diff --git a/src/sat/sat_aig_finder.cpp b/src/sat/sat_aig_finder.cpp
index 162ee9045..6318d18c0 100644
--- a/src/sat/sat_aig_finder.cpp
+++ b/src/sat/sat_aig_finder.cpp
@@ -35,15 +35,13 @@ namespace sat {
         return false;
     }
 
-
     void aig_finder::find_aigs(clause_vector& clauses) {
         if (!m_on_aig) {
             return;
         }
         unsigned j = 0;
         for (clause* cp : clauses) {
-            clause& c = *cp;
-            if (!find_aig(c)) {
+            if (!find_aig(*cp)) {
                 clauses[j++] = cp;
             }
         }
@@ -61,9 +59,7 @@ namespace sat {
         for (literal head : c) {
             is_aig = true;
             for (literal tail : c) {
-                if (head == tail) 
-                    continue;
-                if (!implies(head, ~tail)) {
+                if (head != tail && !implies(head, ~tail)) {
                     is_aig = false;
                     break;
                 }
@@ -187,25 +183,28 @@ namespace sat {
             insert_ternary(*cp);
         }
         auto try_ite = [&,this](literal x, literal y, literal z, clause& c) {
-            clause* c1, *c3;
-            if (has_ternary(y, ~z, ~x, c1)) {
-                binary b(~y, x, nullptr);
-                if (!binaries.find(b, b)) {
-                    return false;
-                }
-                for (auto p : *b.use_list) {
-                    literal u = p.first;
-                    clause* c2 = p.second;
-                    if (has_ternary(~u, ~x, ~y, c3)) {
-                        c.mark_used();
-                        if (c1) c1->mark_used();
-                        if (c2) c2->mark_used();
-                        if (c3) c3->mark_used();
-                        // DEBUG_CODE(validate_if(~x, ~y, z, u, c, c1, c2, c3););
-                        m_on_if(~x, ~y, z, u);
-                        return true;
-                    }
+            literal u;
+            clause* c1, *c2, *c3;
+            if (!has_ternary(y, ~z, ~x, c1)) {
+                return false;
+            }
+            binary b(~y, x, nullptr);
+            if (!binaries.find(b, b)) {
+                return false;
+            }
+            for (auto p : *b.use_list) {
+                u  = p.first;
+                c2 = p.second;
+                if (!has_ternary(~u, ~x, ~y, c3)) {
+                    continue;
                 }
+                c.mark_used();
+                if (c1) c1->mark_used();
+                if (c2) c2->mark_used();
+                if (c3) c3->mark_used();
+                // DEBUG_CODE(validate_if(~x, ~y, z, u, c, c1, c2, c3););
+                m_on_if(~x, ~y, z, u);
+                return true;
             }
             return false;
         };
@@ -214,7 +213,7 @@ namespace sat {
             clause& c = *cp;
             if (c.size() != 3 || c.was_used()) continue;
             literal x = c[0], y = c[1], z = c[2];
-            if (try_ite(x, y, z, c)) continue;
+            if (try_ite(x, z, y, c)) continue;
             if (try_ite(y, x, z, c)) continue;
             if (try_ite(z, y, x, c)) continue;            
         }
diff --git a/src/sat/sat_aig_simplifier.cpp b/src/sat/sat_aig_simplifier.cpp
index 3087b2b69..bb55471e9 100644
--- a/src/sat/sat_aig_simplifier.cpp
+++ b/src/sat/sat_aig_simplifier.cpp
@@ -176,7 +176,6 @@ namespace sat {
     void aig_simplifier::aig2clauses(aig_cuts& aigc) {
         vector<cut_set> cuts = aigc.get_cuts(m_config.m_max_cut_size, m_config.m_max_cutset_size);
         map<cut const*, unsigned, cut::hash_proc, cut::eq_proc> cut2id;
-        literal_vector roots(s.num_vars(), null_literal);
         
