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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, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 208 }

B grade: { }

C grade: { }

F grade: { 206, 207 }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 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, 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, 94, 96, 97, 98, 99, 100, 101, 102, 120, 130, 131, 132, 133, 134, 137, 140, 141, 142, 143, 144, 145, 146, 150, 151, 152, 153, 154, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 207, 208 }

B grade: { 21, 55, 56, 57, 58, 59, 60, 88, 89, 90, 93, 105, 106, 110, 126, 127, 128, 129, 158, 179, 206 }

C grade: { 11, 12, 13, 91, 92, 95, 103, 104, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119, 123, 124, 136, 138, 147, 148, 149, 203, 204, 205 }

F grade: { 121, 122, 125, 135, 139 }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 19, 20, 21, 22, 23, 27, 28, 31, 32, 33, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 56, 57, 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, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 161, 162, 163, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 181, 182, 183, 184, 185, 186, 187, 188, 192, 193, 194, 195, 196, 197, 208 }

B grade: { 14, 15, 17, 18, 24, 25, 26, 29, 30, 34, 35, 38, 39, 53, 54, 58, 59, 60, 160, 164, 178, 179, 180, 189, 190, 191, 198, 199, 200, 201, 202 }

C grade: { }

F grade: { 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, 203, 204, 205, 206, 207 }

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, 47, 48, 49, 50, 51, 52, 55, 56, 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, 96, 100, 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, 175, 182, 183, 184, 185, 186, 193, 194, 195, 196, 197, 208 }

B grade: { 53, 54, 57, 58, 59, 60, 87, 88, 89, 90, 99, 181, 192 }

C grade: { }

F grade: { 91, 92, 93, 94, 95, 97, 98, 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, 176, 177, 178, 179, 180, 187, 188, 189, 190, 191, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 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, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 91, 92, 95, 96, 99, 100, 103, 107, 111, 112, 140, 141, 142, 143, 144, 145, 146, 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, 175, 176, 177, 178, 179, 180, 183, 184, 187, 188, 198, 199, 208 }

B grade: { 10, 11, 12, 13, 17, 24, 30, 57, 58, 59, 60, 74, 84, 88, 89, 90, 93, 94, 97, 98, 101, 102, 104, 105, 106, 108, 109, 110, 113, 114, 147, 148, 149, 181, 182, 185, 186, 189, 190, 191, 192, 193, 194, 195, 196, 197, 200, 201, 202 }

C grade: { }

F grade: { 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, 203, 204, 205, 206, 207 }

2.1.6 Sympy

A grade: { 22, 32, 40, 56 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 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, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208 }

2.1.7 Giac

A grade: { 4, 5, 6, 7, 12, 13, 17, 18, 22, 28, 32, 33, 37, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 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, 142, 143, 144, 148, 149, 152, 153, 154, 157, 158, 159, 162, 163, 164, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 198, 199, 200, 201, 202, 208 }

B grade: { 3, 10, 11, 16, 21, 23, 24, 42, 53, 57, 58, 59, 60, 141, 146, 147, 151, 156, 167, 168, 181, 193 }

C grade: { }

F grade: { 1, 2, 8, 9, 14, 15, 19, 20, 25, 26, 27, 29, 30, 31, 34, 35, 36, 38, 39, 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, 145, 150, 155, 160, 161, 165, 166, 203, 204, 205, 206, 207 }

2.1.8 Mupad

A grade: { 208 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 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, 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, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202 }

C grade: { }

F grade: { 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, 203, 204, 205, 206, 207 }

