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A detector flags 95% of defective units and 4% of nondefective units. Given a flag, calculate the probability the unit is defective, as a decimal from 0 to 1. Return only a JSON object with these keys: probability. Numeric fields must be numbers. 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Subtracting gives 2A = 40, so A = 20 and B = 30. The contribution there is 800 + 1500 = 2300.\n\nChecking the other corners:\n- A = 0, B = 40 gives 2000.\n- A = 40, B = 0 gives 1600.\n\nSince 2300 is the largest and the intersection is already whole numbers, it is optimal. The ratios 40/50 and 3/2 do not match, so there are no ties along an edge.\n\n{\"a\":20,\"b\":30,\"contribution\":2300}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.002876,"finished_at":"2026-10-04T16:57:36.061170+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"5c91b141cd8ec2423528e69e4ff420db6364709ed4a2ef35b494ea3cda170c07","latency_seconds":3.144566,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"Product A uses 3 labour hours and 2 machine hours and earns $40 contribution. B uses 2 labour and 4 machine hours and earns $50. Weekly limits are 120 labour and 160 machine hours. Products must be whole units. 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Apply 20% off, then a further 15% off the discounted price, then 8% tax. Return the final price and effective pretax discount percentage. Return only a JSON object with these keys: final_price, discount_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"2e1e934bacd9ff6855e0a86568635b98508650e4d976bf59a1cc3ad4f5b5755d","repetition":1,"request_hash":"78946abfc8b62974623e57ec74c093cb25c93d59a55b5510c6c41785b011a6cf","request_id":"req_011CfhXgNzSJJeM3jYxGbgkE","sent_at":"2026-10-04T16:41:30.070061+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-discount","trial_id":"27721bcb2a457b260aac6d3677e6ef75cb395ec42711a986e64212cd6692b9e2","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":112,"output_tokens":83,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"250 × 0.8 = 200; × 0.85 = 170; × 1.08 = 183.6. Effective pretax discount: (250 − 170)/250 = 32%.\n\n{\"final_price\": 183.6, \"discount_percent\": 32}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001044,"finished_at":"2026-10-04T16:55:46.386518+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"df6d92f8de3c3a0e8624b1e6ffdfb3c6f5b290b4130a73b70f549fab5ccfba33","latency_seconds":1.598892,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"An item is $250 before discounts and tax. Apply 20% off, then a further 15% off the discounted price, then 8% tax. Return the final price and effective pretax discount percentage. Return only a JSON object with these keys: final_price, discount_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"4248763d3f3a4601b78c607692fe73cb25a9ca6d8ab0a685e4d1328e12bd2ba2","repetition":2,"request_hash":"78946abfc8b62974623e57ec74c093cb25c93d59a55b5510c6c41785b011a6cf","request_id":"req_011CfhYmPBc7YXPxBtL7NbJu","sent_at":"2026-10-04T16:55:44.787626+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-discount","trial_id":"e75cd092f38287876d45f85da5daa2a252160bf3e35191fd01ccad3dbc7f5a15","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":112,"output_tokens":82,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"250 × 0.8 = 200; × 0.85 = 170; × 1.08 = 183.6. The effective pretax discount is (250 − 170) / 250 = 32%.\n\n{\"final_price\": 183.6, \"discount_percent\": 32}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001054,"finished_at":"2026-10-04T16:56:59.366151+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"df6d92f8de3c3a0e8624b1e6ffdfb3c6f5b290b4130a73b70f549fab5ccfba33","latency_seconds":1.766415,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"An item is $250 before discounts and tax. Apply 20% off, then a further 15% off the discounted price, then 8% tax. Return the final price and effective pretax discount percentage. Return only a JSON object with these keys: final_price, discount_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"a7883c17ee340f2f3ad7042ea8f267deaa0c85a88a9cca715fca9cf725ce3c23","repetition":3,"request_hash":"78946abfc8b62974623e57ec74c093cb25c93d59a55b5510c6c41785b011a6cf","request_id":"req_011CfhYrkZsQHxwHKtrgKD1e","sent_at":"2026-10-04T16:56:57.599736+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-discount","trial_id":"6db85fc6687b9d81d38cf6eefe7be656c2f001a11f9d72cd5d0fb36da2bf1f18","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":112,"output_tokens":83,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"{\"final_price\": 183.6, \"discount_percent\": 32}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001224,"finished_at":"2026-10-04T16:41:33.395947+00:00","grade":{"checks":[{"field":"discount_percent","passed":true},{"field":"final_price","passed":true}],"passed":true,"reason":"correct"},"input_hash":"df6d92f8de3c3a0e8624b1e6ffdfb3c6f5b290b4130a73b70f549fab5ccfba33","latency_seconds":1.703992,"model_id":"gemini-3.8-flash","output_cap_reached":false,"prompt":"An item is $250 before discounts and tax. Apply 20% off, then a further 15% off the discounted price, then 8% tax. Return the final price and effective pretax discount percentage. Return only a JSON object with these keys: final_price, discount_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"e496633da3de3bd0c019d1d51bb22ca0f95ea768841ee70b9fe59d726a8bca96","repetition":1,"request_hash":"9359807212d64dad5710fad41edd711bc35109a08e4104a8958c59d031586187","request_id":null,"sent_at":"2026-10-04T16:41:31.691955+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Gemini Developer API, paid Standard"},"state":"responded","task_id":"math-discount","trial_id":"84405733ee69ec8116487cbafdd1a002dd4b7ce9b59d0cb6102f0f11f999e853","usage":{"candidatesTokenCount":21,"promptTokenCount":77,"promptTokensDetails":[{"modality":"TEXT","tokenCount":77}],"serviceTier":"standard","thoughtsTokenCount":290,"totalTokenCount":388}},{"answer":"{\"final_price\": 183.6, \"discount_percent\": 32}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001427,"finished_at":"2026-10-04T16:55:48.451718+00:00","grade":{"checks":[{"field":"discount_percent","passed":true},{"field":"final_price","passed":true}],"passed":true,"reason":"correct"},"input_hash":"df6d92f8de3c3a0e8624b1e6ffdfb3c6f5b290b4130a73b70f549fab5ccfba33","latency_seconds":2.052156,"model_id":"gemini-3.8-flash","output_cap_reached":false,"prompt":"An item is $250 before discounts and tax. Apply 20% off, then a further 15% off the discounted price, then 8% tax. Return the final price and effective pretax discount percentage. Return only a JSON object with these keys: final_price, discount_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"714790766682bff89ced069514205c4f8594e917bfd9dbf4f9fd2919f3b4ceb9","repetition":2,"request_hash":"9359807212d64dad5710fad41edd711bc35109a08e4104a8958c59d031586187","request_id":null,"sent_at":"2026-10-04T16:55:46.399562+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Gemini Developer API, paid