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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, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 70, 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, 129, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 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, 190, 191, 192, 193, 194, 195, 197, 198, 199, 200, 202, 203, 204, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 229, 230, 235, 236, 237, 238, 239, 240, 241, 243, 244, 245, 246, 247, 252, 253, 254 }

B grade: { 11, 40, 42, 44, 61, 72, 136, 138, 140, 158, 160 }

C grade: { 10, 12, 32, 41, 43, 69, 71, 123, 124, 125, 126, 127, 128, 137, 139, 159, 187, 188, 189, 196, 214, 227, 228, 231, 232, 233, 234, 242, 248, 249, 250, 251 }

F grade: { 201, 205}

2.1.3 Maple

A grade: { 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 19, 20, 21, 22, 24, 25, 26, 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, 87, 105, 106, 107, 108, 112, 114, 130, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 144, 146, 147, 148, 149, 150, 152, 153, 154, 156, 157, 158, 159, 160, 175, 190, 192, 193, 194, 202, 203, 204, 206, 207, 208, 210, 211, 212, 220, 221, 222, 224, 225, 226, 229, 238, 239, 240, 243, 244, 245, 246 }

B grade: { 1, 3, 13, 15, 17, 23, 27, 73, 74, 75, 76, 77, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 109, 111, 113, 129, 131, 141, 143, 145, 151, 155, 161, 162, 163, 164, 165, 170, 171, 172, 173, 174, 176, 178, 179, 180, 195, 196, 197, 198, 199, 200, 213, 214, 215, 216, 217, 218, 227, 228, 241, 242 }

C grade: { 78, 79, 93, 97, 98, 99, 100, 101, 102, 103, 104, 115, 116, 117, 118, 119, 121, 122, 166, 167, 168, 181, 182, 185, 186, 230, 231, 232, 233, 234, 235, 247, 248, 249, 250, 251, 252 }

F grade: { 80, 81, 94, 95, 96, 110, 120, 123, 124, 125, 126, 127, 128, 169, 177, 183, 184, 187, 188, 189, 191, 201, 205, 209, 219, 223, 236, 237, 253, 254 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 23, 24, 25, 26, 33, 34, 35, 36, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 51, 59, 60, 61, 62, 63, 64, 66, 129, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 145, 151, 152, 153, 154, 190, 194, 212, 240

B grade: { 8, 9, 10, 11, 12, 18, 19, 20, 21, 22, 27, 28, 29, 30, 31, 32, 41, 42, 43, 44, 52, 53, 54, 55, 56, 57, 58, 65, 67, 68, 69, 70, 71, 72, 136, 137, 138, 139, 140, 146, 147, 148, 149, 150, 155, 156, 157, 158, 159, 160, 192, 193, 195, 196, 197, 198, 199, 200, 202, 203, 204, 206, 207, 208, 210, 211, 213, 214, 215, 216, 217, 218, 220, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 238, 239, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252 }

C grade: { }

F grade: { 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, 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, 191, 201, 205, 209, 219, 223, 236, 237, 253, 254 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 72, 77, 78, 79, 80, 94, 95, 96, 101, 102, 103, 104, 115, 116, 120, 121, 122, 129, 130, 131, 132, 133, 134, 135, 140, 141, 142, 143, 144, 145, 146, 147, 149, 151, 152, 153, 154, 155, 156, 157, 165, 166, 167, 168, 182, 183, 184, 190, 192, 193, 194, 195, 196, 197, 199, 202, 203, 204, 206, 207, 208, 210, 211, 212, 213, 215, 216, 217, 218, 220, 221, 222, 224, 225, 226, 227, 229, 238, 239, 240, 241, 242, 243, 244, 245, 246 }

B grade: { 8, 9, 20, 22, 27, 30, 41, 42, 43, 53, 55, 57, 69, 70, 71, 73, 74, 75, 76, 89, 90, 91, 92, 93, 97, 98, 99, 100, 117, 118, 119, 136, 137, 138, 139, 148, 150, 158, 159, 160, 161, 162, 163, 164, 177, 178, 179, 180, 181, 185, 186, 198, 200, 214, 228, 230, 231, 232, 233, 234, 235, 247, 248, 249, 250, 251, 252 }

C grade: { }

F grade: { 81, 82, 83, 84, 85, 86, 87, 88, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 123, 124, 125, 126, 127, 128, 169, 170, 171, 172, 173, 174, 175, 176, 187, 188, 189, 191, 201, 205, 209, 219, 223, 236, 237, 253, 254 }

2.1.6 Sympy

A grade: { 4, 5, 6, 7, 15, 16, 17, 26, 27, 132, 133, 134, 135, 143, 144, 145, 154, 155, 192, 193, 194, 202, 203, 206, 210, 211, 212, 220, 221, 224, 238, 239, 240, 245 }

B grade: { 195, 213, 227, 241 }

C grade: { }

F grade: { 1, 2, 3, 8, 9, 10, 11, 12, 13, 14, 18, 19, 20, 21, 22, 23, 24, 25, 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, 136, 137, 138, 139, 140, 141, 142, 146, 147, 148, 149, 150, 151, 152, 153, 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, 196, 197, 198, 199, 200, 201, 204, 205, 207, 208, 209, 214, 215, 216, 217, 218, 219, 222, 223, 225, 226, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 242, 243, 244, 246, 247, 248, 249, 250, 251, 252, 253, 254 }

2.1.7 Giac

A grade: { 2, 4, 6, 7, 14, 16, 24, 26, 34, 36, 38, 40, 45, 47, 49, 51, 60, 62, 64, 66, 68, 130, 132, 134, 135, 136, 137, 139, 142, 144, 147, 149, 152, 154, 157, 159, 190, 192, 193, 194, 202, 203, 204, 206, 207, 208, 210, 211, 212, 220, 221, 222, 224, 225, 226, 238, 239, 240, 244, 245, 246 }

B grade: { 1, 3, 5, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 35, 37, 39, 41, 42, 43, 44, 46, 48, 50, 52, 53, 54, 55, 56, 57, 58, 59, 61, 63, 65, 67, 69, 70, 71, 129, 131, 133, 138, 140, 141, 143, 145, 146, 148, 150, 151, 153, 155, 156, 158, 160, 195, 196, 197, 198, 199, 200, 213, 214, 215, 216, 217, 218, 227, 228, 229, 233, 234, 235, 241, 242, 243, 250, 251, 252 }

C grade: { }

F grade: { 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, 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, 191, 201, 205, 209, 219, 223, 230, 231, 232, 236, 237, 247, 248, 249, 253, 254 }

