diff --git a/src/sat/sat_ddfw.cpp b/src/sat/sat_ddfw.cpp
index f1493232c80..418070c64c9 100644
--- a/src/sat/sat_ddfw.cpp
+++ b/src/sat/sat_ddfw.cpp
@@ -57,11 +57,11 @@ namespace sat {
         double sec = m_stopwatch.get_current_seconds();        
         double kflips_per_sec = (m_flips - m_last_flips) / (1000.0 * sec);
         if (m_last_flips == 0) {
-            IF_VERBOSE(0, verbose_stream() << "(sat.ddfw :unsat :models :kflips/sec  :flips  :restarts  :reinits  :unsat_vars  :shifts";
+            IF_VERBOSE(1, verbose_stream() << "(sat.ddfw :unsat :models :kflips/sec  :flips  :restarts  :reinits  :unsat_vars  :shifts";
                        if (m_par) verbose_stream() << "  :par";
                        verbose_stream() << ")\n");
         }
-        IF_VERBOSE(0, verbose_stream() << "(sat.ddfw " 
+        IF_VERBOSE(1, verbose_stream() << "(sat.ddfw " 
                    << std::setw(07) << m_min_sz 
                    << std::setw(07) << m_models.size()
                    << std::setw(10) << kflips_per_sec
@@ -106,7 +106,6 @@ namespace sat {
                 if (r > 0) {
                     lim_pos -= score(r);
                     if (lim_pos <= 0) {
-                        if (m_par) update_reward_avg(v);
                         return v;
                     }
                 }
@@ -139,9 +138,8 @@ namespace sat {
     }
 
     void ddfw::add(solver const& s) {
-        for (auto& ci : m_clauses) {
+        for (auto& ci : m_clauses) 
             m_alloc.del_clause(ci.m_clause);
-        }
         m_clauses.reset(); 
         m_use_list.reset();
         m_num_non_binary_clauses = 0;
@@ -281,6 +279,7 @@ namespace sat {
             ci.add(nlit);
         }
         value(v) = !value(v);
+        update_reward_avg(v);
     }
 
     bool ddfw::should_reinit_weights() {
@@ -379,36 +378,35 @@ namespace sat {
         return m_par != nullptr && m_flips >= m_parsync_next;
     }
 
+    void ddfw::save_priorities() {
+        m_probs.reset();
+        for (unsigned v = 0; v < num_vars(); ++v) 
+            m_probs.push_back(-m_vars[v].m_reward_avg);         
+    }
+
     void ddfw::do_parallel_sync() {
-        if (m_par->from_solver(*this)) {
-            // Sum exp(xi) / exp(a) = Sum exp(xi - a)
-            double max_avg = 0;
-            for (unsigned v = 0; v < num_vars(); ++v) {
-                max_avg = std::max(max_avg, (double)m_vars[v].m_reward_avg);
-            }
-            double sum = 0;
-            for (unsigned v = 0; v < num_vars(); ++v) {
-                sum += exp(m_config.m_itau * (m_vars[v].m_reward_avg - max_avg));
-            }
-            if (sum == 0) {
-                sum = 0.01;
-            }
-            m_probs.reset();
-            for (unsigned v = 0; v < num_vars(); ++v) {
-                m_probs.push_back(exp(m_config.m_itau * (m_vars[v].m_reward_avg - max_avg)) / sum);
-            }
+        if (m_par->from_solver(*this)) 
             m_par->to_solver(*this);
-        }
+        
         ++m_parsync_count;
         m_parsync_next *= 3;
         m_parsync_next /= 2;
     }
 
+    void ddfw::save_model() {
+        m_model.reserve(num_vars());
+        for (unsigned i = 0; i < num_vars(); ++i) 
+            m_model[i] = to_lbool(value(i));
+        save_priorities();
+    }
+
+
     void ddfw::save_best_values() {
-        if (m_unsat.empty()) {
-            m_model.reserve(num_vars());
-            for (unsigned i = 0; i < num_vars(); ++i) 
-                m_model[i] = to_lbool(value(i));
+        if (m_unsat.empty()) 
+            save_model();
+        else if (m_unsat.size() < m_min_sz) {
+            if (m_unsat.size() < 50 || m_min_sz * 10 > m_unsat.size() * 11)
+                save_model();
         }
         if (m_unsat.size() < m_min_sz) {
             m_models.reset();
diff --git a/src/sat/sat_ddfw.h b/src/sat/sat_ddfw.h
index ed9936f0ac9..d5e7df77374 100644
--- a/src/sat/sat_ddfw.h
+++ b/src/sat/sat_ddfw.h
@@ -164,6 +164,8 @@ namespace sat {
         bool_var pick_var();       
         void flip(bool_var v);
         void save_best_values();
+        void save_model();
+        void save_priorities();
 
