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2.2.1 Integrals 1 to 100

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 Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 96 73 72 72 72 66 0 69

N.S.

1 1.12 0.85 0.84 0.84 0.84 0.77 0.00 0.80

time (sec)

N/A 0.275 0.032 0.674 0.192 0.247 2.326 0.000 5.254

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 86 65 65 64 64 58 0 61

N.S.

1 1.13 0.86 0.86 0.84 0.84 0.76 0.00 0.80

time (sec)

N/A 0.276 0.026 0.597 0.192 0.236 1.401 0.000 5.361

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 76 57 56 56 56 49 0 53

N.S.

1 1.15 0.86 0.85 0.85 0.85 0.74 0.00 0.80

time (sec)

N/A 0.261 0.023 0.517 0.193 0.252 0.790 0.000 5.263

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 66 48 49 48 48 41 0 46

N.S.

1 1.18 0.86 0.88 0.86 0.86 0.73 0.00 0.82

time (sec)

N/A 0.252 0.021 0.495 0.197 0.249 0.473 0.000 5.436

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 32 26 33 29 29 22 0 32

N.S.

1 1.10 0.90 1.14 1.00 1.00 0.76 0.00 1.10

time (sec)

N/A 0.209 0.013 0.352 0.193 0.252 0.230 0.000 5.241

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A F A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

5 5 5 6 5 0 3 0 5

N.S.

1 1.00 1.00 1.20 1.00 0.00 0.60 0.00 1.00

time (sec)

N/A 0.179 0.002 1.052 0.190 0.000 0.409 0.000 5.064

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 36 40 28 34 24 0 34

N.S.

1 1.00 1.00 1.11 0.78 0.94 0.67 0.00 0.94

time (sec)

N/A 0.222 0.011 0.569 0.193 0.257 0.317 0.000 5.517

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 57 50 57 40 47 42 0 51

N.S.

1 0.98 0.86 0.98 0.69 0.81 0.72 0.00 0.88

time (sec)

N/A 0.254 0.023 0.669 0.192 0.262 0.580 0.000 5.289

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 69 52 68 49 56 51 0 57

N.S.

1 1.01 0.76 1.00 0.72 0.82 0.75 0.00 0.84

time (sec)

N/A 0.263 0.025 0.727 0.196 0.262 1.034 0.000 5.359

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 79 60 76 58 65 60 0 60

N.S.

1 1.01 0.77 0.97 0.74 0.83 0.77 0.00 0.77

time (sec)

N/A 0.268 0.028 0.802 0.194 0.265 1.799 0.000 5.323

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 103 86 78 77 77 0 0 71

N.S.

1 1.17 0.98 0.89 0.88 0.88 0.00 0.00 0.81

time (sec)

N/A 0.341 0.011 0.168 0.196 0.248 0.000 0.000 5.708

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 93 78 69 69 69 0 0 63

N.S.

1 1.19 1.00 0.88 0.88 0.88 0.00 0.00 0.81

time (sec)

N/A 0.333 0.010 0.152 0.194 0.253 0.000 0.000 5.728

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 83 69 62 61 61 0 0 55

N.S.

1 1.22 1.01 0.91 0.90 0.90 0.00 0.00 0.81

time (sec)

N/A 0.313 0.008 0.154 0.208 0.253 0.000 0.000 5.744

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 39 39 41 39 39 0 0 37

N.S.

1 1.15 1.15 1.21 1.15 1.15 0.00 0.00 1.09

time (sec)

N/A 0.266 0.011 0.109 0.199 0.241 0.000 0.000 5.632

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

5 5 5 6 5 0 3 0 0

N.S.

1 1.00 1.00 1.20 1.00 0.00 0.60 0.00 0.00

time (sec)

N/A 0.174 0.002 0.145 0.205 0.000 0.231 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 44 57 33 39 0 0 36

N.S.

1 1.00 0.96 1.24 0.72 0.85 0.00 0.00 0.78

time (sec)

N/A 0.271 0.026 0.121 0.226 0.251 0.000 0.000 5.633

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

70 74 25 90 47 54 0 0 46

N.S.

1 1.06 0.36 1.29 0.67 0.77 0.00 0.00 0.66

time (sec)

N/A 0.306 0.009 0.215 0.197 0.261 0.000 0.000 6.089

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

80 86 25 106 56 63 0 0 62

N.S.

