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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 }

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, 39, 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, 125, 126, 127, 128, 129, 130, 131, 137, 138, 139, 140, 141, 142, 143, 144, 145 }

B grade: { 135, 136 }

C grade: { 40, 41, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 132, 133, 134 }

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, 51, 64, 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, 131, 132, 133, 134, 143, 144, 145 }

B grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130 }

C grade: { 135, 136, 137, 138, 139, 140, 141, 142 }

F grade: { 40, 41 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 37, 38, 39, 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, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145 }

B grade: { }

C grade: { }

F grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 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, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 47, 48, 49, 50, 51, 52, 53, 54, 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, 125, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145 }

B grade: { 37, 38, 39, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124 }

C grade: { }

F grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 46, 68, 73, 126, 127, 128, 129, 130 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 39, 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, 111, 112, 115, 118, 119, 123, 124 }

B grade: { 64, 110, 113, 114, 116, 117, 120, 121, 122 }

C grade: { 133, 134, 135, 136, 141, 142 }

F grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 125, 126, 127, 128, 129, 130, 131, 132, 137, 138, 139, 140, 143, 144, 145 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 47, 48, 49, 50, 51, 52, 53, 54, 61, 62, 63, 64, 65, 66, 67, 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, 125, 132, 133, 134, 139, 140 }

B grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 55, 56, 57, 58, 59, 60, 68, 69, 70, 71, 72, 73, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 141, 142, 143, 144, 145 }

C grade: { }

F grade: { 40, 41, 135, 136, 137, 138 }

2.1.8 Mupad

A grade: { }

B 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, 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 }

