diff --git a/src/sat/sat_aig_finder.cpp b/src/sat/sat_aig_finder.cpp
index 2d1904857..588a27606 100644
--- a/src/sat/sat_aig_finder.cpp
+++ b/src/sat/sat_aig_finder.cpp
@@ -16,9 +16,12 @@
   --*/
 
 #include "sat/sat_aig_finder.h"
+#include "sat/sat_solver.h"
 
 namespace sat {
 
+    aig_finder::aig_finder(solver& s): s(s), m_big(s.rand()) {}
+
     void aig_finder::operator()(clause_vector& clauses) {
         m_big.init(s, true);
         find_aigs(clauses);
diff --git a/src/sat/sat_aig_finder.h b/src/sat/sat_aig_finder.h
index 5a0ccb254..ab29d3c1a 100644
--- a/src/sat/sat_aig_finder.h
+++ b/src/sat/sat_aig_finder.h
@@ -29,11 +29,12 @@
 #include "util/statistics.h"
 #include "sat/sat_clause.h"
 #include "sat/sat_types.h"
-#include "sat/sat_solver.h"
 #include "sat/sat_big.h"
 
 namespace sat {
 
+    class solver;
+
     class aig_finder {
         solver& s;
         big                     m_big;
@@ -50,7 +51,7 @@ namespace sat {
         void validate_clause(literal_vector const& clause, vector<literal_vector> const& clauses);
 
     public:
-        aig_finder(solver& s) : s(s), m_big(s.rand()) {}
+        aig_finder(solver& s);
         ~aig_finder() {}                
         void set(std::function<void (literal head, literal_vector const& ands)>& f) { m_on_aig = f; }
         void set(std::function<void (literal head, literal cond, literal th, literal el)>& f) { m_on_if = f; }
diff --git a/src/sat/sat_aig_simplifier.cpp b/src/sat/sat_aig_simplifier.cpp
index c64d93b95..fac9c8810 100644
--- a/src/sat/sat_aig_simplifier.cpp
+++ b/src/sat/sat_aig_simplifier.cpp
@@ -25,9 +25,8 @@ namespace sat {
     
     struct aig_simplifier::report {
         aig_simplifier& s;
-        aig_cuts&       c;
         stopwatch       m_watch;
-        report(aig_simplifier& s, aig_cuts& c): s(s), c(c) { m_watch.start(); }
+        report(aig_simplifier& s): s(s) { m_watch.start(); }
         ~report() {
             IF_VERBOSE(2, 
                        verbose_stream() << "(sat.aig-simplifier" 
@@ -39,39 +38,53 @@ namespace sat {
         }
     };
 
+    aig_simplifier::aig_simplifier(solver& s):s(s), m_aig_cuts(m_config.m_max_cut_size, m_config.m_max_cutset_size) {        
+    }
+
+    void aig_simplifier::add_and(literal head, unsigned sz, literal const* lits) {
+        m_aig_cuts.add_node(head, and_op, sz, lits);
+    }
+
+    void aig_simplifier::add_or(literal head, unsigned sz, literal const* lits) {
+        m_aig_cuts.add_node(head, and_op, sz, lits);
+    }
+
+    void aig_simplifier::add_xor(literal head, unsigned sz, literal const* lits) {
+        m_aig_cuts.add_node(head, xor_op, sz, lits);
+    }
+
+    void aig_simplifier::add_ite(literal head, literal c, literal t, literal e) {
+        literal lits[3] = { c, t, e };
+        m_aig_cuts.add_node(head, ite_op, 3, lits);
+    }
+
+    void aig_simplifier::add_iff(literal head, literal l1, literal l2) {
+        literal lits[2] = { l1, ~l2 };
+        m_aig_cuts.add_node(head, xor_op, 2, lits);
+    }
+
     void aig_simplifier::operator()() {
-        aig_cuts aigc;
-        report _report(*this, aigc);
+        report _report(*this);
         TRACE("aig_simplifier", s.display(tout););
-        clauses2aig(aigc);
-        aig2clauses(aigc);
+        clauses2aig();
+        aig2clauses();
     }
 
