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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 A B C A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

44 42 52 43 67 162 155 67 55

N.S.

1 0.95 1.18 0.98 1.52 3.68 3.52 1.52 1.25

time (sec)

N/A 0.217 0.063 0.780 0.275 0.281 3.950 0.276 1.508

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

79 77 85 118 138 423 2082 119 200

N.S.

1 0.97 1.08 1.49 1.75 5.35 26.35 1.51 2.53

time (sec)

N/A 0.340 0.238 0.862 0.273 0.282 90.367 0.289 1.632

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

127 137 117 280 315 1347 0 231 0

N.S.

1 1.08 0.92 2.20 2.48 10.61 0.00 1.82 0.00

time (sec)

N/A 0.517 0.245 1.037 0.277 0.302 0.000 0.273 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

174 198 159 494 551 2934 0 357 0

N.S.

1 1.14 0.91 2.84 3.17 16.86 0.00 2.05 0.00

time (sec)

N/A 0.740 0.542 1.439 0.297 0.347 0.000 0.296 0.000

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 185 178 917 0 464 0 0 0

N.S.

1 1.03 0.99 5.12 0.00 2.59 0.00 0.00 0.00

time (sec)

N/A 0.920 0.329 2.230 0.000 0.120 0.000 0.000 0.000

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 151 139 676 0 263 0 0 0

N.S.

1 1.01 0.93 4.51 0.00 1.75 0.00 0.00 0.00

time (sec)

N/A 0.675 0.271 1.682 0.000 0.113 0.000 0.000 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 65 262 0 173 0 0 0

N.S.

1 1.00 1.08 4.37 0.00 2.88 0.00 0.00 0.00

time (sec)

N/A 0.266 0.137 1.923 0.000 0.098 0.000 0.000 0.000

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 60 125 0 61 0 0 0

N.S.

1 1.00 1.00 2.08 0.00 1.02 0.00 0.00 0.00

time (sec)

N/A 0.275 0.150 0.857 0.000 0.080 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 F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 94 81 456 0 407 0 0 0

N.S.

1 1.00 0.86 4.85 0.00 4.33 0.00 0.00 0.00

time (sec)

N/A 0.376 0.126 1.302 0.000 0.112 0.000 0.000 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 205 166 438 0 1291 0 0 0

N.S.

1 1.04 0.84 2.22 0.00 6.55 0.00 0.00 0.00

time (sec)

N/A 0.938 0.477 1.504 0.000 0.127 0.000 0.000 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 128 101 218 0 174 0 0 0

N.S.

1 1.00 0.79 1.70 0.00 1.36 0.00 0.00 0.00

time (sec)

N/A 0.549 0.344 1.536 0.000 0.123 0.000 0.000 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

112 109 100 0 0 126 0 0 0

N.S.

1 0.97 0.89 0.00 0.00 1.12 0.00 0.00 0.00

time (sec)

N/A 0.439 5.037 0.000 0.000 0.315 0.000 0.000 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

81 81 83 0 0 82 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 1.01 0.00 0.00 0.00

time (sec)

N/A 0.354 1.725 0.000 0.000 0.308 0.000 0.000 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

48 52 66 0 0 49 0 0 0

N.S.

1 1.08 1.38 0.00 0.00 1.02 0.00 0.00 0.00

time (sec)

N/A 0.267 0.154 0.000 0.000 0.313 0.000 0.000 0.000

Problem 115

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

23 25 53 26 26 23 15 17 21

N.S.

1 1.09 2.30 1.13 1.13 1.00 0.65 0.74 0.91

time (sec)

N/A 0.238 0.189 0.703 0.193 0.293 0.065 0.281 0.123

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 47 32 36 141 43 53 32 39

N.S.

1 1.09 0.74 0.84 3.28 1.00 1.23 0.74 0.91

time (sec)

N/A 0.260 0.025 0.857 0.200 0.308 0.130 0.268 1.315

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 66 50 51 267 70 82 46 52

N.S.

1 0.97 0.74 0.75 3.93 1.03 1.21 0.68 0.76

time (sec)

N/A 0.327 0.034 1.048 0.204 0.310 0.242 0.261 1.567

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 89 67 66 469 95 110 60 66

N.S.

