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2.2.2 Integrals 101 to 200

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 101

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 46 39 0 147 0 35 35

N.S.

1 1.00 1.21 1.03 0.00 3.87 0.00 0.92 0.92

time (sec)

N/A 0.025 0.027 0.430 0.000 0.361 0.000 0.396 0.172

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 20 13 12 43 0 46 51

N.S.

1 1.00 1.67 1.08 1.00 3.58 0.00 3.83 4.25

time (sec)

N/A 0.030 0.045 0.571 0.264 0.363 0.000 0.421 0.156

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 65 85 0 384 0 85 230

N.S.

1 1.00 1.14 1.49 0.00 6.74 0.00 1.49 4.04

time (sec)

N/A 0.075 0.078 0.769 0.000 0.406 0.000 0.414 1.457

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 50 102 110 434 0 106 88

N.S.

1 1.00 1.25 2.55 2.75 10.85 0.00 2.65 2.20

time (sec)

N/A 0.048 0.123 0.714 0.258 0.386 0.000 0.430 1.442

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 42 118 36 92 0 42 34

N.S.

1 1.00 0.70 1.97 0.60 1.53 0.00 0.70 0.57

time (sec)

N/A 0.048 0.066 0.418 0.260 0.387 0.000 0.421 1.422

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 34 82 27 56 0 25 23

N.S.

1 1.00 1.36 3.28 1.08 2.24 0.00 1.00 0.92

time (sec)

N/A 0.121 0.044 0.378 0.266 0.361 0.000 0.405 1.315

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 24 78 22 51 0 30 22

N.S.

1 1.00 0.63 2.05 0.58 1.34 0.00 0.79 0.58

time (sec)

N/A 0.041 0.038 0.404 0.260 0.363 0.000 0.397 0.107

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 19 42 11 23 0 11 11

N.S.

1 1.00 1.12 2.47 0.65 1.35 0.00 0.65 0.65

time (sec)

N/A 0.077 0.012 0.373 0.266 0.360 0.000 0.412 1.186

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

10 10 16 19 12 23 0 10 10

N.S.

1 1.00 1.60 1.90 1.20 2.30 0.00 1.00 1.00

time (sec)

N/A 0.077 0.019 0.522 0.496 0.333 0.000 0.396 1.281

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 9 36 18 78 0 27 21

N.S.

1 1.00 0.60 2.40 1.20 5.20 0.00 1.80 1.40

time (sec)

N/A 0.026 0.024 0.578 0.484 0.350 0.000 0.410 1.189

Problem 111

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

20 20 20 45 33 140 0 25 22

N.S.

1 1.00 1.00 2.25 1.65 7.00 0.00 1.25 1.10

time (sec)

N/A 0.115 0.030 0.591 0.478 0.349 0.000 0.407 1.255

Problem 112

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

17 17 17 38 75 84 0 18 18

N.S.

1 1.00 1.00 2.24 4.41 4.94 0.00 1.06 1.06

time (sec)

N/A 0.032 0.039 0.593 0.264 0.363 0.000 0.412 0.074

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 133 0 0 231 0 122 -1

N.S.

1 1.00 6.33 0.00 0.00 11.00 0.00 5.81 -0.05

time (sec)

N/A 0.031 13.800 2.089 0.000 0.385 0.000 0.412 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 144 249 154 1229 0 216 135

N.S.

1 1.00 0.98 1.69 1.05 8.36 0.00 1.47 0.92

time (sec)

N/A 0.253 0.402 0.773 0.283 0.363 0.000 0.409 1.743

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 167 176 0 1873 0 164 262

N.S.

1 1.00 1.24 1.30 0.00 13.87 0.00 1.21 1.94

time (sec)

N/A 0.182 1.009 0.730 0.000 0.405 0.000 0.413 2.044

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 73 146 80 334 0 104 82

N.S.

1 1.00 0.86 1.72 0.94 3.93 0.00 1.22 0.96

time (sec)

N/A 0.115 0.168 0.728 0.281 0.360 0.000 0.430 1.398

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 79 92 0 431 0 71 158

N.S.

1 1.00 1.10 1.28 0.00 5.99 0.00 0.99 2.19

time (sec)

N/A 0.082 0.206 0.704 0.000 0.395 0.000 0.415 1.529

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 60 54 0 200 0 48 164

N.S.

1 1.00 1.20 1.08 0.00 4.00 0.00 0.96 3.28

time (sec)

N/A 0.097 0.078 0.796 0.000 0.425 0.000 0.404 3.223

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 27 61 46 117 0 76 323

N.S.

