diff --git a/.gitignore b/.gitignore
index 686bb52..e6ed060 100644
--- a/.gitignore
+++ b/.gitignore
@@ -6,4 +6,6 @@ docs/src/index.md
 /docs/build/
 docs/src/examples/*.md
 test/playground.jl
-*.csv
\ No newline at end of file
+*.csv
+*.png
+*.pdf
\ No newline at end of file
diff --git a/benchmark/Manifest.toml b/benchmark/Manifest.toml
index 026f0ee..0214c82 100644
--- a/benchmark/Manifest.toml
+++ b/benchmark/Manifest.toml
@@ -2,7 +2,7 @@
 
 julia_version = "1.9.2"
 manifest_format = "2.0"
-project_hash = "a8180b49764d10c36ecb13045ad202fb2dd69c55"
+project_hash = "632f199f0bf0f7ae2bb64168d221b93c43f0d0f3"
 
 [[deps.AMD]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse_jll"]
@@ -72,6 +72,17 @@ git-tree-sha1 = "d9a9701b899b30332bbcb3e1679c41cce81fb0e8"
 uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 version = "1.3.2"
 
+[[deps.BitFlags]]
+git-tree-sha1 = "43b1a4a8f797c1cddadf60499a8a077d4af2cd2d"
+uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
+version = "0.1.7"
+
+[[deps.Bzip2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.8+0"
+
 [[deps.CEnum]]
 git-tree-sha1 = "eb4cb44a499229b3b8426dcfb5dd85333951ff90"
 uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
@@ -83,6 +94,12 @@ git-tree-sha1 = "44dbf560808d49041989b8a96cae4cffbeb7966a"
 uuid = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
 version = "0.10.11"
 
+[[deps.Cairo_jll]]
+deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
+git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
+uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
+version = "1.16.1+1"
+
 [[deps.ChainRules]]
 deps = ["Adapt", "ChainRulesCore", "Compat", "Distributed", "GPUArraysCore", "IrrationalConstants", "LinearAlgebra", "Random", "RealDot", "SparseArrays", "Statistics", "StructArrays"]
 git-tree-sha1 = "f98ae934cd677d51d2941088849f0bf2f59e6f6e"
@@ -101,6 +118,34 @@ git-tree-sha1 = "02aa26a4cf76381be7f66e020a3eddeb27b0a092"
 uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
 version = "0.7.2"
 
+[[deps.ColorSchemes]]
+deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
+git-tree-sha1 = "d9a8f86737b665e15a9641ecbac64deef9ce6724"
+uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
+version = "3.23.0"
+
+[[deps.ColorTypes]]
+deps = ["FixedPointNumbers", "Random"]
+git-tree-sha1 = "eb7f0f8307f71fac7c606984ea5fb2817275d6e4"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.11.4"
+
+[[deps.ColorVectorSpace]]
+deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
+git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249"
+uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
+version = "0.10.0"
+weakdeps = ["SpecialFunctions"]
+
+    [deps.ColorVectorSpace.extensions]
+    SpecialFunctionsExt = "SpecialFunctions"
+
+[[deps.Colors]]
+deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
+git-tree-sha1 = "fc08e5930ee9a4e03f84bfb5211cb54e7769758a"
+uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
+version = "0.12.10"
+
 [[deps.CommonSubexpressions]]
 deps = ["MacroTools", "Test"]
 git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
@@ -122,6 +167,17 @@ deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
 version = "1.0.5+0"
 
+[[deps.ConcurrentUtilities]]
+deps = ["Serialization", "Sockets"]
+git-tree-sha1 = "5372dbbf8f0bdb8c700db5367132925c0771ef7e"
+uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
+version = "2.2.1"
+
+[[deps.Contour]]
+git-tree-sha1 = "d05d9e7b7aedff4e5b51a029dced05cfb6125781"
+uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
+version = "0.6.2"
+
 [[deps.Crayons]]
 git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15"
 uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
@@ -153,6 +209,12 @@ version = "1.0.0"
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 
+[[deps.DelimitedFiles]]
+deps = ["Mmap"]
+git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
+uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
+version = "1.9.1"
+
 [[deps.DiffResults]]
 deps = ["StaticArraysCore"]
 git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621"
@@ -180,11 +242,35 @@ deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 version = "1.6.0"
 
+[[deps.ExceptionUnwrapping]]
+deps = ["Test"]
+git-tree-sha1 = "e90caa41f5a86296e014e148ee061bd6c3edec96"
+uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4"
+version = "0.1.9"
+
+[[deps.Expat_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "4558ab818dcceaab612d1bb8c19cee87eda2b83c"
+uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
+version = "2.5.0+0"
+
 [[deps.ExprTools]]
 git-tree-sha1 = "27415f162e6028e81c72b82ef756bf321213b6ec"
 uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
 version = "0.1.10"
 
