Arithmetic Evaluation is faster than let

$ i=0; time while :; do let "i = i + 1"; [[ $i -gt 100000 ]] && break;done

real    0m8.211s
user    0m7.900s
sys     0m0.304s

$ i=0; time while :; do ((i++)); [[ $i -gt 100000 ]] && break;done

real    0m5.287s
user    0m4.980s
sys     0m0.304s

UPDATE: This appears to still be true, but by a different margin. See comments.

List expansion is faster than seq and command substitution (though not always available)

$ time for i in $(seq 0 1000000); do :; done

real    0m28.482s
user    0m28.066s
sys     0m0.412s

$ time for i in {0..1000000}; do :; done

real    0m24.563s
user    0m24.402s
sys     0m0.156s

UPDATE: On BSD systems the apparent seq equivalent (jot) is faster than list expansion. See comments.

: is faster than true

$ i=0; time while true; do ((i++)); [[ $i -gt 1000000 ]] && break;done

real    0m57.360s
user    0m53.967s
sys     0m3.392s

$ i=0; time while :; do ((i++)); [[ $i -gt 1000000 ]] && break;done

real    0m54.138s
user    0m50.571s
sys     0m3.560s

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