Average Error: 58.1 → 0.0
Time: 4.8s
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 r37847 = x;
        double r37848 = exp(r37847);
        double r37849 = -r37847;
        double r37850 = exp(r37849);
        double r37851 = r37848 - r37850;
        double r37852 = r37848 + r37850;
        double r37853 = r37851 / r37852;
        return r37853;
}
↓
double f(double x) {
        double r37854 = x;
        double r37855 = tanh(r37854);
        return r37855;
}

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 2020056 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))