FA-85426 / Ride-hailing fare and surge pricing / Open access

Partial wait minutes not billed · case 01

A rider who kept the driver 61 seconds past grace pays for one minute instead of two.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Billable seconds are floor-divided into minutes.

VERIFIED REPAIR

Bill every started minute (ceiling).

Unsuccessful approach: Rounding to the nearest minute still drops short partial minutes.

Case contract

Wait time starts at driver arrival, or at the scheduled pickup time if the ride was scheduled and the driver arrived early. The first grace seconds are free; beyond that each started minute is billed at per_min cents, up to cap_min billed minutes. Return the wait fee in cents.

Why this case matters

Ride-hailing prices are computed per trip at scale; ordering, unit and boundary slips become systematic over- or under-charging.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(ev, policy):
    start = ev['arrive'] if ev['scheduled'] is None else max(ev['arrive'], ev['scheduled'])
    wait = ev['board'] - start
    if wait <= policy['grace']:
        return 0
    minutes = (wait - policy['grace']) // 60
    return min(minutes, policy['cap_min']) * policy['per_min']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   80),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10421, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 25),
  ('second regression',
   [{'arrive': 10000, 'board': 10401, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   200),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10120, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 0),
  ('normal control 2',
   [{'arrive': 10000, 'board': 10900, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 3',
   [{'arrive': 10000, 'board': 11020, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10060, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}], 0)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10241, 'scheduled': 10120}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 25),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10421, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 40}], 40),
  ('second regression',
   [{'arrive': 10000, 'board': 10121, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 35),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10420, 'scheduled': 10300}, {'cap_min': 10, 'grace': 120, 'per_min': 40}], 0),
  ('normal control 2',
   [{'arrive': 10000, 'board': 11178, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10060, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 0),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10600, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   320)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   80),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 70),
  ('second regression',
   [{'arrive': 10000, 'board': 10121, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 25}], 25),
  ('normal control 1',
   [{'arrive': 10000, 'board': 11020, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 2',
   [{'arrive': 10000, 'board': 10300, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 0),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10900, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   400),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10900, 'scheduled': 9940}, {'cap_min': 5, 'grace': 120, 'per_min': 35}],
   175)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10421, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 40}], 40),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10181, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 40}], 80),
  ('second regression',
   [{'arrive': 10000, 'board': 10642, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   360),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10300, 'scheduled': 10300}, {'cap_min': 10, 'grace': 120, 'per_min': 25}], 0),
  ('normal control 2',
   [{'arrive': 10000, 'board': 10872, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 175),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10060, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 0),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10120, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 35}], 0)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 70),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10181, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 70),
  ('second regression',
   [{'arrive': 10000, 'board': 10121, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 35}], 35),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10900, 'scheduled': 9940}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 175),
  ('normal control 2',
   [{'arrive': 10000, 'board': 11162, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10180, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 25),
  ('normal control 4',
   [{'arrive': 10000, 'board': 11200, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 35}],
   175)]]
for label, args, expected in fixtures[N-1]:
    check(label, 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: started minute billing	`40`	`80`	Failed
partial repair probe: started minute billing	`0`	`25`	Failed
second regression	`160`	`200`	Failed
normal control 1	`0`	`0`	Passed
normal control 2	`250`	`250`	Passed
normal control 3	`250`	`250`	Passed
normal control 4	`0`	`0`	Passed

SHA-256 / 9c6b5940f65cffa0ae6e6db8c493fdbef4d0831750d8efebe7e937596a5fd0cc

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(ev, policy):
    start = ev['arrive'] if ev['scheduled'] is None else max(ev['arrive'], ev['scheduled'])
    wait = ev['board'] - start
    if wait <= policy['grace']:
        return 0
    minutes = round((wait - policy['grace']) / 60)
    return min(minutes, policy['cap_min']) * policy['per_min']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   80),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10421, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 25),
  ('second regression',
   [{'arrive': 10000, 'board': 10401, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   200),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10120, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 0),
  ('normal control 2',
   [{'arrive': 10000, 'board': 10900, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 3',
   [{'arrive': 10000, 'board': 11020, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10060, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}], 0)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10241, 'scheduled': 10120}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 25),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10421, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 40}], 40),
  ('second regression',
   [{'arrive': 10000, 'board': 10121, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 35),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10420, 'scheduled': 10300}, {'cap_min': 10, 'grace': 120, 'per_min': 40}], 0),
  ('normal control 2',
   [{'arrive': 10000, 'board': 11178, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10060, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 0),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10600, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   320)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   80),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 70),
  ('second regression',
   [{'arrive': 10000, 'board': 10121, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 25}], 25),
  ('normal control 1',
   [{'arrive': 10000, 'board': 11020, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 2',
   [{'arrive': 10000, 'board': 10300, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 0),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10900, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   400),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10900, 'scheduled': 9940}, {'cap_min': 5, 'grace': 120, 'per_min': 35}],
   175)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10421, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 40}], 40),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10181, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 40}], 80),
  ('second regression',
   [{'arrive': 10000, 'board': 10642, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   360),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10300, 'scheduled': 10300}, {'cap_min': 10, 'grace': 120, 'per_min': 25}], 0),
  ('normal control 2',
   [{'arrive': 10000, 'board': 10872, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 175),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10060, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 0),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10120, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 35}], 0)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 70),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10181, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 70),
  ('second regression',
   [{'arrive': 10000, 'board': 10121, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 35}], 35),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10900, 'scheduled': 9940}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 175),
  ('normal control 2',
   [{'arrive': 10000, 'board': 11162, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10180, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 25),
  ('normal control 4',
   [{'arrive': 10000, 'board': 11200, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 35}],
   175)]]
for label, args, expected in fixtures[N-1]:
    check(label, 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: started minute billing	`40`	`80`	Failed
partial repair probe: started minute billing	`0`	`25`	Failed
second regression	`200`	`200`	Passed
normal control 1	`0`	`0`	Passed
normal control 2	`250`	`250`	Passed
normal control 3	`250`	`250`	Passed
normal control 4	`0`	`0`	Passed

