Extensible leftarrow accent above math symbols

Question

How can I get a left arrow as a math accent to go over single symbols and groups of symbols, in such a way that:

• the left arrows over a single character and multiple characters have the same heaviness; and
• the left arrow over a single character is not overly long?

Here is what I've tried so far:

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{newtxtext,newtxmath}
\usepackage{accents}
\usepackage{extarrows}

\linespread{1.1} % just to display output here more clearly

\newcommand{\reverse}[1]{\accentset{\leftarrow}{#1}}
\newcommand{\xreverse}[1]{\accentset{\xlongleftarrow{}}{#1}}
\newcommand{\longreverse}[1]{\overleftarrow{#1}}

\begin{document}

Accent single character with left arrow:

\smallskip

$\reverse{\sigma}$ \quad Arrow too short, too light, too small?

$\longreverse{\sigma}$ \quad Arrow too long and heavy!

\medskip

Accent multiple characters with left arrow:

\smallskip

$\xreverse{\sigma \ast \tau}$ \quad Use \verb!\xreverse!: arrow definitely too short. 

$\longreverse{\sigma \ast \tau}$ \quad Use \verb!\longreverse!: arrow long enough, but perhaps too heavy?

\bigskip

Want to use  better arrows in the alternative to \dots
\[(\sigma \ast \tau)^{\leftarrow} \simeq \reverse{\tau} \ast \reverse{\sigma}
\]
\dots that instead puts the long left arrow over the whole group of 3 symbols:

\begin{itemize}

\item $\longreverse{\sigma \ast \tau} \simeq \reverse{\tau} \ast \reverse{\sigma}$ \quad Use \verb!\longreverse! on left, \verb!\reverse! on right.

\item $\longreverse{\sigma \ast \tau} \simeq \longreverse{\tau} \ast \longreverse{\sigma}$ \quad Use \verb!\longreverse! for all.

\end{itemize}

\end{document}

I'd strongly prefer a method that avoids using TikZ or other drawing methods. And I need a method that will be relatively robust when a different font family (e.g., lucidabr, mathtimepro2) is used insstead of newtx. also when unicode-math is used along with a math font requiring xelatex.

I am aware of Configurable and Extensible Accents (Arrows, Dots, Vectors) and the item Dashed left arrow over symbol that is referenced by the accepted answer to it.

Addendum: using halloween command \overscriptleftarrow

Following the comment by @GuM, I tried the \overscriptleftarrow command from the halloween package. This does seem to work with all the font families I've tried, no matter whether I'm using pdflatex or, together with unicode-math, xelatex. For example:

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{fontspec}
%\setmainfont[Ligatures=TeX]{TeX Gyre Termes}
%\setmainfont[Ligatures=TeX,SmallCapsFont={Latin Modern Roman Caps}]{Latin Modern Roman}
\usepackage{unicode-math}
\setmathfont[Ligatures=TeX]{TeX Gyre Termes Math}
%\setmathfont[Ligatures=TeX]{Latin Modern Math}

\usepackage{halloweenmath}
\newcommand{\reverse}[1]{\overscriptleftarrow{#1}}

\begin{document}

$\reverse{\sigma \ast \tau} \eqsim \reverse{\tau} \ast \reverse{\sigma}$

\end{document}

Output:

Answer 1

Here is a solution using the calc and adjustbox packages. You can adjust the thickness of the arrow as well as its height as described below.

First we define the arrow:

\newcommand{\newarrow}{\scalebox{.7}{$\leftarrow$}}

Adjusting the .7 will make the arrow lighter or heavier. Using 1 will give you the original weight of \leftarrow, and will increase the size of the arrowhead.

Next we clip off the body of the arrow using the \clipbox command from the adjustbox package. (Actually it's from the trimclip package which is part of adjustbox.) What remains is .3em of the arrow: mostly just the arrowhead.

After that we scale the arrow body so that the head and body together make up the width of the symbols beneath the arrow. (Actually we clip .1em from the right end because there's some white space there.)

After that we place the reassembled arrow over the symbols using raise and rlap keys from the adjustbox package. If you want to adjust the height of the arrow, you can replace raise=\myheight with raise=1.2\myheight, or any scaling factor.

Here is the macro for \newreverse:

\newcommand{\newreverse}[1]{\settoheight{\myheight}{\ensuremath{#1}}%
\adjustbox{raise=\myheight,rlap}{%
\clipbox*{0 0 {.3em} {1.5\height}}{$\newarrow$}%
\resizebox{\widthof{\ensuremath{#1}}-.3em}{\height}{\clipbox*{{.3em} 0 {\width-.1em} {1.1\height}}{$\newarrow$}}%
}%
#1}

Note that you must define \myheight using \newlength{\myheight}. For some reason, the \adjustbox command doesn't accept raise=\heightof{#1}.

Here is the full code:

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{newtxtext,newtxmath}
\usepackage{calc} % for subtracting lengths
\usepackage{adjustbox} % \adjustbox, \clipbox, \scalebox

\newcommand{\newarrow}{\scalebox{.7}{$\leftarrow$}}
\newcommand{\newreverse}[1]{\settoheight{\myheight}{\ensuremath{#1}}%
   \adjustbox{raise=\myheight,rlap}{%
   \clipbox*{0 0 {.3em} {1.5\height}}{$\newarrow$}%
   \resizebox{\widthof{\ensuremath{#1}}-.3em}{\height}{\clipbox*{{.3em} 0 {\width-.1em} {1.1\height}}{$\newarrow$}}%
   }#1}

\newlength{\myheight}

\begin{document}

\begin{itemize}
\item $\newreverse{\sigma \ast \tau} \simeq \newreverse{\tau} \ast \newreverse{\sigma}$
\item $\newreverse{\mathit{abcdefghijklmnop}}$
\end{itemize}

\end{document}