diff --git a/src/causality.ml b/src/causality.ml
index 9caf44bb4e34c46209c2c34c2a8165d9e2c7c452..30116cee2d154ec729435bc4089299611e9bebb9 100644
--- a/src/causality.ml
+++ b/src/causality.ml
@@ -105,7 +105,10 @@ module ExprDep = struct
      program/schedule, but used to simplify causality analysis *)
   let mk_instance_var eq f =
     incr instance_var_cpt;
-    Format.sprintf "%s_%d_%d" f (fst eq.eq_loc).Lexing.pos_lnum !instance_var_cpt
+    let loc = fst eq.eq_loc in
+    let lin = loc.Lexing.pos_lnum in
+    let col = loc.Lexing.pos_cnum - loc.Lexing.pos_bol in
+    Format.sprintf "%s_%d_%d_%d" f lin col !instance_var_cpt
 
   let mk_call_instance_var id =
     Format.sprintf "?%s" id
diff --git a/src/checks/liveness.ml b/src/checks/liveness.ml
index ab45bf3d4493a30cb28e2721063f489a6e69588f..81203d1ec982fd8b166ce2cd2c4d4fd168258e8f 100644
--- a/src/checks/liveness.ml
+++ b/src/checks/liveness.ml
@@ -147,6 +147,7 @@ let is_aliasable_input node var =
 
 (* replace variable [v] by [v'] in graph [g]. [v'] is a dead variable *)
 let replace_in_dep_graph v v' g =
+  assert (IdentDepGraph.mem_vertex g v);
   IdentDepGraph.add_vertex g v';
   IdentDepGraph.iter_succ (fun s -> IdentDepGraph.add_edge g v' s) g v;
   IdentDepGraph.iter_pred (fun p -> IdentDepGraph.add_edge g p v') g v;
diff --git a/src/optimize_machine.ml b/src/optimize_machine.ml
index 60e6137299c6cc701283186525d34932be501363..bf8b3be3a577ea94c666382537522ab5f6beb102 100644
--- a/src/optimize_machine.ml
+++ b/src/optimize_machine.ml
@@ -1457,6 +1457,7 @@ let optimize params prog node_schs machine_code =
       machine_code)
     else machine_code
   in
+  let consts = Corelang.get_consts prog in
   (* Optimize machine code *)
   let prog, machine_code, removed_table =
     if
@@ -1469,7 +1470,7 @@ let optimize params prog node_schs machine_code =
             "@ @[<v 2>.. machines optimization: const. inlining (partial eval. \
              with const)@ ");
       let machine_code, removed_table =
-        machines_unfold (Corelang.get_consts prog) node_schs machine_code
+        machines_unfold consts node_schs machine_code
       in
       Log.report ~level:3 (fun fmt ->
           Format.fprintf
@@ -1512,7 +1513,7 @@ let optimize params prog node_schs machine_code =
   let machine_code =
     if !Options.optimization >= 3 && not (Backends.is_functional ()) then
       let node_schs =
-        Scheduling.remove_prog_inlined_locals removed_table node_schs
+        Scheduling.remove_prog_inlined_consts_and_locals consts removed_table node_schs
       in
       let reuse_tables = Scheduling.compute_prog_reuse_table node_schs in
       machine_code
diff --git a/src/scheduling.ml b/src/scheduling.ml
index afc8206b8481f68eae71a096db89f208f5e86883..509524f5ade503c4b90745ca56761c6c5d1193f0 100644
--- a/src/scheduling.ml
+++ b/src/scheduling.ml
@@ -161,8 +161,8 @@ let compute_prog_reuse_table report = IMap.map compute_node_reuse_table report
 
 (* removes inlined local variables from schedule report, which are now
    useless *)
-let remove_node_inlined_locals locals report =
-  let is_inlined v = IMap.exists (fun l _ -> v = l) locals in
+let remove_node_inlined_consts_and_locals consts consts_and_locals report =
+  let is_inlined v = IMap.mem v consts_and_locals in
   let schedule' =
     List.fold_right
       (fun heads q ->
@@ -171,16 +171,22 @@ let remove_node_inlined_locals locals report =
       report.schedule
       []
   in
-  IMap.iter (fun v _ -> Hashtbl.remove report.fanin_table v) locals;
+  IMap.iter (fun v _ -> Hashtbl.remove report.fanin_table v) consts_and_locals;
   IMap.iter
     (fun v _ ->
-      let iv = ExprDep.(mk_call_instance_var (mk_call_instance_var v)) in
-      Liveness.replace_in_dep_graph v iv report.dep_graph)
-    locals;
+      if List.exists (fun decl -> Corelang.(const_of_top decl).const_id = v)
+           consts
+      then
+        let iv = ExprDep.(mk_read_var v) in
+        IdentDepGraph.remove_vertex report.dep_graph iv
+      else
+        let iv = ExprDep.(mk_call_instance_var (mk_call_instance_var v)) in
+        Liveness.replace_in_dep_graph v iv report.dep_graph)
+    consts_and_locals;
   { report with schedule = schedule' }
 
-let remove_prog_inlined_locals removed reuse =
-  IMap.mapi (fun id -> remove_node_inlined_locals (IMap.find id removed)) reuse
+let remove_prog_inlined_consts_and_locals consts removed reuse =
+  IMap.mapi (fun id -> remove_node_inlined_consts_and_locals consts (IMap.find id removed)) reuse
 
 let pp_eq_schedule fmt vl =
   match vl with
diff --git a/src/scheduling.mli b/src/scheduling.mli
index 29e66c7690b4ae59614f7edcbba156b20de2ec86..ba3dbef27520969eb82fdb7a2332023af0fa5100 100644
--- a/src/scheduling.mli
+++ b/src/scheduling.mli
@@ -6,8 +6,8 @@ open Scheduling_type
 val schedule_node : node_desc -> schedule_report
 val schedule_prog : program_t -> program_t * schedule_report IMap.t
 
-val remove_prog_inlined_locals :
-  'a IMap.t IMap.t -> schedule_report IMap.t -> schedule_report IMap.t
+val remove_prog_inlined_consts_and_locals :
+  top_decl list -> 'a IMap.t IMap.t -> schedule_report IMap.t -> schedule_report IMap.t
 
 val compute_prog_reuse_table :
   schedule_report IMap.t -> (ident, var_decl) Hashtbl.t IMap.t