awk || logical operator syntax when printing

I saw the following:

'NR==1 || ($11 > 0.01) && ($10 > 0.8) {print}' 

Are the || for "OR" why is everything printed though? Could you explain me the logic of this code snippet? I understand the second part where it imposes numerical conditions on column $11 and $10, but what does NR==1 || do?

When encountering code where order is not determined by brackets like in

'NR==1 || ($11 > 0.01) && ($10 > 0.8) {print}'

Precedence rules are used, && is above || or in other words && is more sticky than || therefore above is equivalent to

'NR==1 || (($11 > 0.01) && ($10 > 0.8)) {print}'

compare that with

'(NR==1 || ($11 > 0.01)) && ($10 > 0.8) {print}'

which would be case if && and || would share same level of precedence.

Infix notation is ambigue, language designers who use it must made rules regarding precedence, which might differ between languages. Using round brackets, even if not strictly necessary, will make your code easier to digest for reader who does not know precedence rules by heart for that particular language. In case of GNU AWK

> The normal precedence of the operators can be overruled by using
> parentheses. Think of the precedence rules as saying where the
> parentheses are assumed to be. In fact, it is wise to always use
> parentheses whenever there is an unusual combination of operators,
> because other people who read the program may not remember what the
> precedence is in this case. Even experienced programmers occasionally
> forget the exact rules, which leads to mistakes. Explicit parentheses
> help prevent any such mistakes.

from The GNU Awk User' Guide

This structure is call Short-circuit evaluation.

It is used extensively in shell programming or C type languages where the truthiness of the first item will effect the evaluation of the remainder of the statement.

Here is an example in awk.

First, this prints multiples of 2:

seq 10 | awk '$1%2==0'
2
4
6
8
10

Now suppose you want to add 3 as being part of the output sequence:

seq 10 | awk '$1==3 || $1%2==0'
2
3
4
6
8
10

Short-circuit evaluation is exensively used in Bash since the conditionals are kinda wordy.

This:

if  [[ -e "$filename" ]]; then
    echo "exists"
else
    echo "file does not exist"
fi

Can be replaced with:

[[ -e "$filename" ]] && echo "file exists" || echo "file does not exist"

While that is functionally equivalent but not exactly equivelent since this is not a replacement for if ... then. The second clause after the && could return a logical negative and then clause after the || would execute perhaps falsely. In the if ... then that does not happen.