Save energy using the information of the time that system uses to turn off the screen automatically.
Crossing info of the last tap on the screen with the time that the system uses to automatically turn off the screen you can make the app to check if the user is looking less often and saving energy.
If is impossible to an app know when the screen is about to turn off why don't use the information of the time that system uses to turn off the screen automatically? If it's impossible to retrieve this information with the system you can make the user set this information on the app.
This is already done with the scan lives system.