The iterated exp(x)-1 seems to work nicely. It takes a minute or two to generate all the helper functions for a 35-term power series, but then I'm able to calculate 505 points for the interval [-248/128, 256/128], step size 1/128, in just over 59 seconds. This was sufficient to produce the following graph of \( {}^{x} e \) in 1 minute:
By the way, I'm using a radius of 0.005, 35 terms. I could take the number of terms out to 50 pretty easily, and still get increased precision with each new term. As it is, precision seems to be about 65-70 decimal digits.
By the way, sorry for the extremely generic appearance of the graph. This was my first attempt at plotting in SAGE, so I haven't tried changing the tick spacings on the axes, adding gridlines and labels, etc. I also plan to add graphs of the derivatives (approximated with secants).
By the way, I'm using a radius of 0.005, 35 terms. I could take the number of terms out to 50 pretty easily, and still get increased precision with each new term. As it is, precision seems to be about 65-70 decimal digits.
By the way, sorry for the extremely generic appearance of the graph. This was my first attempt at plotting in SAGE, so I haven't tried changing the tick spacings on the axes, adding gridlines and labels, etc. I also plan to add graphs of the derivatives (approximated with secants).
~ Jay Daniel Fox