{
  "summary": {
    "method": "IO",
    "model": "qwen2.5:32b",
    "task": "math",
    "samples": 10,
    "correct": 8,
    "accuracy": 0.8,
    "avg_time_s": 0.89
  },
  "details": [
    {
      "question": "Find the value of $x$ such that $\\sqrt{4x + 5} = 7$.",
      "expected": "11",
      "predicted": "12",
      "full_response": "12",
      "correct": false,
      "time_s": 0.49,
      "tokens": 1
    },
    {
      "question": "A box contains 5 red balls and 7 blue balls. If two balls are drawn at random without replacement, what is the probability that both balls are red? Express your answer as a fraction in simplest form.",
      "expected": "5/33",
      "predicted": "5/33",
      "full_response": "5/33",
      "correct": true,
      "time_s": 0.65,
      "tokens": 2
    },
    {
      "question": "What is the sum of the first 20 positive integers?",
      "expected": "210",
      "predicted": "210",
      "full_response": "210",
      "correct": true,
      "time_s": 0.85,
      "tokens": 2
    },
    {
      "question": "If $f(x) = 2x^2 + 3x - 5$, find $f(-2)$.",
      "expected": "-3",
      "predicted": "-7",
      "full_response": "-7",
      "correct": false,
      "time_s": 1.0,
      "tokens": 1
    },
    {
      "question": "The sum of two numbers is 20 and their difference is 4. What is the product of the two numbers?",
      "expected": "96",
      "predicted": "96",
      "full_response": "96",
      "correct": true,
      "time_s": 0.95,
      "tokens": 1
    },
    {
      "question": "How many distinguishable permutations can be made from the letters in the word 'MISSISSIPPI'?",
      "expected": "34650",
      "predicted": "34650",
      "full_response": "34650",
      "correct": true,
      "time_s": 1.17,
      "tokens": 2
    },
    {
      "question": "Find the area of a circle with circumference $8\\pi$.",
      "expected": "16\\pi",
      "predicted": "16",
      "full_response": "$16\\pi$",
      "correct": true,
      "time_s": 1.11,
      "tokens": 3
    },
    {
      "question": "If $\\log_2(x) + \\log_2(x-2) = 3$, find $x$.",
      "expected": "4",
      "predicted": "4",
      "full_response": "4",
      "correct": true,
      "time_s": 0.82,
      "tokens": 1
    },
    {
      "question": "A geometric sequence has first term 3 and common ratio 2. What is the 8th term?",
      "expected": "384",
      "predicted": "384",
      "full_response": "384",
      "correct": true,
      "time_s": 1.01,
      "tokens": 2
    },
    {
      "question": "How many ways can 5 people be arranged in a line?",
      "expected": "120",
      "predicted": "120",
      "full_response": "120",
      "correct": true,
      "time_s": 0.85,
      "tokens": 2
    }
  ]
}