Experimental Comparison of Proof Rules for Checking Differential Invariance of Algebraic Sets

The source files and examples (Mathematica™ Package) can be found here.

We compare all the proof rules experimentally on a heterogeneous collection of 76 invariant varieties of algebraic differential equations.

The full set of benchmarks is sub-divided into 4 classes of invariant sets that were used in the experiments:
  1. Isolated equilibria as a trivial (for humans not machines) equational invariants
  2. Singularities
  3. Regular (smooth) varieties, where Lie is both necessary (and sufficient)
  4. Functional invariants, where DI= is necessary (and sufficient)

The dimension of the vector field is given under Dim in the tables below. Also shown are the polynomial degree of the invariant candidate d.Inv and the degree of the vector field d.VF defined as the maximum degree of all the polynomials of the vector field. True means that the proof rule was able to prove the invariance of the candidate, otherwise it prints (except for DRI which prints False as it is necessary and sufficient). The time out is set to 60s per rule per problem. The benchmarks of different classes are available below. Time is given in second.

Figures compare the number of invariant varieties which each rule could prove within 60 seconds. The vertical axis shows cumulative time spent on the problems (log scale).

1. Isolated Equilibria

Prob. Dim d.Inv d.VF DI P-c SFLie benchmarks_VMCAI2015_14.png benchmarks_VMCAI2015_15.png benchmarks_VMCAI2015_16.png
1 2 18 17
0.009
True
0.005
True
0.019
0.037
True
0.204
True
0.007
True benchmarks_VMCAI2015_17.png
2 1 1 1
benchmarks_VMCAI2015_18.png
benchmarks_VMCAI2015_19.png
True
benchmarks_VMCAI2015_20.png
True
benchmarks_VMCAI2015_21.png
True
benchmarks_VMCAI2015_22.png
True
benchmarks_VMCAI2015_23.png
True benchmarks_VMCAI2015_24.png
3 1 2 3
benchmarks_VMCAI2015_25.png
benchmarks_VMCAI2015_26.png
True
benchmarks_VMCAI2015_27.png
True
benchmarks_VMCAI2015_28.png
True
0.001
True
benchmarks_VMCAI2015_29.png
True benchmarks_VMCAI2015_30.png
4 1 2 3
benchmarks_VMCAI2015_31.png
0.001
0.002
True
0.002
True
0.006
True
0.003
True benchmarks_VMCAI2015_32.png
5 2 2 2
0.004
0.002
True
0.004
0.005
True
0.006
True
0.002
True benchmarks_VMCAI2015_33.png
6 2 46 4
34.470
0.016
benchmarks_VMCAI2015_34.png
Timeout
benchmarks_VMCAI2015_35.png
Timeout
benchmarks_VMCAI2015_36.png
Timeout
0.451
True benchmarks_VMCAI2015_37.png
7 3 2 243
benchmarks_VMCAI2015_38.png
Timeout
0.057
0.023
14.260
True
14.180
True
benchmarks_VMCAI2015_39.png
Timeout
8 2 128 5
0.429
0.050
0.004
0.012
True
0.013
True
benchmarks_VMCAI2015_40.png
Timeout
9 3 2 2
0.009
0.002
0.018
0.016
True
0.026
True
0.062
True benchmarks_VMCAI2015_41.png
10 3 25 2
benchmarks_VMCAI2015_42.png
Timeout
0.007
benchmarks_VMCAI2015_43.png
Timeout
benchmarks_VMCAI2015_44.png
Timeout
benchmarks_VMCAI2015_45.png
Timeout
benchmarks_VMCAI2015_46.png
Timeout
11 3 2 90
benchmarks_VMCAI2015_47.png
Timeout
0.068
0.032
1.153
True
1.082
True
3.233
True benchmarks_VMCAI2015_48.png
12 4 2 4
0.717
0.003
0.014
3.084
True
2.940
True
benchmarks_VMCAI2015_49.png
Timeout
13 4 2 2
0.030
0.005
0.020
0.019
True
0.035
True
0.021
True benchmarks_VMCAI2015_50.png
14 4 2 2
0.002
0.002
0.019
0.023
True
0.027
True
benchmarks_VMCAI2015_51.png
Timeout
15 5 2 6
0.204
0.007
0.016
8.739
True
8.674
True
benchmarks_VMCAI2015_52.png
Timeout
16 5 12 3
0.757
0.013
benchmarks_VMCAI2015_53.png
Timeout
benchmarks_VMCAI2015_54.png
Timeout
benchmarks_VMCAI2015_55.png
Timeout
benchmarks_VMCAI2015_56.png
Timeout
17 5 2 35
benchmarks_VMCAI2015_57.png
Timeout
1.754
0.026
benchmarks_VMCAI2015_58.png
Timeout
benchmarks_VMCAI2015_59.png
Timeout
benchmarks_VMCAI2015_60.png
Timeout

