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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, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 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, 158, 159, 160, 161, 162, 163, 164, 165, 166 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

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, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 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, 149, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166 }

B grade: { 39, 41, 65, 148, 150 }

C grade: { }

F grade: { }

2.1.3 Maple

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, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 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, 75, 76, 77, 81, 82, 83, 87, 88, 89, 93, 94, 95, 96, 100, 101, 102, 106, 107, 108, 112, 113, 114, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 166 }

B grade: { }

C grade: { 130, 131 }

F grade: { 28, 30, 39, 41, 72, 73, 74, 78, 79, 80, 84, 85, 86, 90, 91, 92, 97, 98, 99, 103, 104, 105, 109, 110, 111, 117, 118, 127, 128, 129, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 16, 19, 21, 22, 24, 26, 33, 35, 37, 49, 50, 56, 57, 63, 64, 70, 71, 77, 83, 89, 95, 96, 102, 108, 114, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 132, 133, 134, 135, 136, 138, 139, 140, 141, 166 }

B grade: { }

C grade: { }

F grade: { 6, 13, 15, 17, 18, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 117, 118, 127, 128, 129, 130, 131, 137, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 21, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 56, 57, 63, 64, 70, 71, 115, 116, 119, 120, 121, 126, 132, 133, 134, 135, 136, 139, 140, 141, 166 }

B grade: { 7, 138 }

C grade: { }

F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 117, 118, 122, 123, 124, 125, 127, 128, 129, 130, 131, 137, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 56, 57, 63, 64, 70, 71, 77, 83, 89, 95, 96, 102, 108, 114, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 132, 133, 134, 135, 136, 166 }

B grade: { }

C grade: { }

F grade: { 6, 7, 8, 9, 10, 11, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 117, 118, 127, 128, 129, 130, 131, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

2.1.7 Giac

A grade: { 4, 5, 7, 8, 9, 10, 11, 16, 21, 26, 37, 49, 50, 56, 57, 63, 64, 70, 71, 77, 83, 89, 95, 96, 102, 108, 114, 115, 116, 119, 120, 121, 124, 125, 132, 135, 136, 166 }

B grade: { 19 }

C grade: { }

F grade: { 1, 2, 3, 6, 12, 13, 14, 15, 17, 18, 20, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 117, 118, 122, 123, 126, 127, 128, 129, 130, 131, 133, 134, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

2.1.8 Mupad

A grade: { 49, 50, 56, 57, 63, 64, 70, 71, 77, 83, 89, 95, 96, 102, 108, 114, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 132, 166 }

B grade: { 4, 5, 135, 136 }

C grade: { }

F grade: { 1, 2, 3, 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, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 117, 118, 127, 128, 129, 130, 131, 133, 134, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

