Hyperbolic sine

Average Error: 58.1 → 0.0

Time: 2.9s

Precision: binary64

Math

\[\frac{e^{x} - e^{-x}}{2}\]

↓

\[\frac{2 \cdot \sinh x}{2}\]

Error

Bits error versus x

Derivation

1. Initial program 58.1

   \[\frac{e^{x} - e^{-x}}{2}\]
2. Using strategy rm

3. Applied sinh-undef 0.0

   \[\leadsto \frac{\color{blue}{2 \cdot \sinh x}}{2}\]

4. Final simplification 0.0

   \[\leadsto \frac{2 \cdot \sinh x}{2}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x)
  :name "Hyperbolic sine"
  :precision binary64
  (/ (- (exp x) (exp (neg x))) 2.0))