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Integrals 1 to 91

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 Reduce Mupad

grade

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

verified

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

size

78 80 67 39 0 39 51 53 13 49

N.S.

1 1.03 0.86 0.50 0.00 0.50 0.65 0.68 0.17 0.63

time (sec)

N/A 0.250 0.054 19.886 0.000 0.077 0.101 0.126 0.186 0.856

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

29 31 51 31 0 26 37 71 13 59

N.S.

1 1.07 1.76 1.07 0.00 0.90 1.28 2.45 0.45 2.03

time (sec)

N/A 0.390 0.036 5.505 0.000 0.074 0.096 0.126 0.214 1.020

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

50 52 39 19 0 25 31 41 13 35

N.S.

1 1.04 0.78 0.38 0.00 0.50 0.62 0.82 0.26 0.70

time (sec)

N/A 0.239 0.061 3.025 0.000 0.071 0.093 0.125 0.157 0.791

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

19 23 33 18 0 14 17 33 11 39

N.S.

1 1.21 1.74 0.95 0.00 0.74 0.89 1.74 0.58 2.05

time (sec)

N/A 0.342 0.014 1.474 0.000 0.074 0.073 0.132 0.154 0.847

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B B F A F B

verified

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

size

16 18 31 21 28 25 0 20 11 20

N.S.

1 1.12 1.94 1.31 1.75 1.56 0.00 1.25 0.69 1.25

time (sec)

N/A 0.330 0.025 1.427 0.043 0.087 0.000 0.129 0.156 0.870

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A F B

verified

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

size

18 19 15 20 17 25 0 18 13 19

N.S.

1 1.06 0.83 1.11 0.94 1.39 0.00 1.00 0.72 1.06

time (sec)

N/A 0.214 0.026 2.800 0.031 0.072 0.000 0.127 0.158 0.794

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B B B B F B F B

verified

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

size

24 26 75 42 59 73 0 46 13 41

N.S.

1 1.08 3.12 1.75 2.46 3.04 0.00 1.92 0.54 1.71

time (sec)

N/A 0.386 0.028 5.879 0.037 0.080 0.000 0.133 0.185 0.867

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A F B

verified

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

size

19 19 29 15 12 36 0 12 13 13

N.S.

1 1.00 1.53 0.79 0.63 1.89 0.00 0.63 0.68 0.68

time (sec)

N/A 0.223 0.028 7.690 0.041 0.069 0.000 0.121 0.164 0.790

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A B B F B F B

verified

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

size

40 40 139 58 83 123 0 62 13 57

N.S.

1 1.00 3.48 1.45 2.08 3.08 0.00 1.55 0.32 1.42

time (sec)

N/A 0.412 0.028 164.334 0.047 0.085 0.000 0.129 0.159 0.848

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A F B

verified

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

size

37 37 41 28 24 54 0 24 13 27

N.S.

1 1.00 1.11 0.76 0.65 1.46 0.00 0.65 0.35 0.73

time (sec)

N/A 0.232 0.029 0.342 0.035 0.078 0.000 0.121 0.155 0.749

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

101 101 103 80 91 97 0 10412 113 121

N.S.

1 1.00 1.02 0.79 0.90 0.96 0.00 103.09 1.12 1.20

time (sec)

N/A 0.300 0.062 5.517 0.030 0.095 0.000 1.536 0.156 0.930

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

79 95 82 73 87 74 0 81 116 155

N.S.

1 1.20 1.04 0.92 1.10 0.94 0.00 1.03 1.47 1.96

time (sec)

N/A 0.353 0.087 2.877 0.109 0.095 0.000 0.149 0.158 0.825

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

69 69 71 60 70 74 0 4486 85 87

N.S.

1 1.00 1.03 0.87 1.01 1.07 0.00 65.01 1.23 1.26

time (sec)

N/A 0.266 0.051 1.939 0.051 0.091 0.000 0.761 0.184 0.853

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

46 59 56 52 52 47 0 58 86 50

N.S.

1 1.28 1.22 1.13 1.13 1.02 0.00 1.26 1.87 1.09

time (sec)

N/A 0.271 0.064 0.909 0.133 0.106 0.000 0.142 0.204 0.812

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

37 37 48 40 46 49 0 1020 53 53

N.S.

