Average Error: 60.1 → 60.1
Time: 2.3s
Precision: binary64
\[\sqrt{x - y} - \sqrt{\left(x - y\right) - 1}\]
↓
\[\sqrt{x - y} - \sqrt{\left(x - y\right) - 1}\]
\sqrt{x - y} - \sqrt{\left(x - y\right) - 1}
↓
\sqrt{x - y} - \sqrt{\left(x - y\right) - 1}
double code(double x, double y) {
	return ((double) (((double) sqrt(((double) (x - y)))) - ((double) sqrt(((double) (((double) (x - y)) - 1.0))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) sqrt(((double) (x - y)))) - ((double) sqrt(((double) (((double) (x - y)) - 1.0))))));
}

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 60.1

    \[\sqrt{x - y} - \sqrt{\left(x - y\right) - 1}\]

  2. Final simplification60.1

    \[\leadsto \sqrt{x - y} - \sqrt{\left(x - y\right) - 1}\]

Reproduce

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