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Integrals 1 to 24

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 A A F A B B

verified

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

size

91 98 163 112 145 161 0 155 91 242

N.S.

1 1.08 1.79 1.23 1.59 1.77 0.00 1.70 1.00 2.66

time (sec)

N/A 0.584 0.203 0.291 0.035 0.087 0.000 0.162 0.195 16.427

Problem 2

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

72 85 116 74 87 135 0 123 75 118

N.S.

1 1.18 1.61 1.03 1.21 1.88 0.00 1.71 1.04 1.64

time (sec)

N/A 0.586 0.133 0.221 0.040 0.079 0.000 0.157 0.186 16.089

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

51 59 110 67 80 103 0 93 59 84

N.S.

1 1.16 2.16 1.31 1.57 2.02 0.00 1.82 1.16 1.65

time (sec)

N/A 0.425 0.054 0.177 0.034 0.089 0.000 0.164 0.205 17.358

Problem 4

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

33 41 45 31 50 51 0 47 30 129

N.S.

1 1.24 1.36 0.94 1.52 1.55 0.00 1.42 0.91 3.91

time (sec)

N/A 0.365 0.032 0.252 0.029 0.085 0.000 0.168 0.198 15.858

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

42 50 33 31 47 38 0 79 36 116

N.S.

1 1.19 0.79 0.74 1.12 0.90 0.00 1.88 0.86 2.76

time (sec)

N/A 0.368 0.104 0.246 0.031 0.072 0.000 0.206 0.197 16.244

Problem 6

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

54 68 43 42 60 49 0 95 52 153

N.S.

1 1.26 0.80 0.78 1.11 0.91 0.00 1.76 0.96 2.83

time (sec)

N/A 0.472 0.155 0.290 0.032 0.073 0.000 0.181 0.195 16.786

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

61 64 117 45 120 129 0 107 57 56

N.S.

1 1.05 1.92 0.74 1.97 2.11 0.00 1.75 0.93 0.92

time (sec)

N/A 0.436 0.113 0.150 0.038 0.082 0.000 0.128 0.193 15.432

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

17 17 17 35 42 36 54 15 34 15

N.S.

1 1.00 1.00 2.06 2.47 2.12 3.18 0.88 2.00 0.88

time (sec)

N/A 0.285 0.013 0.098 0.034 0.065 0.921 0.182 0.201 14.570

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

38 38 79 45 68 86 0 101 42 56

N.S.

1 1.00 2.08 1.18 1.79 2.26 0.00 2.66 1.11 1.47

time (sec)

N/A 0.314 0.075 0.117 0.033 0.091 0.000 0.141 0.196 16.030

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

27 22 46 26 40 45 0 60 25 40

N.S.

1 0.81 1.70 0.96 1.48 1.67 0.00 2.22 0.93 1.48

time (sec)

N/A 0.272 0.037 0.136 0.040 0.090 0.000 0.144 0.189 16.186

Problem 11

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

29 29 25 22 37 26 54 35 25 53

N.S.

1 1.00 0.86 0.76 1.28 0.90 1.86 1.21 0.86 1.83

time (sec)

N/A 0.267 0.018 0.125 0.032 0.075 2.729 0.153 0.196 16.187

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

17 17 17 31 36 15 0 56 32 15

N.S.

1 1.00 1.00 1.82 2.12 0.88 0.00 3.29 1.88 0.88

time (sec)

N/A 0.277 0.005 0.153 0.039 0.072 0.000 0.140 0.195 16.125

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

61 64 117 45 120 129 0 107 57 56

N.S.

1 1.05 1.92 0.74 1.97 2.11 0.00 1.75 0.93 0.92

time (sec)

N/A 0.426 0.015 0.092 0.034 0.086 0.000 0.147 0.190 15.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

17 17 17 35 42 36 54 15 34 15

N.S.

1 1.00 1.00 2.06 2.47 2.12 3.18 0.88 2.00 0.88

time (sec)

N/A 0.283 0.010 0.068 0.033 0.063 0.959 0.163 0.181 14.707

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

38 38 79 45 68 86 0 101 42 56

N.S.

1 1.00 2.08 1.18 1.79 2.26 0.00 2.66 1.11 1.47

time (sec)

N/A 0.309 0.013 0.073 0.028 0.076 0.000 0.134 0.187 14.504

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

27 22 46 26 40 45 0 60 25 40

N.S.

1 0.81 1.70 0.96 1.48 1.67 0.00 2.22 0.93 1.48

time (sec)

N/A 0.268 0.012 0.097 0.035 0.085 0.000 0.173 0.178 15.215

Problem 17

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

29 29 25 22 37 26 54 35 25 53

N.S.

1 1.00 0.86 0.76 1.28 0.90 1.86 1.21 0.86 1.83

time (sec)

N/A 0.266 0.006 0.080 0.035 0.070 2.744 0.158 0.178 15.786

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

17 17 17 31 36 15 0 56 32 15

N.S.

1 1.00 1.00 1.82 2.12 0.88 0.00 3.29 1.88 0.88

time (sec)

N/A 0.274 0.004 0.096 0.027 0.073 0.000 0.158 0.195 15.957

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

91 98 163 112 145 161 0 155 91 242

N.S.

1 1.08 1.79 1.23 1.59 1.77 0.00 1.70 1.00 2.66

time (sec)

N/A 0.564 0.102 0.260 0.035 0.080 0.000 0.181 0.189 15.632

Problem 20

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

70 85 116 74 87 135 0 123 75 119

N.S.

1 1.21 1.66 1.06 1.24 1.93 0.00 1.76 1.07 1.70

time (sec)

N/A 0.557 0.063 0.207 0.034 0.084 0.000 0.174 0.185 15.501

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

51 59 110 67 80 103 0 93 59 86

N.S.

1 1.16 2.16 1.31 1.57 2.02 0.00 1.82 1.16 1.69

time (sec)

N/A 0.419 0.054 0.178 0.036 0.075 0.000 0.153 0.195 15.710

Problem 22

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

33 41 45 32 49 51 0 49 30 129

N.S.

1 1.24 1.36 0.97 1.48 1.55 0.00 1.48 0.91 3.91

time (sec)

N/A 0.373 0.011 0.203 0.037 0.085 0.000 0.160 0.188 15.356

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

42 50 35 33 47 38 0 79 36 116

N.S.

1 1.19 0.83 0.79 1.12 0.90 0.00 1.88 0.86 2.76

time (sec)

N/A 0.365 0.115 0.203 0.035 0.074 0.000 0.145 0.200 14.463

Problem 24

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

54 68 44 44 60 49 0 95 52 153

N.S.

1 1.26 0.81 0.81 1.11 0.91 0.00 1.76 0.96 2.83

time (sec)

N/A 0.471 0.123 0.223 0.033 0.079 0.000 0.156 0.188 15.276

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