diff --git a/src/math/lp/lar_solver.cpp b/src/math/lp/lar_solver.cpp
index b31713094..561a94e99 100644
--- a/src/math/lp/lar_solver.cpp
+++ b/src/math/lp/lar_solver.cpp
@@ -16,6 +16,9 @@ namespace lp {
 
     lp_settings const& lar_solver::settings() const { return m_settings; }
 
+    statistics& lar_solver::stats() { return m_settings.stats(); }
+
+
     void lar_solver::updt_params(params_ref const& _p) {
         smt_params_helper p(_p);
         set_track_pivoted_rows(p.arith_bprop_on_pivoted_rows());
@@ -23,17 +26,9 @@ namespace lp {
         m_settings.updt_params(_p);
     }
 
-
-    void clear() {
-        lp_assert(false); // not implemented
-    }
-
     lar_solver::lar_solver() :
-        m_status(lp_status::UNKNOWN),
         m_crossed_bounds_column(-1),
         m_mpq_lar_core_solver(m_settings, *this),
-        m_int_solver(nullptr),
-        m_need_register_terms(false),
         m_var_register(false),
         m_term_register(true),
         m_constraints(*this) {}
@@ -197,11 +192,11 @@ namespace lp {
     void lar_solver::set_status(lp_status s) { m_status = s; }
 
     lp_status lar_solver::find_feasible_solution() {
-        m_settings.stats().m_make_feasible++;
-        if (A_r().column_count() > m_settings.stats().m_max_cols)
-            m_settings.stats().m_max_cols = A_r().column_count();
-        if (A_r().row_count() > m_settings.stats().m_max_rows)
-            m_settings.stats().m_max_rows = A_r().row_count();
+        stats().m_make_feasible++;
+        if (A_r().column_count() > stats().m_max_cols)
+            stats().m_max_cols = A_r().column_count();
+        if (A_r().row_count() > stats().m_max_rows)
+            stats().m_max_rows = A_r().row_count();
         if (strategy_is_undecided())
             decide_on_strategy_and_adjust_initial_state();
 
@@ -248,7 +243,7 @@ namespace lp {
         m_constraints.push();
         m_usage_in_terms.push();
     }
-
+    
     void lar_solver::clean_popped_elements(unsigned n, u_set& set) {
         vector<int> to_remove;
         for (unsigned j : set)
@@ -269,9 +264,8 @@ namespace lp {
         m_crossed_bounds_column.pop(k);
         unsigned n = m_columns_to_ul_pairs.peek_size(k);
         m_var_register.shrink(n);
-        if (m_settings.use_tableau()) {
+        if (m_settings.use_tableau()) 
             pop_tableau();
-        }
         lp_assert(A_r().column_count() == n);
         TRACE("lar_solver_details",
             for (unsigned j = 0; j < n; j++) {
@@ -285,6 +279,10 @@ namespace lp {
         clean_popped_elements(n, m_columns_with_changed_bounds);
         clean_popped_elements(n, m_incorrect_columns);
 
+        for (auto rid : m_row_bounds_to_replay)
+            insert_row_with_changed_bounds(rid);
+        m_row_bounds_to_replay.reset();
+
         unsigned m = A_r().row_count();
         clean_popped_elements(m, m_rows_with_changed_bounds);
         clean_inf_set_of_r_solver_after_pop();
@@ -633,6 +631,9 @@ namespace lp {
                 left_side.push_back(std::make_pair(p.second, p.first));
     }
 
+    void lar_solver::insert_row_with_changed_bounds(unsigned rid) {
+        m_rows_with_changed_bounds.insert(rid);
+    }
 
     void lar_solver::detect_rows_of_bound_change_column_for_nbasic_column(unsigned j) {
         if (A_r().row_count() != m_column_buffer.data_size())
@@ -643,14 +644,14 @@ namespace lp {
 
         m_mpq_lar_core_solver.m_r_solver.solve_Bd(j, m_column_buffer);
         for (unsigned i : m_column_buffer.m_index)
-            m_rows_with_changed_bounds.insert(i);
+            insert_row_with_changed_bounds(i);
     }
 
 
 
     void lar_solver::detect_rows_of_bound_change_column_for_nbasic_column_tableau(unsigned j) {
         for (auto& rc : m_mpq_lar_core_solver.m_r_A.m_columns[j])
-            m_rows_with_changed_bounds.insert(rc.var());
+            insert_row_with_changed_bounds(rc.var());
     }
 
     bool lar_solver::use_tableau() const { return m_settings.use_tableau(); }
@@ -743,7 +744,7 @@ namespace lp {
 
     void lar_solver::detect_rows_with_changed_bounds_for_column(unsigned j) {
         if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) {
-            m_rows_with_changed_bounds.insert(m_mpq_lar_core_solver.m_r_heading[j]);
+            insert_row_with_changed_bounds(m_mpq_lar_core_solver.m_r_heading[j]);
             return;
         }
 
@@ -793,7 +794,7 @@ namespace lp {
             update_x_and_inf_costs_for_columns_with_changed_bounds();
         m_mpq_lar_core_solver.solve();
         set_status(m_mpq_lar_core_solver.m_r_solver.get_status());
-        lp_assert(((m_settings.stats().m_make_feasible% 100) != 0) || m_status != lp_status::OPTIMAL || all_constraints_hold());
+        lp_assert(((stats().m_make_feasible% 100) != 0) || m_status != lp_status::OPTIMAL || all_constraints_hold());
     }
 
 
@@ -974,9 +975,7 @@ namespace lp {
 
     bool lar_solver::the_left_sides_sum_to_zero(const vector<std::pair<mpq, unsigned>>& evidence) const {
         std::unordered_map<var_index, mpq> coeff_map;
-        for (auto& it : evidence) {
-            mpq coeff = it.first;
-            constraint_index con_ind = it.second;
+        for (auto const & [coeff, con_ind] : evidence) {
             lp_assert(m_constraints.valid_index(con_ind));
             register_in_map(coeff_map, m_constraints[con_ind], coeff);
         }
@@ -1337,7 +1336,7 @@ namespace lp {
     void lar_solver::mark_rows_for_bound_prop(lpvar j) {
         auto& column = A_r().m_columns[j];
         for (auto const& r : column) 
-            m_rows_with_changed_bounds.insert(r.var());        
+            insert_row_with_changed_bounds(r.var());        
     }
 
 
@@ -1659,7 +1658,7 @@ namespace lp {
             m_mpq_lar_core_solver.m_r_heading.push_back(m_mpq_lar_core_solver.m_r_basis.size());
             m_mpq_lar_core_solver.m_r_basis.push_back(j);
             if (m_settings.bound_propagation())
-                m_rows_with_changed_bounds.insert(A_r().row_count() - 1);
+                insert_row_with_changed_bounds(A_r().row_count() - 1);
         }
         else {
             m_mpq_lar_core_solver.m_r_heading.push_back(-static_cast<int>(m_mpq_lar_core_solver.m_r_nbasis.size()) - 1);
@@ -1755,7 +1754,7 @@ namespace lp {
         if (use_tableau() && !coeffs.empty()) {
             add_row_from_term_no_constraint(m_terms.back(), ret);
             if (m_settings.bound_propagation())
-                m_rows_with_changed_bounds.insert(A_r().row_count() - 1);
+                insert_row_with_changed_bounds(A_r().row_count() - 1);
         }
         lp_assert(m_var_register.size() == A_r().column_count());
         if (m_need_register_terms) {
diff --git a/src/math/lp/lar_solver.h b/src/math/lp/lar_solver.h
index 6e61354ff..b4c69d783 100644
--- a/src/math/lp/lar_solver.h
+++ b/src/math/lp/lar_solver.h
@@ -76,13 +76,13 @@ class lar_solver : public column_namer {
     
