Gilmoy,
you are right it is not the happiness that account for the 50%, but the Active Core planet trait. The rest (about the build cost points) is correct.
Anyways, you can see that even the game engine itself thinks that "+30 mp" (for an Entertainment Center) means 450 bc rush cost,
which is indeed a rate of 15.0. That's what it tells you in both hover windows. Somehow, it's letting me build a 30 mp thing for 24 mp.
The improvement list and hover windows show the uncorrected raw improvement build cost. These values are not corrected for building cost reduction techs and show the full cost instead of upgrade costs (when you upgrade an improvement). The "Entertainment Center" has no cost reducing techs and it is not an upgrade, so the shown +30mp results in a build cost of 30, which in turn results in a rush cost of 450 credits.
If i would upgrade my "Xeno Factory" to a "Mega Factory". The hover windows would and does show +67mp. However it is an upgrade and i have building cost reducing tech researched (for a total of -40%), the calculations are as follows:
Earth:
Build cost points = (67 - 45) * (100% - 40%) = 22 * 0.6 = 13.2,
Required mp for upgrade = 13.2 / 100% = 13.2 / 1 = 13.2mp,
Rush cost 13.2 * 15 = 198 credits and the game shows this exact value.
On Eagle I:
Build cost points = (67 - 45) * (100% - 40%) = 22 * 0.6 = 13.2,
Required mp for upgrade = 13.2 / (100% + 25%) = 13.2 / 1.25 = 10.6 mp (actually 10.56 mp)
Rush cost 13.2 * 15 = 198 credits and again the game shows this exact value.
Peti I gives 18.75 bc/mp.
On Eagle I:
Rush cost / Required mp = 198 / 10.56 = 18.75 bc/mp.
Rush cost / build cost points = 198 / 13.2 = 15 bc/bcp.
So my results for Eagle I matches your result for Peti I.
This means rush cost are depended on build cost points, not on manufacturing points required for that build.
I have verified it. See screenshots: Earth (no production bonuses) and Eagle I Thin Atmosphere (25% bonus). Look at the required turns for the given mp settings.
Planetary traits are applied after the shown mp calculation.
During the game, from where i have taken these screenshots, i have researched building cost reducing techs (-40% for manufacturing improvements, -25% for population improvements). See the difference between the required building turns, even while the (raw) building cost is the same, namely 30.
Calculated build costs:
- Basic Factory: 30 - 40% = 30 * 0.6 = 18;
- Entertainment Center: 30;
- Colonial Hospital: 30 - 25% = 30 * 0.75 = 22.5;
Earth at 30.2mp
- Basic Factory 1 turn;
- Entertainment Center 1 turn;
- Colonial Hospital 1 turn;

Earth at 29.7mp
- Basic Factory 1 turn;
- Entertainment Center 2 turns;
- Colonial Hospital 1 turn;

Earth at 22.2mp
- Basic Factory 1 turn;
- Entertainment Center 2 turns;
- Colonial Hospital 2 turns;

Earth at 17.7mp
- Basic Factory 2 turns;
- Entertainment Center 2 turns;
- Colonial Hospital 2 turns;

Eagle I at 15mp.
Can even be lower but this is sufficient to demonstrate the difference with Earth (a 0% bonus planet).
Calculated required mp to generate 18 build cost points on Eagle I: 18 / (100% + 25%) = 18 / 1.25 = 14.4 mp;
