Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\left(\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right) \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\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}}}
double f(double x) {
        double r74910 = 2.0;
        double r74911 = x;
        double r74912 = exp(r74911);
        double r74913 = -r74911;
        double r74914 = exp(r74913);
        double r74915 = r74912 + r74914;
        double r74916 = r74910 / r74915;
        return r74916;
}
↓
double f(double x) {
        double r74917 = 2.0;
        double r74918 = x;
        double r74919 = exp(r74918);
        double r74920 = -r74918;
        double r74921 = exp(r74920);
        double r74922 = r74919 + r74921;
        double r74923 = r74917 / r74922;
        double r74924 = cbrt(r74923);
        double r74925 = r74924 * r74924;
        double r74926 = r74925 * r74924;
        return r74926;
}

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

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

Reproduce

herbie shell --seed 2020025 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))