Is it possible to establish, even roughly, what the maximum precision loss would be when dealing with two double values in java (adding/subtracting)? Probably the worst case scenario is when two numbers cannot be represented exactly, and then an operation is performed on them, which results in a value that also cannot be represented exactly.
Have a look at Math.ulp(double). The ulp of a double is the delta to the next highest value. For instance, if you add to numbers and one is smaller than the ulp of the other, you know that the addition will have no effect. If you multiply two doubles, you can multiply their ulps to get the maximum error of the result.