1 0.98 0.74 0.73 5.15 1.04 1.21 0.66 0.73

time (sec)

N/A 0.402 0.040 1.217 0.208 0.317 0.453 0.267 1.791

Problem 119

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

27 28 34 27 27 24 15 18 21

N.S.

1 1.04 1.26 1.00 1.00 0.89 0.56 0.67 0.78

time (sec)

N/A 0.248 0.541 0.754 0.199 0.322 0.068 0.257 0.118

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 53 32 36 141 43 51 32 37

N.S.

1 1.08 0.65 0.73 2.88 0.88 1.04 0.65 0.76

time (sec)

N/A 0.264 0.023 0.922 0.199 0.330 0.130 0.272 1.311

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 74 49 51 267 70 82 46 52

N.S.

1 0.97 0.64 0.67 3.51 0.92 1.08 0.61 0.68

time (sec)

N/A 0.337 0.085 1.023 0.205 0.303 0.240 0.265 1.492

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 99 63 66 469 95 109 60 68

N.S.

1 0.98 0.62 0.65 4.64 0.94 1.08 0.59 0.67

time (sec)

N/A 0.414 0.041 1.280 0.215 0.280 0.452 0.276 1.712

Problem 123

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

66 67 85 126 0 188 0 0 0

N.S.

1 1.02 1.29 1.91 0.00 2.85 0.00 0.00 0.00

time (sec)

N/A 0.292 0.219 5.189 0.000 0.319 0.000 0.000 0.000

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

79 79 105 0 0 264 0 0 0

N.S.

1 1.00 1.33 0.00 0.00 3.34 0.00 0.00 0.00

time (sec)

N/A 0.310 0.335 0.000 0.000 0.306 0.000 0.000 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

110 110 184 0 0 347 0 0 0

N.S.

1 1.00 1.67 0.00 0.00 3.15 0.00 0.00 0.00

time (sec)

N/A 0.405 0.316 0.000 0.000 0.301 0.000 0.000 0.000

Problem 126

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

259 270 241 1878 0 1139 0 0 0

N.S.

1 1.04 0.93 7.25 0.00 4.40 0.00 0.00 0.00

time (sec)

N/A 1.405 0.623 5.224 0.000 0.125 0.000 0.000 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

207 213 196 1037 0 635 0 0 0

N.S.

1 1.03 0.95 5.01 0.00 3.07 0.00 0.00 0.00

time (sec)

N/A 1.025 0.436 4.315 0.000 0.118 0.000 0.000 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 165 151 731 0 324 0 0 0

N.S.

1 1.01 0.92 4.46 0.00 1.98 0.00 0.00 0.00

time (sec)

N/A 0.740 0.350 3.805 0.000 0.110 0.000 0.000 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 60 61 72 124 147 309 75 269

N.S.

1 1.09 1.11 1.31 2.25 2.67 5.62 1.36 4.89

time (sec)

N/A 0.288 0.148 0.528 0.277 0.313 15.112 0.288 1.657

Problem 130

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

74 79 82 113 229 444 0 119 223

N.S.

1 1.07 1.11 1.53 3.09 6.00 0.00 1.61 3.01

time (sec)

N/A 0.342 0.145 0.559 0.288 0.308 0.000 0.282 1.593

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 145 131 314 537 1614 0 279 0

N.S.

1 1.13 1.02 2.45 4.20 12.61 0.00 2.18 0.00

time (sec)

N/A 0.537 0.220 0.656 0.293 0.355 0.000 0.279 0.000

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 218 189 633 982 3870 0 477 0

N.S.

1 1.17 1.01 3.39 5.25 20.70 0.00 2.55 0.00

time (sec)

N/A 0.818 0.326 0.832 0.312 0.419 0.000 0.287 0.000

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 65 66 80 128 154 258 82 331

N.S.

1 1.08 1.10 1.33 2.13 2.57 4.30 1.37 5.52

time (sec)

N/A 0.313 0.110 0.533 0.276 0.289 13.506 0.282 1.955

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

6 6 6 7 128 6 3 6 6

N.S.

1 1.00 1.00 1.17 21.33 1.00 0.50 1.00 1.00

time (sec)

N/A 0.144 0.000 0.393 0.271 0.275 0.074 0.276 0.023

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 12 26 230 58 0 30 49

N.S.

