How to properly walk from PDF to quantile using symbolic representations?

I like to start with the PDF and symbolically reach the quantile of the normal distribution. I discover two unexpected behaviors: 1. My symbolic representation is simplified in an unexpected manner 2. The finverse function fails in the CDF.

Can I stop the simplification and run the functional inverse?

Here is what I am trying:

syms x mu sd;
n_x = (1/sqrt(2*pi*sd^2)) * (1/exp( (x-mu)^2/(2*sd^2) ));
pretty(n_x)

Resulting in:

                 1/2
                2
  ---------------------------------
             /         2 \
      1/2    | (mu - x)  |    2 1/2
  2 pi    exp| --------- | (sd )
             |       2   |
             \   2 sd    /

Equivalent, but not what I have typed. How can I make Matlab maintain the common notation, rather then the "simplified" one?

It becomes even more strange when integrating and then running the function inverse:

int_n_x = int(n_x);
pretty(int_n_x);

Resulting in:

       /  1/2          /  1  \1/2 \
       | 2    (mu - x) | --- |    |
       |               |   2 |    |
       |               \ sd  /    |
    erf| ------------------------ |
       \            2             /
  - -------------------------------
           /  1  \1/2    2 1/2
         2 | --- |    (sd )
           |   2 |
           \ sd  /

Because I can see that this unlikely to match to an inverse function I substitute some simple values and try finverse:

int_n_subs_x= subs(int_n_x, {mu, sd}, {0,1});
pretty(int_n_subs_x);

       /  1/2   \
       | 2    x |
    erf| ------ |
       \   2    /
    -------------
          2
  finverse(int_n_subs_x)
  Warning: Functional inverse cannot be found.

Why does it fail if Matlab knows about icdf and erfinv?