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(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 93 55 52 68 61 76 0 -1
normalized size 1 1.00 0.59 0.56 0.73 0.66 0.82 0.00 -0.01
time (sec) N/A 0.037 0.035 0.017 0.655 0.648 2.115 0.000 0.000
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 77 77 71 99 77 59 68 0 -1
normalized size 1 1.00 0.92 1.29 1.00 0.77 0.88 0.00 -0.01
time (sec) N/A 0.030 0.070 0.015 0.692 0.562 1.037 0.000 0.000
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 46 43 48 52 54 0 -1
normalized size 1 1.00 0.71 0.66 0.74 0.80 0.83 0.00 -0.02
time (sec) N/A 0.023 0.025 0.010 0.316 0.592 0.497 0.000 0.000
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 49 49 61 77 56 48 44 70 39
normalized size 1 1.00 1.24 1.57 1.14 0.98 0.90 1.43 0.80
time (sec) N/A 0.015 0.027 0.013 0.676 0.562 0.226 0.344 0.040
Problem 5 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 30 30 30 29 25 37 26 35 26
normalized size 1 1.00 1.00 0.97 0.83 1.23 0.87 1.17 0.87
time (sec) N/A 0.006 0.018 0.002 0.621 0.526 0.149 0.205 0.318
Problem 6 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 43 43 42 66 0 0 0 0 -1
normalized size 1 1.00 0.98 1.53 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.059 0.037 0.076 0.000 0.627 0.000 0.000 0.000
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 57 51 22 65 0 36 -1
normalized size 1 1.00 1.78 1.59 0.69 2.03 0.00 1.12 -0.03
time (sec) N/A 0.017 0.029 0.015 0.867 0.504 0.000 0.434 0.000
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 35 40 27 38 0 50 -1
normalized size 1 1.00 0.92 1.05 0.71 1.00 0.00 1.32 -0.03
time (sec) N/A 0.013 0.008 0.012 0.873 0.531 0.000 0.419 0.000
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 78 73 43 90 0 62 -1
normalized size 1 1.00 1.20 1.12 0.66 1.38 0.00 0.95 -0.02
time (sec) N/A 0.027 0.081 0.014 0.859 0.801 0.000 0.442 0.000
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 45 50 48 48 0 77 -1
normalized size 1 1.00 0.68 0.76 0.73 0.73 0.00 1.17 -0.02
time (sec) N/A 0.024 0.024 0.011 0.524 0.535 0.000 0.366 0.000
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 93 104 95 63 101 0 85 -1
normalized size 1 1.00 1.12 1.02 0.68 1.09 0.00 0.91 -0.01
time (sec) N/A 0.041 0.050 0.014 0.875 0.677 0.000 0.372 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 80 112 99 99 122 0 -1
normalized size 1 1.00 0.61 0.85 0.75 0.75 0.92 0.00 -0.01
time (sec) N/A 0.490 0.123 0.049 0.685 0.581 3.419 0.000 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 77 92 0 92 99 0 -1
normalized size 1 1.00 0.73 0.87 0.00 0.87 0.93 0.00 -0.01
time (sec) N/A 0.440 0.077 0.036 0.000 0.567 2.058 0.000 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 64 78 70 82 85 0 -1
normalized size 1 1.00 0.71 0.87 0.78 0.91 0.94 0.00 -0.01
time (sec) N/A 0.311 0.104 0.037 0.690 0.624 0.974 0.000 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 58 58 0 73 60 0 -1
normalized size 1 1.00 0.91 0.91 0.00 1.14 0.94 0.00 -0.02
time (sec) N/A 0.251 0.056 0.031 0.000 0.588 0.487 0.000 0.000
Problem 16 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 39 39 39 39 32 59 39 62 -1
normalized size 1 1.00 1.00 1.00 0.82 1.51 1.00 1.59 -0.03
time (sec) N/A 0.127 0.021 0.043 0.602 0.583 0.210 0.326 0.000
Problem 17 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 62 62 63 98 0 0 0 0 -1
normalized size 1 1.00 1.02 1.58 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.093 0.033 0.056 0.000 0.604 0.000 0.000 0.000
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 60 60 92 137 0 0 0 0 -1
normalized size 1 1.00 1.53 2.28 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.209 0.268 0.163 0.000 0.741 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 48 73 39 65 0 98 -1
normalized size 1 1.00 1.00 1.52 0.81 1.35 0.00 2.04 -0.02
time (sec) N/A 0.192 0.021 0.230 0.680 0.643 0.000 0.787 0.000
Problem 20 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 114 114 144 177 0 0 0 0 -1
normalized size 1 1.00 1.26 1.55 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.392 0.265 0.314 0.000 0.657 0.000 0.000 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 69 109 72 85 0 147 -1
normalized size 1 1.00 0.73 1.15 0.76 0.89 0.00 1.55 -0.01
time (sec) N/A 0.365 0.090 0.291 0.618 0.615 0.000 0.493 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 231 231 130 190 165 151 206 0 -1
normalized size 1 1.00 0.56 0.82 0.71 0.65 0.89 0.00 -0.00
time (sec) N/A 0.771 0.126 0.059 0.694 0.753 6.062 0.000 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 143 150 0 142 170 0 -1
normalized size 1 1.00 0.78 0.82 0.00 0.78 0.93 0.00 -0.01
time (sec) N/A 0.666 0.151 0.043 0.000 0.750 3.959 0.000 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 103 128 116 124 138 0 -1
normalized size 1 1.00 0.66 0.83 0.75 0.80 0.89 0.00 -0.01
time (sec) N/A 0.474 0.097 0.042 0.674 0.628 2.042 0.000 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 113 88 0 112 102 0 -1
normalized size 1 1.00 1.06 0.82 0.00 1.05 0.95 0.00 -0.01