1 1.08 0.31 1.32 0.70 0.79 0.00 0.00 0.78

time (sec)

N/A 0.310 0.011 0.231 0.187 0.259 0.000 0.000 6.196

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 84 65 65 62 62 56 0 61

N.S.

1 1.14 0.88 0.88 0.84 0.84 0.76 0.00 0.82

time (sec)

N/A 0.285 0.016 0.658 0.187 0.239 4.685 0.000 4.913

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 74 56 57 54 54 48 0 53

N.S.

1 1.16 0.88 0.89 0.84 0.84 0.75 0.00 0.83

time (sec)

N/A 0.292 0.013 0.295 0.198 0.247 1.623 0.000 5.051

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 47 43 44 40 40 39 0 45

N.S.

1 1.02 0.93 0.96 0.87 0.87 0.85 0.00 0.98

time (sec)

N/A 0.250 0.008 0.445 0.195 0.256 0.589 0.000 4.913

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 10 0 0 0 0 9

N.S.

1 1.00 1.00 0.91 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.175 0.003 1.534 0.000 0.000 0.000 0.000 4.871

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 51 49 43 34 44 37 0 44

N.S.

1 1.04 1.00 0.88 0.69 0.90 0.76 0.00 0.90

time (sec)

N/A 0.261 0.013 0.226 0.197 0.255 0.769 0.000 4.929

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 65 51 52 46 55 49 0 53

N.S.

1 1.02 0.80 0.81 0.72 0.86 0.77 0.00 0.83

time (sec)

N/A 0.282 0.025 0.523 0.205 0.254 2.111 0.000 4.966

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 77 68 62 55 64 58 0 61

N.S.

1 1.04 0.92 0.84 0.74 0.86 0.78 0.00 0.82

time (sec)

N/A 0.297 0.023 1.185 0.210 0.251 5.449 0.000 4.968

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 82 65 63 80 159 94 0 60

N.S.

1 1.12 0.89 0.86 1.10 2.18 1.29 0.00 0.82

time (sec)

N/A 0.275 0.061 0.987 0.290 0.260 60.570 0.000 5.139

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 72 57 55 68 143 83 0 52

N.S.

1 1.14 0.90 0.87 1.08 2.27 1.32 0.00 0.83

time (sec)

N/A 0.269 0.037 0.413 0.283 0.260 18.156 0.000 5.004

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 48 39 43 49 107 60 0 39

N.S.

1 1.20 0.98 1.08 1.22 2.68 1.50 0.00 0.98

time (sec)

N/A 0.220 0.023 0.176 0.276 0.257 4.199 0.000 4.940

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 45 41 39 49 94 184 0 38

N.S.

1 1.07 0.98 0.93 1.17 2.24 4.38 0.00 0.90

time (sec)

N/A 0.232 0.015 0.250 0.276 0.259 15.850 0.000 5.186

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 61 47 47 57 114 275 0 47

N.S.

1 1.09 0.84 0.84 1.02 2.04 4.91 0.00 0.84

time (sec)

N/A 0.240 0.014 0.529 0.289 0.266 72.400 0.000 5.053

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 71 47 53 65 132 0 0 58

N.S.

1 1.08 0.71 0.80 0.98 2.00 0.00 0.00 0.88

time (sec)

N/A 0.253 0.016 1.152 0.281 0.273 0.000 0.000 5.037

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 103 88 80 77 77 0 0 73

N.S.

1 1.17 1.00 0.91 0.88 0.88 0.00 0.00 0.83

time (sec)

N/A 0.369 0.013 0.066 0.196 0.264 0.000 0.000 4.976

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 93 79 72 69 69 0 0 65

N.S.

1 1.19 1.01 0.92 0.88 0.88 0.00 0.00 0.83

time (sec)

N/A 0.363 0.012 0.055 0.197 0.263 0.000 0.000 4.895

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 61 52 56 53 53 0 0 57

N.S.

1 1.02 0.87 0.93 0.88 0.88 0.00 0.00 0.95

time (sec)

N/A 0.315 0.011 0.133 0.204 0.251 0.000 0.000 5.053

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 10 0 0 0 0 9

N.S.

