Tune search at very long time control

This patch is a result of tuning done by user @candirufish after 150k games.

Since the tuned values were really interesting and touched heuristics
that are known for their non-linear scaling I decided to run limited
games LTC match, even if the STC test was really bad (which was expected).
After seeing the results of the LTC match, I also run a VLTC (very long
time control) SPRTtest, which passed.

The main difference is in extensions: this patch allows much more
singular/double extensions, both in terms of allowing them at lower
depths and with lesser margins.

Failed STC:
https://tests.stockfishchess.org/tests/view/620d66643ec80158c0cd3b46
LLR: -2.94 (-2.94,2.94) <0.00,2.50>
Total: 4968 W: 1194 L: 1398 D: 2376
Ptnml(0-2): 47, 633, 1294, 497, 13

Performed well at LTC in a fixed-length match:
https://tests.stockfishchess.org/tests/view/620d66823ec80158c0cd3b4a
ELO: 3.36 +-1.8 (95%) LOS: 100.0%
Total: 30000 W: 7966 L: 7676 D: 14358
Ptnml(0-2): 36, 2936, 8755, 3248, 25

Passed VLTC SPRT test:
https://tests.stockfishchess.org/tests/view/620da11a26f5b17ec884f939
LLR: 2.96 (-2.94,2.94) <0.50,3.00>
Total: 4400 W: 1326 L: 1127 D: 1947
Ptnml(0-2): 13, 309, 1348, 526, 4

closes #3937

Bench: 6318903

Author: Vizvezdenec

src/search.cpp

@@ -63,15 +63,15 @@ namespace {
 
   // Futility margin
   Value futility_margin(Depth d, bool improving) {
-    return Value(147 * (d - improving));
+    return Value(168 * (d - improving));
   }
 
   // Reductions lookup table, initialized at startup
   int Reductions[MAX_MOVES]; // [depth or moveNumber]
 
   Depth reduction(bool i, Depth d, int mn, Value delta, Value rootDelta) {
     int r = Reductions[d] * Reductions[mn];
-    return (r + 1627 - int(delta) * 1024 / int(rootDelta)) / 1024 + (!i && r > 992);
+    return (r + 1463 - int(delta) * 1024 / int(rootDelta)) / 1024 + (!i && r > 1010);
   }
 
   constexpr int futility_move_count(bool improving, Depth depth) {
@@ -80,7 +80,7 @@ namespace {
 
   // History and stats update bonus, based on depth
   int stat_bonus(Depth d) {
-    return std::min((8 * d + 281) * d - 241 , 1949);
+    return std::min((9 * d + 270) * d - 311 , 2145);
   }
 
   // Add a small random component to draw evaluations to avoid 3-fold blindness
@@ -157,7 +157,7 @@ namespace {
 void Search::init() {
 
   for (int i = 1; i < MAX_MOVES; ++i)
-      Reductions[i] = int((21.14 + std::log(Threads.size()) / 2) * std::log(i));
+      Reductions[i] = int((20.81 + std::log(Threads.size()) / 2) * std::log(i));
 }
 
 
@@ -303,10 +303,10 @@ void Thread::search() {
 
   multiPV = std::min(multiPV, rootMoves.size());
 
-  complexityAverage.set(211, 1);
+  complexityAverage.set(202, 1);
 
   trend         = SCORE_ZERO;
-  optimism[ us] = Value(33);
+  optimism[ us] = Value(39);
   optimism[~us] = -optimism[us];
 
   int searchAgainCounter = 0;
@@ -349,16 +349,16 @@ void Thread::search() {
           if (rootDepth >= 4)
           {
               Value prev = rootMoves[pvIdx].averageScore;
-              delta = Value(19) + int(prev) * prev / 18321;
+              delta = Value(16) + int(prev) * prev / 19178;
               alpha = std::max(prev - delta,-VALUE_INFINITE);
               beta  = std::min(prev + delta, VALUE_INFINITE);
 
               // Adjust trend and optimism based on root move's previousScore
-              int tr = sigmoid(prev, 4, 11, 92, 119, 1);
+              int tr = sigmoid(prev, 3, 8, 90, 125, 1);
               trend = (us == WHITE ?  make_score(tr, tr / 2)
                                    : -make_score(tr, tr / 2));
 
-              int opt = sigmoid(prev, 9, 18, 115, 12250, 187);
+              int opt = sigmoid(prev, 8, 17, 144, 13966, 183);
               optimism[ us] = Value(opt);
               optimism[~us] = -optimism[us];
           }
@@ -459,17 +459,17 @@ void Thread::search() {
           && !Threads.stop
           && !mainThread->stopOnPonderhit)
       {
-          double fallingEval = (66 + 12 * (mainThread->bestPreviousAverageScore - bestValue)
-                                    +  6 * (mainThread->iterValue[iterIdx] - bestValue)) / 809.70;
+          double fallingEval = (69 + 12 * (mainThread->bestPreviousAverageScore - bestValue)
+                                    +  6 * (mainThread->iterValue[iterIdx] - bestValue)) / 781.4;
           fallingEval = std::clamp(fallingEval, 0.5, 1.5);
 
