1. A computer-readable recording medium storing therein a computer program for performing circuit delay analysis on a subject using an all-element delay distribution and a correlation delay distribution, the all-element delay distribution indicating delay based on performance of all circuit elements in a path, the correlation delay distribution indicating delay based on correlation between circuit elements in the path, the computer program causing a computer to execute: extracting, from a data set including the all-element delay distributions and the correlation delay distributions of paths in the subject, a first all-element delay distribution and a first correlation delay distribution of a first path among the paths and a second all-element delay distribution and a second correlation delay distribution of a second path among the paths; calculating a total delay distribution representing a total delay of an integrated path formed by combining the first path and the second path, based on the first all-element delay distribution, the first correlation delay distribution, the second all element delay distribution, and the second correlation delay distribution; calculating a third all-element delay distribution of the integrated path based on the first all-element delay distribution and the second all-element delay distribution; and calculating a third correlation delay distribution of the integrated path based on the total delay distribution and the third all-element delay distribution.