Sophia Thanks, glad you like it!
Your Yamaha e373 can do backing tracks similar to BIAB, without the tedium of entering chords for each measure, telling it how to behave, then exporting that form to a DAW, like Sonar or GarageBand, to make the additional tracks, solos, etc. I've tinkered with BIAB since 2009 (the Windows version I'm using), so I've figured out how to use it. But the interface is clunky, and because it does so much, trying to cover all musical possibilities, there's a lot to learn right from the start. The latest version has more features, and even the basic version is probably worth it, IF... you like tinkering and sifting through the minutiae of endless possibilities.
A simpler tool is Ireal Pro. I think it's $20; mainly jazz styles. Just enter the chords, hit play. Bass, drums, and either piano, electric piano, or guitar. Comes with 1300 jazz tunes that you can play along with, has a great support community. I've used it to practice with, handy for slowing down tricky changes.
I would classify "Back In The Day" as part swing, part Bebop (chord changes are similar to other bebop tunes like: Fried Bananas by Dexter Gordon, Groovin' High by Dizzy Gillespie, Confirmation by Charlie Parker). The term "smooth jazz" came about in the 80s when LA studio players, like Lee Rittenour, David Sanborn, Tom Scott, start ed taking rock type changes and adding jazz elements, gave it a more pronounced beat, to make it more accessible to a wider audience, even dance-able. Steely Dan, and the players associated with those albums had a lot of influence, too.