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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, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 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, 158, 159 }

B grade: { 97, 155, 156, 157 }

C grade: { }

F grade: { 111 }

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, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 100, 101, 102, 103, 104, 105, 106, 109, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 157, 158, 159 }

B grade: { 54, 97, 99, 107, 108, 110, 111, 155, 156 }

C grade: { 33, 34, 43, 58, 59, 68, 69, 70, 71, 72, 73, 74, 75, 76, 132 }

F grade: { 139, 140, 141, 144 }

2.1.3 Maple

A grade: { 1, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 51, 52, 53, 55, 58, 60, 61, 62, 63, 65, 70, 88, 95, 102, 104, 109, 143 }

B grade: { 2, 3, 12, 14, 33, 34, 40, 41, 42, 43, 49, 50, 56, 57, 59, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 103, 105, 106, 107, 108, 110, 111, 119, 130, 131, 134, 135 }

C grade: { 22, 23, 24, 25, 26, 54, 64, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159 }

F grade: { 112, 113, 114, 115, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 18, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 143, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159 }

B grade: { 119, 155 }

C grade: { }

F grade: { 12, 13, 14, 19, 20, 21, 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, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 143, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159 }

B grade: { 13, 14, 20, 21, 26, 119, 130, 131, 134, 135 }

C grade: { }

F grade: { 5, 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, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148 }

2.1.6 Sympy

A grade: { 1, 2, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 119 }

B grade: { 3, 13, 20 }

C grade: { 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159 }

F grade: { 4, 5, 14, 21, 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, 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 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 32, 143, 149, 150, 154, 155, 156, 157 }

B grade: { 5, 27, 28, 29, 30, 119, 158, 159 }

C grade: { }

F grade: { 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, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 151, 152, 153 }

2.1.8 Mupad

A grade: { 143 }

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, 119, 130, 131, 134, 135, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159 }

C grade: { }

F grade: { 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, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148 }

