{"abstract":"A nonconstant sample reports zero or an inaccurate variance after its mean is shifted far from zero.","category":"Floating-point arithmetic","checks":7,"contract":"Return statistics.pvariance for a nonempty sequence of finite floats; return None for empty input. This is population variance, so the denominator is n rather than n-1.","evaluation_group":"model-c1c0b2cb858ce0fc","failed_approach":"Clamping negative results to zero prevents an invalid sign but cannot restore precision already lost to cancellation.","family":"num-stable-population-variance","id":"FA-326","implementations":{"attempt":{"sha256":"f3b26229d2adef184b211d022edf05429f17436fa1bff861e2a4f47fa4a8d9c7","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport statistics\nN = 1\nobservations = []\ndef solve(values):\n    if not values:\n        return None\n    mean = sum(values) / len(values)\n    variance = sum(value * value for value in values) / len(values) - mean * mean\n    return max(0.0, variance)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nbase = float(10 ** (N + 6))\ncheck('unit spread on large baseline', solve([base, base + 1, base + 2]), 2 / 3)\ncheck('same spread around zero', solve([0.0, 1.0, 2.0]), 2 / 3)\ncheck('symmetric wider spread on baseline', solve([base - 2, base, base + 2]), 8 / 3)\ncheck('constant sample has zero variance', solve([base] * (N + 1)), 0.0)\ncheck('population denominator for two values', solve([-float(N), float(N)]), float(N * N))\ncheck('single value', solve([base]), 0.0)\ncheck('empty sample', 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":"2e908f94ab6696ac4eab0138b610046288e97dd9858c8af81eeff44a7c45f183","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport statistics\nN = 1\nobservations = []\ndef solve(values):\n    if not values:\n        return None\n    mean = sum(values) / len(values)\n    return sum(value * value for value in values) / len(values) - mean * mean\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nbase = float(10 ** (N + 6))\ncheck('unit spread on large baseline', solve([base, base + 1, base + 2]), 2 / 3)\ncheck('same spread around zero', solve([0.0, 1.0, 2.0]), 2 / 3)\ncheck('symmetric wider spread on baseline', solve([base - 2, base, base + 2]), 8 / 3)\ncheck('constant sample has zero variance', solve([base] * (N + 1)), 0.0)\ncheck('population denominator for two values', solve([-float(N), float(N)]), float(N * N))\ncheck('single value', solve([base]), 0.0)\ncheck('empty sample', 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":"91f9989eaaf3204df309fb82ea1713907cfb1b4c8cd39e448da3c9c448820f32","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport statistics\nN = 1\nobservations = []\ndef solve(values):\n    return statistics.pvariance(values) if values else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nbase = float(10 ** (N + 6))\ncheck('unit spread on large baseline', solve([base, base + 1, base + 2]), 2 / 3)\ncheck('same spread around zero', solve([0.0, 1.0, 2.0]), 2 / 3)\ncheck('symmetric wider spread on baseline', solve([base - 2, base, base + 2]), 8 / 3)\ncheck('constant sample has zero variance', solve([base] * (N + 1)), 0.0)\ncheck('population denominator for two values', solve([-float(N), float(N)]), float(N * N))\ncheck('single value', solve([base]), 0.0)\ncheck('empty sample', 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-stable-population-variance","generated_at":"2026-09-29T14:36:52.102142+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Variance should not change when all observations receive the same offset. Large baselines with small spreads are a direct regression check for cancellation-prone moment formulas.","repair":"Use the standard-library population-variance computation, which avoids cancellation in the raw-moment subtraction.","root_cause":"E[x²] and E[x]² are rounded separately before subtracting two nearly equal large values.","sha256":"088b511816c89ddcc3a6cc30273b2f24325e42cf9201a9f5ceaf6fafe687b9d6","title":"Subtracting two large moments destroys a small variance · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.205,"exit_code":1,"observations":[{"actual":0.671875,"check":"unit spread on large