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 F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 123 147 95 159 0 0 235
normalized size 1 1.00 1.07 1.28 0.83 1.38 0.00 0.00 2.04
time (sec) N/A 0.072 0.447 0.154 0.326 0.445 0.000 0.000 6.628
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 77 96 51 87 0 0 154
normalized size 1 1.00 1.08 1.35 0.72 1.23 0.00 0.00 2.17
time (sec) N/A 0.048 0.117 0.148 0.307 0.462 0.000 0.000 6.469
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 38 29 25 27 0 1456 43
normalized size 1 1.00 1.27 0.97 0.83 0.90 0.00 48.53 1.43
time (sec) N/A 0.021 0.022 0.100 0.301 0.424 0.000 1.175 6.623
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 26 25 22 24 0 23 38
normalized size 1 1.00 1.08 1.04 0.92 1.00 0.00 0.96 1.58
time (sec) N/A 0.020 0.033 0.089 0.355 0.424 0.000 0.219 6.578
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 60 83 45 69 0 60 146
normalized size 1 1.00 1.11 1.54 0.83 1.28 0.00 1.11 2.70
time (sec) N/A 0.037 0.118 0.204 0.302 0.435 0.000 0.413 6.540
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 87 136 69 110 0 82 207
normalized size 1 1.00 1.07 1.68 0.85 1.36 0.00 1.01 2.56
time (sec) N/A 0.048 0.197 0.170 0.647 0.445 0.000 0.548 6.697
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 111 195 91 158 0 104 267
normalized size 1 1.00 0.97 1.70 0.79 1.37 0.00 0.90 2.32
time (sec) N/A 0.059 0.389 0.191 0.305 0.467 0.000 1.464 7.368
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 110 135 87 116 0 0 351
normalized size 1 1.00 1.09 1.34 0.86 1.15 0.00 0.00 3.48
time (sec) N/A 0.092 0.060 0.243 0.405 0.425 0.000 0.000 11.223
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 81 98 65 88 0 0 231
normalized size 1 1.00 1.12 1.36 0.90 1.22 0.00 0.00 3.21
time (sec) N/A 0.074 0.046 0.207 0.418 0.452 0.000 0.000 9.418
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 47 59 39 80 0 1008 111
normalized size 1 1.00 1.21 1.51 1.00 2.05 0.00 25.85 2.85
time (sec) N/A 0.104 0.039 0.171 0.396 0.404 0.000 4.949 6.768
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 75 57 54 84 0 108 108
normalized size 1 1.00 1.83 1.39 1.32 2.05 0.00 2.63 2.63
time (sec) N/A 0.052 0.043 0.101 0.421 0.452 0.000 0.565 6.906
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 125 106 92 160 0 141 228
normalized size 1 1.00 1.52 1.29 1.12 1.95 0.00 1.72 2.78
time (sec) N/A 0.080 0.052 0.120 0.402 0.432 0.000 0.356 6.602
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 164 159 125 222 0 199 291
normalized size 1 1.00 1.34 1.30 1.02 1.82 0.00 1.63 2.39
time (sec) N/A 0.096 0.067 0.127 0.410 0.454 0.000 0.459 6.673
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 75 261 96 168 0 0 283
normalized size 1 1.00 0.63 2.19 0.81 1.41 0.00 0.00 2.38
time (sec) N/A 0.082 0.243 0.197 0.306 0.469 0.000 0.000 6.567
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 54 162 58 90 0 0 204
normalized size 1 1.00 0.75 2.25 0.81 1.25 0.00 0.00 2.83
time (sec) N/A 0.062 0.100 0.174 0.304 0.456 0.000 0.000 7.111
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 40 69 43 45 0 6695 178
normalized size 1 1.00 0.77 1.33 0.83 0.87 0.00 128.75 3.42
time (sec) N/A 0.038 0.038 0.141 0.305 0.430 0.000 19.303 6.669
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 28 94 53 76 0 47 56
normalized size 1 1.00 0.93 3.13 1.77 2.53 0.00 1.57 1.87
time (sec) N/A 0.039 0.041 0.223 0.309 0.411 0.000 0.389 6.669
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 86 313 107 206 0 121 392
normalized size 1 1.00 0.65 2.37 0.81 1.56 0.00 0.92 2.97
time (sec) N/A 0.075 0.220 0.212 0.315 0.457 0.000 0.958 11.182
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 174 251 152 152 0 0 392
normalized size 1 1.00 1.17 1.68 1.02 1.02 0.00 0.00 2.63
time (sec) N/A 0.165 0.839 0.307 0.422 0.455 0.000 0.000 10.917
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 120 120 159 186 120 196 0 0 287
normalized size 1 1.00 1.32 1.55 1.00 1.63 0.00 0.00 2.39
time (sec) N/A 0.203 1.308 0.292 0.403 0.427 0.000 0.000 10.072
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 145 117 84 125 0 5370 213
normalized size 1 1.00 2.04 1.65 1.18 1.76 0.00 75.63 3.00
time (sec) N/A 0.089 0.434 0.245 0.414 0.421 0.000 24.522 8.693
Problem 22 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 45 45 34 52 47 41 78 38 123
normalized size 1 1.00 0.76 1.16 1.04 0.91 1.73 0.84 2.73
time (sec) N/A 0.014 0.190 0.072 0.302 0.420 0.417 0.324 6.583
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 94 89 79 105 0 143 201
normalized size 1 1.00 1.27 1.20 1.07 1.42 0.00 1.93 2.72
time (sec) N/A 0.102 0.577 0.129 0.649 0.436 0.000 0.255 6.520
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 191 190 139 192 0 209 293
normalized size 1 1.00 1.95 1.94 1.42 1.96 0.00 2.13 2.99
time (sec) N/A 0.161 5.275 0.222 0.457 0.466 0.000 0.552 6.517
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 160 160 99 445 133 240 0 0 398
normalized size 1 1.00 0.62 2.78 0.83 1.50 0.00 0.00 2.49
time (sec) N/A 0.109 0.552 0.232 0.316 0.455 0.000 0.000 6.469
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 66 205 72 104 0 0 262
normalized size 1 1.00 0.73 2.25 0.79 1.14 0.00 0.00 2.88
time (sec) N/A 0.071 0.158 0.183 0.303 0.435 0.000 0.000 7.460
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 52 85 57 61 0 0 281
normalized size 1 1.00 0.74 1.21 0.81 0.87 0.00 0.00 4.01
time (sec) N/A 0.045 0.045 0.144 0.310 0.427 0.000 0.000 7.265
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 67 109 80 118 0 94 253
normalized size 1 1.00 0.68 1.11 0.82 1.20 0.00 0.96 2.58
time (sec) N/A 0.065 0.186 0.240 0.301 0.433 0.000 1.431 6.760
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 180 180 243 359 209 289 0 0 438
normalized size 1 1.00 1.35 1.99 1.16 1.61 0.00 0.00 2.43
time (sec) N/A 0.357 5.117 0.377 0.402 0.424 0.000 0.000 11.047
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 177 266 165 220 0 0 371
normalized size 1 1.00 1.49 2.24 1.39 1.85 0.00 0.00 3.12
time (sec) N/A 0.194 2.104 0.359 0.422 0.463 0.000 0.000 10.500
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 115 167 117 154 0 0 288
normalized size 1 1.00 1.29 1.88 1.31 1.73 0.00 0.00 3.24
time (sec) N/A 0.125 0.483 0.314 0.437 0.428 0.000 0.000 10.331
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 63 63 44 74 72 54 121 55 156
normalized size 1 1.00 0.70 1.17 1.14 0.86 1.92 0.87 2.48
time (sec) N/A 0.054 0.315 0.136 0.293 0.401 1.054 0.368 8.919
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 106 105 93 121 0 162 264
normalized size 1 1.00 1.15 1.14 1.01 1.32 0.00 1.76 2.87
time (sec) N/A 0.137 1.088 0.140 0.399 0.451 0.000 1.395 6.774
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 83 387 109 154 0 0 379
normalized size 1 1.00 0.64 3.00 0.84 1.19 0.00 0.00 2.94
time (sec) N/A 0.095 0.446 0.235 0.295 0.451 0.000 0.000 7.880
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 76 245 85 116 0 0 320
normalized size 1 1.00 0.71 2.29 0.79 1.08 0.00 0.00 2.99