+[[deps.FFMPEG]]
+deps = ["FFMPEG_jll"]
+git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
+uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
+version = "0.4.1"
+
+[[deps.FFMPEG_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Pkg", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
+git-tree-sha1 = "74faea50c1d007c85837327f6775bea60b5492dd"
+uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
+version = "4.4.2+2"
+
 [[deps.FastClosures]]
 git-tree-sha1 = "acebe244d53ee1b461970f8910c235b259e772ef"
 uuid = "9aa1b823-49e4-5ca5-8b0f-3971ec8bab6a"
@@ -205,6 +291,24 @@ git-tree-sha1 = "f372472e8672b1d993e93dada09e23139b509f9e"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
 version = "1.5.0"
 
+[[deps.FixedPointNumbers]]
+deps = ["Statistics"]
+git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
+uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
+version = "0.8.4"
+
+[[deps.Fontconfig_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
+uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
+version = "2.13.93+0"
+
+[[deps.Formatting]]
+deps = ["Printf"]
+git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
+uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
+version = "0.4.2"
+
 [[deps.ForwardDiff]]
 deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"]
 git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad"
@@ -217,10 +321,28 @@ version = "0.10.36"
     [deps.ForwardDiff.weakdeps]
     StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
+[[deps.FreeType2_jll]]
+deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
+git-tree-sha1 = "d8db6a5a2fe1381c1ea4ef2cab7c69c2de7f9ea0"
+uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
+version = "2.13.1+0"
+
+[[deps.FriBidi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
+uuid = "559328eb-81f9-559d-9380-de523a88c83c"
+version = "1.0.10+0"
+
 [[deps.Future]]
 deps = ["Random"]
 uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
 
+[[deps.GLFW_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
+git-tree-sha1 = "d972031d28c8c8d9d7b41a536ad7bb0c2579caca"
+uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
+version = "3.3.8+0"
+
 [[deps.GPUArrays]]
 deps = ["Adapt", "GPUArraysCore", "LLVM", "LinearAlgebra", "Printf", "Random", "Reexport", "Serialization", "Statistics"]
 git-tree-sha1 = "2e57b4a4f9cc15e85a24d603256fe08e527f48d1"
@@ -233,6 +355,53 @@ git-tree-sha1 = "2d6ca471a6c7b536127afccfa7564b5b39227fe0"
 uuid = "46192b85-c4d5-4398-a991-12ede77f4527"
 version = "0.1.5"
 
+[[deps.GR]]
+deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Preferences", "Printf", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "UUIDs", "p7zip_jll"]
+git-tree-sha1 = "d73afa4a2bb9de56077242d98cf763074ab9a970"
+uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
+version = "0.72.9"
+
+[[deps.GR_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"]
+git-tree-sha1 = "1596bab77f4f073a14c62424283e7ebff3072eca"
+uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
+version = "0.72.9+1"
+
+[[deps.Gettext_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
+uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
+version = "0.21.0+0"
+
+[[deps.Glib_jll]]
+deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "d3b3624125c1474292d0d8ed0f65554ac37ddb23"
+uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
+version = "2.74.0+2"
+
+[[deps.Graphite2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
+uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
+version = "1.3.14+0"
+
+[[deps.Grisu]]
+git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
+uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
+version = "1.0.2"
+
+[[deps.HTTP]]
+deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
+git-tree-sha1 = "cb56ccdd481c0dd7f975ad2b3b62d9eda088f7e2"
+uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
+version = "1.9.14"
+
+[[deps.HarfBuzz_jll]]
+deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
+git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
+uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
+version = "2.8.1+1"
+
 [[deps.IRTools]]
 deps = ["InteractiveUtils", "MacroTools", "Test"]
 git-tree-sha1 = "eac00994ce3229a464c2847e956d77a2c64ad3a5"
@@ -284,6 +453,12 @@ git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
 uuid = "82899510-4779-5014-852e-03e436cf321d"
 version = "1.0.0"
 
+[[deps.JLFzf]]
+deps = ["Pipe", "REPL", "Random", "fzf_jll"]
+git-tree-sha1 = "f377670cda23b6b7c1c0b3893e37451c5c1a2185"
+uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
+version = "0.1.5"
+
 [[deps.JLLWrappers]]
 deps = ["Preferences"]
 git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1"
@@ -296,18 +471,36 @@ git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
 uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 version = "0.21.4"
 