     /**
        \brief extract AIG definitions from clauses
        Ensure that they are sorted and variables have unique definitions.
      */
-    void aig_simplifier::clauses2aig(aig_cuts& aigc) {
-        struct aig_def {
-            literal head;
-            bool_op  op;
-            unsigned sz;
-            unsigned offset;
-            aig_def(literal h, bool_op op, unsigned sz, unsigned o): head(h), op(op), sz(sz), offset(o) {}
-        };
-        svector<aig_def> aig_defs;
+    void aig_simplifier::clauses2aig() {
         literal_vector literals;
         std::function<void (literal head, literal_vector const& ands)> on_and = 
-            [&,this](literal head, literal_vector const& ands) {            
-            aig_defs.push_back(aig_def(head, and_op, ands.size(), literals.size()));
-            literals.append(ands);
+            [&,this](literal head, literal_vector const& ands) {
+            m_aig_cuts.add_node(head, and_op, ands.size(), ands.c_ptr());
             m_stats.m_num_ands++;
         };
         std::function<void (literal head, literal c, literal t, literal e)> on_ite = 
             [&,this](literal head, literal c, literal t, literal e) {            
-            aig_defs.push_back(aig_def(head, ite_op, 3, literals.size()));
-            literal args[3] = { c, t, e };
-            literals.append(3, args);
+            literal args[3] = { c, t, e };            
+            m_aig_cuts.add_node(head, ite_op, 3, args);
             m_stats.m_num_ites++;
         };
         aig_finder af(s);
@@ -97,88 +110,25 @@ namespace sat {
             // ~head = t1 + t2 + ..
             literal head = ~xors[index];
             unsigned sz = xors.size() - 1;
-            aig_defs.push_back(aig_def(head, xor_op, sz, literals.size()));
             for (unsigned i = xors.size(); i-- > 0; ) {
                 if (i != index) 
                     literals.push_back(xors[i]);
             }
+            m_aig_cuts.add_node(head, xor_op, sz, literals.c_ptr());
+            literals.reset();
             m_stats.m_num_xors++;            
         };
         xor_finder xf(s);
         xf.set(on_xor);
-        xf(clauses);
-
-        svector<bool> outs(s.num_vars(), false);
-        svector<bool> ins(s.num_vars(), false);
-        for (auto a : aig_defs) {
-            outs[a.head.var()] = true;
-        }
-
-        for (auto a : aig_defs) {
-            for (unsigned i = 0; i < a.sz; ++i) {
-                unsigned v = literals[a.offset+i].var();
-                if (!outs[v]) ins[v] = true;
-            }
-        }
-
-        std::function<void(aig_def)> force_var = [&] (aig_def a) {
-            for (unsigned i = 0; i < a.sz; ++i) {
-                unsigned v = literals[a.offset + i].var();
-                if (!ins[v]) {
-                    aigc.add_var(v);
-                    ins[v] = true;
-                }
-            }
-        };
-        std::function<void(unsigned)> add_var = [&] (unsigned v) {
-            if (!outs[v] && ins[v]) {
-                aigc.add_var(v);
-                outs[v] = true;
-            }
-        };
-        for (auto a : aig_defs) {
-            for (unsigned i = 0; i < a.sz; ++i) {
-                add_var(literals[a.offset+i].var());
-            }
-        }
-
-        while (true) {
-            unsigned j = 0;
-            for (auto a : aig_defs) {
-                bool visited = true;
-                for (unsigned i = 0; visited && i < a.sz; ++i) {
-                    visited &= ins[literals[a.offset + i].var()];
-                }
-                unsigned h = a.head.var();                
-                if (!ins[h] && visited) {
-                    ins[h] = true;
-                    aigc.add_node(a.head, a.op, a.sz, literals.c_ptr() + a.offset);
-                }
-                else if (!ins[h]) {
-                    aig_defs[j++] = a;
-                }
-                else {
-                    TRACE("aig_simplifier", tout << "skip " << a.head << " == .. \n";);
-                    force_var(a);                    
-                }
-            }
-            if (j == 0) {
-                break;
-            }
-            if (j == aig_defs.size()) {
-                IF_VERBOSE(2, verbose_stream() << "break cycle " << j << "\n");
-                force_var(aig_defs.back());
-            }
-            aig_defs.shrink(j);
-        }
+        xf(clauses);       
     }
 
