Average Error: 0.0 → 0.0
Time: 10.3s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[{e}^{\left(\sqrt[3]{{\left(\left(y \cdot y\right) \cdot x\right)}^{2}} \cdot \sqrt[3]{\left(y \cdot y\right) \cdot x}\right)}\]
e^{\left(x \cdot y\right) \cdot y}
↓
{e}^{\left(\sqrt[3]{{\left(\left(y \cdot y\right) \cdot x\right)}^{2}} \cdot \sqrt[3]{\left(y \cdot y\right) \cdot x}\right)}
double f(double x, double y) {
        double r270144 = x;
        double r270145 = y;
        double r270146 = r270144 * r270145;
        double r270147 = r270146 * r270145;
        double r270148 = exp(r270147);
        return r270148;
}
↓
double f(double x, double y) {
        double r270149 = exp(1.0);
        double r270150 = y;
        double r270151 = r270150 * r270150;
        double r270152 = x;
        double r270153 = r270151 * r270152;
        double r270154 = 2.0;
        double r270155 = pow(r270153, r270154);
        double r270156 = cbrt(r270155);
        double r270157 = cbrt(r270153);
        double r270158 = r270156 * r270157;
        double r270159 = pow(r270149, r270158);
        return r270159;
}

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-cube0.8

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

  4. Applied add-cbrt-cube0.8

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

  5. Applied add-cbrt-cube14.8

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

  6. Applied cbrt-unprod14.8

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

  7. Applied cbrt-unprod14.8

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

  8. Simplified0.0

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

  10. Applied *-un-lft-identity0.0

    \[\leadsto e^{\sqrt[3]{\color{blue}{1 \cdot {\left(\left(y \cdot y\right) \cdot x\right)}^{3}}}}\]

  11. Applied cbrt-prod0.0

    \[\leadsto e^{\color{blue}{\sqrt[3]{1} \cdot \sqrt[3]{{\left(\left(y \cdot y\right) \cdot x\right)}^{3}}}}\]

  12. Applied exp-prod0.0

    \[\leadsto \color{blue}{{\left(e^{\sqrt[3]{1}}\right)}^{\left(\sqrt[3]{{\left(\left(y \cdot y\right) \cdot x\right)}^{3}}\right)}}\]

  13. Simplified0.0

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

  15. Applied unpow30.0

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

  16. Applied cbrt-prod0.0

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

  17. Simplified0.0

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

  18. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))