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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 A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 119 75 73 84 75 216 92 107

N.S.

1 1.04 0.66 0.64 0.74 0.66 1.89 0.81 0.94

time (sec)

N/A 0.458 0.138 2.449 0.221 0.271 0.343 0.309 16.482

Problem 2

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

92 93 65 64 69 64 168 77 93

N.S.

1 1.01 0.71 0.70 0.75 0.70 1.83 0.84 1.01

time (sec)

N/A 0.374 0.101 2.254 0.242 0.335 0.228 0.331 16.631

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

76 81 73 53 57 53 144 62 79

N.S.

1 1.07 0.96 0.70 0.75 0.70 1.89 0.82 1.04

time (sec)

N/A 0.363 0.065 2.191 0.220 0.277 0.167 0.320 17.686

Problem 4

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

54 55 57 40 46 42 92 47 55

N.S.

1 1.02 1.06 0.74 0.85 0.78 1.70 0.87 1.02

time (sec)

N/A 0.287 0.071 1.662 0.225 0.261 0.120 0.308 14.560

Problem 5

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

38 38 32 29 34 29 66 31 50

N.S.

1 1.00 0.84 0.76 0.89 0.76 1.74 0.82 1.32

time (sec)

N/A 0.189 0.048 0.714 0.217 0.263 0.100 0.301 15.134

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

15 15 26 16 15 17 17 15 15

N.S.

1 1.00 1.73 1.07 1.00 1.13 1.13 1.00 1.00

time (sec)

N/A 0.146 0.003 0.333 0.243 0.256 0.059 0.304 13.686

Problem 7

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

16 16 16 29 28 36 49 43 20

N.S.

1 1.00 1.00 1.81 1.75 2.25 3.06 2.69 1.25

time (sec)

N/A 0.224 0.007 1.144 0.233 0.268 2.511 0.337 13.698

Problem 8

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

24 24 24 30 38 60 0 63 47

N.S.

1 1.00 1.00 1.25 1.58 2.50 0.00 2.62 1.96

time (sec)

N/A 0.285 0.008 1.781 0.220 0.277 0.000 0.324 13.797

Problem 9

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

47 48 47 47 58 74 0 80 75

N.S.

1 1.02 1.00 1.00 1.23 1.57 0.00 1.70 1.60

time (sec)

N/A 0.366 0.011 2.257 0.242 0.278 0.000 0.337 14.610

Problem 10

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

63 64 60 60 70 88 0 96 102

N.S.

1 1.02 0.95 0.95 1.11 1.40 0.00 1.52 1.62

time (sec)

N/A 0.388 0.103 2.284 0.212 0.271 0.000 0.341 16.521

Problem 11

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

85 90 56 73 95 99 0 110 130

N.S.

1 1.06 0.66 0.86 1.12 1.16 0.00 1.29 1.53

time (sec)

N/A 0.485 0.129 2.684 0.231 0.257 0.000 0.321 17.611

Problem 12

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

101 102 65 83 107 110 0 124 158

N.S.

1 1.01 0.64 0.82 1.06 1.09 0.00 1.23 1.56

time (sec)

N/A 0.512 0.199 2.496 0.232 0.261 0.000 0.307 19.005

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

129 129 73 75 121 89 343 106 121

N.S.

1 1.00 0.57 0.58 0.94 0.69 2.66 0.82 0.94

time (sec)

N/A 0.352 0.155 2.974 0.233 0.268 0.370 0.307 16.985

Problem 14

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

103 103 61 64 95 76 221 89 105

N.S.

1 1.00 0.59 0.62 0.92 0.74 2.15 0.86 1.02

time (sec)

N/A 0.312 0.075 2.761 0.217 0.264 0.254 0.342 17.331

Problem 15

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

87 87 53 55 83 63 211 72 89

N.S.

1 1.00 0.61 0.63 0.95 0.72 2.43 0.83 1.02

time (sec)

N/A 0.290 0.084 2.258 0.221 0.259 0.183 0.309 17.201

Problem 16

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

57 75 41 42 61 49 107 54 61

N.S.

1 1.32 0.72 0.74 1.07 0.86 1.88 0.95 1.07

time (sec)

N/A 0.272 0.055 1.422 0.225 0.254 0.126 0.306 13.706

Problem 17

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 45 34 31 45 36 78 38 57

N.S.