         union_find_default_ctx ctx;
         union_find<> uf(ctx);
@@ -212,23 +211,10 @@ namespace sat {
                 cut2id.insert(&cut, i);                
             }
         }        
-        if (old_num_eqs == m_stats.m_num_eqs) {
-            return;
+        if (old_num_eqs < m_stats.m_num_eqs) {
+            elim_eqs elim(s);
+            elim(uf);
         }
-        bool_var_vector to_elim;
-        for (unsigned i = s.num_vars(); i-- > 0; ) {
-            literal l1(i, false);
-            unsigned idx = uf.find(l1.index());
-            if (idx != l1.index()) {
-                roots[i] = to_literal(idx);
-                to_elim.push_back(i);
-            }
-            else {
-                roots[i] = l1;
-            }
-        }
-        elim_eqs elim(s);
-        elim(roots, to_elim);
     }
 
     void aig_simplifier::collect_statistics(statistics& st) const {
diff --git a/src/sat/sat_anf_simplifier.cpp b/src/sat/sat_anf_simplifier.cpp
index 4ff8daeca..a2a39cb3b 100644
--- a/src/sat/sat_anf_simplifier.cpp
+++ b/src/sat/sat_anf_simplifier.cpp
@@ -15,8 +15,10 @@
 
   --*/
 
+#include "util/union_find.h"
 #include "sat/sat_anf_simplifier.h"
 #include "sat/sat_solver.h"
+#include "sat/sat_elim_eqs.h"
 #include "sat/sat_xor_finder.h"
 #include "sat/sat_aig_finder.h"
 #include "math/grobner/pdd_solver.h"
@@ -32,7 +34,7 @@ namespace sat {
             IF_VERBOSE(2, 
                        verbose_stream() << " (sat.anf.simplifier" 
                        << " :num-units " << s.m_stats.m_num_units 
-                       << " :num-eqs " << s.m_stats.m_num_eq 
+                       << " :num-eqs " << s.m_stats.m_num_eqs 
                        << " :mb " << mem_stat() 
                        << m_watch << ")\n");
         }
@@ -61,6 +63,15 @@ namespace sat {
      */
     void anf_simplifier::anf2clauses(pdd_solver& solver) {
 
+        union_find_default_ctx ctx;
+        union_find<> uf(ctx);
+        for (unsigned i = 2*s.num_vars(); i--> 0; ) uf.mk_var();
+        auto add_eq = [&](literal l1, literal l2) {
+            uf.merge(l1.index(), l2.index());
+            uf.merge((~l1).index(), (~l2).index());
+        };
+
+        unsigned old_num_eqs = m_stats.m_num_eqs;
         for (auto* e : solver.equations()) {
             auto const& p = e->poly();
             if (p.is_one()) {
@@ -80,13 +91,17 @@ namespace sat {
                 // x + y + c = 0
                 SASSERT(!p.is_val() && p.hi().is_one() && !p.lo().is_val() && p.lo().hi().is_one() && p.lo().lo().is_val());
                 literal x(p.var(), false);
-                literal y(p.lo().var(), p.lo().lo().is_zero());
-                s.mk_clause(x, y, true);
-                s.mk_clause(~x, ~y, true);
-                ++m_stats.m_num_eq;
+                literal y(p.lo().var(), p.lo().lo().is_one());
+                add_eq(x, y);
+                ++m_stats.m_num_eqs;
                 TRACE("anf_simplifier", tout << "equivalence " << p << " : " << x << " == " << y << "\n";);
             }
         }
+
+        if (old_num_eqs < m_stats.m_num_eqs) {
+            elim_eqs elim(s);
+            elim(uf);
+        }
     }
 
