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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
 2.2 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, 93, 94, 97, 98, 101, 102, 103, 104, 105, 106, 109, 110, 114, 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, 95, 96, 99, 100, 107, 108, 111, 112, 113, 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 }

2.2 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
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 123 147 128 410 0 0
normalized size 1 1. 1.07 1.28 1.11 3.57 0. 0.
time (sec) N/A 0.072 0.446 0.064 1.049 1.552 0. 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 77 96 69 224 0 0
normalized size 1 1. 1.08 1.35 0.97 3.15 0. 0.
time (sec) N/A 0.048 0.108 0.056 0.992 1.532 0. 0.
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 38 29 34 65 0 1966
normalized size 1 1. 1.27 0.97 1.13 2.17 0. 65.53
time (sec) N/A 0.021 0.021 0.031 1.076 1.371 0. 1.611
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 26 25 30 62 0 31
normalized size 1 1. 1.08 1.04 1.25 2.58 0. 1.29
time (sec) N/A 0.02 0.033 0.016 1.092 1.573 0. 1.268
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 60 83 61 167 0 81
normalized size 1 1. 1.11 1.54 1.13 3.09 0. 1.5
time (sec) N/A 0.037 0.118 0.037 1.09 1.496 0. 1.325
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 87 136 93 292 0 111
normalized size 1 1. 1.07 1.68 1.15 3.6 0. 1.37
time (sec) N/A 0.048 0.198 0.036 1.081 1.573 0. 1.389
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 111 195 123 412 0 140
normalized size 1 1. 0.97 1.7 1.07 3.58 0. 1.22
time (sec) N/A 0.059 0.399 0.039 1.153 1.599 0. 1.387
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 110 135 117 300 0 0
normalized size 1 1. 1.09 1.34 1.16 2.97 0. 0.
time (sec) N/A 0.092 0.065 0.071 1.659 1.467 0. 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 81 98 88 224 0 0
normalized size 1 1. 1.12 1.36 1.22 3.11 0. 0.
time (sec) N/A 0.074 0.048 0.057 1.825 1.476 0. 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 47 59 53 194 0 1361
normalized size 1 1. 1.21 1.51 1.36 4.97 0. 34.9
time (sec) N/A 0.104 0.045 0.039 1.688 1.421 0. 3.472
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 75 57 73 236 0 146
normalized size 1 1. 1.83 1.39 1.78 5.76 0. 3.56
time (sec) N/A 0.052 0.048 0.029 2.303 1.438 0. 1.25
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 125 106 124 425 0 190
normalized size 1 1. 1.52 1.29 1.51 5.18 0. 2.32
time (sec) N/A 0.08 0.053 0.034 1.691 1.504 0. 1.278
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 122 122 164 159 169 620 0 269
normalized size 1 1. 1.34 1.3 1.39 5.08 0. 2.2
time (sec) N/A 0.096 0.071 0.038 1.63 1.538 0. 1.293
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 75 261 130 412 0 0
normalized size 1 1. 0.63 2.19 1.09 3.46 0. 0.
time (sec) N/A 0.082 0.245 0.085 1.129 1.557 0. 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 54 162 78 212 0 0
normalized size 1 1. 0.75 2.25 1.08 2.94 0. 0.
time (sec) N/A 0.062 0.103 0.071 1.112 1.482 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 40 69 58 108 0 9038
normalized size 1 1. 0.77 1.33 1.12 2.08 0. 173.81
time (sec) N/A 0.038 0.038 0.042 1.125 1.418 0. 4.572
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 28 94 72 173 0 63
normalized size 1 1. 0.93 3.13 2.4 5.77 0. 2.1
time (sec) N/A 0.039 0.041 0.049 1.113 1.44 0. 1.371
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 86 313 144 508 0 163
normalized size 1 1. 0.65 2.37 1.09 3.85 0. 1.23
time (sec) N/A 0.075 0.216 0.049 1.086 1.768 0. 1.496
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 149 149 174 251 205 382 0 0
normalized size 1 1. 1.17 1.68 1.38 2.56 0. 0.
time (sec) N/A 0.165 0.838 0.078 1.602 1.701 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 120 120 159 186 162 468 0 0
normalized size 1 1. 1.32 1.55 1.35 3.9 0. 0.
time (sec) N/A 0.203 1.306 0.071 1.625 1.471 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 145 117 113 296 0 7250
normalized size 1 1. 2.04 1.65 1.59 4.17 0. 102.11
time (sec) N/A 0.089 0.438 0.049 1.615 1.537 0. 64.982
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 34 52 63 97 78 51
normalized size 1 1. 0.76 1.16 1.4 2.16 1.73 1.13
time (sec) N/A 0.014 0.193 0.023 1.085 1.558 0.697 1.853
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 94 89 107 281 0 193
normalized size 1 1. 1.27 1.2 1.45 3.8 0. 2.61
time (sec) N/A 0.102 0.58 0.036 1.64 1.524 0. 1.732
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 191 190 188 474 0 282
normalized size 1 1. 1.95 1.94 1.92 4.84 0. 2.88
time (sec) N/A 0.161 5.581 0.044 1.647 1.703 0. 1.762
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 160 160 99 445 180 594 0 0
normalized size 1 1. 0.62 2.78 1.12 3.71 0. 0.
time (sec) N/A 0.109 0.564 0.105 1.077 1.575 0. 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 66 205 97 248 0 0
normalized size 1 1. 0.73 2.25 1.07 2.73 0. 0.
time (sec) N/A 0.071 0.157 0.078 1.071 1.599 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 52 85 77 147 0 0
normalized size 1 1. 0.74 1.21 1.1 2.1 0. 0.
time (sec) N/A 0.045 0.045 0.051 1.071 1.516 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 67 109 108 284 0 127
normalized size 1 1. 0.68 1.11 1.1 2.9 0. 1.3
time (sec) N/A 0.065 0.202 0.053 1.06 1.483 0. 1.372
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 180 180 243 359 282 734 0 0
normalized size 1 1. 1.35 1.99 1.57 4.08 0. 0.
time (sec) N/A 0.357 5.614 0.131 1.648 1.598 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 177 266 223 539 0 0
normalized size 1 1. 1.49 2.24 1.87 4.53 0. 0.
