Check out page 3-5 of this paper called How Futile are Mindless Assessments of Roundoff in Floating-Point Computation? [0]. It explains what is happening here better than I can and is where I got this example from.
That reminds of a jokester who replaced all empty cells in small spread sheet with a space. Good lick figuring out why your 5 row table all of a sudden was in the giga bytes of size (obvious exageration for dramatic reasons). Was a good practical joke so!
Create a table in org mode, pass it to Common Lisp (or Perl or Scheme or R or whatever else floats your boat), and finally hand the thing over to graphviz for an in-line view of the results... and you can write up the relevant formulas with LaTeX.