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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 A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 64 58 57 54 63 0 52

N.S.

1 1.00 1.08 0.98 0.97 0.92 1.07 0.00 0.88

time (sec)

N/A 0.023 0.004 0.205 0.464 3.602 0.334 0.000 0.442

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 61 59 56 59 60 0 54

N.S.

1 1.00 1.09 1.05 1.00 1.05 1.07 0.00 0.96

time (sec)

N/A 0.030 0.012 0.052 0.265 2.026 0.265 0.000 0.417

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 53 49 48 47 53 0 44

N.S.

1 1.00 1.10 1.02 1.00 0.98 1.10 0.00 0.92

time (sec)

N/A 0.022 0.004 0.105 0.469 6.432 0.208 0.000 0.210

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 50 50 46 49 49 0 42

N.S.

1 1.00 1.11 1.11 1.02 1.09 1.09 0.00 0.93

time (sec)

N/A 0.023 0.008 0.053 0.265 4.570 0.194 0.000 0.370

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 42 40 37 34 42 0 34

N.S.

1 1.00 1.14 1.08 1.00 0.92 1.14 0.00 0.92

time (sec)

N/A 0.011 0.004 0.112 0.463 3.426 0.138 0.000 0.123

Problem 6

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

29 29 29 28 31 33 26 31 27

N.S.

1 1.00 1.00 0.97 1.07 1.14 0.90 1.07 0.93

time (sec)

N/A 0.009 0.004 0.083 0.256 3.293 0.091 0.415 0.098

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

35 35 35 74 0 0 0 0 28

N.S.

1 1.00 1.00 2.11 0.00 0.00 0.00 0.00 0.80

time (sec)

N/A 0.022 0.004 0.095 0.000 0.000 0.000 0.000 0.287

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

35 35 38 45 39 37 37 0 36

N.S.

1 1.00 1.09 1.29 1.11 1.06 1.06 0.00 1.03

time (sec)

N/A 0.018 0.004 0.078 0.270 0.920 0.267 0.000 0.319

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 46 44 31 26 37 0 42

N.S.

1 1.00 1.24 1.19 0.84 0.70 1.00 0.00 1.14

time (sec)

N/A 0.015 0.005 0.122 0.470 0.712 0.218 0.000 0.332

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 54 57 51 50 61 0 46

N.S.

1 1.00 1.02 1.08 0.96 0.94 1.15 0.00 0.87

time (sec)

N/A 0.025 0.013 0.082 0.266 1.259 0.377 0.000 0.119

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 46 53 46 41 46 0 42

N.S.

1 1.00 0.96 1.10 0.96 0.85 0.96 0.00 0.88

time (sec)

N/A 0.018 0.004 0.131 0.472 0.629 0.296 0.000 0.363

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 64 66 62 59 71 0 56

N.S.

1 1.00 1.00 1.03 0.97 0.92 1.11 0.00 0.88

time (sec)

N/A 0.027 0.015 0.092 0.260 1.296 0.536 0.000 0.371

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 138 171 163 152 199 0 171

N.S.

1 1.00 0.96 1.19 1.13 1.06 1.38 0.00 1.19

time (sec)

N/A 0.217 0.087 0.326 0.483 0.832 0.461 0.000 0.667

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

170 170 169 312 0 0 0 0 -1

N.S.

1 1.00 0.99 1.84 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.206 0.358 0.471 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 A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 111 135 136 121 155 0 134

N.S.

1 1.00 0.99 1.21 1.21 1.08 1.38 0.00 1.20

time (sec)

N/A 0.153 0.046 0.158 0.474 0.958 0.322 0.000 0.316

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 131 276 0 0 0 0 -1

N.S.

1 1.00 0.95 2.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.139 0.196 0.345 0.000 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 75 97 104 83 107 0 88

N.S.

1 1.00 0.99 1.28 1.37 1.09 1.41 0.00 1.16

time (sec)

N/A 0.076 0.035 0.193 0.474 0.768 0.194 0.000 0.410

Problem 18

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

83 83 90 123 0 0 0 0 -1

N.S.

1 1.00 1.08 1.48 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.072 0.050 0.759 0.000 0.000 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 144 1128 0 0 0 0 -1

N.S.

