My guess is that fake( exp(x) - (x^3 / 5) ) is simply :
exp(x) - Constant.
But I have not tried anything yet.
I assume the best possible approximation ( by using fake - for exp(x) - ( x^3 / 5 ) - ) is approximately exp(x) - a x^b - constant.
Where b is between 0 and 1.
Also a possibility is with q_i very small :
1 + q_1 x + q_2 x^2 + q_3 x^3 + x^4/4! + x^5/5! + ...
or
0 + q_1 x + q_2 x^2 + q_3 x^3 + x^4/4! + x^5/5! + ...
I wonder.
It seems 0 + q_1 x + q_2 x^2 + q_3 x^3 + x^4/4! + x^5/5! + ...
cannot be improved.
( because O(x^3) cannot be given by O(x^(3+eps)) )
Therefore it would be a good (benchmark) test for our fake algorithms I guess.
regards
tommy1729
exp(x) - Constant.
But I have not tried anything yet.
I assume the best possible approximation ( by using fake - for exp(x) - ( x^3 / 5 ) - ) is approximately exp(x) - a x^b - constant.
Where b is between 0 and 1.
Also a possibility is with q_i very small :
1 + q_1 x + q_2 x^2 + q_3 x^3 + x^4/4! + x^5/5! + ...
or
0 + q_1 x + q_2 x^2 + q_3 x^3 + x^4/4! + x^5/5! + ...
I wonder.
It seems 0 + q_1 x + q_2 x^2 + q_3 x^3 + x^4/4! + x^5/5! + ...
cannot be improved.
( because O(x^3) cannot be given by O(x^(3+eps)) )
Therefore it would be a good (benchmark) test for our fake algorithms I guess.
regards
tommy1729
