Synthetic pair Ask/Bid calculation

Hello,

I have a little problem with synthetic pairs calculation. Searching the web i found those formulas but something is still wrong:

first:A/C second:B/C
bid = first.Bid / second.Ask;
ask = first.Ask / second.Bid;


first:A/C second:C/B
bid = first.Bid * second.Bid;
ask = first.Ask * first.Ask;


first:C/A second:B/C
bid = 1/(first.Ask * second.Ask);
ask = 1/(first.Bid * second.Bid);


first:C/A second:C/B
bid = second.Bid / first.Ask;
ask = second.Ask / first.Bid;


AB is the pair we calculate the synthetic value combined from AC,BC.

I did the calculations for EURUSD using EURAUD AUDUSD. But the spread i got between bid/ask for synthetic EURUSD was about 14 pips and real spread is 2 pips. Are the formulas wrong or should i adjust the values further after those calculations?


My calculations given real values:
EURUSD ask = 1.5749
EURUSD bid = 1.5747
EURAUD ask = 1.6370
EURAUD bid = 1.6380
AUDUSD ask = 0.9619
AUDUSD bid = 0.9616

synthetic EURUSD
EURUSD ask = 1.6380*0.9619 = 1.5755 (6 pips higher than real value)
EURUSD bid = 1.6370*0.9616 = 1.5741 (6 pips lower than real value)


Any help will appreciated.
Thanks, Victor