Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
Cost: 6720
\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]
\[x \cdot x + y \cdot y \]
↓
\[\mathsf{fma}\left(x, x, y \cdot y\right) \]
(FPCore (x y) :precision binary64 (+ (* x x) (* y y)))
↓
(FPCore (x y) :precision binary64 (fma x x (* y y)))
double code(double x, double y) {
	return (x * x) + (y * y);
}
↓
double code(double x, double y) {
	return fma(x, x, (y * y));
}

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

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

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

Error

Derivation

  1. Initial program 0.0

    \[x \cdot x + y \cdot y \]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, y \cdot y\right)} \]
    Proof
    (fma.f64 x x (*.f64 y y)): 0 points increase in error, 0 points decrease in error
    (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x x) (*.f64 y y))): 1 points increase in error, 0 points decrease in error

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error9.1
Cost588
\[\begin{array}{l} \mathbf{if}\;x \leq -1.8773351392824087 \cdot 10^{+21}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -14988.653602232162:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;x \leq -8.293314044445579 \cdot 10^{-162}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[y \cdot y + x \cdot x \]
Alternative 3
Error27.5
Cost192
\[x \cdot x \]

Error

Reproduce

herbie shell --seed 2022300 
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))