Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Find a minimax approximation of a function
ResourceFunction["MiniMaxApproximation"][expr,{x,{x_{0},x_{1}},m,n}] finds the rational polynomial function of x, with numerator order m and denominator order n, that gives a minimax approximation to expr on the interval x_{0} to x_{1}. 

ResourceFunction["MiniMaxApproximation"][expr,approx,{x,{x_{0},x_{1}},m,n}] finds the minimax approximation to expr, starting the iterative algorithm with approx. 
"Bias"  0  bias in the automatic choice of interpolation points  
"Brake"  {5,5}  braking to apply on the iterative algorithm  
"Derivatives"  Automatic  function to use for derivatives  
MaxIterations  20  maximum number of iterations to use  
"PlotFlag"  False  whether to plot relative error  
"PrintFlag"  False  whether to print status information  
WorkingPrecision  MachinePrecision  precision to use in internal computations 
A list containing the points where the maximum error occurs and the desired interpolation, along with the value of the error:
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The rational approximation:
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The relative error in the approximation over the interval:
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The convergence process does not finish within a small number of iterations without braking:
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With the default brake, the conversion succeeds:
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Supply a function that gives a list of derivatives of the function to be approximated, evaluated at numeric points:
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Because MiniMaxApproximation tries to minimize the maximum of the relative error, it is not possible to find a minimax approximation to a function that has a zero in the interval in question:
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Divide out the zero and then multiply back into the rational function:
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The relative error:
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Wolfram Language 11.3 (March 2018) or above
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