Average Error: 0.0 → 0.1
Time: 13.1s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\left(\sqrt[3]{\sqrt[3]{\frac{2}{e^{x} + e^{-x}} \cdot \left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right)}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right) \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\left(\sqrt[3]{\sqrt[3]{\frac{2}{e^{x} + e^{-x}} \cdot \left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right)}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right) \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}
double f(double x) {
        double r2507414 = 2.0;
        double r2507415 = x;
        double r2507416 = exp(r2507415);
        double r2507417 = -r2507415;
        double r2507418 = exp(r2507417);
        double r2507419 = r2507416 + r2507418;
        double r2507420 = r2507414 / r2507419;
        return r2507420;
}
↓
double f(double x) {
        double r2507421 = 2.0;
        double r2507422 = x;
        double r2507423 = exp(r2507422);
        double r2507424 = -r2507422;
        double r2507425 = exp(r2507424);
        double r2507426 = r2507423 + r2507425;
        double r2507427 = r2507421 / r2507426;
        double r2507428 = r2507427 * r2507427;
        double r2507429 = r2507427 * r2507428;
        double r2507430 = cbrt(r2507429);
        double r2507431 = cbrt(r2507430);
        double r2507432 = cbrt(r2507427);
        double r2507433 = r2507431 * r2507432;
        double r2507434 = r2507433 * r2507432;
        return r2507434;
}

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-cbrt-cube0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019134 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))