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 112 112 112 109 108 142 148 150 115
normalized size 1 1.00 1.00 0.97 0.96 1.27 1.32 1.34 1.03
time (sec) N/A 0.158 0.052 0.001 0.445 0.605 0.094 1.121 2.383
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 123 246 162 163 146 208 174
normalized size 1 1.00 0.98 1.95 1.29 1.29 1.16 1.65 1.38
time (sec) N/A 0.211 0.088 0.005 0.443 0.944 0.580 1.189 2.537
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 85 196 104 117 507 112 105
normalized size 1 1.00 1.01 2.33 1.24 1.39 6.04 1.33 1.25
time (sec) N/A 0.086 0.062 0.009 0.439 0.790 20.494 1.251 2.970
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 102 179 134 160 0 162 127
normalized size 1 1.00 0.94 1.66 1.24 1.48 0.00 1.50 1.18
time (sec) N/A 0.110 0.082 0.010 0.443 152.519 0.000 1.137 4.168
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 164 164 310 0 0 363 317
normalized size 1 1.00 1.01 1.01 1.90 0.00 0.00 2.23 1.94
time (sec) N/A 0.212 0.201 0.010 0.489 0.000 0.000 1.189 6.622
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 23 23 23 20 19 19 20 22 19
normalized size 1 1.00 1.00 0.87 0.83 0.83 0.87 0.96 0.83
time (sec) N/A 0.011 0.006 0.007 0.430 1.013 0.153 1.251 0.076
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 43 43 33 34 34 53 32 31 29
normalized size 1 1.00 0.77 0.79 0.79 1.23 0.74 0.72 0.67
time (sec) N/A 0.037 0.024 0.009 0.433 1.079 0.161 1.176 0.123
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 227 227 205 301 239 649 274 338 413
normalized size 1 1.00 0.90 1.33 1.05 2.86 1.21 1.49 1.82
time (sec) N/A 0.257 0.275 0.010 0.991 1.309 37.787 1.405 0.161
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 146 146 145 176 152 405 167 201 263
normalized size 1 1.00 0.99 1.21 1.04 2.77 1.14 1.38 1.80
time (sec) N/A 0.098 0.183 0.010 0.963 1.150 27.596 1.362 2.621
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 77 77 81 89 91 219 92 105 136
normalized size 1 1.00 1.05 1.16 1.18 2.84 1.19 1.36 1.77
time (sec) N/A 0.024 0.159 0.008 0.979 1.287 25.991 1.328 0.091
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 54 54 55 46 60 111 54 57 45
normalized size 1 1.00 1.02 0.85 1.11 2.06 1.00 1.06 0.83
time (sec) N/A 0.017 0.048 0.007 0.979 1.268 5.984 1.244 0.072
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 101 196 0 449 97 112 2368
normalized size 1 1.00 1.00 1.94 0.00 4.45 0.96 1.11 23.45
time (sec) N/A 0.114 0.122 0.016 0.000 1.650 27.334 1.352 2.871
Problem 13 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 127 127 124 192 0 1018 1204 142 1827
normalized size 1 1.00 0.98 1.51 0.00 8.02 9.48 1.12 14.39
time (sec) N/A 0.109 0.439 0.019 0.000 1.105 133.870 1.423 0.599
Problem 14 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 208 208 260 424 0 2216 0 300 4852
normalized size 1 1.00 1.25 2.04 0.00 10.65 0.00 1.44 23.33
time (sec) N/A 0.274 0.602 0.020 0.000 2.642 0.000 1.394 4.543
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 226 226 204 301 238 641 274 338 413
normalized size 1 1.00 0.90 1.33 1.05 2.84 1.21 1.50 1.83
time (sec) N/A 0.252 0.281 0.011 0.974 0.792 37.946 1.394 2.528
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 145 145 146 176 152 403 167 201 263
normalized size 1 1.00 1.01 1.21 1.05 2.78 1.15 1.39 1.81
time (sec) N/A 0.094 0.179 0.010 0.980 0.958 26.173 1.368 0.089
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 77 77 87 89 90 217 92 105 136
normalized size 1 1.00 1.13 1.16 1.17 2.82 1.19 1.36 1.77
time (sec) N/A 0.024 0.132 0.009 0.979 1.076 25.966 1.262 2.487
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 54 54 55 46 60 111 54 57 45
normalized size 1 1.00 1.02 0.85 1.11 2.06 1.00 1.06 0.83
time (sec) N/A 0.016 0.050 0.007 0.974 0.934 6.083 1.201 0.069
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 100 103 0 450 100 112 2355
normalized size 1 1.00 0.99 1.02 0.00 4.46 0.99 1.11 23.32
time (sec) N/A 0.119 0.227 0.016 0.000 1.120 24.251 1.219 2.819
Problem 20 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 128 128 122 137 0 1008 1149 142 1814
normalized size 1 1.00 0.95 1.07 0.00 7.88 8.98 1.11 14.17
time (sec) N/A 0.116 0.196 0.017 0.000 1.263 142.242 1.323 2.952
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 259 221 0 2211 0 301 4839
normalized size 1 1.00 1.26 1.08 0.00 10.79 0.00 1.47 23.60
time (sec) N/A 0.279 0.532 0.019 0.000 2.479 0.000 1.401 4.632
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 89 132 105 65 484 63 345
normalized size 1 1.00 0.80 1.19 0.95 0.59 4.36 0.57 3.11
time (sec) N/A 0.045 0.089 0.036 0.974 0.879 35.797 1.245 7.778
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 81 111 83 57 393 53 269
normalized size 1 1.00 0.93 1.28 0.95 0.66 4.52 0.61 3.09
time (sec) N/A 0.034 0.031 0.015 0.993 1.224 25.601 1.341 5.922
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 73 90 61 49 269 40 191
normalized size 1 1.00 1.16 1.43 0.97 0.78 4.27 0.63 3.03
time (sec) N/A 0.023 0.030 0.016 0.962 0.636 20.771 1.275 4.527
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 61 70 41 43 133 28 118
normalized size 1 1.00 1.65 1.89 1.11 1.16 3.59 0.76 3.19
time (sec) N/A 0.013 0.026 0.019 0.955 0.954 11.713 1.239 3.447
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 53 69 41 47 71 44 47
normalized size 1 1.00 1.83 2.38 1.41 1.62 2.45 1.52 1.62
time (sec) N/A 0.016 0.025 0.019 0.953 0.977 25.620 1.233 2.985
