Fixed code by openai o1 preview free:

for (size_t i = 0; i < len; ++i) {
    uint64_t carry = 0;
    for (size_t j = 0; j < len; ++j) {
        // Multiply x[i] and y[j]
        uint128_t product = multiply_uint64(x[i], y[j]);

        // Add product.lo to result[i + j]
        uint64_t sum1;
        uint8_t c1 = _addcarry_u64(0, result[i + j], product.lo, &sum1);

        // Add carry to sum1
        uint64_t sum2;
        uint8_t c2 = _addcarry_u64(0, sum1, carry, &sum2);

        result[i + j] = sum2;

        // Compute new carry
        carry = product.hi + c1 + c2;
    }
    result[i + len] = carry;
}