FA-63876 / Medication dosing calculations / Open access
Pediatric mg/kg/day dose divided by interval: daily ceiling · case 01
Large children receive more than the maximum daily amount when the single-dose cap is loose.
ROOT CAUSE
The weight-based daily amount is never limited by max_daily_mg.
VERIFIED REPAIR
Cap the daily amount at max_daily_mg before dividing it into doses.
Unsuccessful approach: Multiplying the daily cap by doses/day treats it as a per-dose limit and never binds.
Case contract
Input {weight_kg, mg_per_kg_day, interval_h (divides 24), max_single_mg, max_daily_mg, round_mg}. Toy rule: doses/day = 24 / interval_h; daily = min(mg_per_kg_day * weight, max_daily_mg); per-dose = min(daily / doses, max_single_mg), then rounded DOWN to a multiple of round_mg. Return {doses_per_day, dose_mg, daily_mg = dose_mg * doses_per_day}.
Why this case matters
Divided-dose calculators must count administrations per day correctly and apply both ceilings before rounding down to a measurable increment.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
w = Fraction(str(x['weight_kg']))
per_day = 24 // x['interval_h']
daily = Fraction(str(x['mg_per_kg_day'])) * w
dose = min(daily / per_day, x['max_single_mg'])
inc = Fraction(str(x['round_mg']))
dose = math.floor(dose / inc) * inc
return {'doses_per_day': per_day, 'dose_mg': float(dose), 'daily_mg': float(dose * per_day)}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('every 8 hours normal order',
{'weight_kg': 21,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 220.0, 'daily_mg': 660.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 11,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 110.0, 'daily_mg': 440.0}),
('daily ceiling limits large child',
{'weight_kg': 61,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 41,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 14,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 10.0, 'daily_mg': 10.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 22,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 165.0, 'daily_mg': 330.0})],
[('every 8 hours normal order',
{'weight_kg': 22,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 230.0, 'daily_mg': 690.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 12,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 120.0, 'daily_mg': 480.0}),
('daily ceiling limits large child',
{'weight_kg': 62,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 42,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 19,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 15.0, 'daily_mg': 15.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 24,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 180.0, 'daily_mg': 360.0})],
[('every 8 hours normal order',
{'weight_kg': 23,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 245.0, 'daily_mg': 735.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 13,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 130.0, 'daily_mg': 520.0}),
('daily ceiling limits large child',
{'weight_kg': 63,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 43,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 24,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 20.0, 'daily_mg': 20.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 26,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 195.0, 'daily_mg': 390.0})],
[('every 8 hours normal order',
{'weight_kg': 24,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 255.0, 'daily_mg': 765.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 14,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 140.0, 'daily_mg': 560.0}),
('daily ceiling limits large child',
{'weight_kg': 64,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 44,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 29,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 25.0, 'daily_mg': 25.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 28,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 210.0, 'daily_mg': 420.0})],
[('every 8 hours normal order',
{'weight_kg': 25,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 265.0, 'daily_mg': 795.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 15,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 150.0, 'daily_mg': 600.0}),
('daily ceiling limits large child',
{'weight_kg': 65,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 45,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 34,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 30.0, 'daily_mg': 30.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 30,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 225.0, 'daily_mg': 450.0})]]
for label, args, expected in fixtures[N-1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| every 8 hours normal order | {'daily_mg': 660.0, 'dose_mg': 220.0, 'doses_per_day': 3} | {'daily_mg': 660.0, 'dose_mg': 220.0, 'doses_per_day': 3} | Passed |
| every 6 hours with 2.5 mg steps | {'daily_mg': 440.0, 'dose_mg': 110.0, 'doses_per_day': 4} | {'daily_mg': 440.0, 'dose_mg': 110.0, 'doses_per_day': 4} | Passed |
| daily ceiling limits large child | {'daily_mg': 3000.0, 'dose_mg': 1500.0, 'doses_per_day': 2} | {'daily_mg': 2000.0, 'dose_mg': 1000.0, 'doses_per_day': 2} | Failed |
| single-dose ceiling | {'daily_mg': 2000.0, 'dose_mg': 1000.0, 'doses_per_day': 2} | {'daily_mg': 2000.0, 'dose_mg': 1000.0, 'doses_per_day': 2} | Passed |
| rounding never exceeds calculated dose | {'daily_mg': 10.0, 'dose_mg': 10.0, 'doses_per_day': 1} | {'daily_mg': 10.0, 'dose_mg': 10.0, 'doses_per_day': 1} | Passed |
