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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 A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 74 61 60 60 68 64 62

N.S.

1 1.00 1.00 0.82 0.81 0.81 0.92 0.86 0.84

time (sec)

N/A 0.054 0.011 0.074 0.275 0.356 0.009 3.787 0.036

Problem 2

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

74 74 74 61 60 60 68 64 62

N.S.

1 1.00 1.00 0.82 0.81 0.81 0.92 0.86 0.84

time (sec)

N/A 0.037 0.009 0.073 0.287 0.377 0.009 4.002 0.030

Problem 3

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

69 69 69 58 57 57 65 61 59

N.S.

1 1.00 1.00 0.84 0.83 0.83 0.94 0.88 0.86

time (sec)

N/A 0.024 0.009 0.041 0.274 0.378 0.010 6.323 0.029

Problem 4

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

65 65 65 60 55 55 63 60 57

N.S.

1 1.00 1.00 0.92 0.85 0.85 0.97 0.92 0.88

time (sec)

N/A 0.027 0.011 0.013 0.281 0.366 0.054 5.962 0.036

Problem 5

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

63 63 63 57 55 62 58 57 56

N.S.

1 1.00 1.00 0.90 0.87 0.98 0.92 0.90 0.89

time (sec)

N/A 0.034 0.015 0.017 0.276 0.361 0.066 6.501 0.037

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

63 63 58 58 55 62 61 58 56

N.S.

1 1.00 0.92 0.92 0.87 0.98 0.97 0.92 0.89

time (sec)

N/A 0.036 0.025 0.014 0.281 0.373 0.149 4.623 0.035

Problem 7

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

63 63 60 55 56 62 63 56 55

N.S.

1 1.00 0.95 0.87 0.89 0.98 1.00 0.89 0.87

time (sec)

N/A 0.035 0.033 0.018 0.283 0.395 0.294 3.905 0.033

Problem 8

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

63 63 62 56 56 62 63 57 56

N.S.

1 1.00 0.98 0.89 0.89 0.98 1.00 0.90 0.89

time (sec)

N/A 0.034 0.020 0.017 0.283 0.372 1.082 3.908 0.048

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

63 63 63 56 56 62 66 57 56

N.S.

1 1.00 1.00 0.89 0.89 0.98 1.05 0.90 0.89

time (sec)

N/A 0.034 0.037 0.016 0.277 0.377 3.153 4.808 0.777

Problem 10

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

68 68 68 59 59 62 70 60 60

N.S.

1 1.00 1.00 0.87 0.87 0.91 1.03 0.88 0.88

time (sec)

N/A 0.031 0.032 0.013 0.275 0.382 9.680 4.202 0.790

Problem 11

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

159 159 159 142 143 143 168 154 141

N.S.

1 1.00 1.00 0.89 0.90 0.90 1.06 0.97 0.89

time (sec)

N/A 0.148 0.029 0.077 0.281 0.397 0.019 3.401 0.817

Problem 12

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

159 159 159 142 143 143 163 154 141

N.S.

1 1.00 1.00 0.89 0.90 0.90 1.03 0.97 0.89

time (sec)

N/A 0.098 0.025 0.087 0.296 0.349 0.019 4.187 0.068

Problem 13

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

154 154 154 139 140 140 165 151 138

N.S.

1 1.00 1.00 0.90 0.91 0.91 1.07 0.98 0.90

time (sec)

N/A 0.074 0.020 0.085 0.279 0.395 0.020 6.004 0.070

Problem 14

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

150 150 150 149 138 138 156 149 135

N.S.

1 1.00 1.00 0.99 0.92 0.92 1.04 0.99 0.90

time (sec)

N/A 0.071 0.026 0.019 0.287 0.366 0.117 4.185 0.799

Problem 15

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

145 145 145 147 137 145 156 147 135

N.S.

1 1.00 1.00 1.01 0.94 1.00 1.08 1.01 0.93

time (sec)

N/A 0.082 0.061 0.022 0.326 0.368 0.133 3.769 0.797

Problem 16

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

149 149 139 146 139 145 153 148 135

N.S.

1 1.00 0.93 0.98 0.93 0.97 1.03 0.99 0.91

time (sec)

N/A 0.083 0.065 0.023 0.289 0.365 0.213 3.334 0.792

Problem 17

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

149 149 151 143 140 145 160 146 137

N.S.

