LOL. 
I started with a Samsung S3 and graduated to a Note 3. I tried many, highly recommended Apps to improve battery life.
IN the end, the result is, "there is NOT an App for that". At least not one that does a better job than self management of tasks and battery sucking services like bluetooth, hot spot, GPS and of course, the big beautiful screen. (Which did improve with an update a few months ago).
MY preference is to purchase a phone with a user replaceable battery, and possibly buy a spare battery for quick switch outs. It hasn't been an issue with the Note 3. The battery lasts a long time and recharges quickly.
knowledge is power.....