Average Error: 58.3 → 0.0
Time: 5.0s
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 r33444 = x;
        double r33445 = exp(r33444);
        double r33446 = -r33444;
        double r33447 = exp(r33446);
        double r33448 = r33445 - r33447;
        double r33449 = r33445 + r33447;
        double r33450 = r33448 / r33449;
        return r33450;
}
↓
double f(double x) {
        double r33451 = x;
        double r33452 = tanh(r33451);
        return r33452;
}

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 2020002 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))