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2.2.5 Integrals 401 to 500

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 401

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A C F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 133 62 94 117 603 0 111 228

N.S.

1 1.58 0.74 1.12 1.39 7.18 0.00 1.32 2.71

time (sec)

N/A 0.257 0.200 0.050 2.526 2.569 0.000 1.124 1.271

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 31 266 0 137 0 0 -1

N.S.

1 1.00 1.00 8.58 0.00 4.42 0.00 0.00 -0.03

time (sec)

N/A 0.010 0.030 0.147 0.000 1.539 0.000 0.000 0.000

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 29 98 0 137 0 0 -1

N.S.

1 1.00 0.94 3.16 0.00 4.42 0.00 0.00 -0.03

time (sec)

N/A 0.010 0.026 0.106 0.000 1.484 0.000 0.000 0.000

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 41 171 0 151 0 0 -1

N.S.

1 1.00 0.91 3.80 0.00 3.36 0.00 0.00 -0.02

time (sec)

N/A 0.019 0.030 0.103 0.000 1.910 0.000 0.000 0.000

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 43 443 0 76 0 0 -1

N.S.

1 1.00 0.91 9.43 0.00 1.62 0.00 0.00 -0.02

time (sec)

N/A 0.065 0.047 0.175 0.000 1.494 0.000 0.000 0.000

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 50 510 0 181 0 0 -1

N.S.

1 1.00 0.82 8.36 0.00 2.97 0.00 0.00 -0.02

time (sec)

N/A 0.056 0.066 0.143 0.000 1.232 0.000 0.000 0.000

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 56 1108 0 205 0 0 -1

N.S.

1 1.00 0.92 18.16 0.00 3.36 0.00 0.00 -0.02

time (sec)

N/A 0.059 0.056 0.162 0.000 1.248 0.000 0.000 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 508 0 39 0 0 18

N.S.

1 1.00 1.00 31.75 0.00 2.44 0.00 0.00 1.12

time (sec)

N/A 0.015 0.025 0.158 0.000 0.921 0.000 0.000 0.562

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 20 286 0 32 0 0 20

N.S.

1 1.00 0.65 9.23 0.00 1.03 0.00 0.00 0.65

time (sec)

N/A 0.028 0.022 0.122 0.000 1.070 0.000 0.000 0.385

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 24 121 0 43 0 0 29

N.S.

1 1.00 0.83 4.17 0.00 1.48 0.00 0.00 1.00

time (sec)

N/A 0.033 0.025 0.092 0.000 1.138 0.000 0.000 0.430

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 95 111 761 0 136 0 0 -1

N.S.

1 1.40 1.63 11.19 0.00 2.00 0.00 0.00 -0.01

time (sec)

N/A 0.622 1.128 0.362 0.000 1.267 0.000 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 29 19 16 6 15 0 0 15

N.S.

1 1.53 1.00 0.84 0.32 0.79 0.00 0.00 0.79

time (sec)

N/A 0.082 0.006 0.201 1.054 0.983 0.000 0.000 0.514

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A B A C F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 204 66 318 0 1006 0 0 -1

N.S.

1 2.22 0.72 3.46 0.00 10.93 0.00 0.00 -0.01

time (sec)

N/A 0.160 0.054 0.255 0.000 48.350 0.000 0.000 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 63 0 13 29 0 0 32

N.S.

1 1.00 1.34 0.00 0.28 0.62 0.00 0.00 0.68

time (sec)

N/A 0.049 0.108 0.378 1.169 1.376 0.000 0.000 3.937

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 35 0 77 101 0 0 110

N.S.

1 1.00 0.50 0.00 1.10 1.44 0.00 0.00 1.57

time (sec)

N/A 0.137 0.041 0.276 1.590 1.501 0.000 0.000 3.552

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 234 105 247 0 611 0 0 -1

N.S.

1 2.17 0.97 2.29 0.00 5.66 0.00 0.00 -0.01

time (sec)

N/A 1.080 0.194 0.523 0.000 11.474 0.000 0.000 0.000

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A NO NO TBD TBD TBD TBD TBD TBD

size

364 665 385 22968 0 0 0 0 -1

N.S.