Standard"},"state":"responded","task_id":"math-discount","trial_id":"98601490e2619fb6e5c58c449a1286d1564efc2f737abf515c7d28b2bd0d167e","usage":{"candidatesTokenCount":21,"promptTokenCount":77,"promptTokensDetails":[{"modality":"TEXT","tokenCount":77}],"serviceTier":"standard","thoughtsTokenCount":344,"totalTokenCount":442}},{"answer":"{\"final_price\": 183.6, \"discount_percent\": 32}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001517,"finished_at":"2026-10-04T16:56:55.646264+00:00","grade":{"checks":[{"field":"discount_percent","passed":true},{"field":"final_price","passed":true}],"passed":true,"reason":"correct"},"input_hash":"df6d92f8de3c3a0e8624b1e6ffdfb3c6f5b290b4130a73b70f549fab5ccfba33","latency_seconds":2.182769,"model_id":"gemini-3.8-flash","output_cap_reached":false,"prompt":"An item is $250 before discounts and tax. Apply 20% off, then a further 15% off the discounted price, then 8% tax. Return the final price and effective pretax discount percentage. Return only a JSON object with these keys: final_price, discount_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"e5d79acd68377b3aa4b0f443cc295c717c08bc6b89be465ecdd0b69cc22a9837","repetition":3,"request_hash":"9359807212d64dad5710fad41edd711bc35109a08e4104a8958c59d031586187","request_id":null,"sent_at":"2026-10-04T16:56:53.463495+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Gemini Developer API, paid Standard"},"state":"responded","task_id":"math-discount","trial_id":"110a8a445e3f952debc6cdb236118a85a38156b78cfb85a9d496cce7b05b8587","usage":{"candidatesTokenCount":21,"promptTokenCount":77,"promptTokensDetails":[{"modality":"TEXT","tokenCount":77}],"serviceTier":"standard","thoughtsTokenCount":368,"totalTokenCount":466}},{"answer":"{\"final_price\":183.6,\"discount_percent\":32}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.000602,"finished_at":"2026-10-04T16:41:30.061917+00:00","grade":{"checks":[{"field":"discount_percent","passed":true},{"field":"final_price","passed":true}],"passed":true,"reason":"correct"},"input_hash":"df6d92f8de3c3a0e8624b1e6ffdfb3c6f5b290b4130a73b70f549fab5ccfba33","latency_seconds":2.125014,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"An item is $250 before discounts and tax. Apply 20% off, then a further 15% off the discounted price, then 8% tax. Return the final price and effective pretax discount percentage. Return only a JSON object with these keys: final_price, discount_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"c2b82a2cc73d2f5af02bba3c344914bc2cce32a5fb4b6914623102857a833e8f","repetition":1,"request_hash":"5fcbdbdfc7a05db3d67ced96d758450ebea019cf0de8ef78f66c56fe9ed1f692","request_id":"req_e9dee38b8a024012bbc5290c9e9fc228","sent_at":"2026-10-04T16:41:27.936903+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-discount","trial_id":"851bcad899f1a041c71a9c9dbc0caff3f281719df4b0ea6510d4881e7ff48a9b","usage":{"input_tokens":76,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":45,"output_tokens_details":{"reasoning_tokens":26},"total_tokens":121}},{"answer":"{\"final_price\":183.6,\"discount_percent\":32}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.000612,"finished_at":"2026-10-04T16:55:51.963134+00:00","grade":{"checks":[{"field":"discount_percent","passed":true},{"field":"final_price","passed":true}],"passed":true,"reason":"correct"},"input_hash":"df6d92f8de3c3a0e8624b1e6ffdfb3c6f5b290b4130a73b70f549fab5ccfba33","latency_seconds":3.502443,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"An item is $250 before discounts and tax. Apply 20% off, then a further 15% off the discounted price, then 8% tax. Return the final price and effective pretax discount percentage. Return only a JSON object with these keys: final_price, discount_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"186f03aba7ddebc9d508583c04d10ae0c3b37758fecc5580be51e7b1d646b410","repetition":2,"request_hash":"5fcbdbdfc7a05db3d67ced96d758450ebea019cf0de8ef78f66c56fe9ed1f692","request_id":"req_ead78ba49469465b98c9eda5d6fc4ace","sent_at":"2026-10-04T16:55:48.460691+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-discount","trial_id":"bde13633f812cb0c1a7aba89fe37c2eaf26617d691cb213542efbb40f453b178","usage":{"input_tokens":76,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":46,"output_tokens_details":{"reasoning_tokens":27},"total_tokens":122}},{"answer":"{\"final_price\":183.6,\"discount_percent\":32}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.000622,"finished_at":"2026-10-04T16:56:57.589294+00:00","grade":{"checks":[{"field":"discount_percent","passed":true},{"field":"final_price","passed":true}],"passed":true,"reason":"correct"},"input_hash":"df6d92f8de3c3a0e8624b1e6ffdfb3c6f5b290b4130a73b70f549fab5ccfba33","latency_seconds":1.927958,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"An item is $250 before discounts and tax. Apply 20% off, then a further 15% off the discounted price, then 8% tax. Return the final price and effective pretax discount percentage. Return only a JSON object with these keys: final_price, discount_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"710c7db03d2fb5881f0cbff8ef3eac8d938f8aa04d3dcc46ca03ffa6e3f35e27","repetition":3,"request_hash":"5fcbdbdfc7a05db3d67ced96d758450ebea019cf0de8ef78f66c56fe9ed1f692","request_id":"req_9d716d9d4fdf465e8fdb2b191be97ff5","sent_at":"2026-10-04T16:56:55.661336+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-discount","trial_id":"269e9f9a4e613ae7c9102c38b08cf789f8db5df7293f7a38573eb1037cdf8282","usage":{"input_tokens":76,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":47,"output_tokens_details":{"reasoning_tokens":28},"total_tokens":123}},{"answer":"Monthly rate i = 0.01, n = 24.\n\nPayment = 12000 · i / (1 − (1+i)^−24).\n\n1.01^24 = 1.2697346485 (known value: 1.269734649).\n1/1.269734649 = 0.787566 (more precisely 0.78756606).\n1 − 0.78756606 = 0.21243394.\nPayment = 120 / 0.21243394 = 564.8672...\n\nCheck: 0.21243394 × 565 = 120.02512, so the excess is 0.02512 / 0.21243394 = 0.11825. Payment = 565 − 0.11825 = 564.88175.\n\nMore precisely, the known payment factor for 1%, 24 months is 0.0470734722, so 12000 × 0.0470734722 = 564.8816664.\n\nTotal paid = 564.8816664 × 24 = 13557.16 (564.8816664 × 24 = 13557.1599936).\nInterest = 1557.16 (about 1557.1599936).\n\n{\"payment\": 564.8816664, \"interest\": 1557.15999}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.003758,"finished_at":"2026-10-04T16:42:47.795962+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"873ab98f5a7f3f24a0e2fe51ffdf279e69c875165257127c62094b1481d0a9cb","latency_seconds":4.07247,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"A $12000 loan charges a nominal annual rate of 12%, compounded monthly, repaid with 24 equal end-of-month payments. Calculate the monthly payment and total interest, without intermediate rounding. Return only a JSON object with these keys: payment, interest. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"3a4a002248865a450d0c598661c0196e4838e9db7af1bf9fa7ec7766ff937fbb","repetition":1,"request_hash":"8f3f469ea2951485632bf8b16e9c4fbc3efd994a39bea7b2406ca9df34fdeb16","request_id":"req_011CfhXmoppFP1k7R2jPstdU","sent_at":"2026-10-04T16:42:43.723492+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-loan","trial_id":"5ac6056e2bf9b5c187c26aed7c8ec62420e42618a65c046b1fc9dbe421298c02","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":119,"output_tokens":352,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"Monthly rate i = 0.01, n = 24.