Average Error: 0.0 → 0.0
Time: 19.8s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[\left(\sqrt[3]{e^{\sqrt[3]{\left(\left(\left(x \cdot y\right) \cdot y\right) \cdot \left(\left(x \cdot y\right) \cdot y\right)\right) \cdot \left(\left(x \cdot y\right) \cdot y\right)}}} \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}\right) \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
\left(\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)}}} \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}\right) \cdot \sqrt[3]{e^{\left(x \cdot y\right) \cdot y}}
double f(double x, double y) {
        double r47124273 = x;
        double r47124274 = y;
        double r47124275 = r47124273 * r47124274;
        double r47124276 = r47124275 * r47124274;
        double r47124277 = exp(r47124276);
        return r47124277;
}
↓
double f(double x, double y) {
        double r47124278 = x;
        double r47124279 = y;
        double r47124280 = r47124278 * r47124279;
        double r47124281 = r47124280 * r47124279;
        double r47124282 = r47124281 * r47124281;
        double r47124283 = r47124282 * r47124281;
        double r47124284 = cbrt(r47124283);
        double r47124285 = exp(r47124284);
        double r47124286 = cbrt(r47124285);
        double r47124287 = exp(r47124281);
        double r47124288 = cbrt(r47124287);
        double r47124289 = r47124286 * r47124288;
        double r47124290 = r47124289 * r47124288;
        return r47124290;
}

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

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

  6. Applied add-cbrt-cube0.7

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

  7. Applied add-cbrt-cube15.4

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

  8. Applied cbrt-unprod15.4

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

  9. Applied cbrt-unprod15.4

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

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