{"abstract":"Employees working long weeks receive an inflated overtime premium.","category":"Payroll withholding rules","checks":8,"contract":"Input weekly {hours, rate, bonus, discretionary, diff_hours, diff}. Straight pay = hours*rate + diff_hours*diff. Regular rate = (straight pay + bonus unless discretionary) / hours. Overtime premium = regular rate * max(0, hours-40) / 2, rounded half-up to the cent. Total = straight pay + bonus + premium. Zero hours returns [0, bonus]. Return [premium, total].","contract_signature":"x","evaluation_group":"w2-payroll-withholding-overtime-regular-rate","failed_approach":"The attempt divides by hours plus overtime hours, understating the regular rate.","family":"w2-payroll-withholding-overtime-regular-rate-regular-rate-divisor","id":"FA-58996","implementations":{"attempt":{"sha256":"0c0460869c7534f9ff0d098dcd180e6aefd5940827f37c2543b7ea7efcde0798","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    h = x['hours']\n    base = h * x['rate'] + x['diff_hours'] * x['diff']\n    included = base + (0 if x['discretionary'] else x['bonus'])\n    if h == 0:\n        return [0, x['bonus']]\n    ot = max(0, h - 40)\n    rr = Fraction(included, h + ot)\n    premium = rr * ot / 2\n    prem_c = math.floor(premium + Fraction(1, 2))\n    total = base + x['bonus'] + prem_c\n    return [prem_c, total]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression', {'hours': 56, 'rate': 2894, 'bonus': 0, 'discretionary': True, 'diff_hours': 20, 'diff': 189}, [23692, 189536]), ('regression', {'hours': 48, 'rate': 2361, 'bonus': 0, 'discretionary': False, 'diff_hours': 15, 'diff': 150}, [9632, 125210]), ('partial-repair probe', {'hours': 45, 'rate': 1070, 'bonus': 6593, 'discretionary': True, 'diff_hours': 3, 'diff': 100}, [2692, 57735]), ('partial-repair probe', {'hours': 60, 'rate': 3726, 'bonus': 328, 'discretionary': False, 'diff_hours': 13, 'diff': 0}, [37315, 261203]), ('normal control', {'hours': 29, 'rate': 3185, 'bonus': 18960, 'discretionary': True, 'diff_hours': 0, 'diff': 235}, [0, 111325]), ('normal control', {'hours': 15, 'rate': 1913, 'bonus': 0, 'discretionary': False, 'diff_hours': 3, 'diff': 100}, [0, 28995]), ('normal control', {'hours': 36, 'rate': 1564, 'bonus': 12440, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [0, 68744]), ('normal control', {'hours': 36, 'rate': 3124, 'bonus': 20788, 'discretionary': False, 'diff_hours': 0, 'diff': 0}, [0, 133252])], [('regression', {'hours': 48, 'rate': 2361, 'bonus': 0, 'discretionary': False, 'diff_hours': 15, 'diff': 150}, [9632, 125210]), ('regression', {'hours': 45, 'rate': 1070, 'bonus': 6593, 'discretionary': True, 'diff_hours': 3, 'diff': 100}, [2692, 57735]), ('partial-repair probe', {'hours': 60, 'rate': 3726, 'bonus': 328, 'discretionary': False, 'diff_hours': 13, 'diff': 0}, [37315, 261203]), ('partial-repair probe', {'hours': 51, 'rate': 1430, 'bonus': 583, 'discretionary': True, 'diff_hours': 17, 'diff': 212}, [8254, 85371]), ('normal control', {'hours': 38, 'rate': 3803, 'bonus': 0, 'discretionary': False, 'diff_hours': 5, 'diff': 175}, [0, 145389]), ('normal control', {'hours': 40, 'rate': 2368, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 0}, [0, 94720]), ('normal control', {'hours': 15, 'rate': 1275, 'bonus': 16297, 'discretionary': False, 'diff_hours': 0, 'diff': 100}, [0, 35422]), ('normal