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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 B B F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 119 458 464 0 0 0 0 0

N.S.

1 0.93 3.58 3.62 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.444 0.939 1.184 0.000 0.000 0.000 0.000 0.000

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 102 314 176 416 150 434 192 222

N.S.

1 0.81 2.49 1.40 3.30 1.19 3.44 1.52 1.76

time (sec)

N/A 0.291 0.287 0.684 0.214 0.262 1.092 0.399 2.210

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

268 204 443 485 848 367 894 440 507

N.S.

1 0.76 1.65 1.81 3.16 1.37 3.34 1.64 1.89

time (sec)

N/A 0.387 0.285 1.053 0.243 0.263 2.110 0.426 2.603

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

418 315 582 892 1419 672 1544 725 1064

N.S.

1 0.75 1.39 2.13 3.39 1.61 3.69 1.73 2.55

time (sec)

N/A 0.475 0.405 1.339 0.291 0.274 11.684 0.514 4.432

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

575 433 666 1179 2123 1035 0 1014 1881

N.S.

1 0.75 1.16 2.05 3.69 1.80 0.00 1.76 3.27

time (sec)

N/A 0.560 0.589 2.322 0.357 0.283 0.000 0.561 7.614

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 29 114 30 158 30 0 1203 25

N.S.

1 1.04 4.07 1.07 5.64 1.07 0.00 42.96 0.89

time (sec)

N/A 0.177 0.044 0.844 0.204 0.251 0.000 34.962 1.058

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 15 61 22 0 320 15

N.S.

1 1.00 1.00 1.00 4.07 1.47 0.00 21.33 1.00

time (sec)

N/A 0.154 0.021 0.530 0.192 0.264 0.000 3.748 0.945

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 17 59 22 0 322 13

N.S.

1 1.00 1.00 1.31 4.54 1.69 0.00 24.77 1.00

time (sec)

N/A 0.157 0.018 0.532 0.203 0.266 0.000 3.572 0.979

Problem 109

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

32 32 34 32 34 52 95 34 34

N.S.

1 1.00 1.06 1.00 1.06 1.62 2.97 1.06 1.06

time (sec)

N/A 0.192 0.562 0.866 0.221 0.257 8.352 13.898 1.855

Problem 110

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

30 30 32 30 32 34 56 32 32

N.S.

1 1.00 1.07 1.00 1.07 1.13 1.87 1.07 1.07

time (sec)

N/A 0.181 0.119 0.766 0.213 0.250 4.428 11.092 1.951

Problem 111

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

32 32 34 32 34 42 61 34 34

N.S.

1 1.00 1.06 1.00 1.06 1.31 1.91 1.06 1.06

time (sec)

N/A 0.197 0.217 0.671 0.227 0.242 2.656 9.026 2.229

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 52 61 0 47 0 0 0

N.S.

1 1.00 1.04 1.22 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 0.292 0.137 1.850 0.000 0.249 0.000 0.000 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 95 89 117 0 130 0 0 0

N.S.

1 0.89 0.83 1.09 0.00 1.21 0.00 0.00 0.00

time (sec)

N/A 0.415 0.254 2.807 0.000 0.257 0.000 0.000 0.000

Problem 114

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

32 32 34 32 305 79 0 34 34

N.S.

1 1.00 1.06 1.00 9.53 2.47 0.00 1.06 1.06

time (sec)

N/A 0.200 0.930 1.062 0.225 0.254 0.000 0.888 4.301

Problem 115

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

30 30 32 30 227 61 274 32 32

N.S.

1 1.00 1.07 1.00 7.57 2.03 9.13 1.07 1.07

time (sec)

N/A 0.181 0.480 1.592 0.222 0.246 15.893 1.184 4.586

Problem 116

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

32 32 34 32 162 83 90 34 34

N.S.

1 1.00 1.06 1.00 5.06 2.59 2.81 1.06 1.06

time (sec)

N/A 0.200 0.401 0.691 0.230 0.278 1.582 0.662 5.580

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 91 87 113 0 199 0 0 0

N.S.

