diff --git a/src/connectivity.jl b/src/connectivity.jl
index 5ffa6273..9d328775 100644
--- a/src/connectivity.jl
+++ b/src/connectivity.jl
@@ -57,6 +57,19 @@ function connectivity(f::Function, x)
     return _connectivity(xt, yt)
 end
 
+"""
+    connectivity(f!, y, x)
+
+Enumerates inputs `x` and primal outputs `y` after `f!(y, x)` and returns sparse connectivity matrix `C` of size `(m, n)`
+where `C[i, j]` is true if the compute graph connects the `i`-th entry in `y` to the `j`-th entry in `x`.
+"""
+function connectivity(f!::Function, y, x)
+    xt = trace_input(x)
+    yt = similar(y, Tracer)
+    f!(yt, xt)
+    return _connectivity(xt, yt)
+end
+
 _connectivity(xt::Tracer, yt::Number) = _connectivity([xt], [yt])
 _connectivity(xt::Tracer, yt::AbstractArray{Number}) = _connectivity([xt], yt)
 _connectivity(xt::AbstractArray{Tracer}, yt::Number) = _connectivity(xt, [yt])
diff --git a/test/Manifest.toml b/test/Manifest.toml
index dd5ad7f5..a6c8189e 100644
--- a/test/Manifest.toml
+++ b/test/Manifest.toml
@@ -2,7 +2,38 @@
 
 julia_version = "1.10.2"
 manifest_format = "2.0"
-project_hash = "1d3f1a9039733a79302ff3b02a00cfd52278c0de"
+project_hash = "a8456878fc5708d860b66d8359b4004e700f22aa"
+
+[[deps.ADTypes]]
+git-tree-sha1 = "016833eb52ba2d6bea9fcb50ca295980e728ee24"
+uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+version = "0.2.7"
+
+[[deps.AbstractTrees]]
+git-tree-sha1 = "2d9c9a55f9c93e8887ad391fbae72f8ef55e1177"
+uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
+version = "0.4.5"
+
+[[deps.Accessors]]
+deps = ["CompositionsBase", "ConstructionBase", "Dates", "InverseFunctions", "LinearAlgebra", "MacroTools", "Markdown", "Test"]
+git-tree-sha1 = "c0d491ef0b135fd7d63cbc6404286bc633329425"
+uuid = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
+version = "0.1.36"
+
+    [deps.Accessors.extensions]
+    AccessorsAxisKeysExt = "AxisKeys"
+    AccessorsIntervalSetsExt = "IntervalSets"
+    AccessorsStaticArraysExt = "StaticArrays"
+    AccessorsStructArraysExt = "StructArrays"
+    AccessorsUnitfulExt = "Unitful"
+
+    [deps.Accessors.weakdeps]
+    AxisKeys = "94b1ba4f-4ee9-5380-92f1-94cde586c3c5"
+    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
+    Requires = "ae029012-a4dd-5104-9daa-d747884805df"
+    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [[deps.Adapt]]
 deps = ["LinearAlgebra", "Requires"]
@@ -24,6 +55,32 @@ version = "0.8.4"
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 version = "1.1.1"
 
+[[deps.ArrayInterface]]
+deps = ["Adapt", "LinearAlgebra", "SparseArrays", "SuiteSparse"]
+git-tree-sha1 = "44691067188f6bd1b2289552a23e4b7572f4528d"
+uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+version = "7.9.0"
+
+    [deps.ArrayInterface.extensions]
+    ArrayInterfaceBandedMatricesExt = "BandedMatrices"
+    ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices"
+    ArrayInterfaceCUDAExt = "CUDA"
+    ArrayInterfaceChainRulesExt = "ChainRules"
+    ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore"
+    ArrayInterfaceReverseDiffExt = "ReverseDiff"
+    ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore"
+    ArrayInterfaceTrackerExt = "Tracker"
+
+    [deps.ArrayInterface.weakdeps]
+    BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+    BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
+    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+    ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
+    GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
+    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+    StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+
 [[deps.Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 
@@ -36,6 +93,11 @@ version = "0.1.0"
 [[deps.Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
+[[deps.Bijections]]
+git-tree-sha1 = "c9b163bd832e023571e86d0b90d9de92a9879088"
+uuid = "e2ed5e7c-b2de-5872-ae92-c73ca462fb04"
+version = "0.1.6"
+
 [[deps.CEnum]]
 git-tree-sha1 = "389ad5c84de1ae7cf0e28e381131c98ea87d54fc"
 uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
@@ -47,6 +109,12 @@ git-tree-sha1 = "b544d62417a99d091c569b95109bc9d8c223e9e3"
 uuid = "00ebfdb7-1f24-5e51-bd34-a7502290713f"
 version = "3.4.2"
 
