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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174 }

B grade: { }

C grade: { 13, 14, 20, 21, 148, 149, 150 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 163, 164, 165, 166, 167, 168, 169, 170, 171, 174 }

B grade: { 48, 161, 162, 172, 173 }

C grade: { }

F grade: { 58, 59, 60, 61 }

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, 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, 50, 51, 52, 53, 54, 55, 56, 57, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 164, 165, 166, 167, 168, 169, 170, 171 }

B grade: { 47, 48, 49, 159, 160, 161, 162, 163, 172, 173, 174 }

C grade: { }

F grade: { 58, 59, 60, 61 }

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, 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, 66, 67, 68, 69, 74, 75, 76, 77, 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, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174 }

B grade: { 107, 108, 109 }

C grade: { }

F grade: { 58, 59, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 78, 79, 80, 81 }

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, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 35, 36, 38, 43, 44, 45, 46, 53, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 105, 106, 110, 111, 112, 113, 114, 116, 117, 120, 123, 124, 125, 126, 127, 128, 129, 130, 133, 134, 135, 136, 137, 138, 139, 140, 143, 144, 145, 146, 147, 153, 154, 155, 156, 169, 170, 171 }

B grade: { 25, 33, 34, 37, 39, 40, 41, 42, 52, 54, 55, 56, 86, 87, 88, 89, 90, 94, 95, 96, 97, 98, 102, 103, 104, 115, 118, 119, 121, 122, 131, 151, 152, 157, 158 }

C grade: { 58, 59, 60, 61 }

F grade: { 47, 48, 49, 50, 51, 57, 91, 92, 93, 99, 100, 101, 107, 108, 109, 132, 141, 142, 148, 149, 150, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 172, 173, 174 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 169, 170, 171, 172, 173, 174 }

B grade: { 7, 14, 28, 35, 45, 150, 156, 157, 158, 166, 167, 168 }

C grade: { }

F grade: { 58, 59, 60, 61 }

2.1.8 Mupad

A grade: { }

B grade: { 4, 5, 6, 7, 11, 12, 13, 14, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 90, 92, 93, 96, 98, 100, 101, 102, 104, 106, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 155, 156, 157, 158, 166, 167, 169, 170, 171 }

C grade: { }

F grade: { 1, 2, 3, 8, 9, 10, 15, 16, 17, 22, 29, 36, 47, 48, 58, 59, 60, 61, 86, 87, 88, 89, 91, 94, 95, 97, 99, 103, 105, 107, 151, 152, 153, 154, 159, 160, 161, 162, 163, 164, 165, 168, 172, 173, 174 }