         // shift activity
         void shift_weights();
diff --git a/src/sat/sat_parallel.cpp b/src/sat/sat_parallel.cpp
index 2f7a195588b..3e493168a0c 100644
--- a/src/sat/sat_parallel.cpp
+++ b/src/sat/sat_parallel.cpp
@@ -214,14 +214,17 @@ namespace sat {
     }
 
 
-    bool parallel::_to_solver(solver& s) {
-        if (m_priorities.empty()) {
-            return false;
-        }
+    void parallel::_to_solver(solver& s) {
+        return;
+#if 0
+        if (m_priorities.empty())
+            return;
+        
         for (bool_var v = 0; v < m_priorities.size(); ++v) {
             s.update_activity(v, m_priorities[v]);
         }
-        return true;
+        s.m_activity_inc = 128;
+#endif
     }
 
     void parallel::from_solver(solver& s) {
@@ -229,16 +232,19 @@ namespace sat {
         _from_solver(s);        
     }
 
-    bool parallel::to_solver(solver& s) {
+    void parallel::to_solver(solver& s) {
         lock_guard lock(m_mux);
-        return _to_solver(s);
+        _to_solver(s);
     }
 
     void parallel::_to_solver(i_local_search& s) {        
+        return;
+#if 0
         m_priorities.reset();
         for (bool_var v = 0; m_solver_copy && v < m_solver_copy->num_vars(); ++v) {
             m_priorities.push_back(s.get_priority(v));
         }
+#endif
     }
 
     bool parallel::_from_solver(i_local_search& s) {
diff --git a/src/sat/sat_parallel.h b/src/sat/sat_parallel.h
index 68266760ba0..65ae091835e 100644
--- a/src/sat/sat_parallel.h
+++ b/src/sat/sat_parallel.h
@@ -51,7 +51,7 @@ namespace sat {
         bool enable_add(clause const& c) const;
         void _get_clauses(solver& s);
         void _from_solver(solver& s);
-        bool _to_solver(solver& s);
+        void _to_solver(solver& s);
         bool _from_solver(i_local_search& s);
         void _to_solver(i_local_search& s);
 
@@ -102,7 +102,7 @@ namespace sat {
 
         // exchange from solver state to local search and back.
         void from_solver(solver& s);
-        bool to_solver(solver& s);
+        void to_solver(solver& s);
         
         bool from_solver(i_local_search& s);
         void to_solver(i_local_search& s);
diff --git a/src/sat/sat_params.pyg b/src/sat/sat_params.pyg
index f9d7c643ac6..6aedf1c89e9 100644
--- a/src/sat/sat_params.pyg
+++ b/src/sat/sat_params.pyg
@@ -2,7 +2,7 @@ def_module_params('sat',
                   export=True,
                   description='propositional SAT solver',
                   params=(max_memory_param(),
-                          ('phase', SYMBOL, 'caching', 'phase selection strategy: always_false, always_true, basic_caching, random, caching'),
+                          ('phase', SYMBOL, 'caching', 'phase selection strategy: always_false, always_true, basic_caching, random, caching, local_search'),
                           ('phase.sticky', BOOL, True, 'use sticky phase caching'),
                           ('search.unsat.conflicts', UINT, 400, 'period for solving for unsat (in number of conflicts)'),
                           ('search.sat.conflicts', UINT, 400, 'period for solving for sat (in number of conflicts)'),
diff --git a/src/sat/sat_prob.h b/src/sat/sat_prob.h
index 305e76b8bcc..f05365e3902 100644
--- a/src/sat/sat_prob.h
+++ b/src/sat/sat_prob.h
@@ -58,7 +58,7 @@ namespace sat {
         clause_vector    m_clause_db;     
         svector<clause_info> m_clauses;
         bool_vector    m_values, m_best_values;
-        unsigned         m_best_min_unsat{ 0 };
+        unsigned         m_best_min_unsat = 0;
         vector<unsigned_vector> m_use_list;
         unsigned_vector  m_flat_use_list;
         unsigned_vector  m_use_list_index;
@@ -67,9 +67,9 @@ namespace sat {
         indexed_uint_set m_unsat;
         random_gen       m_rand;
         unsigned_vector  m_breaks;
-        uint64_t         m_flips{ 0 };
-        uint64_t         m_next_restart{ 0 };
-        unsigned         m_restart_count{ 0 };
+        uint64_t         m_flips = 0;
+        uint64_t         m_next_restart = 0;
+        unsigned         m_restart_count = 0;
         stopwatch        m_stopwatch;
         model            m_model;
 
