I would like to Reverse Engineer a formula, given a set of coordinates.

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I'm trying to find the original function without trial and error, also I know that every single function can be represented as a polynomial function but I am not looking for a best fit as much as an exact match.

Coordinates

Aside from the list of coordinates I know that the original formula contains $\cos$ and $\pi$.

I got within a $2\%$ maximum margin of error with any given point with this formula:

$$y = \cos \frac {1000 \cdot \pi} {5975.00135 \cdot x + 999.6586074}$$

However I don't know where to go from here to make it more accurate. Let me know if there is any more information I can provide.

Edit:

It seems I left out some crucial info.

The formula is a diminishing returns formula and I am unaware of the cap.

The diminishing returns formula begins at $14444.44$ until that point it is a linear formula. the formula converts a rating into a percent value. The formula before $14444.44$ rating is...

\begin{align} \mathrm{Rating} \cdot 0.000045 &= \mathrm{Value}\\ 14444.44 \cdot 0.000045 &= 65\% \end{align}

Beyond $14444.44$ or $65\%$ the coefficient $0.000045$ no longer applies and begins to diminish. Such that at $14125$ Rating above $14444.44$ the coefficient is $0.0000105305$.

For my formula $x$ is the percent rating above $14444.44$ while the $x$ I gave you on the spread sheet was Flat Rating above $14444.44$ (my bad)

the correct formula given $x$ on the spreadsheet would be...

$$y = \cos( 1000 π / ( 5975.00135 ( x / 14444.44 + 1 ) + 999.6586074 ) )$$