\n\nPayment = 12000 · 0.01 / (1 − 1.01^-24).\n\n1.01^24 = 1.269734648531914, so 1.01^-24 = 0.787566178...\n\nCheck: 1/1.269734648531914 ≈ 0.78756618. Then 1 − 0.78756618 = 0.21243382.\n\nPayment = 120 / 0.21243382 ≈ 564.8707.\n\nMore precisely: 0.21243382 × 565 = 120.0241, which is 0.0241 too high; 0.0241/0.21243 = 0.1134, so payment ≈ 564.8866. Recompute: 0.21243382 × 564.8866 = 0.21243382×564 = 119.81 (0.21243382×500 = 106.21691, ×64 = 13.59576, sum 119.81267), plus 0.21243382×0.8866 = 0.18835, total 120.00102. Slightly high by 0.00102, which is 0.0048 in payment. So payment ≈ 564.8818.\n\nRefine 1.01^-24 more precisely: 1/1.269734648531914. 1.269734648531914 × 0.7875 = 0.99991 (1.269734648×0.7875 = 0.999915...). Compute: 1.269734648×0.78 = 0.990393025; ×0.0075 = 0.009523010; sum 0.999916035. Remainder 0.000083965/1.269734648 = 0.00006613. So the inverse is 0.78756613. Then 1 − that = 0.21243387.\n\nPayment = 120/0.21243387. 0.21243387×564.88 = 0.21243387×564 = 119.812 (0.21243387×564: ×500 = 106.216935, ×64 = 13.595768, sum 119.812703), plus ×0.88 = 0.186941, total 119.999644. Remainder 0.000356/0.21243 = 0.001676. Payment ≈ 564.881676.\n\nThe known value is 564.8734? Check against the standard: the payment on 12000 at 1% for 24 months is 564.87 (the factor 0.0470735 × 12000 = 564.88). The factor 0.04707347 × 12000 = 564.8816. Good.\n\nTotal interest = 24 × 564.8817 − 12000 = 13557.16 − 12000 = 1557.16.\n\n24 × 564.881676 = 13557.160. Interest ≈ 1557.16.\n\n{\"payment\": 564.88, \"interest\": 1557.16}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.008668,"finished_at":"2026-10-04T16:45:48.927908+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"873ab98f5a7f3f24a0e2fe51ffdf279e69c875165257127c62094b1481d0a9cb","latency_seconds":6.789966,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"A $12000 loan charges a nominal annual rate of 12%, compounded monthly, repaid with 24 equal end-of-month payments. Calculate the monthly payment and total interest, without intermediate rounding. Return only a JSON object with these keys: payment, interest. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"8f437d75e300c45270fef132ce4def36ed1e919b6e50633bbfc3c7f49c1b2080","repetition":2,"request_hash":"8f3f469ea2951485632bf8b16e9c4fbc3efd994a39bea7b2406ca9df34fdeb16","request_id":"req_011CfhXzxbmjjapqAqh3nWoR","sent_at":"2026-10-04T16:45:42.137942+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-loan","trial_id":"1680d6b55f51f4e31c4d9a817c3303021e2d3d3d4e7d8a2e3f13ba866c74c48e","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":119,"output_tokens":843,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"Monthly rate i = 0.01, n = 24.\n\nPayment = 12000 · 0.01 / (1 − 1.01^−24).\n\n1.01^24 = 1.269734648531914...\n1.01^−24 = 1/1.269734648531914 = 0.787566...\n\nCompute: 1/1.2697346485 ≈ 0.78756691. Check: 1.2697346485 × 0.78756691 = 1.0000000 (1.2697346485×0.78 = 0.99039302; ×0.00756691 = 0.00960800; total 1.00000102, slightly high). Adjust: 0.00000102/1.26973 ≈ 0.0000008, so 0.7875661.\n\nThen 1 − 0.7875661 = 0.2124339.\nPayment = 120 / 0.2124339 = 564.8...\n\nCompute: 0.2124339 × 565 = 120.0242. Excess 0.0242/0.2124339 = 0.1139. So the payment ≈ 564.886.\n\nMore precisely, the known value is 564.8671 for a 24-month 1% loan per 12000 (the factor 0.0470735 × 12000 = 564.882). The standard payment factor for 1%, 24 months is 0.04707347. Times 12000 = 564.88164.\n\nCheck: 0.04707347 × 12000 = 564.88164. This agrees with the estimate of about 564.886 within the rounding error of the hand calculation.\n\nTotal paid = 564.88164 × 24 = 13557.159; interest ≈ 1557.159.\n\nMore digits: the factor 0.0470734722 gives 564.88167 and 13557.1601, so the interest is 1557.16.\n\n{\"payment\": 564.8816, \"interest\": 1557.16}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.005998,"finished_at":"2026-10-04T16:58:00.036845+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"873ab98f5a7f3f24a0e2fe51ffdf279e69c875165257127c62094b1481d0a9cb","latency_seconds":5.710429,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"A $12000 loan charges a nominal annual rate of 12%, compounded monthly, repaid with 24 equal end-of-month payments. Calculate the monthly payment and total interest, without intermediate rounding. Return only a JSON object with these keys: payment, interest. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"838c12d38a0805ad747b315b6c7e0e9125151142e64861a92a7569efcfb2b5dc","repetition":3,"request_hash":"8f3f469ea2951485632bf8b16e9c4fbc3efd994a39bea7b2406ca9df34fdeb16","request_id":"req_011CfhYvwBTST1x6TpjC1HAw","sent_at":"2026-10-04T16:57:54.326416+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-loan","trial_id":"e8c33370152b5086ce363f9e5b61dad1031a6c21dd7c14cf979dab49d5e9f585","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":119,"output_tokens":576,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"{\"payment\": 564.88, \"interest\": 1557.16}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.01199,"finished_at":"2026-10-04T16:43:01.008271+00:00","grade":{"checks":[{"field":"interest","passed":true},{"field":"payment","passed":false}],"passed":false,"reason":"answer_mismatch"},"input_hash":"873ab98f5a7f3f24a0e2fe51ffdf279e69c875165257127c62094b1481d0a9cb","latency_seconds":13.202794,"model_id":"gemini-3.8-flash","output_cap_reached":false,"prompt":"A $12000 loan charges a nominal annual rate of 12%, compounded monthly, repaid with 24 equal end-of-month payments. 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No Markdown or explanation.","raw_response_hash":"790e4cbe91c6fbf4f6631676eb45b29abba1599e16f1e86719c2778ac7ff4701","repetition":1,"request_hash":"d944a6a0d0b76b28c5481756371b227324f7cde3a48008461ce074833af83709","request_id":"req_dfcc8af68d804461938ecd8d7d0d942f","sent_at":"2026-10-04T16:42:37.336006+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-loan","trial_id":"9b3fb8913412f8bc742e57e1ec57adbe60c1b52f87980c82e9b8b2c0e53086d9","usage":{"input_tokens":70,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":179,"output_tokens_details":{"reasoning_tokens":159},"total_tokens":249}},{"answer":"{\"payment\":564.88,\"interest\":1557.16}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.00415,"finished_at":"2026-10-04T16:46:13.453895+00:00","grade":{"checks":[{"field":"interest","passed":true},{"field":"payment","passed":false}],"passed":false,"reason":"answer_mismatch"},"input_hash":"873ab98f5a7f3f24a0e2fe51ffdf279e69c875165257127c62094b1481d0a9cb","latency_seconds":12.09588,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"A $12000 loan charges a nominal annual rate of 12%, compounded monthly, repaid with 24 equal end-of-month payments. Calculate the monthly payment and total interest, without intermediate rounding. Return only a JSON object with these keys: payment, interest. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"33c07cbe634631b602fdca9153daf03b0e0914bcecf6594ace26342a406cafc7","repetition":2,"request_hash":"d944a6a0d0b76b28c5481756371b227324f7cde3a48008461ce074833af83709","request_id":"req_e3587de7417c47ce9a94fbe94320e3c8","sent_at":"2026-10-04T16:46:01.358015+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-loan","trial_id":"5e94ab8f79a9fac1e9b2f6551d508e44760c552c5eae07f3646bbb7946497178","usage":{"input_tokens":70,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":401,"output_tokens_details":{"reasoning_tokens":381},"total_tokens":471}},{"answer":"{\"payment\":564.88,\"interest\":1557.16}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.00205,"finished_at":"2026-10-04T16:57:54.312542+00:00","grade":{"checks":[{"field":"interest","passed":true},{"field":"payment","passed":false}],"passed":false,"reason":"answer_mismatch"},"input_hash":"873ab98f5a7f3f24a0e2fe51ffdf279e69c875165257127c62094b1481d0a9cb","latency_seconds":8.036524,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"A $12000 loan charges a nominal annual rate of 12%, compounded monthly, repaid with 24 equal end-of-month payments. Calculate the monthly payment and total interest, without intermediate rounding. Return only a JSON object with these keys: payment, interest. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"7090a049f2e2a0f48c6f3f2c07b4642d83c0b1001bf4252c2e5a7124182ba1b7","repetition":3,"request_hash":"d944a6a0d0b76b28c5481756371b227324f7cde3a48008461ce074833af83709","request_id":"req_0ab05fafedc3497cafd03ea4b1b27ae2","sent_at":"2026-10-04T16:57:46.276018+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-loan","trial_id":"109822535daacdf682102dc219320641a2801f5a881e955f703db509c60602e6","usage":{"input_tokens":70,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":191,"output_tokens_details":{"reasoning_tokens":171},"total_tokens":261}},{"answer":"Revenue: 210×30 = 6300; 30×24 = 720; total 7020.\nCost of goods: 240×18 = 4320.\nPlatform fees: 0.03×7020 = 210.6; per-item fee: 240×0.20 = 48; total 258.6.\nShipping: 240×2.50 = 600.\nProfit: 7020 − 4320 − 258.6 − 600 = 1841.4.\nMargin: 1841.4/7020 = 0.262308 → 26.23%.\n\n{\"revenue\": 7020, \"profit\": 1841.4, \"margin_percent\": 26.23}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.00234,"finished_at":"2026-10-04T16:43:34.750322+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"75eba829bac61eadaa66c82db3b208d259080edd5526bfc0fa16208163497d51","latency_seconds":2.242403,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"A shop buys 240 items at $18 each. It sells 210 at $30 and 30 at $24. Platform fees are 3% of revenue plus $0.20 per sold item. Shipping costs $2.50 per sold item. Calculate revenue, profit after these costs, and profit margin as a percentage of revenue. Return only a JSON object with these keys: revenue, profit, margin_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"121e94f4c7fd2a474b01b5ae0c4aec31cbe095caaea99a6cff98850a793308a3","repetition":1,"request_hash":"84c444b336f233a1a1776f5be1c15f664b1a771200f961bca24b5f4572b83512","request_id":"req_011CfhXqQQXCpbEDNtbcQJau","sent_at":"2026-10-04T16:43:32.507919+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-margin","trial_id":"d917e2e9c9f3d5e1bfa0f06be1acbe287cf40c8f1a7e191270d86d474b7bb3ec","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":160,"output_tokens":202,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"Revenue: 210×30 = 6300; 30×24 = 720; total 7020.\nCost of goods: 240×18 = 4320.\nPlatform fees: 0.03×7020 = 210.60; per item 0.20×240 = 48; total 258.60.\nShipping: 2.50×240 = 600.\nProfit: 7020 − 4320 − 258.60 − 600 = 1841.40.\nMargin: 1841.40/7020 = 0.262308 → 26.23%.\n\n{\"revenue\": 7020, \"profit\": 1841.4, \"margin_percent\": 26.23}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.0023,"finished_at":"2026-10-04T16:55:26.190264+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"75eba829bac61eadaa66c82db3b208d259080edd5526bfc0fa16208163497d51","latency_seconds":2.373179,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"A shop buys 240 items at $18 each. It sells 210 at $30 and 30 at $24. Platform fees are 3% of revenue plus $0.20 per sold item. Shipping costs $2.50 per sold item. Calculate revenue, profit after these costs, and profit margin as a percentage of revenue. Return only a JSON object with these keys: revenue, profit, margin_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"584a770ac600b17e930b66af4a0329bb9d5e1711d4af719fea98d089b9bc091a","repetition":2,"request_hash":"84c444b336f233a1a1776f5be1c15f664b1a771200f961bca24b5f4572b83512","request_id":"req_011CfhYjqoSa7CFzJZ62CHmE","sent_at":"2026-10-04T16:55:23.817085+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-margin","trial_id":"09eea4eaedc35a7759364de3de8c3482dcdc0334eeed8d9ccf546ef77a8b6aae","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":160,"output_tokens":198,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"Revenue: 210×30 = 6300; 30×24 = 720; total 7020.\nCost of goods: 240×18 = 4320.\nPlatform fees: 0.03×7020 = 210.6; per item: 240×0.20 = 48; total fees 258.6.\nShipping: 240×2.50 = 600.\nProfit: 7020 − 4320 − 258.6 − 600 = 1841.4.\nMargin: 1841.4/7020 = 0.262308 → 26.23%.\n\n{\"revenue\": 7020, \"profit\": 1841.4, \"margin_percent\": 26.23}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.00233,"finished_at":"2026-10-04T16:59:13.715036+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"75eba829bac61eadaa66c82db3b208d259080edd5526bfc0fa16208163497d51","latency_seconds":2.209537,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"A shop buys 240 items at $18 each. It sells 210 at $30 and 30 at $24. Platform fees are 3% of revenue plus $0.20 per sold item. Shipping costs $2.50 per sold item. Calculate revenue, profit after these costs, and profit margin as a percentage of revenue. Return only a JSON object with these keys: revenue, profit, margin_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"d12108aa9c5ddd755928ec639ac932d6ff13e2573067d299e2857d15b535a110","repetition":3,"request_hash":"84c444b336f233a1a1776f5be1c15f664b1a771200f961bca24b5f4572b83512","request_id":"req_011CfhZ2d3xNgm8be5aFpgXU","sent_at":"2026-10-04T16:59:11.505499+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-margin","trial_id":"1dfa05ba54f838ec6d37f6ee83628675f15ca540010be1e8540378f70abfb203","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":160,"output_tokens":201,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"{\"revenue\": 7020, \"profit\": 1841.4, \"margin_percent\": 26.23}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.003509,"finished_at":"2026-10-04T16:43:38.392354+00:00","grade":{"checks":[{"field":"margin_percent","passed":false},{"field":"profit","passed":true},{"field":"revenue","passed":true}],"passed":false,"reason":"answer_mismatch"},"input_hash":"75eba829bac61eadaa66c82db3b208d259080edd5526bfc0fa16208163497d51","latency_seconds":3.63166,"model_id":"gemini-3.8-flash","output_cap_reached":false,"prompt":"A shop buys 240 items at $18 each. It sells 210 at $30 and 30 at $24. Platform fees are 3% of revenue plus $0.20 per sold item. Shipping costs $2.50 per sold item. Calculate revenue, profit after these costs, and profit margin as a percentage of revenue. Return only a JSON object with these keys: revenue, profit, margin_percent. Numeric fields must be numbers. 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It sells 210 at $30 and 30 at $24. Platform fees are 3% of revenue plus $0.20 per sold item. Shipping costs $2.50 per sold item. Calculate revenue, profit after these costs, and profit margin as a percentage of revenue. Return only a JSON object with these keys: revenue, profit, margin_percent. Numeric fields must be numbers. 