Can be run on the command line, but not in a shell script?

I want to use grep to search for matching strings in the file, but because the file is too big, I only search for the first 500 lines.

I wrote in the shell script:

#!/bin/bash

patterns=(
llc_prefetcher_operat
to_prefetch
llc_prefetcher_cache_fill
)


search_file_path="mix1-bimodal-no-bop-lru-4core.txt"
echo ${#patterns[*]}
cmd="head -500 ${search_file_path} | grep -a "
for(( i=0;i<${#patterns[@]};i++)) do
cmd=$cmd" -e "\"${patterns[i]}\"
done;
echo $cmd
$cmd >junk.log

The result of running the script is:

3
head -500 mix1-bimodal-no-bop-lru-4core.txt | grep -a -e "llc_prefetcher_operat" -e "to_prefetch" -e "llc_prefetcher_cache_fill"
head: invalid option -a
Try'head --help' for more information.

On the penultimate line, I printed out the string of the executed command. I ran it directly on the command line and it was successful. That is the following sentence.

 head -500 mix1-bimodal-no-bop-lru-4core.txt | grep -a -e "llc_prefetcher_operat" -e "to_prefetch" -e "llc_prefetcher_cache_fill"

Note that in the grep command, if I do not add the -a option, there will be a problem of matching the binary file.

Why does this problem occur? Thank you!