FA-59701 / Subscription proration billing / Open access

Subscription schedule phases within a period: phase end from next start · case 01

Periods with a phase change are charged for both phases on the overlapping days.

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

ROOT CAUSE

Every phase is assumed to run to the period end.

VERIFIED REPAIR

Restore the contract rule at the phase end from next start step: use `en = ph[i + 1][0] if i + 1 < len(ph) else x['pe']`.

Unsuccessful approach: The attempt ends each phase a day before the next one starts, leaving a gap day uncharged.

Case contract

Input {ps, pe (exclusive), phases: [[start_day, price per full period]]}. Phases are ordered by start; each lasts until the next phase starts (the last until pe). The period charge is sum(price * overlap days with [ps, pe)) / (pe - ps), rounded half-up once. Return cents.

Why this case matters

Phase transitions inside a billing period must be charged exactly for their overlapping days.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    ph = sorted(x['phases'], key=lambda p: p[0])
    L = x['pe'] - x['ps']
    total = 0
    for i, (st, price) in enumerate(ph):
        en = x['pe']
        a, b = max(st, x['ps']), min(en, x['pe'])
        if b > a:
            total += price * (b - a)
    return (total * 2 + L) // (2 * L)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'ps': 30, 'pe': 60, 'phases': [[53, 0], [60, 2000], [12, 3500], [36, 2000]]}, 1833), ('regression', {'ps': 15, 'pe': 45, 'phases': [[45, 3500], [27, 1000], [39, 1957]]}, 791), ('partial-repair probe', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('partial-repair probe', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('normal control', {'ps': 95, 'pe': 125, 'phases': [[126, 434]]}, 0), ('normal control', {'ps': 87, 'pe': 117, 'phases': [[84, 0], [119, 2000]]}, 0), ('normal control', {'ps': 100, 'pe': 130, 'phases': [[84, 6736]]}, 6736), ('normal control', {'ps': 83, 'pe': 114, 'phases': [[82, 3500]]}, 3500)], [('regression', {'ps': 15, 'pe': 45, 'phases': [[45, 3500], [27, 1000], [39, 1957]]}, 791), ('regression', {'ps': 54, 'pe': 84, 'phases': [[70, 3500], [48, 3500], [40, 5707], [49, 0]]}, 1633), ('partial-repair probe', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('partial-repair probe', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('normal control', {'ps': 44, 'pe': 74, 'phases': [[71, 1000], [46, 0], [76, 0], [41, 0]]}, 100), ('normal