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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 76 73 95 99 0 110 130

N.S.

1 1.00 0.89 0.86 1.12 1.16 0.00 1.29 1.53

time (sec)

N/A 0.045 0.180 0.149 0.287 2.272 0.000 0.459 3.941

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 60 60 70 88 0 96 102

N.S.

1 1.00 0.95 0.95 1.11 1.40 0.00 1.52 1.62

time (sec)

N/A 0.035 0.156 0.099 0.293 2.363 0.000 0.447 2.511

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 47 47 58 74 0 80 75

N.S.

1 1.00 1.00 1.00 1.23 1.57 0.00 1.70 1.60

time (sec)

N/A 0.034 0.024 0.087 0.282 2.944 0.000 0.475 1.057

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 24 30 29 60 37 63 47

N.S.

1 1.00 1.00 1.25 1.21 2.50 1.54 2.62 1.96

time (sec)

N/A 0.017 0.015 0.039 0.291 2.515 2.550 0.438 0.685

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 24 23 36 41 49 20

N.S.

1 1.00 1.00 1.50 1.44 2.25 2.56 3.06 1.25

time (sec)

N/A 0.005 0.004 0.026 0.292 2.807 1.087 0.450 0.610

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 26 21 20 17 17 39 15

N.S.

1 1.00 1.73 1.40 1.33 1.13 1.13 2.60 1.00

time (sec)

N/A 0.014 0.010 0.059 0.284 2.613 1.133 0.433 0.600

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 32 38 34 29 0 56 50

N.S.

1 1.00 0.84 1.00 0.89 0.76 0.00 1.47 1.32

time (sec)

N/A 0.025 0.060 0.079 0.279 3.085 0.000 0.409 1.063

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 57 49 46 42 0 72 55

N.S.

1 1.00 1.06 0.91 0.85 0.78 0.00 1.33 1.02

time (sec)

N/A 0.031 0.075 0.093 0.282 3.649 0.000 0.422 0.654

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 73 60 57 53 0 86 79

N.S.

1 1.00 0.96 0.79 0.75 0.70 0.00 1.13 1.04

time (sec)

N/A 0.038 0.112 0.104 0.282 3.052 0.000 0.443 4.170

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 487 111 133 124 0 138 170

N.S.

1 1.00 3.99 0.91 1.09 1.02 0.00 1.13 1.39

time (sec)

N/A 0.070 1.623 0.115 0.278 2.100 0.000 0.454 5.700

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 877 112 145 111 0 122 141

N.S.

1 1.00 9.14 1.17 1.51 1.16 0.00 1.27 1.47

time (sec)

N/A 0.065 6.441 0.072 0.286 2.902 0.000 0.528 3.960

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 318 75 85 96 0 106 112

N.S.

1 1.00 4.30 1.01 1.15 1.30 0.00 1.43 1.51

time (sec)

N/A 0.060 0.707 0.069 0.291 2.745 0.000 0.471 2.466

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 219 70 81 83 0 90 83

N.S.

1 1.00 4.06 1.30 1.50 1.54 0.00 1.67 1.54

time (sec)

N/A 0.041 0.648 0.045 0.280 2.509 0.000 0.459 1.175

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 171 44 41 76 0 79 56

N.S.

1 1.00 5.03 1.29 1.21 2.24 0.00 2.32 1.65

time (sec)

N/A 0.021 0.523 0.052 0.284 2.911 0.000 0.422 0.710

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 47 44 52 53 0 79 33

N.S.

1 1.00 1.38 1.29 1.53 1.56 0.00 2.32 0.97

time (sec)

N/A 0.040 0.017 0.066 0.286 2.809 0.000 0.445 0.700

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 34 52 48 36 0 64 57

N.S.

1 1.00 0.76 1.16 1.07 0.80 0.00 1.42 1.27

time (sec)

N/A 0.046 0.044 0.072 0.291 3.186 0.000 0.443 1.074

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 41 64 61 49 0 80 61

N.S.

