diff --git a/benchmarks/Manifest.toml b/benchmarks/Manifest.toml
new file mode 100644
index 0000000..04a5ca5
--- /dev/null
+++ b/benchmarks/Manifest.toml
@@ -0,0 +1,2090 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.10.0"
+manifest_format = "2.0"
+project_hash = "fc77535352bd75512c0fc34d88a679aed4bdf945"
+
+[[deps.AbstractFFTs]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef"
+uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
+version = "1.5.0"
+weakdeps = ["ChainRulesCore", "Test"]
+
+    [deps.AbstractFFTs.extensions]
+    AbstractFFTsChainRulesCoreExt = "ChainRulesCore"
+    AbstractFFTsTestExt = "Test"
+
+[[deps.Adapt]]
+deps = ["LinearAlgebra", "Requires"]
+git-tree-sha1 = "cde29ddf7e5726c9fb511f340244ea3481267608"
+uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+version = "3.7.2"
+weakdeps = ["StaticArrays"]
+
+    [deps.Adapt.extensions]
+    AdaptStaticArraysExt = "StaticArrays"
+
+[[deps.ArgCheck]]
+git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4"
+uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
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+
+[[deps.ArgTools]]
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+
+[[deps.Arpack]]
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+
+[[deps.Arpack_jll]]
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+[[deps.Artifacts]]
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+
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+
+[[deps.AtomsBase]]
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+
+[[deps.AxisAlgorithms]]
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+
+[[deps.BFloat16s]]
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+version = "0.4.2"
+
+[[deps.BangBang]]
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+
+    [deps.BangBang.extensions]
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+    BangBangDataFramesExt = "DataFrames"
+    BangBangStaticArraysExt = "StaticArrays"
+    BangBangStructArraysExt = "StructArrays"
+    BangBangTypedTablesExt = "TypedTables"
+
+    [deps.BangBang.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+    TypedTables = "9d95f2ec-7b3d-5a63-8d20-e2491e220bb9"
+
+[[deps.Base64]]
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+
+    [deps.CategoricalArrays.extensions]
+    CategoricalArraysJSONExt = "JSON"
+    CategoricalArraysRecipesBaseExt = "RecipesBase"
+    CategoricalArraysSentinelArraysExt = "SentinelArrays"
+    CategoricalArraysStructTypesExt = "StructTypes"
+
+[[deps.ChainRulesCore]]
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diff --git a/benchmarks/Project.toml b/benchmarks/Project.toml
new file mode 100644
index 0000000..657e33a
--- /dev/null
+++ b/benchmarks/Project.toml
@@ -0,0 +1,16 @@
+[deps]
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+Conda = "8f4d0f93-b110-5947-807f-2305c1781a2d"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+ExpectationMaximization = "e1fe09cc-5134-44c2-a941-50f4cd97986a"
+GaussianMixtures = "cc18c42c-b769-54ff-9e2a-b28141a64aae"
+LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
+LogExpFunctions = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
+MLDatasets = "eb30cadb-4394-5ae3-aed4-317e484a6458"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"
+RCall = "6f49c342-dc21-5d91-9882-a32aef131414"
+RDatasets = "ce6b1742-4840-55fa-b093-852dadbb1d8b"
+Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
+StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
+Traceur = "37b6cedf-1f77-55f8-9503-c64b63398394"
diff --git a/benchmarks/benchmark_v2_K2_unidim.jl b/benchmarks/benchmark_v2_K2_unidim.jl
new file mode 100644
index 0000000..759e9d4
--- /dev/null
+++ b/benchmarks/benchmark_v2_K2_unidim.jl
@@ -0,0 +1,165 @@
+# Benchmarking
+
+using Distributions, Random
+using BenchmarkTools, Test
+using RCall
+using GaussianMixtures # v0.3.8
+using StatsPlots
+using ExpectationMaximization # v0.2.2
+using PyCall
+using Conda
+using LinearAlgebra
+using LaTeXStrings
+# @rimport microbenchmark # One could use that to benchmark in R to prevent a potential overhead time of using RCall.
+# timeit = pyimport("timeit")  # One could use that to benchmark in Python to prevent a potential overhead time of using PyCall.
