{"abstract":"Multiplying observations produces infinity or zero even when their geometric mean is a representable positive number.","category":"Floating-point arithmetic","checks":9,"contract":"For a nonempty sequence of finite positive floats, return a logarithm-based geometric mean formatted with ten significant digits. Empty input or any nonpositive observation returns None. Fixtures remain within the representable range of the final mean.","evaluation_group":"model-2f806254a0c0d5a0","failed_approach":"Saturating each product at the largest float discards magnitude and does not repair underflow.","family":"num-geometric-mean-range","id":"FA-346","implementations":{"attempt":{"sha256":"bd6be5f6346a2ab28039ce564d4dc8b237e4f688ae0bb9fe1e74275c6de6989f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport sys\nN = 1\nobservations = []\ndef solve(values):\n    if not values or any(value <= 0 for value in values):\n        return None\n    product = 1.0\n    for value in values:\n        product = min(product * value, sys.float_info.max)\n    return format(product ** (1 / len(values)), '.10g')\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('finite mean despite overflowing product', solve([1e150] * (N + 2)), '1e+150')\ncheck('finite mean despite underflowing product', solve([1e-200] * (N + 1)), '1e-200')\ncheck('balanced reciprocal scales', solve([1e300, 1e-300] * N), '1')\ncheck('ordinary square-root case', solve([4.0, 9.0]), '6')\ncheck('one observation', solve([float(N)]), str(N))\ncheck('unit-valued observations', solve([1.0] * (N + 1)), '1')\ncheck('zero observation rejected', solve([0.0, 1.0]), None)\ncheck('negative observation rejected', solve([-1.0, 2.0]), None)\ncheck('empty sequence', solve([]), None)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"c4d67fdd217aa723bbcec46fb9b20c91693a426d7cbab5cc7f2040ce37584351","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport sys\nN = 1\nobservations = []\ndef solve(values):\n    if not values or any(value <= 0 for value in values):\n        return None\n    return format(math.prod(values) ** (1 / len(values)), '.10g')\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('finite mean despite overflowing product', solve([1e150] * (N + 2)), '1e+150')\ncheck('finite mean despite underflowing product', solve([1e-200] * (N + 1)), '1e-200')\ncheck('balanced reciprocal scales', solve([1e300, 1e-300] * N), '1')\ncheck('ordinary square-root case', solve([4.0, 9.0]), '6')\ncheck('one observation', solve([float(N)]), str(N))\ncheck('unit-valued observations', solve([1.0] * (N + 1)), '1')\ncheck('zero observation rejected', solve([0.0, 1.0]), None)\ncheck('negative observation rejected', solve([-1.0, 2.0]), None)\ncheck('empty sequence', solve([]), None)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"2acc28c9f45f1b5279b9a6852aa70ad62b40789e6f8a4627c7c5f012f3b4bd68","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport sys\nN = 1\nobservations = []\ndef solve(values):\n    if not values or any(value <= 0 for value in values):\n        return None\n    mean_log = math.fsum(math.log(value) for value in values) / len(values)\n    return format(math.exp(mean_log), '.10g')\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('finite mean despite overflowing product', solve([1e150] * (N + 2)), '1e+150')\ncheck('finite mean despite underflowing product', solve([1e-200] * (N + 1)), '1e-200')\ncheck('balanced reciprocal scales', solve([1e300, 1e-300] * N), '1')\ncheck('ordinary square-root case', solve([4.0, 9.0]), '6')\ncheck('one observation', solve([float(N)]), str(N))\ncheck('unit-valued observations', solve([1.0] * (N + 1)), '1')\ncheck('zero observation rejected', solve([0.0, 1.0]), None)\ncheck('negative observation rejected', solve([-1.0, 2.0]), None)\ncheck('empty sequence', solve([]), None)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":" This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"num-geometric-mean-range","generated_at":"2026-09-29T14:36:52.141252+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Multiplicative metrics and ratios can span enormous ranges while their mean stays ordinary. Bounding an intermediate product changes the statistic rather than stabilizing it.","repair":"Average logarithms with accurate summation and exponentiate once, avoiding the unrepresentable intermediate product.","root_cause":"The implementation materializes an extreme product before applying the nth root.","sha256":"c01b36d90aa6f56fd6d12d0a005abb2c3f020135405ba60bcf6bc34138f789c1","title":"A geometric-mean product overflows although the result is finite · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":34.511,"exit_code":1,"observations":[{"actual":"5.643803094e+102","check":"finite mean despite overflowing