Average Error: 0.0 → 0.0
Time: 7.2s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \left(\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right)\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \left(\sqrt[3]{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt[3]{\frac{2}{e^{x} + e^{-x}}}\right)
double f(double x) {
        double r2431146 = 2.0;
        double r2431147 = x;
        double r2431148 = exp(r2431147);
        double r2431149 = -r2431147;
        double r2431150 = exp(r2431149);
        double r2431151 = r2431148 + r2431150;
        double r2431152 = r2431146 / r2431151;
        return r2431152;
}
↓
double f(double x) {
        double r2431153 = 2.0;
        double r2431154 = x;
        double r2431155 = exp(r2431154);
        double r2431156 = -r2431154;
        double r2431157 = exp(r2431156);
        double r2431158 = r2431155 + r2431157;
        double r2431159 = r2431153 / r2431158;
        double r2431160 = cbrt(r2431159);
        double r2431161 = r2431160 * r2431160;
        double r2431162 = r2431160 * r2431161;
        return r2431162;
}

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-cube-cbrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))