FAILURE MAP
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FA-59531 / Subscription proration billing / Open access

Sales tax on proration credit and debit lines: per-line tax rounding · case 01

Invoice tax differs by a cent from the sum of the per-line tax amounts shown.

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

ROOT CAUSE

Tax is rounded once on the invoice total instead of per line.

VERIFIED REPAIR

Restore the contract rule at the per-line tax rounding step: use `tax = sum(hr(n) for n in parts)`.

Unsuccessful approach: The attempt computes per line but floors, rounding negative lines away and positive lines down.

Case contract

Input {lines: [[signed cents, taxable]], rate_bp}. Tax is computed per taxable line, including negative credit lines (negative tax), each rounded half away from zero, then summed. Subtotal is the sum of all lines. Return [subtotal, tax, subtotal + tax].

Why this case matters

Credit lines on a prorated invoice must reverse the tax charged on the original period.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    parts = []
    for amt, taxable in x['lines']:
        if taxable:
            parts.append(amt * x['rate_bp'])
    def hr(n):
        t = (abs(n) * 2 + 10000) // 20000
        return t if n >= 0 else -t
    tax = hr(sum(parts))
    sub = sum(a for a, t in x['lines'])
    return [sub, tax, sub + tax]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'lines': [[27, True], [-11860, True], [-39505, True], [21922, True]], 'rate_bp': 825}, [-29416, -2426, -31842]), ('regression', {'lines': [[-17245, True], [79270, True], [25, True], [-36068, True]], 'rate_bp': 720}, [25982, 1870, 27852]), ('partial-repair probe', {'lines': [[-30768, True], [88008, True], [58540, True], [-18089, False]], 'rate_bp': 50}, [97691, 579, 98270]), ('partial-repair probe', {'lines': [[53, True], [-19388, True], [67, True]], 'rate_bp': 2000}, [-19268, -3854, -23122]), ('normal control', {'lines': [[-51735, False]], 'rate_bp': 2267}, [-51735, 0, -51735]), ('normal control', {'lines': [[-42950, False], [83094, False], [74700, False], [-33526, False]], 'rate_bp': 725}, [81318, 0, 81318]), ('normal control', {'lines': [[1785, False]], 'rate_bp': 1510}, [1785, 0, 1785]), ('normal control', {'lines': [[11, True], [30948, False]], 'rate_bp': 1000}, [30959, 1, 30960])], [('regression', {'lines': [[-17245, True], [79270, True], [25, True], [-36068, True]], 'rate_bp': 720}, [25982, 1870, 27852]), ('regression', {'lines': [[49804, True], [5609, True], [29, True], [-28832, True]], 'rate_bp': 725}, [26610, 1930, 28540]), ('partial-repair probe', {'lines': [[27, True], [-11860, True], [-39505, True], [21922, True]], 'rate_bp': 825}, [-29416, -2426, -31842]), ('partial-repair probe', {'lines': [[74, True], [-48741, True], [16317, True], [-6432, True]], 'rate_bp': 1000}, [-38782, -3878, -42660]), ('normal control', {'lines': [[-25891, False]], 'rate_bp': 50}, [-25891, 0, -25891]), ('normal control', {'lines': [[20, False]], 'rate_bp': 50}, [20, 0, 20]), ('normal control', {'lines': [[13, True]], 'rate_bp': 825}, [13, 1, 14]), ('normal