Organizing Code in your WordPress Theme's functions.php File?

The more customization I make to WordPress the more I start thinking about if I should be organizing this file or splitting it up.

More specifically, if I have a bunch of custom functions which only apply to the admin area and others which just apply to my public website is there any reason to possibly include all admin functions within their own file or group them together?

Would splitting them up into separate files or grouping them together possibly speed up a WordPress website or does WordPress/PHP automatically skip over functions which have an is_admin code prefix?

What’s the best way to deal with a large functions file (mine is 1370 lines long).

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