Average Error: 0.0 → 0.0
Time: 5.4s
Precision: binary64
\[e^{\left(x \cdot y\right) \cdot y} \]
↓
\[\begin{array}{l} t_0 := {\left(\sqrt[3]{{\left(\sqrt[3]{e^{\left(y \cdot y\right) \cdot x}}\right)}^{3}}\right)}^{3}\\ \sqrt[3]{t_0 \cdot \left(t_0 \cdot t_0\right)} \end{array} \]
e^{\left(x \cdot y\right) \cdot y}
↓
\begin{array}{l}
t_0 := {\left(\sqrt[3]{{\left(\sqrt[3]{e^{\left(y \cdot y\right) \cdot x}}\right)}^{3}}\right)}^{3}\\
\sqrt[3]{t_0 \cdot \left(t_0 \cdot t_0\right)}
\end{array}

(FPCore (x y) :precision binary64 (exp (* (* x y) y)))
↓
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (pow (cbrt (pow (cbrt (exp (* (* y y) x))) 3.0)) 3.0)))
   (cbrt (* t_0 (* t_0 t_0)))))
double code(double x, double y) {
	return exp((x * y) * y);
}
↓
double code(double x, double y) {
	double t_0 = pow(cbrt(pow(cbrt(exp((y * y) * x)), 3.0)), 3.0);
	return cbrt(t_0 * (t_0 * t_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

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

  3. Simplified0.0

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

  4. Applied add-cbrt-cube_binary640.0

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

  5. Simplified0.0

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

  6. Applied add-cube-cbrt_binary640.0

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

  7. Applied unpow-prod-down_binary640.0

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

  8. Applied cbrt-prod_binary640.0

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

  9. Applied unpow-prod-down_binary640.0

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

  10. Applied unpow-prod-down_binary640.0

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

  11. Applied cbrt-prod_binary640.0

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

  12. Applied unpow-prod-down_binary640.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2022081 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))