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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 A B F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 33 144 43 132 0 0 0 0

N.S.

1 0.94 4.11 1.23 3.77 0.00 0.00 0.00 0.00

time (sec)

N/A 0.247 0.019 0.452 0.203 0.000 0.000 0.000 0.000

Problem 102

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

168 167 270 599 333 385 644 2333 742

N.S.

1 0.99 1.61 3.57 1.98 2.29 3.83 13.89 4.42

time (sec)

N/A 0.463 0.142 0.559 0.207 0.273 0.697 0.337 5.386

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 128 174 351 207 241 369 973 386

N.S.

1 1.07 1.45 2.92 1.72 2.01 3.08 8.11 3.22

time (sec)

N/A 0.402 0.085 0.485 0.194 0.269 0.520 0.299 4.694

Problem 104

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

97 106 138 121 109 133 173 338 136

N.S.

1 1.09 1.42 1.25 1.12 1.37 1.78 3.48 1.40

time (sec)

N/A 0.351 0.043 0.177 0.208 0.261 0.406 0.283 5.235

Problem 105

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

40 40 48 35 36 60 46 202 48

N.S.

1 1.00 1.20 0.88 0.90 1.50 1.15 5.05 1.20

time (sec)

N/A 0.182 0.010 0.104 0.200 0.260 0.191 0.265 4.561

Problem 106

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

130 148 206 191 0 0 0 0 0

N.S.

1 1.14 1.58 1.47 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.552 0.074 1.223 0.000 0.000 0.000 0.000 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 121 125 137 121 262 1605 472 175

N.S.

1 1.05 1.09 1.19 1.05 2.28 13.96 4.10 1.52

time (sec)

N/A 0.417 0.131 0.633 0.201 0.337 2.457 0.282 5.351

Problem 108

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

167 170 174 198 291 833 19859 2562 422

N.S.

1 1.02 1.04 1.19 1.74 4.99 118.92 15.34 2.53

time (sec)

N/A 0.488 0.205 1.049 0.211 0.806 8.752 0.343 6.126

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

374 374 1115 1411 791 0 0 0 0

N.S.

1 1.00 2.98 3.77 2.11 0.00 0.00 0.00 0.00

time (sec)

N/A 0.800 7.064 0.671 0.417 0.000 0.000 0.000 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

221 231 295 450 400 0 0 0 0

N.S.

1 1.05 1.33 2.04 1.81 0.00 0.00 0.00 0.00

time (sec)

N/A 0.636 0.922 0.362 0.413 0.000 0.000 0.000 0.000

Problem 111

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

97 93 111 174 0 0 0 0 0

N.S.

1 0.96 1.14 1.79 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.503 0.141 0.439 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 C C F F F F F(-1)

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

214 241 1767 1603 0 0 0 0 0

N.S.

1 1.13 8.26 7.49 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.418 13.432 9.717 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 C A F F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

480 491 470 590 0 0 0 0 0

N.S.

1 1.02 0.98 1.23 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.807 5.990 1.184 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 C C F F F F F(-1)

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

546 533 2646 8597 0 0 0 0 0

N.S.

1 0.98 4.85 15.75 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.132 9.608 27.127 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 C C F F F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

326 324 600 7528 0 0 0 0 0

N.S.

1 0.99 1.84 23.09 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.899 3.692 5.556 0.000 0.000 0.000 0.000 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 130 208 372 0 0 0 0 0

N.S.

1 0.98 1.58 2.82 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.729 0.240 0.851 0.000 0.000 0.000 0.000 0.000

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

308 344 0 3250 0 0 0 0 0

N.S.

1 1.12 0.00 10.55 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.477 0.000 12.702 0.000 0.000 0.000 0.000 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

1089 1085 1945 4101 0 0 0 0 0

N.S.

1 1.00 1.79 3.77 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.793 13.648 12.353 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 F F F F F F F(-1)

verified

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

size

162 222 0 0 0 0 0 0 0

N.S.

1 1.37 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.470 0.000 0.000 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 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

20 20 22 20 253 36 19 22 22

N.S.

1 1.00 1.10 1.00 12.65 1.80 0.95 1.10 1.10

time (sec)

N/A 0.313 2.092 0.361 2.550 0.255 85.904 0.342 3.874

Problem 121

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 20 418 52 0 22 22

N.S.

1 1.00 1.10 1.00 20.90 2.60 0.00 1.10 1.10

time (sec)

N/A 0.306 0.316 0.358 4.130 0.257 0.000 0.375 3.862

Problem 122

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 0.250 0.136 0.654 0.799 0.261 8.499 0.730 4.272

Problem 123

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

460 453 0 1681 0 0 0 0 0

N.S.

