Average Error: 58.1 → 0.0
Time: 16.4s
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 r1138703 = x;
        double r1138704 = exp(r1138703);
        double r1138705 = -r1138703;
        double r1138706 = exp(r1138705);
        double r1138707 = r1138704 - r1138706;
        double r1138708 = r1138704 + r1138706;
        double r1138709 = r1138707 / r1138708;
        return r1138709;
}
↓
double f(double x) {
        double r1138710 = x;
        double r1138711 = tanh(r1138710);
        return r1138711;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019155 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))