Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{{\left(\sqrt{2} \cdot \frac{\sqrt{2}}{e^{x} + e^{-x}}\right)}^{3}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{{\left(\sqrt{2} \cdot \frac{\sqrt{2}}{e^{x} + e^{-x}}\right)}^{3}}
double f(double x) {
        double r33583 = 2.0;
        double r33584 = x;
        double r33585 = exp(r33584);
        double r33586 = -r33584;
        double r33587 = exp(r33586);
        double r33588 = r33585 + r33587;
        double r33589 = r33583 / r33588;
        return r33589;
}
↓
double f(double x) {
        double r33590 = 2.0;
        double r33591 = sqrt(r33590);
        double r33592 = x;
        double r33593 = exp(r33592);
        double r33594 = -r33592;
        double r33595 = exp(r33594);
        double r33596 = r33593 + r33595;
        double r33597 = r33591 / r33596;
        double r33598 = r33591 * r33597;
        double r33599 = 3.0;
        double r33600 = pow(r33598, r33599);
        double r33601 = cbrt(r33600);
        return r33601;
}

Error

Bits error versus x

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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

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

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

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

  9. Applied add-sqr-sqrt0.0

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

  10. Applied times-frac0.0

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

  11. Simplified0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2.0 (+ (exp x) (exp (- x)))))