1 1.00 1.30 1.08 1.24 1.32 0.00 27.57 1.43 1.43

time (sec)

N/A 0.230 0.029 0.730 0.035 0.095 0.000 0.233 0.224 0.892

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

26 26 26 40 46 58 0 49 46 86

N.S.

1 1.00 1.00 1.54 1.77 2.23 0.00 1.88 1.77 3.31

time (sec)

N/A 0.218 0.012 0.807 0.039 0.098 0.000 0.157 0.210 0.866

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

25 23 38 26 25 62 0 26 82 25

N.S.

1 0.92 1.52 1.04 1.00 2.48 0.00 1.04 3.28 1.00

time (sec)

N/A 0.255 0.057 0.737 0.040 0.085 0.000 0.149 0.181 0.783

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A A B F B B B

verified

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

size

60 60 107 68 83 142 0 118 98 149

N.S.

1 1.00 1.78 1.13 1.38 2.37 0.00 1.97 1.63 2.48

time (sec)

N/A 0.272 0.054 2.127 0.031 0.114 0.000 0.181 0.152 0.884

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

57 49 78 46 50 122 0 51 127 49

N.S.

1 0.86 1.37 0.81 0.88 2.14 0.00 0.89 2.23 0.86

time (sec)

N/A 0.278 0.050 3.215 0.034 0.113 0.000 0.161 0.154 0.822

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A A B F A B B

verified

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

size

98 98 151 90 123 213 0 177 127 211

N.S.

1 1.00 1.54 0.92 1.26 2.17 0.00 1.81 1.30 2.15

time (sec)

N/A 0.331 0.053 5.382 0.039 0.110 0.000 0.196 0.180 0.931

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

87 73 116 66 72 174 0 73 155 70

N.S.

1 0.84 1.33 0.76 0.83 2.00 0.00 0.84 1.78 0.80

time (sec)

N/A 0.296 0.056 9.488 0.034 0.096 0.000 0.181 0.171 0.974

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A A F A B B

verified

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

size

122 171 250 140 128 137 0 124 241 127

N.S.

1 1.40 2.05 1.15 1.05 1.12 0.00 1.02 1.98 1.04

time (sec)

N/A 0.463 1.943 3.464 0.115 0.101 0.000 0.198 0.207 0.853

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

122 122 152 113 104 126 0 32694 174 174

N.S.

1 1.00 1.25 0.93 0.85 1.03 0.00 267.98 1.43 1.43

time (sec)

N/A 0.353 1.039 2.870 0.039 0.122 0.000 14.654 0.203 3.897

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A A F A B B

verified

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

size

76 101 162 109 82 101 0 89 195 75

N.S.

1 1.33 2.13 1.43 1.08 1.33 0.00 1.17 2.57 0.99

time (sec)

N/A 0.301 1.690 1.793 0.122 0.111 0.000 0.179 0.213 0.818

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

68 68 111 83 67 90 0 2405 129 93

N.S.

1 1.00 1.63 1.22 0.99 1.32 0.00 35.37 1.90 1.37

time (sec)

N/A 0.281 0.523 1.588 0.038 0.121 0.000 0.731 0.218 1.193

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

43 43 43 56 60 102 0 74 91 125

N.S.

1 1.00 1.00 1.30 1.40 2.37 0.00 1.72 2.12 2.91

time (sec)

N/A 0.257 0.025 0.856 0.036 0.116 0.000 0.208 0.210 0.912

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

42 40 91 38 39 96 0 40 132 44

N.S.

1 0.95 2.17 0.90 0.93 2.29 0.00 0.95 3.14 1.05

time (sec)

N/A 0.239 0.945 2.709 0.036 0.092 0.000 0.163 0.188 0.810

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

95 95 250 101 122 230 0 172 225 292

N.S.

1 1.00 2.63 1.06 1.28 2.42 0.00 1.81 2.37 3.07

time (sec)

N/A 0.325 1.622 3.325 0.038 0.116 0.000 0.237 0.216 0.923

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

79 73 127 80 69 174 0 70 201 72

N.S.

1 0.92 1.61 1.01 0.87 2.20 0.00 0.89 2.54 0.91

time (sec)

N/A 0.270 1.737 5.984 0.034 0.095 0.000 0.186 0.198 0.812

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

165 165 994 145 187 333 0 269 269 378

N.S.

