Efficient way to do calculations in bash

Please don't do this in the shell. There is no amount of tweaking that would ever make it remotely efficient. Shell loops are slow and using the shell to parse text is just bad practice. Your whole script can be replaced by this simple awk one-liner which will be orders of magnitude faster:

awk 'BEGIN{E = exp(1);} $1>0{tot+=log($1); c++} END{m=tot/c; printf "%.2f\n", E^m}' file

For example, if I run that on a file containing the numbers from 1 to 100, I get:

$ seq 100 > file
$ awk 'BEGIN{E = exp(1);} $1>0{tot+=log($1); c++} END{m=tot/c; printf "%.2f\n", E^m}' file
37.99

---

In terms of speed, I tested your shell solution, your python solution and the awk I gave above on a file containing the numbers from 1 to 10000:

## Shell
$ time foo.sh
3677.54

real    1m0.720s
user    0m48.720s
sys     0m24.733s

### Python
$ time foo.py
The Geometric Mean is:  3680.827182220091

real    0m0.149s
user    0m0.121s
sys     0m0.027s


### Awk
$ time awk 'BEGIN{E = exp(1);} $1>0{tot+=log($1); c++} END{m=tot/c; printf "%.2f\n", E^m}' input.txt
3680.83

real    0m0.011s
user    0m0.010s
sys     0m0.001s

As you can see, the awk is even faster than the python and far simpler to write. You can also make it into a "shell" script, if you like. Either like this:

#!/bin/awk -f

BEGIN{
    E = exp(1);
} 
$1>0{
    tot+=log($1);
    c++;
}
 
END{
    m=tot/c; printf "%.2f\n", E^m
}

or by saving the command in a shell script:

#!/bin/sh
awk 'BEGIN{E = exp(1);} $1>0{tot+=log($1); c++;} END{m=tot/c; printf "%.2f\n", E^m}' "$1"