+[[deps.Calculus]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
+uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
+version = "0.5.1"
+
 [[deps.ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra"]
 git-tree-sha1 = "575cd02e080939a33b6df6c5853d14924c08e35b"
@@ -74,25 +142,39 @@ deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statist
 git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249"
 uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
 version = "0.10.0"
+weakdeps = ["SpecialFunctions"]
 
     [deps.ColorVectorSpace.extensions]
     SpecialFunctionsExt = "SpecialFunctions"
 
-    [deps.ColorVectorSpace.weakdeps]
-    SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
-
 [[deps.Colors]]
 deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
 git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a"
 uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
 version = "0.12.10"
 
+[[deps.Combinatorics]]
+git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860"
+uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
+version = "1.0.2"
+
 [[deps.CommonMark]]
 deps = ["Crayons", "JSON", "PrecompileTools", "URIs"]
 git-tree-sha1 = "532c4185d3c9037c0237546d817858b23cf9e071"
 uuid = "a80b9123-70ca-4bc0-993e-6e3bcb318db6"
 version = "0.8.12"
 
+[[deps.CommonSolve]]
+git-tree-sha1 = "0eee5eb66b1cf62cd6ad1b460238e60e4b09400c"
+uuid = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
+version = "0.2.4"
+
+[[deps.CommonSubexpressions]]
+deps = ["MacroTools", "Test"]
+git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
+uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
+version = "0.3.0"
+
 [[deps.Compat]]
 deps = ["TOML", "UUIDs"]
 git-tree-sha1 = "c955881e3c981181362ae4088b35995446298b80"
@@ -108,17 +190,52 @@ deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
 version = "1.1.0+0"
 
+[[deps.CompositeTypes]]
+git-tree-sha1 = "02d2316b7ffceff992f3096ae48c7829a8aa0638"
+uuid = "b152e2b5-7a66-4b01-a709-34e65c35f657"
+version = "0.1.3"
+
+[[deps.CompositionsBase]]
+git-tree-sha1 = "802bb88cd69dfd1509f6670416bd4434015693ad"
+uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
+version = "0.1.2"
+weakdeps = ["InverseFunctions"]
+
+    [deps.CompositionsBase.extensions]
+    CompositionsBaseInverseFunctionsExt = "InverseFunctions"
+
+[[deps.ConstructionBase]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "260fd2400ed2dab602a7c15cf10c1933c59930a2"
+uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
+version = "1.5.5"
+weakdeps = ["IntervalSets", "StaticArrays"]
+
+    [deps.ConstructionBase.extensions]
+    ConstructionBaseIntervalSetsExt = "IntervalSets"
+    ConstructionBaseStaticArraysExt = "StaticArrays"
+
 [[deps.Crayons]]
 git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15"
 uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
 version = "4.1.1"
 
+[[deps.DataAPI]]
+git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
+uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
+version = "1.16.0"
+
 [[deps.DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
 git-tree-sha1 = "0f4b5d62a88d8f59003e43c25a8a90de9eb76317"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 version = "0.18.18"
 
+[[deps.DataValueInterfaces]]
+git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
+uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
+version = "1.0.0"
+
 [[deps.Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
@@ -128,6 +245,18 @@ git-tree-sha1 = "9824894295b62a6a4ab6adf1c7bf337b3a9ca34c"
 uuid = "ab62b9b5-e342-54a8-a765-a90f495de1a6"
 version = "1.2.0"
 
