When plotting data with very large values (in my use case I have around 10^55), the pgf backend produces files on which latex chokes saying:

! Number too big.
13653335517
866810233117889238902434402615404068235693260800.000000in
l.97 ...8902434402615404068235693260800.000000in}}
%
I can only go up to 2147483647='17777777777="7FFFFFFF,
so I'm using that number instead of yours.

From a quick look at the code, it apparrently just sets the clipping rectangle and just passes then numbers through otherwise. I suppose some clipping should happen in the backend itself.