time (sec) N/A 0.194 2.25 0.085 1.612 1.583 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 115 167 158 378 0 0
normalized size 1 1. 1.29 1.88 1.78 4.25 0. 0.
time (sec) N/A 0.125 0.49 0.053 1.57 1.42 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 44 74 97 134 121 74
normalized size 1 1. 0.7 1.17 1.54 2.13 1.92 1.17
time (sec) N/A 0.054 0.326 0.027 1.074 1.458 0.655 1.64
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 106 105 126 321 0 219
normalized size 1 1. 1.15 1.14 1.37 3.49 0. 2.38
time (sec) N/A 0.137 1.065 0.043 1.637 1.566 0. 2.059
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 129 129 83 387 147 394 0 0
normalized size 1 1. 0.64 3. 1.14 3.05 0. 0.
time (sec) N/A 0.095 0.469 0.1 1.107 1.672 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 76 245 115 293 0 0
normalized size 1 1. 0.71 2.29 1.07 2.74 0. 0.
time (sec) N/A 0.079 0.155 0.084 1.065 1.532 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 62 101 95 182 0 0
normalized size 1 1. 0.7 1.15 1.08 2.07 0. 0.
time (sec) N/A 0.053 0.07 0.052 1.076 1.538 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 78 125 111 324 0 130
normalized size 1 1. 0.76 1.23 1.09 3.18 0. 1.27
time (sec) N/A 0.067 0.137 0.054 1.118 1.734 0. 1.393
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 143 143 252 360 321 620 0 0
normalized size 1 1. 1.76 2.52 2.24 4.34 0. 0.
time (sec) N/A 0.199 1.651 0.092 1.673 1.563 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 125 231 244 456 0 0
normalized size 1 1. 1.11 2.04 2.16 4.04 0. 0.
time (sec) N/A 0.161 1.126 0.06 1.589 1.589 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 57 111 146 177 224 97
normalized size 1 1. 0.66 1.28 1.68 2.03 2.57 1.11
time (sec) N/A 0.082 0.425 0.029 1.114 1.479 2.074 1.381
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 136 127 158 360 0 262
normalized size 1 1. 1.17 1.09 1.36 3.1 0. 2.26
time (sec) N/A 0.159 1.574 0.045 1.573 1.693 0. 1.396
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 209 190 294 560 0 370
normalized size 1 1. 1.49 1.36 2.1 4. 0. 2.64
time (sec) N/A 0.225 5.36 0.05 1.527 1.977 0. 1.482
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 198 198 283 293 423 770 0 458
normalized size 1 1. 1.43 1.48 2.14 3.89 0. 2.31
time (sec) N/A 0.428 1.52 0.054 1.692 2.085 0. 1.703
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 101 162 236 464 0 184
normalized size 1 1. 0.78 1.25 1.82 3.57 0. 1.42
time (sec) N/A 0.161 1.009 0.059 1.028 2.054 0. 8.07
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 84 126 176 398 0 157
normalized size 1 1. 0.79 1.19 1.66 3.75 0. 1.48
time (sec) N/A 0.136 0.308 0.056 1. 1.836 0. 3.934
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 54 90 120 338 0 130
normalized size 1 1. 0.66 1.1 1.46 4.12 0. 1.59
time (sec) N/A 0.116 0.165 0.053 1. 1.343 0. 2.115
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 58 28 54 63 163 0 78
normalized size 1 1.57 0.76 1.46 1.7 4.41 0. 2.11
time (sec) N/A 0.067 0.039 0.058 1.088 1.636 0. 1.341
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 32 33 42 74 0 45
normalized size 1 1. 1. 1.03 1.31 2.31 0. 1.41
time (sec) N/A 0.039 0.019 0.023 1.047 1.407 0. 1.283
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 24 30 35 73 0 35
normalized size 1 1. 0.75 0.94 1.09 2.28 0. 1.09
time (sec) N/A 0.068 0.033 0.032 1.118 1.37 0. 1.323
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 30 49 62 162 0 62
normalized size 1 1. 0.59 0.96 1.22 3.18 0. 1.22
time (sec) N/A 0.089 0.049 0.085 1.106 1.4 0. 1.321
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 61 67 89 248 0 89
normalized size 1 1. 0.9 0.99 1.31 3.65 0. 1.31
time (sec) N/A 0.093 0.149 0.095 1.128 1.413 0. 1.462
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 77 87 116 343 0 116
normalized size 1 1. 0.92 1.04 1.38 4.08 0. 1.38
time (sec) N/A 0.1 0.209 0.115 1.108 1.517 0. 1.438
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 146 175 456 248 0 232
normalized size 1 1. 1.74 2.08 5.43 2.95 0. 2.76
time (sec) N/A 0.097 0.319 0.057 1.095 1.673 0. 5.32
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 106 130 289 194 0 162
normalized size 1 1. 1.54 1.88 4.19 2.81 0. 2.35
time (sec) N/A 0.092 0.32 0.055 1.081 1.511 0. 2.567
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 106 70 122 127 0 92
normalized size 1 1. 2.12 1.4 2.44 2.54 0. 1.84
time (sec) N/A 0.088 0.164 0.047 1.095 1.371 0. 1.659
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 48 22 36 108 27 28
normalized size 1 1. 2.09 0.96 1.57 4.7 1.17 1.22
time (sec) N/A 0.012 0.041 0.022 1.078 1.46 1.726 1.27
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 69 56 95 173 0 88
normalized size 1 1. 2.38 1.93 3.28 5.97 0. 3.03
time (sec) N/A 0.051 0.218 0.068 1.087 1.539 0. 1.286
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 124 132 209 311 0 171
normalized size 1 1. 2.14 2.28 3.6 5.36 0. 2.95
time (sec) N/A 0.088 0.491 0.075 1.027 1.416 0. 1.416
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 189 208 316 431 0 252
normalized size 1 1. 2.3 2.54 3.85 5.26 0. 3.07
time (sec) N/A 0.106 0.743 0.088 1.02 1.396 0. 1.578
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 284 284 425 545 0 329
normalized size 1 1. 2.68 2.68 4.01 5.14 0. 3.1
time (sec) N/A 0.127 0.914 0.102 1.125 1.579 0. 1.979
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 189 189 112 180 273 599 0 197
