Since you double the table size after failing to insert/displace above a constant threshhold, e.g. 8. You have O(1) insert performance. You don't need to rehash

Since you double the table size after failing to insert/displace above a constant threshhold, e.g. 8. You have O(1) insert performance. You don't need to rehash the table either, you can add additional hash functions on each grow, or reuse your existing hash function and use bit masking, (that one does require a copy of the table, albeit no rehashing, and copying chunks is something our CPUs are really good at)