{"abstract":"Trend is six months short for annual policies.","category":"Insurance premium rating","checks":9,"contract":"Input losses, age (months, positive multiple of 12 else 'invalid'), ldfs (age-to-age *1000, first is 12-24), tail *1000, trend (annual per mille), exp_start and pol_start (months). CDF = tail * product of ldfs from index age/12-1. Trend span = (pol_start+12) - (exp_start+6) months; factor = (1+t)^years * (1+t*rem/12). Return floor(losses*CDF*factor+1/2).","evaluation_group":"w2-insurance_premium_rating-trend-development","failed_approach":"Measuring start to start ignores both midpoints.","family":"w2-insurance_premium_rating-trend-development-trend-midpoints","id":"FA-63001","implementations":{"attempt":{"sha256":"08827aaf4559082be2946e74a2c9164f7c7511a6429db6a662b1343966f7d492","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    age=x['age']\n    if age<=0 or age%12: return 'invalid'\n    k=age//12-1\n    cdf=Fraction(x['tail'],1000)\n    for f in x['ldfs'][k:]:\n        cdf*=Fraction(f,1000)\n    gap=x['pol_start']-x['exp_start']\n    t=Fraction(x['trend'],1000)\n    yrs,rem=divmod(gap,12)\n    tf=(1+t)**yrs*(1+t*rem/12)\n    return math.floor(x['losses']*cdf*tf+Fraction(1,2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['immature year', {'losses': 6101262, 'age': 12, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 41, 'pol_start': 76}, 16756377], ['second evaluation', {'losses': 5233772, 'age': 24, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 8, 'pol_start': 48}, 9260396], ['mid development', {'losses': 6787850, 'age': 48, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 36, 'pol_start': 60}, 8080698], ['fully developed except tail', {'losses': 4698103, 'age': 72, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1020, 'trend': 30, 'exp_start': 28, 'pol_start': 58}, 5236419], ['beyond last factor', {'losses': 4308538, 'age': 84, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1030, 'trend': 50, 'exp_start': 31, 'pol_start': 68}, 5287139], ['trend span whole years', {'losses': 6440858, 'age': 36, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 25, 'pol_start': 37}, 8137012], ['trend span with remainder', {'losses': 8332360, 'age': 36, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 9, 'pol_start': 28}, 10402433], ['non-annual age rejected', {'losses': 7240281, 'age': 18, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 19, 'pol_start': 53}, 'invalid'], ['zero age rejected', {'losses': 1186186, 'age': 0, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 24, 'pol_start': 50}, 'invalid']], [['immature year', {'losses': 8928412, 'age': 12, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 21, 'pol_start': 50}, 23155698], ['second evaluation', {'losses': 8550609, 'age': 24, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 37, 'pol_start': 74}, 13962253], ['mid development', {'losses': 5731401, 'age': 48, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 3, 'pol_start': 21}, 6736901], ['fully developed except tail', {'losses': 2333827, 'age': 72, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1020, 'trend': 45, 'exp_start': 54, 'pol_start': 89}, 2767485], ['beyond last factor', {'losses': 3119424, 'age': 84, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1030, 'trend': 30, 'exp_start': 3, 'pol_start': 30}, 3485374], ['trend span whole years', {'losses': 3522316, 'age': 36, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 2, 'pol_start': 14}, 4326472], ['trend span with remainder', {'losses': 8948897, 'age': 36, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 5, 'pol_start': 24}, 11640088], ['non-annual age rejected', {'losses': 3221043, 'age': 18, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 39, 'pol_start': 74}, 'invalid'], ['zero age rejected', {'losses': 8655065, 'age': 0, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 37, 'pol_start': 56}, 'invalid']], [['immature year', {'losses': 2645801, 'age': 12, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 29, 'pol_start': 65}, 7397130], ['second evaluation', {'losses': 6201911, 'age': 24, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 20, 'pol_start': 39}, 9992863], ['mid development', {'losses': 4311093, 'age': 48, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 52, 'pol_start': 71}, 4888403], ['fully developed except tail', {'losses': 6201749, 'age': 72, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1020, 'trend': 50, 'exp_start': 31, 'pol_start': 67}, 7505958], ['beyond last factor', {'losses': 6770980, 'age': 84, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1030, 'trend': 30, 'exp_start': 32, 'pol_start': 52}, 7435827], ['trend span whole years', {'losses': 5004070, 'age': 36, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 