Average Error: 0.0 → 0.0
Time: 18.6s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[e^{\sqrt[3]{{\left(x \cdot {y}^{2}\right)}^{3}}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
e^{\sqrt[3]{{\left(x \cdot {y}^{2}\right)}^{3}}}
double f(double x, double y) {
        double r121843 = x;
        double r121844 = y;
        double r121845 = r121843 * r121844;
        double r121846 = r121845 * r121844;
        double r121847 = exp(r121846);
        return r121847;
}
↓
double f(double x, double y) {
        double r121848 = x;
        double r121849 = y;
        double r121850 = 2.0;
        double r121851 = pow(r121849, r121850);
        double r121852 = r121848 * r121851;
        double r121853 = 3.0;
        double r121854 = pow(r121852, r121853);
        double r121855 = cbrt(r121854);
        double r121856 = exp(r121855);
        return r121856;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{\left(x \cdot y\right) \cdot y}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.9

    \[\leadsto e^{\left(x \cdot y\right) \cdot \color{blue}{\sqrt[3]{\left(y \cdot y\right) \cdot y}}}\]

  4. Applied add-cbrt-cube0.9

    \[\leadsto e^{\left(x \cdot \color{blue}{\sqrt[3]{\left(y \cdot y\right) \cdot y}}\right) \cdot \sqrt[3]{\left(y \cdot y\right) \cdot y}}\]

  5. Applied add-cbrt-cube14.9

    \[\leadsto e^{\left(\color{blue}{\sqrt[3]{\left(x \cdot x\right) \cdot x}} \cdot \sqrt[3]{\left(y \cdot y\right) \cdot y}\right) \cdot \sqrt[3]{\left(y \cdot y\right) \cdot y}}\]

  6. Applied cbrt-unprod14.9

    \[\leadsto e^{\color{blue}{\sqrt[3]{\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(y \cdot y\right) \cdot y\right)}} \cdot \sqrt[3]{\left(y \cdot y\right) \cdot y}}\]

  7. Applied cbrt-unprod14.9

    \[\leadsto e^{\color{blue}{\sqrt[3]{\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(y \cdot y\right) \cdot y\right)\right) \cdot \left(\left(y \cdot y\right) \cdot y\right)}}}\]

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))