Can PySR constrain the formula with shared f(X) and g(X) in numerator and denominator?

[Swoswowordnewnew]

Hello everyone, I have a modeling scenario where I want to constrain the symbolic expression to a fixed formula structure like this:

$$ y(X) = \frac{(1 + f(X)) \cdot g(X)}{1 + f(X) + g(X)} $$

with the constraint that both the numerator and denominator must share the same f(X) and g(X) functions. Although my input data is X and the target is y, what I actually want is to discover the possible expressions of f(X) and g(X) that fit into a predefined structure. Can PySR enforce that the same f(X) and g(X) appear exactly in both the numerator and denominator? This kind of structure arises from physical constraints (like transmission-line theory), and it would be very helpful to control this behavior.
Thanks in advance for any insights!

[gm89uk]

Hi, yes you can with templateExpressionSpec:

Have a look at the example here:
https://astroautomata.com/PySR/api/#pysr.TemplateExpressionSpec

You can define f_predict and g_predict and use those variables again to return the exact form above, something like here: #865 (comment)

[Swoswowordnewnew]

Thank you for your helpful answer！