{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T17:09:52Z","timestamp":1791220192430,"version":"4.1.0"},"reference-count":84,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2008,9,1]],"date-time":"2008-09-01T00:00:00Z","timestamp":1220227200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Higher-Order Symb Comput"],"published-print":{"date-parts":[[2008,9]]},"DOI":"10.1007\/s10990-008-9034-4","type":"journal-article","created":{"date-parts":[[2008,10,30]],"date-time":"2008-10-30T17:49:02Z","timestamp":1225388942000},"page":"311-331","source":"Crossref","is-referenced-by-count":26,"title":["On the implementation of automatic differentiation tools"],"prefix":"10.1007","volume":"21","author":[{"given":"Christian H.","family":"Bischof","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul D.","family":"Hovland","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Boyana","family":"Norris","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2008,10,31]]},"reference":[{"key":"9034_CR1","doi-asserted-by":"crossref","unstructured":"Abate, J., Bischof, C., Carle, A., Roh, L.: Algorithms and design for a second-order automatic differentiation module. In: Proc. Int. Symposium on Symbolic and Algebraic Computing (ISSAC) \u201997, New York, pp. 149\u2013155. Association of Computing Machinery (1997)","DOI":"10.1145\/258726.258770"},{"key":"9034_CR2","volume-title":"Compilers: Principles, Techniques and Tools","author":"A.V. Aho","year":"1986","unstructured":"Aho, A.V., Sethi, R., Ullman, J.D.: Compilers: Principles, Techniques and Tools. Addison\u2013Wesley, Reading (1986)"},{"key":"9034_CR3","volume-title":"Optimizing Compilers for Modern Architectures: A Dependence-based Approach","author":"R. Allen","year":"2002","unstructured":"Allen, R., Kennedy, K.: Optimizing Compilers for Modern Architectures: A Dependence-based Approach. Morgan Kaufmann, San Mateo (2002)"},{"key":"9034_CR4","doi-asserted-by":"crossref","unstructured":"Amarasinghe, S.P., Anderson, J.M., Lam, M.S., Tseng, C.W.: The SUIF compiler for scalable parallel machine. In: Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing (1995)","DOI":"10.1007\/3-540-57659-2_15"},{"key":"9034_CR5","doi-asserted-by":"crossref","unstructured":"Aubert, P., Di C\u00e9sar\u00e9, N.: Expression templates and forward mode automatic differentiation. In [26], Chap.\u00a037, pp. 311\u2013315 (2001)","DOI":"10.1007\/978-1-4613-0075-5_37"},{"key":"9034_CR6","unstructured":"Bagge, O.S., Kalleberg, K.T., Haveraaen, M., Visser, E.: Design of the CodeBoost transformation system for domain-specific optimisation of C++ programs. In: Binkley, D., Tonella, P. (eds.): Third International Workshop on Source Code Analysis and Manipulation (SCAM 2003). IEEE Computer Society Press, Amsterdam (2003, to appear)"},{"key":"9034_CR7","unstructured":"Bartholomew-Biggs, M.: OPFAD\u2014A users guide to the OPtima forward automatic differentiation tool. Technical report, Numerical Optimization Centre, University of Hertfordsshire (1995)"},{"key":"9034_CR8","unstructured":"Bartholomew-Biggs, M.C., Brown, S., Christianson, B., Dixon, L.C.W.: The efficient calculation of gradients, Jacobians and Hessians. Technical Report NOC TR301, The Numerical Optimisation Center, University of Hertfordshire, Hatfield, U.K. (1995)"},{"issue":"2","key":"9034_CR9","first-page":"61","volume":"8","author":"J.J. Barton","year":"1996","unstructured":"Barton, J.J., Nackman, L.R.: Automatic differentiation. C++ Rep. 8(2), 61\u201363 (1996)","journal-title":"C++ Rep."