Today's Free App of the Day is Battery Stats Plus Pro
This is a battery optimizer. It looks good, and has nice charts. However, one star reviews cite data collection (there's quite a End User Agreement). Despite what some reviews said, I found it still worked if offline. The data collections is to allow it to compare to other devices, as far as I can tell.
5 of 14 reviews are four stars and above.
So we have a bonus pick: GSam Battery Monitor.
This is a popular and well regarded battery manager. I use it. It also has an icon pack ($0.99--works with all editions, per the product page) that you can purchase which will allow you to put an icon somewhere on your screen that shows when the lock screen is on, which I like. 401 of 443 reviews are four stars and above.
These apps are compatible with the original Fire and with my Fire HD 8.9" 4G. To tell if an app works for your Fire HD or other Android device registered to your Amazon account, click on the above link and look on the right side of the web page. Amazon will tell you if it will work with your registered device.
Also check out the other digital deals from Amazon, including great deals on MP3s and videos: