Adjustlimits in combination with smashoperator

Question

I would like to use the method \adjustlimits from the mathtools package in conjunction with the \smashoperator method. In the MWE I don't know how and where to use the \adjustlimits method. Trying to write it at the beginning with and without parentheses always produces errors.

MWE

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[
  \smashoperator{\sum_{i \in X \colon i \neq 5}} \, x_i  - \smashoperator{\sum_{i \in \bar{X} \colon i \neq 8}} \, y_i
\]
\end{document}

Answer 1

The \adjustlimits operation requires the operators to be at the same brace level, which is not possible with \smashoperator. In this case you can easily adjust things manually:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[
\smashoperator{\sum_{i \in X \colon i \neq 5\vphantom{\bar{X}}}} \, x_i  -
\smashoperator{\sum_{i \in \bar{X} \colon i \neq 8}} \, y_i
\]
\end{document}

The \vphantom with the highest object as argument will adjust the size.

However, the documentation of mathtools specifies that operators should immediately follow one another, in order for \adjustlimits to work, so this approach would not work anyway, because of the x_i- between the summation operators.

Here's how I would set this, with \substack:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[
\sum_{\substack{i \in X\vphantom{\bar{X}} \\ i \neq 5}} x_i  -
\sum_{\substack{i \in \bar{X} \\ i \neq 8}} y_i
\]
\end{document}