Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1

Average Error: 0.0 → 0

Time: 1.8s

Precision: binary64

Cost: 6656

Math

\[x - y \cdot y \]

↓

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

FPCore

(FPCore (x y) :precision binary64 (- x (* y y)))

↓

(FPCore (x y) :precision binary64 (fma y (- y) x))

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.0

   \[x - y \cdot y \]

2. Simplified 0

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

3. Final simplification 0

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

Alternatives

Alternative 1
Error	11.2
Cost	520

\[\begin{array}{l} t_0 := y \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -2.6676010255005967 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.811287136641477 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.0
Cost	320

\[x - y \cdot y \]

Alternative 3
Error	21.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022228 
(FPCore (x y)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1"
  :precision binary64
  (- x (* y y)))