1 1.00 1.01 0.96 0.94 0.97 1.07 0.98 0.92

time (sec)

N/A 0.090 0.052 0.021 0.270 0.365 0.397 3.884 0.059

Problem 18

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

148 148 130 139 139 145 153 142 134

N.S.

1 1.00 0.88 0.94 0.94 0.98 1.03 0.96 0.91

time (sec)

N/A 0.097 0.052 0.021 0.267 0.377 1.441 6.232 0.058

Problem 19

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

143 143 142 135 138 145 155 140 136

N.S.

1 1.00 0.99 0.94 0.97 1.01 1.08 0.98 0.95

time (sec)

N/A 0.097 0.053 0.023 0.276 0.358 4.467 5.548 0.054

Problem 20

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

149 149 144 136 140 145 158 141 136

N.S.

1 1.00 0.97 0.91 0.94 0.97 1.06 0.95 0.91

time (sec)

N/A 0.092 0.063 0.021 0.268 0.367 29.622 5.529 0.057

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

339 339 460 331 0 0 0 5305 2588

N.S.

1 1.00 1.36 0.98 0.00 0.00 0.00 15.65 7.63

time (sec)

N/A 1.215 0.386 0.073 0.000 0.000 0.000 6.581 0.958

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

278 278 377 419 0 1329593 0 3520 2696

N.S.

1 1.00 1.36 1.51 0.00 4782.71 0.00 12.66 9.70

time (sec)

N/A 0.317 0.274 0.062 0.000 61.877 0.000 7.757 1.527

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

270 270 360 267 0 861800 0 3844 1890

N.S.

1 1.00 1.33 0.99 0.00 3191.85 0.00 14.24 7.00

time (sec)

N/A 0.569 0.238 0.066 0.000 57.707 0.000 6.789 2.001

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

223 223 240 313 0 845032 0 2368 2500

N.S.

1 1.00 1.08 1.40 0.00 3789.38 0.00 10.62 11.21

time (sec)

N/A 0.163 0.234 0.048 0.000 14.292 0.000 5.187 1.885

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

211 211 234 242 0 578003 0 1712 2500

N.S.

1 1.00 1.11 1.15 0.00 2739.35 0.00 8.11 11.85

time (sec)

N/A 0.174 0.139 0.043 0.000 27.603 0.000 6.855 2.306

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

229 229 285 251 0 0 0 2337 2258

N.S.

1 1.00 1.24 1.10 0.00 0.00 0.00 10.21 9.86

time (sec)

N/A 0.188 0.293 0.059 0.000 0.000 0.000 6.435 1.493

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

260 260 315 325 0 0 0 3508 2588

N.S.

1 1.00 1.21 1.25 0.00 0.00 0.00 13.49 9.95

time (sec)

N/A 0.318 0.693 0.068 0.000 0.000 0.000 7.457 1.022

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

288 288 377 300 0 0 0 3354 2500

N.S.

1 1.00 1.31 1.04 0.00 0.00 0.00 11.65 8.68

time (sec)

N/A 0.335 0.619 0.082 0.000 0.000 0.000 6.262 1.172

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

412 412 444 550 0 0 0 5220 2500

N.S.

1 1.00 1.08 1.33 0.00 0.00 0.00 12.67 6.07

time (sec)

N/A 0.893 0.876 0.082 0.000 0.000 0.000 8.913 1.774

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

347 347 358 458 0 0 0 3229 2500

N.S.

1 1.00 1.03 1.32 0.00 0.00 0.00 9.31 7.20

time (sec)

N/A 0.434 0.572 0.058 0.000 0.000 0.000 5.333 1.613

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

356 356 378 456 0 0 0 4440 2500

N.S.

1 1.00 1.06 1.28 0.00 0.00 0.00 12.47 7.02

time (sec)

N/A 0.630 0.668 0.070 0.000 0.000 0.000 6.104 1.671

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

317 317 335 510 0 0 0 3014 2500

N.S.

1 1.00 1.06 1.61 0.00 0.00 0.00 9.51 7.89

time (sec)

N/A 0.294 0.801 0.157 0.000 0.000 0.000 8.337 1.595

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

368 368 393 579 0 0 0 5158 2500

N.S.

1 1.00 1.07 1.57 0.00 0.00 0.00 14.02 6.79

time (sec)

N/A 0.597 0.796 0.141 0.000 0.000 0.000 7.624 1.675

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

403 403 458 566 0 0 0 6024 2500

N.S.

