Came across this at: shadertoyunofficial.wordpress.com/2016/0...ks-in-shadertoyglsl/
'pow(x,y) is doing exp(y*log(x)): costly, not valid for x<0, not perfect precision.
for x^2, do prefer x*x !
for 2^x use exp2(x). the reverse log2 also exist (both in most langages ).
atan API also includes the 2 parameters version doing atan2(y,x)'
atan2 is I believe the single most expensive intrinsic HLSL function there is. Log and exp are quarter rate instructions, mul is full rate, so pow usually takes 9 cycles. Atan2 is a macro that spawns dozens of instructions, also conditions since it has to consider the signs of both arguments. Inverse trigonometry is to be avoid at all cost so asin, acos, atan.
The person who made that post on the link you posted earlier is Fabrice Neyret, he's a programmer tier that I only wish to ever reach. That being said, none of the stuff he says mentioned you should use atan over pow which do completely different things anyways - he merely mentions that if the base is 2, don't use pow but exp2 and if you square or such, use x*x or x*x*x instead since it's faster. And the part about the atan just says that the atan() is the canonical inverse tangens, defined from 0 to 180 degrees, where atan2 has the full 360 degrees (hence the sign comparisons to determine which quadrant it's in), saying that you don't need to implement such things yourself.