Likely the best tip would to `objdump -d` and inspect the assembly. For something like floating point, a good starting point would be to write and fiddle with small functions until you get rid of (most) branch labels and cvt instructions. A useful metric could be grepping for and eliminating ss instructions. Prepending (__attribute__((used)) will allow you to inspect your functions.

A quick restrict example:

    #define fn __attribute__((used))

    fn void copy1(int* to, const int* from, const int size)
    {
        for(int i = 0; i < size; i++)
            to[i] = from[i];
    }

    fn void copy2(int* to, const int* from)
    {   
        constexpr int size = 1024;
        for(int i = 0; i < size; i++) 
            to[i] = from[i];
    }

    fn void copy3(int* restrict to, const int* restrict from)
    {
        constexpr int size = 1024;
        for(int i = 0; i < size; i++) 
            to[i] = from[i];
    }

    gcc test.c -c -O3 && objdump -d ./test.o

This is a good starting point for self teaching. The impact of your TLB, L1, and overall instruction count (with IPC) can further be measured with `./perf stat -d -d -d ./a.out`