1 1.83 1.06 63.10 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 3.275 7.664 9.418 0.000 0.000 0.000 0.000 0.000

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 141 58 0 60 56 0 0 -1

N.S.

1 1.13 0.46 0.00 0.48 0.45 0.00 0.00 -0.01

time (sec)

N/A 0.651 0.245 1.064 1.799 1.288 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 67 61 56 55 108 0 55 43

N.S.

1 0.92 0.84 0.77 0.75 1.48 0.00 0.75 0.59

time (sec)

N/A 0.030 0.087 0.044 1.541 1.332 0.000 0.791 0.133

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 48 103 53 88 0 41 -1

N.S.

1 1.00 0.70 1.49 0.77 1.28 0.00 0.59 -0.01

time (sec)

N/A 0.037 0.051 0.157 2.214 1.418 0.000 1.735 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 61 82 36 123 0 41 -1

N.S.

1 1.00 1.05 1.41 0.62 2.12 0.00 0.71 -0.02

time (sec)

N/A 0.038 0.051 0.175 3.280 1.227 0.000 1.139 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 37 44 43 51 0 30 28

N.S.

1 1.00 0.67 0.80 0.78 0.93 0.00 0.55 0.51

time (sec)

N/A 0.038 0.062 0.086 2.308 1.352 0.000 0.912 0.658

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 39 58 716 100 0 38 -1

N.S.

1 1.00 1.00 1.49 18.36 2.56 0.00 0.97 -0.03

time (sec)

N/A 0.052 0.072 0.177 1.402 1.469 0.000 1.035 0.000

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 63 53 69 131 0 40 -1

N.S.

1 1.00 1.31 1.10 1.44 2.73 0.00 0.83 -0.02

time (sec)

N/A 0.055 0.222 0.124 1.611 1.301 0.000 1.262 0.000

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 28 46 192 0 0 33 28

N.S.

1 1.00 0.57 0.94 3.92 0.00 0.00 0.67 0.57

time (sec)

N/A 0.078 0.065 0.082 1.064 0.000 0.000 1.234 0.633

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

111 119 295 131 115 0 0 0 -1

N.S.

1 1.07 2.66 1.18 1.04 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.410 1.181 0.304 1.497 0.000 0.000 0.000 0.000

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 131 0 0 195 0 0 -1

N.S.

1 1.00 1.17 0.00 0.00 1.74 0.00 0.00 -0.01

time (sec)

N/A 0.595 0.213 180.000 0.000 1.455 0.000 0.000 0.000

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 29 38 25 26 0 35 -1

N.S.

1 1.00 0.88 1.15 0.76 0.79 0.00 1.06 -0.03

time (sec)

N/A 0.082 0.028 0.144 4.522 0.938 0.000 1.719 0.000

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 32 62 488 77 0 27 -1

N.S.

1 1.00 0.97 1.88 14.79 2.33 0.00 0.82 -0.03

time (sec)

N/A 0.020 0.014 0.147 3.032 1.179 0.000 1.118 0.000

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 49 55 790 103 0 48 29

N.S.

1 1.00 0.89 1.00 14.36 1.87 0.00 0.87 0.53

time (sec)

N/A 0.046 0.066 0.089 3.217 1.520 0.000 0.982 0.419

Problem 431

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

16 16 16 39 90 39 0 22 12

N.S.

1 1.00 1.00 2.44 5.62 2.44 0.00 1.38 0.75

time (sec)

N/A 0.018 0.026 0.151 3.833 1.269 0.000 0.989 0.347

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 49 100 0 118 0 0 -1

N.S.

1 1.00 1.00 2.04 0.00 2.41 0.00 0.00 -0.02

time (sec)

N/A 0.077 0.069 0.162 0.000 1.620 0.000 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 91 62 180 1359 163 0 55 -1

N.S.

1 1.05 0.71 2.07 15.62 1.87 0.00 0.63 -0.01

time (sec)

N/A 0.321 0.141 0.312 2.199 1.775 0.000 0.817 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 115 754 0 130 0 0 -1

N.S.

1 1.00 1.69 11.09 0.00 1.91 0.00 0.00 -0.01

time (sec)

N/A 0.078 0.146 0.458 0.000 1.194 0.000 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 79 473 0 115 0 0 -1

N.S.