C grade: { }

F grade: { 40, 41 }

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 A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 74 61 60 64 68 64 62
normalized size 1 1.00 1.00 0.82 0.81 0.86 0.92 0.86 0.84
time (sec) N/A 0.082 0.015 0.000 0.452 0.663 0.071 0.286 0.036
Problem 2 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 74 74 74 61 60 64 68 64 62
normalized size 1 1.00 1.00 0.82 0.81 0.86 0.92 0.86 0.84
time (sec) N/A 0.057 0.011 0.003 0.465 0.607 0.072 0.227 0.030
Problem 3 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 69 69 69 58 57 61 65 61 59
normalized size 1 1.00 1.00 0.84 0.83 0.88 0.94 0.88 0.86
time (sec) N/A 0.036 0.012 0.000 0.455 0.519 0.069 0.377 0.029
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 Yes TBD TBD TBD TBD TBD TBD
size 65 65 65 60 55 55 63 60 57
normalized size 1 1.00 1.00 0.92 0.85 0.85 0.97 0.92 0.88
time (sec) N/A 0.040 0.015 0.002 0.604 0.749 0.157 0.372 0.036
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 63 63 63 57 55 62 58 57 56
normalized size 1 1.00 1.00 0.90 0.87 0.98 0.92 0.90 0.89
time (sec) N/A 0.051 0.022 0.006 0.680 0.822 0.175 0.299 0.037
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 63 63 58 58 55 62 61 58 56
normalized size 1 1.00 0.92 0.92 0.87 0.98 0.97 0.92 0.89
time (sec) N/A 0.048 0.038 0.010 0.752 0.502 0.294 0.290 0.035
Problem 7 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 63 63 60 57 56 62 63 56 55
normalized size 1 1.00 0.95 0.90 0.89 0.98 1.00 0.89 0.87
time (sec) N/A 0.051 0.045 0.007 0.659 0.742 0.521 0.369 0.033
Problem 8 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 63 63 62 58 56 62 63 57 56
normalized size 1 1.00 0.98 0.92 0.89 0.98 1.00 0.90 0.89
time (sec) N/A 0.051 0.027 0.006 0.752 0.722 1.755 0.288 0.048
Problem 9 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 63 63 63 60 56 62 66 57 56
normalized size 1 1.00 1.00 0.95 0.89 0.98 1.05 0.90 0.89
time (sec) N/A 0.052 0.054 0.007 0.739 0.571 5.698 0.259 0.777
Problem 10 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 68 68 68 63 59 62 70 60 60
normalized size 1 1.00 1.00 0.93 0.87 0.91 1.03 0.88 0.88
time (sec) N/A 0.048 0.045 0.006 0.874 0.659 15.378 0.390 0.790
Problem 11 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 159 159 159 142 143 154 168 154 141
normalized size 1 1.00 1.00 0.89 0.90 0.97 1.06 0.97 0.89
time (sec) N/A 0.214 0.044 0.001 1.134 0.469 0.093 0.406 0.817
Problem 12 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 159 159 159 142 143 154 163 154 141
normalized size 1 1.00 1.00 0.89 0.90 0.97 1.03 0.97 0.89
time (sec) N/A 0.143 0.036 0.001 1.182 0.549 0.094 0.306 0.068
Problem 13 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 154 154 154 139 140 151 165 151 138
normalized size 1 1.00 1.00 0.90 0.91 0.98 1.07 0.98 0.90
time (sec) N/A 0.111 0.029 0.002 0.629 0.554 0.093 0.300 0.070
Problem 14 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 150 150 150 149 138 138 156 149 135
normalized size 1 1.00 1.00 0.99 0.92 0.92 1.04 0.99 0.90
time (sec) N/A 0.107 0.038 0.004 0.843 0.582 0.306 0.364 0.799
Problem 15 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 145 145 145 147 137 145 156 147 135
normalized size 1 1.00 1.00 1.01 0.94 1.00 1.08 1.01 0.93
time (sec) N/A 0.121 0.091 0.007 0.734 0.647 0.322 0.282 0.797
Problem 16 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 149 149 139 148 139 145 153 148 135
normalized size 1 1.00 0.93 0.99 0.93 0.97 1.03 0.99 0.91
time (sec) N/A 0.123 0.094 0.007 0.622 0.684 0.460 0.395 0.792
Problem 17 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 149 149 151 146 140 145 160 146 137
normalized size 1 1.00 1.01 0.98 0.94 0.97 1.07 0.98 0.92
time (sec) N/A 0.137 0.077 0.009 0.681 0.752 0.719 0.284 0.059
Problem 18 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 148 148 130 144 139 145 153 142 134
normalized size 1 1.00 0.88 0.97 0.94 0.98 1.03 0.96 0.91
time (sec) N/A 0.142 0.081 0.008 0.624 0.919 2.349 0.377 0.058
Problem 19 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 143 143 142 144 138 145 155 140 136
normalized size 1 1.00 0.99 1.01 0.97 1.01 1.08 0.98 0.95
time (sec) N/A 0.147 0.077 0.009 0.612 0.760 7.809 0.292 0.054
Problem 20 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 149 149 144 148 140 145 158 141 136
normalized size 1 1.00 0.97 0.99 0.94 0.97 1.06 0.95 0.91
time (sec) N/A 0.143 0.092 0.009 0.688 0.594 27.402 0.396 0.057
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 339 339 460 1622 0 0 0 5304 2588
normalized size 1 1.00 1.36 4.78 0.00 0.00 0.00 15.65 7.63
time (sec) N/A 1.856 0.572 0.065 0.000 0.000 0.000 5.749 0.958
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 278 278 377 1171 0 0 0 3519 2696
normalized size 1 1.00 1.36 4.21 0.00 0.00 0.00 12.66 9.70
time (sec) N/A 0.466 0.420 0.054 0.000 0.000 0.000 5.025 1.527
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 270 270 360 1327 0 0 0 3843 1890
normalized size 1 1.00 1.33 4.91 0.00 0.00 0.00 14.23 7.00
time (sec) N/A 0.835 0.366 0.050 0.000 0.000 0.000 5.566 2.001
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 223 223 240 728 0 0 0 2369 5594