1 1.00 1.14 1.40 0.00 0.00 0.00 14.95 6.20

time (sec)

N/A 0.649 0.931 0.104 0.000 0.000 0.000 7.385 1.838

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

514 514 559 667 0 0 0 9016 2500

N.S.

1 1.00 1.09 1.30 0.00 0.00 0.00 17.54 4.86

time (sec)

N/A 1.073 1.259 0.135 0.000 0.000 0.000 9.025 2.468

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

534 534 655 778 0 0 0 6939 2500

N.S.

1 1.00 1.23 1.46 0.00 0.00 0.00 12.99 4.68

time (sec)

N/A 1.363 1.539 0.142 0.000 0.000 0.000 8.191 2.773

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

399 399 296 5520 611 3898 47658 7808 2500

N.S.

1 1.00 0.74 13.83 1.53 9.77 119.44 19.57 6.27

time (sec)

N/A 0.281 2.106 0.036 0.427 0.427 3.363 3.716 3.280

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

260 260 187 2187 344 1603 16323 3203 1314

N.S.

1 1.00 0.72 8.41 1.32 6.17 62.78 12.32 5.05

time (sec)

N/A 0.156 0.897 0.022 0.335 0.410 1.468 5.223 1.810

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 92 136 155 444 3628 914 527

N.S.

1 1.00 0.67 0.99 1.13 3.24 26.48 6.67 3.85

time (sec)

N/A 0.063 0.279 0.022 0.306 0.380 0.584 6.065 1.075

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

368 368 438 0 0 32 0 0 -1

N.S.

1 1.00 1.19 0.00 0.00 0.09 0.00 0.00 -0.00

time (sec)

N/A 0.432 1.150 0.018 0.000 0.359 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

685 670 242 0 0 57 0 0 -1

N.S.

1 0.98 0.35 0.00 0.00 0.08 0.00 0.00 -0.00

time (sec)

N/A 1.583 1.182 0.006 0.000 0.361 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

356 356 378 456 0 0 0 4440 2500

N.S.

1 1.00 1.06 1.28 0.00 0.00 0.00 12.47 7.02

time (sec)

N/A 0.623 0.676 0.042 0.000 0.000 0.000 7.202 0.004

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

356 356 378 456 0 0 0 4440 2500

N.S.

1 1.00 1.06 1.28 0.00 0.00 0.00 12.47 7.02

time (sec)

N/A 0.270 0.104 0.053 0.000 0.000 0.000 7.457 1.551

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

356 356 378 456 0 0 0 4440 2500

N.S.

1 1.00 1.06 1.28 0.00 0.00 0.00 12.47 7.02

time (sec)

N/A 0.264 0.102 0.053 0.000 0.000 0.000 8.155 1.474

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

356 356 378 456 0 0 0 4440 2500

N.S.

1 1.00 1.06 1.28 0.00 0.00 0.00 12.47 7.02

time (sec)

N/A 0.263 0.102 0.060 0.000 0.000 0.000 7.393 1.389

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

356 356 378 456 0 0 0 4440 2500

N.S.

1 1.00 1.06 1.28 0.00 0.00 0.00 12.47 7.02

time (sec)

N/A 0.257 0.101 0.051 0.000 0.000 0.000 7.193 1.414

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

273 273 260 330 0 900 0 306 2972

N.S.

1 1.00 0.95 1.21 0.00 3.30 0.00 1.12 10.89

time (sec)

N/A 0.550 0.133 0.112 0.000 0.619 0.000 6.447 1.604

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

203 203 193 224 0 677 0 214 2295

N.S.

1 1.00 0.95 1.10 0.00 3.33 0.00 1.05 11.31

time (sec)

N/A 0.288 0.096 0.094 0.000 0.564 0.000 4.283 1.626

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 136 146 0 473 0 141 1689

N.S.

1 1.00 0.94 1.01 0.00 3.28 0.00 0.98 11.73

time (sec)

N/A 0.181 0.067 0.109 0.000 0.494 0.000 3.646 1.300

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 100 101 0 318 0 99 1081

N.S.

1 1.00 0.97 0.98 0.00 3.09 0.00 0.96 10.50

time (sec)

N/A 0.121 0.045 0.062 0.000 0.458 0.000 4.479 1.830

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 178 99 0 309 0 97 2500

N.S.

