Average Error: 58.1 → 0.0
Time: 20.5s
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 r2813328 = x;
        double r2813329 = exp(r2813328);
        double r2813330 = -r2813328;
        double r2813331 = exp(r2813330);
        double r2813332 = r2813329 - r2813331;
        double r2813333 = r2813329 + r2813331;
        double r2813334 = r2813332 / r2813333;
        return r2813334;
}
↓
double f(double x) {
        double r2813335 = x;
        double r2813336 = tanh(r2813335);
        return r2813336;
}

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 2019165 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))