Average Error: 51.7 → 51.7
Time: 2.9s
Precision: binary64
\[\sqrt{x + y} - \sqrt{x - y}\]
↓
\[\sqrt{x + y} - \sqrt{x - y}\]
\sqrt{x + y} - \sqrt{x - y}
↓
\sqrt{x + y} - \sqrt{x - y}
double code(double x, double y) {
	return ((double) (((double) sqrt(((double) (x + y)))) - ((double) sqrt(((double) (x - y))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) sqrt(((double) (x + y)))) - ((double) sqrt(((double) (x - y))))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 51.7

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

  2. Final simplification51.7

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

Reproduce

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