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 F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 107 115 107 206 192 93 -1
normalized size 1 1.00 0.84 0.91 0.84 1.62 1.51 0.73 -0.01
time (sec) N/A 0.082 0.231 0.010 1.407 0.939 16.250 0.509 0.000
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 93 94 86 175 165 81 -1
normalized size 1 1.00 0.89 0.90 0.83 1.68 1.59 0.78 -0.01
time (sec) N/A 0.049 0.192 0.007 1.363 0.632 10.139 0.471 0.000
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 86 75 67 157 124 68 -1
normalized size 1 1.00 1.08 0.94 0.84 1.96 1.55 0.85 -0.01
time (sec) N/A 0.026 0.152 0.005 1.319 0.575 14.405 0.440 0.000
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 67 53 45 128 70 55 52
normalized size 1 1.00 1.00 0.79 0.67 1.91 1.04 0.82 0.78
time (sec) N/A 0.019 0.057 0.006 1.318 1.199 6.510 0.414 1.162
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 79 79 100 78 59 341 107 78 68
normalized size 1 1.00 1.27 0.99 0.75 4.32 1.35 0.99 0.86
time (sec) N/A 0.061 0.253 0.006 1.360 0.990 8.800 0.452 1.236
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 75 75 99 97 59 333 124 102 89
normalized size 1 1.00 1.32 1.29 0.79 4.44 1.65 1.36 1.19
time (sec) N/A 0.059 0.178 0.010 1.386 1.380 11.972 0.474 1.688
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 108 121 83 377 107 163 94
normalized size 1 1.00 1.35 1.51 1.04 4.71 1.34 2.04 1.18
time (sec) N/A 0.060 0.093 0.007 1.362 0.957 5.499 0.482 1.795
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 126 134 126 254 318 115 -1
normalized size 1 1.00 0.84 0.89 0.84 1.69 2.12 0.77 -0.01
time (sec) N/A 0.095 0.258 0.012 1.390 0.951 20.789 0.440 0.000
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 113 113 105 223 287 103 -1
normalized size 1 1.00 0.89 0.89 0.83 1.76 2.26 0.81 -0.01
time (sec) N/A 0.062 0.240 0.009 1.374 0.857 20.411 0.506 0.000
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 107 94 86 205 223 89 -1
normalized size 1 1.00 1.04 0.91 0.83 1.99 2.17 0.86 -0.01
time (sec) N/A 0.033 0.194 0.006 1.351 0.841 22.469 0.473 0.000
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 87 87 88 69 61 176 219 76 54
normalized size 1 1.00 1.01 0.79 0.70 2.02 2.52 0.87 0.62
time (sec) N/A 0.026 0.078 0.005 1.412 1.021 12.912 0.440 1.182
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 106 106 118 107 88 439 218 100 83
normalized size 1 1.00 1.11 1.01 0.83 4.14 2.06 0.94 0.78
time (sec) N/A 0.094 0.306 0.009 1.319 0.979 35.492 0.539 1.312
Problem 13 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 108 108 105 126 88 411 184 124 86
normalized size 1 1.00 0.97 1.17 0.81 3.81 1.70 1.15 0.80
time (sec) N/A 0.089 0.184 0.009 1.386 0.676 13.290 0.602 1.877
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 90 150 112 425 182 191 91
normalized size 1 1.00 0.81 1.35 1.01 3.83 1.64 1.72 0.82
time (sec) N/A 0.085 0.063 0.010 1.279 0.944 15.566 0.550 2.120
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 145 153 145 302 469 140 -1
normalized size 1 1.00 0.84 0.88 0.84 1.75 2.71 0.81 -0.01
time (sec) N/A 0.105 0.402 0.010 1.358 1.026 37.442 0.529 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 131 132 124 271 442 128 -1
normalized size 1 1.00 0.87 0.88 0.83 1.81 2.95 0.85 -0.01
time (sec) N/A 0.069 0.406 0.007 1.373 0.935 61.217 0.460 0.000
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 112 113 105 253 354 114 -1
normalized size 1 1.00 0.89 0.90 0.83 2.01 2.81 0.90 -0.01
time (sec) N/A 0.044 0.550 0.007 1.444 0.954 26.540 0.499 0.000
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 107 107 108 85 77 224 348 101 54
normalized size 1 1.00 1.01 0.79 0.72 2.09 3.25 0.94 0.50
time (sec) N/A 0.037 0.088 0.005 1.397 0.863 26.046 0.608 1.163
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 132 132 139 138 119 539 323 125 101
normalized size 1 1.00 1.05 1.05 0.90 4.08 2.45 0.95 0.77
time (sec) N/A 0.159 0.361 0.007 1.378 0.636 40.753 0.585 1.247
Problem 20 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 136 136 117 158 120 519 318 150 104
normalized size 1 1.00 0.86 1.16 0.88 3.82 2.34 1.10 0.76
time (sec) N/A 0.132 0.232 0.010 1.403 1.018 18.911 0.499 2.164
Problem 21 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 141 141 92 181 143 535 279 219 111
normalized size 1 1.00 0.65 1.28 1.01 3.79 1.98 1.55 0.79
time (sec) N/A 0.117 0.035 0.012 1.382 0.891 12.983 0.569 2.591
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 76 96 88 158 150 74 -1
normalized size 1 1.00 0.73 0.92 0.85 1.52 1.44 0.71 -0.01
time (sec) N/A 0.077 0.051 0.010 1.361 0.672 7.912 0.498 0.000
Problem 23 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 64 75 67 127 94 61 93
normalized size 1 1.00 0.79 0.93 0.83 1.57 1.16 0.75 1.15
time (sec) N/A 0.042 0.060 0.008 1.293 0.906 6.228 0.524 1.467
Problem 24 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 55 47 109 70 50 82
normalized size 1 1.00 1.02 0.98 0.84 1.95 1.25 0.89 1.46
time (sec) N/A 0.023 0.042 0.004 1.326 1.194 6.255 0.479 1.237
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 46 37 29 92 102 39 36
normalized size 1 1.00 1.07 0.86 0.67 2.14 2.37 0.91 0.84
time (sec) N/A 0.015 0.059 0.006 1.355 0.934 2.641 0.547 1.144
Problem 26 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 53 52 33 273 99 58 42
normalized size 1 1.00 1.00 0.98 0.62 5.15 1.87 1.09 0.79
time (sec) N/A 0.040 0.020 0.007 1.377 0.668 5.141 0.499 1.299
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 47 49 37 101 41 65 39
normalized size 1 1.00 1.00 1.04 0.79 2.15 0.87 1.38 0.83
time (sec) N/A 0.033 0.039 0.007 1.306 0.954 2.799 0.511 1.201
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 63 68 56 123 66 146 58
normalized size 1 1.00 0.88 0.94 0.78 1.71 0.92 2.03 0.81
time (sec) N/A 0.053 0.136 0.011 1.315 0.832 7.056 0.431 1.350
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 72 93 85 197 117 70 -1
normalized size 1 1.00 0.89 1.15 1.05 2.43 1.44 0.86 -0.01
time (sec) N/A 0.043 0.063 0.010 1.352 1.004 10.335 0.512 0.000
