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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 B A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 47 17 21 34 19 21 21

N.S.

1 1.00 2.14 0.77 0.95 1.55 0.86 0.95 0.95

time (sec)

N/A 0.014 0.056 1.086 0.482 0.367 0.121 0.384 0.119

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 47 92 21 47 185 21 21

N.S.

1 1.00 2.14 4.18 0.95 2.14 8.41 0.95 0.95

time (sec)

N/A 0.017 0.038 3.348 0.472 0.398 4.095 0.401 0.096

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 47 92 21 47 0 21 21

N.S.

1 1.00 2.14 4.18 0.95 2.14 0.00 0.95 0.95

time (sec)

N/A 0.029 0.064 3.694 0.496 0.414 0.000 0.390 1.486

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 47 92 21 47 0 21 21

N.S.

1 1.00 2.14 4.18 0.95 2.14 0.00 0.95 0.95

time (sec)

N/A 0.027 0.056 3.163 0.497 0.408 0.000 0.399 1.529

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 42 44 69 89 0 51 57

N.S.

1 1.00 1.91 2.00 3.14 4.05 0.00 2.32 2.59

time (sec)

N/A 0.029 0.078 2.497 0.484 0.381 0.000 0.394 0.502

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 47 80 21 47 0 21 21

N.S.

1 1.00 2.14 3.64 0.95 2.14 0.00 0.95 0.95

time (sec)

N/A 0.029 0.079 3.059 0.487 0.374 0.000 0.400 0.175

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 42 164 38 89 0 48 57

N.S.

1 1.00 1.91 7.45 1.73 4.05 0.00 2.18 2.59

time (sec)

N/A 0.029 0.081 2.657 0.475 0.392 0.000 0.388 1.882

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 37 14 13 22 19 29 13

N.S.

1 1.00 2.47 0.93 0.87 1.47 1.27 1.93 0.87

time (sec)

N/A 0.010 0.011 0.358 0.270 0.370 0.066 0.388 0.066

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 19 20 19 68 49 35 19

N.S.

1 1.00 1.00 1.05 1.00 3.58 2.58 1.84 1.00

time (sec)

N/A 0.016 0.007 2.828 0.280 0.385 0.342 0.402 1.548

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 39 0 373 175 638 327 135

N.S.

1 1.00 1.00 0.00 9.56 4.49 16.36 8.38 3.46

time (sec)

N/A 0.032 0.045 2.615 0.517 0.457 1.574 0.442 1.638

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 49 0 686 379 2574 722 255

N.S.

1 1.00 0.83 0.00 11.63 6.42 43.63 12.24 4.32

time (sec)

N/A 0.037 0.138 1.969 0.518 0.409 5.599 0.483 1.750

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 19 20 19 68 49 35 19

N.S.

1 1.00 1.00 1.05 1.00 3.58 2.58 1.84 1.00

time (sec)

N/A 0.020 0.007 1.731 0.263 0.432 0.338 0.404 1.579

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 44 923 293 189 648 325 132

N.S.

1 1.00 1.10 23.08 7.32 4.72 16.20 8.12 3.30

time (sec)

N/A 0.037 0.100 3.867 0.505 0.378 1.580 0.440 0.179

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 77 0 558 407 2351 721 254

N.S.

1 1.00 1.31 0.00 9.46 6.90 39.85 12.22 4.31

time (sec)

N/A 0.052 0.160 1.474 0.521 0.381 6.055 0.453 1.752

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 23 43 39 40 92 32 18

N.S.

1 1.00 0.50 0.93 0.85 0.87 2.00 0.70 0.39

time (sec)

N/A 0.031 0.024 0.599 0.260 0.390 0.181 0.390 0.113

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 40 61 88 90 136 88 43

N.S.

1 1.00 0.58 0.88 1.28 1.30 1.97 1.28 0.62

time (sec)

N/A 0.065 0.058 1.015 0.263 0.385 0.420 0.395 1.641

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 92 52 79 110 138 189 116 53

N.S.

