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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 C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 90 63 68 55 78 210 61

N.S.

1 1.00 1.50 1.05 1.13 0.92 1.30 3.50 1.02

time (sec)

N/A 0.275 0.027 0.262 0.269 0.278 0.256 0.344 1.027

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 31 44 30 29 43 46 111 42

N.S.

1 0.94 1.33 0.91 0.88 1.30 1.39 3.36 1.27

time (sec)

N/A 0.205 0.010 0.207 0.181 0.278 0.139 0.321 1.333

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 120 256 103 133 0 0 0 0

N.S.

1 1.00 2.13 0.86 1.11 0.00 0.00 0.00 0.00

time (sec)

N/A 0.467 0.153 0.389 0.338 0.000 0.000 0.000 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 61 66 61 77 64 167 498 62

N.S.

1 0.98 1.06 0.98 1.24 1.03 2.69 8.03 1.00

time (sec)

N/A 0.241 0.050 0.240 0.289 0.282 0.539 0.417 1.416

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 102 92 83 112 99 381 1309 230

N.S.

1 1.07 0.97 0.87 1.18 1.04 4.01 13.78 2.42

time (sec)

N/A 0.302 0.087 0.310 0.290 0.289 0.798 0.582 1.631

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 136 126 115 165 142 760 3449 285

N.S.

1 1.05 0.98 0.89 1.28 1.10 5.89 26.74 2.21

time (sec)

N/A 0.358 0.108 0.305 0.273 0.272 1.184 1.667 1.490

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

642 721 563 591 8519 0 0 0 0

N.S.

1 1.12 0.88 0.92 13.27 0.00 0.00 0.00 0.00

time (sec)

N/A 1.373 0.413 2.008 4.025 0.000 0.000 0.000 0.000

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 170 325 187 283 0 0 0 0

N.S.

1 1.12 2.14 1.23 1.86 0.00 0.00 0.00 0.00

time (sec)

N/A 0.537 0.200 0.788 0.359 0.000 0.000 0.000 0.000

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

338 481 514 296 280 0 0 0 0

N.S.

1 1.42 1.52 0.88 0.83 0.00 0.00 0.00 0.00

time (sec)

N/A 1.032 7.625 0.672 0.371 0.000 0.000 0.000 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

735 1222 930 728 8518 0 0 0 0

N.S.

1 1.66 1.27 0.99 11.59 0.00 0.00 0.00 0.00

time (sec)

N/A 2.200 0.699 2.795 0.931 0.000 0.000 0.000 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

693 1133 618 364 0 0 0 0 0

N.S.

1 1.63 0.89 0.53 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.418 0.538 0.427 0.000 0.000 0.000 0.000 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

830 1316 809 388 0 0 0 0 0

N.S.

1 1.59 0.97 0.47 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.680 0.528 0.471 0.000 0.000 0.000 0.000 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

367 388 0 959 0 0 0 0 0

N.S.

1 1.06 0.00 2.61 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.125 0.000 2.493 0.000 0.000 0.000 0.000 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 127 127 118 0 0 0 0 0

N.S.

1 0.96 0.96 0.89 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.288 0.133 1.284 0.000 0.000 0.000 0.000 0.000

Problem 115

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

216 155 138 156 0 0 0 0 0

N.S.

1 0.72 0.64 0.72 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.370 0.088 1.305 0.000 0.000 0.000 0.000 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 28 177 26 28 28 29 28 28

N.S.

1 1.00 6.32 0.93 1.00 1.00 1.04 1.00 1.00

time (sec)

N/A 0.255 0.302 0.747 0.275 0.265 0.801 0.440 0.820

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

33 33 180 31 33 33 31 33 33

N.S.

1 1.00 5.45 0.94 1.00 1.00 0.94 1.00 1.00

time (sec)

N/A 0.285 0.141 0.783 0.297 0.285 5.943 0.451 0.838

Problem 118

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

187 177 202 160 0 0 0 0 0

N.S.

