Is it ever worth it to sing to a butterfly?

Singing to a butterfly gives you an indeterminate amount of experience points but it also costs a great deal of energy--seemingly more energy the further into the game you go. So is it ever 'worth' the energy expenditure of singing to a butterfly in order to gain experience?

It seems like it's never going to be more valuable to sing to a butterfly than just to do the regular things (like making recipes, etc.) to gain experience more slowly but with predictable energy expenditure than to gamble on butterfly singing, but I am afraid there is something in the experience I am missing since I have only done it a handful of times in 25 levels.

I think it makes more sense if you look at the third limited resource involved: real time spent playing the game.

Higher levels of Animal Kinship skill will improve the amount of experience you get from singing to a butterfly, but singing is never very efficient in terms of the ratio of energy expended to experience gained.

The main advantage of singing lies in the ratio of experience gain to real time invested. It's possible to get a decent chunk of experience in only a couple seconds on a street full of butterflies - at the expense of a lot of energy.

Since your energy refills at the start of each new game day, you can think of any unused energy at the end of a game day as "wasted". If your game-playing time is limited, singing to butterflies is a good way to quickly use up that energy and at least get some experience for it.

However, if you've got the time to burn through that energy with other, slower activities, you will get more (experience) bang for your (energy) buck.

Actually, singing to butterflies increases their lifespans by a small amount. The usefulness of this relative to the energy cost is debatable, but this is currently the only means of increasing your butterfly's lifespan.