Average Error: 0.0 → 0.1
Time: 41.1s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right) \cdot \frac{2}{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{\left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right) \cdot \frac{2}{e^{x} + e^{-x}}}
double f(double x) {
        double r2788864 = 2.0;
        double r2788865 = x;
        double r2788866 = exp(r2788865);
        double r2788867 = -r2788865;
        double r2788868 = exp(r2788867);
        double r2788869 = r2788866 + r2788868;
        double r2788870 = r2788864 / r2788869;
        return r2788870;
}
↓
double f(double x) {
        double r2788871 = 2.0;
        double r2788872 = x;
        double r2788873 = exp(r2788872);
        double r2788874 = -r2788872;
        double r2788875 = exp(r2788874);
        double r2788876 = r2788873 + r2788875;
        double r2788877 = r2788871 / r2788876;
        double r2788878 = r2788877 * r2788877;
        double r2788879 = r2788878 * r2788877;
        double r2788880 = cbrt(r2788879);
        return r2788880;
}

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-sqr-sqrt0.8

    \[\leadsto \frac{2}{\color{blue}{\sqrt{e^{x} + e^{-x}} \cdot \sqrt{e^{x} + e^{-x}}}}\]

  4. Applied associate-/r*0.5

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

  6. Applied add-cbrt-cube0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019138 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))