+[[deps.JpegTurbo_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "6f2675ef130a300a112286de91973805fcc5ffbc"
+uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
+version = "2.1.91+0"
+
 [[deps.Krylov]]
 deps = ["LinearAlgebra", "Printf", "SparseArrays"]
 git-tree-sha1 = "6dc4ad9cd74ad4ca0a8e219e945dbd22039f2125"
 uuid = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
 version = "0.9.2"
 
+[[deps.LAME_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
+uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
+version = "3.100.1+0"
+
 [[deps.LDLFactorizations]]
 deps = ["AMD", "LinearAlgebra", "SparseArrays", "Test"]
 git-tree-sha1 = "cbf4b646f82bfc58bb48bcca9dcce2eb88da4cd1"
 uuid = "40e66cde-538c-5869-a4ad-c39174c6795b"
 version = "0.10.0"
 
+[[deps.LERC_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "bf36f528eec6634efc60d7ec062008f171071434"
+uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
+version = "3.0.0+1"
+
 [[deps.LLVM]]
 deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Printf", "Unicode"]
 git-tree-sha1 = "8695a49bfe05a2dc0feeefd06b4ca6361a018729"
@@ -320,11 +513,37 @@ git-tree-sha1 = "c35203c1e1002747da220ffc3c0762ce7754b08c"
 uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
 version = "0.0.23+0"
 
+[[deps.LLVMOpenMP_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "f689897ccbe049adb19a065c495e75f372ecd42b"
+uuid = "1d63c593-3942-5779-bab2-d838dc0a180e"
+version = "15.0.4+0"
+
+[[deps.LZO_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
+uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
+version = "2.10.1+0"
+
 [[deps.LaTeXStrings]]
 git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
 uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
 version = "1.3.0"
 
+[[deps.Latexify]]
+deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Printf", "Requires"]
+git-tree-sha1 = "f428ae552340899a935973270b8d98e5a31c49fe"
+uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
+version = "0.16.1"
+
+    [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"
@@ -351,6 +570,54 @@ version = "1.10.2+0"
 [[deps.Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
+[[deps.Libffi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
+uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
+version = "3.2.2+1"
+
+[[deps.Libgcrypt_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
+git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
+uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
+version = "1.8.7+0"
+
+[[deps.Libglvnd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
+git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733"
+uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
+version = "1.6.0+0"
+
+[[deps.Libgpg_error_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
+uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
+version = "1.42.0+0"
+
+[[deps.Libiconv_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "c7cb1f5d892775ba13767a87c7ada0b980ea0a71"
+uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
+version = "1.16.1+2"
+
+[[deps.Libmount_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
+uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
+version = "2.35.0+0"
+
+[[deps.Libtiff_jll]]
+deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"]
+git-tree-sha1 = "2da088d113af58221c52828a80378e16be7d037a"
+uuid = "89763e89-9b03-5906-acba-b20f662cd828"
+version = "4.5.1+1"
+
+[[deps.Libuuid_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
+uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
+version = "2.36.0+0"
+
 [[deps.LinearAlgebra]]
 deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -380,6 +647,12 @@ version = "0.3.24"
 [[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
+[[deps.LoggingExtras]]
+deps = ["Dates", "Logging"]
+git-tree-sha1 = "cedb76b37bc5a6c702ade66be44f831fa23c681e"
+uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
+version = "1.0.0"
+
 [[deps.MacroTools]]
 deps = ["Markdown", "Random"]
 git-tree-sha1 = "42324d08725e200c23d4dfb549e0d5d89dede2d2"
@@ -390,11 +663,22 @@ version = "0.5.10"
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
+[[deps.MbedTLS]]
+deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "Random", "Sockets"]
+git-tree-sha1 = "03a9b9718f5682ecb107ac9f7308991db4ce395b"
+uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
+version = "1.1.7"
+
 [[deps.MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
 version = "2.28.2+0"
 
+[[deps.Measures]]
+git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102"
+uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
+version = "0.3.2"
+
 [[deps.Missings]]
 deps = ["DataAPI"]
 git-tree-sha1 = "f66bdc5de519e8f8ae43bdc598782d35a25b1272"
@@ -418,6 +702,12 @@ version = "1.0.2"
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 version = "1.2.0"
 
+[[deps.Ogg_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
+uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
+version = "1.3.5+1"
+
 [[deps.OpenBLAS_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
@@ -428,28 +718,94 @@ deps = ["Artifacts", "Libdl"]
 uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
 version = "0.8.1+0"
 
+[[deps.OpenSSL]]
+deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]
+git-tree-sha1 = "51901a49222b09e3743c65b8847687ae5fc78eb2"
+uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
+version = "1.4.1"
+
+[[deps.OpenSSL_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "bbb5c2115d63c2f1451cb70e5ef75e8fe4707019"
+uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
+version = "1.1.22+0"
+
 [[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.Opus_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
+uuid = "91d4177d-7536-5919-b921-800302f37372"
+version = "1.3.2+0"
+
 [[deps.OrderedCollections]]
 git-tree-sha1 = "2e73fe17cac3c62ad1aebe70d44c963c3cfdc3e3"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 version = "1.6.2"
 
