[tail] [up]

Integrals 1 to 46

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 A A B B

verified

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

size

54 54 49 53 50 53 63 78 62 41

N.S.

1 1.00 0.91 0.98 0.93 0.98 1.17 1.44 1.15 0.76

time (sec)

N/A 0.377 0.068 0.136 0.032 0.075 1.322 0.115 0.163 24.436

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

75 80 76 109 107 79 73 69 63 61

N.S.

1 1.07 1.01 1.45 1.43 1.05 0.97 0.92 0.84 0.81

time (sec)

N/A 0.420 0.062 0.081 0.036 0.077 2.682 0.126 0.163 24.773

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

31 31 38 43 25 41 41 44 44 33

N.S.

1 1.00 1.23 1.39 0.81 1.32 1.32 1.42 1.42 1.06

time (sec)

N/A 0.346 0.042 0.081 0.028 0.072 1.155 0.114 0.154 24.454

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

47 46 47 85 78 64 29 52 38 39

N.S.

1 0.98 1.00 1.81 1.66 1.36 0.62 1.11 0.81 0.83

time (sec)

N/A 0.378 0.038 0.073 0.029 0.088 1.584 0.116 0.158 24.510

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

24 35 35 113 64 86 48 66 51 36

N.S.

1 1.46 1.46 4.71 2.67 3.58 2.00 2.75 2.12 1.50

time (sec)

N/A 0.344 0.024 0.093 0.027 0.073 0.764 0.116 0.159 24.521

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

38 45 42 107 54 64 41 0 43 34

N.S.

1 1.18 1.11 2.82 1.42 1.68 1.08 0.00 1.13 0.89

time (sec)

N/A 0.386 0.034 0.082 0.032 0.094 2.303 0.000 0.155 24.746

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

40 44 43 145 86 102 37 67 69 42

N.S.

1 1.10 1.08 3.62 2.15 2.55 0.92 1.68 1.72 1.05

time (sec)

N/A 0.371 0.033 0.079 0.033 0.074 0.937 0.116 0.169 24.916

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

31 31 37 42 25 47 48 69 48 42

N.S.

1 1.00 1.19 1.35 0.81 1.52 1.55 2.23 1.55 1.35

time (sec)

N/A 0.340 0.045 0.082 0.028 0.075 1.019 0.133 0.152 24.606

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

65 74 53 173 129 113 95 103 87 61

N.S.

1 1.14 0.82 2.66 1.98 1.74 1.46 1.58 1.34 0.94

time (sec)

N/A 0.408 0.058 0.086 0.032 0.100 1.089 0.122 0.158 24.929

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

51 56 46 52 41 58 58 124 66 61

N.S.

1 1.10 0.90 1.02 0.80 1.14 1.14 2.43 1.29 1.20

time (sec)

N/A 0.411 0.049 0.092 0.032 0.088 1.072 0.151 0.157 24.641

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

85 85 84 127 117 87 82 80 71 73

N.S.

1 1.00 0.99 1.49 1.38 1.02 0.96 0.94 0.84 0.86

time (sec)

N/A 0.875 0.069 0.151 0.028 0.078 2.640 0.140 0.156 24.608

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

38 38 44 59 32 49 51 66 52 40

N.S.

1 1.00 1.16 1.55 0.84 1.29 1.34 1.74 1.37 1.05

time (sec)

N/A 0.721 0.049 0.142 0.037 0.098 1.162 0.119 0.153 24.415

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

52 52 57 98 89 72 36 62 48 51

N.S.

1 1.00 1.10 1.88 1.71 1.38 0.69 1.19 0.92 0.98

time (sec)

N/A 0.756 0.043 0.116 0.036 0.080 1.615 0.138 0.165 24.542

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

43 43 44 129 75 99 63 82 65 52

N.S.

1 1.00 1.02 3.00 1.74 2.30 1.47 1.91 1.51 1.21

time (sec)

N/A 0.645 0.053 0.131 0.029 0.081 1.750 0.123 0.154 24.562

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

47 47 52 112 59 73 49 0 51 47

N.S.

1 1.00 1.11 2.38 1.26 1.55 1.04 0.00 1.09 1.00

time (sec)

N/A 0.529 0.051 0.111 0.030 0.071 1.742 0.000 0.160 24.615

Problem 16

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

38 38 39 164 93 112 87 103 77 44

N.S.

