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2.2.2 Integrals 101 to 200

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 101

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 23 308 0 39 0 0 24

N.S.

1 1.00 0.96 12.83 0.00 1.62 0.00 0.00 1.00

time (sec)

N/A 0.189 0.138 3.383 0.000 0.264 0.000 0.000 21.243

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 55 43 194 0 74 0 0 103

N.S.

1 1.04 0.81 3.66 0.00 1.40 0.00 0.00 1.94

time (sec)

N/A 0.338 0.223 5.353 0.000 0.259 0.000 0.000 23.192

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 86 52 481 0 103 0 0 136

N.S.

1 1.09 0.66 6.09 0.00 1.30 0.00 0.00 1.72

time (sec)

N/A 0.446 0.259 16.418 0.000 0.258 0.000 0.000 23.761

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 117 67 222 0 118 0 0 350

N.S.

1 1.11 0.64 2.11 0.00 1.12 0.00 0.00 3.33

time (sec)

N/A 0.575 0.328 89.889 0.000 0.255 0.000 0.000 24.442

Problem 105

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

106 116 66 204 0 0 0 0 0

N.S.

1 1.09 0.62 1.92 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.427 0.875 22.559 0.000 0.000 0.000 0.000 0.000

Problem 106

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

106 116 76 139 0 0 0 0 0

N.S.

1 1.09 0.72 1.31 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.429 0.507 20.796 0.000 0.000 0.000 0.000 0.000

Problem 107

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

75 82 34 137 0 0 0 0 0

N.S.

1 1.09 0.45 1.83 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.335 0.291 19.631 0.000 0.000 0.000 0.000 0.000

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 77 52 111 0 0 0 0 0

N.S.

1 1.10 0.74 1.59 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.334 0.424 4.717 0.000 0.000 0.000 0.000 0.000

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 37 176 0 155 0 0 0

N.S.

1 1.00 0.84 4.00 0.00 3.52 0.00 0.00 0.00

time (sec)

N/A 0.263 0.278 4.158 0.000 0.098 0.000 0.000 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 62 123 0 103 0 0 0

N.S.

1 1.00 1.29 2.56 0.00 2.15 0.00 0.00 0.00

time (sec)

N/A 0.259 0.361 6.490 0.000 0.093 0.000 0.000 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 78 64 227 0 266 0 0 0

N.S.

1 1.01 0.83 2.95 0.00 3.45 0.00 0.00 0.00

time (sec)

N/A 0.343 0.865 21.935 0.000 0.113 0.000 0.000 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 82 66 154 0 179 0 0 0

N.S.

1 1.06 0.86 2.00 0.00 2.32 0.00 0.00 0.00

time (sec)

N/A 0.339 0.912 39.194 0.000 0.100 0.000 0.000 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

106 112 85 0 0 346 0 0 0

N.S.

1 1.06 0.80 0.00 0.00 3.26 0.00 0.00 0.00

time (sec)

N/A 0.430 1.198 0.000 0.000 0.122 0.000 0.000 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

106 116 86 0 0 235 0 0 0

N.S.

1 1.09 0.81 0.00 0.00 2.22 0.00 0.00 0.00

time (sec)

N/A 0.439 0.839 0.000 0.000 0.111 0.000 0.000 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

190 215 100 441 0 291 0 0 0

N.S.

1 1.13 0.53 2.32 0.00 1.53 0.00 0.00 0.00

time (sec)

N/A 0.932 0.956 105.301 0.000 0.273 0.000 0.000 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 182 84 973 0 280 0 0 0

N.S.

1 1.11 0.51 5.93 0.00 1.71 0.00 0.00 0.00

time (sec)

N/A 0.741 0.550 102.092 0.000 0.269 0.000 0.000 0.000

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 148 70 243 0 268 0 0 0

N.S.

1 1.17 0.55 1.91 0.00 2.11 0.00 0.00 0.00

time (sec)

N/A 0.613 0.328 107.882 0.000 0.265 0.000 0.000 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 118 68 542 0 295 0 0 0

N.S.