benchmarks_VMCAI2015_62.gif

2. Singularities

Prob. Dim d.Inv d.VF DI P-c SFLie benchmarks_VMCAI2015_64.png benchmarks_VMCAI2015_65.png benchmarks_VMCAI2015_66.png
1 2 6 2
0.013
0.005
0.023
0.029
True
0.438
True
0.054
True benchmarks_VMCAI2015_67.png
2 2 4 3
0.006
0.004
True
0.009
0.014
True
0.022
True
0.003
True benchmarks_VMCAI2015_68.png
3 3 6 10
0.016
0.006
0.081
0.081
True
benchmarks_VMCAI2015_69.png
Timeout
benchmarks_VMCAI2015_70.png
Timeout
4 3 4 3
0.010
0.007
0.067
0.072
0.468
0.049
True benchmarks_VMCAI2015_71.png
5 3 4 3
0.004
0.003
0.015
0.017
0.043
0.026
True benchmarks_VMCAI2015_72.png
6 3 4 1
0.004
0.002
0.016
0.017
0.025
0.092
True benchmarks_VMCAI2015_73.png
7 7 14 1
0.003
0.002
True
0.007
0.007
0.007
True
0.002
True benchmarks_VMCAI2015_74.png
8 2 4 2
0.005
0.003
True
0.007
0.011
True
0.037
True
0.004
True benchmarks_VMCAI2015_75.png
9 2 4 2
0.013
0.003
True
0.015
0.030
0.056
True
0.007
True benchmarks_VMCAI2015_76.png
10 3 4 3
0.005
0.004
0.031
0.033
0.055
0.034
True benchmarks_VMCAI2015_77.png
11 3 6 2
0.001
0.001
0.017
0.030
0.049
0.010
True benchmarks_VMCAI2015_78.png
12 5 6 2
0.003
0.002
0.080
0.168
benchmarks_VMCAI2015_79.png
Timeout
0.058
True benchmarks_VMCAI2015_80.png
13 9 18 8
0.013
0.023
benchmarks_VMCAI2015_81.png
Timeout
benchmarks_VMCAI2015_82.png
Timeout
benchmarks_VMCAI2015_83.png
Timeout
benchmarks_VMCAI2015_84.png
Timeout
14 5 4 4
0.096
0.020
0.071
0.228
benchmarks_VMCAI2015_85.png
Timeout
benchmarks_VMCAI2015_86.png
Timeout
15 9 10 4
0.009
0.010
0.708
0.511
benchmarks_VMCAI2015_87.png
Timeout
0.235
True benchmarks_VMCAI2015_88.png
16 3 4 3
0.006
0.003
0.020
0.027
0.050
0.100
True benchmarks_VMCAI2015_89.png
17 6 2 2
0.001
True
benchmarks_VMCAI2015_90.png
True
0.005
0.014
True
0.014
True
0.002
True benchmarks_VMCAI2015_91.png

benchmarks_VMCAI2015_93.gif

3. Regular (Smooth) Varieties

Prob. Dim d.Inv d.VF DI P-c SFLie benchmarks_VMCAI2015_95.png benchmarks_VMCAI2015_96.png benchmarks_VMCAI2015_97.png
1 1 5 1
0.001
0.001
0.002
True
0.002
True
0.004
True
0.005
True benchmarks_VMCAI2015_98.png
2 1 21 1
0.002
0.003
0.001
True
0.001
True
0.003
True
0.035
True benchmarks_VMCAI2015_99.png
3 2 6 1
0.003
0.002
0.004
True
0.005
True
0.008
True
0.023
True benchmarks_VMCAI2015_100.png
4 2 22 1
0.006
0.006
0.004
True
0.005
True
0.007
True
0.419
True benchmarks_VMCAI2015_101.png
5 4 14 1
0.093
0.074
0.062
True
0.128
True
0.169
True
benchmarks_VMCAI2015_102.png
Timeout
6 4 32 1
0.725
0.985
0.062
True
0.137
True
0.190
True
benchmarks_VMCAI2015_103.png
Timeout
7 2 2 1
benchmarks_VMCAI2015_104.png
benchmarks_VMCAI2015_105.png
True
benchmarks_VMCAI2015_106.png
True
benchmarks_VMCAI2015_107.png
True
benchmarks_VMCAI2015_108.png
True
0.002
True benchmarks_VMCAI2015_109.png
8 2 2 1
benchmarks_VMCAI2015_110.png
True
benchmarks_VMCAI2015_111.png
True
0.002
True
0.002
True
0.002
True
benchmarks_VMCAI2015_112.png
True benchmarks_VMCAI2015_113.png
9 3 1 1
benchmarks_VMCAI2015_114.png
True
benchmarks_VMCAI2015_115.png
True
benchmarks_VMCAI2015_116.png
True
benchmarks_VMCAI2015_117.png
True
benchmarks_VMCAI2015_118.png
True
benchmarks_VMCAI2015_119.png
True benchmarks_VMCAI2015_120.png
10 2 1 5
0.002
benchmarks_VMCAI2015_121.png
True
0.002
True
0.002
True
0.002
True
0.001
True benchmarks_VMCAI2015_122.png
11 2 2 3
0.002
0.002
True
0.004
True
0.006
True
0.008
True
0.002
True benchmarks_VMCAI2015_123.png
12 2 6 5
benchmarks_VMCAI2015_124.png
True
benchmarks_VMCAI2015_125.png
True
0.006
True
0.006
True
0.023
True
0.002
True benchmarks_VMCAI2015_126.png
13 3 2 4
0.026
0.003
True
0.008
True
0.012
True
0.024
True
0.004
True benchmarks_VMCAI2015_127.png
14 4 2 4
0.079
0.006
True
0.013
True
0.019
True
0.036
True
0.009
True benchmarks_VMCAI2015_128.png
15 5 2 4
0.669
0.007
True
0.020
True
0.031
True
0.056
True
0.008
True benchmarks_VMCAI2015_129.png
16 3 2 3
benchmarks_VMCAI2015_130.png
True
benchmarks_VMCAI2015_131.png
True
benchmarks_VMCAI2015_132.png
True
benchmarks_VMCAI2015_133.png
True
benchmarks_VMCAI2015_134.png
True
0.001
True benchmarks_VMCAI2015_135.png
17 3 2 3
0.002
benchmarks_VMCAI2015_136.png
True
0.003
True
0.004
True
0.008
True
0.002
True benchmarks_VMCAI2015_137.png
18 2 4 2
0.005
0.002
True
0.005
True
0.006
True
0.016
True
0.003
True benchmarks_VMCAI2015_138.png
19 2 2 2
benchmarks_VMCAI2015_139.png
benchmarks_VMCAI2015_140.png
True
0.002
True
0.002
True
0.004
True
0.001
True benchmarks_VMCAI2015_141.png
20 2 1 3
benchmarks_VMCAI2015_142.png
benchmarks_VMCAI2015_143.png
True
0.001
True
0.001
True
0.001
True
benchmarks_VMCAI2015_144.png
True benchmarks_VMCAI2015_145.png
21 2 1 2
0.002
benchmarks_VMCAI2015_146.png
True
0.002
True
0.002
True
0.002
True
0.001
True benchmarks_VMCAI2015_147.png
22 2 1 2
0.001
benchmarks_VMCAI2015_148.png
True
0.001
True
0.002
True
0.002
True
0.001
True benchmarks_VMCAI2015_149.png
23 2 1 2
benchmarks_VMCAI2015_150.png
benchmarks_VMCAI2015_151.png
True
0.001
True
0.001
True
0.001
True
benchmarks_VMCAI2015_152.png
True benchmarks_VMCAI2015_153.png
24 6 2 2
benchmarks_VMCAI2015_154.png
True
benchmarks_VMCAI2015_155.png
True
0.002
True
0.005
True
0.007
True
0.002
True benchmarks_VMCAI2015_156.png

