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The phrase "has improved by" is grammatically correct and can be used in written English.
It is typically used to indicate the extent or degree to which something has improved. It is often followed by a numerical value or percentage. Example: The company's profits have improved by 20% compared to last year.
Exact(60)
A patient achieves a HAQ 20 outcome, if his HAQ score has improved by at least 20%; a 50% improvement is required for HAQ 50.
The quality of governance has improved by leaps and bounds.
Moore filled in as a starter and has improved by the game.
"My signing has improved by going to deaf events like this one.
According to the organisers, Athens's air quality has improved by 40% in the past decade.
Energy use has dropped by 13% and wastewater quality has improved by more than 30%.
Its business has improved by about 12percentt since the smoking ban took effect.
In most of the swing states, Mr. Obama's forecast has improved by almost exactly that margin.
Britain has improved by switching from coal- to gas-fired power stations.
Therapy also has improved by combining surgery with other types of treatment.
Attainment at GCSE among disadvantaged pupils from Bangladeshi, black African and Chinese pupils has improved by more than 20 percentage points since 2006, while the national average has improved by 13.5 percentage points.
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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