Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]
\[\left(x + y\right) - x \cdot y \]
↓
\[\mathsf{fma}\left(x, 1 - y, y\right) \]
(FPCore (x y) :precision binary64 (- (+ x y) (* x y)))
↓
(FPCore (x y) :precision binary64 (fma x (- 1.0 y) y))
double code(double x, double y) {
	return (x + y) - (x * y);
}
↓
double code(double x, double y) {
	return fma(x, (1.0 - y), y);
}

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

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

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

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022160 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))