Average Error: 58.4 → 0.0
Time: 5.1s
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 r30741 = x;
        double r30742 = exp(r30741);
        double r30743 = -r30741;
        double r30744 = exp(r30743);
        double r30745 = r30742 - r30744;
        double r30746 = r30742 + r30744;
        double r30747 = r30745 / r30746;
        return r30747;
}
↓
double f(double x) {
        double r30748 = x;
        double r30749 = tanh(r30748);
        return r30749;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.4

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2020033 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))