1 1.13 0.65 5.21 0.00 2.84 0.00 0.00 0.00

time (sec)

N/A 0.486 0.273 14.649 0.000 0.267 0.000 0.000 0.000

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 27 192 0 53 0 0 95

N.S.

1 1.00 0.96 6.86 0.00 1.89 0.00 0.00 3.39

time (sec)

N/A 0.191 0.198 13.021 0.000 0.271 0.000 0.000 21.343

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 55 35 482 0 76 0 0 93

N.S.

1 1.00 0.64 8.76 0.00 1.38 0.00 0.00 1.69

time (sec)

N/A 0.280 0.242 13.756 0.000 0.248 0.000 0.000 24.217

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 86 55 222 0 104 0 0 302

N.S.

1 1.06 0.68 2.74 0.00 1.28 0.00 0.00 3.73

time (sec)

N/A 0.475 0.292 60.106 0.000 0.248 0.000 0.000 24.172

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 117 62 560 0 131 0 0 383

N.S.

1 1.09 0.58 5.23 0.00 1.22 0.00 0.00 3.58

time (sec)

N/A 0.588 0.360 139.424 0.000 0.272 0.000 0.000 26.084

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

84 84 602 0 0 0 0 0 0

N.S.

1 1.00 7.17 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.329 6.697 0.000 0.000 0.000 0.000 0.000 0.000

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

84 84 65 0 0 0 0 0 0

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.315 0.587 0.000 0.000 0.000 0.000 0.000 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

82 82 278 0 0 0 0 0 0

N.S.

1 1.00 3.39 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.306 1.433 0.000 0.000 0.000 0.000 0.000 0.000

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

72 72 254 0 0 0 0 0 0

N.S.

1 1.00 3.53 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.299 1.398 0.000 0.000 0.000 0.000 0.000 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

85 85 61 0 0 0 0 0 0

N.S.

1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.318 0.562 0.000 0.000 0.000 0.000 0.000 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

85 85 2308 0 0 0 0 0 0

N.S.

1 1.00 27.15 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.308 17.643 0.000 0.000 0.000 0.000 0.000 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 54 47 111 91 46 270 46 46

N.S.

1 0.89 0.77 1.82 1.49 0.75 4.43 0.75 0.75

time (sec)

N/A 0.273 0.807 4.973 0.218 0.263 25.606 0.315 19.646

Problem 130

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

61 54 47 97 80 73 233 80 45

N.S.

1 0.89 0.77 1.59 1.31 1.20 3.82 1.31 0.74

time (sec)

N/A 0.283 0.380 2.831 0.207 0.264 11.059 0.300 19.708

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 42 37 83 69 36 199 36 36

N.S.

1 0.91 0.80 1.80 1.50 0.78 4.33 0.78 0.78

time (sec)

N/A 0.268 0.300 1.531 0.207 0.255 4.835 0.283 19.471

Problem 132

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

46 42 37 69 58 53 162 58 36

N.S.

1 0.91 0.80 1.50 1.26 1.15 3.52 1.26 0.78

time (sec)

N/A 0.274 0.151 0.891 0.195 0.254 2.042 0.287 0.052

Problem 133

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

31 30 27 55 47 26 128 26 26

N.S.

1 0.97 0.87 1.77 1.52 0.84 4.13 0.84 0.84

time (sec)

N/A 0.266 0.091 0.500 0.193 0.259 0.769 0.459 19.392

Problem 134

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

31 30 27 41 36 33 90 36 26

N.S.

1 0.97 0.87 1.32 1.16 1.06 2.90 1.16 0.84

time (sec)

N/A 0.265 0.071 0.345 0.207 0.249 0.359 0.316 0.035

Problem 135

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

30 30 15 27 26 13 53 13 43

N.S.

1 1.00 0.50 0.90 0.87 0.43 1.77 0.43 1.43

time (sec)

N/A 0.178 0.009 0.224 0.194 0.244 0.173 0.293 19.789

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 42 22 84 30 0 28 12

N.S.

