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# This demo application shows the capabilities of paceval. in terms of its computational excellence. Please examine its calculation power and speed for a formula without limitations in length and number of variables. In addition, it demonstrates how precise and reliable paceval. works. The trusted interval computation “TINC” shows an interval within the true results can be found. And, finally, you can draw the function for a selected variable. Click here>> for the latest version.

## 1. Input formula into the tool and adjust settings

You can either type your formula directly into the editor next to ‘f(…)=’ or you generate a formula for your measure points using the paceval. approximation demo program.  Please use standard mathematical notations, e.g. for

you simply type

-(sin(x*cos(x))^(1/x)) into the editor.

Just have a look at the paceval. product brief>> or select the tab ‘quick reference’ to get a list of all supported arithmetic expressions and functions. Of course, paceval. is not limited to these. paceval. has no limitation for the length or number of variables. If you wish you can change names for the variables in the grid. Just start with a letter (A-Z) or (a-z), subsequent characters can also be digits (0-9).

## 2.  Calculate results

Please specify the value of the variable you are interested in, then select ‘calculate’. If you press ‘calculate’ for the first time, the function is analyzed first, checked for errors, a cache memory is created and the results shows up in “real-time”. When you now re-do the calculation and just change the variable values you will see that the calculation time is now even further reduced, e.g. it takes less than a millisecond due to the caching method. Of course, the exact speed always depends on your processor speed.

## 3. Check the precision of your result using “TINC”

“Computers are not mathematically exact, you should include this in your calculations.”
In general, paceval. uses long double precision. However, if you have a long formula and/ or many variables the result gains haziness. However, paceval. offers a solution for this: the trusted interval computation (TINC) delivers a precise interval in which the “true” result can be found. Just select ‘on’ for ‘use interval’ and press ‘calculate’. paceval. now shows a minimum and maximum value in which the correct value is. If you do not know this you might be surprised about the results and could end up in unforeseen scenarios.

## 4. Draw and investigate the graph

You can draw the graph for a selected variable by pressing ‘graph for (selected) variable’. In our example we have drawn the graph for the variable ‘x’.
Just zoom in and out and select left and right, up and down to investigate your area of interest.