FA-16140 / Floating-point arithmetic / Member archive

Complementary log exponentials lose the distant tail · case 05

Complementary log exponentials lose the distant tail.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Evaluate log(1-exp(x)) for x <= 0; zero maps to negative infinity. Choose a cancellation-safe formula on either side of -log(2). Finite results are rendered to eleven significant decimal digits; modeled domain violations and arithmetic errors are explicit strings.

Why this case matters

An offline floating representation model isolates a reproducible arithmetic fault.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
far tail	`"0"`	`"-1.299581425e-24"`	Failed

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