ΔE 23.3, loose: different enough that you should pick on purpose. Phalanx Yellow is noticeably lighter, much more saturated, warmer than Bile Yellow.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Phalanx Yellow is noticeably lighter, much more saturated, warmer than Bile Yellow.
The same difference applies the other way round: Bile Yellow is noticeably darker, much more muted, cooler.
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 Phalanx Yellow on the colour wheel
All matches: Bile Yellow equivalents · Phalanx Yellow equivalents