Average Error: 58.0 → 0.0
Time: 17.2s
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 r2234761 = x;
        double r2234762 = exp(r2234761);
        double r2234763 = -r2234761;
        double r2234764 = exp(r2234763);
        double r2234765 = r2234762 - r2234764;
        double r2234766 = r2234762 + r2234764;
        double r2234767 = r2234765 / r2234766;
        return r2234767;
}
↓
double f(double x) {
        double r2234768 = x;
        double r2234769 = tanh(r2234768);
        return r2234769;
}

Error

Bits error versus x

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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)))))