I tried gnuplot and amazed by its performance. It allows you to directly plot mathematical formulas into graphs with just one single line of math equation.
#+BEGIN_SRC gnuplot :file images/trigon01.png
plot [-10:10] sin(x),atan(x),cos(atan(x))
#+END_SRC
when set arguments, it might requires one more line:
#+BEGIN_SRC gnuplot :file images/sd01.png
g(x) = exp(-0.5*(x/s)**2)/s
plot s=1 g(x), s=2 g(x), s=3 g(x)
#+END_SRC
I feel frustrated, how I wish could acquainted with such a tool a decade ago while grappling with the challenges of visualizing mathematical formulas.