Tighter futility margins, based on tuning

Bench: 5530025

src/search.cpp

@@ -70,7 +70,11 @@ namespace {
   // Razoring and futility margin based on depth
   // razor_margin[0] is unused as long as depth >= ONE_PLY in search
   const int razor_margin[] = { 0, 570, 603, 554 };
-  Value futility_margin(Depth d) { return Value(150 * d / ONE_PLY); }
+
+  const int FutilityConstant = -40;
+  const int FutilityMaterialSlope = -27;
+  const int FutilityDepthSlope = 102;
+  inline Value futility_margin(Depth d, Value nonPawnMaterial) { return Value(FutilityDepthSlope * d / ONE_PLY + (FutilityMaterialSlope * (int)nonPawnMaterial) / 327680 + FutilityConstant); }
 
   // Futility and reductions lookup tables, initialized at startup
   int FutilityMoveCounts[2][16]; // [improving][depth]
@@ -733,7 +737,7 @@ namespace {
     // Step 7. Futility pruning: child node (skipped when in check)
     if (   !rootNode
         &&  depth < 7 * ONE_PLY
-        &&  eval - futility_margin(depth) >= beta
+        &&  eval - futility_margin(depth, pos.non_pawn_material()) >= beta
         &&  eval < VALUE_KNOWN_WIN  // Do not return unproven wins
         &&  pos.non_pawn_material(pos.side_to_move()))
         return eval;