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Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
  2.1.8 Mupad
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 78, 81, 82, 83, 84, 85, 88, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 117, 124, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 144, 151, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166 }

B grade: { 75, 77, 79, 86, 87, 114, 116, 118, 120, 121, 122, 123, 141, 143, 145, 152 }

C grade: { 74, 76, 80, 113, 115, 119, 140, 142, 146 }

F grade: { 89, 90, 125, 126, 147, 148, 149, 150, 153 }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 160, 161, 162, 163, 164, 165, 166 }

B grade: { 83 }

C grade: { 9, 11, 66, 82, 102, 158, 159 }

F grade: { 81, 84, 85 }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 18, 21, 23, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 80, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 119, 127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 145, 146, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164 }

B grade: { 7, 14, 16, 20, 22, 24, 26, 28, 29, 32, 34, 87, 123, 136, 141, 143, 147, 149, 152, 153, 157, 166 }

C grade: { 19, 25, 27, 30, 31, 33, 64, 86, 100, 122, 144, 148, 150, 151, 165 }

F grade: { 56, 75, 78, 79, 81, 82, 83, 84, 85, 88, 89, 90, 93, 114, 117, 118, 120, 121, 124, 125, 126, 129 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 80, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 119, 127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164 }

B grade: { 157, 165 }

C grade: { }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 56, 64, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 100, 114, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 129, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 166 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 74, 76, 80, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 105, 107, 109, 111, 113, 115, 119, 127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164 }

B grade: { 68, 69, 70, 71, 72, 73, 104, 106, 108, 110, 112, 166 }

C grade: { }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 56, 64, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 100, 114, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 129, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 157, 165 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 80, 97, 98, 99, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 115, 119, 132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 161, 162, 163 }

B grade: { 158, 159, 160, 164 }

C grade: { }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 56, 59, 64, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 100, 103, 113, 114, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 157, 165, 166 }

2.1.7 Giac

A grade: { 6, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 47, 48, 49, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 67, 68, 69, 70, 71, 72, 73, 74, 76, 91, 92, 94, 95, 96, 97, 98, 99, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 127, 128, 130, 131, 132, 133, 135, 137, 138, 139, 146, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164 }

B grade: { 66, 102, 134, 136 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 43, 46, 50, 51, 52, 56, 64, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 100, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 140, 141, 142, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 157, 165, 166 }

2.1.8 Mupad

A grade: { 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 57, 58, 59, 91, 92, 94, 95, 127, 128, 130, 131 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 53, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 80, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 119, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 146, 154, 155, 156, 157, 158, 159, 160, 162, 163, 164, 165 }

C grade: { }

F grade: { 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 56, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 114, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 129, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 161, 166 }

2.2 Detailed conclusion table per each integral for all CAS systems

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 normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)