control', {'ps': 42, 'pe': 72, 'phases': [[73, 0]]}, 0), ('normal control', {'ps': 24, 'pe': 54, 'phases': [[22, 1371]]}, 1371), ('normal control', {'ps': 6, 'pe': 36, 'phases': [[13, 1000]]}, 767)], [('regression', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('regression', {'ps': 54, 'pe': 84, 'phases': [[70, 3500], [48, 3500], [40, 5707], [49, 0]]}, 1633), ('partial-repair probe', {'ps': 21, 'pe': 52, 'phases': [[29, 6784], [10, 1000], [29, 5303], [34, 1000]]}, 1694), ('partial-repair probe', {'ps': 47, 'pe': 77, 'phases': [[42, 1000], [68, 2000]]}, 1300), ('normal control', {'ps': 58, 'pe': 88, 'phases': [[65, 3500]]}, 2683), ('normal control', {'ps': 42, 'pe': 72, 'phases': [[23, 0], [58, 0]]}, 0), ('normal control', {'ps': 81, 'pe': 111, 'phases': [[88, 1000]]}, 767), ('normal control', {'ps': 56, 'pe': 86, 'phases': [[60, 0]]}, 0)], [('regression', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('regression', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('partial-repair probe', {'ps': 74, 'pe': 104, 'phases': [[63, 2000], [89, 1000]]}, 1500), ('partial-repair probe', {'ps': 86, 'pe': 117, 'phases': [[94, 1000], [82, 3500]]}, 1645), ('normal control', {'ps': 86, 'pe': 117, 'phases': [[107, 2000], [119, 2395]]}, 645), ('normal control', {'ps': 51, 'pe': 82, 'phases': [[78, 2000], [64, 0]]}, 258), ('normal control', {'ps': 17, 'pe': 47, 'phases': [[18, 2000]]}, 1933), ('normal control', {'ps': 92, 'pe': 122, 'phases': [[91, 2000]]}, 2000)], [('regression', {'ps': 21, 'pe': 52, 'phases': [[29, 6784], [10, 1000], [29, 5303], [34, 1000]]}, 1694), ('regression', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('partial-repair probe', {'ps': 9, 'pe': 39, 'phases': [[1, 2000], [27, 7018], [24, 2000]]}, 4007), ('partial-repair probe', {'ps': 100, 'pe': 130, 'phases': [[130, 1000], [88, 2000], [96, 2000]]}, 2000), ('normal control', {'ps': 37, 'pe': 67, 'phases': [[69, 1125]]}, 0), ('normal control', {'ps': 29, 'pe': 60, 'phases': [[27, 1965]]}, 1965), ('normal control', {'ps': 56, 'pe': 87, 'phases': [[83, 3500]]}, 452), ('normal control', {'ps': 53, 'pe': 84, 'phases': [[50, 2000]]}, 2000)]]
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	`5100`	`1833`	Failed
regression 1	`991`	`791`	Failed
partial-repair probe 2	`2733`	`1000`	Failed
partial-repair probe 3	`5245`	`2450`	Failed
normal control 4	`0`	`0`	Passed
normal control 5	`0`	`0`	Passed
normal control 6	`6736`	`6736`	Passed
normal control 7	`3500`	`3500`	Passed