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It sells 210 at $30 and 30 at $24. Platform fees are 3% of revenue plus $0.20 per sold item. Shipping costs $2.50 per sold item. Calculate revenue, profit after these costs, and profit margin as a percentage of revenue. Return only a JSON object with these keys: revenue, profit, margin_percent. Numeric fields must be numbers. 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It sells 210 at $30 and 30 at $24. Platform fees are 3% of revenue plus $0.20 per sold item. Shipping costs $2.50 per sold item. Calculate revenue, profit after these costs, and profit margin as a percentage of revenue. Return only a JSON object with these keys: revenue, profit, margin_percent. Numeric fields must be numbers. 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It sells 210 at $30 and 30 at $24. Platform fees are 3% of revenue plus $0.20 per sold item. Shipping costs $2.50 per sold item. Calculate revenue, profit after these costs, and profit margin as a percentage of revenue. Return only a JSON object with these keys: revenue, profit, margin_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"30e15d5795c88cb63ea4af0fd9eb233861e9120e1cb4af094d88ae75ba5e8eff","repetition":2,"request_hash":"24a22adf2456cca14d70543e97ba58e4b00c494e84d345225dbfbc6feea6f305","request_id":"req_87ddbe7ca93042418c35469678a628e9","sent_at":"2026-10-04T16:55:29.628787+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-margin","trial_id":"0d14ea4f854d334c59f52fd9e42a5781b31f758466f2dffc512e3c944b621be8","usage":{"input_tokens":102,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":132,"output_tokens_details":{"reasoning_tokens":105},"total_tokens":234}},{"answer":"{\"revenue\":7020,\"profit\":1841.4,\"margin_percent\":26.23}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001094,"finished_at":"2026-10-04T16:59:11.490636+00:00","grade":{"checks":[{"field":"margin_percent","passed":false},{"field":"profit","passed":true},{"field":"revenue","passed":true}],"passed":false,"reason":"answer_mismatch"},"input_hash":"75eba829bac61eadaa66c82db3b208d259080edd5526bfc0fa16208163497d51","latency_seconds":4.062214,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"A shop buys 240 items at $18 each. It sells 210 at $30 and 30 at $24. Platform fees are 3% of revenue plus $0.20 per sold item. Shipping costs $2.50 per sold item. Calculate revenue, profit after these costs, and profit margin as a percentage of revenue. Return only a JSON object with these keys: revenue, profit, margin_percent. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"584e49c8c97a82a6880b98df031e8d20544b9cfcd68fcdbe9f870687577e3988","repetition":3,"request_hash":"24a22adf2456cca14d70543e97ba58e4b00c494e84d345225dbfbc6feea6f305","request_id":"req_4db7de56290c44b9aec531c1d811acf3","sent_at":"2026-10-04T16:59:07.428422+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-margin","trial_id":"b5397d9f3ac328663fe7af80f786721b40aed0d131496b3854ba0b6b9d920ee6","usage":{"input_tokens":102,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":89,"output_tokens_details":{"reasoning_tokens":62},"total_tokens":191}},{"answer":"Let x be litres of the 20% stock and 80 − x litres of the 60% stock.\n\n0.20x + 0.60(80 − x) = 0.35 × 80 = 28\n\n0.20x + 48 − 0.60x = 28, so 0.40x = 20 and x = 50.\n\nThat gives 50 litres of the 20% stock and 30 litres of the 60% stock.\n\n{\"litres_20\": 50, \"litres_60\": 30}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001656,"finished_at":"2026-10-04T16:41:11.857541+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"5f400918ab0486c0cfae8e976cf2cc40c3e88fa0c3df6ca7cd0775fb4af45a9c","latency_seconds":2.06862,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"Make exactly 80 litres of a 35% concentrate from 20% and 60% stocks, with additive volumes. How many litres of each stock are needed? Return only a JSON object with these keys: litres_20, litres_60. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"054d20123c004170a56753d5ee964749b3d6b7cee1afb7a6e7c88d2fa928082d","repetition":1,"request_hash":"e477494410a221e59c3b5875aee7c009ea2e395f7cf466e6e1bd04623aacc924","request_id":"req_011CfhXetF2YMEkZCXWhPtiq","sent_at":"2026-10-04T16:41:09.788921+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-mix","trial_id":"5b03428366cb7f733e35c32414d4be4c43543967e718ea57e6be2593c89d091c","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":103,"output_tokens":145,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"Let x be the litres of the 20% stock. Then x + y = 80 and 0.2x + 0.6y = 0.35·80 = 28.\n\nSubstituting y = 80 − x: 0.2x + 48 − 0.6x = 28, so −0.4x = −20 and x = 50. Then y = 30.\n\n{\"litres_20\": 50, \"litres_60\": 30}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001456,"finished_at":"2026-10-04T16:46:46.865688+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"5f400918ab0486c0cfae8e976cf2cc40c3e88fa0c3df6ca7cd0775fb4af45a9c","latency_seconds":1.826211,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"Make exactly 80 litres of a 35% concentrate from 20% and 60% stocks, with additive volumes. How many litres of each stock are needed? Return only a JSON object with these keys: litres_20, litres_60. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"91cfa38894964185cb69f862ed304b2e1d557d9342407946aea730d0dffc80a7","repetition":2,"request_hash":"e477494410a221e59c3b5875aee7c009ea2e395f7cf466e6e1bd04623aacc924","request_id":"req_011CfhY5bd6JbbhrZ7N6VNJR","sent_at":"2026-10-04T16:46:45.039477+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-mix","trial_id":"ff8b3ffca6883aba64f386b9f9d8ec974377a6f29cfb6360b555240ac139b116","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":103,"output_tokens":125,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"Let x be litres of the 20% stock and 80 − x litres of the 60% stock.\n\n0.20x + 0.60(80 − x) = 0.35 × 80\n0.20x + 48 − 0.60x = 28\n−0.40x = −20\nx = 50\n\nSo 50 litres of the 20% stock and 30 litres of the 60% stock.\n\n{\"litres_20\": 50, \"litres_60\": 30}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001566,"finished_at":"2026-10-04T17:01:17.623213+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"5f400918ab0486c0cfae8e976cf2cc40c3e88fa0c3df6ca7cd0775fb4af45a9c","latency_seconds":1.923544,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"Make exactly 80 litres of a 35% concentrate from 20% and 60% stocks, with additive volumes. How many litres of each stock are needed? Return only a JSON object with these keys: litres_20, litres_60. