Average Error: 0.0 → 0.0
Time: 10.0s
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 r867326 = 2.0;
        double r867327 = x;
        double r867328 = exp(r867327);
        double r867329 = -r867327;
        double r867330 = exp(r867329);
        double r867331 = r867328 + r867330;
        double r867332 = r867326 / r867331;
        return r867332;
}
↓
double f(double x) {
        double r867333 = 2.0;
        double r867334 = x;
        double r867335 = exp(r867334);
        double r867336 = -r867334;
        double r867337 = exp(r867336);
        double r867338 = r867335 + r867337;
        double r867339 = r867333 / r867338;
        double r867340 = cbrt(r867339);
        double r867341 = r867340 * r867340;
        double r867342 = r867340 * r867341;
        return r867342;
}

Error

Bits error versus x

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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 2019152 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))