           // If the bestMove is stable over several iterations, reduce time accordingly
-          timeReduction = lastBestMoveDepth + 8 < completedDepth ? 1.73 : 0.94;
-          double reduction = (1.66 + mainThread->previousTimeReduction) / (2.35 * timeReduction);
+          timeReduction = lastBestMoveDepth + 10 < completedDepth ? 1.63 : 0.73;
+          double reduction = (1.56 + mainThread->previousTimeReduction) / (2.20 * timeReduction);
           double bestMoveInstability = 1.073 + std::max(1.0, 2.25 - 9.9 / rootDepth)
                                               * totBestMoveChanges / Threads.size();
           int complexity = mainThread->complexityAverage.value();
-          double complexPosition = std::clamp(1.0 + (complexity - 293) / 1525.0, 0.5, 1.5);
+          double complexPosition = std::clamp(1.0 + (complexity - 326) / 1618.1, 0.5, 1.5);
 
           double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability * complexPosition;
 
@@ -490,7 +490,7 @@ void Thread::search() {
           }
           else if (   Threads.increaseDepth
                    && !mainThread->ponder
-                   && Time.elapsed() > totalTime * 0.49)
+                   && Time.elapsed() > totalTime * 0.43)
                    Threads.increaseDepth = false;
           else
                    Threads.increaseDepth = true;
@@ -766,7 +766,7 @@ namespace {
     // margin and the improving flag are used in various pruning heuristics.
     improvement =   (ss-2)->staticEval != VALUE_NONE ? ss->staticEval - (ss-2)->staticEval
                   : (ss-4)->staticEval != VALUE_NONE ? ss->staticEval - (ss-4)->staticEval
-                  :                                    184;
+                  :                                    175;
 
     improving = improvement > 0;
     complexity = abs(ss->staticEval - (us == WHITE ? eg_value(pos.psq_score()) : -eg_value(pos.psq_score())));
@@ -777,8 +777,8 @@ namespace {
     // If eval is really low check with qsearch if it can exceed alpha, if it can't,
     // return a fail low.
     if (   !PvNode
-        && depth <= 6
-        && eval < alpha - 486 - 314 * depth * depth)
+        && depth <= 7
+        && eval < alpha - 348 - 258 * depth * depth)
     {
         value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
         if (value < alpha)
@@ -791,24 +791,24 @@ namespace {
         &&  depth < 8
         &&  eval - futility_margin(depth, improving) - (ss-1)->statScore / 256 >= beta
         &&  eval >= beta
-        &&  eval < 22266) // larger than VALUE_KNOWN_WIN, but smaller than TB wins.
+        &&  eval < 26305) // larger than VALUE_KNOWN_WIN, but smaller than TB wins.
         return eval;
 
     // Step 9. Null move search with verification search (~22 Elo)
     if (   !PvNode
         && (ss-1)->currentMove != MOVE_NULL
-        && (ss-1)->statScore < 15075
+        && (ss-1)->statScore < 14695
         &&  eval >= beta
         &&  eval >= ss->staticEval
-        &&  ss->staticEval >= beta - 18 * depth - improvement / 19 + 215 + complexity / 30
+        &&  ss->staticEval >= beta - 15 * depth - improvement / 15 + 198 + complexity / 28
         && !excludedMove
         &&  pos.non_pawn_material(us)
         && (ss->ply >= thisThread->nmpMinPly || us != thisThread->nmpColor))
     {
         assert(eval - beta >= 0);
 
         // Null move dynamic reduction based on depth, eval and complexity of position
-        Depth R = std::min(int(eval - beta) / 184, 4) + depth / 3 + 4 - (complexity > 799);
+        Depth R = std::min(int(eval - beta) / 147, 5) + depth / 3 + 4 - (complexity > 753);
 
         ss->currentMove = MOVE_NULL;
         ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
@@ -844,7 +844,7 @@ namespace {
         }
     }
 
-    probCutBeta = beta + 204 - 52 * improving;
+    probCutBeta = beta + 179 - 46 * improving;
 
     // Step 10. ProbCut (~4 Elo)
     // If we have a good enough capture and a reduced search returns a value
@@ -920,7 +920,7 @@ namespace {
 moves_loop: // When in check, search starts here
 
     // Step 12. A small Probcut idea, when we are in check (~0 Elo)
-    probCutBeta = beta + 401;
+    probCutBeta = beta + 481;
     if (   ss->inCheck
         && !PvNode
         && depth >= 2
@@ -1014,14 +1014,14 @@ namespace {
               if (   !pos.empty(to_sq(move))
                   && !givesCheck
                   && !PvNode
-                  && lmrDepth < 7
+                  && lmrDepth < 6
                   && !ss->inCheck
-                  && ss->staticEval + 424 + 138 * lmrDepth + PieceValue[EG][pos.piece_on(to_sq(move))]
-                   + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 7 < alpha)
+                  && ss->staticEval + 281 + 179 * lmrDepth + PieceValue[EG][pos.piece_on(to_sq(move))]
+                   + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 6 < alpha)
                   continue;
 
