A secondary question: On a Mitsubishi, is there any way to determine the energy used and delivered separately for heating and DHW so that SCOP can be evaluated for each?  

I really though should monitor how much less it cost in the evening after having the heating on throughout the day.

...  If as a result you can turn the flow temp down then that could make quite a difference!

Iv done a small amount of juggling with times monitoring my hour electricity bill throughout the day. Basically with the heating on during the daytime I’m paying around 30p an hour.

With a 2c setback it’s around 3p an hour.

So that 7hour period it’s approximately £1.75 a day extra to heat all day.

I really though should monitor how much less it cost in the evening after having the heating on throughout the day.

Your DHW COP is 4/2.5 = 1.6

As you imply sacrificing COP for low cost electricity saves money.  Its possible that you would save money by cancelling the daytime setback, its the most efficient time to generate heat and would mean you might be able to drop the FT  bit.  The saving in loss from the house due to a 2C setback for say 8 hours is less than 5%.  Only careful experimentation (which is difficult) will tell you.

below are figures from an typical

day. My initial figures were from a day when I did use a lot more hot water than normal.

As I’m on an EV tariff, 6.7p midnight to 7am I heat my water then at a high of 60c. This way I feel I can make good use of the low rate. Also enables me to turn off legionnaires setting.

I have the heat pump set to 20c but at 18c during the day when no one is home.

Graphs hopefully below.

COP= approximately 2.85

Overall about 43/15 = 2.85

However this is made up of space heating COP and DHW COP, which normally are quoted separately, because they are typically very different and respond to different adjustments.  As you have truncated the bottom plot its impossible to break them out.  Can you post the rest of the plot please and what temperature do you heat your DHW to?  It looks to me like you may be spending more on DHW than you need to, unless of course you actually use a lot.

COP= approximately 2.85

I have assumed that the energy in contributes to the total heat out although this may not be completely correct.

It doesn't directly contribute.

The energy in basically powers the compressor (plus a bit for other things) and the energy out is the heat in the gas/liquid inside the compressor (which is raised to a useful temperature and liquified as a result of being compressed), minus losses in the transfer of this energy to the circulating water.

Of course all of the 'energy out' must, in fact, have gone in somewhere - its a heat pump not a perpetual motion machine.  The excess of 'energy out' over 'energy in' is extracted from the outside ambient air, which is why you have a large fan that blows cold air from the front of the outdoor unit.  

In terms of formulae

COP = energy out/energy in. 

exactly how the figures are reported depends on your heat pump.  Some heat pumps quote energy out and energy in.  Some (eg Vaillant) quote energy in and 'environmental yield' which is energy out-energy in.  So in the latter case the calculation becomes

COP = energy out/energy in = (energy in + environmental yield)/energy in.

This is unfortunately a bit confusing!

A further consideration is that while the heat loss from the building should be proportional to be difference between inside and outside temperature (although this may be influenced by other factors such as wind chill), the heat pump efficiency changes with the difference between outside temperature and the circulating water temperature. This is actually a compound effect. When it's colder outside the heat pump has to work harder but also the circulating water temperature has to rise in order emit more heat into the house which further increases the workload.

FWIW, here's a graph of heat out vs energy in for my heat pump since it started heating the house in mid-October. I have assumed that the energy in contributes to the total heat out although this may

not be completely correct.