Eradication has a 6% proc chance per Corruption tick to increase your haste by 20% for 10s. It has no ICD anymore.
Assume Corruption is up all the time on one target. If we are somewhere in between two corruption ticks (and we always are) then there is a chance of 6% that the last tick gave the buff. If it didn't (94%), there is a chance of 94%*6% that the one before gave it, and if it didn't, there's a 94%*94%*6% chance that the one before did. If we are less than one second from the last corruption tick (this is the case 1/3 of the time) we have to take even one more tick into account (94%*94%*94%*6%). This sums up to
\frac{2}{3} \cdot 0.06 + 0.06\cdot0.94 + 0.06\cdot0.94\cdot0.94 + \frac{1}{3} \cdot 0.06 + 0.06\cdot0.94 + 0.06\cdot0.94\cdot0.94+ 0.06\cdot0.94\cdot0.94\cdot0.94 = 0.1860
So the uptime is about 18.6% giving an average haste multiplier of 18.6%*20% = 3.72%.
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In regards to this particular section, this equation only applies at 0% haste. The higher your haste, the more often Corruption ticks, and thus the higher uptime the effect. The entire system can calculated with a simple uptime equation U = 1 - (1 - P)^(D/T), where T = 3/(1+Haste) (time between ticks), P is the proc chance, and D is the duration of the effect.
This gives a slightly curved line for effective haste that can be approximated with the linearization: EffHaste = 3.76 + 3.03*TotHaste (TotHaste being your decimal haste percent, 50% = 0.5). Thus the line scales from approximately 3.76% at 0% haste to 6.79% at 100% haste.
The proc itself also contributes haste, which further increases uptime. This ends up being a relatively simply differential equation that asymptotes to an addition ~0.1 additional effective haste and an additional ~0.003 per 1% additional static haste.
The final linear approximation is:
EffHaste = 3.86 + 3.04*TotHaste