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When did 役に立つ lexicalize to 役立{やくだ}つ?

Has 役立つ always been a word, and a word that is used more frequently than 役に立つ?
A quick google shows 役立つ is used 3 times more frequently.

I am reading the translation of a speech. The translator always says 役立つ where
I would say 役に立つ. Is there any connotation difference between the two? Maybe
役立つ less formal? My feeling is that initially there could be some association
of lexicalized words with "slang", but as time passes that perception goes
away.
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etymology connotation
Is "役立つ" a recent lexicalization of "役に立つ"? Is it less formal?
My copy of Shogakukan's 国語大辞典 gives a quote from 狂言記{きょうげんき} using the 役立つ
form, dating this term to at least the late 1650s.

As to formality, a native speaker would be able to answer more
authoritatively, but I am not aware of any particular difference in register
between 役立つ and 役に立つ, and none of my resources to hand indicate any such
difference.
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Please refer to the other answer(s) for your main question (etymology).

As for the modern usage, the difference in frequency is not that large. Here
are the hit counts from BCCWJ.

  * 役に立 2302, 役に立つ 1039, 役に立っ 270, 役にたつ 94
  * 役立 3031, 役立つ 1419, 役立っ 447, 役だつ 30

役に立つ and 役立つ are not always interchangeable. As a simple predicate, 役に立つ is
the more common expression, and saying 役立つ sounds formal/literary/stiff.

>   * この辞書は役に立つ。 (perfect)
>   * この辞書は役立つ。 (sounds literary/stiff)
>

But 役立つ is preferred regardless of the formality, when another ～に precedes to
indicate the "type of usefulness". According to BCCWJ, roughly 80-90% of the
instances of 役立つ are preceded by such ～に.

>   * この辞書は勉強に役立つ。 (perfect)
>   * この辞書は勉強の役に立つ。 (also perfect)
>   * [?] この辞書は勉強に役に立つ。 (weird)
>

～に + 役に立つ is allowed in expressions like
「間接的に役に立つ」「私にとって役に立つ」「文法の勉強をするときにも役に立つ」, but the vast majority of the 役に立つ
examples are not preceded by に at all.

So 役立つ as a simple predicate is not as common as you might think.
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To me both ”役に立つ” and “役立(やくだ)つ” mean the same thing, “It helps,” or
“helpful.”

When I consulted how to translate “役立(やくだ)つ” into Japanese with Kenkyusha’s
“New Japanese English Dictionary” for a reference, it simply told “See 役に立つ.”

However, it appears to me there's a bit of difference between their usage and
nuance. The former (役に立つ) is more often used in “predicative” form in a
sentence than the latter (役立つ), which is rather used for “adjective” form in a
phrase.

For instances, we say;

[役に立つ]

救急箱はいざという時に役に立つ – The first-aid kit is effective in emergency.

彼は役に立つ人間だということが解った – I found him being an able person we can rely on.

この芝刈り機は役に立たない – This mower doesn’t work.

果たして私、お役に立ちますか、どうか – I’m not sure if I am of any assistance to you or not.

[役立つ]

英語の勉強に役立つ本 – A book helpful in learning English.

就職に役立つコネ – A connection helpful for job hunting.

問題解決に役立つアドバイス – Advice that helps solving the problem.

世間のために役立つ人間になれ - Be a man who is useful for the world.

Though I don’t have any academic ground, I think 役立つ derived from "役に立つ" as
its contraction.
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