Average Error: 0.0 → 0
Time: 970.0ms
Precision: binary64
\[x \cdot \left(1 - y\right) \]
↓
\[\mathsf{fma}\left(y, -x, x\right) \]
(FPCore (x y) :precision binary64 (* x (- 1.0 y)))
↓
(FPCore (x y) :precision binary64 (fma y (- x) x))
double code(double x, double y) {
	return x * (1.0 - y);
}
↓
double code(double x, double y) {
	return fma(y, -x, x);
}

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

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

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

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{x - x \cdot y} \]

  3. Taylor expanded in x around 0 0.0

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

  4. Simplified0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2022162 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))