     //////////////////// fields //////////////////////////
     lp_settings                                         m_settings;
-    lp_status                                           m_status;
+    lp_status                                           m_status = lp_status::UNKNOWN;
     stacked_value<simplex_strategy_enum>                m_simplex_strategy;
     // such can be found at the initialization step: u < l
     stacked_value<int>                                  m_crossed_bounds_column; 
     lar_core_solver                                     m_mpq_lar_core_solver;
-    int_solver *                                        m_int_solver;
-    bool                                                m_need_register_terms;
+    int_solver *                                        m_int_solver = nullptr;
+    bool                                                m_need_register_terms = false;
     var_register                                        m_var_register;
     var_register                                        m_term_register;
     stacked_vector<ul_pair>                             m_columns_to_ul_pairs;
@@ -90,6 +90,8 @@ class lar_solver : public column_namer {
     // the set of column indices j such that bounds have changed for j
     u_set                                               m_columns_with_changed_bounds;
     u_set                                               m_rows_with_changed_bounds;
+    unsigned_vector                                     m_row_bounds_to_replay;
+    
     u_set                                               m_basic_columns_with_changed_cost;
     // these are basic columns with the value changed, so the the corresponding row in the tableau
     // does not sum to zero anymore
@@ -164,7 +166,6 @@ class lar_solver : public column_namer {
     void adjust_initial_state_for_lu();
     void adjust_initial_state_for_tableau_rows();
     void fill_last_row_of_A_d(static_matrix<double, double> & A, const lar_term* ls);
-    void clear();
     bool use_lu() const;
     bool sizes_are_correct() const;
     bool implied_bound_is_correctly_explained(implied_bound const & be, const vector<std::pair<mpq, unsigned>> & explanation) const;
@@ -219,6 +220,7 @@ class lar_solver : public column_namer {
     void change_basic_columns_dependend_on_a_given_nb_column(unsigned j, const numeric_pair<mpq> & delta);
     void update_x_and_inf_costs_for_column_with_changed_bounds(unsigned j);
     unsigned num_changed_bounds() const { return m_rows_with_changed_bounds.size(); }
+    void insert_row_with_changed_bounds(unsigned rid);
     void detect_rows_with_changed_bounds_for_column(unsigned j);
     void detect_rows_with_changed_bounds();
     void set_value_for_nbasic_column(unsigned j, const impq & new_val);
@@ -368,20 +370,19 @@ public:
         // these two loops should be run sequentially
         // since the first loop might change column bounds
         // and add fixed columns this way
-        if (settings().cheap_eqs()) {
+        if (settings().propagate_eqs()) {
             bp.clear_for_eq();
             for (unsigned i : m_rows_with_changed_bounds) {
-                calculate_cheap_eqs_for_row(i, bp);
+                unsigned offset_eqs = stats().m_offset_eqs;
+                bp.cheap_eq_tree(i);                
                 if (settings().get_cancel_flag())
                     return;
+                if (stats().m_offset_eqs > offset_eqs)
+                    m_row_bounds_to_replay.push_back(i);
             }
         }
         m_rows_with_changed_bounds.clear();
     }
-    template <typename T>
-    void calculate_cheap_eqs_for_row(unsigned i, lp_bound_propagator<T> & bp) {
-        bp.cheap_eq_tree(i);
-    }
     
     bool is_fixed(column_index const& j) const { return column_is_fixed(j); }
     inline column_index to_column_index(unsigned v) const { return column_index(external_to_column_index(v)); }
@@ -515,6 +516,8 @@ public:
     unsigned column_to_reported_index(unsigned j) const;
     lp_settings & settings();
     lp_settings const & settings() const;
+    statistics& stats();
+ 
     void updt_params(params_ref const& p);
     column_type get_column_type(unsigned j) const { return m_mpq_lar_core_solver.m_column_types()[j]; }
     const impq & get_lower_bound(unsigned j) const { return m_mpq_lar_core_solver.m_r_lower_bounds()[j]; }
diff --git a/src/math/lp/lar_term.h b/src/math/lp/lar_term.h
index 8dcb16684..3ef424e24 100644
--- a/src/math/lp/lar_term.h
+++ b/src/math/lp/lar_term.h
@@ -155,7 +155,7 @@ public:
     };
     
     class const_iterator {
-        u_map< mpq>::iterator m_it;
+        u_map<mpq>::iterator m_it;
     public:
         ival operator*() const { return ival(m_it->m_key, m_it->m_value); }        
         const_iterator operator++() { const_iterator i = *this; m_it++; return i;  }
diff --git a/src/math/lp/lp_bound_propagator.h b/src/math/lp/lp_bound_propagator.h
index fec650293..1ea872517 100644
--- a/src/math/lp/lp_bound_propagator.h
+++ b/src/math/lp/lp_bound_propagator.h
@@ -72,14 +72,15 @@ class lp_bound_propagator {
     static int other(int x, int y, int z) { SASSERT(x == z || y == z); return x == z ? y : x; }
     std::ostream& print_vert(std::ostream & out, const vertex* v) const {
         out << "(c = " << v->column() << ", parent = {";
-        if (v->parent()) { out << "(" << v->parent()->column() << ")";}
-        else { out << "null"; }
+        if (v->parent())
+            out << "(" << v->parent()->column() << ")";
+        else
+            out << "null"; 
         out <<  "} , lvl = " << v->level();
-        if (m_pol.contains(v->column())) {
+        if (m_pol.contains(v->column())) 
             out << (pol(v) == -1? " -":" +");
-        } else {
+        else
             out << " not in m_pol";
-        }
         out << ')';
         return out;
     }
@@ -87,13 +88,13 @@ class lp_bound_propagator {
     hashtable<unsigned, u_hash, u_eq>         m_visited_rows;
     hashtable<unsigned, u_hash, u_eq>         m_visited_columns;
     u_map<vertex*>                            m_vertices;
-    vertex*                                   m_root;
+    vertex*                                   m_root = nullptr;
     // At some point we can find a row with a single vertex non fixed vertex
     // then we can fix the whole tree,
     // by adjusting the vertices offsets, so they become absolute.
     // If the tree is fixed then in addition to checking with the m_vals_to_verts
     // we are going to check with the m_fixed_var_tables.
-    const vertex*                             m_fixed_vertex;
+    const vertex*                             m_fixed_vertex = nullptr;
     explanation                               m_fixed_vertex_explanation;
     // a pair (o, j) belongs to m_vals_to_verts iff x[j] = x[m_root->column()] + o
     map<mpq, const vertex*, obj_hash<mpq>, default_eq<mpq>>  m_vals_to_verts;
@@ -111,19 +112,199 @@ class lp_bound_propagator {
     
