Leaving your heat pump on all day can be more energy-efficient and cost-effective if you have a well-insulated and sealed home that can maintain a consistent temperature throughout the day. In this case, the heat pump doesn't have to work as hard to reach the desired temperature, which can save you money on energy costs. However, if your home is poorly insulated or has air leaks, the heat pump will have to work harder to maintain the desired temperature, which can increase energy costs. In this case, it may be more cost-effective when you're not at home or when the temperature outside is mild. It's also important to consider the cost of electricity in your area. If the electricity rates are high, it may be more cost-effective to turn the heat pump off when you're not home or at night when the temperature outside is lower. It's recommended to program your thermostat to maintain a comfortable temperature when you're home and lower the temperature when you're away or sleeping. You can also use a smart thermostat, which can learn your preferences and adjust the temperature accordingly.