More beautiful display of :unknown

[Kolaru]

As discussed in the JuliaInterval call, this PR reintroduces showing more information for :unknown roots in vectors, with fancy connector to group the information.

However, this information is still hidden if the IOContext is :compact, like for matrices:

julia> f(x) = (x < 1) ? x : (x - 2)^2 * (x - 3)
f (generic function with 1 method)

julia> rts = roots(f, interval(-5, 5))
4-element Vector{Root{Interval{Float64}}}:
 Root([0.0, 0.0]_com, :unique)
 Root([1.0, 1.0]_com, :unknown)
 ├ Not converged: region size smaller than the tolerance
 ├ Warning: error encountered during computation (use showerror(root.error) to see the whole stacktrace)
 └ InconclusiveBooleanOperation: The operation `[1.0, 1.0]_com < [1.0, 1.0]_com_NG` cannot be determined unambiguously. See the documentation for more information. See also `strictprecedes`.
 Root([2.0, 2.0]_com_NG, :unknown)
 └ Not converged: region size smaller than the tolerance
 Root([3.0, 3.0]_com_NG, :unique)

julia> reshape(rts, 2, 2)
2×2 Matrix{Root{Interval{Float64}}}:
 Root([0.0, 0.0]_com, :unique)   Root([2.0, 2.0]_com_NG, :unknown)
 Root([1.0, 1.0]_com, :unknown)  Root([3.0, 3.0]_com_NG, :unique)

@dpsanders @OlivierHnt

[github-actions]

Benchmark Results

	master	48f0a82...	master / 48f0a82...
10 dimensional/IntervalRootFinding.Krawczyk	3.14 ± 0.037 s	3.15 ± 0.033 s	0.998 ± 0.016
10 dimensional/IntervalRootFinding.Newton	48.5 s	48.1 s	1.01
Dietmar-Ratz/Dietmar-Ratz 1/IntervalRootFinding.Krawczyk	3.61 ± 0.091 μs	3.63 ± 0.21 μs	0.994 ± 0.063
Dietmar-Ratz/Dietmar-Ratz 1/IntervalRootFinding.Newton	3.65 ± 0.1 μs	3.6 ± 0.13 μs	1.01 ± 0.046
Dietmar-Ratz/Dietmar-Ratz 2/IntervalRootFinding.Krawczyk	0.106 ± 0.0011 ms	0.102 ± 0.0013 ms	1.03 ± 0.017
Dietmar-Ratz/Dietmar-Ratz 2/IntervalRootFinding.Newton	0.248 ± 0.011 ms	0.241 ± 0.013 ms	1.03 ± 0.074
Dietmar-Ratz/Dietmar-Ratz 3/IntervalRootFinding.Krawczyk	0.262 ± 0.014 ms	0.252 ± 0.014 ms	1.04 ± 0.078
Dietmar-Ratz/Dietmar-Ratz 3/IntervalRootFinding.Newton	0.186 ± 0.01 ms	0.181 ± 0.013 ms	1.03 ± 0.092
Dietmar-Ratz/Dietmar-Ratz 4/IntervalRootFinding.Krawczyk	0.0544 ± 0.00072 ms	0.0508 ± 0.00074 ms	1.07 ± 0.021
Dietmar-Ratz/Dietmar-Ratz 4/IntervalRootFinding.Newton	0.0351 ± 0.00078 ms	0.0341 ± 0.0022 ms	1.03 ± 0.071
Dietmar-Ratz/Dietmar-Ratz 5/IntervalRootFinding.Krawczyk	3.5 ± 0.1 μs	3.46 ± 0.11 μs	1.01 ± 0.044
Dietmar-Ratz/Dietmar-Ratz 5/IntervalRootFinding.Newton	3.45 ± 0.1 μs	3.44 ± 0.099 μs	1 ± 0.041
Dietmar-Ratz/Dietmar-Ratz 6/IntervalRootFinding.Krawczyk	13.6 ± 0.25 μs	13.5 ± 0.86 μs	1.01 ± 0.068
Dietmar-Ratz/Dietmar-Ratz 6/IntervalRootFinding.Newton	20.6 ± 0.58 μs	20 ± 0.46 μs	1.03 ± 0.037
Dietmar-Ratz/Dietmar-Ratz 7/IntervalRootFinding.Krawczyk	3.71 ± 0.09 μs	3.73 ± 0.13 μs	0.995 ± 0.042
Dietmar-Ratz/Dietmar-Ratz 7/IntervalRootFinding.Newton	3.71 ± 0.1 μs	3.73 ± 0.12 μs	0.995 ± 0.042
Dietmar-Ratz/Dietmar-Ratz 9/IntervalRootFinding.Krawczyk	4.02 ± 0.099 μs	4.03 ± 0.13 μs	0.998 ± 0.041
Dietmar-Ratz/Dietmar-Ratz 9/IntervalRootFinding.Newton	4.01 ± 0.099 μs	4.06 ± 0.13 μs	0.987 ± 0.04
Rastigrin stationary points/IntervalRootFinding.Krawczyk	0.151 ± 0.0042 s	0.15 ± 0.001 s	1 ± 0.029
Rastigrin stationary points/IntervalRootFinding.Newton	0.143 ± 0.0019 s	0.142 ± 0.0019 s	1.01 ± 0.018
Smiley/Smiley and Chun (2001), Example 2.2/IntervalRootFinding.Krawczyk	2.78 ± 0.058 ms	2.74 ± 0.052 ms	1.01 ± 0.029
Smiley/Smiley and Chun (2001), Example 2.2/IntervalRootFinding.Newton	2.2 ± 0.037 ms	2.13 ± 0.031 ms	1.03 ± 0.023
Smiley/Smiley and Chun (2001), Example 5.2/IntervalRootFinding.Krawczyk	0.0381 ± 0.0036 s	0.0376 ± 0.0036 s	1.01 ± 0.14
Smiley/Smiley and Chun (2001), Example 5.2/IntervalRootFinding.Newton	0.0322 ± 0.0033 s	0.0317 ± 0.0031 s	1.01 ± 0.14
Smiley/Smiley and Chun (2001), Example 5.4/IntervalRootFinding.Krawczyk	1.83 ± 0.03 ms	1.98 ± 0.033 ms	0.924 ± 0.022
Smiley/Smiley and Chun (2001), Example 5.4/IntervalRootFinding.Newton	1.82 ± 0.026 ms	1.81 ± 0.026 ms	1.01 ± 0.021
Smiley/Smiley and Chun (2001), Example 5.5/IntervalRootFinding.Krawczyk	5.67 s	5.55 s	1.02
Smiley/Smiley and Chun (2001), Example 5.5/IntervalRootFinding.Newton	5.21 s	5.09 s	1.03
time_to_load	0.406 ± 0.0062 s	0.4 ± 0.00075 s	1.02 ± 0.016

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[OlivierHnt]

Really nice! There are only a few doctests to fix.