Average Error: 0.0 → 0.0
Time: 16.5s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[\left(\sqrt[3]{e^{\left(x \cdot y\right) \cdot y}} \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}\right) \cdot \sqrt[3]{e^{\sqrt[3]{\left(\left(\left(x \cdot y\right) \cdot y\right) \cdot \left(\left(x \cdot y\right) \cdot y\right)\right) \cdot \left(\left(x \cdot y\right) \cdot y\right)}}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
\left(\sqrt[3]{e^{\left(x \cdot y\right) \cdot y}} \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}\right) \cdot \sqrt[3]{e^{\sqrt[3]{\left(\left(\left(x \cdot y\right) \cdot y\right) \cdot \left(\left(x \cdot y\right) \cdot y\right)\right) \cdot \left(\left(x \cdot y\right) \cdot y\right)}}}
double f(double x, double y) {
        double r32709130 = x;
        double r32709131 = y;
        double r32709132 = r32709130 * r32709131;
        double r32709133 = r32709132 * r32709131;
        double r32709134 = exp(r32709133);
        return r32709134;
}
↓
double f(double x, double y) {
        double r32709135 = x;
        double r32709136 = y;
        double r32709137 = r32709135 * r32709136;
        double r32709138 = r32709137 * r32709136;
        double r32709139 = exp(r32709138);
        double r32709140 = cbrt(r32709139);
        double r32709141 = r32709140 * r32709140;
        double r32709142 = r32709138 * r32709138;
        double r32709143 = r32709142 * r32709138;
        double r32709144 = cbrt(r32709143);
        double r32709145 = exp(r32709144);
        double r32709146 = cbrt(r32709145);
        double r32709147 = r32709141 * r32709146;
        return r32709147;
}

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-cube-cbrt0.0

    \[\leadsto \color{blue}{\left(\sqrt[3]{e^{\left(x \cdot y\right) \cdot y}} \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}\right) \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube0.7

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

  6. Applied add-cbrt-cube0.7

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

  7. Applied add-cbrt-cube15.4

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

  8. Applied cbrt-unprod15.4

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

  9. Applied cbrt-unprod15.4

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  (exp (* (* x y) y)))