+[[deps.DiffResults]]
+deps = ["StaticArraysCore"]
+git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621"
+uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
+version = "1.1.0"
+
+[[deps.DiffRules]]
+deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
+git-tree-sha1 = "23163d55f885173722d1e4cf0f6110cdbaf7e272"
+uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
+version = "1.15.1"
+
 [[deps.Distances]]
 deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
 git-tree-sha1 = "66c4c81f259586e8f002eacebc177e1fb06363b0"
@@ -143,11 +272,61 @@ weakdeps = ["ChainRulesCore", "SparseArrays"]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
+[[deps.Distributions]]
+deps = ["FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SpecialFunctions", "Statistics", "StatsAPI", "StatsBase", "StatsFuns"]
+git-tree-sha1 = "7c302d7a5fec5214eb8a5a4c466dcf7a51fcf169"
+uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
+version = "0.25.107"
+
+    [deps.Distributions.extensions]
+    DistributionsChainRulesCoreExt = "ChainRulesCore"
+    DistributionsDensityInterfaceExt = "DensityInterface"
+    DistributionsTestExt = "Test"
+
+    [deps.Distributions.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    DensityInterface = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
+    Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[[deps.DocStringExtensions]]
+deps = ["LibGit2"]
+git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d"
+uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
+version = "0.9.3"
+
+[[deps.DomainSets]]
+deps = ["CompositeTypes", "IntervalSets", "LinearAlgebra", "Random", "StaticArrays"]
+git-tree-sha1 = "9fd332fb3b276a080e3ebccf0dcd98f4a10bf6a6"
+uuid = "5b8099bc-c8ec-5219-889f-1d9e522a28bf"
+version = "0.7.10"
+
 [[deps.Downloads]]
 deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 version = "1.6.0"
 
+[[deps.DualNumbers]]
+deps = ["Calculus", "NaNMath", "SpecialFunctions"]
+git-tree-sha1 = "5837a837389fccf076445fce071c8ddaea35a566"
+uuid = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
+version = "0.6.8"
+
+[[deps.DynamicPolynomials]]
+deps = ["Future", "LinearAlgebra", "MultivariatePolynomials", "MutableArithmetics", "Pkg", "Reexport", "Test"]
+git-tree-sha1 = "0bb0a6f812213ecc8fbbcf472f4a993036858971"
+uuid = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
+version = "0.5.5"
+
+[[deps.EnumX]]
+git-tree-sha1 = "bdb1942cd4c45e3c678fd11569d5cccd80976237"
+uuid = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
+version = "1.0.4"
+
+[[deps.ExprTools]]
+git-tree-sha1 = "27415f162e6028e81c72b82ef756bf321213b6ec"
+uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
+version = "0.1.10"
+
 [[deps.FileIO]]
 deps = ["Pkg", "Requires", "UUIDs"]
 git-tree-sha1 = "82d8afa92ecf4b52d78d869f038ebfb881267322"
@@ -157,12 +336,54 @@ version = "1.16.3"
 [[deps.FileWatching]]
 uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
 
+[[deps.FillArrays]]
+deps = ["LinearAlgebra", "Random"]
+git-tree-sha1 = "5b93957f6dcd33fc343044af3d48c215be2562f1"
+uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
+version = "1.9.3"
+weakdeps = ["PDMats", "SparseArrays", "Statistics"]
+
+    [deps.FillArrays.extensions]
+    FillArraysPDMatsExt = "PDMats"
+    FillArraysSparseArraysExt = "SparseArrays"
+    FillArraysStatisticsExt = "Statistics"
+
 [[deps.FixedPointNumbers]]
 deps = ["Statistics"]
 git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
 uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
 version = "0.8.4"
 
+[[deps.Format]]
+git-tree-sha1 = "9c68794ef81b08086aeb32eeaf33531668d5f5fc"
+uuid = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8"
+version = "1.3.7"
+
+[[deps.ForwardDiff]]
+deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"]
+git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad"
+uuid = "f6369f11-7733-5829-9624-2563aa707210"
+version = "0.10.36"
+weakdeps = ["StaticArrays"]
+
+    [deps.ForwardDiff.extensions]
+    ForwardDiffStaticArraysExt = "StaticArrays"
+
+[[deps.FunctionWrappers]]
+git-tree-sha1 = "d62485945ce5ae9c0c48f124a84998d755bae00e"
+uuid = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e"
+version = "1.1.3"
+
+[[deps.FunctionWrappersWrappers]]
+deps = ["FunctionWrappers"]
+git-tree-sha1 = "b104d487b34566608f8b4e1c39fb0b10aa279ff8"
+uuid = "77dc65aa-8811-40c2-897b-53d922fa7daf"
+version = "0.1.3"
+
+[[deps.Future]]
+deps = ["Random"]
+uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
+
 [[deps.GPUArraysCore]]
 deps = ["Adapt"]
 git-tree-sha1 = "ec632f177c0d990e64d955ccc1b8c04c485a0950"
@@ -174,6 +395,17 @@ git-tree-sha1 = "97285bbd5230dd766e9ef6749b80fc617126d496"
 uuid = "c27321d9-0574-5035-807b-f59d2c89b15c"
 version = "1.3.1"
 
