Contracting 行っておいで to 行っといで
Grammar: Colloquial and Casual Speech » Contracting 行ってお出で to 行っといで
The phrase 行っておいで, which is a more casual version of 行ってきなさい, may contract as 行っといで.
Examples
Going to say good morning with 行っといで

Ninako confessed her feelings to Ren, even knowing he already has a girlfriend and would turn her down. After not seeing Ren during summer break, Ninako wonders if she’ll still be able to greet him normally. After a boy she turned down greets her normally, Ninako feels more confident.
- つかさ:
- 「ホラっ 仁奈子 今度はあんたの番だよっ」
- “Hey, Ninako, now it's your turn.”
- 「そろそろ連くん 来るんじゃない?」
- “Won't Ren being coming soon?”
- 「行っといで!!」
- “Go for it!!”