     T&                                        m_imp;
     vector<implied_bound>                     m_ibounds;
+
+
+
+    map<mpq, unsigned, obj_hash<mpq>, default_eq<mpq>>  m_val2fixed_row;
+    
+    void try_add_equation_with_internal_fixed_tables(unsigned r1, vertex const* v) {
+        SASSERT(m_fixed_vertex);
+        if (v != m_root)
+            return;
+        unsigned v1 = v->column();
+        unsigned r2 = UINT_MAX;
+        if (!m_val2fixed_row.find(val(v1), r2) || r2 >= lp().row_count()) {
+            m_val2fixed_row.insert(val(v1), r1);
+            return;
+        }
+        unsigned v2, v3;
+        int polarity;
+        if (!is_tree_offset_row(r2, v2, v3, polarity) || !not_set(v3) ||
+            is_int(v1) != is_int(v2) || val(v1) != val(v2)) {
+            m_val2fixed_row.insert(val(v1), r1);
+            return;
+        }
+
+        explanation ex;
+        explain_fixed_in_row(r1, ex);
+        explain_fixed_in_row(r2, ex);
+        add_eq_on_columns(ex, v1, v2, true);
+    }
+    
+    void try_add_equation_with_lp_fixed_tables(unsigned row_index, const vertex *v) {
+        SASSERT(m_fixed_vertex);
+        unsigned v_j = v->column();
+        unsigned j = null_lpvar;
+        if (!lp().find_in_fixed_tables(val(v_j), is_int(v_j), j)) {
+            // try_add_equation_with_internal_fixed_tables(row_index, v);
+            return;
+        }
+       
+        TRACE("cheap_eq",
+              tout << "v_j = "; lp().print_column_info(v_j, tout) << std::endl;
+              tout << "v = "; print_vert(tout, v) << std::endl;
+              tout << "found j " << j << std::endl; lp().print_column_info(j, tout)<< std::endl;
+              tout << "found j = " << j << std::endl;);
+        vector<edge> path = connect_in_tree(v, m_fixed_vertex);
+        explanation ex = get_explanation_from_path(path);
+        ex.add_expl(m_fixed_vertex_explanation);
+        explain_fixed_column(j, ex);
+        add_eq_on_columns(ex, j, v_j, true);         
+    }
+
+    void try_add_equation_with_val_table(const vertex *v) {
+        SASSERT(m_fixed_vertex);
+        unsigned v_j = v->column();
+        const vertex *u = nullptr;
+        if (!m_vals_to_verts.find(val(v_j), u)) {
+            m_vals_to_verts.insert(val(v_j), v);
+            return;
+        }
+        unsigned j = u->column();
+        if (j == v_j || is_int(j) != is_int(v_j))
+            return;
+    
+        TRACE("cheap_eq", tout << "found j=" << j << " for v=";
+              print_vert(tout, v) << "\n in m_vals_to_verts\n";);
+        vector<edge> path = connect_in_tree(u, v);
+        explanation ex = get_explanation_from_path(path);
+        ex.add_expl(m_fixed_vertex_explanation);
+        add_eq_on_columns(ex, j, v_j, true);
+    }
+
+    static bool not_set(unsigned j) { return j == UINT_MAX; }
+    static bool is_set(unsigned j) { return j != UINT_MAX; }
+    
+    void create_root(unsigned row_index) {
+        SASSERT(!m_root && !m_fixed_vertex);
+        unsigned x, y;
+        int polarity;
+        TRACE("cheap_eq_det", print_row(tout, row_index););
+        if (!is_tree_offset_row(row_index, x, y, polarity)) {
+            TRACE("cheap_eq_det", tout << "not an offset row\n";);
+            return;
+        }
+        TRACE("cheap_eq", print_row(tout, row_index););
+        m_root = alloc_v(x);
+        set_polarity(m_root, 1); // keep m_root in the positive table
+        if (not_set(y)) {
+            set_fixed_vertex(m_root);
+            explain_fixed_in_row(row_index, m_fixed_vertex_explanation);
+        }
+        else {            
+            vertex *v = add_child_with_check(row_index, y, m_root, polarity);
+            if (v)
+                explore_under(v);
+        }
+        explore_under(m_root);
+    }
+
+        void explore_under(vertex * v) {
+        check_for_eq_and_add_to_val_tables(v);
+        go_over_vertex_column(v);
+    }
+
+    // In case of only one non fixed column, and the function returns true,
+    // this column would be represened by x.
+    bool is_tree_offset_row(unsigned row_index, unsigned & x, unsigned & y, int & polarity) const {
+        x = y =  UINT_MAX;
+        const row_cell<mpq>* x_cell = nullptr;
+        const row_cell<mpq>* y_cell = nullptr;
+        const auto & row = lp().get_row(row_index);
+        for (unsigned k = 0; k < row.size(); k++) {
+            const auto& c = row[k];
+            if (column_is_fixed(c.var()))
+                continue;
+            if (not_set(x)) {
+                if (c.coeff().is_one() || c.coeff().is_minus_one()) {
+                    x = c.var();
+                    x_cell = & c;
+                }
+                else 
+                    return false;
+            }
+            else if (not_set(y)) {
+                if (c.coeff().is_one() || c.coeff().is_minus_one()) {
+                    y = c.var();
+                    y_cell = & c;
+                }
+                else
+                    return false;
+            }
+            else
+                return false;
+        }
+        if (is_set(x)) {
+            if (is_set(y))
+                polarity = x_cell->coeff().is_pos() == y_cell->coeff().is_pos()? -1 : 1;
+            else
+                polarity = 1;
+            return true;
+        }
+        return false;
+    }
+
+    void go_over_vertex_column(vertex * v) {
+        lpvar j = v->column();
+        if (!check_insert(m_visited_columns, j))
+            return;
+        
+        for (const auto & c : lp().get_column(j)) {
+            unsigned row_index = c.var();
+            if (!check_insert(m_visited_rows, row_index))
+                continue;
+            vertex* u = get_child_from_row(row_index, v);
+            if (u) 
+                explore_under(u);            
+        }
+    }
+
+    void reset_cheap_eq_eh() {
+        if (!m_root)
+            return;
+        delete_tree(m_root);
+        m_root = nullptr;
+        set_fixed_vertex(nullptr);
+        m_fixed_vertex_explanation.clear();
+        m_vals_to_verts.reset();
+        m_vals_to_verts_neg.reset();
+        m_pol.reset();
+        m_vertices.reset();
+    }
+    
+    struct reset_cheap_eq {
+        lp_bound_propagator& p;
+        reset_cheap_eq(lp_bound_propagator& p):p(p) {}
+        ~reset_cheap_eq() { p.reset_cheap_eq_eh(); }
+    };
+
+
 public:
+    
+    lp_bound_propagator(T& imp):
+        m_imp(imp) {}
+
     const vector<implied_bound>& ibounds() const { return m_ibounds; }
+    
     void init() {
         m_improved_upper_bounds.clear();
         m_improved_lower_bounds.clear();
         m_ibounds.reset();
     }
-    lp_bound_propagator(T& imp): m_root(nullptr),
-                                 m_fixed_vertex(nullptr),
-                                 m_imp(imp) {}
-    
+
     const lar_solver& lp() const { return m_imp.lp(); }
     lar_solver& lp() { return m_imp.lp(); }
+    
     column_type get_column_type(unsigned j) const {
         return m_imp.lp().get_column_type(j);
     }
@@ -133,9 +314,8 @@ public:
     }
 
     const mpq & get_lower_bound_rational(unsigned j) const {
-            return m_imp.lp().get_lower_bound(j).x;
+        return m_imp.lp().get_lower_bound(j).x;
     }
-
     
     const impq & get_upper_bound(unsigned j) const {
         return m_imp.lp().get_upper_bound(j);
@@ -167,19 +347,22 @@ public:
                     found_bound = implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict);
                     TRACE("try_add_bound", m_imp.lp().print_implied_bound(found_bound, tout););
                 }
-            } else {
+            }
+            else {
                 m_improved_lower_bounds[j] = m_ibounds.size();
                 m_ibounds.push_back(implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict));
                 TRACE("try_add_bound", m_imp.lp().print_implied_bound(m_ibounds.back(), tout););
             }
-        } else { // the upper bound case
+        }
+        else { // the upper bound case
             if (try_get_value(m_improved_upper_bounds, j, k)) {
                 auto & found_bound = m_ibounds[k];
                 if (v < found_bound.m_bound || (v == found_bound.m_bound && !found_bound.m_strict && strict)) {
                     found_bound = implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict);
                     TRACE("try_add_bound", m_imp.lp().print_implied_bound(found_bound, tout););
                 }
-            } else {
+            }
+            else {
                 m_improved_upper_bounds[j] = m_ibounds.size();
                 m_ibounds.push_back(implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict));
                 TRACE("try_add_bound", m_imp.lp().print_implied_bound(m_ibounds.back(), tout););
@@ -199,54 +382,12 @@ public:
         return val(v->column());
     }
     
