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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, 255, 256, 257, 258, 259, 260, 261, 262, 263 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 30, 32, 33, 35, 38, 40, 41, 43, 46, 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, 74, 76, 77, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 96, 97, 99, 100, 102, 103, 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, 134, 135, 136, 137, 138, 139, 141, 143, 145, 147, 148, 149, 151, 152, 153, 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, 203, 204, 205, 206, 207, 208, 210, 212, 214, 216, 218, 219, 221, 222, 223, 225, 226, 227, 228, 229, 231, 233, 234, 235, 237, 240, 248, 255, 256, 257, 258, 259, 260, 261, 262, 263 }

B grade: { 104, 144, 146, 202, 213, 241 }

C grade: { 26, 28, 29, 31, 34, 36, 37, 39, 42, 44, 45, 47, 73, 75, 78, 80, 93, 95, 98, 101, 133, 140, 142, 150, 154, 209, 211, 215, 217, 220, 224, 230, 232, 236, 238, 239, 242, 243, 244, 245, 246, 247, 249, 250, 251, 252, 253, 254 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 16, 17, 19, 23, 24, 29, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 71, 74, 76, 77, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 139, 140, 141, 142, 143, 149, 150, 151, 152, 153, 154, 155, 161, 162, 163, 164, 165, 166, 167, 170, 171, 172, 173, 174, 180, 182, 184, 202, 203, 204, 205, 206, 207, 257, 258, 260, 261 }

B grade: { 10, 12, 18, 20, 21, 22, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 62, 70, 72, 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, 144, 145, 146, 147, 148, 156, 157, 158, 159, 160, 168, 169, 175, 176, 177, 178, 179, 181, 183, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 208, 209, 210, 211, 212, 213, 219, 220, 221, 222, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 238, 239, 240, 241, 242, 243, 246, 247, 248, 249, 250, 251, 252, 255, 256 }

C grade: { 73, 75, 78, 80, 259, 262, 263 }

F grade: { 214, 215, 216, 217, 218, 223, 224, 235, 236, 237, 244, 245, 253, 254 }

2.1.4 Maxima

A grade: { 5, 6, 49, 50, 51, 52, 53, 54, 66, 68, 74, 76, 77, 79, 81, 86, 94, 102, 138, 139, 140, 150, 172, 174, 176, 178, 202, 204, 206

B grade: { 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 69, 70, 71, 72, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99, 100, 101, 103, 104, 134, 135, 136, 137, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 180, 182, 184, 186, 188, 191, 193, 195, 197, 199, 207, 257, 258 }

C grade: { 203, 205 }

F grade: { 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 73, 75, 78, 80, 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, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 190, 192, 194, 196, 198, 200, 201, 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, 255, 256, 259, 260, 261, 262, 263 }

2.1.5 FriCAS

A grade: { 1, 3, 4, 81, 82, 83, 89, 138, 203, 205, 206, 207 }

B grade: { 2, 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, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 78, 84, 85, 86, 87, 88, 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, 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, 202, 204, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 224, 225, 227, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 247, 248, 249, 250, 251, 252, 254, 255, 257, 258, 260, 261, 262 }

C grade: { 75, 80, 226, 228, 256 }

F grade: { 41, 42, 47, 48, 65, 73, 74, 76, 77, 79, 200, 201, 220, 246, 253, 259, 263 }

2.1.6 Sympy

A grade: { 77, 79, 134, 135, 136, 137, 138, 144, 145, 146, 147, 148, 156, 157, 158, 159, 160, 168, 169, 170, 171, 172, 173, 174, 175, 181, 183, 185, 206, 208, 210, 212, 233, 242, 251, 257 }

B grade: { 140, 219, 221, 258 }

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, 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, 78, 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, 139, 141, 142, 143, 149, 150, 151, 152, 153, 154, 155, 161, 162, 163, 164, 165, 166, 167, 176, 177, 178, 179, 180, 182, 184, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 207, 209, 211, 213, 214, 215, 216, 217, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 241, 243, 244, 245, 246, 247, 248, 249, 250, 252, 253, 254, 255, 256, 259, 260, 261, 262, 263 }

2.1.7 Giac

A grade: { 5, 6, 8, 14, 23, 30, 49, 50, 51, 52, 53, 54, 58, 60, 61, 63, 66, 68, 73, 74, 75, 76, 77, 78, 79, 80, 81, 85, 93, 110, 112, 138, 139, 140, 153, 171, 173, 174, 175, 176, 177, 178, 202, 206, 257, 258 }

B grade: { 1, 2, 3, 4, 7, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 27, 32, 33, 35, 38, 40, 41, 43, 46, 48, 55, 56, 57, 59, 62, 64, 65, 67, 69, 70, 71, 72, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 114, 116, 119, 121, 123, 125, 128, 130, 132, 134, 135, 136, 137, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 204, 225, 227, 255 }

C grade: { 26, 28, 29, 31, 34, 36, 37, 39, 42, 44, 45, 47, 106, 108, 109, 111, 113, 115, 117, 118, 120, 122, 124, 126, 127, 129, 131, 133, 203, 205, 207, 226, 228, 256 }

F grade: { 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 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, 259, 260, 261, 262, 263 }

