Average Error: 58.2 → 0.0
Time: 1.1m
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 r50654 = x;
        double r50655 = exp(r50654);
        double r50656 = -r50654;
        double r50657 = exp(r50656);
        double r50658 = r50655 - r50657;
        double r50659 = r50655 + r50657;
        double r50660 = r50658 / r50659;
        return r50660;
}
↓
double f(double x) {
        double r50661 = x;
        double r50662 = tanh(r50661);
        return r50662;
}

Error

Bits error versus x

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Your Program's Arguments

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 2019179 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))