicide and unjustifiable killings.\n\nThe defendant's defense is that a fellow fraternity " + } + }, + { + "sample_id": "mmlu_pro-law-6", + "predictions": { + "mmlu_pro:law": "E" + }, + "ground_truth": { + "mmlu_pro:law": "C" + }, + "correct": 0, + "total": 1, + "inference_time_s": 63.75306579500102, + "error": null, + "extra": { + "raw_response": "Okay, I need to analyze this scenario carefully. The question is about whether the cab driver should be found guilty or not guilty of attempted rape based on the given situation.\n\nFirst, let's break down the scenario:\n\n1. **Context**: It's raining hard, and a cab driver is looking for a last passenger. A passenger flags him down and directs him to her home.\n2. **Relationship**: The cab driver recognizes the passenger as a former girlfriend.\n3. **Invitation**: The passenger invites him into her house when they arrive.\n4. **Identity**: Unknown to the cab driver, the passenger is an undercover police officer working in the sex crimes unit.\n5. **Behavior Inside**: The cab driver makes sexual advances toward the passenger, who responds by kissing him and holding his hand. This suggests mutual consent or at least no immediate resistance.\n6. **Interruption**: Just as the cab driver is about to kiss her again, she gets up to answer the phone in the kitchen.\n7. **Charge**: The cab driver is arr" + } + }, + { + "sample_id": "mmlu_pro-law-7", + "predictions": { + "mmlu_pro:law": "D" + }, + "ground_truth": { + "mmlu_pro:law": "G" + }, + "correct": 0, + "total": 1, + "inference_time_s": 42.38914736999868, + "error": null, + "extra": { + "raw_response": "Okay, I need to analyze this scenario carefully to determine the correct answer. Let me break it down step by step.\n\nFirst, let's summarize the key elements of the situation:\n\n1. **Properties Involved**:\n - A lemon grove owned by the widower (30 acres).\n - An antebellum mansion located near the southern edge of the lemon grove, which was deeded to the daughter by the widower.\n - A 10-acre farm owned by the farmer, located directly west of the lemon grove.\n - A four-lane highway to the east of the lemon grove.\n - A little-used road running west to east from the lemon grove border to the four-lane highway along the southern boundary of the grove. This road is accessible from the lemon grove and passes through the lemon grove to reach the highway.\n\n2. **Actions and Relationships**:\n - The widower deeded the antebellum mansion to his daughter, who recorded the deed and took immediate possession.\n - The daughter and the farmer (owner of the adjacent farm to the west) fell in l" + } + }, + { + "sample_id": "mmlu_pro-law-8", + "predictions": { + "mmlu_pro:law": "E" + }, + "ground_truth": { + "mmlu_pro:law": "E" + }, + "correct": 1, + "total": 1, + "inference_time_s": 14.530016534001334, + "error": null, + "extra": { + "raw_response": "Okay, I'm trying to figure out this multiple-choice question about a medical malpractice case. The patient is suing the hospital and doctor because they left sponges in her body during surgery, which was discovered during an MRI. The defense is objecting because the patient didn't bring the MRI printouts to court and is instead testifying about what she saw on the MRI. I need to determine the most likely ruling of the trial judge regarding this objection.\n\nFirst, I recall that in legal proceedings, especially in cases involving medical evidence, there are rules about what kind of evidence is admissible. One key rule that comes to mind is the \"best evidence rule.\" This rule states that if a party wants to prove the contents of a document or record, they must produce the original document or a certified copy, rather than just testifying about its contents. This is because the original document is considered the best evidence of its contents.\n\nIn this case, the MRI scan is a crucial piece" + } + }, + { + "sample_id": "mmlu_pro-law-9", + "predictions": { + "mmlu_pro:law": "C" + }, + "ground_truth": { + "mmlu_pro:law": "A" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.36029710599905, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out this multiple-choice question about a defendant's situation regarding his arrest, release, and a motion to discharge. Let me break it down step by step.\n\nFirst, let's summarize the timeline:\n1. **Arrest**: February 1 (let's assume this is a leap year for simplicity, but since the exact year isn't specified, it might not matter).\n2. **Release**: March 1 (one month after arrest).\n3. **Motion to discharge filed**: December 1 of the same year.\n4. **Hearing on the motion**: 3 days after the motion was filed, so December 4.\n\nNow, the question is about whether the defendant should be discharged or brought to trial, and under what timeframe or condition.\n\nI recall that in criminal procedure, there are speedy trial rights and rules that govern how quickly a defendant must be brought to trial after arrest or release. In the U.S., the Sixth Amendment guarantees the right to a speedy trial, and there are also statutory time limits, like those in the Federal Rules of Crim" + } + }, + { + "sample_id": "mmlu_pro-law-10", + "predictions": { + "mmlu_pro:law": "E" + }, + "ground_truth": { + "mmlu_pro:law": "J" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.850342179997824, + "error": null, + "extra": { + "raw_response": "Okay, I'm trying to figure out this multiple-choice question about the admissibility of the court officer's testimony. Let me break this down step by step.\n\nFirst, let's understand the scenario:\n- A defendant is on trial for robbery.\n- He testifies in his own defense.\n- During cross-examination, the prosecutor asks him about committing false pretenses related to unauthorized use of a credit card.\n- The defendant denies it, saying, \"That's a lie, I never did.\"\n- In rebuttal, the prosecutor calls a court officer who testifies that the defendant admitted committing false pretenses.\n- However, the court officer also testifies that the defendant was granted immunity from prosecution in exchange for his testimony against others.\n\nThe question is about the admissibility of the court officer's testimony regarding the defendant's immunity.\n\nNow, let's recall some legal principles related to this scenario:\n1. **Impeachment vs. Substantive Evidence**: Testimony about a defendant's prior inconsist" + } + }, + { + "sample_id": "mmlu_pro-law-11", + "predictions": { + "mmlu_pro:law": "D" + }, + "ground_truth": { + "mmlu_pro:law": "I" + }, + "correct": 0, + "total": 1, + "inference_time_s": 54.38882150800055, + "error": null, + "extra": { + "raw_response": "Okay, I'm trying to figure out this multiple-choice question about a carpenter and a general contractor. The scenario is that the general contractor invited the carpenter to bid on carpentry work for an office building. The carpenter agreed to bid only if the general contractor agreed to give him the job if his bid was the lowest and the general contractor won the main contract. The general contractor agreed to this condition. The carpenter then submitted the lowest bid, and the general contractor used this bid in its successful main bid. Now, the carpenter wants to know why the general contractor is obligated to award him the carpentry subcontract.