Question

I am trying to replicate a functionality of a built-in function, as the built-in functionality is not callable inside scripts, but I can’t seem to figure out the how the 3rd parameter is calculated.

Basically you specify a and b and it returns c. So here is the result of some operations:

a   b   c

1   1   1
1   2   0.75
1   3   0.666667
1   4   0.625
1   5   0.6

2   1   0.75
2   2   0.5
2   3   0.416667
2   4   0.375
2   5   0.35
2   6   0.333333
2   7   0.321429
2   8   0.3125
2   9   0.305556
2   10  0.3

3   1   0.666667
3   2   0.416667
3   3   0.333333

4   1   0.625
4   2   0.375
4   3   0.291667
4   4   0.25

100 1   0.505
100 2   0.255
100 3   0.171667
100 10  0.055

Let me know if you need additional outputs.

Answer 1

For all of your sample the following formula provides the expected result:

C = (A + B) / (2 * A * B)

As ypercube pointed out in the comments this formula is the inverse of the Harmonic mean or the arithmetic mean of the inverses.