1 1.00 0.72 1.12 1.07 0.86 0.00 1.40 1.07

time (sec)

N/A 0.063 0.092 0.088 0.290 3.560 0.000 0.440 0.656

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 53 90 83 63 0 96 89

N.S.

1 1.00 0.61 1.03 0.95 0.72 0.00 1.10 1.02

time (sec)

N/A 0.059 0.148 0.098 0.286 2.907 0.000 0.450 4.193

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 61 96 95 76 0 112 105

N.S.

1 1.00 0.59 0.93 0.92 0.74 0.00 1.09 1.02

time (sec)

N/A 0.085 0.149 0.131 0.288 2.393 0.000 0.458 4.419

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 487 146 179 124 0 138 170

N.S.

1 1.00 4.27 1.28 1.57 1.09 0.00 1.21 1.49

time (sec)

N/A 0.096 1.550 0.095 0.286 2.760 0.000 0.473 5.482

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 877 123 156 111 0 122 141

N.S.

1 1.00 9.43 1.32 1.68 1.19 0.00 1.31 1.52

time (sec)

N/A 0.086 6.432 0.069 0.286 2.136 0.000 0.486 4.053

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 154 94 104 98 0 106 112

N.S.

1 1.00 2.14 1.31 1.44 1.36 0.00 1.47 1.56

time (sec)

N/A 0.056 5.572 0.059 0.286 4.009 0.000 0.515 2.574

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 235 80 91 98 0 100 88

N.S.

1 1.00 3.56 1.21 1.38 1.48 0.00 1.52 1.33

time (sec)

N/A 0.035 0.957 0.050 0.284 4.070 0.000 0.472 0.737

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 211 55 64 91 0 80 57

N.S.

1 1.00 4.40 1.15 1.33 1.90 0.00 1.67 1.19

time (sec)

N/A 0.048 0.901 0.074 0.278 3.170 0.000 0.478 0.700

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 81 71 74 65 0 100 88

N.S.

1 1.00 1.37 1.20 1.25 1.10 0.00 1.69 1.49

time (sec)

N/A 0.049 0.071 0.082 0.292 3.057 0.000 0.481 0.725

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 44 74 71 50 0 80 63

N.S.

1 1.00 0.70 1.17 1.13 0.79 0.00 1.27 1.00

time (sec)

N/A 0.055 0.065 0.095 0.290 3.422 0.000 0.462 0.670

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 51 100 94 63 0 96 89

N.S.

1 1.00 0.60 1.18 1.11 0.74 0.00 1.13 1.05

time (sec)

N/A 0.072 0.133 0.111 0.286 3.494 0.000 0.490 4.173

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 63 121 117 76 0 112 105

N.S.

1 1.00 0.60 1.15 1.11 0.72 0.00 1.07 1.00

time (sec)

N/A 0.080 0.160 0.128 0.284 3.322 0.000 0.439 4.377

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

129 129 73 143 143 89 0 128 121

N.S.

1 1.00 0.57 1.11 1.11 0.69 0.00 0.99 0.94

time (sec)

N/A 0.101 0.207 0.157 0.281 3.641 0.000 0.533 3.492

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 211 204 270 137 0 154 199

N.S.

1 1.00 1.55 1.50 1.99 1.01 0.00 1.13 1.46

time (sec)

N/A 0.136 0.840 0.131 0.283 3.293 0.000 0.467 4.649

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 498 157 190 124 0 138 170

N.S.

1 1.00 4.49 1.41 1.71 1.12 0.00 1.24 1.53

time (sec)

N/A 0.106 1.536 0.086 0.287 2.416 0.000 0.492 5.470

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 877 142 175 111 0 122 141

N.S.

1 1.00 9.14 1.48 1.82 1.16 0.00 1.27 1.47

time (sec)

N/A 0.083 6.426 0.075 0.293 2.782 0.000 0.499 3.989

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 773 104 116 110 0 116 117

N.S.

1 1.00 8.49 1.14 1.27 1.21 0.00 1.27 1.29

time (sec)

N/A 0.062 6.275 0.061 0.301 3.350 0.000 0.442 0.878

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 272 91 110 111 0 129 115

N.S.

