Symlog for PGFPlots

Question

I'm trying to plot data that ranges from [-1e8,1e8] and I would like to represent it using a symmetric log plot. I've found this solution to my problem but it seems the axes fail as soon as the data is >abs(1e5). A very simple MWE even without negative data shows that the y-axis only prints up to 1.64e4 and doesn't seem to be accurate anymore at larger values:

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat = newest}
\usetikzlibrary{math}
\tikzmath
{
  function symlog(\x,\a){
    \yLarge = ((\x>\a) - (\x<-\a)) * (ln(max(abs(\x/\a),1)) + 1);
    \ySmall = (\x >= -\a) * (\x <= \a) * \x / \a ;
    return \yLarge + \ySmall ;
  };
  function symexp(\y,\a){
    \xLarge = ((\y>1) - (\y<-1)) * \a * exp(abs(\y) - 1) ;
    \xSmall = (\y>=-1) * (\y<=1) * \a * \y ;
    return \xLarge + \xSmall ;
  };
}
\begin{document}
\begin{tikzpicture}
  \def\basis{50}
  \pgfplotsset
  {
    y coord trafo/.code={\pgfmathparse{symlog(#1,\basis)}\pgfmathresult},
    y coord inv trafo/.code={\pgfmathparse{symexp(#1,\basis)}\pgfmathresult},
    yticklabel style={/pgf/number format/.cd,int detect,precision=1},
}
\pgfplotstableread{
0 1
1 1e2
2 1e3
3 1e5
4 1e7
}\dataset
  \begin{axis}
    [
      height=.48\textwidth,
      scaled ticks = base 10:0,
      domain=0:4,
      ytick={1e1,1e3,1e5,1e7},
      x tick label style={/pgf/number format/.cd,fixed,fixed zerofill,precision=3}
    ]
              \addplot []
              table [x index = {0}, y index = {1}]
              \dataset;
  \end{axis}
\end{tikzpicture}
\end{document}

where this is the output

Using almost the exact same code as the linked OC but extending the domain past to -5:15 causes the same problem

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{math}
\tikzmath
{
  function symlog(\x,\a){
    \yLarge = ((\x>\a) - (\x<-\a)) * (ln(max(abs(\x/\a),1)) + 1);
    \ySmall = (\x >= -\a) * (\x <= \a) * \x / \a ;
    return \yLarge + \ySmall ;
  };
  function symexp(\y,\a){
    \xLarge = ((\y>1) - (\y<-1)) * \a * exp(abs(\y) - 1) ;
    \xSmall = (\y>=-1) * (\y<=1) * \a * \y ;
    return \xLarge + \xSmall ;
  };
}
\begin{document}
\begin{tikzpicture}
  \def\basis{1}
  \pgfplotsset
  {
    y coord trafo/.code={\pgfmathparse{symlog(#1,\basis)}\pgfmathresult},
    y coord inv trafo/.code={\pgfmathparse{symexp(#1,\basis)}\pgfmathresult},
    yticklabel style={/pgf/number format/.cd,int detect,precision=2},
}
  \begin{axis}
    [
      height=12cm,
      legend pos=north west,
      scaled ticks = base 10:0,
      domain = -5:15,
      ytick = {-100,-10, -1,0,1,10,100,1e6},
      minor ytick = {-90,-80,...,-20,-9,-8,...,-2,-.9,-.8,...,.9,2,3,...,9,20,30,...,90},
      tick label style = {fill=white, fill opacity=.7},
      yminorgrids = true,
      ymajorgrids = true,
      xmajorgrids = true,
      samples=200,
      axis lines=center,
    ]
    \addplot+ [mark=none] {x} ;
    \addplot+ [mark=none] {exp(x)} ;
    \addplot+ [mark=none] {-exp(-x)} ;
    \legend {$x$,$e^x$,$-e^{-x}$}
  \end{axis}
\end{tikzpicture}
\end{document}