control', {'lines': [[49780, False], [72791, False]], 'rate_bp': 725}, [122571, 0, 122571])], [('regression', {'lines': [[49804, True], [5609, True], [29, True], [-28832, True]], 'rate_bp': 725}, [26610, 1930, 28540]), ('regression', {'lines': [[52, True], [19, False], [14472, True], [91, False]], 'rate_bp': 297}, [14634, 432, 15066]), ('partial-repair probe', {'lines': [[74, True], [-48741, True], [16317, True], [-6432, True]], 'rate_bp': 1000}, [-38782, -3878, -42660]), ('partial-repair probe', {'lines': [[70, True]], 'rate_bp': 825}, [70, 6, 76]), ('normal control', {'lines': [[91, False]], 'rate_bp': 12}, [91, 0, 91]), ('normal control', {'lines': [[25, True]], 'rate_bp': 825}, [25, 2, 27]), ('normal control', {'lines': [[19129, False]], 'rate_bp': 725}, [19129, 0, 19129]), ('normal control', {'lines': [[84, False]], 'rate_bp': 1355}, [84, 0, 84])], [('regression', {'lines': [[52, True], [19, False], [14472, True], [91, False]], 'rate_bp': 297}, [14634, 432, 15066]), ('regression', {'lines': [[-46622, True], [77, True], [83716, False], [46, True], [37, True]], 'rate_bp': 1000}, [37254, -4645, 32609]), ('partial-repair probe', {'lines': [[-7052, True]], 'rate_bp': 2000}, [-7052, -1410, -8462]), ('partial-repair probe', {'lines': [[-12837, True], [-41474, True], [88408, True], [-5186, False]], 'rate_bp': 1738}, [28911, 5926, 34837]), ('normal control', {'lines': [[35, True]], 'rate_bp': 50}, [35, 0, 35]), ('normal control', {'lines': [[-17532, True]], 'rate_bp': 50}, [-17532, -88, -17620]), ('normal control', {'lines': [[95, True]], 'rate_bp': 2000}, [95, 19, 114]), ('normal control', {'lines': [[1, False]], 'rate_bp': 50}, [1, 0, 1])], [('regression', {'lines': [[-46622, True], [77, True], [83716, False], [46, True], [37, True]], 'rate_bp': 1000}, [37254, -4645, 32609]), ('regression', {'lines': [[74, True], [81059, True], [70668, True]], 'rate_bp': 825}, [151801, 12523, 164324]), ('partial-repair probe', {'lines': [[30278, True], [-25624, False], [18105, True]], 'rate_bp': 50}, [22759, 242, 23001]), ('partial-repair probe', {'lines': [[73474, True], [48, False], [70693, False], [-3471, True]], 'rate_bp': 725}, [140744, 5075, 145819]), ('normal control', {'lines': [[80389, True]], 'rate_bp': 725}, [80389, 5828, 86217]), ('normal control', {'lines': [[19, False], [1, True], [-36175, False], [25, True]], 'rate_bp': 2000}, [-36130, 5, -36125]), ('normal control', {'lines': [[-28065, False], [42, False]], 'rate_bp': 725}, [-28023, 0, -28023]), ('normal control', {'lines': [[6941, True], [925, False]], 'rate_bp': 725}, [7866, 503, 8369])]]
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 fixtureActualExpectedOutcome
regression 0[-29416, -2427, -31843][-29416, -2426, -31842]Failed
regression 1[25982, 1871, 27853][25982, 1870, 27852]Failed
partial-repair probe 2[97691, 579, 98270][97691, 579, 98270]Passed
partial-repair probe 3[-19268, -3854, -23122][-19268, -3854, -23122]Passed
normal control 4[-51735, 0, -51735][-51735, 0, -51735]Passed
normal control 5[81318, 0, 81318][81318, 0, 81318]Passed
normal control 6[1785, 0, 1785][1785, 0, 1785]Passed
normal control 7[30959, 1, 30960][30959, 1, 30960]Passed