normalized size 1 1.00 1.08 3.26 0.00 0.00 0.00 10.62 25.09
time (sec) N/A 0.213 0.359 0.040 0.000 0.000 0.000 5.359 1.885
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 211 211 234 616 0 0 0 1616 3942
normalized size 1 1.00 1.11 2.92 0.00 0.00 0.00 7.66 18.68
time (sec) N/A 0.266 0.209 0.025 0.000 0.000 0.000 4.372 2.306
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 285 488 0 0 0 2336 2258
normalized size 1 1.00 1.24 2.13 0.00 0.00 0.00 10.20 9.86
time (sec) N/A 0.259 0.445 0.037 0.000 0.000 0.000 5.075 1.493
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 260 260 315 811 0 0 0 3507 2588
normalized size 1 1.00 1.21 3.12 0.00 0.00 0.00 13.49 9.95
time (sec) N/A 0.471 1.080 0.040 0.000 0.000 0.000 5.393 1.022
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 288 288 377 1054 0 0 0 3353 3563
normalized size 1 1.00 1.31 3.66 0.00 0.00 0.00 11.64 12.37
time (sec) N/A 0.474 0.889 0.056 0.000 0.000 0.000 5.872 1.172
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 412 412 444 1429 0 0 0 5219 4754
normalized size 1 1.00 1.08 3.47 0.00 0.00 0.00 12.67 11.54
time (sec) N/A 1.334 1.382 0.062 0.000 0.000 0.000 8.471 1.774
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 347 347 358 831 0 0 0 3228 3278
normalized size 1 1.00 1.03 2.39 0.00 0.00 0.00 9.30 9.45
time (sec) N/A 0.618 0.894 0.044 0.000 0.000 0.000 5.369 1.613
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 356 356 378 1119 0 0 0 4440 3835
normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77
time (sec) N/A 0.902 1.039 0.055 0.000 0.000 0.000 7.049 1.671
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 317 317 335 1344 0 0 0 3013 3198
normalized size 1 1.00 1.06 4.24 0.00 0.00 0.00 9.50 10.09
time (sec) N/A 0.415 1.249 0.177 0.000 0.000 0.000 5.173 1.595
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 368 368 393 1813 0 0 0 5158 4707
normalized size 1 1.00 1.07 4.93 0.00 0.00 0.00 14.02 12.79
time (sec) N/A 0.867 1.224 0.151 0.000 0.000 0.000 7.849 1.675
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 403 403 458 1603 0 0 0 6022 8129
normalized size 1 1.00 1.14 3.98 0.00 0.00 0.00 14.94 20.17
time (sec) N/A 0.932 1.473 0.063 0.000 0.000 0.000 6.553 1.838
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 514 514 559 2398 0 0 0 9015 8684
normalized size 1 1.00 1.09 4.67 0.00 0.00 0.00 17.54 16.89
time (sec) N/A 1.486 2.027 0.085 0.000 0.000 0.000 11.545 2.468
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 534 534 655 2512 0 0 0 6938 10595
normalized size 1 1.00 1.23 4.70 0.00 0.00 0.00 12.99 19.84
time (sec) N/A 1.992 2.470 0.096 0.000 0.000 0.000 7.565 2.773
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 399 399 296 5520 611 3898 0 7808 2443
normalized size 1 1.00 0.74 13.83 1.53 9.77 0.00 19.57 6.12
time (sec) N/A 0.425 0.919 0.013 1.706 1.909 0.000 1.131 3.280
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 260 260 185 2187 344 1603 0 3203 1314
normalized size 1 1.00 0.71 8.41 1.32 6.17 0.00 12.32 5.05
time (sec) N/A 0.223 0.277 0.010 1.731 1.041 0.000 0.725 1.810
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 90 585 155 444 3735 914 527
normalized size 1 1.00 0.66 4.27 1.13 3.24 27.26 6.67 3.85
time (sec) N/A 0.088 0.104 0.005 0.815 1.338 2.575 0.533 1.075
Problem 40 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 368 368 438 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 0.622 0.474 0.035 0.000 1.068 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 685 670 242 0 0 0 0 0 -1
normalized size 1 0.98 0.35 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.378 0.327 0.031 0.000 1.106 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 356 356 378 1119 0 0 0 4440 3835
normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77
time (sec) N/A 0.924 1.038 0.000 0.000 0.000 0.000 7.038 0.004
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 356 356 378 1119 0 0 0 4440 3835
normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77
time (sec) N/A 0.371 0.425 0.036 0.000 0.000 0.000 7.135 1.551
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 356 356 378 1119 0 0 0 4439 3835
normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77
time (sec) N/A 0.370 0.154 0.039 0.000 0.000 0.000 6.896 1.474
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 356 356 378 1119 0 0 0 4439 3835
normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77
time (sec) N/A 0.356 0.154 0.034 0.000 0.000 0.000 7.311 1.389
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 356 356 378 1119 0 0 0 4439 3835
normalized size 1 1.00 1.06 3.14 0.00 0.00 0.00 12.47 10.77
time (sec) N/A 0.359 0.153 0.033 0.000 0.000 0.000 6.836 1.414
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 273 273 260 622 0 900 0 306 2972
normalized size 1 1.00 0.95 2.28 0.00 3.30 0.00 1.12 10.89
time (sec) N/A 0.854 0.199 0.007 0.000 1.846 0.000 1.868 1.604
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 193 474 0 677 0 214 2295
normalized size 1 1.00 0.95 2.33 0.00 3.33 0.00 1.05 11.31
time (sec) N/A 0.424 0.143 0.006 0.000 1.957 0.000 2.005 1.626