\n\nFirst, I need to understand the legal principles at play here. It seems like this is about contracts and possibly promissory estoppel or consideration. The key points are:\n1. The general contractor made a conditional promise to the carpenter.\n2. The carpenter relied on this promise by preparing a bid, which incurred time and expense.\n3. Th" + } + }, + { + "sample_id": "mmlu_pro-law-12", + "predictions": { + "mmlu_pro:law": "C" + }, + "ground_truth": { + "mmlu_pro:law": "I" + }, + "correct": 0, + "total": 1, + "inference_time_s": 54.2884059570024, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out who has standing to challenge the constitutionality of this appropriation. Standing means that a party must have a personal stake in the outcome of the case, meaning they must have suffered or will suffer an actual injury as a result of the action being challenged.\n\nThe law in question legalizes marijuana, imposes a $1 tax per pack, and appropriates all the proceeds to a specific art museum that focuses on war-related artifacts. So, the key elements here are the tax on marijuana and the appropriation of the proceeds to this museum.\n\nLet's go through each option one by one:\n\n**A. An association of tobacco farmers who allege that the legalization of marijuana is impacting their business.**\n- They might have a financial interest, but is this a personal stake in the constitutionality of the appropriation? The appropriation itself is about where the tax money goes, not about the impact on tobacco farmers. They might have a general economic interest, but standing u" + } + }, + { + "sample_id": "mmlu_pro-math-13", + "predictions": { + "mmlu_pro:math": "E" + }, + "ground_truth": { + "mmlu_pro:math": "H" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.70619573099975, + "error": null, + "extra": { + "raw_response": "Okay, I need to answer this multiple-choice question. There are two statements here, and I need to evaluate their truth values based on the options provided.\n\nFirst, let's break down the question:\n\n**Statement 1:** A ring homomorphism is one-to-one if and only if the kernel is {0}.\n\n**Statement 2:** Q is an ideal in R.\n\nThe options are combinations of \"True,\" \"False,\" and \"Not Given\" for each statement. I need to determine the truth value of each statement and then match it with the correct option.\n\n### Evaluating Statement 1: A ring homomorphism is one-to-one if and only if the kernel is {0}.\n\nFirst, I recall that a ring homomorphism is a function between two rings that preserves the ring operations (addition and multiplication). The kernel of a ring homomorphism is the set of elements in the domain that map to the additive identity (0) in the codomain.\n\nNow, the statement says that a ring homomorphism is one-to-one (injective) if and only if its kernel is {0}.\n\nI know from group theo" + } + }, + { + "sample_id": "mmlu_pro-math-14", + "predictions": { + "mmlu_pro:math": "D" + }, + "ground_truth": { + "mmlu_pro:math": "H" + }, + "correct": 0, + "total": 1, + "inference_time_s": 54.12774637899929, + "error": null, + "extra": { + "raw_response": "Okay, I need to analyze two statements about fields and polynomials. Let me break this down.\n\nFirst, Statement 1 says: \"R is a splitting field of some polynomial over Q.\" I need to figure out if this is true or not given. But wait, what is R here? In field theory, R often denotes the field of real numbers. So, is the statement saying that the real numbers are a splitting field of some polynomial over the rationals Q?\n\nI recall that a splitting field of a polynomial is a field extension that contains all the roots of the polynomial and is minimal with this property. For example, the splitting field of x\u00b2 - 2 over Q is Q(\u221a2), which is a quadratic extension of Q.\n\nNow, is R (the real numbers) a splitting field of some polynomial over Q? Well, the real numbers are indeed a splitting field for certain polynomials. For instance, consider a polynomial with roots that are all real numbers, like x\u00b3 - x. The splitting field of x\u00b3 - x over Q is Q(\u221a(5), \u221a5), but that's not R. Hmm, perhaps a better" + } + }, + { + "sample_id": "mmlu_pro-math-15", + "predictions": { + "mmlu_pro:math": "C" + }, + "ground_truth": { + "mmlu_pro:math": "C" + }, + "correct": 1, + "total": 1, + "inference_time_s": 12.437488122999639, + "error": null, + "extra": { + "raw_response": "Okay, I need to evaluate two statements about linear independence and dimension in R^2. Let's break this down.\n\nFirst, Statement 1: \"Any set of two vectors in R^2 is linearly independent.\"\n\nHmm, I know that in R^2, the maximum number of linearly independent vectors is 2 because the dimension is 2. But does that mean any two vectors are linearly independent? No, that's not right. For example, take the vectors (1, 0) and (2, 0). They are both in R^2, but they are linearly dependent because one is just a scalar multiple of the other. So, Statement 1 is false.\n\nNow, Statement 2: \"If V = span(v1, ... , vk) and {v1, ... , vk} are linearly independent, then dim(V) = k.\"\n\nI recall that the dimension of a vector space is the number of vectors in any basis for the space. If {v1, ..., vk} are linearly independent and span V, then they form a basis for V. By definition, the dimension of V is the number of vectors in a basis, so dim(V) should indeed be k. So, Statement 2 seems to be true.\n\nLet me d" + } + }, + { + "sample_id": "mmlu_pro-math-16", + "predictions": { + "mmlu_pro:math": "H" + }, + "ground_truth": { + "mmlu_pro:math": "H" + }, + "correct": 1, + "total": 1, + "inference_time_s": 22.948669813002198, + "error": null, + "extra": { + "raw_response": "Okay, I need to evaluate two statements about permutations and cycles in group theory or combinatorics. The question is about whether every permutation is a cycle and whether every cycle is a permutation.\n\nFirst, let's recall some definitions:\n\n1. **Permutation**: A permutation is a rearrangement of elements in a set. It can be represented as a bijection from a set to itself. For example, if we have a set {1, 2, 3}, a permutation could be (1 2 3), which maps 1 to 2, 2 to 3, and 3 to 1.\n\n2. **Cycle**: A cycle is a specific type of permutation where the permutation is a single cycle. For example, (1 2 3) is a cycle, but (1 2)(3) is not a single cycle because it consists of two disjoint cycles: (1 2) and (3), which is a fixed point.\n\nNow, let's analyze the statements one by one.\n\n**Statement 1: Every permutation is a cycle.