Which is the more accurate way to compute x2 y2: as x2 y2, or as (x + y)(x y)? (Note that this computation arises when squaring a complex number.) Modification: in my mind, there is no clear winner. The first method has a marginally better error constant if |x2 y2|  2 3(x2 + y2), but the second method could be much better if |x2 y2|(x2 + y2). So just derive error estimates for the two approaches and see if you can see why the second method is better when x2 y2.