diff --git a/src/nlsat/nlsat_explain.cpp b/src/nlsat/nlsat_explain.cpp
index 83c5f31b6..3d124864b 100644
--- a/src/nlsat/nlsat_explain.cpp
+++ b/src/nlsat/nlsat_explain.cpp
@@ -1226,6 +1226,7 @@ namespace nlsat {
          * https://arxiv.org/abs/2003.00409 
          */
         void project_cdcac(polynomial_ref_vector & ps, var max_x) {
+            bool first = true;
             if (ps.empty())
                 return;
 
@@ -1256,9 +1257,17 @@ namespace nlsat {
                 }
                 TRACE(nlsat_explain, tout << "project loop, processing var "; display_var(tout, x); tout << "\npolynomials\n";
                       display(tout, ps); tout << "\n";);
-                add_lcs(ps, x);
-                psc_discriminant(ps, x);
-                psc_resultant(ps, x);
+                if (first) {
+                    add_lcs(ps, x);
+                    psc_discriminant(ps, x);
+                    psc_resultant(ps, x);
+                    first = false;
+                }
+                else {
+                    add_lcs(ps, x);
+                    psc_discriminant(ps, x);
+                    psc_resultant_sample(ps, x, samples);
+                }
                 
                 if (m_todo.empty())
                     break;