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2.2.1 Integrals 1 to 100

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 B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 82 79 78 114 189 83 114 106

N.S.

1 0.87 0.84 0.83 1.21 2.01 0.88 1.21 1.13

time (sec)

N/A 0.280 0.312 176.202 0.280 0.236 4.114 0.432 4.023

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 68 63 67 92 153 68 92 149

N.S.

1 0.91 0.84 0.89 1.23 2.04 0.91 1.23 1.99

time (sec)

N/A 0.299 0.097 63.452 0.237 0.228 2.402 0.427 4.202

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 58 55 56 70 117 60 70 112

N.S.

1 0.94 0.89 0.90 1.13 1.89 0.97 1.13 1.81

time (sec)

N/A 0.285 0.093 18.230 0.242 0.233 1.579 0.413 3.708

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 43 45 48 81 48 48 48

N.S.

1 1.00 0.93 0.98 1.04 1.76 1.04 1.04 1.04

time (sec)

N/A 0.281 0.036 3.463 0.238 0.232 1.108 0.407 3.995

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 30 30 28 21 45 37 26 23

N.S.

1 1.11 1.11 1.04 0.78 1.67 1.37 0.96 0.85

time (sec)

N/A 0.259 0.012 0.625 0.237 0.228 0.738 0.379 3.873

Problem 6

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

19 19 19 23 17 18 24 18 17

N.S.

1 1.00 1.00 1.21 0.89 0.95 1.26 0.95 0.89

time (sec)

N/A 0.152 0.010 0.062 0.258 0.238 0.084 0.297 3.720

Problem 7

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 46 48 22 38 23 39 23 22

N.S.

1 1.02 1.07 0.49 0.84 0.51 0.87 0.51 0.49

time (sec)

N/A 0.255 0.036 0.624 0.332 0.240 0.090 0.359 4.170

Problem 8

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

67 72 46 53 61 56 136 103 64

N.S.

1 1.07 0.69 0.79 0.91 0.84 2.03 1.54 0.96

time (sec)

N/A 0.331 0.035 3.062 0.337 0.247 0.156 0.383 3.707

Problem 9

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

89 98 56 63 82 80 211 127 108

N.S.

1 1.10 0.63 0.71 0.92 0.90 2.37 1.43 1.21

time (sec)

N/A 0.405 0.045 14.070 0.340 0.235 0.210 0.415 4.036

Problem 10

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

111 124 68 73 103 104 279 151 152

N.S.

1 1.12 0.61 0.66 0.93 0.94 2.51 1.36 1.37

time (sec)

N/A 0.493 0.149 48.319 0.320 0.240 0.284 0.463 5.553

Problem 11

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

98 107 98 74 106 372 0 181 247

N.S.

1 1.09 1.00 0.76 1.08 3.80 0.00 1.85 2.52

time (sec)

N/A 0.527 0.021 36.220 0.254 0.249 0.000 0.410 8.358

Problem 12

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

76 81 76 64 86 276 0 139 178

N.S.

1 1.07 1.00 0.84 1.13 3.63 0.00 1.83 2.34

time (sec)

N/A 0.434 0.010 8.212 0.239 0.241 0.000 0.370 7.574

Problem 13

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

54 55 54 51 61 180 0 97 107

N.S.

1 1.02 1.00 0.94 1.13 3.33 0.00 1.80 1.98

time (sec)

N/A 0.333 0.011 1.750 0.236 0.241 0.000 0.358 5.955

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 27 34 32 82 41 52 39

N.S.

1 1.00 1.00 1.26 1.19 3.04 1.52 1.93 1.44

time (sec)

N/A 0.238 0.007 0.358 0.247 0.243 2.268 0.366 4.042

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 51 17 22 15 26 84 20

N.S.

1 1.00 1.96 0.65 0.85 0.58 1.00 3.23 0.77

time (sec)

N/A 0.238 0.034 0.349 0.256 0.233 0.074 0.361 3.947

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 46 37 36 42 105 196 54

N.S.

1 1.00 1.00 0.80 0.78 0.91 2.28 4.26 1.17

time (sec)

N/A 0.269 0.006 1.448 0.225 0.251 0.161 0.396 3.706

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 58 62 47 49 66 184 220 70

N.S.

