Explanation of the safe average of two numbers

Question

Whenever I need to average two numbers for an algorithm like binary search, I always do something like this:

int mid = low + ((high - low) / 2);

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Answer 1

Program synthesis techniques appear to solve such problems.

In this video, the programmer specifies constraints a) no overflow, b) no division, and c) no if-then-else. The synthesizer automatically came up with something pretty nice.

https://youtu.be/jZ-mMprVVBU