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With a node tree of shaders, how can I "extract" the resultant BRDF?

Ideally, I wish I could compute an analytical formula from the node tree: BRDF($x$, $\omega_i$, $\omega_o$), but I understand this might be too utopian. Alternatively, can I feed in a bunch of $x$, $\omega_i$, $\omega_o$ and get the BRDF values? This would suffice my task too.

Right now, I am doing this "the brute force way": I turn off multi-bounce and keep direct illumination only, render a LOT of .exr images using different $\omega_i$ and $\omega_o$ configurations, and finally assemble them into an empirical BRDF. This is just toooooo expensive.

If there's no solution to this problem, what if my node tree is really simple? Like a mixture of a glossy and a diffuse shaders? How do I get the underlying analytical/empirical BRDF?

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