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Integrals 101 to 132

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 C F B A A B B

verified

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

size

220 209 185 218 0 1886 332 310 1828 430

N.S.

1 0.95 0.84 0.99 0.00 8.57 1.51 1.41 8.31 1.95

time (sec)

N/A 0.553 0.086 0.623 0.000 0.186 1.970 0.149 0.240 0.861

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

216 200 182 190 0 1822 298 298 1796 349

N.S.

1 0.93 0.84 0.88 0.00 8.44 1.38 1.38 8.31 1.62

time (sec)

N/A 0.541 0.013 0.617 0.000 0.128 1.891 0.150 0.223 0.996

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

26 26 26 47 136 136 155 46 135 134

N.S.

1 1.00 1.00 1.81 5.23 5.23 5.96 1.77 5.19 5.15

time (sec)

N/A 0.245 0.008 0.580 0.046 0.118 1.711 0.142 0.275 0.631

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

207 207 181 216 0 1780 323 286 1829 357

N.S.

1 1.00 0.87 1.04 0.00 8.60 1.56 1.38 8.84 1.72

time (sec)

N/A 0.553 0.009 0.340 0.000 0.182 1.647 0.159 0.245 0.613

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

94 77 66 148 258 474 292 153 1405 249

N.S.

1 0.82 0.70 1.57 2.74 5.04 3.11 1.63 14.95 2.65

time (sec)

N/A 0.345 0.032 0.784 0.049 0.092 2.250 0.148 0.283 1.257

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

237 228 199 219 0 879 445 295 2310 485

N.S.

1 0.96 0.84 0.92 0.00 3.71 1.88 1.24 9.75 2.05

time (sec)

N/A 0.603 0.063 0.870 0.000 0.161 2.717 0.142 0.281 2.041

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

235 225 195 192 0 1051 500 371 2805 563

N.S.

1 0.96 0.83 0.82 0.00 4.47 2.13 1.58 11.94 2.40

time (sec)

N/A 0.610 0.082 0.897 0.000 0.139 4.090 0.154 0.273 2.923

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

116 95 83 165 474 919 578 262 2664 507

N.S.

1 0.82 0.72 1.42 4.09 7.92 4.98 2.26 22.97 4.37

time (sec)

N/A 0.378 0.033 0.855 0.066 0.169 3.782 0.144 0.268 2.820

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

30 30 30 29 28 104 0 62 105 88

N.S.

1 1.00 1.00 0.97 0.93 3.47 0.00 2.07 3.50 2.93

time (sec)

N/A 0.268 0.100 1.216 0.032 0.112 0.000 0.125 0.250 0.605

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

23 29 80 22 21 108 126 25 117 107

N.S.

1 1.26 3.48 0.96 0.91 4.70 5.48 1.09 5.09 4.65

time (sec)

N/A 0.281 0.014 0.629 0.025 0.072 0.035 0.124 0.242 0.067

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

23 23 172 22 21 250 299 21 286 229

N.S.

1 1.00 7.48 0.96 0.91 10.87 13.00 0.91 12.43 9.96

time (sec)

N/A 0.257 0.027 0.625 0.026 0.086 0.061 0.124 0.209 0.506

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

23 23 308 22 21 432 541 21 523 376

N.S.

1 1.00 13.39 0.96 0.91 18.78 23.52 0.91 22.74 16.35

time (sec)

N/A 0.255 0.056 0.642 0.033 0.105 0.078 0.116 0.208 0.289

Problem 113

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

22 22 22 21 20 54 56 20 54 54

N.S.

1 1.00 1.00 0.95 0.91 2.45 2.55 0.91 2.45 2.45

time (sec)

N/A 0.255 0.008 0.556 0.031 0.095 0.174 0.131 0.247 0.102

Problem 114

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

23 23 23 22 21 66 73 21 55 55

N.S.

1 1.00 1.00 0.96 0.91 2.87 3.17 0.91 2.39 2.39

time (sec)

N/A 0.256 0.009 0.582 0.025 0.083 0.847 0.130 0.223 0.583

Problem 115

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

23 23 23 22 21 172 197 21 173 171

N.S.

1 1.00 1.00 0.96 0.91 7.48 8.57 0.91 7.52 7.43

time (sec)

N/A 0.255 0.011 0.620 0.026 0.161 2.291 0.147 0.237 1.555

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

234 227 132 108 0 6315 238 0 460 374

N.S.

1 0.97 0.56 0.46 0.00 26.99 1.02 0.00 1.97 1.60

time (sec)

N/A 0.819 0.038 0.201 0.000 10.892 1.749 0.000 0.240 1.502

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

210 197 81 74 0 4759 158 0 327 437

N.S.

