diff --git a/src/grad.jl b/src/grad.jl
index 7862a18..003ff85 100644
--- a/src/grad.jl
+++ b/src/grad.jl
@@ -76,8 +76,8 @@ function deriv_broadcast!(tape::Tape, op::AbstractOp, i::Int, dy::AbstractOp)
     # 3. record_expr_broadcast!() - record `broadcast` and execute immediately
     ex = to_unbroadcast_expr(tape, op)
     dep_eltypes = [eltype(tape[arg].typ) for arg in op.args[2:end]]
-    dex = deriv_expr(ex, dep_eltypes, i)
-    st = Dict(Symbol("%$i") => i for i in op.args)
+    dex = deriv_expr(ex, dep_eltypes, i-1)
+    st = Dict(Symbol("%$id") => id for id in op.args)
     st[:ds] = dy.id
     ret_id = record_expr!(tape, dex; st=st, bcast=true)
     return tape[ret_id]
@@ -105,7 +105,9 @@ end
 
 
 function back!(tape::Tape)
-    # z - final variable, y - resulting variable of current op, x - dependencies of y
+    # z - final variable (usually a loss)
+    # y - resulting variable of current op
+    # x - dependencies of y
     # dy - derivative of z w.r.t. y
     z = tape[tape.resultid]
     # using Float32 for seed since for 64-bit args it will be expanded anyway
@@ -118,6 +120,7 @@ function back!(tape::Tape)
         if op isa Call # || op isa Bcast
             for i=1:length(op.args)
                 # backpropagate only non-constant vars
+                # note that it also prevents backprop on 1st param of broadcast
                 arg_op = tape[op.args[i]]
                 if !isa(arg_op, Constant)
                     step_back!(tape, op, i)
diff --git a/src/tape.jl b/src/tape.jl
index a63dd51..2d4c9fa 100644
--- a/src/tape.jl
+++ b/src/tape.jl
@@ -140,7 +140,7 @@ function record_expr!(tape::Tape, ex::Expr; st=Dict(), bcast=false)
             new_op_args[i] = st[x]
         elseif Meta.isexpr(x, :call)
             # recursively record arg expression
-            arg_id = record_expr!(tape, x; st=st)
+            arg_id = record_expr!(tape, x; st=st, bcast=bcast)
             new_op_args[i] = arg_id
         else
             # treat as constant
@@ -160,9 +160,9 @@ function record_expr!(tape::Tape, ex::Expr; st=Dict(), bcast=false)
 end
 
 
-function record_expr!(tape::Tape, x::Symbol; st=Dict(), bcast=false)
-    ds_id = st[:ds]
-    return record!(tape, Assign, ds_id, tape[ds_id].val)
+function record_expr!(tape::Tape, x::Symbol; st=Dict(), bcast=false)    
+    id = st[x]
+    return record!(tape, Assign, id, tape[id].val)
 end
 
 
@@ -193,10 +193,12 @@ end
 
 
 """
-Replace a sequence of `broadcasted()` => `materizalize()` calls with a single `broadcast()`
+Recover broadcast operation from Broadcast.broadcasted and Broadcast.materialize
 """
-function squash_broadcast(tape::Tape)
+function recover_broadcast(tape::Tape)
     new_tape = copy_with(tape; ops=AbstractOp[])
+    # TODO: seems like we don't need subs table any more
+    # remove after squash_assigned is implemented
     st = Dict()
     for (id, op) in enumerate(tape)
         if op isa Call && op.fn === Broadcast.broadcasted
@@ -222,9 +224,29 @@ function squash_broadcast(tape::Tape)
 end
 
 
+function squash_assigned(tape::Tape)
+    new_tape = copy_with(tape; ops=AbstractOp[])    
+    st = Dict()
+    for (id, op) in enumerate(tape)
+        if op isa Assign            
+            st[id] = op.src_id        
+        else
+            # record any other operations as is
+            new_id = length(new_tape) + 1
+            push!(new_tape.ops, copy_with(op; id=new_id))
+            st[id] = length(new_tape)
+        end
+    end
+    replace_in_args!(new_tape, st)
+    new_tape.resultid = get(st, tape.resultid, tape.resultid)
+    return new_tape
+end
+
 
 function simplify(tape::Tape)
-    return squash_broadcast(tape)
+    tape = recover_broadcast(tape)
+    tape = squash_assigned(tape)
+    return tape
 end