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2.2.1 Integrals 1 to 98

Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 26 20 37 23 473 31 25

N.S.

1 1.00 0.79 0.61 1.12 0.70 14.33 0.94 0.76

time (sec)

N/A 0.279 0.014 0.660 0.716 0.241 2.195 0.334 2.812

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 16 19 16 14 14 78 14 16

N.S.

1 0.84 1.00 0.84 0.74 0.74 4.11 0.74 0.84

time (sec)

N/A 0.249 0.004 0.119 0.221 0.238 1.250 0.324 2.272

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 18 18 16 21 14 153 22 15

N.S.

1 0.90 0.90 0.80 1.05 0.70 7.65 1.10 0.75

time (sec)

N/A 0.234 0.003 0.075 0.304 0.230 0.782 0.345 2.274

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

7 7 7 8 7 7 12 7 7

N.S.

1 1.00 1.00 1.14 1.00 1.00 1.71 1.00 1.00

time (sec)

N/A 0.223 0.035 0.061 0.207 0.233 0.458 0.310 0.025

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

5 5 5 6 5 5 2 5 5

N.S.

1 1.00 1.00 1.20 1.00 1.00 0.40 1.00 1.00

time (sec)

N/A 0.187 0.001 0.052 0.522 0.228 0.269 0.318 2.557

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 21 9 21 22 19 23 8

N.S.

1 1.00 2.62 1.12 2.62 2.75 2.38 2.88 1.00

time (sec)

N/A 0.220 0.018 0.086 0.316 0.231 0.109 0.317 2.748

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 20 51 21 37 48 0 38 26

N.S.

1 0.91 2.32 0.95 1.68 2.18 0.00 1.73 1.18

time (sec)

N/A 0.282 0.010 0.299 0.217 0.232 0.000 0.336 0.128

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 16 21 18 17 29 0 17 13

N.S.

1 0.84 1.11 0.95 0.89 1.53 0.00 0.89 0.68

time (sec)

N/A 0.254 0.005 0.095 0.223 0.219 0.000 0.344 2.490

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 75 33 51 72 0 47 39

N.S.

1 1.00 2.14 0.94 1.46 2.06 0.00 1.34 1.11

time (sec)

N/A 0.345 0.013 0.129 0.247 0.244 0.000 0.338 0.090

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 78 143 94 87 225 0 99 100

N.S.

1 1.00 1.83 1.21 1.12 2.88 0.00 1.27 1.28

time (sec)

N/A 0.305 0.294 1.267 0.299 0.273 0.000 0.339 2.410

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 116 57 53 152 0 59 65

N.S.

1 1.00 2.15 1.06 0.98 2.81 0.00 1.09 1.20

time (sec)

N/A 0.256 0.184 0.608 0.315 0.262 0.000 0.331 0.104

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 90 34 30 95 0 30 28

N.S.

1 1.00 2.50 0.94 0.83 2.64 0.00 0.83 0.78

time (sec)

N/A 0.223 0.172 0.252 0.326 0.269 0.000 0.328 0.093

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 18 17 73 66 17 18

N.S.

1 1.00 1.00 0.69 0.65 2.81 2.54 0.65 0.69

time (sec)

N/A 0.195 0.036 0.095 0.330 0.246 0.383 0.304 2.760

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 50 56 48 113 0 50 853

N.S.

1 1.00 1.19 1.33 1.14 2.69 0.00 1.19 20.31

time (sec)

N/A 0.220 0.058 0.210 0.334 0.261 0.000 0.335 2.906

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 77 140 95 105 274 0 103 1138

N.S.

1 1.24 2.26 1.53 1.69 4.42 0.00 1.66 18.35

time (sec)

N/A 0.262 0.430 0.409 0.339 0.276 0.000 0.329 3.022

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 125 204 155 200 592 0 178 833

N.S.

1 1.33 2.17 1.65 2.13 6.30 0.00 1.89 8.86

time (sec)

N/A 0.318 1.320 0.821 0.337 0.317 0.000 0.329 6.042

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 114 77 94 112 285 0 119 681

N.S.

