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Integrals 1 to 43

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 B B B B B B

verified

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

size

15 15 15 36 61 66 209 37 45 50

N.S.

1 1.00 1.00 2.40 4.07 4.40 13.93 2.47 3.00 3.33

time (sec)

N/A 0.182 0.115 0.137 0.112 0.085 1.319 0.120 0.153 0.150

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

25 25 24 46 69 113 908 48 140 63

N.S.

1 1.00 0.96 1.84 2.76 4.52 36.32 1.92 5.60 2.52

time (sec)

N/A 0.188 0.247 0.267 0.114 0.092 3.116 0.129 0.152 1.606

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

75 83 127 71 0 247 0 143 273 285

N.S.

1 1.11 1.69 0.95 0.00 3.29 0.00 1.91 3.64 3.80

time (sec)

N/A 0.361 5.168 0.855 0.000 0.094 0.000 0.138 0.167 3.350

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

159 69 64 81 0 618 0 48 767 273

N.S.

1 0.43 0.40 0.51 0.00 3.89 0.00 0.30 4.82 1.72

time (sec)

N/A 0.434 2.149 4.246 0.000 0.115 0.000 0.276 0.183 3.164

Problem 5

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

31 31 21 19 30 38 39 33 25 40

N.S.

1 1.00 0.68 0.61 0.97 1.23 1.26 1.06 0.81 1.29

time (sec)

N/A 0.184 0.029 0.040 0.121 0.084 0.273 0.125 0.157 0.121

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

133 133 156 60 0 158 5697 106 155 225

N.S.

1 1.00 1.17 0.45 0.00 1.19 42.83 0.80 1.17 1.69

time (sec)

N/A 0.433 5.252 0.220 0.000 0.106 41.815 0.135 0.158 3.219

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

233 233 437 90 0 591 0 4948 12 0

N.S.

1 1.00 1.88 0.39 0.00 2.54 0.00 21.24 0.05 0.00

time (sec)

N/A 0.783 5.037 0.217 0.000 0.176 0.000 2.230 0.152 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

2 2 2 8 10 20 14 10 16 10

N.S.

1 1.00 1.00 4.00 5.00 10.00 7.00 5.00 8.00 5.00

time (sec)

N/A 0.219 0.001 0.059 0.035 0.076 0.332 0.120 0.150 2.917

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

135 196 45 36 0 443 0 303 10 205

N.S.

1 1.45 0.33 0.27 0.00 3.28 0.00 2.24 0.07 1.52

time (sec)

N/A 0.499 5.025 0.389 0.000 0.113 0.000 0.170 0.168 1.977

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

151 71 87 47 0 564 0 10 451 325

N.S.

1 0.47 0.58 0.31 0.00 3.74 0.00 0.07 2.99 2.15

time (sec)

N/A 0.510 5.113 2.235 0.000 0.134 0.000 0.123 0.166 5.465

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

411 129 127 64 0 729 0 1 10 0

N.S.

1 0.31 0.31 0.16 0.00 1.77 0.00 0.00 0.02 0.00

time (sec)

N/A 0.457 5.021 3.534 0.000 0.134 0.000 0.125 0.158 0.000

Problem 12

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

30 30 21 19 30 36 39 29 25 40

N.S.

1 1.00 0.70 0.63 1.00 1.20 1.30 0.97 0.83 1.33

time (sec)

N/A 0.177 0.030 0.054 0.113 0.077 0.268 0.125 0.152 0.123

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

139 147 156 60 0 160 5697 102 155 203

N.S.

1 1.06 1.12 0.43 0.00 1.15 40.99 0.73 1.12 1.46

time (sec)

N/A 0.431 5.301 0.355 0.000 0.098 35.323 0.128 0.159 1.731

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

245 245 439 90 0 589 0 4946 10 0

N.S.

1 1.00 1.79 0.37 0.00 2.40 0.00 20.19 0.04 0.00

time (sec)

N/A 0.693 5.039 0.343 0.000 0.156 0.000 2.216 0.148 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

33 33 33 138 0 312 15319 39 98 181

N.S.