Problem 1 Optimal Rubi Mathematica 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 53 57 54 63 0 52
normalized size 1 1.00 1.08 0.90 0.97 0.92 1.07 0.00 0.88
time (sec) N/A 0.032 0.003 0.008 0.431 0.455 1.425 0.000 0.442
Problem 2 Optimal Rubi Mathematica 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 52 56 59 60 0 54
normalized size 1 1.00 1.09 0.93 1.00 1.05 1.07 0.00 0.96
time (sec) N/A 0.042 0.014 0.007 0.330 0.448 1.042 0.000 0.417
Problem 3 Optimal Rubi Mathematica 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 44 48 47 53 0 44
normalized size 1 1.00 1.10 0.92 1.00 0.98 1.10 0.00 0.92
time (sec) N/A 0.027 0.003 0.006 0.470 0.467 0.817 0.000 0.210
Problem 4 Optimal Rubi Mathematica 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 43 46 49 49 0 42
normalized size 1 1.00 1.11 0.96 1.02 1.09 1.09 0.00 0.93
time (sec) N/A 0.032 0.009 0.006 0.321 0.435 0.577 0.000 0.370
Problem 5 Optimal Rubi Mathematica 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 35 37 34 42 0 34
normalized size 1 1.00 1.14 0.95 1.00 0.92 1.14 0.00 0.92
time (sec) N/A 0.016 0.002 0.006 0.469 0.420 0.423 0.000 0.123
Problem 6 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.00 0.97 1.07 1.14 0.90 1.07 0.93
time (sec) N/A 0.011 0.003 0.004 0.324 0.422 0.205 2.958 0.098
Problem 7 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.00 2.11 0.00 0.00 0.00 0.00 0.80
time (sec) N/A 0.029 0.003 0.029 0.000 0.414 0.000 0.000 0.287
Problem 8 Optimal Rubi Mathematica 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 39 39 37 37 0 36
normalized size 1 1.00 1.09 1.11 1.11 1.06 1.06 0.00 1.03
time (sec) N/A 0.023 0.003 0.011 0.327 0.425 0.631 0.000 0.319
Problem 9 Optimal Rubi Mathematica 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 35 31 26 37 0 42
normalized size 1 1.00 1.24 0.95 0.84 0.70 1.00 0.00 1.14
time (sec) N/A 0.020 0.003 0.009 0.435 0.441 0.528 0.000 0.332
Problem 10 Optimal Rubi Mathematica 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 51 51 50 61 0 46
normalized size 1 1.00 1.02 0.96 0.96 0.94 1.15 0.00 0.87
time (sec) N/A 0.033 0.016 0.013 0.340 0.434 1.059 0.000 0.119
Problem 11 Optimal Rubi Mathematica 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 44 46 41 46 0 42
normalized size 1 1.00 0.96 0.92 0.96 0.85 0.96 0.00 0.88
time (sec) N/A 0.025 0.003 0.009 0.427 0.423 0.827 0.000 0.363
Problem 12 Optimal Rubi Mathematica 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 60 62 59 71 0 56
normalized size 1 1.00 1.00 0.94 0.97 0.92 1.11 0.00 0.88
time (sec) N/A 0.038 0.018 0.011 0.335 0.426 1.673 0.000 0.371
Problem 13 Optimal Rubi Mathematica 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
normalized size 1 1.00 0.96 1.19 1.13 1.06 1.38 0.00 1.19
time (sec) N/A 0.310 0.139 0.015 0.458 0.428 2.393 0.000 0.667
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 170 170 169 334 0 0 0 0 -1
normalized size 1 1.00 0.99 1.96 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.289 0.514 0.095 0.000 0.422 0.000 0.000 0.000
Problem 15 Optimal Rubi Mathematica 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
normalized size 1 1.00 0.99 1.21 1.21 1.08 1.38 0.00 1.20
time (sec) N/A 0.209 0.085 0.014 0.432 0.432 1.444 0.000 0.316
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 138 138 131 298 0 0 0 0 -1
normalized size 1 1.00 0.95 2.16 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.194 0.295 0.016 0.000 0.437 0.000 0.000 0.000
Problem 17 Optimal Rubi Mathematica 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
normalized size 1 1.00 0.99 1.28 1.37 1.09 1.41 0.00 1.16
time (sec) N/A 0.106 0.069 0.022 0.474 0.430 0.734 0.000 0.410
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 83 83 90 128 0 0 0 0 -1
normalized size 1 1.00 1.08 1.54 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.098 0.081 0.192 0.000 0.429 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica 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 132 132 144 1128 0 0 0 0 -1
normalized size 1 1.00 1.09 8.55 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.250 0.078 0.513 0.000 0.436 0.000 0.000 0.000
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 82 82 102 323 0 0 0 0 -1
normalized size 1 1.00 1.24 3.94 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.147 0.149 0.018 0.000 0.452 0.000 0.000 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 90 110 98 94 119 0 140
normalized size 1 1.00 1.14 1.39 1.24 1.19 1.51 0.00 1.77
time (sec) N/A 0.128 0.066 0.013 0.442 0.511 1.015 0.000 2.310
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 140 140 153 399 0 0 0 0 -1
normalized size 1 1.00 1.09 2.85 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.230 0.389 0.019 0.000 0.459 0.000 0.000 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 128 147 152 135 170 0 171
normalized size 1 1.00 1.10 1.27 1.31 1.16 1.47 0.00 1.47
time (sec) N/A 0.219 0.093 0.018 0.419 0.453 1.778 0.000 2.257
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 255 255 291 528 0 0 0 0 -1
normalized size 1 1.00 1.14 2.07 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.948 0.829 0.023 0.000 0.427 0.000 0.000 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 271 271 396 3053 0 0 0 0 -1
normalized size 1 1.00 1.46 11.27 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.756 0.900 5.524 0.000 0.425 0.000 0.000 0.000
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 194 194 225 445 0 0 0 0 -1
normalized size 1 1.00 1.16 2.29 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.545 0.559 0.019 0.000 0.469 0.000 0.000 0.000