normalized size 1 1. 0.59 0.95 1.44 3.17 0. 1.04
time (sec) N/A 0.149 1.693 0.096 1.106 1.728 0. 9.844
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 146 146 91 144 225 532 0 170
normalized size 1 1. 0.62 0.99 1.54 3.64 0. 1.16
time (sec) N/A 0.108 0.45 0.084 1.054 1.528 0. 5.289
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 70 108 149 467 0 138
normalized size 1 1. 0.67 1.04 1.43 4.49 0. 1.33
time (sec) N/A 0.086 0.311 0.083 1.055 1.531 0. 2.998
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 36 72 95 274 0 122
normalized size 1 1. 0.6 1.2 1.58 4.57 0. 2.03
time (sec) N/A 0.048 0.081 0.082 1.025 1.456 0. 1.848
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 36 50 62 162 0 61
normalized size 1 1. 0.69 0.96 1.19 3.12 0. 1.17
time (sec) N/A 0.05 0.055 0.034 1.119 1.509 0. 1.795
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 49 66 74 204 0 155
normalized size 1 1. 0.75 1.02 1.14 3.14 0. 2.38
time (sec) N/A 0.059 0.07 0.106 1.384 1.548 0. 2.102
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 38 39 49 138 0 49
normalized size 1 1. 0.69 0.71 0.89 2.51 0. 0.89
time (sec) N/A 0.051 0.074 0.092 0.956 1.466 0. 1.962
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 73 49 62 234 0 62
normalized size 1 1. 1. 0.67 0.85 3.21 0. 0.85
time (sec) N/A 0.057 0.073 0.108 1.072 1.401 0. 2.364
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 78 79 103 331 0 103
normalized size 1 1. 0.61 0.62 0.81 2.61 0. 0.81
time (sec) N/A 0.074 0.143 0.125 1.762 1.446 0. 2.225
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 88 89 116 431 0 116
normalized size 1 1. 0.61 0.61 0.8 2.97 0. 0.8
time (sec) N/A 0.081 0.205 0.139 1.837 1.676 0. 1.931
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 199 199 118 119 157 541 0 157
normalized size 1 1. 0.59 0.6 0.79 2.72 0. 0.79
time (sec) N/A 0.102 0.329 0.165 1.835 1.654 0. 2.161
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 171 171 102 162 254 657 0 184
normalized size 1 1. 0.6 0.95 1.49 3.84 0. 1.08
time (sec) N/A 0.123 0.926 0.106 1.961 1.671 0. 4.824
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 126 82 126 197 586 0 154
normalized size 1 1. 0.65 1. 1.56 4.65 0. 1.22
time (sec) N/A 0.091 0.363 0.092 1.938 1.581 0. 2.552
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 52 90 132 409 0 109
normalized size 1 1. 0.63 1.1 1.61 4.99 0. 1.33
time (sec) N/A 0.057 0.145 0.095 2.143 1.553 0. 2.19
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 52 68 97 284 0 80
normalized size 1 1. 0.7 0.92 1.31 3.84 0. 1.08
time (sec) N/A 0.058 0.175 0.037 1.769 1.607 0. 1.98
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 61 84 108 393 0 208
normalized size 1 1. 0.71 0.98 1.26 4.57 0. 2.42
time (sec) N/A 0.07 0.191 0.129 1.951 1.547 0. 1.734
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 69 97 101 348 0 235
normalized size 1 1. 0.72 1.01 1.05 3.62 0. 2.45
time (sec) N/A 0.071 0.328 0.126 2.056 1.652 0. 2.575
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 48 49 62 208 0 62
normalized size 1 1. 0.66 0.67 0.85 2.85 0. 0.85
time (sec) N/A 0.057 0.099 0.119 1.539 1.461 0. 1.64
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 68 69 89 302 0 89
normalized size 1 1. 0.62 0.63 0.82 2.77 0. 0.82
time (sec) N/A 0.069 0.072 0.136 1.212 1.476 0. 1.619
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 88 89 116 398 0 116
normalized size 1 1. 0.61 0.61 0.8 2.74 0. 0.8
time (sec) N/A 0.081 0.113 0.153 1.965 1.591 0. 2.013
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 88 89 116 498 0 116
normalized size 1 1. 0.61 0.61 0.8 3.43 0. 0.8
time (sec) N/A 0.078 0.118 0.174 2.733 1.669 0. 1.993
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 195 112 180 288 775 0 197
normalized size 1 1. 0.57 0.92 1.48 3.97 0. 1.01
time (sec) N/A 0.135 1.489 0.088 3.476 1.734 0. 5.53
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 50 81 128 250 0 103
normalized size 1 1. 0.38 0.61 0.97 1.89 0. 0.78
time (sec) N/A 0.089 0.115 0.088 2.939 1.354 0. 2.775
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 62 108 163 525 0 123
normalized size 1 1. 0.59 1.03 1.55 5. 0. 1.17
time (sec) N/A 0.065 0.254 0.092 3.157 1.591 0. 2.141
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 73 101 139 522 0 250
normalized size 1 1. 0.69 0.95 1.31 4.92 0. 2.36
time (sec) N/A 0.083 0.839 0.139 2.616 1.583 0. 1.819
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 89 130 128 502 0 313
normalized size 1 1. 0.66 0.96 0.95 3.72 0. 2.32
time (sec) N/A 0.086 0.171 0.148 2.681 1.598 0. 1.93
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 124 158 481 338 0 197
normalized size 1 1. 0.98 1.24 3.79 2.66 0. 1.55
time (sec) N/A 0.31 0.416 0.076 3.082 1.496 0. 2.539
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 315 161 389 992 0 182
normalized size 1 1. 2.92 1.49 3.6 9.19 0. 1.69
time (sec) N/A 0.318 0.42 0.125 3.729 1.597 0. 1.945
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 120 120 589 195 385 1187 0 242
normalized size 1 1. 4.91 1.62 3.21 9.89 0. 2.02
time (sec) N/A 0.249 6.089 0.138 3.069 1.581 0. 2.401
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 133 133 733 229 377 1191 0 275
normalized size 1 1. 5.51 1.72 2.83 8.95 0. 2.07
time (sec) N/A 0.249 6.145 0.149 3.619 1.787 0. 1.735
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 195 394 172 0 548 0 0
normalized size 1 1.2 2.43 1.06 0. 3.38 0. 0.