benchmarks_VMCAI2015_158.gif

4. Functional Invariants (First Integrals)

Prob. Dim d.Inv d.VF DI P-c SFLie benchmarks_VMCAI2015_160.png benchmarks_VMCAI2015_161.png benchmarks_VMCAI2015_162.png
1 2 3 2
benchmarks_VMCAI2015_163.png
True
benchmarks_VMCAI2015_164.png
True
0.004
0.002
True
0.007
True
0.001
True benchmarks_VMCAI2015_165.png
2 2 6 5
benchmarks_VMCAI2015_166.png
True
benchmarks_VMCAI2015_167.png
True
0.007
0.007
True
2.350
True
0.002
True benchmarks_VMCAI2015_168.png
3 2 6 5
0.002
True
0.001
True
0.008
0.009
True
0.030
True
0.002
True benchmarks_VMCAI2015_169.png
4 2 4 1
benchmarks_VMCAI2015_170.png
True
benchmarks_VMCAI2015_171.png
True
0.014
0.014
0.026
0.003
True benchmarks_VMCAI2015_172.png
5 4 3 2
benchmarks_VMCAI2015_173.png
True
benchmarks_VMCAI2015_174.png
True
0.009
0.006
True
0.031
True
0.003
True benchmarks_VMCAI2015_175.png
6 3 6 10
0.002
True
0.002
True
0.028
0.021
True
benchmarks_VMCAI2015_176.png
Timeout
0.005
True benchmarks_VMCAI2015_177.png
7 4 2 1
0.001
True
benchmarks_VMCAI2015_178.png
True
0.001
True
0.002
True
0.002
True
0.002
True benchmarks_VMCAI2015_179.png
8 4 12 11
benchmarks_VMCAI2015_180.png
True
benchmarks_VMCAI2015_181.png
True
0.010
0.006
True
0.025
True
0.003
True benchmarks_VMCAI2015_182.png
9 8 12 11
0.005
True
0.003
True
0.007
True
0.011
True
0.011
True
0.007
True benchmarks_VMCAI2015_183.png
10 8 9 8
0.003
True
0.003
True
benchmarks_VMCAI2015_184.png
Timeout
0.069
True
benchmarks_VMCAI2015_185.png
Timeout
0.011
True benchmarks_VMCAI2015_186.png
11 8 75 74
benchmarks_VMCAI2015_187.png
True
0.192
True
benchmarks_VMCAI2015_188.png
Timeout
benchmarks_VMCAI2015_189.png
Timeout
benchmarks_VMCAI2015_190.png
Timeout
3.498
True benchmarks_VMCAI2015_191.png
12 8 31 30
benchmarks_VMCAI2015_192.png
True
0.006
True
12.710
benchmarks_VMCAI2015_193.png
Timeout
benchmarks_VMCAI2015_194.png
Timeout
0.091
True benchmarks_VMCAI2015_195.png
13 8 29 28
benchmarks_VMCAI2015_196.png
True
0.003
True
7.917
8.896
True
benchmarks_VMCAI2015_197.png
Timeout
0.025
True benchmarks_VMCAI2015_198.png
14 8 18 17
0.032
True
0.029
True
1.463
0.857
True
benchmarks_VMCAI2015_199.png
Timeout
0.045
True benchmarks_VMCAI2015_200.png
15 8 5 4
benchmarks_VMCAI2015_201.png
True
benchmarks_VMCAI2015_202.png
True
benchmarks_VMCAI2015_203.png
Timeout
0.029
True
0.362
True
0.003
True benchmarks_VMCAI2015_204.png
16 8 16 15
benchmarks_VMCAI2015_205.png
True
0.035
True
20.980
True
27.560
True
benchmarks_VMCAI2015_206.png
Timeout
0.180
True benchmarks_VMCAI2015_207.png
17 3 2 1
benchmarks_VMCAI2015_208.png
True
benchmarks_VMCAI2015_209.png
True
0.001
0.001
True
0.002
True
benchmarks_VMCAI2015_210.png
True benchmarks_VMCAI2015_211.png
18 7 6 1
benchmarks_VMCAI2015_212.png
True
benchmarks_VMCAI2015_213.png
True
0.006
0.006
0.005
True
0.001
True benchmarks_VMCAI2015_214.png

