Average Error: 58.1 → 0.0
Time: 7.7s
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 r41092 = x;
        double r41093 = exp(r41092);
        double r41094 = -r41092;
        double r41095 = exp(r41094);
        double r41096 = r41093 - r41095;
        double r41097 = r41093 + r41095;
        double r41098 = r41096 / r41097;
        return r41098;
}
↓
double f(double x) {
        double r41099 = x;
        double r41100 = tanh(r41099);
        return r41100;
}

Error

Bits error versus x

Try it out

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 2019318 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))