I read up on Stockfish NNUE and as far as I understand it, Stockfish NNUE was (at least in early stages) trained by positions which were evaluated by the hand-crafted eval. function by stockfish. The question I have is, why the NNUE is stronger than the hand-crafted eval? Since the ANN was trained using the hand-crafted function, it only represents it using an ANN? Is that correct, or is my understanding wrong?
From what I've read, the search speed with the hand-crafted eval. was around 100 Million Positions. Search speed using the NNUE was around 60. Million. Therefore, the hand-crafted eval should be stronger.
What am I missing?