1 1.00 0.57 0.86 1.20 1.50 2.05 1.26 0.58

time (sec)

N/A 0.080 0.092 1.166 0.268 0.370 0.959 0.393 1.728

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 40 47 88 90 136 88 42

N.S.

1 1.00 0.60 0.70 1.31 1.34 2.03 1.31 0.63

time (sec)

N/A 0.040 0.045 1.944 0.269 0.372 0.430 0.400 1.601

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 33 33 66 97 189 60 32

N.S.

1 1.00 0.37 0.37 0.73 1.08 2.10 0.67 0.36

time (sec)

N/A 0.063 0.033 1.739 0.276 0.354 0.921 0.398 0.203

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 62 75 132 197 231 144 65

N.S.

1 1.00 0.55 0.66 1.17 1.74 2.04 1.27 0.58

time (sec)

N/A 0.103 0.127 2.398 0.262 0.363 1.880 0.401 1.735

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 52 61 110 138 189 116 53

N.S.

1 1.00 0.59 0.69 1.25 1.57 2.15 1.32 0.60

time (sec)

N/A 0.052 0.071 1.809 0.268 0.378 0.940 0.390 1.677

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 62 75 132 195 231 144 65

N.S.

1 1.00 0.56 0.68 1.19 1.76 2.08 1.30 0.59

time (sec)

N/A 0.074 0.094 3.079 0.270 0.346 1.871 0.402 0.260

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 43 47 86 179 277 88 42

N.S.

1 1.00 0.32 0.35 0.64 1.34 2.07 0.66 0.31

time (sec)

N/A 0.095 0.060 2.533 0.263 0.388 3.581 0.417 1.820

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 31 12 50 60 0 41 30

N.S.

1 1.00 2.82 1.09 4.55 5.45 0.00 3.73 2.73

time (sec)

N/A 0.010 0.016 0.617 0.474 0.348 0.000 0.401 0.151

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 26 23 61 155 0 64 52

N.S.

1 1.00 1.13 1.00 2.65 6.74 0.00 2.78 2.26

time (sec)

N/A 0.018 0.027 0.703 0.267 0.379 0.000 0.381 0.089

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 36 23 88 371 0 93 78

N.S.

1 1.00 1.33 0.85 3.26 13.74 0.00 3.44 2.89

time (sec)

N/A 0.018 0.028 0.716 0.473 0.366 0.000 0.382 1.503

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 41 33 108 697 0 88 133

N.S.

1 1.00 1.08 0.87 2.84 18.34 0.00 2.32 3.50

time (sec)

N/A 0.024 0.023 0.872 0.273 0.381 0.000 0.400 1.509

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 46 33 131 1073 0 122 169

N.S.

1 1.00 1.15 0.82 3.28 26.82 0.00 3.05 4.22

time (sec)

N/A 0.023 0.066 0.731 0.467 0.385 0.000 0.402 1.463

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 29 25 43 103 0 54 48

N.S.

1 1.00 1.21 1.04 1.79 4.29 0.00 2.25 2.00

time (sec)

N/A 0.020 0.015 0.743 0.485 0.365 0.000 0.387 1.466

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 13 32 18 81 0 18 18

N.S.

1 1.00 0.57 1.39 0.78 3.52 0.00 0.78 0.78

time (sec)

N/A 0.023 0.015 1.128 0.262 0.386 0.000 0.379 0.084

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 29 95 90 511 0 102 107

N.S.

1 1.00 0.59 1.94 1.84 10.43 0.00 2.08 2.18

time (sec)

N/A 0.030 0.013 1.590 0.484 0.378 0.000 0.396 1.509

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 46 45 94 230 0 60 152

N.S.

1 1.00 1.21 1.18 2.47 6.05 0.00 1.58 4.00

time (sec)

N/A 0.028 0.029 1.415 0.270 0.348 0.000 0.401 1.520

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 29 117 136 1183 0 124 210

N.S.

1 1.00 0.41 1.67 1.94 16.90 0.00 1.77 3.00

time (sec)

N/A 0.042 0.012 1.642 0.479 0.347 0.000 0.392 0.073

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 34 25 91 379 0 93 78

N.S.

