Bullshit, it doesn't increase your battery life from 6 to 20+.
Android isn't inefficient with your battery if you've turned of WiFi, BT and GPS. How did you get down to 6 hours in the first place, doing nothing, and then to 20+ doing the exact same stuff? Did you measure it honestly, and this was the result?
Anyway, since we can't be sure about your measurement results, have you tried turning it off and on again (your battery program)? Did it work? Was it the cause?
If it IS the cause, then it's harmful in a way. I begin to wonder why you haven't decided to delete it yet.
Go and download every conceivable "This will increase your battery, guaranteed!" program and experience the placebo effect, and become one of the people who dismiss Android as slow, malicious and ignoring privacy preferences.