diff --git a/Distance_3/benchmark/Distance_3/bench_thingi10k_3.cpp b/Distance_3/benchmark/Distance_3/bench_thingi10k_3.cpp
index d51b047226c..ad1ad41dab7 100644
--- a/Distance_3/benchmark/Distance_3/bench_thingi10k_3.cpp
+++ b/Distance_3/benchmark/Distance_3/bench_thingi10k_3.cpp
@@ -16,6 +16,20 @@
 #include <cassert>
 #include <iostream>
 
+template <typename K>
+class Old_compare_squared_distance_3
+{
+  typedef typename K::FT                 FT;
+public:
+  typedef typename K::Comparison_result  result_type;
+
+  template <class T1, class T2>
+  CGAL::Needs_FT<result_type>
+  operator()(const T1& p, const T2& q, const FT& d2) const
+  {
+    return CGAL::compare(CGAL::internal::squared_distance(p, q, K()), d2);
+  }
+};
 
 template <typename K>
 struct Test
@@ -41,6 +55,7 @@ struct Test
 public:
    Test() : nb_closed_pairs(0){ }
 
+  template<bool optimized_version>
   void close_triangles(std::vector<P> &points, std::vector<boost::container::small_vector<std::size_t, 3> >& triangles, FT d2){
     std::vector< CBox > boxes;
     auto extend_bbox3=[&](const Iterator it, FT& d2){
@@ -60,9 +75,14 @@ public:
       if(v.size()!=0) //they have common vertices
         return;
 
-      bool comp = K().compare_squared_distance_3_object()(T(points[a[0]], points[a[1]], points[a[2]]),
-                                                 T(points[b[0]], points[b[1]], points[b[2]]),
-                                                 d2)!=CGAL::LARGER;
+      bool comp;
+      T tr1(points[a[0]], points[a[1]], points[a[2]]);
+      T tr2(points[b[0]], points[b[1]], points[b[2]]);
+      if constexpr(optimized_version)
+        comp = K().compare_squared_distance_3_object()(tr1, tr2, d2)!=CGAL::LARGER;
+      else
+        comp = Old_compare_squared_distance_3<K>()(tr1, tr2, d2)!=CGAL::LARGER;
+
       if(comp)
       {
         nb_closed_pairs++;
@@ -88,9 +108,15 @@ public:
     }
     CGAL::Real_timer t;
     t.start();
-    close_triangles(input_points, input_triangles, d2);
+    close_triangles<true>(input_points, input_triangles, d2);
     t.stop();
-    std::cout << "#points = " << input_points.size() << " and #triangles = " << input_triangles.size() << " has " << nb_closed_pairs << " pairs at squared distance " << d2 << " in " << t.time() << " sec." << std::endl;
+    std::cout << "New version: #points = " << input_points.size() << " and #triangles = " << input_triangles.size() << " has " << nb_closed_pairs << " pairs at squared distance " << d2 << " in " << t.time() << " sec." << std::endl;
+    nb_closed_pairs=0;
+    t.reset();
+    t.start();
+    close_triangles<false>(input_points, input_triangles, d2);
+    t.stop();
+    std::cout << "Old version: #points = " << input_points.size() << " and #triangles = " << input_triangles.size() << " has " << nb_closed_pairs << " pairs at squared distance " << d2 << " in " << t.time() << " sec." << std::endl;
   }
 };
 
@@ -139,9 +165,11 @@ int main(int argc, char** argv)
   average_length/=(3*input_triangles.size());
 
   // Test<CGAL::Exact_predicates_inexact_constructions_kernel>().run(filename, 100*max/input_points.size());
+  std::cout << "EPICK" << std::endl;
   Test<CGAL::Exact_predicates_inexact_constructions_kernel>().run(filename, average_length*average_length/256);
   Test<CGAL::Exact_predicates_inexact_constructions_kernel>().run(filename, min_sq_length*4);
 
+  std::cout << "EPECK" << std::endl;
   Test<CGAL::Exact_predicates_exact_constructions_kernel>().run(filename, average_length*average_length/256);
   Test<CGAL::Exact_predicates_exact_constructions_kernel>().run(filename, min_sq_length*4);
 
diff --git a/Distance_3/include/CGAL/Distance_3/Triangle_3_Triangle_3.h b/Distance_3/include/CGAL/Distance_3/Triangle_3_Triangle_3.h
index 6584e669f34..876e0c955ec 100644
--- a/Distance_3/include/CGAL/Distance_3/Triangle_3_Triangle_3.h
+++ b/Distance_3/include/CGAL/Distance_3/Triangle_3_Triangle_3.h
@@ -229,7 +229,7 @@ compare_squared_distance_disjoint(const typename K::Triangle_3& tr1,
   typename K::Comparison_result res(LARGER);
 
   // The tiangle are supposed to be disjoint
-  assertion(!do_intersect(tr1, tr2));
+  assert(!do_intersect(tr1, tr2));
 
   for(int i=0; i<3; ++i)
   {
diff --git a/HalfedgeDS/include/CGAL/boost/graph/properties_HalfedgeDS_base.h b/HalfedgeDS/include/CGAL/boost/graph/properties_HalfedgeDS_base.h
index 3863b149e4f..65eedd6652c 100644
--- a/HalfedgeDS/include/CGAL/boost/graph/properties_HalfedgeDS_base.h
+++ b/HalfedgeDS/include/CGAL/boost/graph/properties_HalfedgeDS_base.h
@@ -20,7 +20,7 @@
 #include <CGAL/number_utils.h>
 #include <memory>
 #include <CGAL/boost/graph/internal/Has_member_id.h>
-#include <CGAL/Distance_3/Point_3_Point_3.h>
+#include <CGAL/Distance_3>
 #include <CGAL/Dynamic_property_map.h>
 
 namespace CGAL {