Average Error: 0.0 → 0.0
Time: 1.7s
Precision: binary64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[\sqrt{e^{y \cdot \left(y \cdot x\right)}} \cdot \sqrt{e^{\sqrt[3]{y \cdot \left(y \cdot x\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot x\right)} \cdot \sqrt[3]{y \cdot \left(y \cdot x\right)}\right)}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
\sqrt{e^{y \cdot \left(y \cdot x\right)}} \cdot \sqrt{e^{\sqrt[3]{y \cdot \left(y \cdot x\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot x\right)} \cdot \sqrt[3]{y \cdot \left(y \cdot x\right)}\right)}}
(FPCore (x y) :precision binary64 (exp (* (* x y) y)))
↓
(FPCore (x y)
 :precision binary64
 (*
  (sqrt (exp (* y (* y x))))
  (sqrt
   (exp
    (* (cbrt (* y (* y x))) (* (cbrt (* y (* y x))) (cbrt (* y (* y x)))))))))
double code(double x, double y) {
	return ((double) exp(((double) (((double) (x * y)) * y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) sqrt(((double) exp(((double) (y * ((double) (y * x)))))))) * ((double) sqrt(((double) exp(((double) (((double) cbrt(((double) (y * ((double) (y * x)))))) * ((double) (((double) cbrt(((double) (y * ((double) (y * x)))))) * ((double) cbrt(((double) (y * ((double) (y * x))))))))))))))));
}

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-sqr-sqrt_binary640.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied add-cube-cbrt_binary640.0

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

  8. Simplified0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020205 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))