time (sec) N/A 0.079 0.151 0.201 0.294 0.459 0.000 0.000 7.564
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 62 101 70 74 0 0 131
normalized size 1 1.00 0.70 1.15 0.80 0.84 0.00 0.00 1.49
time (sec) N/A 0.053 0.069 0.155 0.295 0.437 0.000 0.000 6.633
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 78 125 82 131 0 96 298
normalized size 1 1.00 0.76 1.23 0.80 1.28 0.00 0.94 2.92
time (sec) N/A 0.067 0.130 0.244 0.309 0.445 0.000 0.548 6.398
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 143 143 252 360 238 247 0 0 437
normalized size 1 1.00 1.76 2.52 1.66 1.73 0.00 0.00 3.06
time (sec) N/A 0.199 1.653 0.408 0.422 0.432 0.000 0.000 11.050
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 125 231 181 179 0 0 363
normalized size 1 1.00 1.11 2.04 1.60 1.58 0.00 0.00 3.21
time (sec) N/A 0.161 1.101 0.312 0.454 0.443 0.000 0.000 10.255
Problem 40 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 57 111 108 70 224 72 237
normalized size 1 1.00 0.66 1.28 1.24 0.80 2.57 0.83 2.72
time (sec) N/A 0.082 0.399 0.195 0.296 0.423 1.893 1.531 8.591
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 136 127 117 135 0 194 295
normalized size 1 1.00 1.17 1.09 1.01 1.16 0.00 1.67 2.54
time (sec) N/A 0.159 1.598 0.137 0.400 0.446 0.000 0.714 6.779
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 209 190 218 219 0 274 384
normalized size 1 1.00 1.49 1.36 1.56 1.56 0.00 1.96 2.74
time (sec) N/A 0.225 5.279 0.233 0.400 0.453 0.000 1.292 6.709
Problem 43 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 198 198 283 293 313 291 0 339 454
normalized size 1 1.00 1.43 1.48 1.58 1.47 0.00 1.71 2.29
time (sec) N/A 0.428 1.578 0.231 0.405 0.469 0.000 1.392 6.853
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 101 162 175 167 0 136 388
normalized size 1 1.00 0.78 1.25 1.35 1.28 0.00 1.05 2.98
time (sec) N/A 0.161 0.983 0.182 0.312 0.450 0.000 9.206 10.740
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 84 126 130 147 0 116 281
normalized size 1 1.00 0.79 1.19 1.23 1.39 0.00 1.09 2.65
time (sec) N/A 0.136 0.326 0.176 0.309 0.472 0.000 3.137 10.425
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 54 90 89 125 0 96 172
normalized size 1 1.00 0.66 1.10 1.09 1.52 0.00 1.17 2.10
time (sec) N/A 0.116 0.164 0.169 0.312 0.423 0.000 0.775 9.111
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 58 28 54 47 58 0 58 61
normalized size 1 1.57 0.76 1.46 1.27 1.57 0.00 1.57 1.65
time (sec) N/A 0.067 0.036 0.178 0.353 0.423 0.000 0.295 6.658
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 32 33 31 28 0 33 32
normalized size 1 1.00 1.00 1.03 0.97 0.88 0.00 1.03 1.00
time (sec) N/A 0.039 0.018 0.116 0.302 0.416 0.000 1.101 6.531
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 24 30 26 30 0 26 23
normalized size 1 1.00 0.75 0.94 0.81 0.94 0.00 0.81 0.72
time (sec) N/A 0.068 0.030 0.130 0.302 0.424 0.000 1.124 6.576
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 30 49 46 63 0 46 45
normalized size 1 1.00 0.59 0.96 0.90 1.24 0.00 0.90 0.88
time (sec) N/A 0.089 0.046 0.233 0.307 0.402 0.000 0.271 6.560
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 61 67 66 96 0 66 63
normalized size 1 1.00 0.90 0.99 0.97 1.41 0.00 0.97 0.93
time (sec) N/A 0.093 0.141 0.246 0.302 0.416 0.000 0.972 6.795
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 77 87 86 127 0 86 83
normalized size 1 1.00 0.92 1.04 1.02 1.51 0.00 1.02 0.99
time (sec) N/A 0.100 0.206 0.277 0.305 0.427 0.000 0.374 6.767
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 146 175 338 95 0 172 99
normalized size 1 1.00 1.74 2.08 4.02 1.13 0.00 2.05 1.18
time (sec) N/A 0.097 0.315 0.184 0.383 0.413 0.000 4.391 8.486
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 106 130 214 75 0 120 73
normalized size 1 1.00 1.54 1.88 3.10 1.09 0.00 1.74 1.06
time (sec) N/A 0.092 0.325 0.170 0.319 0.417 0.000 6.776 6.732
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 106 70 90 47 0 68 47
normalized size 1 1.00 2.12 1.40 1.80 0.94 0.00 1.36 0.94
time (sec) N/A 0.088 0.162 0.145 0.303 0.422 0.000 0.660 6.402
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 48 22 27 42 27 21 21
normalized size 1 1.00 2.09 0.96 1.17 1.83 1.17 0.91 0.91
time (sec) N/A 0.012 0.041 0.074 0.331 0.422 0.830 0.341 6.428
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 69 56 70 62 0 65 25
normalized size 1 1.00 2.38 1.93 2.41 2.14 0.00 2.24 0.86
time (sec) N/A 0.051 0.231 0.185 0.297 0.412 0.000 4.004 6.636
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 124 132 155 111 0 127 115
normalized size 1 1.00 2.14 2.28 2.67 1.91 0.00 2.19 1.98
time (sec) N/A 0.088 0.509 0.200 0.298 0.431 0.000 0.228 6.635
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 189 208 234 155 0 187 183
normalized size 1 1.00 2.30 2.54 2.85 1.89 0.00 2.28 2.23
time (sec) N/A 0.106 0.759 0.239 0.498 0.429 0.000 1.963 6.662
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 284 284 315 198 0 244 387
normalized size 1 1.00 2.68 2.68 2.97 1.87 0.00 2.30 3.65
time (sec) N/A 0.127 0.924 0.324 0.327 0.436 0.000 0.317 8.221
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 112 180 202 218 0 146 444
normalized size 1 1.00 0.59 0.95 1.07 1.15 0.00 0.77 2.35
time (sec) N/A 0.149 1.640 0.248 0.315 0.491 0.000 71.382 10.464
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 146 146 91 144 167 198 0 126 361
normalized size 1 1.00 0.62 0.99 1.14 1.36 0.00 0.86 2.47
time (sec) N/A 0.108 0.447 0.235 0.316 0.464 0.000 19.849 10.504
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 70 108 110 178 0 102 240
normalized size 1 1.00 0.67 1.04 1.06 1.71 0.00 0.98 2.31
time (sec) N/A 0.086 0.317 0.236 0.299 0.427 0.000 2.056 10.052
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 36 72 70 104 0 90 116
normalized size 1 1.00 0.60 1.20 1.17 1.73 0.00 1.50 1.93
time (sec) N/A 0.048 0.081 0.239 0.296 0.411 0.000 0.997 7.640
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 36 50 46 59 0 45 87
normalized size 1 1.00 0.69 0.96 0.88 1.13 0.00 0.87 1.67
time (sec) N/A 0.050 0.057 0.152 0.297 0.413 0.000 0.395 6.590
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 49 66 55 76 0 115 103
normalized size 1 1.00 0.75 1.02 0.85 1.17 0.00 1.77 1.58
time (sec) N/A 0.059 0.068 0.323 0.300 0.416 0.000 0.489 6.528
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 38 39 36 57 0 36 36
normalized size 1 1.00 0.69 0.71 0.65 1.04 0.00 0.65 0.65
time (sec) N/A 0.051 0.067 0.247 0.298 0.393 0.000 0.604 6.335
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 73 49 46 94 0 46 46
normalized size 1 1.00 1.00 0.67 0.63 1.29 0.00 0.63 0.63
time (sec) N/A 0.057 0.074 0.287 0.308 0.436 0.000 0.605 6.375
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 78 79 76 127 0 76 76
normalized size 1 1.00 0.61 0.62 0.60 1.00 0.00 0.60 0.60
time (sec) N/A 0.074 0.151 0.325 0.327 0.426 0.000 0.770 6.542
Problem 70 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 145 145 88 89 86 162 0 86 85
normalized size 1 1.00 0.61 0.61 0.59 1.12 0.00 0.59 0.59
