Indeed, it's hard to me to imagine such an expression without any of the following qualities:
- immediately converges to zero
- immediately heads to infinity
- is dominated by only a few terms (thus obviating the needs for the other X million terms)
It sounds like the problem is that it’s dominated by a few terms, but finding them is tricky. If you have 1.0 x + 2.0 x - 3.0 x - 5/4 x + x - x + x - x … (etc for a few GB) and then quadratic terms, it’ll take work to figure out whether the dominant term is linear or quadratic. Cancelling out the potentially important intermediate terms (especially in higher dimensions) sounds like a mess.
- immediately converges to zero - immediately heads to infinity - is dominated by only a few terms (thus obviating the needs for the other X million terms)