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2.2.1 Integrals 1 to 70

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

87 87 81 78 60 74 0 79 56

N.S.

1 1.00 0.93 0.90 0.69 0.85 0.00 0.91 0.64

time (sec)

N/A 0.036 0.208 0.394 0.300 2.786 0.000 0.475 2.438

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

98 98 75 108 126 114 0 121 102

N.S.

1 1.00 0.77 1.10 1.29 1.16 0.00 1.23 1.04

time (sec)

N/A 0.046 0.251 0.454 0.290 3.768 0.000 0.473 2.485

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

65 65 61 58 43 56 0 57 42

N.S.

1 1.00 0.94 0.89 0.66 0.86 0.00 0.88 0.65

time (sec)

N/A 0.033 0.141 0.410 0.284 2.306 0.000 0.438 2.319

Problem 4

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

70 70 54 85 97 95 0 98 77

N.S.

1 1.00 0.77 1.21 1.39 1.36 0.00 1.40 1.10

time (sec)

N/A 0.034 0.093 0.461 0.284 2.410 0.000 0.461 2.447

Problem 5

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

43 43 36 35 34 37 0 34 28

N.S.

1 1.00 0.84 0.81 0.79 0.86 0.00 0.79 0.65

time (sec)

N/A 0.029 0.071 0.316 0.278 1.499 0.000 0.435 2.367

Problem 6

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

40 40 48 55 58 72 0 60 41

N.S.

1 1.00 1.20 1.38 1.45 1.80 0.00 1.50 1.02

time (sec)

N/A 0.018 0.013 0.276 0.281 2.527 0.000 0.435 2.415

Problem 7

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

15 15 15 16 15 31 0 15 17

N.S.

1 1.00 1.00 1.07 1.00 2.07 0.00 1.00 1.13

time (sec)

N/A 0.009 0.003 0.356 0.282 1.498 0.000 0.411 2.345

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

24 24 35 30 38 40 0 40 22

N.S.

1 1.00 1.46 1.25 1.58 1.67 0.00 1.67 0.92

time (sec)

N/A 0.018 0.013 0.299 0.289 2.438 0.000 0.436 0.056

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 33 37 37 28 51 37 25

N.S.

1 1.00 1.06 1.19 1.19 0.90 1.65 1.19 0.81

time (sec)

N/A 0.020 0.026 0.280 0.504 2.234 3.637 0.424 2.358

Problem 10

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

30 30 50 33 27 28 0 34 28

N.S.

1 1.00 1.67 1.10 0.90 0.93 0.00 1.13 0.93

time (sec)

N/A 0.032 0.015 0.388 0.281 2.557 0.000 0.423 0.041

Problem 11

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

61 61 45 65 73 49 0 73 67

N.S.

1 1.00 0.74 1.07 1.20 0.80 0.00 1.20 1.10

time (sec)

N/A 0.028 0.063 0.455 0.526 1.788 0.000 0.424 2.443

Problem 12

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

50 50 74 54 43 45 0 57 43

N.S.

1 1.00 1.48 1.08 0.86 0.90 0.00 1.14 0.86

time (sec)

N/A 0.046 0.020 0.562 0.282 2.236 0.000 0.466 2.368

Problem 13

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

89 89 68 86 103 68 0 96 91

N.S.

1 1.00 0.76 0.97 1.16 0.76 0.00 1.08 1.02

time (sec)

N/A 0.039 0.075 0.578 0.499 2.136 0.000 0.471 2.942

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 26 512 304 33 0 0 42

N.S.

1 1.00 1.00 19.69 11.69 1.27 0.00 0.00 1.62

time (sec)

N/A 0.027 0.224 0.849 0.649 2.257 0.000 0.000 2.856

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 510 296 33 0 0 41

N.S.

1 1.00 1.00 20.40 11.84 1.32 0.00 0.00 1.64

time (sec)

N/A 0.027 0.200 0.619 0.666 2.593 0.000 0.000 2.675

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 84 251 0 142 0 0 -1

N.S.

1 1.00 0.76 2.28 0.00 1.29 0.00 0.00 -0.01

time (sec)

N/A 0.056 0.701 32.662 0.000 0.515 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 184 668 0 143 0 0 -1

N.S.

1 1.00 1.67 6.07 0.00 1.30 0.00 0.00 -0.01

time (sec)

N/A 0.058 0.841 32.345 0.000 0.584 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 58 201 0 111 0 0 -1

N.S.

