Let me try:
Above equation is not true (as per me). Attempt to derive such equation from first priniciple is obviously futile (and
a dead end);
Though the above proposed equation (henceforth called eq. 1) is somewhat true if the 2nd term (expectation) tends to zero. But that doesn't mean i am belittling the importance of expectations in any relationship. For details refer Answer for the 2nd.
First law of relationship is quite vague/crude/absurd/(or a combinatition of all). Theoretically speaking '
reality' also contain the entity 'expectations'. If one is truly
real, his/her expectations are manageable by the other party. likewise he/she knows exactly what is expected of him... (no 'chand taare tod le aao mere liye').
Once it is known that what is 'expected', it is always easier to meet those / bend accordingly OR parting ways amicably.
Hence, for a realistic person, expectations are not antonym with happiness rather 'these' keep relationship's charm intact.
Relationship minus expectations seems something 'robotic' to me.
Reg 2nd law of relationship:
i like this one better.
Critical analysis of this law is not that easy, too many variables u see. Moreover P, E and H are set of multiple variables whose weightages are not defined.
On the sheer face values, 2nd law seems way better than the 1st law.
To maximize the happiness, third law dictates that Objects should be as large as possible and 'desires' should approach zero.
Though it is not defined what is meant by 'desires' (similarly object is undefined); yet going 'critically'

'No desires' represent a sick attitude.. Happiness to me (in conjecture with desires) is having
realistic desires (not the fantasies), giving your 100% to achieve them. If you succeed: u have the
happiness and if you don't then you have 'satisfication' that u tried your level best (
indirect happiness)
4th law of any relationship: Avoid "too much and Too many";
After critically analyzing the data i had on relationship failures, i had come up with one hypothesis that most common cause of failure in these realtionships was the fact that one of them loved (so called love) "
too much" or the other loved "
too many". While loving too much makes the other party 'suffocate' (emotional suffocation

) which eventually leads to so called break-up; Loving 'too many' caused the jealousy, doubts (... and so on) and hence the failure.

(most of the above data involves bf/gf type relationships, so it should be read only in those context. though universality of the 4th law is not established yet, i hope, with little modification, it can be extend to other cases also)
My apologies for NOT defining the 4th law in form of a simple equation.
Anyhow, i have written an algorithm for the same (its too long and too complicated to put up here), those who are interested, kindly contact me in person.
All the above thoughts are purely indigenous, any resembles whatsoever to any material available one internet or otherwise is purely coincidental and unintentional.