Hyperbolic tangent

Average Error: 58.0 → 0.0

Time: 2.9s

Precision: binary64

Math

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

↓

\[\tanh x\]

Error

Bits error versus x

Derivation

1. Initial program 58.0

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

3. Applied tanh-undef 0.0

   \[\leadsto \color{blue}{\tanh x}\]

4. Final simplification 0.0

   \[\leadsto \tanh x\]

Reproduce

herbie shell --seed 2020169 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))))