?

Average Error: 0.02% → 0.01%
Time: 2.7s
Precision: binary64
Cost: 6912

?

\[2 \cdot \left(x \cdot x - x \cdot y\right) \]
↓
\[2 \cdot \mathsf{fma}\left(x, x, x \cdot \left(-y\right)\right) \]
(FPCore (x y) :precision binary64 (* 2.0 (- (* x x) (* x y))))
↓
(FPCore (x y) :precision binary64 (* 2.0 (fma x x (* x (- y)))))
double code(double x, double y) {
	return 2.0 * ((x * x) - (x * y));
}
↓
double code(double x, double y) {
	return 2.0 * fma(x, x, (x * -y));
}

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, x, Float64(x * Float64(-y))))
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 * x + N[(x * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

Error?

Target

Original0.02%
Target0.01%
Herbie0.01%
\[\left(x \cdot 2\right) \cdot \left(x - y\right) \]

Derivation?

  1. Initial program 0.02

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

  2. Applied egg-rr0.01

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

  3. Final simplification0.01

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

Alternatives

Alternative 1
Error12.18%
Cost585
\[\begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-42} \lor \neg \left(y \leq 2.3 \cdot 10^{-77}\right):\\ \;\;\;\;x \cdot \left(y \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot x\right)\\ \end{array} \]
Alternative 2
Error0.02%
Cost576
\[2 \cdot \left(x \cdot x - x \cdot y\right) \]
Alternative 3
Error0.01%
Cost448
\[\left(x - y\right) \cdot \left(2 \cdot x\right) \]
Alternative 4
Error34.2%
Cost320
\[x \cdot \left(y \cdot -2\right) \]

Error

Reproduce?

herbie shell --seed 2023088 
(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))))