Average Error: 0.0 → 0.0
Time: 6.7s
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 r1872528 = 2.0;
        double r1872529 = x;
        double r1872530 = exp(r1872529);
        double r1872531 = -r1872529;
        double r1872532 = exp(r1872531);
        double r1872533 = r1872530 + r1872532;
        double r1872534 = r1872528 / r1872533;
        return r1872534;
}
↓
double f(double x) {
        double r1872535 = 2.0;
        double r1872536 = x;
        double r1872537 = exp(r1872536);
        double r1872538 = -r1872536;
        double r1872539 = exp(r1872538);
        double r1872540 = r1872537 + r1872539;
        double r1872541 = r1872535 / r1872540;
        double r1872542 = cbrt(r1872541);
        double r1872543 = r1872542 * r1872542;
        double r1872544 = r1872542 * r1872543;
        return r1872544;
}

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 2019162 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))