Savings depends a LOT on how it's programmed. I've even done a setup with a contactor, 24v transformer and standard 24v thermostat. Give MANY more options.
Since the sun heats the house to 78f during the day, cutting the power from the time you leave for work until the sun starts heating the space will save the money. You are "paying for" some of the 78f temp by running the heat until the solar gain can take over. By letting the temp fall before the solar gain takes over you may only be 74f during the afternoon.
I've reviewed the data for my own house and on those "shoulder days" the temp will go DOWN until about noon then go back up due to solar gain. Temp @ 3:30 is a cooler than if I would have let the heat run all day. On the colder days the heat will kick on @ 3:30 to bring the temp up to 68f.
Wake @ 5:30: 70f
Day @ 8:30: 60f
Return @ 3:30: 68f
Sleep @ 11:00: 65f