Average Error: 58.1 → 0.0
Time: 22.7s
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 r50296 = x;
        double r50297 = exp(r50296);
        double r50298 = -r50296;
        double r50299 = exp(r50298);
        double r50300 = r50297 - r50299;
        double r50301 = r50297 + r50299;
        double r50302 = r50300 / r50301;
        return r50302;
}
↓
double f(double x) {
        double r50303 = x;
        double r50304 = tanh(r50303);
        return r50304;
}

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 2019325 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))