{"abstract":"Closeness accepts an infinite distance against infinite tolerance.","category":"Floating-point arithmetic","checks":11,"contract":"Symmetric binary64 closeness: equal values including like-signed infinities are close; remaining nonfinite pairs are not. For finite a,b require abs(a-b)<=max(abs_tol,rel_tol*max(abs(a),abs(b))). Negative tolerances return invalid.","evaluation_group":"s3-float-isclose","failed_approach":"The attempted local correction if math.isnan(a) and math.isnan(b): return False still violates the explicit regression fixtures.","family":"s3-floating_point_arithmetic-isclose-nonfinite-distance","id":"FA-17061","implementations":{"attempt":{"sha256":"ca6d3258b028315d5ab3a0d36c2b8aebd828d22620663505e0bdd3211ed4814c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\nN = 1\nobservations = []\ndef solve(a,b,rel_tol,abs_tol):\n    if rel_tol<0 or abs_tol<0: return 'invalid'\n    if a==b: return True\n    if math.isnan(a) and math.isnan(b): return False\n    difference=abs(a-b)\n    relative=rel_tol*max(abs(a),abs(b))\n    return difference<=max(abs_tol,relative)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('equal infinity', solve(math.inf,math.inf,1e-9,0.0), True)\ncheck('opposite infinity', solve(math.inf,-math.inf,1e-9,0.0), False)\ncheck('nan', solve(math.nan,math.nan,1.0,1.0), False)\ncheck('absolute zero', solve(0.0,N*1e-9,0.0,N*1e-9), True)\ncheck('relative boundary', solve(float(N),float(N*2),0.5,0.0), True)\ncheck('reverse relative', solve(float(N*2),float(N),0.5,0.0), True)\ncheck('negative values', solve(-float(N),-float(N*2),0.5,0.0), True)\ncheck('disjoint tolerances', solve(0.0,1.5,0.5,1.0), False)\ncheck('ordinary apart', solve(float(N),float(N+1),1e-6,0.0), False)\ncheck('bad relative', solve(1.0,1.0,-1.0,0.0), \"invalid\")\ncheck('bad absolute', solve(1.0,1.0,0.0,-1.0), \"invalid\")\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":"21f9a3b62bf1323ffe77605d9c378f58b3f74ebd3cd8c1ebc2a19f27e35bcfb8","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\nN = 1\nobservations = []\ndef solve(a,b,rel_tol,abs_tol):\n    if rel_tol<0 or abs_tol<0: return 'invalid'\n    if a==b: return True\n    if math.isnan(a) or math.isnan(b): return False\n    difference=abs(a-b)\n    relative=rel_tol*max(abs(a),abs(b))\n    return difference<=max(abs_tol,relative)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('equal infinity', solve(math.inf,math.inf,1e-9,0.0), True)\ncheck('opposite infinity', solve(math.inf,-math.inf,1e-9,0.0), False)\ncheck('nan', solve(math.nan,math.nan,1.0,1.0), False)\ncheck('absolute zero', solve(0.0,N*1e-9,0.0,N*1e-9), True)\ncheck('relative boundary', solve(float(N),float(N*2),0.5,0.0), True)\ncheck('reverse relative', solve(float(N*2),float(N),0.5,0.0), True)\ncheck('negative values', solve(-float(N),-float(N*2),0.5,0.0), True)\ncheck('disjoint tolerances', solve(0.0,1.5,0.5,1.0), False)\ncheck('ordinary apart', solve(float(N),float(N+1),1e-6,0.0), False)\ncheck('bad relative', solve(1.0,1.0,-1.0,0.0), \"invalid\")\ncheck('bad absolute', solve(1.0,1.0,0.0,-1.0), \"invalid\")\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":"d99becf37aff8567b546848e57dd7b96eb8a46f9a6359a7133a912bf628d5c9f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\nN = 1\nobservations = []\ndef solve(a,b,rel_tol,abs_tol):\n    if rel_tol<0 or abs_tol<0: return 'invalid'\n    if a==b: return True\n    if not math.isfinite(a) or not math.isfinite(b): return False\n    difference=abs(a-b)\n    relative=rel_tol*max(abs(a),abs(b))\n    return difference<=max(abs_tol,relative)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('equal infinity', solve(math.inf,math.inf,1e-9,0.0), True)\ncheck('opposite infinity', solve(math.inf,-math.inf,1e-9,0.0), False)\ncheck('nan', solve(math.nan,math.nan,1.0,1.0), False)\ncheck('absolute zero', solve(0.0,N*1e-9,0.0,N*1e-9), True)\ncheck('relative boundary', solve(float(N),float(N*2),0.5,0.0), True)\ncheck('reverse relative', solve(float(N*2),float(N),0.5,0.0), True)\ncheck('negative values', solve(-float(N),-float(N*2),0.5,0.0), True)\ncheck('disjoint tolerances', solve(0.0,1.5,0.5,1.0), False)\ncheck('ordinary apart', solve(float(N),float(N+1),1e-6,0.0), False)\ncheck('bad relative', solve(1.0,1.0,-1.0,0.0), \"invalid\")\ncheck('bad absolute', solve(1.0,1.0,0.0,-1.0), \"invalid\")\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":"Controlled binary64 or explicitly stipulated miniature format; no hardware exception flags or platform floating environment are modeled. 