1 1.00 1.21 0.89 3.25 13.54 0.00 3.32 2.79

time (sec)

N/A 0.024 0.033 0.866 0.482 0.373 0.000 0.407 0.071

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 68 43 106 709 0 110 111

N.S.

1 1.00 1.39 0.88 2.16 14.47 0.00 2.24 2.27

time (sec)

N/A 0.038 0.026 1.115 0.272 0.357 0.000 0.392 1.459

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 47 43 102 774 0 96 96

N.S.

1 1.00 1.09 1.00 2.37 18.00 0.00 2.23 2.23

time (sec)

N/A 0.032 0.014 1.252 0.478 0.401 0.000 0.410 1.442

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 83 53 149 1573 0 128 192

N.S.

1 1.00 1.26 0.80 2.26 23.83 0.00 1.94 2.91

time (sec)

N/A 0.038 0.026 1.263 0.272 0.380 0.000 0.418 1.437

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 54 53 181 2103 0 171 187

N.S.

1 1.00 0.93 0.91 3.12 36.26 0.00 2.95 3.22

time (sec)

N/A 0.040 0.297 1.286 0.488 0.378 0.000 0.418 0.077

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 33 33 90 515 0 80 129

N.S.

1 1.00 0.89 0.89 2.43 13.92 0.00 2.16 3.49

time (sec)

N/A 0.029 0.013 0.719 0.487 0.383 0.000 0.392 0.076

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 45 45 90 229 0 60 153

N.S.

1 1.00 1.22 1.22 2.43 6.19 0.00 1.62 4.14

time (sec)

N/A 0.029 0.030 1.434 0.269 0.355 0.000 0.388 1.476

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 33 117 132 1176 0 124 187

N.S.

1 1.00 0.50 1.77 2.00 17.82 0.00 1.88 2.83

time (sec)

N/A 0.032 0.011 1.835 0.471 0.372 0.000 0.395 1.558

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 43 45 90 330 0 31 31

N.S.

1 1.00 0.81 0.85 1.70 6.23 0.00 0.58 0.58

time (sec)

N/A 0.029 0.011 1.752 0.266 0.353 0.000 0.404 0.062

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 33 139 178 2092 0 148 291

N.S.

1 1.00 0.37 1.56 2.00 23.51 0.00 1.66 3.27

time (sec)

N/A 0.035 0.012 1.592 0.479 0.367 0.000 0.408 1.465

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 46 33 133 1082 0 122 169

N.S.

1 1.00 1.18 0.85 3.41 27.74 0.00 3.13 4.33

time (sec)

N/A 0.024 0.085 0.727 0.491 0.355 0.000 0.408 0.063

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 105 61 155 1591 0 130 214

N.S.

1 1.00 1.50 0.87 2.21 22.73 0.00 1.86 3.06

time (sec)

N/A 0.043 0.027 0.964 0.260 0.377 0.000 0.409 1.447

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 56 61 179 2114 0 171 187

N.S.

1 1.00 0.97 1.05 3.09 36.45 0.00 2.95 3.22

time (sec)

N/A 0.038 0.131 1.377 0.472 0.397 0.000 0.404 1.472

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 121 71 195 2802 0 152 295

N.S.

1 1.00 1.36 0.80 2.19 31.48 0.00 1.71 3.31

time (sec)

N/A 0.048 0.029 1.120 0.268 0.387 0.000 0.415 0.097

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 77 70 150 2231 0 124 205

N.S.

1 1.00 1.12 1.01 2.17 32.33 0.00 1.80 2.97

time (sec)

N/A 0.041 0.020 1.116 0.480 0.388 0.000 0.400 1.422

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 59 0 0 997 0 0 -1

N.S.

1 1.00 0.56 0.00 0.00 9.41 0.00 0.00 -0.01

time (sec)

N/A 0.084 0.045 0.767 0.000 0.397 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 59 0 0 591 0 0 -1

N.S.

