?

\[x \cdot \left(y + y\right) \]

↓

\[y \cdot \left(x \cdot 2\right) \]

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

↓

(FPCore (x y) :precision binary64 (* y (* x 2.0)))

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

↓

double code(double x, double y) {
	return y * (x * 2.0);
}

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

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * (x * 2.0d0)
end function

public static double code(double x, double y) {
	return x * (y + y);
}

↓

public static double code(double x, double y) {
	return y * (x * 2.0);
}

def code(x, y):
	return x * (y + y)

↓

def code(x, y):
	return y * (x * 2.0)

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

↓

function code(x, y)
	return Float64(y * Float64(x * 2.0))
end

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

↓

function tmp = code(x, y)
	tmp = y * (x * 2.0);
end

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

↓

code[x_, y_] := N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]

x \cdot \left(y + y\right)

↓

y \cdot \left(x \cdot 2\right)

Derivation?

Initial program 0.0
\[x \cdot \left(y + y\right) \]
Taylor expanded in x around 0 0.0
\[\leadsto \color{blue}{2 \cdot \left(y \cdot x\right)} \]
Simplified0.0
\[\leadsto \color{blue}{y \cdot \left(x \cdot 2\right)} \]
Proof
[Start]0.0
\[ 2 \cdot \left(y \cdot x\right) \]
rational.json-simplify-43 [=>]0.0
\[ \color{blue}{y \cdot \left(x \cdot 2\right)} \]
Final simplification0.0
\[\leadsto y \cdot \left(x \cdot 2\right) \]

Alternative 1
Error	0.0
Cost	320

[Start]0.0	\[ 2 \cdot \left(y \cdot x\right) \]
rational.json-simplify-43 [=>]0.0	\[ \color{blue}{y \cdot \left(x \cdot 2\right)} \]

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