First, you should never claim something is faster without actually benchmarking it. Python has many hidden optimizations in built-in functions.

Second, I guess my solution would be faster in most cases because any stops at the first True, and all stops at the first False, so it would only reach the end of the sequence if it consists of all equal elements. Your algorithm will reach the end in any case. Consider the situation [True, False, ...(10000 elements more)]. My algorithm will stop after checking the first two elements; yours will check all the sequence in any case.

On the second thought, it would be faster in any case except, maybe, some very short sequences, because the first value of predicate would be either True or False, so one of the any or all functions is guaranteed to stop after checking it.

For your solution, I missed the iterator part in map. yes, the space complexity will be O(1) but then it is a slower iteration over sequence. a simple loop should be faster. Mind me I understand that they both are O(n) time complexity but simple loop should be a faster O(n) out of those two. let me know what you think.

How exactly creating new structures in memory can be more efficient? This solution has O(1) space complexity.

i think counter method is more efficient space wise. however , it has same time complexity

Unnecessary parentheses.

Bad

Fixed

added two instance of add![x, y]

I suggested 2 instances of add![x, y] with different values of x and y at runtime. Of course, that would still be hardcodable, but just a bit less straightforward...

I can see the problem now but i am afraid i have no ideas of how to stop this problem. Please suggest me if we have standard way of avoiding this problem in codewars.
Thanks in advance.

Added two test cases without values in error messages

How about some tests to make sure solutions aren't hardcoded based on error messages? Something like

let x = ..., y = ...;
... add![x, y];
let x = ..., y = ...;
... add![x, y];