Seems a little clumsy, but I guess distinguishing from 精を出す is useful.

精が出	5968	  
精が出る	3976	  
精が出ます	3225	

精を出し	117354	91.9%
精出し	10332	8.1%

https://www.weblio.jp/content/精が出る
精が出る:懸命に働く。仕事に励む。よく活動する。「朝早くから—◦出ますね」
精を出す：精いっぱい働く。こつこつ物事をする。「仕事に—・す」


仕事にも精が出る
https://ja.hinative.com/questions/21523148
@benkyou47 If it is to be used in place of "頑張ろう！(ganbarou!)," it needs to be changed to "精を出そう(seiodasou)“

精が出るの意味・語源・例文！敬語だとどうなる？
https://kotobaryoku.com/archives/1456

A nice little discussion just on "精が出ますね"
https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1485424244


性が出なかった
https://shukatsu-venture.com/article/306479
このとき、いくつかサークルを転々としてみたけれどあまり馴染めなかった、志望動機も曖昧なまま入学してしまい勉学に精が出なかったなどのネガティブな理由ではいけません。

There's a sort of logical observation here that I think is correct. を出す is to deliberately do something (see the hinative suggestion that 頑張ろう = 精を出そう). 精が出る is an observation in the moment, or after-the-fact. The dictionary examples are all "to a worker in a field", or some such:  精が出ますね "you sure are doing great work today!"

I get the strong impression that this is used as an observation of someone else's performance: "he's really giving it his all today isn't he", "you're really doing exceptional work today", that sort of thing...

As such, I don't think the glosses should match 精を出す.　 You can say　精を出そう, or 精を出すつもり, but there is no way to do this with 精が出る.
精を出すつもり	405	9.5%
精を出そう	3872	90.5%

精が出ますね is potentially an [exp] on its own:
御精が出ますね	66	3.6%
ご精が出ますね	324	17.8%
精が出ますね	1435	78.6%

This is an interesting one.
精が出ない	246	100.0%
粋を出さない	0	0.0%

精が出ない: (a commentary on their own condition)
https://ameblo.jp/spiral-jump/entry-12572684621.html

This is a bit like 元気が出る、元気が出ない.  This might be a legitimate construction(both halves exist, but I made this up):
精を出そうとしても、精が出なかった。

Certainly the negation is a bit more nuanced than "wasn't working hard".  More like "couldn't do my best", "didn't have the willpower to focus on work". hmm

@@ -13,2 +13,3 @@
-<gloss>to work hard</gloss>
-<gloss>to make an effort</gloss>
+<xref type="see" seq="1888080">精を出す</xref>
+<gloss>to be working hard</gloss>
+<gloss>to be doing one's best</gloss>

daij, Luminous