benchmarks_VMCAI2015_216.gif

5. All Examples

Prob. Dim d.Inv d.VF DI P-c SFLie benchmarks_VMCAI2015_219.png benchmarks_VMCAI2015_220.png benchmarks_VMCAI2015_221.png
1 2 18 17
0.004
True
0.004
True
 *
0.015
0.041
True
0.179
True
0.007
True benchmarks_VMCAI2015_222.png
2 1 1 1
benchmarks_VMCAI2015_223.png
benchmarks_VMCAI2015_224.png
True
benchmarks_VMCAI2015_225.png
True
benchmarks_VMCAI2015_226.png
True
benchmarks_VMCAI2015_227.png
True
benchmarks_VMCAI2015_228.png
True benchmarks_VMCAI2015_229.png
3 1 2 3
benchmarks_VMCAI2015_230.png
benchmarks_VMCAI2015_231.png
True
benchmarks_VMCAI2015_232.png
True
benchmarks_VMCAI2015_233.png
True
benchmarks_VMCAI2015_234.png
True
benchmarks_VMCAI2015_235.png
True benchmarks_VMCAI2015_236.png
4 1 2 3
benchmarks_VMCAI2015_237.png
0.001
0.002
True
0.002
True
0.006
True
0.003
True benchmarks_VMCAI2015_238.png
5 2 2 2
0.003
0.001
True
0.006
0.008
True
0.007
True
0.002
True benchmarks_VMCAI2015_239.png
6 2 46 4
30.330
0.018
59.620
59.790
True
58.570
True
0.356
True benchmarks_VMCAI2015_240.png
7 3 2 243
benchmarks_VMCAI2015_241.png
Timeout
0.060
0.025
12.430
True
12.270
True
benchmarks_VMCAI2015_242.png
Timeout
8 2 128 5
0.362
0.053
0.003
0.008
True
0.010
True
benchmarks_VMCAI2015_243.png
Timeout
9 3 2 2
0.008
0.002
0.018
0.018
True
0.025
True
0.060
True benchmarks_VMCAI2015_244.png
10 3 25 2
benchmarks_VMCAI2015_245.png
Timeout
0.007
benchmarks_VMCAI2015_246.png
Timeout
benchmarks_VMCAI2015_247.png
Timeout
benchmarks_VMCAI2015_248.png
Timeout
benchmarks_VMCAI2015_249.png
Timeout
11 3 2 90
benchmarks_VMCAI2015_250.png
Timeout
0.065
0.034
0.737
True
0.790
True
2.816
True benchmarks_VMCAI2015_251.png
12 4 2 4
0.674
0.003
0.009
2.682
True
2.695
True
benchmarks_VMCAI2015_252.png
Timeout
13 4 2 2
0.027
0.003
0.023
0.018
True
0.025
True
0.026
True benchmarks_VMCAI2015_253.png
14 4 2 2
0.001
0.002
0.020
0.024
True
0.024
True
benchmarks_VMCAI2015_254.png
Timeout
15 5 2 6
0.172
0.004
0.015
8.578
True
8.242
True
benchmarks_VMCAI2015_255.png
Timeout
16 5 12 3
0.753
0.010
benchmarks_VMCAI2015_256.png
Timeout
benchmarks_VMCAI2015_257.png
Timeout
benchmarks_VMCAI2015_258.png
Timeout
benchmarks_VMCAI2015_259.png
Timeout
17 5 2 35
benchmarks_VMCAI2015_260.png
Timeout
1.706
0.032
benchmarks_VMCAI2015_261.png
Timeout
benchmarks_VMCAI2015_262.png
Timeout
benchmarks_VMCAI2015_263.png
Timeout
18 1 5 1
0.001
0.001
0.002
True
0.003
True
0.004
True
0.005
True benchmarks_VMCAI2015_264.png
19 1 21 1
0.002
0.003
0.001
True
0.001
True
0.003
True
0.032
True benchmarks_VMCAI2015_265.png
20 2 6 1
0.003
0.002
0.004
True
0.005
True
0.007
True
0.020
True benchmarks_VMCAI2015_266.png
21 2 22 1
0.006
0.006
0.004
True
0.005
True
0.007
True
0.433
True benchmarks_VMCAI2015_267.png
22 4 14 1
0.097
0.085
0.057
True
0.120
True
0.176
True
benchmarks_VMCAI2015_268.png
Timeout
23 4 32 1
0.648
0.968
0.067
True
0.127
True
0.173
True
benchmarks_VMCAI2015_269.png
Timeout
24 2 2 1
benchmarks_VMCAI2015_270.png
0.002
True
benchmarks_VMCAI2015_271.png
True
benchmarks_VMCAI2015_272.png
True
benchmarks_VMCAI2015_273.png
True
0.001
True benchmarks_VMCAI2015_274.png
25 2 2 1
benchmarks_VMCAI2015_275.png
True
benchmarks_VMCAI2015_276.png
True
0.001
True
0.001
True
0.002
True
benchmarks_VMCAI2015_277.png
True benchmarks_VMCAI2015_278.png
26 3 1 1
benchmarks_VMCAI2015_279.png
True
benchmarks_VMCAI2015_280.png
True
benchmarks_VMCAI2015_281.png
True
benchmarks_VMCAI2015_282.png
True
benchmarks_VMCAI2015_283.png
True
benchmarks_VMCAI2015_284.png
True benchmarks_VMCAI2015_285.png
27 2 1 5
0.002
benchmarks_VMCAI2015_286.png
True
0.001
True
0.001
True
0.002
True
0.001
True benchmarks_VMCAI2015_287.png
28 2 2 3
0.004
0.001
