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The phrase "a far higher rate" is correct and usable in written English.
It can be used when comparing rates or levels, indicating that one is significantly greater than another.
Example: "The new marketing strategy resulted in a far higher rate of customer engagement than the previous one."
Alternatives: "a significantly higher rate" or "a much greater rate".
Exact(60)
Already the death toll on the Palestinian side stands at 760, nearly half women and children - a far higher rate of death even than Israel's devastating war in southern Lebanon two years ago.
It was observed that spammers' ratings tend to deviate from the average review rating at a far higher rate than legitimate reviewers, thus identifying user rating deviations may help in detection of dishonest reviewers.
In recent years inflation has risen at a far higher rate than average earnings.
In 2012, African-Americans in Mecklenburg used early voting at a far higher rate than whites.
They won medals at a far higher rate than French soldiers.
Many Americans who made far less paid a far higher rate.
Mortgage-holders who bought council houses have a far higher rate of repossession than other groups of home owners.
Children working in agriculture are killed at a far higher rate than their peers in other industries.
There are gender disparities as well: black men marry outside the race at a far higher rate than black women.
THE Arctic ice cap melted this summer at a shocking pace, disappearing at a far higher rate than predicted by even the most pessimistic experts in global warming.
Blacks cared more than whites about the city's unemployment rate, and that group reported a far higher rate of joblessness than whites did.
More suggestions(15)
a substantially higher rate
a considerably higher rate
a far higher frequency
a far higher level
a far higher prevalence
a dramatically higher rate
a far larger rate
a far higher price
a far greater rate
a far higher ratio
a far higher tempo
a markedly higher rate
a far higher density
a far higher risk
a far higher time
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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