SHA-256 / de64f9a6f1c7f08b5304f387d0810a52439a28646af200037c5eec779ebdee2d

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(ev, policy):
    start = ev['arrive'] if ev['scheduled'] is None else max(ev['arrive'], ev['scheduled'])
    wait = ev['board'] - start
    if wait <= policy['grace']:
        return 0
    minutes = -(-(wait - policy['grace']) // 60)
    return min(minutes, policy['cap_min']) * policy['per_min']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   80),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10421, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 25),
  ('second regression',
   [{'arrive': 10000, 'board': 10401, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   200),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10120, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 0),
  ('normal control 2',
   [{'arrive': 10000, 'board': 10900, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 3',
   [{'arrive': 10000, 'board': 11020, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10060, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}], 0)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10241, 'scheduled': 10120}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 25),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10421, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 40}], 40),
  ('second regression',
   [{'arrive': 10000, 'board': 10121, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 35),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10420, 'scheduled': 10300}, {'cap_min': 10, 'grace': 120, 'per_min': 40}], 0),
  ('normal control 2',
   [{'arrive': 10000, 'board': 11178, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10060, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 0),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10600, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   320)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   80),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 70),
  ('second regression',
   [{'arrive': 10000, 'board': 10121, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 25}], 25),
  ('normal control 1',
   [{'arrive': 10000, 'board': 11020, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 2',
   [{'arrive': 10000, 'board': 10300, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 0),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10900, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   400),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10900, 'scheduled': 9940}, {'cap_min': 5, 'grace': 120, 'per_min': 35}],
   175)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10421, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 40}], 40),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10181, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 40}], 80),
  ('second regression',
   [{'arrive': 10000, 'board': 10642, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 40}],
   360),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10300, 'scheduled': 10300}, {'cap_min': 10, 'grace': 120, 'per_min': 25}], 0),
  ('normal control 2',
   [{'arrive': 10000, 'board': 10872, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 175),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10060, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 0),
  ('normal control 4',
   [{'arrive': 10000, 'board': 10120, 'scheduled': None}, {'cap_min': 10, 'grace': 120, 'per_min': 35}], 0)],
 [('regression: started minute billing',
   [{'arrive': 10000, 'board': 10301, 'scheduled': 10120}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 70),
  ('partial repair probe: started minute billing',
   [{'arrive': 10000, 'board': 10181, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 70),
  ('second regression',
   [{'arrive': 10000, 'board': 10121, 'scheduled': 9940}, {'cap_min': 10, 'grace': 120, 'per_min': 35}], 35),
  ('normal control 1',
   [{'arrive': 10000, 'board': 10900, 'scheduled': 9940}, {'cap_min': 5, 'grace': 120, 'per_min': 35}], 175),
  ('normal control 2',
   [{'arrive': 10000, 'board': 11162, 'scheduled': 10120}, {'cap_min': 10, 'grace': 120, 'per_min': 25}],
   250),
  ('normal control 3',
   [{'arrive': 10000, 'board': 10180, 'scheduled': None}, {'cap_min': 5, 'grace': 120, 'per_min': 25}], 25),
  ('normal control 4',
   [{'arrive': 10000, 'board': 11200, 'scheduled': 10300}, {'cap_min': 5, 'grace': 120, 'per_min': 35}],
   175)]]
for label, args, expected in fixtures[N-1]:
    check(label, 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: started minute billing	`80`	`80`	Passed
partial repair probe: started minute billing	`25`	`25`	Passed
second regression	`200`	`200`	Passed
normal control 1	`0`	`0`	Passed
normal control 2	`250`	`250`	Passed
normal control 3	`250`	`250`	Passed
normal control 4	`0`	`0`	Passed

SHA-256 / dd8dd409caf799bc1b49f0af2b6f6cbbbf8ceb0847e4355578526e6338c7eb42

Verification & scope

A deterministic toy pricing contract stipulated for this example; it does not reproduce the pricing of any real ride-hailing operator or regulator. 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 2026-09-29T14:50:40.272105+00:00.

Case digest / 4ceb104013f949899c0fbd6645277df8ae1b8e330e51d1a2c2c5b8b1ad9bc27c