Calculate sum of squares using shell script in perl/awk

I have 2 files as below.

file1

0.34
0.27
0.32

file2

0.15
0.21
0.15

Now, I would like to calculate the sum of squares between each column. For example,

[(0.34 - 0.15)^2 + (0.27 - 0.21)^2 + (0.32 - 0.15)^2 ] / 3

Where 3 is the total number of lines in the file. I will be having same number of lines in both the files.

I have come up with the below bash script which works perfectly fine, but I want to know if there is some other easier way.

#! /bin/bash   
sum=0.0
while true; do
  read -r lineA <&3
  read -r lineB <&4
  if [ -z "$lineA" -o -z "$lineB" ]; then
    break
  fi
diff=$(bc <<< "scale=5; $lineA - $lineB")
square=$(bc <<< "scale=5; $diff*$diff")
sum=$(bc <<< "scale=5; $sum+$square")
done 3<file1 4<file2
filelen=`wc -l file1 | cut -f1 -d' '`
final=$(bc <<< "scale=5; $sum/$filelen")
echo "$final"

Is there a simpler way in awk or perl?

EDIT

I had 2 million rows in my input file and the input file actually contained scientific numbers like below.

3.59564e-185

My script as well as the suggested answers failed on scientific numbers. However, I could make my script in the question work when I changed the scientific numbers to 10^ notation.

I converted my input file as below.

sed -e 's/[eE]+*/\*10\^/' file1 > file1_converted
sed -e 's/[eE]+*/\*10\^/' file2 > file2_converted

Now, the suggested 2 answers failed giving me the error message as Nan. My script seemed to work but for 2 million rows it is taking a long time to execute.

Is there any efficient way to make it work?