+[[deps.PCRE2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
+version = "10.42.0+0"
+
 [[deps.Parsers]]
 deps = ["Dates", "PrecompileTools", "UUIDs"]
 git-tree-sha1 = "716e24b21538abc91f6205fd1d8363f39b442851"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
 version = "2.7.2"
 
+[[deps.Pipe]]
+git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d"
+uuid = "b98c9c47-44ae-5843-9183-064241ee97a0"
+version = "1.3.0"
+
+[[deps.Pixman_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl"]
+git-tree-sha1 = "64779bc4c9784fee475689a1752ef4d5747c5e87"
+uuid = "30392449-352a-5448-841d-b1acce4e97dc"
+version = "0.42.2+0"
+
 [[deps.Pkg]]
 deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 version = "1.9.2"
 
+[[deps.PlotThemes]]
+deps = ["PlotUtils", "Statistics"]
+git-tree-sha1 = "1f03a2d339f42dca4a4da149c7e15e9b896ad899"
+uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
+version = "3.1.0"
+
+[[deps.PlotUtils]]
+deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"]
+git-tree-sha1 = "f92e1315dadf8c46561fb9396e525f7200cdc227"
+uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
+version = "1.3.5"
+
+[[deps.Plots]]
+deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Preferences", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"]
+git-tree-sha1 = "9f8675a55b37a70aa23177ec110f6e3f4dd68466"
+uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+version = "1.38.17"
+
+    [deps.Plots.extensions]
+    FileIOExt = "FileIO"
+    GeometryBasicsExt = "GeometryBasics"
+    IJuliaExt = "IJulia"
+    ImageInTerminalExt = "ImageInTerminal"
+    UnitfulExt = "Unitful"
+
+    [deps.Plots.weakdeps]
+    FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
+    GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
+    IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
+    ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254"
+    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
+
 [[deps.PooledArrays]]
 deps = ["DataAPI", "Future"]
 git-tree-sha1 = "a6062fe4063cdafe78f4a0a81cfffb89721b30e7"
@@ -482,6 +838,12 @@ uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 deps = ["Printf"]
 uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"
 
+[[deps.Qt6Base_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
+git-tree-sha1 = "364898e8f13f7eaaceec55fd3d08680498c0aa6e"
+uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56"
+version = "6.4.2+3"
+
 [[deps.REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
@@ -496,11 +858,29 @@ git-tree-sha1 = "9f0a1b71baaf7650f4fa8a1d168c7fb6ee41f0c9"
 uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
 version = "0.1.0"
 
+[[deps.RecipesBase]]
+deps = ["PrecompileTools"]
+git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
+uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
+version = "1.3.4"
+
+[[deps.RecipesPipeline]]
+deps = ["Dates", "NaNMath", "PlotUtils", "PrecompileTools", "RecipesBase"]
+git-tree-sha1 = "45cf9fd0ca5839d06ef333c8201714e888486342"
+uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
+version = "0.6.12"
+
 [[deps.Reexport]]
 git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
 version = "1.2.2"
 
+[[deps.RelocatableFolders]]
+deps = ["SHA", "Scratch"]
+git-tree-sha1 = "90bc7a7c96410424509e4263e277e43250c05691"
+uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
+version = "1.0.0"
+
 [[deps.Requires]]
 deps = ["UUIDs"]
 git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
@@ -511,6 +891,12 @@ version = "1.3.0"
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 version = "0.7.0"
 
+[[deps.Scratch]]
+deps = ["Dates"]
+git-tree-sha1 = "30449ee12237627992a99d5e30ae63e4d78cd24a"
+uuid = "6c6a2e73-6563-6170-7368-637461726353"
+version = "1.2.0"
+
 [[deps.SentinelArrays]]
 deps = ["Dates", "Random"]
 git-tree-sha1 = "04bdff0b09c65ff3e06a05e3eb7b120223da3d39"
@@ -520,6 +906,17 @@ version = "1.4.0"
 [[deps.Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
+[[deps.Showoff]]
+deps = ["Dates", "Grisu"]
+git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
+uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
+version = "1.0.3"
+
+[[deps.SimpleBufferStream]]
+git-tree-sha1 = "874e8867b33a00e784c8a7e4b60afe9e037b74e1"
+uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
+version = "1.1.0"
+
 [[deps.SimpleUnPack]]
 git-tree-sha1 = "58e6353e72cde29b90a69527e56df1b5c3d8c437"
 uuid = "ce78b400-467f-4804-87d8-8f486da07d0a"
@@ -558,6 +955,18 @@ deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 version = "1.9.0"
 
