Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{{\left(\sqrt{2}\right)}^{3} \cdot {\left(\frac{\sqrt{2}}{e^{-1 \cdot x} + e^{x}}\right)}^{3}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{{\left(\sqrt{2}\right)}^{3} \cdot {\left(\frac{\sqrt{2}}{e^{-1 \cdot x} + e^{x}}\right)}^{3}}
double f(double x) {
        double r69345 = 2.0;
        double r69346 = x;
        double r69347 = exp(r69346);
        double r69348 = -r69346;
        double r69349 = exp(r69348);
        double r69350 = r69347 + r69349;
        double r69351 = r69345 / r69350;
        return r69351;
}
↓
double f(double x) {
        double r69352 = 2.0;
        double r69353 = sqrt(r69352);
        double r69354 = 3.0;
        double r69355 = pow(r69353, r69354);
        double r69356 = -1.0;
        double r69357 = x;
        double r69358 = r69356 * r69357;
        double r69359 = exp(r69358);
        double r69360 = exp(r69357);
        double r69361 = r69359 + r69360;
        double r69362 = r69353 / r69361;
        double r69363 = pow(r69362, r69354);
        double r69364 = r69355 * r69363;
        double r69365 = cbrt(r69364);
        return r69365;
}

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

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

  4. Applied add-cbrt-cube0.0

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

  5. Applied cbrt-undiv0.0

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

  6. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{2}{e^{-1 \cdot x} + e^{x}}\right)}^{3}}}\]
  7. Using strategy rm

  8. Applied *-un-lft-identity0.0

    \[\leadsto \sqrt[3]{{\left(\frac{2}{\color{blue}{1 \cdot \left(e^{-1 \cdot x} + e^{x}\right)}}\right)}^{3}}\]

  9. Applied add-sqr-sqrt0.1

    \[\leadsto \sqrt[3]{{\left(\frac{\color{blue}{\sqrt{2} \cdot \sqrt{2}}}{1 \cdot \left(e^{-1 \cdot x} + e^{x}\right)}\right)}^{3}}\]

  10. Applied times-frac0.0

    \[\leadsto \sqrt[3]{{\color{blue}{\left(\frac{\sqrt{2}}{1} \cdot \frac{\sqrt{2}}{e^{-1 \cdot x} + e^{x}}\right)}}^{3}}\]

  11. Applied unpow-prod-down0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{\sqrt{2}}{1}\right)}^{3} \cdot {\left(\frac{\sqrt{2}}{e^{-1 \cdot x} + e^{x}}\right)}^{3}}}\]

  12. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\sqrt{2}\right)}^{3}} \cdot {\left(\frac{\sqrt{2}}{e^{-1 \cdot x} + e^{x}}\right)}^{3}}\]

  13. Final simplification0.0

    \[\leadsto \sqrt[3]{{\left(\sqrt{2}\right)}^{3} \cdot {\left(\frac{\sqrt{2}}{e^{-1 \cdot x} + e^{x}}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020027 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))