What is the legal test for "prosecution due diligence" in its search for a witness?

a mechanical definition," but it "connotes persevering application, untiring efforts in good earnest, efforts of a substantial character."' [Citation.] Relevant considerations include the timeliness of the search, the importance of the witness's testimony, and whether leads were competently explored." (Snchez, supra, 63 Cal.4th at p. 440.) Additional factors include whether the prosecution "'reasonably believed prior to trial that the witness would appear willingly and therefore did not subpoena him when he was available'" and "'whether the witness would have been produced if reasonable diligence had been exercised.'" (People v. Sanders (1995) 11 Cal.4th 475, 523.)

"The reviewing court defers to the trial court's determination of the historical facts if supported by substantial evidence, but it reviews the trial court's ultimate finding of due diligence independently, not deferentially." (Snchez, supra, 63 Cal.4th at p. 440; see People v. Cromer (2001) 24 Cal.4th 889, 900-901 [appellate courts apply a deferential standard of review to trial court's factual findings regarding prosecution's efforts to locate the absent witness, while independently reviewing whether the efforts "demonstrate prosecutorial due diligence in locating the absent witness"].)