FA-97286 / Recipe scaling and nutrition / Open access
Macronutrient target splitter: carb from remainder · case 01
Totals drift a few calories from the target because fat rounding is not absorbed.
ROOT CAUSE
Carbs are computed from the ratio independently rather than from energy left after rounded fat.
THE FAILURE
Carbs are computed from the ratio independently rather than from energy left after rounded fat.
Unsuccessful approach: Subtracting 4 kcal per fat gram leaves too much energy for carbs.
Case contract
split = [protein%, carb%, fat%] must sum to 100 else "error: split". protein_g = max(half-up kcal*p/400, ceiling(1.6*weight_kg)). Remaining kcal = kcal - 4*protein_g is divided between carb and fat in the ratio c:f; fat_g = half-up(rem*f/(c+f)/9); carb_g = half-up((rem - 9*fat_g)/4). Return [protein_g, carb_g, fat_g].
Why this case matters
Meal-plan generators turn calorie targets into gram targets with a protein floor by body weight.
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(kcal, weight_kg, split):
p, c, f = split
if p + c + f != 100:
return 'error: split'
def r(x):
return math.floor(x + Fraction(1, 2))
protein_g = max(r(Fraction(kcal * p, 400)), math.ceil(Fraction(16, 10) * weight_kg))
rem = kcal - 4 * protein_g
fat_g = r(Fraction(rem * f, c + f) / 9)
carb_g = r(Fraction(rem * c, c + f) / 4)
return [protein_g, carb_g, fat_g]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['balanced', [2000, 70, [30, 40, 30]], [150, 199, 67]],
['protein floor binds', [1500, 120, [15, 55, 30]], [192, 118, 29]],
['bad split', [2000, 70, [30, 40, 31]], 'error: split'],
['regression: carb from remainder', [2500, 83, [25, 45, 30]], [156, 282, 83]],
['repair check: carb from remainder', [1800, 100, [40, 30, 30]], [180, 135, 60]],
['generated control 1', [3000, 91, [30, 40, 29]], 'error: split'],
['generated control 2', [1800, 118, [30, 40, 29]], 'error: split'],
['generated control 3', [2000, 60, [20, 50, 25]], 'error: split']],
[['protein floor binds', [1500, 120, [15, 55, 30]], [192, 118, 29]],
['bad split', [2000, 70, [30, 40, 31]], 'error: split'],
['split under 100', [2000, 70, [30, 40, 20]], 'error: split'],
['regression: carb from remainder', [2000, 120, [15, 55, 30]], [192, 200, 48]],
['repair check: carb from remainder', [2500, 60, [40, 30, 30]], [250, 188, 83]],
['generated control 1', [2500, 120, [35, 35, 30]], [219, 219, 83]],
['generated control 2', [2200, 60, [10, 60, 30]], [96, 303, 67]],
['generated control 3', [2200, 120, [30, 40, 30]], [192, 205, 68]]],
[['bad split', [2000, 70, [30, 40, 31]], 'error: split'],
['split under 100', [2000, 70, [30, 40, 20]], 'error: split'],
['fractional floor', [1200, 83, [20, 50, 30]], [133, 104, 28]],
['regression: carb from remainder', [2500, 60, [10, 60, 30]], [96, 354, 78]],
['repair check: carb from remainder', [2500, 83, [35, 35, 30]], [219, 219, 83]],
['generated control 1', [3000, 60, [15, 55, 30]], [113, 412, 100]],
['generated control 2', [2500, 100, [30, 40, 31]], 'error: split'],
['generated control 3', [2000, 118, [20, 50, 25]], 'error: split']],
[['split under 100', [2000, 70, [30, 40, 20]], 'error: split'],
['fractional floor', [1200, 83, [20, 50, 30]], [133, 104, 28]],
['balanced', [2000, 70, [30, 40, 30]], [150, 199, 67]],
['regression: carb from remainder', [2000, 72, [30, 40, 30]], [150, 199, 67]],
['repair check: carb from remainder', [1500, 120, [40, 30, 30]], [192, 91, 41]],
['generated control 1', [1800, 72, [15, 55, 30]], [116, 217, 52]],
['generated control 2', [2000, 91, [30, 40, 31]], 'error: split'],
['generated control 3', [2200, 100, [10, 60, 30]], [160, 260, 58]]],
[['fractional floor', [1200, 83, [20, 50, 30]], [133, 104, 28]],
['balanced', [2000, 70, [30, 40, 30]], [150, 199, 67]],
['protein floor binds', [1500, 120, [15, 55, 30]], [192, 118, 29]],
['regression: carb from remainder', [1800, 100, [20, 50, 30]], [160, 182, 48]],
['repair check: carb from remainder', [1500, 118, [20, 50, 30]], [189, 116, 31]],
['generated control 1', [2200, 100, [20, 50, 25]], 'error: split'],
['generated control 2', [3000, 91, [35, 35, 30]], [263, 262, 100]],
['generated control 3', [2500, 72, [25, 45, 30]], [156, 282, 83]]]]
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 |
|---|---|---|---|
| balanced | [150, 200, 67] | [150, 199, 67] | Failed |
| protein floor binds | [192, 118, 29] | [192, 118, 29] | Passed |
| bad split | error: split | error: split | Passed |
| regression: carb from remainder | [156, 281, 83] | [156, 282, 83] | Failed |
| repair check: carb from remainder | [180, 135, 60] | [180, 135, 60] | Passed |
| generated control 1 | error: split | error: split | Passed |