| twice daily control | {'daily_mg': 330.0, 'dose_mg': 165.0, 'doses_per_day': 2} | {'daily_mg': 330.0, 'dose_mg': 165.0, 'doses_per_day': 2} | Passed |
SHA-256 / 89503789f214e3416f70045e38f27f563dfab788bd0a8aede59b13faff1f81f7
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
w = Fraction(str(x['weight_kg']))
per_day = 24 // x['interval_h']
daily = min(Fraction(str(x['mg_per_kg_day'])) * w, x['max_daily_mg'] * per_day)
dose = min(daily / per_day, x['max_single_mg'])
inc = Fraction(str(x['round_mg']))
dose = math.floor(dose / inc) * inc
return {'doses_per_day': per_day, 'dose_mg': float(dose), 'daily_mg': float(dose * per_day)}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('every 8 hours normal order',
{'weight_kg': 21,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 220.0, 'daily_mg': 660.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 11,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 110.0, 'daily_mg': 440.0}),
('daily ceiling limits large child',
{'weight_kg': 61,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 41,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 14,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 10.0, 'daily_mg': 10.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 22,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 165.0, 'daily_mg': 330.0})],
[('every 8 hours normal order',
{'weight_kg': 22,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 230.0, 'daily_mg': 690.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 12,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 120.0, 'daily_mg': 480.0}),
('daily ceiling limits large child',
{'weight_kg': 62,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 42,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 19,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 15.0, 'daily_mg': 15.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 24,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 180.0, 'daily_mg': 360.0})],
[('every 8 hours normal order',
{'weight_kg': 23,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 245.0, 'daily_mg': 735.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 13,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 130.0, 'daily_mg': 520.0}),
('daily ceiling limits large child',
{'weight_kg': 63,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 43,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 24,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 20.0, 'daily_mg': 20.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 26,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 195.0, 'daily_mg': 390.0})],
[('every 8 hours normal order',
{'weight_kg': 24,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 255.0, 'daily_mg': 765.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 14,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 140.0, 'daily_mg': 560.0}),
('daily ceiling limits large child',
{'weight_kg': 64,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 44,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 29,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 25.0, 'daily_mg': 25.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 28,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 210.0, 'daily_mg': 420.0})],
[('every 8 hours normal order',
{'weight_kg': 25,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 265.0, 'daily_mg': 795.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 15,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 150.0, 'daily_mg': 600.0}),
('daily ceiling limits large child',
{'weight_kg': 65,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 45,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 34,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 30.0, 'daily_mg': 30.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 30,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 225.0, 'daily_mg': 450.0})]]
for label, args, expected in fixtures[N-1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| every 8 hours normal order | {'daily_mg': 660.0, 'dose_mg': 220.0, 'doses_per_day': 3} | {'daily_mg': 660.0, 'dose_mg': 220.0, 'doses_per_day': 3} | Passed |
| every 6 hours with 2.5 mg steps | {'daily_mg': 440.0, 'dose_mg': 110.0, 'doses_per_day': 4} | {'daily_mg': 440.0, 'dose_mg': 110.0, 'doses_per_day': 4} | Passed |
| daily ceiling limits large child | {'daily_mg': 3000.0, 'dose_mg': 1500.0, 'doses_per_day': 2} | {'daily_mg': 2000.0, 'dose_mg': 1000.0, 'doses_per_day': 2} | Failed |
| single-dose ceiling | {'daily_mg': 2000.0, 'dose_mg': 1000.0, 'doses_per_day': 2} | {'daily_mg': 2000.0, 'dose_mg': 1000.0, 'doses_per_day': 2} | Passed |
| rounding never exceeds calculated dose | {'daily_mg': 10.0, 'dose_mg': 10.0, 'doses_per_day': 1} | {'daily_mg': 10.0, 'dose_mg': 10.0, 'doses_per_day': 1} | Passed |
| twice daily control | {'daily_mg': 330.0, 'dose_mg': 165.0, 'doses_per_day': 2} | {'daily_mg': 330.0, 'dose_mg': 165.0, 'doses_per_day': 2} | Passed |
SHA-256 / cd0ac88c67b1707d1c37af57d1bce724532093f42a303ee231267dc6518e5eca
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
w = Fraction(str(x['weight_kg']))
per_day = 24 // x['interval_h']
daily = min(Fraction(str(x['mg_per_kg_day'])) * w, x['max_daily_mg'])
dose = min(daily / per_day, x['max_single_mg'])
inc = Fraction(str(x['round_mg']))
dose = math.floor(dose / inc) * inc