1 1.00 0.76 0.69 1.00 0.80 1.73 0.84 1.27

time (sec)

N/A 0.193 0.083 0.701 0.227 0.252 0.092 0.301 14.395

Problem 18

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

34 34 47 44 43 53 0 79 33

N.S.

1 1.00 1.38 1.29 1.26 1.56 0.00 2.32 0.97

time (sec)

N/A 0.329 0.026 1.226 0.213 0.254 0.000 0.330 14.234

Problem 19

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

34 34 28 44 49 76 0 79 56

N.S.

1 1.00 0.82 1.29 1.44 2.24 0.00 2.32 1.65

time (sec)

N/A 0.240 0.017 1.887 0.219 0.257 0.000 0.329 14.195

Problem 20

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

54 54 54 70 88 83 0 90 83

N.S.

1 1.00 1.00 1.30 1.63 1.54 0.00 1.67 1.54

time (sec)

N/A 0.271 0.011 2.236 0.210 0.256 0.000 0.340 14.145

Problem 21

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

66 66 66 75 85 96 0 106 112

N.S.

1 1.00 1.00 1.14 1.29 1.45 0.00 1.61 1.70

time (sec)

N/A 0.283 0.219 3.313 0.245 0.262 0.000 0.352 15.599

Problem 22

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

96 96 58 112 145 111 0 122 141

N.S.

1 1.00 0.60 1.17 1.51 1.16 0.00 1.27 1.47

time (sec)

N/A 0.308 0.297 2.931 0.217 0.263 0.000 0.354 16.990

Problem 23

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

129 129 73 75 143 89 379 106 121

N.S.

1 1.00 0.57 0.58 1.11 0.69 2.94 0.82 0.94

time (sec)

N/A 0.355 0.112 3.378 0.230 0.260 0.385 0.332 16.744

Problem 24

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

105 105 63 66 117 76 272 88 105

N.S.

1 1.00 0.60 0.63 1.11 0.72 2.59 0.84 1.00

time (sec)

N/A 0.320 0.086 2.467 0.204 0.254 0.271 0.319 17.432

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

85 93 51 53 94 63 224 71 89

N.S.

1 1.09 0.60 0.62 1.11 0.74 2.64 0.84 1.05

time (sec)

N/A 0.330 0.080 2.311 0.240 0.255 0.195 0.330 17.364

Problem 26

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

63 63 44 42 70 50 121 55 63

N.S.

1 1.00 0.70 0.67 1.11 0.79 1.92 0.87 1.00

time (sec)

N/A 0.236 0.102 1.619 0.218 0.280 0.126 0.328 14.110

Problem 27

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

59 59 81 59 67 65 0 100 88

N.S.

1 1.00 1.37 1.00 1.14 1.10 0.00 1.69 1.49

time (sec)

N/A 0.255 0.408 1.308 0.214 0.269 0.000 0.371 14.531

Problem 28

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

48 48 211 55 64 91 0 80 57

N.S.

1 1.00 4.40 1.15 1.33 1.90 0.00 1.67 1.19

time (sec)

N/A 0.257 1.078 2.257 0.224 0.301 0.000 0.447 14.895

Problem 29

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

59 59 50 80 99 98 0 100 88

N.S.

1 1.00 0.85 1.36 1.68 1.66 0.00 1.69 1.49

time (sec)

N/A 0.274 0.025 2.544 0.341 0.263 0.000 0.430 14.626

Problem 30

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

72 72 72 94 111 98 0 106 112

N.S.

1 1.00 1.00 1.31 1.54 1.36 0.00 1.47 1.56

time (sec)

N/A 0.284 0.228 3.446 0.238 0.254 0.000 0.367 16.088

Problem 31

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

93 93 93 123 156 111 0 122 141

N.S.

1 1.00 1.00 1.32 1.68 1.19 0.00 1.31 1.52

time (sec)

N/A 0.319 0.314 3.794 0.240 0.267 0.000 0.409 16.968

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 114 114 145 179 124 0 138 170

N.S.

1 1.00 1.00 1.27 1.57 1.09 0.00 1.21 1.49

time (sec)

N/A 0.336 0.433 4.074 0.242 0.252 0.000 0.355 18.351

Problem 33

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

127 127 73 75 165 89 434 106 121

N.S.

1 1.00 0.57 0.59 1.30 0.70 3.42 0.83 0.95

time (sec)

N/A 0.365 0.128 3.733 0.220 0.252 0.391 0.359 16.436

Problem 34

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

102 117 63 66 128 76 280 89 105

N.S.