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 29 25 42 27 107 88 24
normalized size 1 1.00 0.64 0.56 0.93 0.60 2.38 1.96 0.53
time (sec) N/A 0.010 0.013 0.004 0.958 0.924 15.238 1.271 2.747
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 37 33 62 35 189 130 32
normalized size 1 1.00 0.51 0.45 0.85 0.48 2.59 1.78 0.44
time (sec) N/A 0.019 0.016 0.005 0.962 0.617 17.839 1.242 2.731
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 45 41 84 43 274 175 40
normalized size 1 1.00 0.46 0.42 0.87 0.44 2.82 1.80 0.41
time (sec) N/A 0.027 0.018 0.007 0.973 0.706 23.154 1.406 2.766
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 53 49 106 51 359 217 48
normalized size 1 1.00 0.44 0.40 0.88 0.42 2.97 1.79 0.40
time (sec) N/A 0.038 0.019 0.006 0.966 0.933 33.865 1.315 2.829
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 48 44 21 40 117 43 65
normalized size 1 1.00 1.23 1.13 0.54 1.03 3.00 1.10 1.67
time (sec) N/A 0.007 0.016 0.018 0.962 0.818 35.801 1.269 4.080
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 48 44 21 40 117 43 444
normalized size 1 1.00 1.23 1.13 0.54 1.03 3.00 1.10 11.38
time (sec) N/A 0.011 0.006 0.005 0.976 0.821 72.778 1.291 5.273
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 309 624 0 0 0 0 -1
normalized size 1 1.00 2.13 4.30 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.108 1.511 0.049 0.000 0.943 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 221 221 312 940 0 0 0 0 -1
normalized size 1 1.00 1.41 4.25 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.199 2.249 0.045 0.000 1.085 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 281 281 135 160 0 0 0 0 -1
normalized size 1 1.00 0.48 0.57 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.389 0.436 0.053 0.000 1.045 0.000 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 243 243 130 155 0 0 0 0 -1
normalized size 1 1.00 0.53 0.64 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.300 0.283 0.013 0.000 1.161 0.000 0.000 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 125 150 0 0 0 0 -1
normalized size 1 1.00 0.65 0.78 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.077 0.246 0.013 0.000 0.923 0.000 0.000 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 Yes TBD TBD TBD TBD TBD TBD
size 162 162 120 145 0 0 0 0 -1
normalized size 1 1.00 0.74 0.90 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.063 0.180 0.012 0.000 0.920 0.000 0.000 0.000
Problem 39 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 182 182 139 183 0 0 0 0 -1
normalized size 1 1.00 0.76 1.01 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.213 0.818 0.024 0.000 1.092 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 130 320 0 0 0 0 -1
normalized size 1 1.00 0.69 1.69 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.211 0.815 0.029 0.000 0.987 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 227 227 134 461 0 0 0 0 -1
normalized size 1 1.00 0.59 2.03 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.309 0.750 0.031 0.000 0.721 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 263 263 139 602 0 0 0 0 -1
normalized size 1 1.00 0.53 2.29 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.397 0.787 0.033 0.000 1.102 0.000 0.000 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 570 570 1820 3678 0 0 0 0 -1
normalized size 1 1.00 3.19 6.45 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.286 14.191 0.072 0.000 0.000 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(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 243 243 130 155 0 0 0 0 -1
normalized size 1 1.00 0.53 0.64 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.297 0.389 0.026 0.000 1.043 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(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 125 150 0 0 0 0 -1
normalized size 1 1.00 0.61 0.73 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.213 0.318 0.015 0.000 0.822 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(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 120 145 0 0 0 0 -1
normalized size 1 1.00 0.74 0.90 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.062 0.206 0.013 0.000 0.936 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 131 131 115 140 0 0 0 0 -1
normalized size 1 1.00 0.88 1.07 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.051 0.195 0.012 0.000 0.930 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(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 95 76 0 0 0 0 -1
normalized size 1 1.00 0.63 0.50 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.121 0.418 0.015 0.000 0.940 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 130 320 0 0 0 0 -1
normalized size 1 1.00 0.69 1.69 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.214 0.659 0.018 0.000 0.858 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 135 461 0 0 0 0 -1
normalized size 1 1.00 0.60 2.05 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.301 0.580 0.019 0.000 0.915 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(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 125 150 0 0 0 0 -1
normalized size 1 1.00 0.61 0.73 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.212 0.373 0.028 0.000 1.055 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 F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 120 145 0 0 0 0 -1
