Average Error: 58.1 → 0.0
Time: 3.7s
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 r52901 = x;
        double r52902 = exp(r52901);
        double r52903 = -r52901;
        double r52904 = exp(r52903);
        double r52905 = r52902 - r52904;
        double r52906 = r52902 + r52904;
        double r52907 = r52905 / r52906;
        return r52907;
}
↓
double f(double x) {
        double r52908 = x;
        double r52909 = tanh(r52908);
        return r52909;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2020021 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))