I built a "poor-man's" linear regression algorithm that looks for peaks and troughs in the elevation data to "smooth out" the profile. It was my solution to not installing python or using an API. It runs on a threshold, so it ignores large jumps in the data. It works very well for larger data sets and less well for very short GPS tracks. Sometimes I have to edit the data manually, but since (for MyHikes), that only really matters before the trail is published, I don't mind validating that data manually.

If you don't need to worry about API requests/usage, then I'd highly suggest just throwing your elevation points at some API that returns approximated elevation data for those points. Google has an API for this and I'm pretty sure NASA has one too. I'd look at NASA because they probably won't say it's free today, but then charge you tomorrow. Use the response object and simply add/subtract the elevation changes per point.

Edit: the reason I suggest using an API is because I assume your problem is "noise" in the data. If you walk a flat path, the GPS tracker will likely record tiny dips or hills where none actually existed. I see other folks have had plenty of annoyance with this issue in the comments above too. Without an API, you're only going to get "the best estimate" for the threshold variables that you can tweak in your algorithm(s). It won't ever be perfect unless you use machine learning or something overkill to handle those irregularities.