Seeing that you prefer rhythmic songs, so I picked a few, mainly Japanese, some are not anime songs, and some are random songs I found... as follows

スカイクラッドのObserver (Steins Gate)

Departure (Grandson of the Slippery Ghost)

ready to go! (melody)

crossing field (LiSA-Sword Art Online)

oathsign (LiSA-FATE ZERO)

to the beginning (FATE ZERO)

torch (clannad after story)

ほうき星(bleach)

メリッサ (Steelmaking Season 1)

UNDO (COOL JOKE - Steelmaking Season 1)

MEMORIES (one piece)

Butter Fly (Digimon)

Oblivious (Kalafina)

Light Melody (Kalafina)

パーソナルCOLOR

Paradise.Lost

たった1つの思い

夜风ドライブ（UNLIMITS）

Introducing another way to find songs : Search the top series of anime songs and you will get unexpected results