Average Error: 58.1 → 0.0
Time: 4.7s
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 r67254 = x;
        double r67255 = exp(r67254);
        double r67256 = -r67254;
        double r67257 = exp(r67256);
        double r67258 = r67255 - r67257;
        double r67259 = r67255 + r67257;
        double r67260 = r67258 / r67259;
        return r67260;
}
↓
double f(double x) {
        double r67261 = x;
        double r67262 = tanh(r67261);
        return r67262;
}

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 2019352 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))