-    void try_add_equation_with_lp_fixed_tables(const vertex *v) {
-        SASSERT(m_fixed_vertex);
-        unsigned v_j = v->column();
-        unsigned j = null_lpvar;
-        if (!lp().find_in_fixed_tables(val(v_j), is_int(v_j), j)) 
-            return;
-       
-        TRACE("cheap_eq", tout << "v_j = "; lp().print_column_info(v_j, tout) << std::endl;);
-        TRACE("cheap_eq", tout << "v = "; print_vert(tout, v) << std::endl;);        
-        TRACE("cheap_eq", tout << "found j " << j << std::endl;
-              lp().print_column_info(j, tout)<< std::endl;);
-        TRACE("cheap_eq", tout << "found j = " << j << std::endl;);
-        vector<edge> path = connect_in_tree(v, m_fixed_vertex);
-        explanation ex = get_explanation_from_path(path);
-        ex.add_expl(m_fixed_vertex_explanation);
-        explain_fixed_column(j, ex);
-        add_eq_on_columns(ex, j, v->column());
-        
-    }
-
-    void try_add_equation_with_val_table(const vertex *v) {
-        SASSERT(m_fixed_vertex);
-        unsigned v_j = v->column();
-        const vertex *u = nullptr;
-        if (!m_vals_to_verts.find(val(v_j), u)) {
-            m_vals_to_verts.insert(val(v_j), v);
-            return;
-        }
-        unsigned j = u->column();
-        if (j == v_j || is_int(j) != is_int(v_j))
-            return;
-    
-        TRACE("cheap_eq", tout << "found j=" << j << " for v=";
-              print_vert(tout, v) << "\n in m_vals_to_verts\n";);
-        vector<edge> path = connect_in_tree(u, v);
-        explanation ex = get_explanation_from_path(path);
-        ex.add_expl(m_fixed_vertex_explanation);
-        add_eq_on_columns(ex, j, v_j);
-    }
-
-    
     bool tree_contains_r(vertex* root, vertex *v) const {
         if (*root == *v)
             return true;
-        for (auto e : root->edges()) {
+        for (auto e : root->edges()) 
             if (tree_contains_r(e.target(), v))
                 return true;
-        }
         return false;
     }
 
@@ -294,38 +435,12 @@ public:
         return v;
     }
 
-    static bool not_set(unsigned j) { return j == UINT_MAX; }
-    static bool is_set(unsigned j) { return j != UINT_MAX; }
-    
-    void create_root(unsigned row_index) {
-        SASSERT(!m_root && !m_fixed_vertex);
-        unsigned x, y;
-        int polarity;
-        TRACE("cheap_eq_det", print_row(tout, row_index););
-        if (!is_tree_offset_row(row_index, x, y, polarity)) {
-            TRACE("cheap_eq_det", tout << "not an offset row\n";);
-            return;
-        }
-        TRACE("cheap_eq", print_row(tout, row_index););
-        m_root = alloc_v(x);
-        set_polarity(m_root, 1); // keep m_root in the positive table
-        if (not_set(y)) {
-            set_fixed_vertex(m_root);
-            explain_fixed_in_row(row_index, m_fixed_vertex_explanation);
-        } else {            
-            vertex *v = add_child_with_check(row_index, y, m_root, polarity);
-            if (v)
-                explore_under(v);
-        }
-        explore_under(m_root);
-    }
 
     unsigned column(unsigned row, unsigned index) {
         return lp().get_row(row)[index].var();
     }
 
     bool fixed_phase() const { return m_fixed_vertex; }
-
     
     
     // Returns the vertex to start exploration from, or nullptr.
@@ -379,10 +494,12 @@ public:
                 is_int(k->column()) == is_int(v->column()) &&
                 !is_equal(k->column(), v->column())) {
                 report_eq(k, v);
-            } else {
+            }
+            else {
                 TRACE("cheap_eq", tout << "no report\n";);
             }
-        } else {
+        }
+        else {
             TRACE("cheap_eq", tout << "registered: " << val(v) << " -> { "; print_vert(tout, v) << "} \n";);
             table.insert(val(v), v);
         }
@@ -411,37 +528,31 @@ public:
 
     std::ostream& print_path(const vector<edge>& path, std::ostream& out) const {
         out << "path = \n";
-        for (const edge& k : path) {
+        for (const edge& k : path) 
             print_edge(k, out) << "\n";
-        }
         return out;
     }
-
-
-    
     
     // we have v_i and v_j, indices of vertices at the same offsets
     void report_eq(const vertex* v_i, const vertex* v_j) {
         SASSERT(v_i != v_j);
         SASSERT(lp().get_column_value(v_i->column()) == lp().get_column_value(v_j->column()));
         TRACE("cheap_eq", tout << v_i->column() << " = " << v_j->column() << "\nu = ";
-              print_vert(tout, v_i) << "\nv = "; print_vert(tout, v_j) <<"\n";
-              );
+              print_vert(tout, v_i) << "\nv = "; print_vert(tout, v_j) <<"\n");
         
         vector<edge> path = connect_in_tree(v_i, v_j);
         lp::explanation exp = get_explanation_from_path(path);
-        add_eq_on_columns(exp, v_i->column(), v_j->column());
+        add_eq_on_columns(exp, v_i->column(), v_j->column(), false);
         
     }
 
     std::ostream& print_expl(std::ostream & out, const explanation& exp) const {
-        for (auto p : exp) {
+        for (auto p : exp) 
             lp().constraints().display(out, [this](lpvar j) { return lp().get_variable_name(j);}, p.ci());
-        }
         return out;
     }
     
-    void add_eq_on_columns(const explanation& exp, lpvar j, lpvar k) {
+    bool add_eq_on_columns(const explanation& exp, lpvar j, lpvar k, bool is_fixed) {
         SASSERT(j != k);
         unsigned je = lp().column_to_reported_index(j);
         unsigned ke = lp().column_to_reported_index(k);
@@ -452,8 +563,10 @@ public:
               tout << "theory_vars v" << lp().local_to_external(je) << " == v" << lp().local_to_external(ke) << "\n";
               );
         
-        m_imp.add_eq(je, ke, exp);
-        lp().settings().stats().m_cheap_eqs++;
+        bool added = m_imp.add_eq(je, ke, exp, is_fixed);
+        if (added)
+            lp().stats().m_offset_eqs++;
+        return added;
     }
 
     // column to theory_var
@@ -478,14 +591,10 @@ public:
     }
 
     void explain_fixed_in_row(unsigned row, explanation& ex) const {
-                TRACE("cheap_eq",
-        tout << lp().get_row(row) << std::endl;
-              );
-        for (const auto & c : lp().get_row(row)) {
-            if (lp().is_fixed(c.var())) {
+        TRACE("cheap_eq", tout << lp().get_row(row) << std::endl);
+        for (const auto & c : lp().get_row(row)) 
+            if (lp().is_fixed(c.var())) 
                 explain_fixed_column(c.var(), ex);
-            }
-        }
     }
 
     void explain_fixed_column(unsigned j, explanation & ex) const {
@@ -536,10 +645,9 @@ public:
         if (visited_verts.find(v->column()) != visited_verts.end()) 
             return false;
         visited_verts.insert(v->column());
-        for (auto e : v->edges()) {
+        for (auto e : v->edges()) 
             if (!tree_is_correct(e.target(), visited_verts))
                 return false;
-        }
         return true;
     }
     std::ostream& print_tree(std::ostream & out, vertex* v) const {
@@ -553,43 +661,37 @@ public:
         return out;
     }
 
-    void try_add_equation_with_fixed_tables(const vertex* v) {
-        try_add_equation_with_lp_fixed_tables(v);
+    void try_add_equation_with_fixed_tables(unsigned row_index, const vertex* v) {
+        try_add_equation_with_lp_fixed_tables(row_index, v);
         try_add_equation_with_val_table(v);
     }
     
-    void create_fixed_eqs(const vertex* v) {
-        try_add_equation_with_fixed_tables(v);
+    void handle_fixed_phase(unsigned row_index) {
+        if (!fixed_phase())
+            return;
+        const vertex* v = m_root;
+        try_add_equation_with_fixed_tables(row_index, v);
         for (auto e: v->edges())
-            try_add_equation_with_fixed_tables(e.target());
+            try_add_equation_with_fixed_tables(row_index, e.target());
     }
 
