What is the test for a motion to postpone a trial on the ground of the absence of evidence?

Code of Civil Procedure section 595.4 provides in relevant part that a "motion to postpone a trial on the ground of the absence of evidence can only be made upon affidavit showing the materiality of the evidence expected to be obtained, and that due diligence has been used to procure it." A trial court has broad discretion in ruling on a motion for a continuance. (In re Marriage of Johnson (1982) 134 Cal.App.3d 148, 154, 184 Cal.Rptr. 444.) It is the duty of the trial court to vigorously insist upon cases being heard and decided in the most timely manner possible, unless there are compelling reasons to the contrary. (Mann v. Pacific Greyhound Lines (1949) 92 Cal.App.2d 439, 446, 207 P.2d 105.)