Average Error: 58.0 → 0.0
Time: 18.8s
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 r2234788 = x;
        double r2234789 = exp(r2234788);
        double r2234790 = -r2234788;
        double r2234791 = exp(r2234790);
        double r2234792 = r2234789 - r2234791;
        double r2234793 = r2234789 + r2234791;
        double r2234794 = r2234792 / r2234793;
        return r2234794;
}
↓
double f(double x) {
        double r2234795 = x;
        double r2234796 = tanh(r2234795);
        return r2234796;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 58.0

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019163 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))