SHA-256 / 4fc6a3398e7952e3adcfd05c1843e951a1dc5f5a28a23a00f79b646572856cbe

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    parts = []
    for amt, taxable in x['lines']:
        if taxable:
            parts.append(amt * x['rate_bp'])
    def hr(n):
        t = (abs(n) * 2 + 10000) // 20000
        return t if n >= 0 else -t
    tax = sum(n // 10000 for n in parts)
    sub = sum(a for a, t in x['lines'])
    return [sub, tax, sub + tax]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'lines': [[27, True], [-11860, True], [-39505, True], [21922, True]], 'rate_bp': 825}, [-29416, -2426, -31842]), ('regression', {'lines': [[-17245, True], [79270, True], [25, True], [-36068, True]], 'rate_bp': 720}, [25982, 1870, 27852]), ('partial-repair probe', {'lines': [[-30768, True], [88008, True], [58540, True], [-18089, False]], 'rate_bp': 50}, [97691, 579, 98270]), ('partial-repair probe', {'lines': [[53, True], [-19388, True], [67, True]], 'rate_bp': 2000}, [-19268, -3854, -23122]), ('normal control', {'lines': [[-51735, False]], 'rate_bp': 2267}, [-51735, 0, -51735]), ('normal control', {'lines': [[-42950, False], [83094, False], [74700, False], [-33526, False]], 'rate_bp': 725}, [81318, 0, 81318]), ('normal control', {'lines': [[1785, False]], 'rate_bp': 1510}, [1785, 0, 1785]), ('normal control', {'lines': [[11, True], [30948, False]], 'rate_bp': 1000}, [30959, 1, 30960])], [('regression', {'lines': [[-17245, True], [79270, True], [25, True], [-36068, True]], 'rate_bp': 720}, [25982, 1870, 27852]), ('regression', {'lines': [[49804, True], [5609, True], [29, True], [-28832, True]], 'rate_bp': 725}, [26610, 1930, 28540]), ('partial-repair probe', {'lines': [[27, True], [-11860, True], [-39505, True], [21922, True]], 'rate_bp': 825}, [-29416, -2426, -31842]), ('partial-repair probe', {'lines': [[74, True], [-48741, True], [16317, True], [-6432, True]], 'rate_bp': 1000}, [-38782, -3878, -42660]), ('normal control', {'lines': [[-25891, False]], 'rate_bp': 50}, [-25891, 0, -25891]), ('normal control', {'lines': [[20, False]], 'rate_bp': 50}, [20, 0, 20]), ('normal control', {'lines': [[13, True]], 'rate_bp': 825}, [13, 1, 14]), ('normal control', {'lines': [[49780, False], [72791, False]], 'rate_bp': 725}, [122571, 0, 122571])], [('regression', {'lines': [[49804, True], [5609, True], [29, True], [-28832, True]], 'rate_bp': 725}, [26610, 1930, 28540]), ('regression', {'lines': [[52, True], [19, False], [14472, True], [91, False]], 'rate_bp': 297}, [14634, 432, 15066]), ('partial-repair probe', {'lines': [[74, True], [-48741, True], [16317, True], [-6432, True]], 'rate_bp': 1000}, [-38782, -3878, -42660]), ('partial-repair probe', {'lines': [[70, True]], 'rate_bp': 825}, [70, 6, 76]), ('normal control', {'lines': [[91, False]], 'rate_bp': 12}, [91, 0, 91]), ('normal control', {'lines': [[25, True]], 'rate_bp': 825}, [25, 2, 27]), ('normal control', {'lines': [[19129, False]], 'rate_bp': 725}, [19129, 0, 19129]), ('normal control', {'lines': [[84, False]], 'rate_bp': 1355}, [84, 0, 84])], [('regression', {'lines': [[52, True], [19, False], [14472, True], [91, False]], 'rate_bp': 297}, [14634, 432, 15066]), ('regression', {'lines': [[-46622, True], [77, True], [83716, False], [46, True], [37, True]], 'rate_bp': 1000}, [37254, -4645, 32609]), ('partial-repair probe', {'lines': [[-7052, True]], 'rate_bp': 2000}, [-7052, -1410, -8462]), ('partial-repair probe', {'lines': [[-12837, True], [-41474, True], [88408, True], [-5186, False]], 'rate_bp': 1738}, [28911, 5926, 34837]), ('normal control', {'lines': [[35, True]], 'rate_bp': 50}, [35, 0, 35]), ('normal control', {'lines': [[-17532, True]], 'rate_bp': 50}, [-17532, -88, -17620]), ('normal control', {'lines': [[95, True]], 'rate_bp': 2000}, [95, 19, 114]), ('normal control', {'lines': [[1, False]], 'rate_bp': 50}, [1, 0, 1])], [('regression', {'lines': [[-46622, True], [77, True], [83716, False], [46, True], [37, True]], 'rate_bp': 1000}, [37254, -4645, 32609]), ('regression', {'lines': [[74, True], [81059, True], [70668, True]], 'rate_bp': 825}, [151801, 12523, 164324]), ('partial-repair probe', {'lines': [[30278, True], [-25624, False], [18105, True]], 'rate_bp': 50}, [22759, 242, 23001]), ('partial-repair probe', {'lines': [[73474, True], [48, False], [70693, False], [-3471, True]], 'rate_bp': 725}, [140744, 5075, 145819]), ('normal control', {'lines': [[80389, True]], 'rate_bp': 725}, [80389, 5828, 86217]), ('normal control', {'lines': [[19, False], [1, True], [-36175, False], [25, True]], 'rate_bp': 2000}, [-36130, 5, -36125]), ('normal control', {'lines': [[-28065, False], [42, False]], 'rate_bp': 725}, [-28023, 0, -28023]), ('normal control', {'lines': [[6941, True], [925, False]], 'rate_bp': 725}, [7866, 503, 8369])]]
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 fixtureActualExpectedOutcome
regression 0[-29416, -2429, -31845][-29416, -2426, -31842]Failed
regression 1[25982, 1869, 27851][25982, 1870, 27852]Failed
partial-repair probe 2[97691, 578, 98269][97691, 579, 98270]Failed
partial-repair probe 3[-19268, -3855, -23123][-19268, -3854, -23122]Failed
normal control 4[-51735, 0, -51735][-51735, 0, -51735]Passed
normal control 5[81318, 0, 81318][81318, 0, 81318]Passed
normal control 6[1785, 0, 1785][1785, 0, 1785]Passed
normal control 7[30959, 1, 30960][30959, 1, 30960]Passed

