?

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

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

↓

\[\mathsf{fma}\left(z, x, z \cdot y\right) \]

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

↓

(FPCore (x y z) :precision binary64 (fma z x (* z y)))

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

↓

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

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

↓

function code(x, y, z)
	return fma(z, x, Float64(z * y))
end

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

↓

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

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

↓

\mathsf{fma}\left(z, x, z \cdot y\right)

Derivation?

Initial program 0.0
\[\left(x + y\right) \cdot z \]
Applied egg-rr0.0
\[\leadsto \color{blue}{z \cdot y + z \cdot x} \]
Applied egg-rr0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(z, x, z \cdot y\right)} \]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(z, x, z \cdot y\right) \]

Alternative 1
Error	0.0
Cost	448

\[z \cdot y + z \cdot x \]

Alternative 2
Error	10.4
Cost	324

\[\begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-148}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 3
Error	0.0
Cost	320

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

Alternative 4
Error	29.9
Cost	192

\[z \cdot y \]

herbie shell --seed 2023039 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))