1 1.15 0.62 0.65 1.25 0.75 2.75 0.87 1.03

time (sec)

N/A 0.363 0.091 2.794 0.316 0.243 0.277 0.349 17.628

Problem 35

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

87 87 56 55 106 63 224 72 89

N.S.

1 1.00 0.64 0.63 1.22 0.72 2.57 0.83 1.02

time (sec)

N/A 0.281 0.139 2.109 0.223 0.254 0.196 0.306 17.281

Problem 36

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

73 73 91 70 89 80 0 116 93

N.S.

1 1.00 1.25 0.96 1.22 1.10 0.00 1.59 1.27

time (sec)

N/A 0.273 0.750 2.447 0.270 0.255 0.000 0.370 13.996

Problem 37

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

73 73 241 82 85 105 0 129 117

N.S.

1 1.00 3.30 1.12 1.16 1.44 0.00 1.77 1.60

time (sec)

N/A 0.282 2.997 2.186 0.233 0.321 0.000 0.359 14.568

Problem 38

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

73 73 272 91 110 111 0 129 115

N.S.

1 1.00 3.73 1.25 1.51 1.52 0.00 1.77 1.58

time (sec)

N/A 0.281 3.459 2.970 0.251 0.264 0.000 0.379 14.792

Problem 39

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

73 73 61 96 120 110 0 116 117

N.S.

1 1.00 0.84 1.32 1.64 1.51 0.00 1.59 1.60

time (sec)

N/A 0.296 0.029 3.296 0.298 0.275 0.000 0.349 14.642

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 96 96 135 182 111 0 122 141

N.S.

1 1.00 1.00 1.41 1.90 1.16 0.00 1.27 1.47

time (sec)

N/A 0.324 1.276 3.954 0.273 0.298 0.000 0.377 17.745

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 111 111 156 190 124 0 138 170

N.S.

1 1.00 1.00 1.41 1.71 1.12 0.00 1.24 1.53

time (sec)

N/A 0.338 1.574 4.382 0.239 0.272 0.000 0.380 19.710

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 136 136 178 270 137 0 154 199

N.S.

1 1.00 1.00 1.31 1.99 1.01 0.00 1.13 1.46

time (sec)

N/A 0.379 3.760 4.540 0.264 0.278 0.000 0.381 18.603

Problem 43

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

118 119 173 67 217 79 882 101 98

N.S.

1 1.01 1.47 0.57 1.84 0.67 7.47 0.86 0.83

time (sec)

N/A 0.560 0.842 0.805 0.315 0.260 1.934 0.341 16.481

Problem 44

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

94 93 143 54 176 70 570 88 70

N.S.

1 0.99 1.52 0.57 1.87 0.74 6.06 0.94 0.74

time (sec)

N/A 0.453 0.743 0.780 0.490 0.321 1.225 0.329 14.751

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

76 76 117 43 133 57 325 73 89

N.S.

1 1.00 1.54 0.57 1.75 0.75 4.28 0.96 1.17

time (sec)

N/A 0.318 0.722 0.761 0.316 0.256 0.817 0.328 14.376

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 42 89 31 92 46 129 58 66

N.S.

1 0.98 2.07 0.72 2.14 1.07 3.00 1.35 1.53

time (sec)

N/A 0.352 0.474 0.735 0.309 0.259 0.560 0.381 14.916

Problem 47

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

29 29 69 23 49 37 27 28 23

N.S.

1 1.00 2.38 0.79 1.69 1.28 0.93 0.97 0.79

time (sec)

N/A 0.247 0.141 0.717 0.315 0.248 0.359 0.360 14.640

Problem 48

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

22 22 17 17 23 22 20 16 16

N.S.

1 1.00 0.77 0.77 1.05 1.00 0.91 0.73 0.73

time (sec)

N/A 0.180 0.012 0.699 0.214 0.243 0.297 0.356 14.196

Problem 49

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

38 38 103 46 75 65 0 54 31

N.S.

1 1.00 2.71 1.21 1.97 1.71 0.00 1.42 0.82

time (sec)

N/A 0.308 0.282 0.868 0.220 0.322 0.000 0.438 14.482

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 54 188 74 119 97 0 84 67

N.S.

1 1.02 3.55 1.40 2.25 1.83 0.00 1.58 1.26

time (sec)

N/A 0.448 0.783 0.933 0.231 0.254 0.000 0.319 14.798

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 84 244 105 162 112 0 101 95

N.S.