+[[deps.StatsAPI]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "45a7769a04a3cf80da1c1c7c60caf932e6f4c9f7"
+uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
+version = "1.6.0"
+
+[[deps.StatsBase]]
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "75ebe04c5bed70b91614d684259b661c9e6274a4"
+uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+version = "0.34.0"
+
 [[deps.StringManipulation]]
 git-tree-sha1 = "46da2434b41f41ac3594ee9816ce5541c6096123"
 uuid = "892a3eda-7b42-436c-8928-eab12a02cf0e"
@@ -596,6 +1005,12 @@ deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 version = "1.10.0"
 
+[[deps.TensorCore]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
+uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
+version = "0.1.1"
+
 [[deps.Test]]
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
@@ -612,6 +1027,11 @@ git-tree-sha1 = "9a6ae7ed916312b41236fcef7e0af564ef934769"
 uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
 version = "0.9.13"
 
+[[deps.URIs]]
+git-tree-sha1 = "b7a5e99f24892b6824a954199a45e9ffcc1c70f0"
+uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
+version = "1.5.0"
+
 [[deps.UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
@@ -619,6 +1039,49 @@ uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 [[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
+[[deps.UnicodeFun]]
+deps = ["REPL"]
+git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
+uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
+version = "0.4.1"
+
+[[deps.Unitful]]
+deps = ["Dates", "LinearAlgebra", "Random"]
+git-tree-sha1 = "64eb17acef1d9734cf09967539818f38093d9b35"
+uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
+version = "1.16.2"
+
+    [deps.Unitful.extensions]
+    ConstructionBaseUnitfulExt = "ConstructionBase"
+    InverseFunctionsUnitfulExt = "InverseFunctions"
+
+    [deps.Unitful.weakdeps]
+    ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
+    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
+
+[[deps.UnitfulLatexify]]
+deps = ["LaTeXStrings", "Latexify", "Unitful"]
+git-tree-sha1 = "e2d817cc500e960fdbafcf988ac8436ba3208bfd"
+uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728"
+version = "1.6.3"
+
+[[deps.Unzip]]
+git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
+uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
+version = "0.2.0"
+
+[[deps.Wayland_jll]]
+deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
+git-tree-sha1 = "ed8d92d9774b077c53e1da50fd81a36af3744c1c"
+uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
+version = "1.21.0+0"
+
+[[deps.Wayland_protocols_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
+uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
+version = "1.25.0+0"
+
 [[deps.WeakRefStrings]]
 deps = ["DataAPI", "InlineStrings", "Parsers"]
 git-tree-sha1 = "b1be2855ed9ed8eac54e5caff2afcdb442d52c23"
@@ -630,11 +1093,161 @@ git-tree-sha1 = "cd1659ba0d57b71a464a29e64dbc67cfe83d54e7"
 uuid = "76eceee3-57b5-4d4a-8e66-0e911cebbf60"
 version = "1.6.1"
 
+[[deps.XML2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "93c41695bc1c08c46c5899f4fe06d6ead504bb73"
+uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
+version = "2.10.3+0"
+
+[[deps.XSLT_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
+git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
+uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
+version = "1.1.34+0"
+
+[[deps.XZ_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "cf2c7de82431ca6f39250d2fc4aacd0daa1675c0"
+uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
+version = "5.4.4+0"
+
+[[deps.Xorg_libX11_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
+git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
+uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
+version = "1.8.6+0"
+
+[[deps.Xorg_libXau_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
+uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
+version = "1.0.11+0"
+
+[[deps.Xorg_libXcursor_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
+uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
+version = "1.2.0+4"
+
+[[deps.Xorg_libXdmcp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
+uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
+version = "1.1.4+0"
+
+[[deps.Xorg_libXext_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
+uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
+version = "1.3.4+4"
+
+[[deps.Xorg_libXfixes_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
+uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
+version = "5.0.3+4"
+
+[[deps.Xorg_libXi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
+git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
+uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
+version = "1.7.10+4"
+
+[[deps.Xorg_libXinerama_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
+git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
+uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
+version = "1.1.4+4"
+
+[[deps.Xorg_libXrandr_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
+uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
+version = "1.5.2+4"
+
+[[deps.Xorg_libXrender_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
+uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
+version = "0.9.10+4"
+
+[[deps.Xorg_libpthread_stubs_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
+uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
+version = "0.1.1+0"
+
+[[deps.Xorg_libxcb_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
+git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d"
+uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
+version = "1.15.0+0"
+
+[[deps.Xorg_libxkbfile_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
+git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
+uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
+version = "1.1.2+0"
+
+[[deps.Xorg_xcb_util_image_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
+uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
+git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
+uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_keysyms_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
+uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
+version = "0.4.0+1"
+
+[[deps.Xorg_xcb_util_renderutil_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
+uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
+version = "0.3.9+1"
+
+[[deps.Xorg_xcb_util_wm_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
+uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
+version = "0.4.1+1"
+
+[[deps.Xorg_xkbcomp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
+git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
+uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
+version = "1.4.6+0"
+
+[[deps.Xorg_xkeyboard_config_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
+git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
+uuid = "33bec58e-1273-512f-9401-5d533626f822"
+version = "2.39.0+0"
+
+[[deps.Xorg_xtrans_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
+uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
+version = "1.5.0+0"
+
 [[deps.Zlib_jll]]
 deps = ["Libdl"]
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 version = "1.2.13+0"
 