control', {'hours': 0, 'rate': 1235, 'bonus': 452, 'discretionary': False, 'diff_hours': 15, 'diff': 0}, [0, 452])], [('regression', {'hours': 45, 'rate': 1070, 'bonus': 6593, 'discretionary': True, 'diff_hours': 3, 'diff': 100}, [2692, 57735]), ('regression', {'hours': 60, 'rate': 3726, 'bonus': 328, 'discretionary': False, 'diff_hours': 13, 'diff': 0}, [37315, 261203]), ('partial-repair probe', {'hours': 51, 'rate': 1430, 'bonus': 583, 'discretionary': True, 'diff_hours': 17, 'diff': 212}, [8254, 85371]), ('partial-repair probe', {'hours': 42, 'rate': 2619, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [2619, 112617]), ('normal control', {'hours': 25, 'rate': 2784, 'bonus': 431, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [0, 70031]), ('normal control', {'hours': 4, 'rate': 2630, 'bonus': 24821, 'discretionary': False, 'diff_hours': 10, 'diff': 100}, [0, 36341]), ('normal control', {'hours': 36, 'rate': 3824, 'bonus': 0, 'discretionary': False, 'diff_hours': 12, 'diff': 100}, [0, 138864]), ('normal control', {'hours': 36, 'rate': 3363, 'bonus': 0, 'discretionary': True, 'diff_hours': 0, 'diff': 0}, [0, 121068])], [('regression', {'hours': 60, 'rate': 3726, 'bonus': 328, 'discretionary': False, 'diff_hours': 13, 'diff': 0}, [37315, 261203]), ('regression', {'hours': 51, 'rate': 1430, 'bonus': 583, 'discretionary': True, 'diff_hours': 17, 'diff': 212}, [8254, 85371]), ('partial-repair probe', {'hours': 42, 'rate': 1092, 'bonus': 0, 'discretionary': False, 'diff_hours': 2, 'diff': 157}, [1099, 47277]), ('partial-repair probe', {'hours': 41, 'rate': 1051, 'bonus': 26, 'discretionary': False, 'diff_hours': 0, 'diff': 259}, [526, 43643]), ('normal control', {'hours': 25, 'rate': 1555, 'bonus': 17670, 'discretionary': True, 'diff_hours': 0, 'diff': 150}, [0, 56545]), ('normal control', {'hours': 13, 'rate': 3420, 'bonus': 0, 'discretionary': True, 'diff_hours': 0, 'diff': 150}, [0, 44460]), ('normal control', {'hours': 17, 'rate': 3366, 'bonus': 396, 'discretionary': True, 'diff_hours': 8, 'diff': 0}, [0, 57618]), ('normal control', {'hours': 1, 'rate': 1458, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 0}, [0, 1458])], [('regression', {'hours': 51, 'rate': 1430, 'bonus': 583, 'discretionary': True, 'diff_hours': 17, 'diff': 212}, [8254, 85371]), ('regression', {'hours': 42, 'rate': 2619, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [2619, 112617]), ('partial-repair probe', {'hours': 41, 'rate': 1070, 'bonus': 0, 'discretionary': False, 'diff_hours': 14, 'diff': 300}, [586, 48656]), ('partial-repair probe', {'hours': 49, 'rate': 2740, 'bonus': 1615, 'discretionary': True, 'diff_hours': 20, 'diff': 0}, [12330, 148205]), ('normal control', {'hours': 40, 'rate': 2719, 'bonus': 0, 'discretionary': False, 'diff_hours': 13, 'diff': 100}, [0, 110060]), ('normal control', {'hours': 32, 'rate': 3242, 'bonus': 990, 'discretionary': True, 'diff_hours': 0, 'diff': 48}, [0, 104734]), ('normal control', {'hours': 23, 'rate': 2339, 'bonus': 720, 'discretionary': False, 'diff_hours': 0, 'diff': 0}, [0, 54517]), ('normal control', {'hours': 22, 'rate': 2030, 'bonus': 44512, 'discretionary': False, 'diff_hours': 13, 'diff': 183}, [0, 91551])]]\nfor i, (label, args, expected) in enumerate(fixtures[N-1]):\n    check(\"%s %d\" % (label, i), 