There are two scores. The D score - difficulty score and the E score - execution score. They are both added together to get the final score.
The E score is the easiest to understand. It is a score out of 10.0 and points are taken off for mistakes. The deductions are bigger than in JO. the smallest deduction is 0.1 which is taken for things like unpointed toes, slight lack of body tension, crossed legs, small leg separations, small wobbles and so on. For moderate mistakes they lose 0.3 such as bigger arms and leg bends, lack of split in leaps, lack of height in casts and so on. For big mistakes they lose 0.5 this would be something like an arm or knee bent more than 90 degree's, or landing in a really low squat on dismount. For a fall they lose 1.0 a full mark.
The D score is worked out in three parts. First there are the elements. The top 8 elements in the routine, including the dismount are taken. They get 0.1 for an A, 0.2, for a B, 0.3 for a C and so on. On beam and floor at least 3 of the top elements have to be dance so they can't just do really hard tumbling skills. So lets say for example they do 1 E skill, 2 D skills, 4 C skills and a B skill. They would get 2.7.
The second part of the D score are the compositional requirements. There are 5 of them on each apparatus and for each one they get 0.5. For example on bars they need to have. 1. a flight skills from low to high bar and a flight skill from high to low bar. 2. a release skill to catch the same bar. 3. 2 different circling elements and skills in different directions. 4. a 360 pirouette skill. 5. A D value or above dismount. So if they have all their compositional requirements they then get 2.5, this is added to the 2.7.
The final part of the D score are connection bonus's which are either 0.1 or 0.2 for connecting difficult skills together. So then these three things are added together to get the C score and this is added to the E score to get the final score.
It sounds complicated but it really isn't.