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 B A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 47 111 123 238 0 149
normalized size 1 1. 0.77 1.82 2.02 3.9 0. 2.44
time (sec) N/A 0.057 0.466 0.082 1.237 0.53 0. 1.522
Problem 2 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 61 61 47 97 108 132 0 130
normalized size 1 1. 0.77 1.59 1.77 2.16 0. 2.13
time (sec) N/A 0.058 0.325 0.023 1.175 0.522 0. 1.438
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 37 83 93 174 0 111
normalized size 1 1. 0.8 1.8 2.02 3.78 0. 2.41
time (sec) N/A 0.055 0.251 0.012 1.213 0.504 0. 1.38
Problem 4 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 46 46 37 69 78 96 163 92
normalized size 1 1. 0.8 1.5 1.7 2.09 3.54 2.
time (sec) N/A 0.055 0.146 0.013 1.258 0.49 65.169 1.237
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 27 55 63 108 126 73
normalized size 1 1. 0.87 1.77 2.03 3.48 4.06 2.35
time (sec) N/A 0.05 0.09 0.012 1.188 0.481 16.938 1.276
Problem 6 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 31 31 27 41 49 62 92 54
normalized size 1 1. 0.87 1.32 1.58 2. 2.97 1.74
time (sec) N/A 0.05 0.066 0.01 1.231 0.479 4.359 1.294
Problem 7 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 30 30 15 27 35 57 51 35
normalized size 1 1. 0.5 0.9 1.17 1.9 1.7 1.17
time (sec) N/A 0.011 0.032 0.007 1.099 0.471 1.125 1.306
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 20 155 76 0 235
normalized size 1 1. 1. 1.43 11.07 5.43 0. 16.79
time (sec) N/A 0.017 0.005 0.036 1.79 0.485 0. 1.52
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 50 36 319 154 0 556
normalized size 1 1. 1.79 1.29 11.39 5.5 0. 19.86
time (sec) N/A 0.038 0.039 0.032 1.228 0.495 0. 1.643
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 29 55 1091 230 0 1918
normalized size 1 1. 0.59 1.12 22.27 4.69 0. 39.14
time (sec) N/A 0.063 0.017 0.037 1.882 0.5 0. 2.205
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 205 78 2935 302 0 4088
normalized size 1 1. 3.11 1.18 44.47 4.58 0. 61.94
time (sec) N/A 0.067 0.445 0.036 1.391 0.505 0. 4.72
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 31 97 4169 378 0 7623
normalized size 1 1. 0.35 1.09 46.84 4.25 0. 85.65
time (sec) N/A 0.069 0.03 0.038 2.318 0.523 0. 13.169
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 68 86 97 122 0 115
normalized size 1 1. 1.55 1.95 2.2 2.77 0. 2.61
time (sec) N/A 0.069 0.342 0.022 1.192 0.504 0. 1.449
Problem 14 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 76 76 62 75 88 180 0 100
normalized size 1 1. 0.82 0.99 1.16 2.37 0. 1.32
time (sec) N/A 0.068 0.193 0.027 1.128 0.511 0. 1.354
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 48 58 68 88 362 77
normalized size 1 1. 1.66 2. 2.34 3.03 12.48 2.66
time (sec) N/A 0.059 0.114 0.01 1.084 0.483 63.208 1.378
Problem 16 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 49 49 40 47 55 117 231 62
normalized size 1 1. 0.82 0.96 1.12 2.39 4.71 1.27
time (sec) N/A 0.056 0.072 0.009 1.116 0.489 17.447 1.346
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 30 35 58 133 39
normalized size 1 1. 1. 2. 2.33 3.87 8.87 2.6
time (sec) N/A 0.033 0.005 0.009 1.197 0.474 4.491 1.4
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 13 74 36 0 128
normalized size 1 1. 1. 0.93 5.29 2.57 0. 9.14
time (sec) N/A 0.026 0.011 0.022 1.13 0.498 0. 1.507
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 12 72 47 0 205
normalized size 1 1. 1. 0.92 5.54 3.62 0. 15.77
time (sec) N/A 0.035 0.008 0.091 1.113 0.453 0. 1.477
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 36 27 865 155 0 991
normalized size 1 1. 1.2 0.9 28.83 5.17 0. 33.03
time (sec) N/A 0.048 0.036 0.036 1.122 0.499 0. 1.634
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 48 51 416 109 0 1396
normalized size 1 1. 1.14 1.21 9.9 2.6 0. 33.24
time (sec) N/A 0.063 0.054 0.057 1.075 0.47 0. 1.699
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 56 69 4271 289 0 3587
normalized size 1 1. 0.93 1.15 71.18 4.82 0. 59.78
time (sec) N/A 0.071 0.241 0.036 1.531 0.517 0. 2.58
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 37 97 108 204 0 130
normalized size 1 1. 0.8 2.11 2.35 4.43 0. 2.83
time (sec) N/A 0.063 0.374 0.012 1.062 0.515 0. 1.592
Problem 24 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 61 61 47 83 93 130 0 111
normalized size 1 1. 0.77 1.36 1.52 2.13 0. 1.82
time (sec) N/A 0.069 0.226 0.011 1.218 0.503 0. 1.429
Problem 25 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 31 31 27 55 63 138 0 73
normalized size 1 1. 0.87 1.77 2.03 4.45 0. 2.35
time (sec) N/A 0.06 0.142 0.01 1.176 0.489 0. 1.284
Problem 26 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 46 46 37 55 63 95 202 73
normalized size 1 1. 0.8 1.2 1.37 2.07 4.39 1.59
time (sec) N/A 0.064 0.109 0.01 1.149 0.485 73.172 1.307
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 41 46 81 117 54
normalized size 1 1. 1. 2.73 3.07 5.4 7.8 3.6
time (sec) N/A 0.033 0.007 0.009 1.076 0.471 19.165 1.278
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 27 32 167 99 0 834
normalized size 1 1. 0.96 1.14 5.96 3.54 0. 29.79
time (sec) N/A 0.037 0.012 0.026 1.757 0.503 0. 1.611
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 14 112 30 0 431
normalized size 1 1. 1. 1.08 8.62 2.31 0. 33.15
time (sec) N/A 0.035 0.009 0.02 1.149 0.465 0. 1.619
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 38 38 648 163 0 1500
normalized size 1 1. 1.12 1.12 19.06 4.79 0. 44.12
time (sec) N/A 0.041 0.011 0.066 1.72 0.492 0. 2.188
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 61 49 1332 194 0 2854
normalized size 1 1. 1.42 1.14 30.98 4.51 0. 66.37
time (sec) N/A 0.053 0.026 0.035 1.294 0.502 0. 2.825
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 29 76 2437 262 0 5443
normalized size 1 1. 0.41 1.09 34.81 3.74 0. 77.76
time (sec) N/A 0.072 0.035 0.036 2.067 0.509 0. 5.79
Problem 33 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 61 61 119 71 123 136 0 365
normalized size 1 1. 1.95 1.16 2.02 2.23 0. 5.98
time (sec) N/A 0.061 0.094 0.036 1.068 0.538 0. 1.936
Problem 34 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 61 61 48 97 108 207 0 62
normalized size 1 1. 0.79 1.59 1.77 3.39 0. 1.02
time (sec) N/A 0.061 0.214 0.06 1.224 0.52 0. 1.826
Problem 35 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 46 46 89 53 93 99 0 275
normalized size 1 1. 1.93 1.15 2.02 2.15 0. 5.98
time (sec) N/A 0.056 0.058 0.029 1.15 0.503 0. 1.596
Problem 36 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 46 46 38 69 78 142 0 49
normalized size 1 1. 0.83 1.5 1.7 3.09 0. 1.07
time (sec) N/A 0.057 0.098 0.056 1.163 0.495 0. 1.403
Problem 37 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 31 31 59 35 63 63 0 186
normalized size 1 1. 1.9 1.13 2.03 2.03 0. 6.
time (sec) N/A 0.052 0.038 0.029 1.14 0.482 0. 1.4
Problem 38 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 31 31 28 41 49 84 0 35
normalized size 1 1. 0.9 1.32 1.58 2.71 0. 1.13
time (sec) N/A 0.051 0.048 0.047 1.201 0.477 0. 1.348
Problem 39 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 15 15 15 14 31 31 0 70
normalized size 1 1. 1. 0.93 2.07 2.07 0. 4.67
time (sec) N/A 0.037 0.007 0.019 1.172 0.472 0. 1.263
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 23 12 15 24 0 15
normalized size 1 1. 2.09 1.09 1.36 2.18 0. 1.36
time (sec) N/A 0.017 0.008 0.018 1.077 0.468 0. 1.303
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 29 34 315 136 0 653