**\n\nThis statement claims that any permutation can be expressed as a single cycle. However, this is not true. Permutations can be decomposed into disjoint cycles, and n" + } + }, + { + "sample_id": "mmlu_pro-math-17", + "predictions": { + "mmlu_pro:math": "E" + }, + "ground_truth": { + "mmlu_pro:math": "B" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.109347327997966, + "error": null, + "extra": { + "raw_response": "Okay, let's try to figure out this problem. The question is asking for all elements \\( c \\) in \\( \\mathbb{Z}_3 \\) such that the quotient ring \\( \\mathbb{Z}_3[x]/(x^3 + x^2 + c) \\) is a field. \n\nFirst, I remember that a quotient ring \\( R/I \\) is a field if and only if \\( I \\) is a maximal ideal of \\( R \\). Since \\( \\mathbb{Z}_3 \\) is a field (it's a finite field with 3 elements), the polynomial ring \\( \\mathbb{Z}_3[x] \\) is a principal ideal ring, and its maximal ideals are exactly the ideals generated by irreducible polynomials of degree 1 or equal to the characteristic of the field (but since \\( \\mathbb{Z}_3 \\) has characteristic 3, the only maximal ideal of degree 1 would be generated by a linear polynomial, but actually, in a field, the maximal ideals are the ideals generated by irreducible polynomials, and since the base field is a field, the quotient \\( F[x]/(p(x)) \\) is a field if and only if \\( p(x) \\) is irreducible over \\( F \\). \n\nWait, more precisely, for a polynomial ring o" + } + }, + { + "sample_id": "mmlu_pro-math-18", + "predictions": { + "mmlu_pro:math": "E" + }, + "ground_truth": { + "mmlu_pro:math": "D" + }, + "correct": 0, + "total": 1, + "inference_time_s": 58.16678919300102, + "error": null, + "extra": { + "raw_response": "Okay, I need to tackle this multiple-choice question about group theory. The question has two statements, and I need to evaluate their truth values. The options pair the truth values of Statement 1 and Statement 2 with possible combinations, including \"Cannot be determined.\"\n\nFirst, let's recall some group theory concepts that might be relevant here:\n\n1. **Cyclic groups**: A group is cyclic if it can be generated by a single element. For finite groups, a group is cyclic if and only if its order is a product of primes where at most one prime is repeated (i.e., the order is either a prime power or a product of distinct primes). This is related to the structure theorem for finite abelian groups, but here we're dealing with general groups, not necessarily abelian.\n\n2. **Normal subgroups**: A normal subgroup is a subgroup that is normal with respect to conjugation by any element of the group. Every group has trivial normal subgroups (the identity and the group itself), but a nontrivial prop" + } + }, + { + "sample_id": "mmlu_pro-math-19", + "predictions": { + "mmlu_pro:math": "A" + }, + "ground_truth": { + "mmlu_pro:math": "J" + }, + "correct": 0, + "total": 1, + "inference_time_s": 56.383687577003, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out which condition makes a subset H of a group (G, *) a group. Let me recall the group axioms. A group is a set equipped with an operation that combines any two elements to form a third element, satisfying four conditions: closure, associativity, identity, and inverses.\n\nNow, H is a subset of G, and G is already a group under the operation *. For H to be a group under the same operation, it must satisfy the group axioms itself. That means:\n\n1. **Closure**: For any a, b in H, the product a * b must also be in H.\n2. **Associativity**: This is already satisfied because G is a group, and the operation is associative in G. So, associativity doesn't need to be checked separately for H.\n3. **Identity element**: H must contain the identity element of G (usually denoted as e, where a * e = e * a = a for all a in G).\n4. **Inverse element**: For every a in H, its inverse a^-1 must also be in H (where a * a^-1 = a^-1 * a = e).\n\nNow, let's look at the options one by one to s" + } + }, + { + "sample_id": "mmlu_pro-math-20", + "predictions": { + "mmlu_pro:math": "E" + }, + "ground_truth": { + "mmlu_pro:math": "J" + }, + "correct": 0, + "total": 1, + "inference_time_s": 69.19240535099743, + "error": null, + "extra": { + "raw_response": "Okay, I need to tackle this multiple-choice question about statements related to free abelian groups. Let me break it down.\n\nFirst, I need to understand the two statements:\n\n**Statement 1:** \"There exists a free abelian group of every positive integer rank.\"\n\n**Statement 2:** \"A finitely generated abelian group is free abelian if its Betti number equals the number of elements in some generating set.\"\n\nThe options are combinations of \"True,\" \"False,\" \"Cannot be determined,\" or more complex phrases about the statements.\n\n### Understanding Statement 1\n\n**Statement 1** claims that for every positive integer rank, there exists a free abelian group of that rank.\n\nFirst, what is a free abelian group? A free abelian group is a direct sum of copies of the integers, i.e., \\( \\mathbb{Z}^n \\) for some \\( n \\geq 0 \\). The rank of a free abelian group is the number of summands \\( n \\).\n\nNow, does a free abelian group exist for every positive integer rank? Well, for any positive integer \\( n \\), \\( \\" + } + }, + { + "sample_id": "mmlu_pro-math-21", + "predictions": { + "mmlu_pro:math": "I" + }, + "ground_truth": { + "mmlu_pro:math": "I" + }, + "correct": 1, + "total": 1, + "inference_time_s": 53.89131878700209, + "error": null, + "extra": { + "raw_response": "Okay, I need to tackle this multiple-choice question about statements related to the external direct product of cyclic groups and dihedral groups. Let me break this down.\n\nFirst, I need to understand what the statements are saying:\n\n**Statement 1:** \"The external direct product of cyclic groups is cyclic.\"\n\n**Statement 2:** \"The external direct product of D_3 and D_4 is isomorphic to D_12.\"\n\nI need to evaluate the truth value of each statement and then see how they relate to each other based on the options provided.\n\n### Understanding Statement 1: \"The external direct product of cyclic groups is cyclic.\"\n\nFirst, what is an external direct product? From what I recall, the external direct product of groups \\( G \\) and \\( H \\) is the group whose elements are ordered pairs \\((g, h)\\) where \\( g \\in G \\) and \\( h \\in H \\), with the group operation defined component-wise: \\((g_1, h_1)(g_2, h_2) = (g_1 g_2, h_1 h_2)\\).\n\nNow, if \\( G \\) and \\( H \\) are cyclic groups, is their external direct p" + } + }, + { + "sample_id": "mmlu_pro-math-22", + "predictions": { + "mmlu_pro:math": "B" + }, + "ground_truth": { + "mmlu_pro:math": "G" + }, + "correct": 0, + "total": 1, + "inference_time_s": 54.44780092899964, + "error": null, + "extra": { + "raw_response": "Okay, I need to evaluate two statements about free abelian groups and their bases. Let's break this down.