Average Error: 0.0 → 0.0
Time: 1.1s
Precision: binary64
\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]
\[\left(x + y\right) - x \cdot y \]
↓
\[\mathsf{fma}\left(y, 1 - x, x\right) \]
(FPCore (x y) :precision binary64 (- (+ x y) (* x y)))
↓
(FPCore (x y) :precision binary64 (fma y (- 1.0 x) x))
double code(double x, double y) {
	return (x + y) - (x * y);
}
↓
double code(double x, double y) {
	return fma(y, (1.0 - x), x);
}

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

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

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

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{\left(y + x\right) - y \cdot x} \]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2022150 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))