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Integrals 101 to 178

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 Reduce Mupad

grade

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

verified

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

size

20 20 18 21 20 20 17 28 20 20

N.S.

1 1.00 0.90 1.05 1.00 1.00 0.85 1.40 1.00 1.00

time (sec)

N/A 0.277 0.012 0.081 0.026 0.067 1.281 0.112 0.163 0.048

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 20 21 20 64 71 28 75 71

N.S.

1 1.00 0.91 0.95 0.91 2.91 3.23 1.27 3.41 3.23

time (sec)

N/A 0.280 0.015 0.118 0.026 0.069 2.712 0.133 0.152 12.116

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 22 21 20 86 299 20 84 89

N.S.

1 1.00 0.92 0.88 0.83 3.58 12.46 0.83 3.50 3.71

time (sec)

N/A 0.286 0.056 0.135 0.037 0.070 0.215 0.115 0.170 12.290

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 22 21 20 39 109 20 34 20

N.S.

1 1.00 0.92 0.88 0.83 1.62 4.54 0.83 1.42 0.83

time (sec)

N/A 0.280 0.046 0.101 0.026 0.087 0.111 0.123 0.153 12.048

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 20 21 20 20 20 20 19 20

N.S.

1 1.00 0.91 0.95 0.91 0.91 0.91 0.91 0.86 0.91

time (sec)

N/A 0.280 0.040 2.271 0.032 0.069 0.100 0.106 0.157 12.034

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 22 20 21 20 20 22 20 36 20

N.S.

1 1.00 0.91 0.95 0.91 0.91 1.00 0.91 1.64 0.91

time (sec)

N/A 0.276 0.048 0.216 0.027 0.074 0.128 0.111 0.184 11.976

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 24 22 21 20 81 0 36 91 20

N.S.

1 1.00 0.92 0.88 0.83 3.38 0.00 1.50 3.79 0.83

time (sec)

N/A 0.278 0.055 0.229 0.033 0.076 0.000 0.118 0.181 12.213

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

26 26 24 27 26 43 0 26 39 58

N.S.

1 1.00 0.92 1.04 1.00 1.65 0.00 1.00 1.50 2.23

time (sec)

N/A 0.279 0.099 0.194 0.035 0.097 0.000 0.113 0.166 12.038

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1363 1739 1739 2569 1930 1930 3334 3151 2315 2595

N.S.

1 1.28 1.28 1.88 1.42 1.42 2.45 2.31 1.70 1.90

time (sec)

N/A 7.514 0.835 0.382 0.045 0.089 0.245 0.122 0.157 12.351

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

664 671 671 562 735 735 1166 1126 871 891

N.S.

1 1.01 1.01 0.85 1.11 1.11 1.76 1.70 1.31 1.34

time (sec)

N/A 2.507 0.466 0.293 0.037 0.070 0.102 0.137 0.152 12.183

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

158 158 160 151 156 156 219 214 187 168

N.S.

1 1.00 1.01 0.96 0.99 0.99 1.39 1.35 1.18 1.06

time (sec)

N/A 0.720 0.097 0.233 0.047 0.064 0.045 0.113 0.174 0.035

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

141 141 141 141 170 0 0 170 300 166

N.S.

1 1.00 1.00 1.00 1.21 0.00 0.00 1.21 2.13 1.18

time (sec)

N/A 0.728 0.095 0.251 0.037 0.000 0.000 0.112 0.159 14.097

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

421 419 406 456 2660 0 0 2301 17569 58502

N.S.

1 1.00 0.96 1.08 6.32 0.00 0.00 5.47 41.73 138.96

time (sec)

N/A 2.325 0.558 1.240 0.164 0.000 0.000 0.171 0.717 20.592

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1176 1176 1162 1472 16079 0 0 16944 59 202365

N.S.

1 1.00 0.99 1.25 13.67 0.00 0.00 14.41 0.05 172.08

time (sec)

N/A 9.067 2.595 5.310 1.036 0.000 0.000 0.502 200.034 39.692

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1393 0 12161 2037 0 1943 0 0 59 0

N.S.

1 0.00 8.73 1.46 0.00 1.39 0.00 0.00 0.04 0.00

time (sec)

N/A 0.000 39.037 4.022 0.000 0.210 0.000 0.000 200.020 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

505 0 416 575 0 834 0 0 0 0

N.S.

1 0.00 0.82 1.14 0.00 1.65 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 28.242 4.123 0.000 0.148 0.000 0.000 33.768 0.000

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1151 0 9971 4111 0 5532 0 0 59 0

N.S.

1 0.00 8.66 3.57 0.00 4.81 0.00 0.00 0.05 0.00

time (sec)

N/A 0.000 36.974 4.332 0.000 0.371 0.000 0.000 200.032 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A C A A F A F F F B

verified

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

size

498 2634 252 353 0 151 0 0 625 913

N.S.

1 5.29 0.51 0.71 0.00 0.30 0.00 0.00 1.26 1.83

time (sec)

N/A 16.146 10.600 1.125 0.000 0.074 0.000 0.000 0.211 13.532

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A C A A F A F F F B

verified

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

size

321 1783 207 260 0 106 0 0 427 706

N.S.

1 5.55 0.64 0.81 0.00 0.33 0.00 0.00 1.33 2.20

time (sec)

N/A 6.872 8.775 1.257 0.000 0.080 0.000 0.000 0.173 12.881

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A C A A F A F F F B

verified

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

size

205 1338 166 162 0 63 0 0 180 206

N.S.

1 6.53 0.81 0.79 0.00 0.31 0.00 0.00 0.88 1.00

time (sec)

N/A 3.221 10.345 1.041 0.000 0.078 0.000 0.000 0.168 0.064

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A C A A F A F F F B

verified

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

size

319 1923 205 207 0 207 0 0 0 263

N.S.

1 6.03 0.64 0.65 0.00 0.65 0.00 0.00 0.00 0.82

time (sec)

N/A 7.546 10.398 1.248 0.000 0.085 0.000 0.000 0.191 0.042

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

475 2899 233 276 0 358 0 0 0 0

N.S.

1 6.10 0.49 0.58 0.00 0.75 0.00 0.00 0.00 0.00

time (sec)

N/A 19.564 10.525 1.132 0.000 0.080 0.000 0.000 0.184 0.000

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

386 0 0 0 0 0 0 0 31 0

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.00

time (sec)

N/A 0.000 0.000 0.000 0.000 0.000 0.000 0.000 200.022 0.000

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

470 0 0 0 0 0 0 0 59 0

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.13 0.00

time (sec)

N/A 0.000 0.000 0.000 0.000 0.000 0.000 0.000 200.025 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

431 431 431 382 411 411 600 597 335 462

N.S.

1 1.00 1.00 0.89 0.95 0.95 1.39 1.39 0.78 1.07

time (sec)

N/A 1.667 0.236 0.216 0.034 0.088 0.064 0.113 0.167 0.103

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

112 112 112 109 106 106 138 142 99 114

N.S.

1 1.00 1.00 0.97 0.95 0.95 1.23 1.27 0.88 1.02

time (sec)

N/A 0.521 0.055 0.181 0.037 0.063 0.026 0.114 0.155 0.029

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

196 196 192 179 0 613 0 199 10 2467

N.S.

1 1.00 0.98 0.91 0.00 3.13 0.00 1.02 0.05 12.59

time (sec)

N/A 0.848 0.185 0.183 0.000 32.620 0.000 0.117 0.172 18.285

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

676 695 661 1353 0 0 0 1517 983 26278

N.S.

1 1.03 0.98 2.00 0.00 0.00 0.00 2.24 1.45 38.87

time (sec)

N/A 3.130 1.702 1.060 0.000 0.000 0.000 0.147 0.163 17.012

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

995 0 15681 1698 0 1036 0 0 45 0

N.S.

1 0.00 15.76 1.71 0.00 1.04 0.00 0.00 0.05 0.00

time (sec)

N/A 0.000 18.103 8.194 0.000 0.113 0.000 0.000 200.026 0.000

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

504 0 1086 785 0 464 0 0 45 0

N.S.

1 0.00 2.15 1.56 0.00 0.92 0.00 0.00 0.09 0.00

time (sec)

N/A 0.000 17.665 4.122 0.000 0.084 0.000 0.000 200.028 0.000

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

913 0 10146 2423 0 2763 0 0 45 0

N.S.