1 0.98 0.00 3.65 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.198 0.000 1.381 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 F B F F F F F(-1)

verified

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

size

302 305 0 926 0 0 0 0 0

N.S.

1 1.01 0.00 3.07 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.844 0.000 0.898 0.000 0.000 0.000 0.000 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 84 98 372 0 0 0 0 0

N.S.

1 0.94 1.10 4.18 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.292 0.344 0.671 0.000 0.000 0.000 0.000 0.000

Problem 126

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 0.245 0.206 0.566 0.372 0.235 3.650 0.429 3.988

Problem 127

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 36 246 91 126 38 39

N.S.

1 1.00 1.05 0.90 6.15 2.28 3.15 0.95 0.98

time (sec)

N/A 0.236 0.864 0.566 0.426 0.264 10.502 0.824 5.007

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 34 49 38 81 0 90 96

N.S.

1 1.00 0.92 1.32 1.03 2.19 0.00 2.43 2.59

time (sec)

N/A 0.181 0.033 0.210 0.206 0.249 0.000 0.277 4.297

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 20 20 19 19 19 71 19

N.S.

1 1.00 0.87 0.87 0.83 0.83 0.83 3.09 0.83

time (sec)

N/A 0.159 0.013 0.487 0.253 0.251 0.104 0.287 0.141

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 20 20 19 19 39 71 19

N.S.

1 1.00 0.87 0.87 0.83 0.83 1.70 3.09 0.83

time (sec)

N/A 0.179 0.012 0.421 0.254 0.248 0.158 0.278 4.101

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 18 17 16 14 19 69 16

N.S.

1 1.00 1.12 1.06 1.00 0.88 1.19 4.31 1.00

time (sec)

N/A 0.146 0.007 0.555 0.251 0.246 0.072 0.262 3.747

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 19 21 34 15 0 15 59

N.S.

1 1.00 0.90 1.00 1.62 0.71 0.00 0.71 2.81

time (sec)

N/A 0.176 0.014 0.243 0.222 0.240 0.000 0.308 0.194

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 18 20 17 18 14 70 17

N.S.

1 1.00 1.06 1.18 1.00 1.06 0.82 4.12 1.00

time (sec)

N/A 0.149 0.014 0.319 0.253 0.251 0.086 0.287 0.094

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 18 17 19 16 19 71 16

N.S.

1 1.00 0.78 0.74 0.83 0.70 0.83 3.09 0.70

time (sec)

N/A 0.150 0.012 0.306 0.257 0.239 0.177 0.283 3.753

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 20 19 19 16 20 71 19

N.S.

1 1.00 0.87 0.83 0.83 0.70 0.87 3.09 0.83

time (sec)

N/A 0.153 0.012 0.325 0.261 0.259 0.234 0.271 3.767

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 66 62 112 73 264 0 0 203

N.S.

1 0.93 0.87 1.58 1.03 3.72 0.00 0.00 2.86

time (sec)

N/A 0.217 0.122 0.733 0.265 0.253 0.000 0.000 4.013

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 45 37 37 36 48 37 41 36

N.S.

1 1.07 0.88 0.88 0.86 1.14 0.88 0.98 0.86

time (sec)

N/A 0.197 0.028 28.279 0.303 0.249 0.206 0.291 3.839

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 45 37 37 36 48 37 41 36

N.S.

1 1.07 0.88 0.88 0.86 1.14 0.88 0.98 0.86

time (sec)

N/A 0.201 0.034 25.125 0.290 0.249 0.145 0.286 4.218

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 74 37 36 48 41 41 36

N.S.

1 1.00 2.18 1.09 1.06 1.41 1.21 1.21 1.06

time (sec)

N/A 0.193 0.164 24.160 0.304 0.259 0.194 0.290 3.804

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 15 33 39 20 39 33

N.S.

1 1.00 1.00 0.94 2.06 2.44 1.25 2.44 2.06

time (sec)

N/A 0.153 0.006 0.422 0.298 0.240 0.091 0.280 4.174

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

49 50 53 664 38 36 0 37 183

N.S.

1 1.02 1.08 13.55 0.78 0.73 0.00 0.76 3.73

time (sec)

N/A 0.211 0.083 0.181 0.510 0.248 0.000 0.287 0.297

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

39 39 37 647 54 41 0 36 207

N.S.

1 1.00 0.95 16.59 1.38 1.05 0.00 0.92 5.31

time (sec)

N/A 0.197 0.033 0.152 0.247 0.245 0.000 0.291 3.905

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 42 39 34 38 32 37 34

N.S.

