Average Error: 58.0 → 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 r29290 = x;
        double r29291 = exp(r29290);
        double r29292 = -r29290;
        double r29293 = exp(r29292);
        double r29294 = r29291 - r29293;
        double r29295 = r29291 + r29293;
        double r29296 = r29294 / r29295;
        return r29296;
}
↓
double f(double x) {
        double r29297 = x;
        double r29298 = tanh(r29297);
        return r29298;
}

Error

Bits error versus x

Try it out

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 2020046 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))