1 0.88 0.84 1.10 0.00 1.93 0.00 0.00 0.00

time (sec)

N/A 0.359 0.158 2.639 0.000 0.252 0.000 0.000 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

212 174 136 182 0 570 0 0 0

N.S.

1 0.82 0.64 0.86 0.00 2.69 0.00 0.00 0.00

time (sec)

N/A 0.477 0.468 3.918 0.000 0.268 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 B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 156 144 446 885 454 998 490 1025

N.S.

1 0.86 0.79 2.45 4.86 2.49 5.48 2.69 5.63

time (sec)

N/A 0.314 0.065 1.201 0.223 0.330 3.610 59.292 1.707

Problem 120

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

151 132 122 318 647 341 707 355 567

N.S.

1 0.87 0.81 2.11 4.28 2.26 4.68 2.35 3.75

time (sec)

N/A 0.282 0.066 0.883 0.222 0.285 2.039 10.233 1.456

Problem 121

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

120 108 98 210 437 243 517 246 296

N.S.

1 0.90 0.82 1.75 3.64 2.02 4.31 2.05 2.47

time (sec)

N/A 0.262 0.038 0.704 0.356 0.276 1.390 1.813 1.303

Problem 122

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

78 78 72 108 250 148 250 129 120

N.S.

1 1.00 0.92 1.38 3.21 1.90 3.21 1.65 1.54

time (sec)

N/A 0.229 0.027 0.530 0.280 0.261 0.840 0.538 1.114

Problem 123

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

83 83 88 264 0 0 0 0 0

N.S.

1 1.00 1.06 3.18 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.487 0.031 0.704 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 A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 65 111 93 187 110 255 187 108

N.S.

1 1.00 1.71 1.43 2.88 1.69 3.92 2.88 1.66

time (sec)

N/A 0.221 0.035 0.855 0.196 0.273 0.650 0.367 1.975

Problem 125

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

138 137 109 239 307 238 418 268 206

N.S.

1 0.99 0.79 1.73 2.22 1.72 3.03 1.94 1.49

time (sec)

N/A 0.303 0.080 1.214 0.199 0.270 1.028 0.330 1.945

Problem 126

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

177 165 140 379 480 430 677 477 341

N.S.

1 0.93 0.79 2.14 2.71 2.43 3.82 2.69 1.93

time (sec)

N/A 0.324 0.079 1.569 0.206 0.272 1.664 0.337 2.618

Problem 127

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

208 188 162 527 699 654 947 419 579

N.S.

1 0.90 0.78 2.53 3.36 3.14 4.55 2.01 2.78

time (sec)

N/A 0.343 0.118 2.708 0.221 0.287 2.416 0.663 3.313

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

377 448 523 0 2650 0 0 0 0

N.S.

1 1.19 1.39 0.00 7.03 0.00 0.00 0.00 0.00

time (sec)

N/A 0.951 0.318 0.000 0.346 0.000 0.000 0.000 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

319 373 402 0 1948 0 0 0 0

N.S.

1 1.17 1.26 0.00 6.11 0.00 0.00 0.00 0.00

time (sec)

N/A 0.822 0.225 0.000 0.333 0.000 0.000 0.000 0.000

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

255 292 298 0 1326 0 0 0 0

N.S.

1 1.15 1.17 0.00 5.20 0.00 0.00 0.00 0.00

time (sec)

N/A 0.644 0.154 0.000 0.319 0.000 0.000 0.000 0.000

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

188 220 207 0 727 0 0 0 0

N.S.

1 1.17 1.10 0.00 3.87 0.00 0.00 0.00 0.00

time (sec)

N/A 0.488 0.116 0.000 0.305 0.000 0.000 0.000 0.000

Problem 132

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

132 124 259 0 0 0 0 0 0

N.S.

1 0.94 1.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.469 0.931 0.000 0.000 0.000 0.000 0.000 0.000

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 106 321 188 574 200 454 380 228

N.S.

1 0.82 2.47 1.45 4.42 1.54 3.49 2.92 1.75

time (sec)

N/A 0.296 0.272 0.940 0.228 0.272 1.177 0.723 2.817

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

272 208 451 490 1001 410 879 0 503

N.S.

