broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    sp=x['standard']
    if x['max']<x['min']: return 'invalid bounds'
    lim=max(0,sum(min(c,x['loss_limit']) for c in x['claims']))
    basic=Fraction(sp*x['basic'],1000)
    retro=(basic+Fraction(lim*x['lcf'],1000))*Fraction(x['tax'],1000)
    lo=Fraction(sp*x['min'],1000); hi=Fraction(sp*x['max'],1000)
    retro=min(hi,retro)
    return [lim, math.floor(retro+Fraction(1,2))]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['moderate losses between bounds', {'standard': 1208187, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [65251, 117766, 199866, 72604]}, [455487, 827175]], ['large claim limited', {'standard': 1536795, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [7899385, 85219]}, [5085219, 4610385]], ['maximum binds', {'standard': 576969, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3887820, 3676391, 3519603, 3011895]}, [14095709, 692363]], ['no losses minimum binds', {'standard': 783317, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 391659]], ['subrogation recovery offsets', {'standard': 1402360, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [299401, -71949]}, [227452, 581085]], ['net recovery floors at zero', {'standard': 1970882, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13900]}, [0, 591265]], ['inverted bounds rejected', {'standard': 857821, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1032758, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 929482]], ['near-minimum losses', {'standard': 1037917, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [196003]}, [196003, 509523]]], [['moderate losses between bounds', {'standard': 559811, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [168808, 170340, 188681, 153930]}, [681759, 951695]], ['large claim limited', {'standard': 1398667, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [8563900, 72244]}, [5072244, 4196001]], ['maximum binds', {'standard': 1860838, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3974702, 2021857, 3323996, 2741110]}, [12061665, 2233006]], ['no losses minimum binds', {'standard': 1054836, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 527418]], ['subrogation recovery offsets', {'standard': 572933, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215865, -67794]}, [148071, 322920]], ['net recovery floors at zero', {'standard': 1415569, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-23951]}, [0, 424671]], ['inverted bounds rejected', {'standard': 1885857, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1658903, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 1493013]], ['near-minimum losses', {'standard': 1831216, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [255597]}, [255597, 824047]]], [['moderate losses between bounds', {'standard': 1953166, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [130486, 146045, 106267, 80838]}, [463636, 970005]], ['large claim limited', {'standard': 1375996, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [8850428, 26063]}, [5026063, 4127988]], ['maximum binds', {'standard': 1822101, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3010425, 2467545, 2177771, 3447891]}, [11103632, 2186521]], ['no losses minimum binds', {'standard': 1516833, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 758417]], ['subrogation recovery offsets', {'standard': 714829, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [292326, -101272]}, [191054, 370781]], ['net recovery floors at zero', {'standard': 1501098, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-22616]}, [0, 450329]], ['inverted bounds rejected', {'standard': 696781, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802028, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721825]], ['near-minimum losses', {'standard': 715359, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [161153]}, [161153, 346549]]], [['moderate losses between bounds', {'standard': 714988, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [147807, 50783, 101639, 147624]}, [447853, 714442]], ['large claim limited', {'standard': 1075364, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [6621396, 51697]}, [5051697, 3226092]], ['maximum binds', {'standard': 636493, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3206066, 2811387, 2370852, 2596520]}, [10984825, 763792]], ['no losses minimum binds', {'standard': 1974481, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1600, 'loss_limit': 5000000, 'claims': []}, [0, 987241]], ['subrogation recovery offsets', {'standard': 1092045, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [210597, -95806]}, [114791, 366843]], ['net recovery floors at zero', {'standard': 1088467, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13789]}, [0, 326540]], ['inverted bounds rejected', {'standard': 1508678, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 811592, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 730433]], ['near-minimum losses', {'standard': 1513685, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [237641]}, [237641, 681158]]], [['moderate losses between bounds', {'standard': 1863348, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [182396, 119506, 129126, 64521]}, [495549, 1113521]], ['large claim limited', {'standard': 1794820, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [6997029, 30223]}, [5030223, 5384460]], ['maximum binds', {'standard': 1446879, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3226070, 2149089, 2381869, 2566788]}, [10323816, 1736255]], ['no losses minimum binds', {'standard': 1111989, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 555995]], ['subrogation recovery offsets', {'standard': 930668, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215001, -125166]}, [89835, 346057]], ['net recovery floors at zero', {'standard': 790663, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-24524]}, [0, 237199]], ['inverted bounds rejected', {'standard': 901935, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802066, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721859]], ['near-minimum losses', {'standard': 1352189, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [178467]}, [178467, 608485]]]]
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)

