FA-59006 / Payroll withholding rules / Open access

Overtime regular rate with bonuses and differentials: premium cent rounding · case 01

Overtime premiums ending in a half cent or more are a cent short.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The premium is truncated toward zero rather than rounded half-up.

THE FAILURE

The premium is truncated toward zero rather than rounded half-up.

Unsuccessful approach: The attempt uses round(), which rounds exact half cents to even, so half of the tie cases are still short.

Case 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].

Why this case matters

Nondiscretionary bonuses and shift differentials raise the regular rate, and only a half-time premium is owed on top of straight-time pay.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    h = x['hours']
    base = h * x['rate'] + x['diff_hours'] * x['diff']
    included = base + (0 if x['discretionary'] else x['bonus'])
    if h == 0:
        return [0, x['bonus']]
    ot = max(0, h - 40)
    rr = Fraction(included, h)
    premium = rr * ot / 2
    prem_c = int(premium)
    total = base + x['bonus'] + prem_c
    return [prem_c, total]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'hours': 58, 'rate': 1280, 'bonus': 145, 'discretionary': False, 'diff_hours': 5, 'diff': 0}, [11543, 85928]), ('regression', {'hours': 48, 'rate': 2361, 'bonus': 0, 'discretionary': False, 'diff_hours': 15, 'diff': 150}, [9632, 125210]), ('partial-repair probe', {'hours': 55, 'rate': 3779, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [28343, 236188]), ('partial-repair probe', {'hours': 50, 'rate': 3473, 'bonus': 15335, 'discretionary': False, 'diff_hours': 14, 'diff': 0}, [18899, 207884]), ('normal control', {'hours': 56, 'rate': 2894, 'bonus': 0, 'discretionary': True, 'diff_hours': 20, 'diff': 189}, [23692, 189536]), ('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': 42, 'rate': 2619, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [2619, 112617])], [('regression', {'hours': 55, 'rate': 3779, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [28343, 236188]), ('regression', {'hours': 45, 'rate': 1070, 'bonus': 6593, 'discretionary': True, 'diff_hours': 3, 'diff': 100}, [2692, 57735]), ('partial-repair probe', {'hours': 50, 'rate': 3473, 'bonus': 15335, 'discretionary': False, 'diff_hours': 14, 'diff': 0}, [18899, 207884]), ('partial-repair probe', {'hours': 49, 'rate': 2297, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [10337, 122890]), ('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]), ('normal control', {'hours': 38, 'rate': 3803, 'bonus': 0, 'discretionary': False, 'diff_hours': 5, 'diff': 175}, [0, 145389]), ('normal control', {'hours': 42, 'rate': 1092, 'bonus': 0, 'discretionary': False, 'diff_hours': 2, 'diff': 157}, [1099, 47277])], [('regression', {'hours': 50, 'rate': 3473, 'bonus': 15335, 'discretionary': False, 'diff_hours': 14, 'diff': 0}, [18899, 