SHA-256 / 1f4078638176354e2b1cf09a4e3080d2392a1893770e2db1e393695187017b61

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    parts = []
    for amt, taxable in x['lines']:
        if taxable:
            parts.append(amt * x['rate_bp'])
    def hr(n):
        t = (abs(n) * 2 + 10000) // 20000
        return t if n >= 0 else -t
    tax = sum(hr(n) for n in parts)
    sub = sum(a for a, t in x['lines'])
    return [sub, tax, sub + tax]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'lines': [[27, True], [-11860, True], [-39505, True], [21922, True]], 'rate_bp': 825}, [-29416, -2426, -31842]), ('regression', {'lines': [[-17245, True], [79270, True], [25, True], [-36068, True]], 'rate_bp': 720}, [25982, 1870, 27852]), ('partial-repair probe', {'lines': [[-30768, True], [88008, True], [58540, True], [-18089, False]], 'rate_bp': 50}, [97691, 579, 98270]), ('partial-repair probe', {'lines': [[53, True], [-19388, True], [67, True]], 'rate_bp': 2000}, [-19268, -3854, -23122]), ('normal control', {'lines': [[-51735, False]], 'rate_bp': 2267}, [-51735, 0, -51735]), ('normal control', {'lines': [[-42950, False], [83094, False], [74700, False], [-33526, False]], 'rate_bp': 725}, [81318, 0, 81318]), ('normal control', {'lines': [[1785, False]], 'rate_bp': 1510}, [1785, 0, 1785]), ('normal control', {'lines': [[11, True], [30948, False]], 'rate_bp': 1000}, [30959, 1, 30960])], [('regression', {'lines': [[-17245, True], [79270, True], [25, True], [-36068, True]], 'rate_bp': 720}, [25982, 1870, 27852]), ('regression', {'lines': [[49804, True], [5609, True], [29, True], [-28832, True]], 'rate_bp': 725}, [26610, 1930, 28540]), ('partial-repair probe', {'lines': [[27, True], [-11860, True], [-39505, True], [21922, True]], 'rate_bp': 825}, [-29416, -2426, -31842]), ('partial-repair probe', {'lines': [[74, True], [-48741, True], [16317, True], [-6432, True]], 'rate_bp': 1000}, [-38782, -3878, -42660]), ('normal control', {'lines': [[-25891, False]], 'rate_bp': 50}, [-25891, 0, -25891]), ('normal control', {'lines': [[20, False]], 'rate_bp': 50}, [20, 0, 20]), ('normal control', {'lines': [[13, True]], 'rate_bp': 825}, [13, 1, 14]), ('normal control', {'lines': [[49780, False], [72791, False]], 'rate_bp': 725}, [122571, 0, 122571])], [('regression', {'lines': [[49804, True], [5609, True], [29, True], [-28832, True]], 'rate_bp': 725}, [26610, 1930, 28540]), ('regression', {'lines': [[52, True], [19, False], [14472, True], [91, False]], 'rate_bp': 297}, [14634, 432, 15066]), ('partial-repair probe', {'lines': [[74, True], [-48741, True], [16317, True], [-6432, True]], 'rate_bp': 1000}, [-38782, -3878, -42660]), ('partial-repair probe', {'lines': [[70, True]], 'rate_bp': 825}, [70, 6, 76]), ('normal control', {'lines': [[91, False]], 'rate_bp': 12}, [91, 0, 91]), ('normal control', {'lines': [[25, True]], 'rate_bp': 825}, [25, 2, 