Average Error: 58.2 → 0.0
Time: 23.2s
Precision: 64
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
↓
\[\tanh x\]
\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}
↓
\tanh x
double f(double x) {
        double r54714 = x;
        double r54715 = exp(r54714);
        double r54716 = -r54714;
        double r54717 = exp(r54716);
        double r54718 = r54715 - r54717;
        double r54719 = r54715 + r54717;
        double r54720 = r54718 / r54719;
        return r54720;
}
↓
double f(double x) {
        double r54721 = x;
        double r54722 = tanh(r54721);
        return r54722;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.2

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

  3. Applied tanh-undef0.0

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

  4. Final simplification0.0

    \[\leadsto \tanh x\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))