\n\nFirst, recall that a free abelian group is a direct sum of copies of the integers, i.e., \\( \\mathbb{Z}^n \\) for some non-negative integer \\( n \\). The rank of the group is \\( n \\). A basis for a free abelian group is a set of elements that generates the group and is linearly independent over \\( \\mathbb{Z} \\).\n\n**Statement 1:** Every nonzero free abelian group has an infinite number of bases.\n\nA nonzero free abelian group means \\( n \\geq 1 \\). For \\( n = 1 \\), the group is \\( \\mathbb{Z} \\). The standard basis is \\( \\{1\\} \\), but are there other bases? Well, any nonzero integer \\( k \\) generates \\( \\mathbb{Z} \\), so \\( \\{k\\} \\) is also a basis. There are infinitely many choices for \\( k \\) (e.g., \\( \\{1\\}, \\{2\\}, \\{3\\}, \\ldots \\)), so for \\( n = 1 \\), there are indeed infinitely many bases.\n\nFor \\( n \\geq 2 \\), the situation is more complex. A basis for \\( \\mathbb{Z}^n \\) is a set o" + } + }, + { + "sample_id": "mmlu_pro-math-23", + "predictions": { + "mmlu_pro:math": "G" + }, + "ground_truth": { + "mmlu_pro:math": "A" + }, + "correct": 0, + "total": 1, + "inference_time_s": 58.28684933200202, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out which of these options is a binomial random variable. Let me recall what a binomial random variable is. From what I remember, a binomial random variable is the number of successes in a fixed number of independent trials, where each trial has the same probability of success. The key points are:\n\n1. Fixed number of trials (n).\n2. Each trial is independent.\n3. Each trial has the same probability of success (p).\n4. The outcome is binary (success or failure).\n\nNow, let's go through each option one by one.\n\n**Option A: The number of motorists not wearing seat belts in a random sample of five drivers.**\n\n- Fixed number of trials: Yes, it's a sample of five drivers.\n- Independence: Assuming the drivers are independent, this might hold.\n- Same probability of success: Each driver has the same probability of not wearing a seat belt, assuming the sample is random.\n- Binary outcome: Yes, each driver either is or isn't wearing a seat belt.\n\nThis seems to fit the binomial c" + } + }, + { + "sample_id": "mmlu_pro-math-24", + "predictions": { + "mmlu_pro:math": "E" + }, + "ground_truth": { + "mmlu_pro:math": "H" + }, + "correct": 0, + "total": 1, + "inference_time_s": 76.82116685899746, + "error": null, + "extra": { + "raw_response": "Okay, I need to find the standard deviation of the weights of the packed boxes. The problem gives me several pieces of information:\n\n1. Mean weight of books per box: 25 pounds, standard deviation: 2 pounds.\n2. Mean weight of the boxes: 1 pound, standard deviation: 0.15 pounds.\n3. Mean weight of the packing material per box: 2 pounds, standard deviation: 0.25 pounds.\n\nFirst, I need to understand what the weight of a packed box consists of. It seems like the total weight of a packed box would be the sum of the weight of the books, the weight of the box itself, and the weight of the packing material. So, the total weight \\( W \\) can be expressed as:\n\\[ W = \\text{Books} + \\text{Box} + \\text{Packing Material} \\]\n\nNow, the mean of the total weight \\( W \\) would be the sum of the means of the individual components:\n\\[ \\mu_W = \\mu_{\\text{Books}} + \\mu_{\\text{Box}} + \\mu_{\\text{Packing Material}} \\]\nBut the question doesn't ask for the mean, it asks for the standard deviation of the total weigh" + } + }, + { + "sample_id": "mmlu_pro-physics-25", + "predictions": { + "mmlu_pro:physics": "I" + }, + "ground_truth": { + "mmlu_pro:physics": "I" + }, + "correct": 1, + "total": 1, + "inference_time_s": 15.95633376999831, + "error": null, + "extra": { + "raw_response": "Okay, I need to answer this multiple-choice question about the significance of the 1:2:4 resonance in Jupiter's moons system. First, I need to recall what I know about Jupiter's moons and orbital resonances.\n\nI remember that Jupiter has several moons, and some of them are in orbital resonances. The most famous one is the Galilean moons: Io, Europa, and Ganymede. I recall that Io and Europa are in a 1:2 resonance, meaning that for every orbit Io makes around Jupiter, Europa makes exactly two orbits. But the question mentions a 1:2:4 resonance, which likely involves three moons. I think this refers to Io, Europa, and Ganymede, where their orbital periods are in a 1:2:4 ratio.\n\nNow, what does this resonance mean? I recall that orbital resonances can have significant effects on the dynamics of the system. For example, in the case of Io, Europa, and Ganymede, the resonance helps to maintain their orbits and can cause tidal heating in Io due to the gravitational interactions with Jupiter and" + } + }, + { + "sample_id": "mmlu_pro-physics-26", + "predictions": { + "mmlu_pro:physics": "D" + }, + "ground_truth": { + "mmlu_pro:physics": "D" + }, + "correct": 1, + "total": 1, + "inference_time_s": 53.06772609199834, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out how we first accurately measured the diameter of Pluto. Let me think about the options one by one.\n\nFirst, I recall that Pluto is a dwarf planet located in the Kuiper Belt, far from Earth. Measuring its diameter accurately would require precise observations, especially since it's so small and distant.\n\nOption A: Lunar-based observations during Apollo missions. I know the Apollo missions were focused on the Moon, so I don't think they had the capability to measure Pluto's diameter accurately. Probably not this one.\n\nOption B: Voyager 2 spacecraft flyby in the 1980s. I remember that Voyager 2 visited the outer planets like Jupiter, Saturn, Uranus, and Neptune, but I don't recall it visiting Pluto. I think it didn't go that far. So, probably not B.\n\nOption C: Chandra X-ray Observatory. Chandra is an X-ray telescope, and it's used for studying high-energy phenomena like black holes and galaxy clusters. Pluto is not a strong X-ray emitter, so this doesn't seem rel" + } + }, + { + "sample_id": "mmlu_pro-physics-27", + "predictions": { + "mmlu_pro:physics": "D" + }, + "ground_truth": { + "mmlu_pro:physics": "D" + }, + "correct": 1, + "total": 1, + "inference_time_s": 8.523391647999233, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out what makes asteroids stand out in sky surveys. Let me think about the characteristics of asteroids and how they differ from other celestial bodies like stars.\n\nFirst, asteroids are rocky objects that orbit the sun, mainly found in the asteroid belt between Mars and Jupiter. They don't have atmospheres and are much smaller than planets. So, options that mention size (C) or heat emission (G) might not be the best fit because asteroids are not particularly large or hot compared to other celestial bodies.\n\nNow, let's consider the options one by one:\n\nA. They reflect enough of the sun's light to make them brighter than most background stars.