Need to print all the function calls Drupal makes
I would recommend using Xdebug as opposed to any other methods.

Xdebug can easily be installed and then all you have to do is enable profiling and navigate around your site.

Not only does it list all function calls but it counts how many times each is called during a request and also times the function call, so you know exactly where to look to resolve bottlenecks.

The results can be viewed using Webgrind (browser-based) or KCacheGrind (KDE/linux), amongst others.

This is more efficient because you are not tampering with the code and littering it with debug statements.