Consider all programs

• u₀= average of all the probability vectors at the deepest leaf
• N_di is matrix for first function d argument i

  u₁= u₀M₁. And M₁ = u₀N_di

• Average across all functions. Average across both arguments

  Let $N=1/{f}\sum_{j=1}^{j=f} 1/2\sum_{k=\mbox{left}}^{k=\mbox{right}} N_{jk}$

  Where $f = \vert\mbox{function set}\vert$

  So on average M₁=u₀N

  and u₁ = u₀M₁