FA-16368 / Floating-point arithmetic / Member archive

Cosine decrement fails to square the half-angle sine · case 03

Cosine decrement fails to square the half-angle sine.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Evaluate cos(x)-1 for finite x without cancellation using the half-angle identity. 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
tiny	`"-2.7939677238e-09"`	`"-3.9031278209e-18"`	Failed

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