Why are the functions created by set_djordjevic_sarkar_model different from the functions created when you apply the Sarkar model manually?

[lethangomes]

When I create a material and apply the Djordjevic Sarkar model through pyaedt, the material ends up with this equation for relative permittivity:
(4.25 - (4.25 * 0.0267 - 1e-12 / (2 * pi * 1000000000 * e0)) / atan(159154940000.0 / 1000000000) / 2 * ln(159154940000.0**2 / 1000000000**2 + 1)) + (4.25 * 0.0267 - 1e-12 / (2 * pi * 1000000000 * e0)) / atan(159154940000.0 / 1000000000) / 2 * ln((159154940000.0**2 + Freq**2) / ((159154940000.0 / exp(10 * 0.0267 * (4.25 - (4.25 * 0.0267 - 1e-12 / (2 * pi * 1000000000 * e0)) / atan(159154940000.0 / 1000000000) / 2 * ln(159154940000.0**2 / 1000000000**2 + 1)) / ((4.25 * 0.0267 - 1e-12 / (2 * pi * 1000000000 * e0)) / atan(159154940000.0 / 1000000000))))**2 + Freq**2))

However when I apply Djordjevic Sarkar model manually with the same settings relative permittivity is set to:
3.88228+0.0362653*ln((2.53303e+22+Freq*Freq)/(9.77749e+09+Freq*Freq))

This is also the case for Bulk conductivity, which gets this equation when I use pyaedt:
1e-12 + 2 * pi * Freq * e0 * ((4.25 * 0.0267 - 1e-12 / (2 * pi * 1000000000 * e0)) / atan(159154940000.0 / 1000000000)) * (atan(Freq / ((159154940000.0 / exp(10 * 0.0267 * (4.25 - (4.25 * 0.0267 - 1e-12 / (2 * pi * 1000000000 * e0)) / atan(159154940000.0 / 1000000000) / 2 * ln(159154940000.0**2 / 1000000000**2 + 1)) / ((4.25 * 0.0267 - 1e-12 / (2 * pi * 1000000000 * e0)) / atan(159154940000.0 / 1000000000)))))) - atan(Freq / 159154940000.0))
And this one when I apply manually:
1e-12+4.03506e-12*Freq*(atan(Freq/98881.2)-atan(Freq/1.59155e+11))

Why are these equations so different? Does the first simplify to the second, and if not why?

[isaacwaldron]

@hui-zhou-a it looks like you created this function in #3827, I guess the reason for the different formulation is to allow using variables for dk and df which doesn't allow us to use the reduced form that is in AEDT. Would you please comment on the derivation (and therefore equivalence to the reduced form used by AEDT) of this formulation? Thank you.

[hui-zhou-a]

@lethangomes @isaacwaldron they equations are equivalent. When you create the model from pyaedt, you get the complete equation which allows variables. When the model is created from AEDT, the equation is simplified algebraically