Recognizing entities that follow or closely resemble a regular expression (regex) pattern is an important task in information extraction. Common approaches for extraction of such entities require humans to either write a regex recognizing an entity or manually label entity mentions in a document corpus. While human effort is critical to build an entity recognition model, surprisingly little is known about how to best invest that effort given a limited time budget. To get an answer, we consider an iterative human-in-the-loop (HIL) framework that allows users to write a regex or manually label entity mentions, followed by training and refining a classifier based on the provided information. We demonstrate on 5 entity recognition tasks that classification accuracy improves over time with either approach. When a user is allowed to choose between regex construction and manual labeling, we discover that (1) if the time budget is low, spending all time for regex construction is often advantageous, (2) if the time budget is high, spending all time for manual labeling seems to be superior, and (3) between those two extremes, writing regexes followed by manual labeling is typically the best approach. Our code and data is available at https://github.com/nymph332088/HILRecognizer.