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edited Apr 9, 2013 at 14:08

I wanted to write this as a comment in support of Carlo Beenakkers answer but it was too long so I place it as an answer myself.

Simplification might be associated with the concept of expression economy.

In that line of thought, to simplify is to make more economical without loss of mathematical meaning.

But what measure of economy of an expression could one possibly use?

Just to illustrate (surely more eficient representation schemes could be devised), one could take for example the number of symbols in the expression above.

They are 7 symbols: x,(,y,+,),1,3 which means we can represent the expression in base 7 with the number resulting from the concatenation (in the order of the expression) of the algarism associated with each symbol.

The same procedure applied to the above expression once simplified would probably deliver a smaller number (comparing both once converted back to the same base, for example binary)

The concept of economy could therefore be attacched to the product of the number of symbols used and the number of digits of the number representation of the expression, somehow following a criteria for number base economy evaluation (Hayes, 2001) http://www.americanscientist.org/issues/pub/third-base and which reflects in the final binary number obtained.

I wanted to write this as a comment in support of Carlo Beenakkers answer but it was too long so I place it as an answer myself.

Simplification might be associated with the concept of expression economy.

In that line of thought, to simplify is to make more economical without loss of mathematical meaning.

But what measure of economy of an expression could one possibly use?

Just to illustrate (surely more eficient representation schemes could be devised), one could take for example the number of symbols in the expression above.

The same procedure applied to the above expression once simplified would probably deliver a smaller number (comparing both once converted back to the same base, for example binary)

The concept of economy could therefore be attacched to the product of the number of symbols used and the number of digits of the number representation of the expression, somehow following a criteria for number base economy evaluation (Hayes, 2001) and which reflects in the final binary number obtained.

I wanted to write this as a comment in support of Carlo Beenakkers answer but it was too long so I place it as an answer myself.

Simplification might be associated with the concept of expression economy.

In that line of thought, to simplify is to make more economical without loss of mathematical meaning.

But what measure of economy of an expression could one possibly use?

Just to illustrate (surely more eficient representation schemes could be devised), one could take for example the number of symbols in the expression above.

The same procedure applied to the above expression once simplified would probably deliver a smaller number (comparing both once converted back to the same base, for example binary)

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created Apr 4, 2013 at 15:35

Fernando Pimentel

I wanted to write this as a comment in support of Carlo Beenakkers answer but it was too long so I place it as an answer myself.

Simplification might be associated with the concept of expression economy.

In that line of thought, to simplify is to make more economical without loss of mathematical meaning.

But what measure of economy of an expression could one possibly use?

Just to illustrate (surely more eficient representation schemes could be devised), one could take for example the number of symbols in the expression above.

The same procedure applied to the above expression once simplified would probably deliver a smaller number (comparing both once converted back to the same base, for example binary)

The concept of economy could therefore be attacched to the product of the number of symbols used and the number of digits of the number representation of the expression, somehow following a criteria for number base economy evaluation (Hayes, 2001) and which reflects in the final binary number obtained.