+[[deps.HypergeometricFunctions]]
+deps = ["DualNumbers", "LinearAlgebra", "OpenLibm_jll", "SpecialFunctions"]
+git-tree-sha1 = "f218fe3736ddf977e0e772bc9a586b2383da2685"
+uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
+version = "0.3.23"
+
+[[deps.IfElse]]
+git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
+uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
+version = "0.1.1"
+
 [[deps.ImageBase]]
 deps = ["ImageCore", "Reexport"]
 git-tree-sha1 = "eb49b82c172811fd2c86759fa0553a2221feb909"
@@ -190,6 +422,37 @@ version = "0.10.2"
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
+[[deps.IntervalSets]]
+git-tree-sha1 = "dba9ddf07f77f60450fe5d2e2beb9854d9a49bd0"
+uuid = "8197267c-284f-5f27-9208-e0e47529a953"
+version = "0.7.10"
+weakdeps = ["Random", "RecipesBase", "Statistics"]
+
+    [deps.IntervalSets.extensions]
+    IntervalSetsRandomExt = "Random"
+    IntervalSetsRecipesBaseExt = "RecipesBase"
+    IntervalSetsStatisticsExt = "Statistics"
+
+[[deps.InverseFunctions]]
+deps = ["Test"]
+git-tree-sha1 = "896385798a8d49a255c398bd49162062e4a4c435"
+uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
+version = "0.1.13"
+weakdeps = ["Dates"]
+
+    [deps.InverseFunctions.extensions]
+    DatesExt = "Dates"
+
+[[deps.IrrationalConstants]]
+git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
+uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
+version = "0.2.2"
+
+[[deps.IteratorInterfaceExtensions]]
+git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
+uuid = "82899510-4779-5014-852e-03e436cf321d"
+version = "1.0.0"
+
 [[deps.JET]]
 deps = ["InteractiveUtils", "JuliaInterpreter", "LoweredCodeUtils", "MacroTools", "Pkg", "PrecompileTools", "Preferences", "Revise", "Test"]
 git-tree-sha1 = "6ff76fc594051832ce91078686bc0d3def6d42c5"
@@ -250,6 +513,36 @@ git-tree-sha1 = "88b916503aac4fb7f701bb625cd84ca5dd1677bc"
 uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
 version = "0.0.29+0"
 
+[[deps.LaTeXStrings]]
+git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec"
+uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
+version = "1.3.1"
+
+[[deps.LabelledArrays]]
+deps = ["ArrayInterface", "ChainRulesCore", "ForwardDiff", "LinearAlgebra", "MacroTools", "PreallocationTools", "RecursiveArrayTools", "StaticArrays"]
+git-tree-sha1 = "d1f981fba6eb3ec393eede4821bca3f2b7592cd4"
+uuid = "2ee39098-c373-598a-b85f-a56591580800"
+version = "1.15.1"
+
+[[deps.LambertW]]
+git-tree-sha1 = "c5ffc834de5d61d00d2b0e18c96267cffc21f648"
+uuid = "984bce1d-4616-540c-a9ee-88d1112d94c9"
+version = "0.4.6"
+
+[[deps.Latexify]]
+deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"]
+git-tree-sha1 = "cad560042a7cc108f5a4c24ea1431a9221f22c1b"
+uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
+version = "0.16.2"
+
+    [deps.Latexify.extensions]
+    DataFramesExt = "DataFrames"
+    SymEngineExt = "SymEngine"
+
+    [deps.Latexify.weakdeps]
+    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+    SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"
+
 [[deps.LazyArtifacts]]
 deps = ["Artifacts", "Pkg"]
 uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
@@ -290,6 +583,22 @@ uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
+[[deps.LogExpFunctions]]
+deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "18144f3e9cbe9b15b070288eef858f71b291ce37"
+uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
+version = "0.3.27"
+
+    [deps.LogExpFunctions.extensions]
+    LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
+    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
+    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"
+
+    [deps.LogExpFunctions.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
+
 [[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
@@ -319,6 +628,12 @@ deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
 version = "2.28.2+1"
 