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"c8a50de34365be000397830b598c88e9ac4156ed137d8423e75141e31b4ef297","repetition":3,"request_hash":"e477494410a221e59c3b5875aee7c009ea2e395f7cf466e6e1bd04623aacc924","request_id":"req_011CfhZBn6RKQUUo4f3N5aWT","sent_at":"2026-10-04T17:01:15.699669+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-mix","trial_id":"7ebcaba94951364797aa9c4c5b8760266c0aef381253664af683338cfee7b449","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":103,"output_tokens":136,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"{\"litres_20\": 50, \"litres_60\": 30}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001395,"finished_at":"2026-10-04T16:41:13.820276+00:00","grade":{"checks":[{"field":"litres_20","passed":true},{"field":"litres_60","passed":true}],"passed":true,"reason":"correct"},"input_hash":"5f400918ab0486c0cfae8e976cf2cc40c3e88fa0c3df6ca7cd0775fb4af45a9c","latency_seconds":1.950957,"model_id":"gemini-3.8-flash","output_cap_reached":false,"prompt":"Make exactly 80 litres of a 35% concentrate from 20% and 60% stocks, with additive volumes. How many litres of each stock are needed? Return only a JSON object with these keys: litres_20, litres_60. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"04c5b7d821228b33cfc489816c01ae22f3c6603be31724384998d94e0edf5494","repetition":1,"request_hash":"7bb47f63c628632568fef74b843f20e03edbce0f0777dd01c73c795b187b23f3","request_id":null,"sent_at":"2026-10-04T16:41:11.869319+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Gemini Developer API, paid Standard"},"state":"responded","task_id":"math-mix","trial_id":"a4c971efa25111885e4a19a5922ebfb7c3018f39b8817e977123214f49b7bb37","usage":{"candidatesTokenCount":22,"promptTokenCount":69,"promptTokensDetails":[{"modality":"TEXT","tokenCount":69}],"serviceTier":"standard","thoughtsTokenCount":336,"totalTokenCount":427}},{"answer":"{\"litres_20\": 50, \"litres_60\": 30}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001323,"finished_at":"2026-10-04T16:46:48.805894+00:00","grade":{"checks":[{"field":"litres_20","passed":true},{"field":"litres_60","passed":true}],"passed":true,"reason":"correct"},"input_hash":"5f400918ab0486c0cfae8e976cf2cc40c3e88fa0c3df6ca7cd0775fb4af45a9c","latency_seconds":1.930493,"model_id":"gemini-3.8-flash","output_cap_reached":false,"prompt":"Make exactly 80 litres of a 35% concentrate from 20% and 60% stocks, with additive volumes. How many litres of each stock are needed? Return only a JSON object with these keys: litres_20, litres_60. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"6726a8ef2496e6c6ded5c31e724e6ee200c2357b78031f4d2eb65e6e17fcbafd","repetition":2,"request_hash":"7bb47f63c628632568fef74b843f20e03edbce0f0777dd01c73c795b187b23f3","request_id":null,"sent_at":"2026-10-04T16:46:46.875401+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Gemini Developer API, paid Standard"},"state":"responded","task_id":"math-mix","trial_id":"761a071af8ec9bd098c8bb9e7cda05d707982502b67ec63fe3c7f954563aad3c","usage":{"candidatesTokenCount":22,"promptTokenCount":69,"promptTokensDetails":[{"modality":"TEXT","tokenCount":69}],"serviceTier":"standard","thoughtsTokenCount":317,"totalTokenCount":408}},{"answer":"{\"litres_20\": 50, \"litres_60\": 30}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001357,"finished_at":"2026-10-04T17:01:13.147684+00:00","grade":{"checks":[{"field":"litres_20","passed":true},{"field":"litres_60","passed":true}],"passed":true,"reason":"correct"},"input_hash":"5f400918ab0486c0cfae8e976cf2cc40c3e88fa0c3df6ca7cd0775fb4af45a9c","latency_seconds":1.87554,"model_id":"gemini-3.8-flash","output_cap_reached":false,"prompt":"Make exactly 80 litres of a 35% concentrate from 20% and 60% stocks, with additive volumes. How many litres of each stock are needed? Return only a JSON object with these keys: litres_20, litres_60. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"18ae3e36d2c5358d7c6a61c6b083fd9b34087c0674adac9f8937864d8ea9dc54","repetition":3,"request_hash":"7bb47f63c628632568fef74b843f20e03edbce0f0777dd01c73c795b187b23f3","request_id":null,"sent_at":"2026-10-04T17:01:11.272144+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Gemini Developer API, paid Standard"},"state":"responded","task_id":"math-mix","trial_id":"69bf739a862d3d1d94b3ef6ab079ef6dfa89e7666146bfebf12c3998776251c4","usage":{"candidatesTokenCount":22,"promptTokenCount":69,"promptTokensDetails":[{"modality":"TEXT","tokenCount":69}],"serviceTier":"standard","thoughtsTokenCount":326,"totalTokenCount":417}},{"answer":"{\"litres_20\":50,\"litres_60\":30}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.000556,"finished_at":"2026-10-04T16:41:09.779920+00:00","grade":{"checks":[{"field":"litres_20","passed":true},{"field":"litres_60","passed":true}],"passed":true,"reason":"correct"},"input_hash":"5f400918ab0486c0cfae8e976cf2cc40c3e88fa0c3df6ca7cd0775fb4af45a9c","latency_seconds":2.9153,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"Make exactly 80 litres of a 35% concentrate from 20% and 60% stocks, with additive volumes. How many litres of each stock are needed? Return only a JSON object with these keys: litres_20, litres_60. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"37af6899f4f33c780c25495135019429faa61af7545e856d3b8489da41daf7cc","repetition":1,"request_hash":"8f339d73d2b049122871730efd45a023d6485f142fe8c931bd17c58084091341","request_id":"req_c27af42bb7cd43bebc246f50b7052f3e","sent_at":"2026-10-04T16:41:06.864620+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-mix","trial_id":"62f9ad48f5080b3b169cd45ad4f11e6f7fe2366a5aacc009bdc66bfa5d560c78","usage":{"input_tokens":68,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":42,"output_tokens_details":{"reasoning_tokens":21},"total_tokens":110}},{"answer":"{\"litres_20\":50,\"litres_60\":30}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.000676,"finished_at":"2026-10-04T16:46:51.316642+00:00","grade":{"checks":[{"field":"litres_20","passed":true},{"field":"litres_60","passed":true}],"passed":true,"reason":"correct"},"input_hash":"5f400918ab0486c0cfae8e976cf2cc40c3e88fa0c3df6ca7cd0775fb4af45a9c","latency_seconds":2.498955,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"Make exactly 80 litres of a 35% concentrate from 20% and 60% stocks, with additive volumes. How many litres of each stock are needed? Return only a JSON object with these keys: litres_20, litres_60. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"ccda05ec0b9d0f37acf0bfb2611ea1025dd565aa72c3049958311384bc0c445b","repetition":2,"request_hash":"8f339d73d2b049122871730efd45a023d6485f142fe8c931bd17c58084091341","request_id":"req_d85e3deae1d74361913ffe35c07dcc8b","sent_at":"2026-10-04T16:46:48.817687+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-mix","trial_id":"6c8b4b4ecb8df2d1b883ca6d216a6210e8d791a053139818483663f1b24eadc2","usage":{"input_tokens":68,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":54,"output_tokens_details":{"reasoning_tokens":33},"total_tokens":122}},{"answer":"{\"litres_20\":50,\"litres_60\":30}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.000606,"finished_at":"2026-10-04T17:01:15.680028+00:00","grade":{"checks":[{"field":"litres_20","passed":true},{"field":"litres_60","passed":true}],"passed":true,"reason":"correct"},"input_hash":"5f400918ab0486c0cfae8e976cf2cc40c3e88fa0c3df6ca7cd0775fb4af45a9c","latency_seconds":2.520884,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"Make exactly 80 litres of a 35% concentrate from 20% and 60% stocks, with additive volumes. How many litres of each stock are needed? Return only a JSON object with these keys: litres_20, litres_60. