Average Error: 58.1 → 0.0
Time: 4.5s
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 r28155 = x;
        double r28156 = exp(r28155);
        double r28157 = -r28155;
        double r28158 = exp(r28157);
        double r28159 = r28156 - r28158;
        double r28160 = r28156 + r28158;
        double r28161 = r28159 / r28160;
        return r28161;
}
↓
double f(double x) {
        double r28162 = x;
        double r28163 = tanh(r28162);
        return r28163;
}

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 2020003 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))