Average Error: 0.0 → 0.1
Time: 13.9s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\frac{8}{\left(e^{-x} + e^{x}\right) \cdot \left(\left(e^{-x} + e^{x}\right) \cdot \left(e^{-x} + e^{x}\right)\right)}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{\frac{8}{\left(e^{-x} + e^{x}\right) \cdot \left(\left(e^{-x} + e^{x}\right) \cdot \left(e^{-x} + e^{x}\right)\right)}}
double f(double x) {
        double r2572516 = 2.0;
        double r2572517 = x;
        double r2572518 = exp(r2572517);
        double r2572519 = -r2572517;
        double r2572520 = exp(r2572519);
        double r2572521 = r2572518 + r2572520;
        double r2572522 = r2572516 / r2572521;
        return r2572522;
}
↓
double f(double x) {
        double r2572523 = 8.0;
        double r2572524 = x;
        double r2572525 = -r2572524;
        double r2572526 = exp(r2572525);
        double r2572527 = exp(r2572524);
        double r2572528 = r2572526 + r2572527;
        double r2572529 = r2572528 * r2572528;
        double r2572530 = r2572528 * r2572529;
        double r2572531 = r2572523 / r2572530;
        double r2572532 = cbrt(r2572531);
        return r2572532;
}

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-cbrt-cube0.1

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

  4. Applied add-cbrt-cube0.1

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

  5. Applied cbrt-undiv0.1

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

  6. Simplified0.1

    \[\leadsto \sqrt[3]{\color{blue}{\frac{8}{\left(\left(e^{-x} + e^{x}\right) \cdot \left(e^{-x} + e^{x}\right)\right) \cdot \left(e^{-x} + e^{x}\right)}}}\]

  7. Final simplification0.1

    \[\leadsto \sqrt[3]{\frac{8}{\left(e^{-x} + e^{x}\right) \cdot \left(\left(e^{-x} + e^{x}\right) \cdot \left(e^{-x} + e^{x}\right)\right)}}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))