},{"key":"9034_CR10","unstructured":"Beda, L.M., Korolev, L.N., Sukkikh, N.V., Frolova, T.S.: Programs for automatic differentiation for the machine BESM. Technical Report, Institute for Precise Mechanics and Computation Techniques, Academy of Science, Moscow, USSR (1959) (In Russian)"},{"key":"9034_CR11","unstructured":"Bell, B.M.: CppAD User Manual. Available at http:\/\/www.seanet.com\/~bradbell\/CppAD\/ (2003)"},{"key":"9034_CR12","unstructured":"Bendtsen, C., Stauning, O.: FADBAD, a flexible C++ package for automatic differentiation. Technical Report IMM-REP-1996-17, Department of Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark (1996)"},{"key":"9034_CR13","volume-title":"Computational Differentiation: Techniques, Applications, and Tools","year":"1996","unstructured":"Berz, M., Bischof, C., Corliss, G., Griewank, A. (eds.): Computational Differentiation: Techniques, Applications, and Tools. SIAM, Philadelphia (1996)"},{"key":"9034_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0065-2458(08)60641-5","volume":"43","author":"D.W. Binkley","year":"1996","unstructured":"Binkley, D.W., Gallagher, K.B.: Program slicing. Adv. Comput. 43, 1\u201350 (1996)","journal-title":"Adv. Comput."},{"key":"9034_CR15","unstructured":"Bischof, C., Roh, L.: The automatic differentiation intermediate form (AIF). Unpublished Information (1996)"},{"issue":"1","key":"9034_CR16","first-page":"11","volume":"1","author":"C. Bischof","year":"1992","unstructured":"Bischof, C., Carle, A., Corliss, G., Griewank, A., Hovland, P.: ADIFOR: Generating derivative codes from Fortran programs. Sci. Program. 1(1), 11\u201329 (1992)","journal-title":"Sci. Program."},{"issue":"3","key":"9034_CR17","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/99.537089","volume":"3","author":"C. Bischof","year":"1996","unstructured":"Bischof, C., Carle, A., Khademi, P., Mauer, A.: ADIFOR 2.0: Automatic differentiation of Fortran 77 programs. IEEE Comput. Sci. Eng. 3(3), 18\u201332 (1996)","journal-title":"IEEE Comput. Sci. Eng."},{"issue":"12","key":"9034_CR18","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1002\/(SICI)1097-024X(199712)27:12<1427::AID-SPE138>3.0.CO;2-Q","volume":"27","author":"C. Bischof","year":"1997","unstructured":"Bischof, C., Roh, L., Mauer, A.: ADIC\u2014An extensible automatic differentiation tool for ANSI-C. Softw. Pract. Exp. 27(12), 1427\u20131456 (1997)","journal-title":"Softw. Pract. Exp."},{"key":"9034_CR19","unstructured":"Bischof, C.H., B\u00fccker, H.M., Lang, B., Rasch, A.: An interactive environment for supporting the paradigm shift from simulation to optimization. In: 4th Workshop on Parallel\/High-Performance OO Scientific Computing (POOSC\u201901) 14 October 2001, at the ACM Conference on Object-Oriented Programming, Systems, Languages, and Applications (OOPSLA\u201901) 14\u201318 October, Tampa Bay, FL (2001, to appear)"},{"key":"9034_CR20","unstructured":"Bischof, C.H., B\u00fccker, H.M., Lang, B., Rasch, A., Vehreschild, A.: Combining source transformation and operator overloading techniques to compute derivatives for MATLAB programs. Preprint RWTH-CS-SC-02-04, Institute for Scientific Computing, Aachen University of Technology (2002)"},{"key":"9034_CR21","volume-title":"GAMS: A User\u2019s Guide","author":"A. Brooke","year":"1988","unstructured":"Brooke, A., Kendrick, D., Meeraus, A.: GAMS: A User\u2019s Guide. The Scientific Press, South San Francisco (1988)"},{"key":"9034_CR22","unstructured":"Brown, S.: OPRAD\u2014A users guide to the OPtima reverse automatic differentiation tool. Technical report, Numerical Optimization Centre, University of Hertfordsshire (1995)"},{"key":"9034_CR23","unstructured":"Christianson, B., Dixon, L.C.W., Brown, S.: Sharing storage using dirty