It's a good skill for any musician not just pianists to be able to play through a standard tune with these voicings. Getting this basic harmony together on the piano will help greatly with hearing and especially memorizing the chord changes to standard tunes. This is a tune by the great composer (and greatly under appreciated composer) and trumpeter Freddie Hubbard. Have fun!
* Note that on half-diminished chords it is possible to substitute the root for the ninth if that sounds better to you.