1 1.00 0.73 0.00 0.00 7.30 0.00 0.00 -0.01

time (sec)

N/A 0.062 0.035 0.668 0.000 0.365 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 59 0 0 310 0 0 -1

N.S.

1 1.00 0.75 0.00 0.00 3.92 0.00 0.00 -0.01

time (sec)

N/A 0.057 0.037 0.713 0.000 0.361 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 59 0 0 142 0 0 -1

N.S.

1 1.00 1.09 0.00 0.00 2.63 0.00 0.00 -0.02

time (sec)

N/A 0.029 0.024 0.807 0.000 0.391 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 57 0 0 144 0 0 -1

N.S.

1 1.00 1.06 0.00 0.00 2.67 0.00 0.00 -0.02

time (sec)

N/A 0.029 0.020 0.678 0.000 0.379 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 57 0 0 311 0 0 -1

N.S.

1 1.00 0.72 0.00 0.00 3.94 0.00 0.00 -0.01

time (sec)

N/A 0.058 0.023 0.641 0.000 0.367 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 59 0 0 598 0 0 -1

N.S.

1 1.00 0.73 0.00 0.00 7.38 0.00 0.00 -0.01

time (sec)

N/A 0.053 0.023 0.614 0.000 0.385 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 59 0 0 1001 0 0 -1

N.S.

1 1.00 0.56 0.00 0.00 9.44 0.00 0.00 -0.01

time (sec)

N/A 0.075 0.026 0.612 0.000 0.388 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 59 0 0 1042 0 0 -1

N.S.

1 1.00 0.38 0.00 0.00 6.72 0.00 0.00 -0.01

time (sec)

N/A 0.141 0.040 0.522 0.000 0.394 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 59 0 0 751 0 0 -1

N.S.

1 1.00 0.38 0.00 0.00 4.85 0.00 0.00 -0.01

time (sec)

N/A 0.135 0.042 0.528 0.000 0.378 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

243 243 59 0 0 1003 0 0 -1

N.S.

1 1.00 0.24 0.00 0.00 4.13 0.00 0.00 -0.00

time (sec)

N/A 0.186 0.036 0.516 0.000 0.396 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

218 218 59 0 0 727 0 0 -1

N.S.

1 1.00 0.27 0.00 0.00 3.33 0.00 0.00 -0.00

time (sec)

N/A 0.160 0.028 0.501 0.000 0.374 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 59 0 0 572 0 0 -1

N.S.

1 1.00 0.46 0.00 0.00 4.47 0.00 0.00 -0.01

time (sec)

N/A 0.076 0.024 0.502 0.000 0.395 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 59 0 0 578 0 0 -1

N.S.

1 1.00 0.46 0.00 0.00 4.52 0.00 0.00 -0.01

time (sec)

N/A 0.068 0.020 0.446 0.000 0.368 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

218 218 57 0 0 723 0 0 -1

N.S.

1 1.00 0.26 0.00 0.00 3.32 0.00 0.00 -0.00

time (sec)

N/A 0.152 0.019 0.485 0.000 0.401 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

243 243 57 0 0 1013 0 0 -1

N.S.

1 1.00 0.23 0.00 0.00 4.17 0.00 0.00 -0.00

time (sec)

N/A 0.169 0.022 0.517 0.000 0.418 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 59 0 0 749 0 0 -1

N.S.

1 1.00 0.38 0.00 0.00 4.83 0.00 0.00 -0.01

time (sec)

N/A 0.091 0.023 0.511 0.000 0.390 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 59 0 0 1056 0 0 -1

N.S.

1 1.00 0.38 0.00 0.00 6.81 0.00 0.00 -0.01

time (sec)

N/A 0.087 0.026 0.448 0.000 0.421 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 0 61 93 0 0 6

N.S.

1 1.00 1.00 0.00 3.81 5.81 0.00 0.00 0.38

time (sec)

N/A 0.020 0.008 0.241 0.479 0.342 0.000 0.000 1.540

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 0 61 93 0 0 -1

N.S.

