Average Error: 23.6 → 23.6
Time: 1.3s
Precision: binary64
\[\sqrt{\frac{1 - x \cdot x}{1 - y \cdot y}}\]
↓
\[\sqrt{\frac{1 - x \cdot x}{1 - y \cdot y}}\]
\sqrt{\frac{1 - x \cdot x}{1 - y \cdot y}}
↓
\sqrt{\frac{1 - x \cdot x}{1 - y \cdot y}}
double code(double x, double y) {
	return ((double) sqrt(((double) (((double) (1.0 - ((double) (x * x)))) / ((double) (1.0 - ((double) (y * y))))))));
}
↓
double code(double x, double y) {
	return ((double) sqrt(((double) (((double) (1.0 - ((double) (x * x)))) / ((double) (1.0 - ((double) (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

Derivation

  1. Initial program 23.6

    \[\sqrt{\frac{1 - x \cdot x}{1 - y \cdot y}}\]

  2. Final simplification23.6

    \[\leadsto \sqrt{\frac{1 - x \cdot x}{1 - y \cdot y}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y)
  :name "(sqrt (/ (- 1 (* x x)) (- 1 (* y y))))"
  :precision binary64
  (sqrt (/ (- 1.0 (* x x)) (- 1.0 (* y y)))))