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 136 321 0 473 0 141 1689
normalized size 1 1.00 0.94 2.23 0.00 3.28 0.00 0.98 11.73
time (sec) N/A 0.272 0.099 0.006 0.000 1.504 0.000 1.987 1.300
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 100 211 0 318 0 99 1081
normalized size 1 1.00 0.97 2.05 0.00 3.09 0.00 0.96 10.50
time (sec) N/A 0.179 0.066 0.004 0.000 1.337 0.000 1.780 1.830
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 178 165 0 309 0 97 3927
normalized size 1 1.00 1.84 1.70 0.00 3.19 0.00 1.00 40.48
time (sec) N/A 0.200 0.137 0.009 0.000 1.410 0.000 1.903 8.881
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 203 227 0 399 0 135 4437
normalized size 1 1.00 1.72 1.92 0.00 3.38 0.00 1.14 37.60
time (sec) N/A 0.285 0.150 0.010 0.000 1.643 0.000 1.777 7.857
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 314 356 0 609 0 212 6187
normalized size 1 1.00 1.80 2.05 0.00 3.50 0.00 1.22 35.56
time (sec) N/A 0.407 0.345 0.012 0.000 2.538 0.000 1.719 9.917
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 244 244 416 523 0 834 0 313 9141
normalized size 1 1.00 1.70 2.14 0.00 3.42 0.00 1.28 37.46
time (sec) N/A 0.573 0.348 0.013 0.000 5.313 0.000 1.941 13.829
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 369 369 456 1450 0 15467 0 7243 23332
normalized size 1 1.00 1.24 3.93 0.00 41.92 0.00 19.63 63.23
time (sec) N/A 4.577 0.509 0.035 0.000 35.653 0.000 5.025 4.912
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 282 282 365 1035 0 9364 0 5461 15674
normalized size 1 1.00 1.29 3.67 0.00 33.21 0.00 19.37 55.58
time (sec) N/A 3.590 0.492 0.030 0.000 8.048 0.000 4.755 3.359
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 219 219 258 676 0 5788 0 4086 10209
normalized size 1 1.00 1.18 3.09 0.00 26.43 0.00 18.66 46.62
time (sec) N/A 0.637 0.326 0.027 0.000 4.487 0.000 3.908 3.360
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 213 213 253 563 0 5930 0 3988 10170
normalized size 1 1.00 1.19 2.64 0.00 27.84 0.00 18.72 47.75
time (sec) N/A 0.839 0.302 0.025 0.000 2.258 0.000 5.936 3.515
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 267 267 284 727 0 9850 0 3813 15505
normalized size 1 1.00 1.06 2.72 0.00 36.89 0.00 14.28 58.07
time (sec) N/A 1.065 0.339 0.027 0.000 10.542 0.000 3.442 4.763
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 329 329 394 1121 0 15830 0 6718 23019
normalized size 1 1.00 1.20 3.41 0.00 48.12 0.00 20.42 69.97
time (sec) N/A 1.942 0.551 0.033 0.000 38.588 0.000 7.015 6.247
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 320 320 309 1167 0 2111 0 424 3499
normalized size 1 1.00 0.97 3.65 0.00 6.60 0.00 1.32 10.93
time (sec) N/A 1.233 0.497 0.024 0.000 1.656 0.000 1.952 1.333
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 236 236 236 832 0 1455 0 279 2450
normalized size 1 1.00 1.00 3.53 0.00 6.17 0.00 1.18 10.38
time (sec) N/A 0.440 0.356 0.017 0.000 1.014 0.000 1.865 1.811
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 175 336 0 970 0 195 1651
normalized size 1 1.00 1.06 2.04 0.00 5.88 0.00 1.18 10.01
time (sec) N/A 0.287 0.249 0.015 0.000 1.056 0.000 1.838 2.717
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 130 205 0 650 474 140 342
normalized size 1 1.00 1.06 1.67 0.00 5.28 3.85 1.14 2.78
time (sec) N/A 0.184 0.102 0.012 0.000 0.890 38.035 2.167 0.378
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 268 462 0 1103 0 227 8706
normalized size 1 1.00 1.61 2.78 0.00 6.64 0.00 1.37 52.45
time (sec) N/A 0.394 0.445 0.017 0.000 3.256 0.000 2.001 11.849
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 234 234 403 722 0 1764 0 287 11879
normalized size 1 1.00 1.72 3.09 0.00 7.54 0.00 1.23 50.76
time (sec) N/A 0.725 0.658 0.023 0.000 7.130 0.000 1.846 12.979
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 329 329 592 1078 0 2567 0 535 15905
normalized size 1 1.00 1.80 3.28 0.00 7.80 0.00 1.63 48.34
time (sec) N/A 1.157 1.216 0.029 0.000 16.734 0.000 1.888 21.016
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 550 550 648 2558 0 0 0 8957 33799
normalized size 1 1.00 1.18 4.65 0.00 0.00 0.00 16.29 61.45
time (sec) N/A 13.227 2.131 0.056 0.000 0.000 0.000 9.044 4.104
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 436 436 511 1977 0 12597 0 7496 25862
normalized size 1 1.00 1.17 4.53 0.00 28.89 0.00 17.19 59.32
time (sec) N/A 5.541 1.542 0.052 0.000 17.362 0.000 8.250 2.648
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 362 362 414 1300 0 8951 0 6208 19494
normalized size 1 1.00 1.14 3.59 0.00 24.73 0.00 17.15 53.85
time (sec) N/A 2.498 1.103 0.043 0.000 8.443 0.000 6.811 6.543
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 346 346 382 1182 0 8991 0 6356 19589
normalized size 1 1.00 1.10 3.42 0.00 25.99 0.00 18.37 56.62
time (sec) N/A 1.896 1.081 0.040 0.000 8.489 0.000 6.973 6.552
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 399 399 444 1575 0 13111 0 7182 28164
normalized size 1 1.00 1.11 3.95 0.00 32.86 0.00 18.00 70.59
time (sec) N/A 2.203 1.319 0.048 0.000 19.288 0.000 7.093 6.862
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 575 575 548 2180 0 0 0 8660 36097
