Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3

Average Error: 0.0 → 0.0

Time: 4.3s

Precision: binary64

Cost: 6848

Math

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

↓

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

FPCore

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

↓

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

C

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(y, x, ((1.0 - x) * z));
}

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

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

2. Applied egg-rr 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	6720

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

Alternative 2
Error	1.2
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -3878181.6074148905:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.3266663708400847 \cdot 10^{-17}:\\ \;\;\;\;z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	23.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -6.700369726437684 \cdot 10^{-28}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.2642344477458295 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4
Error	0.0
Cost	448

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

Alternative 5
Error	11.7
Cost	320

\[z + y \cdot x \]

Alternative 6
Error	35.0
Cost	64

\[z \]

Reproduce

herbie shell --seed 2022317 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))