1 1.00 1.00 4.18 0.00 9.45 464.21 1.18 2.97 5.48

time (sec)

N/A 0.247 0.480 0.245 0.000 0.088 15.432 0.114 0.157 0.889

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

352 541 148 94 0 779 0 1781 12 1559

N.S.

1 1.54 0.42 0.27 0.00 2.21 0.00 5.06 0.03 4.43

time (sec)

N/A 1.466 2.743 0.481 0.000 0.122 0.000 2.048 0.153 9.649

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

175 175 134 128 0 16401 0 0 12 857

N.S.

1 1.00 0.77 0.73 0.00 93.72 0.00 0.00 0.07 4.90

time (sec)

N/A 0.560 5.044 1.173 0.000 1.228 0.000 0.000 0.156 67.055

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

245 257 160 162 0 661332 0 0 12 0

N.S.

1 1.05 0.65 0.66 0.00 2699.31 0.00 0.00 0.05 0.00

time (sec)

N/A 0.744 5.075 2.774 0.000 3.262 0.000 0.000 0.180 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

37 42 45 35 54 111 110 56 42 49

N.S.

1 1.14 1.22 0.95 1.46 3.00 2.97 1.51 1.14 1.32

time (sec)

N/A 0.211 0.025 0.090 0.117 0.087 2.549 0.125 0.150 0.161

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

250 250 107 79 0 16934 0 0 12 633

N.S.

1 1.00 0.43 0.32 0.00 67.74 0.00 0.00 0.05 2.53

time (sec)

N/A 0.692 5.035 0.444 0.000 0.968 0.000 0.000 0.153 5.407

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

435 435 141 113 0 0 0 0 12 0

N.S.

1 1.00 0.32 0.26 0.00 0.00 0.00 0.00 0.03 0.00

time (sec)

N/A 1.209 5.046 1.365 0.000 0.000 0.000 0.000 0.149 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

11 21 11 19 49 84 104 18 36 18

N.S.

1 1.91 1.00 1.73 4.45 7.64 9.45 1.64 3.27 1.64

time (sec)

N/A 0.225 0.004 0.174 0.041 0.072 0.778 0.118 0.152 0.067

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

19 31 19 25 111 185 260 24 57 24

N.S.

1 1.63 1.00 1.32 5.84 9.74 13.68 1.26 3.00 1.26

time (sec)

N/A 0.238 0.004 0.325 0.039 0.071 1.769 0.122 0.151 0.080

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

37 37 35 60 87 216 2052 62 224 77

N.S.

1 1.00 0.95 1.62 2.35 5.84 55.46 1.68 6.05 2.08

time (sec)

N/A 0.255 0.139 0.191 0.119 0.085 4.769 0.119 0.152 0.187

Problem 25

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

55 60 51 72 111 575 5666 74 396 112

N.S.

1 1.09 0.93 1.31 2.02 10.45 103.02 1.35 7.20 2.04

time (sec)

N/A 0.359 0.309 0.477 0.115 0.087 11.672 0.125 0.154 1.738

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

11 11 11 14 11 2 0 11 9 2

N.S.

1 1.00 1.00 1.27 1.00 0.18 0.00 1.00 0.82 0.18

time (sec)

N/A 0.258 0.017 0.146 0.118 0.085 0.000 0.121 0.153 1.698

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

13 13 13 15 25 14 0 11 11 5

N.S.

1 1.00 1.00 1.15 1.92 1.08 0.00 0.85 0.85 0.38

time (sec)

N/A 0.279 0.016 0.099 0.115 0.096 0.000 0.119 0.152 0.176

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

11 11 11 51 0 0 0 0 11 0

N.S.

1 1.00 1.00 4.64 0.00 0.00 0.00 0.00 1.00 0.00

time (sec)

N/A 0.175 0.020 0.994 0.000 0.000 0.000 0.000 0.151 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

33 33 33 61 0 0 0 0 9 0

N.S.

