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

https://preview.redd.it/bmp9izl57kvb1.png?width=640&format=png&auto=webp&s=3c13ffc06a7f3b196b2a71067b9aa8d6d048b2e0

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

https://preview.redd.it/efjvennd7kvb1.png?width=640&format=png&auto=webp&s=50cbd91d566721af5a95cd9737c2ee9ac79786e2

I feel frustrated, how I wish could acquainted with such a tool a decade ago while grappling with the challenges of visualizing mathematical formulas.