Average Error: 58.1 → 0.0
Time: 15.4s
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 r44711 = x;
        double r44712 = exp(r44711);
        double r44713 = -r44711;
        double r44714 = exp(r44713);
        double r44715 = r44712 - r44714;
        double r44716 = r44712 + r44714;
        double r44717 = r44715 / r44716;
        return r44717;
}
↓
double f(double x) {
        double r44718 = x;
        double r44719 = tanh(r44718);
        return r44719;
}

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 2019303 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))