{"abstract":"Complex exponential uses cosine for its imaginary projection.","category":"Floating-point arithmetic","checks":8,"contract":"Compute exp(x+iy) for finite components using binary exponent splitting. Fixtures keep each final component finite or zero, including cases where exp(x) alone overflows. Return two rendered components; exact trigonometric zeros are preserved. Finite results are rendered to eleven significant decimal digits; modeled domain violations and arithmetic errors are explicit strings.","contract_signature":"x,y","evaluation_group":"s3-float-complex-exp-scaled","failed_approach":"The attempted local correction imag=math.ldexp(scale*abs(s),k) still violates the explicit regression fixtures.","family":"s3-floating_point_arithmetic-complex-exp-scaled-imag-projection","id":"FA-17286","implementations":{"attempt":{"sha256":"ffb9826490b6831b8f1f895b2875ae8eb4214445e0e6edcd6c4e6322eefba99c","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,y):\n    try:\n        k=math.floor(x/math.log(2))\n        f=x-k*math.log(2)\n        scale=math.exp(f)\n        c=math.cos(y); s=math.sin(y)\n        real=math.ldexp(scale*c,k)\n        imag=math.ldexp(scale*abs(s),k)\n        return [render(real),render(imag)]\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('overflowing common factor', solve(710.0,math.pi/4), [render(math.exp(710-math.log(2))*(2*math.cos(math.pi/4))),render(math.exp(710-math.log(2))*(2*math.sin(math.pi/4)))])\ncheck('negative real projection', solve(float(N),2.0), [render(math.exp(N)*math.cos(2)),render(math.exp(N)*math.sin(2))])\ncheck('ordinary', solve(float(N),0.25), [render(math.exp(N)*math.cos(0.25)),render(math.exp(N)*math.sin(0.25))])\ncheck('negative phase', solve(float(N),-0.25), [render(math.exp(N)*math.cos(-0.25)),render(math.exp(N)*math.sin(-0.25))])\ncheck('negative real', solve(-float(N),0.25), [render(math.exp(-N)*math.cos(0.25)),render(math.exp(-N)*math.sin(0.25))])\ncheck('negative zero phase', solve(float(N),-0.0), [render(math.exp(N)),\"-0\"])\ncheck('zero', solve(0.0,0.0), [\"1\",\"0\"])\ncheck('tiny common factor', solve(-744.0,0.25), [render(math.exp(-744)*math.cos(0.25)),render(math.exp(-744)*math.sin(0.25))])\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":"bbb7c0cb73b7963dd4127253eb1eccaa01f13144c6a46d090fc26ec9b99848e3","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,y):\n    try:\n        k=math.floor(x/math.log(2))\n        f=x-k*math.log(2)\n        scale=math.exp(f)\n        c=math.cos(y); s=math.sin(y)\n        real=math.ldexp(scale*c,k)\n        imag=math.ldexp(scale*c,k)\n        return [render(real),render(imag)]\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('overflowing common factor', solve(710.0,math.pi/4), [render(math.exp(710-math.log(2))*(2*math.cos(math.pi/4))),render(math.exp(710-math.log(2))*(2*math.sin(math.pi/4)))])\ncheck('negative real projection', solve(float(N),2.0), [render(math.exp(N)*math.cos(2)),render(math.exp(N)*math.sin(2))])\ncheck('ordinary', solve(float(N),0.25), [render(math.exp(N)*math.cos(0.25)),render(math.exp(N)*math.sin(0.25))])\ncheck('negative phase', solve(float(N),-0.25), [render(math.exp(N)*math.cos(-0.25)),render(math.exp(N)*math.sin(-0.25))])\ncheck('negative real', solve(-float(N),0.25), [render(math.exp(-N)*math.cos(0.25)),render(math.exp(-N)*math.sin(0.25))])\ncheck('negative zero phase', solve(float(N),-0.0), [render(math.exp(N)),\"-0\"])\ncheck('zero', solve(0.0,0.0), [\"1\",\"0\"])\ncheck('tiny common factor', solve(-744.0,0.25), [render(math.exp(-744)*math.cos(0.25)),render(math.exp(-744)*math.sin(0.25))])\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-complex-exp-scaled-imag-projection","generated_at":"2026-09-29T14:39:45.049801+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.","root_cause":"Complex exponential uses cosine for its imaginary projection. The faulty expression is imag=math.ldexp(scale*c,k).","sha256":"ad87b096aa22c8f61151ce0e32d9d44e305cdf0c7774ac7794026774e8a067b2","title":"Complex exponential uses cosine for its imaginary projection · 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":45.96,"exit_code":1,"observations":[{"actual":["1.5796728483e+308","1.5796728483e+308"],"check":"overflowing common factor","expected":["1.5796728483e+308","1.5796728483e+308"],"passed":true},{"actual":["-1.1312043838","2.471726672"],"check":"negative