ΔE 19.0, loose: different enough that you should pick on purpose. Dorn Yellow is noticeably lighter, more saturated than Bile Yellow.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Dorn Yellow is noticeably lighter, more saturated than Bile Yellow.
The same difference applies the other way round: Bile Yellow is noticeably darker, more muted.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Bile Yellow on the colour wheel See Dorn Yellow on the colour wheel
All matches: Bile Yellow equivalents · Dorn Yellow equivalents