FA-68411 / Toll and parking fee computation / Open access

Early bird flat rate: late evening exits keep the early bird · case 01

Early bird flat rate returns a wrong result when late evening exits keep the early bird.

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

ROOT CAUSE

Without the upper exit bound a car leaving at midnight still pays the early bird rate.

VERIFIED REPAIR

Restore the exit window rule so that the step reads `900 <= xm <= 1140`.

Unsuccessful approach: Excluding exactly 15:00 moves the error to the opening of the exit window.

Case contract

Input {entry: [day, minute], exit: [day, minute], hourly, daily_max, early}; day % 7 == 0 is Monday. Regular fee = min(started hours*hourly, started 24h periods (at least 1)*daily_max). Early bird applies on weekdays when entry is 06:00-09:00 inclusive and exit is the same day 15:00-19:00 inclusive; the customer pays min(regular, early). Negative durations are 'invalid'.

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):
    ed, em = x['entry']
    xd, xm = x['exit']
    dur = (xd - ed) * 1440 + xm - em
    if dur < 0:
        return 'invalid'
    hours = -(-dur // 60)
    days = max(1, -(-dur // 1440))
    regular = min(hours * x['hourly'], days * x['daily_max'])
    eligible = ed % 7 < 5 and 360 <= em <= 540 and xd == ed and 900 <= xm
    if eligible:
        return min(regular, x['early'])
    return regular
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'entry': [2, 427], 'exit': [2, 900], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 900), ({'entry': [0, 480], 'exit': [0, 1300], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [13, 359], 'exit': [15, 1140], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 5400), ({'entry': [1, 0], 'exit': [2, 0], 'hourly': 300, 'daily_max': 1800, 'early': 1000}, 1800), ({'entry': [9, 539], 'exit': [9, 1141], 'hourly': 200, 'daily_max': 1200, 'early': 1000}, 1200), ({'entry': [1, 539], 'exit': [1, 1141], 'hourly': 200, 'daily_max': 2500, 'early': 1400}, 2200), ({'entry': [11, 540], 'exit': [11, 900], 'hourly': 300, 'daily_max': 2500, 'early': 1400}, 1400)], [({'entry': [4, 464], 'exit': [4, 900], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 900), ({'entry': [10, 540], 'exit': [10, 1141], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 200, 'daily_max': 2500, 'early': 1400}, 2500), ({'entry': [5, 400], 'exit': [5, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 360], 'exit': [3, 900], 'hourly': 400, 'daily_max': 2500, 'early': 1400}, 1400), ({'entry': [1, 360], 'exit': [1, 1140], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [11, 540], 'exit': [11, 1141], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1800), ({'entry': [2, 540], 'exit': [2, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 1000)], [({'entry': [4, 540], 'exit': [4, 1141], 'hourly': 400, 'daily_max': 1200, 'early': 1000}, 1200), ({'entry': [2, 540], 'exit': [2, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 1000), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 400, 'daily_max': 1200, 'early': 1000}, 1200), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 200, 'daily_max': 1800, 'early': 900}, 1800), ({'entry': [10, 360], 'exit': [10, 900], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [1, 0], 'exit': [2, 0], 'hourly': 300, 'daily_max': 1800, 'early': 1000}, 1800), ({'entry': [7, 360], 'exit': [7, 900], 'hourly': 300, 'daily_max': 1800, 'early': 1000}, 1000)], [({'entry': [9, 540], 'exit': [9, 900], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [5, 400], 'exit': [5, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [0, 540], 'exit': [0, 1141], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 2200), ({'entry': [2, 376], 'exit': [4, 1141], 'hourly': 300, 'daily_max': 1200, 'early': 900}, 3600), ({'entry': [0, 360], 'exit': [0, 1141], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [0, 480], 'exit': [0, 1300], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [0, 540], 'exit': [0, 900], 'hourly': 200, 'daily_max': 1800, 'early': 1000}, 1000)], [({'entry': [8, 540], 'exit': [8, 900], 'hourly': 200, 'daily_max': 2500, 'early': 1000}, 1000), ({'entry': [7, 360], 'exit': [7, 1141], 'hourly': 400, 'daily_max': 1800, 'early': 900}, 1800), ({'entry': [1, 360], 'exit': [1, 1140], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [5, 400], 'exit': [5, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 400, 'daily_max': 2500, 'early': 1400}, 2500), ({'entry': [9, 436], 'exit': [9, 900], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 900), ({'entry': [11, 540], 'exit': [11, 1141], 'hourly': 200, 'daily_max': 1800, 'early': 1000}, 1800)]]
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	`900`	`900`	Passed
fee oracle 1	`1000`	`2500`	Failed
fee oracle 2	`3600`	`3600`	Passed
fee oracle 3	`5400`	`5400`	Passed
fee oracle 4	`1800`	`1800`	Passed
fee oracle 5	`1000`	`1200`	Failed
fee oracle 6	`1400`	`2200`	Failed
fee oracle 7	`1400`	`1400`	Passed