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":"s3-floating_point_arithmetic-isclose-nonfinite-distance","generated_at":"2026-09-29T14:39:42.497129+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"An offline floating representation model isolates a reproducible arithmetic fault.","repair":"Apply the contract at this fault site using if not math.isfinite(a) or not math.isfinite(b): return False.","root_cause":"Closeness accepts an infinite distance against infinite tolerance. The faulty expression is if math.isnan(a) or math.isnan(b): return False.","sha256":"0727e5ebe67d7ef6e4129aa705d733658b2b90a894e4878de9fd3f3f691b2c0c","title":"Closeness accepts an infinite distance against infinite tolerance · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.624,"exit_code":1,"observations":[{"actual":true,"check":"equal infinity","expected":true,"passed":true},{"actual":true,"check":"opposite infinity","expected":false,"passed":false},{"actual":false,"check":"nan","expected":false,"passed":true},{"actual":true,"check":"absolute zero","expected":true,"passed":true},{"actual":true,"check":"relative boundary","expected":true,"passed":true},{"actual":true,"check":"reverse relative","expected":true,"passed":true},{"actual":true,"check":"negative values","expected":true,"passed":true},{"actual":false,"check":"disjoint tolerances","expected":false,"passed":true},{"actual":false,"check":"ordinary apart","expected":false,"passed":true},{"actual":"invalid","check":"bad relative","expected":"invalid","passed":true},{"actual":"invalid","check":"bad absolute","expected":"invalid","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"equal infinity\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"opposite infinity\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"nan\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"absolute zero\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"relative boundary\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"reverse relative\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"negative values\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"disjoint tolerances\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"ordinary apart\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"bad relative\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"bad absolute\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.847,"exit_code":1,"observations":[{"actual":true,"check":"equal infinity","expected":true,"passed":true},{"actual":true,"check":"opposite infinity","expected":false,"passed":false},{"actual":false,"check":"nan","expected":false,"passed":true},{"actual":true,"check":"absolute zero","expected":true,"passed":true},{"actual":true,"check":"relative boundary","expected":true,"passed":true},{"actual":true,"check":"reverse relative","expected":true,"passed":true},{"actual":true,"check":"negative values","expected":true,"passed":true},{"actual":false,"check":"disjoint tolerances","expected":false,"passed":true},{"actual":false,"check":"ordinary apart","expected":false,"passed":true},{"actual":"invalid","check":"bad relative","expected":"invalid","passed":true},{"actual":"invalid","check":"bad absolute","expected":"invalid","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"equal infinity\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"opposite infinity\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"nan\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"absolute zero\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"relative boundary\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"reverse relative\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"negative values\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"disjoint tolerances\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"ordinary apart\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"bad relative\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"bad absolute\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.458,"exit_code":0,"observations":[{"actual":true,"check":"equal infinity","expected":true,"passed":true},{"actual":false,"check":"opposite infinity","expected":false,"passed":true},{"actual":false,"check":"nan","expected":false,"passed":true},{"actual":true,"check":"absolute zero","expected":true,"passed":true},{"actual":true,"check":"relative boundary","expected":true,"passed":true},{"actual":true,"check":"reverse relative","expected":true,"passed":true},{"actual":true,"check":"negative values","expected":true,"passed":true},{"actual":false,"check":"disjoint tolerances","expected":false,"passed":true},{"actual":false,"check":"ordinary apart","expected":false,"passed":true},{"actual":"invalid","check":"bad relative","expected":"invalid","passed":true},{"actual":"invalid","check":"bad absolute","expected":"invalid","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"equal infinity\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"opposite infinity\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"nan\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"absolute zero\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"relative boundary\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"reverse relative\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"negative values\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"disjoint tolerances\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"ordinary apart\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"bad relative\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"bad absolute\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}