1 1.00 3.00 1.57 6.00 2.14 0.00 2.00 0.86

time (sec)

N/A 0.215 0.019 0.345 0.195 0.247 0.000 0.300 20.996

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 23 29 31 233 50 0 38 26

N.S.

1 0.82 1.04 1.11 8.32 1.79 0.00 1.36 0.93

time (sec)

N/A 0.244 0.061 0.569 0.310 0.255 0.000 0.328 0.061

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 54 143 53 974 96 0 63 49

N.S.

1 1.10 2.92 1.08 19.88 1.96 0.00 1.29 1.00

time (sec)

N/A 0.268 0.522 1.181 0.215 0.260 0.000 0.412 0.077

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 31 69 1780 130 0 72 61

N.S.

1 1.00 0.47 1.05 26.97 1.97 0.00 1.09 0.92

time (sec)

N/A 0.279 0.031 2.510 0.376 0.252 0.000 0.297 19.601

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 97 268 89 3846 148 0 85 78

N.S.

1 1.09 3.01 1.00 43.21 1.66 0.00 0.96 0.88

time (sec)

N/A 0.300 0.733 5.290 0.331 0.251 0.000 0.286 0.128

Problem 141

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

44 42 68 74 72 36 597 36 35

N.S.

1 0.95 1.55 1.68 1.64 0.82 13.57 0.82 0.80

time (sec)

N/A 0.289 0.413 2.984 0.220 0.262 11.304 0.304 19.369

Problem 142

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 86 62 66 65 66 434 68 109

N.S.

1 1.13 0.82 0.87 0.86 0.87 5.71 0.89 1.43

time (sec)

N/A 0.382 0.143 1.654 0.209 0.251 4.913 0.296 21.142

Problem 143

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

28 30 48 52 50 26 362 26 26

N.S.

1 1.07 1.71 1.86 1.79 0.93 12.93 0.93 0.93

time (sec)

N/A 0.274 0.091 0.941 0.193 0.251 2.053 0.463 0.053

Problem 144

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

49 54 40 44 43 47 231 46 43

N.S.

1 1.10 0.82 0.90 0.88 0.96 4.71 0.94 0.88

time (sec)

N/A 0.303 0.077 0.536 0.221 0.247 0.822 0.313 19.742

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 30 26 13 133 13 13

N.S.

1 1.00 1.00 2.00 1.73 0.87 8.87 0.87 0.87

time (sec)

N/A 0.232 0.007 0.350 0.218 0.243 0.367 0.277 0.051

Problem 146

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

14 16 27 13 82 14 0 13 14

N.S.

1 1.14 1.93 0.93 5.86 1.00 0.00 0.93 1.00

time (sec)

N/A 0.222 0.008 0.475 0.226 0.260 0.000 0.278 0.061

Problem 147

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

13 13 13 12 53 19 0 13 11

N.S.

1 1.00 1.00 0.92 4.08 1.46 0.00 1.00 0.85

time (sec)

N/A 0.231 0.011 1.240 0.244 0.251 0.000 0.346 19.813

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 27 43 24 656 65 0 41 36

N.S.

1 0.90 1.43 0.80 21.87 2.17 0.00 1.37 1.20

time (sec)

N/A 0.258 0.038 0.919 0.224 0.259 0.000 0.432 19.641

Problem 149

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

42 34 48 46 308 54 0 35 37

N.S.

1 0.81 1.14 1.10 7.33 1.29 0.00 0.83 0.88

time (sec)

N/A 0.278 0.353 5.418 0.231 0.249 0.000 0.322 19.599

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

60 47 54 62 3188 138 0 74 82

N.S.

1 0.78 0.90 1.03 53.13 2.30 0.00 1.23 1.37

time (sec)

N/A 0.285 0.388 2.806 0.282 0.245 0.000 0.297 19.599

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 42 37 82 80 36 447 36 36

N.S.

1 0.91 0.80 1.78 1.74 0.78 9.72 0.78 0.78

time (sec)

N/A 0.291 0.396 5.408 0.210 0.261 25.731 0.341 20.849

Problem 152

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

61 54 47 70 69 63 366 69 45

N.S.