1 1.01 2.94 1.27 1.95 1.35 0.00 1.22 1.14

time (sec)

N/A 0.568 1.167 0.992 0.243 0.260 0.000 0.320 14.756

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 101 368 132 205 124 0 114 96

N.S.

1 0.98 3.57 1.28 1.99 1.20 0.00 1.11 0.93

time (sec)

N/A 0.590 3.134 1.044 0.208 0.270 0.000 0.314 14.585

Problem 53

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

124 136 115 77 207 108 700 108 135

N.S.

1 1.10 0.93 0.62 1.67 0.87 5.65 0.87 1.09

time (sec)

N/A 0.707 0.528 0.872 0.309 0.257 2.879 0.332 14.881

Problem 54

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

114 120 107 66 164 99 413 95 113

N.S.

1 1.05 0.94 0.58 1.44 0.87 3.62 0.83 0.99

time (sec)

N/A 0.513 0.423 0.789 0.353 0.306 1.774 0.454 14.579

Problem 55

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

80 85 97 55 118 90 201 79 91

N.S.

1 1.06 1.21 0.69 1.48 1.12 2.51 0.99 1.14

time (sec)

N/A 0.624 0.450 0.791 0.304 0.255 1.080 0.319 14.330

Problem 56

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

57 61 87 36 72 80 56 50 35

N.S.

1 1.07 1.53 0.63 1.26 1.40 0.98 0.88 0.61

time (sec)

N/A 0.397 0.256 0.703 0.313 0.256 0.650 0.303 14.215

Problem 57

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

55 54 36 31 47 51 48 31 30

N.S.

1 0.98 0.65 0.56 0.85 0.93 0.87 0.56 0.55

time (sec)

N/A 0.279 0.079 0.677 0.232 0.242 0.491 0.298 14.362

Problem 58

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

55 54 53 31 46 49 44 31 30

N.S.

1 0.98 0.96 0.56 0.84 0.89 0.80 0.56 0.55

time (sec)

N/A 0.258 0.036 0.629 0.238 0.245 0.427 0.304 14.060

Problem 59

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

66 67 152 62 98 114 0 77 43

N.S.

1 1.02 2.30 0.94 1.48 1.73 0.00 1.17 0.65

time (sec)

N/A 0.431 0.437 0.900 0.227 0.325 0.000 0.332 14.080

Problem 60

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

81 89 239 92 145 146 0 106 92

N.S.

1 1.10 2.95 1.14 1.79 1.80 0.00 1.31 1.14

time (sec)

N/A 0.633 1.073 0.839 0.250 0.297 0.000 0.312 14.369

Problem 61

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

119 125 292 120 190 162 0 122 122

N.S.

1 1.05 2.45 1.01 1.60 1.36 0.00 1.03 1.03

time (sec)

N/A 0.803 1.590 1.052 0.279 0.273 0.000 0.322 14.364

Problem 62

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

133 145 343 152 234 172 0 135 153

N.S.

1 1.09 2.58 1.14 1.76 1.29 0.00 1.02 1.15

time (sec)

N/A 0.872 2.911 1.261 0.240 0.262 0.000 0.329 14.297

Problem 63

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

153 167 127 77 184 135 473 113 137

N.S.

1 1.09 0.83 0.50 1.20 0.88 3.09 0.74 0.90

time (sec)

N/A 0.745 2.026 0.838 0.332 0.267 3.889 0.313 14.301

Problem 64

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

119 124 107 66 137 126 240 96 113

N.S.

1 1.04 0.90 0.55 1.15 1.06 2.02 0.81 0.95

time (sec)

N/A 0.882 0.488 0.785 0.308 0.252 2.377 0.315 14.279

Problem 65

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

96 106 108 51 92 116 75 68 81

N.S.

1 1.10 1.12 0.53 0.96 1.21 0.78 0.71 0.84

time (sec)

N/A 0.672 0.816 0.808 0.318 0.269 1.362 0.308 14.227

Problem 66

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 85 46 45 67 75 68 46 45

N.S.

1 1.02 0.55 0.54 0.81 0.90 0.82 0.55 0.54

time (sec)

N/A 0.417 0.130 0.707 0.232 0.245 1.035 0.307 14.536

Problem 67

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 87 44 31 47 73 48 31 30

N.S.

