Average Error: 58.1 → 0.0

Time: 15.2s

Precision: 64

Internal Precision: 128

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

↓

\[\tanh x\]

Error

The X axis uses an exponential scale — Bits error versus x

The X axis uses an exponential scale — Bits error versus x

Derivation

Initial program 58.1
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
Using strategy rm
Applied tanh-undef0.0
\[\leadsto \color{blue}{\tanh x}\]
Final simplification0.0
\[\leadsto \tanh x\]

Reproduce

herbie shell --seed 2019050 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))