1 1.00 0.81 2.79 0.00 1.54 0.00 0.00 -0.01

time (sec)

N/A 0.040 0.260 33.550 0.000 0.535 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 126 588 0 99 0 0 -1

N.S.

1 1.00 1.85 8.65 0.00 1.46 0.00 0.00 -0.01

time (sec)

N/A 0.041 0.488 34.898 0.000 0.325 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 66 198 0 100 0 0 -1

N.S.

1 1.00 0.88 2.64 0.00 1.33 0.00 0.00 -0.01

time (sec)

N/A 0.046 0.197 20.783 0.000 0.651 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 133 614 0 108 0 0 -1

N.S.

1 1.00 1.73 7.97 0.00 1.40 0.00 0.00 -0.01

time (sec)

N/A 0.045 0.765 22.272 0.000 0.748 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 79 241 0 119 0 0 -1

N.S.

1 1.00 0.71 2.15 0.00 1.06 0.00 0.00 -0.01

time (sec)

N/A 0.061 0.470 20.996 0.000 0.998 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 143 636 0 129 0 0 -1

N.S.

1 1.00 1.28 5.68 0.00 1.15 0.00 0.00 -0.01

time (sec)

N/A 0.064 0.953 23.046 0.000 1.196 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 21 41 0 19 0 46 21

N.S.

1 1.00 1.00 1.95 0.00 0.90 0.00 2.19 1.00

time (sec)

N/A 0.016 0.093 1.209 0.000 3.381 0.000 0.480 0.210

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 21 506 305 32 0 0 37

N.S.

1 1.00 1.00 24.10 14.52 1.52 0.00 0.00 1.76

time (sec)

N/A 0.021 0.184 0.849 0.624 2.181 0.000 0.000 2.755

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 19 70 46 21 0 22 42

N.S.

1 1.00 1.00 3.68 2.42 1.11 0.00 1.16 2.21

time (sec)

N/A 0.017 0.046 0.464 0.336 3.408 0.000 0.476 2.456

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 19 56 33 21 0 30 19

N.S.

1 1.00 1.00 2.95 1.74 1.11 0.00 1.58 1.00

time (sec)

N/A 0.017 0.028 0.401 0.317 3.032 0.000 0.465 2.387

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 19 47 36 21 0 23 23

N.S.

1 1.00 1.00 2.47 1.89 1.11 0.00 1.21 1.21

time (sec)

N/A 0.017 0.024 0.404 0.293 4.047 0.000 0.479 2.375

Problem 29

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

19 19 19 34 22 21 0 20 21

N.S.

1 1.00 1.00 1.79 1.16 1.11 0.00 1.05 1.11

time (sec)

N/A 0.017 0.043 0.337 0.297 2.665 0.000 0.436 2.399

Problem 30

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

17 17 17 18 24 21 0 24 22

N.S.

1 1.00 1.00 1.06 1.41 1.24 0.00 1.41 1.29

time (sec)

N/A 0.011 0.013 0.299 0.293 3.736 0.000 0.454 0.058

Problem 31

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

11 11 11 12 12 21 0 11 11

N.S.

1 1.00 1.00 1.09 1.09 1.91 0.00 1.00 1.00

time (sec)

N/A 0.007 0.004 0.229 0.288 2.956 0.000 0.419 2.417

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 23 12 12 12 14 11 11

N.S.

1 1.00 2.09 1.09 1.09 1.09 1.27 1.00 1.00

time (sec)

N/A 0.003 0.007 0.125 0.301 3.937 0.041 0.413 0.020

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 33 18 25 19 49 14 14

N.S.

1 1.00 1.94 1.06 1.47 1.12 2.88 0.82 0.82

time (sec)

N/A 0.015 0.010 0.341 0.291 3.589 5.219 0.409 2.378

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

19 19 46 32 23 21 0 21 22

N.S.

1 1.00 2.42 1.68 1.21 1.11 0.00 1.11 1.16

time (sec)

N/A 0.016 0.018 0.431 0.286 3.159 0.000 0.460 0.036

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 31 45 36 21 0 23 19

N.S.

1 1.00 1.63 2.37 1.89 1.11 0.00 1.21 1.00

time (sec)

N/A 0.016 0.025 0.447 0.285 2.709 0.000 0.423 2.348

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 59 52 33 21 0 30 23

N.S.