normalized size 1 1. 1.04 1.21 11.25 4.86 0. 23.32
time (sec) N/A 0.041 0.017 0.03 1.8 0.491 0. 1.601
Problem 42 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 49 49 143 57 1315 262 0 1791
normalized size 1 1. 2.92 1.16 26.84 5.35 0. 36.55
time (sec) N/A 0.059 0.259 0.032 1.088 0.5 0. 1.927
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 31 76 2403 342 0 4095
normalized size 1 1. 0.47 1.15 36.41 5.18 0. 62.05
time (sec) N/A 0.063 0.021 0.035 1.95 0.505 0. 4.398
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 268 99 5192 417 0 7393
normalized size 1 1. 3.01 1.11 58.34 4.69 0. 83.07
time (sec) N/A 0.072 0.512 0.037 1.788 0.519 0. 12.218
Problem 45 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 155 155 85 111 117 244 0 128
normalized size 1 1. 0.55 0.72 0.75 1.57 0. 0.83
time (sec) N/A 0.171 0.248 0.06 1.115 0.546 0. 1.89
Problem 46 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 44 44 48 53 97 97 0 247
normalized size 1 1. 1.09 1.2 2.2 2.2 0. 5.61
time (sec) N/A 0.065 0.172 0.027 1.081 0.511 0. 1.679
Problem 47 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 111 111 62 83 88 177 0 101
normalized size 1 1. 0.56 0.75 0.79 1.59 0. 0.91
time (sec) N/A 0.12 0.198 0.052 1.199 0.513 0. 1.557
Problem 48 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 29 29 48 35 68 61 0 188
normalized size 1 1. 1.66 1.21 2.34 2.1 0. 6.48
time (sec) N/A 0.057 0.124 0.025 1.121 0.49 0. 1.451
Problem 49 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 60 60 40 55 58 115 0 74
normalized size 1 1. 0.67 0.92 0.97 1.92 0. 1.23
time (sec) N/A 0.074 0.099 0.05 1.199 0.485 0. 1.39
Problem 50 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 13 13 13 14 35 28 0 93
normalized size 1 1. 1. 1.08 2.69 2.15 0. 7.15
time (sec) N/A 0.041 0.006 0.02 1.099 0.462 0. 1.339
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 21 21 20 28 24 53 0 39
normalized size 1 1. 0.95 1.33 1.14 2.52 0. 1.86
time (sec) N/A 0.034 0.024 0.025 1.126 0.476 0. 1.297
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 20 13 109 36 0 74
normalized size 1 1. 1.67 1.08 9.08 3. 0. 6.17
time (sec) N/A 0.02 0.015 0.02 1.217 0.484 0. 1.308
Problem 53 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 30 30 34 27 886 176 0 1098
normalized size 1 1. 1.13 0.9 29.53 5.87 0. 36.6
time (sec) N/A 0.042 0.052 0.03 1.225 0.5 0. 1.47
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 48 51 416 136 0 1457
normalized size 1 1. 1.14 1.21 9.9 3.24 0. 34.69
time (sec) N/A 0.059 0.08 0.032 1.208 0.467 0. 1.546
Problem 55 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 60 60 54 69 4304 367 0 3791
normalized size 1 1. 0.9 1.15 71.73 6.12 0. 63.18
time (sec) N/A 0.067 0.36 0.035 1.456 0.521 0. 2.237
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 90 87 1656 228 0 4651
normalized size 1 1. 1.25 1.21 23. 3.17 0. 64.6
time (sec) N/A 0.07 0.054 0.038 1.257 0.482 0. 3.423
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 76 111 10328 514 0 8605
normalized size 1 1. 0.84 1.23 114.76 5.71 0. 95.61
time (sec) N/A 0.082 0.406 0.037 2.621 0.535 0. 7.276
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 132 123 3659 324 0 10094
normalized size 1 1. 1.29 1.21 35.87 3.18 0. 98.96
time (sec) N/A 0.084 0.07 0.041 1.654 0.517 0. 13.248
Problem 59 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 61 61 119 71 123 142 0 424
normalized size 1 1. 1.95 1.16 2.02 2.33 0. 6.95
time (sec) N/A 0.072 0.146 0.04 1.062 0.57 0. 2.309
Problem 60 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 76 76 58 107 123 246 0 76
normalized size 1 1. 0.76 1.41 1.62 3.24 0. 1.
time (sec) N/A 0.077 0.329 0.058 1.075 0.53 0. 2.153
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 104 53 108 104 0 335
normalized size 1 1. 2.26 1.15 2.35 2.26 0. 7.28
time (sec) N/A 0.067 0.098 0.032 1.058 0.523 0. 1.869
Problem 62 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 61 61 48 79 93 176 0 62
normalized size 1 1. 0.79 1.3 1.52 2.89 0. 1.02
time (sec) N/A 0.071 0.167 0.029 1.104 0.511 0. 1.733
Problem 63 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 31 31 27 35 63 63 0 246
normalized size 1 1. 0.87 1.13 2.03 2.03 0. 7.94
time (sec) N/A 0.061 0.146 0.029 1.041 0.492 0. 1.651
Problem 64 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 46 46 37 51 63 116 0 49
normalized size 1 1. 0.8 1.11 1.37 2.52 0. 1.07
time (sec) N/A 0.066 0.108 0.029 1.037 0.484 0. 1.365
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 14 46 32 0 100
normalized size 1 1. 1. 0.93 3.07 2.13 0. 6.67
time (sec) N/A 0.044 0.01 0.023 1.068 0.48 0. 1.422
Problem 66 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 27 27 28 22 31 55 0 30
normalized size 1 1. 1.04 0.81 1.15 2.04 0. 1.11
time (sec) N/A 0.039 0.011 0.025 1.066 0.474 0. 1.351
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 44 34 124 112 0 77
normalized size 1 1. 1.83 1.42 5.17 4.67 0. 3.21
time (sec) N/A 0.043 0.026 0.029 1.052 0.504 0. 1.25
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 14 113 28 0 18
normalized size 1 1. 1. 1.27 10.27 2.55 0. 1.64
time (sec) N/A 0.026 0.01 0.019 1.038 0.454 0. 1.204
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 31 47 1126 254 0 2830
normalized size 1 1. 0.72 1.09 26.19 5.91 0. 65.81
time (sec) N/A 0.049 0.018 0.032 1.782 0.502 0. 2.102
Problem 70 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 70 70 129 78 3020 374 0 5096
normalized size 1 1. 1.84 1.11 43.14 5.34 0. 72.8
time (sec) N/A 0.073 4.633 0.036 1.343 0.509 0. 4.403
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 31 97 4178 458 0 8529
normalized size 1 1. 0.38 1.2 51.58 5.65 0. 105.3
time (sec) N/A 0.073 0.035 0.039 2.32 0.516 0. 11.886
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 278 120 5762 529 0 0
normalized size 1 1. 2.48 1.07 51.45 4.72 0. 0.
time (sec) N/A 0.087 0.834 0.04 1.94 0.532 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 98 183661406 0 803 0 0
normalized size 1 1. 0.72 6 1.35045 10 0. 5.9 0. 0.
time (sec) N/A 0.094 0.288 59.26 0. 0.564 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 86 65166864 0 771 0 0
normalized size 1 1. 0.78 592426. 0. 7.01 0. 0.
time (sec) N/A 0.068 0.194 15.386 0. 0.556 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 72 6219390 0 737 0 0
normalized size 1 1. 0.86 74040.4 0. 8.77 0. 0.
time (sec) N/A 0.043 0.072 1.171 0. 0.538 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 50 15979424 0 657 0 0
normalized size 1 1. 0.86 275507. 0. 11.33 0. 0.
time (sec) N/A 0.021 0.049 1.424 0. 0.526 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 22 59131270 0 107 0 0
normalized size 1 1. 0.96 6 2.57092 10 0. 4.65 0. 0.
time (sec) N/A 0.018 0.018 8.56 0. 0.487 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 43 597 0 184 0 0
normalized size 1 1. 0.81 11.26 0. 3.47 0. 0.
time (sec) N/A 0.04 0.103 18.474 0. 0.51 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 52 308 0 231 0 0
normalized size 1 1. 0.66 3.9 0. 2.92 0. 0.
time (sec) N/A 0.059 0.189 257.353 0. 0.515 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 67 0 0 300 0 0
normalized size 1 1. 0.64 0. 0. 2.86 0. 0.
time (sec) N/A 0.083 0.146 180. 0. 0.526 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 96 0 0 0 0 0
normalized size 1 1. 0.98 0. 0. 0. 0. 0.
time (sec) N/A 0.06 0.394 180. 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 66 278672995 0 0 0 0
normalized size 1 1. 0.96 6 4.03874 10 0. 0. 0. 0.
