fix error and deprecate

examples/notebooks/experimental_engines/Tutorial-Solution-Optimization.ipynb

@@ -0,0 +1,176 @@
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+   "source": [
+    "## Tutorial: Running Solution Optimization\n",
+    "\n",
+    "![TextGrad](https://github.com/vinid/data/blob/master/logo_full.png?raw=true)\n",
+    "\n",
+    "An autograd engine -- for textual gradients!\n",
+    "\n",
+    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/zou-group/TextGrad/blob/main/examples/notebooks/Prompt-Optimization.ipynb)\n",
+    "[![GitHub license](https://img.shields.io/badge/License-MIT-blue.svg)](https://lbesson.mit-license.org/)\n",
+    "[![Arxiv](https://img.shields.io/badge/arXiv-2406.07496-B31B1B.svg)](https://arxiv.org/abs/2406.07496)\n",
+    "[![Documentation Status](https://readthedocs.org/projects/textgrad/badge/?version=latest)](https://textgrad.readthedocs.io/en/latest/?badge=latest)\n",
+    "[![PyPI - Python Version](https://img.shields.io/pypi/pyversions/textgrad)](https://pypi.org/project/textgrad/)\n",
+    "[![PyPI](https://img.shields.io/pypi/v/textgrad)](https://pypi.org/project/textgrad/)\n",
+    "\n",
+    "**Objectives:**\n",
+    "\n",
+    "* In this tutorial, we will implement a solution optimization pipeline.\n",
+    "\n",
+    "**Requirements:**\n",
+    "\n",
+    "* You need to have an OpenAI API key to run this tutorial. This should be set as an environment variable as OPENAI_API_KEY.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "1f6e021565d0c914",
+   "metadata": {
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+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/federicobianchi/.pyenv/versions/3.11.9/lib/python3.11/site-packages/pydantic/_internal/_config.py:341: UserWarning: Valid config keys have changed in V2:\n",
+      "* 'underscore_attrs_are_private' has been removed\n",
+      "  warnings.warn(message, UserWarning)\n"
+     ]
+    }
+   ],
+   "source": [
+    "#!pip install textgrad # you might need to restart the notebook after installing textgrad\n",
+    "\n",
+    "from dotenv import load_dotenv\n",
+    "load_dotenv()\n",
+    "import textgrad as tg\n",
+    "tg.set_backward_engine(tg.get_engine(\"experimental:gpt-4o\"))\n",
+    "\n",
+    "initial_solution = \"\"\"To solve the equation 3x^2 - 7x + 2 = 0, we use the quadratic formula:\n",
+    "x = (-b ± √(b^2 - 4ac)) / 2a\n",
+    "a = 3, b = -7, c = 2\n",
+    "x = (7 ± √((-7)^2 + 4(3)(2))) / 6\n",
+    "x = (7 ± √73) / 6\n",
+    "The solutions are:\n",
+    "x1 = (7 + √73)\n",
+    "x2 = (7 - √73)\"\"\"\n",
+    "\n",
+    "solution = tg.Variable(initial_solution,\n",
+    "                       requires_grad=True,\n",
+    "                       role_description=\"solution to the math question\")\n",
+    "\n",
+    "loss_system_prompt = tg.Variable(\"\"\"You will evaluate a solution to a math question. \n",
+    "Do not attempt to solve it yourself, do not give a solution, only identify errors. Be super concise.\"\"\",\n",
+    "                                 requires_grad=False,\n",
+    "                                 role_description=\"system prompt\")\n",
+    "                              \n",
+    "loss_fn = tg.TextLoss(loss_system_prompt)\n",
+    "optimizer = tg.TGD([solution])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "169c07c1-a01d-4309-9fd4-a6f9fb52daf4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Variable(value=There are calculation errors in applying the quadratic formula and in the final solutions:\n",
+       "\n",
+       "1. **Quadratic Formula Error**: The discriminant calculation is incorrect. It should be \\( b^2 - 4ac \\), not \\( b^2 + 4ac \\).\n",
+       "\n",
+       "2. **Discriminant Error**: The discriminant is calculated incorrectly. It should be \\( (-7)^2 - 4(3)(2) = 49 - 24 = 25 \\).\n",
+       "\n",
+       "3. **Square Root Error**: The square root of the discriminant should be \\( \\sqrt{25} = 5 \\), not \\( \\sqrt{73} \\).\n",
+       "\n",
+       "4. **Solutions Error**: The solutions do not incorporate the division by 6. The correct expressions for the solutions should involve \\((7 ± 5) / 6\\).\n",
+       "\n",
+       "5. **Final Numerical Error**: The final solutions provided do not simplify after dividing by 6. Adjust the ± part before dividing., role=response from the language model, grads=set())"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "loss = loss_fn(solution)\n",
+    "loss"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "a2fce8c1-6838-4aaf-b830-de34effe44db",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "To solve the equation 3x^2 - 7x + 2 = 0, we use the quadratic formula:\n",
+      "\\[ x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a} \\]\n",
+      "a = 3, b = -7, c = 2\n",
+      "\\[ x = \\frac{7 \\pm \\sqrt{(-7)^2 - 4(3)(2)}}{6} \\]\n",
+      "\\[ x = \\frac{7 \\pm \\sqrt{25}}{6} \\]\n",
+      "\\[ x = \\frac{7 \\pm 5}{6} \\]\n",
+      "The solutions are:\n",
+      "\\[ x1 = \\frac{7 + 5}{6} = 2 \\]\n",
+      "\\[ x2 = \\frac{7 - 5}{6} = \\frac{1}{3} \\]\n"
+     ]
+    }
+   ],
+   "source": [
+    "loss.backward()\n",
+    "optimizer.step()\n",
+    "print(solution.value)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4e9e4cb2-1c6e-499f-bfd6-efa47461f6a6",
+   "metadata": {},
+   "outputs": [],
+   "source": []
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