![](bg8.png)
also be tried, such as exponentially decreasing T.
Finally, we believe that the use of domain specific
knowledge can be fruitfully explored if the expression
has sufficient structure. To confirm this belief more
research is needed.
This work is supported in part by the ERC Ad-
vanced Grant no. 320651, “HEPGAME”.
REFERENCES
Aho, A. V., Sethi, R., and Ullman, J. D. (1988). Compilers:
Principles, Techniques and Tools. Addison-Wesley.
Breuer, M. A. (1969). Generation of Optimal Code
for Expressions via Factorization. Commun. ACM,
12(6):333–340.
Browne, C., Powley, E., Whitehouse, D., Lucas, S., Cowl-
ing, P., Rohlfshagen, P., Tavener, S., Perez, D.,
Samothrakis, S., and Colton, S. (2012). A Survey of
Monte Carlo Tree Search Methods. Comp. Int. and AI
in Games, IEEE Trans. on, 4(1):1–43.
Ceberio, M. and Kreinovich, V. (2004). Greedy Algo-
rithms for Optimizing Multivariate Horner Schemes.
SIGSAM Bull., 38(1):8–15.
Coulom, R. (2007). Efficient Selectivity and Backup Op-
erators in Monte-Carlo Tree Search. In Proceedings
of the 5th International Conference on Computers and
Games, CG’06, pages 72–83, Berlin. Springer-Verlag.
Hashimoto, J., Kishimoto, A., Yoshizoe, K., and Ikeda, K.
(2012). Accelerated UCT and Its Application to Two-
Player Games. Lecture Notes in C.S., 7168:1 – 12.
Horner, W. (1819). A New Method of Solving Numerical
Equations of All Orders by Continuous Approxima-
tion. W. Bulmer & Co. Dover reprint, 2 vols 1959.
Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983). Op-
timization by simulated annealing. Science, 220:671–
680.
Knuth, D. E. (1997). The Art of Computer Program-
ming, Volume 2 (3rd Ed.): Seminumerical Algorithms.
Addison-Wesley Longman Pub. Co., Inc., Boston.
Kocsis, L. and Szepesv
´
ari, C. (2006a). Bandit based Monte-
Carlo Planning. In In: ECML-06. LNCS 4212, pages
282–293. Springer.
Kocsis, L. and Szepesv
´
ari, C. (2006b). Discounted UCB.
Video Lecture. In the lectures of PASCAL Second
Challenges Workshop 2006.
Kuipers, J., Plaat, A., Vermaseren, J., and van den Herik, J.
(2013a). Improving multivariate Horner schemes with
Monte Carlo Tree Search. Computer Physics Commu-
nications.
Kuipers, J., Ueda, T., and Vermaseren, J. (2013b). Code Op-
timization in FORM. http://arxiv.org/abs/1310.7007.
Lee, C.-S., Wang, M.-H., Chaslot, G., Hoock, J.-B., Rim-
mel, A., Teytaud, O., Tsai, S.-R., Hsu, S.-C., and
Hong, T.-P. (2009). The Computational Intelligence
of MoGo Revealed in Taiwan’s Computer Go Tour-
naments. IEEE Trans. Comput. Intellig. and AI in
Games, 1(1):73–89.
Leiserson, C. E., Li, L., Maza, M. M., and Xie, Y. (2010).
Efficient Evaluation of Large Polynomials. In In Proc.
International Congress of Mathematical Software -
ICMS 2010. Springer.
Ruijl, B., Plaat, A., van den Herik, J., and Vermaseren,
J. (2013). Combining Simulated Annealing and
Monte Carlo Tree Search for Expression Simplifica-
tion. http://arxiv.org/abs/1312.0841.
van den Herik, J., Kuipers, J., Vermaseren, J., and Plaat, A.
(2013a). Investigations with Monte Carlo Tree Search
for finding better multivariate Horner schemes. Com-
mun. in Computer and Information Science 2013. In
press.
van den Herik, J., Plaat, A., Kuipers, J., and Vermaseren,
J. (2013b). Connecting Sciences. In ICAART 2013
- Proceedings of the 5th International Conference on
Agents and Artificial Intelligence, pages IS–7 – IS–16.
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