+
+@rimport mixtools # https://www.rdocumentation.org/packages/mixtools/versions/2.0.0
+
+os = pyimport("os")
+os.environ["OMP_NUM_THREADS"] = "1"
+
+np = pyimport("numpy")
+sklearn = pyimport("sklearn.mixture") # scikit-learn 1.3.2
+mixem = pyimport("mixem")
+
+# GaussianMixtures.jl
+function jl_GMM(y, mu, sigma, alpha, iters=100)
+    gmm = GMM(length(mu), 1)  # initialize an empty GMM object
+    # stick in our starting values
+    gmm.μ[:, 1] .= mu
+    gmm.Σ[:, 1] .= sigma
+    gmm.w[:, 1] .= alpha
+
+    # run em!
+    # em!(gmm, y[:, :], nIter=iters)
+    res = copy(gmm)
+    em!(res, y[:,:], nIter=iters)
+    time = @belapsed $em!(g, $(y[:,:]), nIter=iters) setup=(g = copy($gmm))
+    return time, res
+end
+
+py_EM = sklearn.GaussianMixture
+function py_sklearn(y, mu, sigma, alpha, iters=100; infos=0, verbose_interval=1, tol=1e-5)
+    precisions_init = [inv(Diagonal(sigma .^ 2))[i, i] for i in eachindex(mu)]
+    K = length(mu)
+    Y = reshape(y, (length(y), 1))
+    MU = reshape(mu, (length(mu), 1))
+    invsigma2 = reshape(precisions_init, (length(precisions_init), 1))
+    g₀ = py_EM(n_components=K, covariance_type="diag", weights_init=alpha, means_init=MU, precisions_init=invsigma2, max_iter=iters, warm_start=false, verbose=infos, verbose_interval=verbose_interval, tol=tol).fit
+    g = g₀
+    res = g(Y)
+    time = @belapsed g($Y) setup=(g = $g₀)
+    return time, res
+end
+
+# py_mixemEM = mixem.em
+# function py_mixem(y, mu, sigma, alpha, iters=100)
+#     K = length(mu)
+#     dists = [mixem.distribution.NormalDistribution(mu=mu[i], sigma=sigma[i]) for i in 1:K]
+#     return @belapsed $py_mixemEM($y, dists, initial_weights=alpha, max_iterations=iters, progress_callback = :none, tol=1e-5, tol_iters=1)
+# end
+
+function my_em(y, mu, sigma, alpha, iters=100)
+    mix = MixtureModel([Normal(mu[i], sigma[i]) for i in eachindex(mu)], alpha)
+    res = fit_mle(mix, y, maxiter=iters, atol=1e-5)
+    time = @belapsed $fit_mle($mix, $y, maxiter=$iters, atol=$1e-5)
+    return time, res
+end
+
+# function in question
+R_EM = mixtools.normalmixEM
+
+function R_mixtools(y, mu, sigma, alpha, iters=100)
+    K = length(mu)
+    res = R_EM(y, k=K, lambda=alpha, mu=mu, sigma=sigma, maxit=iters, epsilon=1e-5)
+    time = @belapsed $R_EM($y, k=$K, lambda=$alpha, mu=$mu, sigma=$sigma, maxit=$iters, epsilon=$1e-5)
+    return time, res
+end
+
+Names = ["ExpectationMaximization.jl", "GaussianMixtureModel.jl", "mixtools.R", "Sklearn.py", "mixem.py"]
+# true values
+μ = [-4, 10]
+σ = [2, 10]
+α = [0.8, 0.2]
+mi = MixtureModel([Normal(μ[i], σ[i]) for i in eachindex(μ)], α)
+
+# guess 
+mu = [-1, 1]
+sigma = [1, 1]
+alpha = [0.5, 0.5]
+
+iters = 8
+NN = Int[500, 1000, 5000, 1e4, 5e4, 1e5, 5e5, 1e6]
+
+KK = [2]
+
+d = Dict{String,Matrix}()
+for key in Names
+    d[key] = ones(length(NN), length(KK))
+end
+
+for j in eachindex(KK)
+    K = KK[j]
+    for i in eachindex(NN)
+        rtol = 1e-2
+        Random.seed!(3333)
+        n = NN[i]
+        y = rand(mi, n)
+        @show n
+
+        # I found that @belapsed was suspect (sometimes asking to define y while it was already defined)
+        d["ExpectationMaximization.jl"][i, j], res_my = my_em(y, mu, sigma, alpha, iters)
+        d["GaussianMixtureModel.jl"][i, j], res_gmm = jl_GMM(y, mu, sigma, alpha, iters)
+
+        # This is suspect since it triggers a warning regarding Kmean which I do not want to use. 
