(- (sin (+ x eps)) (sin x))

Average Error: 37.1 → 37.1

Time: 3.4s

Precision: binary64

Math

\[\sin \left(x + \varepsilon\right) - \sin x\]

↓

\[\sin \left(x + \varepsilon\right) - \sin x\]

C

double code(double x, double eps) {
	return ((double) (((double) sin(((double) (x + eps)))) - ((double) sin(x))));
}

↓

double code(double x, double eps) {
	return ((double) (((double) sin(((double) (x + eps)))) - ((double) sin(x))));
}

Error

Bits error versus x

Bits error versus eps

Derivation

1. Initial program 37.1

   \[\sin \left(x + \varepsilon\right) - \sin x\]

2. Final simplification 37.1

   \[\leadsto \sin \left(x + \varepsilon\right) - \sin x\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x eps)
  :name "(- (sin (+ x eps)) (sin x))"
  :precision binary64
  (- (sin (+ x eps)) (sin x)))