1 0.00 11.11 2.65 0.00 3.03 0.00 0.00 0.05 0.00

time (sec)

N/A 0.000 36.315 2.592 0.000 0.197 0.000 0.000 200.025 0.000

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A C C C F C F F F B

verified

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

size

270 252 655 325 0 57 0 0 174 879

N.S.

1 0.93 2.43 1.20 0.00 0.21 0.00 0.00 0.64 3.26

time (sec)

N/A 0.914 10.714 1.275 0.000 0.087 0.000 0.000 0.193 0.130

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

532 0 0 0 0 0 0 0 0 0

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.781 0.000

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

110 118 149 129 122 146 189 152 188 124

N.S.

1 1.07 1.35 1.17 1.11 1.33 1.72 1.38 1.71 1.13

time (sec)

N/A 0.832 0.168 0.430 0.039 0.068 0.060 0.121 0.157 0.050

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

108 82 96 76 72 87 107 90 96 73

N.S.

1 0.76 0.89 0.70 0.67 0.81 0.99 0.83 0.89 0.68

time (sec)

N/A 0.569 0.045 0.303 0.027 0.069 0.051 0.114 0.168 0.031

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

35 35 34 33 32 39 42 32 38 32

N.S.

1 1.00 0.97 0.94 0.91 1.11 1.20 0.91 1.09 0.91

time (sec)

N/A 0.281 0.000 0.178 0.030 0.082 0.031 0.118 0.150 0.023

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

106 96 94 97 91 106 107 102 144 106

N.S.

1 0.91 0.89 0.92 0.86 1.00 1.01 0.96 1.36 1.00

time (sec)

N/A 0.505 0.089 0.392 0.027 0.069 0.551 0.113 0.163 11.967

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

110 100 112 99 95 143 122 203 185 108

N.S.

1 0.91 1.02 0.90 0.86 1.30 1.11 1.85 1.68 0.98

time (sec)

N/A 0.507 0.071 0.431 0.035 0.074 0.889 0.114 0.155 12.235

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

194 230 423 70 0 316 247850 0 3061 1077

N.S.

1 1.19 2.18 0.36 0.00 1.63 1277.58 0.00 15.78 5.55

time (sec)

N/A 1.233 1.070 0.563 0.000 0.130 10.775 0.000 0.156 13.204

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

218 227 460 75 0 387 95302 0 3275 1147

N.S.

1 1.04 2.11 0.34 0.00 1.78 437.17 0.00 15.02 5.26

time (sec)

N/A 1.044 1.109 0.557 0.000 0.098 7.555 0.000 0.170 13.069

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

139 148 277 64 0 200 3281 0 1625 177

N.S.

1 1.06 1.99 0.46 0.00 1.44 23.60 0.00 11.69 1.27

time (sec)

N/A 0.704 0.683 0.481 0.000 0.096 1.464 0.000 0.160 12.263

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

88 97 167 56 0 102 184 0 498 132

N.S.

1 1.10 1.90 0.64 0.00 1.16 2.09 0.00 5.66 1.50

time (sec)

N/A 0.520 0.387 0.417 0.000 0.078 0.597 0.000 0.151 0.157

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

211 226 621 187 0 1738 0 0 11241 12009

N.S.

1 1.07 2.94 0.89 0.00 8.24 0.00 0.00 53.27 56.91

time (sec)

N/A 1.173 4.527 1.302 0.000 6.912 0.000 0.000 0.182 48.638

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

275 298 1347 383 0 5609 0 0 44312 0

N.S.

1 1.08 4.90 1.39 0.00 20.40 0.00 0.00 161.13 0.00

time (sec)

N/A 1.558 7.427 3.329 0.000 93.959 0.000 0.000 0.258 0.000

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

404 424 914 703 0 2724 0 0 15132 645

N.S.

1 1.05 2.26 1.74 0.00 6.74 0.00 0.00 37.46 1.60

time (sec)

N/A 2.034 6.909 2.584 0.000 0.160 0.000 0.000 0.191 1.954

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

284 293 451 382 0 1615 2183 0 7954 466

N.S.

1 1.03 1.59 1.35 0.00 5.69 7.69 0.00 28.01 1.64

time (sec)

N/A 1.301 5.975 2.401 0.000 0.130 162.570 0.000 0.159 1.006

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

179 188 238 211 0 638 462 0 2729 346

N.S.