vectors. In [13], pp. 107\u2013115"},{"key":"9034_CR24","unstructured":"Christianson, D.B.: Automatic Hessians by reverse accumulation in ada. IMA J. Numer. Anal. (1991) Presented at SIAM Workshop on Automatic Differentiation of Algorithms, Breckenridge, CO, January 1991"},{"issue":"1","key":"9034_CR25","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1145\/347837.347879","volume":"26","author":"T.F. Coleman","year":"2000","unstructured":"Coleman, T.F., Verma, A.: ADMIT-1: Automatic differentiation and MATLAB interface toolbox. ACM Trans. Math. Softw. 26(1), 150\u2013175 (2000)","journal-title":"ACM Trans. Math. Softw."},{"key":"9034_CR26","series-title":"Computer and Information Science","volume-title":"Automatic Differentiation: From Simulation to Optimization","year":"2001","unstructured":"Corliss, G., Faure, C., Griewank, A., Hasco\u00ebt, L., Naumann, U. (eds.): Automatic Differentiation: From Simulation to Optimization. Computer and Information Science Springer, New York (2001)"},{"key":"9034_CR27","unstructured":"Edison Design Group: EDG C++ Front End (2003). http:\/\/www.edg.com\/cpp.html"},{"key":"9034_CR28","unstructured":"Faure, C.: Adjoining strategies for multi-layered programs. Optim. Methods Softw. (2001, to appear). Also appeared as INRIA Rapport de recherche no. 3781, BP 105-78153 Le Chesnay Cedex, France (1999)"},{"key":"9034_CR29","doi-asserted-by":"crossref","unstructured":"Faure, C., Naumann, U.: Minimizing the tape size. In [26], Chap. 34, pp. 293\u2013298 (2001)","DOI":"10.1007\/978-1-4613-0075-5_34"},{"key":"9034_CR30","unstructured":"Forth, S.: An efficient implementation of AD in MATLAB. Presentation at Joint University of Hertfordshire\/Cranfield University (RMCS Shrivenham) Automatic Differentiation Symposium (2001). Available at http:\/\/www.rmcs.cranfield.ac.uk\/esd\/amor\/workshop\/alldatastore\/ADDAYmay01forth.pdf"},{"key":"9034_CR31","volume-title":"AMPL: A Modeling Language for Mathematical Programming","author":"R. Fourer","year":"1993","unstructured":"Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: A Modeling Language for Mathematical Programming. The Scientific Press, South San Francisco (1993)"},{"key":"9034_CR32","unstructured":"Frazier, Z.: PyAD User manual. Available at http:\/\/students.washington.edu\/zfrazier\/projects\/pyad\/pyad-doc\/ (2003)"},{"issue":"4","key":"9034_CR33","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1145\/293686.293695","volume":"24","author":"R. Giering","year":"1998","unstructured":"Giering, R., Kaminski, T.: Recipes for adjoint code construction. ACM TOMS 24(4), 437\u2013474 (1998)","journal-title":"ACM TOMS"},{"key":"9034_CR34","doi-asserted-by":"crossref","unstructured":"Giering, R., Kaminski, T.: Applying TAF to generate efficient derivative code of Fortran 77-95 programs. In: Proceedings of GAMM 2002, Augsburg, Germany (2002)","DOI":"10.1002\/pamm.200310014"},{"key":"9034_CR35","first-page":"83","volume-title":"Mathematical Programming: Recent Developments and Applications","author":"A. Griewank","year":"1989","unstructured":"Griewank, A.: On automatic differentiation. In: Mathematical Programming: Recent Developments and Applications, pp. 83\u2013108. Kluwer Academic, Amsterdam (1989)"},{"key":"9034_CR36","unstructured":"Griewank, A.: Personal communication (1998)"},{"key":"9034_CR37","volume-title":"Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation","author":"A. Griewank","year":"2000","unstructured":"Griewank, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia (2000)"},{"key":"9034_CR38","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1080\/10556789208805505","volume":"1","author":"A. Griewank","year":"1992","unstructured":"Griewank, A.: Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation. Optim. Methods Softw. 