Why mixing + and cast does not produce an error in "+(int)+(long)-1"?

You are not adding nor substracting. Those + and - operators are unary sign operators.

See documentation at The Unary Operators section.

The sequence at stake:

(byte)+(short)-(int)+(long)-1

is evaluated from right to left like this:

the initial value is -1
casting to long (which is still -1)
unary + sign (still -1)
casting to int (still -1)
unary - sign (now the value is 1)
so on (the value remains 1 until the end)

These + and - are unary ones.

More specifically, it is in fact:

System.out.println((byte) (+((short) (-((int) (+((long) -1)))))));

if you remove all casting from your example, because in this case it will do nothing

System.out.println((byte)+(short)-(int)+(long)-1);

will become

System.out.println( + - + -1);

now you can see that just the operators are still there and because minus and minus are plus your result will be 1

basically you can think of it like:

var mylong  = +(long)-1;      <- -1
var myint   = -(int)mylong;   <-  1
var myshort = +(short)myint;  <-  1
var mybyte  =  (byte)myshort; <-  1