+[[deps.Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl"]
+git-tree-sha1 = "49ce682769cd5de6c72dcf1b94ed7790cd08974c"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.5+0"
+
 [[deps.Zygote]]
 deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "GPUArrays", "GPUArraysCore", "IRTools", "InteractiveUtils", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NaNMath", "PrecompileTools", "Random", "Requires", "SparseArrays", "SpecialFunctions", "Statistics", "ZygoteRules"]
 git-tree-sha1 = "5be3ddb88fc992a7d8ea96c3f10a49a7e98ebc7b"
@@ -657,11 +1270,47 @@ git-tree-sha1 = "977aed5d006b840e2e40c0b48984f7463109046d"
 uuid = "700de1a5-db45-46bc-99cf-38207098b444"
 version = "0.2.3"
 
+[[deps.fzf_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
+uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
+version = "0.29.0+0"
+
+[[deps.libaom_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
+uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
+version = "3.4.0+0"
+
+[[deps.libass_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
+uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
+version = "0.15.1+0"
+
 [[deps.libblastrampoline_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
 version = "5.8.0+0"
 
+[[deps.libfdk_aac_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "2.0.2+0"
+
+[[deps.libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.38+0"
+
+[[deps.libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+1"
+
 [[deps.nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
@@ -671,3 +1320,21 @@ version = "1.48.0+0"
 deps = ["Artifacts", "Libdl"]
 uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 version = "17.4.0+0"
+
+[[deps.x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2021.5.5+0"
+
+[[deps.x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.5.0+0"
+
+[[deps.xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "1.4.1+0"
diff --git a/benchmark/Project.toml b/benchmark/Project.toml
index b96449c..77815b1 100644
--- a/benchmark/Project.toml
+++ b/benchmark/Project.toml
@@ -6,6 +6,7 @@ ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 ImplicitDifferentiation = "57b37032-215b-411a-8a7c-41a003a55207"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SimpleUnPack = "ce78b400-467f-4804-87d8-8f486da07d0a"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
diff --git a/benchmark/benchmarks.jl b/benchmark/benchmarks.jl
index cff2cbc..42e7582 100644
--- a/benchmark/benchmarks.jl
+++ b/benchmark/benchmarks.jl
@@ -1,72 +1,176 @@
+using Pkg
+Pkg.activate(@__DIR__)
+
 using AbstractDifferentiation: ForwardDiffBackend
 using BenchmarkTools
 using CSV
 using DataFrames
-using ForwardDiff: ForwardDiff
+using ForwardDiff: ForwardDiff, Dual
 using ImplicitDifferentiation
+using Plots
 using Random
 using SimpleUnPack
 using Zygote: Zygote
 
-forward(x) = sqrt.(abs.(x))
-conditions(x, y) = abs2.(y) .- abs.(x)
+forward(x) = sqrt.(x)
+conditions(x, y) = abs2.(y) .- x
+
+forward_sum(x) = [sqrt(sum(x))]
+conditions_sum(x, y) = [abs2(only(y)) - sum(x)]
+
+forward_fill(x, output_size) = fill(sqrt(only(x)), output_size...)
+conditions_fill(x, y, output_size) = abs2.(y) .- only(x)
+
+function get_linear_solver(linear_solver_symbol::Symbol)
+    if linear_solver_symbol == :direct
+        return DirectLinearSolver()
+    elseif linear_solver_symbol == :iterative
+        return IterativeLinearSolver()
+    end
+end
+
+function get_conditions_backend(conditions_backend_symbol::Symbol)
+    if conditions_backend_symbol == :nothing
+        return nothing
+    elseif conditions_backend_symbol == :ForwardDiff
+        return ForwardDiffBackend()
+    end
+end
+
+function create_benchmarkable(;
+    scenario_symbol,
+    linear_solver_symbol,
+    backend_symbol,
+    conditions_backend_symbol,
+    input_size,
+)
+    linear_solver = get_linear_solver(linear_solver_symbol)
+    conditions_backend = get_conditions_backend(conditions_backend_symbol)
 
