diff --git a/benchmark/Manifest.toml b/benchmark/Manifest.toml
index 02eb6659..6e3a3a69 100644
--- a/benchmark/Manifest.toml
+++ b/benchmark/Manifest.toml
@@ -153,9 +153,9 @@ version = "6.2.1+2"
 
 [[deps.Groebner]]
 deps = ["AbstractAlgebra", "Atomix", "Combinatorics", "ExprTools", "HostCPUFeatures", "Logging", "MultivariatePolynomials", "Nemo", "PrecompileTools", "PrettyTables", "Primes", "Printf", "Random", "TimerOutputs"]
-path = ".."
+git-tree-sha1 = "5eb13678ae76a60d70090a4c50d1dc3eab0ce180"
 uuid = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
-version = "0.6.3"
+version = "0.6.4"
 
 [[deps.GroupsCore]]
 deps = ["Markdown", "Random"]
diff --git a/benchmark/README.md b/benchmark/README.md
index 4bc65262..34cd9ac3 100644
--- a/benchmark/README.md
+++ b/benchmark/README.md
@@ -4,10 +4,10 @@ Benchmarks for `Groebner.jl`, `Maple`, `msolve`, `OpenF4`, `Singular`.
 
 The definitions of benchmark systems can be found in `benchmark_systems.jl`.
 
-Computed bases will be verified against short certificates that are assumed to
+Computed bases will be verified against short SHA certificate, which are assumed to
 be correct.
 
-For running the benchmarks, you will need a Julia client v1.6+ installed.
+For running the benchmarks, you will need a Julia client v1.6+ installed (preferably 1.9).
 See the official installation guide at
 https://julialang.org/downloads/platform/.
 
diff --git a/benchmark/benchmark_systems.jl b/benchmark/benchmark_systems.jl
index 5a174ad9..10157d4f 100644
--- a/benchmark/benchmark_systems.jl
+++ b/benchmark/benchmark_systems.jl
@@ -36,10 +36,10 @@ end
 function benchmark_set_0()
     (
         name="dummy benchmark set",
-        field=AbstractAlgebra.QQ,
+        field=AbstractAlgebra.GF(7),
         systems=[
-            dummy_system("dummy 1", AbstractAlgebra.QQ),
-            dummy_system("dummy 2", AbstractAlgebra.QQ)
+            dummy_system("dummy 1", AbstractAlgebra.GF(7)),
+            dummy_system("dummy 2", AbstractAlgebra.GF(7))
         ]
     )
 end
@@ -52,7 +52,7 @@ function benchmark_set_1()
         ("cyclic 7", Groebner.cyclicn(7, k=ground_field)),
         ("cyclic 8", Groebner.cyclicn(8, k=ground_field)),
         ("cyclic 9", Groebner.cyclicn(9, k=ground_field)),
-        ("cyclic 10", Groebner.cyclicn(10, k=ground_field)),
+        # ("cyclic 10", Groebner.cyclicn(10, k=ground_field)),
         ("katsura 10", Groebner.katsuran(10, k=ground_field)),
         ("katsura 11", Groebner.katsuran(11, k=ground_field)),
         ("katsura 12", Groebner.katsuran(12, k=ground_field)),
@@ -65,7 +65,7 @@ function benchmark_set_1()
         ("noon 8", Groebner.noonn(8, k=ground_field)),
         ("noon 9", Groebner.noonn(9, k=ground_field)),
         ("noon 10", Groebner.noonn(10, k=ground_field)),
-        ("noon 11", Groebner.noonn(11, k=ground_field)),
+        # ("noon 11", Groebner.noonn(11, k=ground_field)),
         ("henrion 5", Groebner.henrion5(k=ground_field)),
         ("henrion 6", Groebner.henrion6(k=ground_field)),
         ("henrion 7", Groebner.henrion7(k=ground_field)),
@@ -73,7 +73,7 @@ function benchmark_set_1()
         ("reimer 6", Groebner.reimern(6, k=ground_field)),
         ("reimer 7", Groebner.reimern(7, k=ground_field)),
         ("reimer 8", Groebner.reimern(8, k=ground_field)),
-        ("reimer 9", Groebner.reimern(9, k=ground_field)),
+        # ("reimer 9", Groebner.reimern(9, k=ground_field)),
         ("chandra 11", Groebner.chandran(11, k=ground_field)),
         ("chandra 12", Groebner.chandran(12, k=ground_field)),
         ("chandra 13", Groebner.chandran(13, k=ground_field)),
@@ -91,7 +91,7 @@ function benchmark_set_2()
         ("cyclic 7", Groebner.cyclicn(7, k=ground_field)),
         ("cyclic 8", Groebner.cyclicn(8, k=ground_field)),
         ("cyclic 9", Groebner.cyclicn(9, k=ground_field)),
-        ("cyclic 10", Groebner.cyclicn(10, k=ground_field)),
+        # ("cyclic 10", Groebner.cyclicn(10, k=ground_field)),
         ("katsura 10", Groebner.katsuran(10, k=ground_field)),
         ("katsura 11", Groebner.katsuran(11, k=ground_field)),
         ("katsura 12", Groebner.katsuran(12, k=ground_field)),
@@ -104,7 +104,7 @@ function benchmark_set_2()
         ("noon 8", Groebner.noonn(8, k=ground_field)),
         ("noon 9", Groebner.noonn(9, k=ground_field)),
         ("noon 10", Groebner.noonn(10, k=ground_field)),
-        ("noon 11", Groebner.noonn(11, k=ground_field)),
+        # ("noon 11", Groebner.noonn(11, k=ground_field)),
         ("henrion 5", Groebner.henrion5(k=ground_field)),
         ("henrion 6", Groebner.henrion6(k=ground_field)),
         ("henrion 7", Groebner.henrion7(k=ground_field)),
@@ -112,7 +112,7 @@ function benchmark_set_2()
         ("reimer 6", Groebner.reimern(6, k=ground_field)),
         ("reimer 7", Groebner.reimern(7, k=ground_field)),
         ("reimer 8", Groebner.reimern(8, k=ground_field)),
-        ("reimer 9", Groebner.reimern(9, k=ground_field)),
+        # ("reimer 9", Groebner.reimern(9, k=ground_field)),
         ("chandra 11", Groebner.chandran(11, k=ground_field)),
         ("chandra 12", Groebner.chandran(12, k=ground_field)),
         ("chandra 13", Groebner.chandran(13, k=ground_field)),
diff --git a/benchmark/generate/benchmark_systems/biomodels/parser.jl b/benchmark/generate/benchmark_systems/biomodels/parser.jl
index aff9fad1..e42fdea5 100644
--- a/benchmark/generate/benchmark_systems/biomodels/parser.jl
+++ b/benchmark/generate/benchmark_systems/biomodels/parser.jl
@@ -4,19 +4,19 @@ import AbstractAlgebra
 function read_BIOMDs(nspecies)
     @info "Reading biomodels"
     systems = []
-    for smth in readdir(abspath("benchmark/biomodels"))
+    for smth in readdir((@__DIR__))
         system = []
 
         @info "" smth
         !(occursin("BIOMD", smth)) && continue
 
-        io = open(abspath("benchmark/biomodels/$smth/species_map.txt"), "r")
+        io = open((@__DIR__) * "/$smth/species_map.txt", "r")
         vs = map(strip ∘ first, map(split, readlines(io)))
         close(io)
         # @info "variables" vs
         !(length(vs) in nspecies) && continue
 
-        io = open(abspath("benchmark/biomodels/$smth/parameters.txt"), "r")
+        io = open((@__DIR__) * "/$smth/parameters.txt", "r")
         params = readlines(io)
         params = map(p -> replace(p, "/" => "//"), params)
         params = map(params) do p
@@ -30,7 +30,7 @@ function read_BIOMDs(nspecies)
         end
         close(io)
 
-        io = open(abspath("benchmark/biomodels/$smth/odes.txt"), "r")
+        io = open((@__DIR__) * "/$smth/odes.txt", "r")
         odes = readlines(io)
         close(io)
 
diff --git a/benchmark/generate/groebner/Manifest.toml b/benchmark/generate/groebner/Manifest.toml
index 83416cb7..ce7eb53f 100644
--- a/benchmark/generate/groebner/Manifest.toml
+++ b/benchmark/generate/groebner/Manifest.toml
@@ -153,9 +153,9 @@ version = "6.2.1+2"
 
 [[deps.Groebner]]
 deps = ["AbstractAlgebra", "Atomix", "Combinatorics", "ExprTools", "HostCPUFeatures", "Logging", "MultivariatePolynomials", "Nemo", "PrecompileTools", "PrettyTables", "Primes", "Printf", "Random", "TimerOutputs"]
-path = "../../.."
+git-tree-sha1 = "5eb13678ae76a60d70090a4c50d1dc3eab0ce180"
 uuid = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
-version = "0.6.3"
+version = "0.6.4"
 
