I am trying to reproduce published results in a paper. Those results come from numerical simulations. The original authors and I do not use the same software, and theirs is proprietary (I don't have access to it). I have tried to reproduce their results, and it works qualitatively but not quantitatively: the differences between their results and mine on typical quantities of interest are between 2 and 5 times the expected accuracy of the method.
So far, I have communicated with the original authors, trying to clear out all possible sources of error I could think of (checked that I got the tricky parts of the algorithms right, checked that the “usual” parameters that were missing from their paper had the “usual” values, everything I could think of). They are forthcoming enough, and reply to my questions quickly, but it's clear they don't want to invest time in doing any serious follow-up on their side. And without access to their software, it appears I'm stuck.
Now, my question is on how to proceed. The “ideal case” for unreproducible results is to make a detailed analysis of how and why they cannot be reproduced, and possibly find out a source of failure (or at least plausible issues). This advances the field, and is probably publishable (not in a very high-profile journal). Here, this is not possible.
I have, however, nice results that I have obtained (extending their work far beyond what was already published), and if I didn't have these differences with their paper, it would make a very attractive paper. What can I do with those? Is it possible to publish them, merely noting the different with their paper without more comment? Or are my results simply unpublishable? I welcome any comment, especially from people who have found themselves in such an uncomfortable situation!