Average Error: 58.0 → 0.0
Time: 16.5s
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 r49538 = x;
        double r49539 = exp(r49538);
        double r49540 = -r49538;
        double r49541 = exp(r49540);
        double r49542 = r49539 - r49541;
        double r49543 = r49539 + r49541;
        double r49544 = r49542 / r49543;
        return r49544;
}
↓
double f(double x) {
        double r49545 = x;
        double r49546 = tanh(r49545);
        return r49546;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.0

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019294 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))