1 1.00 1.03 4.32 2.45 2.95 2.29 2.71 2.03 1.16

time (sec)

N/A 0.697 0.063 0.143 0.035 0.073 1.995 0.132 0.155 24.692

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

34 33 46 56 28 57 58 75 56 51

N.S.

1 0.97 1.35 1.65 0.82 1.68 1.71 2.21 1.65 1.50

time (sec)

N/A 0.719 0.051 0.141 0.028 0.068 1.207 0.149 0.153 24.527

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

73 73 73 189 139 121 109 112 95 68

N.S.

1 1.00 1.00 2.59 1.90 1.66 1.49 1.53 1.30 0.93

time (sec)

N/A 0.798 0.054 0.137 0.033 0.086 1.233 0.125 0.162 24.631

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

58 58 54 65 52 67 71 134 74 67

N.S.

1 1.00 0.93 1.12 0.90 1.16 1.22 2.31 1.28 1.16

time (sec)

N/A 0.785 0.057 0.142 0.028 0.071 1.260 0.164 0.163 24.528

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

96 96 74 222 180 131 117 121 114 89

N.S.

1 1.00 0.77 2.31 1.88 1.36 1.22 1.26 1.19 0.93

time (sec)

N/A 0.838 0.080 0.136 0.035 0.094 1.289 0.148 0.158 24.763

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

64 64 57 0 0 0 76 0 95 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 1.19 0.00 1.48 0.00

time (sec)

N/A 0.816 0.078 0.000 0.000 0.000 3.251 0.000 0.176 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

52 52 54 0 0 0 65 0 32 0

N.S.

1 1.00 1.04 0.00 0.00 0.00 1.25 0.00 0.62 0.00

time (sec)

N/A 0.411 0.046 0.000 0.000 0.000 2.941 0.000 0.166 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 53 55 0 0 0 0 0 23 0

N.S.

1 53.00 55.00 0.00 0.00 0.00 0.00 0.00 23.00 0.00

time (sec)

N/A 0.572 0.045 0.000 0.000 0.000 0.000 0.000 0.159 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 64 57 0 0 0 0 0 36 0

N.S.

1 64.00 57.00 0.00 0.00 0.00 0.00 0.00 36.00 0.00

time (sec)

N/A 0.799 0.060 0.000 0.000 0.000 0.000 0.000 0.179 0.000

Problem 25

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

202 209 112 150 0 89 48 0 55 0

N.S.

1 1.03 0.55 0.74 0.00 0.44 0.24 0.00 0.27 0.00

time (sec)

N/A 0.692 0.315 0.536 0.000 0.080 1.175 0.000 0.156 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

52 51 53 94 81 70 36 57 190 42

N.S.

1 0.98 1.02 1.81 1.56 1.35 0.69 1.10 3.65 0.81

time (sec)

N/A 0.367 0.073 0.102 0.028 0.082 1.820 0.118 0.155 25.073

Problem 27

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

86 88 113 104 0 56 41 0 47 0

N.S.

1 1.02 1.31 1.21 0.00 0.65 0.48 0.00 0.55 0.00

time (sec)

N/A 0.461 0.344 0.349 0.000 0.083 1.037 0.000 0.157 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

40 40 42 116 71 88 58 61 175 43

N.S.

1 1.00 1.05 2.90 1.78 2.20 1.45 1.52 4.38 1.08

time (sec)

N/A 0.398 0.040 0.090 0.032 0.087 2.949 0.122 0.154 25.150

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

165 179 96 146 0 0 42 0 48 24

N.S.

1 1.08 0.58 0.88 0.00 0.00 0.25 0.00 0.29 0.15

time (sec)

N/A 0.579 0.189 0.474 0.000 0.000 0.528 0.000 0.161 24.207

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 47 22 86 54 74 54 66 126 36

N.S.

1 1.02 0.48 1.87 1.17 1.61 1.17 1.43 2.74 0.78

time (sec)

N/A 0.375 0.059 0.111 0.035 0.071 5.028 0.124 0.159 24.661

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

91 93 96 111 0 57 42 0 53 27

N.S.

