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The phrase "about as rapidly" is correct and usable in written English.
It can be used to compare the speed of two actions or events, indicating that they occur at a similar pace.
Example: "The train arrived about as rapidly as the bus, making the wait time minimal."
Alternatives: "roughly as quickly" or "approximately as fast".
Exact(3)
The carousel has spun as quickly as a tight spiral and — no coincidence — about as rapidly as coaches are hired and fired.
GNP per capita grows about as rapidly as the support ratio during the first dividend period.
The indications are that such bone as becomes necrotic at the ends of vascularized fragments is rapidly revascularized by ingrowth from the living bone and is absorbed and reduced in density about as rapidly as is the adjacent living bone from atrophy of disuse.
Similar(56)
Type I supernovae may be up to three times brighter than Type II; they also differ from Type II supernovae in that their spectra contain no hydrogen lines and they expand about twice as rapidly.
After glucose challenge, blood glucose returned to normal about twice as rapidly in Pten+/− mice.
Both found that, within the age group 25 74 years, the logarithm of the death rate increased in direct proportion to the logarithm of the age, but about six times as rapidly; in other words, the death rate increased proportionally with the sixth power of the age.
As a French exploit developer puts it, those liable to be rapidly detected are about as useful as a "disposable gun" that can be fired just once.
During the session US lawmakers voiced concerns about "who owns" data they couched as "rapidly becoming me".
Nails grow about 0.1 millimetre per day, or roughly one-third as rapidly as hair.
At 20 days after planting, chamber pressures were pumped down as rapidly as possible, reaching 5 kPa after about 5 min and ∼1.5 kPa after about 10 min.
What is being talked about, he said, is a "a smart, thoughtful way to rapidly, as rapidly as possible, while maintaining progress, shift responsibilities to Afghans," he said.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com