The disclosure relates to technology for facilitating query optimization in a distributed data processing system to efficiently and precisely compute predicate push down and partition pruning A query operation is performed to locate data in the data processing system, thereby generating a predicate. Critical points of the predicate are determined based on data stored in the system, and critical point ranges are formed from a sorted sequence of each of the critical points. The predicate is evaluated using the critical points to qualify the critical point ranges, and a reduction is applied to the predicate during partial evaluation to produce reduced predicates on the qualified critical point ranges. The qualified critical point ranges are compared and matched to range partitions of data stored in the distributed system to qualify the range partitions. The reduced predicate is processed against the data in the qualified range partitions to obtain a query result.