time (sec) N/A 0.081 0.214 0.378 0.309 0.437 0.000 1.754 6.633
Problem 71 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 199 199 118 119 116 195 0 116 116
normalized size 1 1.00 0.59 0.60 0.58 0.98 0.00 0.58 0.58
time (sec) N/A 0.102 0.342 0.422 0.304 0.468 0.000 1.327 6.849
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 171 171 102 162 188 248 0 136 418
normalized size 1 1.00 0.60 0.95 1.10 1.45 0.00 0.80 2.44
time (sec) N/A 0.123 0.676 0.259 0.321 0.457 0.000 24.625 10.051
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 82 126 146 226 0 114 302
normalized size 1 1.00 0.65 1.00 1.16 1.79 0.00 0.90 2.40
time (sec) N/A 0.091 0.361 0.265 0.299 0.445 0.000 1.912 9.925
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 52 90 98 154 0 81 186
normalized size 1 1.00 0.63 1.10 1.20 1.88 0.00 0.99 2.27
time (sec) N/A 0.057 0.151 0.244 0.297 0.437 0.000 0.790 8.819
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 52 68 72 104 0 59 148
normalized size 1 1.00 0.70 0.92 0.97 1.41 0.00 0.80 2.00
time (sec) N/A 0.058 0.182 0.167 0.300 0.451 0.000 0.641 6.648
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 61 84 80 147 0 154 169
normalized size 1 1.00 0.71 0.98 0.93 1.71 0.00 1.79 1.97
time (sec) N/A 0.070 0.191 0.474 0.338 0.446 0.000 0.484 6.701
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 69 97 75 131 0 174 171
normalized size 1 1.00 0.72 1.01 0.78 1.36 0.00 1.81 1.78
time (sec) N/A 0.071 0.314 0.343 0.373 0.434 0.000 0.963 6.717
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 48 49 46 84 0 46 46
normalized size 1 1.00 0.66 0.67 0.63 1.15 0.00 0.63 0.63
time (sec) N/A 0.057 0.097 0.331 0.303 0.414 0.000 0.813 6.693
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 68 69 66 117 0 66 66
normalized size 1 1.00 0.62 0.63 0.61 1.07 0.00 0.61 0.61
time (sec) N/A 0.069 0.076 0.355 0.331 0.419 0.000 2.039 6.629
Problem 80 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 145 145 88 89 86 152 0 86 86
normalized size 1 1.00 0.61 0.61 0.59 1.05 0.00 0.59 0.59
time (sec) N/A 0.081 0.111 0.385 0.306 0.436 0.000 2.483 6.811
Problem 81 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 145 145 88 89 86 185 0 86 85
normalized size 1 1.00 0.61 0.61 0.59 1.28 0.00 0.59 0.59
time (sec) N/A 0.078 0.120 0.427 0.305 0.464 0.000 6.359 6.822
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 195 112 180 213 290 0 146 476
normalized size 1 1.00 0.57 0.92 1.09 1.49 0.00 0.75 2.44
time (sec) N/A 0.135 1.446 0.240 0.534 0.468 0.000 7.591 10.661
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 50 81 95 102 0 76 172
normalized size 1 1.00 0.38 0.61 0.72 0.77 0.00 0.58 1.30
time (sec) N/A 0.089 0.104 0.239 0.369 0.451 0.000 2.337 7.508
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 62 108 121 198 0 91 240
normalized size 1 1.00 0.59 1.03 1.15 1.89 0.00 0.87 2.29
time (sec) N/A 0.065 0.256 0.249 0.331 0.443 0.000 0.718 10.070
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 73 101 103 196 0 185 228
normalized size 1 1.00 0.69 0.95 0.97 1.85 0.00 1.75 2.15
time (sec) N/A 0.083 0.802 0.337 0.327 0.445 0.000 1.178 6.610
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 89 130 95 186 0 232 235
normalized size 1 1.00 0.66 0.96 0.70 1.38 0.00 1.72 1.74
time (sec) N/A 0.086 0.161 0.334 0.316 0.447 0.000 1.122 6.807
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 124 158 356 129 0 146 231
normalized size 1 1.00 0.98 1.24 2.80 1.02 0.00 1.15 1.82
time (sec) N/A 0.310 0.428 0.213 0.378 0.445 0.000 1.808 7.577
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 315 161 288 369 0 135 203
normalized size 1 1.00 2.92 1.49 2.67 3.42 0.00 1.25 1.88
time (sec) N/A 0.318 0.423 0.306 0.328 0.439 0.000 0.702 12.052
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 120 120 589 195 285 445 0 179 171
normalized size 1 1.00 4.91 1.62 2.38 3.71 0.00 1.49 1.42
time (sec) N/A 0.249 6.088 0.315 0.331 0.450 0.000 0.418 7.826
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 133 133 733 229 279 439 0 204 209
normalized size 1 1.00 5.51 1.72 2.10 3.30 0.00 1.53 1.57
time (sec) N/A 0.249 6.132 0.337 0.323 0.472 0.000 1.288 7.672
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 195 394 172 0 200 0 0 -1
normalized size 1 1.20 2.43 1.06 0.00 1.23 0.00 0.00 -0.01
time (sec) N/A 0.923 5.568 0.697 0.000 0.471 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 114 89 0 169 0 0 -1
normalized size 1 1.00 1.13 0.88 0.00 1.67 0.00 0.00 -0.01
time (sec) N/A 0.185 0.336 0.728 0.000 0.430 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 206 125 0 279 0 0 -1
normalized size 1 1.00 2.31 1.40 0.00 3.13 0.00 0.00 -0.01
time (sec) N/A 0.192 0.994 0.793 0.000 0.440 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 309 170 0 380 0 0 -1
normalized size 1 1.00 1.90 1.04 0.00 2.33 0.00 0.00 -0.01
time (sec) N/A 0.377 1.603 0.929 0.000 0.443 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-1) A F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 195 141 139 0 239 0 0 -1
normalized size 1 1.17 0.84 0.83 0.00 1.43 0.00 0.00 -0.01
time (sec) N/A 0.975 5.547 0.750 0.000 0.441 0.000 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 46 55 145 48 0 0 -1
normalized size 1 1.00 0.52 0.62 1.65 0.55 0.00 0.00 -0.01
time (sec) N/A 0.196 4.152 0.580 0.584 0.414 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 233 144 0 315 0 0 -1
normalized size 1 1.00 1.93 1.19 0.00 2.60 0.00 0.00 -0.01
time (sec) N/A 0.321 0.756 0.898 0.000 0.430 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 197 197 334 196 0 424 0 0 -1
normalized size 1 1.00 1.70 0.99 0.00 2.15 0.00 0.00 -0.01
time (sec) N/A 0.496 1.628 1.002 0.000 0.451 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 208 112 87 277 98 0 0 -1
normalized size 1 1.38 0.74 0.58 1.83 0.65 0.00 0.00 -0.01
time (sec) N/A 0.979 5.471 0.693 1.291 0.430 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 60 67 191 70 0 0 -1
normalized size 1 1.00 0.51 0.57 1.62 0.59 0.00 0.00 -0.01
time (sec) N/A 0.214 5.473 0.491 0.482 0.426 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 261 162 0 363 0 0 -1
normalized size 1 1.00 1.73 1.07 0.00 2.40 0.00 0.00 -0.01
time (sec) N/A 0.429 1.261 0.726 0.000 0.446 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 227 227 360 222 0 485 0 0 -1
normalized size 1 1.00 1.59 0.98 0.00 2.14 0.00 0.00 -0.00
time (sec) N/A 0.627 1.744 0.909 0.000 0.443 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 241 118 231 0 229 0 0 -1
normalized size 1 1.61 0.79 1.54 0.00 1.53 0.00 0.00 -0.01
time (sec) N/A 0.933 0.689 1.010 0.000 0.437 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 118 130 0 200 0 0 -1
normalized size 1 1.00 1.10 1.21 0.00 1.87 0.00 0.00 -0.01
time (sec) N/A 0.195 0.256 0.576 0.000 0.432 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 138 103 0 263 0 0 -1
normalized size 1 1.00 2.23 1.66 0.00 4.24 0.00 0.00 -0.02
time (sec) N/A 0.110 0.321 0.691 0.000 0.430 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 292 144 0 369 0 0 -1
