“In her online search for ?Mr. Right,? a timid computer programmer builds an algorithm that evolves into a rogue Artificial Intelligence?which the government wants to terminate.”

This logline sets up only a situation. It establishes the beginning status quo of the film, or show(I assume film). Either way, ?at the beginning she has the algorithm/A.I. Now, since the government wants to destroy it, what is the event that alerts the protagonist to this antagonist? ?Do they try to steal it, breaking into her home/lab/whatever? Do they try to kill her? ?As a result of the inciting incident, what does she do? I assume she wants to protect the A.I or use it for something specific. How does she go about doing this?
Is there a specific antagonist who can be identified? The agent in charge, a specific solider, someone? In other words, who is the Darth Vader among the Storm Troopers of your story?
Here’s an example using elements from your post:?After her lab is broken into, a timid computer programmer must track and destroy the rogue A.I she accidentally created before the government kills her for it. (27)

In order to gain a better understanding of loglines, I recommend studying the Formula tab at the top of the page, and even more importantly, reviewing and studying other people’s loglines, and the feedback they receive. Once you can identify what works and what doesn’t in other loglines, then it will help your own.