1 1.00 1.00 2.17 19.17 4.83 0.00 2.50 4.08

time (sec)

N/A 0.197 0.162 0.495 0.281 0.306 0.000 0.283 1.262

Problem 136

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

34 36 28 33 34 42 51 33 48

N.S.

1 1.06 0.82 0.97 1.00 1.24 1.50 0.97 1.41

time (sec)

N/A 0.243 0.067 0.340 0.275 0.279 0.767 0.273 1.270

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 136 109 266 0 183 0 0 0

N.S.

1 1.00 0.80 1.96 0.00 1.35 0.00 0.00 0.00

time (sec)

N/A 0.583 0.394 3.352 0.000 0.088 0.000 0.000 0.000

Problem 138

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

176 185 159 517 0 633 0 0 0

N.S.

1 1.05 0.90 2.94 0.00 3.60 0.00 0.00 0.00

time (sec)

N/A 0.821 0.507 3.628 0.000 0.098 0.000 0.000 0.000

Problem 139

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

251 259 236 806 0 2167 0 0 0

N.S.

1 1.03 0.94 3.21 0.00 8.63 0.00 0.00 0.00

time (sec)

N/A 1.185 0.623 4.202 0.000 0.158 0.000 0.000 0.000

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 56 36 32 53 511 0 120 0

N.S.

1 1.06 0.68 0.60 1.00 9.64 0.00 2.26 0.00

time (sec)

N/A 0.353 0.061 1.195 0.275 0.281 0.000 0.281 0.000

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 26 24 35 226 0 70 0

N.S.

1 1.00 0.76 0.71 1.03 6.65 0.00 2.06 0.00

time (sec)

N/A 0.272 0.052 0.714 0.281 0.287 0.000 0.253 0.000

Problem 142

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

13 13 13 15 17 71 15 34 21

N.S.

1 1.00 1.00 1.15 1.31 5.46 1.15 2.62 1.62

time (sec)

N/A 0.209 0.022 0.875 0.274 0.284 0.113 0.267 1.170

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 30 49 24 110 0 1 0

N.S.

1 1.00 1.76 2.88 1.41 6.47 0.00 0.06 0.00

time (sec)

N/A 0.216 0.034 0.906 0.281 0.323 0.000 0.275 0.000

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 53 71 62 327 0 37 0

N.S.

1 1.00 1.26 1.69 1.48 7.79 0.00 0.88 0.00

time (sec)

N/A 0.290 0.062 0.742 0.276 0.302 0.000 0.278 0.000

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 69 77 89 96 875 0 52 0

N.S.

1 1.13 1.26 1.46 1.57 14.34 0.00 0.85 0.00

time (sec)

N/A 0.383 0.160 0.920 0.277 0.311 0.000 0.285 0.000

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

135 121 67 0 0 823 0 0 0

N.S.

1 0.90 0.50 0.00 0.00 6.10 0.00 0.00 0.00

time (sec)

N/A 0.562 0.158 0.000 0.000 0.106 0.000 0.000 0.000

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

83 85 57 0 0 317 0 0 0

N.S.

1 1.02 0.69 0.00 0.00 3.82 0.00 0.00 0.00

time (sec)

N/A 0.403 0.065 0.000 0.000 0.102 0.000 0.000 0.000

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

62 67 60 0 0 60 0 0 0

N.S.

1 1.08 0.97 0.00 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 0.330 0.082 0.000 0.000 0.084 0.000 0.000 0.000

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

60 63 42 0 0 97 0 0 0

N.S.

1 1.05 0.70 0.00 0.00 1.62 0.00 0.00 0.00

time (sec)

N/A 0.328 0.041 0.000 0.000 0.090 0.000 0.000 0.000

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

87 87 53 0 0 639 0 0 0

N.S.

1 1.00 0.61 0.00 0.00 7.34 0.00 0.00 0.00

time (sec)

N/A 0.400 0.077 0.000 0.000 0.094 0.000 0.000 0.000

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

135 117 69 0 0 1676 0 0 0

N.S.

1 0.87 0.51 0.00 0.00 12.41 0.00 0.00 0.00

time (sec)

N/A 0.554 0.165 0.000 0.000 0.129 0.000 0.000 0.000

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 93 53 171 100 1597 0 114 0

N.S.

1 0.70 0.40 1.30 0.76 12.10 0.00 0.86 0.00

time (sec)

N/A 0.485 0.149 8.387 0.290 0.310 0.000 0.267 0.000

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 61 38 125 63 659 0 50 0

N.S.

1 0.78 0.49 1.60 0.81 8.45 0.00 0.64 0.00

time (sec)

N/A 0.333 0.089 1.635 0.293 0.299 0.000 0.260 0.000

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 30 24 84 27 180 0 26 0

N.S.

1 0.83 0.67 2.33 0.75 5.00 0.00 0.72 0.00

time (sec)

N/A 0.217 0.050 1.826 0.285 0.285 0.000 0.275 0.000

Problem 155

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

16 16 16 29 18 122 0 13 38

N.S.

1 1.00 1.00 1.81 1.12 7.62 0.00 0.81 2.38

time (sec)

N/A 0.222 0.030 1.552 0.286 0.262 0.000 0.276 1.141

Problem 156

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

68 48 34 48 171 1163 0 27 48

N.S.

1 0.71 0.50 0.71 2.51 17.10 0.00 0.40 0.71

time (sec)

N/A 0.250 0.056 1.527 0.289 0.300 0.000 0.289 1.246

Problem 157

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

118 68 47 60 467 3093 0 39 256

N.S.

1 0.58 0.40 0.51 3.96 26.21 0.00 0.33 2.17

time (sec)

N/A 0.263 0.078 1.671 0.289 0.354 0.000 0.274 1.217

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 57 219 186 90 91 124 86 93

N.S.

1 1.14 4.38 3.72 1.80 1.82 2.48 1.72 1.86

time (sec)

N/A 0.345 0.126 0.480 0.198 0.288 0.143 0.266 1.510

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

43 43 42 39 75 72 100 71 77

N.S.

1 1.00 0.98 0.91 1.74 1.67 2.33 1.65 1.79

time (sec)

N/A 0.229 0.024 0.421 0.209 0.292 0.133 0.277 1.391

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 42 131 138 66 67 82 62 67

N.S.

1 1.11 3.45 3.63 1.74 1.76 2.16 1.63 1.76

time (sec)

N/A 0.291 0.185 0.354 0.196 0.272 0.110 0.269 1.304

Problem 161

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

33 33 28 26 51 48 63 47 51

N.S.

1 1.00 0.85 0.79 1.55 1.45 1.91 1.42 1.55

time (sec)

N/A 0.217 0.018 0.360 0.193 0.307 0.093 0.263 1.284

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 27 93 42 42 41 48 38 41

N.S.

1 1.04 3.58 1.62 1.62 1.58 1.85 1.46 1.58

time (sec)

N/A 0.233 0.133 210.698 0.196 0.294 0.079 0.266 0.128

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 14 12 13 27 22 27 23 31

N.S.

1 0.93 0.80 0.87 1.80 1.47 1.80 1.53 2.07

time (sec)

N/A 0.189 0.010 16.026 0.198 0.292 0.068 0.267 1.168

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 34 16 14 17 14 14 7

N.S.

1 1.00 4.25 2.00 1.75 2.12 1.75 1.75 0.88

time (sec)

N/A 0.189 0.036 7.892 0.194 0.274 0.054 0.281 1.177

Problem 165

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

7 7 7 7 5 11 8 11 10

N.S.

1 1.00 1.00 1.00 0.71 1.57 1.14 1.57 1.43

time (sec)

N/A 0.178 0.008 3.332 0.199 0.284 0.040 0.269 1.216

Problem 166

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

24 24 18 30 41 52 0 51 46

N.S.

1 1.00 0.75 1.25 1.71 2.17 0.00 2.12 1.92

time (sec)

N/A 0.212 0.021 8.522 0.194 0.321 0.000 0.273 0.212

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 22 24 53 26 0 29 63

N.S.

1 1.00 0.88 0.96 2.12 1.04 0.00 1.16 2.52

time (sec)

N/A 0.248 0.028 27.193 0.197 0.307 0.000 0.266 1.283

Problem 168

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

52 52 61 63 92 143 0 92 115

N.S.