1 1.00 3.73 1.25 1.51 1.52 0.00 1.77 1.58

time (sec)

N/A 0.057 1.385 0.092 0.287 3.119 0.000 0.488 0.905

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 241 82 85 105 0 129 117

N.S.

1 1.00 3.30 1.12 1.16 1.44 0.00 1.77 1.60

time (sec)

N/A 0.058 1.795 0.106 0.302 2.941 0.000 0.471 0.891

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 91 93 97 80 0 116 93

N.S.

1 1.00 1.25 1.27 1.33 1.10 0.00 1.59 1.27

time (sec)

N/A 0.062 0.108 0.113 0.281 3.391 0.000 0.467 0.687

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 56 111 104 63 0 96 89

N.S.

1 1.00 0.64 1.28 1.20 0.72 0.00 1.10 1.02

time (sec)

N/A 0.074 0.107 0.110 0.282 2.288 0.000 0.457 4.125

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 63 133 128 76 0 112 105

N.S.

1 1.00 0.62 1.30 1.25 0.75 0.00 1.10 1.03

time (sec)

N/A 0.085 0.156 0.151 0.287 2.738 0.000 0.474 4.428

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 73 169 165 89 0 128 121

N.S.

1 1.00 0.57 1.33 1.30 0.70 0.00 1.01 0.95

time (sec)

N/A 0.115 0.208 0.091 0.278 1.972 0.000 0.491 3.418

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 83 185 187 102 0 144 137

N.S.

1 1.00 0.56 1.26 1.27 0.69 0.00 0.98 0.93

time (sec)

N/A 0.120 0.277 0.118 0.298 3.499 0.000 0.513 3.636

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 229 248 314 150 0 170 228

N.S.

1 1.00 1.47 1.59 2.01 0.96 0.00 1.09 1.46

time (sec)

N/A 0.151 1.288 0.147 0.291 2.654 0.000 0.569 4.843

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 374 134 205 124 0 114 96

N.S.

1 1.00 3.63 1.30 1.99 1.20 0.00 1.11 0.93

time (sec)

N/A 0.071 3.352 0.094 0.282 4.572 0.000 0.445 0.933

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 250 108 162 112 0 101 95

N.S.

1 1.00 2.94 1.27 1.91 1.32 0.00 1.19 1.12

time (sec)

N/A 0.069 1.446 0.068 0.294 3.025 0.000 0.440 0.727

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 194 74 119 97 0 84 67

N.S.

1 1.00 3.80 1.45 2.33 1.90 0.00 1.65 1.31

time (sec)

N/A 0.075 0.828 0.049 0.300 2.724 0.000 0.456 0.679

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 109 46 75 65 0 54 31

N.S.

1 1.00 2.87 1.21 1.97 1.71 0.00 1.42 0.82

time (sec)

N/A 0.049 0.193 0.043 0.273 2.710 0.000 0.444 0.647

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 17 17 23 22 0 16 16

N.S.

1 1.00 0.77 0.77 1.05 1.00 0.00 0.73 0.73

time (sec)

N/A 0.017 0.028 0.036 0.293 2.312 0.000 0.436 0.589

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 58 32 49 37 0 28 23

N.S.

1 1.00 2.00 1.10 1.69 1.28 0.00 0.97 0.79

time (sec)

N/A 0.010 0.135 0.038 0.494 2.799 0.000 0.440 0.638

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 89 56 92 46 0 58 66

N.S.

1 1.00 2.02 1.27 2.09 1.05 0.00 1.32 1.50

time (sec)

N/A 0.042 0.242 0.060 0.485 2.877 0.000 0.462 0.662

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 117 74 133 57 0 73 89

N.S.

1 1.00 1.58 1.00 1.80 0.77 0.00 0.99 1.20

time (sec)

N/A 0.066 0.255 0.066 0.498 2.325 0.000 0.446 0.725

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 143 85 176 70 0 88 70

N.S.

1 1.00 1.52 0.90 1.87 0.74 0.00 0.94 0.74

time (sec)

N/A 0.065 0.330 0.072 0.498 3.102 0.000 0.444 0.907

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 173 100 217 79 0 101 98

N.S.