1 0.89 0.77 1.15 1.13 1.03 6.00 1.13 0.74

time (sec)

N/A 0.290 0.221 3.102 0.228 0.259 11.326 0.324 0.068

Problem 153

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

31 30 27 49 47 26 284 26 26

N.S.

1 0.97 0.87 1.58 1.52 0.84 9.16 0.84 0.84

time (sec)

N/A 0.283 0.103 1.610 0.204 0.247 4.921 0.527 19.941

Problem 154

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

46 42 37 48 47 43 202 47 36

N.S.

1 0.91 0.80 1.04 1.02 0.93 4.39 1.02 0.78

time (sec)

N/A 0.282 0.066 0.849 0.206 0.243 2.102 0.358 0.069

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 41 34 13 117 13 13

N.S.

1 1.00 1.00 2.73 2.27 0.87 7.80 0.87 0.87

time (sec)

N/A 0.238 0.009 0.454 0.202 0.254 0.794 0.310 0.053

Problem 156

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

28 23 46 29 92 38 0 36 22

N.S.

1 0.82 1.64 1.04 3.29 1.36 0.00 1.29 0.79

time (sec)

N/A 0.250 0.017 1.060 0.222 0.249 0.000 0.283 0.063

Problem 157

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

13 13 13 14 84 13 0 13 13

N.S.

1 1.00 1.00 1.08 6.46 1.00 0.00 1.00 1.00

time (sec)

N/A 0.250 0.011 2.234 0.213 0.255 0.000 0.348 0.026

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 38 79 39 558 72 0 48 36

N.S.

1 1.12 2.32 1.15 16.41 2.12 0.00 1.41 1.06

time (sec)

N/A 0.303 0.013 5.292 0.215 0.258 0.000 0.437 19.815

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 35 31 41 834 94 0 52 38

N.S.

1 0.81 0.72 0.95 19.40 2.19 0.00 1.21 0.88

time (sec)

N/A 0.275 0.031 10.375 0.322 0.267 0.000 0.328 19.306

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 85 195 71 2237 132 0 73 66

N.S.

1 1.21 2.79 1.01 31.96 1.89 0.00 1.04 0.94

time (sec)

N/A 0.297 0.879 19.832 0.274 0.253 0.000 0.291 19.572

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

136 151 98 221760772 0 290 0 0 0

N.S.

1 1.11 0.72 1630593.91 0.00 2.13 0.00 0.00 0.00

time (sec)

N/A 0.525 0.605 71.553 0.000 0.277 0.000 0.000 0.000

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

110 120 86 85939054 0 281 0 0 0

N.S.

1 1.09 0.78 781264.13 0.00 2.55 0.00 0.00 0.00

time (sec)

N/A 0.402 0.321 16.618 0.000 0.258 0.000 0.000 0.000

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

84 89 70 5537888 0 266 0 0 0

N.S.

1 1.06 0.83 65927.24 0.00 3.17 0.00 0.00 0.00

time (sec)

N/A 0.304 0.202 2.019 0.000 0.259 0.000 0.000 0.000

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

58 58 52 18441891 0 242 0 0 0

N.S.

1 1.00 0.90 317963.64 0.00 4.17 0.00 0.00 0.00

time (sec)

N/A 0.208 0.156 2.068 0.000 0.261 0.000 0.000 0.000

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

24 24 23 57905011 0 39 0 2029 24

N.S.

1 1.00 0.96 2412708.79 0.00 1.62 0.00 84.54 1.00

time (sec)

N/A 0.193 0.023 6.415 0.000 0.258 0.000 13.871 20.158

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 43 194 0 74 0 7875 104

N.S.

1 1.00 0.81 3.66 0.00 1.40 0.00 148.58 1.96

time (sec)

N/A 0.279 0.298 14.079 0.000 0.247 0.000 53.653 23.087

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 84 52 481 0 103 0 18022 136

N.S.

