Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[\sqrt[3]{{\left({\left(\sqrt{e^{y \cdot \left(y \cdot x\right)}}\right)}^{\left({\left(\sqrt[3]{3}\right)}^{2}\right)}\right)}^{\left(\sqrt[3]{3}\right)}} \cdot \sqrt[3]{{\left({\left(\sqrt{e^{y \cdot \left(y \cdot x\right)}}\right)}^{\left({\left(\sqrt[3]{3}\right)}^{2}\right)}\right)}^{\left(\sqrt[3]{3}\right)}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
\sqrt[3]{{\left({\left(\sqrt{e^{y \cdot \left(y \cdot x\right)}}\right)}^{\left({\left(\sqrt[3]{3}\right)}^{2}\right)}\right)}^{\left(\sqrt[3]{3}\right)}} \cdot \sqrt[3]{{\left({\left(\sqrt{e^{y \cdot \left(y \cdot x\right)}}\right)}^{\left({\left(\sqrt[3]{3}\right)}^{2}\right)}\right)}^{\left(\sqrt[3]{3}\right)}}
(FPCore (x y) :precision binary64 (exp (* (* x y) y)))
↓
(FPCore (x y)
 :precision binary64
 (*
  (cbrt (pow (pow (sqrt (exp (* y (* y x)))) (pow (cbrt 3.0) 2.0)) (cbrt 3.0)))
  (cbrt
   (pow (pow (sqrt (exp (* y (* y x)))) (pow (cbrt 3.0) 2.0)) (cbrt 3.0)))))
double code(double x, double y) {
	return exp((x * y) * y);
}
↓
double code(double x, double y) {
	return cbrt(pow(pow(sqrt(exp(y * (y * x))), pow(cbrt(3.0), 2.0)), cbrt(3.0))) * cbrt(pow(pow(sqrt(exp(y * (y * x))), pow(cbrt(3.0), 2.0)), cbrt(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_binary640.0

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

  4. Simplified0.0

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

  6. Applied add-cube-cbrt_binary640.0

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

  7. Applied pow-unpow_binary640.0

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

  8. Simplified0.0

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

  10. Applied add-sqr-sqrt_binary640.0

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

  11. Applied unpow-prod-down_binary640.0

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

  12. Applied unpow-prod-down_binary640.0

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

  13. Applied cbrt-prod_binary640.0

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

  14. Simplified0.0

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

  15. Simplified0.0

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

  16. Final simplification0.0

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

Reproduce

herbie shell --seed 2020233 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))