1 0.95 1.08 0.86 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.446 1.332 1.520 0.000 0.000 0.000 0.000 0.000

Problem 119

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

281 215 207 202 0 0 0 0 0

N.S.

1 0.77 0.74 0.72 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.594 1.030 1.433 0.000 0.000 0.000 0.000 0.000

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

35 35 198 33 35 44 36 35 35

N.S.

1 1.00 5.66 0.94 1.00 1.26 1.03 1.00 1.00

time (sec)

N/A 0.343 0.741 0.884 0.357 0.284 3.454 0.496 0.885

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

40 40 200 38 40 49 37 40 40

N.S.

1 1.00 5.00 0.95 1.00 1.22 0.92 1.00 1.00

time (sec)

N/A 0.405 0.322 0.853 0.373 0.265 24.399 0.513 0.941

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A C B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

52 43 42 42 93 81 99 203 85

N.S.

1 0.83 0.81 0.81 1.79 1.56 1.90 3.90 1.63

time (sec)

N/A 0.266 0.017 0.433 0.255 0.266 0.620 0.374 0.170

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 141 36 52 33 56 100 49

N.S.

1 1.00 3.62 0.92 1.33 0.85 1.44 2.56 1.26

time (sec)

N/A 0.217 0.044 0.247 0.278 0.261 0.380 0.327 1.741

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 43 38 55 112 0 0 100 0

N.S.

1 0.96 0.84 1.22 2.49 0.00 0.00 2.22 0.00

time (sec)

N/A 0.269 0.007 0.475 0.328 0.000 0.000 0.532 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 45 42 41 53 59 139 238 57

N.S.

1 0.96 0.89 0.87 1.13 1.26 2.96 5.06 1.21

time (sec)

N/A 0.240 0.014 0.467 0.197 0.265 1.333 0.333 0.931

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 39 35 37 64 0 0 26 0

N.S.

1 1.11 1.00 1.06 1.83 0.00 0.00 0.74 0.00

time (sec)

N/A 0.260 0.006 0.564 0.318 0.000 0.000 0.297 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 43 38 55 122 0 0 103 0

N.S.

1 0.96 0.84 1.22 2.71 0.00 0.00 2.29 0.00

time (sec)

N/A 0.272 0.007 0.563 0.320 0.000 0.000 0.558 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

18 18 20 16 0 0 17 18 18

N.S.

1 1.00 1.11 0.89 0.00 0.00 0.94 1.00 1.00

time (sec)

N/A 0.187 4.040 0.446 0.000 0.000 3.132 0.304 1.148

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

233 230 157 496 341 325 0 2265 783

N.S.

1 0.99 0.67 2.13 1.46 1.39 0.00 9.72 3.36

time (sec)

N/A 0.513 0.201 0.883 0.276 0.280 0.000 1.731 1.367

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 163 118 294 216 206 376 1161 409

N.S.

1 1.06 0.77 1.91 1.40 1.34 2.44 7.54 2.66

time (sec)

N/A 0.411 0.114 0.676 0.297 0.279 125.905 1.231 1.179

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 103 163 113 113 110 177 451 136

N.S.

1 1.06 1.68 1.16 1.16 1.13 1.82 4.65 1.40

time (sec)

N/A 0.340 0.070 0.353 0.271 0.273 14.479 0.415 1.583

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 49 35 34 52 51 116 48

N.S.

1 1.00 1.29 0.92 0.89 1.37 1.34 3.05 1.26

time (sec)

N/A 0.173 0.010 0.297 0.182 0.268 0.165 0.321 1.498

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 180 336 197 0 0 0 0 0

N.S.

1 1.11 2.07 1.22 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.545 0.328 0.753 0.000 0.000 0.000 0.000 0.000

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 149 118 161 177 223 0 1264 128

N.S.

1 0.97 0.77 1.05 1.16 1.46 0.00 8.26 0.84

time (sec)

N/A 0.435 0.162 0.717 0.266 0.408 0.000 0.689 2.356

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

228 245 180 245 410 728 0 6173 399

N.S.

