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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

Derivation

Initial program 0.1
\[x + \left(y \cdot z\right) \cdot z \]
Applied egg-rr0.1
\[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, z, x\right)} \]
Final simplification0.1
\[\leadsto \mathsf{fma}\left(y \cdot z, z, x\right) \]

Alternatives

Alternative 1
Error	14.6
Cost	848

\[\begin{array}{l} t_0 := z \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.075284003903084 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 78602224326708.78:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	2.2
Cost	712

\[\begin{array}{l} t_0 := z \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+150}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 10^{+120}:\\ \;\;\;\;x + y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.1
Cost	448

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

Alternative 4
Error	20.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022316 
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))

Error

Derivation

Alternatives

Error

Reproduce