add README for prompt engineering example

Author: ZhengyaoJiang

examples/prompt/README.md

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+# AIME 2024 Prompt‑Engineering Example
+This example shows how **Weco** can iteratively improve a prompt for solving American Invitational Mathematics Examination (AIME) problems. The experiment runs locally, requires only two short Python files, and finishes in a few hours on a laptop.
+
+## Files in this folder
+
+| File | Purpose |
+| --- | --- |
+| `optimize.py` | Holds the prompt template, the mutable `EXTRA_INSTRUCTIONS` string, and the LLM call. Weco edits **only** this file during the search. |
+| `eval_aime.py` | Downloads a small slice of the 2024 AIME dataset, calls `optimize.solve` in parallel, prints progress logs, and finally prints an `accuracy:` line that Weco reads. |
+
+## Quick start
+
+1. **Clone the repository and enter the folder.**
+   ```bash
+   git clone https://github.com/your‑fork/weco‑examples.git
+   cd weco‑examples/aime‑2024
+   ```
+2. **Run Weco.**  The command below edits `EXTRA_INSTRUCTIONS` in `optimize.py`, invokes `eval.py` on every iteration, reads the printed accuracy, and keeps the best variants.
+   ```bash
+   weco --source optimize.py \
+        --eval-command "python eval.py" \
+        --metric accuracy \
+        --maximize true \
+        --steps 40 \
+        --model gemini-2.5-pro-exp-03-25
+   ```
+
+During each evaluation round you will see log lines similar to the following.
+
+```text
+[setup] loading 20 problems from AIME 2024 …
+[progress] 5/20 completed, elapsed 7.3 s
+[progress] 10/20 completed, elapsed 14.6 s
+[progress] 15/20 completed, elapsed 21.8 s
+[progress] 20/20 completed, elapsed 28.9 s
+accuracy: 0.0500
+```
+
+Weco then mutates the suffix, tries again, and gradually pushes the accuracy higher. On a modern laptop you can usually double the baseline score within thirty to forty iterations.
+
+## How it works
+
+* `eval_aime.py` slices the **Maxwell‑Jia/AIME_2024** dataset to twenty problems for fast feedback. You can change the slice in one line.
+* The script sends model calls in parallel via `ThreadPoolExecutor`, so network latency is hidden.
+* Every five completed items, the script logs progress and elapsed time.
+* The final line `accuracy: value` is the only part Weco needs for guidance.