source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    sp=x['standard']
    if x['max']<x['min']: return 'invalid bounds'
    lim=max(0,sum(min(c,x['loss_limit']) for c in x['claims']))
    basic=Fraction(sp*x['basic'],1000)
    retro=(basic+Fraction(lim*x['lcf'],1000))*Fraction(x['tax'],1000)
    lo=Fraction(sp*x['min'],1000); hi=Fraction(sp*x['max'],1000)
    retro=max(lo,min(hi,retro)) if lim else retro
    return [lim, math.floor(retro+Fraction(1,2))]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['moderate losses between bounds', {'standard': 1208187, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [65251, 117766, 199866, 72604]}, [455487, 827175]], ['large claim limited', {'standard': 1536795, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [7899385, 85219]}, [5085219, 4610385]], ['maximum binds', {'standard': 576969, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3887820, 3676391, 3519603, 3011895]}, [14095709, 692363]], ['no losses minimum binds', {'standard': 783317, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 391659]], ['subrogation recovery offsets', {'standard': 1402360, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [299401, -71949]}, [227452, 581085]], ['net recovery floors at zero', {'standard': 1970882, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13900]}, [0, 591265]], ['inverted bounds rejected', {'standard': 857821, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1032758, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 929482]], ['near-minimum losses', {'standard': 1037917, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [196003]}, [196003, 509523]]], [['moderate losses between bounds', {'standard': 559811, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [168808, 170340, 188681, 153930]}, [681759, 951695]], ['large claim limited', {'standard': 1398667, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [8563900, 72244]}, [5072244, 4196001]], ['maximum binds', {'standard': 1860838, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3974702, 2021857, 3323996, 2741110]}, [12061665, 2233006]], ['no losses minimum binds', {'standard': 1054836, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 527418]], ['subrogation recovery offsets', {'standard': 572933, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215865, -67794]}, [148071, 322920]], ['net recovery floors at zero', {'standard': 1415569, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-23951]}, [0, 424671]], ['inverted bounds rejected', {'standard': 1885857, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1658903, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 1493013]], ['near-minimum losses', {'standard': 1831216, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [255597]}, [255597, 824047]]], [['moderate losses between bounds', {'standard': 1953166, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [130486, 146045, 106267, 80838]}, [463636, 970005]], ['large claim limited', {'standard': 1375996, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [8850428, 26063]}, [5026063, 4127988]], ['maximum binds', {'standard': 1822101, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3010425, 2467545, 2177771, 3447891]}, [11103632, 2186521]], ['no losses minimum binds', {'standard': 1516833, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 758417]], ['subrogation recovery offsets', {'standard': 714829, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [292326, -101272]}, [191054, 370781]], ['net recovery floors at zero', {'standard': 1501098, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-22616]}, [0, 450329]], ['inverted bounds rejected', {'standard': 696781, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802028, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721825]], ['near-minimum losses', {'standard': 715359, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [161153]}, [161153, 346549]]], [['moderate losses between bounds', {'standard': 714988, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [147807, 50783, 101639, 147624]}, [447853, 714442]], ['large claim limited', {'standard': 1075364, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [6621396, 51697]}, [5051697, 3226092]], ['maximum binds', {'standard': 636493, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3206066, 2811387, 2370852, 2596520]}, [10984825, 763792]], ['no losses minimum binds', {'standard': 1974481, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1600, 'loss_limit': 5000000, 'claims': []}, [0, 987241]], ['subrogation recovery offsets', {'standard': 1092045, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [210597, -95806]}, [114791, 366843]], ['net recovery floors at zero', {'standard': 1088467, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13789]}, [0, 326540]], ['inverted bounds rejected', {'standard': 1508678, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 811592, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 730433]], ['near-minimum losses', {'standard': 1513685, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [237641]}, [237641, 681158]]], [['moderate losses between bounds', {'standard': 1863348, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [182396, 119506, 129126, 64521]}, [495549, 1113521]], ['large claim limited', {'standard': 1794820, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [6997029, 30223]}, [5030223, 5384460]], ['maximum binds', {'standard': 1446879, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3226070, 2149089, 2381869, 2566788]}, [10323816, 1736255]], ['no losses minimum binds', {'standard': 1111989, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 555995]], ['subrogation recovery offsets', {'standard': 930668, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215001, -125166]}, [89835, 346057]], ['net recovery floors at zero', {'standard': 790663, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-24524]}, [0, 237199]], ['inverted bounds rejected', {'standard': 901935, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802066, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721859]], ['near-minimum losses', {'standard': 1352189, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [178467]}, [178467, 608485]]]]
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)

prompt:
Loss-free insureds pay less than the plan minimum.

