FA-16362 / Floating-point arithmetic / Member archive

Cosine decrement forgets half-angle reduction · case 02

Cosine decrement forgets half-angle reduction.

Member previewVariant 2 · 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	`"-6.9388939039e-18"`	`"-1.734723476e-18"`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.