gcc -Wall -Wextra -O3 -msse -msse3 sse.c -lm && ./a.out

499999999500000128.000000
13458ms

499999999500000128.000000
4441ms

.L6:
        pxor    xmm1, xmm1
        cvtsi2ssq       xmm1, rax  ; #1
        mulss   xmm1, xmm1         ; #2
        addss   xmm1, xmm2         ; #3
        sqrtss  xmm1, xmm1         ; #4
        cvtss2sd        xmm1, xmm1
        add     rax, 1
        cmp     rax, 1000000000
        addsd   xmm0, xmm1
        jne     .L6