normalized size 1 1.00 2.16 1.07 0.00 2.73 0.00 0.00 -0.01
time (sec) N/A 0.622 0.608 0.822 0.000 0.443 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-1) A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 177 195 334 289 0 270 0 0 -1
normalized size 1 1.10 1.89 1.63 0.00 1.53 0.00 0.00 -0.01
time (sec) N/A 1.199 0.373 0.802 0.000 0.481 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-1) B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 128 202 0 237 0 0 -1
normalized size 1 1.00 0.96 1.51 0.00 1.77 0.00 0.00 -0.01
time (sec) N/A 0.223 0.456 0.698 0.000 0.466 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 206 134 0 421 0 0 -1
normalized size 1 1.00 1.82 1.19 0.00 3.73 0.00 0.00 -0.01
time (sec) N/A 0.229 2.115 0.801 0.000 0.459 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F(-1) B F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 144 144 294 144 0 383 0 0 -1
normalized size 1 1.00 2.04 1.00 0.00 2.66 0.00 0.00 -0.01
time (sec) N/A 0.553 0.764 0.892 0.000 0.447 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-1) A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 207 260 394 353 0 307 0 0 -1
normalized size 1 1.26 1.90 1.71 0.00 1.48 0.00 0.00 -0.00
time (sec) N/A 1.434 0.541 0.989 0.000 0.484 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-1) A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 284 266 0 279 0 0 -1
normalized size 1 1.00 1.70 1.59 0.00 1.67 0.00 0.00 -0.01
time (sec) N/A 0.303 0.402 0.958 0.000 0.447 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-1) B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 451 219 0 539 0 0 -1
normalized size 1 1.00 3.20 1.55 0.00 3.82 0.00 0.00 -0.01
time (sec) N/A 0.346 0.740 0.688 0.000 0.468 0.000 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-1) B F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 191 191 332 182 0 564 0 0 -1
normalized size 1 1.00 1.74 0.95 0.00 2.95 0.00 0.00 -0.01
time (sec) N/A 0.959 2.411 1.007 0.000 0.461 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 982 982 318 0 0 0 0 0 -1
normalized size 1 1.00 0.32 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.271 3.237 0.273 0.000 0.456 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 290 0 0 0 0 0 -1
normalized size 1 1.00 2.36 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.193 2.709 0.222 0.000 0.444 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 80 80 2692 0 0 0 0 0 -1
normalized size 1 1.00 33.65 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.101 23.710 0.195 0.000 0.000 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 80 80 2796 0 0 0 0 0 -1
normalized size 1 1.00 34.95 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.094 22.335 0.227 0.000 0.000 0.000 0.000 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 551 551 128 0 0 0 0 0 -1
normalized size 1 1.00 0.23 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.494 0.788 0.233 0.000 1.312 0.000 0.000 0.000
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 126 126 100 0 0 0 0 0 -1
normalized size 1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.216 0.499 0.213 0.000 1.690 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F(-1) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 80 80 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.095 12.571 0.199 0.000 0.000 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F(-1) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 80 80 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.094 8.942 0.253 0.000 0.000 0.000 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 269 269 5199 0 0 0 0 0 -1
normalized size 1 1.00 19.33 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.345 58.504 2.675 0.000 1.995 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 187 187 2054 0 0 0 0 0 -1
normalized size 1 1.00 10.98 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.227 18.142 2.243 0.000 1.065 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 129 129 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.139 2.058 1.522 0.000 0.648 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 108 108 232 0 0 0 0 0 -1
normalized size 1 1.00 2.15 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.126 3.925 0.466 0.000 0.486 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 138 138 667 0 0 0 0 0 -1
normalized size 1 1.00 4.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.275 13.956 1.022 0.000 0.480 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 248 248 1276 0 0 0 0 0 -1
normalized size 1 1.00 5.15 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.422 27.816 1.002 0.000 0.453 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 111 111 367 0 0 0 0 0 -1
normalized size 1 1.00 3.31 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.124 2.178 1.324 0.000 0.473 0.000 0.000 0.000
Problem 130 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 163 163 105 0 0 0 0 0 -1
normalized size 1 1.00 0.64 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.149 0.257 0.265 0.000 0.438 0.000 0.000 0.000
Problem 131 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 72 72 63 0 0 0 0 0 -1
normalized size 1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.050 0.069 1.368 0.000 0.481 0.000 0.000 0.000
Problem 132 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 43 43 43 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.044 0.055 1.425 0.000 0.452 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 F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 68 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 0.069 0.192 0.418 0.000 0.436 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 83 0 0 0 0 0 -1
normalized size 1 1.00 0.67 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.098 0.263 0.529 0.000 0.458 0.000 0.000 0.000
Problem 135 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 311 311 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 0.355 1.123 0.259 0.000 0.441 0.000 0.000 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 157 157 4043 0 0 0 0 0 -1
normalized size 1 1.00 25.75 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.248 6.325 0.219 0.000 0.442 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 F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 90 0 0 0 0 0 -1
normalized size 1 1.00 1.22 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.035 0.154 0.450 0.000 0.480 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 89 89 5048 0 0 0 0 0 -1
normalized size 1 1.00 56.72 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.102 26.447 0.351 0.000 0.450 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 F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 89 89 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.099 0.781 0.442 0.000 0.503 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 77 96 73 90 0 0 176
normalized size 1 1.00 0.88 1.09 0.83 1.02 0.00 0.00 2.00
time (sec) N/A 0.077 0.126 0.095 1.625 0.504 0.000 0.000 6.735