1 1.00 1.00 0.91 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.178 0.003 0.085 0.000 0.000 0.000 0.000 4.824

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 65 60 68 41 51 0 0 54

N.S.

1 1.03 0.95 1.08 0.65 0.81 0.00 0.00 0.86

time (sec)

N/A 0.315 0.022 0.138 0.207 0.253 0.000 0.000 4.911

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

78 84 30 98 55 64 0 0 65

N.S.

1 1.08 0.38 1.26 0.71 0.82 0.00 0.00 0.83

time (sec)

N/A 0.352 0.011 0.206 0.198 0.254 0.000 0.000 5.267

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

88 96 30 115 64 73 0 0 73

N.S.

1 1.09 0.34 1.31 0.73 0.83 0.00 0.00 0.83

time (sec)

N/A 0.359 0.015 0.193 0.201 0.261 0.000 0.000 5.893

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 101 77 144 95 189 0 0 72

N.S.

1 1.16 0.89 1.66 1.09 2.17 0.00 0.00 0.83

time (sec)

N/A 0.333 0.131 0.173 0.286 0.268 0.000 0.000 5.179

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 91 69 136 81 173 0 0 64

N.S.

1 1.18 0.90 1.77 1.05 2.25 0.00 0.00 0.83

time (sec)

N/A 0.317 0.118 0.187 0.280 0.260 0.000 0.000 5.141

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 60 50 119 59 133 0 0 49

N.S.

1 1.20 1.00 2.38 1.18 2.66 0.00 0.00 0.98

time (sec)

N/A 0.270 0.078 0.180 0.279 0.253 0.000 0.000 5.236

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 60 50 112 58 112 0 0 53

N.S.

1 1.11 0.93 2.07 1.07 2.07 0.00 0.00 0.98

time (sec)

N/A 0.282 0.073 0.187 0.280 0.263 0.000 0.000 5.142

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 80 61 125 66 132 0 0 59

N.S.

1 1.14 0.87 1.79 0.94 1.89 0.00 0.00 0.84

time (sec)

N/A 0.301 0.073 0.196 0.270 0.266 0.000 0.000 5.416

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 90 69 138 74 150 0 0 70

N.S.

1 1.12 0.86 1.72 0.92 1.88 0.00 0.00 0.88

time (sec)

N/A 0.310 0.081 0.201 0.287 0.272 0.000 0.000 5.744

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 74 69 108 0 0 0 0 0

N.S.

1 1.04 0.97 1.52 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.266 0.037 1.455 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 74 69 108 0 0 0 0 0

N.S.

1 1.04 0.97 1.52 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.258 0.033 0.658 0.000 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 51 88 0 0 0 0 0

N.S.

1 1.00 0.94 1.63 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.241 0.037 0.443 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 0 11 0 0 0

N.S.

1 1.00 1.00 1.09 0.00 1.00 0.00 0.00 0.00

time (sec)

N/A 0.179 0.003 0.550 0.000 0.271 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 70 60 106 0 0 0 0 0

N.S.

1 1.01 0.87 1.54 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.266 0.043 0.722 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 81 61 108 0 0 0 0 0

N.S.

1 1.04 0.78 1.38 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.272 0.044 1.500 0.000 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 79 61 108 0 0 0 0 0

N.S.

1 1.04 0.80 1.42 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.271 0.043 3.164 0.000 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 94 41 132 0 0 0 0 0

N.S.

1 1.07 0.47 1.50 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.341 0.023 0.327 0.000 0.000 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 94 41 132 0 0 0 0 0

N.S.

1 1.07 0.47 1.50 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.325 0.010 0.289 0.000 0.000 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 67 39 105 0 0 0 0 0

N.S.

1 0.97 0.57 1.52 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.297 0.009 0.300 0.000 0.000 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 0 11 0 0 0

N.S.

1 1.00 1.00 1.09 0.00 1.00 0.00 0.00 0.00

time (sec)

N/A 0.181 0.004 0.428 0.000 0.267 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 85 37 129 0 0 0 0 0

N.S.

1 1.01 0.44 1.54 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.334 0.009 0.294 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 101 41 132 0 0 0 0 0

N.S.

1 1.06 0.43 1.39 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.331 0.011 0.313 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 99 41 132 0 0 0 0 0

N.S.

