Average Error: 58.3 → 0.0
Time: 25.7s
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 r37533 = x;
        double r37534 = exp(r37533);
        double r37535 = -r37533;
        double r37536 = exp(r37535);
        double r37537 = r37534 - r37536;
        double r37538 = r37534 + r37536;
        double r37539 = r37537 / r37538;
        return r37539;
}
↓
double f(double x) {
        double r37540 = x;
        double r37541 = tanh(r37540);
        return r37541;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.3

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019212 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))