Average Error: 58.2 → 0.0
Time: 23.8s
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 r29434 = x;
        double r29435 = exp(r29434);
        double r29436 = -r29434;
        double r29437 = exp(r29436);
        double r29438 = r29435 - r29437;
        double r29439 = r29435 + r29437;
        double r29440 = r29438 / r29439;
        return r29440;
}
↓
double f(double x) {
        double r29441 = x;
        double r29442 = tanh(r29441);
        return r29442;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.2

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  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 2019323 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))