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proofs/87709.json
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{"schema": 2, "epoch": 87709, "nonce": "ada3f30c789b5c3a", "hotkey": "5Dq9NdL3ZABAy1FDavc9UqEJz1XUV1SgCRpqr1JqmmeCCCw8", "source_hash": "24837b9ae6895829747c5eb448673693fedbeb2e3e62a5ca170051a512053fc0", "weights_hash": "dce18c768f5dca6835c0784f990235d96ea2f1bb905ab6341841d9cccece15a7", "model_id": "router", "total_cost_usd": 0.001014495, "n_calls": 6, "call_log_hash": "4059b246641fb1005ccdf0fae64cf89e341f97628b70907cb29c4d70e3f1eee8", "measurement": "1449fadb4821cadef93f7eecc8c3b040e2cd244e01a2607ea531e5f7055c38d8", "confined": true, "latency_s": 73.204, "tokens_in": 1482, "tokens_out": 3189, "results": [{"benchmark": "mmlu", "task_id": "mmlu-8142", "answer": "D", "cost_usd": 2.394e-05, "chosen_rung": 1, "rungs_used": [1], "distribution": [0.101252, 0.89498, 1e-06, 1e-06, 0.001349, 1e-06, 0.002417]}, {"benchmark": "mmlu", "task_id": "mmlu-8163", "answer": "B", "cost_usd": 8.2e-06, "chosen_rung": 4, "rungs_used": [4], "distribution": [0.006548, 0.000519, 0.0, 0.0, 0.992927, 0.0, 5e-06]}, {"benchmark": "math", "task_id": "gsm8k-696", "answer": "- Adam: 50 points \n- Betty: \\(50 \\times 1.3 = 65\\) points \n- Tom: \\(65 - 30 = 35\\) points \n- Marta: \\(35 \\times 3 = 105\\) points \n- Total: \\(50 + 65 + 35 + 105 = 255\\) points \n- Missing: \\(400 - 255 = 145\\) points \n\n145", "cost_usd": 0.0001235, "chosen_rung": 4, "rungs_used": [4], "distribution": [0.016685, 0.000135, 1e-06, 1e-06, 0.981143, 1e-06, 0.002035]}, {"benchmark": "math", "task_id": "gsm8k-747", "answer": "Step 1: Find the savings per tomato.\nOld price = $0.50\nNew price = $0.40\nSavings per tomato = $0.50 - $0.40 = $0.10\n\nStep 2: Calculate the daily savings.\nDaily quantity = 500 tomatoes\nDaily savings = 500 \u00d7 $0.10 = $50\n\nStep 3: Calculate the weekly savings.\nAssuming a standard 7-day week:\nWeekly savings = $50/day \u00d7 7 days = $350\n\n350", "cost_usd": 0.00013226, "chosen_rung": 0, "rungs_used": [0], "distribution": [0.549204, 0.017508, 6e-06, 6e-06, 0.397156, 6e-06, 0.036114]}, {"benchmark": "code", "task_id": "lcb-abc395_b", "answer": "n = int(input().strip())\n\ngrid = [['?' for _ in range(n)] for _ in range(n)]\n\nfor i in range(1, n + 1):\n j = n + 1 - i\n if i <= j:\n color = '#' if i % 2 == 1 else '.'\n for r in range(i - 1, j):\n for c in range(i - 1, j):\n grid[r][c] = color\n\nfor row in grid:\n print(''.join(row))", "cost_usd": 0.0002232, "chosen_rung": 4, "rungs_used": [4], "distribution": [7e-06, 3.2e-05, 0.0, 0.0, 0.999919, 0.0, 4.1e-05]}, {"benchmark": "code", "task_id": "lcb-abc392_d", "answer": "```python\nimport sys\nfrom collections import Counter\n\ndef solve() -> None:\n data = sys.stdin.read().split()\n it = iter(data)\n N = int(next(it))\n dice = []\n K_list = []\n for _ in range(N):\n K = int(next(it))\n faces = [int(next(it)) for _ in range(K)]\n dice.append(Counter(faces))\n K_list.append(K)\n\n max_prob = 0.0\n for i in range(N):\n Ki = K_list[i]\n di = dice[i]\n for j in range(i + 1, N):\n Kj = K_list[j]\n dj = dice[j]\n # iterate over the smaller dictionary\n if len(di) > len(dj):\n small, large = dj, di\n else:\n small, large = di, dj\n dot = 0\n for x, cnt in small.items():\n if x in large:\n dot += cnt * large[x]\n prob = dot / (Ki * Kj)\n if prob > max_prob:\n max_prob = prob\n\n print(\"{:.15f}\".format(max_prob))\n\nif __name__ == \"__main__\":\n solve()\n```", "cost_usd": 0.000503395, "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": "4645be69d3863d9be443298e054455a1b154a2b6e3462c302d0921559752ce46", "platform_sig": 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