normalized size 1 1.00 0.95 3.79 0.00 0.00 0.00 15.06 62.78
time (sec) N/A 9.906 1.797 0.065 0.000 0.000 0.000 8.591 7.370
Problem 74 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 68 68 62 56 58 82 61 63 57
normalized size 1 1.00 0.91 0.82 0.85 1.21 0.90 0.93 0.84
time (sec) N/A 0.126 0.028 0.017 0.602 0.785 0.172 0.362 0.056
Problem 75 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 61 61 61 51 53 77 56 58 53
normalized size 1 1.00 1.00 0.84 0.87 1.26 0.92 0.95 0.87
time (sec) N/A 0.118 0.027 0.016 0.719 0.829 0.171 0.323 0.039
Problem 76 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 54 46 48 72 48 53 47
normalized size 1 1.00 1.00 0.85 0.89 1.33 0.89 0.98 0.87
time (sec) N/A 0.108 0.024 0.016 1.075 0.708 0.173 0.367 0.897
Problem 77 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 49 49 49 41 43 67 44 45 43
normalized size 1 1.00 1.00 0.84 0.88 1.37 0.90 0.92 0.88
time (sec) N/A 0.086 0.022 0.015 0.514 0.901 0.174 0.390 0.038
Problem 78 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 42 36 38 57 36 40 37
normalized size 1 1.00 1.00 0.86 0.90 1.36 0.86 0.95 0.88
time (sec) N/A 0.049 0.017 0.016 0.522 1.045 0.166 0.354 0.049
Problem 79 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 44 44 44 38 44 71 41 47 40
normalized size 1 1.00 1.00 0.86 1.00 1.61 0.93 1.07 0.91
time (sec) N/A 0.077 0.022 0.016 0.724 0.901 0.183 0.377 0.041
Problem 80 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 50 45 53 92 51 53 50
normalized size 1 1.00 0.91 0.82 0.96 1.67 0.93 0.96 0.91
time (sec) N/A 0.104 0.025 0.017 0.792 0.980 0.205 0.374 0.044
Problem 81 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 64 64 56 50 56 97 56 66 55
normalized size 1 1.00 0.88 0.78 0.88 1.52 0.88 1.03 0.86
time (sec) N/A 0.111 0.027 0.019 0.679 1.053 0.213 0.341 0.919
Problem 82 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 70 70 71 56 58 79 68 58 58
normalized size 1 1.00 1.01 0.80 0.83 1.13 0.97 0.83 0.83
time (sec) N/A 0.085 0.044 0.012 1.639 1.087 0.210 0.331 0.952
Problem 83 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 57 57 58 49 51 74 54 51 50
normalized size 1 1.00 1.02 0.86 0.89 1.30 0.95 0.89 0.88
time (sec) N/A 0.082 0.048 0.012 1.621 0.865 0.207 0.314 0.054
Problem 84 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 56 56 57 46 48 69 54 48 48
normalized size 1 1.00 1.02 0.82 0.86 1.23 0.96 0.86 0.86
time (sec) N/A 0.073 0.042 0.013 1.635 0.909 0.210 0.306 0.918
Problem 85 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 49 49 50 41 43 64 48 43 42
normalized size 1 1.00 1.02 0.84 0.88 1.31 0.98 0.88 0.86
time (sec) N/A 0.066 0.038 0.011 1.633 0.914 0.207 0.340 0.068
Problem 86 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 48 48 46 38 40 59 46 40 40
normalized size 1 1.00 0.96 0.79 0.83 1.23 0.96 0.83 0.83
time (sec) N/A 0.028 0.040 0.012 1.529 1.075 0.203 0.339 0.072
Problem 87 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 53 53 51 43 45 68 49 45 45
normalized size 1 1.00 0.96 0.81 0.85 1.28 0.92 0.85 0.85
time (sec) N/A 0.073 0.049 0.013 1.554 0.916 0.219 0.384 0.070
Problem 88 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 62 62 56 48 52 79 56 52 51
normalized size 1 1.00 0.90 0.77 0.84 1.27 0.90 0.84 0.82
time (sec) N/A 0.084 0.051 0.015 1.597 0.906 0.240 0.386 0.923
Problem 89 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 69 69 61 53 57 84 61 57 57
normalized size 1 1.00 0.88 0.77 0.83 1.22 0.88 0.83 0.83
time (sec) N/A 0.090 0.058 0.017 1.764 0.873 0.254 0.343 0.916
Problem 90 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 76 76 77 58 62 89 66 62 61
normalized size 1 1.00 1.01 0.76 0.82 1.17 0.87 0.82 0.80
time (sec) N/A 0.100 0.055 0.016 1.528 0.877 0.276 0.450 0.074
Problem 91 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 81 81 71 64 71 114 75 61 70
normalized size 1 1.00 0.88 0.79 0.88 1.41 0.93 0.75 0.86
time (sec) N/A 0.112 0.056 0.013 1.584 0.877 0.258 0.317 0.059
Problem 92 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 80 80 66 62 68 109 76 58 68
normalized size 1 1.00 0.82 0.78 0.85 1.36 0.95 0.72 0.85
time (sec) N/A 0.100 0.054 0.013 1.914 0.862 0.256 0.414 0.052
Problem 93 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 75 75 60 56 63 104 70 53 63
normalized size 1 1.00 0.80 0.75 0.84 1.39 0.93 0.71 0.84
time (sec) N/A 0.091 0.061 0.013 1.850 0.642 0.255 0.324 0.928
Problem 94 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 72 72 55 54 60 99 65 50 59
normalized size 1 1.00 0.76 0.75 0.83 1.38 0.90 0.69 0.82
time (sec) N/A 0.068 0.058 0.011 1.527 0.851 0.262 0.345 0.928
Problem 95 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 72 72 56 53 60 99 66 50 60
normalized size 1 1.00 0.78 0.74 0.83 1.38 0.92 0.69 0.83
time (sec) N/A 0.066 0.061 0.013 1.744 0.686 0.251 0.379 0.071
Problem 96 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 72 72 56 53 60 99 65 50 59
normalized size 1 1.00 0.78 0.74 0.83 1.38 0.90 0.69 0.82
time (sec) N/A 0.037 0.059 0.013 1.671 0.897 0.248 0.328 0.070
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 79 79 63 58 65 108 71 55 65
normalized size 1 1.00 0.80 0.73 0.82 1.37 0.90 0.70 0.82
time (sec) N/A 0.103 0.065 0.014 1.797 0.856 0.276 0.338 0.920
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 86 86 78 64 72 119 76 62 71
normalized size 1 1.00 0.91 0.74 0.84 1.38 0.88 0.72 0.83
time (sec) N/A 0.119 0.059 0.016 1.527 1.013 0.293 0.361 0.923
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 93 93 73 68 77 124 82 67 77
normalized size 1 1.00 0.78 0.73 0.83 1.33 0.88 0.72 0.83
time (sec) N/A 0.134 0.076 0.015 1.737 1.224 0.312 0.356 0.935
Problem 100 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 86 86 78 74 71 95 87 76 75
normalized size 1 1.00 0.91 0.86 0.83 1.10 1.01 0.88 0.87
time (sec) N/A 0.135 0.045 0.010 1.333 1.051 0.183 1.018 0.901
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 81 81 73 69 66 90 80 71 69
normalized size 1 1.00 0.90 0.85 0.81 1.11 0.99 0.88 0.85
time (sec) N/A 0.127 0.030 0.009 1.824 1.011 0.185 1.169 0.051
Problem 102 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 74 74 66 64 59 85 73 66 65
normalized size 1 1.00 0.89 0.86 0.80 1.15 0.99 0.89 0.88
time (sec) N/A 0.121 0.029 0.009 1.585 1.057 0.180 1.090 0.045
Problem 103 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 65 65 61 59 54 80 68 54 60
normalized size 1 1.00 0.94 0.91 0.83 1.23 1.05 0.83 0.92
time (sec) N/A 0.105 0.026 0.010 1.718 0.973 0.181 1.184 0.919
Problem 104 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 58 58 58 54 49 70 60 49 69
normalized size 1 1.00 1.00 0.93 0.84 1.21 1.03 0.84 1.19
time (sec) N/A 0.067 0.022 0.010 1.406 0.787 0.179 1.133 0.048
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 93 58 55 84 65 62 59
normalized size 1 1.00 1.41 0.88 0.83 1.27 0.98 0.94 0.89
time (sec) N/A 0.108 0.062 0.012 1.685 0.775 0.198 1.103 0.907
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 97 63 66 105 76 66 68
normalized size 1 1.00 1.37 0.89 0.93 1.48 1.07 0.93 0.96
time (sec) N/A 0.134 0.050 0.013 1.427 0.582 0.212 1.072 0.061
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 105 68 71 110 80 79 72
normalized size 1 1.00 1.31 0.85 0.89 1.38 1.00 0.99 0.90
time (sec) N/A 0.137 0.060 0.014 2.381 0.804 0.226 1.165 0.060
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 110 73 76 115 85 84 78
normalized size 1 1.00 1.26 0.84 0.87 1.32 0.98 0.97 0.90
time (sec) N/A 0.149 0.066 0.014 2.474 0.841 0.241 1.165 0.065
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 248 248 145 427 0 519 71 585 171
normalized size 1 1.00 0.58 1.72 0.00 2.09 0.29 2.36 0.69
time (sec) N/A 0.345 0.172 0.119 0.000 0.810 0.611 1.887 0.106
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 237 237 132 419 0 476 1205 576 164
normalized size 1 1.00 0.56 1.77 0.00 2.01 5.08 2.43 0.69
time (sec) N/A 0.293 0.158 0.032 0.000 0.757 1.360 1.851 0.943
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 232 232 129 416 0 508 60 573 162
normalized size 1 1.00 0.56 1.79 0.00 2.19 0.26 2.47 0.70
time (sec) N/A 0.292 0.159 0.030 0.000 1.091 0.615 1.854 0.095
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 121 412 0 459 51 566 156
normalized size 1 1.00 0.54 1.83 0.00 2.04 0.23 2.52 0.69
time (sec) N/A 0.297 0.164 0.034 0.000 0.845 0.602 1.825 0.958
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 224 224 115 408 0 454 1185 565 153
normalized size 1 1.00 0.51 1.82 0.00 2.03 5.29 2.52 0.68
time (sec) N/A 0.215 0.264 0.029 0.000 0.601 1.291 1.818 0.127
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 126 414 0 471 1192 572 159
normalized size 1 1.00 0.55 1.81 0.00 2.06 5.21 2.50 0.69
time (sec) N/A 0.310 0.176 0.033 0.000 0.832 1.323 1.937 0.136
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 238 238 131 419 0 528 60 579 165
normalized size 1 1.00 0.55 1.76 0.00 2.22 0.25 2.43 0.69
time (sec) N/A 0.335 0.291 0.035 0.000 0.852 0.653 1.851 0.137
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 245 245 140 424 0 496 1202 584 171
normalized size 1 1.00 0.57 1.73 0.00 2.02 4.91 2.38 0.70
time (sec) N/A 0.329 0.290 0.034 0.000 0.790 1.332 1.785 0.143
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 243 243 156 429 0 561 1204 588 184
normalized size 1 1.00 0.64 1.77 0.00 2.31 4.95 2.42 0.76
time (sec) N/A 0.360 0.216 0.035 0.000 0.760 1.350 2.694 0.111
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 242 242 155 426 0 557 82 585 182
normalized size 1 1.00 0.64 1.76 0.00 2.30 0.34 2.42 0.75
time (sec) N/A 0.310 0.204 0.033 0.000 0.840 0.680 2.588 0.942
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 235 235 138 422 0 551 71 580 176
normalized size 1 1.00 0.59 1.80 0.00 2.34 0.30 2.47 0.75
time (sec) N/A 0.300 0.317 0.035 0.000 0.946 0.656 2.612 0.992
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 238 238 129 418 0 546 1198 577 173
normalized size 1 1.00 0.54 1.76 0.00 2.29 5.03 2.42 0.73
time (sec) N/A 0.290 0.297 0.032 0.000 0.878 1.306 2.600 0.146
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 246 246 133 418 0 570 1200 577 174
normalized size 1 1.00 0.54 1.70 0.00 2.32 4.88 2.35 0.71
time (sec) N/A 0.284 0.297 0.032 0.000 0.872 1.332 2.688 1.012
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 248 248 129 418 0 576 1195 577 173