Input standard premium, basic, lcf, tax (x1000), min and max (per mille of standard), loss_limit, claims (negative = recovery). max<min -> 'invalid bounds'. Limited losses = max(0, sum(min(claim, limit))). Retro = (standard*basic + limited*lcf)*tax, bounded by [standard*min, standard*max] (bounds already include tax), rounded half-up. Return [limited, retro].

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    sp=x['standard']
    if x['max']<x['min']: return 'invalid bounds'
    lim=sum(min(c,x['loss_limit']) for c in x['claims'])
    basic=Fraction(sp*x['basic'],1000)
    retro=(basic+Fraction(lim*x['lcf'],1000))*Fraction(x['tax'],1000)
    lo=Fraction(sp*x['min'],1000); hi=Fraction(sp*x['max'],1000)
    retro=max(lo,min(hi,retro))
    return [lim, math.floor(retro+Fraction(1,2))]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['moderate losses between bounds', {'standard': 1208187, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [65251, 117766, 199866, 72604]}, [455487, 827175]], ['large claim limited', {'standard': 1536795, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [7899385, 85219]}, [5085219, 4610385]], ['maximum binds', {'standard': 576969, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3887820, 3676391, 3519603, 3011895]}, [14095709, 692363]], ['no losses minimum binds', {'standard': 783317, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 391659]], ['subrogation recovery offsets', {'standard': 1402360, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [299401, -71949]}, [227452, 581085]], ['net recovery floors at zero', {'standard': 1970882, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13900]}, [0, 591265]], ['inverted bounds rejected', {'standard': 857821, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1032758, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 929482]], ['near-minimum losses', {'standard': 1037917, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [196003]}, [196003, 509523]]], [['moderate losses between bounds', {'standard': 559811, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [168808, 170340, 188681, 153930]}, [681759, 951695]], ['large claim limited', {'standard': 1398667, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [8563900, 72244]}, [5072244, 4196001]], ['maximum binds', {'standard': 1860838, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3974702, 2021857, 3323996, 2741110]}, [12061665, 2233006]], ['no losses minimum binds', {'standard': 1054836, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 527418]], ['subrogation recovery offsets', {'standard': 572933, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215865, -67794]}, [148071, 322920]], ['net recovery floors at zero', {'standard': 1415569, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-23951]}, [0, 424671]], ['inverted bounds rejected', {'standard': 1885857, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1658903, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 1493013]], ['near-minimum losses', {'standard': 1831216, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [255597]}, [255597, 824047]]], [['moderate losses between bounds', {'standard': 1953166, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [130486, 146045, 106267, 80838]}, [463636, 970005]], ['large claim limited', {'standard': 1375996, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [8850428, 26063]}, [5026063, 4127988]], ['maximum binds', {'standard': 1822101, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3010425, 2467545, 2177771, 3447891]}, [11103632, 2186521]], ['no losses minimum binds', {'standard': 1516833, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 758417]], ['subrogation recovery offsets', {'standard': 714829, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [292326, -101272]}, [191054, 370781]], ['net recovery floors at zero', {'standard': 1501098, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-22616]}, [0, 450329]], ['inverted bounds rejected', {'standard': 696781, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802028, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721825]], ['near-minimum losses', {'standard': 715359, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [161153]}, [161153, 346549]]], [['moderate losses between bounds', {'standard': 714988, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [147807, 50783, 101639, 147624]}, [447853, 714442]], ['large claim limited', {'standard': 1075364, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [6621396, 51697]}, [5051697, 3226092]], ['maximum binds', {'standard': 636493, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3206066, 2811387, 2370852, 2596520]}, [10984825, 763792]], ['no losses minimum binds', {'standard': 1974481, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1600, 'loss_limit': 5000000, 'claims': []}, [0, 987241]], ['subrogation recovery offsets', {'standard': 1092045, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [210597, -95806]}, [114791, 366843]], ['net recovery floors at zero', {'standard': 1088467, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13789]}, [0, 326540]], ['inverted bounds rejected', {'standard': 1508678, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 811592, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 730433]], ['near-minimum losses', {'standard': 1513685, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [237641]}, [237641, 681158]]], [['moderate losses between bounds', {'standard': 1863348, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [182396, 119506, 129126, 64521]}, [495549, 1113521]], ['large claim limited', {'standard': 1794820, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [6997029, 30223]}, [5030223, 5384460]], ['maximum binds', {'standard': 1446879, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3226070, 2149089, 2381869, 2566788]}, [10323816, 1736255]], ['no losses minimum binds', {'standard': 1111989, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 555995]], ['subrogation recovery offsets', {'standard': 930668, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215001, -125166]}, [89835, 346057]], ['net recovery floors at zero', {'standard': 790663, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-24524]}, [0, 237199]], ['inverted bounds rejected', {'standard': 901935, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802066, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721859]], ['near-minimum losses', {'standard': 1352189, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [178467]}, [178467, 608485]]]]
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)