1 1.00 6.02 0.88 1.13 2.02 0.00 1.63 1.63 2.29

time (sec)

N/A 0.396 6.684 9.386 0.042 0.122 0.000 0.255 0.153 0.929

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

122 112 114 119 104 240 0 105 245 107

N.S.

1 0.92 0.93 0.98 0.85 1.97 0.00 0.86 2.01 0.88

time (sec)

N/A 0.308 1.746 17.295 0.041 0.099 0.000 0.204 0.160 1.105

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

205 205 289 184 173 188 0 66584 406 291

N.S.

1 1.00 1.41 0.90 0.84 0.92 0.00 324.80 1.98 1.42

time (sec)

N/A 0.460 5.564 4.288 0.042 0.104 0.000 117.946 0.166 3.686

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

103 125 203 163 113 149 0 128 496 151

N.S.

1 1.21 1.97 1.58 1.10 1.45 0.00 1.24 4.82 1.47

time (sec)

N/A 0.320 2.976 2.722 0.135 0.097 0.000 0.221 0.166 0.836

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F B B B

verified

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

size

133 133 241 144 128 144 0 12476 340 193

N.S.

1 1.00 1.81 1.08 0.96 1.08 0.00 93.80 2.56 1.45

time (sec)

N/A 0.358 3.627 2.254 0.060 0.106 0.000 7.554 0.207 3.125

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

86 86 86 107 111 148 0 144 269 278

N.S.

1 1.00 1.00 1.24 1.29 1.72 0.00 1.67 3.13 3.23

time (sec)

N/A 0.303 0.057 0.882 0.036 0.119 0.000 0.267 0.197 1.328

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

64 59 126 55 56 127 0 57 235 62

N.S.

1 0.92 1.97 0.86 0.88 1.98 0.00 0.89 3.67 0.97

time (sec)

N/A 0.251 1.641 3.612 0.032 0.111 0.000 0.202 0.231 0.811

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F B B B

verified

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

size

141 141 897 140 171 299 0 304 466 581

N.S.

1 1.00 6.36 0.99 1.21 2.12 0.00 2.16 3.30 4.12

time (sec)

N/A 0.369 6.831 5.871 0.048 0.158 0.000 0.279 0.204 1.095

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

113 104 212 106 98 237 0 99 452 103

N.S.

1 0.92 1.88 0.94 0.87 2.10 0.00 0.88 4.00 0.91

time (sec)

N/A 0.300 2.607 10.041 0.050 0.100 0.000 0.209 0.219 0.790

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

229 229 1229 198 250 427 0 373 533 698

N.S.

1 1.00 5.37 0.86 1.09 1.86 0.00 1.63 2.33 3.05

time (sec)

N/A 0.465 7.010 16.484 0.047 0.178 0.000 0.308 0.207 1.112

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

167 154 515 165 142 343 0 143 545 146

N.S.

1 0.92 3.08 0.99 0.85 2.05 0.00 0.86 3.26 0.87

time (sec)

N/A 0.341 2.148 28.849 0.032 0.106 0.000 0.222 0.207 0.932

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

275 275 1017 267 218 224 0 0 591 319

N.S.

1 1.00 3.70 0.97 0.79 0.81 0.00 0.00 2.15 1.16

time (sec)

N/A 0.550 7.174 8.026 0.043 0.102 0.000 0.000 0.223 4.529

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

139 157 263 250 154 186 0 178 780 161

N.S.

1 1.13 1.89 1.80 1.11 1.34 0.00 1.28 5.61 1.16

time (sec)

N/A 0.346 6.192 5.326 0.127 0.126 0.000 0.274 0.155 0.904

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A A F B B B

verified

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

size

180 180 383 217 166 176 0 19074 354 268

N.S.

1 1.00 2.13 1.21 0.92 0.98 0.00 105.97 1.97 1.49

time (sec)

N/A 0.411 4.046 4.220 0.040 0.107 0.000 8.112 0.154 4.448

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A A F A B B

verified

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

size

118 118 352 170 139 175 0 193 426 496

N.S.

