The route you indicate will have two grades. One just past Mountain home about 26 miles from Fairfield. It is a short 6% climb. The second is just before the Craters of the Moon NM. Another short 6% grade. You can miss the first grade if you stay on I84 to Bliss then take US 26 to US 20 at Cary then on to Craters of the Moon NM.
I have not been on the road from Mountain Home to Cary in a long time. I have traveled the road from Bliss to Arco many times recently. The road is a very good two lane highway with light traffic most of the time.