One day my colleague, Todd Eisworth, walked into my office and showed this to me:
This is, of course, ridiculous. I tried listing some values of n·sin(2π·e·n!) using MAPLE and they went all over the place. That shouldn’t surprise anyone; to take the sine of a really big number, we have to get an accurate value of that number modulo 2π, and thus we need far more significant figures than any software is inclined to give us.