1 1.00 1.17 1.21 1.77 2.75 0.00 1.77 2.21

time (sec)

N/A 0.228 0.035 177.479 0.194 0.306 0.000 0.270 1.660

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 40 35 93 205 62 0 53 231

N.S.

1 1.08 0.95 2.51 5.54 1.68 0.00 1.43 6.24

time (sec)

N/A 0.270 0.051 0.434 0.198 0.266 0.000 0.266 1.784

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 80 94 137 140 245 0 118 249

N.S.

1 1.00 1.18 1.71 1.75 3.06 0.00 1.48 3.11

time (sec)

N/A 0.253 0.057 2.349 0.197 0.305 0.000 0.270 2.656

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 50 121 112 54 55 65 50 54

N.S.

1 1.25 3.02 2.80 1.35 1.38 1.62 1.25 1.35

time (sec)

N/A 0.324 0.144 0.379 0.194 0.317 0.103 0.279 0.170

Problem 172

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

14 14 18 12 39 34 44 35 37

N.S.

1 1.00 1.29 0.86 2.79 2.43 3.14 2.50 2.64

time (sec)

N/A 0.191 0.016 0.393 0.200 0.297 0.085 0.263 0.103

Problem 173

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

30 31 46 29 30 31 29 26 28

N.S.

1 1.03 1.53 0.97 1.00 1.03 0.97 0.87 0.93

time (sec)

N/A 0.265 0.060 89.743 0.194 0.279 0.073 0.261 1.203

Problem 174

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

14 14 14 25 23 26 26 21 24

N.S.

1 1.00 1.00 1.79 1.64 1.86 1.86 1.50 1.71

time (sec)

N/A 0.208 0.011 25.100 0.191 0.296 0.090 0.277 1.262

Problem 175

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

14 14 69 13 12 16 8 10 12

N.S.

1 1.00 4.93 0.93 0.86 1.14 0.57 0.71 0.86

time (sec)

N/A 0.184 0.045 13.097 0.185 0.309 0.051 0.262 1.316

Problem 176

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

10 10 10 10 8 16 19 10 12

N.S.

1 1.00 1.00 1.00 0.80 1.60 1.90 1.00 1.20

time (sec)

N/A 0.179 0.023 10.888 0.200 0.290 0.054 0.261 1.247

Problem 177

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

34 34 26 45 70 103 0 66 86

N.S.

1 1.00 0.76 1.32 2.06 3.03 0.00 1.94 2.53

time (sec)

N/A 0.211 0.033 24.110 0.195 0.313 0.000 0.265 1.457

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 48 31 30 117 44 0 41 109

N.S.

1 1.30 0.84 0.81 3.16 1.19 0.00 1.11 2.95

time (sec)

N/A 0.333 0.018 49.599 0.207 0.282 0.000 0.279 1.386

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 68 116 120 201 0 105 198

N.S.

1 1.00 1.13 1.93 2.00 3.35 0.00 1.75 3.30

time (sec)

N/A 0.235 0.037 0.625 0.207 0.304 0.000 0.274 1.852

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 65 47 116 317 80 0 65 139

N.S.

1 1.33 0.96 2.37 6.47 1.63 0.00 1.33 2.84

time (sec)

N/A 0.359 0.032 0.408 0.209 0.284 0.000 0.272 0.528

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 47 26 33 50 31 21 41

N.S.

1 1.00 1.68 0.93 1.18 1.79 1.11 0.75 1.46

time (sec)

N/A 0.216 0.076 60.849 0.192 0.299 0.090 0.277 0.189

Problem 182

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

20 20 16 19 53 28 34 16 19

N.S.

1 1.00 0.80 0.95 2.65 1.40 1.70 0.80 0.95

time (sec)

N/A 0.190 0.046 57.380 0.210 0.293 0.072 0.275 1.407

Problem 183

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

16 16 14 13 10 30 37 12 16

N.S.

1 1.00 0.88 0.81 0.62 1.88 2.31 0.75 1.00

time (sec)

N/A 0.182 0.039 58.272 0.198 0.282 0.072 0.261 1.406

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 28 43 26 33 50 31 21 39

N.S.

1 1.08 1.65 1.00 1.27 1.92 1.19 0.81 1.50

time (sec)

N/A 0.212 0.073 59.068 0.198 0.292 0.089 0.258 0.173

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 16 19 53 28 34 16 19

N.S.

