[next] [prev] [prev-tail] [tail] [up]

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