Problem 30 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 66 66 67 72 64 164 83 58 61
normalized size 1 1.00 1.02 1.09 0.97 2.48 1.26 0.88 0.92
time (sec) N/A 0.036 0.059 0.007 1.296 0.982 16.608 0.547 1.342
Problem 31 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 64 54 46 147 66 48 53
normalized size 1 1.00 1.33 1.12 0.96 3.06 1.38 1.00 1.10
time (sec) N/A 0.020 0.081 0.007 1.309 1.418 15.185 0.498 1.055
Problem 32 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 28 28 27 26 31 35 46 23 24
normalized size 1 1.00 0.96 0.93 1.11 1.25 1.64 0.82 0.86
time (sec) N/A 0.007 0.032 0.003 1.366 0.782 10.223 0.443 0.909
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 47 60 48 146 206 59 50
normalized size 1 1.00 1.00 1.28 1.02 3.11 4.38 1.26 1.06
time (sec) N/A 0.038 0.048 0.009 1.299 1.158 11.294 0.445 1.291
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 72 80 68 169 235 96 70
normalized size 1 1.00 1.03 1.14 0.97 2.41 3.36 1.37 1.00
time (sec) N/A 0.057 0.044 0.009 1.319 1.152 15.826 0.502 1.448
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 75 101 89 211 124 171 94
normalized size 1 1.00 0.79 1.06 0.94 2.22 1.31 1.80 0.99
time (sec) N/A 0.078 0.223 0.010 1.353 1.229 10.795 0.497 1.592
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 69 91 102 239 400 70 -1
normalized size 1 1.00 0.87 1.15 1.29 3.03 5.06 0.89 -0.01
time (sec) N/A 0.042 0.124 0.010 1.409 1.056 18.323 0.482 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 44 41 70 63 141 36 51
normalized size 1 1.00 0.83 0.77 1.32 1.19 2.66 0.68 0.96
time (sec) N/A 0.022 0.055 0.006 1.360 0.917 17.325 0.482 0.967
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 47 32 29 51 49 95 26 34
normalized size 1 0.94 0.64 0.58 1.02 0.98 1.90 0.52 0.68
time (sec) N/A 0.014 0.023 0.003 1.311 0.660 13.983 0.518 0.924
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 43 40 48 62 146 37 41
normalized size 1 1.00 0.84 0.78 0.94 1.22 2.86 0.73 0.80
time (sec) N/A 0.010 0.047 0.004 1.367 0.608 13.203 0.478 0.929
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 69 92 80 239 840 82 80
normalized size 1 1.00 0.91 1.21 1.05 3.14 11.05 1.08 1.05
time (sec) N/A 0.063 0.098 0.008 1.367 0.666 25.923 0.540 1.375
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 95 112 100 264 910 119 96
normalized size 1 1.00 0.91 1.08 0.96 2.54 8.75 1.14 0.92
time (sec) N/A 0.088 0.073 0.010 1.342 0.742 24.183 0.553 1.579
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 106 134 122 307 1034 197 123
normalized size 1 1.00 0.82 1.04 0.95 2.38 8.02 1.53 0.95
time (sec) N/A 0.119 0.215 0.011 1.342 0.726 24.756 0.534 1.621
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 24 29 28 31 24 19 20
normalized size 1 1.00 0.89 1.07 1.04 1.15 0.89 0.70 0.74
time (sec) N/A 0.008 0.030 0.008 2.969 0.594 0.240 0.471 0.040
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 24 29 28 31 24 19 20
normalized size 1 1.00 0.89 1.07 1.04 1.15 0.89 0.70 0.74
time (sec) N/A 0.017 0.020 0.005 2.889 0.618 0.294 0.417 0.033
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 33 15 22 26 27 30 14
normalized size 1 1.00 1.94 0.88 1.29 1.53 1.59 1.76 0.82
time (sec) N/A 0.006 0.009 0.003 2.876 0.617 0.186 0.410 0.919
Problem 46 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 6 6 6 7 6 6 5 6 6
normalized size 1 1.00 1.00 1.17 1.00 1.00 0.83 1.00 1.00
time (sec) N/A 0.003 0.005 0.003 2.972 0.691 0.153 0.458 0.039
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 213 213 165 265 435 522 0 204 -1
normalized size 1 1.00 0.77 1.24 2.04 2.45 0.00 0.96 -0.00
time (sec) N/A 0.324 0.649 0.048 1.680 1.106 0.000 0.539 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 147 277 447 467 0 138 -1
normalized size 1 1.00 0.98 1.85 2.98 3.11 0.00 0.92 -0.01
time (sec) N/A 0.165 0.408 0.013 1.635 0.885 0.000 0.527 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 89 95 240 137 0 112 196
normalized size 1 1.00 0.67 0.72 1.82 1.04 0.00 0.85 1.48
time (sec) N/A 0.166 0.114 0.005 1.443 1.026 0.000 0.624 1.274
Problem 50 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 149 149 78 76 253 122 0 81 186
normalized size 1 1.00 0.52 0.51 1.70 0.82 0.00 0.54 1.25
time (sec) N/A 0.181 0.104 0.008 1.418 0.593 0.000 0.580 1.192
Problem 51 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 139 139 84 85 179 131 0 95 133
normalized size 1 1.00 0.60 0.61 1.29 0.94 0.00 0.68 0.96
time (sec) N/A 0.151 0.126 0.008 1.380 0.634 0.000 0.586 1.138
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 139 139 87 88 197 134 904 94 133
normalized size 1 1.00 0.63 0.63 1.42 0.96 6.50 0.68 0.96
time (sec) N/A 0.131 0.142 0.008 1.420 0.514 118.646 0.518 1.094
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 75 73 123 119 796 82 99
normalized size 1 1.00 0.63 0.61 1.03 1.00 6.69 0.69 0.83
time (sec) N/A 0.088 0.088 0.005 1.341 0.692 85.296 0.604 1.049
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 92 96 153 137 1880 112 115
normalized size 1 1.00 0.72 0.76 1.20 1.08 14.80 0.88 0.91
time (sec) N/A 0.069 0.086 0.007 1.334 0.710 94.218 0.504 1.033
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 120 169 157 465 6613 152 159
normalized size 1 1.00 0.87 1.22 1.14 3.37 47.92 1.10 1.15
time (sec) N/A 0.162 0.229 0.012 1.448 0.768 107.414 0.573 1.620
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 188 188 158 240 228 525 6922 239 225
normalized size 1 1.00 0.84 1.28 1.21 2.79 36.82 1.27 1.20
time (sec) N/A 0.381 0.217 0.012 1.412 0.755 165.702 0.511 2.095
Problem 57 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 219 219 178 288 265 688 0 325 279
normalized size 1 1.00 0.81 1.32 1.21 3.14 0.00 1.48 1.27
time (sec) N/A 0.480 0.534 0.015 1.495 0.932 0.000 0.484 2.518
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 43 0 0 0 97 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 2.16 0.00 -0.02
time (sec) N/A 0.017 0.009 0.071 0.000 0.690 1.970 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 82 0 0 0 192 0 -1