1 1.00 1.17 1.08 0.94 1.06 0.89 1.03 0.94

time (sec)

N/A 0.199 0.030 0.293 0.304 0.247 0.184 0.297 4.060

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 34 33 36 40 37 38 32

N.S.

1 1.00 1.10 1.06 1.16 1.29 1.19 1.23 1.03

time (sec)

N/A 0.167 0.029 0.257 0.305 0.240 0.226 0.287 3.810

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 37 36 36 40 39 38 36

N.S.

1 1.00 0.58 0.56 0.56 0.62 0.61 0.59 0.56

time (sec)

N/A 0.223 0.021 0.297 0.320 0.245 0.299 0.292 3.809

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 95 97 197 109 627 0 0 332

N.S.

1 0.86 0.88 1.79 0.99 5.70 0.00 0.00 3.02

time (sec)

N/A 0.289 0.112 6.026 0.312 0.258 0.000 0.000 4.041

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

61 67 54 0 54 88 56 77 53

N.S.

1 1.10 0.89 0.00 0.89 1.44 0.92 1.26 0.87

time (sec)

N/A 0.242 0.023 0.000 0.335 0.248 0.444 0.288 3.921

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

61 67 54 0 54 88 58 77 53

N.S.

1 1.10 0.89 0.00 0.89 1.44 0.95 1.26 0.87

time (sec)

N/A 0.246 0.019 0.000 0.328 0.251 0.314 0.297 4.245

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

53 61 54 0 54 88 56 77 53

N.S.

1 1.15 1.02 0.00 1.02 1.66 1.06 1.45 1.00

time (sec)

N/A 0.238 0.017 0.000 0.346 0.260 0.209 0.298 3.853

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 99 54 54 87 41 77 53

N.S.

1 1.00 2.91 1.59 1.59 2.56 1.21 2.26 1.56

time (sec)

N/A 0.186 0.173 25.289 0.343 0.257 0.261 0.289 0.124

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 15 51 76 20 75 47

N.S.

1 1.00 1.00 0.94 3.19 4.75 1.25 4.69 2.94

time (sec)

N/A 0.153 0.006 25.865 0.346 0.241 0.118 0.277 3.833

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

77 79 104 3294 74 75 0 74 306

N.S.

1 1.03 1.35 42.78 0.96 0.97 0.00 0.96 3.97

time (sec)

N/A 0.260 0.098 0.287 0.539 0.247 0.000 0.297 0.163

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

68 68 62 3248 124 79 0 74 372

N.S.

1 1.00 0.91 47.76 1.82 1.16 0.00 1.09 5.47

time (sec)

N/A 0.253 0.028 0.256 0.426 0.251 0.000 0.295 3.884

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

60 61 66 3227 72 77 0 71 383

N.S.

1 1.02 1.10 53.78 1.20 1.28 0.00 1.18 6.38

time (sec)

N/A 0.246 0.033 0.275 0.309 0.251 0.000 0.300 3.995

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 55 60 56 52 75 51 73 51

N.S.

1 1.00 1.09 1.02 0.95 1.36 0.93 1.33 0.93

time (sec)

N/A 0.244 0.023 0.993 0.347 0.242 0.231 0.294 3.859

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C B C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 50 49 53 75 56 74 48

N.S.

1 1.00 1.61 1.58 1.71 2.42 1.81 2.39 1.55

time (sec)

N/A 0.173 0.028 1.015 0.342 0.260 0.293 0.298 4.180

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 54 53 54 75 60 74 53

N.S.

1 1.00 0.84 0.83 0.84 1.17 0.94 1.16 0.83

time (sec)

N/A 0.237 0.032 0.962 0.354 0.251 0.402 0.328 0.133

Problem 158

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

53 53 51 0 0 0 0 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.194 0.060 0.000 0.000 0.000 0.000 0.000 0.000

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

81 87 79 130774 85 90 0 81 354

N.S.

1 1.07 0.98 1614.49 1.05 1.11 0.00 1.00 4.37

time (sec)

N/A 0.305 0.034 1.417 0.377 0.245 0.000 0.295 0.135

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

56 59 55 28786 51 51 0 50 234

N.S.

1 1.05 0.98 514.04 0.91 0.91 0.00 0.89 4.18

time (sec)

N/A 0.247 0.030 0.370 0.366 0.248 0.000 0.300 0.286

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

31 31 31 4303 30 30 0 28 108

N.S.

1 1.00 1.00 138.81 0.97 0.97 0.00 0.90 3.48

time (sec)

N/A 0.192 0.024 0.197 0.360 0.255 0.000 0.285 3.914

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 12 13 16 16 17 14 12

N.S.

1 1.00 1.00 1.08 1.33 1.33 1.42 1.17 1.00

time (sec)

N/A 0.149 0.093 0.215 0.284 0.249 0.198 0.304 3.802

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

44 44 29 972 37 28 0 31 113

N.S.

1 1.00 0.66 22.09 0.84 0.64 0.00 0.70 2.57

time (sec)

N/A 0.215 0.021 7.070 0.358 0.253 0.000 0.287 5.786

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

65 81 45 0 65 50 0 62 220

N.S.

1 1.25 0.69 0.00 1.00 0.77 0.00 0.95 3.38

time (sec)

N/A 0.267 0.022 0.000 0.358 0.249 0.000 0.296 6.122

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F C C F C B

verified

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

size

92 121 66 0 106 95 0 107 300

N.S.

1 1.32 0.72 0.00 1.15 1.03 0.00 1.16 3.26

time (sec)

N/A 0.348 0.023 0.000 0.376 0.247 0.000 0.281 7.206

Problem 166

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

65 65 51 0 0 0 0 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.234 0.825 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 A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

98 110 106 131085 179 212 0 135 669

N.S.

1 1.12 1.08 1337.60 1.83 2.16 0.00 1.38 6.83

time (sec)

N/A 0.364 0.075 1.565 0.510 0.252 0.000 0.313 3.899

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

75 82 83 29109 123 151 0 97 490

N.S.

1 1.09 1.11 388.12 1.64 2.01 0.00 1.29 6.53

time (sec)

N/A 0.294 0.041 0.383 0.517 0.253 0.000 0.293 0.181

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

50 54 56 4626 81 95 0 66 302

N.S.

1 1.08 1.12 92.52 1.62 1.90 0.00 1.32 6.04

time (sec)

N/A 0.237 0.055 0.204 0.527 0.254 0.000 0.287 3.962

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 27 35 46 53 36 47 28

N.S.

1 1.00 0.96 1.25 1.64 1.89 1.29 1.68 1.00

time (sec)

N/A 0.186 0.119 0.142 0.537 0.256 12.365 0.289 0.100

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 15 18 19 20 19 14

N.S.

1 1.00 1.00 1.07 1.29 1.36 1.43 1.36 1.00

time (sec)

N/A 0.150 0.006 0.181 0.289 0.235 12.295 0.287 3.839

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

70 88 53 0 78 93 0 78 421

N.S.

1 1.26 0.76 0.00 1.11 1.33 0.00 1.11 6.01

time (sec)

N/A 0.286 0.112 0.000 0.518 0.246 0.000 0.291 7.715

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

102 135 70 5357 135 157 0 136 453

N.S.

1 1.32 0.69 52.52 1.32 1.54 0.00 1.33 4.44

time (sec)

N/A 0.354 0.047 0.352 0.511 0.257 0.000 0.285 6.677

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

143 187 92 0 190 245 0 203 689

N.S.

1 1.31 0.64 0.00 1.33 1.71 0.00 1.42 4.82

time (sec)

N/A 0.462 0.032 0.000 0.533 0.268 0.000 0.290 7.852

Problem 175

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

94 97 51 0 0 0 0 0 0

N.S.

1 1.03 0.54 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.296 0.878 0.000 0.000 0.000 0.000 0.000 0.000

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

92 107 114 29456 198 265 0 163 867

N.S.

1 1.16 1.24 320.17 2.15 2.88 0.00 1.77 9.42

time (sec)

N/A 0.354 0.041 0.433 0.777 0.243 0.000 0.302 4.336

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

71 81 86 4977 146 195 0 123 620

N.S.

1 1.14 1.21 70.10 2.06 2.75 0.00 1.73 8.73

time (sec)

N/A 0.296 0.048 0.245 0.798 0.246 0.000 0.305 4.096

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 52 49 54 96 123 54 92 46

N.S.

1 1.11 1.04 1.15 2.04 2.62 1.15 1.96 0.98

time (sec)

N/A 0.232 0.032 0.172 0.772 0.251 24.640 0.301 3.859

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 27 26 63 60 42 61 25

N.S.

1 1.00 0.79 0.76 1.85 1.76 1.24 1.79 0.74

time (sec)

N/A 0.187 0.105 0.156 0.771 0.238 24.808 0.301 0.098

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 15 28 44 24 44 14

N.S.

1 1.00 1.00 0.94 1.75 2.75 1.50 2.75 0.88

time (sec)

N/A 0.152 0.006 0.211 0.300 0.244 24.853 0.287 3.803

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C F C B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

97 134 74 5655 171 231 0 173 902

N.S.