1 0.76 1.66 1.80 3.68 1.51 3.23 0.00 1.85

time (sec)

N/A 0.392 0.290 1.514 0.259 0.273 2.076 0.000 2.680

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

429 326 595 1019 1575 719 1561 0 1069

N.S.

1 0.76 1.39 2.38 3.67 1.68 3.64 0.00 2.49

time (sec)

N/A 0.485 0.399 2.112 0.313 0.261 12.152 0.000 4.783

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

587 445 680 1486 2279 1084 0 874 1883

N.S.

1 0.76 1.16 2.53 3.88 1.85 0.00 1.49 3.21

time (sec)

N/A 0.553 0.581 3.497 0.372 0.295 0.000 1.067 7.763

Problem 137

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

34 34 36 34 36 75 258 36 36

N.S.

1 1.00 1.06 1.00 1.06 2.21 7.59 1.06 1.06

time (sec)

N/A 0.199 0.103 0.718 0.217 0.246 14.055 0.526 2.267

Problem 138

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

32 32 34 32 34 57 165 34 34

N.S.

1 1.00 1.06 1.00 1.06 1.78 5.16 1.06 1.06

time (sec)

N/A 0.190 0.081 0.628 0.220 0.290 4.835 0.577 2.450

Problem 139

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

34 34 36 34 36 65 170 36 36

N.S.

1 1.00 1.06 1.00 1.06 1.91 5.00 1.06 1.06

time (sec)

N/A 0.206 0.104 0.679 0.220 0.268 4.859 0.423 2.643

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

94 91 0 0 0 0 0 0 0

N.S.

1 0.97 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.305 0.000 0.000 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 F F F F F F F(-1)

verified

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

size

152 137 0 0 0 0 0 0 0

N.S.

1 0.90 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.428 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 142

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

34 34 36 34 308 125 0 36 36

N.S.

1 1.00 1.06 1.00 9.06 3.68 0.00 1.06 1.06

time (sec)

N/A 0.196 0.321 0.663 0.227 0.269 0.000 0.643 6.234

Problem 143

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

32 32 34 32 230 107 558 34 34

N.S.

1 1.00 1.06 1.00 7.19 3.34 17.44 1.06 1.06

time (sec)

N/A 0.186 0.239 0.625 0.231 0.269 22.193 0.529 6.396

Problem 144

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

34 34 36 34 166 129 156 36 36

N.S.

1 1.00 1.06 1.00 4.88 3.79 4.59 1.06 1.06

time (sec)

N/A 0.199 0.151 0.615 0.223 0.246 2.862 0.473 7.564

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

150 135 0 0 0 0 0 0 0

N.S.

1 0.90 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.374 0.000 0.000 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 F F F F F(-1) F F(-1)

verified

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

size

266 225 0 0 0 0 0 0 0

N.S.

1 0.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.483 0.000 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 A B B B B F(-2) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 153 364 832 671 563 0 507 936

N.S.

1 0.89 2.13 4.87 3.92 3.29 0.00 2.96 5.47

time (sec)

N/A 0.298 0.540 134.474 0.220 0.263 0.000 7.178 1.428

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 129 273 664 467 417 0 363 520

N.S.

1 0.91 1.92 4.68 3.29 2.94 0.00 2.56 3.66

time (sec)

N/A 0.275 0.323 52.803 0.215 0.282 0.000 2.068 1.184

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 105 194 462 294 282 0 241 262

N.S.

1 0.93 1.72 4.09 2.60 2.50 0.00 2.13 2.32

time (sec)

N/A 0.248 0.193 18.612 0.203 0.275 0.000 0.830 1.033

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 81 126 265 154 163 0 131 127

N.S.

1 0.96 1.50 3.15 1.83 1.94 0.00 1.56 1.51

time (sec)

N/A 0.229 0.101 5.399 0.192 0.263 0.000 0.410 0.911

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

79 79 129 523 0 0 0 0 0

N.S.

1 1.00 1.63 6.62 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.470 0.071 2.591 0.000 0.000 0.000 0.000 0.000

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 107 89 130 116 107 0 111 97

N.S.

1 1.10 0.92 1.34 1.20 1.10 0.00 1.14 1.00

time (sec)

N/A 0.270 0.063 5.723 0.194 0.273 0.000 0.299 1.525

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

137 137 121 334 230 296 0 243 192

N.S.

1 1.00 0.88 2.44 1.68 2.16 0.00 1.77 1.40

time (sec)

N/A 0.295 0.203 19.185 0.202 0.273 0.000 0.325 1.239

Problem 154

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

166 162 143 504 400 540 0 454 317

N.S.

1 0.98 0.86 3.04 2.41 3.25 0.00 2.73 1.91

time (sec)

N/A 0.314 0.235 54.431 0.198 0.285 0.000 0.289 1.579

Problem 155

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

195 185 165 2309 618 820 0 718 555

N.S.

1 0.95 0.85 11.84 3.17 4.21 0.00 3.68 2.85

time (sec)

N/A 0.334 0.219 135.602 0.212 0.291 0.000 0.314 1.956

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

322 383 1709 10586 1871 0 0 0 0

N.S.

1 1.19 5.31 32.88 5.81 0.00 0.00 0.00 0.00

time (sec)

N/A 0.912 0.993 269.189 0.729 0.000 0.000 0.000 0.000

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

263 306 1149 7208 1284 0 0 0 0

N.S.

1 1.16 4.37 27.41 4.88 0.00 0.00 0.00 0.00

time (sec)

N/A 0.768 0.642 107.027 0.695 0.000 0.000 0.000 0.000

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

195 224 656 4394 779 0 0 0 0

N.S.

1 1.15 3.36 22.53 3.99 0.00 0.00 0.00 0.00

time (sec)

N/A 0.566 0.521 37.570 0.686 0.000 0.000 0.000 0.000

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

131 123 269 0 0 0 0 0 0

N.S.

1 0.94 2.05 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.569 0.140 0.000 0.000 0.000 0.000 0.000 0.000

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

129 107 236 299 449 339 0 0 200

N.S.

1 0.83 1.83 2.32 3.48 2.63 0.00 0.00 1.55

time (sec)

N/A 0.383 0.268 7.258 0.222 0.281 0.000 0.000 1.984

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

274 221 332 871 899 919 0 0 444

N.S.

1 0.81 1.21 3.18 3.28 3.35 0.00 0.00 1.62

time (sec)

N/A 0.487 0.353 21.602 0.238 0.303 0.000 0.000 2.122

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

427 342 432 1400 1500 1635 0 0 911

N.S.

1 0.80 1.01 3.28 3.51 3.83 0.00 0.00 2.13

time (sec)

N/A 0.577 0.475 57.746 0.285 0.329 0.000 0.000 3.506

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

587 470 1011 4946 2238 2458 0 0 1579

N.S.

1 0.80 1.72 8.43 3.81 4.19 0.00 0.00 2.69

time (sec)

N/A 0.657 0.604 142.586 0.337 0.371 0.000 0.000 6.745

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

809 747 6885 0 0 0 0 0 0

N.S.

1 0.92 8.51 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.212 2.318 0.000 0.000 0.000 0.000 0.000 0.000

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

614 573 4802 0 0 0 0 0 0

N.S.

1 0.93 7.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.912 1.379 0.000 0.000 0.000 0.000 0.000 0.000

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

376 352 2984 0 0 0 0 0 0

N.S.

1 0.94 7.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.649 0.740 0.000 0.000 0.000 0.000 0.000 0.000

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

186 174 2513 0 0 0 0 0 0

N.S.

1 0.94 13.51 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.651 0.567 0.000 0.000 0.000 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(-1) F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

184 150 524 543 1129 825 0 0 474

N.S.

1 0.82 2.85 2.95 6.14 4.48 0.00 0.00 2.58

time (sec)

N/A 0.444 0.505 38.576 0.259 0.287 0.000 0.000 2.761

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

390 315 693 1622 2246 2244 0 0 966

N.S.