normalized size 1 1.00 0.90 0.00 0.00 0.00 2.11 0.00 -0.01
time (sec) N/A 0.043 0.041 0.067 0.000 0.696 6.404 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 56 0 0 0 204 0 -1
normalized size 1 1.00 0.74 0.00 0.00 0.00 2.68 0.00 -0.01
time (sec) N/A 0.039 0.072 0.067 0.000 0.656 6.475 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 99 0 0 0 298 0 -1
normalized size 1 1.00 0.82 0.00 0.00 0.00 2.46 0.00 -0.01
time (sec) N/A 0.122 0.095 0.066 0.000 0.633 7.602 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 65 54 53 0 60 57 57
normalized size 1 1.00 1.00 0.83 0.82 0.00 0.92 0.88 0.88
time (sec) N/A 0.074 0.031 0.003 1.341 0.000 0.101 0.369 1.205
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 65 54 53 0 60 57 57
normalized size 1 1.00 1.00 0.83 0.82 0.00 0.92 0.88 0.88
time (sec) N/A 0.076 0.016 0.002 1.325 0.000 0.091 0.379 1.184
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 65 54 53 0 60 57 57
normalized size 1 1.00 1.00 0.83 0.82 0.00 0.92 0.88 0.88
time (sec) N/A 0.061 0.010 0.003 1.312 0.000 0.136 0.318 1.185
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 60 51 50 0 56 54 54
normalized size 1 1.00 1.00 0.85 0.83 0.00 0.93 0.90 0.90
time (sec) N/A 0.041 0.009 0.000 1.322 0.000 0.121 0.361 1.164
Problem 66 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 56 53 48 48 54 53 52
normalized size 1 1.00 1.00 0.95 0.86 0.86 0.96 0.95 0.93
time (sec) N/A 0.040 0.016 0.003 1.354 0.722 0.325 0.410 1.170
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 50 48 55 49 50 49
normalized size 1 1.00 1.00 0.93 0.89 1.02 0.91 0.93 0.91
time (sec) N/A 0.048 0.055 0.006 1.343 0.727 0.280 0.386 1.145
Problem 68 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 51 48 48 55 51 48 47
normalized size 1 1.00 0.94 0.89 0.89 1.02 0.94 0.89 0.87
time (sec) N/A 0.048 0.037 0.007 1.316 0.625 0.507 0.375 1.138
Problem 69 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 51 49 55 54 50 50
normalized size 1 1.00 1.02 0.94 0.91 1.02 1.00 0.93 0.93
time (sec) N/A 0.049 0.037 0.004 1.328 0.592 1.010 0.432 1.148
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 98 102 101 0 110 105 108
normalized size 1 1.00 0.90 0.94 0.93 0.00 1.01 0.96 0.99
time (sec) N/A 0.124 0.057 0.001 1.365 0.000 0.135 0.350 1.130
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 92 102 101 0 110 105 108
normalized size 1 1.00 0.84 0.94 0.93 0.00 1.01 0.96 0.99
time (sec) N/A 0.112 0.070 0.001 1.305 0.000 0.142 0.369 1.111
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 92 102 101 0 110 105 107
normalized size 1 1.00 0.88 0.98 0.97 0.00 1.06 1.01 1.03
time (sec) N/A 0.074 0.044 0.002 1.389 0.000 0.088 0.360 1.111
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 88 99 98 0 107 102 105
normalized size 1 1.00 0.89 1.00 0.99 0.00 1.08 1.03 1.06
time (sec) N/A 0.072 0.056 0.002 1.348 0.000 0.089 0.379 1.106
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 92 92 88 100 96 96 104 100 103
normalized size 1 1.00 0.96 1.09 1.04 1.04 1.13 1.09 1.12
time (sec) N/A 0.069 0.079 0.003 1.384 0.531 0.318 0.464 1.106
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 90 90 88 98 96 103 99 98 92
normalized size 1 1.00 0.98 1.09 1.07 1.14 1.10 1.09 1.02
time (sec) N/A 0.080 0.060 0.007 1.315 0.481 0.351 0.378 1.107
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 98 98 87 97 96 103 100 97 103
normalized size 1 1.00 0.89 0.99 0.98 1.05 1.02 0.99 1.05
time (sec) N/A 0.086 0.044 0.007 1.325 0.496 0.578 0.335 1.106
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 98 98 83 97 97 103 100 97 106
normalized size 1 1.00 0.85 0.99 0.99 1.05 1.02 0.99 1.08
time (sec) N/A 0.086 0.056 0.007 1.370 0.743 1.456 0.430 1.275
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 149 150 145 0 163 153 153
normalized size 1 1.00 1.00 1.01 0.97 0.00 1.09 1.03 1.03
time (sec) N/A 0.186 0.026 0.002 1.328 0.000 0.167 0.459 1.299
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 125 150 145 0 165 153 153
normalized size 1 1.00 0.84 1.01 0.97 0.00 1.11 1.03 1.03
time (sec) N/A 0.141 0.065 0.000 1.361 0.000 0.138 0.461 1.275
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 124 150 145 0 163 153 153
normalized size 1 1.00 0.90 1.09 1.05 0.00 1.18 1.11 1.11
time (sec) N/A 0.095 0.063 0.002 1.336 0.000 0.136 0.362 1.278
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 133 133 121 147 142 0 158 149 149
normalized size 1 1.00 0.91 1.11 1.07 0.00 1.19 1.12 1.12
time (sec) N/A 0.093 0.050 0.001 1.341 0.000 0.135 0.401 1.259
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 129 129 121 148 140 140 158 148 147
normalized size 1 1.00 0.94 1.15 1.09 1.09 1.22 1.15 1.14
time (sec) N/A 0.090 0.067 0.004 1.321 0.710 0.399 0.327 1.264
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 124 124 123 145 139 147 150 145 121
normalized size 1 1.00 0.99 1.17 1.12 1.19 1.21 1.17 0.98
time (sec) N/A 0.109 0.081 0.007 1.348 0.635 0.456 0.406 1.184
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 135 135 124 144 139 147 151 144 143
normalized size 1 1.00 0.92 1.07 1.03 1.09 1.12 1.07 1.06
time (sec) N/A 0.112 0.062 0.007 1.357 0.541 0.674 0.409 1.257
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 139 139 124 146 142 147 155 146 148
normalized size 1 1.00 0.89 1.05 1.02 1.06 1.12 1.05 1.06
time (sec) N/A 0.114 0.050 0.009 1.317 0.817 1.086 0.396 1.368
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 130 176 145 332 316 161 -1
normalized size 1 1.00 0.86 1.17 0.96 2.20 2.09 1.07 -0.01
time (sec) N/A 0.145 0.082 0.007 2.962 0.707 1.434 0.431 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 114 152 127 270 274 137 -1
normalized size 1 1.00 0.88 1.17 0.98 2.08 2.11 1.05 -0.01
time (sec) N/A 0.124 0.104 0.006 2.932 0.613 1.349 0.350 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 95 128 98 238 245 112 -1
normalized size 1 1.00 0.86 1.15 0.88 2.14 2.21 1.01 -0.01
time (sec) N/A 0.113 0.057 0.005 3.002 0.688 1.647 0.399 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 81 106 82 180 211 88 -1