1 1.30 0.88 1.07 1.27 3.24 0.00 1.35 7.74

time (sec)

N/A 0.332 0.177 1.402 0.333 0.273 0.000 0.320 2.788

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 74 52 61 62 211 0 80 126

N.S.

1 1.23 0.87 1.02 1.03 3.52 0.00 1.33 2.10

time (sec)

N/A 0.272 0.108 0.653 0.319 0.265 0.000 0.321 2.630

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 41 37 36 33 177 0 50 108

N.S.

1 1.02 0.92 0.90 0.82 4.42 0.00 1.25 2.70

time (sec)

N/A 0.238 0.087 0.206 0.311 0.275 0.000 0.340 3.109

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 29 21 20 163 10924 37 24

N.S.

1 1.00 0.97 0.70 0.67 5.43 364.13 1.23 0.80

time (sec)

N/A 0.186 0.476 0.127 0.322 0.263 18.672 0.319 2.624

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 40 39 38 228 0 55 34

N.S.

1 1.00 0.98 0.95 0.93 5.56 0.00 1.34 0.83

time (sec)

N/A 0.222 0.104 0.293 0.312 0.268 0.000 0.351 2.356

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 59 57 70 396 0 90 67

N.S.

1 1.00 0.97 0.93 1.15 6.49 0.00 1.48 1.10

time (sec)

N/A 0.278 0.185 0.510 0.318 0.281 0.000 0.352 2.382

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 90 83 127 610 0 156 101

N.S.

1 1.00 1.01 0.93 1.43 6.85 0.00 1.75 1.13

time (sec)

N/A 0.307 0.298 0.764 0.310 0.303 0.000 0.330 2.924

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 100 79 35 89 71 85 60 75

N.S.

1 1.02 0.81 0.36 0.91 0.72 0.87 0.61 0.77

time (sec)

N/A 0.327 0.149 0.182 0.328 0.284 0.803 0.373 0.450

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

4 4 4 5 6 8 14 6 4

N.S.

1 1.00 1.00 1.25 1.50 2.00 3.50 1.50 1.00

time (sec)

N/A 0.200 0.002 0.086 0.210 0.230 0.277 0.308 2.657

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 17 14 14 25 34 14 10

N.S.

1 1.00 1.31 1.08 1.08 1.92 2.62 1.08 0.77

time (sec)

N/A 0.215 0.003 0.116 0.243 0.246 0.804 0.318 2.334

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 27 20 20 37 54 20 17

N.S.

1 1.00 1.29 0.95 0.95 1.76 2.57 0.95 0.81

time (sec)

N/A 0.223 0.004 0.158 0.222 0.239 1.828 0.310 2.262

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 78 111 78 91 259 0 96 86

N.S.

1 1.00 1.42 1.00 1.17 3.32 0.00 1.23 1.10

time (sec)

N/A 0.280 0.330 2.002 0.293 0.271 0.000 0.299 0.146

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 86 50 67 191 0 65 51

N.S.

1 1.00 1.54 0.89 1.20 3.41 0.00 1.16 0.91

time (sec)

N/A 0.256 0.156 0.898 0.291 0.255 0.000 0.317 2.773

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 38 33 50 134 0 41 30

N.S.

1 1.00 1.00 0.87 1.32 3.53 0.00 1.08 0.79

time (sec)

N/A 0.216 0.028 0.434 0.304 0.255 0.000 0.321 0.124

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 29 21 39 95 55508 31 21

N.S.

1 1.00 1.00 0.72 1.34 3.28 1914.07 1.07 0.72

time (sec)

N/A 0.197 0.011 0.188 0.286 0.249 61.710 0.321 0.110

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 38 47 64 119 0 57 414

N.S.

1 1.00 0.93 1.15 1.56 2.90 0.00 1.39 10.10

time (sec)

N/A 0.219 0.049 0.392 0.300 0.254 0.000 0.321 2.687

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 73 152 82 92 186 0 85 483

N.S.