baseline","expected":0.6666666666666666,"passed":false},{"actual":0.6666666666666667,"check":"same spread around zero","expected":0.6666666666666666,"passed":false},{"actual":2.671875,"check":"symmetric wider spread on baseline","expected":2.6666666666666665,"passed":false},{"actual":0.0,"check":"constant sample has zero variance","expected":0.0,"passed":true},{"actual":1.0,"check":"population denominator for two values","expected":1.0,"passed":true},{"actual":0.0,"check":"single value","expected":0.0,"passed":true},{"actual":null,"check":"empty sample","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"unit spread on large baseline\", \"actual\": 0.671875, \"expected\": 0.6666666666666666, \"passed\": false}, {\"check\": \"same spread around zero\", \"actual\": 0.6666666666666667, \"expected\": 0.6666666666666666, \"passed\": false}, {\"check\": \"symmetric wider spread on baseline\", \"actual\": 2.671875, \"expected\": 2.6666666666666665, \"passed\": false}, {\"check\": \"constant sample has zero variance\", \"actual\": 0.0, \"expected\": 0.0, \"passed\": true}, {\"check\": \"population denominator for two values\", \"actual\": 1.0, \"expected\": 1.0, \"passed\": true}, {\"check\": \"single value\", \"actual\": 0.0, \"expected\": 0.0, \"passed\": true}, {\"check\": \"empty sample\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.071,"exit_code":1,"observations":[{"actual":0.671875,"check":"unit spread on large baseline","expected":0.6666666666666666,"passed":false},{"actual":0.6666666666666667,"check":"same spread around zero","expected":0.6666666666666666,"passed":false},{"actual":2.671875,"check":"symmetric wider spread on baseline","expected":2.6666666666666665,"passed":false},{"actual":0.0,"check":"constant sample has zero variance","expected":0.0,"passed":true},{"actual":1.0,"check":"population denominator for two values","expected":1.0,"passed":true},{"actual":0.0,"check":"single value","expected":0.0,"passed":true},{"actual":null,"check":"empty sample","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"unit spread on large baseline\", \"actual\": 0.671875, \"expected\": 0.6666666666666666, \"passed\": false}, {\"check\": \"same spread around zero\", \"actual\": 0.6666666666666667, \"expected\": 0.6666666666666666, \"passed\": false}, {\"check\": \"symmetric wider spread on baseline\", \"actual\": 2.671875, \"expected\": 2.6666666666666665, \"passed\": false}, {\"check\": \"constant sample has zero variance\", \"actual\": 0.0, \"expected\": 0.0, \"passed\": true}, {\"check\": \"population denominator for two values\", \"actual\": 1.0, \"expected\": 1.0, \"passed\": true}, {\"check\": \"single value\", \"actual\": 0.0, \"expected\": 0.0, \"passed\": true}, {\"check\": \"empty sample\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.019,"exit_code":0,"observations":[{"actual":0.6666666666666666,"check":"unit spread on large baseline","expected":0.6666666666666666,"passed":true},{"actual":0.6666666666666666,"check":"same spread around zero","expected":0.6666666666666666,"passed":true},{"actual":2.6666666666666665,"check":"symmetric wider spread on baseline","expected":2.6666666666666665,"passed":true},{"actual":0.0,"check":"constant sample has zero variance","expected":0.0,"passed":true},{"actual":1.0,"check":"population denominator for two values","expected":1.0,"passed":true},{"actual":0.0,"check":"single value","expected":0.0,"passed":true},{"actual":null,"check":"empty sample","expected":null,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"unit spread on large baseline\", \"actual\": 0.6666666666666666, \"expected\": 0.6666666666666666, \"passed\": true}, {\"check\": \"same spread around zero\", \"actual\": 0.6666666666666666, \"expected\": 0.6666666666666666, \"passed\": true}, {\"check\": \"symmetric wider spread on baseline\", \"actual\": 2.6666666666666665, \"expected\": 2.6666666666666665, \"passed\": true}, {\"check\": \"constant sample has zero variance\", \"actual\": 0.0, \"expected\": 0.0, \"passed\": true}, {\"check\": \"population denominator for two values\", \"actual\": 1.0, \"expected\": 1.0, \"passed\": true}, {\"check\": \"single value\", \"actual\": 0.0, \"expected\": 0.0, \"passed\": true}, {\"check\": \"empty sample\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}