So I have a curve like picrel, i.e. Ik now how it looks like. And I know that at 0.5 x value it returns 0.321 y value

It has 2 defining points with following parameters:
[P1]
"X": 0,
"Y": 0.15,
"Arrive": 0,
"ArriveWeight": 0,
"Leave": 0,
"LeaveWeight": 0

[P2]
"X": 1,
"Y": 1,
"Arrive": 2.0334492,
"ArriveWeight": 0,
"Leave": 2.0334492,
"LeaveWeight": 0

In this particular case Arrive and Leave are the value of tangent handle (as in UI handle) that is used to adjust curve in the graphical interface.

What I need is to replicate the function in code to get the value at specific input (X)

I'm having hard time figuring it out. I know the interpolation is cubic with flat tangents