Average Error: 39.3 → 39.3
Time: 1.2s
Precision: binary64
\[\sqrt{2 \cdot \left(\sqrt{x \cdot x + y \cdot y} + x\right)}\]
↓
\[\sqrt{2 \cdot \left(\sqrt{x \cdot x + y \cdot y} + x\right)}\]
\sqrt{2 \cdot \left(\sqrt{x \cdot x + y \cdot y} + x\right)}
↓
\sqrt{2 \cdot \left(\sqrt{x \cdot x + y \cdot y} + x\right)}
double code(double x, double y) {
	return ((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y)))))) + x))))));
}
↓
double code(double x, double y) {
	return ((double) sqrt(((double) (2.0 * ((double) (((double) sqrt(((double) (((double) (x * x)) + ((double) (y * 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 39.3

    \[\sqrt{2 \cdot \left(\sqrt{x \cdot x + y \cdot y} + x\right)}\]

  2. Final simplification39.3

    \[\leadsto \sqrt{2 \cdot \left(\sqrt{x \cdot x + y \cdot y} + x\right)}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(sqrt (* 2 (+ (sqrt (+ (* x x) (* y y))) x)))"
  :precision binary64
  (sqrt (* 2.0 (+ (sqrt (+ (* x x) (* y y))) x))))