1 0.81 1.78 4.16 5.76 5.75 0.00 0.00 2.48

time (sec)

N/A 0.550 0.692 48.694 0.331 0.356 0.000 0.000 5.298

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

611 493 1003 2687 3630 4008 0 0 2069

N.S.

1 0.81 1.64 4.40 5.94 6.56 0.00 0.00 3.39

time (sec)

N/A 0.678 0.856 95.365 0.429 0.410 0.000 0.000 7.731

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

830 669 1370 8292 5280 6057 0 0 4257

N.S.

1 0.81 1.65 9.99 6.36 7.30 0.00 0.00 5.13

time (sec)

N/A 0.788 1.251 191.847 0.572 0.528 0.000 0.000 8.175

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

96 94 0 0 0 62 0 0 0

N.S.

1 0.98 0.00 0.00 0.00 0.65 0.00 0.00 0.00

time (sec)

N/A 0.409 0.000 0.000 0.000 0.285 0.000 0.000 0.000

Problem 173

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

180 154 142 442 619 433 969 2030 1008

N.S.

1 0.86 0.79 2.46 3.44 2.41 5.38 11.28 5.60

time (sec)

N/A 0.305 0.069 1.155 0.227 0.348 3.778 0.475 1.621

Problem 174

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

149 130 120 314 436 320 706 1506 566

N.S.

1 0.87 0.81 2.11 2.93 2.15 4.74 10.11 3.80

time (sec)

N/A 0.286 0.057 0.928 0.203 0.294 2.219 0.448 1.355

Problem 175

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

118 106 99 206 278 223 491 1056 290

N.S.

1 0.90 0.84 1.75 2.36 1.89 4.16 8.95 2.46

time (sec)

N/A 0.258 0.036 0.786 0.221 0.276 1.478 0.400 1.227

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 78 69 111 143 127 253 627 126

N.S.

1 0.96 0.85 1.37 1.77 1.57 3.12 7.74 1.56

time (sec)

N/A 0.232 0.027 0.645 0.198 0.278 0.935 0.456 1.077

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 81 95 149 0 0 0 617 0

N.S.

1 1.00 1.17 1.84 0.00 0.00 0.00 7.62 0.00

time (sec)

N/A 0.486 0.034 1.358 0.000 0.000 0.000 37.793 0.000

Problem 178

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

64 74 86 81 134 87 231 116 106

N.S.

1 1.16 1.34 1.27 2.09 1.36 3.61 1.81 1.66

time (sec)

N/A 0.206 0.035 0.733 0.198 0.270 0.652 0.583 1.849

Problem 179

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

144 138 128 225 255 221 422 234 208

N.S.

1 0.96 0.89 1.56 1.77 1.53 2.93 1.62 1.44

time (sec)

N/A 0.306 0.063 1.043 0.203 0.269 1.173 0.449 1.932

Problem 180

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

175 163 141 330 428 412 656 447 339

N.S.

1 0.93 0.81 1.89 2.45 2.35 3.75 2.55 1.94

time (sec)

N/A 0.345 0.096 1.269 0.208 0.276 1.770 0.437 2.610

Problem 181

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

206 186 166 437 647 637 944 751 578

N.S.

1 0.90 0.81 2.12 3.14 3.09 4.58 3.65 2.81

time (sec)

N/A 0.355 0.127 2.204 0.224 0.269 2.667 0.831 3.251

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

503 697 512 0 2395 0 0 0 0

N.S.

1 1.39 1.02 0.00 4.76 0.00 0.00 0.00 0.00

time (sec)

N/A 1.738 0.322 0.000 0.314 0.000 0.000 0.000 0.000

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

420 515 392 0 1735 0 0 0 0

N.S.

1 1.23 0.93 0.00 4.13 0.00 0.00 0.00 0.00

time (sec)

N/A 1.260 0.218 0.000 0.312 0.000 0.000 0.000 0.000

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

335 361 290 0 1172 0 0 0 0

N.S.

1 1.08 0.87 0.00 3.50 0.00 0.00 0.00 0.00

time (sec)

N/A 0.888 0.152 0.000 0.308 0.000 0.000 0.000 0.000

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

202 227 203 0 619 0 0 0 0

N.S.

