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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 A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 165 119 240 362 3465 0 310 535

N.S.

1 1.11 0.80 1.61 2.43 23.26 0.00 2.08 3.59

time (sec)

N/A 0.350 11.476 6.984 0.280 0.282 0.000 0.405 1.996

Problem 102

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

67 59 67 227 71 786 0 347 1050

N.S.

1 0.88 1.00 3.39 1.06 11.73 0.00 5.18 15.67

time (sec)

N/A 0.263 0.253 21.438 0.187 0.271 0.000 0.430 2.036

Problem 103

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

198 197 158 291 553 6114 0 485 951

N.S.

1 0.99 0.80 1.47 2.79 30.88 0.00 2.45 4.80

time (sec)

N/A 0.408 13.015 43.363 0.298 0.318 0.000 0.408 1.988

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 91 218 269 1847 1185 0 447 1424

N.S.

1 0.89 2.14 2.64 18.11 11.62 0.00 4.38 13.96

time (sec)

N/A 0.304 2.891 80.580 0.217 0.264 0.000 0.436 1.956

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 153 115 273 514 2180 0 0 967

N.S.

1 1.28 0.96 2.28 4.28 18.17 0.00 0.00 8.06

time (sec)

N/A 0.363 0.948 11.204 0.327 0.303 0.000 0.000 2.503

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 75 79 230 0 1850 0 0 2194

N.S.

1 0.94 0.99 2.88 0.00 23.12 0.00 0.00 27.42

time (sec)

N/A 0.318 0.564 3.968 0.000 0.298 0.000 0.000 3.439

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 97 77 159 316 948 0 0 880

N.S.

1 1.26 1.00 2.06 4.10 12.31 0.00 0.00 11.43

time (sec)

N/A 0.305 0.745 1.238 0.298 0.288 0.000 0.000 2.556

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 51 53 149 0 766 0 0 154

N.S.

1 0.96 1.00 2.81 0.00 14.45 0.00 0.00 2.91

time (sec)

N/A 0.246 0.136 0.576 0.000 0.286 0.000 0.000 2.240

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 36 102 0 511 0 0 147

N.S.

1 1.00 1.00 2.83 0.00 14.19 0.00 0.00 4.08

time (sec)

N/A 0.228 0.046 0.904 0.000 0.268 0.000 0.000 0.279

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 32 114 36 455 0 0 81

N.S.

1 1.00 1.00 3.56 1.12 14.22 0.00 0.00 2.53

time (sec)

N/A 0.242 0.550 3.195 0.276 0.286 0.000 0.000 2.056

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 53 55 144 0 540 0 0 449

N.S.

1 0.96 1.00 2.62 0.00 9.82 0.00 0.00 8.16

time (sec)

N/A 0.255 0.312 8.707 0.000 0.293 0.000 0.000 2.298

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 48 50 197 63 649 0 0 176

N.S.

1 0.96 1.00 3.94 1.26 12.98 0.00 0.00 3.52

time (sec)

N/A 0.250 0.567 21.085 0.300 0.284 0.000 0.000 2.221

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 94 79 236 0 1584 0 0 1012

N.S.

1 1.09 0.92 2.74 0.00 18.42 0.00 0.00 11.77

time (sec)

N/A 0.303 0.769 50.330 0.000 0.294 0.000 0.000 2.597

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 70 71 252 140 2032 0 0 252

N.S.

1 0.93 0.95 3.36 1.87 27.09 0.00 0.00 3.36

time (sec)

N/A 0.281 0.868 115.364 0.301 0.298 0.000 0.000 2.238

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 120 111 378 0 6934 0 0 0

N.S.

1 0.94 0.87 2.95 0.00 54.17 0.00 0.00 0.00

time (sec)

N/A 0.367 1.304 26.642 0.000 0.344 0.000 0.000 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 162 110 386 840 4324 0 0 0

N.S.

1 1.16 0.79 2.76 6.00 30.89 0.00 0.00 0.00

time (sec)

N/A 0.358 1.606 4.574 0.384 0.344 0.000 0.000 0.000

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 96 84 286 0 3502 0 0 0

N.S.

1 0.95 0.83 2.83 0.00 34.67 0.00 0.00 0.00

time (sec)

N/A 0.327 0.853 1.817 0.000 0.355 0.000 0.000 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 81 78 252 0 2041 0 0 0

N.S.

1 0.98 0.94 3.04 0.00 24.59 0.00 0.00 0.00

time (sec)

N/A 0.256 0.340 4.077 0.000 0.295 0.000 0.000 0.000

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 64 63 210 125 1515 0 0 0

N.S.

1 0.97 0.95 3.18 1.89 22.95 0.00 0.00 0.00

time (sec)

N/A 0.248 1.028 14.326 0.326 0.296 0.000 0.000 0.000

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 70 69 183 0 1555 0 0 0

N.S.

1 0.97 0.96 2.54 0.00 21.60 0.00 0.00 0.00

time (sec)

N/A 0.261 0.193 35.269 0.000 0.286 0.000 0.000 0.000

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 75 83 259 127 1443 0 0 0

N.S.

1 0.97 1.08 3.36 1.65 18.74 0.00 0.00 0.00

time (sec)

N/A 0.258 1.020 73.200 0.342 0.284 0.000 0.000 0.000

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 107 203 273 0 2140 0 0 0

N.S.

1 1.05 1.99 2.68 0.00 20.98 0.00 0.00 0.00

time (sec)

N/A 0.306 0.641 136.479 0.000 0.345 0.000 0.000 0.000

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 92 102 306 209 2869 0 0 0

N.S.

1 0.95 1.05 3.15 2.15 29.58 0.00 0.00 0.00

time (sec)

N/A 0.314 1.387 258.305 0.393 0.315 0.000 0.000 0.000

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 163 265 351 0 6396 0 0 0

N.S.

1 1.05 1.71 2.26 0.00 41.26 0.00 0.00 0.00

time (sec)

N/A 0.399 1.672 0.304 0.000 0.373 0.000 0.000 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

198 238 164 501 1806 13887 0 0 0

N.S.

1 1.20 0.83 2.53 9.12 70.14 0.00 0.00 0.00

time (sec)

N/A 0.470 2.408 27.890 0.568 0.458 0.000 0.000 0.000

Problem 126

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 Yes TBD TBD TBD TBD TBD

size

154 146 136 375 0 11392 0 0 0

N.S.

1 0.95 0.88 2.44 0.00 73.97 0.00 0.00 0.00

time (sec)

N/A 0.393 2.223 7.195 0.000 0.433 0.000 0.000 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 154 134 394 0 7909 0 0 0

N.S.

1 1.07 0.93 2.74 0.00 54.92 0.00 0.00 0.00

time (sec)

N/A 0.321 1.223 19.445 0.000 0.370 0.000 0.000 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 99 77 284 366 5840 0 0 0

N.S.

1 1.03 0.80 2.96 3.81 60.83 0.00 0.00 0.00

time (sec)

N/A 0.265 2.613 63.990 0.401 0.344 0.000 0.000 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 121 123 342 0 6614 0 0 0

N.S.

1 0.94 0.95 2.65 0.00 51.27 0.00 0.00 0.00

time (sec)

N/A 0.313 0.832 103.406 0.000 0.364 0.000 0.000 0.000

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 113 115 334 360 5659 0 0 0

N.S.

1 0.98 1.00 2.90 3.13 49.21 0.00 0.00 0.00

time (sec)

N/A 0.283 1.962 185.475 0.456 0.336 0.000 0.000 0.000

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 107 87 276 0 5077 0 0 0

N.S.

1 1.03 0.84 2.65 0.00 48.82 0.00 0.00 0.00

time (sec)

N/A 0.279 0.466 0.221 0.000 0.323 0.000 0.000 0.000

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 143 128 376 332 5233 0 0 0

N.S.

1 1.09 0.98 2.87 2.53 39.95 0.00 0.00 0.00

time (sec)

N/A 0.319 1.960 0.189 0.489 0.340 0.000 0.000 0.000

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 170 317 389 0 8070 0 0 0

N.S.

1 1.09 2.03 2.49 0.00 51.73 0.00 0.00 0.00

time (sec)

N/A 0.400 3.688 0.207 0.000 0.377 0.000 0.000 0.000

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 49 97 68 199 339 82 134 50

N.S.

