Average Error: 58.2 → 0.0
Time: 22.3s
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 r49330 = x;
        double r49331 = exp(r49330);
        double r49332 = -r49330;
        double r49333 = exp(r49332);
        double r49334 = r49331 - r49333;
        double r49335 = r49331 + r49333;
        double r49336 = r49334 / r49335;
        return r49336;
}
↓
double f(double x) {
        double r49337 = x;
        double r49338 = tanh(r49337);
        return r49338;
}

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