diff --git a/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h b/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h
index 601dcf5c9a0..7e49bb62376 100644
--- a/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h
+++ b/Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h
@@ -55,10 +55,10 @@ equal_lineC2(const FT &l1a, const FT &l1b, const FT &l1c,
         return false; // Not parallel.
     typename Sgn<FT>::result_type s1a = CGAL_NTS sign(l1a);
     if (s1a != ZERO)
-        return s1a == CGAL_NTS sign(l2a)
-            && sign_of_determinant(l1a, l1c, l2a, l2c) == ZERO;
-    return CGAL_NTS sign(l1b) == CGAL_NTS sign(l2b)
-        && sign_of_determinant(l1b, l1c, l2b, l2c) == ZERO;
+        return CGAL_AND(s1a == CGAL_NTS sign(l2a),
+                        sign_of_determinant(l1a, l1c, l2a, l2c) == ZERO);
+    return CGAL_AND(CGAL_NTS sign(l1b) == CGAL_NTS sign(l2b),
+                    sign_of_determinant(l1b, l1c, l2b, l2c) == ZERO);
 }
 
 template < class FT >
@@ -230,7 +230,7 @@ compare_y_at_x_segment_C2(const FT &px,
     CGAL_kernel_precondition(are_ordered(s1sx, px, s1tx));
     CGAL_kernel_precondition(are_ordered(s2sx, px, s2tx));
 
-    if (s1sx != s1tx && s2sx != s2tx) {
+    if (CGAL_AND(s1sx != s1tx, s2sx != s2tx)) {
         FT s1stx = s1sx-s1tx;
         FT s2stx = s2sx-s2tx;
 
@@ -265,9 +265,9 @@ typename Equal_to<FT>::result_type
 equal_directionC2(const FT &dx1, const FT &dy1,
                   const FT &dx2, const FT &dy2)
 {
-  return CGAL_NTS sign(dx1) == CGAL_NTS sign(dx2)
-      && CGAL_NTS sign(dy1) == CGAL_NTS sign(dy2)
-      && sign_of_determinant(dx1, dy1, dx2, dy2) == ZERO;
+  return CGAL_AND_3( CGAL_NTS sign(dx1) == CGAL_NTS sign(dx2),
+                     CGAL_NTS sign(dy1) == CGAL_NTS sign(dy2),
+                     sign_of_determinant(dx1, dy1, dx2, dy2) == ZERO );
 }
 
 template < class FT >
@@ -391,7 +391,9 @@ typename Compare<FT>::result_type
 compare_lexicographically_xyC2(const FT &px, const FT &py,
                                const FT &qx, const FT &qy)
 {
-  typename Compare<FT>::result_type c = CGAL_NTS compare(px,qx);
+  typedef typename Compare<FT>::result_type Cmp;
+  Cmp c = CGAL_NTS compare(px,qx);
+  if (is_indeterminate(c)) return indeterminate<Cmp>();
   return (c != EQUAL) ? c : CGAL_NTS compare(py,qy);
 }
 
diff --git a/Cartesian_kernel/include/CGAL/predicates/kernel_ftC3.h b/Cartesian_kernel/include/CGAL/predicates/kernel_ftC3.h
index ba15fd30790..8765d0cb587 100644
--- a/Cartesian_kernel/include/CGAL/predicates/kernel_ftC3.h
+++ b/Cartesian_kernel/include/CGAL/predicates/kernel_ftC3.h
@@ -61,8 +61,10 @@ compare_lexicographically_xyzC3(const FT &px, const FT &py, const FT &pz,
 {
   typedef typename Compare<FT>::result_type Cmp;
   Cmp c = CGAL_NTS compare(px, qx);
+  if (is_indeterminate(c)) return indeterminate<Cmp>();
   if (c != EQUAL) return c;
   c = CGAL_NTS compare(py, qy);
+  if (is_indeterminate(c)) return indeterminate<Cmp>();
   if (c != EQUAL) return c;
   return CGAL_NTS compare(pz, qz);
 }
@@ -288,12 +290,12 @@ typename Equal_to<FT>::result_type
 equal_directionC3(const FT &dx1, const FT &dy1, const FT &dz1,
                   const FT &dx2, const FT &dy2, const FT &dz2)
 {
-  return sign_of_determinant(dx1, dy1, dx2, dy2) == ZERO
-      && sign_of_determinant(dx1, dz1, dx2, dz2) == ZERO
-      && sign_of_determinant(dy1, dz1, dy2, dz2) == ZERO
-      && CGAL_NTS sign(dx1) == CGAL_NTS sign(dx2)
-      && CGAL_NTS sign(dy1) == CGAL_NTS sign(dy2)
-      && CGAL_NTS sign(dz1) == CGAL_NTS sign(dz2);
+  return CGAL_AND_6(sign_of_determinant(dx1, dy1, dx2, dy2) == ZERO,
+                    sign_of_determinant(dx1, dz1, dx2, dz2) == ZERO,
+                    sign_of_determinant(dy1, dz1, dy2, dz2) == ZERO,
+                    CGAL_NTS sign(dx1) == CGAL_NTS sign(dx2),
+                    CGAL_NTS sign(dy1) == CGAL_NTS sign(dy2),
+                    CGAL_NTS sign(dz1) == CGAL_NTS sign(dz2) );
 }
 
 template < class FT >
@@ -313,10 +315,10 @@ equal_planeC3(const FT &ha, const FT &hb, const FT &hc, const FT &hd,
                          sign_of_determinant(pa, pd, ha, hd) == ZERO );
     Sg s1b = CGAL_NTS sign(hb);
     if (s1b != ZERO)
-        return s1b == CGAL_NTS sign(pb)
-            && sign_of_determinant(pb, pd, hb, hd) == ZERO;
-    return CGAL_NTS sign(pc) == CGAL_NTS sign(hc)
-        && sign_of_determinant(pc, pd, hc, hd) == ZERO;
+        return CGAL_AND(s1b == CGAL_NTS sign(pb),
+                        sign_of_determinant(pb, pd, hb, hd) == ZERO );
+    return CGAL_AND( CGAL_NTS sign(pc) == CGAL_NTS sign(hc),
+                     sign_of_determinant(pc, pd, hc, hd) == ZERO );
 }
 
 template <class FT >
diff --git a/Filtered_kernel/include/CGAL/Lazy_kernel.h b/Filtered_kernel/include/CGAL/Lazy_kernel.h
index 89a84b5f150..0e9bb380f6a 100644
--- a/Filtered_kernel/include/CGAL/Lazy_kernel.h
+++ b/Filtered_kernel/include/CGAL/Lazy_kernel.h
@@ -480,6 +480,16 @@ public:
 
   };
 
+  struct Less_xyz_3 : public BaseClass::Less_xyz_3
+  {
+    typedef typename Kernel_::Point_3 Point_3;
+
+    bool operator()(const Point_3& p, const Point_3& q) const
+    {
+      if (p.rep().identical(q.rep())) { return false; }
+      return BaseClass::Less_xyz_3::operator()(p,q);
+    }
+  };
 
   Construct_point_2 construct_point_2_object() const
   {
@@ -502,7 +512,6 @@ public:
     return Compute_weight_3();
   }
 
-
   Assign_2
   assign_2_object() const
   { return Assign_2(); }
@@ -534,6 +543,10 @@ public:
   Compute_approximate_area_3
   compute_approximate_area_3_object() const
   { return Compute_approximate_area_3(); }
+
+  Less_xyz_3
+  less_xyz_3_object() const
+  { return Less_xyz_3(); }
 }; // end class Lazy_kernel_base<EK_, AK_, E2A_, Kernel_2>
 