time (sec) N/A 0.923 5.54 0.464 0. 2.006 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 114 89 0 459 0 0
normalized size 1 1. 1.13 0.88 0. 4.54 0. 0.
time (sec) N/A 0.185 0.328 0.502 0. 1.822 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 206 125 0 749 0 570
normalized size 1 1. 2.31 1.4 0. 8.42 0. 6.4
time (sec) N/A 0.192 0.955 0.55 0. 1.936 0. 2.091
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 309 170 0 1025 0 950
normalized size 1 1. 1.9 1.04 0. 6.29 0. 5.83
time (sec) N/A 0.377 1.568 0.701 0. 1.816 0. 2.115
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 195 141 139 0 648 0 0
normalized size 1 1.17 0.84 0.83 0. 3.88 0. 0.
time (sec) N/A 0.975 5.562 0.574 0. 1.902 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 46 55 196 123 0 0
normalized size 1 1. 0.52 0.62 2.23 1.4 0. 0.
time (sec) N/A 0.196 3.992 0.402 1.547 1.754 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 233 144 0 833 0 671
normalized size 1 1. 1.93 1.19 0. 6.88 0. 5.55
time (sec) N/A 0.321 0.76 0.642 0. 1.846 0. 2.634
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 197 197 334 196 0 1123 0 1058
normalized size 1 1. 1.7 0.99 0. 5.7 0. 5.37
time (sec) N/A 0.496 1.356 0.651 0. 1.723 0. 3.102
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 208 112 87 374 246 0 0
normalized size 1 1.38 0.74 0.58 2.48 1.63 0. 0.
time (sec) N/A 0.979 5.459 0.404 1.764 1.432 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 60 67 258 173 0 0
normalized size 1 1. 0.51 0.57 2.19 1.47 0. 0.
time (sec) N/A 0.214 5.463 0.412 1.663 1.423 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 261 162 0 934 0 714
normalized size 1 1. 1.73 1.07 0. 6.19 0. 4.73
time (sec) N/A 0.429 1.193 0.733 0. 1.571 0. 2.906
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 227 227 360 222 0 1249 0 1135
normalized size 1 1. 1.59 0.98 0. 5.5 0. 5.
time (sec) N/A 0.627 1.899 0.694 0. 1.732 0. 3.194
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 150 241 118 231 0 624 0 1056
normalized size 1 1.61 0.79 1.54 0. 4.16 0. 7.04
time (sec) N/A 0.933 0.673 0.766 0. 1.639 0. 5.889
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 118 130 0 549 0 594
normalized size 1 1. 1.1 1.21 0. 5.13 0. 5.55
time (sec) N/A 0.195 0.269 0.462 0. 1.543 0. 2.823
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 138 103 0 706 0 502
normalized size 1 1. 2.23 1.66 0. 11.39 0. 8.1
time (sec) N/A 0.11 0.308 0.59 0. 1.609 0. 2.219
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F(-1) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 292 144 0 987 0 819
normalized size 1 1. 2.16 1.07 0. 7.31 0. 6.07
time (sec) N/A 0.622 0.58 0.638 0. 1.463 0. 2.373
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 177 195 334 289 0 726 0 0
normalized size 1 1.1 1.89 1.63 0. 4.1 0. 0.
time (sec) N/A 1.199 0.356 0.619 0. 1.62 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 128 202 0 644 0 0
normalized size 1 1. 0.96 1.51 0. 4.81 0. 0.
time (sec) N/A 0.223 0.444 0.607 0. 1.635 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 206 134 0 1133 0 656
normalized size 1 1. 1.82 1.19 0. 10.03 0. 5.81
time (sec) N/A 0.229 2.198 0.591 0. 1.764 0. 2.485
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F(-1) B F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 144 144 294 144 0 1003 0 828
normalized size 1 1. 2.04 1. 0. 6.97 0. 5.75
time (sec) N/A 0.553 0.761 0.621 0. 1.572 0. 3.131
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 207 260 394 353 0 830 0 0
normalized size 1 1.26 1.9 1.71 0. 4.01 0. 0.
time (sec) N/A 1.434 0.546 0.843 0. 1.901 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 284 266 0 751 0 0
normalized size 1 1. 1.7 1.59 0. 4.5 0. 0.
time (sec) N/A 0.303 0.408 0.648 0. 1.697 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 451 219 0 1436 0 0
normalized size 1 1. 3.2 1.55 0. 10.18 0. 0.
time (sec) N/A 0.346 0.718 0.57 0. 1.859 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 191 191 332 182 0 1504 0 975
normalized size 1 1. 1.74 0.95 0. 7.87 0. 5.1
time (sec) N/A 0.959 2.389 0.722 0. 1.745 0. 3.16
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 982 982 318 0 0 0 0 0
normalized size 1 1. 0.32 0. 0. 0. 0. 0.
time (sec) N/A 1.271 3.273 0.128 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 290 0 0 0 0 0
normalized size 1 1. 2.36 0. 0. 0. 0. 0.
time (sec) N/A 0.193 2.746 0.104 0. 0. 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 80 80 2692 0 0 0 0 0
normalized size 1 1. 33.65 0. 0. 0. 0. 0.
time (sec) N/A 0.101 23.898 0.095 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 80 80 2796 0 0 0 0 0
normalized size 1 1. 34.95 0. 0. 0. 0. 0.
time (sec) N/A 0.094 22.599 0.102 0. 0. 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 551 551 128 0 0 0 0 0
normalized size 1 1. 0.23 0. 0. 0. 0. 0.
time (sec) N/A 0.494 0.796 0.119 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 126 100 0 0 0 0 0
normalized size 1 1. 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.216 0.513 0.105 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 80 80 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.095 12.766 0.093 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-1) F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 80 80 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.094 9.129 0.105 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 269 269 5199 0 0 0 0 0
normalized size 1 1. 19.33 0. 0. 0. 0. 0.
time (sec) N/A 0.345 58.895 1.709 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 187 187 2054 0 0 0 0 0
normalized size 1 1. 10.98 0. 0. 0. 0. 0.