1 0.94 1.00 0.76 0.79 1.06 2.97 3.55 1.13

time (sec)

N/A 0.273 0.008 6.787 0.253 0.232 0.242 0.534 5.998

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 66 76 57 58 90 253 244 93

N.S.

1 0.87 1.00 0.75 0.76 1.18 3.33 3.21 1.22

time (sec)

N/A 0.286 0.025 27.385 0.268 0.234 0.321 0.525 6.665

Problem 19

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

109 94 79 80 108 189 0 108 151

N.S.

1 0.86 0.72 0.73 0.99 1.73 0.00 0.99 1.39

time (sec)

N/A 0.291 0.544 114.000 0.227 0.228 0.000 0.555 4.316

Problem 20

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

82 72 63 69 95 151 0 95 132

N.S.

1 0.88 0.77 0.84 1.16 1.84 0.00 1.16 1.61

time (sec)

N/A 0.267 0.358 34.889 0.260 0.233 0.000 0.545 3.696

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

55 50 34 58 56 113 0 56 56

N.S.

1 0.91 0.62 1.05 1.02 2.05 0.00 1.02 1.02

time (sec)

N/A 0.253 0.170 8.362 0.251 0.234 0.000 0.503 3.825

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

27 27 50 47 21 75 0 42 35

N.S.

1 1.00 1.85 1.74 0.78 2.78 0.00 1.56 1.30

time (sec)

N/A 0.224 0.092 1.974 0.262 0.227 0.000 0.461 4.062

Problem 23

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

38 38 34 40 41 56 53 66 29

N.S.

1 1.00 0.89 1.05 1.08 1.47 1.39 1.74 0.76

time (sec)

N/A 0.251 0.133 0.091 0.368 0.237 0.132 0.382 3.635

Problem 24

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

25 25 31 19 32 17 36 17 18

N.S.

1 1.00 1.24 0.76 1.28 0.68 1.44 0.68 0.72

time (sec)

N/A 0.219 0.132 1.348 0.362 0.234 0.102 0.495 3.820

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 71 52 44 67 41 87 257 50

N.S.

1 1.13 0.83 0.70 1.06 0.65 1.38 4.08 0.79

time (sec)

N/A 0.273 0.207 6.554 0.373 0.237 0.147 0.559 3.818

Problem 26

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

117 115 99 79 92 78 185 169 88

N.S.

1 0.98 0.85 0.68 0.79 0.67 1.58 1.44 0.75

time (sec)

N/A 0.310 0.306 26.162 0.355 0.245 0.220 0.605 3.639

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 159 142 114 115 106 270 342 144

N.S.

1 0.93 0.83 0.67 0.67 0.62 1.58 2.00 0.84

time (sec)

N/A 0.336 0.362 82.579 0.377 0.247 0.275 0.677 4.951

Problem 28

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

118 121 108 133 181 364 0 237 290

N.S.

1 1.03 0.92 1.13 1.53 3.08 0.00 2.01 2.46

time (sec)

N/A 0.611 0.243 19.593 0.280 0.249 0.000 0.553 7.897

Problem 29

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

94 95 84 111 130 256 0 173 198

N.S.

1 1.01 0.89 1.18 1.38 2.72 0.00 1.84 2.11

time (sec)

N/A 0.492 0.131 3.992 0.285 0.245 0.000 0.513 7.315

Problem 30

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

68 65 56 86 83 148 0 107 104

N.S.

1 0.96 0.82 1.26 1.22 2.18 0.00 1.57 1.53

time (sec)

N/A 0.363 0.141 0.788 0.490 0.255 0.000 0.426 4.632

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 180 56 61 52 68 56 41

N.S.

1 1.00 3.91 1.22 1.33 1.13 1.48 1.22 0.89

time (sec)

N/A 0.279 0.522 0.631 0.358 0.240 0.177 0.456 3.748

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 52 38 52 34 75 531 78

N.S.

1 1.00 1.02 0.75 1.02 0.67 1.47 10.41 1.53

time (sec)

N/A 0.275 0.076 3.128 0.654 0.235 0.152 0.520 3.710

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 66 68 67 79 62 153 613 71

N.S.

1 0.96 0.99 0.97 1.14 0.90 2.22 8.88 1.03

time (sec)

N/A 0.304 0.133 14.235 0.315 0.250 0.232 0.598 5.115

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 78 85 102 98 90 238 641 256

N.S.

