Argonne Labs is a national resource, part of the Department of Energy, that conducts well documented engineering studies including the BMW i3-REx.

So here are the datafiles of interest:
61504034SSS 0-80-0 0% Grade6.24
61504059UDDS #1, Ph 1+27.43450.165
61504060UDDS #2, Ph 1+27.4851.60.145
61504061UDDS #3, Ph 1+27.4850.70.147
61504062Hwyx2 with Coastdowns Ph 210.2450.40.203
61504063US06x2, Ph 3+48.0336.40.221

Vehicle Efficiency

For vehicle efficiency, test 61504034, as the speed sweeps from 0-80-0 mph:

The dyno merics provides the kW as a function of speed. So we can map the miles per kWh, exactly the same metric reported by the BMW i3-REx.

This chart was used to adjust earlier benchmarks and has been confirmed in the field.

REx Efficiency

To looks at the range extender (REx) efficiency, I used 61504062, a highway test with the longest distance:
The available REx power is a function of oil temperature: The REx initally runs at a reduced power level for ~250 seconds (just under 5 minutes.) Once the engine oil temperature reaches 94C, it can output full power, ~20.5kW. This suggests the car should be operated in reduced speed, enough to keep the REx on, ~6kW but not so high as to have the REx turn off.

A typical EPA test consists of two phases: warm-up and for the numbers. So the 600 seconds covers the warm-up and after a 100 second pause, it is repeated starting at seconds 700. The data suggests there are finite number of power bands. The "W/cc" is the watts divided by the fuel cc/second, a measure of power per unit of fuel. But these are not standard metrics such as Brake Specific Fuel Consumption (BSFC).

So plotting the BSFC over the test duration gives:

Converting the "cc/sec" to "g/sec" and the power gives gives BSFC grams per second, divided by the Watts.

So scatter plotting the power versus BSFC, we get:

So we see four distinct power groups:

What we can do is identify the flat-land, speed that requires 17kW. Using the earlier 0-80-0 metrics:

Now these are the measured electrical output which is typically 96% of the mechanical energy. This suggests the actual BSFC is about 5% higher. Regardless, this is in the 30% thermoldynamic efficiency range suggesting there may be more, low-hanging fruit. BMW has already announced going to 0-20W engine oil. But cooled Exhaust Gas Recirculation (EGR) is an obvious trick and one I might try.

My first Prius modification was a 1 kW inverter to provide emergency power which we used every year since 2005. So I started research how to do the same modification with our 2014 BMW i3-REx:

Looking at the REx output, it looks good except for the 440W vehicle overhead. Assuming 1kW of 120VAC output and the vehicle overhead, we're looking at generating 1.4kW. Assuming we're looking at 10kWh/gal, 1.0kW / 1.4kW ~= 7.1 kWh/gal. To keep things in perspective, this is the 2003 Prius performance: