Search for a mathematical algorithm matching input and output

Question

As a final result, I need a computer program that can receive a list of inputs and outputs, and then apply the same algorithm that was included in this input / output on another number, Ie:

If a given I / O list

2:4
4:8
100:200

It would be clear that the algorithm would be (input * 2) or (output / 2) depending on what we wanted.

So, if you set the number 16 and ask for an output, the program will answer 32. And if you set the number 10 and ask for input, it will answer 5.

Obviously, it would be quite simple to “hard-write” this into a program, although I would like to know how the program will teach itself what an algorithm is. I understand that it will be quite complicated pretty quickly.

Answer 1

/ , , - + > ...

:

• • ( /)
  • y=a0+a1*x+a2*x*x+a3*x*x*x

• • y=a0+a1^x

• • , sin- .., , , .

, , 3

• , a0+a1*x+a2*x*x+a3*x*x*x=y 4

, , , . :

• x0<x1<x2<x3,... y0,y1,y2,y3,..
• k0=y0/x0,k1=y1/x1,...
• if k0<<k1<<k2<<k3<<... k0>>k1>>k2>>k3>>... , ,
• ...

, , , , , - , . , , ,

[]

, :

• (, , )
• (, ..)
• /.
• x, y