time (sec) N/A 0.381 0.090 0.035 0.000 0.479 0.983 0.000 0.000
Problem 26 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 68 68 68 61 57 90 63 98 -1
normalized size 1 1.00 1.00 0.90 0.84 1.32 0.93 1.44 -0.01
time (sec) N/A 0.183 0.027 0.061 0.313 0.592 0.480 0.391 0.000
Problem 27 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 87 87 82 132 0 0 0 0 -1
normalized size 1 1.00 0.94 1.52 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.105 0.055 0.089 0.000 0.807 0.000 0.000 0.000
Problem 28 Optimal Rubi Mathematica 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 104 104 128 0 0 0 0 0 -1
normalized size 1 1.00 1.23 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.310 0.182 0.201 0.000 0.570 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 98 98 92 113 0 0 0 0 -1
normalized size 1 1.00 0.94 1.15 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.317 0.869 0.263 0.000 0.551 0.000 0.000 0.000
Problem 30 Optimal Rubi Mathematica 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 183 183 201 0 0 0 0 0 -1
normalized size 1 1.00 1.10 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.577 0.578 0.398 0.000 0.583 0.000 0.000 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 174 174 220 180 0 0 0 0 -1
normalized size 1 1.00 1.26 1.03 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.578 0.673 0.354 0.000 0.679 0.000 0.000 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 306 306 175 256 0 208 275 0 -1
normalized size 1 1.00 0.57 0.84 0.00 0.68 0.90 0.00 -0.00
time (sec) N/A 2.193 0.163 0.057 0.000 0.598 16.788 0.000 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 274 274 158 228 201 189 248 0 -1
normalized size 1 1.00 0.58 0.83 0.73 0.69 0.91 0.00 -0.00
time (sec) N/A 1.628 0.138 0.050 0.701 0.579 9.975 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 214 214 143 180 0 176 197 0 -1
normalized size 1 1.00 0.67 0.84 0.00 0.82 0.92 0.00 -0.00
time (sec) N/A 1.314 0.124 0.049 0.000 0.559 6.453 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 182 182 122 152 143 154 165 0 -1
normalized size 1 1.00 0.67 0.84 0.79 0.85 0.91 0.00 -0.01
time (sec) N/A 0.881 0.123 0.043 0.546 0.497 3.569 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 120 120 104 104 0 138 110 0 -1
normalized size 1 1.00 0.87 0.87 0.00 1.15 0.92 0.00 -0.01
time (sec) N/A 0.603 0.081 0.037 0.000 0.539 2.053 0.000 0.000
Problem 37 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 77 77 77 71 73 112 70 125 -1
normalized size 1 1.00 1.00 0.92 0.95 1.45 0.91 1.62 -0.01
time (sec) N/A 0.298 0.031 0.061 0.316 0.579 0.948 0.440 0.000
Problem 38 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 103 103 103 165 0 0 0 0 -1
normalized size 1 1.00 1.00 1.60 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.120 0.035 0.085 0.000 0.671 0.000 0.000 0.000
Problem 39 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 150 150 478 0 0 0 0 0 -1
normalized size 1 1.00 3.19 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.335 0.701 0.193 0.000 0.502 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 115 115 112 149 0 0 0 0 -1
normalized size 1 1.00 0.97 1.30 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.358 1.159 0.245 0.000 0.598 0.000 0.000 0.000
Problem 41 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 268 268 595 0 0 0 0 0 -1
normalized size 1 1.00 2.22 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.802 3.406 0.401 0.000 0.742 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 40 40 0 0 0 0 -1
normalized size 1 1.00 0.73 0.73 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.096 0.101 0.108 0.000 0.604 0.000 0.000 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 33 33 0 0 0 0 -1
normalized size 1 1.00 0.77 0.77 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.084 0.088 0.104 0.000 0.496 0.000 0.000 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 31 31 0 0 0 0 -1
normalized size 1 1.00 0.76 0.76 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.080 0.081 0.031 0.000 0.539 0.000 0.000 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 24 24 0 0 0 0 -1
normalized size 1 1.00 0.83 0.83 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.066 0.068 0.031 0.000 0.649 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 20 22 0 0 0 0 -1
normalized size 1 1.00 0.74 0.81 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.064 0.059 0.031 0.000 0.560 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 13 0 0 0 0 -1
normalized size 1 1.00 1.00 0.93 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.037 0.025 0.028 0.000 0.480 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 10 0 0 0 0 -1
normalized size 1 1.00 1.00 1.11 0.00 0.00 0.00 0.00 -0.11
time (sec) N/A 0.017 0.025 0.024 0.000 0.635 0.000 0.000 0.000
Problem 49 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 0.014 0.218 0.116 0.000 0.782 0.000 0.000 0.000
Problem 50 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 0.014 0.462 0.194 0.000 0.574 0.000 0.000 0.000
