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proofs/87724.json
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{"schema": 2, "epoch": 87724, "nonce": "d8bbf9b0e21e4401", "hotkey": "5Dq9NdL3ZABAy1FDavc9UqEJz1XUV1SgCRpqr1JqmmeCCCw8", "source_hash": "24837b9ae6895829747c5eb448673693fedbeb2e3e62a5ca170051a512053fc0", "weights_hash": "dce18c768f5dca6835c0784f990235d96ea2f1bb905ab6341841d9cccece15a7", "model_id": "router", "total_cost_usd": 0.0011893688, "n_calls": 6, "call_log_hash": "01e16c4f1bac6fa003669e36dd3eeefd77075f3e62cbfc23a5137780416558d4", "measurement": "1449fadb4821cadef93f7eecc8c3b040e2cd244e01a2607ea531e5f7055c38d8", "confined": true, "latency_s": 59.612, "tokens_in": 1502, "tokens_out": 3924, "results": [{"benchmark": "mmlu", "task_id": "mmlu-9275", "answer": "D", "cost_usd": 8.25e-05, "chosen_rung": 1, "rungs_used": [1], "distribution": [0.302456, 0.684911, 1e-06, 1e-06, 0.01188, 1e-06, 0.00075]}, {"benchmark": "mmlu", "task_id": "mmlu-8065", "answer": "A", "cost_usd": 2.0999999999999995e-05, "chosen_rung": 0, "rungs_used": [0], "distribution": [0.61149, 0.155163, 5e-06, 5e-06, 0.226427, 5e-06, 0.006905]}, {"benchmark": "math", "task_id": "gsm8k-184", "answer": "The probability of rolling a number greater than 3 on a six-sided die is \\(\\frac{3}{6} = \\frac{1}{2} = 50\\%\\). The probability of rolling two even numbers in a row is \\(\\left(\\frac{3}{6}\\right)^2 = \\left(\\frac{1}{2}\\right)^2 = \\frac{1}{4} = 25\\%\\). The relative difference is \\(\\frac{50\\% - 25\\%}{25\\%} = \\frac{25\\%}{25\\%} = 1 = 100\\%\\). Thus, rolling a number greater than 3 is 100% more likely than rolling two even numbers in a row.\n\n100", "cost_usd": 0.00028964880000000004, "chosen_rung": 1, "rungs_used": [1], "distribution": [0.164051, 0.809361, 3e-06, 3e-06, 0.013432, 3e-06, 0.013148]}, {"benchmark": "math", "task_id": "gsm8k-1289", "answer": "Small shirts: 11 \u00d7 3 = 33 square feet \nMedium shirts: 8 \u00d7 4 = 32 square feet \nLarge shirts: 6 \u00d7 6 = 36 square feet \n\nTotal: 33 + 32 + 36 = 101\n\n101", "cost_usd": 7.880000000000002e-05, "chosen_rung": 4, "rungs_used": [4], "distribution": [0.20183, 0.008571, 3e-06, 3e-06, 0.784324, 3e-06, 0.005267]}, {"benchmark": "code", "task_id": "lcb-abc399_b", "answer": "import sys\n\ndef main():\n input = sys.stdin.readline\n n = int(input())\n scores = list(map(int, input().split()))\n\n rank = [0] * n\n current_rank = 1\n\n for score in sorted(set(scores), reverse=True):\n indices = [i for i, value in enumerate(scores) if value == score]\n for i in indices:\n rank[i] = current_rank\n current_rank += len(indices)\n\n sys.stdout.write(\"\\n\".join(map(str, rank)))\n\nif __name__ == \"__main__\":\n main()\n", "cost_usd": 0.00013950000000000003, "chosen_rung": 4, "rungs_used": [4], "distribution": [4.2e-05, 2e-05, 0.0, 0.0, 0.999927, 0.0, 1.1e-05]}, {"benchmark": "code", "task_id": "lcb-abc392_d", "answer": "```python\nimport sys\n\ndef solve() -> None:\n data = sys.stdin.read().split()\n it = iter(data)\n N = int(next(it))\n dice = [] # list of (K, dict[number -> count])\n for _ in range(N):\n K = int(next(it))\n cnt = {}\n for _ in range(K):\n a = int(next(it))\n cnt[a] = cnt.get(a, 0) + 1\n dice.append((K, cnt))\n\n max_prob = 0.0\n for i in range(N):\n Ki, ci = dice[i]\n for j in range(i + 1, N):\n Kj, cj = dice[j]\n # iterate over the smaller dictionary\n if len(ci) <= len(cj):\n small, large = ci, cj\n else:\n small, large = cj, ci\n sum_prod = 0\n for num, f in small.items():\n if num in large:\n sum_prod += f * large[num]\n prob = sum_prod / (Ki * Kj)\n if prob > max_prob:\n max_prob = prob\n\n # output with sufficient precision\n print(\"{:.15f}\".format(max_prob))\n\nif __name__ == \"__main__\":\n solve()\n```", "cost_usd": 0.0005779199999999999, "chosen_rung": 1, "rungs_used": [1], "distribution": [3.3e-05, 0.999811, 0.0, 0.0, 7.7e-05, 0.0, 7.9e-05]}], "quote": {"measurement": "1449fadb4821cadef93f7eecc8c3b040e2cd244e01a2607ea531e5f7055c38d8", "report_data": "a4b9fca9aa854bc715a3b9ea42d85ada0f91a26ae9ea2bdb383a1a9253575cce", "platform_sig": 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