This is properly tested std::set implementation, based on self-balansing AVL-tree.
It supports standart std::set operations in guaranteed O(log(n)).
Benchmark was compiled with g++ -std=c++17 -O2.
About 1.5 times slower.
About 1.6 times slower.
About 3% faster in average.
Memory difference is negligible (less than 0.03 MB per 1e6 elements), which is understandable due to equal amount of information, storing in each node (left, right child pointers, parent pointer, and data themselves).