1 1.00 3.11 2.74 1.74 1.11 0.00 1.58 1.21

time (sec)

N/A 0.016 0.025 0.572 0.281 2.728 0.000 0.451 2.423

Problem 37

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

85 85 76 73 95 99 0 164 153

N.S.

1 1.00 0.89 0.86 1.12 1.16 0.00 1.93 1.80

time (sec)

N/A 0.050 0.166 0.388 0.281 2.733 0.000 0.455 4.941

Problem 38

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

63 63 60 60 70 88 0 122 109

N.S.

1 1.00 0.95 0.95 1.11 1.40 0.00 1.94 1.73

time (sec)

N/A 0.041 0.111 0.413 0.281 2.685 0.000 0.484 4.186

Problem 39

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

47 47 47 47 58 74 0 107 85

N.S.

1 1.00 1.00 1.00 1.23 1.57 0.00 2.28 1.81

time (sec)

N/A 0.031 0.019 0.369 0.290 4.001 0.000 0.457 3.044

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 24 32 31 60 0 57 47

N.S.

1 1.00 1.00 1.33 1.29 2.50 0.00 2.38 1.96

time (sec)

N/A 0.012 0.011 0.326 0.279 3.993 0.000 0.489 2.411

Problem 41

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

16 16 16 29 37 36 0 43 57

N.S.

1 1.00 1.00 1.81 2.31 2.25 0.00 2.69 3.56

time (sec)

N/A 0.018 0.005 0.238 0.285 2.932 0.000 0.447 2.428

Problem 42

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

15 15 26 21 20 17 0 39 17

N.S.

1 1.00 1.73 1.40 1.33 1.13 0.00 2.60 1.13

time (sec)

N/A 0.022 0.007 0.279 0.300 2.919 0.000 0.461 2.411

Problem 43

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

38 38 35 38 34 29 0 82 31

N.S.

1 1.00 0.92 1.00 0.89 0.76 0.00 2.16 0.82

time (sec)

N/A 0.028 0.048 0.342 0.286 1.902 0.000 0.460 2.453

Problem 44

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

54 54 57 49 46 42 0 98 55

N.S.

1 1.00 1.06 0.91 0.85 0.78 0.00 1.81 1.02

time (sec)

N/A 0.034 0.048 0.459 0.285 1.903 0.000 0.472 2.511

Problem 45

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

76 76 73 60 57 53 0 140 75

N.S.

1 1.00 0.96 0.79 0.75 0.70 0.00 1.84 0.99

time (sec)

N/A 0.043 0.087 0.571 0.295 2.427 0.000 0.454 2.504

Problem 46

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

92 92 92 70 69 64 0 154 113

N.S.

1 1.00 1.00 0.76 0.75 0.70 0.00 1.67 1.23

time (sec)

N/A 0.046 0.059 0.599 0.273 2.474 0.000 0.450 6.313

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

169 169 102 526 0 207 0 0 -1

N.S.

1 1.00 0.60 3.11 0.00 1.22 0.00 0.00 -0.01

time (sec)

N/A 0.100 0.321 33.612 0.000 0.663 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 90 508 0 183 0 0 -1

N.S.

1 1.00 0.67 3.76 0.00 1.36 0.00 0.00 -0.01

time (sec)

N/A 0.085 0.193 34.704 0.000 0.744 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 73 456 0 143 0 0 -1

N.S.

1 1.00 0.67 4.18 0.00 1.31 0.00 0.00 -0.01

time (sec)

N/A 0.073 0.131 34.091 0.000 0.628 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 57 450 0 122 0 0 -1

N.S.

1 1.00 0.67 5.29 0.00 1.44 0.00 0.00 -0.01

time (sec)

N/A 0.061 0.062 22.105 0.000 0.387 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 81 470 0 150 0 0 -1

N.S.

1 1.00 0.70 4.05 0.00 1.29 0.00 0.00 -0.01

time (sec)

N/A 0.078 0.124 23.177 0.000 0.382 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 91 482 0 164 0 0 -1

N.S.

1 1.00 0.62 3.28 0.00 1.12 0.00 0.00 -0.01

time (sec)

N/A 0.091 0.376 23.312 0.000 1.211 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 104 493 0 175 0 0 -1

N.S.