32, 'pol_start': 44}, 6333340], ['trend span with remainder', {'losses': 7309289, 'age': 36, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 1, 'pol_start': 20}, 9516030], ['non-annual age rejected', {'losses': 6899078, 'age': 18, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 13, 'pol_start': 37}, 'invalid'], ['zero age rejected', {'losses': 6441743, 'age': 0, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 39, 'pol_start': 71}, 'invalid']], [['immature year', {'losses': 6749109, 'age': 12, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 58, 'pol_start': 77}, 17320043], ['second evaluation', {'losses': 2964503, 'age': 24, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 23, 'pol_start': 52}, 5029129], ['mid development', {'losses': 1958599, 'age': 48, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 8, 'pol_start': 45}, 2445504], ['fully developed except tail', {'losses': 7303981, 'age': 72, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1020, 'trend': 50, 'exp_start': 46, 'pol_start': 76}, 8624376], ['beyond last factor', {'losses': 5438017, 'age': 84, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1030, 'trend': 45, 'exp_start': 33, 'pol_start': 56}, 6231290], ['trend span whole years', {'losses': 3936734, 'age': 36, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 18, 'pol_start': 30}, 4951143], ['trend span with remainder', {'losses': 3870348, 'age': 36, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 36, 'pol_start': 53}, 4821242], ['non-annual age rejected', {'losses': 8705484, 'age': 18, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 56, 'pol_start': 83}, 'invalid'], ['zero age rejected', {'losses': 8329864, 'age': 0, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 0, 'pol_start': 30}, 'invalid']], [['immature year', {'losses': 2993216, 'age': 12, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 42, 'pol_start': 72}, 8419435], ['second evaluation', {'losses': 8759921, 'age': 24, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 24, 'pol_start': 53}, 14668335], ['mid development', {'losses': 7728493, 'age': 48, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 21, 'pol_start': 45}, 9200501], ['fully developed except tail', {'losses': 8451860, 'age': 72, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1020, 'trend': 45, 'exp_start': 16, 'pol_start': 46}, 9837876], ['beyond last factor', {'losses': 5895078, 'age': 84, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1030, 'trend': 30, 'exp_start': 17, 'pol_start': 56}, 6784249], ['trend span whole years', {'losses': 4683619, 'age': 36, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 55, 'pol_start': 67}, 5895820], ['trend span with remainder', {'losses': 5208228, 'age': 36, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 58, 'pol_start': 77}, 6525771], ['non-annual age rejected', {'losses': 2071597, 'age': 18, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 44, 'pol_start': 71}, 'invalid'], ['zero age rejected', {'losses': 2191426, 'age': 0, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 13, 'pol_start': 49}, 'invalid']]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"97e128c0ffd7bbf7df5d98fc9cbbb3dc14c647048b4a90b6fd01ba1e67ffc4bf","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    age=x['age']\n    if age<=0 or age%12: return 'invalid'\n    k=age//12-1\n    cdf=Fraction(x['tail'],1000)\n    for f in x['ldfs'][k:]:\n        cdf*=Fraction(f,1000)\n    gap=(x['pol_start']+6)-(x['exp_start']+6)\n    t=Fraction(x['trend'],1000)\n    yrs,rem=divmod(gap,12)\n    tf=(1+t)**yrs*(1+t*rem/12)\n    return math.floor(x['losses']*cdf*tf+Fraction(1,2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['immature year', {'losses': 6101262, 'age': 12, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 41, 'pol_start': 76}, 16756377], ['second evaluation', {'losses': 5233772, 'age': 24, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 8, 'pol_start': 48}, 9260396], ['mid development', {'losses': 6787850, 'age': 48, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 36, 'pol_start': 60}, 8080698], ['fully developed except tail', {'losses': 4698103, 'age': 72, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1020, 'trend': 30, 'exp_start': 28, 'pol_start': 58}, 5236419], ['beyond last factor', {'losses': 4308538, 'age': 84, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1030, 'trend': 50, 'exp_start': 31, 'pol_start': 68}, 5287139], ['trend span whole years', {'losses': 6440858, 'age': 36, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 25, 'pol_start': 37}, 8137012], ['trend span with remainder', {'losses': 8332360, 'age': 36, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 9, 'pol_start': 28}, 10402433], ['non-annual age rejected', {'losses': 