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Integrals 101 to 122

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 A C F(-1) B B B

verified

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

size

172 180 221 108 224 334837 0 339 570 1393

N.S.

1 1.05 1.28 0.63 1.30 1946.73 0.00 1.97 3.31 8.10

time (sec)

N/A 0.664 0.458 0.111 0.107 21.129 0.000 0.128 0.167 6.753

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

236 235 263 147 284 343626 0 387 912 1002

N.S.

1 1.00 1.11 0.62 1.20 1456.04 0.00 1.64 3.86 4.25

time (sec)

N/A 0.969 0.399 0.113 0.117 31.067 0.000 0.141 0.162 6.532

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

281 285 313 188 345 343822 0 435 1255 1056

N.S.

1 1.01 1.11 0.67 1.23 1223.57 0.00 1.55 4.47 3.76

time (sec)

N/A 1.139 0.224 0.122 0.111 44.661 0.000 0.133 0.174 6.512

Problem 104

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

179 179 152 186 184 184 216 188 189 180

N.S.

1 1.00 0.85 1.04 1.03 1.03 1.21 1.05 1.06 1.01

time (sec)

N/A 0.709 0.063 0.154 0.031 0.095 0.037 0.119 0.168 0.265

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

131 131 111 127 126 126 146 128 129 126

N.S.

1 1.00 0.85 0.97 0.96 0.96 1.11 0.98 0.98 0.96

time (sec)

N/A 0.580 0.024 0.155 0.033 0.092 0.039 0.118 0.173 5.651

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

82 82 77 67 66 66 76 68 69 67

N.S.

1 1.00 0.94 0.82 0.80 0.80 0.93 0.83 0.84 0.82

time (sec)

N/A 0.403 0.016 0.132 0.033 0.080 0.023 0.122 0.166 0.041

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

247 319 311 58 328 622377 0 338 550 5042

N.S.

1 1.29 1.26 0.23 1.33 2519.74 0.00 1.37 2.23 20.41

time (sec)

N/A 0.901 0.221 0.098 0.112 34.261 0.000 0.127 0.169 6.605

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

269 349 319 105 350 352423 0 360 1082 1383

N.S.

1 1.30 1.19 0.39 1.30 1310.12 0.00 1.34 4.02 5.14

time (sec)

N/A 0.900 0.128 0.109 0.120 24.428 0.000 0.132 0.172 6.725

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

334 408 366 144 412 358509 0 410 1681 1001

N.S.

1 1.22 1.10 0.43 1.23 1073.38 0.00 1.23 5.03 3.00

time (sec)

N/A 1.179 0.196 0.119 0.120 40.344 0.000 0.133 0.173 0.721

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

377 456 411 185 472 358702 0 459 2279 1053

N.S.

1 1.21 1.09 0.49 1.25 951.46 0.00 1.22 6.05 2.79

time (sec)

N/A 1.355 0.240 0.112 0.131 72.053 0.000 0.137 0.169 6.520

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

121 121 79 96 0 72 61 0 72 0

N.S.

1 1.00 0.65 0.79 0.00 0.60 0.50 0.00 0.60 0.00

time (sec)

N/A 0.442 10.042 0.449 0.000 0.125 1.261 0.000 0.169 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

127 127 85 101 0 82 66 0 57 0

N.S.

1 1.00 0.67 0.80 0.00 0.65 0.52 0.00 0.45 0.00

time (sec)

N/A 0.443 10.043 0.458 0.000 0.118 1.420 0.000 0.179 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

87 87 81 90 0 79 95 0 88 0

N.S.

1 1.00 0.93 1.03 0.00 0.91 1.09 0.00 1.01 0.00

time (sec)

N/A 0.406 10.040 0.455 0.000 0.114 1.451 0.000 0.239 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

89 89 83 95 0 73 90 0 79 0

N.S.

1 1.00 0.93 1.07 0.00 0.82 1.01 0.00 0.89 0.00

time (sec)

N/A 0.411 10.038 0.466 0.000 0.114 1.365 0.000 0.182 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

258 257 131 193 0 128 102 0 99 0

N.S.

1 1.00 0.51 0.75 0.00 0.50 0.40 0.00 0.38 0.00

time (sec)

N/A 0.615 10.097 0.691 0.000 0.112 1.561 0.000 0.188 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

14 14 14 13 12 12 80 12 20 12

N.S.

1 1.00 1.00 0.93 0.86 0.86 5.71 0.86 1.43 0.86

time (sec)

N/A 0.237 1.174 0.646 0.061 0.087 3.421 0.148 0.174 5.970

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

27 29 27 24 25 34 104 22 31 23

N.S.

1 1.07 1.00 0.89 0.93 1.26 3.85 0.81 1.15 0.85

time (sec)

N/A 0.307 10.031 0.900 0.062 0.098 4.965 0.137 0.171 5.714

Problem 118

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

34 25 27 24 23 33 109 22 31 20

N.S.

1 0.74 0.79 0.71 0.68 0.97 3.21 0.65 0.91 0.59

time (sec)

N/A 0.307 10.033 0.875 0.062 0.091 5.654 0.128 0.175 5.830

Problem 119

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

47 38 38 35 44 44 133 30 42 29

N.S.

1 0.81 0.81 0.74 0.94 0.94 2.83 0.64 0.89 0.62

time (sec)

N/A 0.324 10.047 1.017 0.076 0.094 7.068 0.127 0.169 5.472

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

388 385 281 287 0 204 260 0 259 0

N.S.

1 0.99 0.72 0.74 0.00 0.53 0.67 0.00 0.67 0.00

time (sec)

N/A 1.232 10.162 2.921 0.000 0.237 3.833 0.000 0.216 0.000

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

21 22 21 20 21 21 165 21 27 19

N.S.

1 1.05 1.00 0.95 1.00 1.00 7.86 1.00 1.29 0.90

time (sec)

N/A 0.320 10.047 1.584 0.062 0.089 5.989 0.136 0.178 5.381

Problem 122

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

38 27 27 24 25 25 196 27 33 23

N.S.

1 0.71 0.71 0.63 0.66 0.66 5.16 0.71 0.87 0.61

time (sec)

N/A 0.333 10.046 1.638 0.063 0.086 8.400 0.132 0.172 5.437

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