FA-68431 / Toll and parking fee computation / Open access

Time-band rate with calendar day cap: band minutes are rounded down to quarters · case 01

Time-band rate with calendar day cap returns a wrong result when band minutes are rounded down to quarters.

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

ROOT CAUSE

Partial quarter hours are free.

VERIFIED REPAIR

Restore the quarter-hour ceiling rule so that the step reads `-(-m // 15) * rate`.

Unsuccessful approach: Rounding up to whole hours overcharges short stays.

Case contract

Input {bands: [[start minute of day, cents per quarter hour]] sorted with first start 0, entry, exit (absolute minutes), daily_max}. Minutes of the stay are totalled per calendar day and band; each total is rounded up to whole quarter hours and priced at its band rate. Each calendar day's charge is capped at daily_max.

Why this case matters

Fee engines bill customers in integer cents; a wrong boundary, rounding stage or cap scope silently over- or under-charges.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    bands = x['bands']
    per = {}
    t = x['entry']
    while t < x['exit']:
        day, tod = divmod(t, 1440)
        i = max(k for k in range(len(bands)) if bands[k][0] <= tod)
        nxt = bands[i + 1][0] if i + 1 < len(bands) else 1440
        step = min(x['exit'] - t, nxt - tod)
        key = (day, bands[i][1])
        per[key] = per.get(key, 0) + step
        t += step
    days = {}
    for (day, rate), m in per.items():
        days[day] = days.get(day, 0) + m // 15 * rate
    return sum(min(v, x['daily_max']) for v in days.values())
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'bands': [[0, 50], [630, 100], [1380, 100]], 'entry': 1427, 'exit': 1817, 'daily_max': 1500}, 1400), ({'bands': [[0, 50], [330, 100]], 'entry': 656, 'exit': 1034, 'daily_max': 2500}, 2500), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [300, 50]], 'entry': 1203, 'exit': 1320, 'daily_max': 4000}, 400), ({'bands': [[0, 50], [600, 50], [900, 25]], 'entry': 1880, 'exit': 4249, 'daily_max': 1500}, 3000), ({'bands': [[0, 50], [1320, 100]], 'entry': 1793, 'exit': 2565, 'daily_max': 1500}, 1500), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550)], [({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 25], [270, 50]], 'entry': 1500, 'exit': 2160, 'daily_max': 1500}, 1500), ({'bands': [[0, 50], [390, 100]], 'entry': 1045, 'exit': 1320, 'daily_max': 4000}, 1900), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [1290, 25]], 'entry': 715, 'exit': 1515, 'daily_max': 2500}, 1350), ({'bands': [[0, 25], [960, 100], [1200, 100]], 'entry': 748, 'exit': 2538, 'daily_max': 2500}, 5000), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 25], [1170, 100]], 'entry': 408, 'exit': 1419, 'daily_max': 2500}, 2500)], [({'bands': [[0, 25], [300, 100], [780, 50], [1380, 25]], 'entry': 410, 'exit': 992, 'daily_max': 2500}, 2500), ({'bands': [[0, 25], [90, 100]], 'entry': 15, 'exit': 2161, 'daily_max': 2500}, 5000), ({'bands': [[0, 50], [990, 50]], 'entry': 1775, 'exit': 1955, 'daily_max': 1500}, 600), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [480, 50], [1080, 50]], 'entry': 361, 'exit': 2927, 'daily_max': 1500}, 3200), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 50], [780, 50], [870, 25], [900, 100]], 'entry': 540, 'exit': 797, 'daily_max': 1500}, 900)], [({'bands': [[0, 50], [150, 50], [570, 50], [1320, 50]], 'entry': 615, 'exit': 735, 'daily_max': 2500}, 400), ({'bands': [[0, 25], [420, 100]], 'entry': 364, 'exit': 610, 'daily_max': 2500}, 1400), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [480, 100], [750, 50]], 'entry': 1968, 'exit': 2797, 'daily_max': 1500}, 1500), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [210, 25]], 'entry': 1069, 'exit': 3448, 'daily_max': 1500}, 3425), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [360, 100], [570, 100]], 'entry': 629, 'exit': 2400, 'daily_max': 2500}, 5000)], [({'bands': [[0, 50], [480, 25], [1200, 50], [1230, 50]], 'entry': 1584, 'exit': 3685, 'daily_max': 1500}, 3000), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [900, 50]], 'entry': 347, 'exit': 388, 'daily_max': 4000}, 150), ({'bands': [[0, 50], [60, 100], [450, 100], [1260, 25]], 'entry': 1372, 'exit': 4316, 'daily_max': 2500}, 5125), ({'bands': [[0, 50], [1170, 25]], 'entry': 1899, 'exit': 2697, 'daily_max': 1500}, 1500), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 50], [330, 50]], 'entry': 901, 'exit': 3378, 'daily_max': 1500}, 4500)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('fee oracle' + ' %d' % 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
fee oracle 0	`1250`	`1400`	Failed
fee oracle 1	`2500`	`2500`	Passed
fee oracle 2	`4000`	`4000`	Passed
fee oracle 3	`400`	`500`	Failed
fee oracle 4	`350`	`400`	Failed
fee oracle 5	`3000`	`3000`	Passed
fee oracle 6	`1500`	`1500`	Passed
fee oracle 7	`4550`	`4550`	Passed