7240281, 'age': 18, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 19, 'pol_start': 53}, 'invalid'], ['zero age rejected', {'losses': 1186186, 'age': 0, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 24, 'pol_start': 50}, 'invalid']], [['immature year', {'losses': 8928412, 'age': 12, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 21, 'pol_start': 50}, 23155698], ['second evaluation', {'losses': 8550609, 'age': 24, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 37, 'pol_start': 74}, 13962253], ['mid development', {'losses': 5731401, 'age': 48, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 3, 'pol_start': 21}, 6736901], ['fully developed except tail', {'losses': 2333827, 'age': 72, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1020, 'trend': 45, 'exp_start': 54, 'pol_start': 89}, 2767485], ['beyond last factor', {'losses': 3119424, 'age': 84, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1030, 'trend': 30, 'exp_start': 3, 'pol_start': 30}, 3485374], ['trend span whole years', {'losses': 3522316, 'age': 36, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 2, 'pol_start': 14}, 4326472], ['trend span with remainder', {'losses': 8948897, 'age': 36, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 5, 'pol_start': 24}, 11640088], ['non-annual age rejected', {'losses': 3221043, 'age': 18, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 39, 'pol_start': 74}, 'invalid'], ['zero age rejected', {'losses': 8655065, 'age': 0, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 37, 'pol_start': 56}, 'invalid']], [['immature year', {'losses': 2645801, 'age': 12, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 29, 'pol_start': 65}, 7397130], ['second evaluation', {'losses': 6201911, 'age': 24, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 20, 'pol_start': 39}, 9992863], ['mid development', {'losses': 4311093, 'age': 48, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 52, 'pol_start': 71}, 4888403], ['fully developed except tail', {'losses': 6201749, 'age': 72, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1020, 'trend': 50, 'exp_start': 31, 'pol_start': 67}, 7505958], ['beyond last factor', {'losses': 6770980, 'age': 84, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1030, 'trend': 30, 'exp_start': 32, 'pol_start': 52}, 7435827], ['trend span whole years', {'losses': 5004070, 'age': 36, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 32, 'pol_start': 44}, 6333340], ['trend span with remainder', {'losses': 7309289, 'age': 36, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 1, 'pol_start': 20}, 9516030], ['non-annual age rejected', {'losses': 6899078, 'age': 18, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 13, 'pol_start': 37}, 'invalid'], ['zero age rejected', {'losses': 6441743, 'age': 0, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 39, 'pol_start': 71}, 'invalid']], [['immature year', {'losses': 6749109, 'age': 12, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 58, 'pol_start': 77}, 17320043], ['second evaluation', {'losses': 2964503, 'age': 24, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 23, 'pol_start': 52}, 5029129], ['mid development', {'losses': 1958599, 'age': 48, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 8, 'pol_start': 45}, 2445504], ['fully developed except tail', {'losses': 7303981, 'age': 72, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1020, 'trend': 50, 'exp_start': 46, 'pol_start': 76}, 8624376], ['beyond last factor', {'losses': 5438017, 'age': 84, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1030, 'trend': 45, 'exp_start': 33, 'pol_start': 56}, 6231290], ['trend span whole years', {'losses': 3936734, 'age': 36, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 18, 'pol_start': 30}, 4951143], ['trend span with remainder', {'losses': 3870348, 'age': 36, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 36, 'pol_start': 53}, 4821242], ['non-annual age rejected', {'losses': 8705484, 'age': 18, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 56, 'pol_start': 83}, 'invalid'], ['zero age rejected', {'losses': 8329864, 'age': 0, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 0, 'pol_start': 30}, 'invalid']], [['immature year', {'losses': 2993216, 'age': 12, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 42, 'pol_start': 72}, 8419435], ['second evaluation', {'losses': 8759921, 'age': 24, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 24, 'pol_start': 53}, 14668335], ['mid development', {'losses': 7728493, 'age': 48, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 21, 'pol_start': 45}, 9200501], ['fully developed except tail', {'losses': 8451860, 'age': 72, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1020, 'trend': 45, 'exp_start': 16, 