-    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);
+    void aig_simplifier::aig2clauses() {
+        vector<cut_set> const& cuts = m_aig_cuts.get_cuts();
         map<cut const*, unsigned, cut::hash_proc, cut::eq_proc> cut2id;
         
         union_find_default_ctx ctx;
-        union_find<> uf(ctx);
+        union_find<> uf(ctx), uf2(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());
@@ -212,8 +162,31 @@ namespace sat {
             }
         }        
         if (old_num_eqs < m_stats.m_num_eqs) {
-            elim_eqs elim(s);
-            elim(uf);
+            // extract equivalences over non-eliminated literals.
+            bool new_eq = false;
+            for (unsigned idx = 0; idx < uf.get_num_vars(); ++idx) {
+                if (!uf.is_root(idx) || 1 == uf.size(idx)) continue;
+                literal root = null_literal;
+                unsigned first = idx;
+                do {
+                    literal lit = to_literal(idx);
+                    if (!s.was_eliminated(lit)) {
+                        if (root == null_literal) {
+                            root = lit;
+                        }
+                        else {
+                            uf2.merge(lit.index(), root.index());
+                            new_eq = true;
+                        }
+                    }
+                    idx = uf.next(idx);
+                }
+                while (first != idx);
+            }
+            if (new_eq) {
+                elim_eqs elim(s);
+                elim(uf2);
+            }
         }
     }
 
@@ -224,28 +197,18 @@ namespace sat {
         st.update("sat-aig.ites", m_stats.m_num_ites);
         st.update("sat-aig.xors", m_stats.m_num_xors);
     }
-
-    vector<cut_set> aig_cuts::get_cuts(unsigned max_cut_size, unsigned max_cutset_size) {
-        unsigned_vector sorted = top_sort();
-        vector<cut_set> cuts(m_aig.size());
+    
+    aig_cuts::aig_cuts(unsigned max_cut_size, unsigned max_cutset_size) {
         m_max_cut_size = std::min(cut().max_cut_size, max_cut_size);
         m_max_cutset_size = max_cutset_size;
+    }
+
+    vector<cut_set> const& aig_cuts::get_cuts() {
+        unsigned_vector node_ids = filter_valid_nodes();
         m_cut_set1.init(m_region, m_max_cutset_size + 1);
         m_cut_set2.init(m_region, m_max_cutset_size + 1);
-
-        unsigned j = 0;
-        for (unsigned id : sorted) {
-            node const& n = m_aig[id];
-            if (n.is_valid()) {
-                auto& cut_set = cuts[id];
-                cut_set.init(m_region, m_max_cutset_size + 1);
-                cut_set.push_back(cut(id));
-                sorted[j++] = id;
-            }
-        }
-        sorted.shrink(j);
-        augment(sorted, cuts);
-        return cuts;
+        augment(node_ids, m_cuts);
+        return m_cuts;
     }
 
     void aig_cuts::augment(unsigned_vector const& ids, vector<cut_set>& cuts) {
@@ -259,6 +222,12 @@ namespace sat {
             else if (n.is_ite()) {
                 augment_ite(n, cut_set, cuts);
             }
+            else if (n.num_children() == 0) {
+                augment_aig0(n, cut_set, cuts);
+            }
+            else if (n.num_children() == 1) {
+                augment_aig1(n, cut_set, cuts);
+            }
             else if (n.num_children() == 2) {
                 augment_aig2(n, cut_set, cuts);
             }
@@ -299,6 +268,28 @@ namespace sat {
         }
     }
 
