Thanks for the good comments and suggestions. I have a suspicion that the problem comes from some domain issue having to do with the adaptive parameter, which is consistent with your ideas, but don't have good data to support that. Specific responses to some of the questions here:
- I tried explicitly setting test points in the problem to extreme values, and was unable to get anything that showed a non-zero difference between the student and correct answers (other than is noted below);
- The independent variables as written (and with the answer submitted) are {C, c, s, x}, plus the adaptive parameter; it may be that eliminating one of the variables would help, but it doesn't seem as if that should be necessary;
- The problem doesn't use any non-standard graders, and the past answer is reported as incorrect. I've been testing it since with the "check answers" button.
The only time when I see (inconsequential, but non-zero) differences between the student's and correct answers is with the adaptive parameters, which can have (inconsequential) errors that result in differences of on the order of 10^(-12).
The biggest issue is, of course, that this is for all intents and purposes an irreproducible error: I don't know what test points were used on the submission that was marked incorrect. [Side note: in that the test points vary between submissions now, it would be nice to have them logged somewhere; maybe in the answer log.]
I'd love to hear additional thoughts on this.
Thanks
Gavin