{"abstract":"Semi-annual and monthly targets are divided by their frequency.","category":"Bond day-count conventions","checks":8,"contract":"Inputs a nominal rate, from/to day-count year basis (360 or 365), from/to compounding frequency (0 = continuous). First rescale the nominal rate by to_basis/from_basis, then convert compounding through the effective annual rate: EAR = (1+r/m)^m - 1 or e^r - 1; target nominal = m*((1+EAR)^(1/m)-1) or ln(1+EAR). Return rounded to 10 decimals.","evaluation_group":"w2-bond_day_count_conventions-rate-basis-conversion","failed_approach":"Dividing the EAR by m ignores compounding altogether.","family":"w2-bond_day_count_conventions-rate-basis-conversion-nominal-from-periodic","id":"FA-61291","implementations":{"attempt":{"sha256":"2cc092573a7994cc47ca0a80911de0d39ab718c0eeb48af2fb070f4f50aab422","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(rate, from_basis, to_basis, from_comp, to_comp):\n    def ear(r, m):\n        return math.exp(r) - 1 if m == 0 else (1 + r / m) ** m - 1\n    def nominal(e, m):\n        return math.log(1 + e) if m == 0 else e / m\n    scaled = rate * to_basis / from_basis\n    return round(nominal(ear(scaled, from_comp), to_comp), 10)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression nominal from periodic 1', [0.03, 365, 365, 2, 2], 0.03], ['regression nominal from periodic 2', [0.08, 360, 365, 0, 12], 0.0813858553], ['partial repair probe 1', [0.15, 365, 360, 2, 2], 0.1479452055], ['partial repair probe 2', [0.08, 360, 360, 2, 2], 0.08], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 365, 365, 0, 0], 0.05], ['normal control 1', [0.0475, 360, 360, 4, 1], 0.0483528119], ['normal control 2', [0.001, 365, 365, 12, 1], 0.0010004585]], [['regression nominal from periodic 1', [0.15, 365, 360, 2, 12], 0.1435811627], ['regression nominal from periodic 2', [0.0475, 360, 360, 0, 12], 0.0475941346], ['partial repair probe 1', [0.0475, 360, 360, 2, 12], 0.0470366575], ['partial repair probe 2', [0.001, 365, 365, 4, 4], 0.001], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 365, 365, 0, 0], 0.05], ['normal control 1', [0.15, 365, 365, 4, 1], 0.158650415], ['normal control 2', [0.0475, 360, 365, 0, 1], 0.0493382446]], [['regression nominal from periodic 1', [0.08, 360, 360, 2, 4], 0.0792156109], ['regression nominal from periodic 2', [0.0125, 365, 365, 2, 2], 0.0125], ['partial repair probe 1', [0.0125, 365, 360, 4, 4], 0.0123287671], ['partial repair probe 2', [0.0475, 360, 365, 1, 2], 0.0475934384], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 365, 1, 1], 0.0506944444], ['normal control 1', [0.001, 365, 360, 2, 0], 0.0009860583], ['normal control 2', [0.03, 365, 360, 2, 0], 0.0293722984]], [['regression nominal from periodic 1', [0.0475, 360, 360, 12, 12], 0.0475], ['regression nominal from periodic 2', [0.08, 365, 360, 1, 2], 0.0774061804], ['partial repair probe 1', [0.03, 360, 360, 2, 12], 0.0298142007], ['partial repair probe 2', [0.001, 365, 365, 4, 12], 0.0009999167], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 365, 1, 1], 0.0506944444], ['normal control 1', [0.0125, 360, 360, 2, 1], 0.0125390625], ['normal control 2', [0.001, 365, 365, 0, 0], 0.001]], [['regression nominal from periodic 1', [0.001, 365, 365, 2, 12], 0.0009997917], ['regression nominal from periodic 2', [0.03, 365, 360, 12, 4], 0.0296620603], ['partial repair probe 1', [0.03, 360, 360, 1, 12], 0.0295952373], ['partial repair probe 2', [0.08, 360, 360, 0, 4], 0.0808053601], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 365, 1, 1], 0.0506944444], ['normal control 1', [0.03, 365, 360, 1, 1], 0.0295890411], ['normal control 2', [0.15, 365, 365, 12, 1], 0.1607545177]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\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":"d99ff7dfe4790736dcb11a3d1dce986d402c2d09193710f4894b2b4e51a98c29","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(rate, from_basis, to_basis, from_comp, to_comp):\n    