[tail] [up]

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 A F(-2) A A A F B

verified

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

size

78 80 60 39 0 39 54 63 13 48

N.S.

1 1.03 0.77 0.50 0.00 0.50 0.69 0.81 0.17 0.62

time (sec)

N/A 0.273 0.229 0.367 0.000 0.077 0.095 0.108 0.158 9.985

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

29 31 42 29 0 26 36 69 13 74

N.S.

1 1.07 1.45 1.00 0.00 0.90 1.24 2.38 0.45 2.55

time (sec)

N/A 0.423 0.095 0.239 0.000 0.068 0.099 0.148 0.156 10.191

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

50 52 32 19 0 27 34 51 13 36

N.S.

1 1.04 0.64 0.38 0.00 0.54 0.68 1.02 0.26 0.72

time (sec)

N/A 0.253 0.179 0.247 0.000 0.075 0.075 0.113 0.187 9.423

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

19 23 19 16 0 14 17 31 11 40

N.S.

1 1.21 1.00 0.84 0.00 0.74 0.89 1.63 0.58 2.11

time (sec)

N/A 0.347 0.009 0.173 0.000 0.071 0.073 0.112 0.158 9.448

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

18 18 44 33 45 33 0 29 11 21

N.S.

1 1.00 2.44 1.83 2.50 1.83 0.00 1.61 0.61 1.17

time (sec)

N/A 0.346 0.061 0.210 0.029 0.087 0.000 0.139 0.159 9.470

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

20 19 16 13 12 36 0 53 13 12

N.S.

1 0.95 0.80 0.65 0.60 1.80 0.00 2.65 0.65 0.60

time (sec)

N/A 0.234 0.047 0.198 0.031 0.079 0.000 0.138 0.159 9.338

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

22 26 27 49 94 73 0 55 13 47

N.S.

1 1.18 1.23 2.23 4.27 3.32 0.00 2.50 0.59 2.14

time (sec)

N/A 0.416 0.120 0.198 0.029 0.082 0.000 0.114 0.155 9.391

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

19 19 16 15 13 30 0 13 13 13

N.S.

1 1.00 0.84 0.79 0.68 1.58 0.00 0.68 0.68 0.68

time (sec)

N/A 0.223 0.051 0.206 0.027 0.071 0.000 0.147 0.188 9.111

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

40 40 37 66 167 123 0 87 13 81

N.S.

1 1.00 0.92 1.65 4.18 3.08 0.00 2.18 0.32 2.02

time (sec)

N/A 0.415 0.099 0.230 0.036 0.082 0.000 0.136 0.161 9.557

Problem 10

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

37 37 30 28 25 48 0 25 13 27

N.S.

1 1.00 0.81 0.76 0.68 1.30 0.00 0.68 0.35 0.73

time (sec)

N/A 0.232 0.069 0.197 0.026 0.090 0.000 0.123 0.163 9.637

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

123 123 112 170 279 214 0 201 188 291

N.S.

1 1.00 0.91 1.38 2.27 1.74 0.00 1.63 1.53 2.37

time (sec)

N/A 0.790 0.789 2.035 0.120 0.101 0.000 0.136 0.166 9.599

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

65 65 61 81 105 144 0 94 92 93

N.S.

1 1.00 0.94 1.25 1.62 2.22 0.00 1.45 1.42 1.43

time (sec)

N/A 0.455 0.129 0.390 0.112 0.097 0.000 0.166 0.165 9.074

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

47 47 76 63 98 140 0 90 96 408

N.S.

1 1.00 1.62 1.34 2.09 2.98 0.00 1.91 2.04 8.68

time (sec)

N/A 0.362 0.115 0.332 0.110 0.112 0.000 0.168 0.174 9.744

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

79 79 192 150 203 166 0 158 213 346

N.S.

1 1.00 2.43 1.90 2.57 2.10 0.00 2.00 2.70 4.38

time (sec)

N/A 0.447 0.479 1.492 0.112 0.138 0.000 0.150 0.165 9.267

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 145 400 311 396 236 0 329 679 1971

N.S.

1 145.00 400.00 311.00 396.00 236.00 0.00 329.00 679.00 1971.00

time (sec)

N/A 0.554 1.930 12.032 0.118 0.215 0.000 0.142 0.176 10.033

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

126 211 179 172 240 178 0 270 242 279

N.S.

1 1.67 1.42 1.37 1.90 1.41 0.00 2.14 1.92 2.21

time (sec)

N/A 0.570 0.584 4.654 0.112 0.140 0.000 0.147 0.168 9.478

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

73 124 82 98 122 95 0 155 121 118

N.S.

1 1.70 1.12 1.34 1.67 1.30 0.00 2.12 1.66 1.62

time (sec)

N/A 0.362 0.271 0.837 0.106 0.103 0.000 0.120 0.193 9.289

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

29 35 19 21 20 57 0 21 60 20

N.S.

1 1.21 0.66 0.72 0.69 1.97 0.00 0.72 2.07 0.69

time (sec)

N/A 0.248 0.073 0.554 0.026 0.093 0.000 0.121 0.166 8.857

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

73 81 56 56 56 106 0 60 322 55

N.S.

1 1.11 0.77 0.77 0.77 1.45 0.00 0.82 4.41 0.75

time (sec)

N/A 0.302 0.178 4.218 0.033 0.102 0.000 0.112 0.170 8.902

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 130 95 117 111 170 0 121 784 118

N.S.

1 130.00 95.00 117.00 111.00 170.00 0.00 121.00 784.00 118.00

time (sec)

N/A 0.361 0.454 32.538 0.031 0.104 0.000 0.122 0.176 8.874

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

25 25 57 37 67 66 0 54 49 54

N.S.

1 1.00 2.28 1.48 2.68 2.64 0.00 2.16 1.96 2.16

time (sec)

N/A 0.312 0.081 0.199 0.110 0.129 0.000 0.142 0.164 9.109

[front] [up]