1 1.00 1.98 11.82 0.00 2.88 0.00 0.00 -0.02

time (sec)

N/A 0.032 0.087 0.442 0.000 1.154 0.000 0.000 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 75 975 0 97 0 0 -1

N.S.

1 1.00 0.80 10.37 0.00 1.03 0.00 0.00 -0.01

time (sec)

N/A 0.266 0.433 1.355 0.000 1.266 0.000 0.000 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F C B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 36 64 63 33 0 133 20

N.S.

1 1.00 0.92 1.64 1.62 0.85 0.00 3.41 0.51

time (sec)

N/A 0.211 0.055 0.535 3.429 1.033 0.000 0.611 0.759

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B F B F B F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

73 73 255 1611 0 257 0 121 -1

N.S.

1 1.00 3.49 22.07 0.00 3.52 0.00 1.66 -0.01

time (sec)

N/A 1.455 4.015 1.528 0.000 1.454 0.000 0.723 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 116 117 47 84 0 0 113

N.S.

1 1.00 2.04 2.05 0.82 1.47 0.00 0.00 1.98

time (sec)

N/A 0.746 0.695 0.667 2.711 1.559 0.000 0.000 1.473

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 49 61 0 50 0 52 90

N.S.

1 1.00 0.74 0.92 0.00 0.76 0.00 0.79 1.36

time (sec)

N/A 0.048 0.055 0.046 0.000 1.250 0.000 0.549 1.569

Problem 441

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

54 54 71 41 0 76 46 36 172

N.S.

1 1.00 1.31 0.76 0.00 1.41 0.85 0.67 3.19

time (sec)

N/A 0.040 0.303 0.047 0.000 1.292 3.248 0.529 0.511

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 105 0 0 0 0 186 250

N.S.

1 1.00 0.79 0.00 0.00 0.00 0.00 1.40 1.88

time (sec)

N/A 0.103 0.098 0.034 0.000 0.000 0.000 0.595 1.447

Problem 443

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 42 0 0 117 0 79 101

N.S.

1 1.00 0.61 0.00 0.00 1.70 0.00 1.14 1.46

time (sec)

N/A 0.057 0.070 0.030 0.000 2.301 0.000 0.553 0.717

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 256 0 71 0 0 73 46

N.S.

1 1.00 4.92 0.00 1.37 0.00 0.00 1.40 0.88

time (sec)

N/A 0.053 0.217 0.038 2.643 0.000 0.000 0.718 0.414

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 245 0 74 0 0 76 -1

N.S.

1 1.00 4.54 0.00 1.37 0.00 0.00 1.41 -0.02

time (sec)

N/A 0.054 0.213 0.039 3.691 0.000 0.000 0.696 0.000

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

133 174 6084 0 0 0 0 0 -1

N.S.

1 1.31 45.74 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 3.372 42.296 180.000 0.000 0.000 0.000 0.000 0.000

Problem 447

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 208 169 559 0 271 0 193 -1

N.S.

1 2.08 1.69 5.59 0.00 2.71 0.00 1.93 -0.01

time (sec)

N/A 0.719 3.379 0.643 0.000 1.010 0.000 0.862 0.000

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 47 127 136 185 0 0 -1

N.S.

1 1.00 0.42 1.13 1.21 1.65 0.00 0.00 -0.01

time (sec)

N/A 0.112 0.033 0.307 4.788 0.796 0.000 0.000 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 162 154 0 145 0 0 146 -1

N.S.

1 1.71 1.62 0.00 1.53 0.00 0.00 1.54 -0.01

time (sec)

N/A 0.194 0.096 0.115 4.011 0.000 0.000 0.862 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 30 0 37 46 0 37 -1

N.S.

1 1.00 0.61 0.00 0.76 0.94 0.00 0.76 -0.02

time (sec)

N/A 0.072 0.358 0.832 2.115 1.081 0.000 0.692 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 42 26 86 35 0 25 43

N.S.

1 1.00 2.10 1.30 4.30 1.75 0.00 1.25 2.15

time (sec)

N/A 0.147 0.150 0.054 5.422 1.294 0.000 0.886 0.621

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 35 58 0 0 93 0 40 -1

N.S.