1 0.91 1.80 1.26 3.69 6.28 1.52 2.48 0.93

time (sec)

N/A 0.351 0.055 0.079 0.209 0.272 0.142 0.316 1.863

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 59 43 71 168 1205 88 92 53

N.S.

1 1.20 0.88 1.45 3.43 24.59 1.80 1.88 1.08

time (sec)

N/A 0.362 0.290 0.073 0.286 0.268 0.116 0.327 0.110

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 65 45 105 160 54 86 34

N.S.

1 1.00 1.81 1.25 2.92 4.44 1.50 2.39 0.94

time (sec)

N/A 0.274 0.036 0.064 0.201 0.271 0.104 0.305 1.803

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 40 41 49 76 399 60 57 37

N.S.

1 1.29 1.32 1.58 2.45 12.87 1.94 1.84 1.19

time (sec)

N/A 0.273 0.038 0.084 0.276 0.270 0.091 0.287 1.795

Problem 138

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 28 22 31 37 20 29 18

N.S.

1 1.00 1.47 1.16 1.63 1.95 1.05 1.53 0.95

time (sec)

N/A 0.168 0.001 0.040 0.190 0.255 0.089 0.290 0.069

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 39 33 24 35 70 0 46 228

N.S.

1 1.56 1.32 0.96 1.40 2.80 0.00 1.84 9.12

time (sec)

N/A 0.274 0.055 0.232 0.198 0.264 0.000 0.286 1.854

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 32 27 31 38 90 30 25

N.S.

1 1.00 1.78 1.50 1.72 2.11 5.00 1.67 1.39

time (sec)

N/A 0.214 0.035 0.115 0.199 0.271 4.275 0.321 1.784

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 44 39 35 106 407 0 58 76

N.S.

1 1.42 1.26 1.13 3.42 13.13 0.00 1.87 2.45

time (sec)

N/A 0.280 0.131 0.245 0.197 0.272 0.000 0.310 1.818

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 61 39 105 156 0 86 162

N.S.

1 1.00 1.69 1.08 2.92 4.33 0.00 2.39 4.50

time (sec)

N/A 0.277 0.050 0.212 0.200 0.254 0.000 0.330 1.814

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 63 51 56 206 1216 0 93 177

N.S.

1 1.29 1.04 1.14 4.20 24.82 0.00 1.90 3.61

time (sec)

N/A 0.366 0.377 0.273 0.190 0.269 0.000 0.338 1.827

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 81 190 135 369 796 165 300 91

N.S.

1 0.98 2.29 1.63 4.45 9.59 1.99 3.61 1.10

time (sec)

N/A 0.301 0.101 0.118 0.205 0.259 0.211 0.380 0.167

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 66 130 333 3441 170 191 100

N.S.

1 1.00 0.87 1.71 4.38 45.28 2.24 2.51 1.32

time (sec)

N/A 0.303 0.500 0.096 0.279 0.302 0.191 0.376 0.214

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 65 137 97 231 483 117 218 67

N.S.

1 1.03 2.17 1.54 3.67 7.67 1.86 3.46 1.06

time (sec)

N/A 0.281 0.082 0.093 0.198 0.259 0.155 0.346 1.829

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 60 50 92 186 1638 122 116 76

N.S.

1 1.05 0.88 1.61 3.26 28.74 2.14 2.04 1.33

time (sec)

N/A 0.262 0.370 0.103 0.280 0.285 0.127 0.334 1.835

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 47 65 60 114 201 68 103 47

N.S.

1 1.09 1.51 1.40 2.65 4.67 1.58 2.40 1.09

time (sec)

N/A 0.230 0.894 0.061 0.184 0.274 0.112 0.296 1.841

Problem 149

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

49 54 48 59 104 668 0 141 210

N.S.

1 1.10 0.98 1.20 2.12 13.63 0.00 2.88 4.29

time (sec)

N/A 0.275 0.162 0.176 0.272 0.266 0.000 0.337 1.961

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 40 64 36 64 97 0 71 59

N.S.

1 1.11 1.78 1.00 1.78 2.69 0.00 1.97 1.64

time (sec)

N/A 0.270 0.122 0.254 0.197 0.269 0.000 0.346 1.826

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

52 55 50 62 134 677 0 141 211

N.S.