product","expected":"1e+150","passed":false},{"actual":"0","check":"finite mean despite underflowing product","expected":"1e-200","passed":false},{"actual":"1","check":"balanced reciprocal scales","expected":"1","passed":true},{"actual":"6","check":"ordinary square-root case","expected":"6","passed":true},{"actual":"1","check":"one observation","expected":"1","passed":true},{"actual":"1","check":"unit-valued observations","expected":"1","passed":true},{"actual":null,"check":"zero observation rejected","expected":null,"passed":true},{"actual":null,"check":"negative observation rejected","expected":null,"passed":true},{"actual":null,"check":"empty sequence","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"finite mean despite overflowing product\", \"actual\": \"5.643803094e+102\", \"expected\": \"1e+150\", \"passed\": false}, {\"check\": \"finite mean despite underflowing product\", \"actual\": \"0\", \"expected\": \"1e-200\", \"passed\": false}, {\"check\": \"balanced reciprocal scales\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"ordinary square-root case\", \"actual\": \"6\", \"expected\": \"6\", \"passed\": true}, {\"check\": \"one observation\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"unit-valued observations\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"zero observation rejected\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"negative observation rejected\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"empty sequence\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":36.292,"exit_code":1,"observations":[{"actual":"inf","check":"finite mean despite overflowing product","expected":"1e+150","passed":false},{"actual":"0","check":"finite mean despite underflowing product","expected":"1e-200","passed":false},{"actual":"1","check":"balanced reciprocal scales","expected":"1","passed":true},{"actual":"6","check":"ordinary square-root case","expected":"6","passed":true},{"actual":"1","check":"one observation","expected":"1","passed":true},{"actual":"1","check":"unit-valued observations","expected":"1","passed":true},{"actual":null,"check":"zero observation rejected","expected":null,"passed":true},{"actual":null,"check":"negative observation rejected","expected":null,"passed":true},{"actual":null,"check":"empty sequence","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"finite mean despite overflowing product\", \"actual\": \"inf\", \"expected\": \"1e+150\", \"passed\": false}, {\"check\": \"finite mean despite underflowing product\", \"actual\": \"0\", \"expected\": \"1e-200\", \"passed\": false}, {\"check\": \"balanced reciprocal scales\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"ordinary square-root case\", \"actual\": \"6\", \"expected\": \"6\", \"passed\": true}, {\"check\": \"one observation\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"unit-valued observations\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"zero observation rejected\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"negative observation rejected\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"empty sequence\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":35.971,"exit_code":0,"observations":[{"actual":"1e+150","check":"finite mean despite overflowing product","expected":"1e+150","passed":true},{"actual":"1e-200","check":"finite mean despite underflowing product","expected":"1e-200","passed":true},{"actual":"1","check":"balanced reciprocal scales","expected":"1","passed":true},{"actual":"6","check":"ordinary square-root case","expected":"6","passed":true},{"actual":"1","check":"one observation","expected":"1","passed":true},{"actual":"1","check":"unit-valued observations","expected":"1","passed":true},{"actual":null,"check":"zero observation rejected","expected":null,"passed":true},{"actual":null,"check":"negative observation rejected","expected":null,"passed":true},{"actual":null,"check":"empty sequence","expected":null,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"finite mean despite overflowing product\", \"actual\": \"1e+150\", \"expected\": \"1e+150\", \"passed\": true}, {\"check\": \"finite mean despite underflowing product\", \"actual\": \"1e-200\", \"expected\": \"1e-200\", \"passed\": true}, {\"check\": \"balanced reciprocal scales\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"ordinary square-root case\", \"actual\": \"6\", \"expected\": \"6\", \"passed\": true}, {\"check\": \"one observation\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"unit-valued observations\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"zero observation rejected\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"negative observation rejected\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"empty sequence\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}