(+ (cos x) (cos x))

Average Error: 0 → 0

Time: 987.0ms

Precision: binary64

Math

\[\cos x + \cos x\]

↓

\[2 \cdot \cos x\]

C

double code(double x) {
	return ((double) (((double) cos(x)) + ((double) cos(x))));
}

↓

double code(double x) {
	return ((double) (2.0 * ((double) cos(x))));
}

Error

Bits error versus x

Derivation

1. Initial program 0

   \[\cos x + \cos x\]

2. Simplified 0

   \[\leadsto \color{blue}{2 \cdot \cos x}\]

3. Final simplification 0

   \[\leadsto 2 \cdot \cos x\]

Reproduce

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