1 1.30 2.15 0.00 0.00 3.44 0.00 1.48 -0.04

time (sec)

N/A 0.629 2.853 0.421 0.000 1.710 0.000 0.970 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 126 89 0 100 461 0 0 -1

N.S.

1 1.25 0.88 0.00 0.99 4.56 0.00 0.00 -0.01

time (sec)

N/A 0.918 0.287 0.697 3.128 51.854 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 140 0 0 26 0 25 -1

N.S.

1 1.00 5.60 0.00 0.00 1.04 0.00 1.00 -0.04

time (sec)

N/A 0.038 8.254 0.128 0.000 0.769 0.000 0.973 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 154 153 0 0 0 0 120 -1

N.S.

1 1.51 1.50 0.00 0.00 0.00 0.00 1.18 -0.01

time (sec)

N/A 0.128 0.083 0.309 0.000 0.000 0.000 1.189 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 18 45 88 259 50 0 85 -1

N.S.

1 1.06 2.65 5.18 15.24 2.94 0.00 5.00 -0.06

time (sec)

N/A 0.013 0.053 0.280 2.231 1.356 0.000 1.246 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 52 242 0 115 0 138 -1

N.S.

1 1.00 1.62 7.56 0.00 3.59 0.00 4.31 -0.03

time (sec)

N/A 0.026 0.052 0.478 0.000 0.848 0.000 1.063 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 31 24 27 30 24 32 24

N.S.

1 1.00 1.00 0.77 0.87 0.97 0.77 1.03 0.77

time (sec)

N/A 0.011 0.003 0.081 1.080 0.707 0.040 0.759 0.308

Problem 459

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 39 29 30 32 32 30 30

N.S.

1 1.00 1.00 0.74 0.77 0.82 0.82 0.77 0.77

time (sec)

N/A 0.010 0.009 0.081 2.028 0.998 0.051 0.991 0.035

Problem 460

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

58 58 40 60 46 73 41 42 44

N.S.

1 1.00 0.69 1.03 0.79 1.26 0.71 0.72 0.76

time (sec)

N/A 0.022 0.015 0.088 2.502 0.583 0.058 0.970 0.082

Problem 461

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

52 52 46 37 33 65 984 35 34

N.S.

1 1.00 0.88 0.71 0.63 1.25 18.92 0.67 0.65

time (sec)

N/A 0.018 0.046 0.112 2.458 0.594 2.177 0.750 0.471

Problem 462

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

61 61 49 46 42 47 165 46 46

N.S.

1 1.00 0.80 0.75 0.69 0.77 2.70 0.75 0.75

time (sec)

N/A 0.021 0.042 0.136 2.956 0.740 3.882 0.760 0.467

Problem 463

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

16 16 15 16 14 15 15 14 24

N.S.

1 1.00 0.94 1.00 0.88 0.94 0.94 0.88 1.50

time (sec)

N/A 0.002 0.002 0.006 0.281 1.135 0.007 0.780 0.456

Problem 464

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

46 46 36 33 35 49 32 36 35

N.S.

1 1.00 0.78 0.72 0.76 1.07 0.70 0.78 0.76

time (sec)

N/A 0.017 0.011 0.082 1.734 1.016 0.039 0.806 0.055

Problem 465

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

40 40 23 58 36 36 32 21 36

N.S.

1 1.00 0.58 1.45 0.90 0.90 0.80 0.52 0.90

time (sec)

N/A 0.025 0.008 0.074 0.962 0.903 0.046 0.975 0.066

Problem 466

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

27 27 25 17 19 21 41 19 20

N.S.

1 1.00 0.93 0.63 0.70 0.78 1.52 0.70 0.74

time (sec)

N/A 0.008 0.016 0.079 1.257 0.640 3.831 1.095 0.378

Problem 467

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

38 38 25 22 28 33 82 26 21

N.S.

1 1.00 0.66 0.58 0.74 0.87 2.16 0.68 0.55

time (sec)

N/A 0.011 0.021 0.076 1.203 1.393 1.026 1.076 0.454

Problem 468

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

33 33 24 26 25 34 61 19 99

N.S.

