Average Error: 58.1 → 0.0
Time: 26.0s
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 r51191 = x;
        double r51192 = exp(r51191);
        double r51193 = -r51191;
        double r51194 = exp(r51193);
        double r51195 = r51192 - r51194;
        double r51196 = r51192 + r51194;
        double r51197 = r51195 / r51196;
        return r51197;
}
↓
double f(double x) {
        double r51198 = x;
        double r51199 = tanh(r51198);
        return r51199;
}

Error

Bits error versus x

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Results

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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 2019195 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))