1 1.00 1.47 0.85 1.84 0.67 0.00 0.86 0.83

time (sec)

N/A 0.072 0.321 0.080 0.507 2.659 0.000 0.431 2.454

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 300 120 190 162 0 122 122

N.S.

1 1.00 2.44 0.98 1.54 1.32 0.00 0.99 0.99

time (sec)

N/A 0.127 1.998 0.087 0.281 3.747 0.000 0.510 0.735

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 247 92 145 146 0 106 92

N.S.

1 1.00 2.78 1.03 1.63 1.64 0.00 1.19 1.03

time (sec)

N/A 0.109 1.260 0.069 0.281 2.947 0.000 0.460 0.688

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 160 62 98 114 0 77 43

N.S.

1 1.00 2.42 0.94 1.48 1.73 0.00 1.17 0.65

time (sec)

N/A 0.083 0.375 0.073 0.283 3.117 0.000 0.469 0.643

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 45 32 46 49 0 31 30

N.S.

1 1.00 0.82 0.58 0.84 0.89 0.00 0.56 0.55

time (sec)

N/A 0.046 0.074 0.047 0.274 3.301 0.000 0.493 0.596

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 60 32 47 51 0 31 30

N.S.

1 1.00 1.09 0.58 0.85 0.93 0.00 0.56 0.55

time (sec)

N/A 0.036 0.143 0.048 0.284 2.408 0.000 0.457 0.597

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 112 46 72 80 0 50 35

N.S.

1 1.00 1.96 0.81 1.26 1.40 0.00 0.88 0.61

time (sec)

N/A 0.049 0.295 0.046 0.502 2.992 0.000 0.439 0.630

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 151 72 118 90 0 79 91

N.S.

1 1.00 2.10 1.00 1.64 1.25 0.00 1.10 1.26

time (sec)

N/A 0.095 0.510 0.069 0.500 2.807 0.000 0.455 0.698

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 177 88 164 99 0 95 113

N.S.

1 1.00 1.61 0.80 1.49 0.90 0.00 0.86 1.03

time (sec)

N/A 0.124 0.383 0.077 0.513 2.484 0.000 0.441 0.735

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 199 101 207 108 0 108 135

N.S.

1 1.00 1.60 0.81 1.67 0.87 0.00 0.87 1.09

time (sec)

N/A 0.133 0.357 0.083 0.492 2.482 0.000 0.460 0.782

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 351 135 211 206 0 139 141

N.S.

1 1.00 2.17 0.83 1.30 1.27 0.00 0.86 0.87

time (sec)

N/A 0.201 1.021 0.119 0.294 2.247 0.000 0.453 0.679

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 294 105 165 190 0 122 111

N.S.

1 1.00 2.30 0.82 1.29 1.48 0.00 0.95 0.87

time (sec)

N/A 0.178 1.334 0.089 0.282 3.957 0.000 0.518 0.682

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 209 75 119 158 0 94 58

N.S.

1 1.00 1.99 0.71 1.13 1.50 0.00 0.90 0.55

time (sec)

N/A 0.155 0.514 0.076 0.299 2.709 0.000 0.502 0.688

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 57 45 67 75 0 46 45

N.S.

1 1.00 0.69 0.54 0.81 0.90 0.00 0.55 0.54

time (sec)

N/A 0.085 0.116 0.065 0.281 2.876 0.000 0.488 0.616

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 71 32 47 73 0 31 30

N.S.

1 1.00 0.86 0.39 0.57 0.88 0.00 0.37 0.36

time (sec)

N/A 0.065 0.178 0.078 0.283 2.876 0.000 0.481 0.597

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 86 45 67 75 0 46 45

N.S.

1 1.00 1.04 0.54 0.81 0.90 0.00 0.55 0.54

time (sec)

N/A 0.056 0.235 0.055 0.288 2.504 0.000 0.476 0.619

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 162 59 92 116 0 68 81

N.S.

1 1.00 1.84 0.67 1.05 1.32 0.00 0.77 0.92

time (sec)

N/A 0.079 0.285 0.056 0.497 1.892 0.000 0.429 0.692

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 169 85 137 126 0 96 113

N.S.

