diff --git a/examples/speed_tests_numba_and_cython.ipynb b/examples/speed_tests_numba_and_cython.ipynb
index 665ad7f..d7e0c28 100644
--- a/examples/speed_tests_numba_and_cython.ipynb
+++ b/examples/speed_tests_numba_and_cython.ipynb
@@ -36,13 +36,72 @@
     },
     {
       "cell_type": "code",
-      "execution_count": null,
+      "execution_count": 2,
       "metadata": {
         "cellView": "form",
         "collapsed": true,
-        "id": "oDEK94GOaK4Q"
+        "id": "oDEK94GOaK4Q",
+        "outputId": "60a49850-f2f7-4e7a-b827-1686d291a681",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        }
       },
-      "outputs": [],
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Collecting fast_wave\n",
+            "  Downloading fast_wave-1.5.1-py3-none-any.whl.metadata (14 kB)\n",
+            "Collecting llvmlite==0.42.0 (from fast_wave)\n",
+            "  Downloading llvmlite-0.42.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (4.8 kB)\n",
+            "Requirement already satisfied: mpmath==1.3.0 in /usr/local/lib/python3.10/dist-packages (from fast_wave) (1.3.0)\n",
+            "Collecting numba==0.59.1 (from fast_wave)\n",
+            "  Downloading numba-0.59.1-cp310-cp310-manylinux2014_x86_64.manylinux_2_17_x86_64.whl.metadata (2.7 kB)\n",
+            "Requirement already satisfied: numpy==1.26.4 in /usr/local/lib/python3.10/dist-packages (from fast_wave) (1.26.4)\n",
+            "Collecting sympy==1.12 (from fast_wave)\n",
+            "  Downloading sympy-1.12-py3-none-any.whl.metadata (12 kB)\n",
+            "Collecting cython==3.0.10 (from fast_wave)\n",
+            "  Downloading Cython-3.0.10-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (3.2 kB)\n",
+            "Downloading fast_wave-1.5.1-py3-none-any.whl (320 kB)\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m320.7/320.7 kB\u001b[0m \u001b[31m5.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25hDownloading Cython-3.0.10-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (3.6 MB)\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m3.6/3.6 MB\u001b[0m \u001b[31m33.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25hDownloading llvmlite-0.42.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (43.8 MB)\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m43.8/43.8 MB\u001b[0m \u001b[31m15.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25hDownloading numba-0.59.1-cp310-cp310-manylinux2014_x86_64.manylinux_2_17_x86_64.whl (3.7 MB)\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m3.7/3.7 MB\u001b[0m \u001b[31m41.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25hDownloading sympy-1.12-py3-none-any.whl (5.7 MB)\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m5.7/5.7 MB\u001b[0m \u001b[31m50.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25hInstalling collected packages: sympy, llvmlite, cython, numba, fast_wave\n",
+            "  Attempting uninstall: sympy\n",
+            "    Found existing installation: sympy 1.13.1\n",
+            "    Uninstalling sympy-1.13.1:\n",
+            "      Successfully uninstalled sympy-1.13.1\n",
+            "  Attempting uninstall: llvmlite\n",
+            "    Found existing installation: llvmlite 0.43.0\n",
+            "    Uninstalling llvmlite-0.43.0:\n",
+            "      Successfully uninstalled llvmlite-0.43.0\n",
+            "  Attempting uninstall: cython\n",
+            "    Found existing installation: Cython 3.0.11\n",
+            "    Uninstalling Cython-3.0.11:\n",
+            "      Successfully uninstalled Cython-3.0.11\n",
+            "  Attempting uninstall: numba\n",
+            "    Found existing installation: numba 0.60.0\n",
+            "    Uninstalling numba-0.60.0:\n",
+            "      Successfully uninstalled numba-0.60.0\n",
+            "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
+            "torch 2.5.1+cu121 requires sympy==1.13.1; python_version >= \"3.9\", but you have sympy 1.12 which is incompatible.\u001b[0m\u001b[31m\n",
+            "\u001b[0mSuccessfully installed cython-3.0.10 fast_wave-1.5.1 llvmlite-0.42.0 numba-0.59.1 sympy-1.12\n",
+            "Collecting mrmustard\n",
+            "  Downloading mrmustard-0.7.3-py3-none-any.whl.metadata (15 kB)\n",
+            "Downloading mrmustard-0.7.3-py3-none-any.whl (217 kB)\n",
+            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m217.6/217.6 kB\u001b[0m \u001b[31m4.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25hInstalling collected packages: mrmustard\n",
+            "Successfully installed mrmustard-0.7.3\n"
+          ]
+        }
+      ],
       "source": [
         "#@title Installation\n",
         "!pip install fast_wave\n",
@@ -51,12 +110,24 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 50,
+      "execution_count": 3,
       "metadata": {
         "cellView": "form",
-        "id": "xKirGWMNdvAs"
+        "id": "xKirGWMNdvAs",
+        "outputId": "4bb2598f-c155-4698-dbc7-dcf1dd82a693",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        }
       },
-      "outputs": [],
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Functionality Test Passed: True\n"
+          ]
+        }
+      ],
       "source": [
         "#@title Imports and Definitions\n",
         "import time\n",
@@ -292,7 +363,7 @@
         "n = 5 #@param\n",
         "x_max = 5.0 #@param\n",
         "x_min = -5.0 #@param\n",
-        "number_of_points = 5000 #@param\n",
+        "number_of_points = 50 #@param\n",
         "\n",
         "x_values = np.linspace(x_min, x_max, number_of_points)\n",
         "\n",
@@ -321,7 +392,7 @@
         ")])\n",
         "\n",
         "fig.update_layout(\n",
-        "    title=\"Runtime Comparison\",\n",
+        "    title=\"Performance Comparison\",\n",
         "    xaxis_title=\"Approach\",\n",
         "    yaxis_title=\"Runtime (s)\",\n",
         "    bargap=0.6,\n",
@@ -339,13 +410,13 @@
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         "cellView": "form",
-        "outputId": "d37e2558-0e0c-41a5-d849-e5fee91c8e1b",
+        "outputId": "6f05682e-5053-4c1b-d546-907dad5ab645",
         "colab": {
           "base_uri": "https://localhost:8080/",
           "height": 437
         }
       },
-      "execution_count": 60,
+      "execution_count": 11,
       "outputs": [
         {
           "output_type": "display_data",
@@ -355,9 +426,9 @@
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