1 0.90 0.98 1.17 1.13 1.03 2.74 7.37 2.94

time (sec)

N/A 0.322 0.146 49.181 0.280 0.232 0.314 0.670 4.098

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 86 104 131 119 118 314 669 330

N.S.

1 0.82 0.99 1.25 1.13 1.12 2.99 6.37 3.14

time (sec)

N/A 0.323 0.315 135.736 0.271 0.237 0.387 0.721 6.135

Problem 36

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

109 94 79 91 108 215 0 108 151

N.S.

1 0.86 0.72 0.83 0.99 1.97 0.00 0.99 1.39

time (sec)

N/A 0.272 0.644 182.417 0.483 0.232 0.000 0.596 3.798

Problem 37

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

82 72 63 80 108 177 0 108 151

N.S.

1 0.88 0.77 0.98 1.32 2.16 0.00 1.32 1.84

time (sec)

N/A 0.264 0.367 64.761 0.392 0.239 0.000 0.539 4.170

Problem 38

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

55 50 34 69 82 139 0 82 114

N.S.

1 0.91 0.62 1.25 1.49 2.53 0.00 1.49 2.07

time (sec)

N/A 0.242 0.300 19.529 0.510 0.232 0.000 0.543 3.867

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 50 58 21 101 0 56 56

N.S.

1 1.00 1.85 2.15 0.78 3.74 0.00 2.07 2.07

time (sec)

N/A 0.216 0.153 4.088 0.267 0.233 0.000 0.489 3.847

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 67 46 51 76 97 94 118 41

N.S.

1 1.06 0.73 0.81 1.21 1.54 1.49 1.87 0.65

time (sec)

N/A 0.326 0.148 0.096 0.363 0.239 0.162 0.399 4.199

Problem 41

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

49 43 40 50 62 36 61 36 39

N.S.

1 0.88 0.82 1.02 1.27 0.73 1.24 0.73 0.80

time (sec)

N/A 0.244 0.108 2.852 0.380 0.239 0.169 0.614 3.635

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 24 38 57 34 80 135 36

N.S.

1 1.00 0.89 1.41 2.11 1.26 2.96 5.00 1.33

time (sec)

N/A 0.222 0.079 13.760 0.375 0.237 0.174 0.708 3.944

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 93 65 62 105 55 131 457 77

N.S.

1 1.03 0.72 0.69 1.17 0.61 1.46 5.08 0.86

time (sec)

N/A 0.284 0.245 47.766 0.461 0.234 0.202 0.814 4.152

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 137 137 97 128 92 226 514 125

N.S.

1 0.95 0.95 0.67 0.89 0.64 1.57 3.57 0.87

time (sec)

N/A 0.314 0.312 133.412 0.428 0.237 0.291 0.919 4.011

Problem 45

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

127 134 102 122 155 310 0 189 228

N.S.

1 1.06 0.80 0.96 1.22 2.44 0.00 1.49 1.80

time (sec)

N/A 0.670 1.723 8.870 0.293 0.238 0.000 0.518 7.624

Problem 46

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

99 102 93 100 109 202 0 125 136

N.S.

1 1.03 0.94 1.01 1.10 2.04 0.00 1.26 1.37

time (sec)

N/A 0.501 1.476 1.834 0.272 0.244 0.000 0.484 6.255

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 62 123 93 82 107 107 234 102

N.S.

1 1.02 2.02 1.52 1.34 1.75 1.75 3.84 1.67

time (sec)

N/A 0.370 1.564 1.460 0.291 0.253 0.195 0.604 4.196

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 31 19 75 17 36 901 66

N.S.

1 1.00 0.97 0.59 2.34 0.53 1.12 28.16 2.06

time (sec)

N/A 0.221 0.192 6.812 0.313 0.225 0.132 0.707 3.984

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 87 145 56 105 48 116 929 130

N.S.

1 0.99 1.65 0.64 1.19 0.55 1.32 10.56 1.48

time (sec)

N/A 0.414 0.746 26.521 0.355 0.227 0.217 0.851 4.788

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 99 180 85 123 76 190 465 134

N.S.