1 1.00 1.64 0.83 1.33 1.22 0.00 0.93 1.10

time (sec)

N/A 0.149 0.574 0.077 0.487 2.025 0.000 0.494 0.728

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 181 101 184 135 0 113 137

N.S.

1 1.00 1.23 0.69 1.25 0.92 0.00 0.77 0.93

time (sec)

N/A 0.193 0.577 0.092 0.519 2.641 0.000 0.510 0.758

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

193 193 403 148 231 250 0 155 160

N.S.

1 1.00 2.09 0.77 1.20 1.30 0.00 0.80 0.83

time (sec)

N/A 0.274 1.497 0.069 0.285 2.985 0.000 0.485 0.754

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 349 118 186 234 0 139 130

N.S.

1 1.00 2.19 0.74 1.17 1.47 0.00 0.87 0.82

time (sec)

N/A 0.245 1.263 0.060 0.292 3.286 0.000 0.467 0.702

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 193 88 139 202 0 110 83

N.S.

1 1.00 1.42 0.65 1.02 1.49 0.00 0.81 0.61

time (sec)

N/A 0.217 0.915 0.095 0.298 4.541 0.000 0.516 0.668

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 69 56 87 99 0 59 58

N.S.

1 1.00 0.58 0.47 0.72 0.82 0.00 0.49 0.48

time (sec)

N/A 0.114 0.208 0.075 0.274 9.540 0.000 0.493 0.673

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 87 58 87 99 0 59 58

N.S.

1 1.00 0.78 0.52 0.78 0.88 0.00 0.53 0.52

time (sec)

N/A 0.107 0.245 0.086 0.284 4.039 0.000 0.476 0.662

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 99 58 87 99 0 59 58

N.S.

1 1.00 0.88 0.52 0.78 0.88 0.00 0.53 0.52

time (sec)

N/A 0.088 0.273 0.077 0.277 2.200 0.000 0.455 0.675

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 112 58 87 99 0 59 58

N.S.

1 1.00 1.00 0.52 0.78 0.88 0.00 0.53 0.52

time (sec)

N/A 0.081 0.257 0.059 0.293 5.492 0.000 0.502 0.669

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 224 72 112 152 0 83 102

N.S.

1 1.00 2.02 0.65 1.01 1.37 0.00 0.75 0.92

time (sec)

N/A 0.121 0.399 0.059 0.512 3.103 0.000 0.457 0.725

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 263 98 158 162 0 112 137

N.S.

1 1.00 2.09 0.78 1.25 1.29 0.00 0.89 1.09

time (sec)

N/A 0.208 0.461 0.102 0.540 6.683 0.000 0.461 0.755

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 289 114 204 171 0 128 159

N.S.

1 1.00 1.64 0.65 1.16 0.97 0.00 0.73 0.90

time (sec)

N/A 0.270 0.564 0.099 0.498 8.727 0.000 0.483 0.811

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

200 200 401 131 206 278 0 155 149

N.S.

1 1.00 2.00 0.66 1.03 1.39 0.00 0.78 0.74

time (sec)

N/A 0.325 1.847 0.066 0.279 6.533 0.000 0.532 0.715

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 219 101 159 246 0 126 99

N.S.

1 1.00 1.24 0.57 0.90 1.39 0.00 0.71 0.56

time (sec)

N/A 0.294 1.858 0.067 0.288 7.016 0.000 0.517 0.691

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 97 71 107 123 0 72 127

N.S.

1 1.00 0.61 0.45 0.67 0.77 0.00 0.45 0.80

time (sec)

N/A 0.150 0.178 0.054 0.292 4.098 0.000 0.497 0.764

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 97 58 87 123 0 59 58

N.S.

1 1.00 0.61 0.36 0.55 0.77 0.00 0.37 0.36

time (sec)

N/A 0.150 0.220 0.103 0.282 4.044 0.000 0.527 0.720

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 110 45 67 123 0 46 45

N.S.

