I added a second benchmark, using a Thornburg04 patch system, 8th order finite differencing, and 4th order patch interpolation. The results are
original: 8.53935e-06 sec
rewrite: 8.55188e-06 sec
this time with 1 thread per MPI process, since that was most efficient in both cases. Most of the time is spent in inter-patch interpolation, which is much more expensive than in a "regular" case since this benchmark is run on a single node and hence with very small grids.
With these numbers under our belt, can we merge the rewrite branch?
The "jacobian" benchmark that I gave you was still a pure kernel benchmark, involving no interpatch interpolation. It just measured the speed of the RHSs when Jacobians were included. I would also not use a single-threaded benchmark with very small grid sizes; this might have been fastest in this artificial case, but in practice I don't think we would use that configuration. The benchmark you have now run seems to be more of a "complete system" benchmark, which is useful, but different.
I think it is important that the kernel itself has not gotten slower, even if the kernel is not currently a major contributor to runtime. We specifically split out the advection derivatives because they made the code with 8th order and Jacobians a fair bit slower. I would just like to see that this is not still the case with the new version, which has changed the way this is handled.