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 B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 56 96 208 327 0 196
normalized size 1 1. 0.77 1.32 2.85 4.48 0. 2.68
time (sec) N/A 0.076 0.341 0.041 1.202 1.85 0. 1.323
Problem 2 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 47 47 73 73 184 246 0 162
normalized size 1 1. 1.55 1.55 3.91 5.23 0. 3.45
time (sec) N/A 0.055 0.05 0.034 1.152 1.999 0. 1.302
Problem 3 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 44 44 41 66 136 193 0 147
normalized size 1 1. 0.93 1.5 3.09 4.39 0. 3.34
time (sec) N/A 0.051 0.189 0.033 1.126 1.959 0. 1.27
Problem 4 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 25 25 45 43 90 115 0 107
normalized size 1 1. 1.8 1.72 3.6 4.6 0. 4.28
time (sec) N/A 0.032 0.045 0.033 1.108 1.905 0. 1.206
Problem 5 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 26 26 52 44 54 483 0 70
normalized size 1 1. 2. 1.69 2.08 18.58 0. 2.69
time (sec) N/A 0.033 0.027 0.037 1.08 2.084 0. 1.33
Problem 6 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 24 24 24 23 53 238 0 61
normalized size 1 1. 1. 0.96 2.21 9.92 0. 2.54
time (sec) N/A 0.033 0.02 0.036 1.141 1.886 0. 1.264
Problem 7 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 51 51 87 50 205 2480 0 153
normalized size 1 1. 1.71 0.98 4.02 48.63 0. 3.
time (sec) N/A 0.059 0.046 0.044 1.101 2.219 0. 1.208
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 61 55 153 657 0 108
normalized size 1 1. 1.39 1.25 3.48 14.93 0. 2.45
time (sec) N/A 0.043 0.068 0.046 1.164 2.04 0. 1.215
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 118 118 94 166 398 1021 0 398
normalized size 1 1. 0.8 1.41 3.37 8.65 0. 3.37
time (sec) N/A 0.133 1.374 0.049 1.118 2.068 0. 1.726
Problem 10 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 77 77 71 162 358 664 0 392
normalized size 1 1. 0.92 2.1 4.65 8.62 0. 5.09
time (sec) N/A 0.098 0.517 0.052 1.192 2.055 0. 1.646
Problem 11 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 79 79 70 118 293 747 0 290
normalized size 1 1. 0.89 1.49 3.71 9.46 0. 3.67
time (sec) N/A 0.111 0.85 0.05 1.243 2.059 0. 1.465
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 46 113 231 424 0 219
normalized size 1 1. 0.94 2.31 4.71 8.65 0. 4.47
time (sec) N/A 0.053 0.308 0.046 1.137 2.058 0. 1.371
Problem 13 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 51 51 50 97 265 2331 0 170
normalized size 1 1. 0.98 1.9 5.2 45.71 0. 3.33
time (sec) N/A 0.065 0.155 0.05 1.042 2.003 0. 1.335
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 43 68 184 683 0 116
normalized size 1 1. 0.93 1.48 4. 14.85 0. 2.52
time (sec) N/A 0.057 0.449 0.048 1.054 1.859 0. 1.35
Problem 15 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 82 82 96 103 244 6384 0 227
normalized size 1 1. 1.17 1.26 2.98 77.85 0. 2.77
time (sec) N/A 0.119 1.54 0.062 1.057 2.32 0. 1.373
Problem 16 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 72 72 59 81 284 1011 0 193
normalized size 1 1. 0.82 1.12 3.94 14.04 0. 2.68
time (sec) N/A 0.079 0.48 0.059 1.051 1.932 0. 1.417
Problem 17 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 182 182 125 246 648 2273 0 684
normalized size 1 1. 0.69 1.35 3.56 12.49 0. 3.76
time (sec) N/A 0.222 3.978 0.053 1.077 2.075 0. 2.748
Problem 18 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 105 105 91 287 593 1388 0 597
normalized size 1 1. 0.87 2.73 5.65 13.22 0. 5.69
time (sec) N/A 0.123 0.291 0.052 1.101 1.967 0. 2.437
Problem 19 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 122 139 95 180 509 1854 0 533
normalized size 1 1.14 0.78 1.48 4.17 15.2 0. 4.37
time (sec) N/A 0.185 2.159 0.053 1.1 2.102 0. 2.176
Problem 20 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 70 70 63 219 433 959 0 435
normalized size 1 1. 0.9 3.13 6.19 13.7 0. 6.21
time (sec) N/A 0.068 0.829 0.049 1.092 1.984 0. 1.774
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 79 186 756 5895 0 354
normalized size 1 1. 0.94 2.21 9. 70.18 0. 4.21
time (sec) N/A 0.084 0.302 0.052 1.05 2.251 0. 1.643
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 70 141 470 1449 0 273
normalized size 1 1. 1.09 2.2 7.34 22.64 0. 4.27
time (sec) N/A 0.064 0.679 0.053 1.113 1.875 0. 1.713
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 152 152 127 174 544 12984 0 379
normalized size 1 1. 0.84 1.14 3.58 85.42 0. 2.49
time (sec) N/A 0.225 6.175 0.063 1.093 2.476 0. 1.77
Problem 24 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 98 98 87 136 666 2385 0 347
normalized size 1 1. 0.89 1.39 6.8 24.34 0. 3.54
time (sec) N/A 0.097 1.218 0.058 1.158 2.14 0. 1.783
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 93 865 0 5158 0 406
normalized size 1 1. 0.79 7.33 0. 43.71 0. 3.44
time (sec) N/A 0.172 0.254 0.108 0. 2.314 0. 2.395
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 135 202 0 3729 0 5603
normalized size 1 1. 1.8 2.69 0. 49.72 0. 74.71
time (sec) N/A 0.128 0.539 0.069 0. 2.451 0. 1.888
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 67 605 0 2475 0 238
normalized size 1 1. 0.86 7.76 0. 31.73 0. 3.05
time (sec) N/A 0.104 0.142 0.076 0. 2.441 0. 1.658
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 107 104 0 1906 0 6017
normalized size 1 1. 2.02 1.96 0. 35.96 0. 113.53
time (sec) N/A 0.063 0.242 0.055 0. 2.201 0. 1.559
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 123 69 0 1673 0 5242
