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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

11 11 11 12 11 19 0 12 23

N.S.

1 1.00 1.00 1.09 1.00 1.73 0.00 1.09 2.09

time (sec)

N/A 0.003 0.003 0.237 0.260 0.350 0.000 0.389 0.076

Problem 2

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

10 10 10 19 18 41 0 18 18

N.S.

1 1.00 1.00 1.90 1.80 4.10 0.00 1.80 1.80

time (sec)

N/A 0.007 0.003 0.916 0.260 0.381 0.000 0.389 0.079

Problem 3

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 68 65 267 0 76 81

N.S.

1 1.00 1.00 2.00 1.91 7.85 0.00 2.24 2.38

time (sec)

N/A 0.011 0.009 1.095 0.490 0.349 0.000 0.396 0.083

Problem 4

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

26 26 26 32 90 164 0 31 31

N.S.

1 1.00 1.00 1.23 3.46 6.31 0.00 1.19 1.19

time (sec)

N/A 0.009 0.006 1.085 0.270 0.347 0.000 0.394 0.062

Problem 5

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 47 93 112 812 0 102 189

N.S.

1 1.00 0.85 1.69 2.04 14.76 0.00 1.85 3.44

time (sec)

N/A 0.020 0.029 1.047 0.465 0.378 0.000 0.396 1.305

Problem 6

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

41 41 41 43 205 344 0 42 42

N.S.

1 1.00 1.00 1.05 5.00 8.39 0.00 1.02 1.02

time (sec)

N/A 0.011 0.008 1.133 0.263 0.344 0.000 0.386 1.354

Problem 7

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

19 19 19 19 49 116 0 18 30

N.S.

1 1.00 1.00 1.00 2.58 6.11 0.00 0.95 1.58

time (sec)

N/A 0.007 0.004 0.930 0.252 0.343 0.000 0.382 0.096

Problem 8

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

35 35 35 31 137 280 0 30 30

N.S.

1 1.00 1.00 0.89 3.91 8.00 0.00 0.86 0.86

time (sec)

N/A 0.010 0.004 1.186 0.283 0.400 0.000 0.390 1.518

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 51 217 0 190 0 0 -1

N.S.

1 1.00 0.77 3.29 0.00 2.88 0.00 0.00 -0.02

time (sec)

N/A 0.024 0.058 1.458 0.000 0.148 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 49 103 0 96 0 0 -1

N.S.

1 1.00 0.79 1.66 0.00 1.55 0.00 0.00 -0.02

time (sec)

N/A 0.023 0.035 1.675 0.000 0.088 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 40 135 0 24 0 0 -1

N.S.

1 1.00 1.00 3.38 0.00 0.60 0.00 0.00 -0.02

time (sec)

N/A 0.015 0.024 1.246 0.000 0.129 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 40 135 0 150 0 0 -1

N.S.

1 1.00 1.00 3.38 0.00 3.75 0.00 0.00 -0.02

time (sec)

N/A 0.015 0.027 1.123 0.000 0.083 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 53 174 0 223 0 0 -1

N.S.

1 1.00 0.80 2.64 0.00 3.38 0.00 0.00 -0.02

time (sec)

N/A 0.024 0.034 1.463 0.000 0.130 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 59 188 0 370 0 0 -1

N.S.

1 1.00 0.89 2.85 0.00 5.61 0.00 0.00 -0.02

time (sec)

N/A 0.025 0.053 1.658 0.000 0.089 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 68 0 0 478 0 0 -1

N.S.

1 1.00 0.67 0.00 0.00 4.69 0.00 0.00 -0.01

time (sec)

N/A 0.046 0.147 1.528 0.000 0.095 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 56 0 0 215 0 0 -1

N.S.

1 1.00 0.76 0.00 0.00 2.91 0.00 0.00 -0.01

time (sec)

N/A 0.027 0.052 1.330 0.000 0.139 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 52 0 0 107 0 0 -1

N.S.

1 1.00 0.74 0.00 0.00 1.53 0.00 0.00 -0.01

time (sec)

N/A 0.029 0.031 1.306 0.000 0.090 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 42 0 0 27 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.64 0.00 0.00 -0.02

time (sec)

N/A 0.016 0.018 1.539 0.000 0.124 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 42 244 0 154 0 0 -1

N.S.

1 1.00 1.00 5.81 0.00 3.67 0.00 0.00 -0.02

time (sec)

N/A 0.016 0.025 2.360 0.000 0.084 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 63 0 0 231 0 0 -1

N.S.

1 1.00 0.83 0.00 0.00 3.04 0.00 0.00 -0.01

time (sec)

N/A 0.028 0.048 1.389 0.000 0.132 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 64 0 0 379 0 0 -1

N.S.

1 1.00 0.84 0.00 0.00 4.99 0.00 0.00 -0.01

time (sec)

N/A 0.026 0.061 1.550 0.000 0.106 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 70 0 0 483 0 0 -1

N.S.

1 1.00 0.67 0.00 0.00 4.64 0.00 0.00 -0.01

time (sec)

N/A 0.041 0.091 1.470 0.000 0.141 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 60 0 0 0 0 0 -1

N.S.

1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.033 0.046 1.254 0.000 0.000 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 81 230 156 1604 0 124 -1

N.S.

1 1.00 0.90 2.56 1.73 17.82 0.00 1.38 -0.01

time (sec)

N/A 0.025 0.076 2.601 0.489 0.363 0.000 0.381 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 55 208 112 812 0 102 -1

N.S.

1 1.00 0.85 3.20 1.72 12.49 0.00 1.57 -0.02

time (sec)

N/A 0.017 0.084 2.348 0.459 0.352 0.000 0.391 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 46 183 65 267 0 76 -1

N.S.

1 1.00 1.15 4.58 1.62 6.68 0.00 1.90 -0.02

time (sec)

N/A 0.013 0.036 2.417 0.477 0.372 0.000 0.403 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B C A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 29 130 11 19 0 12 -1

N.S.

1 1.00 2.64 11.82 1.00 1.73 0.00 1.09 -0.09

time (sec)

N/A 0.009 0.013 2.489 0.264 0.374 0.000 0.391 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 22 97 26 10 29 23 53

N.S.

1 1.00 1.00 4.41 1.18 0.45 1.32 1.05 2.41

time (sec)

N/A 0.011 0.019 2.414 0.309 0.390 12.131 0.392 0.155

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 44 201 54 32 54 48 -1

N.S.

1 1.00 0.86 3.94 1.06 0.63 1.06 0.94 -0.02

time (sec)

N/A 0.014 0.047 2.544 0.324 0.363 12.289 0.374 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 54 305 82 66 80 70 -1

N.S.

1 1.00 0.71 4.01 1.08 0.87 1.05 0.92 -0.01

time (sec)

N/A 0.020 0.071 2.495 0.274 0.378 14.511 0.394 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 64 409 100 108 104 92 -1

N.S.

1 1.00 0.63 4.05 0.99 1.07 1.03 0.91 -0.01

time (sec)

N/A 0.025 0.110 2.466 0.265 0.364 35.117 0.387 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 42 127 72 1082 0 65 -1

N.S.

1 1.00 0.65 1.95 1.11 16.65 0.00 1.00 -0.02

time (sec)

N/A 0.023 0.025 0.989 0.518 0.396 0.000 0.399 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 29 106 39 310 0 48 -1

N.S.

1 1.00 0.63 2.30 0.85 6.74 0.00 1.04 -0.02

time (sec)

N/A 0.016 0.015 0.853 0.513 0.384 0.000 0.387 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 21 72 8 145 0 8 -1

N.S.

1 1.00 0.84 2.88 0.32 5.80 0.00 0.32 -0.04

time (sec)

N/A 0.012 0.005 1.024 0.571 0.389 0.000 0.393 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

13 13 13 58 17 79 12 14 33

N.S.

1 1.00 1.00 4.46 1.31 6.08 0.92 1.08 2.54

time (sec)

N/A 0.021 0.005 1.038 0.473 0.398 0.244 0.393 0.120

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 27 130 35 277 31 29 -1

N.S.

1 1.00 0.75 3.61 0.97 7.69 0.86 0.81 -0.03

time (sec)

N/A 0.015 0.016 0.865 0.466 0.366 0.378 0.387 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 36 196 53 580 49 41 -1

N.S.

1 1.00 0.65 3.56 0.96 10.55 0.89 0.75 -0.02

time (sec)

N/A 0.021 0.028 0.849 0.465 0.389 1.607 0.392 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 42 262 71 970 66 53 -1

N.S.

1 1.00 0.57 3.54 0.96 13.11 0.89 0.72 -0.01

time (sec)

N/A 0.027 0.036 1.164 0.478 0.402 12.864 0.374 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 63 0 0 1382 0 0 -1

N.S.

1 1.00 0.52 0.00 0.00 11.42 0.00 0.00 -0.01

time (sec)

N/A 0.041 0.068 1.054 0.000 0.115 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 47 0 0 391 0 0 -1

N.S.

1 1.00 0.68 0.00 0.00 5.67 0.00 0.00 -0.01

time (sec)

N/A 0.028 0.028 0.831 0.000 0.152 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 36 0 0 60 0 0 -1

N.S.

1 1.00 0.78 0.00 0.00 1.30 0.00 0.00 -0.02

time (sec)

N/A 0.021 0.015 1.005 0.000 0.097 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 38 0 0 126 0 0 -1

N.S.

1 1.00 0.79 0.00 0.00 2.62 0.00 0.00 -0.02

time (sec)

N/A 0.021 0.031 1.001 0.000 0.131 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 47 0 0 407 0 0 -1

N.S.

1 1.00 0.61 0.00 0.00 5.29 0.00 0.00 -0.01

time (sec)

N/A 0.031 0.064 0.838 0.000 0.163 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 63 0 0 718 0 0 -1

N.S.

1 1.00 0.52 0.00 0.00 5.93 0.00 0.00 -0.01

time (sec)

N/A 0.044 0.064 0.840 0.000 0.188 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 54 72 620 2804 0 51 498

N.S.

1 1.00 0.33 0.44 3.80 17.20 0.00 0.31 3.06

time (sec)

N/A 0.030 0.122 0.993 0.539 0.439 0.000 0.392 1.453

Problem 46

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

117 117 42 60 322 1475 0 39 356

N.S.

1 1.00 0.36 0.51 2.75 12.61 0.00 0.33 3.04

time (sec)

N/A 0.025 0.069 0.864 0.488 0.387 0.000 0.420 1.374

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

61 61 30 46 120 516 0 27 46

N.S.

1 1.00 0.49 0.75 1.97 8.46 0.00 0.44 0.75

time (sec)

N/A 0.017 0.040 0.862 0.492 0.368 0.000 0.398 1.344

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 29 13 81 0 13 71

N.S.

1 1.00 1.00 1.93 0.87 5.40 0.00 0.87 4.73

time (sec)

N/A 0.012 0.005 0.994 0.492 0.417 0.000 0.394 0.058

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 23 89 30 253 0 28 -1

N.S.

1 1.00 0.64 2.47 0.83 7.03 0.00 0.78 -0.03

time (sec)

N/A 0.012 0.017 1.043 0.490 0.393 0.000 0.400 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 38 230 65 1141 0 52 -1

N.S.

1 1.00 0.44 2.67 0.76 13.27 0.00 0.60 -0.01

time (sec)

N/A 0.024 0.027 0.931 0.514 0.403 0.000 0.388 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 55 362 103 2600 0 76 -1

N.S.

1 1.00 0.42 2.74 0.78 19.70 0.00 0.58 -0.01

time (sec)

N/A 0.038 0.054 0.931 0.475 0.384 0.000 0.387 0.000

Problem 52

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

44 44 28 105 54 36 0 42 59

N.S.

1 1.00 0.64 2.39 1.23 0.82 0.00 0.95 1.34

time (sec)

N/A 0.097 0.080 0.595 0.293 0.347 0.000 0.404 1.483

Problem 53

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

23 23 23 67 46 30 0 37 53

N.S.

1 1.00 1.00 2.91 2.00 1.30 0.00 1.61 2.30

time (sec)

N/A 0.088 0.035 0.523 0.297 0.384 0.000 0.391 1.359

Problem 54

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

27 27 16 65 42 14 0 28 41

N.S.

1 1.00 0.59 2.41 1.56 0.52 0.00 1.04 1.52

time (sec)

N/A 0.076 0.048 0.585 0.265 0.368 0.000 0.389 1.341

Problem 55

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

17 17 16 23 35 50 0 32 15

N.S.

1 1.00 0.94 1.35 2.06 2.94 0.00 1.88 0.88

time (sec)

N/A 0.053 0.013 0.589 0.267 0.360 0.000 0.388 0.068

Problem 56

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

33 33 44 20 48 103 0 52 51

N.S.

1 1.00 1.33 0.61 1.45 3.12 0.00 1.58 1.55

time (sec)

N/A 0.072 0.037 0.709 0.262 0.372 0.000 0.383 1.439

Problem 57

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

23 23 25 23 90 71 0 31 91

N.S.

1 1.00 1.09 1.00 3.91 3.09 0.00 1.35 3.96

time (sec)

N/A 0.087 0.028 0.770 0.302 0.350 0.000 0.389 1.352

Problem 58

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

46 46 59 38 99 630 0 90 121

N.S.

1 1.00 1.28 0.83 2.15 13.70 0.00 1.96 2.63

time (sec)

N/A 0.116 0.148 0.796 0.268 0.361 0.000 0.387 1.351

Problem 59

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

34 34 39 39 292 219 0 59 236

N.S.

1 1.00 1.15 1.15 8.59 6.44 0.00 1.74 6.94

time (sec)

N/A 0.101 0.044 0.810 0.265 0.352 0.000 0.392 1.376

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 219 310 0 1812 0 197 275

N.S.

1 1.00 1.66 2.35 0.00 13.73 0.00 1.49 2.08

time (sec)

N/A 0.256 0.500 0.711 0.000 0.394 0.000 0.394 2.006

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 66 209 128 490 0 87 123

N.S.

1 1.00 1.08 3.43 2.10 8.03 0.00 1.43 2.02

time (sec)

N/A 0.123 0.091 0.659 0.271 0.366 0.000 0.393 1.602

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 76 160 0 536 0 100 173

N.S.

1 1.00 0.93 1.95 0.00 6.54 0.00 1.22 2.11

time (sec)

N/A 0.131 0.128 0.683 0.000 0.368 0.000 0.388 1.670

Problem 63

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

20 20 19 31 46 78 0 34 20

N.S.

1 1.00 0.95 1.55 2.30 3.90 0.00 1.70 1.00

time (sec)

N/A 0.057 0.008 0.625 0.261 0.368 0.000 0.383 1.350

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

53 53 37 48 59 58 0 65 148

N.S.

1 1.00 0.70 0.91 1.11 1.09 0.00 1.23 2.79

time (sec)

N/A 0.079 0.051 0.789 0.267 0.372 0.000 0.384 1.744

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 75 77 0 452 0 64 151

N.S.

1 1.00 1.14 1.17 0.00 6.85 0.00 0.97 2.29

time (sec)

N/A 0.099 0.175 0.826 0.000 0.386 0.000 0.385 1.561

Problem 66

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

85 85 86 82 148 828 0 174 255

N.S.

1 1.00 1.01 0.96 1.74 9.74 0.00 2.05 3.00

time (sec)

N/A 0.163 0.233 0.875 0.291 0.446 0.000 0.390 1.831

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 156 127 0 2340 0 149 295

N.S.

1 1.00 1.41 1.14 0.00 21.08 0.00 1.34 2.66

time (sec)

N/A 0.202 0.397 0.861 0.000 0.404 0.000 0.400 1.747

Problem 68

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

67 67 63 110 80 139 0 86 88

N.S.

1 1.00 0.94 1.64 1.19 2.07 0.00 1.28 1.31

time (sec)

N/A 0.060 0.062 0.832 0.263 0.459 0.000 0.394 1.447

Problem 69

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

54 54 53 86 66 100 0 70 70

N.S.

1 1.00 0.98 1.59 1.22 1.85 0.00 1.30 1.30

time (sec)

N/A 0.056 0.051 0.795 0.261 0.424 0.000 0.382 1.358

Problem 70

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

41 41 45 70 56 70 0 51 52

N.S.

1 1.00 1.10 1.71 1.37 1.71 0.00 1.24 1.27

time (sec)

N/A 0.052 0.036 0.774 0.282 0.378 0.000 0.394 1.360

Problem 71

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

26 26 32 46 41 47 0 35 34

N.S.

1 1.00 1.23 1.77 1.58 1.81 0.00 1.35 1.31

time (sec)

N/A 0.036 0.043 0.769 0.268 0.400 0.000 0.374 1.312

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

11 11 10 9 12 14 0 11 11

N.S.

1 1.00 0.91 0.82 1.09 1.27 0.00 1.00 1.00

time (sec)

N/A 0.018 0.010 0.424 0.283 0.375 0.000 0.388 1.311

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

20 20 22 19 23 29 0 20 31

N.S.

1 1.00 1.10 0.95 1.15 1.45 0.00 1.00 1.55

time (sec)

N/A 0.042 0.021 0.503 0.483 0.390 0.000 0.391 1.305

Problem 74

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

26 26 45 33 45 127 0 36 58

N.S.

1 1.00 1.73 1.27 1.73 4.88 0.00 1.38 2.23

time (sec)

N/A 0.070 0.064 0.521 0.475 0.459 0.000 0.383 1.318

Problem 75

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

45 45 51 46 73 325 0 48 73

N.S.

1 1.00 1.13 1.02 1.62 7.22 0.00 1.07 1.62

time (sec)

N/A 0.054 0.059 0.671 0.479 0.382 0.000 0.385 1.345

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

29 29 58 46 33 48 0 29 24

N.S.

1 1.00 2.00 1.59 1.14 1.66 0.00 1.00 0.83

time (sec)

N/A 0.011 0.103 2.155 0.290 0.359 0.000 0.379 1.299

Problem 77

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 59 48 35 50 0 29 24

N.S.

1 1.00 1.97 1.60 1.17 1.67 0.00 0.97 0.80

time (sec)

N/A 0.011 0.101 1.721 0.261 0.420 0.000 0.385 1.263

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 99 0 0 924 0 151 -1

N.S.

1 1.00 1.01 0.00 0.00 9.43 0.00 1.54 -0.01

time (sec)

N/A 0.086 0.233 2.743 0.000 0.533 0.000 0.463 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 75 0 0 697 0 118 -1

N.S.

1 1.00 1.14 0.00 0.00 10.56 0.00 1.79 -0.02

time (sec)

N/A 0.028 0.137 2.525 0.000 0.489 0.000 0.453 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 60 0 0 637 0 83 -1

N.S.

1 1.00 1.62 0.00 0.00 17.22 0.00 2.24 -0.03

time (sec)

N/A 0.014 0.065 2.958 0.000 0.487 0.000 0.429 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 118 0 0 868 0 0 -1

N.S.

1 1.00 1.39 0.00 0.00 10.21 0.00 0.00 -0.01

time (sec)

N/A 0.054 0.828 2.627 0.000 0.406 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 231 0 0 1190 0 316 -1

N.S.

1 1.00 2.03 0.00 0.00 10.44 0.00 2.77 -0.01

time (sec)

N/A 0.093 1.146 2.536 0.000 0.439 0.000 0.477 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 70 0 0 642 0 101 -1

N.S.

1 1.00 1.84 0.00 0.00 16.89 0.00 2.66 -0.03

time (sec)

N/A 0.018 1.638 2.825 0.000 0.451 0.000 0.414 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 118 0 0 871 0 0 -1

N.S.

1 1.00 1.36 0.00 0.00 10.01 0.00 0.00 -0.01

time (sec)

N/A 0.054 1.266 2.279 0.000 0.431 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 39 0 0 233 0 52 -1

N.S.

1 1.00 2.05 0.00 0.00 12.26 0.00 2.74 -0.05

time (sec)

N/A 0.013 0.027 1.214 0.000 0.396 0.000 0.385 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 51 0 0 235 0 69 -1

N.S.

1 1.00 2.43 0.00 0.00 11.19 0.00 3.29 -0.05

time (sec)

N/A 0.015 0.382 1.197 0.000 0.445 0.000 0.380 0.000

Problem 87

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

107 107 78 182 211 1028 0 141 233

N.S.

1 1.00 0.73 1.70 1.97 9.61 0.00 1.32 2.18

time (sec)

N/A 0.085 0.178 1.494 0.483 0.401 0.000 0.396 1.409

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 55 142 114 521 0 92 165

N.S.

1 1.00 0.75 1.95 1.56 7.14 0.00 1.26 2.26

time (sec)

N/A 0.036 0.096 1.503 0.490 0.417 0.000 0.388 1.398

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 32 64 41 157 0 43 70

N.S.

1 1.00 0.97 1.94 1.24 4.76 0.00 1.30 2.12

time (sec)

N/A 0.020 0.045 1.502 0.266 0.424 0.000 0.388 0.106

Problem 90

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

16 16 16 17 16 26 0 17 38

N.S.

1 1.00 1.00 1.06 1.00 1.62 0.00 1.06 2.38

time (sec)

N/A 0.006 0.003 0.832 0.270 0.401 0.000 0.394 1.299

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 60 83 0 270 0 56 131

N.S.

1 1.00 1.02 1.41 0.00 4.58 0.00 0.95 2.22

time (sec)

N/A 0.042 0.077 1.655 0.000 0.394 0.000 0.390 0.399

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 203 164 0 1207 0 134 296

N.S.

1 1.00 1.86 1.50 0.00 11.07 0.00 1.23 2.72

time (sec)

N/A 0.116 0.279 1.503 0.000 0.409 0.000 0.395 1.849

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

173 173 205 251 0 4125 0 261 -1

N.S.

1 1.00 1.18 1.45 0.00 23.84 0.00 1.51 -0.01

time (sec)

N/A 0.239 0.484 1.776 0.000 0.444 0.000 0.413 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 168 0 0 0 0 0 -1

N.S.

1 1.00 1.58 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.020 3.430 2.608 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

146 146 126 299 0 2402 0 182 251

N.S.

1 1.00 0.86 2.05 0.00 16.45 0.00 1.25 1.72

time (sec)

N/A 0.446 0.187 0.837 0.000 0.406 0.000 0.398 1.851

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 99 203 0 1562 0 133 209

N.S.

1 1.00 0.88 1.81 0.00 13.95 0.00 1.19 1.87

time (sec)

N/A 0.287 0.113 0.833 0.000 0.405 0.000 0.394 1.713

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 78 153 0 860 0 92 167

N.S.

1 1.00 0.92 1.80 0.00 10.12 0.00 1.08 1.96

time (sec)

N/A 0.182 0.085 0.812 0.000 0.385 0.000 0.386 1.579

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 57 94 0 430 0 62 139

N.S.

1 1.00 0.92 1.52 0.00 6.94 0.00 1.00 2.24

time (sec)

N/A 0.065 0.077 0.816 0.000 0.390 0.000 0.406 1.481

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 41 36 0 165 0 32 43

N.S.

1 1.00 0.98 0.86 0.00 3.93 0.00 0.76 1.02

time (sec)

N/A 0.038 0.018 0.422 0.000 0.382 0.000 0.391 0.116

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 54 51 0 219 0 45 286

N.S.

1 1.00 1.00 0.94 0.00 4.06 0.00 0.83 5.30

time (sec)

N/A 0.072 0.037 0.569 0.000 0.403 0.000 0.391 4.006

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