宿題をやりさえすればいい

宿題をやってさえいたらいい

What is the difference/nuance between these two ways to use さえ with verbs?
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nuances
Difference between 連用形＋さえ and テ形＋さえ
I think it is almost interchangeable though, if there was the difference in
some cases, it similar to the difference between deductive reasoning and
inductive reasoning.

> 宿題をやりさえすればいい

宿題をやりさえすればいい may imply that you only have to do homework in order to achieve
something. If you have done homework, you can do something. This is kind of
deduction. Doing X takes you Y.

> 宿題をやってさえいたらいい

宿題をやってさえいたらいい may imply if you are doing homework, something is more likely to
happen. This time, Doing X is likely to take you Y.
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>   * 宿題をやりさえすれば
>   * 宿題をやってさえいたら
>

These are both complicated with さえ (="only"), [whose grammar rule may be
difficult](http://maggiesensei.com/2015/03/28/how-to-
use-%E3%81%95%E3%81%88sae/), but after removing さえ, these sentences are:

>   * 宿題をやれば = If you (will) do your homework ...
>   * 宿題をやっていたら = If you have done/finished your homework ...
>

The essential difference is that only the latter has a subsidiary verb
**～ている** , which describes "the continuation of a state" in this case. See
this question for the basics for ～ている: [When is Vている the continuation of
action and when is it the continuation of
state?](https://japanese.stackexchange.com/q/3122/5010)

Compare the following two sentences:

>   1. 明日の昼に宿題をやりさえすればいい。
>   2. 明日の昼(まで)に宿題をやってさえいたらいい。
>

Sentence 1 rather simply refers to your future action. It means you have to do
your homework tomorrow at noon. Sentence 2 means you have to finish your
homework by noon tomorrow; you have to do your homework tonight or tomorrow
morning.
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