Average Error: 58.2 → 0.0
Time: 34.6s
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 r6297822 = x;
        double r6297823 = exp(r6297822);
        double r6297824 = -r6297822;
        double r6297825 = exp(r6297824);
        double r6297826 = r6297823 - r6297825;
        double r6297827 = r6297823 + r6297825;
        double r6297828 = r6297826 / r6297827;
        return r6297828;
}
↓
double f(double x) {
        double r6297829 = x;
        double r6297830 = tanh(r6297829);
        return r6297830;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 58.2

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019128 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))