SHA-256 / c9a41aef628d3d9ec44baa7046862c1b1ecfeae7b76c045fae9619694727650a

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    bands = x['bands']
    per = {}
    t = x['entry']
    while t < x['exit']:
        day, tod = divmod(t, 1440)
        i = max(k for k in range(len(bands)) if bands[k][0] <= tod)
        nxt = bands[i + 1][0] if i + 1 < len(bands) else 1440
        step = min(x['exit'] - t, nxt - tod)
        key = (day, bands[i][1])
        per[key] = per.get(key, 0) + step
        t += step
    days = {}
    for (day, rate), m in per.items():
        days[day] = days.get(day, 0) + -(-m // 60) * 4 * rate
    return sum(min(v, x['daily_max']) for v in days.values())
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'bands': [[0, 50], [630, 100], [1380, 100]], 'entry': 1427, 'exit': 1817, 'daily_max': 1500}, 1400), ({'bands': [[0, 50], [330, 100]], 'entry': 656, 'exit': 1034, 'daily_max': 2500}, 2500), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [300, 50]], 'entry': 1203, 'exit': 1320, 'daily_max': 4000}, 400), ({'bands': [[0, 50], [600, 50], [900, 25]], 'entry': 1880, 'exit': 4249, 'daily_max': 1500}, 3000), ({'bands': [[0, 50], [1320, 100]], 'entry': 1793, 'exit': 2565, 'daily_max': 1500}, 1500), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550)], [({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 25], [270, 50]], 'entry': 1500, 'exit': 2160, 'daily_max': 1500}, 1500), ({'bands': [[0, 50], [390, 100]], 'entry': 1045, 'exit': 1320, 'daily_max': 4000}, 1900), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [1290, 25]], 'entry': 715, 'exit': 1515, 'daily_max': 2500}, 1350), ({'bands': [[0, 25], [960, 100], [1200, 100]], 'entry': 748, 'exit': 2538, 'daily_max': 2500}, 5000), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 25], [1170, 100]], 'entry': 408, 'exit': 1419, 'daily_max': 2500}, 2500)], [({'bands': [[0, 25], [300, 100], [780, 50], [1380, 25]], 'entry': 410, 'exit': 992, 'daily_max': 2500}, 2500), ({'bands': [[0, 25], [90, 100]], 'entry': 15, 'exit': 2161, 'daily_max': 2500}, 5000), ({'bands': [[0, 50], [990, 50]], 'entry': 1775, 'exit': 1955, 'daily_max': 1500}, 600), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [480, 50], [1080, 50]], 'entry': 361, 'exit': 2927, 'daily_max': 1500}, 3200), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 50], [780, 50], [870, 25], [900, 100]], 'entry': 540, 'exit': 797, 'daily_max': 1500}, 900)], [({'bands': [[0, 50], [150, 50], [570, 50], [1320, 50]], 'entry': 615, 'exit': 735, 'daily_max': 2500}, 400), ({'bands': [[0, 25], [420, 100]], 'entry': 364, 'exit': 610, 'daily_max': 2500}, 1400), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [480, 100], [750, 50]], 'entry': 1968, 'exit': 2797, 'daily_max': 1500}, 1500), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [210, 25]], 'entry': 1069, 'exit': 3448, 'daily_max': 1500}, 3425), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [360, 100], [570, 100]], 'entry': 629, 'exit': 2400, 'daily_max': 2500}, 5000)], [({'bands': [[0, 50], [480, 25], [1200, 50], [1230, 50]], 'entry': 1584, 'exit': 3685, 'daily_max': 1500}, 3000), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [900, 50]], 'entry': 347, 'exit': 388, 'daily_max': 4000}, 150), ({'bands': [[0, 50], [60, 100], [450, 100], [1260, 25]], 'entry': 1372, 'exit': 4316, 'daily_max': 2500}, 5125), ({'bands': [[0, 50], [1170, 25]], 'entry': 1899, 'exit': 2697, 'daily_max': 1500}, 1500), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 50], [330, 50]], 'entry': 901, 'exit': 3378, 'daily_max': 1500}, 4500)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('fee oracle' + ' %d' % 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
fee oracle 0	`1800`	`1400`	Failed
fee oracle 1	`2500`	`2500`	Passed
fee oracle 2	`4000`	`4000`	Passed
fee oracle 3	`600`	`500`	Failed
fee oracle 4	`400`	`400`	Passed
fee oracle 5	`3000`	`3000`	Passed
fee oracle 6	`1500`	`1500`	Passed
fee oracle 7	`4600`	`4550`	Failed