normalized size 1 1.00 0.72 0.87 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.145 0.300 0.017 0.000 0.913 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 Yes TBD TBD TBD TBD TBD TBD
size 131 131 115 140 0 0 0 0 -1
normalized size 1 1.00 0.88 1.07 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.051 0.193 0.015 0.000 0.944 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 111 55 0 0 0 0 -1
normalized size 1 1.00 2.36 1.17 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.015 0.364 0.014 0.000 0.893 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 Yes TBD TBD TBD TBD TBD TBD
size 103 103 70 56 0 0 0 0 -1
normalized size 1 1.00 0.68 0.54 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.096 0.424 0.017 0.000 1.259 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 130 320 0 0 0 0 -1
normalized size 1 1.00 0.69 1.69 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.210 0.691 0.022 0.000 0.953 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 142 461 0 0 0 0 -1
normalized size 1 1.00 0.63 2.05 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.310 0.461 0.023 0.000 1.042 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 293 293 202 382 0 0 0 0 -1
normalized size 1 1.00 0.69 1.30 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.504 1.770 0.051 0.000 0.000 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 449 449 1198 968 0 0 0 0 -1
normalized size 1 1.00 2.67 2.16 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.672 7.744 0.033 0.000 0.000 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 203 203 125 150 0 0 0 0 -1
normalized size 1 1.00 0.62 0.74 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.216 0.530 0.030 0.000 1.404 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 165 165 120 145 0 0 0 0 -1
normalized size 1 1.00 0.73 0.88 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.153 0.372 0.019 0.000 1.406 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 129 129 115 140 0 0 0 0 -1
normalized size 1 1.00 0.89 1.09 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.063 0.257 0.020 0.000 1.255 0.000 0.000 0.000
Problem 63 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 98 98 187 57 0 0 0 0 -1
normalized size 1 1.00 1.91 0.58 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.037 0.478 0.019 0.000 1.218 0.000 0.000 0.000
Problem 64 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 48 48 79 36 0 0 0 0 -1
normalized size 1 1.00 1.65 0.75 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.014 0.112 0.016 0.000 1.072 0.000 0.000 0.000
Problem 65 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 51 51 99 37 0 0 0 0 -1
normalized size 1 1.00 1.94 0.73 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.070 0.487 0.018 0.000 1.015 0.000 0.000 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 130 320 0 0 0 0 -1
normalized size 1 1.00 0.69 1.69 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.220 0.703 0.023 0.000 0.970 0.000 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 142 461 0 0 0 0 -1
normalized size 1 1.00 0.63 2.05 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.310 0.460 0.021 0.000 0.816 0.000 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 180 552 0 0 0 0 -1
normalized size 1 1.00 1.31 4.03 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.061 0.599 0.027 0.000 0.892 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 284 284 319 559 0 0 0 0 -1
normalized size 1 1.00 1.12 1.97 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.169 1.974 0.039 0.000 1.116 0.000 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-1) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 226 223 0 0 0 0 -1
normalized size 1 1.00 1.37 1.35 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.374 1.405 0.030 0.000 0.000 0.000 0.000 0.000
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 393 393 322 2842 0 0 0 0 -1
normalized size 1 1.00 0.82 7.23 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.624 4.051 0.085 0.000 0.000 0.000 0.000 0.000
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 875 875 721 17330 0 0 0 0 -1
normalized size 1 1.00 0.82 19.81 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.339 15.768 0.283 0.000 0.000 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 203 184 0 0 0 0 -1
normalized size 1 1.00 2.74 2.49 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.160 0.905 0.105 0.000 0.000 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 203 181 0 0 0 0 -1
normalized size 1 1.00 2.74 2.45 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.176 0.168 0.028 0.000 0.000 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 218 212 0 0 0 0 -1
normalized size 1 1.00 2.53 2.47 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.160 0.858 0.147 0.000 0.000 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 218 205 0 0 0 0 -1
normalized size 1 1.00 2.53 2.38 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.175 0.162 0.030 0.000 0.000 0.000 0.000 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 471 471 350 895 0 0 0 0 -1
normalized size 1 1.00 0.74 1.90 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.665 4.599 0.081 0.000 1.272 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 429 429 345 890 0 0 0 0 -1
