Hi MArinus
With the equation provided by Jack, we can´t make a reciprocal, unfortunately. The divisor is another polynomial.
Jack, i gave a try using Log10(5+1) with the formula and the precision is something around 5 digits after the "." only. If you input 5 as x, the result of log(x+1) = log(6) will turn onto:
(0.434294481903251828+(1.0658978447365901+(0.944333131990812123+(0.365595021795863521+(0.589858567636932956e-1+(0.298394177553741882e-2+0.100435574013167601e-4*x)*x)*x)*x)*x)*x)*x, x=5
= 607.096994200488817
(1+(2.95432048794495173+(3.31823430318176310+(1.76615730286299464+(0.451400626940937546+(0.492131362215352252e-1+0.158489557252300951e-2*x)*x)*x)*x)*x)*x) , x=5
= 780.177558728198735
607.096994200488817/780.177558728198735 = 0.778152341615854664455814528055710104487791345037987518732
Expected log10(6) = 0.7781512503836436325087667979796083359683187456528044061402931014.
0.
778152341615854664455814528055710104487791345037987518732 ; result using maple
0.
7781512503836436325087667979796083359683187456528044061402931014 ; expected result
Can you please give a try to see if the precision can be extended to at least 14 digits after the "." and also keeping the amount of polynomial "x" to be used (or simplifying would be better) ? I mean it is a equation where the numerator is a equation on the form of x^7+x^6+... and the divisor x^6+x^5... It can be reformulated as:
where A, B, C...are the values you posted and "x" the inputed value to calculate. We could try to put the numerator on a matrix and the divisor on other matrix and try to divide the matrix using the inversal of the divisor (The equation with x^6+...), but calculating the inverse matrix and also needing to check later if it can be divided will take a lot of time to process too.
Please, see if the numbers you created with Maple can be extended to at least 14 digits precision (after the "."), and also try simplifying the equation so we can try to see if it´s faster then the one i made.
