diff --git a/CHANGELOG.md b/CHANGELOG.md
index 36e50713..24baddd6 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,19 +1,27 @@
+## Groebner v0.6.4 Release notes
+
+Minor performance improvements, especially over finite fields of large characteristic.
+
+Versions of dependencies:
+- Updated dependency on AbstractAlgebra.jl and Nemo.jl.
+- Now Groebmer.jl depends on HostCPUFeatures.jl v0.1+.
+
 ## Groebner v0.6.3 Release notes
 
 Now we handle both `Nemo.GF` and `Nemo.Native.GF` as the coefficient ring.
 
 ## Groebner v0.6.1-2 Release notes
 
-Bug fixes.
+Some bug fixes.
 
 ## Groebner v0.6.0 Release notes
 
 New features:
 - Adds the possibility of parallel computation, can be activated by the `threaded` keyword argument in function `groebner`.
-- Major speed-ups over the rationals thanks to the new learn & apply strategy and rational number reconstruction from Nemo.
+- Major speed-ups over the rationals thanks to the new learn & apply strategy and the use of rational number reconstruction from Nemo.
 - Marginal speed-ups over some finite fields due to the new implementations of arithmetic in Z/pZ.
 
-Other:
+Versions of dependencies:
 - Added a dependency on Nemo.jl.
 
 ## Groebner v0.5.0 Release notes
diff --git a/benchmark/Manifest.toml b/benchmark/Manifest.toml
index 263899f1..02eb6659 100644
--- a/benchmark/Manifest.toml
+++ b/benchmark/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"
@@ -146,7 +152,7 @@ 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"]
+deps = ["AbstractAlgebra", "Atomix", "Combinatorics", "ExprTools", "HostCPUFeatures", "Logging", "MultivariatePolynomials", "Nemo", "PrecompileTools", "PrettyTables", "Primes", "Printf", "Random", "TimerOutputs"]
 path = ".."
 uuid = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
 version = "0.6.3"
@@ -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"
@@ -369,6 +386,12 @@ 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/groebner/Manifest.toml b/benchmark/generate/groebner/Manifest.toml
index da093534..83416cb7 100644
--- a/benchmark/generate/groebner/Manifest.toml
+++ b/benchmark/generate/groebner/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"
@@ -146,7 +152,7 @@ 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"]
+deps = ["AbstractAlgebra", "Atomix", "Combinatorics", "ExprTools", "HostCPUFeatures", "Logging", "MultivariatePolynomials", "Nemo", "PrecompileTools", "PrettyTables", "Primes", "Printf", "Random", "TimerOutputs"]
 path = "../../.."
 uuid = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
 version = "0.6.3"
@@ -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/results/benchmark_result_0.md b/benchmark/results/benchmark_result_0.md
index 71ee995b..dcbc540f 100644
--- a/benchmark/results/benchmark_result_0.md
+++ b/benchmark/results/benchmark_result_0.md
@@ -1,21 +1,21 @@
 ## Benchmark results
 
-2024-01-24T03:13:43.861
+2024-01-26T23:39:30.428
 
 Benchmarked backends: Any["groebner", "maple", "msolve"]
 
 Benchmark suite: dummy benchmark set
 
 - Workers: 16
-- Timeout: 600 s
+- Timeout: 1800 s
 - Aggregated over: 1 runs
 
 **All timings in seconds.**
 
 |Model|groebner|maple|msolve|
 |:----|---|---|---|
-|dummy 1|0.00|0.01|0.04|
-|dummy 2|0.00|0.02|0.03|
+|dummy 1|0.00|0.24|0.03|
+|dummy 2|0.00|0.23|0.03|
 
 *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/groebner/benchmark_result_0.md b/benchmark/results/groebner/benchmark_result_0.md
index fae7ea54..cec188c6 100644
--- a/benchmark/results/groebner/benchmark_result_0.md
+++ b/benchmark/results/groebner/benchmark_result_0.md
@@ -1,13 +1,13 @@
 ## Benchmark results
 
-2024-01-24T03:13:25.755
+2024-01-26T23:39:00.057
 
 Benchmarked backend: groebner
 
 Benchmark suite: dummy benchmark set
 
 - Workers: 16
-- Timeout: 600 s
+- Timeout: 1800 s
 - Aggregated over: 1 runs
 
 **All timings in seconds.**
@@ -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/maple/benchmark_result_0.md b/benchmark/results/maple/benchmark_result_0.md
index 65ac798c..fdd02ec1 100644
--- a/benchmark/results/maple/benchmark_result_0.md
+++ b/benchmark/results/maple/benchmark_result_0.md
@@ -1,21 +1,21 @@
 ## Benchmark results
 
-2024-01-26T14:25:53.125
+2024-01-26T23:39:14.885
 
 Benchmarked backend: maple
 
 Benchmark suite: dummy benchmark set
 
 - Workers: 16
-- Timeout: 120 s
-- Aggregated over: 3 runs
+- Timeout: 1800 s
+- Aggregated over: 1 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|dummy 1|0.22|
-|dummy 2|0.20|
+|dummy 1|0.24|
+|dummy 2|0.23|
 
 *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/msolve/benchmark_result_0.md b/benchmark/results/msolve/benchmark_result_0.md
index ea8bfa3b..0e203dbc 100644
--- a/benchmark/results/msolve/benchmark_result_0.md
+++ b/benchmark/results/msolve/benchmark_result_0.md
@@ -1,20 +1,20 @@
 ## Benchmark results
 
-2024-01-24T03:13:42.132
+2024-01-26T23:39:28.793
 
 Benchmarked backend: msolve
 
 Benchmark suite: dummy benchmark set
 
 - Workers: 16
-- Timeout: 600 s
+- Timeout: 1800 s
 - Aggregated over: 1 runs
 
 **All timings in seconds.**
 
 |Model|Total, s|
 |:----|---|
-|dummy 1|0.04|
+|dummy 1|0.03|
 |dummy 2|0.03|
 
 *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/src/utils/simd.jl b/src/utils/simd.jl
index 6d4bbc9c..42cf5b92 100644
--- a/src/utils/simd.jl
+++ b/src/utils/simd.jl
@@ -264,6 +264,12 @@ end
     B = sizeof(T)
     llvm_t = j_to_llvm_t(T)
     mask = typemax_saturated(Int, N)
+    typecast_iN_to_i64(varname) =
+        if N == 64
+            ""
+        else
+            "$(varname)64 = zext i$(N) $(varname)$(N) to i64\n"
+        end
     textir = """
     declare i$N @llvm.cttz.i$N(i$N, i1);
     define i8 @entry(i64 %0, i64 %1, i64 %2) #0 {
@@ -293,7 +299,7 @@ end
 
     L17:
         %tz$N = call i$N @llvm.cttz.i$N(i$N %compressed, i1 true)
-        %tz64 = zext i$N %tz$N to i64
+        $(typecast_iN_to_i64("%tz"))
         %vis = add nuw i64 %i, %tz64
         %sapi2 = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %vis
         %sbpi2 = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %vis
@@ -372,6 +378,13 @@ end
     B = sizeof(T)
     llvm_t = j_to_llvm_t(T)
     mask = typemax_saturated(Int, N)
+    typecast_iN_to_i64(varname) =
+        if N == 64
+            ""
+        else
+            "$(varname)64 = zext i$(N) $(varname)$(N) to i64\n"
+        end
+
     textir = """
     declare i$N @llvm.ctlz.i$N(i$N, i1);
     define i8 @entry(i64 %0, i64 %1, i64 %2) #0 {
@@ -402,9 +415,9 @@ end
         br i1 %matchfnotound, label %L30, label %L17
 
     L17:
-        %tz$N = call i$N @llvm.ctlz.i$N(i$N %compressed, i1 true)
-        %tz$N.rev = sub i$N $(N-1), %tz$N
-        %tz64 = zext i$N %tz$N.rev to i64
+        %tz$N.rev = call i$N @llvm.ctlz.i$N(i$N %compressed, i1 true)
+        %tz$N = sub i$N $(N-1), %tz$N.rev
+        $(typecast_iN_to_i64("%tz"))
         %vis = add nsw i64 %i, %tz64
         %sapi2 = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %vis
         %sbpi2 = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %vis
diff --git a/test/runtests.jl b/test/runtests.jl
index ac277db5..c66b7995 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -21,14 +21,11 @@ function try_import(name::Symbol)
     end
 end
 
-# @test isempty(Test.detect_unbound_args(Groebner))
 @test isempty(Test.detect_ambiguities(Groebner))
 
 ⊂(xs, ys) = all(in(ys), xs)
 ≂(xs, ys) = ⊂(xs, ys) && ⊂(ys, xs)
 
-# Groebner.versioninfo()
-
 @time @testset "All tests" verbose = true begin
     # Basic tests for addition in Zp
     @time @includetests ["arithmetic/Zp"]