[Python] Model Inversion using fitted parameters [closed]

I am trying to invert the following function to find RMSE between x_pred and x:

y = Ax^a (1 - e^{-Bx}) + (C x^c + D) e^{-Bx}
​

The values of parameters are known from curve fitting (using differential evolution) from the data as follows:

A = 0.099810
B = 0.038429
C = 0.039706
D = -0.012183
a = -0.045634
b = 0.072347


I have tried the following methods for inversion, but they are underfitting x:

1. Look up table
2. Newton-Raphson method
3. Bisection method

Please suggest ways/methods to invert and obtain x = f(y).

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