(- (sqrt (+ x 1)) (cos x))

Average Error: 39.3 → 39.3

Time: 1.5s

Precision: binary64

Math

\[\sqrt{x + 1} - \cos x\]

↓

\[\sqrt{x + 1} - \cos x\]

C

double code(double x) {
	return ((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) cos(x))));
}

↓

double code(double x) {
	return ((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) cos(x))));
}

Error

Bits error versus x

Derivation

1. Initial program 39.3

   \[\sqrt{x + 1} - \cos x\]

2. Final simplification 39.3

   \[\leadsto \sqrt{x + 1} - \cos x\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (sqrt (+ x 1)) (cos x))"
  :precision binary64
  (- (sqrt (+ x 1.0)) (cos x)))