 [[deps.GroupsCore]]
 deps = ["Markdown", "Random"]
diff --git a/benchmark/generate/learn_apply/Manifest.toml b/benchmark/generate/learn_apply/Manifest.toml
index da093534..ce7eb53f 100644
--- a/benchmark/generate/learn_apply/Manifest.toml
+++ b/benchmark/generate/learn_apply/Manifest.toml
@@ -50,6 +50,12 @@ git-tree-sha1 = "f1f03a9fa24271160ed7e73051fba3c1a759b53f"
 uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 version = "1.4.0"
 
+[[deps.BitTwiddlingConvenienceFunctions]]
+deps = ["Static"]
+git-tree-sha1 = "0c5f81f47bbbcf4aea7b2959135713459170798b"
+uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b"
+version = "0.1.5"
+
 [[deps.Calcium_jll]]
 deps = ["Antic_jll", "Arb_jll", "Artifacts", "FLINT_jll", "GMP_jll", "JLLWrappers", "Libdl", "MPFR_jll", "Pkg"]
 git-tree-sha1 = "37fd335ecca9bd6ab25a2a4d26b7b2f6fe64c246"
@@ -146,10 +152,10 @@ uuid = "781609d7-10c4-51f6-84f2-b8444358ff6d"
 version = "6.2.1+2"
 
 [[deps.Groebner]]
-deps = ["AbstractAlgebra", "Atomix", "Combinatorics", "ExprTools", "Logging", "MultivariatePolynomials", "Nemo", "PrecompileTools", "PrettyTables", "Primes", "Printf", "Random", "TimerOutputs"]
-path = "../../.."
+deps = ["AbstractAlgebra", "Atomix", "Combinatorics", "ExprTools", "HostCPUFeatures", "Logging", "MultivariatePolynomials", "Nemo", "PrecompileTools", "PrettyTables", "Primes", "Printf", "Random", "TimerOutputs"]
+git-tree-sha1 = "5eb13678ae76a60d70090a4c50d1dc3eab0ce180"
 uuid = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
-version = "0.6.3"
+version = "0.6.4"
 
 [[deps.GroupsCore]]
 deps = ["Markdown", "Random"]
@@ -157,6 +163,17 @@ git-tree-sha1 = "6df9cd6ee79fc59feab33f63a1b3c9e95e2461d5"
 uuid = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
 version = "0.4.2"
 
+[[deps.HostCPUFeatures]]
+deps = ["BitTwiddlingConvenienceFunctions", "IfElse", "Libdl", "Static"]
+git-tree-sha1 = "eb8fed28f4994600e29beef49744639d985a04b2"
+uuid = "3e5b6fbb-0976-4d2c-9146-d79de83f2fb0"
+version = "0.1.16"
+
+[[deps.IfElse]]
+git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
+uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
+version = "0.1.1"
+
 [[deps.IntegerMathUtils]]
 git-tree-sha1 = "b8ffb903da9f7b8cf695a8bead8e01814aa24b30"
 uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
@@ -364,6 +381,12 @@ uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
+[[deps.Static]]
+deps = ["IfElse"]
+git-tree-sha1 = "f295e0a1da4ca425659c57441bcb59abb035a4bc"
+uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
+version = "0.8.8"
+
 [[deps.Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
diff --git a/benchmark/generate/learn_apply/run_in_learn_apply.jl b/benchmark/generate/learn_apply/run_in_learn_apply.jl
index 703c7445..a1a08afd 100644
--- a/benchmark/generate/learn_apply/run_in_learn_apply.jl
+++ b/benchmark/generate/learn_apply/run_in_learn_apply.jl
@@ -60,6 +60,12 @@ function process_system()
         timing3 = @timed flag, _ =
             groebner_apply!(trace, (system, system, system, system), threaded=:no)
         @assert flag
+        timing4 = @timed flag, _ = groebner_apply!(
+            trace,
+            (system, system, system, system, system, system, system, system),
+            threaded=:no
+        )
+        @assert flag
         @debug "Result is" gb
         if VALIDATE
             output_fn = (@__DIR__) * "/$BENCHMARK_DIR/$PROBLEM_NAME/$(output_filename())"
@@ -92,6 +98,8 @@ function process_system()
             min(runtime[PROBLEM_NAME][:total_time_apply], timing2.time)
         runtime[PROBLEM_NAME][:total_time_apply_4x] =
             min(runtime[PROBLEM_NAME][:total_time_apply_4x], timing3.time)
+        runtime[PROBLEM_NAME][:total_time_apply_8x] =
+            min(runtime[PROBLEM_NAME][:total_time_apply_8x], timing4.time)
     end
     # for cat in ID_TIME_CATEGORIES
     #     if haskey(runtime[PROBLEM_NAME], cat)
@@ -104,8 +112,13 @@ function dump_timings()
     timings = ""
     timings *= "$PROBLEM_NAME\n"
     for (key, model_runtime) in runtime
-        for c in
-            [:total_time_F4, :total_time_learn, :total_time_apply, :total_time_apply_4x]
+        for c in [
+            :total_time_F4,
+            :total_time_learn,
+            :total_time_apply,
+            :total_time_apply_4x,
+            :total_time_apply_8x
+        ]
             timings *= "$c, "
             timings *= string(model_runtime[c]) * "\n"
         end
diff --git a/benchmark/generate/openf4/Manifest.toml b/benchmark/generate/openf4/Manifest.toml
index 2fab36a3..2e5f839b 100644
--- a/benchmark/generate/openf4/Manifest.toml
+++ b/benchmark/generate/openf4/Manifest.toml
@@ -2,7 +2,7 @@
 
 julia_version = "1.9.2"
 manifest_format = "2.0"
-project_hash = "eb2490cccda0f14cdfe8e2f4733f8e311a7e9319"
+project_hash = "623d5d4f83b54da08b7ad95e49fa725c6b1f466a"
 
 [[deps.AbstractAlgebra]]
 deps = ["GroupsCore", "InteractiveUtils", "LinearAlgebra", "MacroTools", "Preferences", "Random", "RandomExtensions", "SparseArrays", "Test"]
@@ -32,27 +32,6 @@ git-tree-sha1 = "d9a9701b899b30332bbcb3e1679c41cce81fb0e8"
 uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 version = "1.3.2"
 
-[[deps.ChainRulesCore]]
-deps = ["Compat", "LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "e30f2f4e20f7f186dc36529910beaedc60cfa644"
-uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.16.0"
-
-[[deps.Combinatorics]]
-git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860"
-uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
-version = "1.0.2"
-
-[[deps.Compat]]
-deps = ["UUIDs"]
-git-tree-sha1 = "e460f044ca8b99be31d35fe54fc33a5c33dd8ed7"
-uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "4.9.0"
-weakdeps = ["Dates", "LinearAlgebra"]
-
-    [deps.Compat.extensions]
-    CompatLinearAlgebraExt = "LinearAlgebra"
-
 [[deps.CompilerSupportLibraries_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
@@ -64,12 +43,6 @@ git-tree-sha1 = "fcbb72b032692610bfbdb15018ac16a36cf2e406"
 uuid = "adafc99b-e345-5852-983c-f28acb93d879"
 version = "0.3.1"
 
-[[deps.DataStructures]]
-deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "3dbd312d370723b6bb43ba9d02fc36abade4518d"
-uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.18.15"
-
 [[deps.Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
@@ -83,31 +56,15 @@ deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 version = "1.6.0"
 
-[[deps.ExprTools]]
-git-tree-sha1 = "27415f162e6028e81c72b82ef756bf321213b6ec"
-uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
-version = "0.1.10"
-
 [[deps.FileWatching]]
 uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
 
-[[deps.Groebner]]
-deps = ["AbstractAlgebra", "Combinatorics", "ExprTools", "Logging", "MultivariatePolynomials", "Primes", "Random", "SIMD", "SnoopPrecompile"]
-git-tree-sha1 = "44f595de4f6485ab5ba71fe257b5eadaa3cf161e"
-uuid = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
-version = "0.4.4"
-
 [[deps.GroupsCore]]
 deps = ["Markdown", "Random"]
 git-tree-sha1 = "9e1a5e9f3b81ad6a5c613d181664a0efc6fe6dd7"
 uuid = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
 version = "0.4.0"
 
-[[deps.IntegerMathUtils]]
-git-tree-sha1 = "b8ffb903da9f7b8cf695a8bead8e01814aa24b30"
-uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
-version = "0.1.2"
-
 [[deps.InteractiveUtils]]
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
@@ -169,18 +126,6 @@ uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 version = "2022.10.11"
 
