Any suggestions for how to clean up this search bar while retaining functionality would be of great help.
What kind of questions should I be trying to answer in order to remove or change things around.
By "retaining functionality" I imply that you want us to tell you how to clean up this search bar without cleaning it up: The Filter for where to search in should remain, the boolean options should remain, and the sorting should remain.
If this is what you want you can stop reading this post right now.
Still here? Get rid of the options. Offer them as a helpful link on the results page, like YouTube's filter button:
There are two scenarios in which an advanced search makes sense:
In any other scenario, the added functionality is a) confusing and b) burdening the user with decisions your search algorithm should make. Your search should be sophisticated, not the user. Take the hard work off the user's hand.
A simple search box is good enough for Amazon: Tens of thousands of products. A simple search box is good enough for YouTube: Billions of videos. A simple search box is good enough for Google: Amazon, plus YouTube, plus the internet.
And while yes, in Google's search you can use boolean operators. And yes, in YouTube you can further filter your results, as you can in Amazon, for the vast majority of all searches, the best and most efficient solution is this:
If you have some power users who use boolean operators and exact matching, offer them the same functionality google does and let them type those queries in the search field.
If you have only power users, see above: They will learn fast and also have an easier time typing the query than "selecting" it.
And last, but really actually first: All your casual users will appreciate the simplicity. Of all your current users probably 1–3 % will miss the additional functionality on this form, while the remaining 97-99 % will be happy to find an easy, familiar search box.