@@ -139,6 +139,8 @@ namespace sat {
         void add(solver const& s) override;
 
         model const& get_model() const override { return m_model; }
+
+        double get_priority(bool_var v) const { return 0; }
        
         std::ostream& display(std::ostream& out) const;
 
diff --git a/src/sat/sat_solver.cpp b/src/sat/sat_solver.cpp
index 29710ed29ed..373885f341b 100644
--- a/src/sat/sat_solver.cpp
+++ b/src/sat/sat_solver.cpp
@@ -40,6 +40,26 @@ Revision History:
 
 namespace sat {
 
+    /**
+    * Special cases of kissat style general backoff calculation.
+    * The version here calculates
+    * limit := value*log(C)^2*n*log(n)
+    * (effort calculation in kissat is based on ticks not clauses)
+    *
+    * respectively
+    * limit := conflicts + value*log(C)^2*n*log(n)
+    */
+    void backoff::delta_effort(solver& s) {
+        count++;
+        unsigned d = value * count * log2(count + 1);
+        unsigned cl = log2(s.num_clauses() + 2);
+        limit = cl * cl * d;
+    }
+
+    void backoff::delta_conflicts(solver& s) {
+        delta_effort(s);
+        limit += s.m_conflicts_since_init;
+    }
 
     solver::solver(params_ref const & p, reslimit& l):
         solver_core(l),
@@ -1349,16 +1369,43 @@ namespace sat {
         m_local_search->updt_params(m_params);
         m_local_search->set_seed(m_rand());
         scoped_rl.push_child(&(m_local_search->rlimit()));
-        m_local_search->rlimit().push(500000);
+
+        m_backoffs.m_local_search.delta_effort(*this);
+        m_local_search->rlimit().push(m_backoffs.m_local_search.limit);
+
         m_local_search->reinit(*this);
         lbool r = m_local_search->check(_lits.size(), _lits.data(), nullptr);
-        for (unsigned i = 0; i < m_phase.size(); ++i)
-            m_best_phase[i] = m_local_search->get_value(i);
-        if (r == l_true) {
-            m_conflicts_since_restart = 0;
-            m_conflicts_since_gc = 0;
-            m_next_simplify = std::max(m_next_simplify, m_conflicts_since_init + 1);
+        auto const& mdl = m_local_search->get_model();
+        if (mdl.size() == m_best_phase.size()) {
+            for (unsigned i = 0; i < m_best_phase.size(); ++i)
+                m_best_phase[i] = l_true == mdl[i];
+
+            if (r == l_true) {
+                m_conflicts_since_restart = 0;
+                m_conflicts_since_gc = 0;
+                m_next_simplify = std::max(m_next_simplify, m_conflicts_since_init + 1);
+            }
             do_restart(true);
+#if 0
+            // move higher priority variables to front
+            // eg., move the first 10% variables to front
+            svector<std::pair<double, bool_var>> priorities(mdl.size());
+            for (unsigned i = 0; i < mdl.size(); ++i) 
+                priorities[i] = { m_local_search->get_priority(i), i };
+            std::sort(priorities.begin(), priorities.end(), [](auto& x, auto& y) { return x.first > y.first; });
+            for (unsigned i = priorities.size() / 10; i-- > 0; )
+                move_to_front(priorities[i].second);
+#endif
+
+
+            if (l_true == r) {
+                for (clause const* cp : m_clauses) {
+                    bool is_true = any_of(*cp, [&](auto lit) { return lit.sign() != m_best_phase[lit.var()]; });
+                    if (!is_true) {
+                        verbose_stream() << "clause is false " << *cp << "\n";
+                    }
+                }
+            }
         }
     }
 
