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I am assuming that box office grade animation (Moana, Zootopia, etc.) used ray tracing physically based renderer like Blender's Cycles, and so the amount of tries to sample per pixel is needed. I would like to know what amount of sample setting they usually use to achieve that level of quality? Basically I have never seen anything like fireflies noise in theater like in my personal rendering.(If you know a rough number of computer specs, # of computer in a cluster they use that would be really helpful)

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Depends.

The thing that you noticed was that it looked good. That is the target, not a certain number of samples.

You may have noticed for instance that a glass shader typically needs more samples than a diffuse shader. Once you have determined a ratio of samples that looks good (assuming you are using branched path-tracing which separates out the number of samples each type of shader uses per pass), then you can turn up the samples to produce higher quality results.

If you are trying to reduce fireflies, that is a separate question that has already been answered here.

Computer specs don't really matter either, as it is more a matter of what gets the job done in a certain amount of time within budget. The more computers and/or more powerful computers you throw at the "problem" of rendering, the easier it becomes to quickly produce animation.

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As mentioned the number of samples is something that will vary between every shot, you can also expect any flaws would be fixed before a cinematic release.

You can find some information online about different render farms used by studios, the details are also something that is always changing.

For Toy Story Pixar started with 53 processors, which expanded to about 300 before completing the film. According to this post it originally took about 4 hours per frame and re-rendering it on more recent machines took 2-4 minutes per frame.

Cars 2 averaged 11.5 hours per frame, with some shots taking up to 90 hours per frame and used a 12,500 core render farm.

Monsters University had 24,000 cores in the farm, and one frame took up to 29 hours, think of all that fur - "Sully now has 5.5 million individual hairs in his fur"

You can see that Toy Story was at the beginning of rendering and would have used various tricks to emulate an effect, same as home users still do to reduce render times, newer movies get better render results and leave more work to the renderer to get accurate results.

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