1 1.00 1.09 8.55 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.181 0.052 8.300 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 102 318 0 0 0 0 -1

N.S.

1 1.00 1.24 3.88 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.107 0.097 0.799 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 90 115 98 94 119 0 140

N.S.

1 1.00 1.14 1.46 1.24 1.19 1.51 0.00 1.77

time (sec)

N/A 0.091 0.036 0.239 0.474 0.782 0.341 0.000 2.310

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 153 365 0 0 0 0 -1

N.S.

1 1.00 1.09 2.61 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.166 0.268 0.840 0.000 0.000 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 128 152 152 135 170 0 171

N.S.

1 1.00 1.10 1.31 1.31 1.16 1.47 0.00 1.47

time (sec)

N/A 0.159 0.052 0.250 0.475 1.154 0.507 0.000 2.257

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

255 255 291 494 0 0 0 0 -1

N.S.

1 1.00 1.14 1.94 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.655 0.554 0.474 0.000 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

271 271 396 2951 0 0 0 0 -1

N.S.

1 1.00 1.46 10.89 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.513 0.636 18.189 0.000 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

194 194 225 411 0 0 0 0 -1

N.S.

1 1.00 1.16 2.12 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.383 0.414 0.535 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

206 206 269 1921 0 0 0 0 -1

N.S.

1 1.00 1.31 9.33 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.313 0.420 5.489 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

131 131 152 323 0 0 0 0 -1

N.S.

1 1.00 1.16 2.47 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.172 0.195 0.374 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 B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 192 254 0 0 0 0 -1

N.S.

1 1.00 1.61 2.13 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.152 0.058 1.516 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

206 206 212 2309 0 0 0 0 -1

N.S.

1 1.00 1.03 11.21 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.289 0.099 4.770 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 214 2126 0 0 0 0 -1

N.S.

1 1.00 1.84 18.33 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.187 0.256 3.302 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 176 422 0 0 0 0 -1

N.S.

1 1.00 1.32 3.17 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.199 0.218 1.055 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

213 213 321 5807 0 0 0 0 -1

N.S.

1 1.00 1.51 27.26 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.331 0.618 19.816 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

198 198 265 512 0 0 0 0 -1

N.S.

1 1.00 1.34 2.59 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.412 0.489 1.583 0.000 0.000 0.000 0.000 0.000

Problem 35

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

11 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 -0.09

time (sec)

N/A 0.006 0.483 1.810 0.000 0.000 0.000 0.000 0.000

Problem 36

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

9 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 -0.11

time (sec)

N/A 0.002 0.011 1.324 0.000 0.000 0.000 0.000 0.000

Problem 37

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

13 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 -0.08

time (sec)

N/A 0.010 0.314 1.341 0.000 0.000 0.000 0.000 0.000

Problem 38

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

11 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 -0.09

time (sec)

N/A 0.006 0.442 2.015 0.000 0.000 0.000 0.000 0.000

Problem 39

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

9 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 -0.11

time (sec)

N/A 0.002 0.650 0.460 0.000 0.000 0.000 0.000 0.000

Problem 40

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

13 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 -0.08

time (sec)

N/A 0.010 0.765 1.384 0.000 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

13 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 -0.08

time (sec)

N/A 0.005 1.508 1.301 0.000 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

11 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 -0.09

time (sec)

N/A 0.002 1.331 0.694 0.000 0.000 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 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 -0.07

time (sec)

N/A 0.009 0.927 0.840 0.000 0.000 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

13 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 -0.08

time (sec)

N/A 0.005 0.708 1.239 0.000 0.000 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

11 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 -0.09

time (sec)

N/A 0.003 1.606 0.685 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 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 -0.07

time (sec)

N/A 0.009 0.822 0.802 0.000 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

13 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 -0.08

time (sec)

N/A 0.005 0.937 1.360 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

11 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 -0.09

time (sec)

N/A 0.002 0.018 0.705 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 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 -0.07

time (sec)

N/A 0.009 0.854 0.836 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

13 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 -0.08

time (sec)

N/A 0.005 1.096 1.335 0.000 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

11 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 -0.09

time (sec)

N/A 0.002 1.911 0.708 0.000 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

15 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 -0.07

time (sec)

N/A 0.009 2.022 0.799 0.000 0.000 0.000 0.000 0.000

Problem 53

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

117 117 108 69 86 118 104 86 49

N.S.