def ear(r, m):\n        return math.exp(r) - 1 if m == 0 else (1 + r / m) ** m - 1\n    def nominal(e, m):\n        return math.log(1 + e) if m == 0 else (1 + e) ** (1 / m) - 1\n    scaled = rate * to_basis / from_basis\n    return round(nominal(ear(scaled, from_comp), to_comp), 10)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression nominal from periodic 1', [0.03, 365, 365, 2, 2], 0.03], ['regression nominal from periodic 2', [0.08, 360, 365, 0, 12], 0.0813858553], ['partial repair probe 1', [0.15, 365, 360, 2, 2], 0.1479452055], ['partial repair probe 2', [0.08, 360, 360, 2, 2], 0.08], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 365, 365, 0, 0], 0.05], ['normal control 1', [0.0475, 360, 360, 4, 1], 0.0483528119], ['normal control 2', [0.001, 365, 365, 12, 1], 0.0010004585]], [['regression nominal from periodic 1', [0.15, 365, 360, 2, 12], 0.1435811627], ['regression nominal from periodic 2', [0.0475, 360, 360, 0, 12], 0.0475941346], ['partial repair probe 1', [0.0475, 360, 360, 2, 12], 0.0470366575], ['partial repair probe 2', [0.001, 365, 365, 4, 4], 0.001], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 365, 365, 0, 0], 0.05], ['normal control 1', [0.15, 365, 365, 4, 1], 0.158650415], ['normal control 2', [0.0475, 360, 365, 0, 1], 0.0493382446]], [['regression nominal from periodic 1', [0.08, 360, 360, 2, 4], 0.0792156109], ['regression nominal from periodic 2', [0.0125, 365, 365, 2, 2], 0.0125], ['partial repair probe 1', [0.0125, 365, 360, 4, 4], 0.0123287671], ['partial repair probe 2', [0.0475, 360, 365, 1, 2], 0.0475934384], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 365, 1, 1], 0.0506944444], ['normal control 1', [0.001, 365, 360, 2, 0], 0.0009860583], ['normal control 2', [0.03, 365, 360, 2, 0], 0.0293722984]], [['regression nominal from periodic 1', [0.0475, 360, 360, 12, 12], 0.0475], ['regression nominal from periodic 2', [0.08, 365, 360, 1, 2], 0.0774061804], ['partial repair probe 1', [0.03, 360, 360, 2, 12], 0.0298142007], ['partial repair probe 2', [0.001, 365, 365, 4, 12], 0.0009999167], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 365, 1, 1], 0.0506944444], ['normal control 1', [0.0125, 360, 360, 2, 1], 0.0125390625], ['normal control 2', [0.001, 365, 365, 0, 0], 0.001]], [['regression nominal from periodic 1', [0.001, 365, 365, 2, 12], 0.0009997917], ['regression nominal from periodic 2', [0.03, 365, 360, 12, 4], 0.0296620603], ['partial repair probe 1', [0.03, 360, 360, 1, 12], 0.0295952373], ['partial repair probe 2', [0.08, 360, 360, 0, 4], 0.0808053601], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 365, 1, 1], 0.0506944444], ['normal control 1', [0.03, 365, 360, 1, 1], 0.0295890411], ['normal control 2', [0.15, 365, 365, 12, 1], 0.1607545177]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\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":"f9499f556553106090a587999cbf0a1bb268f6a3dbd5a0026819dc19e59bb76d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(rate, from_basis, to_basis, from_comp, to_comp):\n    def ear(r, m):\n        return math.exp(r) - 1 if m == 0 else (1 + r / m) ** m - 1\n    def nominal(e, m):\n        return math.log(1 + e) if m == 0 else m * ((1 + e) ** (1 / m) - 1)\n    scaled = rate * to_basis / from_basis\n    return round(nominal(ear(scaled, from_comp), to_comp), 10)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression nominal from periodic 1', [0.03, 365, 365, 2, 2], 0.03], ['regression nominal from periodic 2', [0.08, 360, 365, 0, 12], 0.0813858553], ['partial repair probe 1', [0.15, 365, 360, 2, 2], 0.1479452055], ['partial repair probe 2', [0.08, 360, 360, 2, 2], 0.08], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 365, 365, 0, 0], 0.05], ['normal control 1', [0.0475, 360, 360, 4, 1], 0.0483528119], ['normal control 2', [0.001, 365, 365, 12, 1], 0.0010004585]], [['regression nominal from periodic 1', [0.15, 365, 360, 2, 12], 0.1435811627], ['regression