Overall, this is pretty cool stuff.

I think, however, that a reference to the work presented at AD 2004
on runtime activity analysis done by Adifor should be listed.
(Rice technical report TR04-21, Dept of Computational and Applied
Mathematics).

Author response:  reference added.

I also had 1 minor presentation improvement to suggest, with regard to Table 1:

  I wasn't sure what size was telling me. Is it the number of
  independent variables? If so, why write "400" 1 place, and
  "20x20" in another? If size means something else, I'd like to
  know what it is.

Author response:  The size column attempts to not only indicate the number of independent variables, but also their dimensionality.  The size of the individual dimensions are included for reference should a reader attempt to reproduce our results.