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 206 206 269 2020 0 0 0 0 -1
normalized size 1 1.00 1.31 9.81 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.434 0.618 2.526 0.000 0.416 0.000 0.000 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 131 131 152 352 0 0 0 0 -1
normalized size 1 1.00 1.16 2.69 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.239 0.303 0.018 0.000 0.425 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 119 119 192 270 0 0 0 0 -1
normalized size 1 1.00 1.61 2.27 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.209 0.098 0.227 0.000 0.428 0.000 0.000 0.000
Problem 30 Optimal Rubi Mathematica 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 206 206 212 2309 0 0 0 0 -1
normalized size 1 1.00 1.03 11.21 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.427 0.151 0.243 0.000 0.420 0.000 0.000 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-1) F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 116 116 214 2159 0 0 0 0 -1
normalized size 1 1.00 1.84 18.61 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.267 0.399 0.291 0.000 0.422 0.000 0.000 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 133 133 176 457 0 0 0 0 -1
normalized size 1 1.00 1.32 3.44 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.285 0.341 0.021 0.000 0.444 0.000 0.000 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-1) F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 213 213 321 5974 0 0 0 0 -1
normalized size 1 1.00 1.51 28.05 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.476 0.881 3.190 0.000 0.421 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 198 198 265 550 0 0 0 0 -1
normalized size 1 1.00 1.34 2.78 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.601 0.724 0.024 0.000 0.429 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.09
time (sec) N/A 0.008 0.652 0.466 0.000 0.418 0.000 0.000 0.000
Problem 36 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.11
time (sec) N/A 0.003 0.012 0.269 0.000 0.416 0.000 0.000 0.000
Problem 37 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.015 0.448 0.321 0.000 0.420 0.000 0.000 0.000
Problem 38 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.09
time (sec) N/A 0.008 0.619 0.708 0.000 0.403 0.000 0.000 0.000
Problem 39 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.11
time (sec) N/A 0.003 0.914 0.264 0.000 0.417 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.013 1.063 0.382 0.000 0.404 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.007 2.107 0.966 0.000 0.000 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.09
time (sec) N/A 0.003 1.928 0.488 0.000 0.000 0.000 0.000 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.013 1.349 0.999 0.000 0.000 0.000 0.000 0.000
Problem 44 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.007 1.022 0.952 0.000 0.000 0.000 0.000 0.000
Problem 45 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.09
time (sec) N/A 0.003 2.371 0.448 0.000 0.000 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.013 1.172 1.136 0.000 0.000 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.007 1.340 0.977 0.000 0.000 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.09
time (sec) N/A 0.003 0.019 0.452 0.000 0.000 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.014 1.218 0.716 0.000 0.000 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 13 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.007 1.582 0.977 0.000 0.000 0.000 0.000 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 11 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.09
time (sec) N/A 0.003 2.717 0.508 0.000 0.000 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.013 2.951 1.138 0.000 0.000 0.000 0.000 0.000
Problem 53 Optimal Rubi Mathematica 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 74 86 118 104 86 49
normalized size 1 1.00 0.92 0.63 0.74 1.01 0.89 0.74 0.42
time (sec) N/A 0.067 0.028 0.025 0.411 0.476 3.224 0.995 0.321
Problem 54 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.022 4.115 3.371 0.000 0.451 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.021 2.655 2.928 0.000 0.430 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica 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
normalized size 1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.031 0.033 2.771 0.000 0.426 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.024 0.280 1.127 0.000 0.430 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.005 0.461 0.696 0.000 0.435 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica 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 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.021 0.360 1.359 0.000 0.444 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.09 0.93 1.00 0.94 1.07 1.11 0.91
time (sec) N/A 0.035 0.008 0.031 0.413 0.426 65.098 0.164 0.357
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 52 45 48 51 80 47 44
normalized size 1 1.00 1.11 0.96 1.02 1.09 1.70 1.00 0.94
time (sec) N/A 0.031 0.013 0.035 0.307 0.434 46.372 0.171 0.349
Problem 62 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.12 0.95 1.00 0.88 1.12 1.00 0.93
time (sec) N/A 0.027 0.006 0.029 0.411 0.429 23.237 0.200 0.327
Problem 63 Optimal Rubi Mathematica 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 41 36 38 39 66 40 35
normalized size 1 1.00 1.14 1.00 1.06 1.08 1.83 1.11 0.97
time (sec) N/A 0.014 0.007 0.023 0.308 0.417 13.502 0.151 0.314
