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

Average Accuracy: 100.0% → 100.0%

Time: 1.7s

Precision: binary64

Cost: 13120

Math

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

↓

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

FPCore

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

↓

(FPCore (x y) :precision binary64 (pow E (* y (* y x))))

C

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

↓

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

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.E, (y * (y * x)));
}

Python

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

↓

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

Julia

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

↓

function code(x, y)
	return exp(1) ^ Float64(y * Float64(y * x))
end

MATLAB

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

↓

function tmp = code(x, y)
	tmp = 2.71828182845904523536 ^ (y * (y * x));
end

Wolfram

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

↓

code[x_, y_] := N[Power[E, N[(y * 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%

   \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(y \cdot \left(x \cdot y\right)\right)}} \]
   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	\[ \color{blue}{{\left(e^{1}\right)}^{\left(\left(x \cdot y\right) \cdot y\right)}} \]
   *-commutative [=>] 100.0	\[ {\left(e^{1}\right)}^{\color{blue}{\left(y \cdot \left(x \cdot y\right)\right)}} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	6720

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

Alternative 2
Accuracy	67.0%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023135 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))