1 1.07 0.79 1.07 1.80 3.19 0.00 27.07 1.75

time (sec)

N/A 0.593 0.473 1.422 0.273 1.206 0.000 2.130 8.331

Problem 136

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 Yes TBD TBD TBD TBD TBD

size

382 383 586 1072 0 0 0 0 0

N.S.

1 1.00 1.53 2.81 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.766 6.667 1.340 0.000 0.000 0.000 0.000 0.000

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

220 227 286 427 0 0 0 0 0

N.S.

1 1.03 1.30 1.94 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.589 1.054 0.884 0.000 0.000 0.000 0.000 0.000

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 102 118 184 0 0 0 0 123

N.S.

1 1.00 1.16 1.80 0.00 0.00 0.00 0.00 1.21

time (sec)

N/A 0.477 0.150 0.843 0.000 0.000 0.000 0.000 1.167

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

261 288 0 1911 0 0 0 0 0

N.S.

1 1.10 0.00 7.32 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.419 0.000 14.056 0.000 0.000 0.000 0.000 0.000

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

567 586 454 784 0 0 0 0 0

N.S.

1 1.03 0.80 1.38 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.547 6.116 4.178 0.000 0.000 0.000 0.000 0.000

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

565 551 2309 6248 0 0 0 0 0

N.S.

1 0.98 4.09 11.06 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.133 14.560 101.639 0.000 0.000 0.000 0.000 0.000

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

337 334 630 1051 0 0 0 0 0

N.S.

1 0.99 1.87 3.12 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.840 5.420 13.322 0.000 0.000 0.000 0.000 0.000

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 141 228 395 0 0 0 0 0

N.S.

1 0.99 1.59 2.76 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.674 0.256 2.461 0.000 0.000 0.000 0.000 0.000

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

372 408 0 3903 0 0 0 0 0

N.S.

1 1.10 0.00 10.49 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.467 0.000 16.365 0.000 0.000 0.000 0.000 0.000

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1233 1266 0 4229 0 0 0 0 0

N.S.

1 1.03 0.00 3.43 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.423 0.000 28.029 0.000 0.000 0.000 0.000 0.000

Problem 146

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

177 236 162 0 0 0 0 0 0

N.S.

1 1.33 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.476 0.304 0.000 0.000 0.000 0.000 0.000 0.000

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 20 618 36 0 22 22

N.S.

1 1.00 1.10 1.00 30.90 1.80 0.00 1.10 1.10

time (sec)

N/A 0.301 4.821 0.469 5.113 0.260 0.000 0.660 0.843

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 20 880 52 0 22 22

N.S.

1 1.00 1.10 1.00 44.00 2.60 0.00 1.10 1.10

time (sec)

N/A 0.291 0.520 0.551 7.835 0.283 0.000 0.721 0.796

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

42 34 37 37 35 51 60 127 230

N.S.

1 0.81 0.88 0.88 0.83 1.21 1.43 3.02 5.48

time (sec)

N/A 0.282 0.014 0.340 0.194 0.271 0.568 0.403 0.940

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

45 36 40 149 38 56 0 60 58

N.S.

1 0.80 0.89 3.31 0.84 1.24 0.00 1.33 1.29

time (sec)

N/A 0.287 0.027 6.300 0.197 0.282 0.000 0.348 1.726

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

40 40 42 36 39 38 34 38 39

N.S.

1 1.00 1.05 0.90 0.98 0.95 0.85 0.95 0.98

time (sec)

N/A 0.253 0.151 1.408 0.884 0.274 3.353 0.416 1.195

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

488 486 0 1640 0 0 0 0 0

N.S.

1 1.00 0.00 3.36 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.121 0.000 1.319 0.000 0.000 0.000 0.000 0.000

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

321 323 0 903 0 0 0 0 0

N.S.

1 1.01 0.00 2.81 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.788 0.000 0.701 0.000 0.000 0.000 0.000 0.000

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 93 93 363 0 0 0 0 0

N.S.

