I remember reading about this some time back and being amazed. I forgot about it in the meantime. Now I see it and I am like wait that is "just" genetic programming. A month or so ago I spent about a day playing with genetic programming with F# so I decided to test it against Gelman's broken dataset in link1 with same restriction - dont use pow or sqrt. Now what I have is not as impressive or polished as theirs but for the time I spent on it (not very much) I am happy with its result.
After 5 mins it got stuck at MSE 0.1 with: x2x2/(x1 + x2) + (x - sin(2300)). To test it properly I've built another 40 points with the correct equation data and am going to leave it over night since I'm too tired to wait its full cycle which will be more than an hour.
currently (17mins in) its at MSE 0.07 with (x2 + 0.7325/x2) - 0.6839 + x (x/(x+x2)) another equivalent interesting expression it arrived at was: ((x2 + 0.7325/x2) - cos(cos(sin(x2))) + x * (x/(x+x2)). I told it to stop at 0.025, now I think it will hit it and I set the bar too low. mayb