1 1.38 0.76 58.30 1.76 2.38 0.00 1.78 9.30

time (sec)

N/A 0.360 0.141 0.353 0.820 0.249 0.000 0.308 9.788

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

131 181 93 0 245 340 0 258 1074

N.S.

1 1.38 0.71 0.00 1.87 2.60 0.00 1.97 8.20

time (sec)

N/A 0.458 0.040 0.000 0.875 0.250 0.000 0.328 8.287

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

170 231 107 0 331 461 0 343 1251

N.S.

1 1.36 0.63 0.00 1.95 2.71 0.00 2.02 7.36

time (sec)

N/A 0.573 0.031 0.000 0.783 0.257 0.000 0.312 10.019

Problem 184

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

79 79 71 0 0 0 0 0 0

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.225 0.104 0.000 0.000 0.000 0.000 0.000 0.000

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B C C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 150 146 420 380 828 0 0 546

N.S.

1 0.91 0.88 2.55 2.30 5.02 0.00 0.00 3.31

time (sec)

N/A 0.442 0.088 16.412 0.376 0.257 0.000 0.000 4.815

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B C C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 116 106 277 257 498 0 0 418

N.S.

1 0.96 0.88 2.29 2.12 4.12 0.00 0.00 3.45

time (sec)

N/A 0.346 0.052 10.861 0.379 0.259 0.000 0.000 4.204

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 71 163 166 276 0 0 304

N.S.

1 1.00 0.87 1.99 2.02 3.37 0.00 0.00 3.71

time (sec)

N/A 0.275 0.053 9.523 0.374 0.258 0.000 0.000 3.984

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 41 77 102 130 0 0 205

N.S.

1 1.00 0.85 1.60 2.12 2.71 0.00 0.00 4.27

time (sec)

N/A 0.206 0.036 9.098 0.439 0.246 0.000 0.000 3.909

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C C B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 21 65 58 51 27 121

N.S.

1 1.00 1.00 1.05 3.25 2.90 2.55 1.35 6.05

time (sec)

N/A 0.157 0.012 9.137 0.349 0.249 0.268 0.275 3.891

Problem 190

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

64 64 60 0 0 0 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.198 0.061 0.000 0.000 0.000 0.000 0.000 0.000

Problem 191

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

71 71 67 0 0 0 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.229 0.029 0.000 0.000 0.000 0.000 0.000 0.000

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

101 98 67 0 0 0 0 0 0

N.S.

1 0.97 0.66 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.290 0.033 0.000 0.000 0.000 0.000 0.000 0.000

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 34 49 38 81 0 90 96

N.S.

1 1.00 0.92 1.32 1.03 2.19 0.00 2.43 2.59

time (sec)

N/A 0.175 0.018 0.148 0.215 0.245 0.000 0.285 0.002

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 20 20 13 13 76 13 19

N.S.

1 1.00 0.87 0.87 0.57 0.57 3.30 0.57 0.83

time (sec)

N/A 0.163 0.016 0.309 0.240 0.239 4.413 0.262 3.755

Problem 195

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

23 23 20 20 13 13 180 13 19

N.S.

1 1.00 0.87 0.87 0.57 0.57 7.83 0.57 0.83

time (sec)

N/A 0.179 0.012 0.280 0.195 0.204 2.642 0.265 0.059

Problem 196

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 19 10 10 78 10 16

N.S.

1 1.00 1.12 1.19 0.62 0.62 4.88 0.62 1.00

time (sec)

N/A 0.151 0.006 0.355 0.185 0.208 1.471 0.271 0.128

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 19 21 8 8 0 9 58

N.S.

1 1.00 0.90 1.00 0.38 0.38 0.00 0.43 2.76

time (sec)

N/A 0.174 0.014 0.171 0.181 0.236 0.000 0.267 4.257

Problem 198

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

17 17 18 21 11 13 68 12 17

N.S.

1 1.00 1.06 1.24 0.65 0.76 4.00 0.71 1.00

time (sec)

N/A 0.159 0.013 0.262 0.182 0.237 2.611 0.264 3.750

Problem 199

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

23 23 18 20 11 11 80 11 16

N.S.

1 1.00 0.78 0.87 0.48 0.48 3.48 0.48 0.70

time (sec)

N/A 0.158 0.011 0.255 0.187 0.228 4.361 0.272 4.130

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 40 39 36 33 57 0 0 0

N.S.

1 1.48 1.44 1.33 1.22 2.11 0.00 0.00 0.00

time (sec)

N/A 0.303 0.011 0.295 0.241 0.252 0.000 0.000 0.000

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