'pol_start': 46}, 9837876], ['beyond last factor', {'losses': 5895078, 'age': 84, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1030, 'trend': 30, 'exp_start': 17, 'pol_start': 56}, 6784249], ['trend span whole years', {'losses': 4683619, 'age': 36, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 55, 'pol_start': 67}, 5895820], ['trend span with remainder', {'losses': 5208228, 'age': 36, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 58, 'pol_start': 77}, 6525771], ['non-annual age rejected', {'losses': 2071597, 'age': 18, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 44, 'pol_start': 71}, 'invalid'], ['zero age rejected', {'losses': 2191426, 'age': 0, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 13, 'pol_start': 49}, 'invalid']]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"3418058ae8bb9a8b2ed6d503f09eb47a89a3fe2683291e97205c878166b5d293","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    age=x['age']\n    if age<=0 or age%12: return 'invalid'\n    k=age//12-1\n    cdf=Fraction(x['tail'],1000)\n    for f in x['ldfs'][k:]:\n        cdf*=Fraction(f,1000)\n    gap=(x['pol_start']+12)-(x['exp_start']+6)\n    t=Fraction(x['trend'],1000)\n    yrs,rem=divmod(gap,12)\n    tf=(1+t)**yrs*(1+t*rem/12)\n    return math.floor(x['losses']*cdf*tf+Fraction(1,2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['immature year', {'losses': 6101262, 'age': 12, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 41, 'pol_start': 76}, 16756377], ['second evaluation', {'losses': 5233772, 'age': 24, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 8, 'pol_start': 48}, 9260396], ['mid development', {'losses': 6787850, 'age': 48, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 36, 'pol_start': 60}, 8080698], ['fully developed except tail', {'losses': 4698103, 'age': 72, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1020, 'trend': 30, 'exp_start': 28, 'pol_start': 58}, 5236419], ['beyond last factor', {'losses': 4308538, 'age': 84, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1030, 'trend': 50, 'exp_start': 31, 'pol_start': 68}, 5287139], ['trend span whole years', {'losses': 6440858, 'age': 36, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 25, 'pol_start': 37}, 8137012], ['trend span with remainder', {'losses': 8332360, 'age': 36, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 9, 'pol_start': 28}, 10402433], ['non-annual age rejected', {'losses': 7240281, 'age': 18, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 19, 'pol_start': 53}, 'invalid'], ['zero age rejected', {'losses': 1186186, 'age': 0, 'ldfs': [1610, 1250, 1101, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 24, 'pol_start': 50}, 'invalid']], [['immature year', {'losses': 8928412, 'age': 12, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 21, 'pol_start': 50}, 23155698], ['second evaluation', {'losses': 8550609, 'age': 24, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 37, 'pol_start': 74}, 13962253], ['mid development', {'losses': 5731401, 'age': 48, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 3, 'pol_start': 21}, 6736901], ['fully developed except tail', {'losses': 2333827, 'age': 72, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1020, 'trend': 45, 'exp_start': 54, 'pol_start': 89}, 2767485], ['beyond last factor', {'losses': 3119424, 'age': 84, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1030, 'trend': 30, 'exp_start': 3, 'pol_start': 30}, 3485374], ['trend span whole years', {'losses': 3522316, 'age': 36, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 2, 'pol_start': 14}, 4326472], ['trend span with remainder', {'losses': 8948897, 'age': 36, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 5, 'pol_start': 24}, 11640088], ['non-annual age rejected', {'losses': 3221043, 'age': 18, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 39, 'pol_start': 74}, 'invalid'], ['zero age rejected', {'losses': 8655065, 'age': 0, 'ldfs': [1620, 1250, 1102, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 37, 'pol_start': 56}, 'invalid']], [['immature year', {'losses': 2645801, 'age': 12, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 29, 'pol_start': 65}, 7397130], ['second evaluation', {'losses': 6201911, 'age': 24, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 20, 'pol_start': 39}, 9992863], ['mid development', {'losses': 4311093, 'age': 48, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 52, 'pol_start': 71}, 4888403], ['fully developed except tail', {'losses': 6201749, 'age': 72, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1020, 'trend': 50, 'exp_start': 31, 'pol_start': 67}, 7505958], ['beyond last factor', {'losses': 6770980, 'age': 84, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1030, 'trend': 30, 'exp_start': 32, 