normalized size 1 1.00 0.88 1.15 0.89 1.96 2.29 0.96 -0.01
time (sec) N/A 0.085 0.071 0.006 3.007 0.715 0.988 0.423 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 68 83 64 157 219 66 79
normalized size 1 1.00 0.93 1.14 0.88 2.15 3.00 0.90 1.08
time (sec) N/A 0.065 0.043 0.003 2.929 0.681 0.881 0.460 1.425
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 73 80 65 158 0 66 -1
normalized size 1 1.00 1.01 1.11 0.90 2.19 0.00 0.92 -0.01
time (sec) N/A 0.098 0.056 0.007 2.931 0.680 0.000 0.451 0.000
Problem 92 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 76 76 75 83 67 165 0 68 78
normalized size 1 1.00 0.99 1.09 0.88 2.17 0.00 0.89 1.03
time (sec) N/A 0.098 0.048 0.008 3.001 0.820 0.000 0.383 1.212
Problem 93 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 92 92 84 102 76 205 0 80 97
normalized size 1 1.00 0.91 1.11 0.83 2.23 0.00 0.87 1.05
time (sec) N/A 0.109 0.084 0.008 3.052 0.561 0.000 0.386 1.304
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 176 176 139 201 150 468 335 159 -1
normalized size 1 1.00 0.79 1.14 0.85 2.66 1.90 0.90 -0.01
time (sec) N/A 0.268 0.134 0.011 2.835 0.583 4.769 0.432 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 128 177 127 372 289 131 -1
normalized size 1 1.00 0.83 1.15 0.82 2.42 1.88 0.85 -0.01
time (sec) N/A 0.241 0.083 0.010 2.999 0.695 3.868 0.377 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 100 154 108 357 284 111 152
normalized size 1 1.00 0.75 1.15 0.81 2.66 2.12 0.83 1.13
time (sec) N/A 0.226 0.082 0.010 2.963 0.621 4.611 0.390 1.292
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 92 127 84 287 212 81 -1
normalized size 1 1.00 0.91 1.26 0.83 2.84 2.10 0.80 -0.01
time (sec) N/A 0.118 0.051 0.010 3.016 0.604 5.763 0.431 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 93 83 97 89 257 233 88 110
normalized size 1 1.00 0.89 1.04 0.96 2.76 2.51 0.95 1.18
time (sec) N/A 0.065 0.091 0.008 2.945 0.688 3.094 0.375 1.316
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 85 125 87 296 0 93 -1
normalized size 1 1.00 0.89 1.32 0.92 3.12 0.00 0.98 -0.01
time (sec) N/A 0.122 0.076 0.013 2.914 0.761 0.000 0.348 0.000
Problem 100 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 110 110 110 136 105 336 0 103 133
normalized size 1 1.00 1.00 1.24 0.95 3.05 0.00 0.94 1.21
time (sec) N/A 0.142 0.074 0.014 2.985 0.678 0.000 0.342 1.410
Problem 101 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 135 135 112 169 117 441 0 126 158
normalized size 1 1.00 0.83 1.25 0.87 3.27 0.00 0.93 1.17
time (sec) N/A 0.204 0.103 0.016 2.945 0.821 0.000 0.422 1.348
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 185 185 139 235 165 574 357 157 232
normalized size 1 1.00 0.75 1.27 0.89 3.10 1.93 0.85 1.25
time (sec) N/A 0.338 0.117 0.013 3.075 0.762 29.587 0.410 1.556
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 126 206 136 480 282 122 -1
normalized size 1 1.00 0.81 1.33 0.88 3.10 1.82 0.79 -0.01
time (sec) N/A 0.232 0.076 0.012 2.984 0.741 29.728 0.385 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 122 133 146 447 304 128 195
normalized size 1 1.00 0.90 0.98 1.07 3.29 2.24 0.94 1.43
time (sec) N/A 0.158 0.095 0.010 2.977 0.763 20.010 0.422 1.391
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 99 110 111 357 178 97 -1
normalized size 1 1.00 0.83 0.92 0.93 3.00 1.50 0.82 -0.01
time (sec) N/A 0.114 0.134 0.010 2.993 0.731 16.372 0.391 0.000
Problem 106 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 116 116 104 111 122 346 184 106 163
normalized size 1 1.00 0.90 0.96 1.05 2.98 1.59 0.91 1.41
time (sec) N/A 0.068 0.114 0.009 2.998 0.727 11.272 0.386 1.327
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 117 184 133 488 0 128 -1
normalized size 1 1.00 0.90 1.42 1.02 3.75 0.00 0.98 -0.01
time (sec) N/A 0.135 0.109 0.015 2.904 0.813 0.000 0.479 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 141 195 152 524 0 141 202
normalized size 1 1.00 0.98 1.35 1.06 3.64 0.00 0.98 1.40
time (sec) N/A 0.228 0.099 0.016 2.986 0.698 0.000 0.490 1.400
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 147 250 172 696 0 162 229
normalized size 1 1.00 0.84 1.44 0.99 4.00 0.00 0.93 1.32
time (sec) N/A 0.311 0.163 0.018 2.991 1.021 0.000 0.380 1.456
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 19 18 24 15 25 20
normalized size 1 1.00 1.00 0.95 0.90 1.20 0.75 1.25 1.00
time (sec) N/A 0.023 0.007 0.010 1.339 0.638 0.174 0.317 0.912
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 18 15 22 14 22 17 14
normalized size 1 1.00 0.78 0.65 0.96 0.61 0.96 0.74 0.61
time (sec) N/A 0.021 0.009 0.006 1.344 0.691 0.694 0.401 0.102
Problem 112 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 25 25 25 21 20 20 20 20 20
normalized size 1 1.00 1.00 0.84 0.80 0.80 0.80 0.80 0.80
time (sec) N/A 0.024 0.013 0.004 2.920 0.627 0.141 0.355 0.038
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 30 25 24 24 22 24 24
normalized size 1 1.00 1.00 0.83 0.80 0.80 0.73 0.80 0.80
time (sec) N/A 0.025 0.007 0.003 2.899 0.560 0.111 0.389 0.035
Problem 114 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 210 210 210 278 213 452 384 250 289
normalized size 1 1.00 1.00 1.32 1.01 2.15 1.83 1.19 1.38
time (sec) N/A 0.161 0.156 0.005 2.897 0.565 1.652 0.457 0.929
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 172 172 162 230 172 368 337 200 243
normalized size 1 1.00 0.94 1.34 1.00 2.14 1.96 1.16 1.41
time (sec) N/A 0.123 0.121 0.006 2.930 0.592 1.321 0.368 0.944
Problem 116 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 136 136 128 182 133 286 185 152 193
normalized size 1 1.00 0.94 1.34 0.98 2.10 1.36 1.12 1.42
time (sec) N/A 0.105 0.097 0.003 2.964 0.686 1.128 0.416 0.912
Problem 117 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 100 100 98 135 94 236 160 106 96
normalized size 1 1.00 0.98 1.35 0.94 2.36 1.60 1.06 0.96
time (sec) N/A 0.062 0.083 0.003 2.972 0.724 1.149 0.448 0.936
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 83 114 80 211 150 86 76
normalized size 1 1.00 0.99 1.36 0.95 2.51 1.79 1.02 0.90
