What is the correct phrase for "speaks well to the"
Solution 1:
The expression 'speak well of' is idiomatic:
speak well of / for
to show that something is correct or effective
The lower crime rate speaks well for the police department’s new strategy.
{Macmillan}
Of course, this has the alternative meaning 'praise'.
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Alternatively, 'testify well to' may be used:
The difficulties Leibniz and Varignon found in giving an analytic form to dynamics testify well to the fact that their effort was not trivial.
{The Development of Newtonian Calculus in Britain, 1700-1800}
testify to
testify 2 to provide evidence that something exists or is true
testify to: These ruins testify to the existence of Roman occupation.
{Macmillan}