+        # I asked a question [here](https://github.com/scikit-learn/scikit-learn/discussions/25916)
+        # Plus there seem to have a long compilation time
+        d["Sklearn.py"][i, j], res_sk = py_sklearn(y, mu, sigma, alpha, iters)
+
+        # this one seems to overflow for n larger than ~500, I believe it is due to the way log(sum(exp))...
+        # def logsumexp(X,axis=None,keepdims=1,log=1):
+        # d["mixem.py"][i, j] = py_mixem(y, mu, sigma, alpha, iters)
+
+        # this seems to work just fine (just print an annoying warning about convergence that I could not remove)
+        d["mixtools.R"][i, j], res_R = R_mixtools(y, mu, sigma, alpha, iters)
+
+        # mixtools vs EM.jl
+        @test mean.(res_my.components) ≈  res_R[3][1:K] rtol = rtol
+        @test std.(res_my.components) ≈ res_R[4][1:K] rtol = rtol
+        @test probs(res_my) ≈ res_R[2][1:K] rtol = rtol
+
+        # mixtools vs py_sklearn
+        @test vec(res_sk.means_) ≈  res_R[3][1:K] rtol = rtol
+        @test sqrt.(vec(res_sk.covariances_)) ≈ res_R[4][1:K] rtol = rtol
+        @test res_sk.weights_ ≈ res_R[2][1:K] rtol = rtol
+
+        # mixtools vs gmm.jl
+        @test vec(res_gmm.μ) ≈  res_R[3][1:K] rtol = rtol
+        @test sqrt.(vec(res_gmm.Σ)) ≈ res_R[4][1:K] rtol = rtol
+        @test res_gmm.w ≈ res_R[2][1:K] rtol = rtol
+    end
+end
+
+# Random.seed!(3333)
+# n = 500
+# i = 1
+# j =1
+# y = rand(mi, n)
+# d["mixem.py"][i, j] = py_mixem(y, mu, sigma, alpha, iters)
+
+xNN = 10 .^ (2:6)
+yti = 10 .^ (-4.0:1)
+default(fontfamily="Computer Modern", linewidth=1, label=nothing)
+begin
+    K = 2
+    plot(legend=:topleft, size=(900, 800), legendfontsize = 16)
+    [plot!(NN, d[key][:, 1], label=key, c=na) for (na, key) in collect(enumerate(Names))[1:end-1]]
+    # scatter!([NN[1]], [d[Names[end]][1, 1]], label=Names[end], c=length(Names))
+    ylabel!("Time (s)", ylabelfontsize = 16)
+    yaxis!(:log10)
+    xaxis!(:log10)
+    xlabel!(L"n", xlabelfontsize = 18)
+    xticks!(xNN, xtickfontsize = 16)
+    yticks!(yti, ytickfontsize = 16, minorticks=9, minorgrid=true, gridalpha=0.3, minorgridalpha=0.15)
+end
+savefig("timing_K_2.svg")
diff --git a/docs/src/benchmarks.md b/docs/src/benchmarks.md
index a6a5c00..2cc4423 100644
--- a/docs/src/benchmarks.md
+++ b/docs/src/benchmarks.md
@@ -21,7 +21,7 @@ You can find the benchmark code [here](https://github.com/dmetivie/ExpectationMa
 
 **Conclusion: for Gaussian mixtures, `ExpectationMaximization.jl` is about 2 to 10 times faster than Python or R implementations** and about as fast as the specialized Julia package `GaussianMixturesModel.jl`.
 
-![timing_K_2_rudimentary_wo_memory_leak](https://user-images.githubusercontent.com/46794064/227195619-c75b9276-932b-4029-8b49-6cce919acc87.svg)
+![timing_K_2](https://github.com/dmetivie/ExpectationMaximization.jl/assets/46794064/57bd5671-1082-4514-9a9e-c611f9c923df)
 
 [^1]: Note that `@btime` with `RCall` and `PyCall` might produce a small-time overhead compared to the pure R/Python time; see [here for example](https://discourse.julialang.org/t/benchmarking-julia-vs-python-vs-r-with-pycall-and-rcall/37308).
 I did compare with `R` `microbenchmark` and Python `timeit` and they produced very similar timing but in my experience `BenchmarkTools.jl` is smarter and simpler to use, i.e. it will figure out alone the number of repetition to do in function of the run.
diff --git a/img/timing_K_2.svg b/img/timing_K_2.svg
new file mode 100644
index 0000000..dfc9b2c
--- /dev/null
+++ b/img/timing_K_2.svg
@@ -0,0 +1,178 @@
+<?xml version="1.0" encoding="utf-8"?>
+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="900" height="800" viewBox="0 0 3600 3200">
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