Problem 51 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 73 73 101 83 0 0 0 0 -1
normalized size 1 1.00 1.38 1.14 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.064 0.226 0.108 0.000 0.527 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 61 61 58 54 0 0 0 0 -1
normalized size 1 1.00 0.95 0.89 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.050 0.255 0.085 0.000 0.558 0.000 0.000 0.000
Problem 53 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 59 59 58 59 0 0 0 0 -1
normalized size 1 1.00 0.98 1.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.047 0.251 0.036 0.000 0.432 0.000 0.000 0.000
Problem 54 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 42 42 44 28 0 0 0 0 -1
normalized size 1 1.00 1.05 0.67 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.025 0.256 0.029 0.000 0.596 0.000 0.000 0.000
Problem 55 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 39 39 60 33 0 0 0 0 -1
normalized size 1 1.00 1.54 0.85 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.184 0.122 0.028 0.000 0.560 0.000 0.000 0.000
Problem 56 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 4.742 0.097 0.000 0.647 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 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 0.014 8.690 0.196 0.000 0.509 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 107 123 0 0 0 0 -1
normalized size 1 1.00 1.05 1.21 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.645 0.147 0.108 0.000 0.724 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 75 82 0 0 0 0 -1
normalized size 1 1.00 0.86 0.94 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.598 0.182 0.082 0.000 0.555 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 69 84 0 0 0 0 -1
normalized size 1 1.00 0.81 0.99 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.504 0.158 0.034 0.000 0.557 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 67 43 0 0 0 0 -1
normalized size 1 1.00 0.99 0.63 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.393 0.055 0.029 0.000 0.499 0.000 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 55 45 0 0 0 0 -1
normalized size 1 1.00 1.00 0.82 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.188 0.047 0.030 0.000 0.552 0.000 0.000 0.000
Problem 63 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 0.014 0.725 0.117 0.000 0.703 0.000 0.000 0.000
Problem 64 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 2.383 0.195 0.000 0.455 0.000 0.000 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 170 170 356 175 0 0 0 0 -1
normalized size 1 1.00 2.09 1.03 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.617 0.396 0.115 0.000 0.539 0.000 0.000 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 155 155 188 114 0 0 0 0 -1
normalized size 1 1.00 1.21 0.74 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.588 0.418 0.082 0.000 0.683 0.000 0.000 0.000
Problem 67 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 153 153 183 121 0 0 0 0 -1
normalized size 1 1.00 1.20 0.79 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.676 0.396 0.039 0.000 0.606 0.000 0.000 0.000
Problem 68 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 105 105 131 60 0 0 0 0 -1
normalized size 1 1.00 1.25 0.57 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.396 0.322 0.098 0.000 0.599 0.000 0.000 0.000
Problem 69 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 86 86 114 67 0 0 0 0 -1
normalized size 1 1.00 1.33 0.78 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.378 0.212 0.033 0.000 0.529 0.000 0.000 0.000
Problem 70 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 0.014 10.408 0.120 0.000 0.505 0.000 0.000 0.000
Problem 71 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 12.481 0.202 0.000 0.576 0.000 0.000 0.000
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 182 182 162 0 0 0 0 0 -1
normalized size 1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.475 0.105 180.000 0.000 0.000 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 139 139 101 0 0 0 0 0 -1
normalized size 1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.403 0.092 180.000 0.000 0.000 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 120 120 100 0 0 0 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.397 0.094 180.000 0.000 0.000 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 93 93 65 73 0 0 0 0 -1
normalized size 1 1.00 0.70 0.78 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.350 0.082 0.202 0.000 0.000 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 53 53 45 43 0 0 0 0 -1
normalized size 1 1.00 0.85 0.81 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.219 0.041 0.132 0.000 0.000 0.000 0.000 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.013 0.326 0.153 0.000 0.000 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 345 345 152 0 0 0 0 0 -1
normalized size 1 1.00 0.44 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.115 0.123 180.000 0.000 0.000 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 209 209 101 0 0 0 0 0 -1
