Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\left(\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \left(\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right)}\]
\frac{2}{e^{x} + e^{-x}}
↓
\left(\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right) \cdot \sqrt[3]{\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 r2820478 = 2.0;
        double r2820479 = x;
        double r2820480 = exp(r2820479);
        double r2820481 = -r2820479;
        double r2820482 = exp(r2820481);
        double r2820483 = r2820480 + r2820482;
        double r2820484 = r2820478 / r2820483;
        return r2820484;
}
↓
double f(double x) {
        double r2820485 = 2.0;
        double r2820486 = x;
        double r2820487 = exp(r2820486);
        double r2820488 = -r2820486;
        double r2820489 = exp(r2820488);
        double r2820490 = r2820487 + r2820489;
        double r2820491 = r2820485 / r2820490;
        double r2820492 = cbrt(r2820491);
        double r2820493 = r2820492 * r2820492;
        double r2820494 = r2820492 * r2820493;
        double r2820495 = cbrt(r2820494);
        double r2820496 = r2820493 * r2820495;
        return r2820496;
}

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. Using strategy rm

  5. Applied add-cube-cbrt0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))