Can't find my Sims 3 Pets EP code on regedit

Okay, so I recently bought a new computer and I got Origin and I got all my Sims 3 Expansion Packs on it except one: Pets. I looked up online to see how to retrieve that code, so I did. I went to windows button then typed regedit, then went to Computer then HKEY_LOCAL_MACHINE, then SOFTWARE, then Wow6432Node then Electronic Arts, then Sims and I couldn't find the Pets Expansion Pack. I went onto Sims and to the home page when you click "Play", the page after that. Anyways, on that page it said at the bottom that I had pets installed and everything. So then I went to play Sims to make sure and I had all the clothes and furniture from Pets. It was perfectly fine. I have no idea what it wrong so if you could give me some advice or give me a new code, I would really appreciate it. Thanks!