Sometimes do a reduced search if LMR is skipped

If the node doesn't go through LMR and r is too big,
reduce search depth by one ply.

STC:
LLR: 2.94 (-2.94,2.94) <0.00,2.00>
Total: 664888 W: 176375 L: 175169 D: 313344
Ptnml(0-2): 1965, 73754, 179851, 74858, 2016
https://tests.stockfishchess.org/tests/view/6399414c93ed41c57ede8fb8

LTC:
LLR: 2.94 (-2.94,2.94) <0.50,2.50>
Total: 150784 W: 40553 L: 40031 D: 70200
Ptnml(0-2): 76, 14668, 45387, 15180, 81
https://tests.stockfishchess.org/tests/view/639dee6e11c576d919dc2b38

closes https://github.com/official-stockfish/Stockfish/pull/4290

Bench: 3727508

src/search.cpp

@@ -1120,6 +1120,52 @@ moves_loop: // When in check, search starts here
       // Step 16. Make the move
       pos.do_move(move, st, givesCheck);
 
+      Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
+
+      // Decrease reduction if position is or has been on the PV
+      // and node is not likely to fail low. (~3 Elo)
+      if (   ss->ttPv
+          && !likelyFailLow)
+          r -= 2;
+
+      // Decrease reduction if opponent's move count is high (~1 Elo)
+      if ((ss-1)->moveCount > 7)
+          r--;
+
+      // Increase reduction for cut nodes (~3 Elo)
+      if (cutNode)
+          r += 2;
+
+      // Increase reduction if ttMove is a capture (~3 Elo)
+      if (ttCapture)
+          r++;
+
+      // Decrease reduction for PvNodes based on depth
+      if (PvNode)
+          r -= 1 + 11 / (3 + depth);
+
+      // Decrease reduction if ttMove has been singularly extended (~1 Elo)
+      if (singularQuietLMR)
+          r--;
+
+      // Decrease reduction if we move a threatened piece (~1 Elo)
+      if (   depth > 9
+          && (mp.threatenedPieces & from_sq(move)))
+          r--;
+
+      // Increase reduction if next ply has a lot of fail high
+      if ((ss+1)->cutoffCnt > 3)
+          r++;
+
+      ss->statScore =  2 * thisThread->mainHistory[us][from_to(move)]
+                     + (*contHist[0])[movedPiece][to_sq(move)]
+                     + (*contHist[1])[movedPiece][to_sq(move)]
+                     + (*contHist[3])[movedPiece][to_sq(move)]
+                     - 4433;
+
+      // Decrease/increase reduction for moves with a good/bad history (~30 Elo)
+      r -= ss->statScore / (13000 + 4152 * (depth > 7 && depth < 19));
+
       // Step 17. Late moves reduction / extension (LMR, ~98 Elo)
       // We use various heuristics for the sons of a node after the first son has
       // been searched. In general we would like to reduce them, but there are many
@@ -1130,52 +1176,6 @@ moves_loop: // When in check, search starts here
               || !capture
               || (cutNode && (ss-1)->moveCount > 1)))
       {
-          Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
-
-          // Decrease reduction if position is or has been on the PV
-          // and node is not likely to fail low. (~3 Elo)
-          if (   ss->ttPv
-              && !likelyFailLow)
-              r -= 2;
-
-          // Decrease reduction if opponent's move count is high (~1 Elo)
-          if ((ss-1)->moveCount > 7)
-              r--;
-
-          // Increase reduction for cut nodes (~3 Elo)
-          if (cutNode)
-              r += 2;
-
-          // Increase reduction if ttMove is a capture (~3 Elo)
-          if (ttCapture)
-              r++;
-
-          // Decrease reduction for PvNodes based on depth
-          if (PvNode)
-              r -= 1 + 11 / (3 + depth);
-
-          // Decrease reduction if ttMove has been singularly extended (~1 Elo)
-          if (singularQuietLMR)
-              r--;
-
-          // Decrease reduction if we move a threatened piece (~1 Elo)
-          if (   depth > 9
-              && (mp.threatenedPieces & from_sq(move)))
-              r--;
-
-          // Increase reduction if next ply has a lot of fail high
-          if ((ss+1)->cutoffCnt > 3)
-              r++;
-
-          ss->statScore =  2 * thisThread->mainHistory[us][from_to(move)]
-                         + (*contHist[0])[movedPiece][to_sq(move)]
-                         + (*contHist[1])[movedPiece][to_sq(move)]
-                         + (*contHist[3])[movedPiece][to_sq(move)]
-                         - 4433;
-
-          // Decrease/increase reduction for moves with a good/bad history (~30 Elo)
-          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
           // beyond the first move depth. This may lead to hidden double extensions.
@@ -1209,10 +1209,10 @@ moves_loop: // When in check, search starts here
           }
       }
 
-      // Step 18. Full depth search when LMR is skipped
+      // Step 18. Full depth search when LMR is skipped. If expected reduction is high, reduce its depth by 1.
       else if (!PvNode || moveCount > 1)
       {
-              value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth, !cutNode);
+               value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth - (r > 4), !cutNode);
       }
 
       // For PV nodes only, do a full PV search on the first move or after a fail