1 1.05 1.33 1.18 0.00 3.56 2.58 0.00 15.25 1.93

time (sec)

N/A 0.728 3.697 2.398 0.000 0.088 2.413 0.000 0.159 0.613

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

500 518 2761 2312 0 0 0 0 40 0

N.S.

1 1.04 5.52 4.62 0.00 0.00 0.00 0.00 0.08 0.00

time (sec)

N/A 4.264 10.470 18.921 0.000 0.000 0.000 0.000 200.031 0.000

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

564 590 4351 3757 0 0 0 0 40 0

N.S.

1 1.05 7.71 6.66 0.00 0.00 0.00 0.00 0.07 0.00

time (sec)

N/A 6.165 15.919 46.138 0.000 0.000 0.000 0.000 200.025 0.000

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

496 386 17362 350 0 281 0 1711 0 0

N.S.

1 0.78 35.00 0.71 0.00 0.57 0.00 3.45 0.00 0.00

time (sec)

N/A 1.247 17.221 0.572 0.000 0.124 0.000 0.170 3.125 0.000

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

312 268 9146 116 0 155 0 933 0 0

N.S.

1 0.86 29.31 0.37 0.00 0.50 0.00 2.99 0.00 0.00

time (sec)

N/A 0.861 16.739 0.408 0.000 0.113 0.000 0.130 1.303 0.000

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

187 189 1461 75 0 78 0 359 1228 0

N.S.

1 1.01 7.81 0.40 0.00 0.42 0.00 1.92 6.57 0.00

time (sec)

N/A 0.569 2.849 0.230 0.000 0.131 0.000 0.122 0.515 0.000

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

365 313 13435 0 0 1033 0 0 40 0

N.S.

1 0.86 36.81 0.00 0.00 2.83 0.00 0.00 0.11 0.00

time (sec)

N/A 0.948 16.693 0.000 0.000 0.229 0.000 0.000 200.024 0.000

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

435 372 5628 0 0 1309 0 0 40 0

N.S.

1 0.86 12.94 0.00 0.00 3.01 0.00 0.00 0.09 0.00

time (sec)

N/A 0.949 16.252 0.000 0.000 0.330 0.000 0.000 200.019 0.000

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

374 349 1754 0 0 2078 0 0 0 0

N.S.

1 0.93 4.69 0.00 0.00 5.56 0.00 0.00 0.00 0.00

time (sec)

N/A 1.654 17.486 0.000 0.000 0.211 0.000 0.000 29.120 0.000

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

224 226 1497 0 0 1130 0 0 0 0

N.S.

1 1.01 6.68 0.00 0.00 5.04 0.00 0.00 0.00 0.00

time (sec)

N/A 0.693 11.913 0.000 0.000 0.160 0.000 0.000 13.965 0.000

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

124 162 934 0 0 368 0 59 0 0

N.S.

1 1.31 7.53 0.00 0.00 2.97 0.00 0.48 0.00 0.00

time (sec)

N/A 0.484 0.424 0.000 0.000 0.107 0.000 0.124 5.110 0.000

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

329 307 1352 0 0 3961 0 0 40 0

N.S.

1 0.93 4.11 0.00 0.00 12.04 0.00 0.00 0.12 0.00

time (sec)

N/A 0.907 20.363 0.000 0.000 0.495 0.000 0.000 200.021 0.000

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

493 470 451671 0 0 15167 0 0 40 0

N.S.

1 0.95 916.17 0.00 0.00 30.76 0.00 0.00 0.08 0.00

time (sec)

N/A 1.309 88.263 0.000 0.000 4.511 0.000 0.000 200.028 0.000

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

549 498 0 0 0 3837 0 0 40 0

N.S.

1 0.91 0.00 0.00 0.00 6.99 0.00 0.00 0.07 0.00

time (sec)

N/A 1.482 0.000 0.000 0.000 0.363 0.000 0.000 200.031 0.000

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

461 428 0 0 0 2326 0 0 38 0

N.S.

1 0.93 0.00 0.00 0.00 5.05 0.00 0.00 0.08 0.00

time (sec)

N/A 0.975 0.000 0.000 0.000 0.284 0.000 0.000 200.034 0.000

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

399 392 0 0 0 607 0 0 32 0

N.S.

1 0.98 0.00 0.00 0.00 1.52 0.00 0.00 0.08 0.00

time (sec)

N/A 0.755 0.000 0.000 0.000 0.106 0.000 0.000 200.050 0.000

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

846 806 0 0 0 43371 0 0 40 0

N.S.