time (sec) N/A 0.227 18.053 1.421 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 129 129 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.139 2.025 0.907 0. 0. 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 108 108 232 0 0 0 0 0
normalized size 1 1. 2.15 0. 0. 0. 0. 0.
time (sec) N/A 0.126 4.033 0.178 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 138 138 667 0 0 0 0 0
normalized size 1 1. 4.83 0. 0. 0. 0. 0.
time (sec) N/A 0.275 14.178 0.41 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 248 248 1276 0 0 0 0 0
normalized size 1 1. 5.15 0. 0. 0. 0. 0.
time (sec) N/A 0.422 31.232 0.451 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 111 111 367 0 0 0 0 0
normalized size 1 1. 3.31 0. 0. 0. 0. 0.
time (sec) N/A 0.124 2.198 0.847 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 105 0 0 0 0 0
normalized size 1 1. 0.64 0. 0. 0. 0. 0.
time (sec) N/A 0.149 0.267 0.144 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 63 0 0 0 0 0
normalized size 1 1. 0.88 0. 0. 0. 0. 0.
time (sec) N/A 0.05 0.071 0.76 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 43 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.044 0.059 0.821 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 68 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.069 0.188 0.268 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 83 0 0 0 0 0
normalized size 1 1. 0.67 0. 0. 0. 0. 0.
time (sec) N/A 0.098 0.275 0.352 0. 0. 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 311 311 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.355 1.064 0.152 0. 0. 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 157 157 11184 0 0 0 0 0
normalized size 1 1. 71.24 0. 0. 0. 0. 0.
time (sec) N/A 0.248 34.458 0.12 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 90 0 0 0 0 0
normalized size 1 1. 1.22 0. 0. 0. 0. 0.
time (sec) N/A 0.035 0.181 0.286 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 89 89 47487 0 0 0 0 0
normalized size 1 1. 533.56 0. 0. 0. 0. 0.
time (sec) N/A 0.102 99.938 0.231 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 89 89 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.099 0.741 0.294 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 77 96 99 236 0 0
normalized size 1 1. 0.88 1.09 1.12 2.68 0. 0.
time (sec) N/A 0.077 0.119 0.032 1.901 1.68 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 38 46 58 124 0 1966
normalized size 1 1. 0.69 0.84 1.05 2.25 0. 35.75
time (sec) N/A 0.038 0.016 0.025 1.943 1.61 0. 2.827
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 43 25 30 62 0 31
normalized size 1 1. 1.79 1.04 1.25 2.58 0. 1.29
time (sec) N/A 0.021 0.033 0.019 1.698 1.505 0. 2.282
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 60 83 61 167 0 81
normalized size 1 1. 1.11 1.54 1.13 3.09 0. 1.5
time (sec) N/A 0.041 0.21 0.039 1.44 1.601 0. 2.007
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 87 136 93 292 0 111
normalized size 1 1. 1.07 1.68 1.15 3.6 0. 1.37
time (sec) N/A 0.052 0.239 0.04 1.281 1.536 0. 2.1
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 81 98 88 182 0 0
normalized size 1 1. 1.12 1.36 1.22 2.53 0. 0.
time (sec) N/A 0.078 0.038 0.032 2.133 1.815 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 47 59 53 108 0 1361
normalized size 1 1. 1.24 1.55 1.39 2.84 0. 35.82
time (sec) N/A 0.059 0.033 0.026 2.723 1.705 0. 8.562
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 75 57 73 236 0 146
normalized size 1 1. 1.83 1.39 1.78 5.76 0. 3.56
time (sec) N/A 0.053 0.031 0.029 2.207 1.836 0. 2.308
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 125 106 124 425 0 190
normalized size 1 1. 1.52 1.29 1.51 5.18 0. 2.32
time (sec) N/A 0.08 0.042 0.036 1.873 1.864 0. 2.177
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 122 122 164 159 169 620 0 269
normalized size 1 1. 1.34 1.3 1.39 5.08 0. 2.2
time (sec) N/A 0.097 0.06 0.039 2.7 1.706 0. 2.224
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 108 172 142 348 0 0
normalized size 1 1. 0.97 1.55 1.28 3.14 0. 0.
time (sec) N/A 0.173 0.432 0.049 1.676 1.548 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 64 82 95 186 0 10604
normalized size 1 1. 0.82 1.05 1.22 2.38 0. 135.95
time (sec) N/A 0.071 0.136 0.039 1.631 1.609 0. 5.72
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 46 45 54 108 0 55
normalized size 1 1. 1. 0.98 1.17 2.35 0. 1.2
time (sec) N/A 0.039 0.023 0.023 1.893 1.58 0. 2.322
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 70 120 93 271 0 134
normalized size 1 1. 0.83 1.43 1.11 3.23 0. 1.6
time (sec) N/A 0.073 0.236 0.053 1.568 1.521 0. 2.313
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 126 107 220 142 437 0 186
normalized size 1 1. 0.85 1.75 1.13 3.47 0. 1.48
time (sec) N/A 0.104 0.757 0.047 1.403 1.629 0. 2.223
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 149 149 176 185 161 281 0 0
normalized size 1 1. 1.18 1.24 1.08 1.89 0. 0.
time (sec) N/A 0.162 0.687 0.044 2.5 1.464 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 77 116 112 190 0 10355
normalized size 1 1. 0.82 1.23 1.19 2.02 0. 110.16
time (sec) N/A 0.122 0.457 0.039 2.52 1.37 0. 30.612
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 116 102 107 308 0 200
normalized size 1 1. 1.49 1.31 1.37 3.95 0. 2.56
time (sec) N/A 0.086 0.416 0.039 2.595 1.65 0. 2.237
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 133 133 293 199 186 539 0 325
normalized size 1 1. 2.2 1.5 1.4 4.05 0. 2.44
time (sec) N/A 0.149 6.233 0.049 2.453 1.827 0. 2.059
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 202 202 351 302 247 786 0 455
normalized size 1 1. 1.74 1.5 1.22 3.89 0. 2.25
time (sec) N/A 0.169 1.093 0.052 1.676 1.639 0. 2.779
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 150 150 141 279 219 470 0 0
normalized size 1 1. 0.94 1.86 1.46 3.13 0. 0.