1 1.00 1.00 0.00 3.81 5.81 0.00 0.00 -0.06

time (sec)

N/A 0.020 0.012 0.251 0.475 0.352 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

10 10 10 7 0 54 0 17 31

N.S.

1 1.00 1.00 0.70 0.00 5.40 0.00 1.70 3.10

time (sec)

N/A 0.024 0.007 0.419 0.000 0.372 0.000 0.395 1.459

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 23 21 41 86 0 32 49

N.S.

1 1.00 1.00 0.91 1.78 3.74 0.00 1.39 2.13

time (sec)

N/A 0.011 0.009 0.898 0.475 0.372 0.000 0.385 1.471

Problem 71

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

21 21 21 33 54 31 0 41 49

N.S.

1 1.00 1.00 1.57 2.57 1.48 0.00 1.95 2.33

time (sec)

N/A 0.020 0.025 0.866 0.262 0.377 0.000 0.383 1.485

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 48 93 91 463 0 97 107

N.S.

1 1.00 0.98 1.90 1.86 9.45 0.00 1.98 2.18

time (sec)

N/A 0.023 0.039 1.417 0.479 0.364 0.000 0.403 1.464

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 37 51 98 93 0 67 131

N.S.

1 1.00 1.00 1.38 2.65 2.51 0.00 1.81 3.54

time (sec)

N/A 0.022 0.028 1.044 0.267 0.368 0.000 0.398 1.497

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 25 25 56 197 0 60 48

N.S.

1 1.00 0.89 0.89 2.00 7.04 0.00 2.14 1.71

time (sec)

N/A 0.018 0.014 1.121 0.479 0.397 0.000 0.401 0.080

Problem 75

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

40 40 31 39 64 54 0 71 50

N.S.

1 1.00 0.78 0.98 1.60 1.35 0.00 1.78 1.25

time (sec)

N/A 0.034 0.079 1.135 0.266 0.336 0.000 0.408 1.475

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 35 41 103 742 0 99 97

N.S.

1 1.00 0.81 0.95 2.40 17.26 0.00 2.30 2.26

time (sec)

N/A 0.033 0.036 1.102 0.479 0.385 0.000 0.426 1.496

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 38 33 71 290 0 55 77

N.S.

1 1.00 1.00 0.87 1.87 7.63 0.00 1.45 2.03

time (sec)

N/A 0.019 0.012 1.196 0.478 0.352 0.000 0.404 0.090

Problem 78

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

38 38 40 52 79 63 0 63 78

N.S.

1 1.00 1.05 1.37 2.08 1.66 0.00 1.66 2.05

time (sec)

N/A 0.029 0.026 0.937 0.263 0.420 0.000 0.409 1.539

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 65 122 116 851 0 117 136

N.S.

1 1.00 0.98 1.85 1.76 12.89 0.00 1.77 2.06

time (sec)

N/A 0.031 0.075 1.487 0.474 0.377 0.000 0.431 1.523

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 34 33 81 457 0 84 77

N.S.

1 1.00 0.85 0.82 2.02 11.42 0.00 2.10 1.92

time (sec)

N/A 0.023 0.022 1.168 0.484 0.362 0.000 0.407 0.115

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 11 12 23 54 17 23 24

N.S.

1 1.00 1.00 1.09 2.09 4.91 1.55 2.09 2.18

time (sec)

N/A 0.009 0.007 0.415 0.266 0.346 0.086 0.389 1.439

Problem 82

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

15 15 15 14 13 84 22 27 13

N.S.

1 1.00 1.00 0.93 0.87 5.60 1.47 1.80 0.87

time (sec)

N/A 0.015 0.010 0.415 0.270 0.348 0.131 0.397 0.072

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 17 36 115 39 0 31

N.S.

1 1.00 1.00 1.06 2.25 7.19 2.44 0.00 1.94

time (sec)

N/A 0.022 0.025 1.058 0.504 0.371 0.158 0.000 1.477

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 32 13 138 0 31 31

N.S.