True
0.003
True
0.005
True
0.007
True
0.004
True benchmarks_VMCAI2015_288.png
29 2 6 5
0.002
True
0.001
True
0.008
True
0.007
True
0.029
True
0.002
True benchmarks_VMCAI2015_289.png
30 3 2 4
0.028
0.004
True
0.011
True
0.017
True
0.017
True
0.004
True benchmarks_VMCAI2015_290.png
31 4 2 4
0.078
0.005
True
0.012
True
0.020
True
0.030
True
0.005
True benchmarks_VMCAI2015_291.png
32 5 2 4
0.655
0.007
True
0.021
True
0.041
True
0.057
True
0.007
True benchmarks_VMCAI2015_292.png
33 3 2 3
benchmarks_VMCAI2015_293.png
True
benchmarks_VMCAI2015_294.png
True
benchmarks_VMCAI2015_295.png
True
benchmarks_VMCAI2015_296.png
True
benchmarks_VMCAI2015_297.png
True
benchmarks_VMCAI2015_298.png
True benchmarks_VMCAI2015_299.png
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benchmarks_VMCAI2015_303.png
benchmarks_VMCAI2015_304.png
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benchmarks_VMCAI2015_306.png
benchmarks_VMCAI2015_307.png
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benchmarks_VMCAI2015_308.png
True benchmarks_VMCAI2015_309.png
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benchmarks_VMCAI2015_314.png
benchmarks_VMCAI2015_315.png
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benchmarks_VMCAI2015_317.png
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True benchmarks_VMCAI2015_319.png
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benchmarks_VMCAI2015_320.png
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benchmarks_VMCAI2015_321.png
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True benchmarks_VMCAI2015_322.png
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benchmarks_VMCAI2015_323.png
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benchmarks_VMCAI2015_324.png
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True benchmarks_VMCAI2015_325.png
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benchmarks_VMCAI2015_326.png
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benchmarks_VMCAI2015_327.png
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True benchmarks_VMCAI2015_328.png
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benchmarks_VMCAI2015_329.png
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benchmarks_VMCAI2015_330.png
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benchmarks_VMCAI2015_332.png
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benchmarks_VMCAI2015_333.png
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benchmarks_VMCAI2015_335.png
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benchmarks_VMCAI2015_337.png
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benchmarks_VMCAI2015_340.png
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True benchmarks_VMCAI2015_342.png
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True benchmarks_VMCAI2015_343.png
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benchmarks_VMCAI2015_344.png
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benchmarks_VMCAI2015_345.png
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benchmarks_VMCAI2015_347.png
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benchmarks_VMCAI2015_348.png
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benchmarks_VMCAI2015_349.png
Timeout
benchmarks_VMCAI2015_350.png
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True benchmarks_VMCAI2015_351.png
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benchmarks_VMCAI2015_352.png
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benchmarks_VMCAI2015_353.png
Timeout
benchmarks_VMCAI2015_354.png
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True benchmarks_VMCAI2015_355.png
