Average Error: 0.0 → 0.1
Time: 1.0s
Precision: binary64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[\sqrt[3]{e^{\left(y \cdot \left(y \cdot x\right)\right) \cdot 3}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
\sqrt[3]{e^{\left(y \cdot \left(y \cdot x\right)\right) \cdot 3}}
(FPCore (x y) :precision binary64 (exp (* (* x y) y)))
↓
(FPCore (x y) :precision binary64 (cbrt (exp (* (* y (* y x)) 3.0))))
double code(double x, double y) {
	return exp((x * y) * y);
}
↓
double code(double x, double y) {
	return cbrt(exp((y * (y * x)) * 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. Using strategy rm

  3. Applied add-cbrt-cube_binary640.1

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

  4. Simplified0.1

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

  6. Applied pow-exp_binary640.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020224 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))