1 1.00 1.84 1.02 0.00 3.19 0.00 1.00 25.77

time (sec)

N/A 0.134 0.085 0.050 0.000 0.625 0.000 6.102 8.881

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 203 132 0 399 0 135 2500

N.S.

1 1.00 1.72 1.12 0.00 3.38 0.00 1.14 21.19

time (sec)

N/A 0.188 0.096 0.054 0.000 0.600 0.000 3.389 7.857

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

174 174 314 203 0 609 0 212 2500

N.S.

1 1.00 1.80 1.17 0.00 3.50 0.00 1.22 14.37

time (sec)

N/A 0.266 0.218 0.074 0.000 0.912 0.000 4.700 9.917

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

244 244 416 294 0 834 0 313 2500

N.S.

1 1.00 1.70 1.20 0.00 3.42 0.00 1.28 10.25

time (sec)

N/A 0.376 0.216 0.079 0.000 1.642 0.000 6.809 13.829

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

369 369 456 453 0 15467 0 7243 2500

N.S.

1 1.00 1.24 1.23 0.00 41.92 0.00 19.63 6.78

time (sec)

N/A 3.115 0.323 0.057 0.000 40.747 0.000 6.118 4.912

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

282 282 365 333 0 9364 0 5461 2500

N.S.

1 1.00 1.29 1.18 0.00 33.21 0.00 19.37 8.87

time (sec)

N/A 2.418 0.310 0.056 0.000 8.230 0.000 5.952 3.359

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

219 219 258 224 0 5788 0 4086 2500

N.S.

1 1.00 1.18 1.02 0.00 26.43 0.00 18.66 11.42

time (sec)

N/A 0.442 0.204 0.043 0.000 4.058 0.000 7.595 3.360

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

213 213 253 220 0 5930 0 3988 2500

N.S.

1 1.00 1.19 1.03 0.00 27.84 0.00 18.72 11.74

time (sec)

N/A 0.572 0.194 0.062 0.000 1.683 0.000 8.507 3.515

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

267 267 284 244 0 9850 0 3813 2500

N.S.

1 1.00 1.06 0.91 0.00 36.89 0.00 14.28 9.36

time (sec)

N/A 0.699 0.221 0.071 0.000 11.021 0.000 7.057 4.763

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

329 329 394 360 0 15830 0 6718 2500

N.S.

1 1.00 1.20 1.09 0.00 48.12 0.00 20.42 7.60

time (sec)

N/A 1.299 0.358 0.075 0.000 42.362 0.000 5.530 6.247

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) B F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

320 320 309 432 0 2111 0 424 2500

N.S.

1 1.00 0.97 1.35 0.00 6.60 0.00 1.32 7.81

time (sec)

N/A 0.813 0.320 0.154 0.000 0.626 0.000 5.527 1.333

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) B F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

236 236 236 309 0 1455 0 279 2450

N.S.

1 1.00 1.00 1.31 0.00 6.17 0.00 1.18 10.38

time (sec)

N/A 0.294 0.230 0.102 0.000 0.462 0.000 5.877 1.811

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) B F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

165 165 175 228 0 970 0 195 1651

N.S.

1 1.00 1.06 1.38 0.00 5.88 0.00 1.18 10.01

time (sec)

N/A 0.190 0.165 0.082 0.000 0.412 0.000 3.724 2.717

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) B F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 130 139 0 650 0 140 342

N.S.

1 1.00 1.06 1.13 0.00 5.28 0.00 1.14 2.78

time (sec)

N/A 0.122 0.067 0.054 0.000 0.388 0.000 3.637 0.378

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) B F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 268 228 0 1103 0 227 2500

N.S.

1 1.00 1.61 1.37 0.00 6.64 0.00 1.37 15.06

time (sec)

N/A 0.266 0.289 0.073 0.000 1.016 0.000 3.872 11.849

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) B F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

234 234 403 316 0 1764 0 287 2500

N.S.

1 1.00 1.72 1.35 0.00 7.54 0.00 1.23 10.68

time (sec)

N/A 0.483 0.416 0.089 0.000 2.024 0.000 5.063 12.979

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F(-2) B F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

329 329 592 466 0 2567 0 535 2500

N.S.

1 1.00 1.80 1.42 0.00 7.80 0.00 1.63 7.60

time (sec)

N/A 0.779 0.777 0.112 0.000 4.313 0.000 5.454 21.016

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

550 550 648 682 0 18909 0 8957 2500

N.S.

