Nomenclature of aldehydes with double bonds and stereoisomerism I'm struggling to name this compound shown below:

I'll post my chain of thought here so it can be corrected!

longest chain is marked as below:



this is because the functional group with the highest priority is the aldehyde (HCO) functional group, so the chain should contain this functional group
the chain continues down to to bottom-right to obtain the maximum length with the greatest number of substituents (although actually looking at it now, could the carbon chain go left and skip the double bond?)
there's a butyl side chain on carbon 3
there's a double bond at carbon 3
there's an ethyl side chain on carbon 4
there are two methyl groups on carbon 5
following CIP rules, the groups with highest priority are arranged opposite each other, so the molecule is E

Therefore, would the molecule be (E)-3-butyl-4-ethyl-5,5-dimethylhex-3-enal?
Or have I got myself completely mixed up...
Thanks for any help!
IUPAC has changed some of the rules of nomenclature as of 2013. In aldehyde 1 both the aldehyde group and double bond are included in the base name (noun) and the methyl group is the substituent (adjective) because both chains are $\ce{C4}$. In structure 2 the methyl group of 1 has been changed to ethyl. Now the longest chain is $\ce{C5}$ containing the aldehyde group and the double bond, as a substituent is the modifier methylene. In structure 3 the branch at $\ce{C3}$ has two $\ce{C3}$ units. The one containing the double bond takes priority as the &quot;noun&quot;. In structure 4 the chain containing the double bond is shorter, which becomes the &quot;adjective&quot;. In your compound 5, the noun is heptanal (in black) and the adjective, which contains the double bond, is in red. The two entities are numbered independently.