1 0.95 0.95 3.70 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.329 0.029 0.431 0.000 0.000 0.000 0.000 0.000

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

40 40 42 36 39 48 61 38 39

N.S.

1 1.00 1.05 0.90 0.98 1.20 1.52 0.95 0.98

time (sec)

N/A 0.251 0.220 0.767 0.449 0.260 2.832 0.378 0.892

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

40 40 42 36 163 91 126 38 39

N.S.

1 1.00 1.05 0.90 4.08 2.28 3.15 0.95 0.98

time (sec)

N/A 0.246 1.029 0.909 0.500 0.275 6.396 0.530 1.693

Problem 157

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

16 16 18 20 17 15 48 30 21

N.S.

1 1.00 1.12 1.25 1.06 0.94 3.00 1.88 1.31

time (sec)

N/A 0.160 0.008 0.304 0.195 0.235 0.069 0.274 0.087

Problem 158

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 No TBD TBD TBD TBD TBD

size

403 519 371 8038 0 1965 0 0 0

N.S.

1 1.29 0.92 19.95 0.00 4.88 0.00 0.00 0.00

time (sec)

N/A 1.533 2.459 43.734 0.000 0.323 0.000 0.000 0.000

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

305 396 281 7646 0 1545 0 0 0

N.S.

1 1.30 0.92 25.07 0.00 5.07 0.00 0.00 0.00

time (sec)

N/A 1.105 2.238 4.089 0.000 0.327 0.000 0.000 0.000

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

198 277 549 1138 433 1101 0 0 0

N.S.

1 1.40 2.77 5.75 2.19 5.56 0.00 0.00 0.00

time (sec)

N/A 0.684 0.542 4.354 0.324 0.339 0.000 0.000 0.000

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 15 17 15 17 17 0 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.00 1.13 1.13

time (sec)

N/A 0.295 0.332 0.139 227.568 0.258 0.000 1.510 0.900

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

154 198 136 1448 310 321 0 0 0

N.S.

1 1.29 0.88 9.40 2.01 2.08 0.00 0.00 0.00

time (sec)

N/A 0.808 0.181 2.878 0.210 0.274 0.000 0.000 0.000

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

123 155 110 1413 218 270 0 0 0

N.S.

1 1.26 0.89 11.49 1.77 2.20 0.00 0.00 0.00

time (sec)

N/A 0.633 0.081 2.549 0.202 0.273 0.000 0.000 0.000

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

85 107 967 562 455 199 0 0 0

N.S.

1 1.26 11.38 6.61 5.35 2.34 0.00 0.00 0.00

time (sec)

N/A 0.445 4.192 2.062 0.286 0.282 0.000 0.000 0.000

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 23 19 0 36 0 21 22

N.S.

1 1.00 1.10 0.90 0.00 1.71 0.00 1.00 1.05

time (sec)

N/A 0.277 0.276 0.205 0.000 0.246 0.000 1.106 1.054

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

155 199 141 1449 312 321 0 0 0

N.S.

1 1.28 0.91 9.35 2.01 2.07 0.00 0.00 0.00

time (sec)

N/A 0.804 0.187 3.056 0.204 0.267 0.000 0.000 0.000

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

124 156 111 1414 220 270 0 0 0

N.S.

1 1.26 0.90 11.40 1.77 2.18 0.00 0.00 0.00

time (sec)

N/A 0.639 0.067 2.635 0.201 0.268 0.000 0.000 0.000

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

86 108 847 595 450 201 0 0 0

N.S.

1 1.26 9.85 6.92 5.23 2.34 0.00 0.00 0.00

time (sec)

N/A 0.444 2.352 2.142 0.294 0.263 0.000 0.000 0.000

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

22 22 24 20 0 36 0 22 22

N.S.

1 1.00 1.09 0.91 0.00 1.64 0.00 1.00 1.00

time (sec)

N/A 0.337 0.693 0.228 0.000 0.259 0.000 1.151 1.237

Problem 170

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

16 16 18 17 10 10 19 10 16

N.S.

