BibTeX
@ARTICLE{
         Hogan2014FRM,
       author = "Robin J. Hogan",
       title = "Fast Reverse-Mode Automatic Differentiation Using Expression Templates in {C++}",
       journal = "{ACM} Transactions on Mathematical Software",
       pages = "26:1--26:24",
       url = "http://doi.acm.org/10.1145/2560359",
       accepted = "9 December 2013",
       abstract = "Gradient-based optimization problems are encountered in many fields, but the
         associated task of differentiating large computer algorithms can be formidable. The
         operator-overloading approach to performing reverse-mode automatic differentiation is the most
         convenient for the user but current implementations are typically 10-35 times slower than the
         original algorithm. In this paper a fast new operator-overloading method is presented that uses the
         \textit{expression template} programming technique in C++ to provide a compile-time
         representation of each mathematical expression as a computational graph that can be efficiently
         traversed in either direction. Benchmarking with four different numerical algorithms shows this
         approach to be 2.6--9 times faster than current operator-overloading libraries, and 1.3--7.7 times
         more efficient in memory usage. It is typically less than 4 times the computational cost of the
         original algorithm, although poorer performance is found for all libraries in the case of simple
         loops containing no mathematical functions. An implementation is freely available in the
         \textit{Adept} C++ software library.",
       volume = "40",
       number = "4",
       year = "2014",
       month = "jun",
       ad_tools = "Adept"
}