-    void handle_fixed_phase() {
-        create_fixed_eqs(m_root);
-    }
     
     void cheap_eq_tree(unsigned row_index) {
-        TRACE("cheap_eq_det", tout << "row_index = " << row_index << "\n";);        
-        if (!check_insert(m_visited_rows, row_index))
-            return; // already explored
-        create_root(row_index);
-        if (m_root == nullptr) {
+        reset_cheap_eq _reset(*this);
+        TRACE("cheap_eq_det", tout << "row_index = " << row_index << "\n";);
+        if (!check_insert(m_visited_rows, row_index)) 
             return;
-        }
-        TRACE("cheap_eq", tout << "tree = "; print_tree(tout, m_root) << "\n";);
+        create_root(row_index);
+        if (!m_root)
+            return;
+        
+        TRACE("cheap_eq", tout << "tree = "; print_tree(tout, m_root) << "\n";);        
         SASSERT(tree_is_correct());
-        if (fixed_phase())
-            handle_fixed_phase();
-        TRACE("cheap_eq", tout << "done for row_index " << row_index << "\n";);
-        TRACE("cheap_eq", tout << "tree size = " << verts_size(););
-        delete_tree(m_root);
-        m_root = nullptr;
-        set_fixed_vertex(nullptr);
-        m_fixed_vertex_explanation.clear();
-        m_vals_to_verts.reset();
-        m_vals_to_verts_neg.reset();
-        m_pol.reset();
-        m_vertices.reset();
+        handle_fixed_phase(row_index);
+        
+        TRACE("cheap_eq",
+              tout << "done for row_index " << row_index << "\n";
+              tout << "tree size = " << verts_size(););
     }
 
     std::ostream& print_row(std::ostream & out, unsigned row_index) const  {
@@ -643,71 +745,7 @@ public:
             return false;
         table.insert(j);
         return true;
-    }
-    
-    void go_over_vertex_column(vertex * v) {
-        lpvar j = v->column();
-        if (!check_insert(m_visited_columns, j))
-            return;
-        
-        for (const auto & c : lp().get_column(j)) {
-            unsigned row_index = c.var();
-            if (!check_insert(m_visited_rows, row_index))
-                continue;
-            vertex *u = get_child_from_row(row_index, v);
-            if (u) {
-                // debug
-                // if (verts_size() > 3) {
-                //     std::cout << "big tree\n";
-                //     TRACE("cheap_eq", print_tree(tout, m_root););
-                //     exit(1);
-                // } // end debug
-                explore_under(u);
-            }
-        }
-    }
-    
-    void explore_under(vertex * v) {
-        check_for_eq_and_add_to_val_tables(v);
-        go_over_vertex_column(v);
-    }
+    }        
 
-    // In case of only one non fixed column, and the function returns true,
-    // this column would be represened by x.
-    bool is_tree_offset_row( unsigned row_index,
-        unsigned & x, unsigned & y, int & polarity ) const {
-        x = y =  UINT_MAX;
-        const row_cell<mpq>* x_cell = nullptr;
-        const row_cell<mpq>* y_cell = nullptr;
-        const auto & row = lp().get_row(row_index);
-        for (unsigned k = 0; k < row.size(); k++) {
-            const auto& c = row[k];
-            if (column_is_fixed(c.var()))
-                continue;
-            if (not_set(x)) {
-                if (c.coeff().is_one() || c.coeff().is_minus_one()) {
-                    x = c.var();
-                    x_cell = & c;
-                } else {
-                    return false;
-                }
-            } else if (not_set(y)) {
-                if (c.coeff().is_one() || c.coeff().is_minus_one()) {
-                    y = c.var();
-                    y_cell = & c;
-                } else
-                    return false;
-            } else
-                return false;
-        }
-        if (is_set(x)) {
-            if (is_set(y))
-                polarity = x_cell->coeff().is_pos() == y_cell->coeff().is_pos()? -1 : 1;
-            else
-                polarity = 1;
-            return true;
-        }
-        return false;
-    }
 };
 }
diff --git a/src/math/lp/lp_settings.cpp b/src/math/lp/lp_settings.cpp
index ce6edcfd5..592a98983 100644
--- a/src/math/lp/lp_settings.cpp
+++ b/src/math/lp/lp_settings.cpp
@@ -27,7 +27,7 @@ template bool lp::vectors_are_equal<lp::mpq>(vector<lp::mpq > const&, vector<lp:
 void lp::lp_settings::updt_params(params_ref const& _p) {
     smt_params_helper p(_p);
     m_enable_hnf = p.arith_enable_hnf();
-    m_cheap_eqs = p.arith_propagate_eqs();
+    m_propagate_eqs = p.arith_propagate_eqs();
     print_statistics = p.arith_print_stats();
     m_print_external_var_name = p.arith_print_ext_var_names();
     report_frequency = p.arith_rep_freq();
diff --git a/src/math/lp/lp_settings.h b/src/math/lp/lp_settings.h
index 442d10b16..7a0fef5c7 100644
--- a/src/math/lp/lp_settings.h
+++ b/src/math/lp/lp_settings.h
@@ -126,7 +126,7 @@ struct statistics {
     unsigned m_cross_nested_forms;
     unsigned m_grobner_calls;
     unsigned m_grobner_conflicts;
-    unsigned m_cheap_eqs;
+    unsigned m_offset_eqs;
     statistics() { reset(); }
     void reset() { memset(this, 0, sizeof(*this)); }
     void collect_statistics(::statistics& st) const {
@@ -147,7 +147,7 @@ struct statistics {
         st.update("arith-horner-cross-nested-forms", m_cross_nested_forms);
         st.update("arith-grobner-calls", m_grobner_calls);
         st.update("arith-grobner-conflicts", m_grobner_conflicts);
-        st.update("arith-cheap-eqs", m_cheap_eqs);
+        st.update("arith-offset-eqs", m_offset_eqs);
 
     }
 };
@@ -242,10 +242,10 @@ private:
     unsigned         m_nlsat_delay;
     bool             m_enable_hnf { true };
     bool             m_print_external_var_name { false };
-    bool             m_cheap_eqs { false };
+    bool             m_propagate_eqs { false };
 public:
     bool print_external_var_name() const { return m_print_external_var_name; }
-    bool cheap_eqs() const { return m_cheap_eqs;}
+    bool propagate_eqs() const { return m_propagate_eqs;}
     unsigned hnf_cut_period() const { return m_hnf_cut_period; }
     void set_hnf_cut_period(unsigned period) { m_hnf_cut_period = period;  }
     unsigned random_next() { return m_rand(); }
diff --git a/src/sat/smt/arith_solver.cpp b/src/sat/smt/arith_solver.cpp
index 76f1d9a0a..049bf0ce2 100644
--- a/src/sat/smt/arith_solver.cpp
+++ b/src/sat/smt/arith_solver.cpp
@@ -301,26 +301,27 @@ namespace arith {
         m_explanation.add_pair(j, v);
     }
 
-    void solver::add_eq(lpvar u, lpvar v, lp::explanation const& e) {
+    bool solver::add_eq(lpvar u, lpvar v, lp::explanation const& e, bool is_fixed) {
         if (s().inconsistent())
-            return;
+            return false;
         theory_var uv = lp().local_to_external(u); // variables that are returned should have external representations
         theory_var vv = lp().local_to_external(v); // so maybe better to have them already transformed to external form
         if (is_equal(uv, vv))
-            return;
+            return false;
         enode* n1 = var2enode(uv);
         enode* n2 = var2enode(vv);
         expr* e1 = n1->get_expr();
         expr* e2 = n2->get_expr();
-        if (m.is_ite(e1) || m.is_ite(e2))
-            return;
+        if (!is_fixed && !a.is_numeral(e1) && !a.is_numeral(e2) && (m.is_ite(e1) || m.is_ite(e2)))
+            return false;
         if (e1->get_sort() != e2->get_sort())
-            return;
+            return false;
         reset_evidence();
         for (auto ev : e)
             set_evidence(ev.ci(), m_core, m_eqs);
         auto* jst = euf::th_explain::propagate(*this, m_core, m_eqs, n1, n2);
         ctx.propagate(n1, n2, jst->to_index());
+        return true;
     }
 