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 38 46 43 45 0 1456 74
normalized size 1 1.00 0.69 0.84 0.78 0.82 0.00 26.47 1.35
time (sec) N/A 0.038 0.017 0.084 1.153 0.430 0.000 4.249 6.636
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 43 25 22 24 0 23 47
normalized size 1 1.00 1.79 1.04 0.92 1.00 0.00 0.96 1.96
time (sec) N/A 0.021 0.036 0.080 0.606 0.448 0.000 1.274 6.564
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 60 83 45 69 0 60 146
normalized size 1 1.00 1.11 1.54 0.83 1.28 0.00 1.11 2.70
time (sec) N/A 0.041 0.212 0.189 0.957 0.463 0.000 1.790 6.631
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 87 136 69 110 0 82 207
normalized size 1 1.00 1.07 1.68 0.85 1.36 0.00 1.01 2.56
time (sec) N/A 0.052 0.244 0.177 1.402 0.465 0.000 1.844 6.670
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 81 98 65 73 0 0 110
normalized size 1 1.00 1.12 1.36 0.90 1.01 0.00 0.00 1.53
time (sec) N/A 0.078 0.037 0.155 1.703 0.472 0.000 0.000 10.183
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 47 59 39 47 0 1008 55
normalized size 1 1.00 1.24 1.55 1.03 1.24 0.00 26.53 1.45
time (sec) N/A 0.059 0.035 0.136 1.367 0.446 0.000 35.578 6.595
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 75 57 54 84 0 108 158
normalized size 1 1.00 1.83 1.39 1.32 2.05 0.00 2.63 3.85
time (sec) N/A 0.053 0.037 0.098 1.381 0.465 0.000 0.285 6.597
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 125 106 92 160 0 141 225
normalized size 1 1.00 1.52 1.29 1.12 1.95 0.00 1.72 2.74
time (sec) N/A 0.080 0.046 0.115 1.819 0.467 0.000 0.575 6.294
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 164 159 125 222 0 199 288
normalized size 1 1.00 1.34 1.30 1.02 1.82 0.00 1.63 2.36
time (sec) N/A 0.097 0.054 0.129 1.885 0.498 0.000 0.683 6.299
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 108 172 105 140 0 0 232
normalized size 1 1.00 0.97 1.55 0.95 1.26 0.00 0.00 2.09
time (sec) N/A 0.173 0.441 0.146 0.464 0.453 0.000 0.000 6.722
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 64 82 70 74 0 7855 150
normalized size 1 1.00 0.82 1.05 0.90 0.95 0.00 100.71 1.92
time (sec) N/A 0.071 0.132 0.148 0.372 0.473 0.000 12.160 6.366
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 46 45 40 42 0 41 117
normalized size 1 1.00 1.00 0.98 0.87 0.91 0.00 0.89 2.54
time (sec) N/A 0.039 0.025 0.099 0.485 0.461 0.000 0.417 6.436
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 70 120 69 115 0 99 221
normalized size 1 1.00 0.83 1.43 0.82 1.37 0.00 1.18 2.63
time (sec) N/A 0.073 0.259 0.237 0.770 0.486 0.000 0.745 6.385
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 107 220 105 177 0 138 310
normalized size 1 1.00 0.85 1.75 0.83 1.40 0.00 1.10 2.46
time (sec) N/A 0.104 0.732 0.278 0.985 0.497 0.000 0.873 6.444
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 176 185 119 118 0 0 235
normalized size 1 1.00 1.18 1.24 0.80 0.79 0.00 0.00 1.58
time (sec) N/A 0.162 0.724 0.197 1.246 0.445 0.000 0.000 10.036
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 77 116 83 81 0 7670 147
normalized size 1 1.00 0.82 1.23 0.88 0.86 0.00 81.60 1.56
time (sec) N/A 0.122 0.485 0.227 1.037 0.440 0.000 45.199 9.287
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 116 102 79 118 0 148 277
normalized size 1 1.00 1.49 1.31 1.01 1.51 0.00 1.90 3.55
time (sec) N/A 0.086 0.411 0.131 0.727 0.459 0.000 0.199 7.273
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 133 133 293 199 138 218 0 241 584
normalized size 1 1.00 2.20 1.50 1.04 1.64 0.00 1.81 4.39
time (sec) N/A 0.149 6.214 0.246 1.027 0.482 0.000 0.353 8.997
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 202 202 351 302 183 306 0 337 888
normalized size 1 1.00 1.74 1.50 0.91 1.51 0.00 1.67 4.40
time (sec) N/A 0.169 1.120 0.233 2.125 0.520 0.000 0.505 11.280
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 141 279 162 194 0 0 366
normalized size 1 1.00 0.94 1.86 1.08 1.29 0.00 0.00 2.44
time (sec) N/A 0.242 0.249 0.161 0.401 0.492 0.000 0.000 6.981
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 90 139 113 116 0 0 226
normalized size 1 1.00 0.86 1.32 1.08 1.10 0.00 0.00 2.15
time (sec) N/A 0.114 0.199 0.145 0.303 0.470 0.000 0.000 6.746
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 67 64 57 66 0 58 118
normalized size 1 1.00 1.00 0.96 0.85 0.99 0.00 0.87 1.76
time (sec) N/A 0.045 0.027 0.104 1.198 0.467 0.000 0.922 6.678
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 97 165 98 153 0 131 312
normalized size 1 1.00 0.84 1.42 0.84 1.32 0.00 1.13 2.69
time (sec) N/A 0.094 0.289 0.257 1.141 0.466 0.000 0.940 6.946
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 144 316 142 225 0 185 424
normalized size 1 1.00 0.87 1.92 0.86 1.36 0.00 1.12 2.57
time (sec) N/A 0.141 1.037 0.230 0.639 0.498 0.000 2.447 6.969
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 220 220 226 268 167 157 0 0 297
normalized size 1 1.00 1.03 1.22 0.76 0.71 0.00 0.00 1.35
time (sec) N/A 0.224 0.708 0.252 1.263 0.437 0.000 0.000 9.197
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 146 146 113 169 119 116 0 0 249
normalized size 1 1.00 0.77 1.16 0.82 0.79 0.00 0.00 1.71
time (sec) N/A 0.169 0.769 0.286 2.155 0.423 0.000 0.000 9.152
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 143 125 95 143 0 199 289
normalized size 1 1.00 1.40 1.23 0.93 1.40 0.00 1.95 2.83
time (sec) N/A 0.112 1.323 0.143 0.905 0.468 0.000 1.621 6.857
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 194 194 355 264 187 293 0 421 405
normalized size 1 1.00 1.83 1.36 0.96 1.51 0.00 2.17 2.09
time (sec) N/A 0.184 6.234 0.228 1.840 0.486 0.000 0.689 6.809
Problem 169 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 291 291 346 415 252 412 0 471 507
normalized size 1 1.00 1.19 1.43 0.87 1.42 0.00 1.62 1.74
time (sec) N/A 0.231 2.574 0.258 1.890 0.573 0.000 1.051 7.058
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 204 204 184 304 288 261 0 343 498
normalized size 1 1.00 0.90 1.49 1.41 1.28 0.00 1.68 2.44
time (sec) N/A 0.363 1.302 0.180 1.896 0.631 0.000 10.464 7.426
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 117 164 142 157 0 177 217
normalized size 1 1.00 0.93 1.30 1.13 1.25 0.00 1.40 1.72
time (sec) N/A 0.191 0.492 0.180 0.690 0.543 0.000 2.104 7.035
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 87 76 65 63 0 71 91
normalized size 1 1.00 1.18 1.03 0.88 0.85 0.00 0.96 1.23
time (sec) N/A 0.066 0.085 0.180 0.448 0.459 0.000 0.405 6.732
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 34 35 33 31 0 35 48
normalized size 1 1.00 1.00 1.03 0.97 0.91 0.00 1.03 1.41
time (sec) N/A 0.040 0.019 0.112 0.652 0.484 0.000 0.718 6.362
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 65 106 77 118 0 114 144
normalized size 1 1.00 0.77 1.26 0.92 1.40 0.00 1.36 1.71
time (sec) N/A 0.089 0.158 0.221 2.084 0.477 0.000 0.381 6.632
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 148 148 115 216 139 271 0 201 281
normalized size 1 1.00 0.78 1.46 0.94 1.83 0.00 1.36 1.90
