doEvenDeeperSearch + tuning

Credit for the main idea of doEvenDeeperSearch goes to Vizvezdenec,
tuning by FauziAkram: Expansion of existing logic of doDeeperSearch -
if value from LMR is really really good do full depth search not
1 ply deeper but rather 2 instead.

Passed STC:
LLR: 2.93 (-2.94,2.94) <0.00,2.00>
Total: 330048 W: 87672 L: 86942 D: 155434
Ptnml(0-2): 1012, 36739, 88912, 37229, 1132
https://tests.stockfishchess.org/tests/view/638a1cadd2b9c924c4c621d2

Passed LTC:
LLR: 2.95 (-2.94,2.94) <0.50,2.50>
Total: 216696 W: 57891 L: 57240 D: 101565
Ptnml(0-2): 72, 21221, 65152, 21790, 113
https://tests.stockfishchess.org/tests/view/638c7d52a971f1f096c68fe2

closes https://github.com/official-stockfish/Stockfish/pull/4256

Bench: 3461830

src/search.cpp

@@ -81,7 +81,7 @@ namespace {
 
   // History and stats update bonus, based on depth
   int stat_bonus(Depth d) {
-    return std::min((12 * d + 282) * d - 349 , 1594);
+    return std::min((12 * d + 282) * d - 349 , 1480);
   }
 
   // Add a small random component to draw evaluations to avoid 3-fold blindness
@@ -1172,7 +1172,7 @@ moves_loop: // When in check, search starts here
                          - 4433;
 
           // Decrease/increase reduction for moves with a good/bad history (~30 Elo)
-          r -= ss->statScore / (13628 + 4000 * (depth > 7 && depth < 19));
+          r -= ss->statScore / (13000 + 4152 * (depth > 7 && depth < 19));
 
           // In general we want to cap the LMR depth search at newDepth, but when
           // reduction is negative, we allow this move a limited search extension
@@ -1187,9 +1187,10 @@ moves_loop: // When in check, search starts here
               // Adjust full depth search based on LMR results - if result
               // was good enough search deeper, if it was bad enough search shallower
               const bool doDeeperSearch = value > (alpha + 64 + 11 * (newDepth - d));
+              const bool doEvenDeeperSearch = value > alpha + 582;
               const bool doShallowerSearch = value < bestValue + newDepth;
 
-              newDepth += doDeeperSearch - doShallowerSearch;
+              newDepth += doDeeperSearch - doShallowerSearch + doEvenDeeperSearch;
 
               if (newDepth > d)
                   value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth, !cutNode);