SHA-256 / e527005ae36f80870b69613fc7f75a3e194f6594c07c2bf281c1c7323ce4e8e8

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    ph = sorted(x['phases'], key=lambda p: p[0])
    L = x['pe'] - x['ps']
    total = 0
    for i, (st, price) in enumerate(ph):
        en = ph[i + 1][0] - 1 if i + 1 < len(ph) else x['pe']
        a, b = max(st, x['ps']), min(en, x['pe'])
        if b > a:
            total += price * (b - a)
    return (total * 2 + L) // (2 * L)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'ps': 30, 'pe': 60, 'phases': [[53, 0], [60, 2000], [12, 3500], [36, 2000]]}, 1833), ('regression', {'ps': 15, 'pe': 45, 'phases': [[45, 3500], [27, 1000], [39, 1957]]}, 791), ('partial-repair probe', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('partial-repair probe', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('normal control', {'ps': 95, 'pe': 125, 'phases': [[126, 434]]}, 0), ('normal control', {'ps': 87, 'pe': 117, 'phases': [[84, 0], [119, 2000]]}, 0), ('normal control', {'ps': 100, 'pe': 130, 'phases': [[84, 6736]]}, 6736), ('normal control', {'ps': 83, 'pe': 114, 'phases': [[82, 3500]]}, 3500)], [('regression', {'ps': 15, 'pe': 45, 'phases': [[45, 3500], [27, 1000], [39, 1957]]}, 791), ('regression', {'ps': 54, 'pe': 84, 'phases': [[70, 3500], [48, 3500], [40, 5707], [49, 0]]}, 1633), ('partial-repair probe', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('partial-repair probe', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('normal control', {'ps': 44, 'pe': 74, 'phases': [[71, 1000], [46, 0], [76, 0], [41, 0]]}, 100), ('normal control', {'ps': 42, 'pe': 72, 'phases': [[73, 0]]}, 0), ('normal control', {'ps': 24, 'pe': 54, 'phases': [[22, 1371]]}, 1371), ('normal control', {'ps': 6, 'pe': 36, 'phases': [[13, 1000]]}, 767)], [('regression', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('regression', {'ps': 54, 'pe': 84, 'phases': [[70, 3500], [48, 3500], [40, 5707], [49, 0]]}, 1633), ('partial-repair probe', {'ps': 21, 'pe': 52, 'phases': [[29, 6784], [10, 1000], [29, 5303], [34, 1000]]}, 1694), ('partial-repair probe', {'ps': 47, 'pe': 77, 'phases': [[42, 1000], [68, 2000]]}, 1300), ('normal control', {'ps': 58, 'pe': 88, 'phases': [[65, 3500]]}, 2683), ('normal control', {'ps': 42, 'pe': 72, 'phases': [[23, 0], [58, 0]]}, 0), ('normal control', {'ps': 81, 'pe': 111, 'phases': [[88, 1000]]}, 767), ('normal control', {'ps': 56, 'pe': 86, 'phases': [[60, 0]]}, 0)], [('regression', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('regression', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('partial-repair probe', {'ps': 74, 'pe': 104, 'phases': [[63, 2000], [89, 1000]]}, 1500), ('partial-repair probe', {'ps': 86, 'pe': 117, 'phases': [[94, 1000], [82, 3500]]}, 1645), ('normal control', {'ps': 86, 'pe': 117, 'phases': [[107, 2000], [119, 2395]]}, 645), ('normal control', {'ps': 51, 'pe': 82, 'phases': [[78, 2000], [64, 0]]}, 258), ('normal control', {'ps': 17, 'pe': 47, 'phases': [[18, 2000]]}, 1933), ('normal control', {'ps': 92, 'pe': 122, 'phases': [[91, 2000]]}, 2000)], [('regression', {'ps': 21, 'pe': 52, 'phases': [[29, 6784], [10, 1000], [29, 5303], [34, 1000]]}, 1694), ('regression', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('partial-repair probe', {'ps': 9, 'pe': 39, 'phases': [[1, 2000], [27, 7018], [24, 2000]]}, 4007), ('partial-repair probe', {'ps': 100, 'pe': 130, 'phases': [[130, 1000], [88, 2000], [96, 2000]]}, 2000), ('normal control', {'ps': 37, 'pe': 67, 'phases': [[69, 1125]]}, 0), ('normal control', {'ps': 29, 'pe': 60, 'phases': [[27, 1965]]}, 1965), ('normal control', {'ps': 56, 'pe': 87, 'phases': [[83, 3500]]}, 452), ('normal control', {'ps': 53, 'pe': 84, 'phases': [[50, 2000]]}, 2000)]]
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	`1650`	`1833`	Failed
regression 1	`693`	`791`	Failed
partial-repair probe 2	`967`	`1000`	Failed
partial-repair probe 3	`2130`	`2450`	Failed
normal control 4	`0`	`0`	Passed
normal control 5	`0`	`0`	Passed
normal control 6	`6736`	`6736`	Passed
normal control 7	`3500`	`3500`	Passed