1 1.00 1.00 2.13 0.87 9.20 0.00 2.07 2.07

time (sec)

N/A 0.020 0.005 1.577 0.262 0.364 0.000 0.402 0.071

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 34 13 208 44 37 230

N.S.

1 1.00 1.00 2.27 0.87 13.87 2.93 2.47 15.33

time (sec)

N/A 0.021 0.004 1.088 0.263 0.360 0.331 0.410 0.108

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 19 20 19 69 0 38 42

N.S.

1 1.00 1.00 1.05 1.00 3.63 0.00 2.00 2.21

time (sec)

N/A 0.027 0.015 1.186 0.282 0.362 0.000 0.421 1.531

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 27 34 148 172 41 45 48

N.S.

1 1.00 1.00 1.26 5.48 6.37 1.52 1.67 1.78

time (sec)

N/A 0.017 0.027 0.984 0.275 0.352 0.227 0.408 1.412

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 31 34 214 345 46 45 251

N.S.

1 1.00 1.00 1.10 6.90 11.13 1.48 1.45 8.10

time (sec)

N/A 0.026 0.042 1.045 0.280 0.347 0.523 0.414 1.542

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 32 275 345 219 0 0 101

N.S.

1 1.00 0.89 7.64 9.58 6.08 0.00 0.00 2.81

time (sec)

N/A 0.040 0.095 3.082 0.536 0.397 0.000 0.000 1.569

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 56 54 276 304 0 53 270

N.S.

1 1.00 1.81 1.74 8.90 9.81 0.00 1.71 8.71

time (sec)

N/A 0.023 0.031 1.415 0.270 0.348 0.000 0.398 0.126

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

35 35 29 0 352 551 0 148 168

N.S.

1 1.00 0.83 0.00 10.06 15.74 0.00 4.23 4.80

time (sec)

N/A 0.029 0.080 3.500 0.508 0.366 0.000 0.415 1.634

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 73 535 504 180 0 0 115

N.S.

1 1.00 1.82 13.38 12.60 4.50 0.00 0.00 2.88

time (sec)

N/A 0.031 0.630 3.579 0.502 0.374 0.000 0.000 1.608

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 34 69 66 269 0 76 82

N.S.

1 1.00 1.00 2.03 1.94 7.91 0.00 2.24 2.41

time (sec)

N/A 0.023 0.013 1.193 0.469 0.375 0.000 0.400 0.086

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 59 93 112 814 0 102 186

N.S.

1 1.00 1.07 1.69 2.04 14.80 0.00 1.85 3.38

time (sec)

N/A 0.033 0.125 1.345 0.474 0.380 0.000 0.417 1.438

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 55 91 110 808 0 98 215

N.S.

1 1.00 1.00 1.65 2.00 14.69 0.00 1.78 3.91

time (sec)

N/A 0.035 0.015 1.280 0.495 0.388 0.000 0.409 1.459

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 21 28 191 185 29 35 129

N.S.

1 1.00 1.00 1.33 9.10 8.81 1.38 1.67 6.14

time (sec)

N/A 0.014 0.010 0.363 0.258 0.338 0.344 0.402 1.433

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 28 371 634 34 35 520

N.S.

1 1.00 1.00 1.12 14.84 25.36 1.36 1.40 20.80

time (sec)

N/A 0.024 0.012 0.460 0.269 0.385 2.598 0.379 1.547

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 48 64 85 925 0 73 200

N.S.

1 1.00 1.26 1.68 2.24 24.34 0.00 1.92 5.26

time (sec)

N/A 0.042 0.008 0.540 0.484 0.363 0.000 0.396 0.056

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 36 64 85 925 0 73 206

N.S.

1 1.00 1.00 1.78 2.36 25.69 0.00 2.03 5.72

time (sec)

N/A 0.031 0.008 0.508 0.472 0.369 0.000 0.390 1.445

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 67 67 857 778 0 66 820

N.S.

1 1.00 2.03 2.03 25.97 23.58 0.00 2.00 24.85

time (sec)

N/A 0.024 0.018 0.540 0.281 0.353 0.000 0.389 1.455

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