1 1.24 2.58 1.39 1.56 3.15 0.00 1.44 8.19

time (sec)

N/A 0.266 0.316 0.919 0.300 0.280 0.000 0.297 2.980

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 117 215 137 145 270 0 127 969

N.S.

1 1.30 2.39 1.52 1.61 3.00 0.00 1.41 10.77

time (sec)

N/A 0.331 0.846 1.763 0.308 0.286 0.000 0.329 2.682

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 116 76 92 97 273 0 104 1036

N.S.

1 1.33 0.87 1.06 1.11 3.14 0.00 1.20 11.91

time (sec)

N/A 0.376 0.175 1.248 0.312 0.286 0.000 0.315 3.122

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 74 52 59 54 213 0 72 291

N.S.

1 1.23 0.87 0.98 0.90 3.55 0.00 1.20 4.85

time (sec)

N/A 0.271 0.095 0.557 0.310 0.291 0.000 0.308 2.710

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 36 34 31 183 0 48 425

N.S.

1 1.00 0.95 0.89 0.82 4.82 0.00 1.26 11.18

time (sec)

N/A 0.274 0.434 0.183 0.328 0.267 0.000 0.333 2.905

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 29 21 20 163 10924 37 24

N.S.

1 1.00 0.97 0.70 0.67 5.43 364.13 1.23 0.80

time (sec)

N/A 0.186 0.016 0.000 0.296 0.266 20.820 0.332 0.004

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 38 33 32 216 0 36 30

N.S.

1 1.00 1.03 0.89 0.86 5.84 0.00 0.97 0.81

time (sec)

N/A 0.228 0.313 0.542 0.294 0.257 0.000 0.345 2.540

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 55 49 48 276 0 71 51

N.S.

1 1.00 0.98 0.88 0.86 4.93 0.00 1.27 0.91

time (sec)

N/A 0.278 0.347 1.187 0.327 0.265 0.000 0.341 2.768

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 79 80 78 74 348 0 104 84

N.S.

1 1.00 1.01 0.99 0.94 4.41 0.00 1.32 1.06

time (sec)

N/A 0.300 0.515 2.431 0.332 0.269 0.000 0.327 2.363

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 65 70 60 72 326 0 69 52

N.S.

1 1.00 1.08 0.92 1.11 5.02 0.00 1.06 0.80

time (sec)

N/A 0.289 5.108 0.602 0.304 0.284 0.000 0.309 2.401

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 120 106 117 186 616 0 149 123

N.S.

1 1.12 0.99 1.09 1.74 5.76 0.00 1.39 1.15

time (sec)

N/A 0.462 5.399 1.421 0.392 0.292 0.000 0.305 3.057

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 16 15 14 13 31 63 46 26

N.S.

1 0.47 0.44 0.41 0.38 0.91 1.85 1.35 0.76

time (sec)

N/A 0.174 0.060 0.141 0.397 0.253 0.352 0.332 2.797

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 35 35 27 26 57 218 59 40

N.S.

1 0.64 0.64 0.49 0.47 1.04 3.96 1.07 0.73

time (sec)

N/A 0.239 0.103 0.301 0.374 0.235 1.179 0.326 2.363

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 56 51 35 41 81 439 68 53

N.S.

1 0.79 0.72 0.49 0.58 1.14 6.18 0.96 0.75

time (sec)

N/A 0.340 0.174 0.573 0.305 0.238 4.223 0.325 2.389

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 12 13 10 4 0 24 10

N.S.

1 1.00 1.00 1.08 0.83 0.33 0.00 2.00 0.83

time (sec)

N/A 0.246 0.024 0.470 0.316 0.242 0.000 0.315 0.037

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A F F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 14 12 0 0 28 39

N.S.

1 1.00 1.00 1.00 0.86 0.00 0.00 2.00 2.79

time (sec)

N/A 0.241 0.016 0.402 0.314 0.000 0.000 0.329 2.690

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 23 19 11 11 0 45 0

N.S.

