Do you guys know any way to calculate the intersection of two HLL instances? The algorithm allows merging two sets but it's not that easy to take the intersection of them. A + B - (A U B) is not the optimal way so I would love to hear your suggestions.
Neustar Research has a good article on this which may be of interest to you. However, I think the approach they took was still based on the inclusion-exclusion principle (still a good read though).
Another approach if you have the flexibility of changing your implementation, is to use a different type of data-sketch that is more amenable to set expressions. There is some discussion (and references) here:
