Why is Stockfish unable to solve this relatively easy study?

Hi.
The position is here : lichess.org/analysis/1q6/6pQ/1p4Pb/p1p2p2/k5p1/P1R5/KPP5/8_w_-_-#0

White's winning move is 1. Rh3 and when you make this move Stockfish recognizes that it is winning, but it takes too much time to find it by itself from the initial position...

My engine finds Rh3 on depth 25 which it reaches in under 4 seconds on my laptop. But indeed sometimes the engines fail to find quite trivial solutions. Example:

lichess.org/editor/2qN4/k2p4/2pP4/1pP3B1/pP6/P3K3/8/8_w_-_-_0_1

Even on depth 75 my engine doesnt find the win and instead moves back and forth with the king. For humans it is obvious how to win.

BTW Leela seems to be able to solve this. However she sucks at other studies (at least last time i checked). Example:

lichess.org/editor/1B6/1p1k4/pPp5/P1Pp1b2/3Pp3/4Pp1p/5PrP/5K2_w_-_-_0_1

Leela plays the idiotic Ke1. While other engines keep the king on f1 but think that black has a winning advantage.

There are still a lot of unsolved secrets in chess.

@nh78 What does the icon to the left of your name mean?

@Irishman964 Which icon are you referring to?

@badnen Because engines can't calculate all the lines and prune some lines if they contain "blunders", which is similar to what humans do. In this case it is the line 1. Rh3!! gh 2. Qh8!! Qxh8 which most humans won't even look at, because both white moves seem huge blunders, and engine euristics prunes this at low depths. Humans eventually can notice this after analyzing the weakness of black's king and how it can be exploited, and engines periodically explore the lines pruned before at higher depths.

Thank you for your interesting replies! A special thank to @Wolfram_EP for your succint but deep explanation.

Well, you can possibly get a deep explanation if you visit the fishcooking forum and ask there (groups.google.com/forum/#!forum/fishcooking), where some developers can reproduce and debug the issue and figure out exactly what quirks in the Stockfish code caused the pruning. Sometimes such analysis and attempts to mitigate the issue help to improve the engine. But note that they might not be really interested in the position if it is well-known or is not from a real game.

@nh78 Yes, indeed! So many secrets especially related to positional understanding. This and the example you have given in your commentary prove that our mind is much more valuable the computers' processors which rely basically on brute calculation of variations. And even if, in the future, we succeed in "teaching" that to computers, I am sure that there would still remain a lot of additional secrets.

@badnen couldnt agree more.

A chess engine is designed to win as many games as possible, rather than solve tactical puzzles. As a consequence of that, sometimes it won't see the optimal move in a situation like this, until you get to a certain depth.