The :eprof module is part of the :tools application (see eprof — tools v4.1.1). So :tools is the application you want to add to extra_applications if your application generally needs access to eprof. If you just need it on occasion you can also use Mix.ensure_application!/1.
Afaik some of these modules had been shuffled around a bit in recent OTP version – not sure when exactly. E.g. :observer used to be in :runtime_tools instead of its own application.