While coding my own auto clicker I noticed an extreme inaccuracy with the click speed. When nothing I tried worked, I downloaded more auto clickers. I saw that every auto clicker I tested has extremely inaccurate CPS outputs, including mine. The inaccuracy seems to scale almost exponentially with the input CPS value.
I confirmed that my click speed tester works correctly by using different ones. Here are my test results: (Bumps in the graph are due to inaccuracies) https://i.stack.imgur.com/SDP5x.png
My question is: How would I calculate the "Input CPS" needed to reach the desired measurement?
First of all, Welcome to the site !
You are facing the typical problem of data regression.
Just looking at your data, it seems that simple hyperbolic models such as $$y=x \,\frac{\sum_{n=0}^p a_n\,x^n}{1+\sum_{n=1}^p b_n\,x^n}$$ could be adequate.
Minimizing the sum of squares of absolute errors, for example, the simplest one $(p=1)$ would give (I made the coefficients rational) $$a_0=\frac{3170}{3543} \qquad \text{and} \qquad b_1=-\frac{25}{1801} $$ to which corresponds to $R^2=0.9988$ which is good.