Are you aware of any work that tries to model the difficulty of evaluating a formula mentally (for your average, numerate, person, not a trained mental calculator)?

For instance, evaluating an arithmetic expression requires in general three registers, but some only require two and are considerably easier to deal with. Additions is easier than subtraction which is easier than multiplication which is easier than division. Multiplication by small integer number is easy, as are multiplications and divisions by 2,5,10...

Many rule of thumbs are intuitive, but I'm looking for a more comprehensive work on the topic.

mighthelp? probably nothing comprehensive. have you looked at front.math.ucdavis.edu/0904.3740? – john mangual Jun 27 '12 at 13:35