diff --git a/benchmark/experiments/normalform_f4.jl b/benchmark/experiments/normalform_f4.jl
new file mode 100644
index 00000000..a998ef01
--- /dev/null
+++ b/benchmark/experiments/normalform_f4.jl
@@ -0,0 +1,26 @@
+
+include("../../src/Groebner.jl")
+
+if !isdefined(Main, :Groebner)
+    import Groebner
+end
+
+import AbstractAlgebra
+using Nemo
+using BenchmarkTools
+using Logging
+global_logger(ConsoleLogger(stderr, Logging.Error))
+
+BenchmarkTools.DEFAULT_PARAMETERS.samples = 4
+
+system = Groebner.cyclicn(7, ground=Nemo.QQ, ordering=:degrevlex)
+gb = Groebner.groebner(system);
+xs = gens(parent(system[1]))
+
+@time Groebner.normalform(gb, system, check=false);
+collect([AbstractAlgebra.normal_form(s, gb) for s in system])
+
+@benchmark Groebner.normalform($gb, $system, check=false)
+@benchmark for s in system
+    AbstractAlgebra.normal_form(s, gb)
+end
diff --git a/src/arithmetic/QQ.jl b/src/arithmetic/QQ.jl
index ea7b63e2..1385f533 100644
--- a/src/arithmetic/QQ.jl
+++ b/src/arithmetic/QQ.jl
@@ -3,4 +3,15 @@
 # All implementations of arithmetic in QQ are a subtype of it. 
 abstract type AbstractArithmeticQQ end
 
-struct BuiltinArithmeticQQ <: AbstractArithmeticQQ end
+struct BuiltinArithmeticQQ <: AbstractArithmeticQQ
+    buf1::BigInt
+    buf2::Rational{BigInt}
+    function BuiltinArithmeticQQ()
+        new(BigInt(0), Rational{BigInt}(0))
+    end
+end
+
+# arithmetic over rational numbers
+function select_arithmetic(coeffs::Vector{Vector{T}}, ch) where {T <: CoeffQQ}
+    BuiltinArithmeticQQ()
+end
diff --git a/src/arithmetic/Zp.jl b/src/arithmetic/Zp.jl
index 968ccf01..1c6739fa 100644
--- a/src/arithmetic/Zp.jl
+++ b/src/arithmetic/Zp.jl
@@ -66,8 +66,3 @@ end
 function select_arithmetic(coeffs::Vector{Vector{T}}, ch) where {T <: CoeffFF}
     SpecializedBuiltinArithmeticZp(convert(T, ch))
 end
-
-# arithmetic over rational numbers
-function select_arithmetic(coeffs::Vector{Vector{T}}, ch) where {T <: CoeffQQ}
-    ch
-end
diff --git a/src/f4/matrix.jl b/src/f4/matrix.jl
index 67f78f0a..e8132afc 100644
--- a/src/f4/matrix.jl
+++ b/src/f4/matrix.jl
@@ -215,15 +215,16 @@ function reduce_by_pivot!(
     row::Vector{T},
     indices::Vector{ColumnIdx},
     cfs::Vector{T},
-    ch
+    arithmetic::BuiltinArithmeticQQ
 ) where {T <: CoeffQQ}
     @inbounds mul = -row[indices[1]]
-
+    buf2 = arithmetic.buf2
     @inbounds for j in 1:length(indices)
         idx = indices[j]
         row[idx] = row[idx] + mul * cfs[j]
+        # Base.GMP.MPQ.mul!(buf2, cfs[j], mul)
+        # row[idx] = row[idx] + buf2
     end
-
     nothing
 end