Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[e^{\left(\left(x \cdot y\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
e^{\left(\left(x \cdot y\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}}
double code(double x, double y) {
	return ((double) exp(((double) (((double) (x * y)) * y))));
}
↓
double code(double x, double y) {
	return ((double) exp(((double) (((double) (((double) (x * y)) * ((double) (((double) cbrt(y)) * ((double) cbrt(y)))))) * ((double) cbrt(y))))));
}

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

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

  4. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020173 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))