Average Error: 0.0 → 0.0
Time: 8.1s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\frac{\frac{8}{e^{x} + \frac{1}{e^{x}}}}{\left(e^{x} + \frac{1}{e^{x}}\right) \cdot \left(e^{x} + \frac{1}{e^{x}}\right)}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{\frac{\frac{8}{e^{x} + \frac{1}{e^{x}}}}{\left(e^{x} + \frac{1}{e^{x}}\right) \cdot \left(e^{x} + \frac{1}{e^{x}}\right)}}
double f(double x) {
        double r2176589 = 2.0;
        double r2176590 = x;
        double r2176591 = exp(r2176590);
        double r2176592 = -r2176590;
        double r2176593 = exp(r2176592);
        double r2176594 = r2176591 + r2176593;
        double r2176595 = r2176589 / r2176594;
        return r2176595;
}
↓
double f(double x) {
        double r2176596 = 8.0;
        double r2176597 = x;
        double r2176598 = exp(r2176597);
        double r2176599 = 1.0;
        double r2176600 = r2176599 / r2176598;
        double r2176601 = r2176598 + r2176600;
        double r2176602 = r2176596 / r2176601;
        double r2176603 = r2176601 * r2176601;
        double r2176604 = r2176602 / r2176603;
        double r2176605 = cbrt(r2176604);
        return r2176605;
}

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-cube0.0

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

  4. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{8}{e^{x} + \frac{1}{e^{x}}}}{\left(e^{x} + \frac{1}{e^{x}}\right) \cdot \left(e^{x} + \frac{1}{e^{x}}\right)}}}\]

  5. Final simplification0.0

    \[\leadsto \sqrt[3]{\frac{\frac{8}{e^{x} + \frac{1}{e^{x}}}}{\left(e^{x} + \frac{1}{e^{x}}\right) \cdot \left(e^{x} + \frac{1}{e^{x}}\right)}}\]

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))