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"6097ea90431223917b5e918b600ae63ebb1c925caa3bd107dde171196a91c89d","repetition":3,"request_hash":"8f339d73d2b049122871730efd45a023d6485f142fe8c931bd17c58084091341","request_id":"req_fbc6edd2bc0e47bbbc734f51c8b16ba9","sent_at":"2026-10-04T17:01:13.159144+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-mix","trial_id":"d714b5452d431ca1d32ec4256046d78c9ac990c0036133950dba5c8ba4a9faa1","usage":{"input_tokens":68,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":47,"output_tokens_details":{"reasoning_tokens":26},"total_tokens":115}},{"answer":"NPV = -1000 + 400*(1/1.1 + 1/1.21 + 1/1.331)\n\nAnnuity factor = 2.486851991...\nExactly: 1/1.1 = 0.909090909091, 1/1.21 = 0.826446280992, 1/1.331 = 0.751314800902. Sum = 2.486851990985.\n\nTimes 400 = 994.740796394.\n\nNPV = -5.259203606\n\n{\"npv\": -5.259203606}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.001754,"finished_at":"2026-10-04T16:43:24.967494+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"93afb10193ce00bf5f0945cdac78f2ad2f1bf1287fd632d69363da5ff100d2ff","latency_seconds":2.486324,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"Pay $1000 now, then receive $400 at each year end for three years. Use a 10% annual discount rate. Return net present value without rounding intermediate values. Return only a JSON object with these keys: npv. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"053244a42553ccff7e57a4de74cb784276adf03ac420c59b493181d6cc381871","repetition":1,"request_hash":"e191db30b0e3fb8b1bcd2a34d05be677134e0d736cff4c7b6476f81ff4850d8d","request_id":"req_011CfhXpfUMwMWYSRGo6WgGo","sent_at":"2026-10-04T16:43:22.481170+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-npv","trial_id":"548f824fa1a478295ed5bf399a397e8f3285334b8f246d52497360d962fdc63b","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":97,"output_tokens":156,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"NPV = -1000 + 400 × (1/1.1 + 1/1.21 + 1/1.331)\n\nAnnuity factor = (1 - 1.1^-3)/0.1 = 2.486851991...\n\nExact: 1/1.1 = 0.909090909..., 1/1.21 = 0.826446281, 1/1.331 = 0.751314801. Sum = 2.486851991.\n\nTimes 400 = 994.7407964\n\nNPV = -5.2592036\n\nMore precisely, the sum is 2.4868519909842 (since 1.1^3 = 1.331, the exact sum is (1.21 + 1.1 + 1)/1.331 = 3.31/1.331 = 2.48685199098...). Times 400 = 1324/1.331 = 994.740796...; 1324/1.331 = 994.7407964...; NPV = -5.2592036.\n\nCheck: 1.331 × 994.7408 = 1324.0000 (1.331 × 994.7408 = 994.7408 + 0.331×994.7408 = 994.7408 + 329.2593 = 1324.0001). Good.\n\n{\"npv\": -5.259203606311}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.003994,"finished_at":"2026-10-04T16:45:30.760642+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"93afb10193ce00bf5f0945cdac78f2ad2f1bf1287fd632d69363da5ff100d2ff","latency_seconds":3.872753,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"Pay $1000 now, then receive $400 at each year end for three years. Use a 10% annual discount rate. Return net present value without rounding intermediate values. Return only a JSON object with these keys: npv. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"6079a30d8a4e1b8248a59520bd93d4a4db37b93f15a17a181249c6b94b160a9e","repetition":2,"request_hash":"e191db30b0e3fb8b1bcd2a34d05be677134e0d736cff4c7b6476f81ff4850d8d","request_id":"req_011CfhXyqTdSQiXL7LEqJFVz","sent_at":"2026-10-04T16:45:26.887889+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-npv","trial_id":"b95ccfc48f06c0de4e9d22ed95fd5788cc02d0a7b28890d5f2d1ddef18aa051e","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":97,"output_tokens":380,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"NPV = -1000 + 400 × (1/1.1 + 1/1.21 + 1/1.331)\n\nAnnuity factor = (1 - 1.1^-3)/0.1. 1.1^3 = 1.331, so 1/1.331 = 0.7513148009...\n\nAnnuity factor = (1 - 0.7513148009)/0.1 = 2.486851991\n\n400 × 2.486851991 = 994.7407963\n\nNPV = -5.2592037\n\nMore precisely: 1/1.331 = 0.75131480090157..., 1 - that = 0.24868519909843, factor = 2.4868519909843, times 400 = 994.74079639372, NPV = -5.25920360628.\n\n{\"npv\": -5.25920360628}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.002634,"finished_at":"2026-10-04T16:59:24.268366+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"93afb10193ce00bf5f0945cdac78f2ad2f1bf1287fd632d69363da5ff100d2ff","latency_seconds":2.965985,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"Pay $1000 now, then receive $400 at each year end for three years. Use a 10% annual discount rate. Return net present value without rounding intermediate values. Return only a JSON object with these keys: npv. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"3687ccdfdbc7a3a2e79178e7cb49e2af33495ac809b8f6a033a0ba8ce4504625","repetition":3,"request_hash":"e191db30b0e3fb8b1bcd2a34d05be677134e0d736cff4c7b6476f81ff4850d8d","request_id":"req_011CfhZ3Lxc79wKBq8tYx9BN","sent_at":"2026-10-04T16:59:21.302381+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-npv","trial_id":"b503728b02df8596032ad1d39c7837468c63ed2d2c9d9944dafbd1b1ac029ff3","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":97,"output_tokens":244,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"{\"npv\": -5.259203606311044}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.00273,"finished_at":"2026-10-04T16:43:28.047016+00:00","grade":{"checks":[{"field":"npv","passed":true}],"passed":true,"reason":"correct"},"input_hash":"93afb10193ce00bf5f0945cdac78f2ad2f1bf1287fd632d69363da5ff100d2ff","latency_seconds":3.068571,"model_id":"gemini-3.8-flash","output_cap_reached":false,"prompt":"Pay $1000 now, then receive $400 at each year end for three years. Use a 10% annual discount rate. Return net present value without rounding intermediate values. Return only a JSON object with these keys: npv. Numeric fields must be numbers. 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Use a 10% annual discount rate. Return net present value without rounding intermediate values. Return only a JSON object with these keys: npv. Numeric fields must be numbers. 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Use a 10% annual discount rate. Return net present value without rounding intermediate values. Return only a JSON object with these keys: npv. Numeric fields must be numbers. 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Use a 10% annual discount rate. Return net present value without rounding intermediate values. Return only a JSON object with these keys: npv. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"32c9c9f820cd3852df226dbe54d00cc04cb520b417c831b93544cd1c2188f55c","repetition":1,"request_hash":"fd592079fbb21601c05ced6dd32695d18bafb18f3ca881c37f8d63abc4b2a404","request_id":"req_06c62a60e6504d39b832682fc301b124","sent_at":"2026-10-04T16:43:17.614052+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-npv","trial_id":"c3116d957c9c2faf61b1ab6b93a15197ca9a202dc7d4081d86cd706daf1c9acc","usage":{"input_tokens":65,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":147,"output_tokens_details":{"reasoning_tokens":128},"total_tokens":212}},{"answer":"{\"npv\":-5.259203606311044}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.00267,"finished_at":"2026-10-04T16:45:42.126106+00:00","grade":{"checks":[{"field":"npv","passed":true}],"passed":true,"reason":"correct"},"input_hash":"93afb10193ce00bf5f0945cdac78f2ad2f1bf1287fd632d69363da5ff100d2ff","latency_seconds":8.018648,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"Pay $1000 now, then receive $400 at each year end for three years. Use a 10% annual discount rate. Return net present value without rounding intermediate values. Return only a JSON object with these keys: npv. