I rather doubt a battery saver would ever achieve a 100% increase in life as you suggest (from 1day to 2days). It may comfortably get you through the day and a half perhaps.
Most smartphones suggest it will last a day, whilst many will get much less depending on use.
I would suggest that you carry one of the power banks, I have an EasyAcc power bank that has a capacity of 9200 mAh and that can charge my Samsung Galaxy Nexus 3 to 4 times. That should allow you to let the battery get much lower, as you can hook it up whilst out in needed.
That way you should be able to let the battery get lower before fully recharging it.