The ADMB project supports the application of automatic differentiation (AD) for solutions to non-linear statistical modeling and optimization problems.
AD Model Builder, or ADMB, is a statistical application that implements AD using C++ classes and a native template language. ADMB can be downloaded here and is developed on GitHub. For further information, see this site and the ADMB paper:
Fournier, D.A., Skaug, H.J., Ancheta, J., Ianelli, J., Magnusson, A., Maunder, M.N., Nielsen, A., and Sibert, J. 2012. AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models. Optim. Methods Softw. 27:233-249.
Template Model Builder, or TMB, is an R package that implements AD using C++ templates. TMB can be downloaded from CRAN and is developed on GitHub. For further information, see the Wiki and the TMB paper:
Kristensen, K., Nielsen, A., Berg, C.W., Skaug, H.J., and Bell, B.M. 2016. TMB: Automatic Differentiation and Laplace Approximation. J. Stat. Softw. 70(5):1-21.