1 1.00 0.73 0.79 0.76 1.03 1.85 0.58 3.00

time (sec)

N/A 0.003 0.036 0.066 2.528 1.007 0.879 1.272 0.045

Problem 469

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 26 36 51 61 0 21 22

N.S.

1 1.00 0.60 0.84 1.19 1.42 0.00 0.49 0.51

time (sec)

N/A 0.004 0.155 0.125 1.862 0.539 0.000 0.943 0.283

Problem 470

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

47 47 28 36 35 40 153 62 24

N.S.

1 1.00 0.60 0.77 0.74 0.85 3.26 1.32 0.51

time (sec)

N/A 0.008 0.038 0.079 1.693 0.629 1.631 1.112 0.449

Problem 471

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

28 28 19 17 16 15 24 16 17

N.S.

1 1.00 0.68 0.61 0.57 0.54 0.86 0.57 0.61

time (sec)

N/A 0.004 0.014 0.056 1.523 0.895 1.090 0.674 0.272

Problem 472

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

52 52 49 47 53 74 49 58 51

N.S.

1 1.00 0.94 0.90 1.02 1.42 0.94 1.12 0.98

time (sec)

N/A 0.021 0.019 0.082 1.412 0.686 0.069 0.843 0.052

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 22 0 21 0 0 15

N.S.

1 1.00 1.00 0.88 0.00 0.84 0.00 0.00 0.60

time (sec)

N/A 0.037 6.553 0.107 0.000 0.866 0.000 0.000 0.450

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 35 121 79 69 0 98 -1

N.S.

1 1.00 0.70 2.42 1.58 1.38 0.00 1.96 -0.02

time (sec)

N/A 0.010 0.216 0.139 0.924 0.636 0.000 0.868 0.000

Problem 475

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

24 24 30 22 21 41 49 29 54

N.S.

1 1.00 1.25 0.92 0.88 1.71 2.04 1.21 2.25

time (sec)

N/A 0.004 0.046 0.104 1.244 0.616 0.181 0.637 0.303

Problem 476

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

40 40 46 58 45 45 32 77 33

N.S.

1 1.00 1.15 1.45 1.12 1.12 0.80 1.92 0.82

time (sec)

N/A 0.006 0.059 0.111 1.435 0.762 0.443 0.665 0.041

Problem 477

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

49 49 28 38 37 44 291 35 179

N.S.

1 1.00 0.57 0.78 0.76 0.90 5.94 0.71 3.65

time (sec)

N/A 0.006 0.176 0.076 0.787 0.828 3.843 0.576 0.276

Problem 478

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

47 47 31 40 59 47 0 35 29

N.S.

1 1.00 0.66 0.85 1.26 1.00 0.00 0.74 0.62

time (sec)

N/A 0.005 0.145 0.155 1.143 0.693 0.000 0.735 0.289

Problem 479

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

36 36 36 33 32 32 34 32 32

N.S.

1 1.00 1.00 0.92 0.89 0.89 0.94 0.89 0.89

time (sec)

N/A 0.008 0.002 0.123 1.107 1.153 0.008 0.786 0.033

Problem 480

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 39 30 29 29 34 29 29

N.S.

1 1.00 1.00 0.77 0.74 0.74 0.87 0.74 0.74

time (sec)

N/A 0.010 0.001 0.104 1.209 0.921 0.009 1.022 0.029

Problem 481

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

47 47 33 54 59 73 0 27 29

N.S.

1 1.00 0.70 1.15 1.26 1.55 0.00 0.57 0.62

time (sec)

N/A 0.006 0.208 0.176 0.979 1.287 0.000 1.215 0.365

Problem 482

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

45 45 33 86 76 73 0 41 29

N.S.

1 1.00 0.73 1.91 1.69 1.62 0.00 0.91 0.64

time (sec)

N/A 0.014 0.380 0.145 0.877 0.940 0.000 1.195 0.187

Problem 483

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

83 83 67 70 55 57 112 55 69

N.S.

1 1.00 0.81 0.84 0.66 0.69 1.35 0.66 0.83

time (sec)

N/A 0.061 0.039 0.136 1.075 0.887 0.471 1.069 0.396

Problem 484

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

73 73 51 57 49 52 92 49 59

N.S.

