{"abstract":"Positive softplus drops its linear asymptote.","category":"Floating-point arithmetic","checks":6,"contract":"Evaluate log(1+exp(x)) without overflowing or erasing a small positive tail. Finite results are rendered to eleven significant decimal digits; modeled domain violations and arithmetic errors are explicit strings.","evaluation_group":"s3-float-softplus","failed_approach":"The attempted local correction result=x still violates the explicit regression fixtures.","family":"s3-floating_point_arithmetic-softplus-linear-term","id":"FA-16171","implementations":{"attempt":{"sha256":"86e7f15396dcff807f2ceaaa81ad3f58a516f0c759b91ae138afea389853f886","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\ndef render(x):\n    if math.isnan(x): return 'nan'\n    if math.isinf(x): return '-infinity' if x<0 else '+infinity'\n    return format(x,'.11g')\n\nN = 1\nobservations = []\ndef solve(x):\n    try:\n        if x>0:\n            result=x\n        else:\n            result=math.log1p(math.exp(x))\n        return render(result)\n    except (ValueError, OverflowError, ZeroDivisionError, TypeError):\n        return \"arithmetic-error\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive huge', solve(1000.0*N), render(1000.0*N))\ncheck('negative tail', solve(-50.0-N), render(math.exp(-50.0-N)))\ncheck('zero', solve(0.0), render(math.log(2)))\ncheck('positive moderate', solve(float(N)), render(math.log1p(math.exp(float(N)))))\ncheck('negative moderate', solve(-float(N)), render(math.log1p(math.exp(-float(N)))))\ncheck('small positive', solve(N*1e-8), render(math.log1p(math.exp(N*1e-8))))\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":"621e8316c2ca3ab64a7f70aa0c20f2a2c96e88c3ff036614a3576409dbafffbd","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\ndef render(x):\n    if math.isnan(x): return 'nan'\n    if math.isinf(x): return '-infinity' if x<0 else '+infinity'\n    return format(x,'.11g')\n\nN = 1\nobservations = []\ndef solve(x):\n    try:\n        if x>0:\n            result=math.log1p(math.exp(-x))\n        else:\n            result=math.log1p(math.exp(x))\n        return render(result)\n    except (ValueError, OverflowError, ZeroDivisionError, TypeError):\n        return \"arithmetic-error\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive huge', solve(1000.0*N), render(1000.0*N))\ncheck('negative tail', solve(-50.0-N), render(math.exp(-50.0-N)))\ncheck('zero', solve(0.0), render(math.log(2)))\ncheck('positive moderate', solve(float(N)), render(math.log1p(math.exp(float(N)))))\ncheck('negative moderate', solve(-float(N)), render(math.log1p(math.exp(-float(N)))))\ncheck('small positive', solve(N*1e-8), render(math.log1p(math.exp(N*1e-8))))\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":"b3e0d0ed0bb46c46fb9f2ef65916ed9a364d4676147e96f2f123c6ab89501610","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\ndef render(x):\n    if math.isnan(x): return 'nan'\n    if math.isinf(x): return '-infinity' if x<0 else '+infinity'\n    return format(x,'.11g')\n\nN = 1\nobservations = []\ndef solve(x):\n    try:\n        if x>0:\n            result=x+math.log1p(math.exp(-x))\n        else:\n            result=math.log1p(math.exp(x))\n        return render(result)\n    except (ValueError, OverflowError, ZeroDivisionError, TypeError):\n        return \"arithmetic-error\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive huge', solve(1000.0*N), render(1000.0*N))\ncheck('negative tail', solve(-50.0-N), render(math.exp(-50.0-N)))\ncheck('zero', solve(0.0), render(math.log(2)))\ncheck('positive moderate', solve(float(N)), render(math.log1p(math.exp(float(N)))))\ncheck('negative moderate', solve(-float(N)), render(math.log1p(math.exp(-float(N)))))\ncheck('small positive', solve(N*1e-8), render(math.log1p(math.exp(N*1e-8))))\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-softplus-linear-term","generated_at":"2026-09-29T14:39:33.920199+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 result=x+math.log1p(math.exp(-x)).","root_cause":"Positive softplus drops its linear asymptote. The faulty expression is result=math.log1p(math.exp(-x)).","sha256":"8aa749afc46abbc2e64be59d03c0512dbdaa714d0052af5c7cdb069362dead1f","title":"Positive softplus drops its linear asymptote · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.057,"exit_code":1,"observations":[{"actual":"1000","check":"positive huge","expected":"1000","passed":true},{"actual":"7.0954741623e-23","check":"negative tail","expected":"7.0954741623e-23","passed":true},{"actual":"0.69314718056","check":"zero","expected":"0.69314718056","passed":true},{"actual":"1","check":"positive moderate","expected":"1.3132616875","passed":false},{"actual":"0.31326168752","check":"negative moderate","expected":"0.31326168752","passed":true},{"actual":"1e-08","check":"small positive","expected":"0.69314718556","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive huge\", \"actual\": \"1000\", \"expected\": \"1000\", \"passed\": true}, {\"check\": \"negative tail\", \"actual\": \"7.0954741623e-23\", \"expected\": \"7.0954741623e-23\", \"passed\": true}, {\"check\": \"zero\", \"actual\": \"0.69314718056\", \"expected\": \"0.69314718056\", \"passed\": true}, {\"check\": \"positive moderate\", \"actual\": \"1\", \"expected\": \"1.3132616875\", \"passed\": false}, {\"check\": \"negative moderate\", \"actual\": \"0.31326168752\", \"expected\": \"0.31326168752\", \"passed\": true}, {\"check\": \"small positive\", \"actual\": \"1e-08\", \"expected\": \"0.69314718556\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.227,"exit_code":1,"observations":[{"actual":"0","check":"positive huge","expected":"1000","passed":false},{"actual":"7.0954741623e-23","check":"negative tail","expected":"7.0954741623e-23","passed":true},{"actual":"0.69314718056","check":"zero","expected":"0.69314718056","passed":true},{"actual":"0.31326168752","check":"positive moderate","expected":"1.3132616875","passed":false},{"actual":"0.31326168752","check":"negative moderate","expected":"0.31326168752","passed":true},{"actual":"0.69314717556","check":"small positive","expected":"0.69314718556","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive huge\", \"actual\": \"0\", \"expected\": \"1000\", \"passed\": false}, {\"check\": \"negative tail\", \"actual\": \"7.0954741623e-23\", \"expected\": \"7.0954741623e-23\", \"passed\": true}, {\"check\": \"zero\", \"actual\": \"0.69314718056\", \"expected\": \"0.69314718056\", \"passed\": true}, {\"check\": \"positive moderate\", \"actual\": \"0.31326168752\", \"expected\": \"1.3132616875\", \"passed\": false}, {\"check\": \"negative moderate\", \"actual\": \"0.31326168752\", \"expected\": \"0.31326168752\", \"passed\": true}, {\"check\": \"small positive\", \"actual\": \"0.69314717556\", \"expected\": \"0.69314718556\", \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.573,"exit_code":0,"observations":[{"actual":"1000","check":"positive huge","expected":"1000","passed":true},{"actual":"7.0954741623e-23","check":"negative tail","expected":"7.0954741623e-23","passed":true},{"actual":"0.69314718056","check":"zero","expected":"0.69314718056","passed":true},{"actual":"1.3132616875","check":"positive moderate","expected":"1.3132616875","passed":true},{"actual":"0.31326168752","check":"negative moderate","expected":"0.31326168752","passed":true},{"actual":"0.69314718556","check":"small positive","expected":"0.69314718556","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive huge\", \"actual\": \"1000\", \"expected\": \"1000\", \"passed\": true}, {\"check\": \"negative tail\", \"actual\": \"7.0954741623e-23\", \"expected\": \"7.0954741623e-23\", \"passed\": true}, {\"check\": \"zero\", \"actual\": \"0.69314718056\", \"expected\": \"0.69314718056\", \"passed\": true}, {\"check\": \"positive moderate\", \"actual\": \"1.3132616875\", \"expected\": \"1.3132616875\", \"passed\": true}, {\"check\": \"negative moderate\", \"actual\": \"0.31326168752\", \"expected\": \"0.31326168752\", \"passed\": true}, {\"check\": \"small positive\", \"actual\": \"0.69314718556\", \"expected\": \"0.69314718556\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}