-[[deps.MultivariatePolynomials]]
-deps = ["ChainRulesCore", "DataStructures", "LinearAlgebra", "MutableArithmetics"]
-git-tree-sha1 = "6c2e970692b6f4fed2508865c43a0f67f3820cf4"
-uuid = "102ac46a-7ee4-5c85-9060-abc95bfdeaa3"
-version = "0.5.2"
-
-[[deps.MutableArithmetics]]
-deps = ["LinearAlgebra", "SparseArrays", "Test"]
-git-tree-sha1 = "6985021d02ab8c509c841bb8b2becd3145a7b490"
-uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
-version = "1.3.3"
-
 [[deps.NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 version = "1.2.0"
@@ -190,11 +135,6 @@ deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
 version = "0.3.21+4"
 
-[[deps.OrderedCollections]]
-git-tree-sha1 = "2e73fe17cac3c62ad1aebe70d44c963c3cfdc3e3"
-uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
-version = "1.6.2"
-
 [[deps.Parsers]]
 deps = ["Dates", "PrecompileTools", "UUIDs"]
 git-tree-sha1 = "716e24b21538abc91f6205fd1d8363f39b442851"
@@ -218,12 +158,6 @@ git-tree-sha1 = "00805cd429dcb4870060ff49ef443486c262e38e"
 uuid = "21216c6a-2e73-6563-6e65-726566657250"
 version = "1.4.1"
 
-[[deps.Primes]]
-deps = ["IntegerMathUtils"]
-git-tree-sha1 = "4c9f306e5d6603ae203c2000dd460d81a5251489"
-uuid = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
-version = "0.5.4"
-
 [[deps.Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
@@ -256,21 +190,9 @@ version = "0.4.3"
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 version = "0.7.0"
 
-[[deps.SIMD]]
-deps = ["PrecompileTools"]
-git-tree-sha1 = "0e270732477b9e551d884e6b07e23bb2ec947790"
-uuid = "fdea26ae-647d-5447-a871-4b548cad5224"
-version = "3.4.5"
-
 [[deps.Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
-[[deps.SnoopPrecompile]]
-deps = ["Preferences"]
-git-tree-sha1 = "e760a70afdcd461cf01a575947738d359234665c"
-uuid = "66db9d55-30c0-4569-8b51-7e840670fc0c"
-version = "1.0.3"
-
 [[deps.Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
diff --git a/benchmark/generate/openf4/Project.toml b/benchmark/generate/openf4/Project.toml
index 9aa0ae60..dbfdb4ed 100644
--- a/benchmark/generate/openf4/Project.toml
+++ b/benchmark/generate/openf4/Project.toml
@@ -5,7 +5,6 @@ BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 CpuId = "adafc99b-e345-5852-983c-f28acb93d879"
 Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
 Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
-Groebner = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
 Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
diff --git a/benchmark/generate/singular/Manifest.toml b/benchmark/generate/singular/Manifest.toml
index 882f1197..2459f9f4 100644
--- a/benchmark/generate/singular/Manifest.toml
+++ b/benchmark/generate/singular/Manifest.toml
@@ -56,6 +56,12 @@ git-tree-sha1 = "7c08e585f2d50e3c74bc2491474d3f897d2ebec8"
 uuid = "f01c122e-0ea1-4f85-ad8f-907073ad7a9f"
 version = "0.1.2"
 
+[[deps.BitTwiddlingConvenienceFunctions]]
+deps = ["Static"]
+git-tree-sha1 = "0c5f81f47bbbcf4aea7b2959135713459170798b"
+uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b"
+version = "0.1.5"
+
 [[deps.Calcium_jll]]
 deps = ["Antic_jll", "Arb_jll", "Artifacts", "FLINT_jll", "GMP_jll", "JLLWrappers", "Libdl", "MPFR_jll", "Pkg"]
 git-tree-sha1 = "37fd335ecca9bd6ab25a2a4d26b7b2f6fe64c246"
@@ -164,10 +170,10 @@ uuid = "781609d7-10c4-51f6-84f2-b8444358ff6d"
 version = "6.2.1+2"
 
 [[deps.Groebner]]
-deps = ["AbstractAlgebra", "Atomix", "Combinatorics", "ExprTools", "Logging", "MultivariatePolynomials", "Nemo", "PrecompileTools", "PrettyTables", "Primes", "Printf", "Random", "TimerOutputs"]
-path = "../../.."
+deps = ["AbstractAlgebra", "Atomix", "Combinatorics", "ExprTools", "HostCPUFeatures", "Logging", "MultivariatePolynomials", "Nemo", "PrecompileTools", "PrettyTables", "Primes", "Printf", "Random", "TimerOutputs"]
+git-tree-sha1 = "5eb13678ae76a60d70090a4c50d1dc3eab0ce180"
 uuid = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
-version = "0.6.3"
+version = "0.6.4"
 
 [[deps.GroupsCore]]
 deps = ["Markdown", "Random"]
@@ -175,6 +181,17 @@ git-tree-sha1 = "6df9cd6ee79fc59feab33f63a1b3c9e95e2461d5"
 uuid = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
 version = "0.4.2"
 
+[[deps.HostCPUFeatures]]
+deps = ["BitTwiddlingConvenienceFunctions", "IfElse", "Libdl", "Static"]
+git-tree-sha1 = "eb8fed28f4994600e29beef49744639d985a04b2"
+uuid = "3e5b6fbb-0976-4d2c-9146-d79de83f2fb0"
+version = "0.1.16"
+
+[[deps.IfElse]]
+git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
+uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
+version = "0.1.1"
+
 [[deps.IntegerMathUtils]]
 git-tree-sha1 = "b8ffb903da9f7b8cf695a8bead8e01814aa24b30"
 uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
@@ -406,6 +423,12 @@ uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
+[[deps.Static]]
+deps = ["IfElse"]
+git-tree-sha1 = "f295e0a1da4ca425659c57441bcb59abb035a4bc"
+uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
+version = "0.8.8"
+
 [[deps.Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
diff --git a/benchmark/generate/utils.jl b/benchmark/generate/utils.jl
index d6813a47..ff889f33 100644
--- a/benchmark/generate/utils.jl
+++ b/benchmark/generate/utils.jl
@@ -23,7 +23,8 @@ const TIME_CATEGORIES = [
     :total_time_F4,
     :total_time_learn,
     :total_time_apply,
-    :total_time_apply_4x
+    :total_time_apply_4x,
+    :total_time_apply_8x
 ]
 const DATA_CATEGORIES = []
 const ALL_CATEGORIES = union(TIME_CATEGORIES, DATA_CATEGORIES)
@@ -33,6 +34,7 @@ const HUMAN_READABLE_CATEGORIES = Dict(
     :total_time_learn => "Learn, s",
     :total_time_apply => "Apply, s",
     :total_time_apply_4x => "Apply 4x, s",
+    :total_time_apply_8x => "Apply 8x, s",
     :total_time_F4 => "F4, s"
 )
 const CATEGORY_FORMAT = Dict()
diff --git a/benchmark/one_script_to_run_them_all.jl b/benchmark/one_script_to_run_them_all.jl
index bad27974..017de5f2 100644
--- a/benchmark/one_script_to_run_them_all.jl
+++ b/benchmark/one_script_to_run_them_all.jl
@@ -34,8 +34,8 @@ progressbar_enabled() =
 
 const _available_backends = ["groebner", "singular", "maple", "msolve", "openf4"]
 
-const _skip_singular = true
-const _skip_openf4 = true
+const _skip_singular = false
+const _skip_openf4 = false
 
 # Parses command-line arguments
 #! format: off
@@ -350,7 +350,7 @@ function run_benchmarks(args)
     Benchmark systems:
     $systems_to_benchmark"""
 
-    timeout = timeout + 10  # add 10 seconds for compilation time :)
+    timeout = timeout + added_timeout_time  # add 10 seconds for compilation time :)
     seconds_passed(from_t) = round((time_ns() - from_t) / 1e9, digits=2)
 
     queue = [(problem_id=problem,) for problem in indices_to_benchmark]
@@ -591,8 +591,13 @@ function collect_timings(args, names)
     benchmark_name = get_benchmark_suite(benchmark_id).name
 
     if backend == "learn_apply"
-        targets =
-            [:total_time_F4, :total_time_learn, :total_time_apply, :total_time_apply_4x]
+        targets = [
+            :total_time_F4,
+            :total_time_learn,
+            :total_time_apply,
+            :total_time_apply_4x,
+            :total_time_apply_8x
+        ]
     else
         targets = [:total_time]
     end
@@ -894,7 +899,8 @@ end
 
 function check_args(args)
     backend = args["backend"]
-    @assert backend in ("groebner", "singular", "maple", "openf4", "msolve", "ALL")
+    @assert backend in
+            ("groebner", "singular", "maple", "openf4", "msolve", "learn_apply", "ALL")
     if backend == "openf4" && args["suite"] in [3, 7]
         throw("Running benchmarks over the rationals is not possible for openf4")
     end
diff --git a/benchmark/results/benchmark_result_0.md b/benchmark/results/benchmark_result_0.md
index ba8ac69e..4729b9e6 100644
--- a/benchmark/results/benchmark_result_0.md
+++ b/benchmark/results/benchmark_result_0.md
@@ -1,21 +1,21 @@
 ## Benchmark results
 
