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Discover Ludwig"improved on" is a correct and common phrase used in written English.
You can use it to describe when you have done something to make it better or greater than before. For example: "I improved on my last score by ten points."
Exact(56)
Indeed, its researchers have improved on nature.
But whatever he stole he improved on.
"Then we improved on that".
Einbaum's health actually improved on camp rations.
"We have improved on that front.
The Box improved on its routine.
And maybe even improved on Lemaire's tactics.
All faculties improved on their 1996 rating.
Nor have matters improved on land.
He promptly improved on those figures.
Similar(1)
He greatly improved on-time ratings.
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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