1, 35\u201354 (1992)","journal-title":"Optim. Methods Softw."},{"key":"9034_CR39","volume-title":"Automatic Differentiation of Algorithms: Theory, Implementation, and Application","author":"A. Griewank","year":"1991","unstructured":"Griewank, A., Corliss, G.F.: Automatic Differentiation of Algorithms: Theory, Implementation, and Application. SIAM, Philadelphia (1991)"},{"key":"9034_CR40","unstructured":"Griewank, A., Reese, S.: On the calculation of Jacobian matrices by the Markowitz rule. In [39], pp. 126\u2013135 (1991)"},{"issue":"2","key":"9034_CR41","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1145\/229473.229474","volume":"22","author":"A. Griewank","year":"1996","unstructured":"Griewank, A., Juedes, D., Utke, J.: ADOL-C, a package for the automatic differentiation of algorithms written in C\/C++. ACM Trans. Math. Softw. 22(2), 131\u2013167 (1996)","journal-title":"ACM Trans. Math. Softw."},{"key":"9034_CR42","unstructured":"Grimm, J., Pottier, L., Rostaing-Schmidt, N.: Optimal time and minimum space-time product for reversing a certain class of programs. In [13], pp. 95\u2013106 (1996)"},{"key":"9034_CR43","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/3-540-45574-4_15","volume-title":"Optimizing the use of high performance software libraries","author":"S.Z. Guyer","year":"2001","unstructured":"Guyer, S.Z., Lin, C.: Optimizing the use of high performance software libraries. Lecture Notes in Computer Science, vol. 2017, pp. 227\u2013243. Springer, Berlin (2001)"},{"key":"9034_CR44","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0168-9274(92)90065-L","volume":"9","author":"D.R. Hill","year":"1992","unstructured":"Hill, D.R., Rich, L.C.: Automatic differentiation in MATLAB. Appl. Numer. Math. 9, 33\u201343 (1992)","journal-title":"Appl. Numer. Math."},{"key":"9034_CR45","doi-asserted-by":"crossref","unstructured":"Hinkins, R.L.: Parallel computation of automatic differentiation applied to magnetic field calculations. Master\u2019s thesis, University of California, Berkeley (1994)","DOI":"10.2172\/10107439"},{"key":"9034_CR46","unstructured":"Hinsen, K.: Scientific python collection. Module Scientific. Functions. Derivatives (2003). Available at http:\/\/starship.python.net\/~hinsen\/ScientificPython\/"},{"key":"9034_CR47","unstructured":"Hovland, P.D., Naumann, U., Norris, B.: An XML-based platform for semantic transformation of numerical programs. Preprint ANL\/MCS-P950-0402, Mathematics and Computer Science Division, Argonne National Laboratory. Proceedings of Software Engineering and Applications (SEA 2002) (2002, to appear)"},{"issue":"2","key":"9034_CR48","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0096-3003(90)90112-G","volume":"35","author":"R.E. Huss","year":"1990","unstructured":"Huss, R.E.: An ADA library for automatic evaluation of derivatives. Appl. Math. Comput. 35(2), 103\u2013123 (1990)","journal-title":"Appl. Math. Comput."},{"key":"9034_CR49","doi-asserted-by":"crossref","unstructured":"Jerrell, M.: Automatic differentiation using almost any language. ACM SIGNUM Newsl. pp. 2\u20139 (1989)","DOI":"10.1145\/1057967.1057968"},{"key":"9034_CR50","unstructured":"Juedes, D.W.: A taxonomy of automatic differentiation tools. In [39], pp. 315\u2013329 (1991)"},{"key":"9034_CR51","unstructured":"Kahrimanian, H.G.: Analytical differentiation by a digital computer. Master\u2019s thesis, Temple University (1953)"},{"key":"9034_CR52","unstructured":"Kalman, D., Lindell, R.: Automatic