1 1.06 0.66 6.09 0.00 1.30 0.00 228.13 1.72

time (sec)

N/A 0.382 0.385 231.201 0.000 0.254 0.000 181.760 23.298

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 115 67 222 0 118 0 0 350

N.S.

1 1.10 0.64 2.11 0.00 1.12 0.00 0.00 3.33

time (sec)

N/A 0.499 0.509 157.895 0.000 0.277 0.000 0.000 24.201

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

98 108 96 0 0 0 0 0 0

N.S.

1 1.10 0.98 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.410 0.722 0.000 0.000 0.000 0.000 0.000 0.000

Problem 170

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 No TBD TBD TBD TBD TBD

size

69 74 66 364390662 0 0 0 0 0

N.S.

1 1.07 0.96 5281024.09 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.322 0.568 152.693 0.000 0.000 0.000 0.000 0.000

Problem 171

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 No TBD TBD TBD TBD TBD

size

69 74 76 198204147 0 0 0 0 0

N.S.

1 1.07 1.10 2872523.87 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.326 0.776 49.126 0.000 0.000 0.000 0.000 0.000

Problem 172

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 No TBD TBD TBD TBD TBD

size

40 40 34 26159851 0 0 0 0 0

N.S.

1 1.00 0.85 653996.28 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.252 0.352 5.164 0.000 0.000 0.000 0.000 0.000

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

40 40 54 67488705 0 0 0 0 0

N.S.

1 1.00 1.35 1687217.62 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.259 1.559 9.333 0.000 0.000 0.000 0.000 0.000

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

46 46 39 107396897 0 156 0 0 0

N.S.

1 1.00 0.85 2334715.15 0.00 3.39 0.00 0.00 0.00

time (sec)

N/A 0.264 0.348 11.489 0.000 0.097 0.000 0.000 0.000

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 62 123 0 103 0 0 0

N.S.

1 1.00 1.29 2.56 0.00 2.15 0.00 0.00 0.00

time (sec)

N/A 0.265 0.888 27.506 0.000 0.090 0.000 0.000 0.000

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 78 64 227 0 266 0 0 0

N.S.

1 1.01 0.83 2.95 0.00 3.45 0.00 0.00 0.00

time (sec)

N/A 0.343 1.088 145.204 0.000 0.106 0.000 0.000 0.000

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

136 151 99 523275790 0 291 0 0 0

N.S.

1 1.11 0.73 3847616.10 0.00 2.14 0.00 0.00 0.00

time (sec)

N/A 0.528 0.628 204.947 0.000 0.267 0.000 0.000 0.000

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

110 120 84 103475646 0 280 0 0 0

N.S.

1 1.09 0.76 940687.69 0.00 2.55 0.00 0.00 0.00

time (sec)

N/A 0.411 0.355 18.148 0.000 0.275 0.000 0.000 0.000

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

84 89 73 213968312 0 268 0 0 0

N.S.

1 1.06 0.87 2547241.81 0.00 3.19 0.00 0.00 0.00

time (sec)

N/A 0.304 0.345 36.608 0.000 0.265 0.000 0.000 0.000

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

82 87 70 211562444 0 295 0 0 0

N.S.

1 1.06 0.85 2580029.80 0.00 3.60 0.00 0.00 0.00

time (sec)

N/A 0.400 0.347 35.435 0.000 0.270 0.000 0.000 0.000

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 27 192 0 53 0 15292 94

N.S.

1 1.00 0.96 6.86 0.00 1.89 0.00 546.14 3.36

time (sec)

N/A 0.198 0.378 68.588 0.000 0.260 0.000 104.028 22.263

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 55 35 482 0 76 0 0 93

N.S.

1 1.00 0.64 8.76 0.00 1.38 0.00 0.00 1.69

time (sec)

N/A 0.285 0.562 230.854 0.000 0.278 0.000 0.000 23.660

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

81 86 55 0 0 104 0 0 302

N.S.