normalized size 1 1. 2.24 1.25 0. 30.42 0. 95.31
time (sec) N/A 0.078 0.199 0.063 0. 2.395 0. 1.526
Problem 30 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 48 48 48 413 0 1636 0 93
normalized size 1 1. 1. 8.6 0. 34.08 0. 1.94
time (sec) N/A 0.063 0.115 0.076 0. 2.204 0. 1.42
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 170 181 0 4872 0 7173
normalized size 1 1. 2. 2.13 0. 57.32 0. 84.39
time (sec) N/A 0.119 0.638 0.077 0. 2.651 0. 1.822
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 71 750 0 4307 0 178
normalized size 1 1. 1.01 10.71 0. 61.53 0. 2.54
time (sec) N/A 0.088 0.289 0.089 0. 2.386 0. 1.419
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 192 192 132 1246 0 17565 0 709
normalized size 1 1. 0.69 6.49 0. 91.48 0. 3.69
time (sec) N/A 0.252 0.933 0.119 0. 3.304 0. 3.392
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 160 267 0 12417 0 8694
normalized size 1 1. 1.29 2.15 0. 100.14 0. 70.11
time (sec) N/A 0.218 1.22 0.095 0. 3.063 0. 2.472
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 105 1128 0 9441 0 540
normalized size 1 1. 0.8 8.55 0. 71.52 0. 4.09
time (sec) N/A 0.165 0.65 0.099 0. 2.677 0. 2.253
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 133 167 0 5933 0 6742
normalized size 1 1. 1.45 1.82 0. 64.49 0. 73.28
time (sec) N/A 0.075 0.684 0.079 0. 2.585 0. 1.698
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 175 331 0 6604 0 7329
normalized size 1 1. 1.7 3.21 0. 64.12 0. 71.16
time (sec) N/A 0.144 0.663 0.092 0. 3.284 0. 1.704
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 86 552 0 6218 0 306
normalized size 1 1. 1.05 6.73 0. 75.83 0. 3.73
time (sec) N/A 0.076 0.42 0.102 0. 2.409 0. 1.653
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 203 367 0 15776 0 5650
normalized size 1 1. 1.44 2.6 0. 111.89 0. 40.07
time (sec) N/A 0.209 4.089 0.108 0. 3.304 0. 1.973
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 114 1012 0 12585 0 298
normalized size 1 1. 1.01 8.96 0. 111.37 0. 2.64
time (sec) N/A 0.154 0.775 0.119 0. 2.786 0. 1.61
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 240 240 184 2366 0 0 0 1246
normalized size 1 1. 0.77 9.86 0. 0. 0. 5.19
time (sec) N/A 0.345 0.763 0.128 0. 0. 0. 4.662
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F(-1) F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 166 166 227 341 0 0 0 8107
normalized size 1 1. 1.37 2.05 0. 0. 0. 48.84
time (sec) N/A 0.286 1.812 0.109 0. 0. 0. 3.143
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 185 185 158 2110 0 29831 0 788
normalized size 1 1. 0.85 11.41 0. 161.25 0. 4.26
time (sec) N/A 0.251 1.209 0.115 0. 3.844 0. 3.103
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 126 157 252 0 17194 0 8412
normalized size 1 1. 1.25 2. 0. 136.46 0. 66.76
time (sec) N/A 0.097 1.737 0.089 0. 3.084 0. 2.003
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 156 236 1132 0 25141 0 9281
normalized size 1 1. 1.51 7.26 0. 161.16 0. 59.49
time (sec) N/A 0.254 1.288 0.104 0. 4.358 0. 1.981
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 109 816 0 19301 0 474
normalized size 1 1. 0.97 7.29 0. 172.33 0. 4.23
time (sec) N/A 0.087 0.882 0.116 0. 3.142 0. 1.916
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 196 196 269 1083 0 0 0 8479
normalized size 1 1. 1.37 5.53 0. 0. 0. 43.26
time (sec) N/A 0.334 4.095 0.118 0. 0. 0. 2.445
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 149 1416 0 0 0 549
normalized size 1 1. 0.99 9.38 0. 0. 0. 3.64
time (sec) N/A 0.201 1.244 0.135 0. 0. 0. 1.918
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 92 122 262 4209 0 278
normalized size 1 1. 0.7 0.92 1.98 31.89 0. 2.11
time (sec) N/A 0.172 0.19 0.047 1.608 2.49 0. 1.374
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 104 129 235 2942 0 192
normalized size 1 1. 1.06 1.32 2.4 30.02 0. 1.96
time (sec) N/A 0.12 0.257 0.043 1.541 2.334 0. 1.3
Problem 51 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 100 100 69 79 190 2453 0 192
normalized size 1 1. 0.69 0.79 1.9 24.53 0. 1.92
time (sec) N/A 0.117 0.107 0.041 1.584 2.351 0. 1.266
Problem 52 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 63 63 72 85 142 1473 0 128
normalized size 1 1. 1.14 1.35 2.25 23.38 0. 2.03
time (sec) N/A 0.076 0.121 0.04 1.611 2.361 0. 1.217
Problem 53 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 49 49 75 65 112 1453 0 100
normalized size 1 1. 1.53 1.33 2.29 29.65 0. 2.04
time (sec) N/A 0.074 0.031 0.049 1.516 2.634 0. 1.217
Problem 54 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 29 29 29 34 59 375 0 61
normalized size 1 1. 1. 1.17 2.03 12.93 0. 2.1
time (sec) N/A 0.034 0.025 0.05 1.043 2.445 0. 1.212
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 71 71 95 62 211 3216 0 193
normalized size 1 1. 1.34 0.87 2.97 45.3 0. 2.72
time (sec) N/A 0.09 0.026 0.059 1.531 2.795 0. 1.222
Problem 56 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 56 56 74 60 248 4702 0 201
normalized size 1 1. 1.32 1.07 4.43 83.96 0. 3.59
time (sec) N/A 0.058 0.197 0.061 1.577 2.454 0. 1.236
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 170 206 156 243 512 13666 0 508
normalized size 1 1.21 0.92 1.43 3.01 80.39 0. 2.99
time (sec) N/A 0.297 2.809 0.058 1.586 2.942 0. 2.273
Problem 58 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 182 182 121 296 470 9211 0 405
normalized size 1 1. 0.66 1.63 2.58 50.61 0. 2.23
time (sec) N/A 0.225 0.72 0.058 1.555 2.777 0. 2.041
Problem 59 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 129 159 137 173 406 9671 0 402
normalized size 1 1.23 1.06 1.34 3.15 74.97 0. 3.12
time (sec) N/A 0.205 1.55 0.056 1.578 2.871 0. 1.836
Problem 60 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 123 123 90 225 342 5998 0 289
normalized size 1 1. 0.73 1.83 2.78 48.76 0. 2.35
time (sec) N/A 0.147 0.393 0.054 1.584 2.512 0. 1.617
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 106 180 603 6643 0 240
normalized size 1 1. 1.08 1.84 6.15 67.79 0. 2.45
time (sec) N/A 0.136 0.157 0.072 1.535 2.673 0. 1.511
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 94 105 346 1334 0 165
normalized size 1 1. 2. 2.23 7.36 28.38 0. 3.51
time (sec) N/A 0.058 0.221 0.067 1.055 2.178 0. 1.613
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 138 154 510 12523 0 259
normalized size 1 1. 1.29 1.44 4.77 117.04 0. 2.42
time (sec) N/A 0.16 0.151 0.085 1.561 2.992 0. 1.593
Problem 64 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 97 97 147 146 632 11420 0 336
normalized size 1 1. 1.52 1.51 6.52 117.73 0. 3.46
time (sec) N/A 0.098 0.186 0.083 1.582 2.815 0. 1.693
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 275 306 294 385 873 0 0 956
normalized size 1 1.11 1.07 1.4 3.17 0. 0. 3.48
time (sec) N/A 0.494 6.239 0.076 1.807 0. 0. 4.874
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 351 351 291 554 815 23883 0 811
normalized size 1 1. 0.83 1.58 2.32 68.04 0. 2.31
time (sec) N/A 0.35 6.545 0.13 1.787 3.607 0. 3.952
Problem 67 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 220 241 244 289 734 25608 0 799
normalized size 1 1.1 1.11 1.31 3.34 116.4 0. 3.63
time (sec) N/A 0.315 6.22 0.073 1.751 4.052 0. 3.473
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 269 269 233 458 653 17484 0 655
normalized size 1 1. 0.87 1.7 2.43 65. 0. 2.43
time (sec) N/A 0.249 6.289 0.067 1.747 3.985 0. 2.633
Problem 69 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 219 219 154 387 883 19499 0 570
normalized size 1 1. 0.7 1.77 4.03 89.04 0. 2.6
time (sec) N/A 0.264 2.886 0.096 1.72 3.6 0. 2.286
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 113 223 917 3071 0 420
normalized size 1 1. 1.59 3.14 12.92 43.25 0. 5.92
time (sec) N/A 0.065 0.687 0.086 1.195 2.234 0. 2.492
Problem 71 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 232 232 243 334 791 30318 0 586
normalized size 1 1. 1.05 1.44 3.41 130.68 0. 2.53
time (sec) N/A 0.316 6.316 0.099 1.778 3.905 0. 2.564
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 213 275 1346 25978 0 590
normalized size 1 1. 1.54 1.99 9.75 188.25 0. 4.28
time (sec) N/A 0.115 0.169 0.106 1.81 3.63 0. 2.877
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 491 491 645 603 0 0 0 489
normalized size 1 1. 1.31 1.23 0. 0. 0. 1.
time (sec) N/A 0.892 4.377 0.128 0. 0. 0. 2.33
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) F(-1) A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 32 0 826 346 0 0 0 473
normalized size 1 0. 25.81 10.81 0. 0. 0. 14.78
time (sec) N/A 0.046 0.484 0.11 0. 0. 0. 2.058
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F C F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 384 384 423 356 0 22579 0 301
normalized size 1 1. 1.1 0.93 0. 58.8 0. 0.78
time (sec) N/A 0.629 3.391 0.109 0. 16.062 0. 1.784
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) F(-1) A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 30 0 409 164 0 0 0 263
normalized size 1 0. 13.63 5.47 0. 0. 0. 8.77
time (sec) N/A 0.028 0.226 0.108 0. 0. 0. 1.621
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) A A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 30 0 319 98 0 0 0 207
normalized size 1 0. 10.63 3.27 0. 0. 0. 6.9
time (sec) N/A 0.041 0.158 0.105 0. 0. 0. 1.453
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 157 157 190 121 0 1801 0 28
normalized size 1 1. 1.21 0.77 0. 11.47 0. 0.18
time (sec) N/A 0.14 0.135 0.112 0. 2.665 0. 1.33
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) A A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 32 0 201 144 0 0 0 0
normalized size 1 0. 6.28 4.5 0. 0. 0. 0.
time (sec) N/A 0.047 0.362 0.125 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F C F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 215 215 322 187 0 4415 0 243
normalized size 1 1. 1.5 0.87 0. 20.53 0. 1.13
time (sec) N/A 0.239 3.157 0.131 0. 17.102 0. 1.423
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 63 63 44 82 140 169 0 144
normalized size 1 1. 0.7 1.3 2.22 2.68 0. 2.29
time (sec) N/A 0.05 0.163 0.039 1.144 1.825 0. 1.279
Problem 82 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 30 30 44 53 112 119 0 127
normalized size 1 1. 1.47 1.77 3.73 3.97 0. 4.23
time (sec) N/A 0.036 0.016 0.036 1.097 1.813 0. 1.246
Problem 83 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 33 33 32 54 93 80 0 109
normalized size 1 1. 0.97 1.64 2.82 2.42 0. 3.3
time (sec) N/A 0.039 0.057 0.033 1.11 1.861 0. 1.219
Problem 84 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 27 27 47 37 74 296 0 76
normalized size 1 1. 1.74 1.37 2.74 10.96 0. 2.81
time (sec) N/A 0.032 0.029 0.034 1.61 1.865 0. 1.265
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 48 65 108 883 0 85