time (sec) N/A 0.242 0.263 0.056 1.546 1.721 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 90 139 153 277 0 0
normalized size 1 1. 0.86 1.32 1.46 2.64 0. 0.
time (sec) N/A 0.114 0.19 0.046 1.707 1.606 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 67 64 77 158 0 78
normalized size 1 1. 1. 0.96 1.15 2.36 0. 1.16
time (sec) N/A 0.045 0.025 0.027 1.567 1.492 0. 2.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 97 165 132 358 0 177
normalized size 1 1. 0.84 1.42 1.14 3.09 0. 1.53
time (sec) N/A 0.094 0.321 0.065 1.9 1.563 0. 2.022
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 165 144 316 192 536 0 250
normalized size 1 1. 0.87 1.92 1.16 3.25 0. 1.52
time (sec) N/A 0.141 1.164 0.062 1.354 1.6 0. 2.141
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 220 220 226 268 225 369 0 0
normalized size 1 1. 1.03 1.22 1.02 1.68 0. 0.
time (sec) N/A 0.224 0.678 0.058 1.824 1.593 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 146 146 113 169 161 271 0 0
normalized size 1 1. 0.77 1.16 1.1 1.86 0. 0.
time (sec) N/A 0.169 0.729 0.047 3.013 1.485 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 143 125 128 370 0 269
normalized size 1 1. 1.4 1.23 1.25 3.63 0. 2.64
time (sec) N/A 0.112 1.295 0.052 1.515 1.605 0. 2.628
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 194 194 355 264 252 699 0 568
normalized size 1 1. 1.83 1.36 1.3 3.6 0. 2.93
time (sec) N/A 0.184 6.236 0.062 2.21 1.652 0. 2.652
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 291 291 346 415 340 1014 0 636
normalized size 1 1. 1.19 1.43 1.17 3.48 0. 2.19
time (sec) N/A 0.231 2.578 0.063 2.641 1.832 0. 2.013
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 204 204 184 304 389 594 0 463
normalized size 1 1. 0.9 1.49 1.91 2.91 0. 2.27
time (sec) N/A 0.363 1.462 0.066 1.826 2.474 0. 5.118
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 126 117 164 192 367 0 239
normalized size 1 1. 0.93 1.3 1.52 2.91 0. 1.9
time (sec) N/A 0.191 0.484 0.059 1.536 1.961 0. 1.98
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 87 76 88 157 0 96
normalized size 1 1. 1.18 1.03 1.19 2.12 0. 1.3
time (sec) N/A 0.066 0.086 0.049 1.551 1.611 0. 1.3
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 34 35 45 80 0 47
normalized size 1 1. 1. 1.03 1.32 2.35 0. 1.38
time (sec) N/A 0.04 0.02 0.026 1.465 1.57 0. 1.695
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 65 106 104 271 0 154
normalized size 1 1. 0.77 1.26 1.24 3.23 0. 1.83
time (sec) N/A 0.089 0.161 0.063 1.616 1.596 0. 2.011
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 148 148 115 216 188 629 0 271
normalized size 1 1. 0.78 1.46 1.27 4.25 0. 1.83
time (sec) N/A 0.138 3.847 0.063 1.463 1.663 0. 1.538
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 177 177 195 269 0 1054 0 325
normalized size 1 1. 1.1 1.52 0. 5.95 0. 1.84
time (sec) N/A 0.239 1.419 0.067 0. 1.639 0. 3.306
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 152 117 0 684 0 144
normalized size 1 1. 1.58 1.22 0. 7.12 0. 1.5
time (sec) N/A 0.099 0.203 0.053 0. 1.67 0. 2.053
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 108 155 0 801 0 174
normalized size 1 1. 1.35 1.94 0. 10.01 0. 2.17
time (sec) N/A 0.243 0.236 0.06 0. 1.742 0. 1.87
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) A F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 154 154 350 348 0 1507 0 369
normalized size 1 1. 2.27 2.26 0. 9.79 0. 2.4
time (sec) N/A 0.426 6.119 0.069 0. 2.929 0. 1.911
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 307 307 504 629 0 2566 0 662
normalized size 1 1. 1.64 2.05 0. 8.36 0. 2.16
time (sec) N/A 1.106 1.386 0.073 0. 4.834 0. 2.212
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 242 242 240 318 682 1231 0 667
normalized size 1 1. 0.99 1.31 2.82 5.09 0. 2.76
time (sec) N/A 0.633 6.252 0.093 1.828 3.386 0. 4.672
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 161 145 182 370 869 0 335
normalized size 1 1. 0.9 1.13 2.3 5.4 0. 2.08
time (sec) N/A 0.312 0.719 0.087 1.753 2.394 0. 1.843
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 162 132 167 463 0 211
normalized size 1 1. 1.49 1.21 1.53 4.25 0. 1.94
time (sec) N/A 0.096 0.287 0.078 1.764 1.695 0. 1.284
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 42 54 63 176 0 69
normalized size 1 1. 0.79 1.02 1.19 3.32 0. 1.3
time (sec) N/A 0.053 0.076 0.038 1.47 1.637 0. 1.499
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 96 150 157 599 0 223
normalized size 1 1. 0.84 1.32 1.38 5.25 0. 1.96
time (sec) N/A 0.115 0.608 0.089 1.364 1.619 0. 1.976
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 188 188 187 282 255 1241 0 375
normalized size 1 1. 0.99 1.5 1.36 6.6 0. 1.99
time (sec) N/A 0.181 6.144 0.098 1.734 2.294 0. 1.811
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 333 333 341 382 0 1790 0 548
normalized size 1 1. 1.02 1.15 0. 5.38 0. 1.65
time (sec) N/A 0.627 1.967 0.098 0. 2.504 0. 2.784
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 200 200 169 282 0 1261 0 339
normalized size 1 1. 0.84 1.41 0. 6.3 0. 1.7
time (sec) N/A 0.301 1.012 0.088 0. 1.958 0. 2.152
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 139 245 0 1681 0 294
normalized size 1 1. 1.21 2.13 0. 14.62 0. 2.56
time (sec) N/A 0.453 0.746 0.086 0. 2.816 0. 1.715
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 238 238 403 527 0 2639 0 481
normalized size 1 1. 1.69 2.21 0. 11.09 0. 2.02
time (sec) N/A 0.695 6.295 0.096 0. 3.101 0. 1.859
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 424 424 361 897 0 4674 0 805
normalized size 1 1. 0.85 2.12 0. 11.02 0. 1.9
time (sec) N/A 1.493 1.592 0.108 0. 5.532 0. 1.37
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 321 321 304 465 986 2206 0 790
normalized size 1 1. 0.95 1.45 3.07 6.87 0. 2.46
time (sec) N/A 0.877 6.341 0.116 1.303 6.427 0. 3.708
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 232 232 196 323 595 1727 0 626
normalized size 1 1. 0.84 1.39 2.56 7.44 0. 2.7
time (sec) N/A 0.482 2.189 0.109 1.876 3.964 0. 2.1
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 149 149 213 198 308 995 0 347
normalized size 1 1. 1.43 1.33 2.07 6.68 0. 2.33
time (sec) N/A 0.132 2.02 0.1 1.915 2.649 0. 1.582
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 60 74 109 365 0 93
normalized size 1 1. 0.8 0.99 1.45 4.87 0. 1.24
time (sec) N/A 0.06 0.262 0.046 1.547 2.004 0. 1.746
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 121 194 211 911 0 208
normalized size 1 1. 0.83 1.34 1.46 6.28 0. 1.43
time (sec) N/A 0.133 0.931 0.111 1.921 2.342 0. 1.8
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 221 221 195 348 319 1708 0 441
normalized size 1 1. 0.88 1.57 1.44 7.73 0. 2.