Problem 64 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.00 1.62 0.00 0.00 0.00 0.00 0.82
time (sec) N/A 0.045 0.005 0.109 0.000 0.409 0.000 0.000 0.327
Problem 65 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.13 1.00 1.05 1.10 1.92 1.54 0.97
time (sec) N/A 0.024 0.007 0.030 0.317 0.437 30.285 0.174 0.343
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 48 39 35 30 42 74 41
normalized size 1 1.00 1.17 0.95 0.85 0.73 1.02 1.80 1.00
time (sec) N/A 0.025 0.007 0.032 0.418 0.403 24.120 2.810 0.356
Problem 67 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.09 0.93 0.96 0.98 1.67 1.25 0.91
time (sec) N/A 0.032 0.013 0.033 0.324 0.438 81.386 0.142 0.365
Problem 68 Optimal Rubi Mathematica 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 161 161 179 140 147 372 184 169 64
normalized size 1 1.00 1.11 0.87 0.91 2.31 1.14 1.05 0.40
time (sec) N/A 0.113 0.064 0.039 0.445 0.462 33.026 2.852 0.363
Problem 69 Optimal Rubi Mathematica 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 159 159 177 138 145 337 173 165 62
normalized size 1 1.00 1.11 0.87 0.91 2.12 1.09 1.04 0.39
time (sec) N/A 0.101 0.037 0.027 0.433 0.442 17.684 3.075 0.392
Problem 70 Optimal Rubi Mathematica 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 140 140 107 125 127 319 930 149 49
normalized size 1 1.00 0.76 0.89 0.91 2.28 6.64 1.06 0.35
time (sec) N/A 0.105 0.046 0.029 0.428 0.443 10.228 0.180 0.390
Problem 71 Optimal Rubi Mathematica 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 143 143 158 125 132 322 151 138 55
normalized size 1 1.00 1.10 0.87 0.92 2.25 1.06 0.97 0.38
time (sec) N/A 0.086 0.046 0.026 0.421 0.448 20.443 0.209 0.201
Problem 72 Optimal Rubi Mathematica 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 159 159 177 132 142 389 590 159 63
normalized size 1 1.00 1.11 0.83 0.89 2.45 3.71 1.00 0.40
time (sec) N/A 0.104 0.057 0.033 0.413 0.449 38.521 5.357 0.428
Problem 73 Optimal Rubi Mathematica 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 159 159 177 138 138 350 185 150 63
normalized size 1 1.00 1.11 0.87 0.87 2.20 1.16 0.94 0.40
time (sec) N/A 0.103 0.054 0.032 0.414 0.467 63.234 0.245 0.452
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A A A A A A B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 124 731 121 151 169 137 199 145 150
normalized size 1 5.90 0.98 1.22 1.36 1.10 1.60 1.17 1.21
time (sec) N/A 1.627 0.125 0.051 0.490 0.449 98.996 0.177 1.016
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F(-2) F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 154 647 141 0 0 0 0 0 -1
normalized size 1 4.20 0.92 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.366 0.335 180.000 0.000 0.422 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A A A A A A B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 90 612 85 113 126 100 155 100 112
normalized size 1 6.80 0.94 1.26 1.40 1.11 1.72 1.11 1.24
time (sec) N/A 1.042 0.070 0.035 0.488 0.445 34.914 1.333 0.683
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A A F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 101 255 107 146 0 0 0 0 -1
normalized size 1 2.52 1.06 1.45 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.554 0.074 0.206 0.000 0.429 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.321 0.112 0.356 0.000 0.424 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 97 290 127 0 0 0 0 0 -1
normalized size 1 2.99 1.31 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.653 0.157 0.595 0.000 0.427 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A A A A A F B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 87 419 98 118 110 115 167 0 152
normalized size 1 4.82 1.13 1.36 1.26 1.32 1.92 0.00 1.75
time (sec) N/A 1.136 0.083 0.056 0.519 0.440 52.408 0.000 0.613
Problem 81 Optimal Rubi Mathematica 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
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.602 5.175 0.357 0.000 0.438 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica 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 1191 1191 5504 0 0 0 0 0 -1
normalized size 1 1.00 4.62 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.778 31.540 0.307 0.000 0.425 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica 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 5535 0 0 0 0 0 -1
normalized size 1 1.00 4.76 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.622 30.755 0.326 0.000 0.439 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica 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
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.227 2.942 0.333 0.000 0.417 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica 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
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.427 2.891 0.346 0.000 0.430 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A C F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 149 951 170 690 0 0 0 0 -1
normalized size 1 6.38 1.14 4.63 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 4.736 0.172 1.560 0.000 0.416 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 144 545 224 306 0 0 0 0 -1
normalized size 1 3.78 1.56 2.12 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 2.545 0.126 0.243 0.000 0.421 0.000 0.000 0.000
Problem 88 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.07 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.529 0.207 0.403 0.000 0.417 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 138 0 239 0 0 0 0 0 -1