normalized size 1 1.00 0.80 2.07 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.542 4.331 0.023 0.000 0.876 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 391 391 340 885 0 0 0 0 -1
normalized size 1 1.00 0.87 2.26 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.429 4.267 0.020 0.000 1.181 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 351 351 347 880 0 0 0 0 -1
normalized size 1 1.00 0.99 2.51 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.324 3.069 0.035 0.000 1.261 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 349 349 330 875 0 0 0 0 -1
normalized size 1 1.00 0.95 2.51 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.319 2.977 0.046 0.000 0.953 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 391 391 366 1149 0 0 0 0 -1
normalized size 1 1.00 0.94 2.94 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.429 3.226 0.047 0.000 0.934 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 330 330 251 973 0 0 0 0 -1
normalized size 1 1.00 0.76 2.95 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.395 2.458 0.048 0.000 0.641 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 370 370 259 1160 0 0 0 0 -1
normalized size 1 1.00 0.70 3.14 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.515 2.806 0.051 0.000 0.742 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 429 429 345 890 0 0 0 0 -1
normalized size 1 1.00 0.80 2.07 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.526 3.852 0.042 0.000 0.831 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 391 391 340 885 0 0 0 0 -1
normalized size 1 1.00 0.87 2.26 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.412 3.771 0.024 0.000 0.753 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 351 351 347 880 0 0 0 0 -1
normalized size 1 1.00 0.99 2.51 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.316 4.214 0.022 0.000 0.807 0.000 0.000 0.000
Problem 88 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 365 365 318 875 0 0 0 0 -1
normalized size 1 1.00 0.87 2.40 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.216 1.289 0.026 0.000 0.881 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 279 279 326 870 0 0 0 0 -1
normalized size 1 1.00 1.17 3.12 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.195 2.467 0.029 0.000 0.756 0.000 0.000 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 290 290 246 786 0 0 0 0 -1
normalized size 1 1.00 0.85 2.71 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.320 1.950 0.030 0.000 0.947 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 330 330 251 973 0 0 0 0 -1
normalized size 1 1.00 0.76 2.95 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.398 1.868 0.031 0.000 0.752 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 370 370 258 1160 0 0 0 0 -1
normalized size 1 1.00 0.70 3.14 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.521 2.451 0.035 0.000 0.705 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 391 391 340 885 0 0 0 0 -1
normalized size 1 1.00 0.87 2.26 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.421 2.617 0.041 0.000 0.956 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 351 351 349 880 0 0 0 0 -1
normalized size 1 1.00 0.99 2.51 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.322 3.341 0.027 0.000 0.811 0.000 0.000 0.000
Problem 95 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 365 365 347 875 0 0 0 0 -1
normalized size 1 1.00 0.95 2.40 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.202 1.472 0.026 0.000 0.894 0.000 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 101 101 170 172 0 0 0 0 -1
normalized size 1 1.00 1.68 1.70 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.037 0.588 0.028 0.000 0.817 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B B B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 195 237 330 0 0 0 0 -1
normalized size 1 3.25 3.95 5.50 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.131 1.860 0.030 0.000 0.759 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 290 290 248 786 0 0 0 0 -1
normalized size 1 1.00 0.86 2.71 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.296 1.916 0.032 0.000 0.878 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 721 721 6667 18077 0 0 0 0 -1
normalized size 1 1.00 9.25 25.07 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.675 15.046 0.157 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 B F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 208 206 4590 0 0 0 0 -1
normalized size 1 1.29 1.28 28.51 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.093 5.206 0.128 0.000 3.356 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 351 351 347 880 0 0 0 0 -1
normalized size 1 1.00 0.99 2.51 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.319 2.606 0.041 0.000 0.714 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 469 469 347 875 0 0 0 0 -1
normalized size 1 1.00 0.74 1.87 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.280 1.323 0.029 0.000 0.654 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 95 170 0 0 0 0 -1
normalized size 1 1.00 0.95 1.70 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.038 0.171 0.026 0.000 0.781 0.000 0.000 0.000
Problem 104 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 71 71 90 134 0 0 0 0 -1