1 0.93 1.70 0.80 1.16 0.72 1.79 4.39 1.26

time (sec)

N/A 0.417 0.613 81.925 0.406 0.238 0.311 0.941 5.109

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 107 226 120 145 104 275 1039 330

N.S.

1 0.86 1.82 0.97 1.17 0.84 2.22 8.38 2.66

time (sec)

N/A 0.417 0.910 215.938 0.312 0.251 0.421 0.780 5.731

Problem 52

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

163 173 171 133 246 364 0 237 290

N.S.

1 1.06 1.05 0.82 1.51 2.23 0.00 1.45 1.78

time (sec)

N/A 0.834 2.055 20.175 0.278 0.241 0.000 0.598 8.388

Problem 53

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

133 139 237 111 180 256 0 173 198

N.S.

1 1.05 1.78 0.83 1.35 1.92 0.00 1.30 1.49

time (sec)

N/A 0.649 1.533 3.806 0.309 0.249 0.000 0.556 7.601

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 100 906 107 137 162 153 372 159

N.S.

1 1.03 9.34 1.10 1.41 1.67 1.58 3.84 1.64

time (sec)

N/A 0.494 6.766 3.187 0.274 0.267 0.244 0.665 6.342

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 85 246 79 121 68 109 1299 88

N.S.

1 1.09 3.15 1.01 1.55 0.87 1.40 16.65 1.13

time (sec)

N/A 0.405 0.944 13.925 0.435 0.249 0.244 0.972 4.155

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 145 38 118 34 80 915 130

N.S.

1 1.00 2.20 0.58 1.79 0.52 1.21 13.86 1.97

time (sec)

N/A 0.334 0.552 47.411 0.416 0.239 0.227 1.083 4.878

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 107 181 74 149 62 156 1327 186

N.S.

1 1.05 1.77 0.73 1.46 0.61 1.53 13.01 1.82

time (sec)

N/A 0.435 0.608 131.887 0.314 0.248 0.286 0.756 4.932

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 119 216 233 181 90 228 1409 145

N.S.

1 0.99 1.80 1.94 1.51 0.75 1.90 11.74 1.21

time (sec)

N/A 0.455 0.911 0.825 0.295 0.237 0.392 0.809 6.090

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 94 81 377 160 267 0 160 146

N.S.

1 0.86 0.74 3.46 1.47 2.45 0.00 1.47 1.34

time (sec)

N/A 0.283 0.842 1.150 0.297 0.233 0.000 0.863 4.235

Problem 60

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

82 72 63 102 108 229 0 108 151

N.S.

1 0.88 0.77 1.24 1.32 2.79 0.00 1.32 1.84

time (sec)

N/A 0.261 0.529 181.819 0.347 0.236 0.000 0.809 4.047

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 50 36 91 108 191 0 108 151

N.S.

1 0.91 0.65 1.65 1.96 3.47 0.00 1.96 2.75

time (sec)

N/A 0.246 0.382 66.858 0.335 0.237 0.000 0.777 3.893

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 72 80 21 153 0 82 114

N.S.

1 1.00 2.67 2.96 0.78 5.67 0.00 3.04 4.22

time (sec)

N/A 0.215 0.345 20.703 0.359 0.229 0.000 0.749 3.750

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 125 71 72 165 177 178 222 73

N.S.

1 1.07 0.61 0.62 1.41 1.51 1.52 1.90 0.62

time (sec)

N/A 0.547 0.179 0.151 0.459 0.248 0.249 0.399 4.399

Problem 64

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

83 78 62 85 86 125 131 146 70

N.S.

1 0.94 0.75 1.02 1.04 1.51 1.58 1.76 0.84

time (sec)

N/A 0.260 0.594 14.134 0.451 0.237 0.242 0.939 3.722

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 65 49 68 88 51 102 450 64

N.S.

1 0.89 0.67 0.93 1.21 0.70 1.40 6.16 0.88

time (sec)

N/A 0.268 0.270 48.941 0.392 0.249 0.252 0.704 4.011

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 50 36 38 93 34 80 187 53

N.S.

1 0.91 0.65 0.69 1.69 0.62 1.45 3.40 0.96

time (sec)

N/A 0.251 0.116 135.100 0.514 0.234 0.256 0.699 4.173

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 24 301 103 62 162 267 63

N.S.

