If United fly user prefered tracks as does Qantas, there is every chance that the resulting flight plan bears absolutely no resemblance to a great circle. Some of the tracks YSSY - KLAX I've seen can go over Noumea (NWWW) and Hilo (PHTO), while others are almost in the circuit at Raratonga (NCRG) and way west of Pago Pago (NSTU).
Remember, it's min fuel the flight plan looks for, not min distance.