nominal from periodic 2', [0.0475, 360, 360, 0, 12], 0.0475941346], ['partial repair probe 1', [0.0475, 360, 360, 2, 12], 0.0470366575], ['partial repair probe 2', [0.001, 365, 365, 4, 4], 0.001], ['boundary control 1', [0.05, 360, 365, 1, 1], 0.0506944444], ['boundary control 2', [0.05, 365, 365, 0, 0], 0.05], ['normal control 1', [0.15, 365, 365, 4, 1], 0.158650415], ['normal control 2', [0.0475, 360, 365, 0, 1], 0.0493382446]], [['regression nominal from periodic 1', [0.08, 360, 360, 2, 4], 0.0792156109], ['regression nominal from periodic 2', [0.0125, 365, 365, 2, 2], 0.0125], ['partial repair probe 1', [0.0125, 365, 360, 4, 4], 0.0123287671], ['partial repair probe 2', [0.0475, 360, 365, 1, 2], 0.0475934384], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 365, 1, 1], 0.0506944444], ['normal control 1', [0.001, 365, 360, 2, 0], 0.0009860583], ['normal control 2', [0.03, 365, 360, 2, 0], 0.0293722984]], [['regression nominal from periodic 1', [0.0475, 360, 360, 12, 12], 0.0475], ['regression nominal from periodic 2', [0.08, 365, 360, 1, 2], 0.0774061804], ['partial repair probe 1', [0.03, 360, 360, 2, 12], 0.0298142007], ['partial repair probe 2', [0.001, 365, 365, 4, 12], 0.0009999167], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 365, 1, 1], 0.0506944444], ['normal control 1', [0.0125, 360, 360, 2, 1], 0.0125390625], ['normal control 2', [0.001, 365, 365, 0, 0], 0.001]], [['regression nominal from periodic 1', [0.001, 365, 365, 2, 12], 0.0009997917], ['regression nominal from periodic 2', [0.03, 365, 360, 12, 4], 0.0296620603], ['partial repair probe 1', [0.03, 360, 360, 1, 12], 0.0295952373], ['partial repair probe 2', [0.08, 360, 360, 0, 4], 0.0808053601], ['boundary control 1', [0.05, 365, 365, 0, 0], 0.05], ['boundary control 2', [0.05, 360, 365, 1, 1], 0.0506944444], ['normal control 1', [0.03, 365, 360, 1, 1], 0.0295890411], ['normal control 2', [0.15, 365, 365, 12, 1], 0.1607545177]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\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":"A deterministic toy contract stated explicitly in the contract field; no claim of conformance to any published convention text. 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":"w2-bond_day_count_conventions-rate-basis-conversion-nominal-from-periodic","generated_at":"2026-09-29T14:46:53.844994+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Bond accrual and pricing systems depend on exact day-count arithmetic; a single-day error changes settlement cash.","repair":"Annualize the per-period rate by multiplying by m.","root_cause":"The inverse conversion omits the multiplication by m.","sha256":"f1c0c165ac4a41cc470eaa239b540fa1bdad4f01fe332816e7ca9e621bb3e7fb","title":"Rate conversion across day-count basis and compounding: the target is returned as a per-period rate · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.113,"exit_code":1,"observations":[{"actual":0.0151125,"check":"regression nominal from periodic 1","expected":0.03,"passed":false},{"actual":0.0070409491,"check":"regression nominal from periodic 2","expected":0.0813858553,"passed":false},{"actual":0.0767085757,"check":"partial repair probe 1","expected":0.1479452055,"passed":false},{"actual":0.0408,"check":"partial repair probe 2","expected":0.08,"passed":false},{"actual":0.0506944444,"check":"boundary control 1","expected":0.0506944444,"passed":true},{"actual":0.05,"check":"boundary control 2","expected":0.05,"passed":true},{"actual":0.0483528119,"check":"normal control 1","expected":0.0483528119,"passed":true},{"actual":0.0010004585,"check":"normal control 2","expected":0.0010004585,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression nominal from periodic 1\", \"actual\": 0.0151125, \"expected\": 0.03, \"passed\": false}, {\"check\": \"regression nominal from periodic 2\", \"actual\": 0.0070409491, \"expected\": 0.0813858553, \"passed\": false}, {\"check\": \"partial repair probe 