time (sec) N/A 0.138 1.060 0.202 0.608 0.473 0.000 0.455 6.409
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 177 177 195 269 0 476 0 241 372
normalized size 1 1.00 1.10 1.52 0.00 2.69 0.00 1.36 2.10
time (sec) N/A 0.239 1.401 0.193 0.000 0.539 0.000 3.699 9.547
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 152 117 0 305 0 107 148
normalized size 1 1.00 1.58 1.22 0.00 3.18 0.00 1.11 1.54
time (sec) N/A 0.099 0.197 0.158 0.000 0.464 0.000 1.790 6.369
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 108 155 0 314 0 129 204
normalized size 1 1.00 1.35 1.94 0.00 3.92 0.00 1.61 2.55
time (sec) N/A 0.243 0.245 0.172 0.000 0.526 0.000 0.416 7.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) A F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 154 154 350 348 0 633 0 273 654
normalized size 1 1.00 2.27 2.26 0.00 4.11 0.00 1.77 4.25
time (sec) N/A 0.426 6.121 0.198 0.000 0.636 0.000 0.390 7.144
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 307 307 504 629 0 1079 0 490 1099
normalized size 1 1.00 1.64 2.05 0.00 3.51 0.00 1.60 3.58
time (sec) N/A 1.106 1.414 0.206 0.000 1.041 0.000 0.597 7.130
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 242 242 240 318 505 555 0 494 755
normalized size 1 1.00 0.99 1.31 2.09 2.29 0.00 2.04 3.12
time (sec) N/A 0.633 6.255 0.270 1.061 0.970 0.000 9.560 7.782
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 145 182 274 388 0 248 351
normalized size 1 1.00 0.90 1.13 1.70 2.41 0.00 1.54 2.18
time (sec) N/A 0.312 0.794 0.264 1.452 0.680 0.000 1.981 7.245
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 162 132 124 195 0 156 158
normalized size 1 1.00 1.49 1.21 1.14 1.79 0.00 1.43 1.45
time (sec) N/A 0.096 0.299 0.243 0.924 0.542 0.000 0.460 6.758
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 42 54 47 69 0 51 105
normalized size 1 1.00 0.79 1.02 0.89 1.30 0.00 0.96 1.98
time (sec) N/A 0.053 0.081 0.146 0.604 0.508 0.000 0.416 6.376
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 96 150 116 259 0 165 235
normalized size 1 1.00 0.84 1.32 1.02 2.27 0.00 1.45 2.06
time (sec) N/A 0.115 0.631 0.291 0.304 0.533 0.000 0.431 6.379
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 188 188 187 282 189 542 0 278 439
normalized size 1 1.00 0.99 1.50 1.01 2.88 0.00 1.48 2.34
time (sec) N/A 0.181 6.139 0.273 0.806 0.548 0.000 0.416 6.900
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 333 333 341 382 0 815 0 406 722
normalized size 1 1.00 1.02 1.15 0.00 2.45 0.00 1.22 2.17
time (sec) N/A 0.627 2.027 0.259 0.000 0.575 0.000 2.980 9.895
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 200 200 169 282 0 569 0 251 313
normalized size 1 1.00 0.84 1.41 0.00 2.84 0.00 1.26 1.56
time (sec) N/A 0.301 1.057 0.306 0.000 0.552 0.000 0.874 8.675
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 139 245 0 768 0 218 1616
normalized size 1 1.00 1.21 2.13 0.00 6.68 0.00 1.90 14.05
time (sec) N/A 0.453 0.764 0.279 0.000 0.660 0.000 0.396 8.317
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 238 238 403 527 0 1149 0 356 973
normalized size 1 1.00 1.69 2.21 0.00 4.83 0.00 1.50 4.09
time (sec) N/A 0.695 6.198 0.287 0.000 0.715 0.000 0.542 6.830
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 424 424 361 897 0 2011 0 596 1424
normalized size 1 1.00 0.85 2.12 0.00 4.74 0.00 1.41 3.36
time (sec) N/A 1.493 1.566 0.323 0.000 1.063 0.000 0.899 6.905
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 321 321 304 465 730 981 0 585 1229
normalized size 1 1.00 0.95 1.45 2.27 3.06 0.00 1.82 3.83
time (sec) N/A 0.877 6.341 0.327 1.438 1.349 0.000 6.814 10.735
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 232 232 196 323 441 788 0 464 690
normalized size 1 1.00 0.84 1.39 1.90 3.40 0.00 2.00 2.97
time (sec) N/A 0.482 2.277 0.305 0.740 0.861 0.000 2.390 7.464
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 213 198 228 462 0 257 304
normalized size 1 1.00 1.43 1.33 1.53 3.10 0.00 1.72 2.04
time (sec) N/A 0.132 2.161 0.293 0.659 0.661 0.000 0.530 6.854
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 60 74 81 154 0 69 369
normalized size 1 1.00 0.80 0.99 1.08 2.05 0.00 0.92 4.92
time (sec) N/A 0.060 0.262 0.175 0.687 0.518 0.000 1.083 6.537
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 121 194 156 404 0 154 334
normalized size 1 1.00 0.83 1.34 1.08 2.79 0.00 1.06 2.30
time (sec) N/A 0.133 0.940 0.329 0.735 0.581 0.000 0.536 6.790
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 221 221 195 348 236 754 0 327 563
normalized size 1 1.00 0.88 1.57 1.07 3.41 0.00 1.48 2.55
time (sec) N/A 0.211 5.306 0.350 0.700 0.631 0.000 0.835 7.262
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 474 474 351 922 0 1249 0 632 1099
normalized size 1 1.00 0.74 1.95 0.00 2.64 0.00 1.33 2.32
time (sec) N/A 0.872 1.045 0.316 0.000 0.641 0.000 2.416 11.220
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 350 350 212 766 0 934 0 384 627
normalized size 1 1.00 0.61 2.19 0.00 2.67 0.00 1.10 1.79
time (sec) N/A 0.539 3.221 0.289 0.000 0.592 0.000 1.821 10.358
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 202 202 195 729 0 1394 0 339 1762
normalized size 1 1.00 0.97 3.61 0.00 6.90 0.00 1.68 8.72
time (sec) N/A 0.788 5.783 0.303 0.000 1.038 0.000 0.500 7.853
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 289 289 459 780 0 2027 0 451 1261
normalized size 1 1.00 1.59 2.70 0.00 7.01 0.00 1.56 4.36
time (sec) N/A 1.072 6.211 0.332 0.000 1.045 0.000 0.920 7.311
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 492 492 448 1252 0 2571 0 731 1614
normalized size 1 1.00 0.91 2.54 0.00 5.23 0.00 1.49 3.28
time (sec) N/A 2.127 1.758 0.411 0.000 1.175 0.000 1.518 7.301
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 271 271 4791 0 0 0 0 0 -1
normalized size 1 1.00 17.68 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.380 16.096 2.629 0.000 0.496 0.000 0.000 0.000
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 186 186 2464 0 0 0 0 0 -1
normalized size 1 1.00 13.25 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.242 14.236 2.489 0.000 0.490 0.000 0.000 0.000
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 129 129 849 0 0 0 0 0 -1
normalized size 1 1.00 6.58 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.148 9.534 1.533 0.000 0.463 0.000 0.000 0.000
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F B F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 284 0 858 0 0 0 0 0 -1
normalized size 1 0.00 3.02 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.048 13.590 0.796 0.000 0.459 0.000 0.000 0.000
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A F A F F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 737 0 866 0 0 0 0 0 -1
normalized size 1 0.00 1.18 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.045 14.397 1.567 0.000 0.596 0.000 0.000 0.000
Problem 208 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 26 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 -0.04
time (sec) N/A 0.040 3.129 1.523 0.000 0.714 0.000 0.000 0.000

