Use equations for PushAway and PushClose

[protonspring]

This is a functional simplification. I was trying to replace all of the tables, but in doing so, found that this particular version seems to do very well at LTC. I think we should commit this, then I can continue. This version is slightly simplified from the one that passed STC.

Both LTC tests are included. I honestly can't explain the difference. The change is pretty minimal.

STC
LLR: 2.95 (-2.94,2.94) {-1.50,0.50}
Total: 57864 W: 11092 L: 11001 D: 35771
Ptnml(0-2): 826, 6458, 14320, 6455, 873
http://tests.stockfishchess.org/tests/view/5e5da5b6e42a5c3b3ca2e05c

LTC
LLR: 2.95 (-2.94,2.94) {-1.50,0.50}
Total: 7198 W: 982 L: 883 D: 5333
Ptnml(0-2): 33, 575, 2296, 650, 45
http://tests.stockfishchess.org/tests/view/5e5df13ae42a5c3b3ca2e077

LTC (This exact version. . . more simplified)
LLR: 2.95 (-2.94,2.94) {-1.50,0.50}
Total: 5392 W: 729 L: 631 D: 4032
Ptnml(0-2): 23, 405, 1751, 485, 32
http://tests.stockfishchess.org/tests/view/5e5ead99e42a5c3b3ca2e0e4

Bench 5123316

[adentong]

This looks pretty legit.

[ddugovic]

My guess is that these parameter values are significantly better in endgames where search affects the result (likely KQKP, probably not KXK or KBNK). Congrats!

[protonspring]

probably, but even the values themselves are barely different.

[vondele]

Thanks! I'm inclined to think these very strong LTC results are lucky runs.... but we'll see in later regression tests.

[xoto10]

I wonder if arrays are just slower than we expect? A lot of my changes add arrays to make things more flexible, but they often perform poorly.

[vondele]

@xoto10 in would say in a code like SF, a single memory access that is not in cache has a measurable performance penalty (that's why we prefetch the TT entries). Apart from reducing the number of parameters, that's why we should encourage such arrays -> equation changes IMO. However, it seems very unlikely to me to gain 5 Elo from a mere speedup, by accessing less certain arrays in the endgame.

[adentong]

This is interesting because it was not one, but two extremely strong LTCs. I wonder if it's still due to luck.

[ddugovic]

I'd expect this to perform better at LTC than STC since being able to prune away entire endgame search trees from middlegame and opening positions is useful in slower games.