differentiation in astrodynamical modeling. In [39], pp. 228\u2013243 (1991)"},{"key":"9034_CR53","first-page":"35","volume":"14","author":"J. Karczmarczuk","year":"2001","unstructured":"Karczmarczuk, J.: Functional differentiation of computer programs. J. HOSC 14, 35\u201357 (2001)","journal-title":"J. HOSC"},{"issue":"12","key":"9034_CR54","doi-asserted-by":"crossref","first-page":"1803","DOI":"10.1006\/jpdc.2001.1724","volume":"61","author":"K. Kennedy","year":"2001","unstructured":"Kennedy, K., Broom, B., Cooper, K., Dongarra, J., Fowler, R., Gannon, D., Johnsson, L., Mellor-Crummey, J., Torczon, L.: Telescoping languages: A strategy for automatic generation of scientific problem-solving systems from annotated libraries. J. Parallel Distrib. Comput. 61(12), 1803\u20131826 (2001)","journal-title":"J. Parallel Distrib. Comput."},{"key":"9034_CR55","doi-asserted-by":"crossref","unstructured":"Korelc, J.: Hybrid system for multi-language and multi-environment generation of numerical codes. In: Proceedings of the 2001 International Symposium on Symbolic and algebraic computation, pp. 209\u2013216. ACM Press (2001)","DOI":"10.1145\/384101.384130"},{"key":"9034_CR56","unstructured":"Lawson, C.L.: Computing derivatives using W-arithmetic and U-arithmetic. Internal computing memorandum CM\u2013286, Jet Propulsion Laboratory, Pasadena (1971)"},{"issue":"9","key":"9034_CR57","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1145\/363566.363693","volume":"10","author":"A.M. Lesk","year":"1967","unstructured":"Lesk, A.M.: Dynamic computation of derivatives. Commun. ACM 10(9), 571\u2013572 (1967)","journal-title":"Commun. ACM"},{"key":"9034_CR58","unstructured":"Maany, Z.: Ada automatic differentiation package for the optimization of functions of many variables. Technical Report NOC TR209, The Numerical Optimisation Center, Hatfield Polytechnic, Hatfield, UK (1989)"},{"key":"9034_CR59","doi-asserted-by":"crossref","unstructured":"Martins, J.R.R.A., Kroo, I.M., Alonso, J.J.: An automated method for sensitivity analysis using complex variables. In: Proceedings of the 38th Aerospace Sciences Meeting, Reno, NV (2000)","DOI":"10.2514\/6.2000-689"},{"key":"9034_CR60","unstructured":"Martins, J.R.R.A., Sturdza, P., Alonso, J.J.: The connection between the complex-step derivative approximation and algorithmic differentiation. In: Proceedings of the 39th Aerospace Sciences Meeting, Reno, NV (2001). Complexify.h and derivify.h available at http:\/\/mdolab.utias.utoronto.ca\/c++.html"},{"key":"9034_CR61","unstructured":"Michelotti, L.: MXYZPTLK: A C++ Hacker\u2019s implementation of automatic differentiation. In [39], pp.\u00a0218\u2013227 (1991). Software available at http:\/\/www.netlib.org\/c++\/mxyzptlk\/"},{"key":"9034_CR62","first-page":"353","volume-title":"Computational Differentiation: Techniques, Applications, and Tools","author":"M. Monagan","year":"1996","unstructured":"Monagan, M., Rodoni, R.R.: An implementation of the forward and reverse mode of automatic differentiation in maple. In: Berz, M., Bischof, C., Corliss, G., Griewank, A. (eds.) Computational Differentiation: Techniques, Applications, and Tools, pp. 353\u2013362. SIAM, Philadelphia (1996)"},{"key":"9034_CR63","volume-title":"Advanced Compiler Design and Implementation","author":"S.S. Muchnick","year":"1997","unstructured":"Muchnick, S.S.: Advanced Compiler Design and Implementation. Morgan Kaufmann, San Mateo (1997)"},{"key":"9034_CR64","unstructured":"NAG-AD: Differentiation enabled Fortran compiler technology (2003). http:\/\/www.nag.co.uk\/nagware\/research\/ad_overview.asp"},{"key":"9034_CR65","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1007\/3-540-46080-2_109","volume-title":"Proceedings