normalized size 1 0.00 1.73 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.831 0.461 0.559 0.000 0.431 0.000 0.000 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 149 0 196 0 0 0 0 0 -1
normalized size 1 0.00 1.32 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.659 0.349 1.182 0.000 0.423 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.023 1.962 0.265 0.000 0.434 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.024 1.284 0.250 0.000 0.424 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica 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 75 75 65 0 0 0 0 0 -1
normalized size 1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.041 0.066 0.241 0.000 0.435 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.027 0.335 0.145 0.000 0.408 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.026 0.357 0.189 0.000 0.430 0.000 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 59 50 54 51 0 60 49
normalized size 1 1.00 1.09 0.93 1.00 0.94 0.00 1.11 0.91
time (sec) N/A 0.039 0.009 0.031 0.417 0.414 0.000 0.163 0.454
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 52 45 48 51 133 47 44
normalized size 1 1.00 1.11 0.96 1.02 1.09 2.83 1.00 0.94
time (sec) N/A 0.036 0.014 0.033 0.315 0.417 177.260 0.807 0.379
Problem 98 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.12 0.95 1.00 0.88 1.12 1.00 0.93
time (sec) N/A 0.029 0.006 0.028 0.413 0.424 89.853 0.169 0.405
Problem 99 Optimal Rubi Mathematica 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 41 36 38 39 117 40 35
normalized size 1 1.00 1.14 1.00 1.06 1.08 3.25 1.11 0.97
time (sec) N/A 0.021 0.007 0.026 0.313 0.416 47.589 0.709 0.100
Problem 100 Optimal Rubi Mathematica 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
normalized size 1 1.00 1.00 1.62 0.00 0.00 0.00 0.00 0.82
time (sec) N/A 0.050 0.005 0.103 0.000 0.426 0.000 0.000 0.351
Problem 101 Optimal Rubi Mathematica 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 43 126 60 38
normalized size 1 1.00 1.13 1.00 1.05 1.10 3.23 1.54 0.97
time (sec) N/A 0.025 0.007 0.031 0.318 0.469 96.086 2.010 0.377
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 48 39 35 30 42 74 41
normalized size 1 1.00 1.17 0.95 0.85 0.73 1.02 1.80 1.00
time (sec) N/A 0.027 0.007 0.037 0.424 0.410 88.005 0.170 0.386
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 60 51 53 54 0 69 50
normalized size 1 1.00 1.09 0.93 0.96 0.98 0.00 1.25 0.91
time (sec) N/A 0.035 0.014 0.034 0.326 0.444 0.000 0.156 0.401
Problem 104 Optimal Rubi Mathematica 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 174 174 179 165 148 399 311 167 114
normalized size 1 1.00 1.03 0.95 0.85 2.29 1.79 0.96 0.66
time (sec) N/A 0.325 0.057 0.156 0.428 0.459 58.103 3.785 1.164
Problem 105 Optimal Rubi Mathematica 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 101 101 131 98 92 234 898 95 91
normalized size 1 1.00 1.30 0.97 0.91 2.32 8.89 0.94 0.90
time (sec) N/A 0.098 0.045 0.026 0.421 0.459 31.243 0.160 2.295
Problem 106 Optimal Rubi Mathematica 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 165 165 170 148 137 505 301 137 107
normalized size 1 1.00 1.03 0.90 0.83 3.06 1.82 0.83 0.65
time (sec) N/A 0.294 0.052 0.108 0.416 0.480 73.747 0.179 0.909
Problem 107 Optimal Rubi Mathematica 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 115 115 183 105 102 121 352 108 118
normalized size 1 1.00 1.59 0.91 0.89 1.05 3.06 0.94 1.03
time (sec) N/A 0.091 0.052 0.038 0.413 0.430 144.506 4.327 2.567
Problem 108 Optimal Rubi Mathematica 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 176 176 181 167 152 439 320 171 122
normalized size 1 1.00 1.03 0.95 0.86 2.49 1.82 0.97 0.69
time (sec) N/A 0.431 0.086 0.108 0.423 0.455 149.056 2.989 1.002
Problem 109 Optimal Rubi Mathematica 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 117 117 185 113 106 137 359 119 106
normalized size 1 1.00 1.58 0.97 0.91 1.17 3.07 1.02 0.91
time (sec) N/A 0.096 0.029 0.030 0.424 0.448 71.605 3.953 1.936
Problem 110 Optimal Rubi Mathematica 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 165 165 170 154 137 408 303 157 113
normalized size 1 1.00 1.03 0.93 0.83 2.47 1.84 0.95 0.68
time (sec) N/A 0.393 0.028 0.108 0.431 0.467 39.660 2.110 0.689
Problem 111 Optimal Rubi Mathematica 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 104 104 170 104 98 90 328 91 99
normalized size 1 1.00 1.63 1.00 0.94 0.87 3.15 0.88 0.95
time (sec) N/A 0.085 0.040 0.026 0.421 0.439 58.274 3.822 1.828
Problem 112 Optimal Rubi Mathematica 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 174 174 179 159 147 595 320 161 120
normalized size 1 1.00 1.03 0.91 0.84 3.42 1.84 0.93 0.69
time (sec) N/A 0.413 0.054 0.105 0.420 0.516 109.838 2.985 0.706
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A A A A F(-1) A B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 124 731 121 151 169 129 0 145 150
normalized size 1 5.90 0.98 1.22 1.36 1.04 0.00 1.17 1.21
time (sec) N/A 1.655 0.102 0.047 0.518 0.471 0.000 0.189 1.140
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F(-2) F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 154 647 141 0 0 0 0 0 -1
normalized size 1 4.20 0.92 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.394 0.314 180.000 0.000 0.427 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A A A A A A B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 90 612 85 113 126 91 209 100 112
normalized size 1 6.80 0.94 1.26 1.40 1.01 2.32 1.11 1.24
time (sec) N/A 1.052 0.068 0.043 0.515 0.445 122.135 1.601 0.724
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A A F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 104 255 107 148 0 0 0 0 -1
normalized size 1 2.45 1.03 1.42 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.644 0.074 0.234 0.000 0.419 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica 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 154 154 167 0 0 0 0 0 -1
normalized size 1 1.00 1.08 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.316 0.124 0.400 0.000 0.416 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 100 290 125 0 0 0 0 0 -1
normalized size 1 2.90 1.25 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.661 0.168 0.592 0.000 0.442 0.000 0.000 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A A A A A F B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 87 419 98 118 110 102 223 0 152
normalized size 1 4.82 1.13 1.36 1.26 1.17 2.56 0.00 1.75
time (sec) N/A 1.122 0.083 0.045 0.540 0.461 173.366 0.000 0.691
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 154 536 167 0 0 0 0 0 -1
normalized size 1 3.48 1.08 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.450 0.412 0.418 0.000 0.433 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A F F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 240 1867 346 0 0 0 0 0 -1
normalized size 1 7.78 1.44 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 7.034 0.562 0.411 0.000 0.426 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A C F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 147 951 170 867 0 0 0 0 -1
normalized size 1 6.47 1.16 5.90 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 4.733 0.176 1.776 0.000 0.445 0.000 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 139 545 224 303 0 0 0 0 -1
normalized size 1 3.92 1.61 2.18 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 2.702 0.100 0.244 0.000 0.428 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica 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 232 232 248 0 0 0 0 0 -1
normalized size 1 1.00 1.07 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.523 0.217 0.394 0.000 0.418 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 133 0 240 0 0 0 0 0 -1
normalized size 1 0.00 1.80 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.860 0.424 0.570 0.000 0.451 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 146 0 196 0 0 0 0 0 -1
normalized size 1 0.00 1.34 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.670 0.352 0.885 0.000 0.445 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.024 1.982 0.268 0.000 0.436 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.024 1.298 0.243 0.000 0.438 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica 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 75 75 65 0 0 0 0 0 -1
normalized size 1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.042 0.067 0.227 0.000 0.435 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.027 0.341 0.151 0.000 0.408 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica 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
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.026 0.363 0.181 0.000 0.420 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica 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 50 50 55 46 45 41 46 84 45
normalized size 1 1.00 1.10 0.92 0.90 0.82 0.92 1.68 0.90
time (sec) N/A 0.031 0.011 0.042 0.416 0.401 0.495 4.012 0.411
Problem 133 Optimal Rubi Mathematica 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 55 43 40 41 69 40
normalized size 1 1.00 1.12 1.28 1.00 0.93 0.95 1.60 0.93
time (sec) N/A 0.030 0.008 0.047 0.435 0.416 0.368 1.998 0.352
Problem 134 Optimal Rubi Mathematica 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 39 39 44 37 36 31 36 74 36
normalized size 1 1.00 1.13 0.95 0.92 0.79 0.92 1.90 0.92
time (sec) N/A 0.017 0.008 0.037 0.416 0.416 0.289 0.182 0.344
Problem 135 Optimal Rubi Mathematica 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 27 38 27 25 22 46 25
normalized size 1 1.00 1.00 1.41 1.00 0.93 0.81 1.70 0.93
time (sec) N/A 0.012 0.003 0.036 0.318 0.420 0.178 1.759 0.303
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 39 94 0 0 0 74 32
normalized size 1 1.00 1.00 2.41 0.00 0.00 0.00 1.90 0.82
time (sec) N/A 0.045 0.006 0.052 0.000 0.433 0.000 3.960 0.338
Problem 137 Optimal Rubi Mathematica 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 34 34 37 36 38 41 36 39 43
normalized size 1 1.00 1.09 1.06 1.12 1.21 1.06 1.15 1.26
time (sec) N/A 0.019 0.012 0.024 0.322 0.429 0.646 0.167 0.344
Problem 138 Optimal Rubi Mathematica 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 42 37 44 67 50
normalized size 1 1.00 1.12 0.95 0.98 0.86 1.02 1.56 1.16
time (sec) N/A 0.024 0.011 0.033 0.415 0.440 0.851 1.796 0.384
Problem 139 Optimal Rubi Mathematica 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 45 54 55 60 51 56
normalized size 1 1.00 1.09 0.82 0.98 1.00 1.09 0.93 1.02
time (sec) N/A 0.036 0.010 0.033 0.314 0.433 1.095 0.204 0.369
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A A A A A F B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 122 862 111 157 134 125 144 0 140
normalized size 1 7.07 0.91 1.29 1.10 1.02 1.18 0.00 1.15
time (sec) N/A 1.791 0.101 0.056 0.431 0.434 0.814 0.000 0.473
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 152 787 152 445 0 0 0 0 -1
normalized size 1 5.18 1.00 2.93 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 1.490 0.355 0.128 0.000 0.426 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A A A A A F B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 82 663 73 116 104 88 97 0 98
