NavList:

I just ran yesterday the examples, quoted here-after, by Modris Fersters yesterday ( https://navlist.net/Lunar44-vs-Franks-online-calculator-Fersters-may-2023-g54219 )

"Here are some examples. Position: 57°N; 26°E; 10°C; 1010mbar
1) Sun-Moon near limbs; 30.04.2023; 16:20:00; Frank’s distance: 120° 28,59'; Paul’s Lunar4.4: 120° 28,77'; Difference: 0,18’. "

My own result : 120°28,74' 

"2)Capella-Moon near limb; 03.05.2023; 19:20:00; Frank’s distance: 114° 58,44'; Paul’s Lunar4.4: 114° 58,58'; Difference: 0,14'."

My own result : 114°58,58' 

"But on 30.04.2023 Marss, Pollux and Regulus lunar distances differs only 0,01'...0,05'  from Paul's Lunar4.4."

Mars, my own result : 52°05,68' 
Pollux, my own result : 47°17.53' 
Regulus, Own result : 11°16,21' 

In spite of having a software slightly less accurate than Paul's, my results fully back up Modris' investigation results.

Hence it might be worth investigating the software behind https://clockwk.com/apps/clear/. As clear discrepancies appear only for lunar Distances in excess of 90°, check for :
- Earlier mentioned Interface error about displaying angles superior to 90° . That's the easy case.
- Lunar reduction method actual ability to accurately solve for LD's in excess of 90°. That's a much more uneasy case.

When the Sine function is used, it returns the same value for α  and for 90 - α   , e.g.  sin 85° = sin 95°, altogether with the same drawback if the Asin function is used since in the vicinity of 90° it always returns the smallest angle. This is the one reason for which - except in simple clear cut cases - I avoid the use of the Sine/Cosine and Asin/Acos functions to all the extent possible, highly preferring the use of the P⇾R and  R⇾P functions which are absolutely undefeatable and unbeatable over the full 0°- 360° range.

Good luck in your investigations.

[Note from FER: Antoine sent this message yesterday. It was accidentally (automated software) trapped as spam at a top level (which I only check now and then because it almost never traps real messages). I am re-posting with some formatting changes which maybe will reduce its accidental and erroneous "spam score"]