Average Error: 0.0 → 0.0
Time: 36.9s
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 r4790406 = 2.0;
        double r4790407 = x;
        double r4790408 = exp(r4790407);
        double r4790409 = -r4790407;
        double r4790410 = exp(r4790409);
        double r4790411 = r4790408 + r4790410;
        double r4790412 = r4790406 / r4790411;
        return r4790412;
}
↓
double f(double x) {
        double r4790413 = 2.0;
        double r4790414 = x;
        double r4790415 = exp(r4790414);
        double r4790416 = -r4790414;
        double r4790417 = exp(r4790416);
        double r4790418 = r4790415 + r4790417;
        double r4790419 = r4790413 / r4790418;
        double r4790420 = cbrt(r4790419);
        double r4790421 = r4790420 * r4790420;
        double r4790422 = r4790420 * r4790421;
        return r4790422;
}

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. 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 2019112 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))