1 1.00 1.12 1.06 0.62 0.62 1.19 0.62 1.00

time (sec)

N/A 0.161 0.006 0.654 0.175 0.214 0.060 0.274 0.799

Problem 171

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 No TBD TBD TBD TBD TBD

size

399 515 360 7868 0 1589 0 0 0

N.S.

1 1.29 0.90 19.72 0.00 3.98 0.00 0.00 0.00

time (sec)

N/A 1.511 2.325 53.611 0.000 0.455 0.000 0.000 0.000

Problem 172

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 No TBD TBD TBD TBD TBD

size

303 394 275 7488 0 1289 0 0 0

N.S.

1 1.30 0.91 24.71 0.00 4.25 0.00 0.00 0.00

time (sec)

N/A 1.099 1.892 4.436 0.000 0.403 0.000 0.000 0.000

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

198 277 1649 1146 532 965 0 0 0

N.S.

1 1.40 8.33 5.79 2.69 4.87 0.00 0.00 0.00

time (sec)

N/A 0.660 12.133 4.579 0.355 0.399 0.000 0.000 0.000

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 15 17 15 0 17 0 17 17

N.S.

1 1.00 1.13 1.00 0.00 1.13 0.00 1.13 1.13

time (sec)

N/A 0.280 0.300 0.194 0.000 0.257 0.000 3.495 0.908

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

154 198 140 1448 0 174 0 0 0

N.S.

1 1.29 0.91 9.40 0.00 1.13 0.00 0.00 0.00

time (sec)

N/A 0.799 0.161 3.115 0.000 0.276 0.000 0.000 0.000

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

123 155 110 1413 0 152 0 0 0

N.S.

1 1.26 0.89 11.49 0.00 1.24 0.00 0.00 0.00

time (sec)

N/A 0.623 0.093 2.616 0.000 0.272 0.000 0.000 0.000

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

85 107 929 587 0 116 0 0 0

N.S.

1 1.26 10.93 6.91 0.00 1.36 0.00 0.00 0.00

time (sec)

N/A 0.427 4.892 1.566 0.000 0.261 0.000 0.000 0.000

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 21 23 26 0 42 0 28 25

N.S.

1 1.00 1.10 1.24 0.00 2.00 0.00 1.33 1.19

time (sec)

N/A 0.282 0.326 0.099 0.000 0.254 0.000 2.381 1.434

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

155 199 136 1449 0 174 0 0 0

N.S.

1 1.28 0.88 9.35 0.00 1.12 0.00 0.00 0.00

time (sec)

N/A 0.819 0.165 3.421 0.000 0.271 0.000 0.000 0.000

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

124 156 110 1414 0 152 0 0 0

N.S.

1 1.26 0.89 11.40 0.00 1.23 0.00 0.00 0.00

time (sec)

N/A 0.636 0.091 2.865 0.000 0.262 0.000 0.000 0.000

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

86 108 872 630 0 116 0 0 0

N.S.

1 1.26 10.14 7.33 0.00 1.35 0.00 0.00 0.00

time (sec)

N/A 0.447 2.405 1.367 0.000 0.267 0.000 0.000 0.000

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

22 22 24 25 0 42 0 27 25

N.S.

1 1.00 1.09 1.14 0.00 1.91 0.00 1.23 1.14

time (sec)

N/A 0.297 0.365 0.059 0.000 0.272 0.000 2.724 1.544

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

299 327 600 3570 0 1460 0 0 0

N.S.

1 1.09 2.01 11.94 0.00 4.88 0.00 0.00 0.00

time (sec)

N/A 1.200 0.233 33.571 0.000 0.376 0.000 0.000 0.000

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

229 251 375 2668 0 1002 0 0 0

N.S.

1 1.10 1.64 11.65 0.00 4.38 0.00 0.00 0.00

time (sec)

N/A 0.847 0.135 24.430 0.000 0.338 0.000 0.000 0.000

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

159 175 237 1776 0 600 0 0 0

N.S.