     bool solver::bound_is_interesting(unsigned vi, lp::lconstraint_kind kind, const rational& bval) const {
diff --git a/src/sat/smt/arith_solver.h b/src/sat/smt/arith_solver.h
index b449e049e..759c85fae 100644
--- a/src/sat/smt/arith_solver.h
+++ b/src/sat/smt/arith_solver.h
@@ -450,7 +450,7 @@ namespace arith {
         lp::lar_solver& lp() { return *m_solver; }
         lp::lar_solver const& lp() const { return *m_solver; }
         bool is_equal(theory_var x, theory_var y) const;
-        void add_eq(lpvar u, lpvar v, lp::explanation const& e);
+        bool add_eq(lpvar u, lpvar v, lp::explanation const& e, bool is_fixed);
         void consume(rational const& v, lp::constraint_index j);
         bool bound_is_interesting(unsigned vi, lp::lconstraint_kind kind, const rational& bval) const;
     };
diff --git a/src/smt/smt_context_pp.cpp b/src/smt/smt_context_pp.cpp
index a5a42ee7a..4499752e5 100644
--- a/src/smt/smt_context_pp.cpp
+++ b/src/smt/smt_context_pp.cpp
@@ -262,22 +262,30 @@ namespace smt {
     }
 
     void context::display_eqc(std::ostream & out) const {
-        bool first = true;
-        for (enode * x : m_enodes) {
-            expr * n = x->get_expr();
-            expr * r = x->get_root()->get_expr();
-            if (n != r) {
-                if (first) {
-                    out << "equivalence classes:\n";
-                    first = false;
-                }
-                out << "#" << n->get_id() << " -> #" << r->get_id() << ": ";
-                out << mk_pp(n, m) << " -> " << mk_pp(r, m) << "\n";
+        if (m_enodes.empty())
+            return;
+        unsigned count = 0;
+        for (enode * r : m_enodes) 
+            if (r->is_root())
+                ++count;
+            
+        out << "equivalence classes: " << count << "\n";        
+        for (enode * r : m_enodes) {
+            if (!r->is_root())
+                continue;
+            out << "#" << enode_pp(r, *this) << "\n";
+            if (r->get_class_size() == 1)
+                continue;
+            for (enode* n : *r) {
+                if (n != r)
+                    out << "   #" << enode_pp(n, *this) << "\n";
             }
         }
     }
 
     void context::display_app_enode_map(std::ostream & out) const {
+        return;
+        // mainly useless 
         if (!m_e_internalized_stack.empty()) {
             out << "expression -> enode:\n";
             unsigned sz = m_e_internalized_stack.size();
diff --git a/src/smt/smt_theory.h b/src/smt/smt_theory.h
index c47a7bcf7..500c47f5e 100644
--- a/src/smt/smt_theory.h
+++ b/src/smt/smt_theory.h
@@ -453,9 +453,6 @@ namespace smt {
         
         std::ostream& display_flat_app(std::ostream & out, app * n) const;
         
-        std::ostream& display_var_def(std::ostream & out, theory_var v) const { return display_app(out, get_enode(v)->get_expr()); }
-        
-        std::ostream& display_var_flat_def(std::ostream & out, theory_var v) const { return display_flat_app(out, get_enode(v)->get_expr());  }
 
     protected:
         void log_axiom_instantiation(app * r, unsigned axiom_id = UINT_MAX, unsigned num_bindings = 0, 
diff --git a/src/smt/theory_arith_aux.h b/src/smt/theory_arith_aux.h
index f152c2430..4b57f043e 100644
--- a/src/smt/theory_arith_aux.h
+++ b/src/smt/theory_arith_aux.h
@@ -2239,17 +2239,17 @@ namespace smt {
 
         ctx.push_trail(value_trail<unsigned>(m_assume_eq_head));
         while (m_assume_eq_head < m_assume_eq_candidates.size()) {
-            std::pair<theory_var, theory_var> const & p = m_assume_eq_candidates[m_assume_eq_head];
-            theory_var v1 = p.first;
-            theory_var v2 = p.second;
+            auto const& [v1, v2] = m_assume_eq_candidates[m_assume_eq_head];
+            enode* n1 = get_enode(v1);
+            enode* n2 = get_enode(v2);
             m_assume_eq_head++;
             CTRACE("func_interp_bug", 
                    get_value(v1) == get_value(v2) && 
-                   get_enode(v1)->get_root() != get_enode(v2)->get_root(),
-                   tout << "assuming eq: #" << get_enode(v1)->get_owner_id() << " = #" << get_enode(v2)->get_owner_id() << "\n";);
+                   n1->get_root() != n2->get_root(),
+                   tout << "assuming eq: #" << n1->get_owner_id() << " = #" << n2->get_owner_id() << "\n";);
             if (get_value(v1) == get_value(v2) && 
-                get_enode(v1)->get_root() != get_enode(v2)->get_root() &&
-                assume_eq(get_enode(v1), get_enode(v2))) {
+                n1->get_root() != n2->get_root() &&
+                assume_eq(n1, n2)) {
                 ++m_stats.m_assume_eqs;
                 return true;
             }
diff --git a/src/smt/theory_arith_pp.h b/src/smt/theory_arith_pp.h
index a4dba46d0..049528f79 100644
--- a/src/smt/theory_arith_pp.h
+++ b/src/smt/theory_arith_pp.h
@@ -82,18 +82,17 @@ namespace smt {
 
     template<typename Ext>
     void theory_arith<Ext>::display_row(std::ostream & out, row const & r, bool compact) const {
-        typename vector<row_entry>::const_iterator it  = r.begin_entries();
-        typename vector<row_entry>::const_iterator end = r.end_entries();
+        
         out << "(v" << r.get_base_var() << ") : ";
         bool first = true;
-        for (; it != end; ++it) {
-            if (!it->is_dead()) {
+        for (auto const& e : r) {
+            if (!e.is_dead()) {
                 if (first)
                     first = false;
                 else
                     out << " + ";
-                theory_var s      = it->m_var;
-                numeral const & c = it->m_coeff;
+                theory_var s      = e.m_var;
+                numeral const & c = e.m_coeff;
                 if (!c.is_one())
                     out << c << "*";
                 if (compact) {
@@ -103,7 +102,7 @@ namespace smt {
                     }
                 }
                 else
-                    display_var_flat_def(out, s);
+                    out << enode_pp(get_enode(s), ctx);
             }
         }
         out << "\n";
@@ -117,20 +116,16 @@ namespace smt {
         else
             out << "rows (expanded view):\n";
         unsigned num = m_rows.size();
-        for (unsigned r_id = 0; r_id < num; r_id++) {
-            if (m_rows[r_id].m_base_var != null_theory_var) {
+        for (unsigned r_id = 0; r_id < num; r_id++) 
+            if (m_rows[r_id].m_base_var != null_theory_var) 
                 display_row(out, r_id, compact);
-            }
-        }
     }
 
     template<typename Ext>
     void theory_arith<Ext>::display_row_shape(std::ostream & out, row const & r) const {
-        typename vector<row_entry>::const_iterator it  = r.begin_entries();
-        typename vector<row_entry>::const_iterator end = r.end_entries();
-        for (; it != end; ++it) {
-            if (!it->is_dead()) {
-                numeral const & c = it->m_coeff;
+        for (auto const& e : r) {
+            if (!e.is_dead()) {
+                numeral const & c = e.m_coeff;
                 if (c.is_one())
                     out << "1";
                 else if (c.is_minus_one())
@@ -150,11 +145,9 @@ namespace smt {
 