1 1.00 0.89 11.15 3.81 2.30 6.00 9.89 2.33

time (sec)

N/A 0.223 0.176 1.381 0.594 0.236 0.308 0.785 3.741

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 137 123 331 164 83 209 857 122

N.S.

1 0.95 0.85 2.30 1.14 0.58 1.45 5.95 0.85

time (sec)

N/A 0.308 0.332 0.696 1.334 0.248 0.373 0.902 4.743

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 181 159 361 187 120 301 914 171

N.S.

1 0.91 0.80 1.82 0.94 0.61 1.52 4.62 0.86

time (sec)

N/A 0.347 0.639 0.788 0.430 0.260 0.492 0.883 5.556

Problem 70

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

167 176 115 122 215 310 0 189 228

N.S.

1 1.05 0.69 0.73 1.29 1.86 0.00 1.13 1.37

time (sec)

N/A 0.805 2.105 8.776 0.330 0.249 0.000 0.722 7.799

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 137 151 118 173 216 197 510 222

N.S.

1 1.05 1.16 0.91 1.33 1.66 1.52 3.92 1.71

time (sec)

N/A 0.645 1.781 7.326 0.317 0.240 0.292 0.812 8.254

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 103 130 111 154 122 148 1683 162

N.S.

1 1.05 1.33 1.13 1.57 1.24 1.51 17.17 1.65

time (sec)

N/A 0.533 1.965 26.349 0.301 0.246 0.320 1.176 6.136

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 31 19 152 17 36 1669 104

N.S.

1 1.00 0.97 0.59 4.75 0.53 1.12 52.16 3.25

time (sec)

N/A 0.219 0.420 81.448 0.631 0.233 0.204 0.887 4.313

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 104 122 56 187 48 121 1697 186

N.S.

1 1.03 1.21 0.55 1.85 0.48 1.20 16.80 1.84

time (sec)

N/A 0.457 0.615 212.039 0.405 0.236 0.321 0.935 4.712

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 140 146 287 217 76 192 1725 79

N.S.

1 0.99 1.04 2.04 1.54 0.54 1.36 12.23 0.56

time (sec)

N/A 0.559 0.730 0.793 0.309 0.243 0.399 0.947 4.862

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 148 170 317 246 104 265 1807 139

N.S.

1 0.93 1.07 1.99 1.55 0.65 1.67 11.36 0.87

time (sec)

N/A 0.566 1.043 0.668 0.349 0.250 0.492 1.030 5.811

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 94 56 611 186 345 0 186 153

N.S.

1 0.86 0.51 5.61 1.71 3.17 0.00 1.71 1.40

time (sec)

N/A 0.288 1.929 0.593 0.282 0.242 0.000 1.200 5.595

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 72 44 475 173 307 0 173 190

N.S.

1 0.88 0.54 5.79 2.11 3.74 0.00 2.11 2.32

time (sec)

N/A 0.270 1.012 0.582 0.339 0.234 0.000 1.113 5.868

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 50 34 124 134 269 0 134 107

N.S.

1 0.91 0.62 2.25 2.44 4.89 0.00 2.44 1.95

time (sec)

N/A 0.246 0.721 286.484 0.352 0.241 0.000 1.130 4.728

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 102 113 21 231 0 120 83

N.S.

1 1.00 3.78 4.19 0.78 8.56 0.00 4.44 3.07

time (sec)

N/A 0.228 0.667 111.631 0.302 0.238 0.000 1.064 4.383

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

200 212 100 103 121 297 301 378 113

N.S.

1 1.06 0.50 0.52 0.60 1.48 1.50 1.89 0.56

time (sec)

N/A 0.966 0.509 0.338 0.475 0.235 0.379 0.536 4.289

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 121 96 118 124 245 257 302 102

N.S.

1 0.91 0.72 0.89 0.93 1.84 1.93 2.27 0.77

time (sec)

N/A 0.297 0.890 84.154 0.355 0.258 0.366 0.907 3.795

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 113 86 114 135 179 216 785 111

N.S.

1 0.91 0.69 0.92 1.09 1.44 1.74 6.33 0.90

time (sec)

N/A 0.297 1.513 219.138 0.366 0.244 0.381 1.044 4.114

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 101 77 319 146 113 172 799 103

N.S.

