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# Remez exchange toolbox

The Remez exchange algorithm is a fast method for approximating functions in a Chebyshev space. The Lol Engine provides its own implementation of the Remez exchange algorithm to find **polynomial approximations to real functions**. Such polynomials are also known as minimax polynomials.

## Example

The following graph shows approximations of `sin(x)`

over [-π, π] using three different polynomials:

- the Taylor series to the 5th order:
*x-x³/6+x⁵/120* - the Taylor series to the 7th order:
*x-x³/6+x⁵/120-x⁷/5040* - the minimax polynomial to the 5th order:
*x-0.1587164x³+0.00585375x⁵*

It is obvious that the polynomial found using the Remez method is closer to the sine curve than the Taylor series of same order, and even better than the next order.

## Download

AVAILABLE SOON

## Tutorial

Before you start reading the tutorial, I suggest you have a quick look at the Lol Engine real numbers? documentation.

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