1 1.00 1.18 1.24 0.00 34.38 0.00 16.29 4.55

time (sec)

N/A 9.873 1.304 0.098 0.000 75.856 0.000 7.932 4.104

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

436 436 511 522 0 12597 0 7496 2500

N.S.

1 1.00 1.17 1.20 0.00 28.89 0.00 17.19 5.73

time (sec)

N/A 3.601 0.960 0.072 0.000 22.844 0.000 7.058 2.648

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

362 362 414 415 0 8951 0 6208 2500

N.S.

1 1.00 1.14 1.15 0.00 24.73 0.00 17.15 6.91

time (sec)

N/A 1.737 0.676 0.063 0.000 12.980 0.000 6.066 6.543

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

346 346 382 387 0 8991 0 6356 2500

N.S.

1 1.00 1.10 1.12 0.00 25.99 0.00 18.37 7.23

time (sec)

N/A 1.259 0.663 0.060 0.000 11.408 0.000 6.986 6.552

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

399 399 444 438 0 13111 0 7182 2500

N.S.

1 1.00 1.11 1.10 0.00 32.86 0.00 18.00 6.27

time (sec)

N/A 1.397 0.824 0.114 0.000 26.383 0.000 8.214 6.862

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

575 575 548 570 0 19333 0 8660 2500

N.S.

1 1.00 0.95 0.99 0.00 33.62 0.00 15.06 4.35

time (sec)

N/A 6.511 1.117 0.134 0.000 84.860 0.000 8.753 7.370

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

68 68 62 56 58 82 61 63 57

N.S.

1 1.00 0.91 0.82 0.85 1.21 0.90 0.93 0.84

time (sec)

N/A 0.085 0.019 0.040 0.281 0.373 0.059 4.832 0.056

Problem 75

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

61 61 61 51 53 77 56 58 53

N.S.

1 1.00 1.00 0.84 0.87 1.26 0.92 0.95 0.87

time (sec)

N/A 0.078 0.019 0.029 0.280 0.375 0.061 5.196 0.039

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

54 54 54 46 48 72 48 53 47

N.S.

1 1.00 1.00 0.85 0.89 1.33 0.89 0.98 0.87

time (sec)

N/A 0.077 0.017 0.039 0.264 0.362 0.059 3.831 0.897

Problem 77

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

49 49 49 41 43 67 44 45 43

N.S.

1 1.00 1.00 0.84 0.88 1.37 0.90 0.92 0.88

time (sec)

N/A 0.058 0.015 0.027 0.271 0.368 0.061 2.654 0.038

Problem 78

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

42 42 42 36 38 57 36 40 37

N.S.

1 1.00 1.00 0.86 0.90 1.36 0.86 0.95 0.88

time (sec)

N/A 0.033 0.012 0.025 0.296 0.360 0.057 3.007 0.049

Problem 79

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

44 44 44 38 44 71 41 47 40

N.S.

1 1.00 1.00 0.86 1.00 1.61 0.93 1.07 0.91

time (sec)

N/A 0.051 0.016 0.030 0.273 0.364 0.065 4.166 0.041

Problem 80

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 50 45 53 92 51 53 50

N.S.

1 1.00 0.91 0.82 0.96 1.67 0.93 0.96 0.91

time (sec)

N/A 0.071 0.018 0.031 0.270 0.369 0.075 5.429 0.044

Problem 81

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

64 64 56 50 56 97 56 66 55

N.S.

1 1.00 0.88 0.78 0.88 1.52 0.88 1.03 0.86

time (sec)

N/A 0.071 0.018 0.033 0.277 0.365 0.082 6.024 0.919

Problem 82

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

70 70 71 56 58 79 68 58 58

N.S.

1 1.00 1.01 0.80 0.83 1.13 0.97 0.83 0.83

time (sec)

N/A 0.055 0.031 0.033 0.490 0.366 0.082 5.877 0.952

Problem 83

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

57 57 58 49 51 74 54 51 50

N.S.

1 1.00 1.02 0.86 0.89 1.30 0.95 0.89 0.88

time (sec)

N/A 0.051 0.032 0.044 0.482 0.371 0.081 5.192 0.054

Problem 84

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

56 56 57 46 48 69 54 48 48

N.S.