time (sec) N/A 0.094 0.066 0.007 2.929 0.516 1.638 0.337 1.067
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 83 115 79 216 151 81 80
normalized size 1 1.00 1.01 1.40 0.96 2.63 1.84 0.99 0.98
time (sec) N/A 0.087 0.087 0.009 2.938 0.677 2.266 0.355 0.111
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 103 142 97 246 167 105 94
normalized size 1 1.00 0.99 1.37 0.93 2.37 1.61 1.01 0.90
time (sec) N/A 0.102 0.088 0.007 3.090 0.779 6.728 0.367 1.203
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 139 190 134 292 301 151 127
normalized size 1 1.00 1.01 1.39 0.98 2.13 2.20 1.10 0.93
time (sec) N/A 0.130 0.124 0.010 3.031 0.648 21.646 0.455 0.981
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 175 175 174 238 175 374 354 201 161
normalized size 1 1.00 0.99 1.36 1.00 2.14 2.02 1.15 0.92
time (sec) N/A 0.146 0.144 0.010 3.006 0.749 32.721 0.423 1.018
Problem 123 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 211 211 211 286 214 458 398 249 197
normalized size 1 1.00 1.00 1.36 1.01 2.17 1.89 1.18 0.93
time (sec) N/A 0.175 0.171 0.010 2.952 0.668 84.142 0.356 0.988
Problem 124 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 240 240 227 309 227 572 444 252 413
normalized size 1 1.00 0.95 1.29 0.95 2.38 1.85 1.05 1.72
time (sec) N/A 0.294 0.128 0.013 3.007 0.571 3.070 0.387 0.099
Problem 125 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 202 202 187 258 183 478 257 201 288
normalized size 1 1.00 0.93 1.28 0.91 2.37 1.27 1.00 1.43
time (sec) N/A 0.235 0.104 0.012 3.006 0.705 4.762 0.417 0.966
Problem 126 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 163 163 148 212 140 418 221 152 153
normalized size 1 1.00 0.91 1.30 0.86 2.56 1.36 0.93 0.94
time (sec) N/A 0.229 0.089 0.012 2.957 0.645 3.036 0.373 1.002
Problem 127 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 118 118 122 177 117 364 201 126 113
normalized size 1 1.00 1.03 1.50 0.99 3.08 1.70 1.07 0.96
time (sec) N/A 0.120 0.098 0.011 2.967 0.654 2.877 0.403 0.100
Problem 128 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 112 112 115 165 117 354 197 122 112
normalized size 1 1.00 1.03 1.47 1.04 3.16 1.76 1.09 1.00
time (sec) N/A 0.132 0.070 0.013 2.992 0.614 9.465 0.360 0.996
Problem 129 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 121 121 125 182 130 378 212 123 119
normalized size 1 1.00 1.03 1.50 1.07 3.12 1.75 1.02 0.98
time (sec) N/A 0.158 0.079 0.015 3.023 0.746 25.992 0.483 0.131
Problem 130 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 152 152 151 219 151 438 226 151 145
normalized size 1 1.00 0.99 1.44 0.99 2.88 1.49 0.99 0.95
time (sec) N/A 0.213 0.091 0.015 2.989 0.713 32.024 0.490 0.999
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 190 268 194 488 394 201 181
normalized size 1 1.00 1.01 1.42 1.03 2.58 2.08 1.06 0.96
time (sec) N/A 0.293 0.109 0.019 3.047 0.619 99.022 0.433 0.987
Problem 132 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 230 230 230 318 238 582 0 252 219
normalized size 1 1.00 1.00 1.38 1.03 2.53 0.00 1.10 0.95
time (sec) N/A 0.376 0.124 0.016 2.985 0.668 0.000 0.378 1.010
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 287 287 272 394 281 762 503 301 506
normalized size 1 1.00 0.95 1.37 0.98 2.66 1.75 1.05 1.76
time (sec) N/A 0.492 0.186 0.016 3.104 0.582 16.433 0.400 0.999
Problem 134 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 247 247 232 343 237 668 316 250 348
normalized size 1 1.00 0.94 1.39 0.96 2.70 1.28 1.01 1.41
time (sec) N/A 0.411 0.152 0.015 2.991 0.644 18.216 0.470 0.107
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 207 207 176 294 193 614 280 200 206
normalized size 1 1.00 0.85 1.42 0.93 2.97 1.35 0.97 1.00
time (sec) N/A 0.334 0.177 0.014 3.038 0.505 17.840 0.509 0.954
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 156 259 169 555 260 173 163
normalized size 1 1.00 0.93 1.55 1.01 3.32 1.56 1.04 0.98
time (sec) N/A 0.262 0.134 0.012 3.021 0.742 13.069 0.448 1.018
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 147 147 141 234 154 504 243 149 148
normalized size 1 1.00 0.96 1.59 1.05 3.43 1.65 1.01 1.01
time (sec) N/A 0.150 0.122 0.010 2.996 0.808 10.095 0.457 1.047
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 155 237 161 517 250 153 149
normalized size 1 1.00 1.01 1.55 1.05 3.38 1.63 1.00 0.97
time (sec) N/A 0.176 0.132 0.013 2.992 0.632 26.563 0.449 1.094
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 168 168 169 264 181 570 270 170 166
normalized size 1 1.00 1.01 1.57 1.08 3.39 1.61 1.01 0.99
time (sec) N/A 0.242 0.159 0.015 3.073 0.795 70.490 0.449 1.027
Problem 140 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 196 196 196 300 202 628 284 198 192
normalized size 1 1.00 1.00 1.53 1.03 3.20 1.45 1.01 0.98
time (sec) N/A 0.350 0.124 0.018 2.978 0.567 150.751 0.439 1.043
Problem 141 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 234 234 234 351 247 678 0 250 230
normalized size 1 1.00 1.00 1.50 1.06 2.90 0.00 1.07 0.98
time (sec) N/A 0.486 0.147 0.019 3.026 0.853 0.000 0.466 1.046
Problem 142 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 277 277 276 401 291 772 0 301 268
normalized size 1 1.00 1.00 1.45 1.05 2.79 0.00 1.09 0.97
time (sec) N/A 0.603 0.158 0.022 3.090 0.510 0.000 0.403 1.070
Problem 143 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 214 214 158 193 347 177 442 264 186
normalized size 1 1.00 0.74 0.90 1.62 0.83 2.07 1.23 0.87
time (sec) N/A 0.252 0.174 0.008 1.401 0.716 4.676 0.449 1.191
Problem 144 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 167 167 122 145 263 134 340 197 146
normalized size 1 1.00 0.73 0.87 1.57 0.80 2.04 1.18 0.87
time (sec) N/A 0.194 0.123 0.008 1.449 0.659 2.905 0.508 1.107
Problem 145 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 121 121 89 99 180 94 238 130 103
normalized size 1 1.00 0.74 0.82 1.49 0.78 1.97 1.07 0.85
time (sec) N/A 0.133 0.085 0.004 1.349 0.644 2.189 0.407 1.064
Problem 146 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 103 103 86 134 122 205 102 127 99