normalized size 1 1.00 0.48 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.874 0.092 180.000 0.000 0.000 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 189 189 100 0 0 0 0 0 -1
normalized size 1 1.00 0.53 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.640 0.093 180.000 0.000 0.000 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 127 127 84 105 0 0 0 0 -1
normalized size 1 1.00 0.66 0.83 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.438 0.131 0.297 0.000 0.000 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 86 86 45 68 0 0 0 0 -1
normalized size 1 1.00 0.52 0.79 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.220 0.032 0.203 0.000 0.000 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.013 0.327 0.145 0.000 0.000 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 394 394 162 0 0 0 0 0 -1
normalized size 1 1.00 0.41 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.822 0.103 180.000 0.000 0.000 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 257 257 101 0 0 0 0 0 -1
normalized size 1 1.00 0.39 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.375 0.094 180.000 0.000 0.000 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 220 220 100 0 0 0 0 0 -1
normalized size 1 1.00 0.45 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.055 0.090 180.000 0.000 0.000 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 157 157 92 139 0 0 0 0 -1
normalized size 1 1.00 0.59 0.89 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.709 0.186 0.273 0.000 0.000 0.000 0.000 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 99 99 45 81 0 0 0 0 -1
normalized size 1 1.00 0.45 0.82 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.395 0.040 0.211 0.000 0.000 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.333 0.147 0.000 0.000 0.000 0.000 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 163 163 150 0 0 0 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.199 0.120 180.000 0.000 0.000 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 109 109 101 0 0 0 0 0 -1
normalized size 1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.146 0.096 180.000 0.000 0.000 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 105 105 100 0 0 0 0 0 -1
normalized size 1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.140 0.092 180.000 0.000 0.000 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 49 37 0 0 0 0 -1
normalized size 1 1.00 0.78 0.59 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.077 0.043 0.120 0.000 0.000 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 43 43 45 26 0 0 0 0 -1
normalized size 1 1.00 1.05 0.60 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.047 0.032 0.085 0.000 0.000 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.259 0.146 0.000 0.000 0.000 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.669 0.339 0.000 0.000 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 193 193 201 0 0 0 0 0 -1
normalized size 1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.184 0.313 180.000 0.000 0.000 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 143 143 124 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 0.128 0.169 180.000 0.000 0.000 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 135 135 139 0 0 0 0 0 -1
normalized size 1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.124 0.182 180.000 0.000 0.000 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 89 89 63 83 0 0 0 0 -1
normalized size 1 1.00 0.71 0.93 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.066 0.110 0.266 0.000 0.000 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 68 68 76 66 0 0 0 0 -1
normalized size 1 1.00 1.12 0.97 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.218 0.068 0.209 0.000 0.000 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.383 0.140 0.000 0.000 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 228 228 278 0 0 0 0 0 -1
normalized size 1 1.00 1.22 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.864 1.665 180.000 0.000 0.000 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 172 172 175 0 0 0 0 0 -1
normalized size 1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.755 0.796 180.000 0.000 0.000 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 166 166 194 0 0 0 0 0 -1
normalized size 1 1.00 1.17 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.627 0.735 180.000 0.000 0.000 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 123 123 83 122 0 0 0 0 -1
normalized size 1 1.00 0.67 0.99 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.483 0.284 0.326 0.000 0.000 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 89 89 121 84 0 0 0 0 -1
normalized size 1 1.00 1.36 0.94 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.234 0.169 0.204 0.000 0.000 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.015 0.397 0.142 0.000 0.000 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 300 300 374 0 0 0 0 0 -1