+    void aig_cuts::augment_aig0(node const& n, cut_set& cs, vector<cut_set>& cuts) {
+        SASSERT(n.is_and());
+        cut c;
+        cs.reset();
+        if (!n.sign()) {
+            c.m_table = 3;
+        }
+        cs.insert(c);
+    }
+
+    void aig_cuts::augment_aig1(node const& n, cut_set& cs, vector<cut_set>& cuts) {
+        SASSERT(n.is_and());
+        literal lit = child(n, 0);
+        for (auto const& a : cuts[lit.var()]) {
+            if (cs.size() >= m_max_cutset_size) break;
+            cut c;
+            c.set_table(a.m_table);
+            if (n.sign()) c.negate();
+            cs.insert(c);
+        }
+    }
+
     void aig_cuts::augment_aig2(node const& n, cut_set& cs, vector<cut_set>& cuts) {
         SASSERT(n.is_and() || n.is_xor());
         literal l1 = child(n, 0);
@@ -363,7 +354,11 @@ namespace sat {
 
     void aig_cuts::add_var(unsigned v) {
         m_aig.reserve(v + 1);
-        m_aig[v] = node(v);
+        m_cuts.reserve(v + 1);
+        if (!m_aig[v].is_valid()) {
+            m_aig[v] = node(v);
+            init_cut_set(v);
+        }
         SASSERT(m_aig[v].is_valid());
     }
 
@@ -371,49 +366,45 @@ namespace sat {
         TRACE("aig_simplifier", tout << head << " == " << op << " " << literal_vector(sz, args) << "\n";);
         unsigned v = head.var();
         m_aig.reserve(v + 1);
-        m_aig[v] = node(head.sign(), op, sz, m_literals.size());        
+        unsigned offset = m_literals.size();
+        node n(head.sign(), op, sz, offset);
         m_literals.append(sz, args);
-        DEBUG_CODE(
-            for (unsigned i = 0; i < sz; ++i) {
-                SASSERT(m_aig[args[i].var()].is_valid());
-            });
+        for (unsigned i = 0; i < sz; ++i) {
+            if (!m_aig[args[i].var()].is_valid()) {
+                add_var(args[i].var());
+            }
+        }
+        if (!m_aig[v].is_valid() || m_aig[v].is_var()) {
+            m_aig[v] = n;
+            init_cut_set(v);
+        }
+        else {
+            insert_aux(v, n);
+        }
         SASSERT(m_aig[v].is_valid());
     }
 
-    unsigned_vector aig_cuts::top_sort() {
-        unsigned_vector result;
-        svector<bool> visit;
-        visit.reserve(m_aig.size(), false);
-        unsigned_vector todo;
+    void aig_cuts::init_cut_set(unsigned id) {
+        node const& n = m_aig[id];
+        SASSERT(n.is_valid());
+        auto& cut_set = m_cuts[id];
+        cut_set.init(m_region, m_max_cutset_size + 1);
+        cut_set.push_back(cut(id));        
+    }
+
+    void aig_cuts::insert_aux(unsigned v, node const& n) {
+        // TBD: throttle and replacement strategy
+        m_aux_aig.reserve(v + 1);
+        m_aux_aig[v].push_back(n);
+    }
+
+    unsigned_vector aig_cuts::filter_valid_nodes() {
         unsigned id = 0;
+        unsigned_vector result;
         for (node const& n : m_aig) {
-            if (n.is_valid()) todo.push_back(id);
+            if (n.is_valid()) result.push_back(id);
             ++id;
         }
-        while (!todo.empty()) {
-            unsigned id = todo.back();
-            if (visit[id]) {
-                todo.pop_back();
-                continue;
-            }
-            bool all_visit = true;
-            node const& n = m_aig[id];
-            SASSERT(n.is_valid());
-            if (!n.is_var()) {
-                for (unsigned i = 0; i < n.num_children(); ++i) {
-                    bool_var v = child(n, i).var();
-                    if (!visit[v]) {
-                        todo.push_back(v); 
-                        all_visit = false;
-                    }
-                }
-            }
-            if (all_visit) {
-                visit[id] = true;
-                result.push_back(id);
-                todo.pop_back();
-            }
-        }
         return result;
     }
 }
diff --git a/src/sat/sat_aig_simplifier.h b/src/sat/sat_aig_simplifier.h
index 3800f3ac8..72b04986a 100644
--- a/src/sat/sat_aig_simplifier.h
+++ b/src/sat/sat_aig_simplifier.h
@@ -61,18 +61,26 @@ namespace sat {
         unsigned           m_max_cut_size;
         unsigned           m_max_cutset_size;
         cut_set            m_cut_set1, m_cut_set2;
+        vector<cut_set>    m_cuts;
 