'pol_start': 52}, 7435827], ['trend span whole years', {'losses': 5004070, 'age': 36, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 32, 'pol_start': 44}, 6333340], ['trend span with remainder', {'losses': 7309289, 'age': 36, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 1, 'pol_start': 20}, 9516030], ['non-annual age rejected', {'losses': 6899078, 'age': 18, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 13, 'pol_start': 37}, 'invalid'], ['zero age rejected', {'losses': 6441743, 'age': 0, 'ldfs': [1630, 1250, 1103, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 39, 'pol_start': 71}, 'invalid']], [['immature year', {'losses': 6749109, 'age': 12, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 58, 'pol_start': 77}, 17320043], ['second evaluation', {'losses': 2964503, 'age': 24, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 23, 'pol_start': 52}, 5029129], ['mid development', {'losses': 1958599, 'age': 48, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 8, 'pol_start': 45}, 2445504], ['fully developed except tail', {'losses': 7303981, 'age': 72, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1020, 'trend': 50, 'exp_start': 46, 'pol_start': 76}, 8624376], ['beyond last factor', {'losses': 5438017, 'age': 84, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1030, 'trend': 45, 'exp_start': 33, 'pol_start': 56}, 6231290], ['trend span whole years', {'losses': 3936734, 'age': 36, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 18, 'pol_start': 30}, 4951143], ['trend span with remainder', {'losses': 3870348, 'age': 36, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 36, 'pol_start': 53}, 4821242], ['non-annual age rejected', {'losses': 8705484, 'age': 18, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 56, 'pol_start': 83}, 'invalid'], ['zero age rejected', {'losses': 8329864, 'age': 0, 'ldfs': [1640, 1250, 1104, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 0, 'pol_start': 30}, 'invalid']], [['immature year', {'losses': 2993216, 'age': 12, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 42, 'pol_start': 72}, 8419435], ['second evaluation', {'losses': 8759921, 'age': 24, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 24, 'pol_start': 53}, 14668335], ['mid development', {'losses': 7728493, 'age': 48, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 21, 'pol_start': 45}, 9200501], ['fully developed except tail', {'losses': 8451860, 'age': 72, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1020, 'trend': 45, 'exp_start': 16, 'pol_start': 46}, 9837876], ['beyond last factor', {'losses': 5895078, 'age': 84, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1030, 'trend': 30, 'exp_start': 17, 'pol_start': 56}, 6784249], ['trend span whole years', {'losses': 4683619, 'age': 36, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 45, 'exp_start': 55, 'pol_start': 67}, 5895820], ['trend span with remainder', {'losses': 5208228, 'age': 36, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 58, 'pol_start': 77}, 6525771], ['non-annual age rejected', {'losses': 2071597, 'age': 18, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 50, 'exp_start': 44, 'pol_start': 71}, 'invalid'], ['zero age rejected', {'losses': 2191426, 'age': 0, 'ldfs': [1650, 1250, 1105, 1040, 1015], 'tail': 1010, 'trend': 30, 'exp_start': 13, 'pol_start': 49}, 'invalid']]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic bounded teaching model of a stipulated toy rating contract. Amounts are integer cents and factors exact rationals; it makes no claim of conformance with any filed rating plan, bureau manual or jurisdiction. 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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-insurance_premium_rating-trend-development-trend-midpoints","generated_at":"2026-09-29T14:47:10.166209+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Projected ultimate trended losses drive the indicated rate level for the prospective policy period.","repair":"Measure from experience midpoint (+6) to policy-period average accident date (+12).","root_cause":"The average accident date of an annual policy period is placed at +6 instead of +12 months.","sha256":"b7d10e3ea712104f3dfc12d410d5c4b2e38e8587b4758bc0676c92c08320cdd4","title":"Loss development and trend to rating period: Policy period midpoint treated like an accident year · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":47.653,"exit_code":1,"observations":[{"actual":16388954,"check":"immature year","expected":16756377,"passed":false},{"actual":9038146,"check":"second evaluation","expected":9260396,"passed":false},{"actual":7902883,"check":"mid development","expected":8080698,"passed":false},{"actual":5160160,"check":"fully developed except