Not all numbers in the vicinity of large values can be exactly represented in double precision. In particular 12345678901234567 is not exactly representable in double.
v = [1:9 0:7];
format longg
p = polyval(v, 10)
s = sym(p)
What's the distance between p and the next largest representable number?
eps(p)
If we add something smaller than eps(p) to p it's not enough to get us to the next largest double precision number.
p2 = p + 0.5;
p == p2 % true