 
diff --git a/Kernel_23/benchmark/Kernel_23/CMakeLists.txt b/Kernel_23/benchmark/Kernel_23/CMakeLists.txt
new file mode 100644
index 00000000000..d061469c729
--- /dev/null
+++ b/Kernel_23/benchmark/Kernel_23/CMakeLists.txt
@@ -0,0 +1,12 @@
+# Created by the script cgal_create_cmake_script
+# This is the CMake script for compiling a CGAL application.
+
+cmake_minimum_required(VERSION 3.1...3.14)
+project( benchmark )
+
+find_package(CGAL REQUIRED QUIET OPTIONAL_COMPONENTS Core )
+
+  include_directories (BEFORE "../include")
+
+create_single_source_cgal_program( "cmp_epeck_points.cpp" )
+
diff --git a/Kernel_23/benchmark/Kernel_23/cmp_epeck_points.cpp b/Kernel_23/benchmark/Kernel_23/cmp_epeck_points.cpp
new file mode 100644
index 00000000000..86e8fec5f9c
--- /dev/null
+++ b/Kernel_23/benchmark/Kernel_23/cmp_epeck_points.cpp
@@ -0,0 +1,36 @@
+#define TEST_IDENTICAL
+
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/Timer.h>
+
+#include <vector>
+#include <algorithm>
+
+typedef CGAL::Exact_predicates_exact_constructions_kernel K;
+typedef K::Point_3 Point_3;
+typedef K::Vector_3 Vector_3;
+
+
+int main(){
+
+  int N = 10000000;
+
+  std::vector<Point_3> points(N);
+
+  int count = 0;
+  for(int i = 0; i < N; i+=10){
+    points[i] = Point_3((N-i) * CGAL_PI , 0, 0) + Vector_3(i * (CGAL_PI/2.0), 0, 0);
+    if(points[i].approx().x().inf() != points[i].approx().x().sup()){
+      ++count;
+    }
+    for(int j = 1; j < 10; j++){
+      points[i+j] =  points[i];
+    }
+  }
+  std::cout << count << " points approx().x().inf() != approx().x().sup()" << std::endl;
+  CGAL::Timer t;
+  t.start();
+  std::sort(points.begin(), points.end());
+  std::cout << t.time() << " sec." << std::endl;
+  return 0;
+}
diff --git a/Kernel_23/include/CGAL/Kernel/function_objects.h b/Kernel_23/include/CGAL/Kernel/function_objects.h
index 1a803d094ae..40d05f8094d 100644
--- a/Kernel_23/include/CGAL/Kernel/function_objects.h
+++ b/Kernel_23/include/CGAL/Kernel/function_objects.h
@@ -3111,7 +3111,7 @@ namespace CommonKernelFunctors {
     result_type
     operator()(const Iso_rectangle_2& i1, const Iso_rectangle_2& i2) const
     {
-      return ((i1.min)() == (i2.min)()) && ((i1.max)() == (i2.max)());
+      return CGAL_AND((i1.min)() == (i2.min)(), (i1.max)() == (i2.max)());
     }
   };
 
@@ -3138,7 +3138,7 @@ namespace CommonKernelFunctors {
     result_type
     operator()(const Point_3 &p, const Point_3 &q) const
     {
-      return p.x() == q.x() && p.y() == q.y() && p.z() == q.z();
+      return CGAL_AND_3(p.x() == q.x(), p.y() == q.y(), p.z() == q.z());
     }
 
     result_type
diff --git a/STL_Extension/include/CGAL/Uncertain.h b/STL_Extension/include/CGAL/Uncertain.h
index 21f46a9196a..1a7539b2b24 100644
--- a/STL_Extension/include/CGAL/Uncertain.h
+++ b/STL_Extension/include/CGAL/Uncertain.h
@@ -348,6 +348,7 @@ Uncertain<bool> operator&(Uncertain<bool> a, bool b)
 #endif
 
 #define CGAL_AND_3(X, Y, Z)  CGAL_AND(X, CGAL_AND(Y, Z))
+#define CGAL_AND_6(A, B, C, D, E, F)  CGAL_AND(CGAL_AND_3(A, B, C), CGAL_AND_3(D, E,F))
 #define CGAL_OR_3(X, Y, Z)   CGAL_OR(X, CGAL_OR(Y, Z))