Its a very easy algorthym.
Should take but 10 seconds for a person to enter the rate info into a spread sheet.
And get the answer. For at what temp the switch over should be.
Of course. If you want to be accurate. You now also must account for the homes load change from day time to night time.
Plus, HPs go into defrost more often at night time then during the day time.
Also when its snowing, or sleeting.
This effects performance efficiency, so they need to build in a weather sensor, and photo sensor to determine solar effect.
Or, by adding pressure and temp transducers. Along with flow sensors. They could determine the output of the heat pump at any give time. And along with the additional sensors to know the actual efficiency of the furnace when it last ran.
Determine which one in reality would be cheapest to run.
All this could be done as an add on to the equoipment and thermostat. So only those that want it. Would have to pay the premiumn price for the few dollars it would save.
All those efficiency ratings you read or hear about, are lab ratings.
Unless your house is a lab. You won't get any of those efficiencies.