-2024-01-27T00:31:15.423
+2024-01-27T13:24:45.699
 
-Benchmarked backends: Any["groebner", "maple", "msolve"]
+Benchmarked backends: Any["groebner", "maple", "msolve", "openf4", "singular"]
 
 Benchmark suite: dummy benchmark set
 
-- Workers: 16
-- Timeout: 60 s
-- Aggregated over: 1 runs
+- Workers: 1
+- Timeout: 1800 s
+- Aggregated over: 3 runs
 
 **All timings in seconds.**
 
-|Model|groebner|maple|msolve|
-|:----|---|---|---|
-|dummy 1|0.00|0.23|0.03|
-|dummy 2|0.00|0.21|0.03|
+|Model|groebner|maple|msolve|openf4|singular|
+|:----|---|---|---|---|---|
+|dummy 1|0.00|0.22|0.01|0.01|0.00|
+|dummy 2|0.00|0.21|0.01|0.01|0.00|
 
 *Benchmarking environment:*
 
diff --git a/benchmark/results/benchmark_result_1.md b/benchmark/results/benchmark_result_1.md
index 2781c028..66a67bb6 100644
--- a/benchmark/results/benchmark_result_1.md
+++ b/benchmark/results/benchmark_result_1.md
@@ -1,49 +1,46 @@
 ## Benchmark results
 
-2024-01-26T15:22:47.295
+2024-01-27T02:48:25.710
 
 Benchmarked backends: Any["groebner", "maple", "msolve"]
 
 Benchmark suite: Integers modulo 2^30 + 3
 
 - Workers: 16
-- Timeout: 600 s
-- Aggregated over: 3 runs
+- Timeout: 60 s
+- Aggregated over: 1 runs
 
 **All timings in seconds.**
 
 |Model|groebner|maple|msolve|
 |:----|---|---|---|
-|chandra 11|0.48|0.76|0.88|
-|chandra 12|2.73|2.89|3.84|
-|chandra 13|14.95|14.09|20.56|
-|chandra 14|98.81|82.15|133.08|
-|cyclic 7|0.09|0.24|0.15|
-|cyclic 8|1.17|1.38|1.36|
-|cyclic 9|120.54|195.46|118.97|
-|cyclic 10| - | - | - |
+|chandra 11|0.76|0.97|0.96|
+|chandra 12|3.69|4.18|4.78|
+|chandra 13| - |25.59|30.71|
+|chandra 14| - | - | - |
+|cyclic 7|0.11|0.30|0.15|
+|cyclic 8|1.62|1.66|1.48|
+|cyclic 9| - | - | - |
 |dummy|0.00|0.18|0.01|
-|eco 11|0.30|0.53|0.52|
-|eco 12|1.98|2.08|2.59|
-|eco 13|9.00|10.52|13.42|
-|eco 14|93.24|86.25|127.94|
-|henrion 5|0.00|0.20|0.02|
-|henrion 6|0.03|0.22|0.06|
-|henrion 7|1.97|5.31|3.26|
+|eco 11|0.33|0.54|0.58|
+|eco 12|2.61|2.35|3.92|
+|eco 13|17.10|20.51|23.67|
+|eco 14| - | - | - |
+|henrion 5|0.00|0.19|0.02|
+|henrion 6|0.03|0.25|0.08|
+|henrion 7|2.70|7.20|3.91|
 |henrion 8| - | - | - |
-|katsura 10|0.75|1.21|1.08|
-|katsura 11|5.14|7.51|6.15|
-|katsura 12|35.77|49.28|43.52|
-|katsura 13| - |634.70| - |
-|noon 7|0.17|0.36|0.22|
-|noon 8|1.37|1.75|1.88|
-|noon 9|13.44|15.72|16.01|
-|noon 10| - |225.13| - |
-|noon 11| - | - | - |
-|reimer 6|0.05|0.23|0.08|
-|reimer 7|0.69|1.41|1.21|
-|reimer 8|18.28|26.74|30.17|
-|reimer 9| - | - | - |
+|katsura 10|0.86|1.73|1.19|
+|katsura 11| - |15.16|10.34|
+|katsura 12| - | - | - |
+|katsura 13| - | - | - |
+|noon 7|0.18| - |0.23|
+|noon 8|1.55|2.09|2.05|
+|noon 9| - |19.33|25.39|
+|noon 10| - | - | - |
+|reimer 6|0.07|0.23| - |
+|reimer 7|0.80|1.75|1.32|
+|reimer 8| - |54.01|47.06|
 
 *Benchmarking environment:*
 
@@ -58,6 +55,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/benchmark_result_3.md b/benchmark/results/benchmark_result_3.md
index 399b1e88..1b65944b 100644
--- a/benchmark/results/benchmark_result_3.md
+++ b/benchmark/results/benchmark_result_3.md
@@ -1,44 +1,44 @@
 ## Benchmark results
 
-2024-01-26T16:58:14.560
+2024-01-27T08:58:45.352
 
-Benchmarked backends: Any["groebner", "maple", "msolve"]
+Benchmarked backends: Any["groebner", "maple", "msolve", "singular"]
 
 Benchmark suite: The rationals
 
-- Workers: 16
-- Timeout: 1800 s
+- Workers: 8
+- Timeout: 3600 s
 - Aggregated over: 3 runs
 
 **All timings in seconds.**
 
-|Model|groebner|maple|msolve|
-|:----|---|---|---|
-|chandra 9|1.18|4.84|1.25|
-|chandra 10|2.88|21.17|4.53|
-|chandra 11|10.28|111.70|19.83|
-|chandra 12|82.21|886.62|105.81|
-|chandra 13| - | - | - |
-|cyclic 7|0.80|1.43|1.20|
-|cyclic 8|20.81|20.50|27.28|
-|cyclic 9| - | - | - |
-|dummy|0.00|0.14|0.02|
-|eco 10|0.44|0.93|0.65|
-|eco 11|3.04|4.79|4.02|
-|eco 12|20.65|31.59|28.25|
-|eco 13|320.03|352.97|314.83|
-|henrion 6|0.53|2.03|0.65|
-|henrion 7| - | - |404.00|
-|ipp|61.74|91.40|14.18|
-|katsura 9|2.79|7.70|2.21|
-|katsura 10|20.30|76.88|17.29|
-|katsura 11|297.12|1218.94|206.39|
-|noon 7|0.46|1.09|1.53|
-|noon 8|3.84|8.15|11.80|
-|noon 9|24.66|66.52|100.94|
-|reimer 6|0.41|0.77|0.30|
-|reimer 7|6.79|24.22|6.14|
-|reimer 8| - | - |358.83|
+|Model|groebner|maple|msolve|singular|
+|:----|---|---|---|---|
+|chandra 9|1.28|5.53|1.44|3.10|
+|chandra 10|4.20|25.24|5.25|35.13|
+|chandra 11|13.27|137.17|21.87|284.97|
+|chandra 12|82.00|927.56|115.73| - |
+|chandra 13|415.78| - |709.91| - |
+|cyclic 7|1.11|1.60|1.11| - |
+|cyclic 8|27.19|22.57|27.03| - |
+|cyclic 9| - | - | - | - |
+|dummy|0.00|0.16|0.03|0.00|
+|eco 10|0.47|0.78|0.66|43.90|
+|eco 11|3.16|5.30|4.00| - |
+|eco 12|26.92|39.84|29.09| - |
+|eco 13|281.37|420.79|344.04| - |
+|henrion 6|0.63|1.91|0.63|6.16|
+|henrion 7|346.59|3205.31|364.54| - |
+|ipp|93.93|82.50|16.44|870.29|
+|katsura 9|3.49|8.71|2.52|284.81|
+|katsura 10|24.64|93.27|19.68| - |
+|katsura 11|269.47|1439.72|198.94| - |
+|noon 7|0.66|1.18|1.75|1.11|
+|noon 8|5.37|9.32|11.94|13.23|
+|noon 9|36.32|75.82|102.60|172.35|
+|reimer 6|0.55|0.80|0.28| - |
+|reimer 7|10.48|31.54|6.43| - |
+|reimer 8|661.18|3425.27|296.64| - |
 
 *Benchmarking environment:*
 
@@ -53,6 +53,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/groebner/benchmark_result_0.md b/benchmark/results/groebner/benchmark_result_0.md
index fa5e79a4..baecb57c 100644
--- a/benchmark/results/groebner/benchmark_result_0.md
+++ b/benchmark/results/groebner/benchmark_result_0.md
@@ -1,14 +1,14 @@
 ## Benchmark results
 