1 1.05 0.53 0.37 0.57 0.88 0.58 0.37 0.36

time (sec)

N/A 0.369 0.074 0.837 0.575 0.295 0.808 0.305 14.316

Problem 68

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 87 65 45 67 75 63 46 45

N.S.

1 1.05 0.78 0.54 0.81 0.90 0.76 0.55 0.54

time (sec)

N/A 0.352 0.056 0.659 0.229 0.234 0.687 0.293 14.604

Problem 69

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

97 107 201 75 119 158 0 94 58

N.S.

1 1.10 2.07 0.77 1.23 1.63 0.00 0.97 0.60

time (sec)

N/A 0.633 0.550 0.894 0.228 0.254 0.000 0.331 14.175

Problem 70

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

112 123 286 105 165 190 0 122 111

N.S.

1 1.10 2.55 0.94 1.47 1.70 0.00 1.09 0.99

time (sec)

N/A 0.895 1.129 1.025 0.344 0.259 0.000 0.322 14.306

Problem 71

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

156 170 343 135 211 206 0 139 141

N.S.

1 1.09 2.20 0.87 1.35 1.32 0.00 0.89 0.90

time (sec)

N/A 1.103 2.914 1.102 0.289 0.259 0.000 0.322 14.377

Problem 72

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

184 202 137 88 204 171 530 128 159

N.S.

1 1.10 0.74 0.48 1.11 0.93 2.88 0.70 0.86

time (sec)

N/A 1.006 6.175 0.934 0.356 0.266 9.079 0.321 14.851

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

150 171 135 77 158 162 280 112 137

N.S.

1 1.14 0.90 0.51 1.05 1.08 1.87 0.75 0.91

time (sec)

N/A 1.193 1.664 0.830 0.327 0.267 5.596 0.337 14.974

Problem 74

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

127 142 117 64 112 152 95 83 102

N.S.

1 1.12 0.92 0.50 0.88 1.20 0.75 0.65 0.80

time (sec)

N/A 0.958 3.187 0.650 0.330 0.269 3.261 0.343 14.835

Problem 75

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

114 121 56 57 87 99 88 59 58

N.S.

1 1.06 0.49 0.50 0.76 0.87 0.77 0.52 0.51

time (sec)

N/A 0.701 1.227 0.692 0.248 0.258 2.401 0.320 15.080

Problem 76

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

112 118 56 58 87 99 87 59 58

N.S.

1 1.05 0.50 0.52 0.78 0.88 0.78 0.53 0.52

time (sec)

N/A 0.534 0.877 0.777 0.258 0.252 1.890 0.317 14.941

Problem 77

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

112 120 56 57 87 99 85 59 58

N.S.

1 1.07 0.50 0.51 0.78 0.88 0.76 0.53 0.52

time (sec)

N/A 0.477 0.163 0.780 0.230 0.243 1.585 0.307 14.939

Problem 78

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

112 120 77 56 87 99 83 59 58

N.S.

1 1.07 0.69 0.50 0.78 0.88 0.74 0.53 0.52

time (sec)

N/A 0.458 0.120 0.630 0.228 0.283 1.431 0.297 15.283

Problem 79

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

120 135 185 88 139 202 0 110 83

N.S.

1 1.12 1.54 0.73 1.16 1.68 0.00 0.92 0.69

time (sec)

N/A 0.850 0.901 1.026 0.229 0.265 0.000 0.333 14.901

Problem 80

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

135 159 341 118 186 234 0 139 130

N.S.

1 1.18 2.53 0.87 1.38 1.73 0.00 1.03 0.96

time (sec)

N/A 1.115 3.376 1.065 0.249 0.260 0.000 0.326 14.974

Problem 81

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

185 203 455 148 231 250 0 155 160

N.S.

1 1.10 2.46 0.80 1.25 1.35 0.00 0.84 0.86

time (sec)

N/A 1.370 6.781 1.271 0.329 0.261 0.000 0.337 15.503

Problem 82

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

225 250 143 98 224 207 588 145 181

N.S.

1 1.11 0.64 0.44 1.00 0.92 2.61 0.64 0.80

time (sec)

N/A 1.274 8.033 0.997 0.339 0.257 19.695 0.346 15.425

Problem 83

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

191 220 149 88 178 198 320 129 159

N.S.

1 1.15 0.78 0.46 0.93 1.04 1.68 0.68 0.83

time (sec)

N/A 1.496 7.982 0.743 0.324 0.268 11.539 0.432 15.056

Problem 84

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

168 196 127 77 132 188 116 100 125

N.S.