1 0.94 0.39 0.35 0.00 22.66 0.75 0.00 1.56 2.08

time (sec)

N/A 0.773 0.021 0.198 0.000 0.774 0.624 0.000 0.258 0.706

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

180 171 79 72 0 1950 83 0 232 145

N.S.

1 0.95 0.44 0.40 0.00 10.83 0.46 0.00 1.29 0.81

time (sec)

N/A 0.618 0.018 0.188 0.000 0.730 0.417 0.000 0.203 0.657

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

140 131 116 71 0 442 26 160 111 144

N.S.

1 0.94 0.83 0.51 0.00 3.16 0.19 1.14 0.79 1.03

time (sec)

N/A 0.462 0.009 0.178 0.000 0.110 0.160 0.121 0.198 0.003

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

224 241 119 105 0 4370 0 0 1347 553

N.S.

1 1.08 0.53 0.47 0.00 19.51 0.00 0.00 6.01 2.47

time (sec)

N/A 0.886 0.036 0.250 0.000 0.780 0.000 0.000 0.223 0.537

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

312 315 173 143 0 8919 0 0 3657 1588

N.S.

1 1.01 0.55 0.46 0.00 28.59 0.00 0.00 11.72 5.09

time (sec)

N/A 1.200 0.064 0.275 0.000 1.146 0.000 0.000 0.276 0.719

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

388 380 244 200 0 14765 0 0 6603 1328

N.S.

1 0.98 0.63 0.52 0.00 38.05 0.00 0.00 17.02 3.42

time (sec)

N/A 1.413 0.104 0.312 0.000 3.838 0.000 0.000 0.305 0.884

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

361 349 1258 4787 0 0 0 0 403 0

N.S.

1 0.97 3.48 13.26 0.00 0.00 0.00 0.00 1.12 0.00

time (sec)

N/A 0.770 15.652 18.929 0.000 0.000 0.000 0.000 0.300 0.000

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

326 318 553 2153 0 0 0 0 473 0

N.S.

1 0.98 1.70 6.60 0.00 0.00 0.00 0.00 1.45 0.00

time (sec)

N/A 0.676 11.671 5.142 0.000 0.000 0.000 0.000 0.325 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

154 152 389 1528 0 0 0 0 186 0

N.S.

1 0.99 2.53 9.92 0.00 0.00 0.00 0.00 1.21 0.00

time (sec)

N/A 0.466 10.377 3.628 0.000 0.000 0.000 0.000 0.294 0.000

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

111 111 90 1036 0 0 0 0 96 56

N.S.

1 1.00 0.81 9.33 0.00 0.00 0.00 0.00 0.86 0.50

time (sec)

N/A 0.296 10.040 2.385 0.000 0.000 0.000 0.000 0.288 0.843

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

413 436 442 1582 0 0 0 0 19 0

N.S.

1 1.06 1.07 3.83 0.00 0.00 0.00 0.00 0.05 0.00

time (sec)

N/A 1.154 10.534 3.066 0.000 0.000 0.000 0.000 200.040 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

629 658 1385 5348 0 0 0 0 19 0

N.S.

1 1.05 2.20 8.50 0.00 0.00 0.00 0.00 0.03 0.00

time (sec)

N/A 1.979 13.871 13.339 0.000 0.000 0.000 0.000 200.037 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

55 61 64 864 0 379 0 134 131 0

N.S.

1 1.11 1.16 15.71 0.00 6.89 0.00 2.44 2.38 0.00

time (sec)

N/A 0.328 0.324 10.571 0.000 0.342 0.000 0.154 0.213 0.000

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

55 62 64 864 0 379 0 134 131 0

N.S.

1 1.13 1.16 15.71 0.00 6.89 0.00 2.44 2.38 0.00

time (sec)

N/A 0.339 0.003 2.330 0.000 0.405 0.000 0.161 0.220 0.000

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

55 34 64 864 0 379 0 134 131 0

N.S.

1 0.62 1.16 15.71 0.00 6.89 0.00 2.44 2.38 0.00

time (sec)

N/A 0.527 0.006 2.227 0.000 0.358 0.000 0.159 0.232 0.000

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

56 62 64 864 0 379 0 134 131 0

N.S.

1 1.11 1.14 15.43 0.00 6.77 0.00 2.39 2.34 0.00

time (sec)

N/A 0.551 0.004 2.195 0.000 0.348 0.000 0.159 0.199 0.000

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