That much logging is not necessary. There's no reason (in production) to know when each method starts and ends. Maybe you need that on certain methods, but having that much noise in the log files makes them nearly impossible to analyze effectively.
You should log when important things happen such as errors, user logins (audit log), transactions started, important data updated... so on and so forth. If you have a problem that you can't figure out from the logs, then you can add more to it if necessary... but only if necessary.
Also, just for your information, the adding logging in at compile time would be an example of what is called Aspect Oriented Programming. Logging would be the "cross cutting concern".