normalized size 1 1.00 0.52 1.69 0.00 2.32 4.82 2.33 0.70
time (sec) N/A 0.254 0.291 0.032 0.000 0.857 1.337 2.618 1.008
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 253 253 140 424 0 630 75 582 179
normalized size 1 1.00 0.55 1.68 0.00 2.49 0.30 2.30 0.71
time (sec) N/A 0.343 0.366 0.034 0.000 0.909 0.672 3.266 0.993
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 139 429 0 652 80 589 185
normalized size 1 1.00 0.53 1.64 0.00 2.49 0.31 2.25 0.71
time (sec) N/A 0.366 0.315 0.036 0.000 0.866 0.689 2.991 1.022
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 142 357 0 486 0 146 1834
normalized size 1 1.00 0.95 2.40 0.00 3.26 0.00 0.98 12.31
time (sec) N/A 0.295 0.116 0.006 0.000 1.071 0.000 1.898 1.685
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 594 594 721 3028 0 0 0 10761 47339
normalized size 1 1.00 1.21 5.10 0.00 0.00 0.00 18.12 79.70
time (sec) N/A 14.113 2.641 0.060 0.000 0.000 0.000 9.953 4.731
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 471 471 575 2300 0 0 0 9170 36589
normalized size 1 1.00 1.22 4.88 0.00 0.00 0.00 19.47 77.68
time (sec) N/A 6.662 1.946 0.047 0.000 0.000 0.000 8.921 4.218
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 449 449 512 1760 0 0 0 8913 32587
normalized size 1 1.00 1.14 3.92 0.00 0.00 0.00 19.85 72.58
time (sec) N/A 2.867 1.651 0.053 0.000 0.000 0.000 8.514 5.821
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 460 460 529 2045 0 0 0 9176 40860
normalized size 1 1.00 1.15 4.45 0.00 0.00 0.00 19.95 88.83
time (sec) N/A 2.791 2.434 0.055 0.000 0.000 0.000 8.303 7.761
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 542 542 612 2503 0 0 0 10422 51386
normalized size 1 1.00 1.13 4.62 0.00 0.00 0.00 19.23 94.81
time (sec) N/A 7.265 2.153 0.067 0.000 0.000 0.000 9.055 8.467
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 21 31 31 0 58 31
normalized size 1 1.00 1.00 1.05 1.55 1.55 0.00 2.90 1.55
time (sec) N/A 0.036 0.141 0.010 1.028 1.059 0.000 0.609 1.098
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 210 278 265 145 295 138 0 269 287
normalized size 1 1.32 1.26 0.69 1.40 0.66 0.00 1.28 1.37
time (sec) N/A 0.315 1.379 0.009 1.026 1.019 0.000 0.894 1.645
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 159 213 232 109 217 104 367 194 215
normalized size 1 1.34 1.46 0.69 1.36 0.65 2.31 1.22 1.35
time (sec) N/A 0.189 1.069 0.007 1.062 0.857 135.140 0.749 1.494
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 149 194 73 139 71 350 121 143
normalized size 1 1.37 1.78 0.67 1.28 0.65 3.21 1.11 1.31
time (sec) N/A 0.122 0.691 0.006 1.032 1.031 90.666 0.626 1.377
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C A A C F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 151 217 143 105 80 304 0 161
normalized size 1 1.62 2.33 1.54 1.13 0.86 3.27 0.00 1.73
time (sec) N/A 0.165 0.880 0.042 1.004 0.963 91.279 0.000 2.949
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C A A C F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 155 233 163 123 98 270 0 422
normalized size 1 1.57 2.35 1.65 1.24 0.99 2.73 0.00 4.26
time (sec) N/A 0.252 0.213 0.024 1.017 0.801 133.790 0.000 5.151
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-1) F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 182 134 222 193 102 0 0 932
normalized size 1 1.44 1.06 1.76 1.53 0.81 0.00 0.00 7.40
time (sec) N/A 0.277 0.161 0.030 1.034 0.798 0.000 0.000 10.816
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-1) F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 212 248 173 306 271 137 0 0 1621
normalized size 1 1.17 0.82 1.44 1.28 0.65 0.00 0.00 7.65
time (sec) N/A 0.373 0.192 0.036 1.033 0.815 0.000 0.000 20.051
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 216 245 202 273 190 134 0 208 1132
normalized size 1 1.13 0.94 1.26 0.88 0.62 0.00 0.96 5.24
time (sec) N/A 0.205 0.791 0.037 1.106 0.850 0.000 0.749 23.121
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 128 179 157 191 113 100 0 135 651
normalized size 1 1.40 1.23 1.49 0.88 0.78 0.00 1.05 5.09
time (sec) N/A 0.091 0.562 0.020 1.018 0.947 0.000 0.595 12.861
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 155 135 148 73 90 287 257 306
normalized size 1 1.52 1.32 1.45 0.72 0.88 2.81 2.52 3.00
time (sec) N/A 0.122 0.555 0.023 1.052 0.959 104.024 1.046 7.002
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 81 146 85 90 257 555 138
normalized size 1 1.00 0.52 0.93 0.54 0.57 1.64 3.54 0.88
time (sec) N/A 0.125 0.124 0.026 1.005 0.832 116.433 1.467 2.268
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 160 160 87 82 148 76 0 1103 146
normalized size 1 1.00 0.54 0.51 0.92 0.48 0.00 6.89 0.91
time (sec) N/A 0.145 0.118 0.005 1.019 0.858 0.000 2.546 1.732
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 226 226 124 118 226 110 0 1517 218
normalized size 1 1.00 0.55 0.52 1.00 0.49 0.00 6.71 0.96
time (sec) N/A 0.178 0.142 0.007 1.010 0.972 0.000 4.731 1.817
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 292 292 158 154 304 144 0 1931 290
normalized size 1 1.00 0.54 0.53 1.04 0.49 0.00 6.61 0.99
time (sec) N/A 0.242 0.176 0.007 1.031 1.024 0.000 7.348 1.873