\n - Asteroids do reflect sunlight, but are they brighter than most background stars? Stars are much farther away, but they emit their own light, which can be very bright. Asteroids reflect sunlight, but they are not necessarily brighter than stars. This might not be the best answer.\n\nB. Asteroids rotate at a high speed, makin" + } + }, + { + "sample_id": "mmlu_pro-physics-28", + "predictions": { + "mmlu_pro:physics": "I" + }, + "ground_truth": { + "mmlu_pro:physics": "B" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.76141119100066, + "error": null, + "extra": { + "raw_response": "Okay, I need to answer this multiple-choice question about the distance to the Andromeda Galaxy. I remember that the Andromeda Galaxy is one of the closest galaxies to our Milky Way. I recall that it's often mentioned to be around 2.5 million light-years away, but I'm not entirely sure. Let me think about this carefully.\n\nFirst, I recall that the Andromeda Galaxy is also known as M31. I think I've heard that it's the nearest major galaxy to the Milky Way. I remember reading that it's about 2.5 million light-years away, but I'm not sure if that's exact or if it's an approximation.\n\nI also recall that the distance to Andromeda has been measured using various methods, including the observation of variable stars like Cepheids. I think the most commonly cited figure is around 2.5 million light-years, but I'm not sure if that's the exact value or if it's been updated more recently.\n\nLooking at the options, option B is 2.5 million light-years, and option C is 2.1 million light-years. I'm not " + } + }, + { + "sample_id": "mmlu_pro-physics-29", + "predictions": { + "mmlu_pro:physics": "J" + }, + "ground_truth": { + "mmlu_pro:physics": "J" + }, + "correct": 1, + "total": 1, + "inference_time_s": 20.123942767997505, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out the correct answer for this multiple-choice question about the source of material that causes meteor showers. Let me go through each option one by one and think about whether it makes sense or not.\n\nFirst, I recall that meteor showers are usually associated with comets. I remember something about comets leaving a trail of dust and debris as they orbit the sun. When Earth passes through this trail, the debris burns up in our atmosphere, creating a meteor shower. That sounds familiar, but I need to verify this against the options.\n\nLet's look at option A: \"Large meteorites disintegrate in the Earth's atmosphere, creating smaller particles that cause a meteor shower.\"\nHmm, large meteorites disintegrating would create smaller particles, but I don't think this is the primary cause of meteor showers. Meteor showers are more about periodic events, not just random disintegration of large meteorites. So, probably not A.\n\nOption B: \"Near-Earth asteroids gradually disin" + } + }, + { + "sample_id": "mmlu_pro-physics-30", + "predictions": { + "mmlu_pro:physics": "F" + }, + "ground_truth": { + "mmlu_pro:physics": "F" + }, + "correct": 1, + "total": 1, + "inference_time_s": 19.539291639997828, + "error": null, + "extra": { + "raw_response": "Okay, I need to understand how the greenhouse effect works to answer this question correctly. The greenhouse effect is a process where certain gases in the Earth's atmosphere trap heat, making the planet warmer than it would be without them.\n\nFirst, I recall that greenhouse gases, like carbon dioxide and methane, play a key role in this process. They don't absorb visible light directly, but they do absorb infrared radiation. So, when sunlight reaches the Earth's surface, it's mostly visible light that heats up the surface. The Earth then re-radiates this heat as infrared light. Greenhouse gases absorb this infrared light and re-emit it in all directions, including back towards the Earth's surface, which traps heat and warms the atmosphere and surface.\n\nNow, let's look at the options:\n\nA. Ozone absorbs infrared light from the Sun and then re-emits it, heating the atmosphere and the surface.\n - Ozone does absorb some infrared light, but its main role is in absorbing ultraviolet (UV) li" + } + }, + { + "sample_id": "mmlu_pro-physics-31", + "predictions": { + "mmlu_pro:physics": "I" + }, + "ground_truth": { + "mmlu_pro:physics": "G" + }, + "correct": 0, + "total": 1, + "inference_time_s": 55.027140439000505, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out which wavelength is most strongly reflected when white light hits a puddle of water with a thin layer of oil on top. The oil layer is 500 nm thick, and the indices of refraction are given: water is 1.33, oil is 1.5.\n\nFirst, I recall that when light reflects off a thin film, interference occurs between the light reflected from the top surface of the film and the light reflected from the bottom surface of the film (where the film meets the water). This is called thin-film interference.\n\nFor constructive interference (which leads to strong reflection), the path difference between these two reflected rays should be an integer multiple of the wavelength in the film. But I also need to consider the phase changes that occur upon reflection.\n\nLet me break this down:\n\n1. **Phase Change on Reflection**:\n - When light reflects off a medium with a higher refractive index, there's a 180-degree phase shift (or \u03c0 radians).\n - When light reflects off a medium with a lowe" + } + }, + { + "sample_id": "mmlu_pro-physics-32", + "predictions": { + "mmlu_pro:physics": "E" + }, + "ground_truth": { + "mmlu_pro:physics": "E" + }, + "correct": 1, + "total": 1, + "inference_time_s": 56.811949281000125, + "error": null, + "extra": { + "raw_response": "Okay, I need to solve this problem about a coin on a turntable. The question is asking for the maximum distance from the center where the coin won't slide, given the coefficient of static friction and the rotational speed.\n\nFirst, I recall that when an object is on a rotating surface, the static friction provides the centripetal force needed to keep it moving in a circular path without sliding. The maximum static friction force is given by \\( f_{s, max} = \\mu_s \\cdot N \\), where \\( \\mu_s \\) is the coefficient of static friction and \\( N \\) is the normal force. Since the coin is on a horizontal surface, the normal force \\( N \\) is equal to the weight of the coin, \\( mg \\), where \\( m \\) is the mass of the coin and \\( g \\) is the acceleration due to gravity.\n\nSo, the maximum static friction force is \\( \\mu_s \\cdot mg \\).\n\nNow, the centripetal force required to keep the coin moving in a circle of radius \\( r \\) at angular velocity \\( \\omega \\) is \\( F_c = m \\omega^2 r \\).\n\nAt the point wh" + } + }, + { + "sample_id": "mmlu_pro-physics-33", + "predictions": { + "mmlu_pro:physics": "I" + }, + "ground_truth": { + "mmlu_pro:physics": "C" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.70315273899905, + "error": null, + "extra": { + "raw_response": "Okay, let's break this down step by step.