time (sec) N/A 0.047 0.217 103.249 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 76 172329442 0 0 0 0
normalized size 1 1. 1.1 6 2.49753 10 0. 0. 0. 0.
time (sec) N/A 0.047 0.345 48.767 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 34 16542587 0 0 0 0
normalized size 1 1. 0.85 413565. 0. 0. 0. 0.
time (sec) N/A 0.036 0.083 3.85 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 75 53350427 0 0 0 0
normalized size 1 1. 1.88 6 1.33376 10 0. 0. 0. 0.
time (sec) N/A 0.037 0.245 8.632 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 41 83117872 0 0 0 0
normalized size 1 1. 0.91 6 1.84706 10 0. 0. 0. 0.
time (sec) N/A 0.037 0.096 9.329 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 83 123 0 0 0 0
normalized size 1 1. 1.73 2.56 0. 0. 0. 0.
time (sec) N/A 0.038 0.19 11.461 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 66 227 0 0 0 0
normalized size 1 1. 0.86 2.95 0. 0. 0. 0.
time (sec) N/A 0.046 0.815 58.739 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 98 322248039 0 805 0 0
normalized size 1 1. 0.72 6 2.36947 10 0. 5.92 0. 0.
time (sec) N/A 0.101 0.34 127.454 0. 0.569 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 86 47430975 0 774 0 0
normalized size 1 1. 0.78 431191. 0. 7.04 0. 0.
time (sec) N/A 0.078 0.219 15.251 0. 0.551 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 74 155734626 0 740 0 0
normalized size 1 1. 0.88 6 1.85398 10 0. 8.81 0. 0.
time (sec) N/A 0.054 0.141 33.727 0. 0.547 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 72 149404972 0 815 0 0
normalized size 1 1. 0.89 6 1.84451 10 0. 10.06 0. 0.
time (sec) N/A 0.078 0.091 30.918 0. 0.536 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 27 727 0 132 0 0
normalized size 1 1. 0.96 25.96 0. 4.71 0. 0.
time (sec) N/A 0.028 0.054 44.19 0. 0.493 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 35 0 0 147 0 0
normalized size 1 1. 0.64 0. 0. 2.67 0. 0.
time (sec) N/A 0.049 0.096 180. 0. 0.503 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 55 0 0 213 0 0
normalized size 1 1. 0.68 0. 0. 2.63 0. 0.
time (sec) N/A 0.069 0.107 180. 0. 0.517 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 62 0 0 263 0 0
normalized size 1 1. 0.58 0. 0. 2.46 0. 0.
time (sec) N/A 0.092 0.163 180. 0. 0.536 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 98 973 0 806 0 0
normalized size 1 1. 0.72 7.15 0. 5.93 0. 0.
time (sec) N/A 0.123 0.322 4.362 0. 0.579 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 86 243 0 768 0 0
normalized size 1 1. 0.78 2.21 0. 6.98 0. 0.
time (sec) N/A 0.095 0.19 2.911 0. 0.557 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 70 362 0 734 0 0
normalized size 1 1. 0.86 4.47 0. 9.06 0. 0.
time (sec) N/A 0.072 0.086 1.805 0. 0.542 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 52 157 0 657 0 0
normalized size 1 1. 0.98 2.96 0. 12.4 0. 0.
time (sec) N/A 0.047 0.041 1.042 0. 0.52 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 23 308 0 103 0 0
normalized size 1 1. 0.96 12.83 0. 4.29 0. 0.
time (sec) N/A 0.024 0.047 1.546 0. 0.491 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 43 194 0 192 0 0
normalized size 1 1. 0.81 3.66 0. 3.62 0. 0.
time (sec) N/A 0.064 0.1 2.469 0. 0.498 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 52 481 0 267 0 0
normalized size 1 1. 0.66 6.09 0. 3.38 0. 0.
time (sec) N/A 0.086 0.124 5.486 0. 0.514 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 67 222 0 320 0 0
normalized size 1 1. 0.64 2.11 0. 3.05 0. 0.
time (sec) N/A 0.108 0.138 30.944 0. 0.53 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 66 204 0 0 0 0
normalized size 1 1. 0.62 1.92 0. 0. 0. 0.
time (sec) N/A 0.058 0.295 7.493 0. 0. 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 76 139 0 0 0 0
normalized size 1 1. 0.72 1.31 0. 0. 0. 0.
time (sec) N/A 0.059 0.258 5.161 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 34 137 0 0 0 0
normalized size 1 1. 0.45 1.83 0. 0. 0. 0.
time (sec) N/A 0.047 0.078 3.971 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 73 111 0 0 0 0
normalized size 1 1. 1.04 1.59 0. 0. 0. 0.
time (sec) N/A 0.048 0.86 2.622 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 37 176 0 0 0 0
normalized size 1 1. 0.84 4. 0. 0. 0. 0.
time (sec) N/A 0.036 0.127 2.096 0. 0. 0. 0.
Problem 110 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 48 48 82 0 0 0 0 0
normalized size 1 1. 1.71 0. 0. 0. 0. 0.
time (sec) N/A 0.037 0.951 180. 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 64 227 0 0 0 0
normalized size 1 1. 0.83 2.95 0. 0. 0. 0.
time (sec) N/A 0.047 0.58 6.056 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 66 154 0 0 0 0
normalized size 1 1. 0.86 2. 0. 0. 0. 0.
time (sec) N/A 0.048 0.461 9.525 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 85 240 0 0 0 0
normalized size 1 1. 0.8 2.26 0. 0. 0. 0.
time (sec) N/A 0.058 0.814 30.493 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 86 167 0 0 0 0
normalized size 1 1. 0.81 1.58 0. 0. 0. 0.
time (sec) N/A 0.059 0.344 47.27 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 190 190 100 441 0 802 0 0
normalized size 1 1. 0.53 2.32 0. 4.22 0. 0.
time (sec) N/A 0.186 0.435 26.75 0. 0.574 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 164 164 84 973 0 772 0 0
normalized size 1 1. 0.51 5.93 0. 4.71 0. 0.
time (sec) N/A 0.156 0.22 19.125 0. 0.56 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 70 243 0 737 0 0
normalized size 1 1. 0.55 1.91 0. 5.8 0. 0.
time (sec) N/A 0.131 0.13 7.616 0. 0.54 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 68 542 0 814 0 0
normalized size 1 1. 0.65 5.21 0. 7.83 0. 0.
time (sec) N/A 0.102 0.098 6.01 0. 0.53 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 27 192 0 140 0 0
normalized size 1 1. 0.96 6.86 0. 5. 0. 0.
time (sec) N/A 0.028 0.049 3.405 0. 0.488 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 35 0 0 198 0 0
normalized size 1 1. 0.64 0. 0. 3.6 0. 0.
time (sec) N/A 0.053 0.092 180. 0. 0.498 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 55 222 0 281 0 0
normalized size 1 1. 0.68 2.74 0. 3.47 0. 0.
time (sec) N/A 0.092 0.116 9.663 0. 0.507 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 62 560 0 356 0 0
normalized size 1 1. 0.58 5.23 0. 3.33 0. 0.
time (sec) N/A 0.116 0.091 18.636 0. 0.527 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 84 84 602 0 0 0 0 0
normalized size 1 1. 7.17 0. 0. 0. 0. 0.
time (sec) N/A 0.074 5.625 1.214 0. 0. 0. 0.
Problem 124 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 84 84 602 0 0 0 0 0
normalized size 1 1. 7.17 0. 0. 0. 0. 0.
time (sec) N/A 0.077 3.596 0.848 0. 0. 0. 0.
Problem 125 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 82 82 152 0 0 0 0 0
normalized size 1 1. 1.85 0. 0. 0. 0. 0.
time (sec) N/A 0.064 0.268 0.957 0. 0. 0. 0.
Problem 126 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 72 72 254 0 0 0 0 0
normalized size 1 1. 3.53 0. 0. 0. 0. 0.
time (sec) N/A 0.07 0.889 0.517 0. 0. 0. 0.
Problem 127 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 85 85 938 0 0 0 0 0
normalized size 1 1. 11.04 0. 0. 0. 0. 0.
time (sec) N/A 0.082 5.515 0.326 0. 0. 0. 0.
Problem 128 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 85 85 2421 0 0 0 0 0
normalized size 1 1. 28.48 0. 0. 0. 0. 0.
time (sec) N/A 0.081 14.423 0.345 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 47 111 123 136 0 149
normalized size 1 1. 0.77 1.82 2.02 2.23 0. 2.44
time (sec) N/A 0.06 0.454 0.024 1.082 0.538 0. 1.664