1 1.00 0.79 0.32 0.48 0.88 0.00 0.33 0.32

time (sec)

N/A 0.131 0.251 0.096 0.283 3.066 0.000 0.491 0.656

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 125 58 87 123 0 59 58

N.S.

1 1.00 0.87 0.41 0.61 0.86 0.00 0.41 0.41

time (sec)

N/A 0.113 0.260 0.085 0.302 15.421 0.000 0.505 0.689

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 138 71 107 123 0 72 127

N.S.

1 1.00 0.97 0.50 0.75 0.86 0.00 0.50 0.89

time (sec)

N/A 0.102 0.290 0.066 0.281 4.586 0.000 0.508 0.763

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 280 85 132 188 0 100 125

N.S.

1 1.00 1.94 0.59 0.92 1.31 0.00 0.69 0.87

time (sec)

N/A 0.145 0.549 0.068 0.502 3.736 0.000 0.465 0.798

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 319 111 178 198 0 129 159

N.S.

1 1.00 2.01 0.70 1.12 1.25 0.00 0.81 1.00

time (sec)

N/A 0.275 0.684 0.096 0.518 2.541 0.000 0.485 0.832

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

215 215 345 127 224 207 0 145 181

N.S.

1 1.00 1.60 0.59 1.04 0.96 0.00 0.67 0.84

time (sec)

N/A 0.347 0.761 0.122 0.506 2.486 0.000 0.510 0.950

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 58 82 0 82 0 120 331

N.S.

1 1.00 0.48 0.67 0.00 0.67 0.00 0.98 2.71

time (sec)

N/A 0.138 0.145 0.324 0.000 2.674 0.000 0.826 5.925

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 48 72 0 72 0 101 115

N.S.

1 1.00 0.56 0.84 0.00 0.84 0.00 1.17 1.34

time (sec)

N/A 0.104 0.124 0.115 0.000 2.679 0.000 0.837 4.458

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 36 62 0 60 0 82 108

N.S.

1 1.00 0.64 1.11 0.00 1.07 0.00 1.46 1.93

time (sec)

N/A 0.056 0.108 0.098 0.000 4.016 0.000 0.794 1.389

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 29 42 0 41 0 62 41

N.S.

1 1.00 1.12 1.62 0.00 1.58 0.00 2.38 1.58

time (sec)

N/A 0.022 0.074 0.080 0.000 3.750 0.000 0.753 0.191

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 60 89 146 133 0 130 -1

N.S.

1 1.00 1.62 2.41 3.95 3.59 0.00 3.51 -0.03

time (sec)

N/A 0.014 0.097 0.133 0.567 3.547 0.000 0.958 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 62 123 791 242 0 282 -1

N.S.

1 1.00 1.00 1.98 12.76 3.90 0.00 4.55 -0.02

time (sec)

N/A 0.044 0.207 0.276 0.592 3.226 0.000 0.814 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 47 221 1059 270 0 378 -1

N.S.

1 1.00 0.46 2.17 10.38 2.65 0.00 3.71 -0.01

time (sec)

N/A 0.085 0.106 0.173 0.628 3.289 0.000 1.023 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 47 310 1921 290 0 475 -1

N.S.

1 1.00 0.34 2.25 13.92 2.10 0.00 3.44 -0.01

time (sec)

N/A 0.123 0.100 0.197 0.749 2.360 0.000 1.022 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B B A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 47 399 6638 310 0 571 -1

N.S.

1 1.00 0.27 2.29 38.15 1.78 0.00 3.28 -0.01

time (sec)

N/A 0.170 0.096 0.228 0.872 2.825 0.000 0.988 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 70 93 0 98 0 180 429

N.S.

1 1.00 0.43 0.57 0.00 0.60 0.00 1.11 2.65

time (sec)

N/A 0.193 0.503 0.121 0.000 2.639 0.000 1.090 6.701

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 60 83 0 87 0 151 346

N.S.

1 1.00 0.52 0.72 0.00 0.75 0.00 1.30 2.98

time (sec)

N/A 0.135 0.181 0.106 0.000 2.632 0.000 1.163 5.084

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