normalized size 1 1. 1.2 1.62 2.7 22.08 0. 2.12
time (sec) N/A 0.031 0.023 0.026 1.65 1.96 0. 1.211
Problem 86 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 28 28 28 53 46 424 0 80
normalized size 1 1. 1. 1.89 1.64 15.14 0. 2.86
time (sec) N/A 0.029 0.011 0.036 1.133 1.818 0. 1.189
Problem 87 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 66 66 93 103 244 2826 0 178
normalized size 1 1. 1.41 1.56 3.7 42.82 0. 2.7
time (sec) N/A 0.046 0.029 0.044 1.616 2.012 0. 1.226
Problem 88 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 48 48 86 75 501 934 0 128
normalized size 1 1. 1.79 1.56 10.44 19.46 0. 2.67
time (sec) N/A 0.04 0.048 0.044 1.108 1.92 0. 1.343
Problem 89 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 85 85 63 124 231 234 0 255
normalized size 1 1. 0.74 1.46 2.72 2.75 0. 3.
time (sec) N/A 0.087 0.293 0.04 1.035 1.96 0. 1.933
Problem 90 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 54 54 71 117 217 1314 0 221
normalized size 1 1. 1.31 2.17 4.02 24.33 0. 4.09
time (sec) N/A 0.06 0.443 0.043 1.674 1.926 0. 1.791
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 54 96 189 261 0 230
normalized size 1 1. 1.06 1.88 3.71 5.12 0. 4.51
time (sec) N/A 0.076 0.371 0.04 1.205 2.008 0. 1.689
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 54 122 205 1967 0 185
normalized size 1 1. 0.9 2.03 3.42 32.78 0. 3.08
time (sec) N/A 0.082 0.179 0.043 1.749 1.993 0. 1.666
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B B F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 91 91 427 173 269 3433 0 212
normalized size 1 1. 4.69 1.9 2.96 37.73 0. 2.33
time (sec) N/A 0.085 7.22 0.036 1.615 2.191 0. 1.396
Problem 94 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 49 49 49 126 72 1023 0 228
normalized size 1 1. 1. 2.57 1.47 20.88 0. 4.65
time (sec) N/A 0.053 0.18 0.052 1.165 1.862 0. 1.411
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B B F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 125 125 792 236 466 7337 0 393
normalized size 1 1. 6.34 1.89 3.73 58.7 0. 3.14
time (sec) N/A 0.152 8.641 0.056 1.72 2.294 0. 1.489
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 83 158 1253 1829 0 321
normalized size 1 1. 1.09 2.08 16.49 24.07 0. 4.22
time (sec) N/A 0.07 0.515 0.057 1.211 1.904 0. 1.456
Problem 97 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 91 91 81 184 360 539 0 385
normalized size 1 1. 0.89 2.02 3.96 5.92 0. 4.23
time (sec) N/A 0.13 0.668 0.042 1.167 2.04 0. 2.677
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 87 87 494 227 383 4523 0 377
normalized size 1 1. 5.68 2.61 4.4 51.99 0. 4.33
time (sec) N/A 0.105 6.901 0.044 1.665 2.207 0. 2.42
Problem 99 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 78 78 69 148 346 903 0 360
normalized size 1 1. 0.88 1.9 4.44 11.58 0. 4.62
time (sec) N/A 0.09 0.85 0.047 1.155 2.042 0. 2.061
Problem 100 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 99 99 89 257 398 5933 0 347
normalized size 1 1. 0.9 2.6 4.02 59.93 0. 3.51
time (sec) N/A 0.116 0.363 0.048 1.701 2.189 0. 1.832
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B B F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 149 149 1341 334 489 8768 0 433
normalized size 1 1. 9. 2.24 3.28 58.85 0. 2.91
time (sec) N/A 0.154 17.289 0.041 1.687 2.322 0. 1.589
Problem 102 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 67 67 67 227 96 2034 0 468
normalized size 1 1. 1. 3.39 1.43 30.36 0. 6.99
time (sec) N/A 0.061 0.167 0.065 1.054 1.99 0. 1.705
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 198 198 158 421 747 16058 0 698
normalized size 1 1. 0.8 2.13 3.77 81.1 0. 3.53
time (sec) N/A 0.239 11.677 0.071 1.668 2.568 0. 1.704
Problem 104 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 102 102 218 269 2493 3218 0 603
normalized size 1 1. 2.14 2.64 24.44 31.55 0. 5.91
time (sec) N/A 0.089 0.826 0.124 1.172 2.014 0. 1.827
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 120 120 115 857 0 5515 0 440
normalized size 1 1. 0.96 7.14 0. 45.96 0. 3.67
time (sec) N/A 0.168 0.275 0.088 0. 2.574 0. 2.795
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 79 468 0 4604 0 6807
normalized size 1 1. 0.99 5.85 0. 57.55 0. 85.09
time (sec) N/A 0.109 0.396 0.087 0. 2.374 0. 2.115
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 77 608 0 2520 0 232
normalized size 1 1. 1. 7.9 0. 32.73 0. 3.01
time (sec) N/A 0.103 0.148 0.083 0. 2.285 0. 1.853
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 53 315 0 2040 0 6017
normalized size 1 1. 1. 5.94 0. 38.49 0. 113.53
time (sec) N/A 0.07 0.092 0.071 0. 2.462 0. 1.584
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 36 235 0 1385 0 6607
normalized size 1 1. 1. 6.53 0. 38.47 0. 183.53
time (sec) N/A 0.044 0.037 0.059 0. 2.398 0. 1.57
Problem 110 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 32 32 32 363 0 1199 0 59
normalized size 1 1. 1. 11.34 0. 37.47 0. 1.84
time (sec) N/A 0.056 0.053 0.07 0. 2.396 0. 1.401
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 55 494 0 1494 0 4938
normalized size 1 1. 1. 8.98 0. 27.16 0. 89.78
time (sec) N/A 0.073 0.195 0.073 0. 2.584 0. 1.793
Problem 112 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 50 50 50 648 0 1750 0 113
normalized size 1 1. 1. 12.96 0. 35. 0. 2.26
time (sec) N/A 0.07 0.133 0.068 0. 2.422 0. 1.38
