Looking at this again, I wrote this example way too quickly and totally screwed it up by putting a plus sign instead of a minus sign in the first computation. The relevant comparison would be something like this:
julia> 1 - (0.9999999999999999 + 0.0000000000000001)
0.0julia> (1 - 0.9999999999999999) - 0.0000000000000001
1.1022302462515656e-17