1 1.00 0.70 0.78 0.67 0.71 1.26 0.67 0.81

time (sec)

N/A 0.056 0.069 0.124 1.283 0.843 0.307 0.972 0.335

Problem 485

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

105 105 70 96 66 72 192 66 88

N.S.

1 1.00 0.67 0.91 0.63 0.69 1.83 0.63 0.84

time (sec)

N/A 0.130 0.059 0.168 0.857 0.962 0.700 0.777 0.398

Problem 486

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 39 32 35 36 53 35 40

N.S.

1 1.00 0.89 0.73 0.80 0.82 1.20 0.80 0.91

time (sec)

N/A 0.027 0.089 0.102 1.086 0.937 0.199 0.994 0.075

Problem 487

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 33 60 0 45 507 206 56

N.S.

1 1.00 1.00 1.82 0.00 1.36 15.36 6.24 1.70

time (sec)

N/A 0.033 0.023 0.150 0.000 0.939 0.741 0.845 0.492

Problem 488

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 104 30 619 47 551 341 35

N.S.

1 1.00 3.47 1.00 20.63 1.57 18.37 11.37 1.17

time (sec)

N/A 0.026 0.086 0.200 0.920 0.816 0.672 0.948 0.496

Problem 489

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 13 132 15 128 53 16

N.S.

1 1.00 1.00 0.81 8.25 0.94 8.00 3.31 1.00

time (sec)

N/A 0.013 0.013 0.095 0.842 0.819 0.419 0.752 0.352

Problem 490

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 57 57 66 113 0 0 -1

N.S.

1 1.00 0.92 0.92 1.06 1.82 0.00 0.00 -0.02

time (sec)

N/A 0.048 0.014 0.082 1.048 1.016 0.000 0.000 0.000

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 54 59 210 138 0 0 -1

N.S.

1 1.00 0.92 1.00 3.56 2.34 0.00 0.00 -0.02

time (sec)

N/A 0.043 0.011 0.274 3.788 1.541 0.000 0.000 0.000

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 14 44 78 13 0 10 -1

N.S.

1 1.00 1.17 3.67 6.50 1.08 0.00 0.83 -0.08

time (sec)

N/A 0.073 0.098 0.869 3.644 0.875 0.000 1.418 0.000

Problem 493

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B A B A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 19 29 69 19 66 39 -1

N.S.

1 1.00 0.95 1.45 3.45 0.95 3.30 1.95 -0.05

time (sec)

N/A 0.024 0.093 0.250 5.016 0.820 0.667 1.309 0.000

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 22 23 0 22 42 325 22

N.S.

1 1.00 1.00 1.05 0.00 1.00 1.91 14.77 1.00

time (sec)

N/A 0.020 0.018 0.033 0.000 0.694 0.282 1.237 0.327

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 41 46 42 0 52 0 436 34

N.S.

1 1.21 1.35 1.24 0.00 1.53 0.00 12.82 1.00

time (sec)

N/A 0.147 0.045 0.042 0.000 0.707 0.000 0.875 0.493

Problem 496

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

9 9 9 8 7 11 7 7 4

N.S.

1 1.00 1.00 0.89 0.78 1.22 0.78 0.78 0.44

time (sec)

N/A 0.003 0.008 0.013 2.089 1.349 0.023 1.465 0.051

Problem 497

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

22 22 22 19 16 21 17 24 8

N.S.

1 1.00 1.00 0.86 0.73 0.95 0.77 1.09 0.36

time (sec)

N/A 0.013 0.009 0.019 2.781 0.902 0.032 1.830 0.056

Problem 498

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 30 24 23 24 24 25 23

N.S.

1 1.00 0.97 0.77 0.74 0.77 0.77 0.81 0.74

time (sec)

N/A 0.014 0.024 0.027 1.178 0.845 0.042 1.460 0.307

Problem 499

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

36 36 37 31 28 31 31 36 28

N.S.

1 1.00 1.03 0.86 0.78 0.86 0.86 1.00 0.78

time (sec)

N/A 0.018 0.038 0.026 2.732 0.708 0.051 1.187 0.344

Problem 500

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

48 52 45 0 0 0 0 0 -1

N.S.

1 1.08 0.94 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.034 0.053 0.007 0.000 0.000 0.000 0.000 0.000

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