Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[{e}^{\left(\left(\sqrt[3]{{y}^{2} \cdot x} \cdot \sqrt[3]{{y}^{2} \cdot x}\right) \cdot \sqrt[3]{{y}^{2} \cdot x}\right)}\]
e^{\left(x \cdot y\right) \cdot y}
↓
{e}^{\left(\left(\sqrt[3]{{y}^{2} \cdot x} \cdot \sqrt[3]{{y}^{2} \cdot x}\right) \cdot \sqrt[3]{{y}^{2} \cdot x}\right)}
double f(double x, double y) {
        double r304999 = x;
        double r305000 = y;
        double r305001 = r304999 * r305000;
        double r305002 = r305001 * r305000;
        double r305003 = exp(r305002);
        return r305003;
}
↓
double f(double x, double y) {
        double r305004 = exp(1.0);
        double r305005 = y;
        double r305006 = 2.0;
        double r305007 = pow(r305005, r305006);
        double r305008 = x;
        double r305009 = r305007 * r305008;
        double r305010 = cbrt(r305009);
        double r305011 = r305010 * r305010;
        double r305012 = r305011 * r305010;
        double r305013 = pow(r305004, r305012);
        return r305013;
}

Error

Bits error versus x

Bits error versus y

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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 pow10.0

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

  4. Applied pow10.0

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

  5. Applied pow10.0

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

  6. Applied pow-prod-down0.0

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

  7. Applied pow-prod-down0.0

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

  8. Simplified0.0

    \[\leadsto e^{{\color{blue}{\left({y}^{2} \cdot x\right)}}^{1}}\]
  9. Using strategy rm

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

    \[\leadsto e^{\color{blue}{1 \cdot {\left({y}^{2} \cdot x\right)}^{1}}}\]

  11. Applied exp-prod0.0

    \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left({\left({y}^{2} \cdot x\right)}^{1}\right)}}\]

  12. Simplified0.0

    \[\leadsto {\color{blue}{e}}^{\left({\left({y}^{2} \cdot x\right)}^{1}\right)}\]
  13. Using strategy rm

  14. Applied add-cube-cbrt0.0

    \[\leadsto {e}^{\left({\color{blue}{\left(\left(\sqrt[3]{{y}^{2} \cdot x} \cdot \sqrt[3]{{y}^{2} \cdot x}\right) \cdot \sqrt[3]{{y}^{2} \cdot x}\right)}}^{1}\right)}\]

  15. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 +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)))