One advantage our fast-check property-based tests have over the fuzzer is they can only reference eight fields. The fuzzer can reference many more.

This means its search space is much smaller, but it is more likely to hit different types of plans. For example with eight fields, covered plans, distinct plans, plans using indexes to satisfy a sort, etc are more likely. I believe this is part of why the fast-check PBTs have been effective.

We could create a new fuzzer variant that can only reference a few fields. Since the fuzzer models many more aggregation stages, it's capable of finding bugs that our core property-based tests cannot. The index grammar, query grammar, and document grammar should reference this smaller set of fields.

One issue we may run into is hitting more covered plans, which have caused lots of fuzzer noise because of SERVER-12869. We could solve this by simply not including null in the collections.