\n\nFirst, the proton is accelerated from rest through a potential difference V. That means it gains kinetic energy, and its velocity will be in the +z-direction because that's the direction it's accelerated in. The kinetic energy gained is eV (where e is the charge of the proton), so the velocity v can be calculated from that.\n\nNext, the proton enters a region with both an electric field E in the +x-direction and a magnetic field B in the +y-direction. The problem states that the proton's trajectory is not affected by these fields. That means the net force on the proton in this region must be zero. So, the electric force and the magnetic force must cancel each other out.\n\nLet's recall the forces:\n- Electric force: F_e = qE (since the proton is positively charged, q = e)\n- Magnetic force: F_m = q(v \u00d7 B)\n\nThe electric field is in the +x-direction, so F_e is in the +x-direction (since q is positive). The magnetic field is in the +y-direction, and th" + } + }, + { + "sample_id": "mmlu_pro-physics-34", + "predictions": { + "mmlu_pro:physics": "B" + }, + "ground_truth": { + "mmlu_pro:physics": "J" + }, + "correct": 0, + "total": 1, + "inference_time_s": 59.58960317200035, + "error": null, + "extra": { + "raw_response": "Okay, the question is about the kinetic energy of electrons needed to observe a diffraction pattern when they impinge on a crystal surface. The lattice spacing is given as 0.4 nm. I need to figure out which of the provided options corresponds to the approximate kinetic energy required for this phenomenon.\n\nFirst, I recall that electron diffraction is a well-known phenomenon, especially in the context of crystallography. The diffraction pattern arises when the wavelength of the electrons is comparable to the lattice spacing of the crystal. So, the key here is to relate the kinetic energy of the electrons to their wavelength and then match that wavelength to the given lattice spacing.\n\nThe de Broglie wavelength (\u03bb) of an electron is given by the equation:\n\u03bb = h / p\nwhere h is Planck's constant and p is the momentum of the electron.\n\nFor non-relativistic electrons, the momentum p can be expressed in terms of the kinetic energy (K) as:\np = sqrt(2 * m * K)\nwhere m is the mass of the electro" + } + }, + { + "sample_id": "mmlu_pro-physics-35", + "predictions": { + "mmlu_pro:physics": "C" + }, + "ground_truth": { + "mmlu_pro:physics": "H" + }, + "correct": 0, + "total": 1, + "inference_time_s": 82.70427421599743, + "error": null, + "extra": { + "raw_response": "Okay, I have this question about an organ pipe that's closed at one end and open at the other. It's designed to have a fundamental frequency of C, which is 131 Hz. The question is asking for the frequency of the next higher harmonic for this pipe.\n\nFirst, I need to recall the properties of organ pipes. I remember that organ pipes can be either open at both ends or closed at one end. The ones that are closed at one end are called \"closed pipes,\" and they have different harmonic series compared to open pipes.\n\nFor a closed pipe, the fundamental frequency (the lowest frequency) is given by the formula:\n\\[ f_1 = \\frac{v}{4L} \\]\nwhere \\( v \\) is the speed of sound in air, and \\( L \\) is the length of the pipe.\n\nThe harmonics for a closed pipe are different from those of an open pipe. For a closed pipe, the harmonics are the odd harmonics of the fundamental frequency. That means the next higher harmonic would be the third harmonic, not the second like in an open pipe.\n\nSo, if the fundamental" + } + }, + { + "sample_id": "mmlu_pro-physics-36", + "predictions": { + "mmlu_pro:physics": "C" + }, + "ground_truth": { + "mmlu_pro:physics": "F" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.90238518499973, + "error": null, + "extra": { + "raw_response": "Okay, I have this problem about two spaceships approaching Earth at the same speed but from opposite directions. There's a meterstick on one spaceship that's measured to be 60 cm long by an occupant of the other spaceship. I need to find out the speed of each spaceship as measured by an observer on Earth. The options are given from A to J, with speeds like 0.4c, 0.1c, etc.\n\nFirst, I recall that when dealing with speeds close to the speed of light, we need to consider special relativity because the speeds are a significant fraction of the speed of light (c). The problem mentions that the meterstick is measured to be shorter by the occupant of the other spaceship, which is a classic case of length contraction.\n\nLet me break this down:\n\n1. **Understanding the scenario**:\n - Two spaceships are moving towards Earth at the same speed, say v, but from opposite directions. So, if one is coming from the left, the other is coming from the right, both at speed v relative to Earth.\n - A meters" + } + }, + { + "sample_id": "mmlu_pro-philosophy-37", + "predictions": { + "mmlu_pro:philosophy": "E" + }, + "ground_truth": { + "mmlu_pro:philosophy": "A" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.88344576000236, + "error": null, + "extra": { + "raw_response": "Okay, I need to translate the statement \"David teaches Chris\" into predicate logic using the given symbols and constants.\n\nFirst, let's recall the given information:\n- c represents Chris.\n- d represents David.\n- Txy is a predicate that means \"x teaches y.\"\n\nThe statement is \"David teaches Chris.\" So, the subject (who teaches) is David, and the object (who is taught) is Chris.\n\nIn predicate logic, the order in the predicate Txy is important. Txy means \"x teaches y,\" so the first argument is the teacher, and the second argument is the student.\n\nSo, for \"David teaches Chris\":\n- x should be David (d).\n- y should be Chris (c).\n\nTherefore, the correct translation should be Tdc, where the first argument is d (David) and the second is c (Chris).\n\nNow, let's look at the options:\nA. Tdc\nB. Tcc\nC. cTd\nD. cTc\nE. dTdc\nF. dTc\nG. Tcd\nH. Tdd\nI. dTcd\nJ. cTdd\n\nFrom our reasoning, the correct translation is Tdc, which corresponds to option A.\n\nBut wait, I need to double-check the order. The predicate is " + } + }, + { + "sample_id": "mmlu_pro-philosophy-38", + "predictions": { + "mmlu_pro:philosophy": "H" + }, + "ground_truth": { + "mmlu_pro:philosophy": "D" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.975865921998775, + "error": null, + "extra": { + "raw_response": "Okay, I need to tackle this logic problem. It's about constructing truth tables for two complex propositions and then determining their logical relationship. The options are about whether they're logically equivalent, contradictory, consistent, or inconsistent. Let me break this down.\n\nFirst, I need to understand the two propositions:\n\n1. (~M \u2283 ~N) \u2228 (O \u2261 N)\n2. (~M \u00b7 N) \u00b7 [(~O \u2228 ~N) \u00b7 (O \u2228 N)]\n\nI need to construct truth tables for both. Since there are three variables (M, N, O), the truth table will have 2^3 = 8 rows.\n\nBut before diving into the truth table, I need to simplify or understand these expressions better.\n\n### Understanding the Propositions\n\n**First Proposition: (~M \u2283 ~N) \u2228 (O \u2261 N)**\n\nLet's break it down:\n- (~M \u2283 ~N): This is an implication. A \u2283 B is equivalent to ~A \u2228 B. So, ~M \u2283 ~N is equivalent to M \u2228 ~N (since ~(~M) is M, and then ~(~N) is N, but wait, no: A \u2283 B is ~A \u2228 B. So here, A is ~M, B is ~N. So ~(~M) \u2228 ~N, which is M \u2228 ~N. Wait, no: A \u2283 B is equivalent to ~A \u2228 B." + } + }, + { + "sample_id": "mmlu_pro-philosophy-39", + "predictions": { + "mmlu_pro:philosophy": "E" + }, + "ground_truth": { + "mmlu_pro:philosophy": "I" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.88438469900211, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out which proposition is an immediate consequence of the given premises in propositional logic (PL). The premises are:\n\n1. U \u2283 W\n2. W \u2283 (X \u2261 ~Y)\n3. (X \u2261 ~Y) \u2283 Z\n4. ~Z\n\nAnd the options are A through J. I need to find which one is a one-step consequence of these premises.\n\nFirst, let me recall what an immediate consequence means. It's a statement that can be derived directly from the premises in one logical step, without needing intermediate steps or additional premises.\n\nLet me list the premises again for clarity:\n\n1. U \u2192 W (I'll use \u2192 for material implication for simplicity)\n2. W \u2192 (X \u2261 \u00acY)\n3. (X \u2261 \u00acY) \u2192 Z\n4. \u00acZ\n\nI need to see which of the options follows directly from these.\n\nLet me think about the structure here. We have a chain of implications:\n\nU \u2192 W \u2192 (X \u2261 \u00acY) \u2192 Z\n\nAnd we're given \u00acZ.\n\nHmm, if we have A \u2192 B and \u00acB, then by modus tollens, we can conclude \u00acA.\n\nLooking at the chain, the last implication is (X \u2261 \u00acY) \u2192 Z, and we have \u00acZ. So, by modus tollens, we " + } + }, + { + "sample_id": "mmlu_pro-philosophy-40", + "predictions": { + "mmlu_pro:philosophy": "A" + }, + "ground_truth": { + "mmlu_pro:philosophy": "A" + }, + "correct": 1, + "total": 1, + "inference_time_s": 7.191275132998271, + "error": null, + "extra": { + "raw_response": "Okay, I need to translate the sentence \"Holly loves Frances\" into predicate logic using the given symbols. The symbols provided are:\n- f: Frances\n- h: Holly\n- Lxy: x loves y\n\nThe sentence is about Holly loving Frances. So, the subject is Holly (h) and the object is Frances (f). The predicate is \"loves,\" which is represented by Lxy, where the first argument is the lover (x) and the second argument is the beloved (y).\n\nSo, in this case, x would be Holly (h) and y would be Frances (f). Therefore, the correct translation should be Lhf, where L is the predicate, h is the first argument (the lover), and f is the second argument (the beloved).\n\nNow, let's look at the options:\nA. Lhf - This matches our reasoning: L (love), h (Holly), f (Frances).\nB. hLf - This seems to have the predicate in the wrong position. It looks like it's saying h loves Lf, which doesn't make sense.\nC. hLh - This would mean Holly loves Holly, which is not the case.\nD. Lfh - This would mean Frances loves Holly, which is " + } + }, + { + "sample_id": "mmlu_pro-philosophy-41", + "predictions": { + "mmlu_pro:philosophy": "E" + }, + "ground_truth": { + "mmlu_pro:philosophy": "E" + }, + "correct": 1, + "total": 1, + "inference_time_s": 10.037987842999428, + "error": null, + "extra": { + "raw_response": "Okay, I need to translate the statement \"Earth isn't bigger than Jupiter\" into predicate logic using the given symbols and options. The symbols provided are:\n- e: Earth\n- j: Jupiter\n- Bxy: x is bigger than y\n\nFirst, I need to understand the structure of the statement. The statement says that Earth is not bigger than Jupiter. In predicate logic, this would typically involve a predicate B (for \"is bigger than\") and two arguments: Earth (e) and Jupiter (j).\n\nThe phrase \"Earth isn't bigger than Jupiter\" can be broken down as follows:\n1. \"Earth is bigger than Jupiter\" would be written as Bej, where B is the predicate, e is the first argument (subject), and j is the second argument (object).\n2. The negation of this statement would be ~Bej, where ~ represents negation.\n\nNow, let's look at the options to see which one matches ~Bej.\n\nOption A: j~Be - This seems to have a different structure. It starts with j, which is Jupiter, followed by ~Be. This doesn't seem to match our expected ~Bej.\n\nOpti" + } + }, + { + "sample_id": "mmlu_pro-philosophy-42", + "predictions": { + "mmlu_pro:philosophy": "I" + }, + "ground_truth": { + "mmlu_pro:philosophy": "I" + }, + "correct": 1, + "total": 1, + "inference_time_s": 15.943554776000383, + "error": null, + "extra": { + "raw_response": "Okay, I need to translate the statement \"All birds live in some nest\" into predicate logic. The predicates given are:\n- Bx: x is a bird\n- Nx: x is a nest\n- Lxy: x lives in y\n\nFirst, I need to understand the original statement. \"All birds live in some nest\" means that for every bird, there exists at least one nest in which it lives.\n\nLet's break it down:\n1. \"All birds\" suggests a universal quantifier (\u2200x) over birds (Bx).\n2. \"live in some nest\" suggests that for each bird, there exists a nest (\u2203y) such that the bird lives in that nest (Lxy).\n\nSo, the structure should be: For all x, if x is a bird (Bx), then there exists a y such that y is a nest (Ny) and x lives in y (Lxy).\n\nNow, let's look at the options to see which one matches this structure.\n\nOption A: (\u2203x)[Bx \u2283 (\u2203y)(Ny \u2022 Lxy)]\nThis says there exists an x such that if x is a bird, then there exists a y that is a nest and x lives in y. This is not correct because it's existential for x, not universal. It's saying \"there is a bird tha" + } + }, + { + "sample_id": "mmlu_pro-philosophy-43", + "predictions": { + "mmlu_pro:philosophy": "D" + }, + "ground_truth": { + "mmlu_pro:philosophy": "D" + }, + "correct": 1, + "total": 1, + "inference_time_s": 53.85483439699965, + "error": null, + "extra": { + "raw_response": "Okay, I need to determine if the given argument is valid using indirect truth tables. If it's invalid, I need to choose the correct counterexample from the options provided.\n\nFirst, let's understand the argument. It's a set of premises and a conclusion. The argument is:\n\n1. L \u2283 [(M \u2228 ~N) \u2283 O]\n2. (N \u2283 O) \u2283 (~P \u2283 Q)\n3. R \u2283 ~Q\n4. Therefore, L \u2283 (R \u2283 P)\n\nI need to check if the conclusion logically follows from the premises. If it doesn't, I need to find a counterexample where all premises are true, but the conclusion is false.