Make the displayed evaluation more symmetric

[atumanian]

This patch simplifies the formulas used to compute the trend and optimism values before each search iteration. Also and more importantly, this removes the parameters which make the relationship between the displayed evaluation value and the expected game result asymmetric. Here by symmetricity we mean that f(x) + f(-x) = 1, where f(x) is the expected score when the evaluation shows x. This has implications in usability for analysis, where more symmetric eval values mean less fluctuations of eval during a traverse of a game.
The patch has passed both STC and LTC simplification tests. The patch in the LTC test (which is functionally equivalent to the version in the present pull request) is slightly different from the patch used in the STC: in the LTC version the change is applied to the latest version of master and the fraction of two integers is rounded to an integer. Both was tested without automatic adjudication.
I've also provided links to the results of isotonic regression analysis of the relationship between the evaluation and game result (statistical data and a graph) for both tests, which demonstrate that the new version has a more symmetric relationship.

STC

Test result
Data and graph

LLR: 2.96 (-2.94,2.94) <-1.75,0.25>
Total: 108016 W: 28903 L: 28760 D: 50353
Ptnml(0-2): 461, 12075, 28850, 12104, 518 

LTC

Test result
Data and graph

LLR: 3.01 (-2.94,2.94) <-1.75,0.25>
Total: 34792 W: 9412 L: 9209 D: 16171
Ptnml(0-2): 24, 3374, 10397, 3577, 24

After the patch is commited I suggest running more tests to verify if the eval-result relationship is symmetric and thinking what can be changed to make it even more symmetric in case it still isn't.
Fixes at least partly: #4142 (but please don't close the issue yet, because the eval may be still asymmetric).
Closes: #4163

Bench: 4425574

[atumanian]

By the way, the patch affects also the calculation of trend, which is used in the classical evaluation. Do we have to test this also without NNUE?

[vondele]

it is not needed to run without NNUE. However, I would like to see one more test, as this changes the optimism quite a bit. Can you run a test of master vs sf 13 and this patch vs sf 13, both 100'000 games at STC, UHO book. Let's see if there is an effect in that case.

[atumanian]

it is not needed to run without NNUE. However, I would like to see one more test, as this changes the optimism quite a bit. Can you run a test of master vs sf 13 and this patch vs sf 13, both 100'000 games at STC, UHO book. Let's see if there is an effect in that case.

Ok, just a minute...
...The tests already started.

[atumanian]

Here are the results:

This patch vs SF 13:

Elo: 141.66 +-1.2 (95%) LOS: 100.0%
Total: 100000 W: 48182 L: 9528 D: 42290
Ptnml(0-2): 96, 1426, 13277, 30130, 5071
nElo: 284.13 +-3.3 (95%) PairsRatio: 23.13 

Master vs SF 13:

Elo: 143.26 +-1.2 (95%) LOS: 100.0%
Total: 100000 W: 48525 L: 9479 D: 41996
Ptnml(0-2): 94, 1537, 13098, 29771, 5500
nElo: 281.70 +-3.3 (95%) PairsRatio: 21.63

The master is better by 1.6 Elo, which, however, is not statistically significant here.

[Disservin]

So no clear regression against weaker version, I guess thats good ;)

[dav1312]

359 more 1.5 pairs and 429 less 2 pairs 🤔 interesting

[atumanian]

@vondele thanks.