(- (sin x) (/ (/ x 2) (- (- (cos x)) (/ 1 2))))

Average Error: 0.3 → 0.3

Time: 2.0s

Precision: binary64

Math

\[\sin x - \frac{\frac{x}{2}}{\left(-\cos x\right) - \frac{1}{2}}\]

↓

\[\sin x - \frac{\frac{x}{2}}{\left(-\cos x\right) - \frac{1}{2}}\]

Error

Bits error versus x

Derivation

1. Initial program 0.3

   \[\sin x - \frac{\frac{x}{2}}{\left(-\cos x\right) - \frac{1}{2}}\]

2. Final simplification 0.3

   \[\leadsto \sin x - \frac{\frac{x}{2}}{\left(-\cos x\right) - \frac{1}{2}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (sin x) (/ (/ x 2) (- (- (cos x)) (/ 1 2))))"
  :precision binary64
  (- (sin x) (/ (/ x 2.0) (- (neg (cos x)) (/ 1.0 2.0)))))