Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2

Average Accuracy: 100.0% → 100.0%

Time: 3.1s

Precision: binary64

Cost: 13312

Math

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

↓

\[{\left(e^{0.5}\right)}^{\left(\left(y + y\right) \cdot \left(y \cdot x\right)\right)} \]

FPCore

(FPCore (x y) :precision binary64 (exp (* (* x y) y)))

↓

(FPCore (x y) :precision binary64 (pow (exp 0.5) (* (+ y y) (* y x))))

C

double code(double x, double y) {
	return exp(((x * y) * y));
}

↓

double code(double x, double y) {
	return pow(exp(0.5), ((y + y) * (y * x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp(((x * y) * y))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp(0.5d0) ** ((y + y) * (y * x))
end function

Java

public static double code(double x, double y) {
	return Math.exp(((x * y) * y));
}

↓

public static double code(double x, double y) {
	return Math.pow(Math.exp(0.5), ((y + y) * (y * x)));
}

Python

def code(x, y):
	return math.exp(((x * y) * y))

↓

def code(x, y):
	return math.pow(math.exp(0.5), ((y + y) * (y * x)))

Julia

function code(x, y)
	return exp(Float64(Float64(x * y) * y))
end

↓

function code(x, y)
	return exp(0.5) ^ Float64(Float64(y + y) * Float64(y * x))
end

MATLAB

function tmp = code(x, y)
	tmp = exp(((x * y) * y));
end

↓

function tmp = code(x, y)
	tmp = exp(0.5) ^ ((y + y) * (y * x));
end

Wolfram

code[x_, y_] := N[Exp[N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]

↓

code[x_, y_] := N[Power[N[Exp[0.5], $MachinePrecision], N[(N[(y + y), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(x \cdot \left(y \cdot y\right)\right)}} \]
   Proof

   [Start] 100.0	\[ e^{\left(x \cdot y\right) \cdot y} \]
   *-un-lft-identity [=>] 100.0	\[ e^{\color{blue}{1 \cdot \left(\left(x \cdot y\right) \cdot y\right)}} \]
   exp-prod [=>] 100.0	\[ \color{blue}{{\left(e^{1}\right)}^{\left(\left(x \cdot y\right) \cdot y\right)}} \]
   associate-*l* [=>] 100.0	\[ {\left(e^{1}\right)}^{\color{blue}{\left(x \cdot \left(y \cdot y\right)\right)}} \]

3. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ {\left(e^{1}\right)}^{\left(x \cdot \left(y \cdot y\right)\right)} \]
   add-sqr-sqrt [=>] 100.0	\[ {\color{blue}{\left(\sqrt{e^{1}} \cdot \sqrt{e^{1}}\right)}}^{\left(x \cdot \left(y \cdot y\right)\right)} \]
   unpow-prod-down [=>] 100.0	\[ \color{blue}{{\left(\sqrt{e^{1}}\right)}^{\left(x \cdot \left(y \cdot y\right)\right)} \cdot {\left(\sqrt{e^{1}}\right)}^{\left(x \cdot \left(y \cdot y\right)\right)}} \]
   exp-1-e [=>] 100.0	\[ {\left(\sqrt{\color{blue}{e}}\right)}^{\left(x \cdot \left(y \cdot y\right)\right)} \cdot {\left(\sqrt{e^{1}}\right)}^{\left(x \cdot \left(y \cdot y\right)\right)} \]
   associate-*r* [=>] 100.0	\[ {\left(\sqrt{e}\right)}^{\color{blue}{\left(\left(x \cdot y\right) \cdot y\right)}} \cdot {\left(\sqrt{e^{1}}\right)}^{\left(x \cdot \left(y \cdot y\right)\right)} \]
   *-commutative [=>] 100.0	\[ {\left(\sqrt{e}\right)}^{\color{blue}{\left(y \cdot \left(x \cdot y\right)\right)}} \cdot {\left(\sqrt{e^{1}}\right)}^{\left(x \cdot \left(y \cdot y\right)\right)} \]
   exp-1-e [=>] 100.0	\[ {\left(\sqrt{e}\right)}^{\left(y \cdot \left(x \cdot y\right)\right)} \cdot {\left(\sqrt{\color{blue}{e}}\right)}^{\left(x \cdot \left(y \cdot y\right)\right)} \]
   associate-*r* [=>] 100.0	\[ {\left(\sqrt{e}\right)}^{\left(y \cdot \left(x \cdot y\right)\right)} \cdot {\left(\sqrt{e}\right)}^{\color{blue}{\left(\left(x \cdot y\right) \cdot y\right)}} \]
   *-commutative [=>] 100.0	\[ {\left(\sqrt{e}\right)}^{\left(y \cdot \left(x \cdot y\right)\right)} \cdot {\left(\sqrt{e}\right)}^{\color{blue}{\left(y \cdot \left(x \cdot y\right)\right)}} \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{{\left(e^{0.5}\right)}^{\left(\left(y \cdot x\right) \cdot \left(y + y\right)\right)}} \]
   Proof

   [Start] 100.0	\[ {\left(\sqrt{e}\right)}^{\left(y \cdot \left(x \cdot y\right)\right)} \cdot {\left(\sqrt{e}\right)}^{\left(y \cdot \left(x \cdot y\right)\right)} \]
   pow-prod-up [=>] 100.0	\[ \color{blue}{{\left(\sqrt{e}\right)}^{\left(y \cdot \left(x \cdot y\right) + y \cdot \left(x \cdot y\right)\right)}} \]
   distribute-rgt-out [=>] 100.0	\[ {\left(\sqrt{e}\right)}^{\color{blue}{\left(\left(x \cdot y\right) \cdot \left(y + y\right)\right)}} \]
   add-exp-log [=>] 100.0	\[ {\color{blue}{\left(e^{\log \left(\sqrt{e}\right)}\right)}}^{\left(\left(x \cdot y\right) \cdot \left(y + y\right)\right)} \]
   pow1/2 [=>] 100.0	\[ {\left(e^{\log \color{blue}{\left({e}^{0.5}\right)}}\right)}^{\left(\left(x \cdot y\right) \cdot \left(y + y\right)\right)} \]
   log-pow [=>] 100.0	\[ {\left(e^{\color{blue}{0.5 \cdot \log e}}\right)}^{\left(\left(x \cdot y\right) \cdot \left(y + y\right)\right)} \]
   log-E [=>] 100.0	\[ {\left(e^{0.5 \cdot \color{blue}{1}}\right)}^{\left(\left(x \cdot y\right) \cdot \left(y + y\right)\right)} \]
   metadata-eval [=>] 100.0	\[ {\left(e^{\color{blue}{0.5}}\right)}^{\left(\left(x \cdot y\right) \cdot \left(y + y\right)\right)} \]
   *-commutative [=>] 100.0	\[ {\left(e^{0.5}\right)}^{\left(\color{blue}{\left(y \cdot x\right)} \cdot \left(y + y\right)\right)} \]

5. Final simplification 100.0%

   \[\leadsto {\left(e^{0.5}\right)}^{\left(\left(y + y\right) \cdot \left(y \cdot x\right)\right)} \]

Alternatives

Alternative 1
Accuracy	100.0%
Cost	13120

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

Alternative 2
Accuracy	100.0%
Cost	6720

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

Alternative 3
Accuracy	66.9%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023151 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))