1 1.00 0.59 2.80 0.00 0.99 0.00 0.00 -0.01

time (sec)

N/A 0.097 0.441 23.065 0.000 0.451 0.000 0.000 0.000

Problem 54

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

122 122 80 104 127 122 0 246 197

N.S.

1 1.00 0.66 0.85 1.04 1.00 0.00 2.02 1.61

time (sec)

N/A 0.072 0.418 0.543 0.297 3.035 0.000 0.450 5.166

Problem 55

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

97 97 71 106 139 117 0 230 160

N.S.

1 1.00 0.73 1.09 1.43 1.21 0.00 2.37 1.65

time (sec)

N/A 0.064 0.173 0.555 0.284 3.400 0.000 0.469 5.032

Problem 56

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

78 78 51 68 79 94 0 162 123

N.S.

1 1.00 0.65 0.87 1.01 1.21 0.00 2.08 1.58

time (sec)

N/A 0.060 0.150 0.519 0.281 2.157 0.000 0.443 4.607

Problem 57

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

51 51 59 63 75 82 0 115 89

N.S.

1 1.00 1.16 1.24 1.47 1.61 0.00 2.25 1.75

time (sec)

N/A 0.038 0.017 0.379 0.278 2.195 0.000 0.438 3.141

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 27 35 34 71 0 60 161

N.S.

1 1.00 1.00 1.30 1.26 2.63 0.00 2.22 5.96

time (sec)

N/A 0.013 0.007 0.382 0.277 3.894 0.000 0.405 2.538

Problem 59

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

27 27 38 37 46 45 0 70 68

N.S.

1 1.00 1.41 1.37 1.70 1.67 0.00 2.59 2.52

time (sec)

N/A 0.035 0.016 0.325 0.270 3.291 0.000 0.420 2.515

Problem 60

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

42 42 55 45 42 33 0 86 34

N.S.

1 1.00 1.31 1.07 1.00 0.79 0.00 2.05 0.81

time (sec)

N/A 0.043 0.042 0.369 0.282 2.461 0.000 0.409 2.503

Problem 61

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

56 56 53 57 55 45 0 138 66

N.S.

1 1.00 0.95 1.02 0.98 0.80 0.00 2.46 1.18

time (sec)

N/A 0.060 0.075 0.474 0.273 2.515 0.000 0.447 2.535

Problem 62

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

88 88 70 84 77 65 0 200 81

N.S.

1 1.00 0.80 0.95 0.88 0.74 0.00 2.27 0.92

time (sec)

N/A 0.062 0.119 0.688 0.276 2.891 0.000 0.432 2.527

Problem 63

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

98 98 87 89 89 73 0 222 104

N.S.

1 1.00 0.89 0.91 0.91 0.74 0.00 2.27 1.06

time (sec)

N/A 0.083 0.107 0.688 0.282 2.479 0.000 0.459 2.580

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 107 115 115 93 0 284 126

N.S.

1 1.00 0.81 0.87 0.87 0.70 0.00 2.15 0.95

time (sec)

N/A 0.071 0.119 0.659 0.290 2.990 0.000 0.427 2.667

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

178 178 308 832 0 225 0 0 -1

N.S.

1 1.00 1.73 4.67 0.00 1.26 0.00 0.00 -0.01

time (sec)

N/A 0.110 4.541 37.257 0.000 0.948 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 252 647 0 193 0 0 -1

N.S.

1 1.00 1.85 4.76 0.00 1.42 0.00 0.00 -0.01

time (sec)

N/A 0.093 1.488 35.315 0.000 1.012 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 156 720 0 153 0 0 -1

N.S.

1 1.00 1.42 6.55 0.00 1.39 0.00 0.00 -0.01

time (sec)

N/A 0.075 0.944 34.996 0.000 0.716 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 154 602 0 160 0 0 -1

N.S.

1 1.00 1.32 5.15 0.00 1.37 0.00 0.00 -0.01

time (sec)

N/A 0.085 1.081 25.298 0.000 0.405 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

150 150 169 766 0 176 0 0 -1

N.S.

1 1.00 1.13 5.11 0.00 1.17 0.00 0.00 -0.01

time (sec)

N/A 0.102 1.296 23.665 0.000 0.512 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

185 185 183 645 0 193 0 0 -1

N.S.

1 1.00 0.99 3.49 0.00 1.04 0.00 0.00 -0.01

time (sec)

N/A 0.118 1.905 22.723 0.000 0.783 0.000 0.000 0.000

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