You understand precisely the first part of the problem ... it looks easy and linear. But, as the article points out, you may need a very large amount of precis

You understand precisely the first part of the problem ... it looks easy and linear. But, as the article points out, you may need a very large amount of precision to figure out which way the difference goes if it is very close. This isn't about computing a really big sum. This is about computing enough digits of irrational numbers. If you have to compute an exponential number of tinier and tinier digits you still can need exponential time for very small values.