We prove that if $$q_1,\dots ,q_m:{\mathbb {R}}^n \rightarrow {\mathbb {R}}$$ are quadratic forms in variables $$x_1,\dots ,x_n$$ such each $$q_k$$ depends on at most r and has common with other forms, then the average value of product $$(1+q_1)\cdots (1+q_m)$$ respect to standard Gaussian measure $${\mathbb {R}}^n$$ can be approximated within relative error $$\epsilon >0$$ quasi-polynomial $$n...