Average Error: 0.0 → 0.0
Time: 3.1s
Precision: binary64
\[x \cdot x + y \cdot y\]
↓
\[\sqrt{y \cdot y + x \cdot x} \cdot \sqrt{y \cdot y + x \cdot x}\]
x \cdot x + y \cdot y
↓
\sqrt{y \cdot y + x \cdot x} \cdot \sqrt{y \cdot y + x \cdot x}
(FPCore (x y) :precision binary64 (+ (* x x) (* y y)))
↓
(FPCore (x y)
 :precision binary64
 (* (sqrt (+ (* y y) (* x x))) (sqrt (+ (* y y) (* x x)))))
double code(double x, double y) {
	return (x * x) + (y * y);
}
↓
double code(double x, double y) {
	return sqrt((y * y) + (x * x)) * sqrt((y * y) + (x * x));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt_binary64_35100.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

    \[\leadsto \sqrt{y \cdot y + x \cdot x} \cdot \sqrt{y \cdot y + x \cdot x}\]

Reproduce

herbie shell --seed 2021047 
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))