Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[e^{\left(x \cdot y\right) \cdot y} \]
↓
\[e^{\sqrt[3]{{\left(y \cdot \left(x \cdot y\right)\right)}^{3}}} \]
e^{\left(x \cdot y\right) \cdot y}
↓
e^{\sqrt[3]{{\left(y \cdot \left(x \cdot y\right)\right)}^{3}}}

(FPCore (x y) :precision binary64 (exp (* (* x y) y)))
↓
(FPCore (x y) :precision binary64 (exp (cbrt (pow (* y (* x y)) 3.0))))
double code(double x, double y) {
	return exp((x * y) * y);
}
↓
double code(double x, double y) {
	return exp(cbrt(pow((y * (x * y)), 3.0)));
}

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. Applied add-cbrt-cube_binary640.0

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

  3. Applied pow3_binary640.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2022088 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))