Average Error: 8.1 → 8.1
Time: 2.3s
Precision: binary64
\[\left(\sqrt{x} + \sqrt{y}\right) - \sqrt{\frac{x}{y}}\]
↓
\[\left(\sqrt{x} + \sqrt{y}\right) - \sqrt{\frac{x}{y}}\]
\left(\sqrt{x} + \sqrt{y}\right) - \sqrt{\frac{x}{y}}
↓
\left(\sqrt{x} + \sqrt{y}\right) - \sqrt{\frac{x}{y}}
double code(double x, double y) {
	return ((double) (((double) (((double) sqrt(x)) + ((double) sqrt(y)))) - ((double) sqrt(((double) (x / y))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) sqrt(x)) + ((double) sqrt(y)))) - ((double) sqrt(((double) (x / 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 8.1

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

  2. Final simplification8.1

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

Reproduce

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