Average Error: 58.1 → 0.0
Time: 36.9s
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 r2837833 = x;
        double r2837834 = exp(r2837833);
        double r2837835 = -r2837833;
        double r2837836 = exp(r2837835);
        double r2837837 = r2837834 - r2837836;
        double r2837838 = r2837834 + r2837836;
        double r2837839 = r2837837 / r2837838;
        return r2837839;
}
↓
double f(double x) {
        double r2837840 = x;
        double r2837841 = tanh(r2837840);
        return r2837841;
}

Error

Bits error versus x

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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 2019112 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))