Song of Celerity unaffected by Wild Embrace

[Flights of Fantasy]

Wild Embrace is supposed to grant an additional three caster levels when active, yet I noticed that if I used Song of Celerity to add a spell to my longsword, the caster level is still set to 30. I ran into the forest to do some tests using Flame Arrow. This spell can send off eight flaming arrows when Wild Embrace is active because it does 1 per 4 caster levels (Caster Level 30 + 3 = 33 / 4 = 8.25). If I just cast the spell, the enemy was struck by fire damage 8 times. But if I cast the spell onto my longsword using Song of Celerity, the enemy will only be struck by fire damage 7 times. I confirmed this in the Combat Log. This might also be true for other PrC abilities that can boost caster level such as Mystic Theurge.