+[[deps.Missings]]
+deps = ["DataAPI"]
+git-tree-sha1 = "f66bdc5de519e8f8ae43bdc598782d35a25b1272"
+uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
+version = "1.1.0"
+
 [[deps.Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
@@ -332,6 +647,18 @@ version = "0.3.4"
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 version = "2023.1.10"
 
+[[deps.MultivariatePolynomials]]
+deps = ["ChainRulesCore", "DataStructures", "LinearAlgebra", "MutableArithmetics"]
+git-tree-sha1 = "769c9175942d91ed9b83fa929eee4fe6a1d128ad"
+uuid = "102ac46a-7ee4-5c85-9060-abc95bfdeaa3"
+version = "0.5.4"
+
+[[deps.MutableArithmetics]]
+deps = ["LinearAlgebra", "SparseArrays", "Test"]
+git-tree-sha1 = "2d106538aebe1c165e16d277914e10c550e9d9b7"
+uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
+version = "1.4.2"
+
 [[deps.NNlib]]
 deps = ["Adapt", "Atomix", "ChainRulesCore", "GPUArraysCore", "KernelAbstractions", "LinearAlgebra", "Pkg", "Random", "Requires", "Statistics"]
 git-tree-sha1 = "1fa1a14766c60e66ab22e242d45c1857c83a3805"
@@ -350,6 +677,12 @@ version = "0.9.13"
     EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
     cuDNN = "02a925ec-e4fe-4b08-9a7e-0d78e3d38ccd"
 
+[[deps.NaNMath]]
+deps = ["OpenLibm_jll"]
+git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4"
+uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
+version = "1.0.2"
+
 [[deps.NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 version = "1.2.0"
@@ -368,11 +701,28 @@ deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
 version = "0.3.23+4"
 
+[[deps.OpenLibm_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
+version = "0.8.1+2"
+
+[[deps.OpenSpecFun_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
+uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
+version = "0.5.5+0"
+
 [[deps.OrderedCollections]]
 git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 version = "1.6.3"
 
+[[deps.PDMats]]
+deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
+git-tree-sha1 = "949347156c25054de2db3b166c52ac4728cbad65"
+uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
+version = "0.11.31"
+
 [[deps.PaddedViews]]
 deps = ["OffsetArrays"]
 git-tree-sha1 = "0fac6313486baae819364c52b4f483450a9d793f"
@@ -390,6 +740,18 @@ deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 version = "1.10.0"
 
+[[deps.PreallocationTools]]
+deps = ["Adapt", "ArrayInterface", "ForwardDiff"]
+git-tree-sha1 = "b6665214f2d0739f2d09a17474dd443b9139784a"
+uuid = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
+version = "0.4.20"
+
+    [deps.PreallocationTools.extensions]
+    PreallocationToolsReverseDiffExt = "ReverseDiff"
+
+    [deps.PreallocationTools.weakdeps]
+    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+
 [[deps.PrecompileTools]]
 deps = ["Preferences"]
 git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f"
@@ -406,6 +768,12 @@ version = "1.4.3"
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
+[[deps.QuadGK]]
+deps = ["DataStructures", "LinearAlgebra"]
+git-tree-sha1 = "9b23c31e76e333e6fb4c1595ae6afa74966a729e"
+uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
+version = "2.9.4"
+
 [[deps.REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
@@ -414,6 +782,36 @@ uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 deps = ["SHA"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
+[[deps.RecipesBase]]
+deps = ["PrecompileTools"]
+git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
+uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
+version = "1.3.4"
+
+[[deps.RecursiveArrayTools]]
+deps = ["Adapt", "ArrayInterface", "DocStringExtensions", "GPUArraysCore", "IteratorInterfaceExtensions", "LinearAlgebra", "RecipesBase", "SparseArrays", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"]
+git-tree-sha1 = "d8f131090f2e44b145084928856a561c83f43b27"
+uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
+version = "3.13.0"
+
+    [deps.RecursiveArrayTools.extensions]
+    RecursiveArrayToolsFastBroadcastExt = "FastBroadcast"
+    RecursiveArrayToolsForwardDiffExt = "ForwardDiff"
+    RecursiveArrayToolsMeasurementsExt = "Measurements"
+    RecursiveArrayToolsMonteCarloMeasurementsExt = "MonteCarloMeasurements"
+    RecursiveArrayToolsReverseDiffExt = ["ReverseDiff", "Zygote"]
+    RecursiveArrayToolsTrackerExt = "Tracker"
+    RecursiveArrayToolsZygoteExt = "Zygote"
+
+    [deps.RecursiveArrayTools.weakdeps]
+    FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
+    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+    Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
+    MonteCarloMeasurements = "0987c9cc-fe09-11e8-30f0-b96dd679fdca"
+    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+
 [[deps.Reexport]]
 git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
@@ -437,21 +835,97 @@ git-tree-sha1 = "12aa2d7593df490c407a3bbd8b86b8b515017f3e"
 uuid = "295af30f-e4ad-537b-8983-00126c2a3abe"
 version = "3.5.14"
 