-2024-01-27T00:30:45.638
+2024-01-27T13:22:27.349
 
 Benchmarked backend: groebner
 
 Benchmark suite: dummy benchmark set
 
-- Workers: 16
-- Timeout: 60 s
-- Aggregated over: 1 runs
+- Workers: 1
+- Timeout: 1800 s
+- Aggregated over: 3 runs
 
 **All timings in seconds.**
 
diff --git a/benchmark/results/groebner/benchmark_result_1.md b/benchmark/results/groebner/benchmark_result_1.md
index cb7b9c9b..9b6e6224 100644
--- a/benchmark/results/groebner/benchmark_result_1.md
+++ b/benchmark/results/groebner/benchmark_result_1.md
@@ -1,49 +1,46 @@
 ## Benchmark results
 
-2024-01-27T00:17:07.455
+2024-01-27T02:44:16.764
 
 Benchmarked backend: groebner
 
 Benchmark suite: Integers modulo 2^30 + 3
 
 - Workers: 16
-- Timeout: 1800 s
+- Timeout: 60 s
 - Aggregated over: 1 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|chandra 11| - |
-|chandra 12| - |
+|chandra 11|0.76|
+|chandra 12|3.69|
 |chandra 13| - |
 |chandra 14| - |
-|cyclic 7|0.09|
-|cyclic 8|1.56|
-|cyclic 9|255.31|
-|cyclic 10| - |
+|cyclic 7|0.11|
+|cyclic 8|1.62|
+|cyclic 9| - |
 |dummy|0.00|
-|eco 11| - |
-|eco 12| - |
-|eco 13| - |
+|eco 11|0.33|
+|eco 12|2.61|
+|eco 13|17.10|
 |eco 14| - |
-|henrion 5| - |
-|henrion 6| - |
-|henrion 7| - |
+|henrion 5|0.00|
+|henrion 6|0.03|
+|henrion 7|2.70|
 |henrion 8| - |
-|katsura 10| - |
+|katsura 10|0.86|
 |katsura 11| - |
-|katsura 12|101.30|
+|katsura 12| - |
 |katsura 13| - |
-|noon 7| - |
-|noon 8| - |
-|noon 9|16.57|
+|noon 7|0.18|
+|noon 8|1.55|
+|noon 9| - |
 |noon 10| - |
-|noon 11| - |
-|reimer 6| - |
-|reimer 7| - |
+|reimer 6|0.07|
+|reimer 7|0.80|
 |reimer 8| - |
-|reimer 9| - |
 
 *Benchmarking environment:*
 
diff --git a/benchmark/results/groebner/benchmark_result_2.md b/benchmark/results/groebner/benchmark_result_2.md
index 3cd5ac0c..890d1610 100644
--- a/benchmark/results/groebner/benchmark_result_2.md
+++ b/benchmark/results/groebner/benchmark_result_2.md
@@ -1,30 +1,46 @@
 ## Benchmark results
 
-2023-12-29T23:35:20.348
+2024-01-27T02:30:44.878
 
 Benchmarked backend: groebner
-Benchmark suite: The rationals
 
-- Workers: 4
-- Timeout: 600 s
-- Aggregated over: 1 runs
+Benchmark suite: Integers modulo 1031
+
+- Workers: 16
+- Timeout: 1800 s
+- Aggregated over: 3 runs
 
 **All timings in seconds.**
 
-|Model|Total|
-|-----|---|
-|cyclic 7|1.35|
-|cyclic 8|26.73|
+|Model|Total, s|
+|:----|---|
+|chandra 11|0.48|
+|chandra 12|2.43|
+|chandra 13|20.02|
+|chandra 14| - |
+|cyclic 7|0.08|
+|cyclic 8|1.19|
+|cyclic 9| - |
 |dummy|0.00|
-|eco 10|0.64|
-|eco 11|3.99|
-|eco 12|29.60|
-|henrion 6|0.93|
-|katsura 10|25.43|
-|katsura 11| - |
-|katsura 9|4.10|
-|noon 8|6.10|
-|noon 9|50.79|
+|eco 11|0.31|
+|eco 12|1.84|
+|eco 13|8.61|
+|eco 14|163.92|
+|henrion 5|0.00|
+|henrion 6|0.04|
+|henrion 7|2.10|
+|henrion 8| - |
+|katsura 10|0.77|
+|katsura 11|5.15|
+|katsura 12|52.61|
+|katsura 13| - |
+|noon 7|0.18|
+|noon 8|1.32|
+|noon 9|12.09|
+|noon 10| - |
+|reimer 6|0.04|
+|reimer 7|0.75|
+|reimer 8|18.54|
 
 *Benchmarking environment:*
 
@@ -39,6 +55,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/groebner/benchmark_result_3.md b/benchmark/results/groebner/benchmark_result_3.md
index b2823a45..3e7ee2f9 100644
--- a/benchmark/results/groebner/benchmark_result_3.md
+++ b/benchmark/results/groebner/benchmark_result_3.md
@@ -1,44 +1,44 @@
 ## Benchmark results
 
-2024-01-26T16:00:02.075
+2024-01-27T04:37:58.855
 
 Benchmarked backend: groebner
 
 Benchmark suite: The rationals
 
-- Workers: 16
-- Timeout: 1800 s
+- Workers: 8
+- Timeout: 3600 s
 - Aggregated over: 3 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|chandra 9|1.18|
-|chandra 10|2.88|
-|chandra 11|10.28|
-|chandra 12|82.21|
-|chandra 13| - |
-|cyclic 7|0.80|
-|cyclic 8|20.81|
+|chandra 9|1.28|
+|chandra 10|4.20|
+|chandra 11|13.27|
+|chandra 12|82.00|
+|chandra 13|415.78|
+|cyclic 7|1.11|
+|cyclic 8|27.19|
 |cyclic 9| - |
 |dummy|0.00|
-|eco 10|0.44|
-|eco 11|3.04|
-|eco 12|20.65|
-|eco 13|320.03|
-|henrion 6|0.53|
-|henrion 7| - |
-|ipp|61.74|
-|katsura 9|2.79|
-|katsura 10|20.30|
-|katsura 11|297.12|
-|noon 7|0.46|
-|noon 8|3.84|
-|noon 9|24.66|
-|reimer 6|0.41|
-|reimer 7|6.79|
-|reimer 8| - |
+|eco 10|0.47|
+|eco 11|3.16|
+|eco 12|26.92|
+|eco 13|281.37|
+|henrion 6|0.63|
+|henrion 7|346.59|
+|ipp|93.93|
+|katsura 9|3.49|
+|katsura 10|24.64|
+|katsura 11|269.47|
+|noon 7|0.66|
+|noon 8|5.37|
+|noon 9|36.32|
+|reimer 6|0.55|
+|reimer 7|10.48|
+|reimer 8|661.18|
 
 *Benchmarking environment:*
 
@@ -53,6 +53,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/learn_apply/benchmark_result_1.md b/benchmark/results/learn_apply/benchmark_result_1.md
index e160dd9d..2048bda6 100644
--- a/benchmark/results/learn_apply/benchmark_result_1.md
+++ b/benchmark/results/learn_apply/benchmark_result_1.md
@@ -1,45 +1,46 @@
 ## Benchmark results
 
-2024-01-12T08:36:22.358
+2024-01-27T03:16:11.080
 
 Benchmarked backend: learn_apply
 
 Benchmark suite: Integers modulo 2^30 + 3
 
-- Workers: 8
-- Timeout: 5400 s
-- Aggregated over: 1 runs
+- Workers: 16
+- Timeout: 600 s
+- Aggregated over: 3 runs
 