normalized size 1 1.00 1.25 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.932 2.173 180.000 0.000 0.000 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 244 244 291 0 0 0 0 0 -1
normalized size 1 1.00 1.19 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.757 0.590 180.000 0.000 0.000 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 237 237 286 0 0 0 0 0 -1
normalized size 1 1.00 1.21 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.848 0.813 180.000 0.000 0.000 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 157 157 91 153 0 0 0 0 -1
normalized size 1 1.00 0.58 0.97 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.495 0.319 0.238 0.000 0.000 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 122 122 147 111 0 0 0 0 -1
normalized size 1 1.00 1.20 0.91 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.444 0.199 0.210 0.000 0.000 0.000 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.017 0.393 0.145 0.000 0.000 0.000 0.000 0.000
Problem 115 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 59 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 -0.02
time (sec) N/A 0.277 1.886 1.004 0.000 0.572 0.000 0.000 0.000
Problem 116 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 59 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 -0.02
time (sec) N/A 0.298 1.787 0.942 0.000 0.632 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 154 167 143 0 0 0 0 0 -1
normalized size 1 1.08 0.93 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.238 0.377 1.142 0.000 0.739 0.000 0.000 0.000
Problem 118 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 91 91 82 0 0 0 0 0 -1
normalized size 1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.055 0.100 1.043 0.000 0.586 0.000 0.000 0.000
Problem 119 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 0.023 1.324 0.720 0.000 0.407 0.000 0.000 0.000
Problem 120 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 0.023 1.337 0.873 0.000 0.465 0.000 0.000 0.000
Problem 121 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 0.020 1.359 0.721 0.000 0.657 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.019 1.998 0.141 0.000 0.000 0.000 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.016 2.267 0.109 0.000 0.000 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.016 2.121 0.115 0.000 0.000 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A 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 0.016 2.037 0.114 0.000 0.000 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A 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 0.019 1.447 0.115 0.000 0.603 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 144 0 0 0 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.247 0.210 180.000 0.000 1.177 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 97 0 0 0 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.191 0.102 180.000 0.000 0.676 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 95 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.182 0.121 180.000 0.000 0.685 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 58 38 0 0 0 0 -1
normalized size 1 1.00 0.98 0.64 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.087 0.052 0.087 0.000 0.837 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 43 40 0 0 0 0 -1
normalized size 1 1.00 0.88 0.82 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.049 0.026 0.052 0.000 0.582 0.000 0.000 0.000
Problem 132 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 0.017 0.353 0.109 0.000 0.564 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 105 109 87 73 87 0 -1
normalized size 1 1.00 1.25 1.30 1.04 0.87 1.04 0.00 -0.01
time (sec) N/A 0.039 0.041 0.016 0.390 0.550 0.981 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 54 55 58 65 71 0 -1
normalized size 1 1.00 0.76 0.77 0.82 0.92 1.00 0.00 -0.01
time (sec) N/A 0.030 0.046 0.004 0.420 0.644 0.537 0.000 0.000
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 55 55 76 86 66 61 61 80 47
normalized size 1 1.00 1.38 1.56 1.20 1.11 1.11 1.45 0.85
time (sec) N/A 0.020 0.038 0.004 0.626 0.921 0.265 0.625 0.411
Problem 136 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 35 35 35 34 30 43 31 41 31
normalized size 1 1.00 1.00 0.97 0.86 1.23 0.89 1.17 0.89
time (sec) N/A 0.014 0.022 0.002 0.536 0.674 0.140 0.431 0.452
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 55 55 48 75 0 0 0 0 -1
normalized size 1 1.00 0.87 1.36 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.077 0.043 0.070 0.000 0.488 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica 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 37 37 65 59 30 74 0 0 -1
normalized size 1 1.00 1.76 1.59 0.81 2.00 0.00 0.00 -0.03
time (sec) N/A 0.024 0.078 0.007 0.837 0.550 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 48 52 36 48 0 0 -1
normalized size 1 1.00 1.12 1.21 0.84 1.12 0.00 0.00 -0.02
