\[x \cdot y + \left(1 - x\right) \cdot z \]

↓

\[\mathsf{fma}\left(1 - x, z, x \cdot y\right) \]

(FPCore (x y z) :precision binary64 (+ (* x y) (* (- 1.0 x) z)))

↓

(FPCore (x y z) :precision binary64 (fma (- 1.0 x) z (* x y)))

double code(double x, double y, double z) {
	return (x * y) + ((1.0 - x) * z);
}

↓

double code(double x, double y, double z) {
	return fma((1.0 - x), z, (x * y));
}

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(Float64(1.0 - x) * z))
end

↓

function code(x, y, z)
	return fma(Float64(1.0 - x), z, Float64(x * y))
end

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(1.0 - x), $MachinePrecision] * z + N[(x * y), $MachinePrecision]), $MachinePrecision]

x \cdot y + \left(1 - x\right) \cdot z

↓

\mathsf{fma}\left(1 - x, z, x \cdot y\right)

Derivation

Initial program 0.0
\[x \cdot y + \left(1 - x\right) \cdot z \]
Applied egg-rr0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(1 - x, z, x \cdot y\right)} \]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(1 - x, z, x \cdot y\right) \]

Alternatives

Alternative 1
Error	23.8
Cost	784

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -142.35294720706634:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.465587340358282 \cdot 10^{-41}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	11.9
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	1.0
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -6.626812523086677:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.9427776562286103:\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -6.626812523086677:\\ \;\;\;\;x \cdot y - x \cdot z\\ \mathbf{elif}\;x \leq 0.9427776562286103:\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - z\right)\\ \end{array} \]

Alternative 5
Error	0.0
Cost	576

\[\left(1 - x\right) \cdot z + x \cdot y \]

Alternative 6
Error	24.0
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -142.35294720706634:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.465587340358282 \cdot 10^{-41}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7
Error	0.0
Cost	448

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

Alternative 8
Error	34.6
Cost	64

\[z \]

Reproduce

herbie shell --seed 2022297 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))

Error

Derivation

Alternatives

Error

Reproduce