Average Error: 58.3 → 0.0
Time: 22.5s
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 r52304 = x;
        double r52305 = exp(r52304);
        double r52306 = -r52304;
        double r52307 = exp(r52306);
        double r52308 = r52305 - r52307;
        double r52309 = r52305 + r52307;
        double r52310 = r52308 / r52309;
        return r52310;
}
↓
double f(double x) {
        double r52311 = x;
        double r52312 = tanh(r52311);
        return r52312;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 58.3

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019194 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))