207884]), ('regression', {'hours': 60, 'rate': 3726, 'bonus': 328, 'discretionary': False, 'diff_hours': 13, 'diff': 0}, [37315, 261203]), ('partial-repair probe', {'hours': 59, 'rate': 1183, 'bonus': 15895, 'discretionary': True, 'diff_hours': 0, 'diff': 111}, [11239, 96931]), ('partial-repair probe', {'hours': 45, 'rate': 3152, 'bonus': 297, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [7897, 150034]), ('normal control', {'hours': 40, 'rate': 2368, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 0}, [0, 94720]), ('normal control', {'hours': 41, 'rate': 1070, 'bonus': 0, 'discretionary': False, 'diff_hours': 14, 'diff': 300}, [586, 48656]), ('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': 49, 'rate': 2297, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [10337, 122890]), ('regression', {'hours': 51, 'rate': 1430, 'bonus': 583, 'discretionary': True, 'diff_hours': 17, 'diff': 212}, [8254, 85371]), ('partial-repair probe', {'hours': 49, 'rate': 1393, 'bonus': 1015, 'discretionary': True, 'diff_hours': 13, 'diff': 0}, [6269, 75541]), ('partial-repair probe', {'hours': 41, 'rate': 3985, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 218}, [1993, 165378]), ('normal control', {'hours': 25, 'rate': 2784, 'bonus': 431, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [0, 70031]), ('normal control', {'hours': 49, 'rate': 2740, 'bonus': 1615, 'discretionary': True, 'diff_hours': 20, 'diff': 0}, [12330, 148205]), ('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])], [('regression', {'hours': 59, 'rate': 1183, 'bonus': 15895, 'discretionary': True, 'diff_hours': 0, 'diff': 111}, [11239, 96931]), ('regression', {'hours': 41, 'rate': 1051, 'bonus': 26, 'discretionary': False, 'diff_hours': 0, 'diff': 259}, [526, 43643]), ('partial-repair probe', {'hours': 41, 'rate': 1613, 'bonus': 28839, 'discretionary': True, 'diff_hours': 0, 'diff': 100}, [807, 95779]), ('partial-repair probe', {'hours': 59, 'rate': 3943, 'bonus': 3183, 'discretionary': True, 'diff_hours': 0, 'diff': 50}, [37459, 273279]), ('normal control', {'hours': 51, 'rate': 3958, 'bonus': 443, 'discretionary': True, 'diff_hours': 0, 'diff': 100}, [21769, 224070]), ('normal control', {'hours': 36, 'rate': 3363, 'bonus': 0, 'discretionary': True, 'diff_hours': 0, 'diff': 0}, [0, 121068]), ('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])]]
for i, (label, args, expected) in enumerate(fixtures[N-1]):
    check("%s %d" % (label, i), solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression 0	`[11542, 85927]`	`[11543, 85928]`	Failed
regression 1	`[9631, 125209]`	`[9632, 125210]`	Failed
partial-repair probe 2	`[28342, 236187]`	`[28343, 236188]`	Failed
partial-repair probe 3	`[18898, 207883]`	`[18899, 207884]`	Failed
normal control 4	`[23692, 189536]`	`[23692, 189536]`	Passed
normal control 5	`[0, 111325]`	`[0, 111325]`	Passed
normal control 6	`[0, 28995]`	`[0, 28995]`	Passed
normal control 7	`[2619, 112617]`	`[2619, 112617]`	Passed