normalized size 1 1.00 0.83 1.30 1.18 1.99 0.99 1.23 0.96
time (sec) N/A 0.140 0.130 0.009 1.346 0.709 37.870 0.398 1.810
Problem 147 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 100 100 131 127 104 210 138 114 99
normalized size 1 1.00 1.31 1.27 1.04 2.10 1.38 1.14 0.99
time (sec) N/A 0.203 0.412 0.010 1.327 0.687 127.426 0.554 1.947
Problem 148 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 114 114 141 162 128 221 0 141 133
normalized size 1 1.00 1.24 1.42 1.12 1.94 0.00 1.24 1.17
time (sec) N/A 0.233 0.374 0.011 1.379 0.868 0.000 0.397 2.191
Problem 149 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 146 146 162 238 193 261 0 232 199
normalized size 1 1.00 1.11 1.63 1.32 1.79 0.00 1.59 1.36
time (sec) N/A 0.276 1.024 0.013 1.388 0.583 0.000 0.391 2.543
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 195 140 320 275 341 0 361 277
normalized size 1 1.00 0.72 1.64 1.41 1.75 0.00 1.85 1.42
time (sec) N/A 0.350 0.336 0.016 1.346 0.997 0.000 0.397 2.913
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 245 245 184 368 339 414 586 224 -1
normalized size 1 1.00 0.75 1.50 1.38 1.69 2.39 0.91 -0.00
time (sec) N/A 0.258 0.238 0.024 1.459 0.989 42.122 0.527 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 194 194 149 284 255 329 444 175 -1
normalized size 1 1.00 0.77 1.46 1.31 1.70 2.29 0.90 -0.01
time (sec) N/A 0.208 0.167 0.010 1.387 0.790 32.562 0.537 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 118 203 174 250 362 129 -1
normalized size 1 1.00 0.81 1.40 1.20 1.72 2.50 0.89 -0.01
time (sec) N/A 0.119 0.114 0.007 1.350 0.704 13.711 0.564 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 103 140 118 216 250 121 -1
normalized size 1 1.00 0.88 1.20 1.01 1.85 2.14 1.03 -0.01
time (sec) N/A 0.136 0.118 0.010 1.259 0.614 9.052 0.522 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 93 117 102 210 197 176 143
normalized size 1 1.00 0.85 1.06 0.93 1.91 1.79 1.60 1.30
time (sec) N/A 0.127 0.113 0.011 1.333 0.790 4.729 0.559 2.199
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 95 136 128 221 456 324 105
normalized size 1 1.00 0.81 1.15 1.08 1.87 3.86 2.75 0.89
time (sec) N/A 0.133 0.113 0.011 1.327 0.788 6.207 0.597 1.724
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 103 111 193 100 891 554 124
normalized size 1 1.00 0.74 0.79 1.38 0.71 6.36 3.96 0.89
time (sec) N/A 0.184 0.081 0.006 1.403 0.806 6.712 0.571 1.280
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 134 157 275 141 1642 667 171
normalized size 1 1.00 0.71 0.83 1.46 0.75 8.69 3.53 0.90
time (sec) N/A 0.254 0.096 0.007 1.386 1.180 7.689 0.603 1.282
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 381 381 273 517 1221 987 0 342 -1
normalized size 1 1.00 0.72 1.36 3.20 2.59 0.00 0.90 -0.00
time (sec) N/A 0.662 0.576 0.296 1.888 1.133 0.000 0.642 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 279 279 229 460 986 816 0 265 -1
normalized size 1 1.00 0.82 1.65 3.53 2.92 0.00 0.95 -0.00
time (sec) N/A 0.455 0.479 0.011 1.787 0.942 0.000 0.593 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 210 210 194 405 753 653 0 203 -1
normalized size 1 1.00 0.92 1.93 3.59 3.11 0.00 0.97 -0.00
time (sec) N/A 0.387 0.497 0.013 1.686 0.956 0.000 0.598 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 179 192 168 363 533 491 0 160 -1
normalized size 1 1.07 0.94 2.03 2.98 2.74 0.00 0.89 -0.01
time (sec) N/A 0.314 0.456 0.010 1.661 0.760 0.000 0.550 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 98 109 335 141 0 131 -1
normalized size 1 1.00 0.73 0.81 2.50 1.05 0.00 0.98 -0.01
time (sec) N/A 0.210 0.107 0.006 1.423 0.710 0.000 0.534 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 185 179 133 157 313 182 0 211 -1
normalized size 1 0.97 0.72 0.85 1.69 0.98 0.00 1.14 -0.01
time (sec) N/A 0.246 0.184 0.008 1.471 0.943 0.000 0.575 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 242 242 165 205 337 225 0 349 -1
normalized size 1 1.00 0.68 0.85 1.39 0.93 0.00 1.44 -0.00
time (sec) N/A 0.322 0.134 0.010 1.468 1.000 0.000 0.557 0.000
Problem 166 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 281 275 202 253 398 270 0 592 405
normalized size 1 0.98 0.72 0.90 1.42 0.96 0.00 2.11 1.44
time (sec) N/A 0.429 0.158 0.009 1.545 1.208 0.000 0.632 2.397
Problem 167 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 334 334 234 301 489 311 0 938 421
normalized size 1 1.00 0.70 0.90 1.46 0.93 0.00 2.81 1.26
time (sec) N/A 0.480 0.161 0.010 1.518 1.900 0.000 0.712 2.836
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 392 380 270 349 579 354 0 1162 -1
normalized size 1 0.97 0.69 0.89 1.48 0.90 0.00 2.96 -0.00
time (sec) N/A 0.546 0.180 0.010 1.574 2.308 0.000 0.736 0.000
Problem 169 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 214 214 158 193 347 177 442 264 186
normalized size 1 1.00 0.74 0.90 1.62 0.83 2.07 1.23 0.87
time (sec) N/A 0.222 0.185 0.007 1.435 0.547 9.372 0.454 1.203
Problem 170 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 167 167 122 145 263 134 340 197 146
normalized size 1 1.00 0.73 0.87 1.57 0.80 2.04 1.18 0.87
time (sec) N/A 0.175 0.131 0.007 1.367 0.674 5.409 0.498 1.140
Problem 171 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 121 121 89 99 180 94 238 130 103
normalized size 1 1.00 0.74 0.82 1.49 0.78 1.97 1.07 0.85
time (sec) N/A 0.150 0.090 0.006 1.355 0.670 3.406 0.398 1.084
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 261 257 221 478 826 705 0 224 -1
normalized size 1 0.98 0.85 1.83 3.16 2.70 0.00 0.86 -0.00
time (sec) N/A 0.716 0.590 0.011 1.747 0.919 0.000 0.559 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 214 250 197 427 597 567 0 204 -1
normalized size 1 1.17 0.92 2.00 2.79 2.65 0.00 0.95 -0.00
time (sec) N/A 0.410 0.514 0.009 1.743 1.175 0.000 0.590 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 138 166 421 187 0 220 -1
normalized size 1 1.00 0.72 0.86 2.18 0.97 0.00 1.14 -0.01
time (sec) N/A 0.341 0.189 0.007 1.540 1.023 0.000 0.602 0.000