1 1.00 2.98 1.44 1.18 1.48 0.00 1.64 3.61 4.20

time (sec)

N/A 0.342 4.690 1.683 0.060 0.126 0.000 0.341 0.155 1.357

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

83 75 162 79 72 159 0 73 312 81

N.S.

1 0.90 1.95 0.95 0.87 1.92 0.00 0.88 3.76 0.98

time (sec)

N/A 0.257 2.235 5.641 0.037 0.097 0.000 0.227 0.178 0.775

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

161 161 1128 157 188 346 0 300 666 670

N.S.

1 1.00 7.01 0.98 1.17 2.15 0.00 1.86 4.14 4.16

time (sec)

N/A 0.400 7.289 9.934 0.043 0.159 0.000 0.382 0.208 1.203

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

137 125 188 133 120 267 0 126 593 132

N.S.

1 0.91 1.37 0.97 0.88 1.95 0.00 0.92 4.33 0.96

time (sec)

N/A 0.318 3.820 17.823 0.040 0.125 0.000 0.255 0.216 0.808

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

274 274 1491 241 304 547 0 479 806 857

N.S.

1 1.00 5.44 0.88 1.11 2.00 0.00 1.75 2.94 3.13

time (sec)

N/A 0.529 7.199 26.997 0.044 0.219 0.000 0.395 0.159 1.243

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

194 178 233 218 171 386 0 177 708 181

N.S.

1 0.92 1.20 1.12 0.88 1.99 0.00 0.91 3.65 0.93

time (sec)

N/A 0.389 4.101 40.719 0.039 0.108 0.000 0.272 0.175 0.959

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD TBD

size

402 402 660 327 387 697 0 647 888 990

N.S.

1 1.00 1.64 0.81 0.96 1.73 0.00 1.61 2.21 2.46

time (sec)

N/A 0.635 7.810 80.345 0.046 0.242 0.000 0.426 0.186 1.235

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

274 251 289 358 658 370 0 464 456 683

N.S.

1 0.92 1.05 1.31 2.40 1.35 0.00 1.69 1.66 2.49

time (sec)

N/A 1.283 3.367 16.872 0.139 0.119 0.000 0.230 0.174 4.071

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A B A F A B B

verified

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

size

168 166 139 202 364 261 0 241 258 324

N.S.

1 0.99 0.83 1.20 2.17 1.55 0.00 1.43 1.54 1.93

time (sec)

N/A 0.874 0.921 3.984 0.143 0.107 0.000 0.219 0.212 3.818

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

90 90 79 101 141 185 0 118 116 110

N.S.

1 1.00 0.88 1.12 1.57 2.06 0.00 1.31 1.29 1.22

time (sec)

N/A 0.511 0.357 1.304 0.113 0.110 0.000 0.213 0.218 0.968

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

66 66 75 63 107 183 0 94 86 174

N.S.

1 1.00 1.14 0.95 1.62 2.77 0.00 1.42 1.30 2.64

time (sec)

N/A 0.388 0.259 1.075 0.119 0.116 0.000 0.206 0.224 1.065

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

122 122 179 140 215 270 0 209 132 764

N.S.

1 1.00 1.47 1.15 1.76 2.21 0.00 1.71 1.08 6.26

time (sec)

N/A 0.559 1.124 1.883 0.136 0.134 0.000 0.215 0.223 1.675

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

158 241 249 208 280 216 0 287 336 313

N.S.

1 1.53 1.58 1.32 1.77 1.37 0.00 1.82 2.13 1.98

time (sec)

N/A 0.610 3.185 8.120 0.118 0.106 0.000 0.170 0.232 1.375

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

94 146 170 122 144 122 0 172 176 147

N.S.

1 1.55 1.81 1.30 1.53 1.30 0.00 1.83 1.87 1.56

time (sec)

N/A 0.379 0.717 1.963 0.117 0.108 0.000 0.150 0.212 1.030

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

50 49 47 48 47 95 0 54 82 39

N.S.

1 0.98 0.94 0.96 0.94 1.90 0.00 1.08 1.64 0.78

time (sec)

N/A 0.266 0.513 1.119 0.032 0.100 0.000 0.156 0.193 0.845

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F A B B

verified

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

size

108 103 95 96 97 208 0 112 227 102

N.S.