1 1.06 0.96 1.19 2.58 13.02 0.00 2.71 4.06

time (sec)

N/A 0.287 0.190 0.196 0.197 0.263 0.000 0.375 0.236

Problem 152

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

43 47 65 43 114 197 0 103 175

N.S.

1 1.09 1.51 1.00 2.65 4.58 0.00 2.40 4.07

time (sec)

N/A 0.276 0.543 0.166 0.209 0.244 0.000 0.368 0.155

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

72 72 58 77 236 1649 0 118 197

N.S.

1 1.00 0.81 1.07 3.28 22.90 0.00 1.64 2.74

time (sec)

N/A 0.307 0.472 0.219 0.186 0.274 0.000 0.417 1.919

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 65 98 58 231 473 0 218 529

N.S.

1 1.03 1.56 0.92 3.67 7.51 0.00 3.46 8.40

time (sec)

N/A 0.293 0.128 0.168 0.191 0.255 0.000 0.418 0.184

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

92 89 74 92 390 3454 0 192 362

N.S.

1 0.97 0.80 1.00 4.24 37.54 0.00 2.09 3.93

time (sec)

N/A 0.317 0.566 0.244 0.199 0.305 0.000 0.461 0.244

Problem 156

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

114 109 123 218 583 1563 260 534 138

N.S.

1 0.96 1.08 1.91 5.11 13.71 2.28 4.68 1.21

time (sec)

N/A 0.315 1.723 0.169 0.208 0.273 0.304 0.513 0.229

Problem 157

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

107 104 98 205 540 7502 279 309 155

N.S.

1 0.97 0.92 1.92 5.05 70.11 2.61 2.89 1.45

time (sec)

N/A 0.314 0.354 0.144 0.289 0.336 0.275 0.462 1.881

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 93 108 164 400 1036 192 418 106

N.S.

1 0.99 1.15 1.74 4.26 11.02 2.04 4.45 1.13

time (sec)

N/A 0.302 2.004 0.130 0.207 0.273 0.224 0.431 1.865

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 83 76 151 351 4298 211 216 123

N.S.

1 1.00 0.92 1.82 4.23 51.78 2.54 2.60 1.48

time (sec)

N/A 0.282 0.308 0.130 0.282 0.296 0.186 0.401 1.854

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 75 95 112 239 567 126 241 86

N.S.

1 1.01 1.28 1.51 3.23 7.66 1.70 3.26 1.16

time (sec)

N/A 0.253 0.717 0.094 0.196 0.273 0.158 0.306 0.159

Problem 161

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

72 74 67 80 214 2381 0 267 380

N.S.

1 1.03 0.93 1.11 2.97 33.07 0.00 3.71 5.28

time (sec)

N/A 0.288 0.620 0.208 0.276 0.295 0.000 0.390 0.364

Problem 162

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

59 60 81 59 147 341 0 135 218

N.S.

1 1.02 1.37 1.00 2.49 5.78 0.00 2.29 3.69

time (sec)

N/A 0.280 2.613 0.199 0.197 0.262 0.000 0.429 1.868

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

72 70 63 77 203 1686 0 274 327

N.S.

1 0.97 0.88 1.07 2.82 23.42 0.00 3.81 4.54

time (sec)

N/A 0.293 0.487 0.246 0.285 0.268 0.000 0.468 2.913

Problem 164

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

59 60 82 56 147 341 0 135 219

N.S.

1 1.02 1.39 0.95 2.49 5.78 0.00 2.29 3.71

time (sec)

N/A 0.278 1.412 0.244 0.209 0.268 0.000 0.492 1.839

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

83 83 67 90 264 2393 0 267 381

N.S.

1 1.00 0.81 1.08 3.18 28.83 0.00 3.22 4.59

time (sec)

N/A 0.310 0.648 0.245 0.212 0.294 0.000 0.523 0.360

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 76 100 72 239 557 0 241 568

N.S.

1 1.03 1.35 0.97 3.23 7.53 0.00 3.26 7.68

time (sec)

N/A 0.302 1.620 0.216 0.205 0.265 0.000 0.567 1.893

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

103 100 76 106 420 4305 0 217 380

N.S.

