The phrase "fast and efficiently" is correct and usable in written English. You can use it when referring to a task that was completed quickly and effectively. For example, "The team was able to finish the project fast and efficiently.".
The cheerful servers move fast and efficiently.
Servers were moving fast and efficiently.
Everything moved very fast and efficiently, and I was lucky it was caught so early.
And all the while Grosjean looked so comfortable on grass, covering the surface as fast and efficiently as the ground staff when the rains came.
With a rights-based approach, combined with utilizing the advancements in science (effective antiretroviral therapy, malarial drugs, rapid diagnostics for TB), we can reach more people in need, faster and efficiently.
Our new President will see that it's done as fast and as efficiently as possible.
You work faster and more efficiently.
When I feel like I can't trust my brain 100%, Ludwig really comes in handy. It makes me translate and proofread faster and my output more reliable.
Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu