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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 C F F F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

670 670 442 1408 0 0 0 0 -1

N.S.

1 1.00 0.66 2.10 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.491 0.682 1.730 0.000 0.000 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

450 450 320 981 0 0 0 0 -1

N.S.

1 1.00 0.71 2.18 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.381 0.793 1.088 0.000 0.000 0.000 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

238 238 219 628 0 0 0 0 -1

N.S.

1 1.00 0.92 2.64 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.179 0.954 1.102 0.000 0.000 0.000 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

725 725 1095 1209 0 0 0 0 -1

N.S.

1 1.00 1.51 1.67 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.322 2.222 0.914 0.000 0.000 0.000 0.000 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

851 851 1116 1573 0 0 0 0 -1

N.S.

1 1.00 1.31 1.85 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.917 6.940 1.302 0.000 0.000 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

959 959 910 2168 0 0 0 0 -1

N.S.

1 1.00 0.95 2.26 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.642 2.679 1.342 0.000 0.000 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

680 680 591 1550 0 0 0 0 -1

N.S.

1 1.00 0.87 2.28 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.490 1.368 1.016 0.000 0.000 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

370 370 337 1012 0 0 0 0 -1

N.S.

1 1.00 0.91 2.74 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.226 1.012 1.058 0.000 0.000 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

1064 1064 3034 2132 0 0 0 0 -1

N.S.

1 1.00 2.85 2.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.549 9.947 0.899 0.000 0.000 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

1281 1281 1144 3051 0 0 0 0 -1

N.S.

1 1.00 0.89 2.38 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.785 4.890 1.434 0.000 0.000 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F(-1) F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

940 940 794 2230 0 0 0 0 -1

N.S.

1 1.00 0.84 2.37 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.609 2.897 1.109 0.000 0.000 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

517 517 526 1419 0 0 0 0 -1

N.S.

1 1.00 1.02 2.74 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.269 1.969 1.086 0.000 0.000 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

1637 1637 6216 4692 0 0 0 0 -1

N.S.

1 1.00 3.80 2.87 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.880 14.515 0.994 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

450 450 342 861 0 0 0 0 -1

N.S.

1 1.00 0.76 1.91 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.399 0.669 1.398 0.000 0.000 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

270 270 266 507 0 0 0 0 -1

N.S.

1 1.00 0.99 1.88 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.285 0.439 0.946 0.000 0.000 0.000 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 172 247 108 0 0 0 -1

N.S.

1 1.00 1.35 1.94 0.85 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.143 0.237 0.683 0.488 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

370 370 930 487 0 0 0 0 -1

N.S.

1 1.00 2.51 1.32 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.392 1.163 0.579 0.000 0.000 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

496 496 1108 1622 0 0 0 0 -1

N.S.

1 1.00 2.23 3.27 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.482 3.280 1.342 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A F(-1) A A

verified

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

size

38 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.125 0.110 2.351 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

496 496 2330 0 0 0 0 0 -1

N.S.

1 1.00 4.70 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.549 24.056 3.494 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

374 374 1248 0 0 0 0 0 -1

N.S.

1 1.00 3.34 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.425 3.658 3.331 0.000 0.000 0.000 0.000 0.000

Problem 22

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

237 237 246 0 0 0 0 0 -1

N.S.

1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.238 0.018 0.020 0.000 0.000 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

38 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.135 0.145 2.768 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 A B A B B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 104 235 333 94 255 242 -1

N.S.

1 1.00 0.76 1.72 2.43 0.69 1.86 1.77 -0.01

time (sec)

N/A 0.139 0.078 0.047 0.486 2.445 0.300 0.409 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 83 161 220 75 170 156 -1

N.S.

1 1.00 0.88 1.71 2.34 0.80 1.81 1.66 -0.01

time (sec)

N/A 0.084 0.058 0.006 0.470 2.670 0.174 0.413 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 69 78 153 59 104 88 -1

N.S.

1 1.00 0.86 0.98 1.91 0.74 1.30 1.10 -0.01

time (sec)

N/A 0.054 0.033 0.007 0.468 2.826 0.111 0.417 0.000

Problem 27

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

36 36 154 33 32 41 46 32 88

N.S.

1 1.00 4.28 0.92 0.89 1.14 1.28 0.89 2.44

time (sec)

N/A 0.013 0.065 0.007 0.468 3.380 0.073 0.411 0.543

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 228 199 0 0 0 0 -1

N.S.

1 1.00 1.29 1.12 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.200 0.143 0.829 0.000 0.000 0.000 0.000 0.000

Problem 29

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

63 63 79 81 0 360 0 79 -1

N.S.

1 1.00 1.25 1.29 0.00 5.71 0.00 1.25 -0.02

time (sec)

N/A 0.055 0.040 0.007 0.000 5.122 0.000 0.410 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 126 124 0 482 0 242 -1

N.S.

1 1.00 1.22 1.20 0.00 4.68 0.00 2.35 -0.01

time (sec)

N/A 0.081 0.125 0.006 0.000 2.306 0.000 0.451 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 168 240 0 580 0 557 -1

N.S.

1 1.00 1.17 1.67 0.00 4.03 0.00 3.87 -0.01

time (sec)

N/A 0.121 0.131 0.005 0.000 1.696 0.000 0.441 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 74 71 0 66 109 78 60

N.S.

1 1.00 0.90 0.87 0.00 0.80 1.33 0.95 0.73

time (sec)

N/A 0.057 0.028 0.098 0.000 1.734 0.151 0.421 0.281

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 49 48 0 53 63 52 44

N.S.

1 1.00 1.04 1.02 0.00 1.13 1.34 1.11 0.94

time (sec)

N/A 0.037 0.018 0.083 0.000 1.047 0.100 0.418 0.253

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 12 13 0 0 0 12 -1

N.S.

1 1.00 1.00 1.08 0.00 0.00 0.00 1.00 -0.08

time (sec)

N/A 0.014 0.024 0.080 0.000 0.000 0.000 0.430 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 40 37 0 0 0 38 -1

N.S.

1 1.00 1.00 0.92 0.00 0.00 0.00 0.95 -0.02

time (sec)

N/A 0.052 0.041 0.082 0.000 0.000 0.000 0.417 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 65 53 0 0 0 57 -1

N.S.

1 1.00 1.00 0.82 0.00 0.00 0.00 0.88 -0.02

time (sec)

N/A 0.054 0.038 0.083 0.000 0.000 0.000 0.441 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 90 140 0 0 0 183 -1

N.S.

1 1.00 0.81 1.26 0.00 0.00 0.00 1.65 -0.01

time (sec)

N/A 0.098 0.037 0.389 0.000 0.000 0.000 0.530 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 76 105 0 0 0 139 -1

N.S.

1 1.00 0.85 1.18 0.00 0.00 0.00 1.56 -0.01

time (sec)

N/A 0.063 0.029 0.174 0.000 0.000 0.000 0.523 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 90 66 0 0 0 95 -1

N.S.

1 1.00 1.64 1.20 0.00 0.00 0.00 1.73 -0.02

time (sec)

N/A 0.053 0.029 0.169 0.000 0.000 0.000 0.442 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 78 28 0 0 0 51 -1

N.S.

1 1.00 2.36 0.85 0.00 0.00 0.00 1.55 -0.03

time (sec)

N/A 0.024 0.035 0.098 0.000 0.000 0.000 0.458 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 97 84 0 0 0 0 -1

N.S.

1 1.00 1.52 1.31 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.061 0.038 0.174 0.000 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 139 120 0 0 0 0 -1

N.S.

1 1.00 1.54 1.33 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.064 0.209 0.182 0.000 0.000 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 128 93 0 0 0 167 -1

N.S.

1 1.00 1.21 0.88 0.00 0.00 0.00 1.58 -0.01

time (sec)

N/A 0.114 0.037 0.513 0.000 0.000 0.000 0.519 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 133 95 0 0 0 171 -1

N.S.

1 1.00 1.23 0.88 0.00 0.00 0.00 1.58 -0.01

time (sec)

N/A 0.084 0.075 0.305 0.000 0.000 0.000 0.514 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 59 92 0 0 0 0 -1

N.S.

1 1.00 0.87 1.35 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.061 0.030 0.316 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 30 33 30 26 39 27 -1

N.S.

1 1.00 0.88 0.97 0.88 0.76 1.15 0.79 -0.03

time (sec)

N/A 0.021 0.012 0.437 0.480 1.206 1.067 0.421 0.000

Problem 47

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

51 51 48 69 79 41 48 46 42

N.S.

1 1.00 0.94 1.35 1.55 0.80 0.94 0.90 0.82

time (sec)

N/A 0.028 0.021 0.079 0.474 1.236 0.189 0.417 0.302

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 63 79 0 33 48 0 -1

N.S.

1 1.00 1.15 1.44 0.00 0.60 0.87 0.00 -0.02

time (sec)

N/A 0.020 0.110 0.007 0.000 0.293 0.750 0.000 0.000

Problem 49

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

35 35 35 32 31 31 32 31 29

N.S.

