I could minimize some of the fields, but the larger point I should have made is that when I was typing the regex the first time, I was looking at the cheat sheet. The workflow I found myself fall into was:

1. Enter the test string.

2. Look at the cheat sheet and type into the regex field.

3. Look at the matches and test field to see if it was correct.

4. If incorrect, look at the explanation.

5. Go back to (2)

So for me, the default layout didn't handle my step (2) very well. I'm not saying that's the workflow you should optimize the UX for, but it's what mine was.