Sorry for gravedigging, looking at these ICs myself, and came over this post, the devil is in the details

I'm looking to make a circuit for myself, and noticed your circuit has a flaw compared to the datasheet, increasing the boost voltage unnecessarily by 4 volts (40mA*100ohm and 0,16W powerloss), in your LED resistors, making the circuit work hard to boost the voltage 4V more than it needs.
They are not needed, as the IC limits the current to 40mA (that's why it was designed in the first place).
Anyway, looking for tips on good efficiency small IC to run some LED with a cell of lithium, Looked at MIC2289, AP3019, MIC2287 so far.
If you came across a better IC, please share

All the best,
Frode.