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Integrals 1 to 21

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 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

57 57 56 96 0 227 688 361 132 1537

N.S.

1 1.00 0.98 1.68 0.00 3.98 12.07 6.33 2.32 26.96

time (sec)

N/A 0.329 0.132 0.178 0.000 0.126 11.756 0.130 0.149 2.988

Problem 2

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 19 17 19 28 17 18 18 18

N.S.

1 1.00 1.00 0.89 1.00 1.47 0.89 0.95 0.95 0.95

time (sec)

N/A 0.260 0.042 0.090 0.028 0.120 0.158 0.111 0.149 1.006

Problem 3

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

23 23 20 28 19 25 27 39 39 30

N.S.

1 1.00 0.87 1.22 0.83 1.09 1.17 1.70 1.70 1.30

time (sec)

N/A 0.275 0.229 0.103 0.034 0.107 0.336 0.116 0.164 1.034

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

58 58 57 97 0 231 804 407 179 2219

N.S.

1 1.00 0.98 1.67 0.00 3.98 13.86 7.02 3.09 38.26

time (sec)

N/A 0.327 0.129 0.183 0.000 0.156 12.188 0.133 0.235 6.932

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

58 58 55 85 0 235 748 103 179 2213

N.S.

1 1.00 0.95 1.47 0.00 4.05 12.90 1.78 3.09 38.16

time (sec)

N/A 0.339 0.200 0.192 0.000 0.150 15.220 0.123 0.239 6.908

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

65 65 61 108 0 263 0 121 159 1540

N.S.

1 1.00 0.94 1.66 0.00 4.05 0.00 1.86 2.45 23.69

time (sec)

N/A 0.359 0.352 0.288 0.000 0.155 0.000 0.125 0.250 3.006

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

100 100 134 96 0 266 0 116 97 419

N.S.

1 1.00 1.34 0.96 0.00 2.66 0.00 1.16 0.97 4.19

time (sec)

N/A 0.394 0.478 0.319 0.000 2.835 0.000 0.129 0.162 1.703

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

99 99 116 95 0 265 0 115 97 417

N.S.

1 1.00 1.17 0.96 0.00 2.68 0.00 1.16 0.98 4.21

time (sec)

N/A 0.523 0.375 0.229 0.000 3.774 0.000 0.127 0.154 1.678

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

247 247 526 484 0 1049 0 607 2335 9992

N.S.

1 1.00 2.13 1.96 0.00 4.25 0.00 2.46 9.45 40.45

time (sec)

N/A 0.716 7.770 1.230 0.000 96.820 0.000 0.207 0.211 6.705

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

170 170 335 291 0 747 0 340 1631 6735

N.S.

1 1.00 1.97 1.71 0.00 4.39 0.00 2.00 9.59 39.62

time (sec)

N/A 0.601 3.542 0.757 0.000 21.484 0.000 0.193 0.181 5.703

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

103 103 135 165 0 505 0 196 445 3577

N.S.

1 1.00 1.31 1.60 0.00 4.90 0.00 1.90 4.32 34.73

time (sec)

N/A 0.531 2.916 0.501 0.000 2.907 0.000 0.170 0.165 4.283

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

76 76 112 92 0 296 0 128 193 345

N.S.

1 1.00 1.47 1.21 0.00 3.89 0.00 1.68 2.54 4.54

time (sec)

N/A 0.462 0.615 0.310 0.000 0.381 0.000 0.133 0.176 1.781

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

121 121 106 108 0 1022 0 507 291 2665

N.S.

1 1.00 0.88 0.89 0.00 8.45 0.00 4.19 2.40 22.02

time (sec)

N/A 0.521 0.954 0.571 0.000 1.647 0.000 0.190 0.173 2.565

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

187 221 205 210 0 2835 0 333 1678 20827

N.S.

1 1.18 1.10 1.12 0.00 15.16 0.00 1.78 8.97 111.37

time (sec)

N/A 0.994 2.053 1.652 0.000 87.078 0.000 0.170 0.215 9.106

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

458 458 319 412 0 0 0 748 4916 52103

N.S.

1 1.00 0.70 0.90 0.00 0.00 0.00 1.63 10.73 113.76

time (sec)

N/A 1.220 4.573 4.630 0.000 0.000 0.000 0.298 0.225 11.950

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

213 213 184 318 0 0 0 0 26 0

N.S.

1 1.00 0.86 1.49 0.00 0.00 0.00 0.00 0.12 0.00

time (sec)

N/A 0.886 10.692 7.799 0.000 0.000 0.000 0.000 0.163 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

102 102 187 206 0 0 0 0 53 0

N.S.

1 1.00 1.83 2.02 0.00 0.00 0.00 0.00 0.52 0.00

time (sec)

N/A 0.451 12.048 4.852 0.000 0.000 0.000 0.000 0.167 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

87 87 82 142 0 326 672 454 26 886

N.S.

1 1.00 0.94 1.63 0.00 3.75 7.72 5.22 0.30 10.18

time (sec)

N/A 0.495 0.473 0.339 0.000 0.118 13.950 0.145 0.151 2.188

Problem 19

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

120 131 115 141 0 444 0 167 173 126

N.S.

1 1.09 0.96 1.18 0.00 3.70 0.00 1.39 1.44 1.05

time (sec)

N/A 0.561 0.598 0.324 0.000 0.119 0.000 0.135 0.161 1.257

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

187 213 175 270 0 830 0 480 504 283

N.S.

1 1.14 0.94 1.44 0.00 4.44 0.00 2.57 2.70 1.51

time (sec)

N/A 0.793 0.908 0.527 0.000 0.187 0.000 0.179 0.159 3.112

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

260 302 302 456 0 1334 0 918 1239 502

N.S.

1 1.16 1.16 1.75 0.00 5.13 0.00 3.53 4.77 1.93

time (sec)

N/A 1.101 1.266 0.917 0.000 0.225 0.000 0.192 0.162 2.876

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