1 1.00 0.93 2.10 1.59 4.03 0.00 2.62 11.14

time (sec)

N/A 0.038 0.068 0.783 0.500 0.348 0.000 0.401 1.584

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 85 121 0 856 0 102 166

N.S.

1 1.00 1.02 1.46 0.00 10.31 0.00 1.23 2.00

time (sec)

N/A 0.166 0.133 0.931 0.000 0.376 0.000 0.399 3.938

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 68 151 133 909 0 201 123

N.S.

1 1.00 0.86 1.91 1.68 11.51 0.00 2.54 1.56

time (sec)

N/A 0.070 0.214 0.830 0.476 0.366 0.000 0.419 1.450

Problem 122

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

31 31 38 41 38 41 0 26 65

N.S.

1 1.00 1.23 1.32 1.23 1.32 0.00 0.84 2.10

time (sec)

N/A 0.073 0.038 1.276 0.496 0.351 0.000 0.414 0.513

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 40 96 55 571 0 47 69

N.S.

1 1.00 0.93 2.23 1.28 13.28 0.00 1.09 1.60

time (sec)

N/A 0.083 0.070 0.572 0.480 0.360 0.000 0.405 1.303

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 33 80 43 354 0 39 35

N.S.

1 1.00 0.89 2.16 1.16 9.57 0.00 1.05 0.95

time (sec)

N/A 0.071 0.041 0.579 0.488 0.359 0.000 0.407 1.206

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 27 65 29 186 0 35 29

N.S.

1 1.00 0.93 2.24 1.00 6.41 0.00 1.21 1.00

time (sec)

N/A 0.056 0.035 0.491 0.485 0.353 0.000 0.402 1.216

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 23 47 17 73 0 17 17

N.S.

1 1.00 1.21 2.47 0.89 3.84 0.00 0.89 0.89

time (sec)

N/A 0.031 0.022 0.510 0.498 0.363 0.000 0.417 1.170

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 18 24 10 26 27 10 14

N.S.

1 1.00 1.12 1.50 0.62 1.62 1.69 0.62 0.88

time (sec)

N/A 0.006 0.020 0.236 0.258 0.367 0.266 0.416 0.002

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 18 24 10 26 27 10 12

N.S.

1 1.00 1.12 1.50 0.62 1.62 1.69 0.62 0.75

time (sec)

N/A 0.015 0.014 0.273 0.273 0.332 0.275 0.412 0.049

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 23 24 24 73 92 18 21

N.S.

1 1.00 1.21 1.26 1.26 3.84 4.84 0.95 1.11

time (sec)

N/A 0.026 0.022 0.257 0.275 0.359 0.362 0.409 0.059

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 27 28 38 196 160 36 21

N.S.

1 1.00 0.87 0.90 1.23 6.32 5.16 1.16 0.68

time (sec)

N/A 0.036 0.032 0.352 0.261 0.376 0.561 0.421 1.164

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 33 32 54 357 197 40 29

N.S.

1 1.00 0.89 0.86 1.46 9.65 5.32 1.08 0.78

time (sec)

N/A 0.050 0.045 0.424 0.269 0.387 0.761 0.403 0.066

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 90 35 0 259 0 135 34

N.S.

1 1.00 2.00 0.78 0.00 5.76 0.00 3.00 0.76

time (sec)

N/A 0.038 0.097 0.599 0.000 0.345 0.000 0.413 1.238

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 53 26 0 131 0 71 25

N.S.

1 1.00 1.66 0.81 0.00 4.09 0.00 2.22 0.78

time (sec)

N/A 0.026 0.080 0.683 0.000 0.362 0.000 0.411 1.197

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 97 25 0 85 0 64 24

N.S.

1 1.00 3.23 0.83 0.00 2.83 0.00 2.13 0.80

time (sec)

N/A 0.027 0.136 0.747 0.000 0.350 0.000 0.408 1.230

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 84 35 0 166 0 89 32

N.S.

1 1.00 1.71 0.71 0.00 3.39 0.00 1.82 0.65

time (sec)

N/A 0.035 0.233 0.688 0.000 0.364 0.000 0.404 1.218

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 70 35 0 436 0 197 34

N.S.

1 1.00 1.56 0.78 0.00 9.69 0.00 4.38 0.76

time (sec)

N/A 0.048 0.176 0.676 0.000 0.378 0.000 0.423 1.248

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 61 26 0 242 0 133 25

N.S.

