Average Error: 58.1 → 0.0
Time: 20.0s
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 r1102679 = x;
        double r1102680 = exp(r1102679);
        double r1102681 = -r1102679;
        double r1102682 = exp(r1102681);
        double r1102683 = r1102680 - r1102682;
        double r1102684 = r1102680 + r1102682;
        double r1102685 = r1102683 / r1102684;
        return r1102685;
}
↓
double f(double x) {
        double r1102686 = x;
        double r1102687 = tanh(r1102686);
        return r1102687;
}

Error

Bits error versus x

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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 2019153 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))