Average Error: 0.1 → 0.1
Time: 4.8s
Precision: binary64
\[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
↓
\[\mathsf{fma}\left(x, y, \left(-y\right) \cdot \left(x \cdot y\right)\right) \]
(FPCore (x y) :precision binary64 (* (* x y) (- 1.0 y)))
↓
(FPCore (x y) :precision binary64 (fma x y (* (- y) (* x y))))
double code(double x, double y) {
	return (x * y) * (1.0 - y);
}
↓
double code(double x, double y) {
	return fma(x, y, (-y * (x * y)));
}

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

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

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

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.1

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

  2. Applied egg-rr0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2022133 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1.0 y)))