what is the scientific name for this fruit/tree?

[Tropicalnut]

Back in 2012 on my trip to the Dominican Republic I saw this tree, it reminded me of the same tree in El Salvador that we call ;"Aceitunas" , They come in purple and white kind of yellowish like these ones, but the fruit is sweet and I used to love to eat them when I was a child. Since they look like the Olive fruit here in the states I was wondering if it is the same family but different variety and I would love to grow those here as well. Thanks in advance! 

[FlyingFoxFruits]

Azadirachta indica

[Tropicalnut]

Thanks Adam; this led me to find the name of the tree I really want which apparently in Florida is known as "paradise tree" or Simarouba Glauca. I had no idea of its many uses, now my challenge is to get a female grafted variety to try to grow in my neck of the woods here in Arizona. Do you know where I can buy one? I supposed I can start with seeds and later on graft female scions to it. Do you or anyone else have any suggestions?  XE

[Tropicdude]

Not sure about the cold hardiness of Neem,  but I can say that this is one of the best trees for greening deserts and arid areas.   consider it an instant shade tree,  2 years and you have a shade.   once established you never have to water them.   people in the very dry areas here in the south west of DR.  plant them in areas you only see cactus and spiny acacias growing.

of course the other benefit, is you can make homemade pest repellent. oil from the tree is used to make soap , to treat skin ailments.  and as a repellent.  you can even find Neem in toothpaste,  supposedly whitens teeth. 

The little berries I have tried, the ripe ones do not taste bad, a bit like Spanish lime, but smaller like miracle fruit.

The other tree I always recommend for the dry areas here, is Moringa.  for being multipurpose.

[Tropicalnut]

Thanks Tropicdude, I already have a moringa tree in my front yard.
Its good to know that Neem tree is so fast growing that is one of the things I like about the Simarouba Glauca, plus it has the added edible fruit that I enjoy as a child.
If I am correct Neem tree or Azadirachta indica is a different species than Simarouba Glauca, the fruit look almost identical but the leaves seem to be different. It seems that both have beneficial properties to boot! or is it the same??? 

[Tropicdude]

Not the same,  Neem has a very distinctive curvature in the leaves.