I'm trying to reproduce the following pyplot figure with pgfplots:

```
import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 1)
plt.plot(np.log(x)-np.log(1-x), np.log(x / (x + (1-x))))
plt.xlim(-3, 3)
plt.show()

```

My attempt so far with pgfplots, using `x coord trafo`:

```
\documentclass[tikz,12pt,preview]{standalone}
\usepackage{tikz,pgfplots}
\pgfplotsset{compat=1.13} 

\begin{document}

\begin{tikzpicture}
\begin{axis}[every axis plot post/.append style={
  mark=none,domain=0:1,samples=200},
  x coord trafo/.code={\pgfmathparse{log10(#1) - log10(1-#1)}},
  ]
  \addplot {log10(x / (x + (1-x)))};
\end{axis}
\end{tikzpicture}

\end{document}

```

I think I'm close, but am unable to set xlim to (-3, 3). I think I'm thinking too much in a pyplot manner! Is there an elegant way to achieve this?