Average Error: 58.1 → 0.0
Time: 32.7s
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 r2267778 = x;
        double r2267779 = exp(r2267778);
        double r2267780 = -r2267778;
        double r2267781 = exp(r2267780);
        double r2267782 = r2267779 - r2267781;
        double r2267783 = r2267779 + r2267781;
        double r2267784 = r2267782 / r2267783;
        return r2267784;
}
↓
double f(double x) {
        double r2267785 = x;
        double r2267786 = tanh(r2267785);
        return r2267786;
}

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 2019146 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))