1 1.12 1.00 0.00 3.06 0.00 0.00 0.00 0.00

time (sec)

N/A 0.589 0.114 0.000 0.305 0.000 0.000 0.000 0.000

Problem 186

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

128 120 252 346 0 0 0 0 0

N.S.

1 0.94 1.97 2.70 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.398 0.890 1.417 0.000 0.000 0.000 0.000 0.000

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 112 314 180 416 154 430 174 223

N.S.

1 0.73 2.05 1.18 2.72 1.01 2.81 1.14 1.46

time (sec)

N/A 0.260 0.270 0.730 0.217 0.269 1.208 0.395 3.152

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

296 219 444 485 847 373 892 369 507

N.S.

1 0.74 1.50 1.64 2.86 1.26 3.01 1.25 1.71

time (sec)

N/A 0.319 0.256 1.094 0.242 0.288 2.271 0.444 2.720

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

399 315 582 836 1420 680 1544 714 1064

N.S.

1 0.79 1.46 2.10 3.56 1.70 3.87 1.79 2.67

time (sec)

N/A 0.444 0.345 1.407 0.292 0.271 12.818 0.708 4.475

Problem 190

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

498 379 666 1112 2122 1045 0 1194 1880

N.S.

1 0.76 1.34 2.23 4.26 2.10 0.00 2.40 3.78

time (sec)

N/A 0.466 0.502 2.376 0.360 0.291 0.000 0.562 7.813

Problem 191

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

32 32 34 32 34 52 95 34 34

N.S.

1 1.00 1.06 1.00 1.06 1.62 2.97 1.06 1.06

time (sec)

N/A 0.189 0.539 1.092 0.222 0.261 2.564 14.765 2.020

Problem 192

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

30 30 32 30 32 34 56 32 32

N.S.

1 1.00 1.07 1.00 1.07 1.13 1.87 1.07 1.07

time (sec)

N/A 0.179 0.115 0.909 0.224 0.252 2.042 11.642 2.312

Problem 193

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

32 32 34 32 34 42 61 34 34

N.S.

1 1.00 1.06 1.00 1.06 1.31 1.91 1.06 1.06

time (sec)

N/A 0.194 0.324 0.780 0.223 0.255 2.920 9.754 3.064

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 50 55 0 50 0 0 0

N.S.

1 1.00 0.94 1.04 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 0.276 0.105 3.164 0.000 0.250 0.000 0.000 0.000

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 97 89 126 0 129 0 0 0

N.S.

1 0.89 0.82 1.16 0.00 1.18 0.00 0.00 0.00

time (sec)

N/A 0.355 0.216 3.355 0.000 0.246 0.000 0.000 0.000

Problem 196

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

32 32 34 32 309 79 400 34 34

N.S.

1 1.00 1.06 1.00 9.66 2.47 12.50 1.06 1.06

time (sec)

N/A 0.193 0.933 1.293 0.227 0.251 11.034 0.696 5.577

Problem 197

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

30 30 32 30 231 61 275 32 32

N.S.

1 1.00 1.07 1.00 7.70 2.03 9.17 1.07 1.07

time (sec)

N/A 0.179 0.458 1.158 0.227 0.252 6.975 1.196 6.859

Problem 198

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

32 32 34 32 166 83 92 34 34

N.S.

1 1.00 1.06 1.00 5.19 2.59 2.88 1.06 1.06

time (sec)

N/A 0.193 0.270 1.046 0.265 0.259 1.711 0.709 8.663

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 93 88 107 0 208 0 142 0

N.S.

1 0.89 0.85 1.03 0.00 2.00 0.00 1.37 0.00

time (sec)

N/A 0.318 0.141 3.787 0.000 0.283 0.000 0.586 0.000

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 199 135 268 0 584 0 291 0

N.S.

1 1.25 0.85 1.69 0.00 3.67 0.00 1.83 0.00

time (sec)

N/A 0.550 0.317 4.999 0.000 0.253 0.000 0.537 0.000

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