1 0.89 0.68 2.80 1.28 0.99 1.51 7.01 0.90

time (sec)

N/A 0.290 0.916 0.839 0.341 0.243 0.406 1.094 4.221

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 42 31 451 136 17 36 381 66

N.S.

1 0.98 0.72 10.49 3.16 0.40 0.84 8.86 1.53

time (sec)

N/A 0.229 1.610 1.405 0.333 0.244 0.346 1.123 3.842

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 70 44 588 152 48 121 409 82

N.S.

1 0.88 0.55 7.35 1.90 0.60 1.51 5.11 1.02

time (sec)

N/A 0.265 0.240 1.177 0.354 0.243 0.447 1.229 4.493

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 50 34 639 162 76 197 437 82

N.S.

1 0.91 0.62 11.62 2.95 1.38 3.58 7.95 1.49

time (sec)

N/A 0.249 0.413 2.809 0.334 0.261 0.522 1.270 3.843

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 116 689 171 104 279 465 105

N.S.

1 1.00 4.30 25.52 6.33 3.85 10.33 17.22 3.89

time (sec)

N/A 0.220 2.932 1.402 0.343 0.276 0.630 1.310 3.898

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

225 203 152 739 246 125 323 1457 195

N.S.

1 0.90 0.68 3.28 1.09 0.56 1.44 6.48 0.87

time (sec)

N/A 0.359 0.976 2.592 0.375 0.297 0.693 1.529 5.673

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

279 247 186 789 269 162 413 1514 231

N.S.

1 0.89 0.67 2.83 0.96 0.58 1.48 5.43 0.83

time (sec)

N/A 0.406 1.170 2.284 0.393 0.319 0.799 1.629 6.040

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

235 248 205 151 396 378 320 924 399

N.S.

1 1.06 0.87 0.64 1.69 1.61 1.36 3.93 1.70

time (sec)

N/A 1.204 2.765 90.461 0.274 0.247 0.434 1.437 9.230

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A A B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

205 215 1540 147 352 284 277 2835 343

N.S.

1 1.05 7.51 0.72 1.72 1.39 1.35 13.83 1.67

time (sec)

N/A 1.012 8.297 253.242 0.288 0.255 0.458 1.346 8.747

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B A A B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

173 182 1162 322 326 190 235 2849 281

N.S.

1 1.05 6.72 1.86 1.88 1.10 1.36 16.47 1.62

time (sec)

N/A 0.845 8.064 2.376 0.277 0.252 0.454 1.421 8.578

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 163 305 385 309 96 187 2863 207

N.S.

1 1.07 2.01 2.53 2.03 0.63 1.23 18.84 1.36

time (sec)

N/A 0.730 3.173 1.562 0.268 0.254 0.484 1.544 8.247

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 146 447 302 34 80 2451 37

N.S.

1 1.00 2.21 6.77 4.58 0.52 1.21 37.14 0.56

time (sec)

N/A 0.338 0.807 1.588 0.265 0.252 0.461 1.615 4.140

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 142 151 567 355 62 162 2863 65

N.S.

1 1.04 1.11 4.17 2.61 0.46 1.19 21.05 0.48

time (sec)

N/A 0.617 0.959 1.875 0.435 0.260 0.575 1.734 4.812

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 218 168 617 405 90 240 2891 93

N.S.

1 1.03 0.80 2.92 1.92 0.43 1.14 13.70 0.44

time (sec)

N/A 0.936 1.784 1.807 0.323 0.272 0.621 1.842 4.837

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

212 209 173 667 453 118 313 2919 222

N.S.

1 0.99 0.82 3.15 2.14 0.56 1.48 13.77 1.05

time (sec)

N/A 0.784 2.106 1.804 0.500 0.283 0.738 1.889 6.412

Problem 99

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

107 92 56 58 87 146 0 87 92

N.S.

1 0.86 0.52 0.54 0.81 1.36 0.00 0.81 0.86

time (sec)

N/A 0.275 0.269 0.451 0.283 0.234 0.000 0.405 4.347

Problem 100

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

80 70 46 47 67 109 0 67 114

N.S.

1 0.88 0.58 0.59 0.84 1.36 0.00 0.84 1.42

time (sec)

N/A 0.270 0.168 0.369 0.255 0.227 0.000 0.392 3.944

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