Average Error: 34.8 → 34.8
Time: 1.8s
Precision: binary64
\[\sqrt{x - y} - \sqrt{x}\]
↓
\[\sqrt{x - y} - \sqrt{x}\]
\sqrt{x - y} - \sqrt{x}
↓
\sqrt{x - y} - \sqrt{x}
double code(double x, double y) {
	return ((double) (((double) sqrt(((double) (x - y)))) - ((double) sqrt(x))));
}
↓
double code(double x, double y) {
	return ((double) (((double) sqrt(((double) (x - y)))) - ((double) sqrt(x))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 34.8

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

  2. Final simplification34.8

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(- (sqrt (- x y)) (sqrt x))"
  :precision binary64
  (- (sqrt (- x y)) (sqrt x)))