1 1.00 0.92 0.59 0.74 1.01 0.89 0.74 0.42

time (sec)

N/A 0.048 0.019 0.093 0.492 5.000 1.315 0.465 0.321

Problem 54

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

19 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 -0.05

time (sec)

N/A 0.016 2.712 1.527 0.000 0.000 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 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 -0.05

time (sec)

N/A 0.015 1.779 1.783 0.000 0.000 0.000 0.000 0.000

Problem 56

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

73 73 60 0 0 0 0 0 -1

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.025 0.024 1.711 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 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 -0.05

time (sec)

N/A 0.017 0.194 0.975 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

13 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 -0.08

time (sec)

N/A 0.004 0.337 0.487 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

19 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 -0.05

time (sec)

N/A 0.015 0.246 1.220 0.000 0.000 0.000 0.000 0.000

Problem 60

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

54 54 59 50 54 51 58 60 49

N.S.

1 1.00 1.09 0.93 1.00 0.94 1.07 1.11 0.91

time (sec)

N/A 0.028 0.008 0.211 0.468 2.638 28.518 0.428 0.357

Problem 61

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

47 47 52 45 48 51 80 47 44

N.S.

1 1.00 1.11 0.96 1.02 1.09 1.70 1.00 0.94

time (sec)

N/A 0.024 0.011 0.198 0.268 2.858 21.110 0.431 0.349

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

43 43 48 41 43 38 48 43 40

N.S.

1 1.00 1.12 0.95 1.00 0.88 1.12 1.00 0.93

time (sec)

N/A 0.020 0.006 0.187 0.464 3.464 10.193 0.430 0.327

Problem 63

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

36 36 41 38 38 39 66 40 35

N.S.

1 1.00 1.14 1.06 1.06 1.08 1.83 1.11 0.97

time (sec)

N/A 0.010 0.008 0.147 0.256 3.686 5.671 0.443 0.314

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 39 63 0 0 0 0 32

N.S.

1 1.00 1.00 1.62 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.036 0.005 0.235 0.000 0.000 0.000 0.000 0.327

Problem 65

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

39 39 44 39 41 43 75 60 38

N.S.

1 1.00 1.13 1.00 1.05 1.10 1.92 1.54 0.97

time (sec)

N/A 0.018 0.007 0.089 0.263 2.432 12.450 0.436 0.343

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 48 39 35 30 42 72 41

N.S.

1 1.00 1.17 0.95 0.85 0.73 1.02 1.76 1.00

time (sec)

N/A 0.018 0.007 0.125 0.465 2.265 10.297 0.460 0.356

Problem 67

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

55 55 60 51 53 54 92 69 50

N.S.

1 1.00 1.09 0.93 0.96 0.98 1.67 1.25 0.91

time (sec)

N/A 0.024 0.011 0.105 0.259 2.203 35.832 0.457 0.365

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 179 140 147 372 153 169 64

N.S.

1 1.00 1.11 0.87 0.91 2.31 0.95 1.05 0.40

time (sec)

N/A 0.081 0.038 0.170 0.484 1.370 14.355 0.487 0.363

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 177 138 145 337 143 165 62

N.S.

1 1.00 1.11 0.87 0.91 2.12 0.90 1.04 0.39

time (sec)

N/A 0.072 0.028 0.085 0.487 2.398 7.254 0.461 0.392

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 107 125 127 319 617 149 49

N.S.

1 1.00 0.76 0.89 0.91 2.28 4.41 1.06 0.35

time (sec)

N/A 0.077 0.030 0.082 0.466 1.387 4.139 0.410 0.390

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 158 125 132 322 121 138 55

N.S.

1 1.00 1.10 0.87 0.92 2.25 0.85 0.97 0.38

time (sec)

N/A 0.065 0.031 0.102 0.485 2.090 8.217 0.452 0.201

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 177 132 142 389 529 159 63

N.S.

1 1.00 1.11 0.83 0.89 2.45 3.33 1.00 0.40

time (sec)

N/A 0.072 0.037 0.109 0.477 1.283 16.586 0.477 0.428

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 177 138 138 350 155 150 63

N.S.