meaning: Fixture-count band, not measured model difficulty

deps: stdlib

source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    sp=x['standard']
    if x['max']<x['min']: return 'invalid bounds'
    lim=sum(min(max(c,0),x['loss_limit']) for c in x['claims'])
    basic=Fraction(sp*x['basic'],1000)
    retro=(basic+Fraction(lim*x['lcf'],1000))*Fraction(x['tax'],1000)
    lo=Fraction(sp*x['min'],1000); hi=Fraction(sp*x['max'],1000)
    retro=max(lo,min(hi,retro))
    return [lim, math.floor(retro+Fraction(1,2))]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['moderate losses between bounds', {'standard': 1208187, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [65251, 117766, 199866, 72604]}, [455487, 827175]], ['large claim limited', {'standard': 1536795, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [7899385, 85219]}, [5085219, 4610385]], ['maximum binds', {'standard': 576969, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3887820, 3676391, 3519603, 3011895]}, [14095709, 692363]], ['no losses minimum binds', {'standard': 783317, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 391659]], ['subrogation recovery offsets', {'standard': 1402360, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [299401, -71949]}, [227452, 581085]], ['net recovery floors at zero', {'standard': 1970882, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13900]}, [0, 591265]], ['inverted bounds rejected', {'standard': 857821, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1032758, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 929482]], ['near-minimum losses', {'standard': 1037917, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [196003]}, [196003, 509523]]], [['moderate losses between bounds', {'standard': 559811, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [168808, 170340, 188681, 153930]}, [681759, 951695]], ['large claim limited', {'standard': 1398667, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [8563900, 72244]}, [5072244, 4196001]], ['maximum binds', {'standard': 1860838, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3974702, 2021857, 3323996, 2741110]}, [12061665, 2233006]], ['no losses minimum binds', {'standard': 1054836, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 527418]], ['subrogation recovery offsets', {'standard': 572933, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215865, -67794]}, [148071, 322920]], ['net recovery floors at zero', {'standard': 1415569, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-23951]}, [0, 424671]], ['inverted bounds rejected', {'standard': 1885857, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1658903, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 1493013]], ['near-minimum losses', {'standard': 1831216, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [255597]}, [255597, 824047]]], [['moderate losses between bounds', {'standard': 1953166, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [130486, 146045, 106267, 80838]}, [463636, 970005]], ['large claim limited', {'standard': 1375996, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [8850428, 26063]}, [5026063, 4127988]], ['maximum binds', {'standard': 1822101, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3010425, 2467545, 2177771, 3447891]}, [11103632, 2186521]], ['no losses minimum binds', {'standard': 1516833, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 758417]], ['subrogation recovery offsets', {'standard': 714829, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [292326, -101272]}, [191054, 370781]], ['net recovery floors at zero', {'standard': 1501098, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-22616]}, [0, 450329]], ['inverted bounds rejected', {'standard': 696781, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802028, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721825]], ['near-minimum losses', {'standard': 715359, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [161153]}, [161153, 346549]]], [['moderate losses between bounds', {'standard': 714988, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [147807, 50783, 101639, 147624]}, [447853, 714442]], ['large claim limited', {'standard': 1075364, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [6621396, 51697]}, [5051697, 3226092]], ['maximum binds', {'standard': 636493, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3206066, 2811387, 2370852, 2596520]}, [10984825, 763792]], ['no losses minimum binds', {'standard': 1974481, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1600, 'loss_limit': 5000000, 'claims': []}, [0, 987241]], ['subrogation recovery offsets', {'standard': 1092045, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [210597, -95806]}, [114791, 366843]], ['net recovery floors at zero', {'standard': 1088467, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13789]}, [0, 326540]], ['inverted bounds rejected', {'standard': 1508678, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 811592, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 730433]], ['near-minimum losses', {'standard': 1513685, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [237641]}, [237641, 681158]]], [['moderate losses between bounds', {'standard': 1863348, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [182396, 119506, 129126, 64521]}, [495549, 1113521]], ['large claim limited', {'standard': 1794820, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [6997029, 30223]}, [5030223, 5384460]], ['maximum binds', {'standard': 1446879, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3226070, 2149089, 2381869, 2566788]}, [10323816, 1736255]], ['no losses minimum binds', {'standard': 1111989, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 555995]], ['subrogation recovery offsets', {'standard': 930668, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215001, -125166]}, [89835, 346057]], ['net recovery floors at zero', {'standard': 790663, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-24524]}, [0, 237199]], ['inverted bounds rejected', {'standard': 901935, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802066, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721859]], ['near-minimum losses', {'standard': 1352189, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [178467]}, [178467, 608485]]]]
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)