normalized size 1 8.09 0.89 1.41 1.27 1.07 1.18 0.00 1.20
time (sec) N/A 1.126 0.058 0.051 0.425 0.422 0.445 0.000 0.404
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 83 478 105 357 0 0 0 0 -1
normalized size 1 5.76 1.27 4.30 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.440 0.115 0.104 0.000 1.103 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 148 148 148 1249 0 0 0 0 -1
normalized size 1 1.00 1.00 8.44 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.294 0.092 0.340 0.000 0.559 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A A F(-1) F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 96 259 107 147 0 0 0 0 -1
normalized size 1 2.70 1.11 1.53 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.528 0.120 0.207 0.000 0.435 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A A A A A A B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 84 836 99 110 120 109 117 140 143
normalized size 1 9.95 1.18 1.31 1.43 1.30 1.39 1.67 1.70
time (sec) N/A 1.294 0.076 0.046 0.429 0.468 1.044 0.232 2.749
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 214 0 253 608 0 0 0 0 -1
normalized size 1 0.00 1.18 2.84 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 4.629 0.653 0.127 0.000 0.434 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 229 0 330 6441 0 0 0 0 -1
normalized size 1 0.00 1.44 28.13 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.520 0.731 1.376 0.000 1.467 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 145 0 174 507 0 0 0 0 -1
normalized size 1 0.00 1.20 3.50 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 2.352 0.289 0.125 0.000 0.419 0.000 0.000 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A C F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 119 0 215 2363 0 0 0 0 -1
normalized size 1 0.00 1.81 19.86 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.739 0.271 0.352 0.000 0.408 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 230 230 219 2542 0 0 0 0 -1
normalized size 1 1.00 0.95 11.05 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.494 0.220 0.236 0.000 0.413 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A B F(-1) F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 136 551 189 306 0 0 0 0 -1
normalized size 1 4.05 1.39 2.25 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 2.359 0.189 0.253 0.000 0.521 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A B F(-1) F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 147 0 178 396 0 0 0 0 -1
normalized size 1 0.00 1.21 2.69 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 2.255 0.293 0.102 0.000 0.469 0.000 0.000 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 34 32 31 27 39 31 31
normalized size 1 1.00 0.67 0.63 0.61 0.53 0.76 0.61 0.61
time (sec) N/A 0.015 0.015 0.029 0.413 0.469 1.969 0.138 0.349
Problem 155 Optimal Rubi Mathematica 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 28 27 26 20 32 26 26
normalized size 1 1.00 0.67 0.64 0.62 0.48 0.76 0.62 0.62
time (sec) N/A 0.010 0.011 0.025 0.413 0.484 1.261 0.161 0.365
Problem 156 Optimal Rubi Mathematica 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 18 17 16 14 19 16 16
normalized size 1 1.00 0.82 0.77 0.73 0.64 0.86 0.73 0.73
time (sec) N/A 0.006 0.007 0.023 0.414 0.412 1.147 0.350 0.074
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 61 35 0 0 0 24
normalized size 1 1.00 1.00 1.97 1.13 0.00 0.00 0.00 0.77
time (sec) N/A 0.035 0.005 0.040 0.418 0.528 0.000 0.000 0.302
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 30 22 21 17 94 21 21
normalized size 1 1.00 1.11 0.81 0.78 0.63 3.48 0.78 0.78
time (sec) N/A 0.012 0.010 0.031 0.411 0.434 1.917 0.303 0.348
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 34 27 26 26 160 26 24
normalized size 1 1.00 0.81 0.64 0.62 0.62 3.81 0.62 0.57
time (sec) N/A 0.014 0.012 0.030 0.408 0.459 4.919 0.165 0.353
Problem 160 Optimal Rubi Mathematica 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 30 25 24 24 85 24 24
normalized size 1 1.00 0.83 0.69 0.67 0.67 2.36 0.67 0.67
time (sec) N/A 0.015 0.016 0.025 0.306 0.481 4.793 0.175 0.351
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 25 20 19 19 24 19 -1
normalized size 1 1.00 0.86 0.69 0.66 0.66 0.83 0.66 -0.03
time (sec) N/A 0.012 0.011 0.031 0.308 0.468 1.239 0.177 0.000
Problem 162 Optimal Rubi Mathematica 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 20 20 20 17 16 16 17 16 16
normalized size 1 1.00 1.00 0.85 0.80 0.80 0.85 0.80 0.80
time (sec) N/A 0.008 0.008 0.025 0.307 0.437 0.325 0.179 0.346
Problem 163 Optimal Rubi Mathematica 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 18 26 20 18 22
normalized size 1 1.00 1.00 0.86 0.82 1.18 0.91 0.82 1.00
time (sec) N/A 0.009 0.012 0.036 0.313 0.431 1.155 0.174 0.358
Problem 164 Optimal Rubi Mathematica 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 37 37 31 26 25 33 143 28 27
normalized size 1 1.00 0.84 0.70 0.68 0.89 3.86 0.76 0.73
time (sec) N/A 0.014 0.020 0.033 0.310 0.479 4.897 0.169 0.354
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 33 57 50 0 0 0 25
normalized size 1 1.00 1.00 1.73 1.52 0.00 0.00 0.00 0.76
time (sec) N/A 0.036 0.007 0.091 0.424 0.451 0.000 0.000 0.336
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 32 94 0 63 0 0 -1
normalized size 1 1.00 0.82 2.41 0.00 1.62 0.00 0.00 -0.03
time (sec) N/A 0.036 0.014 0.046 0.000 0.473 0.000 0.000 0.000

