Theoretically, it DOES cost a bit more with this exception -- if you happen to manually change the temperature at the same time as your thermostat would (e.g. when temps swing towards warm side more than 3 deg).
There is a term called hysteresis: "Hysteresis refers to systems that have memory, where the effects of the current input (or stimulus) to the system are experienced with a certain delay in time."
So when the thermostat has sent the signal to shut off and the compressor is 'asleep", it takes a while for the system to power up and then start the temp lowering again. So, every time the lower temp signal is off too long for comfort, that is lost time to 'get ahead" of the cooling demand.
However, just leaving thermostat set to one temp is wasteful and more costly, especially at the peak of the heat of the day from 10am to say 5pm, depending on where you live.
FWIW, early at wake-up I set to 78, then set my thermostat temp after 10 am to 74 deg F. After 5pm set back to 78 deg F..that works better for me.
However, a good idea would be to use a setback (prog) thermostat which would adjust time intervals to do those specific times and of course would set it to a weekend non-work schedule etc for sake of efficiency.
Then there's the different issue of how AC unit is energized. The cost of electricity during peak-hours would effect the cost to cool, too.