Re: Help with solving a simple black box of two inputs...

Nathan Baulch wrote:
This is a bit of a long shot, but I was hoping somebody would be able to help me figure out the inner workings of a function of two variables, to which I don't have the implementation.
The following table is the input/output map that I've built by profiling it.

x \ y| 0.0 0.2 0.4 0.6 0.8 1.0
-----+-----------------------------------
0.5 | 7.0 7.5 7.9 8.4 8.9 9.3
0.55 | 9.6 10.2 10.9 11.5 12.1 12.8
0.6 | 12.3 13.2 14.0 14.8 15.6 16.4
0.65 | 15.2 16.3 17.3 18.3 19.3 20.3
0.7 | 18.3 19.6 20.8 22.0 23.2 24.4
0.75 | 21.6 23.0 24.5 25.9 27.3 28.8
0.8 | 25.0 26.7 28.3 30.0 31.7 33.3

Unfortunately the outputs are all rounded to a single decimal place.
I know the equation must be quite simple, but I don't know what techniques to use to get there.
Varying y seems to cause a linear change in the output, however varying x seems to be exponential.

Hi Nathan,

The dependence on y is easy to work out: one can observe that the
values for y=1 are 4/3 of those for y=0, so f(x,y) = f(x,0)*(1+y/3).
The dependence on x is not exponential, but quadratic; if you take
the differences in any column, they grow linearly. After a bit of
fiddling, I've come up with this formula:

f(x,y) = (100*x^2 + 50*x - 29)*(y + 3)/9.

The resulting values match yours when rounded to one decimal place,
provided that even rounding is used--it turns out that f(0.65,0) is
exactly 15.25, so it could just as well have been rounded to 15.3.

I hope that helps. I'm also just a little bit curious as to what the
application is.

--
John Garrideb
Moorville, KS
jgarrideb@xxxxxxxxxxxxxx

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