SHA-256 / 082294bb524a93462cc4c54e8aa4965c730c57365d7f453ba2478d351dc4fe21

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    h = x['hours']
    base = h * x['rate'] + x['diff_hours'] * x['diff']
    included = base + (0 if x['discretionary'] else x['bonus'])
    if h == 0:
        return [0, x['bonus']]
    ot = max(0, h - 40)
    rr = Fraction(included, h)
    premium = rr * ot / 2
    prem_c = round(premium)
    total = base + x['bonus'] + prem_c
    return [prem_c, total]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'hours': 58, 'rate': 1280, 'bonus': 145, 'discretionary': False, 'diff_hours': 5, 'diff': 0}, [11543, 85928]), ('regression', {'hours': 48, 'rate': 2361, 'bonus': 0, 'discretionary': False, 'diff_hours': 15, 'diff': 150}, [9632, 125210]), ('partial-repair probe', {'hours': 55, 'rate': 3779, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [28343, 236188]), ('partial-repair probe', {'hours': 50, 'rate': 3473, 'bonus': 15335, 'discretionary': False, 'diff_hours': 14, 'diff': 0}, [18899, 207884]), ('normal control', {'hours': 56, 'rate': 2894, 'bonus': 0, 'discretionary': True, 'diff_hours': 20, 'diff': 189}, [23692, 189536]), ('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': 42, 'rate': 2619, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [2619, 112617])], [('regression', {'hours': 55, 'rate': 3779, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [28343, 236188]), ('regression', {'hours': 45, 'rate': 1070, 'bonus': 6593, 'discretionary': True, 'diff_hours': 3, 'diff': 100}, [2692, 57735]), ('partial-repair probe', {'hours': 50, 'rate': 3473, 'bonus': 15335, 'discretionary': False, 'diff_hours': 14, 'diff': 0}, [18899, 207884]), ('partial-repair probe', {'hours': 49, 'rate': 2297, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [10337, 122890]), ('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]), ('normal control', {'hours': 38, 'rate': 3803, 'bonus': 0, 'discretionary': False, 'diff_hours': 5, 'diff': 175}, [0, 145389]), ('normal control', {'hours': 42, 'rate': 1092, 'bonus': 0, 'discretionary': False, 'diff_hours': 2, 'diff': 157}, [1099, 47277])], [('regression', {'hours': 50, 'rate': 3473, 'bonus': 15335, 'discretionary': False, 'diff_hours': 14, 'diff': 0}, [18899, 207884]), ('regression', {'hours': 60, 'rate': 3726, 'bonus': 328, 'discretionary': False, 'diff_hours': 13, 'diff': 0}, [37315, 261203]), ('partial-repair probe', {'hours': 59, 'rate': 1183, 'bonus': 15895, 'discretionary': True, 'diff_hours': 0, 'diff': 111}, [11239, 96931]), ('partial-repair probe', {'hours': 45, 'rate': 3152, 'bonus': 297, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [7897, 150034]), ('normal control', {'hours': 40, 'rate': 2368, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 0}, [0, 94720]), ('normal control', {'hours': 41, 'rate': 1070, 'bonus': 0, 'discretionary': False, 'diff_hours': 14, 'diff': 300}, [586, 48656]), ('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': 49, 'rate': 2297, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [10337, 122890]), ('regression', {'hours': 51, 'rate': 1430, 'bonus': 583, 'discretionary': True, 'diff_hours': 17, 'diff': 212}, [8254, 85371]), ('partial-repair probe', {'hours': 49, 'rate': 1393, 'bonus': 1015, 'discretionary': True, 'diff_hours': 13, 'diff': 0}, [6269, 75541]), ('partial-repair probe', {'hours': 41, 'rate': 3985, 'bonus': 0, 'discretionary': False, 'diff_hours': 0, 'diff': 218}, [1993, 165378]), ('normal control', {'hours': 25, 'rate': 2784, 'bonus': 431, 'discretionary': False, 'diff_hours': 0, 'diff': 150}, [0, 70031]), ('normal control', {'hours': 49, 'rate': 2740, 'bonus': 1615, 'discretionary': True, 'diff_hours': 20, 'diff': 0}, [12330, 148205]), ('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])], [('regression', {'hours': 59, 'rate': 1183, 'bonus': 15895, 'discretionary': True, 'diff_hours': 0, 'diff': 111}, [11239, 96931]), ('regression', {'hours': 41, 'rate': 1051, 'bonus': 26, 'discretionary': False, 'diff_hours': 0, 'diff': 259}, [526, 43643]), ('partial-repair probe', {'hours': 41, 'rate': 1613, 'bonus': 28839, 'discretionary': True, 'diff_hours': 0, 'diff': 100}, [807, 95779]), ('partial-repair probe', {'hours': 59, 'rate': 3943, 'bonus': 3183, 'discretionary': True, 'diff_hours': 0, 'diff': 50}, [37459, 273279]), ('normal control', {'hours': 51, 'rate': 3958, 'bonus': 443, 'discretionary': True, 'diff_hours': 0, 'diff': 100}, [21769, 224070]), ('normal control', {'hours': 36, 'rate': 3363, 'bonus': 0, 'discretionary': True, 'diff_hours': 0, 'diff': 0}, [0, 121068]), ('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])]]
for i, (label, args, expected) in enumerate(fixtures[N-1]):
    check("%s %d" % (label, i), solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression 0	`[11542, 85927]`	`[11543, 85928]`	Failed
regression 1	`[9632, 125210]`	`[9632, 125210]`	Passed
partial-repair probe 2	`[28342, 236187]`	`[28343, 236188]`	Failed
partial-repair probe 3	`[18898, 207883]`	`[18899, 207884]`	Failed
normal control 4	`[23692, 189536]`	`[23692, 189536]`	Passed
normal control 5	`[0, 111325]`	`[0, 111325]`	Passed
normal control 6	`[0, 28995]`	`[0, 28995]`	Passed
normal control 7	`[2619, 112617]`	`[2619, 112617]`	Passed

SHA-256 / 6ca2712a93337ed2938117878eaca092f4b9d94ead7a67bf9e3abec529d5d6b7

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:46:32.112003+00:00.

Case digest / b836248ad479174e1867a4b701e81e60d79138ec985b9f2716c42f8f5b9f87de