Average Error: 58.2 → 0.0
Time: 17.9s
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 r2719095 = x;
        double r2719096 = exp(r2719095);
        double r2719097 = -r2719095;
        double r2719098 = exp(r2719097);
        double r2719099 = r2719096 - r2719098;
        double r2719100 = r2719096 + r2719098;
        double r2719101 = r2719099 / r2719100;
        return r2719101;
}
↓
double f(double x) {
        double r2719102 = x;
        double r2719103 = tanh(r2719102);
        return r2719103;
}

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 2019172 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))