RESULTS

I ran the program 3 times.

1st run:
Bubble Sort No Temp:   1.147000 ms (4.779167 μs per 240 iterations)
Bubble Sort With Temp: 0.963000 ms (4.012500 μs per 240 iterations)

2nd run:
Bubble Sort No Temp:   1.134000 ms (4.685950 μs per 242 iterations)
Bubble Sort With Temp: 0.980000 ms (4.049587 μs per 242 iterations)

3rd run:
Bubble Sort No Temp:   1.165000 ms (4.814050 μs per 242 iterations)
Bubble Sort With Temp: 0.953000 ms (3.938016 μs per 242 iterations)

You can clearly see that while using a temp variable creates an extra
one, it is faster than doing some arithmetic to swap the variables' values.

sort.c

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#define SIZE 256

int is_sorted(int* arr, int size) {
	for (int i = 1; i < size; i++) {
		if (arr[i] < arr[i - 1])
			return 0;
	}
	return 1;
}

int has_duplicates(int* arr, int size) {
	for (int i = 0; i < size; i++)
		for (int j = 0; j < i; j++)
			if (arr[i] == arr[j])
				return 1;
	return 0;
}

int sort(void (*sorter_cb)(int* arr, int size), int print_iter) {
	printf("Initializing list...\n");
	srand(time(NULL));
	int arr[SIZE];
	for (int i = 0; i < SIZE; i++) {
		arr[i] = rand();
	}

	if (has_duplicates(arr, SIZE)) {
		printf("ERROR: has duplicates!\n");
		exit(1);
	}

	printf("Starting sort...\n");

	int iterations = 0;
	while (!is_sorted(arr, SIZE)) {
		sorter_cb(arr, SIZE);
		iterations++;
		if (print_iter)
			printf("Iteration %d\n", iterations);
	}
	printf("Took %d iterations\n", iterations);
	return iterations;
}

void swap_no_temp(int* a, int* b) {
	*a = *a + *b;
	*b = *a - *b;
	*a = *a - *b;
}

void bubble_sort_no_temp(int* arr, int size) {
	for (int i = 1; i < size; i++)
		if (arr[i] < arr[i - 1])
			swap_no_temp(&arr[i], &arr[i - 1]);
}

void swap_temp(int* a, int* b) {
	int temp = *a;
	*a = *b;
	*b = temp;
}

void bubble_sort_temp(int* arr, int size) {
	for (int i = 1; i < size; i++)
		if (arr[i] < arr[i - 1])
			swap_temp(&arr[i], &arr[i - 1]);
}

void willbe_sort(int* arr, int size) {
	for (int i = 0; i < size; i++)
		arr[i] = size;
}

int main() {
	long start_no_temp = clock();
	int iter_no_temp = sort(bubble_sort_no_temp, 0);
	long end_no_temp = clock();

	long start_temp = clock();
	int iter_temp = sort(bubble_sort_temp, 0);
	long end_temp = clock();

	double no_temp_seconds = (float)(end_no_temp - start_no_temp) / CLOCKS_PER_SEC;
	double    temp_seconds = (float)(end_temp    - start_temp)    / CLOCKS_PER_SEC;

	printf(
		"Results:\n"
		"Bubble Sort No Temp:   %f ms (%f μs per iteration)\n"
		"Bubble Sort With Temp: %f ms (%f μs per iteration)\n",
		no_temp_seconds * 1000,
		(no_temp_seconds / iter_no_temp) * 1e6,
		temp_seconds * 1000,
		(temp_seconds / iter_temp)       * 1e6
	);

	return 0;
}