When calculating the distance between two 3D points in Java, I can compute the distance, or the distance squared between them, avoiding a call to Math.sqrt.
Natively, I've read that sqrt is only a quarter of the speed of multiplication which makes the inconvenience of using the distance squared not worthwhile.
In Java, what is the absolute performance difference between multiplication and calculating a square root?
I Initially wanted to add this as a comment, but it started to get too bid, so here goes:
Try it yourself. Make a loop with 10.000 iterations where you simply calculate a*a + b*b and another separate loop where you calculate Math.sqrt(a*a + b*a). Time it and you'll know. Calculating a square root is an iterative process on its own where the digital (computer bits) square root converges closer to the real square root of the given number until it's sufficiently close (as soon as the difference between each iteration is less than some really small value). There are multiple algorithms out there beside the one the Math library uses and their speed depends on the input and how the algorithm is designed. Stick with Math.sqrt(...) in my opinion, can't go wrong and it's been tested by a LOT of people.
Although this can be done very fast for one square root, there's a definite observable time difference.
On a side note: I cannot think of a reason to calculate the square root more than once, usually at the end. If you want to know the distance between points, just use the squared value of that distance as a default and make comparisons/summations/subtractions or whatever you want based on that default.
PS: Provide more code if you want a more "practical" answer