1 0.95 0.88 0.89 0.90 1.93 0.00 1.04 2.10 0.94

time (sec)

N/A 0.316 2.457 2.243 0.034 0.104 0.000 0.160 0.172 0.926

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

169 160 150 165 168 385 0 183 408 167

N.S.

1 0.95 0.89 0.98 0.99 2.28 0.00 1.08 2.41 0.99

time (sec)

N/A 0.376 5.099 6.944 0.070 0.106 0.000 0.160 0.172 1.401

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

297 405 664 383 799 619 0 575 1222 757

N.S.

1 1.36 2.24 1.29 2.69 2.08 0.00 1.94 4.11 2.55

time (sec)

N/A 1.513 6.575 62.463 0.135 0.153 0.000 0.203 1.190 2.715

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

217 304 392 269 507 444 0 413 886 481

N.S.

1 1.40 1.81 1.24 2.34 2.05 0.00 1.90 4.08 2.22

time (sec)

N/A 0.985 3.730 16.891 0.127 0.135 0.000 0.195 0.291 2.039

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

148 207 246 171 293 292 0 281 620 255

N.S.

1 1.40 1.66 1.16 1.98 1.97 0.00 1.90 4.19 1.72

time (sec)

N/A 0.605 3.164 4.238 0.122 0.107 0.000 0.197 0.207 1.171

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

72 67 109 67 74 293 0 79 235 79

N.S.

1 0.93 1.51 0.93 1.03 4.07 0.00 1.10 3.26 1.10

time (sec)

N/A 0.279 0.722 1.543 0.042 0.099 0.000 0.177 0.224 0.945

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

140 131 244 127 144 442 0 154 488 150

N.S.

1 0.94 1.74 0.91 1.03 3.16 0.00 1.10 3.49 1.07

time (sec)

N/A 0.356 3.476 2.630 0.039 0.111 0.000 0.188 0.163 1.041

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

219 206 589 205 225 787 0 235 772 237

N.S.

1 0.94 2.69 0.94 1.03 3.59 0.00 1.07 3.53 1.08

time (sec)

N/A 0.445 7.025 4.701 0.038 0.129 0.000 0.194 0.171 2.170

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

382 498 746 466 1088 932 0 733 2081 1068

N.S.

1 1.30 1.95 1.22 2.85 2.44 0.00 1.92 5.45 2.80

time (sec)

N/A 2.219 6.429 120.932 0.159 0.191 0.000 0.263 5.697 2.989

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

285 378 521 331 744 705 0 613 1663 717

N.S.

1 1.33 1.83 1.16 2.61 2.47 0.00 2.15 5.84 2.52

time (sec)

N/A 1.403 6.303 36.311 0.131 0.159 0.000 0.250 0.394 2.569

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

206 270 316 236 463 526 0 372 1517 433

N.S.

1 1.31 1.53 1.15 2.25 2.55 0.00 1.81 7.36 2.10

time (sec)

N/A 0.784 2.607 9.989 0.146 0.132 0.000 0.238 0.206 1.809

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

95 86 241 85 108 565 0 99 452 99

N.S.

1 0.91 2.54 0.89 1.14 5.95 0.00 1.04 4.76 1.04

time (sec)

N/A 0.294 2.337 2.273 0.039 0.114 0.000 0.213 0.175 0.893

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

178 165 456 158 192 811 0 185 798 200

N.S.

1 0.93 2.56 0.89 1.08 4.56 0.00 1.04 4.48 1.12

time (sec)

N/A 0.385 3.668 3.975 0.039 0.138 0.000 0.221 0.192 1.438

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A B F A B B

verified

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

size

265 248 494 246 281 1018 0 274 1176 297

N.S.

1 0.94 1.86 0.93 1.06 3.84 0.00 1.03 4.44 1.12

time (sec)

N/A 0.500 4.292 7.074 0.046 0.146 0.000 0.242 0.201 2.608

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

366 464 590 425 997 1053 0 670 3021 962

N.S.

1 1.27 1.61 1.16 2.72 2.88 0.00 1.83 8.25 2.63

time (sec)

N/A 2.032 3.579 89.269 0.150 0.283 0.000 0.302 6.486 2.865

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

264 329 395 288 662 802 0 486 2289 597

N.S.

