composition in after effects running slow and doesnt render properly

Preview duration depends entirely on system resources, comp size, comp frame rate, and source footage specifications. The time it takes to render each frame depends on source footage size, effects, comp frame size, and system resources. After Effects is not a video editing app. It is a Motion Graphics, animation, and visual effects/compositing app designed specifically to create shots that you cannot create in an NLE like Premiere Pro. After Effects looks at every pixel on every layer in every frame and makes calculations for each frame. I did a project a couple of days ago that took a little more than 2 minutes to render each frame when all of the effects were applied and the comp was at full resolution with motion blur turned on. That was acceptable for that project. The design limit for an animated frame for companies like Pixar has historically been 7 minutes a frame for the final frame. If the frame takes longer to render than that, redesign the shot. So how do they get things done? They and I use the "Pencil Sketch / Ink and Paint" workflow animators have used since the very first days of animation and visual effects. Pencil Sketch is a low resolution (comp Magnification Ratio set to 50% or less and Comp Resolution to Auto) preview of the comp without motion blur and minimum effects so you can check the framing, blocking (how things move) and timing of a shot, then Ink and Paint is applied by checking a few of the Hero or most critical frames in the comp at full resolution (Magnification Ration set to 100%, resolution full), motion blur and all effects on. Get a second or two of preview at this resolution if you can, then send the file to be rendered to a lossless digital intermediate so it can be edited in an NLE like Premiere Pro, and the sound can be edited, and the final color grading for the movie can be done. That's how to efficiently use After Effects. Use it to create shots, not edit videos. 

Your screenshot* shows me a timeline that is probably about 10 minutes long, has multiple layers that are shorter than the comp, and it might have some nested comps (pre-comps) in the timeline.  The screenshot is also cropped so I have no idea what is really going on in the comp.

Your screenshot tells me you are trying to use After Effects to edit a movie. It is not designed for that and it will never give you a 10-minute full resolution, full effects preview of a movie unless you spend more for your computer than you would on a new house on the beach in Maui. You have to be satisfied with short ram previews at low resolution, and possibly even skip frames to see more than a few seconds at a time. It is that way with all compositing and animation apps. Preview time is limited to the system resources available on that machne. Some do a better job than After Effects at looking ahead and caching frames, but they all have to render before they playback. An NLE like Final Cut Pro, Avid, Davinci Resolve, or Premiere Pro, on the other hand, does its best to give you a real-time preview of what it can and throws out everything it can to playback in real-time. Even if the NLE will preview in real-time, rendering always takes longer, sometimes significantly longer, than the length of the sequence. I'm working on a section of a documentary feature right now that is just under an hour. I ran a render for the client to review last night and it took about 6 hours. Inside that documentary, I have an 8 second animated graphic I created in After Effects that took about 40 minutes to render. When the final movie is rendered it will have hundreds of 3 to 10 seconds shots created in After Effects as separate comps, but all of the editing will be done in Premiere Pro. 

My suggestion, simplify, keep each comp no longer than one shot unless you must use After Effets to create a transition between shots that cannot be done in an NLE, render your comps, then do the final editing in Premiere Pro.

I hope this helps.

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