Average Error: 58.1 → 0.0
Time: 5.5s
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 r38989 = x;
        double r38990 = exp(r38989);
        double r38991 = -r38989;
        double r38992 = exp(r38991);
        double r38993 = r38990 - r38992;
        double r38994 = r38990 + r38992;
        double r38995 = r38993 / r38994;
        return r38995;
}
↓
double f(double x) {
        double r38996 = x;
        double r38997 = tanh(r38996);
        return r38997;
}

Error

Bits error versus x

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Your Program's Arguments

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 2019347 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))