prompt:
Salvage exceeding losses reduces the retro premium below the basic charge.

Input standard premium, basic, lcf, tax (x1000), min and max (per mille of standard), loss_limit, claims (negative = recovery). max<min -> 'invalid bounds'. Limited losses = max(0, sum(min(claim, limit))). Retro = (standard*basic + limited*lcf)*tax, bounded by [standard*min, standard*max] (bounds already include tax), rounded half-up. Return [limited, retro].

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    sp=x['standard']
    if x['max']<=x['min']: return 'invalid bounds'
    lim=max(0,sum(min(c,x['loss_limit']) for c in x['claims']))
    basic=Fraction(sp*x['basic'],1000)
    retro=(basic+Fraction(lim*x['lcf'],1000))*Fraction(x['tax'],1000)
    lo=Fraction(sp*x['min'],1000); hi=Fraction(sp*x['max'],1000)
    retro=max(lo,min(hi,retro))
    return [lim, math.floor(retro+Fraction(1,2))]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['moderate losses between bounds', {'standard': 1208187, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [65251, 117766, 199866, 72604]}, [455487, 827175]], ['large claim limited', {'standard': 1536795, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [7899385, 85219]}, [5085219, 4610385]], ['maximum binds', {'standard': 576969, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3887820, 3676391, 3519603, 3011895]}, [14095709, 692363]], ['no losses minimum binds', {'standard': 783317, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 391659]], ['subrogation recovery offsets', {'standard': 1402360, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [299401, -71949]}, [227452, 581085]], ['net recovery floors at zero', {'standard': 1970882, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13900]}, [0, 591265]], ['inverted bounds rejected', {'standard': 857821, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1032758, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 929482]], ['near-minimum losses', {'standard': 1037917, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [196003]}, [196003, 509523]]], [['moderate losses between bounds', {'standard': 559811, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [168808, 170340, 188681, 153930]}, [681759, 951695]], ['large claim limited', {'standard': 1398667, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [8563900, 72244]}, [5072244, 4196001]], ['maximum binds', {'standard': 1860838, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3974702, 2021857, 3323996, 2741110]}, [12061665, 2233006]], ['no losses minimum binds', {'standard': 1054836, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 527418]], ['subrogation recovery offsets', {'standard': 572933, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215865, -67794]}, [148071, 322920]], ['net recovery floors at zero', {'standard': 1415569, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-23951]}, [0, 424671]], ['inverted bounds rejected', {'standard': 1885857, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1658903, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 1493013]], ['near-minimum losses', {'standard': 1831216, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [255597]}, [255597, 824047]]], [['moderate losses between bounds', {'standard': 1953166, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [130486, 146045, 106267, 80838]}, [463636, 970005]], ['large claim limited', {'standard': 1375996, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [8850428, 26063]}, [5026063, 4127988]], ['maximum binds', {'standard': 1822101, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3010425, 2467545, 2177771, 3447891]}, [11103632, 2186521]], ['no losses minimum binds', {'standard': 1516833, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 758417]], ['subrogation recovery offsets', {'standard': 714829, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [292326, -101272]}, [191054, 370781]], ['net recovery floors at zero', {'standard': 1501098, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-22616]}, [0, 450329]], ['inverted bounds rejected', {'standard': 696781, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802028, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721825]], ['near-minimum losses', {'standard': 715359, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [161153]}, [161153, 346549]]], [['moderate losses between bounds', {'standard': 714988, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [147807, 50783, 101639, 147624]}, [447853, 714442]], ['large claim limited', {'standard': 1075364, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [6621396, 51697]}, [5051697, 3226092]], ['maximum binds', {'standard': 636493, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3206066, 2811387, 2370852, 2596520]}, [10984825, 763792]], ['no losses minimum binds', {'standard': 1974481, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1600, 'loss_limit': 5000000, 'claims': []}, [0, 987241]], ['subrogation recovery offsets', {'standard': 1092045, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [210597, -95806]}, [114791, 366843]], ['net recovery floors at zero', {'standard': 1088467, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13789]}, [0, 326540]], ['inverted bounds rejected', {'standard': 1508678, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 811592, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 730433]], ['near-minimum losses', {'standard': 1513685, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [237641]}, [237641, 681158]]], [['moderate losses between bounds', {'standard': 1863348, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [182396, 119506, 129126, 64521]}, [495549, 1113521]], ['large claim limited', {'standard': 1794820, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [6997029, 30223]}, [5030223, 5384460]], ['maximum binds', {'standard': 1446879, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3226070, 2149089, 2381869, 2566788]}, [10323816, 1736255]], ['no losses minimum binds', {'standard': 1111989, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 555995]], ['subrogation recovery offsets', {'standard': 930668, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215001, -125166]}, [89835, 346057]], ['net recovery floors at zero', {'standard': 790663, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-24524]}, [0, 237199]], ['inverted bounds rejected', {'standard': 901935, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802066, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721859]], ['near-minimum losses', {'standard': 1352189, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [178467]}, [178467, 608485]]]]
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)

