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

Average Error: 0.0 → 0.0

Time: 3.6s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (fma x (- y z) 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(x, (y - z), 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(x, Float64(y - z), 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[(x * N[(y - z), $MachinePrecision] + z), $MachinePrecision]

Derivation

1. Initial program 0.0

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

2. Simplified 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	24.5
Cost	784

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -151.9358696265468:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.637579584658845 \cdot 10^{-71}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+50}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+97}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2
Error	7.0
Cost	584

\[\begin{array}{l} t_0 := z + x \cdot y\\ \mathbf{if}\;y \leq -2.8242493482857007 \cdot 10^{-129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.0844511696676437 \cdot 10^{-150}:\\ \;\;\;\;z - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	7.0
Cost	584

\[\begin{array}{l} t_0 := z + x \cdot y\\ \mathbf{if}\;y \leq -2.8242493482857007 \cdot 10^{-129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.0844511696676437 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.2
Cost	584

\[\begin{array}{l} t_0 := x \cdot \left(y - z\right)\\ \mathbf{if}\;x \leq -151.9358696265468:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.3048847798148325 \cdot 10^{-14}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	11.7
Cost	520

\[\begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{+55}:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6
Error	23.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.788910637546426 \cdot 10^{-45}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.637579584658845 \cdot 10^{-71}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7
Error	0.0
Cost	448

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

Alternative 8
Error	34.3
Cost	64

\[z \]

Reproduce

herbie shell --seed 2022217 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1.0 x) z)))