               // SEE based pruning (~9 Elo)
-              if (!pos.see_ge(move, Value(-214) * depth))
+              if (!pos.see_ge(move, Value(-203) * depth))
                   continue;
           }
           else
@@ -1040,11 +1040,11 @@ namespace {
               // Futility pruning: parent node (~9 Elo)
               if (   !ss->inCheck
                   && lmrDepth < 11
-                  && ss->staticEval + 147 + 125 * lmrDepth + history / 64 <= alpha)
+                  && ss->staticEval + 122 + 138 * lmrDepth + history / 60 <= alpha)
                   continue;
 
               // Prune moves with negative SEE (~3 Elo)
-              if (!pos.see_ge(move, Value(-23 * lmrDepth * lmrDepth - 31 * lmrDepth)))
+              if (!pos.see_ge(move, Value(-25 * lmrDepth * lmrDepth - 20 * lmrDepth)))
                   continue;
           }
       }
@@ -1059,15 +1059,15 @@ namespace {
           // a reduced search on all the other moves but the ttMove and if the
           // result is lower than ttValue minus a margin, then we will extend the ttMove.
           if (   !rootNode
-              &&  depth >= 6 + 2 * (PvNode && tte->is_pv())
+              &&  depth >= 4 + 2 * (PvNode && tte->is_pv())
               &&  move == ttMove
               && !excludedMove // Avoid recursive singular search
            /* &&  ttValue != VALUE_NONE Already implicit in the next condition */
               &&  abs(ttValue) < VALUE_KNOWN_WIN
               && (tte->bound() & BOUND_LOWER)
               &&  tte->depth() >= depth - 3)
           {
-              Value singularBeta = ttValue - 4 * depth;
+              Value singularBeta = ttValue - 3 * depth;
               Depth singularDepth = (depth - 1) / 2;
 
               ss->excludedMove = move;
@@ -1080,7 +1080,7 @@ namespace {
 
                   // Avoid search explosion by limiting the number of double extensions
                   if (  !PvNode
-                      && value < singularBeta - 52
+                      && value < singularBeta - 26
                       && ss->doubleExtensions <= 8)
                       extension = 2;
               }
@@ -1100,15 +1100,15 @@ namespace {
 
           // Check extensions (~1 Elo)
           else if (   givesCheck
-                   && depth > 8
-                   && abs(ss->staticEval) > 81)
+                   && depth > 9
+                   && abs(ss->staticEval) > 71)
               extension = 1;
 
           // Quiet ttMove extensions (~0 Elo)
           else if (   PvNode
                    && move == ttMove
                    && move == ss->killers[0]
-                   && (*contHist[0])[movedPiece][to_sq(move)] >= 7546)
+                   && (*contHist[0])[movedPiece][to_sq(move)] >= 5491)
               extension = 1;
       }
 
@@ -1170,18 +1170,18 @@ namespace {
                          + (*contHist[0])[movedPiece][to_sq(move)]
                          + (*contHist[1])[movedPiece][to_sq(move)]
                          + (*contHist[3])[movedPiece][to_sq(move)]
-                         - 4123;
+                         - 4334;
 
           // Decrease/increase reduction for moves with a good/bad history (~30 Elo)
-          r -= ss->statScore / 17417;
+          r -= ss->statScore / 15914;
 
           // In general we want to cap the LMR depth search at newDepth. But if reductions
           // are really negative and movecount is low, we allow this move to be searched
           // deeper than the first move (this may lead to hidden double extensions).
           int deeper =   r >= -1                   ? 0
-                       : moveCount <= 5            ? 2
-                       : PvNode && depth > 3       ? 1
-                       : cutNode && moveCount <= 7 ? 1
+                       : moveCount <= 4            ? 2
+                       : PvNode && depth > 4       ? 1
+                       : cutNode && moveCount <= 8 ? 1
                        :                             0;
 
           Depth d = std::clamp(newDepth - r, 1, newDepth + deeper);
@@ -1190,7 +1190,7 @@ namespace {
 
           // If the son is reduced and fails high it will be re-searched at full depth
           doFullDepthSearch = value > alpha && d < newDepth;
-          doDeeperSearch = value > (alpha + 76 + 11 * (newDepth - d));
+          doDeeperSearch = value > (alpha + 78 + 11 * (newDepth - d));
           didLMR = true;
       }
       else
@@ -1342,7 +1342,7 @@ namespace {
         //or fail low was really bad
         bool extraBonus =    PvNode
                           || cutNode
-                          || bestValue < alpha - 71 * depth;
+                          || bestValue < alpha - 70 * depth;
 
         update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, stat_bonus(depth) * (1 + extraBonus));
     }
@@ -1473,7 +1473,7 @@ namespace {
         if (PvNode && bestValue > alpha)
             alpha = bestValue;
 
-        futilityBase = bestValue + 139;
+        futilityBase = bestValue + 118;
     }
 
     const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,