Cache math content in savebox and account for math style

Question

I am using Create a \savebox in a Group and have it available outside of group to cache some math content. However, I realized that there may be a case where the same math content needs to be cached for different math styles.

I attempted to make use of the scalerel package mentioned at Proper-use-of-mathchoice and include that in the style. But, I am not able to get the functionality of \SavedStyle to be applied to the math content. The MWE below produces:

The desired output has a smaller \sqrt in the denominator:

Code:

\documentclass{article}
\usepackage{etoolbox}
\usepackage{xparse}
\usepackage{scalerel}
\NewDocumentCommand{\CachedMathContent}{s O{} m}{%
    % #1 = not used here
    % #2 = String to use to store cached name. 
    %      Declared as optional (for compatibility with another related macro), but 
    %      in this example it is really mandatory. 
    % ---------
    % Code to check that #2 was provided has been omitted here.
    \ThisStyle{% scalerel pacakge
        \begingroup
        \edef\CachedMathBoxName{MathBox #2 \string\SavedStyle}%
        \ifcsdef{\CachedMathBoxName}{%
            %% Cached content already exists
        }{%
            %% https://tex.stackexchange.com/questions/283373/create-a-savebox-in-a-group-and-have-it-available-outside-of-group
            \global\expandafter\newsavebox\csname\CachedMathBoxName\endcsname%
            \global\expandafter\setbox\csname\CachedMathBoxName\endcsname%
                    \hbox{$\SavedStyle#3$}%
        }%
        \expandafter\usebox\csname\CachedMathBoxName\endcsname%
        \endgroup
    }%
}%
\begin{document}
Should be cramped: $\frac{1}{\CachedMathContent[sqrt phi]{\sqrt{\phi}}}$
\medskip
Should NOT be cramped: $\CachedMathContent[sqrt phi]{\sqrt{\phi}}$
\end{document}

Answer 1

\documentclass{article}
\usepackage{etoolbox}
\usepackage{xparse}
\usepackage{scalerel}

\NewDocumentCommand{\CachedMathContent}{s O{} m}{%
    % #1 = not used here
    % #2 = String to use to store cached name. 
    %      Declared as optional (for compatibility with another related macro), but 
    %      in this example it is really mandatory. 
    % ---------
    % Code to check that #2 was provided has been omitted here.
    \ThisStyle{% scalerel pacakge
        \begingroup
\edef\x{\SavedStyle}%
\typeout{\meaning\x}%
        \edef\CachedMathBoxName{MathBox #2 \expandafter\string\x}%
        \ifcsdef{\CachedMathBoxName}{%
            %% Cached content already exists
        }{%
            %% http://tex.stackexchange.com/questions/283373/create-a-savebox-in-a-group-and-have-it-available-outside-of-group
\typeout{\meaning\CachedMathBoxName}%
            \global\expandafter\newsavebox\csname\CachedMathBoxName\endcsname%
            \global\expandafter\setbox\csname\CachedMathBoxName\endcsname%
                    \hbox{$\SavedStyle#3$}%
        }%
        \expandafter\usebox\csname\CachedMathBoxName\endcsname%
        \endgroup
    }%
}%

\begin{document}

Should be cramped: 
$\frac{1}{\CachedMathContent[sqrt phi]{\sqrt{\phi}}}$
$\frac{1}{\sqrt{\phi}}$

\medskip
Should NOT be cramped:
$\CachedMathContent[sqrt phi]{\sqrt{\phi}}$ 
$\sqrt{\phi}$ 

\end{document}

The intention of the code was to save a box based on the supplied argument and the current style but

    \edef\CachedMathBoxName{MathBox #2 \string\SavedStyle}%

uses #2 and the literal string \SavedStyle it does not use the definition of \SavedStyle (it would not need it to be defined at all).

You need to fully expand that macro to something like \textstyle and then apply \string to that hence the \edef and \expandafter.