Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[2 \cdot \left(x \cdot x + x \cdot y\right) \]
↓
\[2 \cdot \mathsf{fma}\left(x, y, x \cdot x\right) \]
(FPCore (x y) :precision binary64 (* 2.0 (+ (* x x) (* x y))))
↓
(FPCore (x y) :precision binary64 (* 2.0 (fma x y (* x x))))
double code(double x, double y) {
	return 2.0 * ((x * x) + (x * y));
}
↓
double code(double x, double y) {
	return 2.0 * fma(x, y, (x * x));
}

function code(x, y)
	return Float64(2.0 * Float64(Float64(x * x) + Float64(x * y)))
end
↓
function code(x, y)
	return Float64(2.0 * fma(x, y, Float64(x * x)))
end

code[x_, y_] := N[(2.0 * N[(N[(x * x), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(2.0 * N[(x * y + N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0.0
Herbie0.0
\[\left(x \cdot 2\right) \cdot \left(x + y\right) \]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x + x \cdot y\right) \]

  2. Applied egg-rr0.0

    \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(x, y, x \cdot x\right)} \]

  3. Final simplification0.0

    \[\leadsto 2 \cdot \mathsf{fma}\left(x, y, x \cdot x\right) \]

Reproduce

herbie shell --seed 2022150 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (* x 2.0) (+ x y))

  (* 2.0 (+ (* x x) (* x y))))