return {'doses_per_day': per_day, 'dose_mg': float(dose), 'daily_mg': float(dose * per_day)}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('every 8 hours normal order',
{'weight_kg': 21,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 220.0, 'daily_mg': 660.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 11,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 110.0, 'daily_mg': 440.0}),
('daily ceiling limits large child',
{'weight_kg': 61,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 41,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 14,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 10.0, 'daily_mg': 10.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 22,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 165.0, 'daily_mg': 330.0})],
[('every 8 hours normal order',
{'weight_kg': 22,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 230.0, 'daily_mg': 690.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 12,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 120.0, 'daily_mg': 480.0}),
('daily ceiling limits large child',
{'weight_kg': 62,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 42,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 19,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 15.0, 'daily_mg': 15.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 24,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 180.0, 'daily_mg': 360.0})],
[('every 8 hours normal order',
{'weight_kg': 23,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 245.0, 'daily_mg': 735.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 13,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 130.0, 'daily_mg': 520.0}),
('daily ceiling limits large child',
{'weight_kg': 63,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 43,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 24,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 20.0, 'daily_mg': 20.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 26,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 195.0, 'daily_mg': 390.0})],
[('every 8 hours normal order',
{'weight_kg': 24,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 255.0, 'daily_mg': 765.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 14,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 140.0, 'daily_mg': 560.0}),
('daily ceiling limits large child',
{'weight_kg': 64,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 44,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 29,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 25.0, 'daily_mg': 25.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 28,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 210.0, 'daily_mg': 420.0})],
[('every 8 hours normal order',
{'weight_kg': 25,
'mg_per_kg_day': 32,
'interval_h': 8,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 5},
{'doses_per_day': 3, 'dose_mg': 265.0, 'daily_mg': 795.0}),
('every 6 hours with 2.5 mg steps',
{'weight_kg': 15,
'mg_per_kg_day': 40,
'interval_h': 6,
'max_single_mg': 500,
'max_daily_mg': 2000,
'round_mg': '2.5'},
{'doses_per_day': 4, 'dose_mg': 150.0, 'daily_mg': 600.0}),
('daily ceiling limits large child',
{'weight_kg': 65,
'mg_per_kg_day': 50,
'interval_h': 12,
'max_single_mg': 1500,
'max_daily_mg': 2000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('single-dose ceiling',
{'weight_kg': 45,
'mg_per_kg_day': 100,
'interval_h': 12,
'max_single_mg': 1000,
'max_daily_mg': 5000,
'round_mg': 5},
{'doses_per_day': 2, 'dose_mg': 1000.0, 'daily_mg': 2000.0}),
('rounding never exceeds calculated dose',
{'weight_kg': 34,
'mg_per_kg_day': 1,
'interval_h': 24,
'max_single_mg': 500,
'max_daily_mg': 500,
'round_mg': 5},
{'doses_per_day': 1, 'dose_mg': 30.0, 'daily_mg': 30.0}),
('twice daily control',
{'weight_kg': 15,
'mg_per_kg_day': 30,
'interval_h': 12,
'max_single_mg': 500,
'max_daily_mg': 1500,
'round_mg': 1},
{'doses_per_day': 2, 'dose_mg': 225.0, 'daily_mg': 450.0})]]
for label, args, expected in fixtures[N-1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| every 8 hours normal order | {'daily_mg': 660.0, 'dose_mg': 220.0, 'doses_per_day': 3} | {'daily_mg': 660.0, 'dose_mg': 220.0, 'doses_per_day': 3} | Passed |
| every 6 hours with 2.5 mg steps | {'daily_mg': 440.0, 'dose_mg': 110.0, 'doses_per_day': 4} | {'daily_mg': 440.0, 'dose_mg': 110.0, 'doses_per_day': 4} | Passed |
| daily ceiling limits large child | {'daily_mg': 2000.0, 'dose_mg': 1000.0, 'doses_per_day': 2} | {'daily_mg': 2000.0, 'dose_mg': 1000.0, 'doses_per_day': 2} | Passed |
| single-dose ceiling | {'daily_mg': 2000.0, 'dose_mg': 1000.0, 'doses_per_day': 2} | {'daily_mg': 2000.0, 'dose_mg': 1000.0, 'doses_per_day': 2} | Passed |
| rounding never exceeds calculated dose | {'daily_mg': 10.0, 'dose_mg': 10.0, 'doses_per_day': 1} | {'daily_mg': 10.0, 'dose_mg': 10.0, 'doses_per_day': 1} | Passed |
| twice daily control | {'daily_mg': 330.0, 'dose_mg': 165.0, 'doses_per_day': 2} | {'daily_mg': 330.0, 'dose_mg': 165.0, 'doses_per_day': 2} | Passed |
SHA-256 / 554b1c8d4d7287825c88725f774ac420ca44def84a74abf15542c063553f9798
Verification & scope
A deterministic toy software model with explicitly stipulated thresholds and formulas; it is not clinical guidance, not a validated medical calculator, and makes no claim of conformance to any published protocol. Numbered variants vary patient and order inputs. 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 2026-09-29T14:47:18.968666+00:00.
Case digest / 8a872d4661bede668d780c7da777234a8b54bf3a7a72715cffdef2fedfa2e800