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 [35] had the largest ratio of [.4643]

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 2 1 1.00 26 0.038
2 A 2 1 1.00 24 0.042
3 A 2 1 1.00 23 0.043
4 A 2 1 1.00 26 0.038
5 A 2 1 1.00 26 0.038
6 A 2 1 1.00 26 0.038
7 A 2 1 1.00 26 0.038
8 A 2 1 1.00 26 0.038
9 A 2 1 1.00 26 0.038
10 A 2 1 1.00 26 0.038
11 A 2 1 1.00 28 0.036
12 A 2 1 1.00 26 0.038
13 A 2 1 1.00 25 0.040
14 A 2 1 1.00 28 0.036
15 A 2 1 1.00 28 0.036
16 A 2 1 1.00 28 0.036
17 A 2 1 1.00 28 0.036
18 A 2 1 1.00 28 0.036
19 A 2 1 1.00 28 0.036
20 A 2 1 1.00 28 0.036
21 A 13 11 1.00 28 0.393
22 A 12 11 1.00 28 0.393
23 A 11 10 1.00 28 0.357
24 A 10 9 1.00 26 0.346
25 A 8 7 1.00 25 0.280
26 A 12 10 1.00 28 0.357
27 A 13 12 1.00 28 0.429
28 A 13 11 1.00 28 0.393
29 A 11 10 1.00 28 0.357
30 A 10 9 1.00 28 0.321
31 A 10 9 1.00 28 0.321
32 A 10 9 1.00 26 0.346
33 A 10 9 1.00 25 0.360
34 A 14 12 1.00 28 0.429
35 A 15 13 1.00 28 0.464
36 A 15 13 1.00 28 0.464
37 A 2 1 1.00 30 0.033
38 A 2 1 1.00 30 0.033
39 A 2 1 1.00 28 0.036
40 A 8 5 1.00 30 0.167
41 A 10 6 0.98 30 0.200
42 A 10 9 1.00 28 0.321
43 A 11 10 1.00 30 0.333
44 A 11 10 1.00 31 0.323
45 A 11 10 1.00 34 0.294
46 A 11 10 1.00 34 0.294
47 A 7 6 1.00 30 0.200
48 A 7 6 1.00 30 0.200
49 A 7 6 1.00 30 0.200
50 A 7 6 1.00 28 0.214
51 A 7 6 1.00 30 0.200
52 A 7 6 1.00 30 0.200
53 A 7 6 1.00 30 0.200
54 A 7 6 1.00 30 0.200
55 A 5 3 1.00 30 0.100
56 A 5 3 1.00 30 0.100
57 A 5 3 1.00 27 0.111
58 A 5 3 1.00 30 0.100
59 A 5 3 1.00 30 0.100
60 A 5 3 1.00 30 0.100
61 A 8 7 1.00 30 0.233
62 A 7 7 1.00 30 0.233
63 A 6 6 1.00 30 0.200
64 A 5 5 1.00 28 0.179
65 A 8 7 1.00 30 0.233
66 A 8 7 1.00 30 0.233
67 A 8 7 1.00 30 0.233
68 A 6 4 1.00 30 0.133
69 A 6 4 1.00 30 0.133
70 A 4 3 1.00 30 0.100
71 A 4 3 1.00 27 0.111
72 A 6 4 1.00 30 0.133
73 A 6 4 1.00 30 0.133
74 A 7 5 1.00 31 0.161
75 A 7 5 1.00 31 0.161
76 A 7 5 1.00 31 0.161
77 A 7 5 1.00 31 0.161
78 A 5 4 1.00 29 0.138
79 A 4 3 1.00 31 0.097
80 A 4 3 1.00 31 0.097
81 A 4 3 1.00 31 0.097
82 A 6 4 1.00 31 0.129
83 A 6 4 1.00 31 0.129
84 A 6 4 1.00 31 0.129
85 A 6 4 1.00 31 0.129
86 A 4 3 1.00 28 0.107
87 A 5 3 1.00 31 0.097
88 A 5 3 1.00 31 0.097
89 A 5 3 1.00 31 0.097
90 A 5 3 1.00 31 0.097
91 A 7 5 1.00 31 0.161
92 A 7 5 1.00 31 0.161
93 A 7 5 1.00 31 0.161
94 A 5 4 1.00 31 0.129
95 A 5 4 1.00 31 0.129
96 A 5 4 1.00 28 0.143
97 A 6 3 1.00 31 0.097
98 A 6 3 1.00 31 0.097
99 A 6 3 1.00 31 0.097
100 A 8 7 1.00 31 0.226
101 A 8 7 1.00 31 0.226
102 A 8 7 1.00 31 0.226
103 A 8 7 1.00 31 0.226
104 A 6 6 1.00 29 0.207
105 A 8 7 1.00 31 0.226
106 A 8 7 1.00 31 0.226
107 A 8 7 1.00 31 0.226
108 A 8 7 1.00 31 0.226
109 A 12 7 1.00 31 0.226
110 A 12 7 1.00 31 0.226
111 A 12 7 1.00 31 0.226
112 A 12 7 1.00 31 0.226
113 A 10 6 1.00 28 0.214
114 A 12 7 1.00 31 0.226
115 A 12 7 1.00 31 0.226
116 A 12 7 1.00 31 0.226
117 A 13 8 1.00 31 0.258
118 A 13 8 1.00 31 0.258
119 A 13 8 1.00 31 0.258
120 A 11 7 1.00 31 0.226
121 A 11 7 1.00 31 0.226
122 A 11 7 1.00 28 0.250
123 A 13 7 1.00 31 0.226
124 A 13 7 1.00 31 0.226
125 A 7 6 1.00 33 0.182
126 A 6 4 1.00 35 0.114
127 A 6 4 1.00 35 0.114
128 A 4 3 1.00 32 0.094
129 A 6 4 1.00 35 0.114
130 A 6 4 1.00 35 0.114
131 A 1 1 1.00 42 0.024
132 A 5 4 1.32 35 0.114
133 A 4 3 1.34 35 0.086
134 A 4 3 1.37 33 0.091
135 A 6 5 1.62 35 0.143
136 A 6 6 1.57 35 0.171
137 A 6 6 1.44 35 0.171
138 A 7 7 1.17 35 0.200
139 A 6 6 1.13 35 0.171
140 A 5 5 1.40 32 0.156
141 A 5 5 1.52 35 0.143
142 A 5 5 1.00 35 0.143
143 A 4 4 1.00 35 0.114
144 A 5 5 1.00 35 0.143
145 A 6 5 1.00 35 0.143

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