SHA-256 / 74b976d76662df7562e96a87c1344db25d9bc9bc6b3d9db76c8cbac4986b659f

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    bands = x['bands']
    per = {}
    t = x['entry']
    while t < x['exit']:
        day, tod = divmod(t, 1440)
        i = max(k for k in range(len(bands)) if bands[k][0] <= tod)
        nxt = bands[i + 1][0] if i + 1 < len(bands) else 1440
        step = min(x['exit'] - t, nxt - tod)
        key = (day, bands[i][1])
        per[key] = per.get(key, 0) + step
        t += step
    days = {}
    for (day, rate), m in per.items():
        days[day] = days.get(day, 0) + -(-m // 15) * rate
    return sum(min(v, x['daily_max']) for v in days.values())
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'bands': [[0, 50], [630, 100], [1380, 100]], 'entry': 1427, 'exit': 1817, 'daily_max': 1500}, 1400), ({'bands': [[0, 50], [330, 100]], 'entry': 656, 'exit': 1034, 'daily_max': 2500}, 2500), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [300, 50]], 'entry': 1203, 'exit': 1320, 'daily_max': 4000}, 400), ({'bands': [[0, 50], [600, 50], [900, 25]], 'entry': 1880, 'exit': 4249, 'daily_max': 1500}, 3000), ({'bands': [[0, 50], [1320, 100]], 'entry': 1793, 'exit': 2565, 'daily_max': 1500}, 1500), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550)], [({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 25], [270, 50]], 'entry': 1500, 'exit': 2160, 'daily_max': 1500}, 1500), ({'bands': [[0, 50], [390, 100]], 'entry': 1045, 'exit': 1320, 'daily_max': 4000}, 1900), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [1290, 25]], 'entry': 715, 'exit': 1515, 'daily_max': 2500}, 1350), ({'bands': [[0, 25], [960, 100], [1200, 100]], 'entry': 748, 'exit': 2538, 'daily_max': 2500}, 5000), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 25], [1170, 100]], 'entry': 408, 'exit': 1419, 'daily_max': 2500}, 2500)], [({'bands': [[0, 25], [300, 100], [780, 50], [1380, 25]], 'entry': 410, 'exit': 992, 'daily_max': 2500}, 2500), ({'bands': [[0, 25], [90, 100]], 'entry': 15, 'exit': 2161, 'daily_max': 2500}, 5000), ({'bands': [[0, 50], [990, 50]], 'entry': 1775, 'exit': 1955, 'daily_max': 1500}, 600), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [480, 50], [1080, 50]], 'entry': 361, 'exit': 2927, 'daily_max': 1500}, 3200), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 50], [780, 50], [870, 25], [900, 100]], 'entry': 540, 'exit': 797, 'daily_max': 1500}, 900)], [({'bands': [[0, 50], [150, 50], [570, 50], [1320, 50]], 'entry': 615, 'exit': 735, 'daily_max': 2500}, 400), ({'bands': [[0, 25], [420, 100]], 'entry': 364, 'exit': 610, 'daily_max': 2500}, 1400), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [480, 100], [750, 50]], 'entry': 1968, 'exit': 2797, 'daily_max': 1500}, 1500), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [210, 25]], 'entry': 1069, 'exit': 3448, 'daily_max': 1500}, 3425), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [360, 100], [570, 100]], 'entry': 629, 'exit': 2400, 'daily_max': 2500}, 5000)], [({'bands': [[0, 50], [480, 25], [1200, 50], [1230, 50]], 'entry': 1584, 'exit': 3685, 'daily_max': 1500}, 3000), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [900, 50]], 'entry': 347, 'exit': 388, 'daily_max': 4000}, 150), ({'bands': [[0, 50], [60, 100], [450, 100], [1260, 25]], 'entry': 1372, 'exit': 4316, 'daily_max': 2500}, 5125), ({'bands': [[0, 50], [1170, 25]], 'entry': 1899, 'exit': 2697, 'daily_max': 1500}, 1500), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 50], [330, 50]], 'entry': 901, 'exit': 3378, 'daily_max': 1500}, 4500)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('fee oracle' + ' %d' % 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
fee oracle 0	`1400`	`1400`	Passed
fee oracle 1	`2500`	`2500`	Passed
fee oracle 2	`4000`	`4000`	Passed
fee oracle 3	`500`	`500`	Passed
fee oracle 4	`400`	`400`	Passed
fee oracle 5	`3000`	`3000`	Passed
fee oracle 6	`1500`	`1500`	Passed
fee oracle 7	`4550`	`4550`	Passed

SHA-256 / a9fafe8adf5464d7bdb09d1be5b160cd31841550d3dba1aed682b5d192f41814

Verification & scope

A deterministic, bounded toy model with a stipulated contract; it makes no claim of conformance to any agency manual or standard. 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 2026-09-29T14:48:02.177188+00:00.

Case digest / 94eff589b7ac3cf534d8f0c6b186ea2652a24fd7f83d7e35cc32d361e03a7e01