     template<typename Ext>
     bool theory_arith<Ext>::is_one_minus_one_row(row const & r) const {
-        typename vector<row_entry>::const_iterator it  = r.begin_entries();
-        typename vector<row_entry>::const_iterator end = r.end_entries();
-        for (; it != end; ++it) {
-            if (!it->is_dead()) {
-                numeral const & c = it->m_coeff;
+        for (auto const& e : r) {
+            if (!e.is_dead()) {
+                numeral const & c = e.m_coeff;
                 if (!c.is_one() && !c.is_minus_one())
                     return false;
             }
@@ -184,11 +177,9 @@ namespace smt {
         for (unsigned r_id = 0; r_id < num; r_id++) {
             row const & r = m_rows[r_id];
             if (r.m_base_var != null_theory_var) {
-                typename vector<row_entry>::const_iterator it  = r.begin_entries();
-                typename vector<row_entry>::const_iterator end = r.end_entries();
-                for (; it != end; ++it) {
-                    if (!it->is_dead()) {
-                        numeral const & c = it->m_coeff;
+                for (auto const& e : r) {
+                    if (!e.is_dead()) {
+                        numeral const & c = e.m_coeff;
                         if (c.to_rational().is_big()) {
                             std::string str = c.to_rational().to_string();
                             if (str.length() > 48) 
@@ -215,11 +206,9 @@ namespace smt {
             row const & r = m_rows[r_id];
             if (r.m_base_var != null_theory_var) {
                 num_rows++;
-                typename vector<row_entry>::const_iterator it  = r.begin_entries();
-                typename vector<row_entry>::const_iterator end = r.end_entries();
-                for (; it != end; ++it) {
-                    if (!it->is_dead()) {
-                        numeral const & c = it->m_coeff;
+                for (auto const& e : r) {
+                    if (!e.is_dead()) {
+                        numeral const & c = e.m_coeff;
                         num_non_zeros++;
                         if (c.is_one())
                             num_ones++;
@@ -284,11 +273,9 @@ namespace smt {
     template<typename Ext>
     void theory_arith<Ext>::display_row_info(std::ostream & out, row const & r) const {
         display_row(out, r, true);
-        typename vector<row_entry>::const_iterator it  = r.begin_entries();
-        typename vector<row_entry>::const_iterator end = r.end_entries();
-        for (; it != end; ++it) 
-            if (!it->is_dead())
-                display_var(out, it->m_var);
+        for (auto const& e : r) 
+            if (!e.is_dead())
+                display_var(out, e.m_var);
     }
 
     /**
@@ -298,15 +285,14 @@ namespace smt {
     void theory_arith<Ext>::display_simplified_row(std::ostream & out, row const & r) const {
         bool has_rat_coeff = false;
         numeral k;
-        typename vector<row_entry>::const_iterator it  = r.begin_entries();
-        typename vector<row_entry>::const_iterator end = r.end_entries();
+        
         out << "(v" << r.get_base_var() << ") : ";
         bool first = true;
-        for (; it != end; ++it) {
-            if (it->is_dead())
+        for (auto const& e : r) {
+            if (e.is_dead())
                 continue;
-            theory_var v      = it->m_var;
-            numeral const & c = it->m_coeff;
+            theory_var v      = e.m_var;
+            numeral const & c = e.m_coeff;
             if (is_fixed(v)) {
                 k += c * lower_bound(v).get_rational(); 
                 continue;
@@ -328,11 +314,9 @@ namespace smt {
         }
         out << "\n";
         if (has_rat_coeff) {
-            typename vector<row_entry>::const_iterator it  = r.begin_entries();
-            typename vector<row_entry>::const_iterator end = r.end_entries();
-            for (; it != end; ++it) 
-                if (!it->is_dead() && (is_base(it->m_var) || (!is_fixed(it->m_var) && (lower(it->m_var) || upper(it->m_var)))))
-                    display_var(out, it->m_var);
+            for (auto const& e : r) 
+                if (!e.is_dead() && (is_base(e.m_var) || (!is_fixed(e.m_var) && (lower(e.m_var) || upper(e.m_var)))))
+                    display_var(out, e.m_var);
         }
     }
 
@@ -385,8 +369,7 @@ namespace smt {
         out << ", shared: " << get_context().is_shared(get_enode(v));
         out << ", unassigned: " << m_unassigned_atoms[v];
         out << ", rel: " << get_context().is_relevant(get_enode(v));
-        out << ", def: ";
-        display_var_flat_def(out, v);
+        out << ", def: " << enode_pp(get_enode(v), ctx);
         out << "\n";
     }
 
@@ -477,28 +460,17 @@ namespace smt {
         theory_var      v = a->get_var();
         inf_numeral const & k = a->get_k();
         enode *         e = get_enode(v);
-        if (show_sign) {
-            if (!a->is_true()) 
-                out << "not ";
-            else 
-                out << "    ";
-        }
+        if (show_sign)
+            out << (a->is_true()?"    ":"not ");
         out << "v";
         out.width(3);
         out << std::left << v << " #";
         out.width(3);
         out << e->get_owner_id();
         out << std::right;
-        out << " ";
-        if (a->get_atom_kind() == A_LOWER)
-            out << ">=";
-        else
-            out << "<=";
-        out << " ";
+        out << " " << ((a->get_atom_kind() == A_LOWER)? ">=" : "<=") << " ";
         out.width(6);
-        out << k << "    ";
-        display_var_flat_def(out, v);
-        out << "\n";
+        out << k << "    " << enode_pp(get_enode(v), ctx) << "\n";
     }
 
     template<typename Ext>
diff --git a/src/smt/theory_lra.cpp b/src/smt/theory_lra.cpp
index 124461189..0abc2870d 100644
--- a/src/smt/theory_lra.cpp
+++ b/src/smt/theory_lra.cpp
@@ -173,8 +173,8 @@ class theory_lra::imp {
     unsigned_vector        m_bounds_trail;
     unsigned               m_asserted_qhead;
 
-    svector<unsigned>       m_to_check;    // rows that should be checked for theory propagation
-
+    svector<unsigned>       m_bv_to_propagate;      // Boolean variables that can be propagated
+    
     svector<std::pair<theory_var, theory_var> >       m_assume_eq_candidates; 
     unsigned                                          m_assume_eq_head;
     lp::u_set                                         m_tmp_var_set;
@@ -233,6 +233,7 @@ class theory_lra::imp {
     resource_limit               m_resource_limit;
     lp_bounds                    m_new_bounds;
     symbol                       m_farkas;
+    vector<parameter>            m_bound_params;
     lp::lp_bound_propagator<imp> m_bp;
 
     context& ctx() const { return th.get_context(); }
@@ -870,6 +871,10 @@ public:
         m_bound_terms(m),
         m_bound_predicate(m)
     {
+        m_bound_params.push_back(parameter(m_farkas));
+        m_bound_params.push_back(parameter(rational(1)));
+        m_bound_params.push_back(parameter(rational(1)));
+
     }
         
     ~imp() {
@@ -1071,7 +1076,7 @@ public:
         lp().pop(num_scopes);
         // VERIFY(l_false != make_feasible());
         m_new_bounds.reset();
-        m_to_check.reset();
+        m_bv_to_propagate.reset();
         if (m_nla)
             m_nla->pop(num_scopes);
         TRACE("arith", tout << "num scopes: " << num_scopes << " new scope level: " << m_scopes.size() << "\n";);
@@ -1493,29 +1498,24 @@ public:
             
         ctx().push_trail(value_trail<unsigned>(m_assume_eq_head));
         while (m_assume_eq_head < m_assume_eq_candidates.size()) {
-            std::pair<theory_var, theory_var> const & p = m_assume_eq_candidates[m_assume_eq_head];
-            theory_var v1 = p.first;
-            theory_var v2 = p.second;
+            auto const [v1, v2] = m_assume_eq_candidates[m_assume_eq_head];
             enode* n1 = get_enode(v1);
             enode* n2 = get_enode(v2);
             m_assume_eq_head++;
             CTRACE("arith", 
                    is_eq(v1, v2) && n1->get_root() != n2->get_root(),
                    tout << "assuming eq: v" << v1 << " = v" << v2 << "\n";);
-            if (is_eq(v1, v2) &&  n1->get_root() != n2->get_root() && th.assume_eq(n1, n2)) {
+            if (is_eq(v1, v2) &&  n1->get_root() != n2->get_root() && th.assume_eq(n1, n2)) 
                 return true;
-            }
         }
         return false;
     }
 
     bool is_eq(theory_var v1, theory_var v2) {
-        if (use_nra_model()) {
+        if (use_nra_model()) 
             return m_nla->am().eq(nl_value(v1, *m_a1), nl_value(v2, *m_a2));
-        }
-        else {
+        else 
             return get_ivalue(v1) == get_ivalue(v2); 
-        }
     }
 
     bool has_delayed_constraints() const {
@@ -1523,6 +1523,8 @@ public:
     }
 
     final_check_status final_check_eh() {
+        if (propagate_core())
+            return FC_CONTINUE;
         m_model_is_initialized = false;
         IF_VERBOSE(12, verbose_stream() << "final-check " << lp().get_status() << "\n");
         lbool is_sat = l_true;
@@ -1534,9 +1536,7 @@ public:
 
         switch (is_sat) {
         case l_true:
-            TRACE("arith", display(tout);
-                  /* ctx().display(tout);*/
-                  );
+            TRACE("arith", display(tout));
 
             switch (check_lia()) {
             case l_true:
@@ -2048,41 +2048,59 @@ public:
         return false;
     }
 
