update example

README.md

@@ -22,13 +22,46 @@ This API is similar to the Pytorch API, making it simple to adapt to your usecas
 
 ## QuickStart
 If you know PyTorch, you know 80% of TextGrad. 
-Let's walk through the key components with a simple example. Say we want to use GPT-4o to improve a solution to a math problem using TextGrad.
+Let's walk through the key components with a simple example. Say we want to use GPT-4o to solve a simple
+reasoning problem.
+
+The question is "If it takes 1 hour to dry 25 shirts under the sun, how long will it take to dry 30 shirts under the sun? Reason step by step."
+If you think about it **the answer is 1 hour**, since the number of shirts doesn't affect the time it takes to dry them.
+
 ```python
 import textgrad as tg
-# Step 1: Get an initial response from an LLM.
+
+tg.set_backward_engine("gpt-4o", override=True)
+
 model = tg.BlackboxLLM("gpt-4o")
-punchline = model(tg.Variable("write a punchline for my github package about optimizing compound AI systems", role_description="prompt", requires_grad=False))
-punchline.set_role_description("a concise punchline that must hook everyone")
+question_string = "If it takes 1 hour to dry 25 shirts under the sun, how long will it take to dry 30 shirts under the sun? Reason step by step"
+question = tg.Variable(question_string, role_description="question to the LLM", requires_grad=False)
+
+answer = model(question)
+# answer: To determine how long it will take to dry 30 shirts under the sun, 
+# we can use a proportional relationship based on the given information. 
+# Here’s the step-by-step reasoning: [.....]
+#  So, it will take 1.2 hours (or 1 hour and 12 minutes) to dry 30 shirts under the sun.
+```
+
+```python
+
+answer.set_role_description("concise and accurate answer to the question")
+
+optimizer = tg.TGD(parameters=[answer])
+evaluation_instruction = f"Here's a question: {question_string}. Evaluate any given answer to this question, be smart, logical, and very critical. Just provide concise feedback."
+loss_fn = tg.TextLoss(evaluation_instruction)
+loss = loss_fn(answer)
+# loss: [...] Your step-by-step reasoning is clear and logical, 
+# but it contains a critical flaw in the assumption that drying time is directly proportional 
+# to the number of shirts. [..]
+
+loss.backward()
+optimizer.step()
+# answer: It will still take 1 hour to dry 30 shirts under the sun, 
+# assuming they are all laid out properly to receive equal sunlight.
+
+
 ```
 
 Initial `punchline` from the model: