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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.

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Perhaps cogsci.stackexchange.com would be a better place for your question. –  Joel Reyes Noche Jun 27 '12 at 13:15
    
some complexity theory might help? probably nothing comprehensive. have you looked at front.math.ucdavis.edu/0904.3740? –  john mangual Jun 27 '12 at 13:35
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Do you include mental prime factorization within "mental calculation"? –  Michael Hardy Oct 16 '13 at 21:23
    
The difficulty of assigning "difficulty" to any such evaluation can be illustrated already by such trivial example as $199556\times 200444+222\times 888$. The point is that without pen and paper we hardly ever try to "compute honestly", so all that stuff about the needed amount of registers and the relative difficulty of elementary operations gets pretty meaningless. –  fedja Oct 16 '13 at 23:27
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closed as off-topic by Tom LaGatta, Steven Landsburg, Chris Godsil, Olivier Benoist, Ryan Budney Oct 17 '13 at 9:44

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