source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    sp=x['standard']
    if x['max']<0: return 'invalid bounds'
    lim=max(0,sum(min(c,x['loss_limit']) for c in x['claims']))
    basic=Fraction(sp*x['basic'],1000)
    retro=(basic+Fraction(lim*x['lcf'],1000))*Fraction(x['tax'],1000)
    lo=Fraction(sp*x['min'],1000); hi=Fraction(sp*x['max'],1000)
    retro=max(lo,min(hi,retro))
    return [lim, math.floor(retro+Fraction(1,2))]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['moderate losses between bounds', {'standard': 1208187, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [65251, 117766, 199866, 72604]}, [455487, 827175]], ['large claim limited', {'standard': 1536795, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [7899385, 85219]}, [5085219, 4610385]], ['maximum binds', {'standard': 576969, 'basic': 250, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3887820, 3676391, 3519603, 3011895]}, [14095709, 692363]], ['no losses minimum binds', {'standard': 783317, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 391659]], ['subrogation recovery offsets', {'standard': 1402360, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [299401, -71949]}, [227452, 581085]], ['net recovery floors at zero', {'standard': 1970882, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13900]}, [0, 591265]], ['inverted bounds rejected', {'standard': 857821, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1032758, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 929482]], ['near-minimum losses', {'standard': 1037917, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [196003]}, [196003, 509523]]], [['moderate losses between bounds', {'standard': 559811, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [168808, 170340, 188681, 153930]}, [681759, 951695]], ['large claim limited', {'standard': 1398667, 'basic': 200, 'lcf': 1150, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [8563900, 72244]}, [5072244, 4196001]], ['maximum binds', {'standard': 1860838, 'basic': 250, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3974702, 2021857, 3323996, 2741110]}, [12061665, 2233006]], ['no losses minimum binds', {'standard': 1054836, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 527418]], ['subrogation recovery offsets', {'standard': 572933, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215865, -67794]}, [148071, 322920]], ['net recovery floors at zero', {'standard': 1415569, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-23951]}, [0, 424671]], ['inverted bounds rejected', {'standard': 1885857, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 1658903, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 1493013]], ['near-minimum losses', {'standard': 1831216, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [255597]}, [255597, 824047]]], [['moderate losses between bounds', {'standard': 1953166, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [130486, 146045, 106267, 80838]}, [463636, 970005]], ['large claim limited', {'standard': 1375996, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [8850428, 26063]}, [5026063, 4127988]], ['maximum binds', {'standard': 1822101, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 600, 'max': 1200, 'loss_limit': 5000000, 'claims': [3010425, 2467545, 2177771, 3447891]}, [11103632, 2186521]], ['no losses minimum binds', {'standard': 1516833, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 758417]], ['subrogation recovery offsets', {'standard': 714829, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [292326, -101272]}, [191054, 370781]], ['net recovery floors at zero', {'standard': 1501098, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-22616]}, [0, 450329]], ['inverted