Use futility margin in razoring margin

Uses futilityMargin * depth to set the razoring margin. This retains the
quadratic depth scaling to preserve mate finding capabilities. This patch is
nice because it increases the elo sensitivity of the futility margin
heuristics.

Passed STC:
https://tests.stockfishchess.org/tests/view/665f9892fd11ae7170b4849c
LLR: 2.93 (-2.94,2.94) <0.00,2.00>
Total: 39392 W: 10348 L: 10030 D: 19014
Ptnml(0-2): 99, 4585, 10009, 4905, 98

Passed LTC:
https://tests.stockfishchess.org/tests/view/665f9d2dfd11ae7170b484a8
LLR: 2.95 (-2.94,2.94) <0.50,2.50>
Total: 107910 W: 27521 L: 27053 D: 53336
Ptnml(0-2): 73, 11835, 29670, 12305, 72

closes official-stockfish#5360

bench 1277173

src/search.cpp

@@ -60,9 +60,9 @@ static constexpr double EvalLevel[10] = {0.981, 0.956, 0.895, 0.949, 0.913,
 
 // Futility margin
 Value futility_margin(Depth d, bool noTtCutNode, bool improving, bool oppWorsening) {
-    Value futilityMult       = 124 - 43 * noTtCutNode;
-    Value improvingDeduction = 60 * improving * futilityMult / 32;
-    Value worseningDeduction = 344 * oppWorsening * futilityMult / 1024;
+    Value futilityMult       = 109 - 40 * noTtCutNode;
+    Value improvingDeduction = 59 * improving * futilityMult / 32;
+    Value worseningDeduction = 328 * oppWorsening * futilityMult / 1024;
 
     return futilityMult * d - improvingDeduction - worseningDeduction;
 }
@@ -554,7 +554,7 @@ Value Search::Worker::search(
     bool     givesCheck, improving, priorCapture, opponentWorsening;
     bool     capture, moveCountPruning, ttCapture;
     Piece    movedPiece;
-    int      moveCount, captureCount, quietCount;
+    int      moveCount, captureCount, quietCount, futilityMargin;
     Bound    singularBound;
 
     // Step 1. Initialize node
@@ -761,10 +761,12 @@ Value Search::Worker::search(
 
     opponentWorsening = ss->staticEval + (ss - 1)->staticEval > 2;
 
+    futilityMargin = futility_margin(depth, cutNode && !ss->ttHit, improving, opponentWorsening);
+
     // Step 7. Razoring (~1 Elo)
     // If eval is really low check with qsearch if it can exceed alpha, if it can't,
     // return a fail low.
-    if (eval < alpha - 512 - 293 * depth * depth)
+    if (eval < alpha - 465 - futilityMargin * depth * 33 / 32)
     {
         value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
         if (value < alpha)
@@ -774,9 +776,7 @@ Value Search::Worker::search(
     // Step 8. Futility pruning: child node (~40 Elo)
     // The depth condition is important for mate finding.
     if (!ss->ttPv && depth < 13
-        && eval - futility_margin(depth, cutNode && !ss->ttHit, improving, opponentWorsening)
-               - (ss - 1)->statScore / 263
-             >= beta
+        && eval - futilityMargin - (ss - 1)->statScore / 263 >= beta
         && eval >= beta && eval < VALUE_TB_WIN_IN_MAX_PLY && (!ttMove || ttCapture))
         return beta > VALUE_TB_LOSS_IN_MAX_PLY ? beta + (eval - beta) / 3 : eval;