1 1.06 0.44 1.42 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.318 0.009 0.338 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 138 90 101 128 190 0 0 0

N.S.

1 1.18 0.77 0.86 1.09 1.62 0.00 0.00 0.00

time (sec)

N/A 0.294 0.094 0.778 0.280 0.288 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 118 75 88 109 143 0 0 0

N.S.

1 1.16 0.74 0.86 1.07 1.40 0.00 0.00 0.00

time (sec)

N/A 0.283 0.068 0.683 0.280 0.266 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 90 63 74 83 135 0 0 0

N.S.

1 1.12 0.79 0.92 1.04 1.69 0.00 0.00 0.00

time (sec)

N/A 0.265 0.076 0.709 0.276 0.273 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 71 51 59 71 132 0 0 0

N.S.

1 1.04 0.75 0.87 1.04 1.94 0.00 0.00 0.00

time (sec)

N/A 0.256 0.064 0.697 0.280 0.272 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 98 57 75 89 150 0 0 0

N.S.

1 1.10 0.64 0.84 1.00 1.69 0.00 0.00 0.00

time (sec)

N/A 0.267 0.078 0.699 0.275 0.274 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 118 65 88 108 170 0 0 0

N.S.

1 1.11 0.61 0.83 1.02 1.60 0.00 0.00 0.00

time (sec)

N/A 0.285 0.080 0.736 0.282 0.292 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 182 98 149 156 279 0 0 0

N.S.

1 1.19 0.64 0.97 1.02 1.82 0.00 0.00 0.00

time (sec)

N/A 0.384 0.216 0.242 0.297 0.288 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 162 88 141 143 229 0 0 0

N.S.

1 1.19 0.65 1.04 1.05 1.68 0.00 0.00 0.00

time (sec)

N/A 0.381 0.181 0.119 0.299 0.271 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 142 73 133 122 173 0 0 0

N.S.

1 1.17 0.60 1.10 1.01 1.43 0.00 0.00 0.00

time (sec)

N/A 0.352 0.165 0.076 0.289 0.277 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 110 57 127 94 161 0 0 0

N.S.

1 1.13 0.59 1.31 0.97 1.66 0.00 0.00 0.00

time (sec)

N/A 0.339 0.115 0.071 0.277 0.270 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 91 58 111 78 156 0 0 0

N.S.

1 1.07 0.68 1.31 0.92 1.84 0.00 0.00 0.00

time (sec)

N/A 0.329 0.099 0.085 0.302 0.276 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 122 64 122 97 175 0 0 0

N.S.

1 1.13 0.59 1.13 0.90 1.62 0.00 0.00 0.00

time (sec)

N/A 0.347 0.095 0.075 0.286 0.270 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 142 72 135 118 195 0 0 0

N.S.

1 1.14 0.58 1.08 0.94 1.56 0.00 0.00 0.00

time (sec)

N/A 0.352 0.118 0.074 0.281 0.272 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

140 168 101 135 160 188 0 0 0

N.S.

1 1.20 0.72 0.96 1.14 1.34 0.00 0.00 0.00

time (sec)

N/A 0.340 0.091 0.457 0.278 0.275 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 149 91 127 139 173 0 0 0

N.S.

1 1.19 0.73 1.02 1.11 1.38 0.00 0.00 0.00

time (sec)

N/A 0.328 0.063 0.459 0.280 0.273 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 137 57 127 128 154 0 0 0

N.S.

1 1.19 0.50 1.10 1.11 1.34 0.00 0.00 0.00

time (sec)

N/A 0.314 0.072 0.484 0.285 0.275 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 117 62 111 123 174 0 0 0

N.S.

1 1.14 0.60 1.08 1.19 1.69 0.00 0.00 0.00

time (sec)

N/A 0.310 0.074 0.470 0.279 0.267 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 125 62 111 125 200 0 0 0

N.S.

1 1.13 0.56 1.00 1.13 1.80 0.00 0.00 0.00

time (sec)

N/A 0.305 0.077 0.421 0.290 0.273 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 144 70 122 151 214 0 0 0

N.S.

1 1.14 0.56 0.97 1.20 1.70 0.00 0.00 0.00

time (sec)

N/A 0.326 0.079 0.431 0.276 0.278 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 198 89 155 178 235 0 0 0

N.S.