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [13] had the largest ratio of [.4000]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 6 5 1.00 20 0.250
2 A 5 5 1.00 20 0.250
3 A 4 4 1.00 18 0.222
4 A 4 4 1.00 17 0.235
5 A 7 7 1.00 20 0.350
6 A 7 7 1.00 20 0.350
7 A 7 7 1.00 20 0.350
8 A 7 5 1.00 20 0.250
9 A 6 5 1.00 20 0.250
10 A 5 4 1.00 18 0.222
11 A 5 4 1.00 17 0.235
12 A 8 7 1.00 20 0.350
13 A 8 8 1.00 20 0.400
14 A 8 7 1.00 20 0.350
15 A 8 5 1.00 20 0.250
16 A 7 5 1.00 20 0.250
17 A 6 4 1.00 18 0.222
18 A 6 4 1.00 17 0.235
19 A 9 7 1.00 20 0.350
20 A 9 8 1.00 20 0.400
21 A 9 8 1.00 20 0.400
22 A 5 4 1.00 20 0.200
23 A 4 4 1.00 20 0.200
24 A 3 3 1.00 18 0.167
25 A 3 3 1.00 17 0.176
26 A 6 6 1.00 20 0.300
27 A 4 4 1.00 20 0.200
28 A 5 5 1.00 20 0.250
29 A 4 4 1.00 20 0.200
30 A 4 4 1.00 20 0.200
31 A 3 3 1.00 18 0.167
32 A 1 1 1.00 17 0.059
33 A 5 5 1.00 20 0.250
34 A 5 5 1.00 20 0.250
35 A 6 6 1.00 20 0.300
36 A 4 4 1.00 20 0.200
37 A 2 2 1.00 20 0.100
38 A 2 2 0.94 18 0.111
39 A 2 2 1.00 17 0.118
40 A 6 5 1.00 20 0.250
41 A 6 5 1.00 20 0.250
42 A 7 6 1.00 20 0.300
43 A 2 2 1.00 18 0.111
44 A 3 3 1.00 19 0.158
45 A 2 2 1.00 13 0.154
46 A 2 2 1.00 13 0.154
47 A 7 5 1.00 25 0.200
48 A 6 5 1.00 25 0.200
49 A 5 4 1.00 25 0.160
50 A 4 4 1.00 25 0.160
51 A 4 4 1.00 25 0.160
52 A 4 4 1.00 25 0.160
53 A 4 4 1.00 23 0.174
54 A 5 4 1.00 22 0.182
55 A 8 6 1.00 25 0.240
56 A 8 5 1.00 25 0.200
57 A 9 6 1.00 25 0.240
58 A 2 2 1.00 16 0.125
59 A 3 2 1.00 20 0.100
60 A 2 2 1.00 22 0.091
61 A 5 3 1.00 25 0.120
62 A 2 1 1.00 26 0.038
63 A 2 1 1.00 26 0.038
64 A 2 1 1.00 24 0.042
65 A 2 1 1.00 23 0.043
66 A 2 1 1.00 26 0.038
67 A 2 1 1.00 26 0.038
68 A 2 1 1.00 26 0.038
69 A 2 1 1.00 26 0.038
70 A 2 1 1.00 28 0.036
71 A 2 1 1.00 28 0.036
72 A 3 2 1.00 26 0.077
73 A 3 2 1.00 25 0.080
74 A 3 2 1.00 28 0.071
75 A 3 2 1.00 28 0.071
76 A 2 1 1.00 28 0.036
77 A 2 1 1.00 28 0.036
78 A 2 1 1.00 28 0.036
79 A 2 1 1.00 28 0.036
80 A 3 2 1.00 26 0.077
81 A 3 2 1.00 25 0.080
82 A 3 2 1.00 28 0.071
83 A 3 2 1.00 28 0.071
84 A 2 1 1.00 28 0.036
85 A 2 1 1.00 28 0.036
86 A 5 4 1.00 28 0.143
87 A 5 4 1.00 28 0.143
88 A 5 4 1.00 28 0.143
89 A 5 4 1.00 26 0.154
90 A 5 4 1.00 25 0.160
91 A 5 4 1.00 28 0.143
92 A 5 4 1.00 28 0.143
93 A 5 4 1.00 28 0.143
94 A 6 5 1.00 28 0.179
95 A 6 5 1.00 28 0.179
96 A 6 5 1.00 28 0.179
97 A 6 5 1.00 26 0.192
98 A 4 4 1.00 25 0.160
99 A 6 5 1.00 28 0.179
100 A 6 5 1.00 28 0.179
101 A 6 5 1.00 28 0.179
102 A 7 5 1.00 28 0.179
103 A 6 5 1.00 28 0.179
104 A 5 4 1.00 28 0.143
105 A 4 4 1.00 26 0.154
106 A 3 3 1.00 25 0.120
107 A 7 6 1.00 28 0.214
108 A 7 5 1.00 28 0.179
109 A 7 5 1.00 28 0.179
110 A 4 3 1.00 17 0.176
111 A 4 3 1.00 17 0.176
112 A 4 4 1.00 21 0.190
113 A 6 5 1.00 15 0.333
114 A 3 2 1.00 30 0.067
115 A 3 2 1.00 30 0.067
116 A 3 2 1.00 30 0.067
117 A 3 2 1.00 27 0.074
118 A 3 2 1.00 30 0.067
119 A 3 2 1.00 30 0.067
120 A 3 2 1.00 30 0.067
121 A 3 2 1.00 30 0.067
122 A 3 2 1.00 30 0.067
123 A 3 2 1.00 30 0.067
124 A 5 4 1.00 30 0.133
125 A 5 4 1.00 30 0.133
126 A 5 4 1.00 30 0.133
127 A 4 3 1.00 27 0.111
128 A 4 3 1.00 30 0.100
129 A 4 3 1.00 30 0.100
130 A 4 3 1.00 30 0.100
131 A 4 3 1.00 30 0.100
132 A 4 3 1.00 30 0.100
133 A 6 5 1.00 30 0.167
134 A 6 5 1.00 30 0.167
135 A 6 5 1.00 30 0.167
136 A 6 5 1.00 30 0.167
137 A 4 4 1.00 27 0.148
138 A 4 4 1.00 30 0.133
139 A 5 4 1.00 30 0.133
140 A 5 3 1.00 30 0.100
141 A 5 3 1.00 30 0.100
142 A 5 3 1.00 30 0.100
143 A 3 2 1.00 32 0.062
144 A 3 2 1.00 32 0.062
145 A 3 2 1.00 30 0.067
146 A 5 4 1.00 32 0.125
147 A 6 5 1.00 32 0.156
148 A 6 6 1.00 32 0.188
149 A 6 6 1.00 32 0.188
150 A 7 7 1.00 32 0.219
151 A 7 6 1.00 32 0.188
152 A 6 6 1.00 32 0.188
153 A 5 5 1.00 29 0.172
154 A 6 6 1.00 32 0.188
155 A 6 6 1.00 32 0.188
156 A 6 6 1.00 32 0.188
157 A 5 3 1.00 32 0.094
158 A 6 4 1.00 32 0.125
159 A 11 9 1.00 32 0.281
160 A 10 9 1.00 32 0.281
161 A 9 9 1.00 32 0.281
162 A 8 8 1.07 32 0.250
163 A 5 4 1.00 29 0.138
164 A 6 5 0.97 32 0.156
165 A 7 5 1.00 32 0.156
166 A 8 4 0.98 32 0.125
167 A 9 5 1.00 32 0.156
168 A 10 5 0.97 32 0.156
169 A 4 3 1.00 33 0.091
170 A 4 3 1.00 33 0.091
171 A 4 3 1.00 31 0.097
172 A 10 9 0.98 37 0.243
173 A 6 5 1.17 34 0.147
174 A 6 4 1.00 37 0.108

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