of the International Conference on Computational Science, Part II","author":"U. Naumann","year":"2002","unstructured":"Naumann, U.: Reducing the memory requirement in reverse mode automatic differentiation by solving TBR flow equations. In: Sloot, P.M.A., Tan, C.J.K., Dongarra, J.J. (eds.) Proceedings of the International Conference on Computational Science, Part II, Amsterdam, The Netherlands, April 21\u201324, 2002. Lecture Notes in Computer Science, vol. 2330, pp. 1039\u20131048. Springer, Berlin (2002)"},{"key":"9034_CR66","unstructured":"Naumann, U.: Statement level optimality of tangent-linear and adjoint models. Preprint ANL-MCS\/P1066-0603, Argonne National Laboratory (2003)"},{"key":"9034_CR67","doi-asserted-by":"crossref","unstructured":"Naumann, U., Gottschling, P.: Simulated annealing for optimal pivot selection in Jacobian accumulation. In: Albrecht, A. (ed.): Stochastic Algorithms, Foundations and Applications\u2014SAGA\u201903. Berlin, Springer (2003, to appear). See also http:\/\/angellib.sourceforge.net\/","DOI":"10.1007\/978-3-540-39816-5_8"},{"issue":"3","key":"9034_CR68","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1080\/07468342.1989.11973240","volume":"20","author":"R.D. Neidinger","year":"1989","unstructured":"Neidinger, R.D.: Automatic differentiation and APL. Coll. Math. J. 20(3), 238\u2013251 (1989)","journal-title":"Coll. Math. J."},{"issue":"9","key":"9034_CR69","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1145\/944746.944720","volume":"38","author":"H. Nilsson","year":"2003","unstructured":"Nilsson, H.: Functional automatic differentiation with Dirac impulses. ACM SIGPLAN Not. 38(9), 153\u2013164 (2003)","journal-title":"ACM SIGPLAN Not."},{"key":"9034_CR70","unstructured":"Nolan, J.F.: Analytical differentiation on a digital computer. Master\u2019s thesis, Massachusetts Institute of Technology (1953)"},{"key":"9034_CR71","unstructured":"Pryce, J.D., Reid, J.K.: ADO1, a Fortran 90 code for automatic differentiation. Technical Report RAL-TR-1998-057, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 OQX, England (1998)"},{"issue":"2\/3","key":"9034_CR72","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1142\/S0129626400000214","volume":"10","author":"D. Quinlan","year":"2000","unstructured":"Quinlan, D.: ROSE: Compiler support for object-oriented frameworks. Parallel Process. Lett. 10(2\/3), 215 (2000)","journal-title":"Parallel Process. Lett."},{"key":"9034_CR73","doi-asserted-by":"crossref","unstructured":"Reps, T., Rosay, G.: Precise interprocedural chopping. In: Kaiser, G.E. (ed.) SIGSOFT\u201995: Proceedings of the Third ACM SIGSOFT Symposium on the Foundations of Software Engineering, pp. 41\u201352. ACM Press (1995)","DOI":"10.1145\/222124.222138"},{"key":"9034_CR74","doi-asserted-by":"crossref","first-page":"1586","DOI":"10.1137\/S1064827595285500","volume":"19","author":"J.M. Restrepo","year":"1998","unstructured":"Restrepo, J.M., Leaf, G.K., Griewank, A.: Circumventing storage limitations in variational data assimilation. SIAM J. Sci. Comput. 