1 1.00 1.00 0.91 0.89 0.89 0.91 0.89 0.83

time (sec)

N/A 0.018 0.011 0.017 0.478 1.535 0.080 0.446 0.328

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 34 65 0 33 44 0 -1

N.S.

1 1.00 0.79 1.51 0.00 0.77 1.02 0.00 -0.02

time (sec)

N/A 0.023 10.009 0.006 0.000 0.490 0.621 0.000 0.000

Problem 51

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

62 62 56 0 0 0 0 0 -1

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.045 0.024 0.054 0.000 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B F A A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 40 57 0 11 44 0 -1

N.S.

1 1.00 1.38 1.97 0.00 0.38 1.52 0.00 -0.03

time (sec)

N/A 0.011 0.029 0.006 0.000 0.686 0.660 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 61 56 72 93 95 77 -1

N.S.

1 1.00 1.05 0.97 1.24 1.60 1.64 1.33 -0.02

time (sec)

N/A 0.027 0.035 0.112 0.472 1.543 1.886 0.441 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 33 39 28 32 48 64 28

N.S.

1 1.00 0.97 1.15 0.82 0.94 1.41 1.88 0.82

time (sec)

N/A 0.013 0.016 0.007 0.468 1.374 0.936 0.438 0.239

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 84 30 45 65 27 55 28

N.S.

1 1.00 3.11 1.11 1.67 2.41 1.00 2.04 1.04

time (sec)

N/A 0.012 0.070 0.007 0.476 1.559 1.065 0.412 0.567

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 60 77 0 0 0 0 -1

N.S.

1 1.00 1.00 1.28 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.038 0.016 0.525 0.000 0.000 0.000 0.000 0.000

Problem 57

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

30 30 30 32 31 36 26 31 28

N.S.

1 1.00 1.00 1.07 1.03 1.20 0.87 1.03 0.93

time (sec)

N/A 0.017 0.014 0.004 0.465 2.228 0.424 0.421 0.028

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 50 47 77 47 100 44 42

N.S.

1 1.00 0.98 0.92 1.51 0.92 1.96 0.86 0.82

time (sec)

N/A 0.025 0.019 0.009 0.468 1.410 1.981 0.439 0.285

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 47 55 49 49 100 52 -1

N.S.

1 1.00 0.84 0.98 0.88 0.88 1.79 0.93 -0.02

time (sec)

N/A 0.029 0.023 0.009 0.463 3.129 1.909 0.435 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 46 53 52 36 82 52 -1

N.S.

1 1.00 0.59 0.68 0.67 0.46 1.05 0.67 -0.01

time (sec)

N/A 0.020 0.027 0.007 0.475 1.468 4.861 0.406 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 41 41 40 31 66 40 -1

N.S.

1 1.00 0.68 0.68 0.67 0.52 1.10 0.67 -0.02

time (sec)

N/A 0.015 0.021 0.007 0.468 1.639 2.141 0.437 0.000

Problem 62

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

37 37 43 26 25 24 29 25 35

N.S.

1 1.00 1.16 0.70 0.68 0.65 0.78 0.68 0.95

time (sec)

N/A 0.008 0.013 0.007 0.471 3.441 0.098 0.412 0.640

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 54 59 0 0 0 0 -1

N.S.

1 1.00 0.96 1.05 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.039 0.026 0.375 0.000 0.000 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 24 22 21 22 44 40 -1

N.S.

1 1.00 0.89 0.81 0.78 0.81 1.63 1.48 -0.04

time (sec)

N/A 0.010 0.015 0.004 0.471 0.959 1.862 0.413 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 43 35 34 28 53 74 -1

N.S.

1 1.00 0.86 0.70 0.68 0.56 1.06 1.48 -0.02

time (sec)

N/A 0.013 0.023 0.013 0.470 1.494 4.662 0.446 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 37 47 46 33 68 106 -1

N.S.

1 1.00 0.54 0.69 0.68 0.49 1.00 1.56 -0.01

time (sec)

N/A 0.016 0.029 0.005 0.478 1.115 11.751 0.433 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 42 59 58 38 80 138 -1

N.S.

1 1.00 0.49 0.69 0.67 0.44 0.93 1.60 -0.01

time (sec)

N/A 0.019 0.031 0.009 0.465 1.970 32.013 0.428 0.000

Problem 68

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

25 25 25 20 19 19 20 19 19

N.S.

1 1.00 1.00 0.80 0.76 0.76 0.80 0.76 0.76

time (sec)

N/A 0.013 0.007 0.003 0.462 1.241 0.101 0.423 0.396

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 141 84 0 0 0 0 -1

N.S.