1 1.00 1.00 1.85 0.00 0.00 0.00 0.00 0.27 0.00

time (sec)

N/A 0.250 0.024 0.747 0.000 0.000 0.000 0.000 0.152 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

29 29 20 21 23 17 0 25 24 0

N.S.

1 1.00 0.69 0.72 0.79 0.59 0.00 0.86 0.83 0.00

time (sec)

N/A 0.322 0.007 0.084 0.114 0.100 0.000 0.117 0.159 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

33 33 22 21 53 26 0 25 27 0

N.S.

1 1.00 0.67 0.64 1.61 0.79 0.00 0.76 0.82 0.00

time (sec)

N/A 0.320 0.006 0.091 0.123 0.106 0.000 0.123 0.154 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

45 48 45 103 0 0 0 0 30 0

N.S.

1 1.07 1.00 2.29 0.00 0.00 0.00 0.00 0.67 0.00

time (sec)

N/A 0.387 0.051 0.635 0.000 0.000 0.000 0.000 0.156 0.000

Problem 33

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

87 90 78 106 0 0 0 0 26 0

N.S.

1 1.03 0.90 1.22 0.00 0.00 0.00 0.00 0.30 0.00

time (sec)

N/A 0.569 0.088 0.768 0.000 0.000 0.000 0.000 0.157 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

14 14 15 15 5 8 0 5 18 0

N.S.

1 1.00 1.07 1.07 0.36 0.57 0.00 0.36 1.29 0.00

time (sec)

N/A 0.269 0.006 0.084 0.151 0.075 0.000 0.124 0.152 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

11 11 11 41 0 42 0 0 22 0

N.S.

1 1.00 1.00 3.73 0.00 3.82 0.00 0.00 2.00 0.00

time (sec)

N/A 0.172 0.027 0.133 0.000 0.105 0.000 0.000 0.154 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

33 33 33 61 0 42 0 0 18 0

N.S.

1 1.00 1.00 1.85 0.00 1.27 0.00 0.00 0.55 0.00

time (sec)

N/A 0.253 0.029 0.116 0.000 0.099 0.000 0.000 0.151 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

16 16 17 34 5 13 0 5 21 0

N.S.

1 1.00 1.06 2.12 0.31 0.81 0.00 0.31 1.31 0.00

time (sec)

N/A 0.277 0.005 0.095 0.169 0.081 0.000 0.127 0.151 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

168 172 173 490 0 0 0 0 56 0

N.S.

1 1.02 1.03 2.92 0.00 0.00 0.00 0.00 0.33 0.00

time (sec)

N/A 1.027 0.388 7.285 0.000 0.000 0.000 0.000 0.164 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

125 124 132 333 0 0 0 0 32 0

N.S.

1 0.99 1.06 2.66 0.00 0.00 0.00 0.00 0.26 0.00

time (sec)

N/A 0.748 0.276 2.742 0.000 0.000 0.000 0.000 0.156 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

43 42 54 109 0 0 0 0 11 0

N.S.

1 0.98 1.26 2.53 0.00 0.00 0.00 0.00 0.26 0.00

time (sec)

N/A 0.280 0.037 1.440 0.000 0.000 0.000 0.000 0.152 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

43 42 53 63 0 136 0 0 22 0

N.S.

1 0.98 1.23 1.47 0.00 3.16 0.00 0.00 0.51 0.00

time (sec)

N/A 0.303 0.040 0.165 0.000 0.097 0.000 0.000 0.153 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

83 82 81 197 0 1183 0 0 34 0

N.S.

1 0.99 0.98 2.37 0.00 14.25 0.00 0.00 0.41 0.00

time (sec)

N/A 0.437 0.076 0.826 0.000 0.108 0.000 0.000 0.151 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

187 192 159 311 0 4717 0 0 46 0

N.S.

1 1.03 0.85 1.66 0.00 25.22 0.00 0.00 0.25 0.00

time (sec)

N/A 1.252 0.506 1.259 0.000 0.231 0.000 0.000 0.150 0.000

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