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

Average Accuracy: 100.0% → 100.0%

Time: 2.4s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 100.0%

   \[\leadsto e^{\color{blue}{{y}^{2} \cdot x}} \]

3. Simplified 100.0%

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

   [Start] 100.0	\[ e^{{y}^{2} \cdot x} \]
   unpow2 [=>] 100.0	\[ e^{\color{blue}{\left(y \cdot y\right)} \cdot x} \]

4. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	6720

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

Alternative 2
Accuracy	66.5%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023138 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))