1 1.00 2.07 1.24 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.041 0.101 0.555 0.000 0.000 0.000 0.000 0.000

Problem 70

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

62 62 56 0 0 0 0 0 -1

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.044 0.026 0.044 0.000 0.000 0.000 0.000 0.000

Problem 71

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

47 47 43 40 39 48 61 39 99

N.S.

1 1.00 0.91 0.85 0.83 1.02 1.30 0.83 2.11

time (sec)

N/A 0.040 0.021 0.022 0.478 1.508 0.203 0.425 0.646

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 43 0 41 59 76 41 111

N.S.

1 1.00 0.90 0.00 0.85 1.23 1.58 0.85 2.31

time (sec)

N/A 0.040 0.031 0.029 0.482 2.571 25.479 0.406 0.354

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 249 0 0 207 0 0 -1

N.S.

1 1.00 1.96 0.00 0.00 1.63 0.00 0.00 -0.01

time (sec)

N/A 0.021 0.153 0.070 0.000 1.011 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 162 0 0 144 0 0 -1

N.S.

1 1.00 1.47 0.00 0.00 1.31 0.00 0.00 -0.01

time (sec)

N/A 0.043 0.083 0.056 0.000 0.937 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 98 0 0 91 0 0 -1

N.S.

1 1.00 1.56 0.00 0.00 1.44 0.00 0.00 -0.02

time (sec)

N/A 0.009 0.043 0.054 0.000 0.985 0.000 0.000 0.000

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

43 43 41 45 45 48 0 55 39

N.S.

1 1.00 0.95 1.05 1.05 1.12 0.00 1.28 0.91

time (sec)

N/A 0.027 0.019 0.011 0.471 1.150 0.000 0.435 0.465

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 85 0 0 0 0 0 -1

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.023 0.082 0.056 0.000 0.000 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

151 151 133 0 0 0 0 0 -1

N.S.

1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.017 0.259 0.054 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

173 173 147 0 0 0 0 0 -1

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.028 0.192 0.055 0.000 0.000 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 249 0 0 207 0 0 -1

N.S.

1 1.00 1.96 0.00 0.00 1.63 0.00 0.00 -0.01

time (sec)

N/A 0.022 0.155 0.054 0.000 0.968 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 162 0 0 144 0 0 -1

N.S.

1 1.00 1.47 0.00 0.00 1.31 0.00 0.00 -0.01

time (sec)

N/A 0.041 0.087 0.053 0.000 0.732 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 98 0 0 91 0 0 -1

N.S.

1 1.00 1.56 0.00 0.00 1.44 0.00 0.00 -0.02

time (sec)

N/A 0.009 0.041 0.054 0.000 0.859 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 41 45 45 48 0 50 39

N.S.

1 1.00 0.95 1.05 1.05 1.12 0.00 1.16 0.91

time (sec)

N/A 0.026 0.020 0.012 0.467 0.669 0.000 0.418 0.435

Problem 84

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

98 98 85 0 0 0 0 0 -1

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.010 0.078 0.056 0.000 0.000 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

149 149 131 0 0 0 0 0 -1

N.S.

1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.014 0.255 0.053 0.000 0.000 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

171 171 149 0 0 0 0 0 -1

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.024 0.172 0.058 0.000 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

249 249 256 0 0 0 0 0 -1

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.072 1.779 0.056 0.000 0.000 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

207 207 200 0 0 0 0 0 -1

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.049 0.472 0.058 0.000 0.000 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 157 0 0 0 0 0 -1

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.016 0.067 0.055 0.000 0.000 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 114 0 0 0 0 0 -1

N.S.

1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.013 0.121 0.058 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 177 0 0 0 0 0 -1

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.022 0.278 0.056 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

221 221 234 0 0 0 0 0 -1

N.S.

1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.038 0.518 0.056 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

269 269 308 0 0 0 0 0 -1

N.S.

1 1.00 1.14 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.045 0.379 0.055 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

249 249 256 0 0 0 0 0 -1

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.044 1.472 0.057 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 F F F(-2) F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

207 207 200 0 0 0 0 0 -1

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.034 0.422 0.062 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 157 0 0 0 0 0 -1

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.016 0.081 0.055 0.000 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 115 0 0 0 0 0 -1

N.S.

1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.013 0.120 0.056 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 161 0 0 0 0 0 -1

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.018 0.236 0.065 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

221 221 233 0 0 0 0 0 -1

N.S.

1 1.00 1.05 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.031 0.416 0.054 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

269 269 309 0 0 0 0 0 -1

N.S.

1 1.00 1.15 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.039 0.384 0.053 0.000 0.000 0.000 0.000 0.000

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