time (sec) N/A 0.211 5.327 0.114 1.612 2.424 0. 2.104
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 474 474 351 922 0 2765 0 853
normalized size 1 1. 0.74 1.95 0. 5.83 0. 1.8
time (sec) N/A 0.872 1.043 0.131 0. 2.853 0. 3.399
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 350 350 212 766 0 2067 0 518
normalized size 1 1. 0.61 2.19 0. 5.91 0. 1.48
time (sec) N/A 0.539 3.291 0.115 0. 2.322 0. 1.956
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 202 202 195 729 0 3044 0 458
normalized size 1 1. 0.97 3.61 0. 15.07 0. 2.27
time (sec) N/A 0.788 5.784 0.116 0. 5.548 0. 1.552
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 289 289 459 780 0 4578 0 609
normalized size 1 1. 1.59 2.7 0. 15.84 0. 2.11
time (sec) N/A 1.072 6.211 0.134 0. 5.542 0. 2.051
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 492 492 448 1252 0 6091 0 987
normalized size 1 1. 0.91 2.54 0. 12.38 0. 2.01
time (sec) N/A 2.127 1.705 0.138 0. 6.517 0. 1.85
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 271 271 4791 0 0 0 0 0
normalized size 1 1. 17.68 0. 0. 0. 0. 0.
time (sec) N/A 0.38 18.403 1.514 0. 0. 0. 0.
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 186 186 2464 0 0 0 0 0
normalized size 1 1. 13.25 0. 0. 0. 0. 0.
time (sec) N/A 0.242 14.208 1.446 0. 0. 0. 0.
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 129 129 849 0 0 0 0 0
normalized size 1 1. 6.58 0. 0. 0. 0. 0.
time (sec) N/A 0.148 8.262 0.904 0. 0. 0. 0.
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 284 0 864 0 0 0 0 0
normalized size 1 0. 3.04 0. 0. 0. 0. 0.
time (sec) N/A 0.048 13.498 0.362 0. 0. 0. 0.
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 737 0 908 0 0 0 0 0
normalized size 1 0. 1.23 0. 0. 0. 0. 0.
time (sec) N/A 0.045 14.227 0.677 0. 0. 0. 0.
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.04 2.695 0.862 0. 0. 0. 0.

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 [ 0.4762 ]

Table 2.1Rubi 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. 19 0.105
2 A 3 2 1. 19 0.105
3 A 3 2 1. 17 0.118
4 A 3 2 1. 17 0.118
5 A 3 2 1. 19 0.105
6 A 3 2 1. 19 0.105
7 A 3 2 1. 19 0.105
8 A 9 5 1. 19 0.263
9 A 8 5 1. 19 0.263
10 A 5 5 1. 19 0.263
11 A 7 6 1. 19 0.316
12 A 9 7 1. 19 0.368
13 A 11 7 1. 19 0.368
14 A 3 2 1. 21 0.095
15 A 3 2 1. 21 0.095
16 A 3 2 1. 19 0.105
17 A 2 2 1. 21 0.095
18 A 3 2 1. 21 0.095
19 A 14 9 1. 21 0.429
20 A 4 4 1. 21 0.19
21 A 6 5 1. 21 0.238
22 A 1 1 1. 12 0.083
23 A 8 6 1. 21 0.286
24 A 12 7 1. 21 0.333
25 A 3 2 1. 21 0.095
26 A 3 2 1. 21 0.095
27 A 3 2 1. 19 0.105
28 A 3 2 1. 21 0.095
29 A 9 7 1. 21 0.333
30 A 10 7 1. 21 0.333
31 A 8 6 1. 21 0.286
32 A 7 5 1. 12 0.417
33 A 10 7 1. 21 0.333
34 A 3 2 1. 21 0.095
35 A 3 2 1. 21 0.095
36 A 3 2 1. 19 0.105
37 A 3 2 1. 21 0.095
38 A 13 7 1. 21 0.333
39 A 11 6 1. 21 0.286
40 A 10 5 1. 12 0.417
41 A 12 6 1. 21 0.286
42 A 17 8 1. 21 0.381
43 A 21 8 1. 21 0.381
44 A 8 5 1. 21 0.238
45 A 7 5 1. 21 0.238
46 A 6 5 1. 21 0.238
47 A 5 5 1.57 19 0.263
48 A 4 4 1. 19 0.21
49 A 5 4 1. 21 0.19
50 A 5 4 1. 21 0.19
51 A 6 5 1. 21 0.238
52 A 6 5 1. 21 0.238
53 A 6 5 1. 21 0.238
54 A 6 5 1. 21 0.238
55 A 5 4 1. 21 0.19
56 A 1 1 1. 12 0.083
57 A 4 4 1. 21 0.19
58 A 5 5 1. 21 0.238
59 A 6 5 1. 21 0.238
60 A 7 5 1. 21 0.238
61 A 4 3 1. 21 0.143