1 1.00 1.02 0.82 0.86 1.23 0.96 0.86 0.86

time (sec)

N/A 0.047 0.029 0.030 0.490 0.355 0.080 5.472 0.918

Problem 85

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

49 49 50 41 43 64 48 43 42

N.S.

1 1.00 1.02 0.84 0.88 1.31 0.98 0.88 0.86

time (sec)

N/A 0.043 0.026 0.030 0.485 0.370 0.081 4.621 0.068

Problem 86

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

48 48 46 38 40 59 46 40 40

N.S.

1 1.00 0.96 0.79 0.83 1.23 0.96 0.83 0.83

time (sec)

N/A 0.018 0.028 0.028 0.487 0.369 0.079 3.700 0.072

Problem 87

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

53 53 51 43 45 68 49 45 45

N.S.

1 1.00 0.96 0.81 0.85 1.28 0.92 0.85 0.85

time (sec)

N/A 0.049 0.034 0.034 0.497 0.357 0.087 3.299 0.070

Problem 88

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

62 62 56 48 52 79 56 52 51

N.S.

1 1.00 0.90 0.77 0.84 1.27 0.90 0.84 0.82

time (sec)

N/A 0.054 0.037 0.042 0.486 0.363 0.096 3.808 0.923

Problem 89

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

69 69 61 53 57 84 61 57 57

N.S.

1 1.00 0.88 0.77 0.83 1.22 0.88 0.83 0.83

time (sec)

N/A 0.060 0.041 0.036 0.496 0.379 0.103 5.112 0.916

Problem 90

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

76 76 77 58 62 89 66 62 61

N.S.

1 1.00 1.01 0.76 0.82 1.17 0.87 0.82 0.80

time (sec)

N/A 0.065 0.038 0.036 0.497 0.384 0.110 4.764 0.074

Problem 91

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

81 81 71 64 71 114 75 61 70

N.S.

1 1.00 0.88 0.79 0.88 1.41 0.93 0.75 0.86

time (sec)

N/A 0.075 0.038 0.034 0.514 0.365 0.103 4.448 0.059

Problem 92

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

80 80 66 62 68 109 76 58 68

N.S.

1 1.00 0.82 0.78 0.85 1.36 0.95 0.72 0.85

time (sec)

N/A 0.081 0.038 0.034 0.503 0.377 0.102 4.482 0.052

Problem 93

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

75 75 60 56 63 104 70 53 63

N.S.

1 1.00 0.80 0.75 0.84 1.39 0.93 0.71 0.84

time (sec)

N/A 0.060 0.043 0.035 0.494 0.376 0.104 2.875 0.928

Problem 94

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

72 72 55 54 60 99 65 50 59

N.S.

1 1.00 0.76 0.75 0.83 1.38 0.90 0.69 0.82

time (sec)

N/A 0.046 0.040 0.032 0.495 0.371 0.101 3.101 0.928

Problem 95

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

72 72 56 53 60 99 66 50 60

N.S.

1 1.00 0.78 0.74 0.83 1.38 0.92 0.69 0.83

time (sec)

N/A 0.045 0.042 0.029 0.496 0.359 0.102 4.320 0.071

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

72 72 56 53 60 99 65 50 59

N.S.

1 1.00 0.78 0.74 0.83 1.38 0.90 0.69 0.82

time (sec)

N/A 0.025 0.041 0.031 0.495 0.371 0.099 4.727 0.070

Problem 97

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

79 79 63 58 65 108 71 55 65

N.S.

1 1.00 0.80 0.73 0.82 1.37 0.90 0.70 0.82

time (sec)

N/A 0.069 0.045 0.037 0.488 0.366 0.112 5.462 0.920

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

86 86 78 64 72 119 76 62 71

N.S.

1 1.00 0.91 0.74 0.84 1.38 0.88 0.72 0.83

time (sec)

N/A 0.077 0.039 0.040 0.493 0.364 0.116 5.315 0.923

Problem 99

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

93 93 73 68 77 124 82 67 77

N.S.

1 1.00 0.78 0.73 0.83 1.33 0.88 0.72 0.83

time (sec)

N/A 0.088 0.051 0.038 0.488 0.362 0.123 4.799 0.935

Problem 100

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

86 86 78 74 71 95 87 76 75

N.S.

1 1.00 0.91 0.86 0.83 1.10 1.01 0.88 0.87

time (sec)

N/A 0.088 0.031 0.030 0.529 0.361 0.067 3.371 0.901

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