Physics Velocity Correction

Question

So, been up all night working on getting the velocity/angle of arrow simulations perfect. Running into an issue with the physics engine I'm using is ever so slightly off (probably a rounding issue)

The Velocity is a fixed 55 "Units"

Correction Required at ranges (Range being the variable):

Range | Correction
30      0.0180
100     0.0055
200     0.0027
300     0.00165

After applying manual corrections on the velocity, I've been able to come up with the above data set.

Would anyone be so kind as to help me figure out a formula which satisfies the above problem?

Minor Background Information

The formulas I am using for the base calculations are https://en.wikipedia.org/wiki/Trajectory_of_a_projectile

Answer 1

Inspired by Frentos's answer, for the time being, let us assume something like $$y=\frac ax+b$$ Using your values, a simple linear regression gives $$y=\frac{0.541976}{x}-0.000038024$$ which gives as predicted corrections $0.01803$, $0.00538$, $0.00267$, $0.00177$.

As said, with more data points, something better could come out.

Edit

Take care; the constant term is not significant. So, $y=\frac{0.540401}{x}$ seems to more than sufficient (predicted values $0.01801$, $0.00540$, $0.00270$, $0.00180$)

Answer 2

As per comments, it's difficult to make a model of the error without more knowledge of the your script.

The first three data points fit an almost perfect inverse relationship:

 30 * 0.0180  = 0.54
100 * 0.0055  = 0.55
200 * 0.0027  = 0.54
300 * 0.00165 = 0.495

The fact that the $300$ range datapoint doesn't fit suggests something more complex is going on, but without more information about the script or more datapoints it's hard to come up with anything substantial.