Average Error: 58.0 → 0.0
Time: 1.9m
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 r20841332 = x;
        double r20841333 = exp(r20841332);
        double r20841334 = -r20841332;
        double r20841335 = exp(r20841334);
        double r20841336 = r20841333 - r20841335;
        double r20841337 = r20841333 + r20841335;
        double r20841338 = r20841336 / r20841337;
        return r20841338;
}
↓
double f(double x) {
        double r20841339 = x;
        double r20841340 = tanh(r20841339);
        return r20841340;
}

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 2019124 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))