MYSQL OR vs IN performance

I am wondering if there is any difference in regards to performance between the following

SELECT ... FROM ... WHERE someFIELD IN(1,2,3,4)

SELECT ... FROM ... WHERE someFIELD between  0 AND 5

SELECT ... FROM ... WHERE someFIELD = 1 OR someFIELD = 2 OR someFIELD = 3 ...

or will MySQL optimize the SQL in the same way compilers will optimize code ?

EDIT: Changed the AND's to OR's for the reason stated in the comments.

I needed to know this for sure, so I benchmarked both methods. I consistenly found IN to be much faster than using OR.

Do not believe people who give their "opinion", science is all about testing and evidence.

I ran a loop of 1000x the equivalent queries (for consistency, I used sql_no_cache):

IN: 2.34969592094s

OR: 5.83781504631s

Update:
(I don't have the source code for the original test, as it was 6 years ago, though it returns a result in the same range as this test)

In request for some sample code to test this, here is the simplest possible use case. Using Eloquent for syntax simplicity, raw SQL equivalent executes the same.

$t = microtime(true); 
for($i=0; $i<10000; $i++):
$q = DB::table('users')->where('id',1)
    ->orWhere('id',2)
    ->orWhere('id',3)
    ->orWhere('id',4)
    ->orWhere('id',5)
    ->orWhere('id',6)
    ->orWhere('id',7)
    ->orWhere('id',8)
    ->orWhere('id',9)
    ->orWhere('id',10)
    ->orWhere('id',11)
    ->orWhere('id',12)
    ->orWhere('id',13)
    ->orWhere('id',14)
    ->orWhere('id',15)
    ->orWhere('id',16)
    ->orWhere('id',17)
    ->orWhere('id',18)
    ->orWhere('id',19)
    ->orWhere('id',20)->get();
endfor;
$t2 = microtime(true); 
echo $t."\n".$t2."\n".($t2-$t)."\n";

1482080514.3635
1482080517.3713
3.0078368186951

$t = microtime(true); 
for($i=0; $i<10000; $i++): 
$q = DB::table('users')->whereIn('id',[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20])->get(); 
endfor; 
$t2 = microtime(true); 
echo $t."\n".$t2."\n".($t2-$t)."\n";

1482080534.0185
1482080536.178
2.1595389842987

I also did a test for future Googlers. Total count of returned results is 7264 out of 10000

SELECT * FROM item WHERE id = 1 OR id = 2 ... id = 10000

This query took 0.1239 seconds

SELECT * FROM item WHERE id IN (1,2,3,...10000)

This query took 0.0433 seconds

IN is 3 times faster than OR

The accepted answer doesn't explain the reason.

Below are quoted from High Performance MySQL, 3rd Edition.

In many database servers, IN() is just a synonym for multiple OR clauses, because the two are logically equivalent. Not so in MySQL, which sorts the values in the IN() list and uses a fast binary search to see whether a value is in the list. This is O(Log n) in the size of the list, whereas an equivalent series of OR clauses is O(n) in the size of the list (i.e., much slower for large lists)

MYSQL OR vs IN performance

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