SHA-256 / 8cd5f0bfe020b38e23c6e855d032f56ea18b80857e42c10a98afec6a4b4e43b0

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    ph = sorted(x['phases'], key=lambda p: p[0])
    L = x['pe'] - x['ps']
    total = 0
    for i, (st, price) in enumerate(ph):
        en = ph[i + 1][0] if i + 1 < len(ph) else x['pe']
        a, b = max(st, x['ps']), min(en, x['pe'])
        if b > a:
            total += price * (b - a)
    return (total * 2 + L) // (2 * L)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'ps': 30, 'pe': 60, 'phases': [[53, 0], [60, 2000], [12, 3500], [36, 2000]]}, 1833), ('regression', {'ps': 15, 'pe': 45, 'phases': [[45, 3500], [27, 1000], [39, 1957]]}, 791), ('partial-repair probe', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('partial-repair probe', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('normal control', {'ps': 95, 'pe': 125, 'phases': [[126, 434]]}, 0), ('normal control', {'ps': 87, 'pe': 117, 'phases': [[84, 0], [119, 2000]]}, 0), ('normal control', {'ps': 100, 'pe': 130, 'phases': [[84, 6736]]}, 6736), ('normal control', {'ps': 83, 'pe': 114, 'phases': [[82, 3500]]}, 3500)], [('regression', {'ps': 15, 'pe': 45, 'phases': [[45, 3500], [27, 1000], [39, 1957]]}, 791), ('regression', {'ps': 54, 'pe': 84, 'phases': [[70, 3500], [48, 3500], [40, 5707], [49, 0]]}, 1633), ('partial-repair probe', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('partial-repair probe', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('normal control', {'ps': 44, 'pe': 74, 'phases': [[71, 1000], [46, 0], [76, 0], [41, 0]]}, 100), ('normal control', {'ps': 42, 'pe': 72, 'phases': [[73, 0]]}, 0), ('normal control', {'ps': 24, 'pe': 54, 'phases': [[22, 1371]]}, 1371), ('normal control', {'ps': 6, 'pe': 36, 'phases': [[13, 1000]]}, 767)], [('regression', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('regression', {'ps': 54, 'pe': 84, 'phases': [[70, 3500], [48, 3500], [40, 5707], [49, 0]]}, 1633), ('partial-repair probe', {'ps': 21, 'pe': 52, 'phases': [[29, 6784], [10, 1000], [29, 5303], [34, 1000]]}, 1694), ('partial-repair probe', {'ps': 47, 'pe': 77, 'phases': [[42, 1000], [68, 2000]]}, 1300), ('normal control', {'ps': 58, 'pe': 88, 'phases': [[65, 3500]]}, 2683), ('normal control', {'ps': 42, 'pe': 72, 'phases': [[23, 0], [58, 0]]}, 0), ('normal control', {'ps': 81, 'pe': 111, 'phases': [[88, 1000]]}, 767), ('normal control', {'ps': 56, 'pe': 86, 'phases': [[60, 0]]}, 0)], [('regression', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('regression', {'ps': 52, 'pe': 82, 'phases': [[60, 0], [44, 1000], [60, 1000], [32, 1000]]}, 1000), ('partial-repair probe', {'ps': 74, 'pe': 104, 'phases': [[63, 2000], [89, 1000]]}, 1500), ('partial-repair probe', {'ps': 86, 'pe': 117, 'phases': [[94, 1000], [82, 3500]]}, 1645), ('normal control', {'ps': 86, 'pe': 117, 'phases': [[107, 2000], [119, 2395]]}, 645), ('normal control', {'ps': 51, 'pe': 82, 'phases': [[78, 2000], [64, 0]]}, 258), ('normal control', {'ps': 17, 'pe': 47, 'phases': [[18, 2000]]}, 1933), ('normal control', {'ps': 92, 'pe': 122, 'phases': [[91, 2000]]}, 2000)], [('regression', {'ps': 21, 'pe': 52, 'phases': [[29, 6784], [10, 1000], [29, 5303], [34, 1000]]}, 1694), ('regression', {'ps': 25, 'pe': 55, 'phases': [[40, 6111], [52, 7893], [43, 3500]]}, 2450), ('partial-repair probe', {'ps': 9, 'pe': 39, 'phases': [[1, 2000], [27, 7018], [24, 2000]]}, 4007), ('partial-repair probe', {'ps': 100, 'pe': 130, 'phases': [[130, 1000], [88, 2000], [96, 2000]]}, 2000), ('normal control', {'ps': 37, 'pe': 67, 'phases': [[69, 1125]]}, 0), ('normal control', {'ps': 29, 'pe': 60, 'phases': [[27, 1965]]}, 1965), ('normal control', {'ps': 56, 'pe': 87, 'phases': [[83, 3500]]}, 452), ('normal control', {'ps': 53, 'pe': 84, 'phases': [[50, 2000]]}, 2000)]]
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	`1833`	`1833`	Passed
regression 1	`791`	`791`	Passed
partial-repair probe 2	`1000`	`1000`	Passed
partial-repair probe 3	`2450`	`2450`	Passed
normal control 4	`0`	`0`	Passed
normal control 5	`0`	`0`	Passed
normal control 6	`6736`	`6736`	Passed
normal control 7	`3500`	`3500`	Passed

SHA-256 / 92e3253f6ebfb7f96d057a83a92f07921fca18ea05ceffadc4419e4529f0708e

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 2026-09-29T14:46:38.823253+00:00.

Case digest / 0d13a7388d5c5b4c14b3165820c0b935fe194a947b0f019da2ae2de7b18d1e94