Calcbot
Today Tapbots finally released an update to Calcbot on iOS. I used Calcbot for many years as an alternative to the stock iOS calculator mainly for the expression view and history tape. Calcbot is also available as a Mac app and can sync your history through iCloud.
When Calcbot wasn’t updated for the iPhone 5/5S, I ditched it in favor of Kalky. Kalky is gesture-based for the delete, clear, use result and save functions. It definitely doesn’t look as nice as Calcbot, but it has the features I want and works fast.
Kalky
Most have agreed that the best calculator on iOS is PCalc, however it is way more than I need on a normal basis. For now I’ll stick with Kalky but Calcbot certainly is a great alternative.
I also have used both Calcbot and Pcalc. Just like to add that Calcbot is free but has an In-App purchase of $2 to upgrade to the Pro version which includes ConvertBot that supports conversion of 200 units in 20 categories. Well worth the upgrade.