fix stats of stabilized RK methods

[ranocha]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

I was wondering why an algorithm became so much slower when supplying an eigen_est although both the number of steps and the number of function evaluations reported in the stats reduced significantly 🙈

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	a0eae4b...	master / a0eae4b...
construction/linear_N50	27.1 ± 0.78 μs	28 ± 14 μs	0.966 ± 0.48
construction/lotka_volterra	18 ± 0.22 μs	18.1 ± 0.27 μs	0.993 ± 0.019
construction/rober	17.9 ± 0.19 μs	18.1 ± 0.23 μs	0.989 ± 0.016
nonstiff/fitzhugh_nagumo/BS3	0.143 ± 0.0097 ms	0.147 ± 0.011 ms	0.975 ± 0.096
nonstiff/fitzhugh_nagumo/DP5	0.0973 ± 0.0093 ms	0.0986 ± 0.0097 ms	0.987 ± 0.13
nonstiff/fitzhugh_nagumo/Tsit5	0.116 ± 0.0081 ms	0.117 ± 0.0092 ms	0.994 ± 0.1
nonstiff/fitzhugh_nagumo/Vern6	0.166 ± 0.0085 ms	0.171 ± 0.0083 ms	0.973 ± 0.069
nonstiff/fitzhugh_nagumo/Vern7	0.112 ± 0.0081 ms	0.117 ± 0.0087 ms	0.957 ± 0.099
nonstiff/lotka_volterra/BS3	0.287 ± 0.01 ms	0.293 ± 0.011 ms	0.979 ± 0.051
nonstiff/lotka_volterra/DP5	0.0466 ± 0.016 ms	0.0465 ± 0.016 ms	1 ± 0.48
nonstiff/lotka_volterra/Tsit5	0.0623 ± 0.023 ms	0.0628 ± 0.024 ms	0.992 ± 0.52
nonstiff/lotka_volterra/Vern6	0.0822 ± 0.011 ms	0.0818 ± 0.011 ms	1.01 ± 0.19
nonstiff/lotka_volterra/Vern7	0.0499 ± 0.021 ms	0.0508 ± 0.021 ms	0.983 ± 0.59
nonstiff/pleiades/BS3	0.0862 ± 0.012 s	0.0865 ± 0.0091 s	0.997 ± 0.17
nonstiff/pleiades/DP5	1.25 ± 0.11 ms	1.27 ± 0.096 ms	0.988 ± 0.11
nonstiff/pleiades/Tsit5	16.2 ± 5.3 ms	15.6 ± 5.9 ms	1.04 ± 0.52
nonstiff/pleiades/Vern6	6.65 s	7.43 s	0.895
nonstiff/pleiades/Vern7	7.87 s	7.96 s	0.988
scaling/brusselator_2d/16x16	0.302 ± 0.029 s	0.306 ± 0.021 s	0.986 ± 0.12
scaling/brusselator_2d/32x32	7.05 s	7.23 s	0.975
scaling/brusselator_2d/8x8	11.1 ± 0.17 ms	11.3 ± 0.27 ms	0.985 ± 0.028
scaling/linear/N10	0.0375 ± 0.017 ms	0.0374 ± 0.017 ms	1 ± 0.64
scaling/linear/N100	0.789 ± 0.016 ms	0.798 ± 0.023 ms	0.989 ± 0.034
scaling/linear/N50	0.213 ± 0.011 ms	0.216 ± 0.01 ms	0.985 ± 0.068
stiff/pollution/FBDF	0.593 ± 0.015 ms	0.599 ± 0.013 ms	0.991 ± 0.033
stiff/pollution/KenCarp4	0.552 ± 0.011 ms	0.553 ± 0.011 ms	0.998 ± 0.027
stiff/pollution/Rodas4	0.764 ± 0.017 ms	0.779 ± 0.013 ms	0.981 ± 0.027
stiff/pollution/Rosenbrock23	1.35 ± 0.033 ms	1.38 ± 0.024 ms	0.981 ± 0.029
stiff/pollution/TRBDF2	0.513 ± 0.012 ms	0.521 ± 0.012 ms	0.985 ± 0.032
stiff/rober/FBDF	0.604 ± 0.01 ms	0.629 ± 0.011 ms	0.961 ± 0.023
stiff/rober/KenCarp4	0.753 ± 0.02 ms	0.749 ± 0.019 ms	1.01 ± 0.037
stiff/rober/Rodas4	0.402 ± 0.012 ms	0.401 ± 0.01 ms	1 ± 0.039
stiff/rober/Rosenbrock23	0.275 ± 0.0096 ms	0.276 ± 0.0094 ms	0.995 ± 0.049
stiff/rober/TRBDF2	1.74 ± 0.012 ms	1.74 ± 0.015 ms	1 ± 0.011
stiff/van_der_pol/FBDF	9.87 ± 0.079 ms	9.9 ± 0.1 ms	0.997 ± 0.013
stiff/van_der_pol/KenCarp4	4.61 ± 0.069 ms	4.68 ± 0.068 ms	0.986 ± 0.02
stiff/van_der_pol/Rodas4	7.31 ± 0.047 ms	7.23 ± 0.089 ms	1.01 ± 0.014
stiff/van_der_pol/Rosenbrock23	21.9 ± 0.17 ms	21.5 ± 0.19 ms	1.02 ± 0.012
stiff/van_der_pol/TRBDF2	2.99 ± 0.087 ms	2.93 ± 0.093 ms	1.02 ± 0.044
time_to_load	3.22 ± 0.027 s	3.3 ± 0.092 s	0.977 ± 0.029

