[mpg_numbers_guy]

The Honda Insight is a vastly different beast, but I have found accelerating "rapidly" to 15-20 MPH, and then slowly going through the gears up to optimal speed was best for fuel economy.

In my Civic I didn't have the best instrumentation, but it was definitely possible to accelerate too slow in the Civic, as well as too fast. Moderate acceleration seemed to be best. Same was true for the Sienna my family used to have.

The 2nd gen Prius seems to return best fuel economy somewhere between slow and moderate acceleration.

Looking at what I did with those cars, the most fuel efficient acceleration was keeping the car at best BSFC - in the Insight's case, ~2K RPMs at 70%-80% load. The other cars' best BSFC was at higher RPMs (I'm not sure where) so that was where it accelerated most efficiently.

I don't think I'm explaining this very well, probably because I don't fully understand it myself. To my knowledge BSFC is a chart that shows you at what RPMs your engine is running most efficiently at, and then if you accelerate within that range, your acceleration will be more fuel efficient.

You could try testing various accelerations and measuring their fuel economy to compare, although I'm not sure how accurate that would be.