1 0.97 0.74 1.03 4.08 41.80 0.00 2.11 3.69

time (sec)

N/A 0.326 0.266 0.270 0.208 0.311 0.000 0.619 0.274

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 108 128 179 410 1176 209 447 133

N.S.

1 0.98 1.16 1.63 3.73 10.69 1.90 4.06 1.21

time (sec)

N/A 0.295 1.195 0.134 0.207 0.279 0.228 0.309 0.184

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

160 155 170 262 624 2133 308 721 188

N.S.

1 0.97 1.06 1.64 3.90 13.33 1.92 4.51 1.18

time (sec)

N/A 0.326 2.720 0.206 0.212 0.297 0.319 0.359 1.950

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 60 79 133 742 415 132 72

N.S.

1 1.00 0.91 1.20 2.02 11.24 6.29 2.00 1.09

time (sec)

N/A 0.312 0.212 0.109 0.277 0.301 10.068 0.346 0.245

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 69 66 87 509 777 428 87 56

N.S.

1 1.17 1.12 1.47 8.63 13.17 7.25 1.47 0.95

time (sec)

N/A 0.300 0.242 0.136 0.389 0.289 4.762 0.325 1.864

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 52 44 49 82 118 306 96 46

N.S.

1 1.13 0.96 1.07 1.78 2.57 6.65 2.09 1.00

time (sec)

N/A 0.311 0.052 0.076 0.278 0.298 2.859 0.351 1.830

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 54 47 72 215 486 253 65 38

N.S.

1 1.17 1.02 1.57 4.67 10.57 5.50 1.41 0.83

time (sec)

N/A 0.268 0.039 0.120 0.302 0.288 2.081 0.313 0.099

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 47 35 44 58 82 146 61 43

N.S.

1 1.12 0.83 1.05 1.38 1.95 3.48 1.45 1.02

time (sec)

N/A 0.254 0.033 0.061 0.200 0.265 1.932 0.307 1.815

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 65 71 57 484 240 63 37

N.S.

1 1.00 1.44 1.58 1.27 10.76 5.33 1.40 0.82

time (sec)

N/A 0.320 0.108 0.104 0.278 0.283 1.999 0.296 0.085

Problem 176

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

60 65 55 65 101 118 0 97 194

N.S.

1 1.08 0.92 1.08 1.68 1.97 0.00 1.62 3.23

time (sec)

N/A 0.302 0.082 0.162 0.200 0.307 0.000 0.310 2.085

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 71 67 89 329 784 0 89 402

N.S.

1 1.18 1.12 1.48 5.48 13.07 0.00 1.48 6.70

time (sec)

N/A 0.298 0.234 0.196 0.347 0.307 0.000 0.323 2.209

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

85 82 60 88 159 747 0 133 313

N.S.

1 0.96 0.71 1.04 1.87 8.79 0.00 1.56 3.68

time (sec)

N/A 0.329 0.212 0.204 0.217 0.340 0.000 0.346 2.244

Problem 179

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

82 96 91 109 1038 2368 0 147 519

N.S.

1 1.17 1.11 1.33 12.66 28.88 0.00 1.79 6.33

time (sec)

N/A 0.363 0.748 0.228 0.419 0.308 0.000 0.352 2.206

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 84 69 91 217 1141 102 194 170

N.S.

1 1.01 0.83 1.10 2.61 13.75 1.23 2.34 2.05

time (sec)

N/A 0.331 0.557 0.114 0.299 0.329 74.908 0.430 2.317

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 105 90 104 1010 1950 0 195 1655

N.S.

1 1.18 1.01 1.17 11.35 21.91 0.00 2.19 18.60

time (sec)

N/A 0.305 0.616 0.192 0.522 0.316 0.000 0.380 2.440

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 71 57 84 170 629 92 149 210

N.S.

1 0.99 0.79 1.17 2.36 8.74 1.28 2.07 2.92

time (sec)

N/A 0.312 0.500 0.106 0.216 0.291 42.147 0.364 0.399

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 99 86 100 614 2025 0 177 106

N.S.

1 1.16 1.01 1.18 7.22 23.82 0.00 2.08 1.25

time (sec)

N/A 0.314 0.445 0.183 0.424 0.311 0.000 0.357 0.606

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 55 86 170 623 92 149 129

N.S.

