Upper and lower limit slots not clear leading to undesirable results

[johnblommers]

Expected: To demonstrate the issue, integrate the simple function x from 0 to 1. The correct answer is 0.5 exactly.

Result: But with accuracy of integration set to maximum the result is -0.501146157. There are three things wrong:

1. It takes perhaps ten seconds to compute this result, much longer than you'd expect from such a simple integration.
2. The exact answer is 0.50000000 but pebbles returns -0.501146157.
3. The sign of the answer is wrong, it should be positive.

Screenshot:

Version

flatpak info com.github.subhadeepjasu.pebbles

Pebbles - Perform advanced calculations with ease

          ID: com.github.subhadeepjasu.pebbles
         Ref: app/com.github.subhadeepjasu.pebbles/x86_64/stable
        Arch: x86_64
      Branch: stable
     Version: 2.0.0
     License: GPL-3.0+
      Origin: flathub
  Collection: org.flathub.Stable
Installation: user
   Installed: 104.3 MB
     Runtime: org.freedesktop.Platform/x86_64/20.08
         Sdk: org.freedesktop.Sdk/x86_64/20.08

      Commit: 43f192a03fa1ac2eed46888d6c60144d6b387b0d851444bf812e633e0cc2ec4f
      Parent: b3de54e093f068bc4146b69d488128b407a9370df3fd06d875f6786aa538699b
     Subject: Temporarily remove elementary stylesheet (734a0d18)
        Date: 2021-08-15 14:52:32 +0000

[SubhadeepJasu]

The answer is partly correct, because you have entered the upper and lower limits in lower and upper slots respectively. Which is definitely still an UX fail and I need to fix it.

As for speed, it doesn't depend on the way we perceive an expression to be simple or complex. Increasing accuracy simply increases the number of subdivisions between the limits and increases the number of calculation iterations even for something as simple as "x". That is where the accuracy slider comes in. If we as humans know that an expression is simple, use low accuracy, otherwise use higher accuracy. Also the result will never be 100% accurate even with the highest accuracy settings. That's just by the nature of the algorithm. I do have plans to look into alternative algorithms to improve accuracy and speed.

[SubhadeepJasu]

Point 1 and 2 are mitigated by #82