Average Error: 58.3 → 0.0
Time: 23.7s
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 r50352 = x;
        double r50353 = exp(r50352);
        double r50354 = -r50352;
        double r50355 = exp(r50354);
        double r50356 = r50353 - r50355;
        double r50357 = r50353 + r50355;
        double r50358 = r50356 / r50357;
        return r50358;
}
↓
double f(double x) {
        double r50359 = x;
        double r50360 = tanh(r50359);
        return r50360;
}

Error

Bits error versus x

Try it out

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 2019212 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))