-        unsigned_vector top_sort();
+        void insert_aux(unsigned v, node const& n);
+        void init_cut_set(unsigned id);
+
+        unsigned_vector filter_valid_nodes();
         void augment(unsigned_vector const& ids, vector<cut_set>& cuts);
         void augment_ite(node const& n, cut_set& cs, vector<cut_set>& cuts);
+        void augment_aig0(node const& n, cut_set& cs, vector<cut_set>& cuts);
+        void augment_aig1(node const& n, cut_set& cs, vector<cut_set>& cuts);
         void augment_aig2(node const& n, cut_set& cs, vector<cut_set>& cuts);
         void augment_aigN(node const& n, cut_set& cs, vector<cut_set>& cuts);
 
     public:
+        aig_cuts(unsigned max_cut_size, unsigned max_cutset_size);
         void add_var(unsigned v);
         void add_node(literal head, bool_op op, unsigned sz, literal const* args);
+
         literal child(node const& n, unsigned idx) const { SASSERT(!n.is_var()); SASSERT(idx < n.num_children()); return m_literals[n.offset() + idx]; }
-        vector<cut_set> get_cuts(unsigned max_cut_size, unsigned max_cutset_size);
+        vector<cut_set> const & get_cuts();
     };
 
     class aig_simplifier {
@@ -91,14 +99,22 @@ namespace sat {
         solver& s;
         stats   m_stats;
         config  m_config;
+        aig_cuts m_aig_cuts;
+
         struct report;
-        void clauses2aig(aig_cuts& aigc);
-        void aig2clauses(aig_cuts& aigc);
+        void clauses2aig();
+        void aig2clauses();
     public:
-        aig_simplifier(solver& s) : s(s) {}
+        aig_simplifier(solver& s);
         ~aig_simplifier() {}                
         void operator()();
         void collect_statistics(statistics& st) const;
+
+        void add_and(literal head, unsigned sz, literal const* args);
+        void add_or(literal head, unsigned sz, literal const* args);
+        void add_xor(literal head, unsigned sz, literal const* args);
+        void add_ite(literal head, literal c, literal t, literal e);
+        void add_iff(literal head, literal l1, literal l2);
     };
 }
 
diff --git a/src/sat/sat_solver.h b/src/sat/sat_solver.h
index 98edec401..cdb1142c9 100644
--- a/src/sat/sat_solver.h
+++ b/src/sat/sat_solver.h
@@ -31,6 +31,7 @@ Revision History:
 #include "sat/sat_simplifier.h"
 #include "sat/sat_scc.h"
 #include "sat/sat_asymm_branch.h"
+#include "sat/sat_aig_simplifier.h"
 #include "sat/sat_iff3_finder.h"
 #include "sat/sat_probing.h"
 #include "sat/sat_mus.h"
@@ -89,6 +90,7 @@ namespace sat {
         config                  m_config;
         stats                   m_stats;
         scoped_ptr<extension>   m_ext;
+        scoped_ptr<aig_simplifier> m_aig_simplifier;
         parallel*               m_par;
         drat                    m_drat;          // DRAT for generating proofs
         clause_allocator        m_cls_allocator[2];
@@ -398,6 +400,7 @@ namespace sat {
         bool is_incremental() const { return m_config.m_incremental; }
         extension* get_extension() const override { return m_ext.get(); }
         void       set_extension(extension* e) override;
+        aig_simplifier* get_aig_simplifier() override { return m_aig_simplifier.get(); }
         bool       set_root(literal l, literal r);
         void       flush_roots();
         typedef std::pair<literal, literal> bin_clause;
diff --git a/src/sat/sat_solver_core.h b/src/sat/sat_solver_core.h
index b3c43ea6a..92be0b19f 100644
--- a/src/sat/sat_solver_core.h
+++ b/src/sat/sat_solver_core.h
@@ -23,7 +23,10 @@ Revision History:
 #include "sat/sat_types.h"
 
 namespace sat {
-    
+
+    class aig_simplifier;
+    class extension;
+
     class solver_core {
     protected:
         reslimit&               m_rlimit;
@@ -89,6 +92,8 @@ namespace sat {
         virtual extension* get_extension() const { return nullptr; }
         virtual void       set_extension(extension* e) { if (e) throw default_exception("optional API not supported"); }
 
