?

Average Error: 0.0 → 0.0
Time: 12.2s
Precision: binary64
Cost: 13056

?

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

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

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

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

Error?

Derivation?

  1. Initial program 0.0

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

  2. Simplified0.0

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

Alternatives

Alternative 1
Error12.3
Cost456
\[\begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-87}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[x \cdot x + y \cdot y \]
Alternative 3
Error27.7
Cost192
\[x \cdot x \]

Error

Reproduce?

herbie shell --seed 2023033 
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))