Bad science.
I'll come back with the details.
OK, as you know, other than the Kodak table that gives time and RF-corrected time from 1-100 seconds, and Ilford's graphs, most mfrs now just give stops or time multipliers at a few points. Some do 1, 10, 100 seconds (powers of ten), and the Japanese films tend to use 2-4-8-16 second (powers of 2).
The Foma film is typical of providing corrections at 1, 10,100 seconds.
If I can see an obvious pattern, I can write an equation 'by inspection'. Some films have correction that 'looks' like a(log)t). Sometimes a=1, sometimes it's something less. This is probably not too far off the method you use, but coming at it from a different angle.
Kodak Plus/Tri-X and the Foma ones don't cooperate well with the method that works most easily for me for most films.
So I take the measly few data points given, for example below are the metered and corrected times for Foma 200 Creative, based on the multiplicative correction and not the f-stop correction. They often don't match. I have heard suggested reasons why, but I wonder if it's easier to use if they give 'easy-to-handle' correction rounded to a convenient fraction of a stop. Most people find 1/3 or 1/2 stop far easier to incorporate than 0.172 for example. So I think mfrs may round off.
0.5 1
1 3
10 90
100 1800
Any method should work, but sometimes software generates 'inconvenient' solutions that are more work to convert to the form one may want.
Excel gives you a choice of several types of curves, and you can place the R^2 fit value as well as an equation on the chart(graph). You know all that; I'm explaining both for other readers and in case I reveal a flaw in my logic.
I use Curve Expert because it uses about 30 different models, creates a graph for each, giving you a quick visual sanity check of models that are ridiculously unsuited, like a sinusoidal model that oscillates but 'hits' the few given values right on. This would be a case of using an unsuitable model relevant to a different phenomena. Such is the risk of plugging numbers into software and yelling Eureka when you get an 'answer'.
I didn't show the few data points in my posted table because I assumed people would immediately check those reference values first for validity.
I am not sure I can figure out how to paste a graph in here. (I have to export it to be able to import it). I'll see what I can figure out.
I usually use a 3rd order polynomial for results that seem close enough to me. Some films don't seem to play well with that so I take what gives me what looks like a better fit to me, or I'll do a piecewise function fit, say, one model for 1-5 seconds, another for 3-20 and another for 10-100 (hypothetically speaking). By overlapping the range of each model, I know that each one doesn't get wild just outside the range it was chosen for (I model a wider range than I use it for when possible).
For this film I chose a MMF model (I don't even know what it is).
MMF Model: y=(a*b+c*x^d)/(b+x^d)
Coefficient Data:
a = -0.3211 use these for 1-100 secs
b = 1838.8295
c = 6017.6488
d = 1.4474
MMF Model: y=(a*b+c*x^d)/(b+x^d)
Residual Table:
0.5 -0.378719081
1 0.050141418
10 0.008148474
100 0.012561275
I tried another set of coefficients for 1-5 seconds but it didn't help much.
Coefficient Data: 1-5 secs
a = -0.24793684 MMF Model: y=(a*b+c*x^d)/(b+x^d)
b = 98.695186
c = 321.83251
d = 1.5084278
Nothing gave a good fit at 0.5; not to worry for my needs. I have poor speed control between 1 and 3 seconds anyway.
So what I get to compare is only meaningful at the small number of points the datasheet gave me. If I did my own film testing as some do, I might be trying to fit different data altogether.
I have to interpolate visually. Today I plotted the modeled vs the given data (I can't show you the graph). You can see from the residual table the fit AT THE DATASHEET REFERENCE VALUES is very good. The 'overlaid' graphs don't match perfectly, but it's a curve fit after all, 0.1 stop is <6% and we can both think of a lot of reasons why published reciprocity failure data is an exercise in estimation anyway.
One of the things I was uncomfortable with in my possible misunderstanding of your graphical method is that it seems to assume many films conform to as assumption then use one initial value.
While my method is a lot different, I feel like I'm checking it at ALL the given datasheet values, and doing a sanity check on the shape of the graph.
Other than my unorthodox presentation, so you see a flaw in my logic and/or results?
I'm well aware of claims that published data don't get updated for emulsion batches, and see drastically different results from others' own field measurements. Thus it seems that it's a holy grail to aim for.
That's why I'm happy trying to aim for the published data as a start.
I just re-read your comment that my data seem to fit but where the beep did it come from? I didn't answer that directly, but hopefully did so indirectly.
It's all artist license based on software-suggested best fit, looking for unsuitable curve shape (like if I had enough data to use a 6th order polynomial - the tendency of high order polynomials to have 'instability' or 'oscillation' seems to show up as nonlinearity in the curve outside the range desired. A model is just a model I guess, but 'funny' shapes don't give me any extra confidence I'm close to a solution.
(A little knowledge is dangerous?)