1 1.00 0.79 0.66 0.38 0.38 0.00 1.55 0.00

time (sec)

N/A 0.291 0.034 0.543 0.349 0.240 0.000 0.361 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F(-1) C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 25 23 0 0 0 55 0

N.S.

1 1.00 0.76 0.70 0.00 0.00 0.00 1.67 0.00

time (sec)

N/A 0.299 0.038 0.520 0.000 0.000 0.000 0.347 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 28 14 35 19 0 21 0

N.S.

1 1.00 1.87 0.93 2.33 1.27 0.00 1.40 0.00

time (sec)

N/A 0.249 0.032 0.403 0.515 0.249 0.000 0.315 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A F(-2) F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 30 34 17 0 0 26 0

N.S.

1 1.00 1.76 2.00 1.00 0.00 0.00 1.53 0.00

time (sec)

N/A 0.253 0.036 0.459 0.524 0.000 0.000 0.328 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 51 37 300 44 0 78 0

N.S.

1 1.00 1.59 1.16 9.38 1.38 0.00 2.44 0.00

time (sec)

N/A 0.309 0.054 0.670 0.479 0.238 0.000 0.393 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B F(-2) F C F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 53 39 284 0 0 90 0

N.S.

1 1.00 1.47 1.08 7.89 0.00 0.00 2.50 0.00

time (sec)

N/A 0.307 0.042 0.635 0.331 0.000 0.000 0.377 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F F F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 11 41 0 0 0 0 7

N.S.

1 1.00 1.22 4.56 0.00 0.00 0.00 0.00 0.78

time (sec)

N/A 0.167 0.038 2.163 0.000 0.000 0.000 0.000 0.014

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 34 75 0 0 0 0 0

N.S.

1 1.00 1.06 2.34 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.234 0.036 2.314 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 46 49 0 0 0 0 0

N.S.

1 1.00 1.10 1.17 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.257 0.062 2.461 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F F F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 46 39 101 0 0 0 0 0

N.S.

1 1.07 0.91 2.35 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.350 0.046 1.094 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 92 66 110 0 0 0 0 0

N.S.

1 1.03 0.74 1.24 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.581 0.057 1.324 0.000 0.000 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 122 123 192 0 0 0 0 0

N.S.

1 1.01 1.02 1.59 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.695 0.360 2.966 0.000 0.000 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 11 41 0 87 0 0 0

N.S.

1 1.00 1.22 4.56 0.00 9.67 0.00 0.00 0.00

time (sec)

N/A 0.162 0.030 0.566 0.000 0.091 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 33 62 0 41 0 0 0

N.S.

1 1.00 1.03 1.94 0.00 1.28 0.00 0.00 0.00

time (sec)

N/A 0.226 0.035 0.578 0.000 0.075 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 46 48 0 276 0 0 0

N.S.

1 1.00 1.10 1.14 0.00 6.57 0.00 0.00 0.00

time (sec)

N/A 0.253 0.050 0.502 0.000 0.092 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 35 70 0 247 0 0 0

N.S.

1 1.00 1.09 2.19 0.00 7.72 0.00 0.00 0.00

time (sec)

N/A 0.233 0.052 0.841 0.000 0.100 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 43 101 0 168 0 0 0

N.S.

1 1.00 0.77 1.80 0.00 3.00 0.00 0.00 0.00

time (sec)

N/A 0.325 0.035 1.114 0.000 0.085 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 78 75 73 0 775 0 0 0

N.S.

1 1.00 0.96 0.94 0.00 9.94 0.00 0.00 0.00

time (sec)

N/A 0.351 0.145 1.367 0.000 0.141 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 33 8 49 0 23 0

N.S.

1 1.00 1.00 3.67 0.89 5.44 0.00 2.56 0.00

time (sec)

N/A 0.182 0.008 0.384 0.302 0.249 0.000 0.381 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 57 11 89 0 0 0

N.S.

