ITE operator and continuity on operators

[Vahan-tech]

Hello to everyone, I have some questions i was not able to answer from myself from the documentation.
Does pysr takes into account the continuity of the expression while using operators like max, min, cond ?
Or to get something that is continuos i should use something like
"smoothed_max(x, y) = 0.5*(x + y + sqrt((x - y)^2 + 1e-6f0))"?

The other question is that sometimes i get ITE operation even if i don't have any "conditional" operator like max,min, cond and the logical ones, it is normal ?

Last question is a bit off-topic with respect to the title and is about fractional user defined operators.
As an example i write something like

"poly3(x) = x/(x^3 + x^2 + x)"

and for example the regression chose poly3(x) but the feature x start from 0, pysr doesn't take in account that the operator poly3 is not defined in 0 right ? So i am obbligated to add at least a +1f0 to the denominator? Or there are better solutions ?

[MilesCranmer]

Q1:

No need for operators to be continuous. It can help if they are though, as the constant optimisation is smoother.

max and min are continuous, but cond is not.

Q2:

Not sure I understand, could you give an example?

Q3:

What you should do is return NaN for invalid inputs. Like:

poly3(x) = x != 0 ? (x / (x^3 + x^2 + x)) : convert(typeof(x), NaN)

Then the evaluation will automatically flag invalid inputs and eliminate those expressions.

[Vahan-tech]

Thank you a lot for the reply and the amazing work, so

1)Unfortunally i need to use the expression in an envirorment in which conitnuity at least C^1 is a must any idea on how to make cond continuous ?
2)Sometimes when i run a regression it appears a operator called ITE(cond,arg1,0) it is like a cond, but i don't have any operators like that. It usually appear when i use large dataset only the + operator and 0 unary operator
3) Thanks a lot :) very usefull instead if I want pysr to ad a number chose trough regression like (x / (x^3 + x^2 + x +k), what should i use ?

I have matured 2 another question (maybe I am exaggerating, hope i'd be forgiven)

4)If for example I define a sigmoid operator "sig(x) = 1f0/(1f0 + exp(x))", or in general user defined operator, i can put costrain in them ?
For example for the sig(x) i would want to research onli elements of the type 1/(1+exp(coeff*x+coeff2))

5)There is a way to put a limit on decimals ? For example i would like pysr to only find constant and coefficent with only 3 decimal elements, i usually get coefficent and constant with 6 digits after the comma

Thank you in advance for the reply, hope i am not exaggerating with the questions