Is it practical to implement the Lorenz-Mie(LM) phase function in a renderer ?

$p(\cos\theta)=\frac{|S_1(\theta)|^2+|S_2(\theta)|^2}{4\pi\sum_{n=1}^\infty (2n+1)(|a_n|^2+|b_n|^2)}$

I'll spare you the details but: $S_1(\theta), S_2(\theta), a_n, b_n$ are complex numbers involving Legendre polynomials, and their derivatives. All of that to say the computations are quite involved.

So do the benefit of LM phase function(Physical accuracies mainly) outweighs the cost to computed them, or I better off with the standard Henyey-Greenstein or some modified version of it ?