Average Error: 0.0 → 0.0
Time: 3.8s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\left(\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \left(\sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}} \cdot \sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}}\right)\right) \cdot \sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\left(\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \left(\sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}} \cdot \sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}}\right)\right) \cdot \sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}}
double f(double x) {
        double r75341 = 2.0;
        double r75342 = x;
        double r75343 = exp(r75342);
        double r75344 = -r75342;
        double r75345 = exp(r75344);
        double r75346 = r75343 + r75345;
        double r75347 = r75341 / r75346;
        return r75347;
}
↓
double f(double x) {
        double r75348 = 2.0;
        double r75349 = x;
        double r75350 = exp(r75349);
        double r75351 = -r75349;
        double r75352 = exp(r75351);
        double r75353 = r75350 + r75352;
        double r75354 = r75348 / r75353;
        double r75355 = sqrt(r75354);
        double r75356 = cbrt(r75355);
        double r75357 = r75356 * r75356;
        double r75358 = r75355 * r75357;
        double r75359 = r75358 * r75356;
        return r75359;
}

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-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.0

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

  6. Applied associate-*r*0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))