+        virtual aig_simplifier* get_aig_simplifier() { return nullptr; }
+
 
         // The following methods are used when converting the state from the SAT solver back
         // to a set of assertions. 
diff --git a/src/sat/tactic/goal2sat.cpp b/src/sat/tactic/goal2sat.cpp
index a3e6b857c..73f000193 100644
--- a/src/sat/tactic/goal2sat.cpp
+++ b/src/sat/tactic/goal2sat.cpp
@@ -35,6 +35,7 @@ Notes:
 #include "ast/for_each_expr.h"
 #include "sat/tactic/goal2sat.h"
 #include "sat/ba_solver.h"
+#include "sat/sat_aig_simplifier.h"
 #include "model/model_evaluator.h"
 #include "model/model_v2_pp.h"
 #include "tactic/tactic.h"
@@ -53,6 +54,7 @@ struct goal2sat::imp {
     ast_manager &               m;
     pb_util                     pb;
     sat::ba_solver*             m_ext;
+    sat::aig_simplifier*        m_aig;
     svector<frame>              m_frame_stack;
     svector<sat::literal>       m_result_stack;
     obj_map<app, sat::literal>  m_cache;
@@ -73,6 +75,7 @@ struct goal2sat::imp {
         m(_m),
         pb(m),
         m_ext(nullptr),
+        m_aig(nullptr),
         m_solver(s),
         m_map(map),
         m_dep2asm(dep2asm),
@@ -82,6 +85,7 @@ struct goal2sat::imp {
         m_is_lemma(false) {
         updt_params(p);
         m_true = sat::null_literal;
+        m_aig = s.get_aig_simplifier();
     }
         
     void updt_params(params_ref const & p) {
@@ -252,6 +256,9 @@ struct goal2sat::imp {
             sat::literal  l(k, false);
             m_cache.insert(t, l);
             sat::literal * lits = m_result_stack.end() - num;
+
+            if (m_aig) m_aig->add_or(l, num, lits);
+
             for (unsigned i = 0; i < num; i++) {
                 mk_clause(~lits[i], l);
             }
@@ -290,8 +297,11 @@ struct goal2sat::imp {
             sat::bool_var k = m_solver.add_var(false);
             sat::literal  l(k, false);
             m_cache.insert(t, l);
-            // l => /\ lits
             sat::literal * lits = m_result_stack.end() - num;
+
+            if (m_aig) m_aig->add_and(l, num, lits);
+
+            // l => /\ lits
             for (unsigned i = 0; i < num; i++) {
                 mk_clause(~l, lits[i]);
             }
@@ -341,6 +351,7 @@ struct goal2sat::imp {
                 mk_clause(~t, ~e, l, false);
                 mk_clause(t,  e, ~l, false);
             }
+            if (m_aig) m_aig->add_ite(l, c, t, e);
             m_result_stack.shrink(sz-3);
             if (sign)
                 l.neg();
@@ -374,6 +385,7 @@ struct goal2sat::imp {
             mk_clause(~l, ~l1, l2);
             mk_clause(l,  l1, l2);
             mk_clause(l, ~l1, ~l2);
+            if (m_aig) m_aig->add_iff(l, l1, l2);
             m_result_stack.shrink(sz-2);
             if (sign)
                 l.neg();
@@ -400,6 +412,7 @@ struct goal2sat::imp {
         }
         ensure_extension();
         m_ext->add_xr(lits);
+        if (m_aig) m_aig->add_xor(~lits.back(), lits.size() - 1, lits.c_ptr() + 1);
         sat::literal lit(v, sign);
         if (root) {            
             m_result_stack.reset();
@@ -634,7 +647,7 @@ struct goal2sat::imp {
                 m_ext = alloc(sat::ba_solver);
                 m_solver.set_extension(m_ext);
             }
-        }
+        }        
     }
 
     void convert(app * t, bool root, bool sign) {