time (sec) N/A 0.020 0.019 0.005 0.533 0.745 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 101 82 52 100 0 0 -1
normalized size 1 1.00 1.42 1.15 0.73 1.41 0.00 0.00 -0.01
time (sec) N/A 0.033 0.106 0.006 0.736 0.518 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 50 62 57 60 0 0 -1
normalized size 1 1.00 0.69 0.86 0.79 0.83 0.00 0.00 -0.01
time (sec) N/A 0.032 0.032 0.005 0.681 0.507 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 213 213 214 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.788 0.508 180.000 0.000 0.000 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 136 0 0 0 0 0 -1
normalized size 1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.649 0.416 0.169 0.000 0.000 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 102 102 100 0 0 0 0 0 -1
normalized size 1 1.00 0.98 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.412 0.238 0.095 0.000 0.000 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 292 292 540 0 0 0 0 0 -1
normalized size 1 1.00 1.85 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.251 2.390 180.000 0.000 0.000 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 184 184 165 0 0 0 0 0 -1
normalized size 1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.816 1.107 0.158 0.000 0.000 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 140 140 269 0 0 0 0 0 -1
normalized size 1 1.00 1.92 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.428 0.708 0.099 0.000 0.000 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F(-2) F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 337 337 924 0 0 0 0 0 -1
normalized size 1 1.00 2.74 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.090 11.124 180.000 0.000 0.000 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 228 228 207 0 0 0 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.328 2.044 0.156 0.000 0.000 0.000 0.000 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 160 160 452 0 0 0 0 0 -1
normalized size 1 1.00 2.82 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.751 2.552 0.095 0.000 0.000 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 194 194 195 0 0 0 0 0 -1
normalized size 1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.360 0.371 180.000 0.000 0.000 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 104 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.185 0.244 0.161 0.000 0.000 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 88 88 100 0 0 0 0 0 -1
normalized size 1 1.00 1.14 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.105 0.105 0.096 0.000 0.000 0.000 0.000 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 231 231 247 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 0.310 0.710 180.000 0.000 0.000 0.000 0.000 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 140 140 135 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.155 1.289 0.138 0.000 0.000 0.000 0.000 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 120 120 132 0 0 0 0 0 -1
normalized size 1 1.00 1.10 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.410 0.263 0.095 0.000 0.000 0.000 0.000 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 276 276 340 0 0 0 0 0 -1
normalized size 1 1.00 1.23 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.330 2.216 180.000 0.000 0.000 0.000 0.000 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 188 188 157 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.893 1.652 0.135 0.000 0.000 0.000 0.000 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 148 148 192 0 0 0 0 0 -1
normalized size 1 1.00 1.30 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.456 1.083 0.100 0.000 0.000 0.000 0.000 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 361 361 394 0 0 0 0 0 -1
normalized size 1 1.00 1.09 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.627 2.593 180.000 0.000 0.000 0.000 0.000 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 229 229 175 0 0 0 0 0 -1
normalized size 1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.870 1.745 0.135 0.000 0.000 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 188 188 214 0 0 0 0 0 -1
normalized size 1 1.00 1.14 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.772 0.745 0.099 0.000 0.000 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 128 141 118 0 0 0 0 0 -1
normalized size 1 1.10 0.92 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.285 0.426 180.000 0.000 0.477 0.000 0.000 0.000
Problem 164 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 181 194 164 0 0 0 0 0 -1
normalized size 1 1.07 0.91 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.310 0.263 3.194 0.000 0.561 0.000 0.000 0.000
Problem 165 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 106 106 87 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 0.053 0.146 2.961 0.000 1.555 0.000 0.000 0.000
Problem 166 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 0.028 0.504 1.181 0.000 1.074 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 [41] had the largest ratio of [1.000]

