Gymnastics on a horse
Equestrian vaulting was an Olympic sport during the 1920s Olympic games. It is essentially gymnastics on a horse.
It dates back to Roman times but is still practised today in Europe and the USA.
Riders are scored on their ability to perform moves such as the mount, basic seat, flag, mill, scissors, stand and flank. Horses also receive a score based on their movement and behaviour. The whole thing is choreographed to music.
https://equimanagement.com/news/saturday-competition-wrap-up-for-weg-tryon-2018