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 79 836 0 4316 0 5747
normalized size 1 1. 0.92 9.72 0. 50.19 0. 66.83
time (sec) N/A 0.12 0.557 0.076 0. 2.825 0. 1.844
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 71 1077 0 5189 0 207
normalized size 1 1. 0.95 14.36 0. 69.19 0. 2.76
time (sec) N/A 0.092 0.341 0.078 0. 2.65 0. 1.449
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 128 128 111 875 0 16069 0 9686
normalized size 1 1. 0.87 6.84 0. 125.54 0. 75.67
time (sec) N/A 0.182 1.053 0.105 0. 3.215 0. 2.513
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 110 1146 0 10118 0 606
normalized size 1 1. 0.79 8.19 0. 72.27 0. 4.33
time (sec) N/A 0.194 0.748 0.107 0. 2.861 0. 2.307
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 84 729 0 8197 0 8317
normalized size 1 1. 0.83 7.22 0. 81.16 0. 82.35
time (sec) N/A 0.139 0.697 0.096 0. 2.532 0. 1.88
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 78 666 0 4917 0 6892
normalized size 1 1. 0.94 8.02 0. 59.24 0. 83.04
time (sec) N/A 0.071 0.275 0.082 0. 2.302 0. 1.681
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 63 498 0 3663 0 186
normalized size 1 1. 0.95 7.55 0. 55.5 0. 2.82
time (sec) N/A 0.066 0.239 0.096 0. 2.308 0. 1.618
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 69 375 0 4026 0 4585
normalized size 1 1. 0.96 5.21 0. 55.92 0. 63.68
time (sec) N/A 0.077 0.138 0.101 0. 2.274 0. 1.938
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 83 746 0 3452 0 211
normalized size 1 1. 1.08 9.69 0. 44.83 0. 2.74
time (sec) N/A 0.079 0.279 0.095 0. 2.221 0. 1.668
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 203 1007 0 5292 0 5392
normalized size 1 1. 1.99 9.87 0. 51.88 0. 52.86
time (sec) N/A 0.127 0.483 0.099 0. 2.587 0. 2.16
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 102 1283 0 6589 0 335
normalized size 1 1. 1.05 13.23 0. 67.93 0. 3.45
time (sec) N/A 0.129 0.585 0.092 0. 2.597 0. 1.665
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 265 1477 0 15050 0 6431
normalized size 1 1. 1.71 9.53 0. 97.1 0. 41.49
time (sec) N/A 0.249 1.303 0.102 0. 3.933 0. 2.158
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 198 198 164 2132 0 31513 0 803
normalized size 1 1. 0.83 10.77 0. 159.16 0. 4.06
time (sec) N/A 0.31 1.279 0.121 0. 4.53 0. 3.207
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 136 1570 0 25858 0 10338
normalized size 1 1. 0.88 10.19 0. 167.91 0. 67.13
time (sec) N/A 0.223 1.857 0.111 0. 3.783 0. 2.144
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 134 1676 0 18148 0 7417
normalized size 1 1. 0.93 11.64 0. 126.03 0. 51.51
time (sec) N/A 0.141 0.943 0.086 0. 3.184 0. 1.896
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 77 764 0 13154 0 432
normalized size 1 1. 0.8 7.96 0. 137.02 0. 4.5
time (sec) N/A 0.075 0.748 0.108 0. 3.048 0. 1.917
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 129 129 123 1226 0 15408 0 7308
normalized size 1 1. 0.95 9.5 0. 119.44 0. 56.65
time (sec) N/A 0.12 0.742 0.12 0. 2.877 0. 2.428
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 115 1270 0 12604 0 448
normalized size 1 1. 1. 11.04 0. 109.6 0. 3.9
time (sec) N/A 0.097 0.963 0.111 0. 2.974 0. 1.916
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 88 634 0 12057 0 5954
normalized size 1 1. 0.85 6.1 0. 115.93 0. 57.25
time (sec) N/A 0.091 0.295 0.116 0. 2.782 0. 2.297
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 128 1776 0 11889 0 456
normalized size 1 1. 0.98 13.56 0. 90.76 0. 3.48
time (sec) N/A 0.124 0.894 0.114 0. 2.869 0. 1.938
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 156 317 1907 0 18573 0 6677
normalized size 1 1. 2.03 12.22 0. 119.06 0. 42.8
time (sec) N/A 0.228 3.171 0.112 0. 3.353 0. 2.466
Problem 134 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 54 54 97 128 269 938 82 181
normalized size 1 1. 1.8 2.37 4.98 17.37 1.52 3.35
time (sec) N/A 0.052 0.034 0.006 1.036 1.953 0.933 1.194
Problem 135 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 49 49 43 104 227 3336 88 130
normalized size 1 1. 0.88 2.12 4.63 68.08 1.8 2.65
time (sec) N/A 0.059 0.236 0.004 1.665 2.154 0.64 1.214
Problem 136 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 36 36 65 100 142 428 54 116
normalized size 1 1. 1.81 2.78 3.94 11.89 1.5 3.22
time (sec) N/A 0.04 0.025 0.005 1.138 1.83 0.381 1.166
Problem 137 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 31 31 41 76 103 1114 60 82
normalized size 1 1. 1.32 2.45 3.32 35.94 1.94 2.65
time (sec) N/A 0.032 0.023 0.004 1.698 1.9 0.32 1.165
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 28 47 42 96 20 46
normalized size 1 1. 1.47 2.47 2.21 5.05 1.05 2.42
time (sec) N/A 0.013 0.007 0.002 1.092 2.054 0.191 1.166
Problem 139 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 25 25 33 26 47 178 0 66
normalized size 1 1. 1.32 1.04 1.88 7.12 0. 2.64
time (sec) N/A 0.041 0.04 0.041 1.103 2.029 0. 1.176
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 32 28 42 97 49 43
normalized size 1 1. 1.78 1.56 2.33 5.39 2.72 2.39
time (sec) N/A 0.029 0.026 0.033 1.041 1.934 60.368 1.217
Problem 141 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 31 31 39 40 143 1114 0 84
normalized size 1 1. 1.26 1.29 4.61 35.94 0. 2.71
time (sec) N/A 0.042 0.104 0.046 1.079 2.106 0. 1.184
