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The phrase "freely based on" is correct and can be used in written English.
It is typically used to indicate that something is loosely or loosely inspired by something else, rather than being an exact or direct representation. Example: The movie was freely based on the novel, taking some liberties with the plot and characters.
Exact(4)
The post-reform retail market will be perfectly liberalized, and retailers will be able to price freely based on retail electricity load.
They receive what's given freely based on mutual want.
By continually standing up to and challenging this internal enemy, we become stronger in our ability to live life freely based on our own desires, passions, and goals.
The femur bone rotated freely based on the soft tissue tension (Fig. 2C).
Similar(55)
Raymond Chandler once complained that Holmes was little more than a few lines of unforgettable dialogue and an attitude: the drug habit, the boredom, the violin playing, the show-offy logical deductions, which Conan Doyle freely admitted were based on one of his medical school professors.
A second repeated measures ANOVA for experiment 1 investigated the effects of rule-selection (either specified or freely chosen) based on height or color.
His central argument in the Citizens United case was that the right to speak freely cannot vary based on the identity of the speaker.
Our major emphasis is to help scientific community by developing freely accessible webserver/softwares based on our study.
This unique relationship enables us to determine the precision of synchronization in cortical spike data of a freely viewing monkey based on the analysis for a single setting of tolerated temporal spread.
Coding of comments provided in response to the open-ended question was done freely rather than based on a pre-developed framework.
In the absence of core randomized data, decisions must be made about combined use of these freely available therapies based on the existing preclinical and clinical evidence, which suggests that safety is not substantially compromised and that there may be a survival benefit.
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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