This doesn't directly answer your question bu seems to b a highly accurate calculator for heating costs:
SWIMMING POOL ENERGY TEMPERATURE CALCULATOR | Neil Anderson
At about $2.65 per degree (if you get 3 degrees an hour) it will depend how many days between uses I suspect.
Here, in Michigan with a cover on and even freezing temps but inside a dome, I'm not losing much more than 5 degrees a day or less right now over a 14 hr period with heater off. (My nat gas is only .70 per CCF so about $1.50 per degree.)
So for me to swim daily its $7.50 at the moment. BUT I heat it to 94 for 5-6 hrs and then turn heater off, without Thermostatting, which is IMHO cheaper at least in these kind of extremes.
If I let it drop to 40 from 94 over a few days, (degree differential of air to water, times surface area of pool, x 5 btu into volume of your btu to equal 1 degree for your water...eg in my case, one degree in 24k is worth about 200,000 btu) ...
It would take me at least 54 hours at 1.50 to get back up to temp IF my 266k btu heater could stay at 1 degree an hour (depends on differential). So that's $82...or more than ten days of heat
Make sense?