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [159] had the largest ratio of [.4762]

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 3 2 1.00 19 0.105
2 A 3 2 1.00 19 0.105
3 A 3 2 1.00 17 0.118
4 A 3 2 1.00 17 0.118
5 A 3 2 1.00 19 0.105
6 A 3 2 1.00 19 0.105
7 A 3 2 1.00 19 0.105
8 A 9 5 1.00 19 0.263
9 A 8 5 1.00 19 0.263
10 A 5 5 1.00 19 0.263
11 A 7 6 1.00 19 0.316
12 A 9 7 1.00 19 0.368
13 A 11 7 1.00 19 0.368
14 A 3 2 1.00 21 0.095
15 A 3 2 1.00 21 0.095
16 A 3 2 1.00 19 0.105
17 A 2 2 1.00 21 0.095
18 A 3 2 1.00 21 0.095
19 A 14 9 1.00 21 0.429
20 A 4 4 1.00 21 0.190
21 A 6 5 1.00 21 0.238
22 A 1 1 1.00 12 0.083
23 A 8 6 1.00 21 0.286
24 A 12 7 1.00 21 0.333
25 A 3 2 1.00 21 0.095
26 A 3 2 1.00 21 0.095
27 A 3 2 1.00 19 0.105
28 A 3 2 1.00 21 0.095
29 A 9 7 1.00 21 0.333
30 A 10 7 1.00 21 0.333
31 A 8 6 1.00 21 0.286
32 A 7 5 1.00 12 0.417
33 A 10 7 1.00 21 0.333
34 A 3 2 1.00 21 0.095
35 A 3 2 1.00 21 0.095
36 A 3 2 1.00 19 0.105
37 A 3 2 1.00 21 0.095
38 A 13 7 1.00 21 0.333
39 A 11 6 1.00 21 0.286
40 A 10 5 1.00 12 0.417
41 A 12 6 1.00 21 0.286
42 A 17 8 1.00 21 0.381
43 A 21 8 1.00 21 0.381
44 A 8 5 1.00 21 0.238
45 A 7 5 1.00 21 0.238
46 A 6 5 1.00 21 0.238
47 A 5 5 1.57 19 0.263
48 A 4 4 1.00 19 0.210
49 A 5 4 1.00 21 0.190
50 A 5 4 1.00 21 0.190
51 A 6 5 1.00 21 0.238
52 A 6 5 1.00 21 0.238
53 A 6 5 1.00 21 0.238
54 A 6 5 1.00 21 0.238
55 A 5 4 1.00 21 0.190
56 A 1 1 1.00 12 0.083
57 A 4 4 1.00 21 0.190
58 A 5 5 1.00 21 0.238
59 A 6 5 1.00 21 0.238
60 A 7 5 1.00 21 0.238
61 A 4 3 1.00 21 0.143
62 A 4 3 1.00 21 0.143
63 A 4 3 1.00 21 0.143
64 A 4 3 1.00 19 0.158
65 A 3 2 1.00 19 0.105
66 A 3 2 1.00 21 0.095
67 A 3 2 1.00 21 0.095
68 A 3 2 1.00 21 0.095
69 A 3 2 1.00 21 0.095
70 A 3 2 1.00 21 0.095
71 A 3 2 1.00 21 0.095
72 A 4 3 1.00 21 0.143
73 A 4 3 1.00 21 0.143
74 A 4 3 1.00 19 0.158
75 A 3 2 1.00 19 0.105
76 A 3 2 1.00 21 0.095
77 A 3 2 1.00 21 0.095
78 A 3 2 1.00 21 0.095
79 A 3 2 1.00 21 0.095
80 A 3 2 1.00 21 0.095
81 A 3 2 1.00 21 0.095
82 A 4 3 1.00 21 0.143
83 A 3 2 1.00 21 0.095
84 A 4 3 1.00 19 0.158
85 A 3 2 1.00 21 0.095
86 A 3 2 1.00 21 0.095
87 A 17 5 1.00 21 0.238
88 A 14 8 1.00 21 0.381
89 A 14 8 1.00 21 0.381
90 A 16 6 1.00 21 0.286
91 A 15 10 1.20 23 0.435
92 A 4 4 1.00 23 0.174
93 A 4 4 1.00 23 0.174
94 A 7 7 1.00 23 0.304
95 A 14 9 1.17 23 0.391
96 A 3 3 1.00 23 0.130
97 A 5 5 1.00 23 0.217
98 A 8 8 1.00 23 0.348
99 A 10 7 1.38 23 0.304
100 A 4 4 1.00 23 0.174
101 A 6 5 1.00 23 0.217
102 A 10 8 1.00 23 0.348
103 A 17 9 1.61 23 0.391
104 A 4 4 1.00 23 0.174
105 A 4 4 1.00 23 0.174
106 A 11 7 1.00 23 0.304
107 A 20 9 1.10 23 0.391
108 A 5 5 1.00 23 0.217
109 A 6 5 1.00 23 0.217
110 A 10 6 1.00 23 0.261
111 A 23 9 1.26 23 0.391
112 A 6 6 1.00 23 0.261
113 A 7 6 1.00 23 0.261
114 A 16 8 1.00 23 0.348
115 A 10 9 1.00 23 0.391
116 A 4 4 1.00 23 0.174
117 A 3 3 1.00 23 0.130
118 A 3 3 1.00 23 0.130
119 A 8 7 1.00 23 0.304
120 A 4 4 1.00 23 0.174
121 A 3 3 1.00 23 0.130
122 A 3 3 1.00 23 0.130
123 A 10 6 1.00 23 0.261
124 A 8 6 1.00 23 0.261
125 A 6 5 1.00 21 0.238
126 A 4 4 1.00 23 0.174
127 A 10 6 1.00 23 0.261
128 A 13 6 1.00 23 0.261
129 A 4 3 1.00 23 0.130
130 A 4 4 1.00 21 0.190
131 A 3 3 1.00 19 0.158
132 A 2 2 1.00 19 0.105
133 A 3 3 1.00 21 0.143
134 A 4 4 1.00 21 0.190
135 A 6 6 1.00 21 0.286
136 A 5 5 1.00 21 0.238
137 A 2 2 1.00 12 0.167
138 A 3 3 1.00 21 0.143
139 A 3 3 1.00 21 0.143
140 A 6 5 1.00 19 0.263
141 A 5 4 1.00 17 0.235
142 A 3 2 1.00 17 0.118
143 A 3 2 1.00 19 0.105
144 A 3 2 1.00 19 0.105
145 A 8 5 1.00 19 0.263
146 A 7 5 1.00 19 0.263
147 A 7 6 1.00 19 0.316
148 A 9 7 1.00 19 0.368
149 A 11 7 1.00 19 0.368
150 A 7 5 1.00 21 0.238
151 A 6 4 1.00 19 0.210
152 A 3 2 1.00 19 0.105
153 A 3 2 1.00 21 0.095
154 A 3 2 1.00 21 0.095
155 A 13 9 1.00 21 0.429
156 A 11 9 1.00 21 0.429
157 A 9 7 1.00 21 0.333
158 A 13 9 1.00 21 0.429
159 A 16 10 1.00 21 0.476
160 A 7 5 1.00 21 0.238
161 A 6 4 1.00 19 0.210
162 A 3 2 1.00 19 0.105
163 A 3 2 1.00 21 0.095
164 A 3 2 1.00 21 0.095
165 A 16 9 1.00 21 0.429
166 A 14 10 1.00 21 0.476
167 A 11 9 1.00 21 0.429
168 A 17 10 1.00 21 0.476
169 A 21 10 1.00 21 0.476
170 A 5 3 1.00 21 0.143
171 A 4 3 1.00 21 0.143
172 A 3 2 1.00 19 0.105
173 A 4 4 1.00 19 0.210
174 A 3 2 1.00 21 0.095
175 A 3 2 1.00 21 0.095
176 A 13 9 1.00 21 0.429
177 A 8 7 1.00 21 0.333
178 A 7 7 1.00 21 0.333
179 A 7 7 1.00 21 0.333
180 A 9 7 1.00 21 0.333
181 A 5 3 1.00 21 0.143
182 A 4 3 1.00 21 0.143
183 A 3 2 1.00 19 0.105
184 A 3 2 1.00 19 0.105
185 A 3 2 1.00 21 0.095
186 A 3 2 1.00 21 0.095
187 A 16 8 1.00 21 0.381
188 A 12 7 1.00 21 0.333
189 A 8 7 1.00 21 0.333
190 A 8 7 1.00 21 0.333
191 A 10 7 1.00 21 0.333
192 A 5 3 1.00 21 0.143
193 A 4 3 1.00 21 0.143
194 A 3 2 1.00 19 0.105
195 A 3 2 1.00 19 0.105
196 A 3 2 1.00 21 0.095
197 A 3 2 1.00 21 0.095
198 A 22 9 1.00 21 0.429
199 A 18 8 1.00 21 0.381
200 A 9 8 1.00 21 0.381
201 A 9 7 1.00 21 0.333
202 A 11 7 1.00 21 0.333
203 A 10 6 1.00 23 0.261
204 A 8 6 1.00 23 0.261
205 A 6 5 1.00 21 0.238
206 F 0 0 N/A 0 N/A
207 F 0 0 N/A 0 N/A
208 A 0 0 0.00 0 0.000

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