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":"319e68e7975f301b7e48455236bc66ca7387957dba9da10ce31c045b0c285f43","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    h = x['hours']\n    base = h * x['rate'] + x['diff_hours'] * x['diff']\n    included = base + (0 if x['discretionary'] else x['bonus'])\n    if h == 0:\n        return [0, x['bonus']]\n    ot = max(0, h - 40)\n    rr = Fraction(included, 40)\n    premium = rr * ot / 2\n    prem_c = math.floor(premium + Fraction(1, 2))\n    total = base + x['bonus'] + prem_c\n    return [prem_c, total]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression', {'hours': 56, 'rate': 2894, 'bonus': 0, 'discretionary': True, 'diff_hours': 20, 'diff': 189}, [23692, 189536]), ('regression', {'hours': 48, 'rate': 2361, 'bonus': 0, 'discretionary': False, 'diff_hours': 15, 'diff': 150}, [9632, 125210]), ('partial-repair probe', {'hours': 45, 'rate': 1070, 'bonus': 6593, 'discretionary': True, 'diff_hours': 3, 'diff': 100}, [2692, 57735]), ('partial-repair probe', {'hours': 60, 'rate': 3726, 'bonus': 328, 'discretionary': False, 'diff_hours': 13, 'diff': 0}, [37315, 261203]), ('normal control', {'hours': 29, 'rate': 3185, 'bonus': 18960, 'discretionary': True, 'diff_hours': 0, 'diff': 235}, [0, 111325]), ('normal control', {'hours': 15, 'rate': 1913, 'bonus': 0, 'discretionary': False, 'diff_hours': 3, 'diff': 100}, [0, 28995]), ('normal control', {'hours': 36, 'rate': 1564, 'bonus': 12440, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [0, 68744]), ('normal control', {'hours': 36, 'rate': 3124, 'bonus': 20788, 'discretionary': False, 'diff_hours': 0, 'diff': 0}, [0, 133252])], [('regression', {'hours': 48, 'rate': 2361, 'bonus': 0, 'discretionary': False, 'diff_hours': 15, 'diff': 150}, [9632, 125210]), ('regression', {'hours': 45, 'rate': 1070, 'bonus': 6593, 'discretionary': True, 'diff_hours': 3, 'diff': 100}, [2692, 57735]), ('partial-repair probe', {'hours': 60, 'rate': 3726, 'bonus': 328, 'discretionary': False, 'diff_hours': 13, 'diff': 0}, [37315, 261203]), ('partial-repair probe', {'hours': 51, 'rate': 1430, 'bonus': 583, 'discretionary': True, 'diff_hours': 17, 'diff': 212}, [8254, 85371]), ('normal control', {'hours': 38, 'rate': 3803, 'bonus': 0, 'discretionary': False, 'diff_hours': 5, 'diff': 175}, [0, 145389]), ('normal control', {'hours': 40, 'rate': 2368, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 0}, [0, 94720]), ('normal control', {'hours': 15, 'rate': 1275, 'bonus': 16297, 'discretionary': False, 'diff_hours': 0, 'diff': 100}, [0, 35422]), ('normal control', {'hours': 0, 'rate': 1235, 'bonus': 452, 'discretionary': False, 'diff_hours': 15, 'diff': 0}, [0, 452])], [('regression', {'hours': 45, 'rate': 1070, 'bonus': 6593, 'discretionary': True, 'diff_hours': 3, 'diff': 100}, [2692, 57735]), ('regression', {'hours': 60, 'rate': 3726, 'bonus': 328, 'discretionary': False, 'diff_hours': 13, 'diff': 0}, [37315, 261203]), ('partial-repair probe', {'hours': 51, 'rate': 1430, 'bonus': 583, 'discretionary': True, 'diff_hours': 17, 'diff': 212}, [8254, 85371]), ('partial-repair probe', {'hours': 42, 'rate': 2619, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [2619, 112617]), ('normal control', {'hours': 25, 'rate': 2784, 'bonus': 431, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [0, 70031]), ('normal control', {'hours': 4, 'rate': 2630, 'bonus': 24821, 'discretionary': False, 