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 6 4 1.00 8 0.500
2 A 5 5 1.00 8 0.625
3 A 4 4 1.00 8 0.500
4 A 3 3 1.00 6 0.500
5 A 2 2 1.00 4 0.500
6 A 5 5 1.00 8 0.625
7 A 3 3 1.00 8 0.375
8 A 2 2 1.00 8 0.250
9 A 5 5 1.00 8 0.625
10 A 4 4 1.00 8 0.500
11 A 7 5 1.00 8 0.625
12 A 7 5 1.00 10 0.500
13 A 6 4 1.00 10 0.400
14 A 5 5 1.00 10 0.500
15 A 4 4 1.00 8 0.500
16 A 3 3 1.00 6 0.500
17 A 6 6 1.00 10 0.600
18 A 7 5 1.00 10 0.500
19 A 3 3 1.00 10 0.300
20 A 9 7 1.00 10 0.700
21 A 5 5 1.00 10 0.500
22 A 16 7 1.00 10 0.700
23 A 12 7 1.00 10 0.700
24 A 9 7 1.00 10 0.700
25 A 6 5 1.00 8 0.625
26 A 4 3 1.00 6 0.500
27 A 7 7 1.00 10 0.700
28 A 9 6 1.00 10 0.600
29 A 7 7 1.00 10 0.700
30 A 13 9 1.00 10 0.900
31 A 10 9 1.00 10 0.900
32 A 23 4 1.00 10 0.400
33 A 19 6 1.00 10 0.600
34 A 14 4 1.00 10 0.400
35 A 11 6 1.00 10 0.600
36 A 7 4 1.00 8 0.500
37 A 5 3 1.00 6 0.500
38 A 8 7 1.00 10 0.700
39 A 11 7 1.00 10 0.700
40 A 8 8 1.00 10 0.800
41 A 19 10 1.00 10 1.000
42 A 7 3 1.00 10 0.300
43 A 6 3 1.00 10 0.300
44 A 6 3 1.00 10 0.300
45 A 5 3 1.00 10 0.300
46 A 5 3 1.00 10 0.300
47 A 4 4 1.00 8 0.500
48 A 2 2 1.00 6 0.333
49 A 0 0 0.00 0 0.000
50 A 0 0 0.00 0 0.000
51 A 5 2 1.00 10 0.200
52 A 4 2 1.00 10 0.200
53 A 4 2 1.00 10 0.200
54 A 2 2 1.00 8 0.250
55 A 3 3 1.00 6 0.500
56 A 0 0 0.00 0 0.000
57 A 0 0 0.00 0 0.000
58 A 14 5 1.00 10 0.500
59 A 12 6 1.00 10 0.600
60 A 10 6 1.00 10 0.600
61 A 7 7 1.00 8 0.875
62 A 4 4 1.00 6 0.667
63 A 0 0 0.00 0 0.000
64 A 0 0 0.00 0 0.000
65 A 12 4 1.00 10 0.400
66 A 9 4 1.00 10 0.400
67 A 10 6 1.00 10 0.600
68 A 5 5 1.00 8 0.625
69 A 5 4 1.00 6 0.667
70 A 0 0 0.00 0 0.000
71 A 0 0 0.00 0 0.000
72 A 19 7 1.00 12 0.583
73 A 14 7 1.00 12 0.583
74 A 14 7 1.00 12 0.583
75 A 9 7 1.00 10 0.700
76 A 7 6 1.00 8 0.750
77 A 0 0 0.00 0 0.000
78 A 41 10 1.00 12 0.833
79 A 25 10 1.00 12 0.833
80 A 22 10 1.00 12 0.833
81 A 11 10 1.00 10 1.000
82 A 8 7 1.00 8 0.875
83 A 0 0 0.00 0 0.000
84 A 44 10 1.00 12 0.833
85 A 27 9 1.00 12 0.750
86 A 24 10 1.00 12 0.833
87 A 12 9 1.00 10 0.900
88 A 9 7 1.00 8 0.875
89 A 0 0 0.00 0 0.000
90 A 18 6 1.00 12 0.500
91 A 13 6 1.00 12 0.500
92 A 13 6 1.00 12 0.500
93 A 8 7 1.00 10 0.700
94 A 6 5 1.00 8 0.625
95 A 0 0 0.00 0 0.000
96 A 0 0 0.00 0 0.000
97 A 17 5 1.00 12 0.417
98 A 12 5 1.00 12 0.417
99 A 12 5 1.00 12 0.417
100 A 6 5 1.00 10 0.500
101 A 7 6 1.00 8 0.750
102 A 0 0 0.00 0 0.000
103 A 34 8 1.00 12 0.667
104 A 24 9 1.00 12 0.750
105 A 22 9 1.00 12 0.750
106 A 11 10 1.00 10 1.000
107 A 8 7 1.00 8 0.875
108 A 0 0 0.00 0 0.000
109 A 32 7 1.00 12 0.583
110 A 21 7 1.00 12 0.583
111 A 22 9 1.00 12 0.750
112 A 9 8 1.00 10 0.800
113 A 9 7 1.00 8 0.875
114 A 0 0 0.00 0 0.000
115 A 0 0 0.00 0 0.000
116 A 0 0 0.00 0 0.000
117 A 2 2 1.08 10 0.200
118 A 4 4 1.00 8 0.500
119 A 0 0 0.00 0 0.000
120 A 0 0 0.00 0 0.000
121 A 0 0 0.00 0 0.000
122 A 0 0 0.00 0 0.000
123 A 0 0 0.00 0 0.000
124 A 0 0 0.00 0 0.000
125 A 0 0 0.00 0 0.000
126 A 0 0 0.00 0 0.000
127 A 12 4 1.00 10 0.400
128 A 9 4 1.00 10 0.400
129 A 9 4 1.00 10 0.400
130 A 6 5 1.00 8 0.625
131 A 4 3 1.00 6 0.500
132 A 0 0 0.00 0 0.000
133 A 5 5 1.00 12 0.417
134 A 4 4 1.00 12 0.333
135 A 3 3 1.00 10 0.300
136 A 3 2 1.00 8 0.250
137 A 5 5 1.00 12 0.417
138 A 3 3 1.00 12 0.250
139 A 2 2 1.00 12 0.167
140 A 5 5 1.00 12 0.417
141 A 4 4 1.00 12 0.333
142 A 14 7 1.00 16 0.438
143 A 9 7 1.00 14 0.500
144 A 7 6 1.00 12 0.500
145 A 22 10 1.00 16 0.625
146 A 11 10 1.00 14 0.714
147 A 8 7 1.00 12 0.583
148 A 24 10 1.00 16 0.625
149 A 12 9 1.00 14 0.643
150 A 9 7 1.00 12 0.583
151 A 13 6 1.00 16 0.375
152 A 8 7 1.00 14 0.500
153 A 6 5 1.00 12 0.417
154 A 12 5 1.00 16 0.312
155 A 6 5 1.00 14 0.357
156 A 7 6 1.00 12 0.500
157 A 22 9 1.00 16 0.562
158 A 11 10 1.00 14 0.714
159 A 8 7 1.00 12 0.583
160 A 22 9 1.00 16 0.562
161 A 9 8 1.00 14 0.571
162 A 9 7 1.00 12 0.583
163 A 2 2 1.10 18 0.111
164 A 2 2 1.07 16 0.125
165 A 4 4 1.00 14 0.286
166 A 0 0 0.00 0 0.000

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