1 1.02 1.05 1.22 0.00 0.63 0.46 0.00 0.58 0.30

time (sec)

N/A 0.420 0.185 0.612 0.000 0.080 1.146 0.000 0.159 24.586

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

42 49 24 114 92 101 42 61 281 42

N.S.

1 1.17 0.57 2.71 2.19 2.40 1.00 1.45 6.69 1.00

time (sec)

N/A 0.381 0.062 0.106 0.031 0.078 1.351 0.112 0.159 25.204

Problem 33

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

181 185 114 171 0 97 44 0 53 0

N.S.

1 1.02 0.63 0.94 0.00 0.54 0.24 0.00 0.29 0.00

time (sec)

N/A 0.627 0.234 0.744 0.000 0.079 1.210 0.000 0.162 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

31 31 39 42 25 49 49 71 175 44

N.S.

1 1.00 1.26 1.35 0.81 1.58 1.58 2.29 5.65 1.42

time (sec)

N/A 0.348 0.055 0.106 0.027 0.071 1.464 0.146 0.153 24.504

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

59 59 55 0 0 0 71 0 60 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 1.20 0.00 1.02 0.00

time (sec)

N/A 0.429 0.062 0.000 0.000 0.000 2.790 0.000 0.153 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

1 52 54 0 0 0 65 0 32 0

N.S.

1 52.00 54.00 0.00 0.00 0.00 65.00 0.00 32.00 0.00

time (sec)

N/A 0.416 0.022 0.000 0.000 0.000 2.972 0.000 0.163 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

85 85 88 0 0 0 0 0 52 0

N.S.

1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 0.61 0.00

time (sec)

N/A 0.566 0.733 0.000 0.000 0.000 0.000 0.000 0.163 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

92 102 85 172 162 90 0 89 73 79

N.S.

1 1.11 0.92 1.87 1.76 0.98 0.00 0.97 0.79 0.86

time (sec)

N/A 0.560 0.133 0.438 0.118 0.074 0.000 0.125 0.160 24.742

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

72 77 64 125 49 58 0 85 56 61

N.S.

1 1.07 0.89 1.74 0.68 0.81 0.00 1.18 0.78 0.85

time (sec)

N/A 0.551 0.088 0.420 0.038 0.077 0.000 0.114 0.170 24.760

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

59 64 54 138 107 68 0 61 46 51

N.S.

1 1.08 0.92 2.34 1.81 1.15 0.00 1.03 0.78 0.86

time (sec)

N/A 0.480 0.115 0.391 0.116 0.084 0.000 0.117 0.155 24.738

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

36 36 35 89 31 38 0 44 28 31

N.S.

1 1.00 0.97 2.47 0.86 1.06 0.00 1.22 0.78 0.86

time (sec)

N/A 0.419 0.060 0.381 0.037 0.073 0.000 0.133 0.148 24.783

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

27 27 38 85 61 38 0 34 24 21

N.S.

1 1.00 1.41 3.15 2.26 1.41 0.00 1.26 0.89 0.78

time (sec)

N/A 0.423 0.195 0.386 0.114 0.067 0.000 0.121 0.143 24.687

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

33 38 37 170 0 80 0 70 58 38

N.S.

1 1.15 1.12 5.15 0.00 2.42 0.00 2.12 1.76 1.15

time (sec)

N/A 0.402 0.132 0.385 0.000 0.102 0.000 0.118 0.143 24.620

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

30 33 30 157 34 41 42 43 33 29

N.S.

1 1.10 1.00 5.23 1.13 1.37 1.40 1.43 1.10 0.97

time (sec)

N/A 0.444 0.120 0.397 0.115 0.094 2.175 0.137 0.146 24.436

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

60 81 58 216 0 130 0 114 96 61

N.S.

1 1.35 0.97 3.60 0.00 2.17 0.00 1.90 1.60 1.02

time (sec)

N/A 0.552 0.148 0.401 0.000 0.070 0.000 0.112 0.146 24.601

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

61 77 54 197 56 70 102 82 68 57

N.S.

1 1.26 0.89 3.23 0.92 1.15 1.67 1.34 1.11 0.93

time (sec)

N/A 0.538 0.180 0.388 0.122 0.102 2.261 0.127 0.146 24.497

[front] [up]