diff --git a/lib/codegen/transform/pipeline.cc b/lib/codegen/transform/pipeline.cc
index 39b058ae7..8b9fe1a5d 100644
--- a/lib/codegen/transform/pipeline.cc
+++ b/lib/codegen/transform/pipeline.cc
@@ -23,6 +23,18 @@ void recursive_deps(ir::value* v, ir::basic_block* block, std::vector<ir::instru
    recursive_deps(u, block, ret);
 }
 
+void get_induction_vars(ir::value* cond, std::set<ir::phi_node*>& phis) {
+  auto instr = dynamic_cast<ir::instruction*>(cond);
+  for (auto op : instr->ops()) {
+    if (auto phi_op = dynamic_cast<ir::phi_node*>(op)) {
+      phis.insert(phi_op);
+      return;
+    }
+    if (dynamic_cast<ir::instruction*>(op))
+      get_induction_vars(op, phis);
+  }
+}
+
 /// assume incoming block is 1
 ir::value* rematerialize_vals(ir::builder& builder, ir::value* v, 
                               std::map<ir::phi_node*, ir::value*>& prev_phi_vals) {
@@ -46,37 +58,6 @@ ir::value* rematerialize_vals(ir::builder& builder, ir::value* v,
   return ret;
 }
 
-void get_induction_vars(ir::value* cond, std::set<ir::phi_node*>& phis) {
-  auto instr = dynamic_cast<ir::instruction*>(cond);
-  for (auto op : instr->ops()) {
-    if (auto phi_op = dynamic_cast<ir::phi_node*>(op)) {
-      phis.insert(phi_op);
-      return;
-    }
-    if (dynamic_cast<ir::instruction*>(op))
-      get_induction_vars(op, phis);
-  }
-}
-
-/// Returns phi_val if sees a phi node
-ir::value* rematerialize_val(ir::builder& builder, ir::value* v, ir::value* phi_val) {
-  ir::instruction* i = dynamic_cast<ir::instruction*>(v);
-  if(!i)
-    return v;
-  if(ir::phi_node* phi = dynamic_cast<ir::phi_node*>(v))
-    return phi_val;
-
-  std::vector<ir::value*> new_ops;
-  for(ir::value* op: i->ops()){
-    new_ops.push_back(rematerialize_val(builder, op, phi_val));
-  }
-  ir::instruction* ret = i->clone();
-  for(size_t k = 0; k < new_ops.size(); k++)
-    ret->set_operand(k, new_ops[k]);
-  builder.insert(ret);
-  return ret;
-}
-
 ir::value* rematerialize(ir::builder& builder, ir::value* v, size_t phi_idx){
   ir::instruction* i = dynamic_cast<ir::instruction*>(v);
   if(!i)
@@ -96,11 +77,13 @@ ir::value* rematerialize(ir::builder& builder, ir::value* v, size_t phi_idx){
 }
 
 /// moving the prev phi vals to the next iteration
-void update_prev_phi_vals(ir::builder& builder, std::map<ir::phi_node*, ir::value*>& prev_phi_vals) {
-  for (auto& [phi, val] : prev_phi_vals) {
-    // TODO: handling nested phis
-    val = rematerialize_val(builder, phi->get_incoming_value(1), val);
+std::map<ir::phi_node*, ir::value*> update_prev_phi_vals(
+  ir::builder& builder, std::map<ir::phi_node*, ir::value*>& prev_phi_vals) {
+  std::map<ir::phi_node*, ir::value*> next_phi_vals;
+  for (auto &[phi, val] : prev_phi_vals) {
+    next_phi_vals[phi] = rematerialize_vals(builder, phi->get_incoming_value(1), prev_phi_vals);
   }
+  return next_phi_vals;
 }
 
 void finalize_iv_vals(ir::builder& builder, std::map<ir::phi_node*, ir::value*>& load_ivs,
@@ -163,12 +146,10 @@ void pipeline::run(ir::module &mod) {
 
       std::map<ir::phi_node*, ir::value*> prev_phi_vals;
       // initialize prev_phi_vals
-      // note: we assume that ptr & other values only depend on ptr & iv (phis)
-      // TODO: can we just add all phis here?
-      prev_phi_vals[ptr] = ptr->get_value_for_block(header);
-      for (ir::phi_node* iv : induction_vars)
-        prev_phi_vals[iv] = iv->get_value_for_block(header);
-      prev_phi_vals[ptr] = ptr->get_value_for_block(header);
+      // Add all phi nodes. The following DCE pass will delete dead ones.
+      for (ir::instruction *instr : block->get_inst_list())
+        if (auto *phi = dynamic_cast<ir::phi_node*>(instr))
+          prev_phi_vals[phi] = phi->get_value_for_block(header);
 
       builder.set_insert_point(header->get_inst_list().back());
       first_ptrs[0] = ptr->get_value_for_block(header);
@@ -188,7 +169,7 @@ void pipeline::run(ir::module &mod) {
       for (int stage = 1; stage < num_stages-1; ++stage) {
         // mask is the loop condition of the previous iteration
         loop_conds[stage] = rematerialize_vals(builder, block_cond, prev_phi_vals);
-        update_prev_phi_vals(builder, prev_phi_vals);
+        prev_phi_vals = update_prev_phi_vals(builder, prev_phi_vals);
         first_ptrs[stage] = rematerialize_vals(builder, ptr, prev_phi_vals);
         first_masks[stage] = builder.create_splat(loop_conds[stage], ty->get_block_shapes());
         if (auto* masked_load = dynamic_cast<ir::masked_load_inst*>(load)) {
@@ -330,4 +311,4 @@ void pipeline::run(ir::module &mod) {
 
 }
 }
-}
+}
\ No newline at end of file