+[[deps.Rmath]]
+deps = ["Random", "Rmath_jll"]
+git-tree-sha1 = "f65dcb5fa46aee0cf9ed6274ccbd597adc49aa7b"
+uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
+version = "0.7.1"
+
+[[deps.Rmath_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "6ed52fdd3382cf21947b15e8870ac0ddbff736da"
+uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
+version = "0.4.0+0"
+
+[[deps.RuntimeGeneratedFunctions]]
+deps = ["ExprTools", "SHA", "Serialization"]
+git-tree-sha1 = "6aacc5eefe8415f47b3e34214c1d79d2674a0ba2"
+uuid = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
+version = "0.5.12"
+
 [[deps.SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 version = "0.7.0"
 
+[[deps.SciMLBase]]
+deps = ["ADTypes", "ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "EnumX", "FunctionWrappersWrappers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "PrecompileTools", "Preferences", "Printf", "RecipesBase", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLOperators", "SciMLStructures", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"]
+git-tree-sha1 = "d15c65e25615272e1b1c5edb1d307484c7942824"
+uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+version = "2.31.0"
+
+    [deps.SciMLBase.extensions]
+    SciMLBaseChainRulesCoreExt = "ChainRulesCore"
+    SciMLBaseMakieExt = "Makie"
+    SciMLBasePartialFunctionsExt = "PartialFunctions"
+    SciMLBasePyCallExt = "PyCall"
+    SciMLBasePythonCallExt = "PythonCall"
+    SciMLBaseRCallExt = "RCall"
+    SciMLBaseZygoteExt = "Zygote"
+
+    [deps.SciMLBase.weakdeps]
+    ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
+    PartialFunctions = "570af359-4316-4cb7-8c74-252c00c2016b"
+    PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"
+    PythonCall = "6099a3de-0909-46bc-b1f4-468b9a2dfc0d"
+    RCall = "6f49c342-dc21-5d91-9882-a32aef131414"
+    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+
+[[deps.SciMLOperators]]
+deps = ["ArrayInterface", "DocStringExtensions", "LinearAlgebra", "MacroTools", "Setfield", "SparseArrays", "StaticArraysCore"]
+git-tree-sha1 = "10499f619ef6e890f3f4a38914481cc868689cd5"
+uuid = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
+version = "0.3.8"
+
+[[deps.SciMLStructures]]
+git-tree-sha1 = "5833c10ce83d690c124beedfe5f621b50b02ba4d"
+uuid = "53ae85a6-f571-4167-b2af-e1d143709226"
+version = "1.1.0"
+
 [[deps.Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
+[[deps.Setfield]]
+deps = ["ConstructionBase", "Future", "MacroTools", "StaticArraysCore"]
+git-tree-sha1 = "e2cc6d8c88613c05e1defb55170bf5ff211fbeac"
+uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
+version = "1.1.1"
+
 [[deps.Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
+[[deps.SortingAlgorithms]]
+deps = ["DataStructures"]
+git-tree-sha1 = "66e0a8e672a0bdfca2c3f5937efb8538b9ddc085"
+uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
+version = "1.2.1"
+
 [[deps.SparseArrays]]
 deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 version = "1.10.0"
 
