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proofs/87863.json
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{"schema": 2, "epoch": 87863, "nonce": "190ad6e110526d8d", "hotkey": "5FRE1kqMJz8ddModcXUsCquuWhB8QHnjYib2iK2VfiFetkC5", "source_hash": "24837b9ae6895829747c5eb448673693fedbeb2e3e62a5ca170051a512053fc0", "weights_hash": "2e4d6a88063177a0a7a564f24e10b347ef48e87c9595a209162369a4fa4d4477", "model_id": "router", "total_cost_usd": 0.003174644, "n_calls": 6, "call_log_hash": "682fab3f406eea6affd11d2e4e2d1174dcb95180f6fd30a30cd9e85e1b5c964d", "measurement": "1449fadb4821cadef93f7eecc8c3b040e2cd244e01a2607ea531e5f7055c38d8", "confined": true, "latency_s": 99.742, "tokens_in": 1172, "tokens_out": 8412, "results": [{"benchmark": "mmlu", "task_id": "mmlu-11079", "answer": "A", "cost_usd": 0.00012448, "chosen_rung": 0, "rungs_used": [0], "distribution": [0.998954, 6.4e-05, 0.0, 0.0, 0.000979, 3e-06, 0.0]}, {"benchmark": "mmlu", "task_id": "mmlu-11396", "answer": "C", "cost_usd": 0.00027886, "chosen_rung": 0, "rungs_used": [0], "distribution": [0.999365, 0.000267, 0.0, 0.0, 0.000364, 5e-06, 0.0]}, {"benchmark": "math", "task_id": "gsm8k-1011", "answer": "We are given: A tank capacity = 18000 gallons. Two days of pumping. First day: Wanda filled 1/4 of tank's capacity. So Wanda pumped (1/4)*18000 = 4500 gallons. Ms. B pumped 3/4 as much water as Wanda pumped that day. So Ms. B pumped (3/4)*4500 = 3375 gallons. So total first day = 4500+3375 = 7875 gallons.\n\nSecond day: Wanda pumped 2/3 of the amount she pumped on previous day. So Wanda second day = (2/3)*4500 = 3000 gallons. Ms. B pumped 1/3 of the number of gallons she pumped on first day. So Ms. B second day = (1/3)*3375 = 1125 gallons. Total second day = 3000+1125 = 4125 gallons.\n\nTotal pumped over two days = 7875+4125 = 12000 gallons. Tank capacity = 18000, so remaining = 18000-12000 = 6000 gallons.\n\nThus answer: 6000.The tank's capacity is 18,000 gallons. On the first day, Wanda pumped \\(\\frac{1}{4}\\) of the capacity, which is \\(18,000 \\times \\frac{1}{4} = 4,500\\) gallons. Ms. B pumped \\(\\frac{3}{4}\\) of Wanda's amount, so \\(4,500 \\times \\frac{3}{4} = 3,375\\) gallons. Total for the first day: \\(4,500 + 3,375 = 7,875\\) gallons.\n\nOn the second day, Wanda pumped \\(\\frac{2}{3}\\) of her first-day amount: \\(4,500 \\times \\frac{2}{3} = 3,000\\) gallons. Ms. B pumped \\(\\frac{1}{3}\\) of her first-day amount: \\(3,375 \\times \\frac{1}{3} = 1,125\\) gallons. Total for the second day: \\(3,000 + 1,125 = 4,125\\) gallons.\n\nOverall, the total water pumped is \\(7,875 + 4,125 = 12,000\\) gallons. The remaining capacity is \\(18,000 - 12,000 = 6,000\\) gallons.\n\n\\boxed{6000}", "cost_usd": 0.00016617999999999998, "chosen_rung": 1, "rungs_used": [1], "distribution": [0.000596, 0.999311, 0.0, 0.0, 5.6e-05, 3.6e-05, 0.0]}, {"benchmark": "math", "task_id": "gsm8k-1028", "answer": "Tom buys a bedroom set for $3000. He sells his old bedroom set for $1000, which he uses as a partial payment, so the remaining amount owed is $3000 - $1000 = $2000. He then has to pay 10% a month for the bedroom set, meaning he pays 10% of the remaining balance each month. Therefore, the monthly payment is 10% of $2000, which is $200.\n\n200", "cost_usd": 0.001210824, "chosen_rung": 1, "rungs_used": [1], "distribution": [0.000137, 0.999825, 0.0, 0.0, 1.7e-05, 2.2e-05, 0.0]}, {"benchmark": "code", "task_id": "lcb-abc391_a", "answer": "import sys\n\ndef main():\n d = sys.stdin.read().strip()\n opposite = {\n 'N': 'S',\n 'S': 'N',\n 'E': 'W',\n 'W': 'E',\n 'NE': 'SW',\n 'SW': 'NE',\n 'NW': 'SE',\n 'SE': 'NW'\n }\n print(opposite[d])\n\nif __name__ == '__main__':\n main()", "cost_usd": 0.0011895, "chosen_rung": 5, "rungs_used": [5], "distribution": [5.5e-05, 4.3e-05, 0.0, 0.0, 0.000612, 0.99929, 0.0]}, {"benchmark": "code", "task_id": "lcb-abc399_c", "answer": "import sys\n\ndef main():\n data = list(map(int, sys.stdin.buffer.read().split()))\n if not data:\n return\n\n n, m = data[0], data[1]\n parent = list(range(n + 1))\n size = [1] * (n + 1)\n\n def find(x):\n while parent[x] != x:\n parent[x] = parent[parent[x]]\n x = parent[x]\n return x\n\n deleted = 0\n idx = 2\n\n for _ in range(m):\n u, v = data[idx], data[idx + 1]\n idx += 2\n\n ru, rv = find(u), find(v)\n if ru == rv:\n deleted += 1\n else:\n if size[ru] < size[rv]:\n ru, rv = rv, ru\n parent[rv] = ru\n size[ru] += size[rv]\n\n print(deleted)\n\nif __name__ == \"__main__\":\n main()\n", "cost_usd": 0.00020479999999999977, "chosen_rung": 4, "rungs_used": [4], "distribution": [0.000534, 0.000281, 0.0, 0.0, 0.997795, 0.00139, 0.0]}], "quote": {"measurement": "1449fadb4821cadef93f7eecc8c3b040e2cd244e01a2607ea531e5f7055c38d8", "report_data": "6412e1fbfdcfbb493c91bfabd7b0ad6b7073c8c6c89096c63d0a7375c1c663ab", "platform_sig": 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