(+ (+ 1 (sin x)) (sin x))

Average Error: 0.3 → 0.2

Time: 1.1s

Precision: binary64

Math

\[\left(1 + \sin x\right) + \sin x\]

↓

\[2 \cdot \sin x + 1\]

C

double code(double x) {
	return ((double) (((double) (1.0 + ((double) sin(x)))) + ((double) sin(x))));
}

↓

double code(double x) {
	return ((double) (((double) (2.0 * ((double) sin(x)))) + 1.0));
}

Error

Bits error versus x

Derivation

1. Initial program 0.3

   \[\left(1 + \sin x\right) + \sin x\]

2. Simplified 0.2

   \[\leadsto \color{blue}{2 \cdot \sin x + 1}\]

3. Final simplification 0.2

   \[\leadsto 2 \cdot \sin x + 1\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (+ 1 (sin x)) (sin x))"
  :precision binary64
  (+ (+ 1.0 (sin x)) (sin x)))