1 1.00 1.79 0.76 0.00 7.12 0.00 3.91 0.74

time (sec)

N/A 0.034 0.123 0.786 0.000 0.362 0.000 0.434 1.195

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 81 35 0 189 0 88 36

N.S.

1 1.00 1.93 0.83 0.00 4.50 0.00 2.10 0.86

time (sec)

N/A 0.042 0.254 0.770 0.000 0.358 0.000 0.416 1.256

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 86 35 0 166 0 113 31

N.S.

1 1.00 1.76 0.71 0.00 3.39 0.00 2.31 0.63

time (sec)

N/A 0.058 0.241 0.756 0.000 0.356 0.000 0.422 1.232

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 105 190 146 1294 0 141 163

N.S.

1 1.00 1.08 1.96 1.51 13.34 0.00 1.45 1.68

time (sec)

N/A 0.356 0.246 0.681 0.509 0.398 0.000 0.414 1.612

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 88 138 94 637 0 97 111

N.S.

1 1.00 1.16 1.82 1.24 8.38 0.00 1.28 1.46

time (sec)

N/A 0.223 0.229 0.658 0.509 0.397 0.000 0.410 1.511

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 64 111 67 264 0 74 73

N.S.

1 1.00 1.07 1.85 1.12 4.40 0.00 1.23 1.22

time (sec)

N/A 0.128 0.105 0.639 0.479 0.373 0.000 0.418 1.450

Problem 143

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

51 51 46 88 50 73 0 57 58

N.S.

1 1.00 0.90 1.73 0.98 1.43 0.00 1.12 1.14

time (sec)

N/A 0.058 0.069 0.638 0.472 0.383 0.000 0.408 0.324

Problem 144

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

39 39 29 55 37 42 148 43 42

N.S.

1 1.00 0.74 1.41 0.95 1.08 3.79 1.10 1.08

time (sec)

N/A 0.031 0.045 0.277 0.277 0.357 0.496 0.414 0.084

Problem 145

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

39 39 29 55 36 43 134 43 42

N.S.

1 1.00 0.74 1.41 0.92 1.10 3.44 1.10 1.08

time (sec)

N/A 0.042 0.045 0.289 0.274 0.379 0.505 0.405 0.064

Problem 146

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

63 63 49 60 63 76 372 59 57

N.S.

1 1.00 0.78 0.95 1.00 1.21 5.90 0.94 0.90

time (sec)

N/A 0.066 0.062 0.292 0.278 0.400 0.865 0.413 1.480

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 64 67 82 271 636 76 74

N.S.

1 1.00 1.00 1.05 1.28 4.23 9.94 1.19 1.16

time (sec)

N/A 0.092 0.098 0.435 0.276 0.380 1.317 0.429 1.509

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 88 76 119 648 882 100 110

N.S.

1 1.00 1.16 1.00 1.57 8.53 11.61 1.32 1.45

time (sec)

N/A 0.158 0.152 0.389 0.288 0.376 1.818 0.410 1.627

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

94 94 108 95 169 1299 1013 143 164

N.S.

1 1.00 1.15 1.01 1.80 13.82 10.78 1.52 1.74

time (sec)

N/A 0.266 0.225 0.380 0.294 0.416 3.021 0.436 1.631

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 49 73 68 184 0 169 68

N.S.

1 1.00 0.91 1.35 1.26 3.41 0.00 3.13 1.26

time (sec)

N/A 0.062 0.136 1.303 0.412 0.418 0.000 0.423 1.282

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 64 24 36 28 0 24 23

N.S.

1 1.00 2.13 0.80 1.20 0.93 0.00 0.80 0.77

time (sec)

N/A 0.028 0.019 0.438 0.272 0.367 0.000 0.410 1.251

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 64 83 48 62 0 54 39

N.S.

1 1.00 1.42 1.84 1.07 1.38 0.00 1.20 0.87

time (sec)

N/A 0.030 0.168 0.714 0.514 0.359 0.000 0.402 1.213

Problem 153

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

23 23 26 37 36 33 0 37 25

N.S.

1 1.00 1.13 1.61 1.57 1.43 0.00 1.61 1.09

time (sec)

N/A 0.020 0.140 0.569 0.283 0.354 0.000 0.414 1.226

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 58 71 45 58 0 51 36

N.S.

1 1.00 1.45 1.78 1.12 1.45 0.00 1.28 0.90

time (sec)

N/A 0.014 0.132 0.708 0.489 0.359 0.000 0.418 1.186

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 21 26 10 18 27 21 18

N.S.

