The NumWorks graphing calculator

My point is that, for any given level of accuracy/precision, there's arithmetic you can feed it that will reveal its deficiencies. If the goal is to cleanly have the "square" and "square root" operations neutralize each other, that requires symbolic processing to be reliable. Otherwise, it's just a question of how far you can stretch the implementation before it breaks, and non-symbolic systems tend to break that way silently. Such systems yield results that are very close to the proper one but with bewildering notation (like the ones in the article).