Problem 130 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 61 61 47 97 108 205 0 130
normalized size 1 1. 0.77 1.59 1.77 3.36 0. 2.13
time (sec) N/A 0.061 0.315 0.036 1.121 0.519 0. 1.528
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 37 83 93 99 0 111
normalized size 1 1. 0.8 1.8 2.02 2.15 0. 2.41
time (sec) N/A 0.055 0.264 0.023 1.027 0.504 0. 1.386
Problem 132 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 46 46 37 69 78 142 162 92
normalized size 1 1. 0.8 1.5 1.7 3.09 3.52 2.
time (sec) N/A 0.054 0.131 0.027 1.052 0.504 76.047 1.265
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 27 55 63 62 128 73
normalized size 1 1. 0.87 1.77 2.03 2. 4.13 2.35
time (sec) N/A 0.05 0.09 0.019 1.011 0.478 22.704 1.245
Problem 134 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 31 31 27 41 49 84 90 54
normalized size 1 1. 0.87 1.32 1.58 2.71 2.9 1.74
time (sec) N/A 0.048 0.063 0.022 1.033 0.478 6.312 1.252
Problem 135 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 30 30 15 27 35 31 53 35
normalized size 1 1. 0.5 0.9 1.17 1.03 1.77 1.17
time (sec) N/A 0.011 0.006 0.014 1.067 0.483 1.329 1.251
Problem 136 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 14 14 42 22 113 93 0 22
normalized size 1 1. 3. 1.57 8.07 6.64 0. 1.57
time (sec) N/A 0.016 0.012 0.019 1.158 0.491 0. 1.193
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 29 34 315 136 0 51
normalized size 1 1. 1.04 1.21 11.25 4.86 0. 1.82
time (sec) N/A 0.038 0.018 0.023 1.818 0.498 0. 1.235
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 143 57 1315 262 0 189
normalized size 1 1. 2.92 1.16 26.84 5.35 0. 3.86
time (sec) N/A 0.055 0.255 0.027 1.255 0.499 0. 1.275
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 31 76 2403 343 0 97
normalized size 1 1. 0.47 1.15 36.41 5.2 0. 1.47
time (sec) N/A 0.059 0.024 0.027 2.169 0.515 0. 1.301
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 268 99 5192 419 0 282
normalized size 1 1. 3.01 1.11 58.34 4.71 0. 3.17
time (sec) N/A 0.067 0.489 0.032 1.863 0.519 0. 1.348
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 68 86 97 96 0 115
normalized size 1 1. 1.55 1.95 2.2 2.18 0. 2.61
time (sec) N/A 0.067 0.402 0.021 1.15 0.511 0. 1.415
Problem 142 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 76 76 62 75 88 177 0 100
normalized size 1 1. 0.82 0.99 1.16 2.33 0. 1.32
time (sec) N/A 0.064 0.189 0.03 1.156 0.511 0. 1.341
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 48 58 68 61 359 77
normalized size 1 1. 1.71 2.07 2.43 2.18 12.82 2.75
time (sec) N/A 0.057 0.122 0.017 1.11 0.493 174.245 1.231
Problem 144 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 49 49 40 47 58 116 231 62
normalized size 1 1. 0.82 0.96 1.18 2.37 4.71 1.27
time (sec) N/A 0.054 0.094 0.023 1.201 0.491 28.56 1.285
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 30 35 31 131 39
normalized size 1 1. 1. 2. 2.33 2.07 8.73 2.6
time (sec) N/A 0.033 0.006 0.013 1.121 0.475 5.989 1.29
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 22 13 111 39 0 76
normalized size 1 1. 1.57 0.93 7.93 2.79 0. 5.43
time (sec) N/A 0.025 0.015 0.014 1.18 0.491 0. 1.281
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 12 72 49 0 18
normalized size 1 1. 1. 0.92 5.54 3.77 0. 1.38
time (sec) N/A 0.033 0.013 0.02 1.15 0.458 0. 1.194
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 34 27 886 177 0 161
normalized size 1 1. 1.13 0.9 29.53 5.9 0. 5.37
time (sec) N/A 0.047 0.044 0.023 1.202 0.5 0. 1.285
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 48 51 416 136 0 47
normalized size 1 1. 1.14 1.21 9.9 3.24 0. 1.12
time (sec) N/A 0.06 0.052 0.03 1.137 0.469 0. 1.264
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 54 69 4304 369 0 313
normalized size 1 1. 0.9 1.15 71.73 6.15 0. 5.22
time (sec) N/A 0.068 0.367 0.027 1.507 0.517 0. 1.296
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 37 97 108 103 0 130
normalized size 1 1. 0.8 2.11 2.35 2.24 0. 2.83
time (sec) N/A 0.061 0.39 0.024 1.126 0.519 0. 1.408
Problem 152 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 61 61 47 83 93 174 0 111
normalized size 1 1. 0.77 1.36 1.52 2.85 0. 1.82
time (sec) N/A 0.065 0.212 0.03 1.166 0.511 0. 1.213
Problem 153 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 31 31 27 55 63 62 0 73
normalized size 1 1. 0.87 1.77 2.03 2. 0. 2.35
time (sec) N/A 0.056 0.136 0.017 1.106 0.499 0. 1.3
Problem 154 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 46 46 37 55 63 115 202 73
normalized size 1 1. 0.8 1.2 1.37 2.5 4.39 1.59
time (sec) N/A 0.06 0.092 0.026 1.097 0.481 77.694 1.222
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 41 46 31 117 54
normalized size 1 1. 1. 2.73 3.07 2.07 7.8 3.6
time (sec) N/A 0.033 0.008 0.014 1.121 0.491 19.201 1.216
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 46 34 124 115 0 77
normalized size 1 1. 1.64 1.21 4.43 4.11 0. 2.75
time (sec) N/A 0.035 0.019 0.022 1.121 0.5 0. 1.244
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 14 113 31 0 18
normalized size 1 1. 1. 1.08 8.69 2.38 0. 1.38
time (sec) N/A 0.035 0.012 0.017 1.061 0.459 0. 1.232
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 79 40 753 203 0 124
normalized size 1 1. 2.32 1.18 22.15 5.97 0. 3.65
time (sec) N/A 0.041 0.015 0.048 1.206 0.493 0. 1.315
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 31 47 1126 254 0 70
normalized size 1 1. 0.72 1.09 26.19 5.91 0. 1.63
time (sec) N/A 0.051 0.018 0.027 2.416 0.502 0. 1.233
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 195 78 3020 375 0 220
normalized size 1 1. 2.79 1.11 43.14 5.36 0. 3.14
time (sec) N/A 0.07 0.338 0.03 1.495 0.507 0. 1.312
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 98 199880296 0 806 0 0
normalized size 1 1. 0.72 6 1.46971 10 0. 5.93 0. 0.
time (sec) N/A 0.091 0.357 61.386 0. 0.573 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 86 74316378 0 768 0 0
normalized size 1 1. 0.78 675603. 0. 6.98 0. 0.
time (sec) N/A 0.067 0.186 18.977 0. 0.551 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 70 5339854 0 736 0 0
normalized size 1 1. 0.83 63569.7 0. 8.76 0. 0.
time (sec) N/A 0.043 0.097 1.177 0. 0.533 0. 0.
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 52 622763 0 657 0 0
normalized size 1 1. 0.9 10737.3 0. 11.33 0. 0.
time (sec) N/A 0.021 0.047 0.355 0. 0.53 0. 0.
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 23 55926091 0 108 0 0
normalized size 1 1. 0.96 6 2.33025 10 0. 4.5 0. 0.
time (sec) N/A 0.018 0.02 6.793 0. 0.491 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 43 194 0 193 0 0
normalized size 1 1. 0.81 3.66 0. 3.64 0. 0.
time (sec) N/A 0.038 0.102 6.571 0. 0.504 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 52 481 0 269 0 0
normalized size 1 1. 0.66 6.09 0. 3.41 0. 0.
time (sec) N/A 0.059 0.121 89.464 0. 0.514 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 67 222 0 320 0 0
normalized size 1 1. 0.64 2.11 0. 3.05 0. 0.
time (sec) N/A 0.08 0.143 183.381 0. 0.535 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 96 0 0 0 0 0
normalized size 1 1. 0.98 0. 0. 0. 0. 0.
time (sec) N/A 0.057 0.385 180. 0. 0. 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 66 336654858 0 0 0 0
normalized size 1 1. 0.96 6 4.87906 10 0. 0. 0. 0.
time (sec) N/A 0.045 0.208 110.597 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 76 174364218 0 0 0 0
normalized size 1 1. 1.1 6 2.52702 10 0. 0. 0. 0.
time (sec) N/A 0.045 0.348 33.345 0. 0. 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 34 24847123 0 0 0 0
