Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \left(\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right)\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \left(\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right)
double f(double x) {
        double r2727707 = 2.0;
        double r2727708 = x;
        double r2727709 = exp(r2727708);
        double r2727710 = -r2727708;
        double r2727711 = exp(r2727710);
        double r2727712 = r2727709 + r2727711;
        double r2727713 = r2727707 / r2727712;
        return r2727713;
}
↓
double f(double x) {
        double r2727714 = 2.0;
        double r2727715 = x;
        double r2727716 = exp(r2727715);
        double r2727717 = -r2727715;
        double r2727718 = exp(r2727717);
        double r2727719 = r2727716 + r2727718;
        double r2727720 = r2727714 / r2727719;
        double r2727721 = cbrt(r2727720);
        double r2727722 = r2727721 * r2727721;
        double r2727723 = r2727721 * r2727722;
        return r2727723;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{2}{e^{x} + e^{-x}}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.0

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right) \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}}\]

  4. Final simplification0.0

    \[\leadsto \sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \left(\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))