\n\n### Step 1: Understand the structure\nThe argument has three premises and one conclusion. To check validity, I need to see if there's any scenario where all premises are true, but the conclusion is false.\n\n### Step 2: Analyze the conclusion\nThe conclusion is L \u2283 (R \u2283 P). This can be read as \"If L is true, then if R is true, P must be true.\" In logical terms, this is equivalent to ~L \u2228 ~R \u2228 P (by material implication).\n\nFor the conclusion to be false, all of L, R, and" + } + }, + { + "sample_id": "mmlu_pro-philosophy-44", + "predictions": { + "mmlu_pro:philosophy": "I" + }, + "ground_truth": { + "mmlu_pro:philosophy": "J" + }, + "correct": 0, + "total": 1, + "inference_time_s": 55.08722270499857, + "error": null, + "extra": { + "raw_response": "Okay, I need to identify the conclusion of the given argument. The argument is about whether it's wrong for society to kill a murderer. The text says: \"It is wrong for society to kill a murderer. This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer. And a murderer is wrong in killing his victim.\"\n\nFirst, I need to understand the structure of this argument. It seems to be a syllogism or a logical argument with a premise and a conclusion. The conclusion is usually the statement that is being argued for, and it's often preceded by phrases like \"therefore,\" \"thus,\" or \"hence.\" However, in this case, the conclusion is stated first: \"It is wrong for society to kill a murderer.\"\n\nBut the argument also includes a reasoning part: \"This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer. And a murderer is wrong in killing his victim.\"\n\nSo, the arg" + } + }, + { + "sample_id": "mmlu_pro-philosophy-45", + "predictions": { + "mmlu_pro:philosophy": "J" + }, + "ground_truth": { + "mmlu_pro:philosophy": "D" + }, + "correct": 0, + "total": 1, + "inference_time_s": 27.045506946000387, + "error": null, + "extra": { + "raw_response": "Okay, I need to answer this multiple-choice question about Reiman's take on van den Haag's argument regarding the death penalty. I'm not entirely sure about the exact details of Reiman's and van den Haag's views, but I can try to reason through this based on what I know about their general positions.\n\nFirst, I recall that van den Haag is a prominent figure who has argued in favor of the death penalty. His arguments often revolve around the idea that capital punishment is a necessary evil, serving as a deterrent and providing retribution for heinous crimes. He might also argue that the death penalty is the ultimate form of justice, especially for the worst offenders.\n\nNow, Reiman is likely critiquing or interpreting van den Haag's argument. I remember that Reiman is known for his critical perspectives on punishment and criminal justice. He might challenge the notion that the death penalty is justified or effective. But the question is about what Reiman concludes based on van den Haag's " + } + }, + { + "sample_id": "mmlu_pro-philosophy-46", + "predictions": { + "mmlu_pro:philosophy": "C" + }, + "ground_truth": { + "mmlu_pro:philosophy": "H" + }, + "correct": 0, + "total": 1, + "inference_time_s": 52.858646914999554, + "error": null, + "extra": { + "raw_response": "Okay, I'm trying to figure out this multiple-choice question about Ashford's article. The question is asking what particular paralysis Ashford's article is meant to address. I need to look at the options and see which one fits best.\n\nFirst, I recall that Ashford is likely referring to a philosopher or scholar, possibly related to ethics or moral philosophy, given the context of the options. The options seem to revolve around moral dilemmas, economic issues, and global challenges.\n\nLet's break down the options:\n\nA. The daunting task of solving worldwide economic imbalance. This seems more about economic policy than moral philosophy. Maybe not the best fit.\n\nB. The impossibility of meeting everyone's basic needs. This is a broad issue, but it's more about feasibility than paralysis in moral reasoning.\n\nC. Having to give up so much of our own wealth in light of Singer's arguments. Peter Singer is known for his work on moral obligation to charity, especially regarding global poverty. This " + } + }, + { + "sample_id": "mmlu_pro-philosophy-47", + "predictions": { + "mmlu_pro:philosophy": "B" + }, + "ground_truth": { + "mmlu_pro:philosophy": "D" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.1585497140004, + "error": null, + "extra": { + "raw_response": "Okay, I need to answer this multiple-choice question about Reiman's critique of van den Haag's arguments in favor of the death penalty. I'm not entirely sure about the exact details of Reiman's and van den Haag's arguments, but I can try to reason through this based on what I know about the topic.\n\nFirst, I recall that van den Haag was a prominent defender of the death penalty. His arguments often revolved around retribution and deterrence. Retribution is the idea that punishment, especially capital punishment, is justified because it gives society a way to retaliate against criminals for their crimes. Deterrence is the notion that the death penalty prevents future crimes by serving as a strong deterrent.\n\nNow, Reiman is likely a critic of the death penalty. I remember that some critics argue that van den Haag's arguments are flawed, particularly in terms of empirical evidence. For example, there's a lot of debate about whether the death penalty actually deters crime more effectively t" + } + }, + { + "sample_id": "mmlu_pro-philosophy-48", + "predictions": { + "mmlu_pro:philosophy": "J" + }, + "ground_truth": { + "mmlu_pro:philosophy": "G" + }, + "correct": 0, + "total": 1, + "inference_time_s": 53.57613648500046, + "error": null, + "extra": { + "raw_response": "Okay, I need to figure out Pence's main objective in his article \"Will Cloning Harm People?\" based on the given options. I don't have the actual article, but I can infer from the title and the options provided.\n\nFirst, the title \"Will Cloning Harm People?\" suggests that the article is concerned with the ethical implications of cloning, specifically whether it causes harm to people. The word \"harm\" implies that the focus is on the negative consequences or moral acceptability of cloning.\n\nNow, let's look at the options:\n\nA. to use Kant's humanity formulation to show that cloning is morally acceptable\nB. to argue for the potential benefits of cloning\nC. to use consequentialist arguments to show that cloning is immoral\nD. to use virtue ethics to prove that cloning is morally unacceptable\nE. to use Kant's humanity formulation to show that cloning is immoral\nF. to use utilitarian arguments to show that cloning is immoral\nG. to object to consequentialist arguments against cloning\nH. to argue " + } + } + ], + "metrics": { + "gsm8k_acc": 0.86, + "mmlu_pro_acc": 0.3125 + } +} \ No newline at end of file