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For queries like select * from a, b on a.x = b.x and a.y = b.x, we can push down a filter before side a with condition a.x=a.y and only keep one of the two join condition in hash join executor.
Such optimization can apply to almost all kinds of hash join with the exception of anti-join.
For anti-join we can not push down a filter or keep let join key. Instead, we need to evaluate the predicate in hash join executor. If a.x=a.y is false, we know the join condition a.x = b.x and a.y = b.x is false.