{"abstract":"Overlapping area is counted twice.","category":"Planar geometry","checks":4,"contract":"Integer coordinates and lengths, with exact arithmetic except for indicated division results. Lengths are nonnegative. Rectangles are (xmin,ymin,xmax,ymax) with ordered bounds; coordinate vectors have matching dimensions. Rectangle union area. Exact operational definition: (a[2]-a[0])*(a[3]-a[1])+(b[2]-b[0])*(b[3]-b[1])-max(0,min(a[2],b[2])-max(a[0],b[0]))*max(0,min(a[3],b[3])-max(a[1],b[1]))","contract_signature":"a, b","evaluation_group":"model-8c1da95c9468dfb0","failed_approach":"The bounding rectangle includes uncovered space.","family":"xn-rectangle-union-area","id":"FA-5776","implementations":{"attempt":{"sha256":"36fa408e7e9456e6532f3c1c6b86e506a9acccf61b7d3edc0fdc3a986cca5f0b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(a, b):\n    return (max(a[2],b[2])-min(a[0],b[0]))*(max(a[3],b[3])-min(a[1],b[1]))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ((0, 0, 2, 2), (1, 1, 3, 3))', solve(*((0, 0, 2, 2), (1, 1, 3, 3))), 7)\ncheck('fixture 2: ((0, 0, 1, 1), (2, 2, 3, 3))', solve(*((0, 0, 1, 1), (2, 2, 3, 3))), 2)\ncheck('fixture 3: ((0, 0, 2, 2), (0, 0, 2, 2))', solve(*((0, 0, 2, 2), (0, 0, 2, 2))), 4)\ncheck('fixture 4: ((0, 0, 4, 4), (1, 1, 2, 2))', solve(*((0, 0, 4, 4), (1, 1, 2, 2))), 16)\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":"afa240c10371f01d100558ffecdbc5050866da07f429d39a5f9b3c0ab15da405","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(a, b):\n    return (a[2]-a[0])*(a[3]-a[1])+(b[2]-b[0])*(b[3]-b[1])\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ((0, 0, 2, 2), (1, 1, 3, 3))', solve(*((0, 0, 2, 2), (1, 1, 3, 3))), 7)\ncheck('fixture 2: ((0, 0, 1, 1), (2, 2, 3, 3))', solve(*((0, 0, 1, 1), (2, 2, 3, 3))), 2)\ncheck('fixture 3: ((0, 0, 2, 2), (0, 0, 2, 2))', solve(*((0, 0, 2, 2), (0, 0, 2, 2))), 4)\ncheck('fixture 4: ((0, 0, 4, 4), (1, 1, 2, 2))', solve(*((0, 0, 4, 4), (1, 1, 2, 2))), 16)\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":"xn-rectangle-union-area","generated_at":"2026-09-29T14:37:53.590630+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Planar geometry results depend on the stated convention.","root_cause":"Overlapping area is counted twice.","sha256":"acadca15372b47dd95285eb4f2df8bf2507210041d4a769db55a04627dc77138","title":"Rectangle union area · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":46.076,"exit_code":1,"observations":[{"actual":9,"check":"fixture 1: ((0, 0, 2, 2), (1, 1, 3, 3))","expected":7,"passed":false},{"actual":9,"check":"fixture 2: ((0, 0, 1, 1), (2, 2, 3, 3))","expected":2,"passed":false},{"actual":4,"check":"fixture 3: ((0, 0, 2, 2), (0, 0, 2, 2))","expected":4,"passed":true},{"actual":16,"check":"fixture 4: ((0, 0, 4, 4), (1, 1, 2, 2))","expected":16,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ((0, 0, 2, 2), (1, 1, 3, 3))\", \"actual\": 9, \"expected\": 7, \"passed\": false}, {\"check\": \"fixture 2: ((0, 0, 1, 1), (2, 2, 3, 3))\", \"actual\": 9, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 3: ((0, 0, 2, 2), (0, 0, 2, 2))\", \"actual\": 4, \"expected\": 4, \"passed\": true}, {\"check\": \"fixture 4: ((0, 0, 4, 4), (1, 1, 2, 2))\", \"actual\": 16, \"expected\": 16, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":51.829,"exit_code":1,"observations":[{"actual":8,"check":"fixture 1: ((0, 0, 2, 2), (1, 1, 3, 3))","expected":7,"passed":false},{"actual":2,"check":"fixture 2: ((0, 0, 1, 1), (2, 2, 3, 3))","expected":2,"passed":true},{"actual":8,"check":"fixture 3: ((0, 0, 2, 2), (0, 0, 2, 2))","expected":4,"passed":false},{"actual":17,"check":"fixture 4: ((0, 0, 4, 4), (1, 1, 2, 2))","expected":16,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ((0, 0, 2, 2), (1, 1, 3, 3))\", \"actual\": 8, \"expected\": 7, \"passed\": false}, {\"check\": \"fixture 2: ((0, 0, 1, 1), (2, 2, 3, 3))\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 3: ((0, 0, 2, 2), (0, 0, 2, 2))\", \"actual\": 8, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 4: ((0, 0, 4, 4), (1, 1, 2, 2))\", \"actual\": 17, \"expected\": 16, \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}