Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[\sqrt{x + y}\]
↓
\[\sqrt{y + x}\]
\sqrt{x + y}
↓
\sqrt{y + x}
(FPCore (x y) :precision binary64 (sqrt (+ x y)))
↓
(FPCore (x y) :precision binary64 (sqrt (+ y x)))
double code(double x, double y) {
	return sqrt(x + y);
}
↓
double code(double x, double y) {
	return sqrt(y + 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

    \[\sqrt{x + y}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube_binary64_147821.4

    \[\leadsto \color{blue}{\sqrt[3]{\left(\sqrt{x + y} \cdot \sqrt{x + y}\right) \cdot \sqrt{x + y}}}\]

  4. Simplified21.4

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\sqrt{y + x}\right)}^{3}}}\]
  5. Using strategy rm

  6. Applied rem-cbrt-cube_binary64_14660.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2021076 
(FPCore (x y)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, A"
  :precision binary64
  (sqrt (+ x y)))