You are doing the polynomial evaluation wrong for Taylor Series. First of all you should be using Horner's Method to reduce the number of multiplications needed

You are doing the polynomial evaluation wrong for Taylor Series. First of all you should be using Horner's Method to reduce the number of multiplications needed and then you should be using FMA to increase precision of the solution. https://momentsingraphics.de/FMA.html https://momentsingraphics.de/FMA.html