Average Error: 58.2 → 0.0
Time: 24.0s
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 r38664 = x;
        double r38665 = exp(r38664);
        double r38666 = -r38664;
        double r38667 = exp(r38666);
        double r38668 = r38665 - r38667;
        double r38669 = r38665 + r38667;
        double r38670 = r38668 / r38669;
        return r38670;
}
↓
double f(double x) {
        double r38671 = x;
        double r38672 = tanh(r38671);
        return r38672;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))