tikzpicture has a node whose text is a tree: unevenly formatting

Question

I want to typeset a picture similar to the following one, using tikz.

For that purpose I have written the following latex document

\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{chains}

\begin{document}

\begin{tikzpicture}[
  level distance=10mm,
  op/.style={circle,draw,fill=red!20},
  leaf/.style={circle,fill=blue!20,font=\ttfamily},
  ]
  \node (in) [fill=green!10] {\texttt{1 + 2*3}};
  \node (out) [fill=green!10,right=30mm of in] {
    \tikz{
      \node [op] {$+$}
        child { node [leaf] {1} }
        child { node [op] {$\times$}
          child { node [leaf] {2} }
          child { node [leaf] {3} }};
    }
  };
  \draw[->] (in) -- node [above] {\emph{parsing}} (out);
\end{tikzpicture}

\end{document}

which gives me the output

Notice that in the tree, the left and right edges from each node are not symmetric: the left one is shorter than the right one. When the same tree is drawn outside of the out node, they are symmetric.

Why am I getting this effect, and how to fix this issue?

Answer 1

Say it backwards:

\begin{tikzpicture}[
  level distance=10mm,
  op/.style={circle,draw,fill=red!20},
  leaf/.style={circle,fill=blue!20,font=\ttfamily},
  ]
  \node (out) [fill=green!10] {
    \tikz{
      \node [op] {$+$}
        child { node [leaf] {1} }
        child { node [op] {$\times$}
          child { node [leaf] {2} }
          child { node [leaf] {3} }};
    }
  };
  \node (in) [fill=green!10,left=30mm of out] {\texttt{1 + 2*3}};
  \draw[->] (in) -- node [above] {\emph{parsing}} (out);
\end{tikzpicture}

I really don't know why it works.