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [142] had the largest ratio of [2.286]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 4 3 1.00 12 0.250
2 A 4 3 1.00 12 0.250
3 A 4 3 1.00 12 0.250
4 A 4 3 1.00 12 0.250
5 A 3 3 1.00 10 0.300
6 A 3 2 1.00 8 0.250
7 A 3 2 1.00 12 0.167
8 A 5 5 1.00 12 0.417
9 A 3 3 1.00 12 0.250
10 A 4 3 1.00 12 0.250
11 A 4 3 1.00 12 0.250
12 A 4 3 1.00 12 0.250
13 A 16 7 1.00 14 0.500
14 A 14 9 1.00 14 0.643
15 A 11 7 1.00 14 0.500
16 A 9 8 1.00 14 0.571
17 A 6 5 1.00 12 0.417
18 A 5 5 1.00 10 0.500
19 A 6 5 1.00 14 0.357
20 A 4 4 1.00 14 0.286
21 A 8 7 1.00 14 0.500
22 A 8 7 1.00 14 0.500
23 A 13 8 1.00 14 0.571
24 A 33 11 1.00 14 0.786
25 A 24 11 1.00 14 0.786
26 A 18 10 1.00 14 0.714
27 A 12 9 1.00 14 0.643
28 A 8 8 1.00 12 0.667
29 A 5 6 1.00 10 0.600
30 A 8 6 1.00 14 0.429
31 A 5 6 1.00 14 0.429
32 A 7 6 1.00 14 0.429
33 A 14 11 1.00 14 0.786
34 A 16 8 1.00 14 0.571
35 A 0 0 0.00 0 0.000
36 A 0 0 0.00 0 0.000
37 A 0 0 0.00 0 0.000
38 A 0 0 0.00 0 0.000
39 A 0 0 0.00 0 0.000
40 A 0 0 0.00 0 0.000
41 A 0 0 0.00 0 0.000
42 A 0 0 0.00 0 0.000
43 A 0 0 0.00 0 0.000
44 A 0 0 0.00 0 0.000
45 A 0 0 0.00 0 0.000
46 A 0 0 0.00 0 0.000
47 A 0 0 0.00 0 0.000
48 A 0 0 0.00 0 0.000
49 A 0 0 0.00 0 0.000
50 A 0 0 0.00 0 0.000
51 A 0 0 0.00 0 0.000
52 A 0 0 0.00 0 0.000
53 A 12 9 1.00 8 1.125
54 A 0 0 0.00 0 0.000
55 A 0 0 0.00 0 0.000
56 A 2 2 1.00 14 0.143
57 A 0 0 0.00 0 0.000
58 A 0 0 0.00 0 0.000
59 A 0 0 0.00 0 0.000
60 A 5 4 1.00 14 0.286
61 A 4 3 1.00 14 0.214
62 A 4 4 1.00 14 0.286
63 A 2 2 1.00 12 0.167
64 A 4 3 1.00 14 0.214
65 A 5 5 1.00 14 0.357
66 A 4 4 1.00 14 0.286
67 A 4 3 1.00 14 0.214
68 A 11 8 1.00 14 0.571
69 A 11 8 1.00 14 0.571
70 A 11 7 1.00 10 0.700
71 A 10 7 1.00 14 0.500
72 A 11 8 1.00 14 0.571
73 A 11 8 1.00 14 0.571
74 C 62 19 5.90 16 1.187
75 B 53 19 4.20 16 1.187
76 C 44 16 6.80 16 1.000
77 B 28 12 2.52 14 0.857
78 A 7 6 1.00 16 0.375
79 B 24 13 2.99 16 0.812
80 C 46 23 4.82 16 1.438
81 A 86 27 1.00 16 1.687
82 A 69 23 1.00 12 1.917
83 A 47 23 1.00 16 1.438
84 A 64 25 1.00 16 1.562
85 A 77 25 1.00 16 1.562
86 B 155 30 6.38 16 1.875
87 B 82 23 3.78 14 1.643
88 A 9 7 1.00 16 0.438
89 F 0 0 N/A 0 N/A
90 F 0 0 N/A 0 N/A
91 A 0 0 0.00 0 0.000
92 A 0 0 0.00 0 0.000
93 A 3 3 1.00 16 0.188
94 A 0 0 0.00 0 0.000
95 A 0 0 0.00 0 0.000
96 A 5 4 1.00 14 0.286
97 A 4 3 1.00 14 0.214
98 A 4 4 1.00 14 0.286
99 A 2 2 1.00 14 0.143
100 A 4 3 1.00 14 0.214
101 A 5 5 1.00 14 0.357
102 A 4 4 1.00 14 0.286
103 A 4 3 1.00 14 0.214
104 A 12 8 1.00 14 0.571
105 A 9 8 1.00 10 0.800
106 A 11 7 1.00 14 0.500
107 A 9 9 1.00 14 0.643
108 A 12 8 1.00 14 0.571
109 A 9 9 1.00 14 0.643
110 A 11 7 1.00 12 0.583
111 A 8 8 1.00 14 0.571
112 A 12 8 1.00 14 0.571
113 C 62 19 5.90 16 1.187
114 B 53 19 4.20 16 1.187
115 C 44 16 6.80 16 1.000
116 B 28 12 2.45 16 0.750
117 A 7 6 1.00 16 0.375
118 B 24 13 2.90 16 0.812
119 C 46 23 4.82 16 1.438
120 B 59 24 3.48 16 1.500
121 B 239 32 7.78 16 2.000
122 B 155 30 6.47 16 1.875
123 B 82 23 3.92 16 1.438
124 A 9 7 1.00 16 0.438
125 F 0 0 N/A 0 N/A
126 F 0 0 N/A 0 N/A
127 A 0 0 0.00 0 0.000
128 A 0 0 0.00 0 0.000
129 A 3 3 1.00 16 0.188
130 A 0 0 0.00 0 0.000
131 A 0 0 0.00 0 0.000
132 A 5 4 1.00 14 0.286
133 A 5 4 1.00 14 0.286
134 A 4 4 1.00 12 0.333
135 A 4 3 1.00 10 0.300
136 A 4 3 1.00 14 0.214
137 A 2 2 1.00 14 0.143
138 A 4 4 1.00 14 0.286
139 A 5 4 1.00 14 0.286
140 C 88 34 7.07 16 2.125
141 B 73 34 5.18 16 2.125
142 C 58 32 8.09 14 2.286
143 B 31 14 5.76 12 1.167
144 A 7 6 1.00 16 0.375
145 B 28 12 2.70 16 0.750
146 C 66 23 9.95 16 1.438
147 F 0 0 N/A 0 N/A
148 F 0 0 N/A 0 N/A
149 F 0 0 N/A 0 N/A
150 F 0 0 N/A 0 N/A
151 A 9 7 1.00 16 0.438
152 B 82 23 4.05 16 1.438
153 F 0 0 N/A 0 N/A
154 A 6 4 1.00 10 0.400
155 A 5 4 1.00 8 0.500
156 A 4 4 1.00 6 0.667
157 A 4 3 1.00 10 0.300
158 A 4 4 1.00 10 0.400
159 A 5 4 1.00 10 0.400
160 A 3 2 1.00 12 0.167
161 A 3 2 1.00 12 0.167
162 A 2 2 1.00 12 0.167
163 A 4 4 1.00 12 0.333
164 A 3 2 1.00 12 0.167
165 A 4 3 1.00 10 0.300
166 A 4 3 1.00 10 0.300

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