$\begingroup$

When I was a child, I wanted to be a mathematician so I asked my parents to buy me a computer to make super complex calculations. Of course, they were not crazy enough to buy an expensive super computer, so they bought me a way cheaper Stupid Computer™. In the TV ad, they said that «Stupid Computer™ can perform any operations a Super Computer™ can do !». As trusting as a 8 years old kid can be toward marketing, I trusted them.

In fact, and I realized that years later, Stupid Computer™ was just a Super Computer™ with a production defect.

With a Super Computer™ you can compute every polynomial functions like $ x^7-42x^3+3x$.

A bug in Stupid Computer™ prevents you to use the $x$ key more than once. For example, you can't enter $x²+x$ but you can enter $(x+1/2)^2-1/4$ instead.

Super and Stupid computer can only use operations like addition, multiplication, exponent... and their opposite : subtraction, division, roots, logarithm...

The question is : Can really a Stupid Computer do everything a Super Computer can ?