bounds rejected', {'standard': 696781, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802028, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721825]], ['near-minimum losses', {'standard': 715359, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [161153]}, [161153, 346549]]], [['moderate losses between bounds', {'standard': 714988, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [147807, 50783, 101639, 147624]}, [447853, 714442]], ['large claim limited', {'standard': 1075364, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 600, 'max': 3000, 'loss_limit': 5000000, 'claims': [6621396, 51697]}, [5051697, 3226092]], ['maximum binds', {'standard': 636493, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3206066, 2811387, 2370852, 2596520]}, [10984825, 763792]], ['no losses minimum binds', {'standard': 1974481, 'basic': 200, 'lcf': 1200, 'tax': 1050, 'min': 500, 'max': 1600, 'loss_limit': 5000000, 'claims': []}, [0, 987241]], ['subrogation recovery offsets', {'standard': 1092045, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [210597, -95806]}, [114791, 366843]], ['net recovery floors at zero', {'standard': 1088467, 'basic': 250, 'lcf': 1200, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-13789]}, [0, 326540]], ['inverted bounds rejected', {'standard': 1508678, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 811592, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 730433]], ['near-minimum losses', {'standard': 1513685, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [237641]}, [237641, 681158]]], [['moderate losses between bounds', {'standard': 1863348, 'basic': 250, 'lcf': 1200, 'tax': 1050, 'min': 400, 'max': 2000, 'loss_limit': 5000000, 'claims': [182396, 119506, 129126, 64521]}, [495549, 1113521]], ['large claim limited', {'standard': 1794820, 'basic': 200, 'lcf': 1100, 'tax': 1030, 'min': 500, 'max': 3000, 'loss_limit': 5000000, 'claims': [6997029, 30223]}, [5030223, 5384460]], ['maximum binds', {'standard': 1446879, 'basic': 200, 'lcf': 1200, 'tax': 1030, 'min': 500, 'max': 1200, 'loss_limit': 5000000, 'claims': [3226070, 2149089, 2381869, 2566788]}, [10323816, 1736255]], ['no losses minimum binds', {'standard': 1111989, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 500, 'max': 1400, 'loss_limit': 5000000, 'claims': []}, [0, 555995]], ['subrogation recovery offsets', {'standard': 930668, 'basic': 250, 'lcf': 1150, 'tax': 1030, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [215001, -125166]}, [89835, 346057]], ['net recovery floors at zero', {'standard': 790663, 'basic': 200, 'lcf': 1100, 'tax': 1050, 'min': 300, 'max': 2500, 'loss_limit': 5000000, 'claims': [-24524]}, [0, 237199]], ['inverted bounds rejected', {'standard': 901935, 'basic': 200, 'lcf': 1150, 'tax': 1050, 'min': 1300, 'max': 1200, 'loss_limit': 5000000, 'claims': [100000]}, 'invalid bounds'], ['flat plan with equal bounds', {'standard': 802066, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 900, 'max': 900, 'loss_limit': 5000000, 'claims': [100000]}, [100000, 721859]], ['near-minimum losses', {'standard': 1352189, 'basic': 250, 'lcf': 1150, 'tax': 1050, 'min': 450, 'max': 1800, 'loss_limit': 5000000, 'claims': [178467]}, [178467, 608485]]]]
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)

prompt:
A fixed-cost plan with identical bounds is refused.

Input standard premium, basic, lcf, tax (x1000), min and max (per mille of standard), loss_limit, claims (negative = recovery). max<min -> 'invalid bounds'. Limited losses = max(0, sum(min(claim, limit))). Retro = (standard*basic + limited*lcf)*tax, bounded by [standard*min, standard*max] (bounds already include tax), rounded half-up. Return [limited, retro].

split: open-access