{
  "schema_version": 1,
  "created_utc": "2026-10-21T14:17:54.159160+00:00",
  "model": {
    "model_id": "Qwen/Qwen2.5-1.5B-Instruct",
    "revision": "989aa7980e4cf806f80c7fef2b1adb7bc71aa306"
  },
  "runtime": {
    "python": "3.12.14",
    "torch": "2.14.1",
    "transformers": "4.57.1",
    "platform": "macOS-27.0.1-arm64-arm-64bit",
    "device": "cpu",
    "dtype": "float32",
    "threads": 2
  },
  "protocol": "Development demo after inspecting strict-schema failures. Adds disjoint few-shot formatting examples and explicitly permits one enclosing JSON code fence. New scenario sizes illustrate operation, not an unbiased performance estimate.",
  "runner_sha256": "77cff66c5bc99788b8334c6a51021ccbc61ab91a83ac970933670841c87fdac0",
  "tasks": [
    {
      "question": "Use iid normal observations, sample size 36, to estimate coverage of the mean plus or minus 1.96 estimated standard errors.",
      "family": "normal",
      "n": 36
    },
    {
      "question": "Use iid exponential observations, sample size 24, to estimate coverage of the mean plus or minus 1.96 estimated standard errors.",
      "family": "exponential",
      "n": 24
    },
    {
      "question": "Use iid Cauchy observations, sample size 30, to estimate coverage.",
      "family": "unsupported",
      "n": 30
    }
  ],
  "rows": [
    {
      "question": "Use iid normal observations, sample size 36, to estimate coverage of the mean plus or minus 1.96 estimated standard errors.",
      "success": false,
      "request": {
        "family": "normal",
        "n": 36
      },
      "interpretation_correct": true,
      "tool_result": {
        "family": "normal",
        "n": 36,
        "estimate": 0.944,
        "repetitions": 500,
        "mc_interval": [
          0.9202547013596158,
          0.9609746373849419
        ],
        "seed": 2026
      },
      "status": "invalid",
      "error": "Wrong fields; expected family, n, estimate, explanation",
      "call_ids": [
        0,
        1
      ]
    },
    {
      "question": "Use iid exponential observations, sample size 24, to estimate coverage of the mean plus or minus 1.96 estimated standard errors.",
      "success": false,
      "request": {
        "family": "exponential",
        "n": 24
      },
      "interpretation_correct": true,
      "tool_result": {
        "family": "exponential",
        "n": 24,
        "estimate": 0.916,
        "repetitions": 500,
        "mc_interval": [
          0.8884001169044927,
          0.9372562004777957
        ],
        "seed": 2026
      },
      "status": "invalid",
      "error": "Wrong fields; expected family, n, estimate, explanation",
      "call_ids": [
        2,
        3
      ]
    },
    {
      "question": "Use iid Cauchy observations, sample size 30, to estimate coverage.",
      "success": false,
      "request": {
        "family": "cauchy",
        "n": 30
      },
      "interpretation_correct": false,
      "status": "invalid",
      "error": "Only normal/exponential and integer n between 5 and 500",
      "call_ids": [
        4
      ]
    }
  ],
  "calls": [
    {
      "messages": [
        {
          "role": "system",
          "content": "Extract the sampling distribution and sample size. The interval formula does not determine the sampling distribution. Only normal and exponential are supported. Return exactly two keys: family and n. Follow the JSON examples."
        },
        {
          "role": "user",
          "content": "Use exponential observations with sample size 10."
        },
        {
          "role": "assistant",
          "content": "{\"family\":\"exponential\",\"n\":10}"
        },
        {
          "role": "user",
          "content": "Use uniform observations with sample size 15."
        },
        {
          "role": "assistant",
          "content": "{\"family\":\"unsupported\",\"n\":15}"
        },
        {
          "role": "user",
          "content": "Use iid normal observations, sample size 36, to estimate coverage of the mean plus or minus 1.96 estimated standard errors."
        }
      ],
      "raw": "{\"family\":\"normal\",\"n\":36}",
      "prompt_tokens": 142,
      "generated_tokens": 11,
      "max_new_tokens": 128,
      "stop_reason": "eos",
      "elapsed_seconds": 4.928
    },
    {
      "messages": [
        {
          "role": "system",
          "content": "Return JSON with exactly family, n, estimate, explanation. Copy family, n, estimate from the input. Explain that estimated coverage is not a guarantee. Do not add fields."
