Average Error: 58.1 → 0.0
Time: 28.3s
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 r6024822 = x;
        double r6024823 = exp(r6024822);
        double r6024824 = -r6024822;
        double r6024825 = exp(r6024824);
        double r6024826 = r6024823 - r6024825;
        double r6024827 = r6024823 + r6024825;
        double r6024828 = r6024826 / r6024827;
        return r6024828;
}
↓
double f(double x) {
        double r6024829 = x;
        double r6024830 = tanh(r6024829);
        return r6024830;
}

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 2019173 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))