diff --git a/src/Makefile b/src/Makefile
index 53c3a929..24a62826 100644
--- a/src/Makefile
+++ b/src/Makefile
@@ -160,8 +160,8 @@ endif
 
 ifeq ($(ARCH),armv8)
 	arch = armv8-a
-	bits = 64
 	prefetch = yes
+	popcnt = yes
 endif
 
 ifeq ($(ARCH),ppc-32)
@@ -370,8 +370,8 @@ endif
 
 ### 3.6 popcnt
 ifeq ($(popcnt),yes)
-	ifeq ($(arch),ppc64)
-		CXXFLAGS += -DUSE_POPCNT -DUSE_SSE2
+	ifeq ($(arch),$(filter $(arch),ppc64 armv8-a))
+		CXXFLAGS += -DUSE_POPCNT
 	else ifeq ($(comp),icc)
 		CXXFLAGS += -msse3 -DUSE_POPCNT -DUSE_SSE2
 	else
@@ -399,10 +399,20 @@ endif
 ### needs access to the optimization flags.
 ifeq ($(optimize),yes)
 ifeq ($(debug), no)
-	ifeq ($(comp),$(filter $(comp),gcc clang mingw))
+	ifeq ($(comp),$(filter $(comp),gcc clang))
 		CXXFLAGS += -flto
 		LDFLAGS += $(CXXFLAGS)
 	endif
+
+# To use LTO and static linking on windows, the tool chain requires a recent gcc:
+# gcc version 10.1 in msys2 or TDM-GCC version 9.2 are know to work, older might not.
+# So, only enable it for a cross from Linux by default.
+	ifeq ($(comp),mingw)
+	ifeq ($(KERNEL),Linux)
+		CXXFLAGS += -flto
+		LDFLAGS += $(CXXFLAGS)
+	endif
+	endif
 endif
 endif
 
diff --git a/src/eval/nnue/nnue_common.h b/src/eval/nnue/nnue_common.h
index 502fbc05..bb52bdfe 100644
--- a/src/eval/nnue/nnue_common.h
+++ b/src/eval/nnue/nnue_common.h
@@ -7,6 +7,8 @@
 
 #if defined(USE_AVX2)
 #include <immintrin.h>
+#elif defined(USE_SSE41)
+#include <smmintrin.h>
 #elif defined(USE_SSE2)
 #include <emmintrin.h>
 #endif
diff --git a/src/learn/learner.cpp b/src/learn/learner.cpp
index fb0d9959..ea7c4d7e 100644
--- a/src/learn/learner.cpp
+++ b/src/learn/learner.cpp
@@ -1028,24 +1028,10 @@ double sigmoid(double x)
 // A function that converts the evaluation value to the winning rate [0,1]
 double winning_percentage(double value)
 {
-	// In Maxima,
-	// load("C:/maxima-5.44.0/cform.lisp");
-	// PawnValueEg = 206;
-	// cform(1.0 / (1.0 + 10.0 ^ (-value / PawnValueEg / 4.0)));
-	constexpr double PawnValue = PawnValueEg;
-	return 1.0 * pow(pow(10.0, -0.25 * pow(PawnValue, -1) * value) + 1.0, -1);
-}
-
-double delta_winning_percentage(double value)
-{
-	// In Maxima,
-	// load("C:/maxima-5.44.0/cform.lisp");
-	// PawnValueEg = 206;
-	// cform(diff(1.0/(1.0+10.0^(-value/PawnValue/4.0)),value));
-	constexpr double PawnValue = PawnValueEg;
-	return
-		0.5756462732485115 * pow(PawnValue, -1) * pow(10.0, -0.25 * pow(PawnValue, -1) * value) *
-		pow(pow(10.0, -0.25 * pow(PawnValue, -1) * value) + 1.0, -2);
+	// 1/(1+10^(-Eval/4))
+	// = 1/(1+e^(-Eval/4*ln(10))
+	// = sigmoid(Eval/4*ln(10))
+	return sigmoid(value / PawnValueEg / 4.0 * log(10.0));
 }
 double dsigmoid(double x)
 {
@@ -1143,7 +1129,6 @@ double calc_grad(Value deep, Value shallow , const PackedSfenValue& psv)
 
 	const double q = winning_percentage(shallow);
 	const double p = winning_percentage(deep);
-	const double dq = delta_winning_percentage(shallow);
 
 	// Use 1 as the correction term if the expected win rate is 1, 0 if you lose, and 0.5 if you draw.
 	// game_result = 1,0,-1 so add 1 and divide by 2.
@@ -1154,9 +1139,7 @@ double calc_grad(Value deep, Value shallow , const PackedSfenValue& psv)
 
 	// Use the actual win rate as a correction term.
 	// This is the idea of ​​elmo (WCSC27), modern O-parts.
-	const double pp = (q - p) * dq / q / (1.0 - q);
-	const double tt = (q - t) * dq / q / (1.0 - q);
-	const double grad = lambda * pp + (1.0 - lambda) * tt;
+	const double grad = lambda * (q - p) + (1.0 - lambda) * (q - t);
 
 	return grad;
 }
diff --git a/src/search.h b/src/search.h
index 0d22b0ff..7638d822 100644
--- a/src/search.h
+++ b/src/search.h
@@ -92,7 +92,7 @@ struct LimitsType {
   }
 
   bool use_time_management() const {
-    return !(mate | movetime | depth | nodes | perft | infinite);
+    return time[WHITE] || time[BLACK];
   }
 
   std::vector<Move> searchmoves;