19, 1586\u20131605 (1998)","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"9034_CR75","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1034\/j.1600-0870.1993.00016.x","volume":"45a","author":"N. Rostaing","year":"1993","unstructured":"Rostaing, N., Dalmas, S., Galligo, A.: Automatic differentiation in Odyssee. Tellus 45a(5), 558\u2013568 (1993)","journal-title":"Tellus"},{"key":"9034_CR76","doi-asserted-by":"crossref","unstructured":"Rote, G.: Path problems in graphs. In: Tinhofer, G., Mayr, E., Noltemeier, H., M.M.S. in cooperation with Albrecht, R. (eds.) Computational Graphs Theory, Springer-Verlag Computing Supplementum 7. Springer (1990)","DOI":"10.1007\/978-3-7091-9076-0_9"},{"key":"9034_CR77","unstructured":"SGI: WHIRL intermediate language specification (1999). Available at http:\/\/open64.sourceforge.net\/documentation.html"},{"issue":"2&3","key":"9034_CR78","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0010-4655(99)00513-5","volume":"127","author":"S. Stamatiadis","year":"2000","unstructured":"Stamatiadis, S., Prosmiti, R., Farantos, S.C.: auto_deriv: Tool for automatic differentiation of a fortran code. Comput. Phys. Commun. 127(2&3), 343\u2013355 (2000). Catalog number: ADLS","journal-title":"Comput. Phys. Commun."},{"key":"9034_CR79","series-title":"Lecture Notes in Computer Science","first-page":"95","volume-title":"Proceedings of the International Conference on Computational Science and its Applications, Part\u00a0II","author":"M. Tadjouddine","year":"2003","unstructured":"Tadjouddine, M., Forth, S.A., Pryce, J.D.: Hierarchicalal automatic differentiation by vertex elimination and source transformation. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K. (eds.) Proceedings of the International Conference on Computational Science and its Applications, Part\u00a0II, Montreal, Canada, May 18\u201321, 2003. Lecture Notes in Computer Science, vol.\u00a02668, pp.\u00a095\u2013104. Springer, Berlin (2003)"},{"key":"9034_CR80","unstructured":"TAPENADE: TAPENADE tutorial (2002). http:\/\/www-sop.inria.fr\/tropics\/tapenade\/tutorial.html"},{"issue":"13","key":"9034_CR81","doi-asserted-by":"crossref","first-page":"1949","DOI":"10.1002\/nme.647","volume":"56","author":"I.M.H. Tsukanov","year":"2003","unstructured":"Tsukanov, I.M.H.: Data structure and algorithms for fast automatic differentiation. Int. J. Numer. Methods Eng. 56(13), 1949\u20131972 (2003)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"5","key":"9034_CR82","first-page":"26","volume":"7","author":"T. Veldhuizen","year":"1995","unstructured":"Veldhuizen, T.: Expression templates. C++ Rep. 7(5), 26\u201331 (1995)","journal-title":"C++ Rep."},{"issue":"8","key":"9034_CR83","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1145\/355586.364791","volume":"7","author":"R.E. Wengert","year":"1964","unstructured":"Wengert, R.E.: A simple automatic derivative evaluation program. Commun. ACM 7(8), 463\u2013464 (1964)","journal-title":"Commun. ACM"},{"issue":"8","key":"9034_CR84","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1145\/355586.364792","volume":"7","author":"R.D. Wilkins","year":"1964","unstructured":"Wilkins, R.D.: Investigation of a new analytic model for numerical derivative evaluation. Commun. ACM 7(8), 465\u2013471 (1964)","journal-title":"Commun. ACM"}],"container-title":["Higher-Order and Symbolic Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10990-008-9034-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10990-008-9034-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10990-008-9034-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,2]],"date-time":"2024-03-02T06:26:34Z","timestamp":1709360794000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10990-008-9034-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9]]},"references-count":84,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,9]]}},"alternative-id":["9034"],"URL":"https:\/\/doi.org\/10.1007\/s10990-008-9034-4","relation":{},"ISSN":["1388-3690","1573-0557"],"issn-type":[{"value":"1388-3690","type":"print"},{"value":"1573-0557","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9]]}}}