normalized size 1 1.00 1.27 1.89 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.043 0.163 0.026 0.000 0.760 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 270 237 599 0 0 0 0 -1
normalized size 1 1.38 1.22 3.07 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.183 1.691 0.032 0.000 0.589 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 288 288 246 786 0 0 0 0 -1
normalized size 1 1.00 0.85 2.73 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.303 1.826 0.035 0.000 0.699 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 968 968 6638 16526 0 0 0 0 -1
normalized size 1 1.00 6.86 17.07 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.882 14.158 0.102 0.000 0.000 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 228 228 584 2465 0 0 0 0 -1
normalized size 1 1.00 2.56 10.81 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.150 5.576 0.060 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 A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 198 227 270 0 0 0 0 -1
normalized size 1 1.23 1.41 1.68 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.082 1.337 0.066 0.000 5.871 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 429 429 3247 4660 0 0 0 0 -1
normalized size 1 1.00 7.57 10.86 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.256 14.142 0.113 0.000 0.947 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B B F F F(-1) F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 786 0 7075 21102 0 0 0 0 -1
normalized size 1 0.00 9.00 26.85 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.010 17.287 0.253 0.000 6.358 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 319 319 285 0 0 0 0 0 -1
normalized size 1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.279 0.986 0.261 0.000 0.802 0.000 0.000 0.000
Problem 113 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 216 216 174 0 0 0 0 0 -1
normalized size 1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.154 0.427 0.275 0.000 0.718 0.000 0.000 0.000
Problem 114 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 158 158 153 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 0.107 0.074 0.252 0.000 0.965 0.000 0.000 0.000
Problem 115 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 124 124 116 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 0.039 0.036 0.247 0.000 0.948 0.000 0.000 0.000
Problem 116 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 124 124 116 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 0.033 0.033 0.248 0.000 0.870 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 175 175 170 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 0.119 0.192 0.248 0.000 0.875 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(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 222 222 177 0 0 0 0 0 -1
normalized size 1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.151 0.278 0.249 0.000 0.720 0.000 0.000 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 149 726 474 877 8221 1665 819
normalized size 1 1.00 0.89 4.35 2.84 5.25 49.23 9.97 4.90
time (sec) N/A 0.131 0.231 0.010 0.542 0.923 8.124 1.028 2.945
Problem 120 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 134 134 120 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 0.086 0.198 0.277 0.000 0.939 0.000 0.000 0.000
Problem 121 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 140 140 115 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 0.059 0.079 0.253 0.000 0.799 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 224 224 193 0 0 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.195 0.369 0.260 0.000 0.854 0.000 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 104 0 0 0 0 0 -1
normalized size 1 1.00 0.74 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.123 0.231 0.250 0.000 0.722 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 266 266 195 0 0 0 0 0 -1
normalized size 1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.165 0.240 0.244 0.000 0.958 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 245 245 195 0 0 0 0 0 -1
normalized size 1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.155 0.265 0.238 0.000 0.918 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 235 235 189 0 0 0 0 0 -1
normalized size 1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.138 0.218 0.240 0.000 1.104 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 261 261 221 0 0 0 0 0 -1
normalized size 1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.186 0.208 0.242 0.000 0.910 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 205 198 0 0 0 0 0 -1
normalized size 1 1.01 0.98 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.107 0.231 0.289 0.000 0.997 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 246 246 237 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.160 0.322 0.260 0.000 0.943 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 362 362 220 894 0 1659 0 0 1895
normalized size 1 1.00 0.61 2.47 0.00 4.58 0.00 0.00 5.23
time (sec) N/A 0.362 0.478 0.010 0.000 1.079 0.000 0.000 4.487
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 507 507 279 2343 0 3441 0 0 3720
normalized size 1 1.00 0.55 4.62 0.00 6.79 0.00 0.00 7.34
time (sec) N/A 0.586 0.702 0.017 0.000 1.177 0.000 0.000 6.752
Problem 132 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 815 803 3579 0 0 0 0 0 -1