 **All timings in seconds.**
 
-|Model|F4, s|Learn, s|Apply, s|Apply 4x, s|
-|:----|---|---|---|---|
-|cyclic 7|0.12|0.19|0.03|0.06|
-|cyclic 8|1.44|4.01|0.58|0.75|
-|cyclic 9|104.46|643.68|73.29|245.08|
-|cyclic 10| - | - | - | - |
-|dummy|0.00|0.00|0.00|0.00|
-|eco 11|0.37|1.16|0.16|0.28|
-|eco 12|2.80|12.76|1.19|1.91|
-|eco 13|10.69|133.29|4.89|7.66|
-|eco 14|124.62|833.97|66.71|100.08|
-|henrion 5|0.00|0.00|0.00|0.00|
-|henrion 6|0.07|0.07|0.02|0.05|
-|henrion 7|3.08|9.28|1.05|1.98|
-|henrion 8| - | - | - | - |
-|katsura 10|0.78|5.30|0.31|0.58|
-|katsura 11|5.46|74.63|3.36|6.33|
-|katsura 12|56.40|592.94|24.49|36.21|
-|katsura 13| - | - | - | - |
-|noon 7|0.25|0.24|0.04|0.12|
-|noon 8|2.05|2.07|0.34|0.74|
-|noon 9|15.37|16.85|1.54|2.87|
-|noon 10|189.33|194.49|11.82|27.34|
-|noon 11| - | - | - | - |
-|reimer 6|0.05|0.17|0.01|0.02|
-|reimer 7|1.30|1.91|0.18|0.26|
-|reimer 8|19.21|58.04|2.55|3.99|
-|reimer 9| - | - | - | - |
+|Model|F4, s|Learn, s|Apply, s|Apply 4x, s|Apply 8x, s|
+|:----|---|---|---|---|---|
+|chandra 11|0.48|1.15|0.05|0.12|0.20|
+|chandra 12|2.68|7.36|0.18|0.45|0.69|
+|chandra 13|15.06|49.39|0.84|2.16|3.31|
+|chandra 14| - | - | - | - | - |
+|cyclic 7|0.08|0.18|0.03|0.04|0.06|
+|cyclic 8|1.17|3.64|0.50|0.72|1.35|
+|cyclic 9| - | - | - | - | - |
+|dummy|0.00|0.00|0.00|0.00|0.00|
+|eco 11|0.32|1.12|0.14|0.21|0.33|
+|eco 12|2.08|9.40|0.85|1.28|2.28|
+|eco 13|8.84|88.53|3.58|5.68|12.92|
+|eco 14| - | - | - | - | - |
+|henrion 5|0.00|0.00|0.00|0.00|0.00|
+|henrion 6|0.03|0.05|0.01|0.02|0.06|
+|henrion 7|1.93|5.29|0.71|1.13|1.79|
+|henrion 8| - | - | - | - | - |
+|katsura 10|0.76|4.92|0.30|0.51|0.85|
+|katsura 11|4.99|46.82|1.99|3.44|6.24|
+|katsura 12| - | - | - | - | - |
+|katsura 13| - | - | - | - | - |
+|noon 7|0.16|0.19|0.03|0.04|0.08|
+|noon 8|1.34|1.56|0.19|0.33|0.46|
+|noon 9|12.49|13.06|1.32|2.29|4.06|
+|noon 10| - | - | - | - | - |
+|reimer 6|0.04|0.08|0.01|0.02|0.02|
+|reimer 7|0.77|1.32|0.10|0.16|0.21|
+|reimer 8|17.86|42.05|1.70|2.69|4.46|
 
 *Benchmarking environment:*
 
@@ -54,6 +55,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/maple/benchmark_result_0.md b/benchmark/results/maple/benchmark_result_0.md
index d1c70cb3..d2b89266 100644
--- a/benchmark/results/maple/benchmark_result_0.md
+++ b/benchmark/results/maple/benchmark_result_0.md
@@ -1,20 +1,20 @@
 ## Benchmark results
 
-2024-01-27T00:30:59.875
+2024-01-27T13:23:56.875
 
 Benchmarked backend: maple
 
 Benchmark suite: dummy benchmark set
 
-- Workers: 16
-- Timeout: 60 s
-- Aggregated over: 1 runs
+- Workers: 1
+- Timeout: 1800 s
+- Aggregated over: 3 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|dummy 1|0.23|
+|dummy 1|0.22|
 |dummy 2|0.21|
 
 *Benchmarking environment:*
diff --git a/benchmark/results/maple/benchmark_result_1.md b/benchmark/results/maple/benchmark_result_1.md
index 72b5967f..374fc48f 100644
--- a/benchmark/results/maple/benchmark_result_1.md
+++ b/benchmark/results/maple/benchmark_result_1.md
@@ -1,49 +1,46 @@
 ## Benchmark results
 
-2024-01-26T15:11:24.864
+2024-01-27T02:46:22.712
 
 Benchmarked backend: maple
 
 Benchmark suite: Integers modulo 2^30 + 3
 
 - Workers: 16
-- Timeout: 600 s
-- Aggregated over: 3 runs
+- Timeout: 60 s
+- Aggregated over: 1 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|chandra 11|0.76|
-|chandra 12|2.89|
-|chandra 13|14.09|
-|chandra 14|82.15|
-|cyclic 7|0.24|
-|cyclic 8|1.38|
-|cyclic 9|195.46|
-|cyclic 10| - |
+|chandra 11|0.97|
+|chandra 12|4.18|
+|chandra 13|25.59|
+|chandra 14| - |
+|cyclic 7|0.30|
+|cyclic 8|1.66|
+|cyclic 9| - |
 |dummy|0.18|
-|eco 11|0.53|
-|eco 12|2.08|
-|eco 13|10.52|
-|eco 14|86.25|
-|henrion 5|0.20|
-|henrion 6|0.22|
-|henrion 7|5.31|
+|eco 11|0.54|
+|eco 12|2.35|
+|eco 13|20.51|
+|eco 14| - |
+|henrion 5|0.19|
+|henrion 6|0.25|
+|henrion 7|7.20|
 |henrion 8| - |
-|katsura 10|1.21|
-|katsura 11|7.51|
-|katsura 12|49.28|
-|katsura 13|634.70|
-|noon 7|0.36|
-|noon 8|1.75|
-|noon 9|15.72|
-|noon 10|225.13|
-|noon 11| - |
+|katsura 10|1.73|
+|katsura 11|15.16|
+|katsura 12| - |
+|katsura 13| - |
+|noon 7| - |
+|noon 8|2.09|
+|noon 9|19.33|
+|noon 10| - |
 |reimer 6|0.23|
-|reimer 7|1.41|
-|reimer 8|26.74|
-|reimer 9| - |
+|reimer 7|1.75|
+|reimer 8|54.01|
 
 *Benchmarking environment:*
 
@@ -58,6 +55,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/maple/benchmark_result_3.md b/benchmark/results/maple/benchmark_result_3.md
index 8a904cb0..ce06d908 100644
--- a/benchmark/results/maple/benchmark_result_3.md
+++ b/benchmark/results/maple/benchmark_result_3.md
@@ -1,44 +1,44 @@
 ## Benchmark results
 
-2024-01-26T16:31:09.203
+2024-01-27T07:56:37.996
 
 Benchmarked backend: maple
 
 Benchmark suite: The rationals
 
-- Workers: 16
-- Timeout: 1800 s
+- Workers: 8
+- Timeout: 3600 s
 - Aggregated over: 3 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|chandra 9|4.84|
-|chandra 10|21.17|
-|chandra 11|111.70|
-|chandra 12|886.62|
+|chandra 9|5.53|
+|chandra 10|25.24|
+|chandra 11|137.17|
+|chandra 12|927.56|
 |chandra 13| - |
-|cyclic 7|1.43|
-|cyclic 8|20.50|
+|cyclic 7|1.60|
+|cyclic 8|22.57|
 |cyclic 9| - |
-|dummy|0.14|
-|eco 10|0.93|
-|eco 11|4.79|
-|eco 12|31.59|
-|eco 13|352.97|
-|henrion 6|2.03|
-|henrion 7| - |
-|ipp|91.40|
-|katsura 9|7.70|
-|katsura 10|76.88|
-|katsura 11|1218.94|
-|noon 7|1.09|
-|noon 8|8.15|
-|noon 9|66.52|
-|reimer 6|0.77|
-|reimer 7|24.22|
-|reimer 8| - |
+|dummy|0.16|
+|eco 10|0.78|
+|eco 11|5.30|
+|eco 12|39.84|
+|eco 13|420.79|
+|henrion 6|1.91|
+|henrion 7|3205.31|
+|ipp|82.50|
+|katsura 9|8.71|
+|katsura 10|93.27|
+|katsura 11|1439.72|
+|noon 7|1.18|
+|noon 8|9.32|
+|noon 9|75.82|
+|reimer 6|0.80|
+|reimer 7|31.54|
+|reimer 8|3425.27|
 
 *Benchmarking environment:*
 
@@ -53,6 +53,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/msolve/benchmark_result_0.md b/benchmark/results/msolve/benchmark_result_0.md
index aed138ce..1e6d8138 100644
--- a/benchmark/results/msolve/benchmark_result_0.md
+++ b/benchmark/results/msolve/benchmark_result_0.md
@@ -1,21 +1,21 @@
 ## Benchmark results
 
-2024-01-27T00:31:13.800
+2024-01-27T13:24:19.795
 
 Benchmarked backend: msolve
 
 Benchmark suite: dummy benchmark set
 
-- Workers: 16
-- Timeout: 60 s
-- Aggregated over: 1 runs
+- Workers: 1
+- Timeout: 1800 s
+- Aggregated over: 3 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|dummy 1|0.03|
-|dummy 2|0.03|
+|dummy 1|0.01|
+|dummy 2|0.01|
 