SHA-256 / 377201e719f2e5d1c8f2cf6399d31f2c2d2f43073e8afca201ab9b26dfe800bb

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    ed, em = x['entry']
    xd, xm = x['exit']
    dur = (xd - ed) * 1440 + xm - em
    if dur < 0:
        return 'invalid'
    hours = -(-dur // 60)
    days = max(1, -(-dur // 1440))
    regular = min(hours * x['hourly'], days * x['daily_max'])
    eligible = ed % 7 < 5 and 360 <= em <= 540 and xd == ed and 900 < xm <= 1140
    if eligible:
        return min(regular, x['early'])
    return regular
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'entry': [2, 427], 'exit': [2, 900], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 900), ({'entry': [0, 480], 'exit': [0, 1300], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [13, 359], 'exit': [15, 1140], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 5400), ({'entry': [1, 0], 'exit': [2, 0], 'hourly': 300, 'daily_max': 1800, 'early': 1000}, 1800), ({'entry': [9, 539], 'exit': [9, 1141], 'hourly': 200, 'daily_max': 1200, 'early': 1000}, 1200), ({'entry': [1, 539], 'exit': [1, 1141], 'hourly': 200, 'daily_max': 2500, 'early': 1400}, 2200), ({'entry': [11, 540], 'exit': [11, 900], 'hourly': 300, 'daily_max': 2500, 'early': 1400}, 1400)], [({'entry': [4, 464], 'exit': [4, 900], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 900), ({'entry': [10, 540], 'exit': [10, 1141], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 200, 'daily_max': 2500, 'early': 1400}, 2500), ({'entry': [5, 400], 'exit': [5, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 360], 'exit': [3, 900], 'hourly': 400, 'daily_max': 2500, 'early': 1400}, 1400), ({'entry': [1, 360], 'exit': [1, 1140], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [11, 540], 'exit': [11, 1141], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1800), ({'entry': [2, 540], 'exit': [2, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 1000)], [({'entry': [4, 540], 'exit': [4, 1141], 'hourly': 400, 'daily_max': 1200, 'early': 1000}, 1200), ({'entry': [2, 540], 'exit': [2, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 1000), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 400, 'daily_max': 1200, 'early': 1000}, 1200), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 200, 'daily_max': 1800, 'early': 900}, 1800), ({'entry': [10, 360], 'exit': [10, 900], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [1, 0], 'exit': [2, 0], 'hourly': 300, 'daily_max': 1800, 'early': 1000}, 1800), ({'entry': [7, 360], 'exit': [7, 900], 'hourly': 300, 'daily_max': 1800, 'early': 1000}, 1000)], [({'entry': [9, 540], 'exit': [9, 900], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [5, 400], 'exit': [5, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [0, 540], 'exit': [0, 1141], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 2200), ({'entry': [2, 376], 'exit': [4, 1141], 'hourly': 300, 'daily_max': 1200, 'early': 900}, 3600), ({'entry': [0, 360], 'exit': [0, 1141], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [0, 480], 'exit': [0, 1300], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [0, 540], 'exit': [0, 900], 'hourly': 200, 'daily_max': 1800, 'early': 1000}, 1000)], [({'entry': [8, 540], 'exit': [8, 900], 'hourly': 200, 'daily_max': 2500, 'early': 1000}, 1000), ({'entry': [7, 360], 'exit': [7, 1141], 'hourly': 400, 'daily_max': 1800, 'early': 900}, 1800), ({'entry': [1, 360], 'exit': [1, 1140], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [5, 400], 'exit': [5, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 400, 'daily_max': 2500, 'early': 1400}, 2500), ({'entry': [9, 436], 'exit': [9, 900], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 900), ({'entry': [11, 540], 'exit': [11, 1141], 'hourly': 200, 'daily_max': 1800, 'early': 1000}, 1800)]]
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	`1600`	`900`	Failed
fee oracle 1	`2500`	`2500`	Passed
fee oracle 2	`3600`	`3600`	Passed
fee oracle 3	`5400`	`5400`	Passed
fee oracle 4	`1800`	`1800`	Passed
fee oracle 5	`1200`	`1200`	Passed
fee oracle 6	`2200`	`2200`	Passed
fee oracle 7	`1800`	`1400`	Failed