1 0.95 0.00 0.00 0.00 51.27 0.00 0.00 0.05 0.00

time (sec)

N/A 2.377 0.000 0.000 0.000 24.608 0.000 0.000 200.102 0.000

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1153 1113 0 0 0 81003 0 0 40 0

N.S.

1 0.97 0.00 0.00 0.00 70.25 0.00 0.00 0.03 0.00

time (sec)

N/A 3.447 0.000 0.000 0.000 129.875 0.000 0.000 200.022 0.000

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

171 171 171 146 151 151 172 179 177 148

N.S.

1 1.00 1.00 0.85 0.88 0.88 1.01 1.05 1.04 0.87

time (sec)

N/A 0.805 0.047 0.229 0.027 0.060 0.045 0.108 0.149 21.626

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

119 119 118 104 104 104 121 125 123 106

N.S.

1 1.00 0.99 0.87 0.87 0.87 1.02 1.05 1.03 0.89

time (sec)

N/A 0.597 0.032 0.171 0.034 0.059 0.033 0.117 0.164 0.060

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

71 71 71 58 61 61 61 69 69 57

N.S.

1 1.00 1.00 0.82 0.86 0.86 0.86 0.97 0.97 0.80

time (sec)

N/A 0.414 0.018 0.133 0.032 0.073 0.026 0.114 0.153 0.034

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

297 920 68 47 0 7641 298 0 100 369

N.S.

1 3.10 0.23 0.16 0.00 25.73 1.00 0.00 0.34 1.24

time (sec)

N/A 14.029 0.025 0.066 0.000 1.546 8.271 0.000 0.150 0.660

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

816 1777 161 114 0 5331 343 0 797 997

N.S.

1 2.18 0.20 0.14 0.00 6.53 0.42 0.00 0.98 1.22

time (sec)

N/A 54.904 0.053 0.087 0.000 1.500 12.045 0.000 0.160 0.601

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

520 1899 0 0 0 0 0 0 0 0

N.S.

1 3.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.148 0.000 0.000 0.000 0.000 0.000 0.000 0.161 0.000

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

171 171 171 146 151 151 172 179 177 145

N.S.

1 1.00 1.00 0.85 0.88 0.88 1.01 1.05 1.04 0.85

time (sec)

N/A 0.401 0.041 0.232 0.035 0.065 0.036 0.134 0.146 0.145

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

118 118 118 102 104 104 114 124 123 101

N.S.

1 1.00 1.00 0.86 0.88 0.88 0.97 1.05 1.04 0.86

time (sec)

N/A 0.319 0.032 0.172 0.038 0.068 0.028 0.112 0.158 0.057

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

71 71 71 56 61 61 61 68 69 55

N.S.

1 1.00 1.00 0.79 0.86 0.86 0.86 0.96 0.97 0.77

time (sec)

N/A 0.237 0.016 0.133 0.028 0.062 0.022 0.135 0.147 0.031

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

706 681 68 47 0 7620 296 0 100 365

N.S.

1 0.96 0.10 0.07 0.00 10.79 0.42 0.00 0.14 0.52

time (sec)

N/A 3.646 0.025 0.064 0.000 1.502 8.061 0.000 0.154 21.930

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1237 1268 160 114 0 5342 342 0 797 989

N.S.

1 1.03 0.13 0.09 0.00 4.32 0.28 0.00 0.64 0.80

time (sec)

N/A 8.601 0.054 0.088 0.000 1.540 8.461 0.000 0.168 22.116

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

960 1284 0 0 0 0 0 0 0 0

N.S.

1 1.34 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.888 0.000 0.000 0.000 0.000 0.000 0.000 0.175 0.000

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

19 19 25 18 17 17 17 20 17 17

N.S.

1 1.00 1.32 0.95 0.89 0.89 0.89 1.05 0.89 0.89

time (sec)

N/A 0.202 0.010 0.064 0.033 0.076 0.071 0.120 0.159 0.062

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

42 42 22 25 24 24 20 24 41 24

N.S.

1 1.00 0.52 0.60 0.57 0.57 0.48 0.57 0.98 0.57

time (sec)

N/A 0.330 0.066 0.113 0.035 0.077 13.482 0.137 0.152 0.123

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