Average Error: 58.2 → 0.0
Time: 4.2s
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 r32152 = x;
        double r32153 = exp(r32152);
        double r32154 = -r32152;
        double r32155 = exp(r32154);
        double r32156 = r32153 - r32155;
        double r32157 = r32153 + r32155;
        double r32158 = r32156 / r32157;
        return r32158;
}
↓
double f(double x) {
        double r32159 = x;
        double r32160 = tanh(r32159);
        return r32160;
}

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 2020059 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))