 *Benchmarking environment:*
 
diff --git a/benchmark/results/msolve/benchmark_result_1.md b/benchmark/results/msolve/benchmark_result_1.md
index b8ed2a8f..8b9624b1 100644
--- a/benchmark/results/msolve/benchmark_result_1.md
+++ b/benchmark/results/msolve/benchmark_result_1.md
@@ -1,49 +1,46 @@
 ## Benchmark results
 
-2024-01-26T15:22:43.818
+2024-01-27T02:48:22.410
 
 Benchmarked backend: msolve
 
 Benchmark suite: Integers modulo 2^30 + 3
 
 - Workers: 16
-- Timeout: 600 s
-- Aggregated over: 3 runs
+- Timeout: 60 s
+- Aggregated over: 1 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|chandra 11|0.88|
-|chandra 12|3.84|
-|chandra 13|20.56|
-|chandra 14|133.08|
+|chandra 11|0.96|
+|chandra 12|4.78|
+|chandra 13|30.71|
+|chandra 14| - |
 |cyclic 7|0.15|
-|cyclic 8|1.36|
-|cyclic 9|118.97|
-|cyclic 10| - |
+|cyclic 8|1.48|
+|cyclic 9| - |
 |dummy|0.01|
-|eco 11|0.52|
-|eco 12|2.59|
-|eco 13|13.42|
-|eco 14|127.94|
+|eco 11|0.58|
+|eco 12|3.92|
+|eco 13|23.67|
+|eco 14| - |
 |henrion 5|0.02|
-|henrion 6|0.06|
-|henrion 7|3.26|
+|henrion 6|0.08|
+|henrion 7|3.91|
 |henrion 8| - |
-|katsura 10|1.08|
-|katsura 11|6.15|
-|katsura 12|43.52|
+|katsura 10|1.19|
+|katsura 11|10.34|
+|katsura 12| - |
 |katsura 13| - |
-|noon 7|0.22|
-|noon 8|1.88|
-|noon 9|16.01|
+|noon 7|0.23|
+|noon 8|2.05|
+|noon 9|25.39|
 |noon 10| - |
-|noon 11| - |
-|reimer 6|0.08|
-|reimer 7|1.21|
-|reimer 8|30.17|
-|reimer 9| - |
+|reimer 6| - |
+|reimer 7|1.32|
+|reimer 8|47.06|
 
 *Benchmarking environment:*
 
@@ -58,6 +55,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/msolve/benchmark_result_3.md b/benchmark/results/msolve/benchmark_result_3.md
index b2783a3d..21704d89 100644
--- a/benchmark/results/msolve/benchmark_result_3.md
+++ b/benchmark/results/msolve/benchmark_result_3.md
@@ -1,44 +1,44 @@
 ## Benchmark results
 
-2024-01-26T16:58:11.224
+2024-01-27T08:58:42.262
 
 Benchmarked backend: msolve
 
 Benchmark suite: The rationals
 
-- Workers: 16
-- Timeout: 1800 s
+- Workers: 8
+- Timeout: 3600 s
 - Aggregated over: 3 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|chandra 9|1.25|
-|chandra 10|4.53|
-|chandra 11|19.83|
-|chandra 12|105.81|
-|chandra 13| - |
-|cyclic 7|1.20|
-|cyclic 8|27.28|
+|chandra 9|1.44|
+|chandra 10|5.25|
+|chandra 11|21.87|
+|chandra 12|115.73|
+|chandra 13|709.91|
+|cyclic 7|1.11|
+|cyclic 8|27.03|
 |cyclic 9| - |
-|dummy|0.02|
-|eco 10|0.65|
-|eco 11|4.02|
-|eco 12|28.25|
-|eco 13|314.83|
-|henrion 6|0.65|
-|henrion 7|404.00|
-|ipp|14.18|
-|katsura 9|2.21|
-|katsura 10|17.29|
-|katsura 11|206.39|
-|noon 7|1.53|
-|noon 8|11.80|
-|noon 9|100.94|
-|reimer 6|0.30|
-|reimer 7|6.14|
-|reimer 8|358.83|
+|dummy|0.03|
+|eco 10|0.66|
+|eco 11|4.00|
+|eco 12|29.09|
+|eco 13|344.04|
+|henrion 6|0.63|
+|henrion 7|364.54|
+|ipp|16.44|
+|katsura 9|2.52|
+|katsura 10|19.68|
+|katsura 11|198.94|
+|noon 7|1.75|
+|noon 8|11.94|
+|noon 9|102.60|
+|reimer 6|0.28|
+|reimer 7|6.43|
+|reimer 8|296.64|
 
 *Benchmarking environment:*
 
@@ -53,6 +53,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/openf4/benchmark_result_0.md b/benchmark/results/openf4/benchmark_result_0.md
index 6fb6d195..fb615067 100644
--- a/benchmark/results/openf4/benchmark_result_0.md
+++ b/benchmark/results/openf4/benchmark_result_0.md
@@ -1,21 +1,21 @@
 ## Benchmark results
 
-2024-01-22T20:54:59.328
+2024-01-27T13:24:44.120
 
 Benchmarked backend: openf4
 
 Benchmark suite: dummy benchmark set
 
-- Workers: 8
-- Timeout: 600 s
-- Aggregated over: 1 runs
+- Workers: 1
+- Timeout: 1800 s
+- Aggregated over: 3 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|dummy 1| - |
-|dummy 2| - |
+|dummy 1|0.01|
+|dummy 2|0.01|
 
 *Benchmarking environment:*
 
@@ -30,6 +30,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/singular/benchmark_result_0.md b/benchmark/results/singular/benchmark_result_0.md
index d2fef652..3d2d9c61 100644
--- a/benchmark/results/singular/benchmark_result_0.md
+++ b/benchmark/results/singular/benchmark_result_0.md
@@ -1,20 +1,20 @@
 ## Benchmark results
 
-2024-01-11T10:12:01.109
+2024-01-27T13:23:32.554
 
 Benchmarked backend: singular
 
 Benchmark suite: dummy benchmark set
 
-- Workers: 4
-- Timeout: 20 s
-- Aggregated over: 1 runs
+- Workers: 1
+- Timeout: 1800 s
+- Aggregated over: 3 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
-|-----|---|
-|dummy 1| - |
+|:----|---|
+|dummy 1|0.00|
 |dummy 2|0.00|
 
 *Benchmarking environment:*
@@ -30,6 +30,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/results/singular/benchmark_result_3.md b/benchmark/results/singular/benchmark_result_3.md
index 3c34b466..324abc34 100644
--- a/benchmark/results/singular/benchmark_result_3.md
+++ b/benchmark/results/singular/benchmark_result_3.md
@@ -1,31 +1,44 @@
 ## Benchmark results
 
-2023-12-31T02:48:35.724
+2024-01-27T06:50:31.803
 
 Benchmarked backend: singular
 
 Benchmark suite: The rationals
 
 - Workers: 8
-- Timeout: 100 s
-- Aggregated over: 1 runs
+- Timeout: 3600 s
+- Aggregated over: 3 runs
 
 **All timings in seconds.**
 
-|Model|Total|
-|-----|---|
+|Model|Total, s|
+|:----|---|
+|chandra 9|3.10|
+|chandra 10|35.13|
+|chandra 11|284.97|
+|chandra 12| - |
+|chandra 13| - |
 |cyclic 7| - |
 |cyclic 8| - |
+|cyclic 9| - |
 |dummy|0.00|
-|eco 10|30.60|
+|eco 10|43.90|
 |eco 11| - |
 |eco 12| - |
-|henrion 6|5.22|
-|katsura 9| - |
+|eco 13| - |
+|henrion 6|6.16|
+|henrion 7| - |
+|ipp|870.29|
+|katsura 9|284.81|
 |katsura 10| - |
 |katsura 11| - |
-|noon 8|13.60|
-|noon 9| - |
+|noon 7|1.11|
+|noon 8|13.23|
+|noon 9|172.35|
+|reimer 6| - |
+|reimer 7| - |
+|reimer 8| - |
 
