diff --git a/src/greedy.jl b/src/greedy.jl
index d784133..fac568e 100644
--- a/src/greedy.jl
+++ b/src/greedy.jl
@@ -160,10 +160,45 @@ function analyze_contraction(incidence_list::IncidenceList{Int,ET}, vi::Int, vj:
     return LegInfo(leg1, leg2, leg12, leg01, leg02, leg012)
 end
 
+function analyze_contraction_fast(incidence_list::IncidenceList{Int,ET}, vi::Int, vj::Int, log2_edge_sizes::AbstractDict{ET, T}) where {ET, T}
+    ei = edges(incidence_list, vi)
+    ej = edges(incidence_list, vj)
+
+    D1 = D2 = D12 = D01 = D02 = D012 = zero(T)
+
+    # external legs
+    for leg in ei ∪ ej
+        dim = log2_edge_sizes[leg]
+        isext = leg ∈ incidence_list.openedges || !all(x->x==vi || x==vj, vertices(incidence_list, leg))
+
+        if isext
+            if leg ∈ ei
+                if leg ∈ ej
+                    D012 += dim
+                else
+                    D01 += dim
+                end
+            else
+                D02 += dim
+            end
+        else
+            if leg ∈ ei
+                if leg ∈ ej
+                    D12 += dim
+                else
+                    D1 += dim
+                end
+            else
+                D2 += dim
+            end
+        end
+    end
+
+    return D1, D2, D12, D01, D02, D012
+end
+
 function greedy_loss(α, incidence_list, log2_edge_sizes, vi, vj)
-    log2dim(legs) = isempty(legs) ? 0 : sum(l->log2_edge_sizes[l], legs)  # for 1.5, you need this patch because `init` kw is not allowed.
-    legs = analyze_contraction(incidence_list, vi, vj)
-    D1,D2,D12,D01,D02,D012 = log2dim.(getfield.(Ref(legs), 1:6))
+    D1, D2, D12, D01, D02, D012 = analyze_contraction_fast(incidence_list, vi, vj, log2_edge_sizes)
     loss = exp2(D01+D02+D012) - α * (exp2(D01+D12+D012) + exp2(D02+D12+D012))  # out - in
     return loss
 end
@@ -251,7 +286,26 @@ function optimize_greedy(ixs::AbstractVector{<:AbstractVector}, iy::AbstractVect
     parse_eincode!(incidence_list, tree, 1:length(ixs), size_dict)[2]
 end
 
-function optimize_greedy(code::E, size_dict; α, temperature) where E <: NestedEinsum
+function optimize_greedy_log2(code::EinCode{L}, size_dict::Dict{L}, size_dict_log2::Dict{L}; α, temperature) where {L}
+    ixs = getixsv(code)
+    iy = getiyv(code)
+
+    if length(ixs) <= 2
+        return NestedEinsum(NestedEinsum{L}.(1:length(ixs)), EinCode(ixs, iy))
+    end
+
+    incidence_list = IncidenceList(Dict([i=>ixs[i] for i=1:length(ixs)]); openedges=iy)
+    tree, _, _ = tree_greedy(incidence_list, size_dict_log2; α, temperature)
+    return parse_eincode!(incidence_list, tree, 1:length(ixs), size_dict)[2]
+end
+
+function optimize_greedy(code::E, size_dict::AbstractDict{L}; α, temperature) where {E <: NestedEinsum, L}
+    size_dict_log2 = Dict{L, Float64}()
+
+    for (lbl, dim) in size_dict
+        size_dict_log2[lbl] = log2(dim)
+    end
+
     # construct first-child next-sibling representation of `code`
     queue = [code]
     child = [0]
@@ -296,7 +350,7 @@ function optimize_greedy(code::E, size_dict; α, temperature) where E <: NestedE
             end
 
             if length(args) > 2
-                code = replace_args(optimize_greedy(code.eins, size_dict; α, temperature), args)
+                code = replace_args(optimize_greedy_log2(code.eins, size_dict, size_dict_log2; α, temperature), args)
             else
                 code = NestedEinsum(args, code.eins)
             end