The common phrases on a daily basis and on a regular basis are wordy for daily and regularly. The same applies to similar constructions such as on an hourly basis, on a yearly basis, and so on. Such phrases can usually be shortened to single-word adverbial equivalents.
Wordier basis-based phrases are appropriate where no one-word adjective exists, such as with on an adjusted basis and on a trial basis. But these are rare.
These instances of on a daily basis or on a regular basis could be shortened to just daily or regularly:
How much desktop software do you generally use on a daily basis? [CNN Money]
The use of gestation crates is without a doubt one of the worst offenses committed on a daily basis in factory farming. [The Dish is Veg]
Though we fall short of our ideals on a daily basis, Americans are committed to the principle of the level playing field. [Forbes]
Blood, knives and carcasses surround Tommy Estevez on a daily basis. [The Independent Florida Alligator]
And the similar constructions in these sentences could likewise be shortened to single-word equivalents:
A former Healdsburg police chief will run the Santa Rosa Junior College police department on a temporary basis [temporarily]. [KSRO]
One area we expect to do better on a relative basis [relatively] this year is the US. [Market Minder]