Average Error: 0.0 → 0
Time: 853.0ms
Precision: binary64
\[x - y \cdot y \]
↓
\[\mathsf{fma}\left(y, -y, x\right) \]
(FPCore (x y) :precision binary64 (- x (* y y)))
↓
(FPCore (x y) :precision binary64 (fma y (- y) x))
double code(double x, double y) {
	return x - (y * y);
}
↓
double code(double x, double y) {
	return fma(y, -y, x);
}

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

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

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

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x - y \cdot y \]

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2022160 
(FPCore (x y)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1"
  :precision binary64
  (- x (* y y)))