HP 42S Integration

[lrdheat]

When integrating x^1/3 from -3 to 1, using
SIGN
LAST X
3
1/X
Y^X
ABS
*

The program, using ACC of 1e-5 was very much slowed down compared to the simpler program if the integral is calculated for a range falling entirely within a positive domain. The accuracy was also lessened.

On the Free42 on my iPad, the program for -3 to 1 ran quickly, and accuracy did not appear to be lessened. I did note that, even on the iPad, using an ACC of 1e-9 produced a noticeable delay in achieving an answer. I am left wondering what makes the program so much more time consuming, and why it impacts the accuracy on the physical calculator?