1\", \"actual\": 0.0767085757, \"expected\": 0.1479452055, \"passed\": false}, {\"check\": \"partial repair probe 2\", \"actual\": 0.0408, \"expected\": 0.08, \"passed\": false}, {\"check\": \"boundary control 1\", \"actual\": 0.0506944444, \"expected\": 0.0506944444, \"passed\": true}, {\"check\": \"boundary control 2\", \"actual\": 0.05, \"expected\": 0.05, \"passed\": true}, {\"check\": \"normal control 1\", \"actual\": 0.0483528119, \"expected\": 0.0483528119, \"passed\": true}, {\"check\": \"normal control 2\", \"actual\": 0.0010004585, \"expected\": 0.0010004585, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.451,"exit_code":1,"observations":[{"actual":0.015,"check":"regression nominal from periodic 1","expected":0.03,"passed":false},{"actual":0.0067821546,"check":"regression nominal from periodic 2","expected":0.0813858553,"passed":false},{"actual":0.0739726027,"check":"partial repair probe 1","expected":0.1479452055,"passed":false},{"actual":0.04,"check":"partial repair probe 2","expected":0.08,"passed":false},{"actual":0.0506944444,"check":"boundary control 1","expected":0.0506944444,"passed":true},{"actual":0.05,"check":"boundary control 2","expected":0.05,"passed":true},{"actual":0.0483528119,"check":"normal control 1","expected":0.0483528119,"passed":true},{"actual":0.0010004585,"check":"normal control 2","expected":0.0010004585,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression nominal from periodic 1\", \"actual\": 0.015, \"expected\": 0.03, \"passed\": false}, {\"check\": \"regression nominal from periodic 2\", \"actual\": 0.0067821546, \"expected\": 0.0813858553, \"passed\": false}, {\"check\": \"partial repair probe 1\", \"actual\": 0.0739726027, \"expected\": 0.1479452055, \"passed\": false}, {\"check\": \"partial repair probe 2\", \"actual\": 0.04, \"expected\": 0.08, \"passed\": false}, {\"check\": \"boundary control 1\", \"actual\": 0.0506944444, \"expected\": 0.0506944444, \"passed\": true}, {\"check\": \"boundary control 2\", \"actual\": 0.05, \"expected\": 0.05, \"passed\": true}, {\"check\": \"normal control 1\", \"actual\": 0.0483528119, \"expected\": 0.0483528119, \"passed\": true}, {\"check\": \"normal control 2\", \"actual\": 0.0010004585, \"expected\": 0.0010004585, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.557,"exit_code":0,"observations":[{"actual":0.03,"check":"regression nominal from periodic 1","expected":0.03,"passed":true},{"actual":0.0813858553,"check":"regression nominal from periodic 2","expected":0.0813858553,"passed":true},{"actual":0.1479452055,"check":"partial repair probe 1","expected":0.1479452055,"passed":true},{"actual":0.08,"check":"partial repair probe 2","expected":0.08,"passed":true},{"actual":0.0506944444,"check":"boundary control 1","expected":0.0506944444,"passed":true},{"actual":0.05,"check":"boundary control 2","expected":0.05,"passed":true},{"actual":0.0483528119,"check":"normal control 1","expected":0.0483528119,"passed":true},{"actual":0.0010004585,"check":"normal control 2","expected":0.0010004585,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression nominal from periodic 1\", \"actual\": 0.03, \"expected\": 0.03, \"passed\": true}, {\"check\": \"regression nominal from periodic 2\", \"actual\": 0.0813858553, \"expected\": 0.0813858553, \"passed\": true}, {\"check\": \"partial repair probe 1\", \"actual\": 0.1479452055, \"expected\": 0.1479452055, \"passed\": true}, {\"check\": \"partial repair probe 2\", \"actual\": 0.08, \"expected\": 0.08, \"passed\": true}, {\"check\": \"boundary control 1\", \"actual\": 0.0506944444, \"expected\": 0.0506944444, \"passed\": true}, {\"check\": \"boundary control 2\", \"actual\": 0.05, \"expected\": 0.05, \"passed\": true}, {\"check\": \"normal control 1\", \"actual\": 0.0483528119, \"expected\": 0.0483528119, \"passed\": true}, {\"check\": \"normal control 2\", \"actual\": 0.0010004585, \"expected\": 0.0010004585, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}