-function make_suite(; linear_solvers, conditions_backends, input_sizes)
+    if scenario_symbol == :jacobian && prod(input_size) >= 1000
+        return nothing
+    end
+
+    x, implicit = nothing, nothing
+    if scenario_symbol == :jacobian
+        x = rand(input_size...)
+        implicit = ImplicitFunction(forward, conditions; linear_solver, conditions_backend)
+    elseif scenario_symbol == :pullback
+        x = rand(input_size...)
+        implicit = ImplicitFunction(
+            forward_sum, conditions_sum; linear_solver, conditions_backend
+        )
+    elseif scenario_symbol == :pushforward
+        @show input_size
+        x = Array{Float64,length(input_size)}(undef, ones(Int, length(input_size))...)
+        x[only(eachindex(x))] = rand()
+        implicit = ImplicitFunction(
+            x -> forward_fill(x, input_size),
+            (x, y) -> conditions_fill(x, y, input_size);
+            linear_solver,
+            conditions_backend,
+        )
+    end
+
+    x_and_dx = Dual.(x, (one(eltype(x)),))
+    y = implicit(x)
+    dy = zero(y)
+
+    if scenario_symbol == :jacobian && backend_symbol == :ForwardDiff
+        return @benchmarkable ForwardDiff.jacobian($implicit, $x) seconds = 1
+    elseif scenario_symbol == :jacobian && backend_symbol == :Zygote
+        return @benchmarkable Zygote.jacobian($implicit, $x) seconds = 1
+    elseif scenario_symbol == :pullback && backend_symbol == :Zygote
+        return @benchmarkable begin
+            _, back = Zygote.pullback($implicit, $x)
+            back($dy)
+        end seconds = 1
+    elseif scenario_symbol == :pushforward && backend_symbol == :ForwardDiff
+        return @benchmarkable $implicit($x_and_dx) seconds = 1
+    else
+        return nothing
+    end
+end
+
+function make_suite(;
+    scenario_symbols,
+    linear_solver_symbols,
+    backend_symbols,
+    conditions_backend_symbols,
+    input_sizes,
+)
     SUITE = BenchmarkGroup()
-    for linear_solver in linear_solvers
-        ls = string(typeof(linear_solver))
-        SUITE[ls] = BenchmarkGroup()
-        for conditions_backend in conditions_backends
-            implicit = ImplicitFunction(
-                forward, conditions; linear_solver, conditions_backend
-            )
-            cb = string(typeof(conditions_backend))
-            SUITE[ls][cb] = BenchmarkGroup()
-            for input_size in input_sizes
-                x = rand(input_size...)
-                is = string(input_size)
-                g = BenchmarkGroup()
-                g["ForwardDiff"] = @benchmarkable ForwardDiff.jacobian($implicit, $x) seconds =
-                    1
-                g["Zygote"] = @benchmarkable Zygote.jacobian($implicit, $x) seconds = 1
-                SUITE[ls][cb][is] = g
-            end
+
+    for sc in scenario_symbols,
+        ls in linear_solver_symbols,
+        ba in backend_symbols,
+        cb in conditions_backend_symbols,
+        is in input_sizes
+
+        bench = create_benchmarkable(;
+            scenario_symbol=sc,
+            linear_solver_symbol=ls,
+            backend_symbol=ba,
+            conditions_backend_symbol=cb,
+            input_size=is,
+        )
+
+        isnothing(bench) && continue
+
+        if !haskey(SUITE, sc)
+            SUITE[sc] = BenchmarkGroup()
+        end
+        if !haskey(SUITE[sc], ls)
+            SUITE[sc][ls] = BenchmarkGroup()
+        end
+        if !haskey(SUITE[sc][ls], ba)
+            SUITE[sc][ls][ba] = BenchmarkGroup()
         end
+        if !haskey(SUITE[sc][ls][ba], cb)
+            SUITE[sc][ls][ba][cb] = BenchmarkGroup()
+        end
+        SUITE[sc][ls][ba][cb][is] = bench
     end
     return SUITE
 end
 