+[[deps.SpecialFunctions]]
+deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
+git-tree-sha1 = "e2cfc4012a19088254b3950b85c3c1d8882d864d"
+uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
+version = "2.3.1"
+weakdeps = ["ChainRulesCore"]
+
+    [deps.SpecialFunctions.extensions]
+    SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"
+
 [[deps.StackViews]]
 deps = ["OffsetArrays"]
 git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
@@ -485,16 +959,85 @@ git-tree-sha1 = "1ff449ad350c9c4cbc756624d6f8a8c3ef56d3ed"
 uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
 version = "1.7.0"
 
+[[deps.StatsBase]]
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "1d77abd07f617c4868c33d4f5b9e1dbb2643c9cf"
+uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+version = "0.34.2"
+
+[[deps.StatsFuns]]
+deps = ["HypergeometricFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "cef0472124fab0695b58ca35a77c6fb942fdab8a"
+uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
+version = "1.3.1"
+weakdeps = ["ChainRulesCore", "InverseFunctions"]
+
+    [deps.StatsFuns.extensions]
+    StatsFunsChainRulesCoreExt = "ChainRulesCore"
+    StatsFunsInverseFunctionsExt = "InverseFunctions"
+
+[[deps.SuiteSparse]]
+deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
+uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
+
 [[deps.SuiteSparse_jll]]
 deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
 uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
 version = "7.2.1+1"
 
+[[deps.SymbolicIndexingInterface]]
+deps = ["Accessors", "ArrayInterface", "MacroTools", "RuntimeGeneratedFunctions", "StaticArraysCore"]
+git-tree-sha1 = "4b7f4c80449d8baae8857d55535033981862619c"
+uuid = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
+version = "0.3.15"
+
+[[deps.SymbolicLimits]]
+deps = ["SymbolicUtils"]
+git-tree-sha1 = "89aa6b25a75418c8fffc42073b2e7dce69847394"
+uuid = "19f23fe9-fdab-4a78-91af-e7b7767979c3"
+version = "0.2.0"
+
+[[deps.SymbolicUtils]]
+deps = ["AbstractTrees", "Bijections", "ChainRulesCore", "Combinatorics", "ConstructionBase", "DataStructures", "DocStringExtensions", "DynamicPolynomials", "IfElse", "LabelledArrays", "LinearAlgebra", "MultivariatePolynomials", "NaNMath", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicIndexingInterface", "TimerOutputs", "Unityper"]
+git-tree-sha1 = "669e43e90df46fcee4aa859b587da7a7948272ac"
+uuid = "d1185830-fcd6-423d-90d6-eec64667417b"
+version = "1.5.1"
+
+[[deps.Symbolics]]
+deps = ["ArrayInterface", "Bijections", "ConstructionBase", "DataStructures", "DiffRules", "Distributions", "DocStringExtensions", "DomainSets", "DynamicPolynomials", "ForwardDiff", "IfElse", "LaTeXStrings", "LambertW", "Latexify", "Libdl", "LinearAlgebra", "LogExpFunctions", "MacroTools", "Markdown", "NaNMath", "PrecompileTools", "RecipesBase", "Reexport", "Requires", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicIndexingInterface", "SymbolicLimits", "SymbolicUtils"]
+git-tree-sha1 = "280c17e091a24283a59eedfc00a02026ec984b09"
+uuid = "0c5d862f-8b57-4792-8d23-62f2024744c7"
+version = "5.27.1"
+
+    [deps.Symbolics.extensions]
+    SymbolicsGroebnerExt = "Groebner"
+    SymbolicsLuxCoreExt = "LuxCore"
+    SymbolicsPreallocationToolsExt = "PreallocationTools"
+    SymbolicsSymPyExt = "SymPy"
+
+    [deps.Symbolics.weakdeps]
+    Groebner = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
+    LuxCore = "bb33d45b-7691-41d6-9220-0943567d0623"
+    PreallocationTools = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
+    SymPy = "24249f21-da20-56a4-8eb1-6a02cf4ae2e6"
+
 [[deps.TOML]]
 deps = ["Dates"]
 uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
 version = "1.0.3"
 