SHA-256 / b2d6d5edd4ea7603b280db6eb93f1188940ab185597dde1961d1b9a757286dc0

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    ed, em = x['entry']
    xd, xm = x['exit']
    dur = (xd - ed) * 1440 + xm - em
    if dur < 0:
        return 'invalid'
    hours = -(-dur // 60)
    days = max(1, -(-dur // 1440))
    regular = min(hours * x['hourly'], days * x['daily_max'])
    eligible = ed % 7 < 5 and 360 <= em <= 540 and xd == ed and 900 <= xm <= 1140
    if eligible:
        return min(regular, x['early'])
    return regular
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'entry': [2, 427], 'exit': [2, 900], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 900), ({'entry': [0, 480], 'exit': [0, 1300], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [13, 359], 'exit': [15, 1140], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 5400), ({'entry': [1, 0], 'exit': [2, 0], 'hourly': 300, 'daily_max': 1800, 'early': 1000}, 1800), ({'entry': [9, 539], 'exit': [9, 1141], 'hourly': 200, 'daily_max': 1200, 'early': 1000}, 1200), ({'entry': [1, 539], 'exit': [1, 1141], 'hourly': 200, 'daily_max': 2500, 'early': 1400}, 2200), ({'entry': [11, 540], 'exit': [11, 900], 'hourly': 300, 'daily_max': 2500, 'early': 1400}, 1400)], [({'entry': [4, 464], 'exit': [4, 900], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 900), ({'entry': [10, 540], 'exit': [10, 1141], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 200, 'daily_max': 2500, 'early': 1400}, 2500), ({'entry': [5, 400], 'exit': [5, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 360], 'exit': [3, 900], 'hourly': 400, 'daily_max': 2500, 'early': 1400}, 1400), ({'entry': [1, 360], 'exit': [1, 1140], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [11, 540], 'exit': [11, 1141], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1800), ({'entry': [2, 540], 'exit': [2, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 1000)], [({'entry': [4, 540], 'exit': [4, 1141], 'hourly': 400, 'daily_max': 1200, 'early': 1000}, 1200), ({'entry': [2, 540], 'exit': [2, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 1000), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 400, 'daily_max': 1200, 'early': 1000}, 1200), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 200, 'daily_max': 1800, 'early': 900}, 1800), ({'entry': [10, 360], 'exit': [10, 900], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [1, 0], 'exit': [2, 0], 'hourly': 300, 'daily_max': 1800, 'early': 1000}, 1800), ({'entry': [7, 360], 'exit': [7, 900], 'hourly': 300, 'daily_max': 1800, 'early': 1000}, 1000)], [({'entry': [9, 540], 'exit': [9, 900], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [5, 400], 'exit': [5, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [0, 540], 'exit': [0, 1141], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 2200), ({'entry': [2, 376], 'exit': [4, 1141], 'hourly': 300, 'daily_max': 1200, 'early': 900}, 3600), ({'entry': [0, 360], 'exit': [0, 1141], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [0, 480], 'exit': [0, 1300], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [0, 540], 'exit': [0, 900], 'hourly': 200, 'daily_max': 1800, 'early': 1000}, 1000)], [({'entry': [8, 540], 'exit': [8, 900], 'hourly': 200, 'daily_max': 2500, 'early': 1000}, 1000), ({'entry': [7, 360], 'exit': [7, 1141], 'hourly': 400, 'daily_max': 1800, 'early': 900}, 1800), ({'entry': [1, 360], 'exit': [1, 1140], 'hourly': 400, 'daily_max': 1800, 'early': 1000}, 1000), ({'entry': [5, 400], 'exit': [5, 1000], 'hourly': 300, 'daily_max': 2500, 'early': 1000}, 2500), ({'entry': [3, 420], 'exit': [4, 960], 'hourly': 300, 'daily_max': 1800, 'early': 900}, 3600), ({'entry': [1, 360], 'exit': [1, 1141], 'hourly': 400, 'daily_max': 2500, 'early': 1400}, 2500), ({'entry': [9, 436], 'exit': [9, 900], 'hourly': 200, 'daily_max': 2500, 'early': 900}, 900), ({'entry': [11, 540], 'exit': [11, 1141], 'hourly': 200, 'daily_max': 1800, 'early': 1000}, 1800)]]
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	`900`	`900`	Passed
fee oracle 1	`2500`	`2500`	Passed
fee oracle 2	`3600`	`3600`	Passed
fee oracle 3	`5400`	`5400`	Passed
fee oracle 4	`1800`	`1800`	Passed
fee oracle 5	`1200`	`1200`	Passed
fee oracle 6	`2200`	`2200`	Passed
fee oracle 7	`1400`	`1400`	Passed

SHA-256 / ccfc79fd340dac3314f5bddf5bfea75a1be822d0f81ac32391a971042be88de2

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 2026-09-29T14:48:01.895874+00:00.

Case digest / 77265b90ad6115a9b0245b878690e1a2a926c582d23697eba7d8a385a0994eef