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

Average Error: 0.4 → 0.4

Time: 2.0s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Derivation

1. Initial program 0.4

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

2. Final simplification 0.4

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

Reproduce

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