1 1.06 0.68 0.00 0.00 1.28 0.00 0.00 3.73

time (sec)

N/A 0.394 0.803 0.000 0.000 0.255 0.000 0.000 23.989

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

107 117 62 0 0 131 0 0 383

N.S.

1 1.09 0.58 0.00 0.00 1.22 0.00 0.00 3.58

time (sec)

N/A 0.515 1.054 0.000 0.000 0.255 0.000 0.000 25.365

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 29 98 0 137 0 0 0

N.S.

1 1.00 0.94 3.16 0.00 4.42 0.00 0.00 0.00

time (sec)

N/A 0.181 0.054 0.629 0.000 0.255 0.000 0.000 0.000

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 33 25 99 0 137 0 0 0

N.S.

1 1.32 1.00 3.96 0.00 5.48 0.00 0.00 0.00

time (sec)

N/A 0.241 0.043 0.497 0.000 0.274 0.000 0.000 0.000

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

85 85 2472 0 0 0 0 0 0

N.S.

1 1.00 29.08 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.335 13.908 0.000 0.000 0.000 0.000 0.000 0.000

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

85 85 63 0 0 0 0 0 0

N.S.

1 1.00 0.74 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.324 0.693 0.000 0.000 0.000 0.000 0.000 0.000

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

83 83 567 0 0 0 0 0 0

N.S.

1 1.00 6.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.309 5.282 0.000 0.000 0.000 0.000 0.000 0.000

Problem 190

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

46 42 37 60 58 36 318 36 36

N.S.

1 0.91 0.80 1.30 1.26 0.78 6.91 0.78 0.78

time (sec)

N/A 0.313 0.274 3.158 0.240 0.250 10.970 0.334 19.541

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

293 287 182 0 0 0 0 0 0

N.S.

1 0.98 0.62 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.983 2.756 0.000 0.000 0.000 0.000 0.000 0.000

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 86 84 916 122 921 84 311

N.S.

1 1.00 0.95 0.92 10.07 1.34 10.12 0.92 3.42

time (sec)

N/A 0.266 0.631 0.799 0.292 0.254 1.853 0.279 21.328

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 69 57 414 71 408 56 98

N.S.

1 1.00 1.11 0.92 6.68 1.15 6.58 0.90 1.58

time (sec)

N/A 0.234 0.810 0.532 0.246 0.257 0.667 0.296 20.801

Problem 194

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

43 43 43 40 40 42 153 40 84

N.S.

1 1.00 1.00 0.93 0.93 0.98 3.56 0.93 1.95

time (sec)

N/A 0.203 0.231 0.343 0.247 0.248 0.308 0.287 20.713

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 28 26 68 108 31 333 236 111

N.S.

1 1.08 1.00 2.62 4.15 1.19 12.81 9.08 4.27

time (sec)

N/A 0.232 0.184 1.061 0.288 0.279 4.450 0.303 20.651

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 90 115 454 71 3264 349 252

N.S.

1 1.00 2.50 3.19 12.61 1.97 90.67 9.69 7.00

time (sec)

N/A 0.280 0.125 1.375 0.288 0.261 54.943 0.316 25.174

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 35 63 399 47 0 145 0

N.S.

1 1.00 0.90 1.62 10.23 1.21 0.00 3.72 0.00

time (sec)

N/A 0.291 0.226 1.697 0.224 0.242 0.000 0.310 0.000

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 63 67 189 1773 141 0 2221 0

N.S.

1 0.94 1.00 2.82 26.46 2.10 0.00 33.15 0.00

time (sec)

N/A 0.366 0.632 3.848 0.300 0.259 0.000 0.324 0.000

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 52 58 97 1076 75 0 301 0

N.S.

1 0.87 0.97 1.62 17.93 1.25 0.00 5.02 0.00

time (sec)

N/A 0.314 0.430 3.747 0.237 0.256 0.000 0.320 0.000

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 89 79 257 3879 197 0 8035 0

N.S.

1 0.95 0.84 2.73 41.27 2.10 0.00 85.48 0.00

time (sec)

N/A 0.468 1.347 13.880 0.427 0.259 0.000 0.364 0.000

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