Average Error: 0.1 → 0.1
Time: 2.3s
Precision: binary64
\[\sqrt{x + 1} \cdot \sqrt{y} - \sqrt{x}\]
↓
\[\sqrt{x + 1} \cdot \sqrt{y} - \sqrt{x}\]
\sqrt{x + 1} \cdot \sqrt{y} - \sqrt{x}
↓
\sqrt{x + 1} \cdot \sqrt{y} - \sqrt{x}
double code(double x, double y) {
	return ((double) (((double) (((double) sqrt(((double) (x + 1.0)))) * ((double) sqrt(y)))) - ((double) sqrt(x))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) sqrt(((double) (x + 1.0)))) * ((double) sqrt(y)))) - ((double) sqrt(x))));
}

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 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(- (* (sqrt (+ x 1)) (sqrt y)) (sqrt x))"
  :precision binary64
  (- (* (sqrt (+ x 1.0)) (sqrt y)) (sqrt x)))