normalized size 1 0.99 4.39 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.435 44.242 0.240 0.000 0.990 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 572 566 422 0 0 0 0 0 -1
normalized size 1 0.99 0.74 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.662 1.907 0.237 0.000 1.052 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 363 360 227 906 0 1608 0 0 1890
normalized size 1 0.99 0.63 2.50 0.00 4.43 0.00 0.00 5.21
time (sec) N/A 0.397 0.548 0.010 0.000 1.051 0.000 0.000 4.277
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 188 186 181 509 0 905 0 0 869
normalized size 1 0.99 0.96 2.71 0.00 4.81 0.00 0.00 4.62
time (sec) N/A 0.098 0.128 0.010 0.000 0.870 0.000 0.000 3.407
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 177 190 199 0 0 0 0 0 -1
normalized size 1 1.07 1.12 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.119 0.399 0.247 0.000 0.600 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 233 220 174 0 0 0 0 0 -1
normalized size 1 0.94 0.75 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.127 0.140 0.254 0.000 0.664 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 250 250 184 0 0 0 0 0 -1
normalized size 1 1.00 0.74 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.217 0.226 0.257 0.000 1.030 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 530 530 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.179 4.532 0.361 0.000 3.375 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 393 393 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.493 1.529 0.251 0.000 3.521 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 256 256 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.210 0.834 0.256 0.000 2.275 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 121 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 0.083 0.133 0.000 0.000 1.056 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 32 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 -0.03
time (sec) N/A 0.008 0.252 0.262 0.000 0.811 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 268 268 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.212 0.646 0.252 0.000 1.193 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 283 283 208 0 0 0 0 0 -1
normalized size 1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.208 0.326 0.287 0.000 1.238 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 277 277 215 0 0 0 0 0 -1
normalized size 1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.147 0.435 0.253 0.000 1.486 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 263 261 223 0 0 0 0 0 -1
normalized size 1 0.99 0.85 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.227 0.271 0.250 0.000 2.173 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 558 558 508 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 0.981 1.942 0.253 0.000 2.547 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 57 139 87 78 313 101 244
normalized size 1 1.00 0.72 1.76 1.10 0.99 3.96 1.28 3.09
time (sec) N/A 0.142 0.066 0.043 0.967 0.787 82.403 1.339 7.441
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 45 117 57 67 282 76 232
normalized size 1 1.00 0.71 1.86 0.90 1.06 4.48 1.21 3.68
time (sec) N/A 0.061 0.035 0.020 0.970 0.537 49.786 1.315 6.988
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 48 96 57 81 245 0 122
normalized size 1 1.00 1.00 2.00 1.19 1.69 5.10 0.00 2.54
time (sec) N/A 0.184 0.060 0.028 0.969 0.614 55.199 0.000 3.924
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 48 97 57 84 221 0 114
normalized size 1 1.00 1.00 2.02 1.19 1.75 4.60 0.00 2.38
time (sec) N/A 0.183 0.060 0.023 0.971 0.844 49.853 0.000 3.741
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 56 108 98 65 218 0 312
normalized size 1 1.00 0.79 1.52 1.38 0.92 3.07 0.00 4.39
time (sec) N/A 0.188 0.050 0.022 0.967 0.702 80.293 0.000 5.854
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A C A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 87 151 149 137 100 73 308 105 318
normalized size 1 1.74 1.71 1.57 1.15 0.84 3.54 1.21 3.66
time (sec) N/A 0.146 0.349 0.026 0.434 0.578 78.825 1.303 12.354
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B B C B A C A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 52 135 126 120 90 61 277 80 312
normalized size 1 2.60 2.42 2.31 1.73 1.17 5.33 1.54 6.00
time (sec) N/A 0.071 0.225 0.018 0.426 0.762 48.292 1.253 12.400
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B B C A A C A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 55 135 128 95 56 73 240 71 118
normalized size 1 2.45 2.33 1.73 1.02 1.33 4.36 1.29 2.15
time (sec) N/A 0.184 0.418 0.023 0.962 0.599 47.403 1.295 3.975
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B A C A A C A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 55 135 89 96 56 82 216 83 118
normalized size 1 2.45 1.62 1.75 1.02 1.49 3.93 1.51 2.15
time (sec) N/A 0.182 0.185 0.023 0.965 0.642 45.925 1.347 3.859
Problem 158 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 83 129 82 103 61 69 212 145 316
normalized size 1 1.55 0.99 1.24 0.73 0.83 2.55 1.75 3.81
time (sec) N/A 0.189 0.144 0.023 0.972 0.589 74.795 1.350 9.891
Problem 159 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 116 171 94 123 86 90 219 197 304
normalized size 1 1.47 0.81 1.06 0.74 0.78 1.89 1.70 2.62
time (sec) N/A 0.221 0.133 0.023 0.983 0.626 129.782 1.348 9.436