1 1.00 1.11 0.87 0.87 2.20 0.97 0.94 0.40

time (sec)

N/A 0.074 0.040 0.117 0.481 1.948 27.329 0.495 0.452

Problem 74

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

124 124 121 151 169 137 199 145 150

N.S.

1 1.00 0.98 1.22 1.36 1.10 1.60 1.17 1.21

time (sec)

N/A 0.183 0.055 0.224 0.516 1.184 41.041 0.453 1.016

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

154 154 141 367 0 0 0 0 -1

N.S.

1 1.00 0.92 2.38 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.169 0.234 0.432 0.000 0.000 0.000 0.000 0.000

Problem 76

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

90 90 85 113 126 100 155 100 112

N.S.

1 1.00 0.94 1.26 1.40 1.11 1.72 1.11 1.24

time (sec)

N/A 0.103 0.043 0.133 0.522 1.802 14.779 0.427 0.683

Problem 77

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

101 101 107 142 0 0 0 0 -1

N.S.

1 1.00 1.06 1.41 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.096 0.061 0.181 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 F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 165 0 0 0 0 0 -1

N.S.

1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.213 0.072 0.013 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 F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 127 0 0 0 0 0 -1

N.S.

1 1.00 1.31 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.133 0.104 0.015 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 A A A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 98 118 110 115 167 0 152

N.S.

1 1.00 1.13 1.36 1.26 1.32 1.92 0.00 1.75

time (sec)

N/A 0.117 0.046 0.134 0.537 2.367 21.552 0.000 0.613

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

1393 1393 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.845 4.143 0.027 0.000 0.000 0.000 0.000 0.000

Problem 82

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

1191 1191 5293 0 0 0 0 0 -1

N.S.

1 1.00 4.44 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.232 30.757 0.027 0.000 0.000 0.000 0.000 0.000

Problem 83

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

1164 1164 5293 0 0 0 0 0 -1

N.S.

1 1.00 4.55 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.151 30.545 0.033 0.000 0.000 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

1360 1360 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.549 2.000 0.079 0.000 0.000 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

1444 1444 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.690 2.033 0.048 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 C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 170 758 0 0 0 0 -1

N.S.

1 1.00 1.14 5.09 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.214 0.295 0.471 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 B F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 224 289 0 0 0 0 -1

N.S.

1 1.00 1.56 2.01 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.181 0.044 0.407 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 F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

229 229 245 0 0 0 0 0 -1

N.S.

1 1.00 1.07 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.342 0.132 0.014 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 F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 239 0 0 0 0 0 -1

N.S.

1 1.00 1.73 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.218 0.288 0.015 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 F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 196 0 0 0 0 0 -1

N.S.

1 1.00 1.32 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.226 0.219 0.015 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 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 -0.05

time (sec)

N/A 0.015 1.271 0.014 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

21 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 -0.05

time (sec)

N/A 0.016 0.825 0.014 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 F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 65 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 0.027 0.042 0.014 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 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 -0.05

time (sec)

N/A 0.018 0.221 0.013 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

21 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 -0.05

time (sec)

N/A 0.018 0.233 0.013 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 A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 59 50 54 51 58 60 49

N.S.

1 1.00 1.09 0.93 1.00 0.94 1.07 1.11 0.91

time (sec)

N/A 0.025 0.007 0.047 0.487 1.468 125.815 0.420 0.454

Problem 97

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

47 47 52 45 48 51 117 47 44

N.S.

1 1.00 1.11 0.96 1.02 1.09 2.49 1.00 0.94

time (sec)

N/A 0.023 0.011 0.041 0.262 1.082 69.177 0.438 0.379

Problem 98

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

43 43 48 41 43 38 48 43 40

N.S.

1 1.00 1.12 0.95 1.00 0.88 1.12 1.00 0.93

time (sec)

N/A 0.019 0.006 0.063 0.470 1.406 35.579 0.441 0.405

Problem 99

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

36 36 41 38 38 39 102 40 35

N.S.

1 1.00 1.14 1.06 1.06 1.08 2.83 1.11 0.97

time (sec)

N/A 0.014 0.008 0.029 0.260 1.294 19.447 0.404 0.100

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 39 63 0 0 0 0 32

N.S.

1 1.00 1.00 1.62 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.033 0.005 0.044 0.000 0.000 0.000 0.000 0.351

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