tail","expected":5236419,"passed":false},{"actual":5158707,"check":"beyond last factor","expected":5287139,"passed":false},{"actual":7938548,"check":"trend span whole years","expected":8137012,"passed":false},{"actual":10250564,"check":"trend span with remainder","expected":10402433,"passed":false},{"actual":"invalid","check":"non-annual age rejected","expected":"invalid","passed":true},{"actual":"invalid","check":"zero age rejected","expected":"invalid","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"immature year\", \"actual\": 16388954, \"expected\": 16756377, \"passed\": false}, {\"check\": \"second evaluation\", \"actual\": 9038146, \"expected\": 9260396, \"passed\": false}, {\"check\": \"mid development\", \"actual\": 7902883, \"expected\": 8080698, \"passed\": false}, {\"check\": \"fully developed except tail\", \"actual\": 5160160, \"expected\": 5236419, \"passed\": false}, {\"check\": \"beyond last factor\", \"actual\": 5158707, \"expected\": 5287139, \"passed\": false}, {\"check\": \"trend span whole years\", \"actual\": 7938548, \"expected\": 8137012, \"passed\": false}, {\"check\": \"trend span with remainder\", \"actual\": 10250564, \"expected\": 10402433, \"passed\": false}, {\"check\": \"non-annual age rejected\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"zero age rejected\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.671,"exit_code":1,"observations":[{"actual":16388954,"check":"immature year","expected":16756377,"passed":false},{"actual":9038146,"check":"second evaluation","expected":9260396,"passed":false},{"actual":7902883,"check":"mid development","expected":8080698,"passed":false},{"actual":5160160,"check":"fully developed except tail","expected":5236419,"passed":false},{"actual":5158707,"check":"beyond last factor","expected":5287139,"passed":false},{"actual":7938548,"check":"trend span whole years","expected":8137012,"passed":false},{"actual":10250564,"check":"trend span with remainder","expected":10402433,"passed":false},{"actual":"invalid","check":"non-annual age rejected","expected":"invalid","passed":true},{"actual":"invalid","check":"zero age rejected","expected":"invalid","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"immature year\", \"actual\": 16388954, \"expected\": 16756377, \"passed\": false}, {\"check\": \"second evaluation\", \"actual\": 9038146, \"expected\": 9260396, \"passed\": false}, {\"check\": \"mid development\", \"actual\": 7902883, \"expected\": 8080698, \"passed\": false}, {\"check\": \"fully developed except tail\", \"actual\": 5160160, \"expected\": 5236419, \"passed\": false}, {\"check\": \"beyond last factor\", \"actual\": 5158707, \"expected\": 5287139, \"passed\": false}, {\"check\": \"trend span whole years\", \"actual\": 7938548, \"expected\": 8137012, \"passed\": false}, {\"check\": \"trend span with remainder\", \"actual\": 10250564, \"expected\": 10402433, \"passed\": false}, {\"check\": \"non-annual age rejected\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"zero age rejected\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.151,"exit_code":0,"observations":[{"actual":16756377,"check":"immature year","expected":16756377,"passed":true},{"actual":9260396,"check":"second evaluation","expected":9260396,"passed":true},{"actual":8080698,"check":"mid development","expected":8080698,"passed":true},{"actual":5236419,"check":"fully developed except tail","expected":5236419,"passed":true},{"actual":5287139,"check":"beyond last factor","expected":5287139,"passed":true},{"actual":8137012,"check":"trend span whole years","expected":8137012,"passed":true},{"actual":10402433,"check":"trend span with remainder","expected":10402433,"passed":true},{"actual":"invalid","check":"non-annual age rejected","expected":"invalid","passed":true},{"actual":"invalid","check":"zero age rejected","expected":"invalid","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"immature year\", \"actual\": 16756377, \"expected\": 16756377, \"passed\": true}, {\"check\": \"second evaluation\", \"actual\": 9260396, \"expected\": 9260396, \"passed\": true}, {\"check\": \"mid development\", \"actual\": 8080698, \"expected\": 8080698, \"passed\": true}, {\"check\": \"fully developed except tail\", \"actual\": 5236419, \"expected\": 5236419, \"passed\": true}, {\"check\": \"beyond last factor\", \"actual\": 5287139, \"expected\": 5287139, \"passed\": true}, {\"check\": \"trend span whole years\", \"actual\": 8137012, \"expected\": 8137012, \"passed\": true}, {\"check\": \"trend span with remainder\", \"actual\": 10402433, \"expected\": 10402433, \"passed\": true}, {\"check\": \"non-annual age rejected\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}, {\"check\": \"zero age rejected\", \"actual\": \"invalid\", \"expected\": \"invalid\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}