        },
        {
          "role": "user",
          "content": "{\"family\":\"normal\",\"n\":10,\"estimate\":0.9}"
        },
        {
          "role": "assistant",
          "content": "{\"family\":\"normal\",\"n\":10,\"estimate\":0.9,\"explanation\":\"This Monte Carlo estimate describes the specified procedure; it is not a coverage guarantee.\"}"
        },
        {
          "role": "user",
          "content": "{\"family\": \"normal\", \"n\": 36, \"estimate\": 0.944, \"repetitions\": 500, \"mc_interval\": [0.9202547013596158, 0.9609746373849419], \"seed\": 2026}"
        }
      ],
      "raw": "{\"family\":\"normal\",\"n\":36,\"estimate\":0.944,\"repetitions\":500,\"mc_interval\":[0.9202547013596158,0.9609746373849419],\"seed\":2026,\"explanation\":\"The provided data includes an estimate of 0.944 for a normal distribution with 36 samples and 500 repetitions using a seed value of 2026. The interval represents the range within which the true parameter likely falls with a certain level of confidence (92% to 96%).\"}",
      "prompt_tokens": 197,
      "generated_tokens": 145,
      "max_new_tokens": 160,
      "stop_reason": "eos",
      "elapsed_seconds": 21.464
    },
    {
      "messages": [
        {
          "role": "system",
          "content": "Extract the sampling distribution and sample size. The interval formula does not determine the sampling distribution. Only normal and exponential are supported. Return exactly two keys: family and n. Follow the JSON examples."
        },
        {
          "role": "user",
          "content": "Use exponential observations with sample size 10."
        },
        {
          "role": "assistant",
          "content": "{\"family\":\"exponential\",\"n\":10}"
        },
        {
          "role": "user",
          "content": "Use uniform observations with sample size 15."
        },
        {
          "role": "assistant",
          "content": "{\"family\":\"unsupported\",\"n\":15}"
        },
        {
          "role": "user",
          "content": "Use iid exponential observations, sample size 24, to estimate coverage of the mean plus or minus 1.96 estimated standard errors."
        }
      ],
      "raw": "{\"family\":\"exponential\",\"n\":24}",
      "prompt_tokens": 142,
      "generated_tokens": 12,
      "max_new_tokens": 128,
      "stop_reason": "eos",
      "elapsed_seconds": 1.585
    },
    {
      "messages": [
        {
          "role": "system",
          "content": "Return JSON with exactly family, n, estimate, explanation. Copy family, n, estimate from the input. Explain that estimated coverage is not a guarantee. Do not add fields."
        },
        {
          "role": "user",
          "content": "{\"family\":\"normal\",\"n\":10,\"estimate\":0.9}"
        },
        {
          "role": "assistant",
          "content": "{\"family\":\"normal\",\"n\":10,\"estimate\":0.9,\"explanation\":\"This Monte Carlo estimate describes the specified procedure; it is not a coverage guarantee.\"}"
        },
        {
          "role": "user",
          "content": "{\"family\": \"exponential\", \"n\": 24, \"estimate\": 0.916, \"repetitions\": 500, \"mc_interval\": [0.8884001169044927, 0.9372562004777957], \"seed\": 2026}"
        }
      ],
      "raw": "{\"family\":\"exponential\",\"n\":24,\"estimate\":0.916,\"repetitions\":500,\"mc_interval\":[0.8884001169044927,0.9372562004777957],\"seed\":2026,\"explanation\":\"The exponential distribution's estimate of 0.916 was obtained through 500 repetitions using a seed value of 2026. The interval suggests a range within which the true parameter likely falls.\"}",
      "prompt_tokens": 198,
      "generated_tokens": 124,
      "max_new_tokens": 160,
      "stop_reason": "eos",
      "elapsed_seconds": 31.033
    },
    {
      "messages": [
        {
          "role": "system",
          "content": "Extract the sampling distribution and sample size. The interval formula does not determine the sampling distribution. Only normal and exponential are supported. Return exactly two keys: family and n. Follow the JSON examples."
        },
        {
          "role": "user",
          "content": "Use exponential observations with sample size 10."
        },
        {
          "role": "assistant",
          "content": "{\"family\":\"exponential\",\"n\":10}"
        },
        {
          "role": "user",
          "content": "Use uniform observations with sample size 15."
        },
        {
          "role": "assistant",
          "content": "{\"family\":\"unsupported\",\"n\":15}"
        },
        {
          "role": "user",
          "content": "Use iid Cauchy observations, sample size 30, to estimate coverage."
        }
      ],
      "raw": "{\"family\":\"cauchy\",\"n\":30}",
      "prompt_tokens": 130,
      "generated_tokens": 13,
      "max_new_tokens": 128,
      "stop_reason": "eos",
      "elapsed_seconds": 2.471
    }
  ]
}