-    bool m_new_def{ false };
+    bool m_new_def = false ;
+
+    bool adaptive() const { return ctx().get_fparams().m_arith_adaptive; }
+    double adaptive_assertion_threshold() const { return ctx().get_fparams().m_arith_adaptive_assertion_threshold; }
+
+    bool process_atoms() const {
+        if (!adaptive())
+            return true;
+        unsigned total_conflicts = ctx().get_num_conflicts();
+        if (total_conflicts < 10)
+            return true;
+        double f = static_cast<double>(m_num_conflicts)/static_cast<double>(total_conflicts);
+        return f >= adaptive_assertion_threshold();
+    }
 
     bool can_propagate() {
+        return process_atoms() && can_propagate_core();
+    }
+    
+    bool can_propagate_core() {
         return m_asserted_atoms.size() > m_asserted_qhead || m_new_def;
     }
 
-    void propagate() {
+    bool propagate() {
+        return process_atoms() && propagate_core();        
+    }
+
+    bool propagate_core() {
         m_model_is_initialized = false;
         flush_bound_axioms();
-        if (!can_propagate()) {
-            return;
-        }
-        m_new_def = false;
+        if (!can_propagate_core())
+            return false;
+        m_new_def = false;        
         while (m_asserted_qhead < m_asserted_atoms.size() && !ctx().inconsistent() && m.inc()) {
-            bool_var bv = m_asserted_atoms[m_asserted_qhead].m_bv;
-            bool is_true = m_asserted_atoms[m_asserted_qhead].m_is_true;
-            m_to_check.push_back(bv);
+            auto [bv, is_true] = m_asserted_atoms[m_asserted_qhead];
+            
+            m_bv_to_propagate.push_back(bv);
+            
             api_bound* b = nullptr;
-            TRACE("arith", tout << "propagate: " << literal(bv, !is_true) << "\n";);
-            if (m_bool_var2bound.find(bv, b)) {
+            TRACE("arith", tout << "propagate: " << literal(bv, !is_true) << "\n";
+                  if (!m_bool_var2bound.contains(bv)) tout << "not found\n");
+            if (m_bool_var2bound.find(bv, b)) 
                 assert_bound(bv, is_true, *b);
-            }
-            else {
-                TRACE("arith", tout << "not found " << bv << "\n";);
-            }
             ++m_asserted_qhead;
         }
         if (ctx().inconsistent()) {
-            m_to_check.reset();
-            return;
+            m_bv_to_propagate.reset();
+            return true;
         }
 
         lbool lbl = make_feasible();
         if (!m.inc())
-            return;
+            return false;
         
         switch(lbl) {
         case l_false:
@@ -2096,7 +2114,7 @@ public:
         case l_undef:
             break;
         }
-            
+        return true;            
     }
 
     bool should_propagate() const {
@@ -2246,26 +2264,28 @@ public:
         assign(bound, m_core, m_eqs, m_params);              
     }
 
-    void add_eq(lpvar u, lpvar v, lp::explanation const& e) {
+    bool add_eq(lpvar u, lpvar v, lp::explanation const& e, bool is_fixed) {
         if (ctx().inconsistent())
-            return;
+            return false;
         theory_var uv = lp().local_to_external(u); // variables that are returned should have external representations
         theory_var vv = lp().local_to_external(v); // so maybe better to have them already transformed to external form
         enode* n1 = get_enode(uv);
         enode* n2 = get_enode(vv);
+
         TRACE("arith", tout << "add-eq " << mk_pp(n1->get_expr(), m) << " == " << mk_pp(n2->get_expr(), m) << " " << n1->get_expr_id() << " == " << n2->get_expr_id() << "\n";);
         if (n1->get_root() == n2->get_root())
-            return;
+            return false;
         expr* e1 = n1->get_expr();
         expr* e2 = n2->get_expr();
         if (e1->get_sort() != e2->get_sort())
-            return;
-        if (m.is_ite(e1) || m.is_ite(e2))
-            return;
+            return false;
+        if (!is_fixed && !a.is_numeral(e1) && !a.is_numeral(e2) && (m.is_ite(e1) || m.is_ite(e2))) 
+            return false;
         reset_evidence();
         for (auto ev : e) 
             set_evidence(ev.ci(), m_core, m_eqs);
         assign_eq(uv, vv);
+        return true;
     }
 
     literal_vector m_core2;
@@ -2440,6 +2460,7 @@ public:
     typedef lp_bounds::iterator iterator;
 
     void flush_bound_axioms() {
+        
         CTRACE("arith", !m_new_bounds.empty(), tout << "flush bound axioms\n";);
 
         while (!m_new_bounds.empty()) {
@@ -2458,7 +2479,7 @@ public:
             CTRACE("arith", atoms.size() > 1, 
                    for (auto* a : atoms) a->display(tout) << "\n";);
             lp_bounds occs(m_bounds[v]);
-                
+            
             std::sort(atoms.begin(), atoms.end(), compare_bounds());
             std::sort(occs.begin(), occs.end(), compare_bounds());
                 
@@ -2558,14 +2579,15 @@ public:
     }
 
     void propagate_basic_bounds() {
-        for (auto const& bv : m_to_check) {
+        for (auto const& bv : m_bv_to_propagate) {
             api_bound* b = nullptr;
             if (m_bool_var2bound.find(bv, b)) {
                 propagate_bound(bv, ctx().get_assignment(bv) == l_true, *b);
-                if (ctx().inconsistent()) break;
+                if (ctx().inconsistent())
+                    break;
             }
         }
-        m_to_check.reset();
+        m_bv_to_propagate.reset();
     }
         
     // for glb lo': lo' < lo:
@@ -2633,10 +2655,7 @@ public:
               ctx().display_literals_verbose(tout, m_core);
               ctx().display_literal_verbose(tout << " => ", lit2);
               tout << "\n";);
-        m_params.push_back(parameter(m_farkas));
-        m_params.push_back(parameter(rational(1)));
-        m_params.push_back(parameter(rational(1)));
-        assign(lit2, m_core, m_eqs, m_params);
+        assign(lit2, m_core, m_eqs, m_bound_params);
         ++m_stats.m_bounds_propagations;
     }
 
@@ -3194,7 +3213,7 @@ public:
         m_assume_eq_head = 0;
         m_scopes.reset();
         m_stats.reset();
-        m_to_check.reset();
+        m_bv_to_propagate.reset();
         m_model_is_initialized = false;
     }
 
@@ -3661,7 +3680,7 @@ public:
             else if (can_get_value(v)) out << " = " << get_value(v); 
             if (is_int(v)) out << ", int";
             if (ctx().is_shared(get_enode(v))) out << ", shared";
-            out << " := "; th.display_var_flat_def(out, v) << "\n";
+            out << " := " << enode_pp(get_enode(v), ctx()) << "\n";
         }
     }