Problem 142 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 36 36 61 46 142 408 0 116
normalized size 1 1. 1.69 1.28 3.94 11.33 0. 3.22
time (sec) N/A 0.039 0.036 0.042 1.172 1.915 0. 1.198
Problem 143 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 49 49 51 68 278 3336 0 131
normalized size 1 1. 1.04 1.39 5.67 68.08 0. 2.67
time (sec) N/A 0.062 0.313 0.046 1.165 2.172 0. 1.201
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 190 236 498 2140 165 405
normalized size 1 1. 2.29 2.84 6. 25.78 1.99 4.88
time (sec) N/A 0.079 0.077 0.006 1.161 1.975 1.518 1.314
Problem 145 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 76 76 66 196 450 8982 170 262
normalized size 1 1. 0.87 2.58 5.92 118.18 2.24 3.45
time (sec) N/A 0.11 0.408 0.004 1.79 2.342 1.217 1.308
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 137 189 312 1245 117 294
normalized size 1 1. 2.17 3. 4.95 19.76 1.86 4.67
time (sec) N/A 0.076 0.048 0.005 1.163 2.092 0.92 1.248
Problem 147 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 57 57 50 149 251 4165 122 162
normalized size 1 1. 0.88 2.61 4.4 73.07 2.14 2.84
time (sec) N/A 0.073 0.307 0.004 1.723 2.166 0.704 1.268
Problem 148 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 43 43 65 144 154 509 68 139
normalized size 1 1. 1.51 3.35 3.58 11.84 1.58 3.23
time (sec) N/A 0.031 0.707 0.006 1.058 1.849 0.42 1.191
Problem 149 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 49 49 48 60 140 1715 0 198
normalized size 1 1. 0.98 1.22 2.86 35. 0. 4.04
time (sec) N/A 0.077 0.125 0.053 1.529 2.093 0. 1.265
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 64 49 86 243 0 99
normalized size 1 1. 1.78 1.36 2.39 6.75 0. 2.75
time (sec) N/A 0.067 0.096 0.043 1.074 1.901 0. 1.308
Problem 151 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 52 52 50 60 181 1715 0 198
normalized size 1 1. 0.96 1.15 3.48 32.98 0. 3.81
time (sec) N/A 0.095 0.153 0.058 1.018 2.036 0. 1.295
Problem 152 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 43 43 65 59 154 489 0 139
normalized size 1 1. 1.51 1.37 3.58 11.37 0. 3.23
time (sec) N/A 0.071 0.571 0.05 1.067 2.067 0. 1.274
Problem 153 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 72 72 58 91 319 4165 0 165
normalized size 1 1. 0.81 1.26 4.43 57.85 0. 2.29
time (sec) N/A 0.099 0.391 0.054 1.036 2.184 0. 1.315
Problem 154 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 63 63 98 87 312 1206 0 294
normalized size 1 1. 1.56 1.38 4.95 19.14 0. 4.67
time (sec) N/A 0.077 0.079 0.056 1.069 2.043 0. 1.289
Problem 155 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 92 92 74 138 527 8982 0 263
normalized size 1 1. 0.8 1.5 5.73 97.63 0. 2.86
time (sec) N/A 0.113 0.484 0.059 1.072 2.455 0. 1.307
Problem 156 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 114 114 123 365 787 4166 260 721
normalized size 1 1. 1.08 3.2 6.9 36.54 2.28 6.32
time (sec) N/A 0.101 1.432 0.007 1.151 2.19 2.827 1.453
Problem 157 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 107 107 98 307 729 19047 279 421
normalized size 1 1. 0.92 2.87 6.81 178.01 2.61 3.93
time (sec) N/A 0.152 0.289 0.007 1.592 3.118 2.4 1.464
Problem 158 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 94 94 108 299 540 2693 192 564
normalized size 1 1. 1.15 3.18 5.74 28.65 2.04 6.
time (sec) N/A 0.093 1.613 0.005 1.069 1.977 1.698 1.461
Problem 159 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 83 83 76 241 474 10689 211 296
normalized size 1 1. 0.92 2.9 5.71 128.78 2.54 3.57
time (sec) N/A 0.101 0.214 0.006 1.6 2.623 1.404 1.386
Problem 160 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 74 74 95 235 323 1412 126 325
normalized size 1 1. 1.28 3.18 4.36 19.08 1.7 4.39
time (sec) N/A 0.046 0.57 0.004 1.107 2.044 0.904 1.187
Problem 161 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 72 72 67 111 289 5854 0 366
normalized size 1 1. 0.93 1.54 4.01 81.31 0. 5.08
time (sec) N/A 0.098 0.518 0.055 1.706 2.221 0. 1.413
Problem 162 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 59 59 81 80 198 811 0 186
normalized size 1 1. 1.37 1.36 3.36 13.75 0. 3.15
time (sec) N/A 0.08 2.181 0.049 1.158 1.951 0. 1.428
Problem 163 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 72 72 63 94 274 4113 0 375
normalized size 1 1. 0.88 1.31 3.81 57.12 0. 5.21
time (sec) N/A 0.108 0.437 0.06 1.573 2.173 0. 1.421
Problem 164 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 59 59 82 80 198 811 0 186
normalized size 1 1. 1.39 1.36 3.36 13.75 0. 3.15
time (sec) N/A 0.081 1.187 0.05 1.074 2.006 0. 1.428
Problem 165 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 83 83 67 111 356 5854 0 366
normalized size 1 1. 0.81 1.34 4.29 70.53 0. 4.41
time (sec) N/A 0.117 0.555 0.062 1.076 2.37 0. 1.502
Problem 166 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 74 74 100 100 323 1372 0 325
normalized size 1 1. 1.35 1.35 4.36 18.54 0. 4.39
time (sec) N/A 0.089 1.672 0.065 1.07 2.101 0. 1.511
Problem 167 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 103 103 76 161 567 10689 0 297
normalized size 1 1. 0.74 1.56 5.5 103.78 0. 2.88
time (sec) N/A 0.129 0.238 0.062 1.074 2.878 0. 1.53
Problem 168 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 110 110 128 344 554 2954 209 603
normalized size 1 1. 1.16 3.13 5.04 26.85 1.9 5.48
time (sec) N/A 0.07 1.673 0.006 1.118 2.525 1.608 1.194