1 1.23 0.55 0.96 1.11 1.46 0.00 0.00 0.00

time (sec)

N/A 0.430 0.101 0.197 0.275 0.291 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 194 89 155 175 208 0 0 0

N.S.

1 1.20 0.55 0.96 1.09 1.29 0.00 0.00 0.00

time (sec)

N/A 0.420 0.086 0.152 0.264 0.278 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

146 175 68 147 153 188 0 0 0

N.S.

1 1.20 0.47 1.01 1.05 1.29 0.00 0.00 0.00

time (sec)

N/A 0.400 0.086 0.168 0.275 0.270 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 159 68 147 141 169 0 0 0

N.S.

1 1.19 0.51 1.10 1.05 1.26 0.00 0.00 0.00

time (sec)

N/A 0.395 0.079 0.242 0.268 0.291 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 139 71 131 132 188 0 0 0

N.S.

1 1.14 0.58 1.07 1.08 1.54 0.00 0.00 0.00

time (sec)

N/A 0.380 0.082 0.276 0.269 0.283 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 151 71 131 134 214 0 0 0

N.S.

1 1.14 0.54 0.99 1.02 1.62 0.00 0.00 0.00

time (sec)

N/A 0.376 0.089 0.285 0.283 0.279 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 170 79 142 163 228 0 0 0

N.S.

1 1.16 0.54 0.97 1.11 1.55 0.00 0.00 0.00

time (sec)

N/A 0.390 0.090 0.157 0.286 0.295 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 172 84 142 168 228 0 0 0

N.S.

1 1.17 0.57 0.97 1.14 1.55 0.00 0.00 0.00

time (sec)

N/A 0.402 0.090 0.161 0.286 0.297 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 104 82 121 0 0 0 0 0

N.S.

1 1.03 0.81 1.20 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.286 0.104 0.493 0.000 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 103 82 121 0 0 0 0 0

N.S.

1 1.03 0.82 1.21 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.286 0.097 0.505 0.000 0.000 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 94 48 109 0 0 0 0 0

N.S.

1 1.01 0.52 1.17 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.292 0.027 0.572 0.000 0.000 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 99 48 121 0 0 0 0 0

N.S.

1 1.02 0.49 1.25 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.294 0.033 0.592 0.000 0.000 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 109 48 121 0 0 0 0 0

N.S.

1 1.04 0.46 1.15 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.296 0.036 0.972 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 131 50 145 0 0 0 0 0

N.S.

1 1.05 0.40 1.16 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.370 0.041 0.356 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 130 50 145 0 0 0 0 0

N.S.

1 1.05 0.40 1.17 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.356 0.033 0.379 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 117 50 133 0 0 0 0 0

N.S.

1 1.02 0.43 1.16 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.356 0.028 0.372 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 122 50 145 0 0 0 0 0

N.S.

1 1.03 0.42 1.22 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.366 0.036 0.344 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

129 136 50 145 0 0 0 0 0

N.S.

1 1.05 0.39 1.12 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.366 0.034 0.346 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

7 7 9 5 7 7 7 7 7

N.S.

1 1.00 1.29 0.71 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.256 0.007 0.019 0.196 0.244 0.232 0.270 5.195

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

7 7 9 5 7 7 7 7 7

N.S.

1 1.00 1.29 0.71 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.209 0.008 0.020 0.208 0.261 0.224 0.283 5.182

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

7 7 9 5 7 7 8 7 7

N.S.

1 1.00 1.29 0.71 1.00 1.00 1.14 1.00 1.00

time (sec)

N/A 0.159 0.007 0.020 0.189 0.246 0.233 0.270 4.964

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

7 7 9 5 7 7 8 7 7

N.S.

1 1.00 1.29 0.71 1.00 1.00 1.14 1.00 1.00

time (sec)

N/A 0.206 0.007 0.020 0.180 0.234 0.210 0.271 4.962

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

7 7 9 5 7 7 8 7 7

N.S.

1 1.00 1.29 0.71 1.00 1.00 1.14 1.00 1.00

time (sec)

N/A 0.251 0.008 0.020 0.197 0.226 0.246 0.273 5.027

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