| generated control 2 | error: split | error: split | Passed |
| generated control 3 | error: split | error: split | Passed |
SHA-256 / 0eaaa659ac9561d8a8f9abf6c255c63ee78d4ea8b0173b628c47434a2f150192
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(kcal, weight_kg, split):
p, c, f = split
if p + c + f != 100:
return 'error: split'
def r(x):
return math.floor(x + Fraction(1, 2))
protein_g = max(r(Fraction(kcal * p, 400)), math.ceil(Fraction(16, 10) * weight_kg))
rem = kcal - 4 * protein_g
fat_g = r(Fraction(rem * f, c + f) / 9)
carb_g = r(Fraction(rem - 4 * fat_g, 4))
return [protein_g, carb_g, fat_g]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['balanced', [2000, 70, [30, 40, 30]], [150, 199, 67]],
['protein floor binds', [1500, 120, [15, 55, 30]], [192, 118, 29]],
['bad split', [2000, 70, [30, 40, 31]], 'error: split'],
['regression: carb from remainder', [2500, 83, [25, 45, 30]], [156, 282, 83]],
['repair check: carb from remainder', [1800, 100, [40, 30, 30]], [180, 135, 60]],
['generated control 1', [3000, 91, [30, 40, 29]], 'error: split'],
['generated control 2', [1800, 118, [30, 40, 29]], 'error: split'],
['generated control 3', [2000, 60, [20, 50, 25]], 'error: split']],
[['protein floor binds', [1500, 120, [15, 55, 30]], [192, 118, 29]],
['bad split', [2000, 70, [30, 40, 31]], 'error: split'],
['split under 100', [2000, 70, [30, 40, 20]], 'error: split'],
['regression: carb from remainder', [2000, 120, [15, 55, 30]], [192, 200, 48]],
['repair check: carb from remainder', [2500, 60, [40, 30, 30]], [250, 188, 83]],
['generated control 1', [2500, 120, [35, 35, 30]], [219, 219, 83]],
['generated control 2', [2200, 60, [10, 60, 30]], [96, 303, 67]],
['generated control 3', [2200, 120, [30, 40, 30]], [192, 205, 68]]],
[['bad split', [2000, 70, [30, 40, 31]], 'error: split'],
['split under 100', [2000, 70, [30, 40, 20]], 'error: split'],
['fractional floor', [1200, 83, [20, 50, 30]], [133, 104, 28]],
['regression: carb from remainder', [2500, 60, [10, 60, 30]], [96, 354, 78]],
['repair check: carb from remainder', [2500, 83, [35, 35, 30]], [219, 219, 83]],
['generated control 1', [3000, 60, [15, 55, 30]], [113, 412, 100]],
['generated control 2', [2500, 100, [30, 40, 31]], 'error: split'],
['generated control 3', [2000, 118, [20, 50, 25]], 'error: split']],
[['split under 100', [2000, 70, [30, 40, 20]], 'error: split'],
['fractional floor', [1200, 83, [20, 50, 30]], [133, 104, 28]],
['balanced', [2000, 70, [30, 40, 30]], [150, 199, 67]],
['regression: carb from remainder', [2000, 72, [30, 40, 30]], [150, 199, 67]],
['repair check: carb from remainder', [1500, 120, [40, 30, 30]], [192, 91, 41]],
['generated control 1', [1800, 72, [15, 55, 30]], [116, 217, 52]],
['generated control 2', [2000, 91, [30, 40, 31]], 'error: split'],
['generated control 3', [2200, 100, [10, 60, 30]], [160, 260, 58]]],
[['fractional floor', [1200, 83, [20, 50, 30]], [133, 104, 28]],
['balanced', [2000, 70, [30, 40, 30]], [150, 199, 67]],
['protein floor binds', [1500, 120, [15, 55, 30]], [192, 118, 29]],
['regression: carb from remainder', [1800, 100, [20, 50, 30]], [160, 182, 48]],
['repair check: carb from remainder', [1500, 118, [20, 50, 30]], [189, 116, 31]],
['generated control 1', [2200, 100, [20, 50, 25]], 'error: split'],
['generated control 2', [3000, 91, [35, 35, 30]], [263, 262, 100]],
['generated control 3', [2500, 72, [25, 45, 30]], [156, 282, 83]]]]
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 |
|---|---|---|---|
| balanced | [150, 283, 67] | [150, 199, 67] | Failed |
| protein floor binds | [192, 154, 29] | [192, 118, 29] | Failed |
| bad split | error: split | error: split | Passed |
| regression: carb from remainder | [156, 386, 83] | [156, 282, 83] | Failed |
| repair check: carb from remainder | [180, 210, 60] | [180, 135, 60] | Failed |
| generated control 1 | error: split | error: split | Passed |
| generated control 2 | error: split | error: split | Passed |
| generated control 3 | error: split | error: split | Passed |
SHA-256 / 7a744a3753cd1ef5f299b67eebc5c52e0be4583511a6d8f5d291f94e5611c8a9
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.
Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.
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Sign in to the archive ↗Verification & scope
A deterministic toy contract stated in full here; it is a bounded teaching model, not an authoritative reference or standards implementation. 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 2026-09-29T14:52:30.723097+00:00.
Case digest / 181441ba20fbcd382b9571ebbf9033223ec3f5a6dd1fe27e1323280fc99a59c7