I tried some simple algebra, but I'm not getting the result I expected (or 
given by macsyma).

The problem is to invert the Normal distribution:

In [11]: solve (Eq (1/(sqrt(2*pi)*s) * exp (-(x**2)/(2*(s**2))),y), x)
Out[11]: [I*2**(1/2)*(s**2)**(1/2)*log(s*y*2**(1/2)*pi**(1/2))**(1/2)]

The expected answer is sqrt(-2 s**2 log(sqrt(2 pi) s y)

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