-function run_suite(;
-    linear_solvers, conditions_backends, input_sizes, path=joinpath(@__DIR__, "results.csv")
+function export_results(
+    results;
+    scenario_symbols,
+    linear_solver_symbols,
+    backend_symbols,
+    conditions_backend_symbols,
+    input_sizes,
+    path=joinpath(@__DIR__, "benchmark_results.csv"),
 )
-    SUITE = make_suite(; linear_solvers, conditions_backends, input_sizes)
-
-    results = BenchmarkTools.run(SUITE; verbose=true, evals=1)
     min_results = minimum(results)
 
     data = DataFrame()
-    for linear_solver in linear_solvers,
-        conditions_backend in conditions_backends,
-        input_size in input_sizes,
-        backend in ["ForwardDiff", "Zygote"]
-
-        ls = string(typeof(linear_solver))
-        cb = string(typeof(conditions_backend))
-        is = string(input_size)
-        perf = min_results[ls][cb][is][backend]
-        @unpack time, gctime, memory, allocs = perf
-        row = (;
-            func="sqrt",
-            linear_solver=ls,
-            backend=backend,
-            conditions_backend=cb,
-            input_size=is,
-            time,
-            gctime,
-            memory,
-            allocs,
-        )
-        push!(data, row)
+
+    for sc in scenario_symbols,
+        ls in linear_solver_symbols,
+        ba in backend_symbols,
+        cb in conditions_backend_symbols,
+        is in input_sizes
+
+        try
+            perf = min_results[sc][ls][ba][cb][is]
+            @unpack time, gctime, memory, allocs = perf
+            row = (;
+                scenario=sc,
+                linear_solver=ls,
+                backend=ba,
+                conditions_backend=cb,
+                input_size=is,
+                time,
+                gctime,
+                memory,
+                allocs,
+            )
+            push!(data, row)
+        catch KeyError
+            nothing
+        end
     end
 
     if !isnothing(path)
@@ -77,13 +181,85 @@ function run_suite(;
     return data
 end
 
-linear_solvers = (DirectLinearSolver(), IterativeLinearSolver())
-conditions_backends = (nothing, ForwardDiffBackend())
-input_sizes = vcat(
-    [(n,) for n in (10, 100, 1_000, 10_000)], #
-    [(n, n) for n in (10, 30, 90)], #
+function plot_results(
+    data;
+    scenario_symbols,
+    linear_solver_symbols,
+    backend_symbols,
+    conditions_backend_symbols,
+    path=joinpath(
+        @__DIR__,
+        "benchmark_plot_$(scenario_symbols)_$(linear_solver_symbols)_$(backend_symbols)_$(conditions_backend_symbols).pdf",
+    ),
+)
+    pl = plot(;
+        size=(1000, 500),
+        xlabel="Input dimension (log scale)",
+        ylabel="Time [s] (log scale)",
+        title="ImplicitDifferentiation.jl benchmarks",
+        legendtitle="scen - linsol - back - condback",
+        legend=:outerright,
+        xaxis=:log10,
+        yaxis=:log10,
+        margin=5Plots.mm,
+    )
+    for sc in scenario_symbols,
+        ls in linear_solver_symbols,
+        ba in backend_symbols,
+        cb in conditions_backend_symbols
+
+        filtered_data = subset(
+            data,
+            :scenario => _col -> _col .== sc,
+            :linear_solver => _col -> _col .== ls,
+            :backend => _col -> _col .== ba,
+            :conditions_backend => _col -> _col .== cb,
+        )
+
+        if !isempty(filtered_data)
+            x = map(prod, filtered_data[!, :input_size])
+            y = filtered_data[!, :time] ./ 1e9
+            plot!(
+                pl, x, y; linestyle=:auto, markershape=:auto, label="$sc - $ls - $ba - $cb"
+            )
+        end
+    end
+
+    if !isnothing(path)
+        savefig(pl, path)
+    end
+    return pl
+end
+
+scenario_symbols = (:jacobian, :pullback, :pushforward)
+linear_solver_symbols = (:direct, :iterative)
+backend_symbols = (:Zygote, :ForwardDiff)
+conditions_backend_symbols = (:nothing, :ForwardDiff)
+input_sizes = [(n,) for n in (1, 10, 100, 1_000, 10_000)]
+
+SUITE = make_suite(;
+    scenario_symbols,
+    linear_solver_symbols,
+    backend_symbols,
+    conditions_backend_symbols,
+    input_sizes,
 )
 
-SUITE = make_suite(; linear_solvers, conditions_backends, input_sizes)
+results = run(SUITE; verbose=true, evals=1)
+
+# data = export_results(
+#     results;
+#     scenario_symbols,
+#     linear_solver_symbols,
+#     backend_symbols,
+#     conditions_backend_symbols,
+#     input_sizes,
+# )
 
-# data = run_suite(; linear_solvers, conditions_backends, input_sizes)
+# plot_results(
+#     data;
+#     scenario_symbols=[:pullback],
+#     linear_solver_symbols=[:direct, :iterative],
+#     backend_symbols=[:FowardDiff, :Zygote],
+#     conditions_backend_symbols=[:nothing],
+# )