1 1.00 1.00 3.80 0.73 5.93 0.00 0.00 0.00

time (sec)

N/A 0.188 0.022 0.651 0.290 0.252 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 53 8 39 0 29 0

N.S.

1 1.00 1.00 5.89 0.89 4.33 0.00 3.22 0.00

time (sec)

N/A 0.185 0.009 0.674 0.288 0.241 0.000 0.362 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

487 541 121 101 0 809 0 307 926

N.S.

1 1.11 0.25 0.21 0.00 1.66 0.00 0.63 1.90

time (sec)

N/A 1.263 2.847 0.741 0.000 0.353 0.000 0.396 3.564

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F(-1) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 156 109 72 0 817 0 299 938

N.S.

1 1.54 1.08 0.71 0.00 8.09 0.00 2.96 9.29

time (sec)

N/A 0.311 0.441 0.668 0.000 0.353 0.000 0.384 3.143

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

292 200 45 126 0 117 0 170 214

N.S.

1 0.68 0.15 0.43 0.00 0.40 0.00 0.58 0.73

time (sec)

N/A 0.468 5.025 0.501 0.000 0.265 0.000 0.531 3.207

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 25 24 21 20 43 78 53 20

N.S.

1 0.56 0.53 0.47 0.44 0.96 1.73 1.18 0.44

time (sec)

N/A 0.178 1.067 0.262 0.295 0.248 0.628 0.335 2.847

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F F(-2) F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

494 494 130 150 0 0 0 0 1520

N.S.

1 1.00 0.26 0.30 0.00 0.00 0.00 0.00 3.08

time (sec)

N/A 0.971 5.096 1.645 0.000 0.000 0.000 0.000 10.835

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F(-1) B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 171 146 60 0 15483 0 0 184

N.S.

1 1.00 0.85 0.35 0.00 90.54 0.00 0.00 1.08

time (sec)

N/A 0.494 5.055 2.006 0.000 1.629 0.000 0.000 3.511

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

245 257 172 76 0 665467 0 0 216

N.S.

1 1.05 0.70 0.31 0.00 2716.19 0.00 0.00 0.88

time (sec)

N/A 0.665 5.091 4.374 0.000 6.129 0.000 0.000 4.605

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F F(-2) F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

494 494 130 148 0 0 0 0 1518

N.S.

1 1.00 0.26 0.30 0.00 0.00 0.00 0.00 3.07

time (sec)

N/A 0.776 5.146 1.622 0.000 0.000 0.000 0.000 8.982

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F(-1) B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

175 175 146 62 0 16679 0 0 184

N.S.

1 1.00 0.83 0.35 0.00 95.31 0.00 0.00 1.05

time (sec)

N/A 0.493 5.161 1.892 0.000 1.657 0.000 0.000 3.831

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

213 213 172 78 0 643291 0 0 216

N.S.

1 1.00 0.81 0.37 0.00 3020.15 0.00 0.00 1.01

time (sec)

N/A 0.484 3.965 4.313 0.000 6.081 0.000 0.000 3.730

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B F(-1) F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

223 223 378 62 0 789 0 0 535

N.S.

1 1.00 1.70 0.28 0.00 3.54 0.00 0.00 2.40

time (sec)

N/A 0.701 5.068 0.351 0.000 0.396 0.000 0.000 3.282

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F(-1) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 83 79 73 72 138 0 185 99

N.S.

1 1.00 0.95 0.88 0.87 1.66 0.00 2.23 1.19

time (sec)

N/A 0.339 5.078 1.354 0.310 0.260 0.000 0.343 3.358

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B F(-1) F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 129 141 67 0 885 0 0 1025

N.S.

1 1.00 1.09 0.52 0.00 6.86 0.00 0.00 7.95

time (sec)

N/A 0.417 5.041 3.133 0.000 0.383 0.000 0.000 3.380

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B F(-1) F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 205 378 62 0 748 0 0 403

N.S.

1 1.00 1.84 0.30 0.00 3.65 0.00 0.00 1.97

time (sec)

N/A 0.626 5.046 0.331 0.000 0.370 0.000 0.000 2.692

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 71 117 51 0 239 728 199 95

N.S.

1 1.00 1.65 0.72 0.00 3.37 10.25 2.80 1.34

time (sec)

N/A 0.479 1.359 0.414 0.000 0.289 8.914 0.362 3.158

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F(-1) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 69 64 176 0 166 0 222 241

N.S.

1 0.78 0.72 1.98 0.00 1.87 0.00 2.49 2.71

time (sec)

N/A 0.428 5.081 2.677 0.000 0.291 0.000 0.542 2.911

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 19 17 16 19 19 0 16 9

N.S.

1 1.12 1.00 0.94 1.12 1.12 0.00 0.94 0.53

time (sec)

N/A 0.200 0.022 0.613 0.209 0.246 0.000 0.301 2.438

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 45 40 43 95 90 0 38 0

N.S.

1 1.12 1.00 1.08 2.38 2.25 0.00 0.95 0.00

time (sec)

N/A 0.234 0.032 0.580 0.433 0.354 0.000 0.306 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 26 17 17 47 21 0 45 0

N.S.

1 1.30 0.85 0.85 2.35 1.05 0.00 2.25 0.00

time (sec)

N/A 0.262 0.059 0.576 0.383 0.248 0.000 0.299 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 30 81 67 0 24 0

N.S.

1 1.00 1.00 1.20 3.24 2.68 0.00 0.96 0.00

time (sec)

N/A 0.237 0.029 0.583 0.434 0.287 0.000 0.314 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 10 60 16 0 27 0

N.S.

1 1.00 1.00 0.91 5.45 1.45 0.00 2.45 0.00

time (sec)

N/A 0.207 0.026 0.479 0.293 0.255 0.000 0.302 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 14 8 39 17 0 33 0

N.S.

1 1.00 1.56 0.89 4.33 1.89 0.00 3.67 0.00

time (sec)

N/A 0.253 0.030 0.377 0.305 0.235 0.000 0.288 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C A C F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 153 217 109 151 823 0 143 1281

N.S.

1 1.00 1.42 0.71 0.99 5.38 0.00 0.93 8.37

time (sec)

N/A 0.424 0.364 5.555 0.303 0.942 0.000 0.319 5.950

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A F A F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

45 45 45 0 52 123 0 38 0

N.S.

1 1.00 1.00 0.00 1.16 2.73 0.00 0.84 0.00

time (sec)

N/A 0.255 0.023 0.000 0.604 1.575 0.000 0.337 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A F(-2) F A F(-1)

verified

N/A Yes Yes N/A TBD TBD TBD TBD TBD

size

28 28 28 0 39 0 0 24 0

N.S.

1 1.00 1.00 0.00 1.39 0.00 0.00 0.86 0.00

time (sec)

N/A 0.242 0.015 0.000 0.552 0.000 0.000 0.315 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 45 44 43 90 0 38 0

N.S.

1 1.00 1.00 0.98 0.96 2.00 0.00 0.84 0.00

time (sec)

N/A 0.244 0.029 0.781 0.225 0.319 0.000 0.297 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 28 31 0 67 0 24 0

N.S.

1 1.00 1.00 1.11 0.00 2.39 0.00 0.86 0.00

time (sec)

N/A 0.243 0.013 0.400 0.000 0.320 0.000 0.318 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 46 46 39 58 97 0 46 0

N.S.

1 0.98 0.98 0.83 1.23 2.06 0.00 0.98 0.00

time (sec)

N/A 0.251 0.029 0.701 0.385 0.247 0.000 0.370 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 29 24 42 74 0 27 0

N.S.

1 1.00 1.00 0.83 1.45 2.55 0.00 0.93 0.00

time (sec)

N/A 0.249 0.014 0.190 0.428 0.243 0.000 0.322 0.000

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