@@ -1693,7 +1740,7 @@ namespace sat {
         
         if (!is_pos)
             next_lit.neg();
-        
+
         TRACE("sat_decide", tout << scope_lvl() << ": next-case-split: " << next_lit << "\n";);
         assign_scoped(next_lit);
         return true;
@@ -1913,6 +1960,7 @@ namespace sat {
         m_rephase_lim             = 0;
         m_rephase_inc             = 0;
         m_reorder_lim             = m_config.m_reorder_base;
+        m_backoffs.m_local_search.value = 500;
         m_reorder_inc             = 0;
         m_conflicts_since_restart = 0;
         m_force_conflict_analysis = false;
@@ -1928,6 +1976,7 @@ namespace sat {
         m_next_simplify           = m_config.m_simplify_delay;
         m_min_d_tk                = 1.0;
         m_search_lvl              = 0;
+
         if (m_learned.size() <= 2*m_clauses.size())
             m_conflicts_since_gc      = 0;
         m_restart_next_out        = 0;
@@ -2030,9 +2079,7 @@ namespace sat {
 
         if (m_par) {
             m_par->from_solver(*this);
-            if (m_par->to_solver(*this)) {
-                m_activity_inc = 128;
-            }
+            m_par->to_solver(*this);
         }
 
         if (m_config.m_binspr && !inconsistent()) {
@@ -2944,14 +2991,19 @@ namespace sat {
         case PS_SAT_CACHING:
             if (m_search_state == s_sat) 
                 for (unsigned i = 0; i < m_phase.size(); ++i) 
-                    m_phase[i] = m_best_phase[i];                            
+                    m_phase[i] = m_best_phase[i];  
             break;
         case PS_RANDOM:
             for (auto& p : m_phase) p = (m_rand() % 2) == 0;
             break;
         case PS_LOCAL_SEARCH:
-            if (m_search_state == s_sat) 
-                bounded_local_search();
+            if (m_search_state == s_sat) {
+                if (m_rand() % 2 == 0)
+                    bounded_local_search();
+                for (unsigned i = 0; i < m_phase.size(); ++i) 
+                    m_phase[i] = m_best_phase[i];              
+            }
+
             break;
         default:
             UNREACHABLE();
diff --git a/src/sat/sat_solver.h b/src/sat/sat_solver.h
index 524f6b06de3..ca738ce9b14 100644
--- a/src/sat/sat_solver.h
+++ b/src/sat/sat_solver.h
@@ -87,10 +87,23 @@ namespace sat {
     struct no_drat_params : public params_ref {
         no_drat_params() { set_bool("drat.disable", true); }
     };
+
+    struct backoff {
+        unsigned value = 1;
+        unsigned lo    = 0;
+        unsigned hi    = 0;
+        unsigned limit = 0;
+        unsigned count = 0;    
+        void delta_effort(solver& s);
+        void delta_conflicts(solver& s);
+    };
     
     class solver : public solver_core {
     public:
         struct abort_solver {};
+        struct backoffs {
+            backoff m_local_search;
+        };
     protected:
         enum search_state { s_sat, s_unsat };
 
@@ -159,6 +172,7 @@ namespace sat {
         unsigned                m_search_next_toggle;
         unsigned                m_phase_counter; 
         unsigned                m_best_phase_size;
+        backoffs                m_backoffs;
         unsigned                m_rephase_lim;
         unsigned                m_rephase_inc;
         unsigned                m_reorder_lim;
@@ -237,6 +251,7 @@ namespace sat {
         friend class lut_finder;
         friend class npn3_finder;
         friend class proof_trim;
+        friend struct backoff;
     public:
         solver(params_ref const & p, reslimit& l);
         ~solver() override;
diff --git a/src/sat/sat_types.h b/src/sat/sat_types.h
index c92a8bbeb4f..3026b3c5e00 100644
--- a/src/sat/sat_types.h
+++ b/src/sat/sat_types.h
@@ -90,7 +90,7 @@ namespace sat {
         virtual reslimit& rlimit() = 0;
         virtual model const& get_model() const = 0;
         virtual void collect_statistics(statistics& st) const = 0;        
-        virtual double get_priority(bool_var v) const { return 0; }
+        virtual double get_priority(bool_var v) const = 0;
         virtual bool get_value(bool_var v) const { return true; }
     };