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This is interesting. I have two comments that grew too long for the comment box, so I'll post them here instead. Is it possible that the discrepancy in your point (2) is only due to roundoff error? After all the difference is less than $MachineEpsilon. I made the following weird discovery: if you calculate the result of the ImageMeasurements expression, ...
Mathematica uses the SUNDIALS/CVODES libraries. I would recommend the following paper and the references therein. Quoting from the introduction, The forward sensitivity module in CVODES implements the simultaneous corrector method, as well as two flavors of staggered corrector methods. Its adjoint sensitivity module provides a combination of ...
This was not acknowledged (yet) by Wolfram but appears to have been fixed on version 10.2.0.0
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