Sorry i've been super busy lately. KP708, what you were probably looking at was one of the plots of the sinusoidal part of the curve. As jdegre mentioned, the level->tt value function has the form y=sin(x)*z+*x*exp(x) from 550 to at least 7.5k. Somewhere above 7.5k the nature of the function changes significantly. Unfortunately, no one fit of the x*exp(x) curve fits the entire range from 550 to 7k, so i have been breaking it into segments and fitting the segments with their own exp() function. The sin function remains the same except for a possible change in factor at a couple places, though.
I do have to disagree with jdegre that a poly fit will be sufficient for getting optimal results (at least not without breaking it into short enough segments to approximate the sine, which we don't have enough data for at high levels). You can see that the error is greatly reduced by including the sin function in the fit:
The average error is much smaller with the sin and exp fit (black line) vs just the exp() function (red line). Sure the sine can be ignored for low skill values, but by the time you get to ~8k skills, the magnitude of the function is about 20 PEDs, which as a percentage may not be much, but in absolute terms is huge. With my fit that includes a sine wave i get less than 1% error over almost the entire range we have data for.
Here's the fit of my current function to the data we have:
I spent some time creating a new spreadsheet to simplify trying different fits and data sets. When we have a good fit to 8k+ i will focus on the chip calculator i have been wanting to do, and been detoured by the need to finish the skill<->tt fit.
This is
not the function currently used by the php script i have linked earlier. I will update that script when i'm satisfied with the 900-1.1k range, which is a bit high with the parameters i'm using now.