(- (cos (+ x e)) (cos x))

Average Error: 39.3 → 39.3

Time: 3.2s

Precision: binary64

Math

\[\cos \left(x + e\right) - \cos x\]

↓

\[\cos \left(x + e\right) - \cos x\]

C

double code(double x, double e) {
	return ((double) (((double) cos(((double) (x + e)))) - ((double) cos(x))));
}

↓

double code(double x, double e) {
	return ((double) (((double) cos(((double) (x + e)))) - ((double) cos(x))));
}

Error

Bits error versus x

Bits error versus e

Derivation

1. Initial program 39.3

   \[\cos \left(x + e\right) - \cos x\]

2. Final simplification 39.3

   \[\leadsto \cos \left(x + e\right) - \cos x\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x e)
  :name "(- (cos (+ x e)) (cos x))"
  :precision binary64
  (- (cos (+ x e)) (cos x)))