1 1.10 1.49 11.17 0.00 3.77 0.00 0.00 0.00

time (sec)

N/A 0.608 0.095 2.572 0.000 0.311 0.000 0.000 0.000

Problem 186

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

73 79 91 184 0 334 0 0 0

N.S.

1 1.08 1.25 2.52 0.00 4.58 0.00 0.00 0.00

time (sec)

N/A 0.343 0.023 1.737 0.000 0.297 0.000 0.000 0.000

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

15 15 17 15 17 17 14 3 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.93 0.20 1.13

time (sec)

N/A 0.217 0.675 0.240 1.561 0.270 3.143 90.586 0.832

Problem 188

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 No TBD TBD TBD TBD TBD

size

355 441 438 6916 0 1289 0 0 0

N.S.

1 1.24 1.23 19.48 0.00 3.63 0.00 0.00 0.00

time (sec)

N/A 1.416 0.347 42.430 0.000 0.343 0.000 0.000 0.000

Problem 189

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 No TBD TBD TBD TBD TBD

size

267 343 330 6566 0 1067 0 0 0

N.S.

1 1.28 1.24 24.59 0.00 4.00 0.00 0.00 0.00

time (sec)

N/A 1.022 0.723 4.506 0.000 0.354 0.000 0.000 0.000

Problem 190

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

174 237 288 352 0 825 0 0 0

N.S.

1 1.36 1.66 2.02 0.00 4.74 0.00 0.00 0.00

time (sec)

N/A 0.659 0.275 3.026 0.000 0.403 0.000 0.000 0.000

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 15 17 15 17 17 0 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.00 1.13 1.13

time (sec)

N/A 0.280 3.872 0.155 1.047 0.244 0.000 0.578 0.883

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

142 167 134 1405 129 292 0 0 0

N.S.

1 1.18 0.94 9.89 0.91 2.06 0.00 0.00 0.00

time (sec)

N/A 0.791 0.147 2.531 1.275 0.267 0.000 0.000 0.000

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

113 132 103 1369 107 246 0 0 0

N.S.

1 1.17 0.91 12.12 0.95 2.18 0.00 0.00 0.00

time (sec)

N/A 0.616 0.059 1.962 1.382 0.288 0.000 0.000 0.000

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 93 71 544 80 186 0 0 0

N.S.

1 1.18 0.90 6.89 1.01 2.35 0.00 0.00 0.00

time (sec)

N/A 0.420 0.099 1.833 1.314 0.270 0.000 0.000 0.000

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

19 19 21 17 81 36 0 19 20

N.S.

1 1.00 1.11 0.89 4.26 1.89 0.00 1.00 1.05

time (sec)

N/A 0.282 3.107 0.105 0.642 0.250 0.000 0.370 1.063

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

145 170 134 1409 129 292 0 0 0

N.S.

1 1.17 0.92 9.72 0.89 2.01 0.00 0.00 0.00

time (sec)

N/A 0.784 0.158 2.473 1.441 0.276 0.000 0.000 0.000

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

116 136 103 1373 106 246 0 0 0

N.S.

1 1.17 0.89 11.84 0.91 2.12 0.00 0.00 0.00

time (sec)

N/A 0.620 0.087 2.032 1.347 0.270 0.000 0.000 0.000

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 95 71 517 80 186 0 0 0

N.S.

1 1.16 0.87 6.30 0.98 2.27 0.00 0.00 0.00

time (sec)

N/A 0.424 0.086 1.855 1.276 0.271 0.000 0.000 0.000

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

22 22 24 20 73 36 0 19 20

N.S.

1 1.00 1.09 0.91 3.32 1.64 0.00 0.86 0.91

time (sec)

N/A 0.295 3.190 0.128 0.628 0.250 0.000 0.375 1.055

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

299 327 600 3570 0 1460 0 0 0

N.S.

1 1.09 2.01 11.94 0.00 4.88 0.00 0.00 0.00

time (sec)

N/A 1.165 0.219 33.246 0.000 0.332 0.000 0.000 0.000

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