Average Error: 0.0 → 0.1
Time: 6.2s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{{\left(\frac{2}{e^{x} + e^{-x}}\right)}^{3}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{{\left(\frac{2}{e^{x} + e^{-x}}\right)}^{3}}
double f(double x) {
        double r35423 = 2.0;
        double r35424 = x;
        double r35425 = exp(r35424);
        double r35426 = -r35424;
        double r35427 = exp(r35426);
        double r35428 = r35425 + r35427;
        double r35429 = r35423 / r35428;
        return r35429;
}
↓
double f(double x) {
        double r35430 = 2.0;
        double r35431 = x;
        double r35432 = exp(r35431);
        double r35433 = -r35431;
        double r35434 = exp(r35433);
        double r35435 = r35432 + r35434;
        double r35436 = r35430 / r35435;
        double r35437 = 3.0;
        double r35438 = pow(r35436, r35437);
        double r35439 = cbrt(r35438);
        return r35439;
}

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

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))