normalized size 1 1. 0.85 621178. 0. 0. 0. 0.
time (sec) N/A 0.035 0.058 3.975 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 76 59635246 0 0 0 0
normalized size 1 1. 1.9 6 1.49088 10 0. 0. 0. 0.
time (sec) N/A 0.035 0.864 8.96 0. 0. 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 39 94273592 0 0 0 0
normalized size 1 1. 0.85 6 2.04943 10 0. 0. 0. 0.
time (sec) N/A 0.036 0.114 9.786 0. 0. 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 82 123 0 0 0 0
normalized size 1 1. 1.71 2.56 0. 0. 0. 0.
time (sec) N/A 0.036 1.007 11.904 0. 0. 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 64 227 0 0 0 0
normalized size 1 1. 0.83 2.95 0. 0. 0. 0.
time (sec) N/A 0.046 0.562 71.1 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 99 0 0 803 0 0
normalized size 1 1. 0.73 0. 0. 5.9 0. 0.
time (sec) N/A 0.099 0.328 180. 0. 0.562 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 84 88762396 0 774 0 0
normalized size 1 1. 0.76 806931. 0. 7.04 0. 0.
time (sec) N/A 0.076 0.182 19.511 0. 0.55 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 73 190984194 0 738 0 0
normalized size 1 1. 0.87 6 2.27362 10 0. 8.79 0. 0.
time (sec) N/A 0.052 0.11 38.924 0. 0.545 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 70 179366588 0 815 0 0
normalized size 1 1. 0.85 6 2.1874 10 0. 9.94 0. 0.
time (sec) N/A 0.076 0.089 29.262 0. 0.541 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 27 192 0 142 0 0
normalized size 1 1. 0.96 6.86 0. 5.07 0. 0.
time (sec) N/A 0.027 0.054 52.142 0. 0.49 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 35 482 0 200 0 0
normalized size 1 1. 0.64 8.76 0. 3.64 0. 0.
time (sec) N/A 0.047 0.093 213.665 0. 0.501 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 55 0 0 282 0 0
normalized size 1 1. 0.68 0. 0. 3.48 0. 0.
time (sec) N/A 0.068 0.114 180. 0. 0.506 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 62 0 0 358 0 0
normalized size 1 1. 0.58 0. 0. 3.35 0. 0.
time (sec) N/A 0.09 0.094 180. 0. 0.526 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 29 98 0 455 0 0
normalized size 1 1. 0.94 3.16 0. 14.68 0. 0.
time (sec) N/A 0.013 0.025 0.046 0. 0.508 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 99 0 455 0 0
normalized size 1 1. 1. 3.96 0. 18.2 0. 0.
time (sec) N/A 0.03 0.016 0.046 0. 0.508 0. 0.
Problem 187 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 85 85 2472 0 0 0 0 0
normalized size 1 1. 29.08 0. 0. 0. 0. 0.
time (sec) N/A 0.071 13.303 0.992 0. 0. 0. 0.
Problem 188 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 85 85 890 0 0 0 0 0
normalized size 1 1. 10.47 0. 0. 0. 0. 0.
time (sec) N/A 0.071 7.969 0.875 0. 0. 0. 0.
Problem 189 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 83 83 149 0 0 0 0 0
normalized size 1 1. 1.8 0. 0. 0. 0. 0.
time (sec) N/A 0.061 0.244 0.914 0. 0. 0. 0.
Problem 190 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 46 46 37 69 78 95 0 92
normalized size 1 1. 0.8 1.5 1.7 2.07 0. 2.
time (sec) N/A 0.097 0.163 0.023 1.223 0.491 0. 1.858
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 293 293 209 0 0 0 0 0
normalized size 1 1. 0.71 0. 0. 0. 0. 0.
time (sec) N/A 0.848 0.857 1.304 0. 0. 0. 0.
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 86 84 1237 267 921 113
normalized size 1 1. 0.95 0.92 13.59 2.93 10.12 1.24
time (sec) N/A 0.076 0.511 0.027 1.606 0.508 133.383 1.137
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 69 57 559 171 401 76
normalized size 1 1. 1.11 0.92 9.02 2.76 6.47 1.23
time (sec) N/A 0.053 0.714 0.016 1.339 0.494 10.725 1.116
Problem 194 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 43 43 43 40 54 99 153 54
normalized size 1 1. 1. 0.93 1.26 2.3 3.56 1.26
time (sec) N/A 0.035 0.187 0.016 1.249 0.475 3.613 1.141
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 26 325 146 77 335 319
normalized size 1 1. 1. 12.5 5.62 2.96 12.88 12.27
time (sec) N/A 0.027 0.141 0.201 1.337 0.496 18.406 1.211
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 90 890 613 203 0 471
normalized size 1 1. 2.5 24.72 17.03 5.64 0. 13.08
time (sec) N/A 0.033 0.097 0.446 1.283 0.502 0. 1.136
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 35 120 539 113 0 196
normalized size 1 1. 0.9 3.08 13.82 2.9 0. 5.03
time (sec) N/A 0.044 0.19 0.602 1.193 0.47 0. 1.173
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 67 14880 2394 377 0 2998
normalized size 1 1. 1. 222.09 35.73 5.63 0. 44.75
time (sec) N/A 0.046 0.553 2.466 1.655 0.516 0. 1.242
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 58 321 1453 193 0 406
normalized size 1 1. 0.97 5.35 24.22 3.22 0. 6.77
time (sec) N/A 0.047 0.374 1.888 1.574 0.481 0. 1.157
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 79 97954 5237 543 0 10847
normalized size 1 1. 0.84 1042.06 55.71 5.78 0. 115.39
time (sec) N/A 0.058 1.165 10.075 2.231 0.532 0. 1.32
Problem 201 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 410 410 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.973 0.375 1.504 0. 0. 0. 0.
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 80 63 501 155 410 82
normalized size 1 1. 1.18 0.93 7.37 2.28 6.03 1.21
time (sec) N/A 0.054 0.351 0.017 1.149 0.477 18.268 1.138
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 106 83 837 263 1027 108
normalized size 1 1. 1.2 0.94 9.51 2.99 11.67 1.23
time (sec) N/A 0.065 0.792 0.027 1.247 0.512 40.937 1.168
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 158 133 1839 429 0 174
normalized size 1 1. 1.1 0.92 12.77 2.98 0. 1.21
time (sec) N/A 0.097 1.645 0.023 1.461 0.545 0. 1.166
Problem 205 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 600 600 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.722 0.542 1.488 0. 0. 0. 0.
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 91 90 1065 246 957 120
normalized size 1 1. 0.94 0.93 10.98 2.54 9.87 1.24
time (sec) N/A 0.075 0.518 0.024 1.388 0.499 88.981 1.132
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 153 127 1836 427 0 167
normalized size 1 1. 1.11 0.92 13.3 3.09 0. 1.21
time (sec) N/A 0.098 1.672 0.022 1.559 0.534 0. 1.117
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 195 177 184 3526 652 0 244
normalized size 1 1. 0.91 0.94 18.08 3.34 0. 1.25
time (sec) N/A 0.132 1.657 0.046 2.036 0.574 0. 1.121
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 277 277 202 0 0 0 0 0
normalized size 1 1. 0.73 0. 0. 0. 0. 0.
time (sec) N/A 0.589 0.975 0.698 0. 0. 0. 0.
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 87 84 1231 239 923 113
normalized size 1 1. 0.96 0.92 13.53 2.63 10.14 1.24
time (sec) N/A 0.066 0.509 0.019 1.284 0.512 79.467 1.16
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 71 57 559 162 401 76
normalized size 1 1. 1.15 0.92 9.02 2.61 6.47 1.23
time (sec) N/A 0.047 0.781 0.016 1.212 0.491 12.126 1.139
Problem 212 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 43 43 43 40 54 100 155 54
normalized size 1 1. 1. 0.93 1.26 2.33 3.6 1.26
time (sec) N/A 0.036 0.196 0.014 1.178 0.474 2.872 1.135
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 563 99 74 435 213
normalized size 1 1. 1. 20.85 3.67 2.74 16.11 7.89
time (sec) N/A 0.018 0.142 0.201 1.259 0.498 169.994 1.161
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 88 888 522 186 0 335
normalized size 1 1. 2.59 26.12 15.35 5.47 0. 9.85
time (sec) N/A 0.027 0.091 0.424 2.042 0.504 0. 1.178
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 34 150 528 109 0 235
