Distance from a point to a curve

Hello, I am trying to find the minimum distance between a series of data points and a function. I know how to do it symbolically, plug the formula into the distance formula, take the derivative and set to zero to find the minimum and plug into the distance formula, but I am having a hard time figuring out how to do this in excel. One method I can think of is to calculate the distances from the point to the surrounding points on the function and take the minimum. However this would require about 40 distance per data point and I have 8000 data points. Is there a way to do this in one step, and I would prefer not to use macros. Or if you have alternate suggestions I am completely open.

I am comparing recorded (noisy) data to a calculated formula. The formula is a repeating piecewise function formed from lines a circles. The lines are easy enough to solve algebraically but the circles turn out to be a complex forumla due to subbing a square root into another square root and taking the derivative.

where is it

I could not upload the file due to it's size.

zip it or remove unnecessary data

Okay, I trimmed it down and attached it.

Would this give minimum distance between two points? =MIN(ABS(C2-$A$2:$A$722)) (comfirmed with ctrl+shift+enter)?

And then minimum of all points is =MIN(E:E)

That give's me 1E-5 which is probably right for points but if you threat them as lines then it should be 0 due of overlaping....

I don't believe so, to my understanding that formula is simply taking the vertical difference in distance, I need the normal distance. This requires the use of derivatives.

I think that will work. I am not familiar with array functions so I have a quick question, does an array function evaluate by row or evaluate every pair? In this case for instance, will the function select A1 and B2 if that corresponds to a lower value to will solely evaluate A1 and A2 etc?