Commit aa9f290 has a lot of small changes but the primary change is that I removed exceptions:
https://github.com/swharden/ScottPlot/blob/be1d2866f014b5fc1a20b9e72d5496ec80ce5f76/src/ScottPlot/TicksExperimental.cs#L325-L384

and use if/else to determine what type of ticks to generate:
https://github.com/swharden/ScottPlot/blob/aa9f2900142df624954498ef8027d086c4c75e9a/src/ScottPlot/TicksExperimental.cs#L303-L322

I'm happy to merge this if you're okay with the change

This is progressing really well! I just modified Ticks.cs and added a bool we can change to experiment with the new and old tick systems:

https://github.com/swharden/ScottPlot/blob/f3d51c4657268e550b339791883c8edda25b7adc/src/ScottPlot/Ticks.cs#L114

Zooming far out we get:

Am I using your functions incorrectly?
https://github.com/swharden/ScottPlot/blob/f3d51c4657268e550b339791883c8edda25b7adc/src/ScottPlot/Ticks.cs#L209-L222

This is progressing really well! I just modified Ticks.cs and added a bool we can change to experiment with the new and old tick systems:

It's more than possibly a bug, but I need to test it after pulling. I'll see what's the problem.

I am unable to reproduce. Works for me. Are you up with all commits?

I created a new "tick tester 2" winForms app in /demos/

The "Large" button reproduces this error

I modified the console application to reproduce this error

double bigNumber = Math.Pow(23.456, 9);
double smallNumber = Math.Pow(23.456, -9);

DisplayTicksForRange(-bigNumber, bigNumber);
DisplayTicksForRange(9876 * bigNumber, 9877 * bigNumber);
DisplayTicksForRange(-smallNumber, smallNumber);
DisplayTicksForRange(9876 * smallNumber, 9877 * smallNumber);

Value range: [-2149243275732, 2149243275732]
  tick labels: -166666666666.667  -83333333333.333  0  83333333333.333  166666666666.667  
  modifier: x10¹²

Value range: [2.12259265911293E+16, 2.1228075834405E+16]
  tick labels: 0  31250000000  62500000000  93750000000  125000000000  
  modifier: x10¹62.123x10¹6

Value range: [-4.65280041255177E-13, 4.65280041255177E-13]
  tick labels: NaN  8  8  
  modifier: -2.5E-13

Value range: [4.59510568743613E-09, 4.59557096747739E-09]
  tick labels: 4.595  4.595  4.595  4.596  
  modifier: x10??

The bug is on line 96

https://github.com/swharden/ScottPlot/blob/be1d2866f014b5fc1a20b9e72d5496ec80ce5f76/src/ScottPlot/TicksExperimental.cs#L96

which should read:
if (Exponents.Max() != Exponents.Min() & Exponents.Min() !=0 )

For simmetrical plots, the Exponents.Min is 0.

Edit: I made the change you suggested cfa8790

This is much better! However, a few issues remain:

Value range: [-2149243275732, 2149243275732]
  tick labels: -2  -1  0  1  2  
  modifier: x10¹²

Value range: [2.12259265911293E+16, 2.1228075834405E+16]
  tick labels: 0  31250000000  62500000000  93750000000  125000000000  
  modifier: x10¹62.123x10¹6

Value range: [-4.65280041255177E-13, 4.65280041255177E-13]
  tick labels: NaN  8  8  
  modifier: -2.5E-13

Value range: [4.59510568743613E-09, 4.59557096747739E-09]
  tick labels: 4.595  4.595  4.595  4.596  
  modifier: x10??

Line 100 should read:
tickPositionsMantissas[i] = Math.Round((tickPositions[i]) / Math.Pow(10,tickPositionsExponent), 3);

I made the change you suggested. It now looks like:

https://github.com/swharden/ScottPlot/blob/2bb4e3c67ecf412745fc1746d4a520cb05e65951/src/ScottPlot/TicksExperimental.cs#L96-L104

Value range: [-2149243275732, 2149243275732]
  tick labels: -2  -1  0  1  2  
  modifier: x10¹²

Value range: [2.12259265911293E+16, 2.1228075834405E+16]
  tick labels: 0  31250000000  62500000000  93750000000  125000000000  
  modifier: x10¹62.123x10¹6

Value range: [-4.65280041255177E-13, 4.65280041255177E-13]
  tick labels: NaN  8  8  
  modifier: -2.5E-13

Value range: [4.59510568743613E-09, 4.59557096747739E-09]
  tick labels: 4.595  4.595  4.595  4.596  
  modifier: x10??

And line 119 shall have the same correction of line 100

there is still one bug on line 109 to be sorted out.

I made the update but the output is the same.

I know you're going on holiday soon! I don't want to disturb you when you leave. If you're still available, it might be more effective for you to make code changes to this pull request and I can merge it once it's working well. If you've left already, let me know I'll keep working on this and not trouble you about it!

This is the current mantissa-generating function:
https://github.com/swharden/ScottPlot/blob/dc059105046d30d35de7297ddd844c07f8ee35ef/src/ScottPlot/TicksExperimental.cs#L74-L128

There's one remaining bug, when Max and Min are of the same order of magnitude and they require exponentiation. It is a recursion of the same scenario. I'll see into it when I'm back.

This works great now, thanks so much @Padanian!

I'll pull it into the main branch and continue to work on it a bit there.