1 1.17 0.76 0.46 0.79 1.12 0.69 0.60 0.74

time (sec)

N/A 1.248 7.118 0.713 0.309 0.258 7.073 0.420 14.852

Problem 85

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

155 176 66 71 107 123 107 72 127

N.S.

1 1.14 0.43 0.46 0.69 0.79 0.69 0.46 0.82

time (sec)

N/A 0.953 2.737 0.738 0.222 0.247 5.436 0.425 14.121

Problem 86

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

147 159 66 57 87 123 87 59 58

N.S.

1 1.08 0.45 0.39 0.59 0.84 0.59 0.40 0.39

time (sec)

N/A 0.845 2.694 0.843 0.221 0.300 4.125 0.434 14.414

Problem 87

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

139 147 66 45 67 123 68 46 45

N.S.

1 1.06 0.47 0.32 0.48 0.88 0.49 0.33 0.32

time (sec)

N/A 0.672 2.261 0.818 0.261 0.250 3.418 0.358 14.012

Problem 88

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

143 153 66 57 87 123 85 59 58

N.S.

1 1.07 0.46 0.40 0.61 0.86 0.59 0.41 0.41

time (sec)

N/A 0.601 0.224 0.767 0.263 0.253 3.037 0.438 14.056

Problem 89

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

143 153 89 69 107 123 102 72 127

N.S.

1 1.07 0.62 0.48 0.75 0.86 0.71 0.50 0.89

time (sec)

N/A 0.580 0.117 0.780 0.213 0.247 2.758 0.388 14.571

Problem 90

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

153 181 211 101 159 246 0 126 99

N.S.

1 1.18 1.38 0.66 1.04 1.61 0.00 0.82 0.65

time (sec)

N/A 1.089 1.622 1.112 0.246 0.269 0.000 0.437 14.541

Problem 91

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

168 200 393 131 206 278 0 155 149

N.S.

1 1.19 2.34 0.78 1.23 1.65 0.00 0.92 0.89

time (sec)

N/A 1.442 5.518 1.174 0.302 0.289 0.000 0.443 14.776

Problem 92

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

224 249 507 160 251 294 0 171 179

N.S.

1 1.11 2.26 0.71 1.12 1.31 0.00 0.76 0.80

time (sec)

N/A 1.678 7.091 1.223 0.257 0.266 0.000 0.415 14.231

Problem 93

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

184 211 76 83 127 147 129 85 75

N.S.

1 1.15 0.41 0.45 0.69 0.80 0.70 0.46 0.41

time (sec)

N/A 1.244 5.085 0.742 0.233 0.253 11.966 0.422 15.305

Problem 94

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

176 204 76 84 127 147 124 85 151

N.S.

1 1.16 0.43 0.48 0.72 0.84 0.70 0.48 0.86

time (sec)

N/A 1.095 5.085 0.869 0.227 0.250 9.672 0.414 14.791

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 179 92 97 79 72 0 117 0

N.S.

1 1.13 0.58 0.61 0.50 0.46 0.00 0.74 0.00

time (sec)

N/A 0.790 0.202 0.971 0.391 0.243 0.000 0.659 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 138 80 84 65 62 0 96 0

N.S.

1 1.13 0.66 0.69 0.53 0.51 0.00 0.79 0.00

time (sec)

N/A 0.614 0.096 0.797 0.365 0.243 0.000 0.619 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

86 97 68 71 51 52 0 75 0

N.S.

1 1.13 0.79 0.83 0.59 0.60 0.00 0.87 0.00

time (sec)

N/A 0.435 0.064 0.917 0.439 0.303 0.000 0.484 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

56 56 54 58 36 40 0 53 0

N.S.

1 1.00 0.96 1.04 0.64 0.71 0.00 0.95 0.00

time (sec)

N/A 0.281 0.046 0.776 0.388 0.261 0.000 0.547 0.000

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

26 26 29 43 20 32 0 30 33

N.S.

1 1.00 1.12 1.65 0.77 1.23 0.00 1.15 1.27

time (sec)

N/A 0.187 0.020 0.942 0.373 0.242 0.000 0.372 14.123

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 50 182 0 146 0 58 0

N.S.

1 1.00 1.35 4.92 0.00 3.95 0.00 1.57 0.00

time (sec)

N/A 0.232 0.035 1.415 0.000 0.270 0.000 0.381 0.000

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