Clarification on why K * x4/x0 is considered dimensional under dimensionless_constants_only=True

[arasugurlu]

Hi Miles — thanks again for the earlier response. I want to clarify one specific point because I’m still not fully understanding the mechanism behind your explanation.

You wrote:
“Because K * x4 / x0 has dimensions, and therefore exp(K * x4 / x0) is invalid.”

You can see the answer in the following link:
#1078

In my setup, both x4 and x0 have units of length (meters), and K is a pure number. Under normal dimensional analysis, K * x4 / x0 should be dimensionless since the length units cancel. Therefore, I don’t understand in which sense PySR is treating that term as dimensional.

This matters because when I set dimensionless_constants_only=True, PySR produces dimensionally consistent expressions but never produces exp(...). When I set it to False, I do get exponentials, but I also get dimensionally inconsistent structures like:

exp(-10.673[?] / x0[m])

which is inconsistent unless the fitted constant carries a length unit.

So here are the specific points I am trying to understand:

1. When you say “K * x4/x0 has dimensions,” do you mean that PySR internally needs to assign physical units to K (for example 1/m) to satisfy the output-unit constraints elsewhere in the expression, and that this requirement is incompatible with dimensionless_constants_only=True?

2. Is the reason exp becomes “impossible” under dimensionless_constants_only=True that PySR cannot make the exponent dimensionless without giving the constant a unit, which violates the constraint?

3. In other words, is the core issue that the search cannot satisfy simultaneously:

   • exp requires a dimensionless argument,
   • the model must satisfy the target output units,
   • and constants are forced to be strictly dimensionless?

I’m trying to confirm whether this interpretation is correct, or whether I am misunderstanding how PySR assigns or propagates units internally.

I simply want to use the exp function while keeping my resulting expression fully dimensionally consistent.

Thanks for the clarification — I want to fully understand the logic before deciding how to restructure my inputs.

[MilesCranmer]

When I set it to False, I do get exponentials, but I also get dimensionally inconsistent structures like:

exp(-10.673[?] / x0[m])

which is inconsistent unless the fitted constant carries a length unit.

Yeah this is what dimensionless_constants_only=False does. There is now a [m] attached to that 10.673. So it's not dimensionally inconsistent.

Regarding "both x4 and x0 have units of length (meters)", this isn't true, because you wrote:

X_units = ["m","N/m^2","",""]
y_units = "N/m^2"

There is only one feature with units of length.

[arasugurlu]

Hi Miles, thank you again for all your previous explanations — and apologies if I misunderstood parts of your earlier answers.

I would like to clarify just one final point:
Is it possible to simultaneously achieve the following in PySR?

1. All fitted constants are dimensionless (dimensionless_constants_only=True),
2. I can still use the exp operator,
3. And the argument of exp(...) can include my original variables, as long as the entire exponent is dimensionless and the final expression remains fully dimensionally consistent.

In other words, I would like to have expressions like exp(f(x)) where f(x) is dimensionless, without allowing dimensional constants.

Is this combination fundamentally impossible in the current dimensional-analysis system, or is there a correct way to structure inputs so that PySR can still produce such exponential terms?

Thanks again for your patience and clarification.