'diff_hours': 10, 'diff': 100}, [0, 36341]), ('normal control', {'hours': 36, 'rate': 3824, 'bonus': 0, 'discretionary': False, 'diff_hours': 12, 'diff': 100}, [0, 138864]), ('normal control', {'hours': 36, 'rate': 3363, 'bonus': 0, 'discretionary': True, 'diff_hours': 0, 'diff': 0}, [0, 121068])], [('regression', {'hours': 60, 'rate': 3726, 'bonus': 328, 'discretionary': False, 'diff_hours': 13, 'diff': 0}, [37315, 261203]), ('regression', {'hours': 51, 'rate': 1430, 'bonus': 583, 'discretionary': True, 'diff_hours': 17, 'diff': 212}, [8254, 85371]), ('partial-repair probe', {'hours': 42, 'rate': 1092, 'bonus': 0, 'discretionary': False, 'diff_hours': 2, 'diff': 157}, [1099, 47277]), ('partial-repair probe', {'hours': 41, 'rate': 1051, 'bonus': 26, 'discretionary': False, 'diff_hours': 0, 'diff': 259}, [526, 43643]), ('normal control', {'hours': 25, 'rate': 1555, 'bonus': 17670, 'discretionary': True, 'diff_hours': 0, 'diff': 150}, [0, 56545]), ('normal control', {'hours': 13, 'rate': 3420, 'bonus': 0, 'discretionary': True, 'diff_hours': 0, 'diff': 150}, [0, 44460]), ('normal control', {'hours': 17, 'rate': 3366, 'bonus': 396, 'discretionary': True, 'diff_hours': 8, 'diff': 0}, [0, 57618]), ('normal control', {'hours': 1, 'rate': 1458, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 0}, [0, 1458])], [('regression', {'hours': 51, 'rate': 1430, 'bonus': 583, 'discretionary': True, 'diff_hours': 17, 'diff': 212}, [8254, 85371]), ('regression', {'hours': 42, 'rate': 2619, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [2619, 112617]), ('partial-repair probe', {'hours': 41, 'rate': 1070, 'bonus': 0, 'discretionary': False, 'diff_hours': 14, 'diff': 300}, [586, 48656]), ('partial-repair probe', {'hours': 49, 'rate': 2740, 'bonus': 1615, 'discretionary': True, 'diff_hours': 20, 'diff': 0}, [12330, 148205]), ('normal control', {'hours': 40, 'rate': 2719, 'bonus': 0, 'discretionary': False, 'diff_hours': 13, 'diff': 100}, [0, 110060]), ('normal control', {'hours': 32, 'rate': 3242, 'bonus': 990, 'discretionary': True, 'diff_hours': 0, 'diff': 48}, [0, 104734]), ('normal control', {'hours': 23, 'rate': 2339, 'bonus': 720, 'discretionary': False, 'diff_hours': 0, 'diff': 0}, [0, 54517]), ('normal control', {'hours': 22, 'rate': 2030, 'bonus': 44512, 'discretionary': False, 'diff_hours': 13, 'diff': 183}, [0, 91551])]]\nfor i, (label, args, expected) in enumerate(fixtures[N-1]):\n    check(\"%s %d\" % (label, i), 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 teaching model of a stipulated payroll rule with toy thresholds and rates. It makes no claim of conformance to any tax authority, statute or jurisdiction and is not payroll software. 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-payroll-withholding-overtime-regular-rate-regular-rate-divisor","generated_at":"2026-09-29T14:46:32.079870+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Nondiscretionary bonuses and shift differentials raise the regular rate, and only a half-time premium is owed on top of straight-time pay.","root_cause":"The regular rate divides total straight-time compensation by 40 instead of by all hours worked.","sha256":"280f2d0e5a0afd67fab5f7e27eeeb2796e4915e3a3058cebad6312701a1d7863","title":"Overtime regular rate with bonuses and differentials: regular rate divisor · 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":43.261,"exit_code":1,"observations":[{"actual":[18427,184271],"check":"regression 0","expected":[23692,189536],"passed":false},{"actual":[8256,123834],"check":"regression 1","expected":[9632,125210],"passed":false},{"actual":[2423,57466],"check":"partial-repair probe 2","expected":[2692,57735],"passed":false},{"actual":[27986,251874],"check":"partial-repair probe 3","expected":[37315,261203],"passed":false},{"actual":[0,111325],"check":"normal control 4","expected":[0,111325],"passed":true},{"actual":[0,28995],"check":"normal control 5","expected":[0,28995],"passed":true},{"actual":[0,68744],"check":"normal control 6","expected":[0,68744],"passed":true},{"actual":[0,133252],"check":"normal control 7","expected":[0,133252],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 0\", \"actual\": [18427, 184271], \"expected\": [23692, 189536], \"passed\": false}, {\"check\": \"regression 1\", \"actual\": [8256, 123834], \"expected\": [9632, 125210], \"passed\": false}, {\"check\": \"partial-repair probe 2\", \"actual\": [2423, 57466], \"expected\": [2692, 57735], \"passed\": false}, {\"check\": \"partial-repair probe 3\", \"actual\": [27986, 251874], \"expected\": [37315, 261203], \"passed\": false}, {\"check\": \"normal control 4\", \"actual\": [0, 111325], \"expected\": [0, 111325], \"passed\": true}, {\"check\": \"normal control 5\", \"actual\": [0, 28995], \"expected\": [0, 28995], \"passed\": true}, {\"check\": \"normal control 6\", \"actual\": [0, 68744], \"expected\": [0, 68744], \"passed\": true}, {\"check\": \"normal control 7\", \"actual\": [0, 133252], \"expected\": [0, 133252], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.756,"exit_code":1,"observations":[{"actual":[33169,199013],"check":"regression 0","expected":[23692,189536],"passed":false},{"actual":[11558,127136],"check":"regression 1","expected":[9632,125210],"passed":false},{"actual":[3028,58071],"check":"partial-repair probe 2","expected":[2692,57735],"passed":false},{"actual":[55972,279860],"check":"partial-repair probe 3","expected":[37315,261203],"passed":false},{"actual":[0,111325],"check":"normal control 4","expected":[0,111325],"passed":true},{"actual":[0,28995],"check":"normal control 5","expected":[0,28995],"passed":true},{"actual":[0,68744],"check":"normal control 6","expected":[0,68744],"passed":true},{"actual":[0,133252],"check":"normal control 7","expected":[0,133252],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 0\", \"actual\": [33169, 199013], \"expected\": [23692, 189536], \"passed\": false}, {\"check\": \"regression 1\", \"actual\": [11558, 127136], \"expected\": [9632, 125210], \"passed\": false}, {\"check\": \"partial-repair probe 2\", \"actual\": [3028, 58071], \"expected\": [2692, 57735], \"passed\": false}, {\"check\": \"partial-repair probe 3\", \"actual\": [55972, 279860], \"expected\": [37315, 261203], \"passed\": false}, {\"check\": \"normal control 4\", \"actual\": [0, 111325], \"expected\": [0, 111325], \"passed\": true}, {\"check\": \"normal control 5\", \"actual\": [0, 28995], \"expected\": [0, 28995], \"passed\": true}, {\"check\": \"normal control 6\", \"actual\": [0, 68744], \"expected\": [0, 68744], \"passed\": true}, {\"check\": \"normal control 7\", \"actual\": [0, 133252], \"expected\": [0, 133252], \"passed\": true}], \"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."}}