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 [72] had the largest ratio of [.3429]

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 21 0.048
2 A 2 1 1.00 23 0.043
3 A 2 1 1.00 25 0.040
4 A 2 1 1.00 27 0.037
5 A 2 1 1.00 29 0.034
6 A 2 1 1.00 17 0.059
7 A 3 2 1.00 22 0.091
8 A 6 5 1.00 25 0.200
9 A 5 5 1.00 25 0.200
10 A 4 4 1.00 23 0.174
11 A 4 4 1.00 18 0.222
12 A 6 4 1.00 25 0.160
13 A 6 4 1.00 25 0.160
14 A 7 5 1.00 25 0.200
15 A 6 5 1.00 25 0.200
16 A 5 5 1.00 25 0.200
17 A 4 4 1.00 23 0.174
18 A 4 4 1.00 18 0.222
19 A 6 5 1.00 25 0.200
20 A 6 5 1.00 25 0.200
21 A 7 6 1.00 25 0.240
22 A 8 6 1.00 26 0.231
23 A 7 6 1.00 26 0.231
24 A 6 6 1.00 24 0.250
25 A 4 4 1.00 23 0.174
26 A 5 5 1.00 26 0.192
27 A 3 3 1.00 26 0.115
28 A 4 4 1.00 26 0.154
29 A 5 4 1.00 26 0.154
30 A 6 4 1.00 26 0.154
31 A 4 4 1.00 24 0.167
32 A 5 5 1.00 36 0.139
33 A 3 3 1.00 45 0.067
34 A 5 5 1.00 39 0.128
35 A 10 8 1.00 35 0.229
36 A 9 8 1.00 35 0.229
37 A 8 6 1.00 33 0.182
38 A 7 7 1.00 28 0.250
39 A 10 10 1.00 35 0.286
40 A 10 10 1.00 35 0.286
41 A 11 11 1.00 35 0.314
42 A 12 11 1.00 35 0.314
43 A 12 10 1.00 35 0.286
44 A 9 8 1.00 35 0.229
45 A 8 8 1.00 35 0.229
46 A 7 6 1.00 33 0.182
47 A 6 6 1.00 28 0.214
48 A 9 9 1.00 35 0.257
49 A 10 10 1.00 35 0.286
50 A 11 11 1.00 35 0.314
51 A 8 8 1.00 35 0.229
52 A 7 7 1.00 35 0.200
53 A 6 6 1.00 33 0.182
54 A 2 2 1.00 28 0.071
55 A 6 6 1.00 35 0.171
56 A 10 10 1.00 35 0.286
57 A 11 11 1.00 35 0.314
58 A 8 6 1.00 35 0.171
59 A 11 8 1.00 35 0.229
60 A 8 8 1.00 35 0.229
61 A 7 7 1.00 35 0.200
62 A 7 7 1.00 35 0.200
63 A 5 5 1.00 33 0.152
64 A 2 2 1.00 28 0.071
65 A 3 3 1.00 35 0.086
66 A 10 10 1.00 35 0.286
67 A 11 11 1.00 35 0.314
68 A 3 3 1.00 36 0.083
69 A 6 5 1.00 33 0.152
70 A 4 3 1.00 35 0.086
71 A 10 8 1.00 35 0.229
72 A 18 12 1.00 35 0.343
73 A 3 3 1.00 36 0.083
74 A 4 4 1.00 31 0.129
75 A 3 3 1.00 40 0.075
76 A 4 4 1.00 31 0.129
77 A 12 10 1.00 37 0.270
78 A 11 10 1.00 37 0.270
79 A 10 10 1.00 37 0.270
80 A 9 9 1.00 37 0.243
81 A 9 9 1.00 37 0.243
82 A 10 10 1.00 37 0.270
83 A 9 9 1.00 37 0.243
84 A 10 9 1.00 37 0.243
85 A 11 10 1.00 37 0.270
86 A 10 10 1.00 37 0.270
87 A 9 9 1.00 37 0.243
88 A 9 8 1.00 37 0.216
89 A 7 7 1.00 37 0.189
90 A 8 8 1.00 37 0.216
91 A 9 9 1.00 37 0.243
92 A 10 9 1.00 37 0.243
93 A 10 10 1.00 37 0.270
94 A 9 9 1.00 37 0.243
95 A 9 8 1.00 37 0.216
96 A 2 2 1.00 37 0.054
97 B 5 5 3.25 37 0.135
98 A 8 8 1.00 37 0.216
99 A 7 7 1.00 37 0.189
100 A 2 2 1.29 37 0.054
101 A 9 9 1.00 37 0.243
102 A 12 10 1.00 37 0.270
103 A 2 2 1.00 37 0.054
104 A 2 2 1.00 37 0.054
105 A 8 7 1.38 37 0.189
106 A 8 8 1.00 37 0.216
107 A 10 8 1.00 37 0.216
108 A 2 2 1.00 37 0.054
109 A 2 2 1.23 37 0.054
110 A 5 5 1.00 37 0.135
111 F 0 0 N/A 0 N/A
112 A 8 3 1.00 25 0.120
113 A 6 3 1.00 25 0.120
114 A 4 2 1.00 25 0.080
115 A 3 2 1.00 23 0.087
116 A 3 2 1.00 22 0.091
117 A 5 3 1.00 25 0.120
118 A 6 3 1.00 25 0.120
119 A 2 1 1.00 23 0.043
120 A 2 2 1.00 25 0.080
121 A 3 2 1.00 27 0.074
122 A 5 2 1.00 29 0.069
123 A 6 3 1.00 25 0.120
124 A 3 3 1.00 25 0.120
125 A 3 3 1.00 29 0.103
126 A 3 3 1.00 27 0.111
127 A 3 3 1.00 29 0.103
128 A 3 3 1.01 29 0.103
129 A 3 3 1.00 29 0.103
130 A 3 3 1.00 29 0.103
131 A 4 3 1.00 29 0.103
132 A 10 9 0.99 31 0.290
133 A 9 8 0.99 31 0.258
134 A 3 3 0.99 29 0.103
135 A 3 3 0.99 24 0.125
136 A 5 5 1.07 27 0.185
137 A 7 5 0.94 29 0.172
138 A 7 4 1.00 29 0.138
139 A 31 5 1.00 29 0.172
140 A 15 5 1.00 29 0.172
141 A 7 4 1.00 27 0.148
142 A 3 3 1.00 22 0.136
143 A 0 0 0.00 0 0.000
144 A 7 4 1.00 33 0.121
145 A 7 4 1.00 34 0.118
146 A 5 5 1.00 34 0.147
147 A 3 3 0.99 34 0.088
148 A 4 3 1.00 34 0.088
149 A 4 4 1.00 31 0.129
150 A 4 4 1.00 30 0.133
151 A 7 7 1.00 33 0.212
152 A 7 7 1.00 33 0.212
153 A 6 6 1.00 33 0.182
154 A 5 5 1.74 30 0.167
155 B 5 5 2.60 29 0.172
156 B 8 8 2.45 32 0.250
157 B 8 8 2.45 32 0.250
158 A 6 6 1.55 32 0.188
159 A 7 7 1.47 32 0.219

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