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benchmarks_VMCAI2015_356.png
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benchmarks_VMCAI2015_357.png
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True benchmarks_VMCAI2015_358.png
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0.032
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benchmarks_VMCAI2015_359.png
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True benchmarks_VMCAI2015_360.png
56 8 5 4
benchmarks_VMCAI2015_361.png
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benchmarks_VMCAI2015_362.png
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True benchmarks_VMCAI2015_363.png
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benchmarks_VMCAI2015_364.png
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benchmarks_VMCAI2015_365.png
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True benchmarks_VMCAI2015_366.png
58 3 2 1
benchmarks_VMCAI2015_367.png
True
benchmarks_VMCAI2015_368.png
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benchmarks_VMCAI2015_369.png
True benchmarks_VMCAI2015_370.png
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benchmarks_VMCAI2015_371.png
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benchmarks_VMCAI2015_372.png
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True benchmarks_VMCAI2015_373.png
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True benchmarks_VMCAI2015_374.png
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True benchmarks_VMCAI2015_375.png
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benchmarks_VMCAI2015_376.png
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True benchmarks_VMCAI2015_378.png
64 3 4 3
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True benchmarks_VMCAI2015_379.png
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0.003
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True benchmarks_VMCAI2015_380.png
66 7 14 1
0.002
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True benchmarks_VMCAI2015_381.png
67 2 4 2 <|r st}lE='vertical-align: baseline;'>
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True benchmarks_VMCAI2015_382.png
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0.012
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True benchmarks_VMCAI2015_383.png
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True benchmarks_VMCAI2015_384.png
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True benchmarks_VMCAI2015_385.png
71 5 6 2
0.002
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benchmarks_VMCAI2015_386.png
Timeout
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True benchmarks_VMCAI2015_387.png
72 9 18 8
0.010
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benchmarks_VMCAI2015_388.png
Timeout
benchmarks_VMCAI2015_389.png
Timeout
benchmarks_VMCAI2015_390.png
Timeout
benchmarks_VMCAI2015_391.png
Timeout
73 5 4 4
0.103
0.021
0.071
0.220
benchmarks_VMCAI2015_392.png
Timeout
benchmarks_VMCAI2015_393.png
Timeout
74 9 10 4
0.007
0.009
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0.478
benchmarks_VMCAI2015_394.png
Timeout
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True benchmarks_VMCAI2015_395.png
75 3 4 3
0.005
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0.019
0.025
0.054
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True benchmarks_VMCAI2015_396.png
76 6 2 2
0.001
True
benchmarks_VMCAI2015_397.png
True
0.005
0.010
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0.002
True benchmarks_VMCAI2015_398.png

benchmarks_VMCAI2015_400.gif

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