1 1.00 0.80 0.95 2.65 1.40 1.70 0.80 0.95

time (sec)

N/A 0.189 0.051 57.560 0.214 0.286 0.073 0.269 1.269

Problem 186

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

16 16 14 13 10 30 36 12 16

N.S.

1 1.00 0.88 0.81 0.62 1.88 2.25 0.75 1.00

time (sec)

N/A 0.183 0.038 58.086 0.211 0.279 0.073 0.263 0.214

Problem 187

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

138 138 121 146 308 2105 0 254 287

N.S.

1 1.00 0.88 1.06 2.23 15.25 0.00 1.84 2.08

time (sec)

N/A 0.336 0.124 128.980 0.218 0.315 0.000 0.274 2.063

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 169 463 344 283 1486 0 288 302

N.S.

1 1.17 3.19 2.37 1.95 10.25 0.00 1.99 2.08

time (sec)

N/A 0.928 4.677 57.610 0.296 0.320 0.000 0.282 2.007

Problem 189

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

81 80 76 82 180 865 0 139 169

N.S.

1 0.99 0.94 1.01 2.22 10.68 0.00 1.72 2.09

time (sec)

N/A 0.277 0.067 23.125 0.211 0.298 0.000 0.273 1.580

Problem 190

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 113 553 162 170 569 0 168 200

N.S.

1 1.16 5.70 1.67 1.75 5.87 0.00 1.73 2.06

time (sec)

N/A 0.626 1.757 8.007 0.322 0.307 0.000 0.282 1.633

Problem 191

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

38 38 38 37 81 221 0 61 77

N.S.

1 1.00 1.00 0.97 2.13 5.82 0.00 1.61 2.03

time (sec)

N/A 0.242 0.030 2.992 0.246 0.295 0.000 0.278 1.388

Problem 192

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

54 64 396 93 81 171 377 83 87

N.S.

1 1.19 7.33 1.72 1.50 3.17 6.98 1.54 1.61

time (sec)

N/A 0.393 0.581 1.122 0.323 0.319 67.566 0.274 1.316

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 11 27 14 22 11

N.S.

1 1.00 1.00 1.09 1.00 2.45 1.27 2.00 1.00

time (sec)

N/A 0.186 0.006 0.365 0.232 0.301 0.073 0.279 0.070

Problem 194

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 59 99 64 66 57 0 89 93

N.S.

1 1.23 2.06 1.33 1.38 1.19 0.00 1.85 1.94

time (sec)

N/A 0.243 0.075 2.237 0.320 0.295 0.000 0.264 2.124

Problem 195

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

59 64 67 71 89 259 0 87 321

N.S.

1 1.08 1.14 1.20 1.51 4.39 0.00 1.47 5.44

time (sec)

N/A 0.316 0.153 6.923 0.320 0.297 0.000 0.275 1.797

Problem 196

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

87 135 77 161 159 652 0 214 291

N.S.

1 1.55 0.89 1.85 1.83 7.49 0.00 2.46 3.34

time (sec)

N/A 0.342 0.140 17.266 0.291 0.311 0.000 0.281 3.045

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 116 102 182 230 1142 0 180 634

N.S.

1 1.16 1.02 1.82 2.30 11.42 0.00 1.80 6.34

time (sec)

N/A 0.548 0.293 47.077 0.288 0.290 0.000 0.280 2.395

Problem 198

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

135 215 284 313 345 2707 0 369 548

N.S.

1 1.59 2.10 2.32 2.56 20.05 0.00 2.73 4.06

time (sec)

N/A 0.439 0.316 92.654 0.305 0.368 0.000 0.278 5.729

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

146 176 146 350 438 3175 0 323 1010

N.S.

1 1.21 1.00 2.40 3.00 21.75 0.00 2.21 6.92

time (sec)

N/A 0.873 0.384 174.745 0.296 0.313 0.000 0.281 3.019

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 117 660 161 176 833 0 178 256

N.S.

1 1.24 7.02 1.71 1.87 8.86 0.00 1.89 2.72

time (sec)

N/A 0.577 3.597 17.491 0.295 0.308 0.000 0.290 1.602

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