1 1.25 1.50 1.09 2.51 3.04 0.00 1.84 8.67 2.26

time (sec)

N/A 1.016 2.400 29.537 0.129 0.162 0.000 0.280 0.242 2.277

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

116 103 259 103 140 874 0 115 710 131

N.S.

1 0.89 2.23 0.89 1.21 7.53 0.00 0.99 6.12 1.13

time (sec)

N/A 0.317 2.081 3.734 0.047 0.155 0.000 0.242 0.214 1.023

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

205 188 528 184 228 1235 0 227 1158 232

N.S.

1 0.92 2.58 0.90 1.11 6.02 0.00 1.11 5.65 1.13

time (sec)

N/A 0.419 1.824 7.048 0.041 0.174 0.000 0.270 0.244 2.294

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A B A A B F A B B

verified

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

size

300 279 673 280 325 1536 0 303 1650 337

N.S.

1 0.93 2.24 0.93 1.08 5.12 0.00 1.01 5.50 1.12

time (sec)

N/A 0.554 1.989 12.543 0.045 0.209 0.000 0.273 0.273 2.887

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A C A B B F A B B

verified

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

size

26 26 41 26 50 55 0 44 34 38

N.S.

1 1.00 1.58 1.00 1.92 2.12 0.00 1.69 1.31 1.46

time (sec)

N/A 0.306 0.066 0.483 0.118 0.090 0.000 0.159 0.159 0.949

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

229 229 205 0 0 0 0 0 86 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 0.38 0.00

time (sec)

N/A 0.733 1.726 0.000 0.000 0.000 0.000 0.000 0.171 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

179 179 166 0 0 0 0 0 59 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.33 0.00

time (sec)

N/A 0.500 0.797 0.000 0.000 0.000 0.000 0.000 0.171 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

109 109 109 0 0 0 0 0 32 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.29 0.00

time (sec)

N/A 0.362 0.208 0.000 0.000 0.000 0.000 0.000 0.167 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

765 580 0 0 0 0 0 0 23 0

N.S.

1 0.76 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.00

time (sec)

N/A 2.419 0.000 0.000 0.000 0.000 0.000 0.000 0.214 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

21 21 23 21 23 23 20 23 23 23

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.10 1.10

time (sec)

N/A 2.769 4.133 2.125 1.317 0.134 66.264 0.514 0.204 3.719

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

435 476 910 0 0 0 0 0 23 0

N.S.

1 1.09 2.09 0.00 0.00 0.00 0.00 0.00 0.05 0.00

time (sec)

N/A 0.909 6.502 0.000 0.000 0.000 0.000 0.000 0.163 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

276 281 270 0 0 0 0 0 23 0

N.S.

1 1.02 0.98 0.00 0.00 0.00 0.00 0.00 0.08 0.00

time (sec)

N/A 0.484 0.798 0.000 0.000 0.000 0.000 0.000 0.158 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

49 48 48 0 0 0 0 0 23 0

N.S.

1 0.98 0.98 0.00 0.00 0.00 0.00 0.00 0.47 0.00

time (sec)

N/A 0.234 4.257 0.000 0.000 0.000 0.000 0.000 0.158 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

141 147 78 0 0 0 0 0 23 0

N.S.

1 1.04 0.55 0.00 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 0.302 6.395 0.000 0.000 0.000 0.000 0.000 0.174 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

21 21 23 21 23 32 0 23 23 23

N.S.

1 1.00 1.10 1.00 1.10 1.52 0.00 1.10 1.10 1.10

time (sec)

N/A 2.332 3.141 5.200 2.387 0.091 0.000 0.952 0.214 3.632

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

19 19 21 19 21 21 19 21 21 21

N.S.

1 1.00 1.11 1.00 1.11 1.11 1.00 1.11 1.11 1.11

time (sec)

N/A 1.295 1.739 1.244 1.709 0.084 7.200 0.788 0.196 1.455

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

19 19 21 19 21 21 19 21 21 23

N.S.

1 1.00 1.11 1.00 1.11 1.11 1.00 1.11 1.11 1.21

time (sec)

N/A 0.825 2.794 2.165 1.457 0.080 5.148 0.619 0.162 1.010

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

21 21 23 21 23 23 20 23 23 23

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.10 1.10

time (sec)

N/A 2.110 16.379 2.170 3.154 0.098 61.961 0.907 0.158 2.878

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