real projection","expected":["-1.1312043838","2.471726672"],"passed":true},{"actual":["2.6337770293","0.67251368673"],"check":"ordinary","expected":["2.6337770293","0.67251368673"],"passed":true},{"actual":["2.6337770293","0.67251368673"],"check":"negative phase","expected":["2.6337770293","-0.67251368673"],"passed":false},{"actual":["0.35644296024","0.091014830274"],"check":"negative real","expected":["0.35644296024","0.091014830274"],"passed":true},{"actual":["2.7182818285","0"],"check":"negative zero phase","expected":["2.7182818285","-0"],"passed":false},{"actual":["1","0"],"check":"zero","expected":["1","0"],"passed":true},{"actual":["9.8813129168e-324","0"],"check":"tiny common factor","expected":["9.8813129168e-324","0"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"overflowing common factor\", \"actual\": [\"1.5796728483e+308\", \"1.5796728483e+308\"], \"expected\": [\"1.5796728483e+308\", \"1.5796728483e+308\"], \"passed\": true}, {\"check\": \"negative real projection\", \"actual\": [\"-1.1312043838\", \"2.471726672\"], \"expected\": [\"-1.1312043838\", \"2.471726672\"], \"passed\": true}, {\"check\": \"ordinary\", \"actual\": [\"2.6337770293\", \"0.67251368673\"], \"expected\": [\"2.6337770293\", \"0.67251368673\"], \"passed\": true}, {\"check\": \"negative phase\", \"actual\": [\"2.6337770293\", \"0.67251368673\"], \"expected\": [\"2.6337770293\", \"-0.67251368673\"], \"passed\": false}, {\"check\": \"negative real\", \"actual\": [\"0.35644296024\", \"0.091014830274\"], \"expected\": [\"0.35644296024\", \"0.091014830274\"], \"passed\": true}, {\"check\": \"negative zero phase\", \"actual\": [\"2.7182818285\", \"0\"], \"expected\": [\"2.7182818285\", \"-0\"], \"passed\": false}, {\"check\": \"zero\", \"actual\": [\"1\", \"0\"], \"expected\": [\"1\", \"0\"], \"passed\": true}, {\"check\": \"tiny common factor\", \"actual\": [\"9.8813129168e-324\", \"0\"], \"expected\": [\"9.8813129168e-324\", \"0\"], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.411,"exit_code":1,"observations":[{"actual":["1.5796728483e+308","1.5796728483e+308"],"check":"overflowing common factor","expected":["1.5796728483e+308","1.5796728483e+308"],"passed":true},{"actual":["-1.1312043838","-1.1312043838"],"check":"negative real projection","expected":["-1.1312043838","2.471726672"],"passed":false},{"actual":["2.6337770293","2.6337770293"],"check":"ordinary","expected":["2.6337770293","0.67251368673"],"passed":false},{"actual":["2.6337770293","2.6337770293"],"check":"negative phase","expected":["2.6337770293","-0.67251368673"],"passed":false},{"actual":["0.35644296024","0.35644296024"],"check":"negative real","expected":["0.35644296024","0.091014830274"],"passed":false},{"actual":["2.7182818285","2.7182818285"],"check":"negative zero phase","expected":["2.7182818285","-0"],"passed":false},{"actual":["1","1"],"check":"zero","expected":["1","0"],"passed":false},{"actual":["9.8813129168e-324","9.8813129168e-324"],"check":"tiny common factor","expected":["9.8813129168e-324","0"],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"overflowing common factor\", \"actual\": [\"1.5796728483e+308\", \"1.5796728483e+308\"], \"expected\": [\"1.5796728483e+308\", \"1.5796728483e+308\"], \"passed\": true}, {\"check\": \"negative real projection\", \"actual\": [\"-1.1312043838\", \"-1.1312043838\"], \"expected\": [\"-1.1312043838\", \"2.471726672\"], \"passed\": false}, {\"check\": \"ordinary\", \"actual\": [\"2.6337770293\", \"2.6337770293\"], \"expected\": [\"2.6337770293\", \"0.67251368673\"], \"passed\": false}, {\"check\": \"negative phase\", \"actual\": [\"2.6337770293\", \"2.6337770293\"], \"expected\": [\"2.6337770293\", \"-0.67251368673\"], \"passed\": false}, {\"check\": \"negative real\", \"actual\": [\"0.35644296024\", \"0.35644296024\"], \"expected\": [\"0.35644296024\", \"0.091014830274\"], \"passed\": false}, {\"check\": \"negative zero phase\", \"actual\": [\"2.7182818285\", \"2.7182818285\"], \"expected\": [\"2.7182818285\", \"-0\"], \"passed\": false}, {\"check\": \"zero\", \"actual\": [\"1\", \"1\"], \"expected\": [\"1\", \"0\"], \"passed\": false}, {\"check\": \"tiny common factor\", \"actual\": [\"9.8813129168e-324\", \"9.8813129168e-324\"], \"expected\": [\"9.8813129168e-324\", \"0\"], \"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."}}