Average Error: 0.0 → 0.0
Time: 1.4min
Precision: binary64
Cost: 448
\[x \cdot x + y \cdot y\]
↓
\[x \cdot x + y \cdot y\]
x \cdot x + y \cdot y
↓
x \cdot x + y \cdot y
(FPCore (x y) :precision binary64 (+ (* x x) (* y y)))
↓
(FPCore (x y) :precision binary64 (+ (* x x) (* y y)))
double code(double x, double y) {
	return (x * x) + (y * y);
}
↓
double code(double x, double y) {
	return (x * x) + (y * y);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error12.6
Cost785
\[\begin{array}{l} \mathbf{if}\;y \leq -6.118930439520561 \cdot 10^{-70} \lor \neg \left(y \leq -9.475100020882994 \cdot 10^{-116} \lor \neg \left(y \leq -1.7781012792143406 \cdot 10^{-140}\right) \land y \leq 1.1271085824046623 \cdot 10^{-28}\right):\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array}\]
Alternative 2
Error27.4
Cost192
\[x \cdot x\]
Alternative 3
Error55.4
Cost64
\[0\]

Error

Derivation

  1. Initial program 0.0

    \[x \cdot x + y \cdot y\]
  2. Using strategy rm

  3. Applied *-un-lft-identity_binary64_79210.0

    \[\leadsto \color{blue}{1 \cdot \left(x \cdot x + y \cdot y\right)}\]
  4. Using strategy rm

  5. Applied +-commutative_binary64_78510.0

    \[\leadsto 1 \cdot \color{blue}{\left(y \cdot y + x \cdot x\right)}\]

  6. Simplified0.0

    \[\leadsto \color{blue}{x \cdot x + y \cdot y}\]

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2021014 
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))