lower value from the upper, yielding -1 at level one. This also terminates data entry, so the 5 can be immediately entered. This automatically raises the -1 to the second level. When the user then presses (add), the first two levels are added, and the result, 4, appears in the lower. This automatic promotion (and demotion) of data among levels in the stack as each operation is performed automatically sets up successive operators just as they are needed. In many HP calculators, the stack is four levels high. So it is possible to type 3, , type 4, , type 5, , and type 6. The stack now holds all four values in its four levels. One can then hit the button three times, and the sum, 18, will appear in level one. Any new data entry promotes the 18 to level two. This activity is limited only by the "height" of the stack. Careful stack management allows complex parenthesis-filled expressions to be evaluated in a simple linear fashion. It is rarely required that intermediate results be stored and retrieved, as is required usually of algebraic notation systems. This advantage of reverse Polish notation is that it removes the need for parentheses that are required by infix notation, since the stack holds all arguments in a last-in, first out progression. For example, to compute the expression , one would type 3, press , and type 4. Upon pressing (multiply), the intermediate product 12 appears visually at the bottom of the stack. Then one types 5, , and 6. The intermediate result 12 has been promoted to level three, with the 5 at level two and the 6 visible at level one. It is only required to press and then in succession. The intermediate product, 30, appears first in level one, and the final result, 42 appears at level one since the 12 at level two has now been added. Practical implications In comparison, testing of reverse Polish notation with algebraic notation, reverse Polish has been found to lead to faster calculations, for two reasons. The first reason is that reverse Polish calculators do not need expressions to be parenthesized, so fewer operations need to be entered to perform typical calculations. Additionally, users of reverse Polish calculators made fewer mistakes than for other types of calculators. Later research clarified that the increased speed from reverse Polish notation may be attributed to