Average Error: 0.0 → 0.0
Time: 1.8s
Precision: binary64
\[2 \cdot \left(x \cdot x - x \cdot y\right) \]
↓
\[\mathsf{fma}\left(y, x \cdot -2, x \cdot \left(x \cdot 2\right)\right) \]
(FPCore (x y) :precision binary64 (* 2.0 (- (* x x) (* x y))))
↓
(FPCore (x y) :precision binary64 (fma y (* x -2.0) (* x (* x 2.0))))
double code(double x, double y) {
	return 2.0 * ((x * x) - (x * y));
}
↓
double code(double x, double y) {
	return fma(y, (x * -2.0), (x * (x * 2.0)));
}

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

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

2 \cdot \left(x \cdot x - x \cdot y\right)
↓
\mathsf{fma}\left(y, x \cdot -2, x \cdot \left(x \cdot 2\right)\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. Simplified0.0

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

  3. Applied egg-rr1.2

    \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(-2 \cdot \left(y - x\right)\right)}\right)}^{3}} \]

  4. Applied egg-rr0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022166 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

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

  (* 2.0 (- (* x x) (* x y))))