62 A 4 3 1. 21 0.143
63 A 4 3 1. 21 0.143
64 A 4 3 1. 19 0.158
65 A 3 2 1. 19 0.105
66 A 3 2 1. 21 0.095
67 A 3 2 1. 21 0.095
68 A 3 2 1. 21 0.095
69 A 3 2 1. 21 0.095
70 A 3 2 1. 21 0.095
71 A 3 2 1. 21 0.095
72 A 4 3 1. 21 0.143
73 A 4 3 1. 21 0.143
74 A 4 3 1. 19 0.158
75 A 3 2 1. 19 0.105
76 A 3 2 1. 21 0.095
77 A 3 2 1. 21 0.095
78 A 3 2 1. 21 0.095
79 A 3 2 1. 21 0.095
80 A 3 2 1. 21 0.095
81 A 3 2 1. 21 0.095
82 A 4 3 1. 21 0.143
83 A 3 2 1. 21 0.095
84 A 4 3 1. 19 0.158
85 A 3 2 1. 21 0.095
86 A 3 2 1. 21 0.095
87 A 17 5 1. 21 0.238
88 A 14 8 1. 21 0.381
89 A 14 8 1. 21 0.381
90 A 16 6 1. 21 0.286
91 A 15 10 1.2 23 0.435
92 A 4 4 1. 23 0.174
93 A 4 4 1. 23 0.174
94 A 7 7 1. 23 0.304
95 A 14 9 1.17 23 0.391
96 A 3 3 1. 23 0.13
97 A 5 5 1. 23 0.217
98 A 8 8 1. 23 0.348
99 A 10 7 1.38 23 0.304
100 A 4 4 1. 23 0.174
101 A 6 5 1. 23 0.217
102 A 10 8 1. 23 0.348
103 A 17 9 1.61 23 0.391
104 A 4 4 1. 23 0.174
105 A 4 4 1. 23 0.174
106 A 11 7 1. 23 0.304
107 A 20 9 1.1 23 0.391
108 A 5 5 1. 23 0.217
109 A 6 5 1. 23 0.217
110 A 10 6 1. 23 0.261
111 A 23 9 1.26 23 0.391
112 A 6 6 1. 23 0.261
113 A 7 6 1. 23 0.261
114 A 16 8 1. 23 0.348
115 A 10 9 1. 23 0.391
116 A 4 4 1. 23 0.174
117 A 3 3 1. 23 0.13
118 A 3 3 1. 23 0.13
119 A 8 7 1. 23 0.304
120 A 4 4 1. 23 0.174
121 A 3 3 1. 23 0.13
122 A 3 3 1. 23 0.13
123 A 10 6 1. 23 0.261
124 A 8 6 1. 23 0.261
125 A 6 5 1. 21 0.238
126 A 4 4 1. 23 0.174
127 A 10 6 1. 23 0.261
128 A 13 6 1. 23 0.261
129 A 4 3 1. 23 0.13
130 A 4 4 1. 21 0.19
131 A 3 3 1. 19 0.158
132 A 2 2 1. 19 0.105
133 A 3 3 1. 21 0.143
134 A 4 4 1. 21 0.19
135 A 6 6 1. 21 0.286
136 A 5 5 1. 21 0.238
137 A 2 2 1. 12 0.167
138 A 3 3 1. 21 0.143
139 A 3 3 1. 21 0.143
140 A 6 5 1. 19 0.263
141 A 5 4 1. 17 0.235
142 A 3 2 1. 17 0.118
143 A 3 2 1. 19 0.105
144 A 3 2 1. 19 0.105
145 A 8 5 1. 19 0.263
146 A 7 5 1. 19 0.263
147 A 7 6 1. 19 0.316
148 A 9 7 1. 19 0.368
149 A 11 7 1. 19 0.368
150 A 7 5 1. 21 0.238
151 A 6 4 1. 19 0.21
152 A 3 2 1. 19 0.105
153 A 3 2 1. 21 0.095
154 A 3 2 1. 21 0.095
155 A 13 9 1. 21 0.429
156 A 11 9 1. 21 0.429
157 A 9 7 1. 21 0.333
158 A 13 9 1. 21 0.429
159 A 16 10 1. 21 0.476
160 A 7 5 1. 21 0.238
161 A 6 4 1. 19 0.21
162 A 3 2 1. 19 0.105
163 A 3 2 1. 21 0.095
164 A 3 2 1. 21 0.095
165 A 16 9 1. 21 0.429
166 A 14 10 1. 21 0.476
167 A 11 9 1. 21 0.429
168 A 17 10 1. 21 0.476
169 A 21 10 1. 21 0.476
170 A 5 3 1. 21 0.143
171 A 4 3 1. 21 0.143
172 A 3 2 1. 19 0.105
173 A 4 4 1. 19 0.21
174 A 3 2 1. 21 0.095
175 A 3 2 1. 21 0.095
176 A 13 9 1. 21 0.429
177 A 8 7 1. 21 0.333
178 A 7 7 1. 21 0.333
179 A 7 7 1. 21 0.333
180 A 9 7 1. 21 0.333
181 A 5 3 1. 21 0.143
182 A 4 3 1. 21 0.143
183 A 3 2 1. 19 0.105
184 A 3 2 1. 19 0.105
185 A 3 2 1. 21 0.095
186 A 3 2 1. 21 0.095
187 A 16 8 1. 21 0.381
188 A 12 7 1. 21 0.333
189 A 8 7 1. 21 0.333
190 A 8 7 1. 21 0.333
191 A 10 7 1. 21 0.333
192 A 5 3 1. 21 0.143
193 A 4 3 1. 21 0.143
194 A 3 2 1. 19 0.105
195 A 3 2 1. 19 0.105
196 A 3 2 1. 21 0.095
197 A 3 2 1. 21 0.095
198 A 22 9 1. 21 0.429
199 A 18 8 1. 21 0.381
200 A 9 8 1. 21 0.381
201 A 9 7 1. 21 0.333
202 A 11 7 1. 21 0.333
203 A 10 6 1. 23 0.261
204 A 8 6 1. 23 0.261
205 A 6 5 1. 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. 0 0.

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