1 1.00 1.75 2.17 0.83 1.50 2.25 1.75 1.50

time (sec)

N/A 0.010 0.023 0.792 0.269 0.367 0.531 0.393 1.212

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 62 88 47 54 0 52 37

N.S.

1 1.00 1.51 2.15 1.15 1.32 0.00 1.27 0.90

time (sec)

N/A 0.024 0.123 0.704 0.473 0.391 0.000 0.408 1.205

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 27 35 30 38 0 33 25

N.S.

1 1.00 1.29 1.67 1.43 1.81 0.00 1.57 1.19

time (sec)

N/A 0.021 0.113 0.509 0.264 0.338 0.000 0.412 1.214

Problem 158

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 86 41 53 61 0 40 40

N.S.

1 1.00 1.83 0.87 1.13 1.30 0.00 0.85 0.85

time (sec)

N/A 0.046 0.078 0.422 0.273 0.362 0.000 0.411 1.247

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 154 100 66 104 0 72 60

N.S.

1 1.00 2.26 1.47 0.97 1.53 0.00 1.06 0.88

time (sec)

N/A 0.050 2.115 0.589 0.478 0.356 0.000 0.421 1.237

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 163 54 53 74 0 54 42

N.S.

1 1.00 3.98 1.32 1.29 1.80 0.00 1.32 1.02

time (sec)

N/A 0.033 2.140 0.428 0.264 0.350 0.000 0.419 1.226

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 153 86 60 97 0 66 54

N.S.

1 1.00 2.55 1.43 1.00 1.62 0.00 1.10 0.90

time (sec)

N/A 0.029 1.625 0.600 0.479 0.358 0.000 0.399 1.205

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

14 14 28 35 19 28 78 21 28

N.S.

1 1.00 2.00 2.50 1.36 2.00 5.57 1.50 2.00

time (sec)

N/A 0.018 0.041 0.793 0.273 0.334 2.653 0.423 1.188

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 153 104 69 97 0 77 60

N.S.

1 1.00 1.78 1.21 0.80 1.13 0.00 0.90 0.70

time (sec)

N/A 0.043 1.926 0.608 0.479 0.347 0.000 0.401 1.212

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 155 55 50 82 0 57 48

N.S.

1 1.00 2.58 0.92 0.83 1.37 0.00 0.95 0.80

time (sec)

N/A 0.038 2.119 0.383 0.261 0.360 0.000 0.411 1.230

Problem 165

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

59 59 46 0 0 0 0 0 -1

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.026 0.070 0.464 0.000 0.000 0.000 0.000 0.000

Problem 166

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

79 79 77 0 0 0 0 0 -1

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.054 0.124 0.447 0.000 0.000 0.000 0.000 0.000

Problem 167

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

177 177 108 0 0 0 0 0 -1

N.S.

1 1.00 0.61 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.126 0.152 0.596 0.000 0.000 0.000 0.000 0.000

Problem 168

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

79 79 259 0 0 0 0 0 -1

N.S.

1 1.00 3.28 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.030 1.361 0.846 0.000 0.000 0.000 0.000 0.000

Problem 169

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

99 99 126 0 0 0 0 0 -1

N.S.

1 1.00 1.27 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.058 2.148 0.451 0.000 0.000 0.000 0.000 0.000

Problem 170

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

52 52 83 0 0 0 0 0 -1

N.S.

1 1.00 1.60 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.017 0.379 0.848 0.000 0.000 0.000 0.000 0.000

Problem 171

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

108 108 125 0 0 0 0 0 -1

N.S.

1 1.00 1.16 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.057 0.488 0.836 0.000 0.000 0.000 0.000 0.000

Problem 172

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

162 162 142 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 0.088 0.505 0.847 0.000 0.000 0.000 0.000 0.000

Problem 173

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

194 194 176 0 0 0 0 0 -1

N.S.

1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.109 2.036 0.851 0.000 0.000 0.000 0.000 0.000

Problem 174

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

61 61 171 0 0 0 0 0 -1

N.S.

1 1.00 2.80 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.022 1.110 0.842 0.000 0.000 0.000 0.000 0.000

Problem 175

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

61 61 171 0 0 0 0 0 -1

N.S.

1 1.00 2.80 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.025 1.253 0.848 0.000 0.000 0.000 0.000 0.000

Problem 176

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

61 61 171 0 0 0 0 0 -1

N.S.

1 1.00 2.80 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.025 1.320 0.858 0.000 0.000 0.000 0.000 0.000

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 198 0 0 0 0 0 -1

N.S.

1 1.00 3.41 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.047 4.872 0.906 0.000 0.000 0.000 0.000 0.000

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 207 0 0 0 0 0 -1

N.S.

