pgfplots and hyperref clash for complicated figure in book class

Question

When using the book class, pgfplots, hyperref, and section labeling according to "How to reset chapter and section counter with \part", I get the following error

! You can't use `the character -' after \the.
\value ->-
          1.60942
l.51     \end{axis}

in the following MWE

\documentclass[a4paper, 12pt]{book} 

\usepackage{pgfplots}
\pgfplotsset{compat=1.7} % to use more recent defaults

\usepackage{hyperref}

%section restarts at each part
%see https://tex.stackexchange.com/questions/54383/how-to-reset-chapter-and-section-counter-with-part/123777#123777
\makeatletter\@addtoreset{chapter}{part}\makeatother

\begin{document}

\begin{figure}
  \centering
\pgfplotsset{
    colormap/hot,
}%
\pgfmathparse{-ln(0.1)}%
\let\BEMAX=\pgfmathresult

\pgfmathparse{-ln(5)}%
\let\BEMIN=\pgfmathresult

% FIRST: define one color for every value of \be : 
\pgfplotsforeachungrouped \be in {
        0.1,
        0.5,
        0.8,
        1.0,
        2.0,
        5.0} {
    \pgfmathparse{-ln(\be)}
    \let\value=\pgfmathresult
}


\begin{tikzpicture}
    \begin{axis}[ylabel={$p(x)$},
        legend to name={fig:mm_temp_legend}
    ]
      \pgfplotsforeachungrouped \be/\zedd in {
                0.1/12.4595,
                0.5/18.3263,
                0.8/29.6888,
                1.0/43.0372,
                2.0/403.539,
                5.0/1.07923e6 } {
       \addplot+ gnuplot {x};
      }
    \end{axis}
  \end{tikzpicture}
\end{figure}

\end{document}

which was adapted from Christian Feuersänger's answer to "line legend for mesh plots". I tried to make the example as small as possible. In particular, removing any of \usepackage{hyperref}, \makeatletter\@addtoreset{chapter}{part}\makeatother, \let\value=\pgfmathresult or legend to name={fig:mm_temp_legend} makes it compile.

Answer 1

\value is an important command of LaTeX related to counters and redefining it is a bad idea. Use \VALUE or some other name.

---

Note that you can simplify your construct

\pgfmathparse{-ln(0.1)}\let\BEMAX=\pgfmathresult

as

\pgfmathsetmacro\BEMAX{-ln(0.1)}

and similarly for the other alike calls.

It's also a bad idea, in my opinion, to reset chapter numbers for each part, which makes cross references very clumsy

as we saw in chapter 2 of part III

Anyway, with the chngcntr package the change is easier:

\usepackage{chngcntr}
\counterwithin*{chapter}{part}

With the * the chapter counter representation is not modified; it would become \thepart.\arabic{chapter} if the *-variant is not used.