'In the backyard, the dog barked and howled at the cat' is an example of—

This sentence has one subject (the dog) with two verbs joined by 'and' (barked, howled), and a prepositional phrase. It contains only one independent clause with a compound predicate—no subordinate clauses and no additional independent clauses. Therefore it is a simple sentence. A compound predicate does not make a sentence compound; it remains simple.