27]), ('normal control', {'lines': [[19129, False]], 'rate_bp': 725}, [19129, 0, 19129]), ('normal control', {'lines': [[84, False]], 'rate_bp': 1355}, [84, 0, 84])], [('regression', {'lines': [[52, True], [19, False], [14472, True], [91, False]], 'rate_bp': 297}, [14634, 432, 15066]), ('regression', {'lines': [[-46622, True], [77, True], [83716, False], [46, True], [37, True]], 'rate_bp': 1000}, [37254, -4645, 32609]), ('partial-repair probe', {'lines': [[-7052, True]], 'rate_bp': 2000}, [-7052, -1410, -8462]), ('partial-repair probe', {'lines': [[-12837, True], [-41474, True], [88408, True], [-5186, False]], 'rate_bp': 1738}, [28911, 5926, 34837]), ('normal control', {'lines': [[35, True]], 'rate_bp': 50}, [35, 0, 35]), ('normal control', {'lines': [[-17532, True]], 'rate_bp': 50}, [-17532, -88, -17620]), ('normal control', {'lines': [[95, True]], 'rate_bp': 2000}, [95, 19, 114]), ('normal control', {'lines': [[1, False]], 'rate_bp': 50}, [1, 0, 1])], [('regression', {'lines': [[-46622, True], [77, True], [83716, False], [46, True], [37, True]], 'rate_bp': 1000}, [37254, -4645, 32609]), ('regression', {'lines': [[74, True], [81059, True], [70668, True]], 'rate_bp': 825}, [151801, 12523, 164324]), ('partial-repair probe', {'lines': [[30278, True], [-25624, False], [18105, True]], 'rate_bp': 50}, [22759, 242, 23001]), ('partial-repair probe', {'lines': [[73474, True], [48, False], [70693, False], [-3471, True]], 'rate_bp': 725}, [140744, 5075, 145819]), ('normal control', {'lines': [[80389, True]], 'rate_bp': 725}, [80389, 5828, 86217]), ('normal control', {'lines': [[19, False], [1, True], [-36175, False], [25, True]], 'rate_bp': 2000}, [-36130, 5, -36125]), ('normal control', {'lines': [[-28065, False], [42, False]], 'rate_bp': 725}, [-28023, 0, -28023]), ('normal control', {'lines': [[6941, True], [925, False]], 'rate_bp': 725}, [7866, 503, 8369])]]
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 fixtureActualExpectedOutcome
regression 0[-29416, -2426, -31842][-29416, -2426, -31842]Passed
regression 1[25982, 1870, 27852][25982, 1870, 27852]Passed
partial-repair probe 2[97691, 579, 98270][97691, 579, 98270]Passed
partial-repair probe 3[-19268, -3854, -23122][-19268, -3854, -23122]Passed
normal control 4[-51735, 0, -51735][-51735, 0, -51735]Passed
normal control 5[81318, 0, 81318][81318, 0, 81318]Passed
normal control 6[1785, 0, 1785][1785, 0, 1785]Passed
normal control 7[30959, 1, 30960][30959, 1, 30960]Passed

SHA-256 / 2a55d82133ecbb0006fe031fea737a507f8671602b970f1afbb63b765a0863ab

Verification & scope

A deterministic teaching model of a stipulated billing rule. It makes no claim to reproduce any billing provider's exact behaviour and is not billing 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 2026-09-29T14:46:37.209771+00:00.

Case digest / 8efd2aa69a409312b56862c54717d3afbe268228ff7f4eda47296cbd344bf31a