+[[deps.TableTraits]]
+deps = ["IteratorInterfaceExtensions"]
+git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
+uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
+version = "1.0.1"
+
+[[deps.Tables]]
+deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits"]
+git-tree-sha1 = "cb76cf677714c095e535e3501ac7954732aeea2d"
+uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
+version = "1.11.1"
+
 [[deps.Tar]]
 deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
@@ -510,6 +1053,12 @@ version = "0.1.1"
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
+[[deps.TimerOutputs]]
+deps = ["ExprTools", "Printf"]
+git-tree-sha1 = "f548a9e9c490030e545f72074a41edfd0e5bcdd7"
+uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
+version = "0.5.23"
+
 [[deps.Tokenize]]
 git-tree-sha1 = "5b5a892ba7704c0977013bd0f9c30f5d962181e0"
 uuid = "0796e94c-ce3b-5d07-9a54-7f471281c624"
@@ -527,6 +1076,12 @@ uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 [[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
+[[deps.Unityper]]
+deps = ["ConstructionBase"]
+git-tree-sha1 = "25008b734a03736c41e2a7dc314ecb95bd6bbdb0"
+uuid = "a7c27f48-0311-42f6-a7f8-2c11e75eb415"
+version = "0.1.6"
+
 [[deps.UnsafeAtomics]]
 git-tree-sha1 = "6331ac3440856ea1988316b46045303bef658278"
 uuid = "013be700-e6cd-48c3-b4a1-df204f14c38f"
diff --git a/test/Project.toml b/test/Project.toml
index 3c0b9875..18e6ce9a 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -6,4 +6,5 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 NNlib = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReferenceTests = "324d217c-45ce-50fc-942e-d289b448e8cf"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/test/benchmark.jl b/test/benchmark.jl
new file mode 100644
index 00000000..3b5ddaa5
--- /dev/null
+++ b/test/benchmark.jl
@@ -0,0 +1,31 @@
+using BenchmarkTools
+using SparseConnectivityTracer
+using Symbolics: Symbolics
+
+include("brusselator.jl")
+
+function benchmark_brusselator(N::Integer, method=:tracer)
+    dims = (N, N, 2)
+    A = 1.0
+    B = 1.0
+    alpha = 1.0
+    xyd = fill(1.0, N)
+    dx = 1.0
+    p = (A, B, alpha, xyd, dx, N)
+
+    u = rand(dims...)
+    du = similar(u)
+    f!(du, u) = brusselator_2d_loop(du, u, p, nothing)
+
+    if method == :tracer
+        return @benchmark connectivity($f!, $du, $u)
+    elseif method == :symbolics
+        return @benchmark Symbolics.jacobian_sparsity($f!, $du, $u)
+    end
+end
+
+benchmark_brusselator(6, :tracer)
+benchmark_brusselator(6, :symbolics)
+
+benchmark_brusselator(24, :tracer)
+benchmark_brusselator(24, :symbolics)
diff --git a/test/runtests.jl b/test/runtests.jl
index b1037b2e..a5dc97c4 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -9,9 +9,10 @@ using JET
 
 using LinearAlgebra
 using Random
+using Symbolics: Symbolics
 using NNlib
 
-@testset "SparseConnectivityTracer.jl" begin
+@testset verbose = true "SparseConnectivityTracer.jl" begin
     @testset "Code formatting" begin
         @test JuliaFormatter.format(
             SparseConnectivityTracer; verbose=false, overwrite=false
@@ -70,14 +71,14 @@ using NNlib
             p = (A, B, alpha, xyd, dx, N)
 
             u = rand(dims...)
-            du = similar(u, Tracer)
-            function f(u)
-                brusselator_2d_loop(du, u, p, nothing)
-                return du
-            end
+            du = similar(u)
+            f!(du, u) = brusselator_2d_loop(du, u, p, nothing)
 
-            C = connectivity(f, u)
+            C = connectivity(f!, du, u)
             @test_reference "references/connectivity/Brusselator.txt" BitMatrix(C)
+
+            C_ref = Symbolics.jacobian_sparsity(f!, du, u)
+            @test C == C_ref
         end
     end
 end