 *Benchmarking environment:*
 
@@ -40,6 +53,7 @@ Versions of the dependencies:
 * PrecompileTools : 1.2.0
 * MultivariatePolynomials : 0.5.3
 * Combinatorics : 1.0.2
+* HostCPUFeatures : 0.1.16
 * AbstractAlgebra : 0.34.7
 * Nemo : 0.38.3
 * Atomix : 0.1.0
diff --git a/benchmark/validate/benchmark_0/dummy 1/certificate b/benchmark/validate/benchmark_0/dummy 1/certificate
index fcbdc7b4..0e201db6 100644
--- a/benchmark/validate/benchmark_0/dummy 1/certificate	
+++ b/benchmark/validate/benchmark_0/dummy 1/certificate	
@@ -1 +1 @@
-c775cf0260d43aea2cb7d42049708525d924fabf56b18b21a12ed756e8af8814
+48f002a952bef07bb2b36ca58d9618e0a063e945be143d9dfd7632169945c01a
diff --git a/benchmark/validate/benchmark_0/dummy 2/certificate b/benchmark/validate/benchmark_0/dummy 2/certificate
index fcbdc7b4..0e201db6 100644
--- a/benchmark/validate/benchmark_0/dummy 2/certificate	
+++ b/benchmark/validate/benchmark_0/dummy 2/certificate	
@@ -1 +1 @@
-c775cf0260d43aea2cb7d42049708525d924fabf56b18b21a12ed756e8af8814
+48f002a952bef07bb2b36ca58d9618e0a063e945be143d9dfd7632169945c01a
diff --git a/experimental/sparsedense.jl b/experimental/sparsedense.jl
new file mode 100644
index 00000000..8061fc83
--- /dev/null
+++ b/experimental/sparsedense.jl
@@ -0,0 +1,172 @@
+using BenchmarkTools
+
+function addmul!(
+    row::Vector{UInt64},
+    indices::Vector{Int64},
+    coeffs::Vector{UInt32},
+    mul::UInt64
+)
+    @inbounds for j in 1:length(indices)
+        idx = indices[j]
+        a = row[idx] + mul * UInt64(coeffs[j])
+        row[idx] = a
+    end
+    nothing
+end
+
+function addmul_2!(row, indices, coeffs, mul)
+    textir = """
+    ; row, indices, coeffs, mul, len
+    define void @entry(i64 %0, i64 %1, i64 %2, i64 %3, i64 %4) #0 {
+    top:
+        %row = inttoptr i64 %0 to i64*
+        %inds = inttoptr i64 %1 to i64*
+        %coeffs = inttoptr i64 %2 to i32*
+        %lenm7 = add nsw i64 %4, -3
+        %dosimditer = icmp ugt i64 %4, 3
+        br i1 %dosimditer, label %L9.lr.ph, label %L32
+
+    L9.lr.ph:
+        %len8 = and i64 %4, 9223372036854775804
+        br label %L9
+
+    L9:
+        %i = phi i64 [ 0, %L9.lr.ph ], [ %vinc, %L30 ]
+        %indsi = getelementptr inbounds i64, i64* %inds, i64 %i
+        %idx = load i64, i64* %indsi, align 8
+        %coeffsi = getelementptr inbounds i32, i32* %coeffs, i64 %i
+        %coeff = load i32, i32* %coeffsi, align 8
+        %idxm1 = add i64 %idx, -1
+        %rowi = getelementptr inbounds i64, i64* %row, i64 %idxm1
+        %x = load i64, i64* %rowi, align 8
+        %coeff64 = zext i32 %coeff to i64
+        %mulcoeff = mul i64 %coeff64, %3
+        %newx = add i64 %x, %mulcoeff
+        store i64 %newx, i64* %rowi, align 8
+        ;
+        %i2 = add i64 %i, 1
+        %indsi2 = getelementptr inbounds i64, i64* %inds, i64 %i2
+        %idx2 = load i64, i64* %indsi2, align 8
+        %coeffsi2 = getelementptr inbounds i32, i32* %coeffs, i64 %i2
+        %coeff2 = load i32, i32* %coeffsi2, align 8
+        %idxm12 = add i64 %idx2, -1
+        %rowi2 = getelementptr inbounds i64, i64* %row, i64 %idxm12
+        %x2 = load i64, i64* %rowi2, align 8
+        %coeff642 = zext i32 %coeff2 to i64
+        %mulcoeff2 = mul i64 %coeff642, %3
+        %newx2 = add i64 %x2, %mulcoeff2
+        store i64 %newx2, i64* %rowi2, align 8
+        ;
+        %i3 = add i64 %i2, 1
+        %indsi3 = getelementptr inbounds i64, i64* %inds, i64 %i3
+        %idx3 = load i64, i64* %indsi3, align 8
+        %coeffsi3 = getelementptr inbounds i32, i32* %coeffs, i64 %i3
+        %coeff3 = load i32, i32* %coeffsi3, align 8
+        %idxm13 = add i64 %idx3, -1
+        %rowi3 = getelementptr inbounds i64, i64* %row, i64 %idxm13
+        %x3 = load i64, i64* %rowi3, align 8
+        %coeff643 = zext i32 %coeff3 to i64
+        %mulcoeff3 = mul i64 %coeff643, %3
+        %newx3 = add i64 %x3, %mulcoeff3
+        store i64 %newx3, i64* %rowi3, align 8
+        ;
+        %i4 = add i64 %i3, 1
+        %indsi4 = getelementptr inbounds i64, i64* %inds, i64 %i4
+        %idx4 = load i64, i64* %indsi4, align 8
+        %coeffsi4 = getelementptr inbounds i32, i32* %coeffs, i64 %i4
+        %coeff4 = load i32, i32* %coeffsi4, align 8
+        %idxm14 = add i64 %idx4, -1
+        %rowi4 = getelementptr inbounds i64, i64* %row, i64 %idxm14
+        %x4 = load i64, i64* %rowi4, align 8
+        %coeff644 = zext i32 %coeff4 to i64
+        %mulcoeff4 = mul i64 %coeff644, %3
+        %newx4 = add i64 %x4, %mulcoeff4
+        store i64 %newx4, i64* %rowi4, align 8
+        ;
+        br label %L30
+
+    L30:
+        %vinc = add nuw nsw i64 %i, 4
+        %continue = icmp slt i64 %vinc, %lenm7
+        br i1 %continue, label %L9, label %L32
+
+    L32:
+        %cumi = phi i64 [ 0, %top ], [ %len8, %L30 ]
+        %done = icmp eq i64 %cumi, %4
+        br i1 %done, label %common.ret, label %L51
+
+    common.ret:
+        ret void
+
+    L51:
+        %si = phi i64 [ %inc, %L67 ], [ %cumi, %L32 ]
+        %sindsi = getelementptr inbounds i64, i64* %inds, i64 %si
+        %sidx = load i64, i64* %sindsi, align 8
+        %scoeffsi = getelementptr inbounds i32, i32* %coeffs, i64 %si
+        %scoeff = load i32, i32* %scoeffsi, align 8
+        %sidxm1 = add i64 %sidx, -1
+        %srowi = getelementptr inbounds i64, i64* %row, i64 %sidxm1
+        %sx = load i64, i64* %srowi, align 8
+        %scoeff64 = zext i32 %scoeff to i64
+        %smulcoeff = mul i64 %scoeff64, %3
+        %snewx = add i64 %sx, %smulcoeff
+        store i64 %snewx, i64* %srowi, align 8
+        br label %L67
+
+    L67:
+        %inc = add i64 %si, 1
+        %dobreak = icmp eq i64 %inc, %4
+        br i1 %dobreak, label %common.ret, label %L51
+
+    }
+    attributes #0 = { alwaysinline }
+"""
+
+    GC.@preserve row indices coeffs begin
+        Base.llvmcall(
+            (textir, "entry"),
+            Nothing,
+            Tuple{Ptr{UInt64}, Ptr{Int64}, Ptr{UInt32}, UInt64, Int64},
+            Base.unsafe_convert(Ptr{UInt64}, row),
+            Base.unsafe_convert(Ptr{Int64}, indices),
+            Base.unsafe_convert(Ptr{UInt32}, coeffs),
+            mul,
+            length(indices)
+        )
+    end
+end
+
+@code_native debuginfo = :none addmul!(UInt[], Int[], UInt32[], UInt(1))
+@code_native debuginfo = :none addmul_2!(UInt[], Int[], UInt32[], UInt(1))
+
+n = 10_000
+for k in 1:5:200
+    @info "n = $n, k = $k"
+    for _ in 1:100
+        row = rand(UInt.(0:100), n)
+        indices = sort(unique(rand(1:(n), k)))
+        coeffs = rand(UInt32.(1:100), length(indices))
+        mul = rand(UInt)
+        crow = copy(row)
+        # println(row[indices])
+        addmul!(row, indices, coeffs, mul)
+        addmul_2!(crow, indices, coeffs, mul)
+        # println(row[indices])
+        # println(crow[indices])
+        # println(indices)
+        # println(coeffs)
+        @assert row == crow
+    end
+    @btime addmul!(row, indices, coeffs, mul) setup = begin
+        row = rand(UInt, $n)
+        indices = sort(unique(rand(1:($n), $k)))
+        coeffs = rand(UInt32, length(indices))
+        mul = rand(UInt)
+    end
+    @btime addmul_2!(row, indices, coeffs, mul) setup = begin
+        row = rand(UInt, $n)
+        indices = sort(unique(rand(1:($n), $k)))
+        coeffs = rand(UInt32, length(indices))
+        mul = rand(UInt)
+    end
+end