Average Error: 0.0 → 0.0
Time: 13.6s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[{\left({\left(e^{x \cdot {y}^{2}}\right)}^{3}\right)}^{\frac{1}{3}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
{\left({\left(e^{x \cdot {y}^{2}}\right)}^{3}\right)}^{\frac{1}{3}}
double f(double x, double y) {
        double r296131 = x;
        double r296132 = y;
        double r296133 = r296131 * r296132;
        double r296134 = r296133 * r296132;
        double r296135 = exp(r296134);
        return r296135;
}
↓
double f(double x, double y) {
        double r296136 = x;
        double r296137 = y;
        double r296138 = 2.0;
        double r296139 = pow(r296137, r296138);
        double r296140 = r296136 * r296139;
        double r296141 = exp(r296140);
        double r296142 = 3.0;
        double r296143 = pow(r296141, r296142);
        double r296144 = 0.3333333333333333;
        double r296145 = pow(r296143, r296144);
        return r296145;
}

Error

Bits error versus x

Bits error versus y

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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 associate-*l*0.0

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

  4. Simplified0.0

    \[\leadsto e^{x \cdot \color{blue}{{y}^{2}}}\]
  5. Using strategy rm

  6. Applied add-cbrt-cube0.0

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

  7. Simplified0.0

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

  9. Applied pow1/30.0

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

  10. Final simplification0.0

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

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)))