1 1.00 3.34 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.044 3.512 0.944 0.000 0.000 0.000 0.000 0.000

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 193 0 0 0 0 0 -1

N.S.

1 1.00 3.57 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.039 4.748 0.960 0.000 0.000 0.000 0.000 0.000

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 198 0 0 0 0 0 -1

N.S.

1 1.00 3.81 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.037 6.162 0.659 0.000 0.000 0.000 0.000 0.000

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 40 48 24 76 0 74 34

N.S.

1 1.00 1.60 1.92 0.96 3.04 0.00 2.96 1.36

time (sec)

N/A 0.015 0.046 2.287 0.264 0.374 0.000 0.487 1.193

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 197 0 0 0 0 0 -1

N.S.

1 1.00 3.40 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.043 2.607 0.559 0.000 0.000 0.000 0.000 0.000

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 191 0 0 0 0 0 -1

N.S.

1 1.00 3.47 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.043 2.594 0.545 0.000 0.000 0.000 0.000 0.000

Problem 184

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

132 132 155 0 0 0 0 0 -1

N.S.

1 1.00 1.17 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.119 4.925 0.548 0.000 0.000 0.000 0.000 0.000

Problem 185

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

136 136 165 0 0 0 0 0 -1

N.S.

1 1.00 1.21 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.122 3.094 0.552 0.000 0.000 0.000 0.000 0.000

Problem 186

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

130 130 151 0 0 0 0 0 -1

N.S.

1 1.00 1.16 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.112 4.500 0.569 0.000 0.000 0.000 0.000 0.000

Problem 187

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

126 126 160 0 0 0 0 0 -1

N.S.

1 1.00 1.27 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.108 5.695 0.543 0.000 0.000 0.000 0.000 0.000

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 49 63 37 72 0 37 34

N.S.

1 1.00 1.75 2.25 1.32 2.57 0.00 1.32 1.21

time (sec)

N/A 0.021 0.082 2.317 0.324 0.347 0.000 0.479 1.189

Problem 189

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

134 134 158 0 0 0 0 0 -1

N.S.

1 1.00 1.18 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.119 2.463 0.572 0.000 0.000 0.000 0.000 0.000

Problem 190

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

135 135 156 0 0 0 0 0 -1

N.S.

1 1.00 1.16 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.120 2.432 0.424 0.000 0.000 0.000 0.000 0.000

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 52 56 330 572 0 127 95

N.S.

1 1.00 1.21 1.30 7.67 13.30 0.00 2.95 2.21

time (sec)

N/A 0.030 0.157 2.381 0.330 0.350 0.000 0.468 1.225

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 44 69 499 171 0 67 163

N.S.

1 1.00 0.98 1.53 11.09 3.80 0.00 1.49 3.62

time (sec)

N/A 0.030 0.085 2.357 0.352 0.360 0.000 0.498 1.208

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 67 71 855 1576 0 161 229

N.S.

1 1.00 1.02 1.08 12.95 23.88 0.00 2.44 3.47

time (sec)

N/A 0.043 0.202 2.474 0.399 0.363 0.000 0.490 1.199

Problem 194

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

87 87 158 0 0 0 0 0 -1

N.S.

1 1.00 1.82 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.053 9.101 0.574 0.000 0.000 0.000 0.000 0.000

Problem 195

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

168 168 312 0 0 0 0 0 -1

N.S.

1 1.00 1.86 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.147 9.901 0.432 0.000 0.000 0.000 0.000 0.000

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

306 306 600 0 0 0 0 0 -1

N.S.

1 1.00 1.96 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.327 13.208 1.396 0.000 0.000 0.000 0.000 0.000

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

115 115 387 0 0 0 0 0 -1

N.S.

1 1.00 3.37 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.086 2.458 1.181 0.000 0.000 0.000 0.000 0.000

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

135 135 174 0 0 0 0 0 -1

N.S.

1 1.00 1.29 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.106 3.470 1.055 0.000 0.000 0.000 0.000 0.000

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 64 76 0 626 0 0 65

N.S.

1 1.00 0.88 1.04 0.00 8.58 0.00 0.00 0.89

time (sec)

N/A 0.039 0.208 5.122 0.000 0.378 0.000 0.000 2.241

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 57 74 0 334 0 0 51

N.S.

1 1.00 0.81 1.06 0.00 4.77 0.00 0.00 0.73

time (sec)

N/A 0.035 0.108 4.647 0.000 0.374 0.000 0.000 1.860

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