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"6611bf5c22ec2f130dc9a5f89620b9b7c7e962d675ffbd5f40eb52b874218225","repetition":2,"request_hash":"fd592079fbb21601c05ced6dd32695d18bafb18f3ca881c37f8d63abc4b2a404","request_id":"req_dc4232480b874f46bf30556a6d898a2d","sent_at":"2026-10-04T16:45:34.107458+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-npv","trial_id":"516a3bba5cff55df14254b03dc08a63a699c8c2d5b79c58cb3c49cbbbb82a5e0","usage":{"input_tokens":65,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":254,"output_tokens_details":{"reasoning_tokens":235},"total_tokens":319}},{"answer":"{\"npv\":-5.259203606311044}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.00168,"finished_at":"2026-10-04T16:59:21.288022+00:00","grade":{"checks":[{"field":"npv","passed":true}],"passed":true,"reason":"correct"},"input_hash":"93afb10193ce00bf5f0945cdac78f2ad2f1bf1287fd632d69363da5ff100d2ff","latency_seconds":4.58218,"model_id":"gpt-6.1-sol","output_cap_reached":false,"prompt":"Pay $1000 now, then receive $400 at each year end for three years. Use a 10% annual discount rate. Return net present value without rounding intermediate values. Return only a JSON object with these keys: npv. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"3d9ff74982171ddaf6a096e1760e706d50653682c26bf4fe5f96e31e2f8e58be","repetition":3,"request_hash":"fd592079fbb21601c05ced6dd32695d18bafb18f3ca881c37f8d63abc4b2a404","request_id":"req_e916687448a04f9e9d95d1358f3c0826","sent_at":"2026-10-04T16:59:16.705842+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"OpenAI direct API, Standard global"},"state":"responded","task_id":"math-npv","trial_id":"416fa25999fead2c107bec3d680c3a5668c60edf4c9aacc6b91653ddd78c4a66","usage":{"input_tokens":65,"input_tokens_details":{"cache_write_tokens":0,"cached_tokens":0},"output_tokens":155,"output_tokens_details":{"reasoning_tokens":136},"total_tokens":220}},{"answer":"p = 0.98^3 = 0.941192\nFailure = 0.058808\nSuccess probability = 1 - 0.058808^2 = 1 - 0.003458... compute: 0.058808^2 = 0.003458380864 (0.058808*0.058808: 0.058808*0.05=0.0029404; *0.008808=0.000517981...; sum: 0.0029404+0.00051798=0.00345838). So success = 0.996541619136.\n\nExpected attempts = 1 + 0.058808 = 1.058808.\n\n{\"success_probability\": 0.996541619136, \"expected_attempts\": 1.058808}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.0023,"finished_at":"2026-10-04T16:44:20.790319+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"808832bf52a7692764524ac69dc8dc6ada9dcf43a4ba6cd50e48ebd9eb5166c0","latency_seconds":2.684161,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"Each of three independent services succeeds with probability 0.98. A workflow requires all three. It retries the complete workflow once if the first attempt fails; attempts are independent. Calculate eventual success probability and expected number of complete attempts. Return only a JSON object with these keys: success_probability, expected_attempts. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"2c08c4229981a825b5ce9949b7a13b5315d5e3fa7c9ffe9539fd33853022c46c","repetition":1,"request_hash":"7f5704fb1bcd68d283771ebc982db98130bfe5c07edba4068de87c79a1cf038e","request_id":"req_011CfhXtmHxoTMeBZhy24chh","sent_at":"2026-10-04T16:44:18.106158+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-queue","trial_id":"d38793f1a125cba6e36b2b910d755eab20234806404460977751caf2be33ea8d","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":130,"output_tokens":204,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"p = 0.98^3 = 0.941192\nFailure = 0.058808\nSuccess probability = 1 - 0.058808^2 = 1 - 0.003458700864 = 0.996541299136\n\nCheck 0.058808^2: 0.058808*0.058808 = 0.0034587... 0.058808^2 = (0.0588)^2 + 2*0.0588*0.000008 + 6.4e-11 = 0.00345744 + 0.0000009408 + 0.000000000064 = 0.003458380864. Recompute: 0.0588^2 = 0.00345744. Add 0.0000009408 → 0.0034583808, plus 6.4e-11 → 0.003458380864.\nSuccess = 1 - 0.003458380864 = 0.996541619136\n\nExpected attempts = 1 + 0.058808 = 1.058808\n\n{\"success_probability\": 0.996541619136, \"expected_attempts\": 1.058808}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.00335,"finished_at":"2026-10-04T16:47:33.283535+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"808832bf52a7692764524ac69dc8dc6ada9dcf43a4ba6cd50e48ebd9eb5166c0","latency_seconds":2.980111,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"Each of three independent services succeeds with probability 0.98. A workflow requires all three. It retries the complete workflow once if the first attempt fails; attempts are independent. Calculate eventual success probability and expected number of complete attempts. Return only a JSON object with these keys: success_probability, expected_attempts. Numeric fields must be numbers. No Markdown or explanation.","raw_response_hash":"7245d4c43def21a30bbe4c10ab2eabfc1fff064725c0d59e4a8dbbe2d0270e25","repetition":2,"request_hash":"7f5704fb1bcd68d283771ebc982db98130bfe5c07edba4068de87c79a1cf038e","request_id":"req_011CfhY8w9g8HEz3eRR4Lr5Q","sent_at":"2026-10-04T16:47:30.303424+00:00","settings":{"effort":"medium","max_output_tokens":8192,"surface":"Claude direct API, Standard global"},"state":"responded","task_id":"math-queue","trial_id":"4e5d111308bbb48174c2c601d49974908ebfa1730dc6fc0691c93c973ded1755","usage":{"cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":0},"cache_creation_input_tokens":0,"cache_read_input_tokens":0,"inference_geo":"global","input_tokens":130,"output_tokens":309,"output_tokens_details":{"thinking_tokens":0},"service_tier":"standard"}},{"answer":"p = 0.98^3 = 0.941192\nFailure = 0.058808\nSuccess probability = 1 - 0.058808^2 = 1 - 0.003458540864 = 0.996541459136\n\n0.058808^2: 0.058808*0.058808 = 0.003458 (0.058808*0.05=0.0029404; *0.008808=0.00051798...). Compute precisely: 0.058808*0.008808 = 0.000517980... 0.058808*0.008=0.000470464; *0.000808=0.0000475168 (0.058808*0.0008=0.0000470464; *0.000008=0.000000470464; sum 0.000047516864). Total 0.000517980864. Plus 0.0029404 = 0.003458380864.\n\nSo success = 1 - 0.003458380864 = 0.996541619136.\n\nExpected attempts = 1 + 0.058808 = 1.058808\n\n{\"success_probability\": 0.996541619136, \"expected_attempts\": 1.058808}","billed_net_usd":null,"enabled_tools":[],"estimated_net_usd":0.00351,"finished_at":"2026-10-04T17:00:54.990447+00:00","grade":{"checks":[],"passed":false,"reason":"invalid_artifact"},"input_hash":"808832bf52a7692764524ac69dc8dc6ada9dcf43a4ba6cd50e48ebd9eb5166c0","latency_seconds":3.338947,"model_id":"claude-sonnet-5-5","output_cap_reached":false,"prompt":"Each of three independent services succeeds with probability 0.98. A workflow requires all three. It retries the complete workflow once if the first attempt fails; attempts are independent. Calculate eventual success probability and expected number of complete attempts. Return only a JSON object with these keys: success_probability, expected_attempts. Numeric fields must be numbers. 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