normalized size 1 1. 0.89 3.95 13.89 2.87 0. 6.18
time (sec) N/A 0.037 0.174 0.595 1.181 0.49 0. 1.197
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 64 14825 1922 258 0 668
normalized size 1 1. 0.96 221.27 28.69 3.85 0. 9.97
time (sec) N/A 0.042 0.431 2.318 2.161 0.527 0. 1.201
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 48 381 1450 142 0 441
normalized size 1 1. 0.81 6.46 24.58 2.41 0. 7.47
time (sec) N/A 0.051 0.339 1.819 1.191 0.495 0. 1.246
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 78 97703 4180 294 0 1021
normalized size 1 1. 0.83 1039.39 44.47 3.13 0. 10.86
time (sec) N/A 0.07 1.003 9.186 2.661 0.548 0. 1.214
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 386 386 242 0 0 0 0 0
normalized size 1 1. 0.63 0. 0. 0. 0. 0.
time (sec) N/A 0.7 1.786 0.751 0. 0. 0. 0.
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 76 63 501 155 410 82
normalized size 1 1. 1.12 0.93 7.37 2.28 6.03 1.21
time (sec) N/A 0.051 0.784 0.023 1.213 0.489 9.755 1.151
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 108 83 837 246 1027 108
normalized size 1 1. 1.23 0.94 9.51 2.8 11.67 1.23
time (sec) N/A 0.068 0.782 0.028 1.21 0.509 151.378 1.127
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 158 133 1839 393 0 174
normalized size 1 1. 1.1 0.92 12.77 2.73 0. 1.21
time (sec) N/A 0.096 1.826 0.036 1.416 0.527 0. 1.141
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 568 568 329 0 0 0 0 0
normalized size 1 1. 0.58 0. 0. 0. 0. 0.
time (sec) N/A 1.18 24.644 0.762 0. 0. 0. 0.
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 90 90 1060 247 964 120
normalized size 1 1. 0.93 0.93 10.93 2.55 9.94 1.24
time (sec) N/A 0.068 0.523 0.02 1.267 0.505 88.4 1.127
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 153 127 1836 404 0 167
normalized size 1 1. 1.11 0.92 13.3 2.93 0. 1.21
time (sec) N/A 0.096 1.641 0.023 1.43 0.54 0. 1.141
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 195 176 184 3526 591 0 244
normalized size 1 1. 0.9 0.94 18.08 3.03 0. 1.25
time (sec) N/A 0.124 1.602 0.029 1.889 0.588 0. 1.133
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 58 325 143 77 335 651
normalized size 1 1. 2.15 12.04 5.3 2.85 12.41 24.11
time (sec) N/A 0.017 0.173 0.184 1.113 0.501 10.342 1.228
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 90 1062 608 203 0 1326
normalized size 1 1. 2.57 30.34 17.37 5.8 0. 37.89
time (sec) N/A 0.028 0.096 0.452 1.31 0.517 0. 1.332
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 35 55 533 113 0 441
normalized size 1 1. 0.92 1.45 14.03 2.97 0. 11.61
time (sec) N/A 0.043 0.197 0.544 1.122 0.469 0. 1.262
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 70 186 1386 1015 0 0
normalized size 1 1. 0.97 2.58 19.25 14.1 0. 0.
time (sec) N/A 0.071 0.363 0.115 1.976 0.565 0. 0.
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C B B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 109 143 702 857 0 0
normalized size 1 1. 2.48 3.25 15.95 19.48 0. 0.
time (sec) N/A 0.036 0.1 0.083 1.992 0.539 0. 0.
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C B B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 94 99 177 509 0 0
normalized size 1 1. 3.24 3.41 6.1 17.55 0. 0.
time (sec) N/A 0.016 0.049 0.066 1.914 0.517 0. 0.
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 93 95 142 531 0 305
normalized size 1 1. 3.21 3.28 4.9 18.31 0. 10.52
time (sec) N/A 0.016 0.053 0.085 1.164 0.531 0. 1.193
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 111 143 826 859 0 779
normalized size 1 1. 2.41 3.11 17.96 18.67 0. 16.93
time (sec) N/A 0.04 0.097 0.089 1.335 0.553 0. 1.21
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 71 184 1693 987 0 1175
normalized size 1 1. 0.96 2.49 22.88 13.34 0. 15.88
time (sec) N/A 0.072 0.351 0.104 1.249 0.565 0. 1.332
Problem 236 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 143 143 116 0 0 0 0 0
normalized size 1 1. 0.81 0. 0. 0. 0. 0.
time (sec) N/A 0.112 1.787 0.181 0. 0. 0. 0.
Problem 237 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 139 139 260 0 0 0 0 0
normalized size 1 1. 1.87 0. 0. 0. 0. 0.
time (sec) N/A 0.111 3.595 0.208 0. 0. 0. 0.
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 85 84 1234 243 933 113
normalized size 1 1. 0.93 0.92 13.56 2.67 10.25 1.24
time (sec) N/A 0.065 0.486 0.027 1.455 0.511 136.5 1.124
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 69 57 562 147 401 76
normalized size 1 1. 1.11 0.92 9.06 2.37 6.47 1.23
time (sec) N/A 0.045 0.713 0.023 1.248 0.504 12.625 1.119
Problem 240 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 43 43 43 40 54 99 153 54
normalized size 1 1. 1. 0.93 1.26 2.3 3.56 1.26
time (sec) N/A 0.033 0.181 0.019 1.073 0.473 2.412 1.091
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 26 461 100 73 435 594
normalized size 1 1. 1. 17.73 3.85 2.81 16.73 22.85
time (sec) N/A 0.013 0.121 0.199 1.182 0.533 109.34 1.215
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 89 1049 528 185 0 1810
normalized size 1 1. 2.54 29.97 15.09 5.29 0. 51.71
time (sec) N/A 0.029 0.089 0.451 1.868 0.536 0. 1.38
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 35 56 516 108 0 425
normalized size 1 1. 0.92 1.47 13.58 2.84 0. 11.18
time (sec) N/A 0.039 0.191 0.556 1.129 0.485 0. 1.174
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 158 133 1839 370 0 174
normalized size 1 1. 1.1 0.92 12.77 2.57 0. 1.21
time (sec) N/A 0.089 1.639 0.036 1.573 0.533 0. 1.125
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 105 83 837 234 1027 108
normalized size 1 1. 1.19 0.94 9.51 2.66 11.67 1.23
time (sec) N/A 0.069 0.733 0.031 1.279 0.511 35.085 1.128
Problem 246 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 195 176 184 3529 535 0 244
normalized size 1 1. 0.9 0.94 18.1 2.74 0. 1.25
time (sec) N/A 0.135 1.63 0.046 1.879 0.592 0. 1.117
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 70 181 1386 986 0 0
normalized size 1 1. 0.97 2.51 19.25 13.69 0. 0.
time (sec) N/A 0.078 0.363 0.099 2.031 0.571 0. 0.
Problem 248 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C B B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 111 149 710 857 0 0
normalized size 1 1. 2.41 3.24 15.43 18.63 0. 0.
time (sec) N/A 0.039 0.097 0.085 1.969 0.536 0. 0.
Problem 249 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C B B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 93 97 177 531 0 0
normalized size 1 1. 3.1 3.23 5.9 17.7 0. 0.
time (sec) N/A 0.018 0.06 0.066 1.862 0.531 0. 0.
Problem 250 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 94 93 142 510 0 316
normalized size 1 1. 3.24 3.21 4.9 17.59 0. 10.9
time (sec) N/A 0.021 0.051 0.079 1.182 0.519 0. 1.16
Problem 251 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 112 145 828 856 0 846
normalized size 1 1. 2.43 3.15 18. 18.61 0. 18.39
time (sec) N/A 0.041 0.099 0.095 1.329 0.544 0. 1.23
Problem 252 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 71 179 1693 1040 0 1300
normalized size 1 1. 0.97 2.45 23.19 14.25 0. 17.81
time (sec) N/A 0.077 0.336 0.104 1.341 0.56 0. 1.384
Problem 253 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 134 134 142 0 0 0 0 0
normalized size 1 1. 1.06 0. 0. 0. 0. 0.
time (sec) N/A 0.119 1.884 0.175 0. 0. 0. 0.
Problem 254 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 130 130 108 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.12 1.742 0.204 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 [201] had the largest ratio of [ 0.5882 ]