Memory benchmarks

	master	a0eae4b...	master / a0eae4b...
construction/linear_N50	0.071 k allocs: 0.0411 MB	0.071 k allocs: 0.0411 MB	1
construction/lotka_volterra	0.065 k allocs: 2.45 kB	0.065 k allocs: 2.45 kB	1
construction/rober	0.065 k allocs: 2.42 kB	0.065 k allocs: 2.42 kB	1
nonstiff/fitzhugh_nagumo/BS3	3.69 k allocs: 0.164 MB	3.69 k allocs: 0.164 MB	1
nonstiff/fitzhugh_nagumo/DP5	2.63 k allocs: 0.127 MB	2.63 k allocs: 0.127 MB	1
nonstiff/fitzhugh_nagumo/Tsit5	4 k allocs: 0.182 MB	4 k allocs: 0.182 MB	1
nonstiff/fitzhugh_nagumo/Vern6	4.54 k allocs: 0.207 MB	4.54 k allocs: 0.207 MB	1
nonstiff/fitzhugh_nagumo/Vern7	3.91 k allocs: 0.165 MB	3.91 k allocs: 0.165 MB	1
nonstiff/lotka_volterra/BS3	7.88 k allocs: 0.365 MB	7.88 k allocs: 0.365 MB	1
nonstiff/lotka_volterra/DP5	1.21 k allocs: 0.0543 MB	1.21 k allocs: 0.0543 MB	1
nonstiff/lotka_volterra/Tsit5	2.17 k allocs: 0.093 MB	2.17 k allocs: 0.093 MB	1
nonstiff/lotka_volterra/Vern6	2.24 k allocs: 0.0986 MB	2.24 k allocs: 0.0986 MB	1
nonstiff/lotka_volterra/Vern7	1.65 k allocs: 0.0736 MB	1.65 k allocs: 0.0736 MB	1
nonstiff/pleiades/BS3	0.685 M allocs: 0.0675 GB	0.685 M allocs: 0.0675 GB	1
nonstiff/pleiades/DP5	6.63 k allocs: 0.51 MB	6.63 k allocs: 0.51 MB	1
nonstiff/pleiades/Tsit5	0.186 M allocs: 20.4 MB	0.186 M allocs: 20.4 MB	1
nonstiff/pleiades/Vern6	0.038 G allocs: 4.05 GB	0.038 G allocs: 4.05 GB	1
nonstiff/pleiades/Vern7	0.044 G allocs: 4.63 GB	0.044 G allocs: 4.63 GB	1
scaling/brusselator_2d/16x16	3.58 k allocs: 0.152 GB	3.58 k allocs: 0.152 GB	1
scaling/brusselator_2d/32x32	3.4 k allocs: 2.22 GB	3.4 k allocs: 2.22 GB	1
scaling/brusselator_2d/8x8	2.62 k allocs: 8.76 MB	2.62 k allocs: 8.76 MB	1
scaling/linear/N10	0.752 k allocs: 0.0514 MB	0.752 k allocs: 0.0514 MB	1
scaling/linear/N100	2.27 k allocs: 0.901 MB	2.27 k allocs: 0.901 MB	1
scaling/linear/N50	1.66 k allocs: 0.348 MB	1.66 k allocs: 0.348 MB	1
stiff/pollution/FBDF	1.5 k allocs: 0.288 MB	1.5 k allocs: 0.288 MB	1
stiff/pollution/KenCarp4	0.516 k allocs: 0.134 MB	0.516 k allocs: 0.134 MB	1
stiff/pollution/Rodas4	1.28 k allocs: 0.363 MB	1.28 k allocs: 0.363 MB	1
stiff/pollution/Rosenbrock23	2.77 k allocs: 0.819 MB	2.77 k allocs: 0.819 MB	1
stiff/pollution/TRBDF2	0.783 k allocs: 0.168 MB	0.783 k allocs: 0.168 MB	1
stiff/rober/FBDF	2.89 k allocs: 0.137 MB	2.89 k allocs: 0.137 MB	1
stiff/rober/KenCarp4	1.3 k allocs: 0.0575 MB	1.3 k allocs: 0.0575 MB	1
stiff/rober/Rodas4	2.19 k allocs: 0.106 MB	2.19 k allocs: 0.106 MB	1
stiff/rober/Rosenbrock23	2.51 k allocs: 0.117 MB	2.51 k allocs: 0.117 MB	1
stiff/rober/TRBDF2	7.72 k allocs: 0.36 MB	7.72 k allocs: 0.36 MB	1
stiff/van_der_pol/FBDF	0.0444 M allocs: 2.2 MB	0.0444 M allocs: 2.2 MB	1
stiff/van_der_pol/KenCarp4	4.27 k allocs: 0.184 MB	4.27 k allocs: 0.184 MB	1
stiff/van_der_pol/Rodas4	0.0377 M allocs: 1.86 MB	0.0377 M allocs: 1.86 MB	1
stiff/van_der_pol/Rosenbrock23	0.213 M allocs: 9.09 MB	0.213 M allocs: 9.09 MB	1
stiff/van_der_pol/TRBDF2	5.02 k allocs: 0.212 MB	5.02 k allocs: 0.212 MB	1
time_to_load	0.159 k allocs: 11.2 kB	0.159 k allocs: 11.2 kB	1

[ChrisRackauckas]

I was wondering why an algorithm became so much slower when supplying an eigen_est although both the number of steps and the number of function evaluations reported in the stats reduced significantly 🙈

I've seen this before and started looking into the adaptivity algorithm and thought it must have possible improvements but couldn't figure out why it was behaving like that. This explains a lot 😅

[ranocha]

Thanks for your review - and for catching the debug statement I forgot.