The Collaborative International Dictionary
heuristically
heuristically \heu*ris"ti*cal*ly\ (h[-u]*r[i^]s"t[i^]*kal*l[y^]), n. In a heuristic manner; by using a heuristic method; by serving as a heuristic method; as, a heuristically guided search technique; a heuristically valuable theory.
Wiktionary
heuristically
adv. in a heuristic manner
Usage examples of "heuristically".
As is clearly stated in the novel (Chapter 16), HAL stands for Heuristically programmed ALgorithmic computer.