Color intersection between curves using fillbetween

Question

I have two Guassian distribution curves, as shown here and I am attempting to color the areas under the curves as well as the intersection between them, like here:

I assumed fillbetween would be the appropriate tool here, but that produced some strange results. Below is the code

\begin{tikzpicture}
    \begin{axis}[
    axis lines=left,
    domain=0:10, 
    samples=100,
    ymin=0,
    xtick=\empty,
    ytick=\empty,
    enlargelimits=false, 
    clip=false,
    ]

    \addplot [thick, orange, name path=cat] {gauss(x, 3, 1)} node[pos=0.3, above]{cat};
    \addplot [thick, purple!70!black, name path=puma] {gauss(x, 5, 0.5)} node[pos=0.5, above right] {puma};

    \path[name path=axis] (axis cs:0,0) -- (axis cs:10,0);

    \addplot[
        thick,
        color=orange,
        fill=yellow,
        fill opacity=0.25
    ]
    fill between[
        of=cat and axis
    ];

    \addplot[
        thick,
        color=purple!70!black,
        fill=purple!70!black,
        fill opacity=0.25
    ]
    fill between[
        of=puma and axis
    ];

    \addplot[
        thick,
        color=white,
        fill=blue,
        fill opacity=0.25
    ]
    fill between[
        of=cat and puma
    ];
    \end{axis}
\end{tikzpicture}

which produces this:

Every other answer I've found either miraculously makes fillbetween work or avoids it entirely (usually in ways that seem more complicated than is necessary for a simple task such as this).

Can anyone explain to me what is missing to make fillbetween achieve the desired results or recommend a clean alternative? Thanks in advance.

Answer 1

As already mentioned in the comment below the question next time you should either provide a full minimal working example (MWE) or state exactly what you expect from the code and where the error might be.

Here I provide the code to get the I output that I think you are searching for. For more details please have a look at the comments in the code.

% used PGFPlots v1.15
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
    \usepgfplotslibrary{fillbetween}
    \pgfplotsset{
        /pgf/declare function={
            % normal distribution where \mean = mean and \stddev = sd}
            gauss(\mean,\stddev) = 1/sqrt(2*pi*\stddev^2) * exp(-((\x-\mean)^2)/(2*\stddev^2));
        },
    }
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        axis lines=left,
        domain=0:10,
        samples=101,
        ymin=0,
        xtick=\empty,
        ytick=\empty,
        enlargelimits=false,
        clip=false,
    ]

        \addplot [
            thick,
            orange,
            name path=cat,
        ] {gauss(3, 1)}
            node[pos=0.3, above] {cat}
        ;
        \addplot [
            thick,
            purple!70!black,
            name path=puma,
        ] {gauss(5, 0.5)}
            node [pos=0.5, above right] {puma}
        ;

        \path[name path=axis] (axis cs:0,0) -- (axis cs:10,0);

        % because `cat' and `puma' only intersect once and both have a minimum
        % value of 0, both areas can be filled with one call without filling the
        % common area
        \addplot[
            thick,
        ] fill between [
            of=cat and puma,
            split,
            every segment no 0/.style={
                fill=yellow,
                fill opacity=0.25,
            },
            every segment no 1/.style={
                fill=purple!70!black,
                fill opacity=0.25
            },
        ];

        % compute + label the lower area (but do not draw it):
        \path [
            name path=lower,
            intersection segments={
                of=cat and puma,
                sequence=R1 -- L2,
            }
        ];

        % fill the lower area
        \addplot [
            fill=blue,
            fill opacity=0.25,
        ] fill between [
            of=axis and lower,
        ];

    \end{axis}
\end{tikzpicture}
\end{document}