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 4 3 1. 18 0.167
2 A 4 3 1. 18 0.167
3 A 4 3 1. 18 0.167
4 A 4 3 1. 18 0.167
5 A 4 3 1. 18 0.167
6 A 4 3 1. 18 0.167
7 A 1 1 1. 16 0.062
8 A 2 2 1. 16 0.125
9 A 4 4 1. 18 0.222
10 A 5 5 1. 18 0.278
11 A 6 5 1. 18 0.278
12 A 7 5 1. 18 0.278
13 A 5 4 1. 20 0.2
14 A 6 5 1. 20 0.25
15 A 4 3 1. 20 0.15
16 A 5 5 1. 20 0.25
17 A 3 3 1. 18 0.167
18 A 2 2 1. 18 0.111
19 A 3 3 1. 20 0.15
20 A 4 3 1. 20 0.15
21 A 4 3 1. 20 0.15
22 A 5 4 1. 20 0.2
23 A 4 3 1. 20 0.15
24 A 4 3 1. 20 0.15
25 A 4 3 1. 20 0.15
26 A 4 3 1. 20 0.15
27 A 3 3 1. 18 0.167
28 A 4 4 1. 18 0.222
29 A 3 3 1. 20 0.15
30 A 3 3 1. 20 0.15
31 A 5 4 1. 20 0.2
32 A 6 5 1. 20 0.25
33 A 4 3 1. 18 0.167
34 A 4 3 1. 18 0.167
35 A 4 3 1. 18 0.167
36 A 4 3 1. 18 0.167
37 A 4 3 1. 18 0.167
38 A 4 3 1. 18 0.167
39 A 3 3 1. 18 0.167
40 A 2 2 1. 16 0.125
41 A 4 4 1. 16 0.25
42 A 5 5 1. 18 0.278
43 A 6 5 1. 18 0.278
44 A 7 5 1. 18 0.278
45 A 9 4 1. 20 0.2
46 A 5 4 1. 20 0.2
47 A 7 4 1. 20 0.2
48 A 4 3 1. 20 0.15
49 A 5 4 1. 20 0.2
50 A 3 3 1. 20 0.15
51 A 3 3 1. 20 0.15
52 A 2 2 1. 18 0.111
53 A 4 3 1. 18 0.167
54 A 4 3 1. 20 0.15
55 A 5 4 1. 20 0.2
56 A 4 3 1. 20 0.15
57 A 5 4 1. 20 0.2
58 A 4 3 1. 20 0.15
59 A 4 3 1. 20 0.15
60 A 4 3 1. 20 0.15
61 A 4 3 1. 20 0.15
62 A 4 3 1. 20 0.15
63 A 4 3 1. 20 0.15
64 A 4 3 1. 20 0.15
65 A 3 3 1. 20 0.15
66 A 3 2 1. 20 0.1
67 A 4 4 1. 20 0.2
68 A 3 3 1. 18 0.167
69 A 5 4 1. 18 0.222
70 A 6 5 1. 20 0.25
71 A 6 5 1. 20 0.25
72 A 8 5 1. 20 0.25
73 A 4 3 1. 20 0.15
74 A 3 3 1. 20 0.15
75 A 2 2 1. 20 0.1
76 A 1 1 1. 20 0.05
77 A 1 1 1. 20 0.05
78 A 2 2 1. 20 0.1
79 A 3 3 1. 20 0.15
80 A 4 3 1. 20 0.15
81 A 4 3 1. 22 0.136
82 A 3 3 1. 22 0.136
83 A 3 3 1. 22 0.136
84 A 2 2 1. 22 0.091
85 A 2 2 1. 22 0.091
86 A 2 2 1. 22 0.091
87 A 2 2 1. 22 0.091
88 A 3 3 1. 22 0.136
89 A 4 4 1. 22 0.182
90 A 3 3 1. 22 0.136
91 A 2 2 1. 22 0.091
92 A 3 3 1. 22 0.136
93 A 1 1 1. 22 0.045
94 A 2 2 1. 22 0.091
95 A 3 3 1. 22 0.136
96 A 4 4 1. 22 0.182
97 A 5 4 1. 20 0.2
98 A 4 4 1. 20 0.2
99 A 3 3 1. 20 0.15
100 A 2 2 1. 20 0.1
101 A 1 1 1. 20 0.05
102 A 3 3 1. 20 0.15
103 A 4 4 1. 20 0.2
104 A 5 4 1. 20 0.2
105 A 4 3 1. 22 0.136
106 A 4 3 1. 22 0.136
107 A 3 3 1. 22 0.136
108 A 3 3 1. 22 0.136
109 A 2 2 1. 22 0.091
110 A 2 2 1. 22 0.091
111 A 3 3 1. 22 0.136
112 A 3 3 1. 22 0.136
113 A 4 3 1. 22 0.136
114 A 4 3 1. 22 0.136
115 A 7 5 1. 22 0.227
116 A 6 5 1. 22 0.227
117 A 5 5 1. 22 0.227
118 A 4 4 1. 22 0.182
119 A 1 1 1. 22 0.045
120 A 2 2 1. 22 0.091
121 A 4 4 1. 22 0.182
122 A 5 5 1. 22 0.227
123 A 2 2 1. 20 0.1
124 A 2 2 1. 20 0.1
125 A 2 2 1. 18 0.111
126 A 2 2 1. 18 0.111
127 A 2 2 1. 20 0.1
128 A 2 2 1. 20 0.1
129 A 4 3 1. 18 0.167
130 A 4 3 1. 18 0.167
131 A 4 3 1. 18 0.167
132 A 4 3 1. 18 0.167
133 A 4 3 1. 18 0.167
134 A 4 3 1. 18 0.167
135 A 1 1 1. 16 0.062
136 A 2 2 1. 16 0.125
137 A 4 4 1. 18 0.222
138 A 5 5 1. 18 0.278
139 A 6 5 1. 18 0.278
140 A 7 5 1. 18 0.278
141 A 5 4 1. 20 0.2
142 A 6 5 1. 20 0.25
143 A 4 3 1. 20 0.15
144 A 5 5 1. 20 0.25
145 A 3 3 1. 18 0.167
146 A 2 2 1. 18 0.111
147 A 3 3 1. 20 0.15
148 A 4 3 1. 20 0.15
149 A 4 3 1. 20 0.15
150 A 5 4 1. 20 0.2
151 A 4 3 1. 20 0.15
152 A 4 3 1. 20 0.15
153 A 4 3 1. 20 0.15
154 A 4 3 1. 20 0.15
155 A 3 3 1. 18 0.167
156 A 4 4 1. 18 0.222
157 A 3 3 1. 20 0.15
158 A 3 3 1. 20 0.15
159 A 5 4 1. 20 0.2
160 A 6 5 1. 20 0.25
161 A 4 3 1. 20 0.15
162 A 3 3 1. 20 0.15
163 A 2 2 1. 20 0.1
164 A 1 1 1. 20 0.05
165 A 1 1 1. 20 0.05
166 A 2 2 1. 20 0.1
167 A 3 3 1. 20 0.15
168 A 4 3 1. 20 0.15
169 A 4 3 1. 22 0.136
170 A 3 3 1. 22 0.136
171 A 3 3 1. 22 0.136
172 A 2 2 1. 22 0.091
173 A 2 2 1. 22 0.091
174 A 2 2 1. 22 0.091
175 A 2 2 1. 22 0.091
176 A 3 3 1. 22 0.136
177 A 4 4 1. 22 0.182
178 A 3 3 1. 22 0.136
179 A 2 2 1. 22 0.091
180 A 3 3 1. 22 0.136
181 A 1 1 1. 22 0.045
182 A 2 2 1. 22 0.091
183 A 3 3 1. 22 0.136
184 A 4 4 1. 22 0.182
185 A 1 1 1. 11 0.091
186 A 2 2 1. 11 0.182
187 A 2 2 1. 20 0.1
188 A 2 2 1. 20 0.1
189 A 2 2 1. 18 0.111
190 A 4 3 1. 28 0.107
191 A 10 5 1. 15 0.333
192 A 6 2 1. 15 0.133
193 A 5 2 1. 15 0.133
194 A 4 2 1. 13 0.154
195 A 3 3 1. 13 0.231
196 A 4 4 1. 15 0.267
197 A 5 5 1. 15 0.333
198 A 5 5 1. 15 0.333
199 A 5 4 1. 15 0.267
200 A 6 5 1. 15 0.333
201 A 15 10 1. 17 0.588
202 A 5 2 1. 15 0.133
203 A 6 2 1. 17 0.118
204 A 8 2 1. 17 0.118
205 A 18 5 1. 17 0.294
206 A 6 2 1. 15 0.133
207 A 8 2 1. 17 0.118
208 A 10 2 1. 17 0.118
209 A 8 4 1. 15 0.267
210 A 6 2 1. 15 0.133
211 A 5 2 1. 15 0.133
212 A 4 2 1. 13 0.154
213 A 3 3 1. 13 0.231
214 A 4 4 1. 15 0.267
215 A 5 5 1. 15 0.333
216 A 5 5 1. 15 0.333
217 A 5 4 1. 15 0.267
218 A 6 5 1. 15 0.333
219 A 11 7 1. 17 0.412
220 A 5 2 1. 15 0.133
221 A 6 2 1. 17 0.118
222 A 8 2 1. 17 0.118
223 A 14 4 1. 17 0.235
224 A 6 2 1. 15 0.133
225 A 8 2 1. 17 0.118
226 A 10 2 1. 17 0.118
227 A 3 3 1. 13 0.231
228 A 4 4 1. 15 0.267
229 A 5 5 1. 15 0.333
230 A 9 7 1. 15 0.467
231 A 6 6 1. 15 0.4
232 A 3 3 1. 13 0.231
233 A 3 3 1. 13 0.231
234 A 6 6 1. 15 0.4
235 A 9 7 1. 15 0.467
236 A 6 3 1. 13 0.231
237 A 6 3 1. 13 0.231
238 A 6 2 1. 15 0.133
239 A 5 2 1. 15 0.133
240 A 4 2 1. 13 0.154
241 A 3 3 1. 13 0.231
242 A 4 4 1. 15 0.267
243 A 5 5 1. 15 0.333
244 A 8 2 1. 17 0.118
245 A 6 2 1. 17 0.118
246 A 10 2 1. 17 0.118
247 A 9 7 1. 15 0.467
248 A 6 6 1. 15 0.4
249 A 3 3 1. 13 0.231
250 A 3 3 1. 13 0.231
251 A 6 6 1. 15 0.4
252 A 9 7 1. 15 0.467
253 A 6 3 1. 13 0.231
254 A 6 3 1. 13 0.231

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