Average Error: 58.1 → 0.0
Time: 4.8s
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 r32885 = x;
        double r32886 = exp(r32885);
        double r32887 = -r32885;
        double r32888 = exp(r32887);
        double r32889 = r32886 - r32888;
        double r32890 = r32886 + r32888;
        double r32891 = r32889 / r32890;
        return r32891;
}
↓
double f(double x) {
        double r32892 = x;
        double r32893 = tanh(r32892);
        return r32893;
}

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 2020060 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))