1 1.00 0.81 1.26 2.50 9.16 1.35 2.19 1.90

time (sec)

N/A 0.290 0.447 0.102 0.218 0.284 58.576 0.339 2.048

Problem 185

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

89 106 97 103 206 1942 0 195 110

N.S.

1 1.19 1.09 1.16 2.31 21.82 0.00 2.19 1.24

time (sec)

N/A 0.283 0.587 0.183 0.319 0.316 0.000 0.304 2.144

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 94 83 110 235 1148 0 195 0

N.S.

1 0.99 0.87 1.16 2.47 12.08 0.00 2.05 0.00

time (sec)

N/A 0.335 2.130 0.254 0.217 0.356 0.000 0.359 0.000

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 134 111 120 976 3725 0 336 0

N.S.

1 1.13 0.93 1.01 8.20 31.30 0.00 2.82 0.00

time (sec)

N/A 0.382 1.851 0.272 0.434 0.337 0.000 0.369 0.000

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

124 116 93 131 402 3468 0 323 0

N.S.

1 0.94 0.75 1.06 3.24 27.97 0.00 2.60 0.00

time (sec)

N/A 0.358 1.023 0.332 0.223 0.451 0.000 0.395 0.000

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 169 139 142 2345 8482 0 281 0

N.S.

1 1.06 0.87 0.89 14.75 53.35 0.00 1.77 0.00

time (sec)

N/A 0.460 1.637 0.344 0.677 0.379 0.000 0.410 0.000

Problem 190

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 173 144 157 3354 7528 0 408 2669

N.S.

1 1.20 1.00 1.09 23.29 52.28 0.00 2.83 18.53

time (sec)

N/A 0.405 1.341 0.304 1.236 0.395 0.000 0.524 2.553

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 105 91 127 376 2584 0 245 416

N.S.

1 0.96 0.83 1.17 3.45 23.71 0.00 2.25 3.82

time (sec)

N/A 0.352 1.220 0.154 0.238 0.304 0.000 0.472 0.745

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 157 135 148 2432 7757 0 384 2574

N.S.

1 1.15 0.99 1.08 17.75 56.62 0.00 2.80 18.79

time (sec)

N/A 0.371 1.270 0.299 0.947 0.399 0.000 0.460 2.373

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 95 80 115 384 2611 0 245 397

N.S.

1 0.97 0.82 1.17 3.92 26.64 0.00 2.50 4.05

time (sec)

N/A 0.332 0.514 0.168 0.235 0.310 0.000 0.440 2.454

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 162 137 152 1472 7791 0 388 255

N.S.

1 1.18 1.00 1.11 10.74 56.87 0.00 2.83 1.86

time (sec)

N/A 0.349 1.257 0.302 0.599 0.374 0.000 0.424 3.907

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 91 77 116 378 2554 0 245 235

N.S.

1 0.97 0.82 1.23 4.02 27.17 0.00 2.61 2.50

time (sec)

N/A 0.305 0.602 0.146 0.242 0.315 0.000 0.393 2.754

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 170 147 156 507 7496 0 409 260

N.S.

1 1.20 1.04 1.10 3.57 52.79 0.00 2.88 1.83

time (sec)

N/A 0.349 0.345 0.264 0.380 0.366 0.000 0.331 0.809

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 134 117 161 498 4800 0 295 0

N.S.

1 0.97 0.85 1.17 3.61 34.78 0.00 2.14 0.00

time (sec)

N/A 0.372 1.773 0.526 0.229 0.518 0.000 0.438 0.000

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

178 203 166 167 1944 11865 0 437 0

N.S.

1 1.14 0.93 0.94 10.92 66.66 0.00 2.46 0.00

time (sec)

N/A 0.485 6.803 0.417 0.651 0.443 0.000 0.462 0.000

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

171 160 138 184 770 10720 0 474 0

N.S.

1 0.94 0.81 1.08 4.50 62.69 0.00 2.77 0.00

time (sec)

N/A 0.418 2.083 0.688 0.266 0.706 0.000 0.538 0.000

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

228 248 194 189 4285 22038 0 493 0

N.S.

1 1.09 0.85 0.83 18.79 96.66 0.00 2.16 0.00

time (sec)

N/A 0.556 3.911 0.527 1.076 0.554 0.000 0.562 0.000

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