     /**
@@ -104,13 +119,13 @@ namespace sat {
     void anf_simplifier::anf2phase(pdd_solver& solver) {
         if (!m_config.m_anf2phase) 
             return;
-        m_eval_ts = 0;
         reset_eval();
         auto const& eqs = solver.equations();
         for (unsigned i = eqs.size(); i-- > 0; ) {
             dd::pdd const& p = eqs[i]->poly();
             if (!p.is_val() && p.hi().is_one() && s.m_best_phase[p.var()] != eval(p.lo())) {
                 s.m_best_phase[p.var()] = !s.m_best_phase[p.var()];
+                ++m_stats.m_num_phase_flips;
             }
         }
     }
@@ -415,10 +430,11 @@ namespace sat {
     void anf_simplifier::save_statistics(pdd_solver& solver) {
         solver.collect_statistics(m_st);
         m_st.update("sat-anf.units", m_stats.m_num_units);
-        m_st.update("sat-anf.eqs",   m_stats.m_num_eq);
+        m_st.update("sat-anf.eqs",   m_stats.m_num_eqs);
         m_st.update("sat-anf.ands",  m_stats.m_num_aigs);
         m_st.update("sat-anf.ites",  m_stats.m_num_ifs);
         m_st.update("sat-anf.xors",  m_stats.m_num_xors);
+        m_st.update("sat-anf.phase_flips", m_stats.m_num_phase_flips);
     }
 
 }
diff --git a/src/sat/sat_anf_simplifier.h b/src/sat/sat_anf_simplifier.h
index beee9e9b4..5169a4438 100644
--- a/src/sat/sat_anf_simplifier.h
+++ b/src/sat/sat_anf_simplifier.h
@@ -57,8 +57,9 @@ namespace sat {
         struct report;
 
         struct stats {
-            unsigned m_num_units, m_num_eq;
+            unsigned m_num_units, m_num_eqs;
             unsigned m_num_aigs, m_num_xors, m_num_ifs;
+            unsigned m_num_phase_flips;
             stats() { reset(); }
             void reset() { memset(this, 0, sizeof(*this)); }
         };
@@ -109,7 +110,7 @@ namespace sat {
 
 
     public:
-        anf_simplifier(solver& s) : s(s) {}
+        anf_simplifier(solver& s) : s(s), m_eval_ts(0) {}
         ~anf_simplifier() {}
         
         void operator()();
diff --git a/src/sat/sat_elim_eqs.cpp b/src/sat/sat_elim_eqs.cpp
index e577846e0..908304fb5 100644
--- a/src/sat/sat_elim_eqs.cpp
+++ b/src/sat/sat_elim_eqs.cpp
@@ -284,4 +284,21 @@ namespace sat {
         SASSERT(check_clauses(roots));
         TRACE("elim_eqs", tout << "after full cleanup\n"; m_solver.display(tout););
     }
+
+    void elim_eqs::operator()(union_find<>& uf) {
+        literal_vector roots(m_solver.num_vars(), null_literal);
+        bool_var_vector to_elim;
+        for (unsigned i = m_solver.num_vars(); i-- > 0; ) {
+            literal l1(i, false);
+            unsigned idx = uf.find(l1.index());
+            if (idx != l1.index()) {
+                roots[i] = to_literal(idx);
+                to_elim.push_back(i);
+            }
+            else {
+                roots[i] = l1;
+            }
+        }
+        (*this)(roots, to_elim);
+    }
 };
diff --git a/src/sat/sat_elim_eqs.h b/src/sat/sat_elim_eqs.h
index ac132b213..de4e9b848 100644
--- a/src/sat/sat_elim_eqs.h
+++ b/src/sat/sat_elim_eqs.h
@@ -20,6 +20,7 @@ Revision History:
 #define SAT_ELIM_EQS_H_
 
 #include "sat/sat_types.h"
+#include "util/union_find.h"
 
 namespace sat {
     class solver;
@@ -44,6 +45,7 @@ namespace sat {
         elim_eqs(solver & s);
         ~elim_eqs();
         void operator()(literal_vector const & roots, bool_var_vector const & to_elim);
+        void operator()(union_find<>& uf);
     };
 
 };