Solving

There are two kinds of solving: iterative and symbolic. FastFigures uses an iterative approach.

An iterative method attempts to balance an equation and determine an answer, relying on a minimum and maximum guess to "bracket" the answer. An equation is said to be in balance when, tabulated, the value to the left of the equals sign is the same as the value to the right of the equals sign. Because the method is iterative it can take a significant amount of time to complete and may fail to return a result or return a result that is inexact but within the tolerance permitted when using floating point math.

In its simplest form, an iterative solver determines a mid-point between a maximum and minimum guess and evaluates the equation at all three points. It then decides which two points the equation is between – the mid-point and minimum guess or mid-point and maximum guess – and calculates a new mid-point based on those two points. It continues this cycle until it "guesses" the right answer. Although the solver is more advanced than this, it is similar in nature.

In more detail, the iteration methodology is as follows: It will take the mid-point between the minimum and maximum and step towards the maximum bracket until a sign change is detected. It will then search for a root around the sign change using Brent's method. If the search does not yield a sign change then it steps negatively towards the minimum bracket from the mid-point between the bracket values until a sign change is found. It will then search for a root around the sign change using Brent's method. If a sign change is not found it gives up.

FastFigures automatically handles solving when creating templates.

Keep in mind that the solver is only available for real numbers and fractions.