Problem 169 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 160 160 170 472 842 5516 308 973
normalized size 1 1. 1.06 2.95 5.26 34.48 1.92 6.08
time (sec) N/A 0.094 2.148 0.006 1.205 2.671 2.828 1.227
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 60 93 180 1817 425 190
normalized size 1 1. 0.91 1.41 2.73 27.53 6.44 2.88
time (sec) N/A 0.115 0.161 0.018 1.576 3.057 39.448 1.267
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 66 95 0 2043 495 126
normalized size 1 1. 1.12 1.61 0. 34.63 8.39 2.14
time (sec) N/A 0.108 0.172 0.02 0. 2.239 21.121 1.208
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 42 75 111 319 316 136
normalized size 1 1. 0.91 1.63 2.41 6.93 6.87 2.96
time (sec) N/A 0.104 0.034 0.017 1.548 2.435 18.753 1.212
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 47 77 0 1249 294 92
normalized size 1 1. 1.02 1.67 0. 27.15 6.39 2.
time (sec) N/A 0.083 0.029 0.016 0. 1.913 11.628 1.176
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 35 71 78 220 156 84
normalized size 1 1. 0.83 1.69 1.86 5.24 3.71 2.
time (sec) N/A 0.061 0.024 0.018 1.08 1.75 11.396 1.19
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 65 76 0 1249 280 90
normalized size 1 1. 1.44 1.69 0. 27.76 6.22 2.
time (sec) N/A 0.074 0.077 0.017 0. 1.959 11.581 1.161
Problem 176 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 60 60 54 121 136 319 0 138
normalized size 1 1. 0.9 2.02 2.27 5.32 0. 2.3
time (sec) N/A 0.101 0.054 0.076 1.091 2.057 0. 1.215
Problem 177 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 60 60 67 494 0 2043 0 127
normalized size 1 1. 1.12 8.23 0. 34.05 0. 2.12
time (sec) N/A 0.106 0.17 0.084 0. 1.88 0. 1.249
Problem 178 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 85 85 60 180 215 1817 0 190
normalized size 1 1. 0.71 2.12 2.53 21.38 0. 2.24
time (sec) N/A 0.137 0.164 0.086 1.081 2.487 0. 1.199
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 91 580 0 5846 0 203
normalized size 1 1. 1.11 7.07 0. 71.29 0. 2.48
time (sec) N/A 0.177 0.605 0.096 0. 2.219 0. 1.2
Problem 180 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 83 83 69 156 293 2678 0 275
normalized size 1 1. 0.83 1.88 3.53 32.27 0. 3.31
time (sec) N/A 0.15 0.474 0.027 1.638 2.616 0. 1.267
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 90 172 0 4703 2179 274
normalized size 1 1. 1.01 1.93 0. 52.84 24.48 3.08
time (sec) N/A 0.117 0.484 0.026 0. 2.101 101.773 1.213
Problem 182 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 72 72 57 118 230 1611 0 208
normalized size 1 1. 0.79 1.64 3.19 22.38 0. 2.89
time (sec) N/A 0.118 0.439 0.024 1.089 1.797 0. 1.233
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 86 162 0 4747 2144 251
normalized size 1 1. 1.01 1.91 0. 55.85 25.22 2.95
time (sec) N/A 0.108 0.376 0.023 0. 2.147 83.268 1.221
Problem 184 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 68 68 55 113 230 1611 0 208
normalized size 1 1. 0.81 1.66 3.38 23.69 0. 3.06
time (sec) N/A 0.086 0.371 0.027 1.092 1.956 0. 1.223
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 97 172 0 4703 2086 274
normalized size 1 1. 1.09 1.93 0. 52.84 23.44 3.08
time (sec) N/A 0.088 0.495 0.024 0. 2.092 151.002 1.19
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 83 325 317 2678 0 279
normalized size 1 1. 0.87 3.42 3.34 28.19 0. 2.94
time (sec) N/A 0.149 1.858 0.102 1.128 3.142 0. 1.218
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 111 1061 0 8676 0 464
normalized size 1 1. 0.93 8.92 0. 72.91 0. 3.9
time (sec) N/A 0.194 1.559 0.108 0. 2.731 0. 1.252
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 93 383 543 7919 0 450
normalized size 1 1. 0.75 3.09 4.38 63.86 0. 3.63
time (sec) N/A 0.189 0.8 0.113 1.165 4.111 0. 1.283
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 159 159 139 1137 0 19919 0 393
normalized size 1 1. 0.87 7.15 0. 125.28 0. 2.47
time (sec) N/A 0.283 1.327 0.122 0. 3.247 0. 1.269
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 144 352 0 17204 0 566
normalized size 1 1. 1. 2.44 0. 119.47 0. 3.93
time (sec) N/A 0.208 1.182 0.027 0. 3.475 0. 1.266
Problem 191 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 109 109 91 234 508 6044 0 339
normalized size 1 1. 0.83 2.15 4.66 55.45 0. 3.11
time (sec) N/A 0.17 0.984 0.027 1.241 2.45 0. 1.265
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 135 340 0 17383 0 533
normalized size 1 1. 0.99 2.48 0. 126.88 0. 3.89
time (sec) N/A 0.195 1.06 0.029 0. 3.193 0. 1.257
Problem 193 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 98 98 80 196 518 6130 0 339
normalized size 1 1. 0.82 2. 5.29 62.55 0. 3.46
time (sec) N/A 0.138 0.453 0.027 1.313 2.437 0. 1.268
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 137 340 0 17383 0 539
normalized size 1 1. 1. 2.48 0. 126.88 0. 3.93
time (sec) N/A 0.157 1.069 0.026 0. 3.33 0. 1.264
Problem 195 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 77 193 510 6044 0 339
normalized size 1 1. 0.82 2.05 5.43 64.3 0. 3.61
time (sec) N/A 0.105 0.514 0.029 1.37 2.547 0. 1.24
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 147 352 0 17204 0 567
normalized size 1 1. 1.04 2.48 0. 121.15 0. 3.99
time (sec) N/A 0.163 0.277 0.031 0. 3.367 0. 1.221
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 117 952 672 10714 0 417
normalized size 1 1. 0.85 6.9 4.87 77.64 0. 3.02
time (sec) N/A 0.205 1.569 0.117 1.308 5.282 0. 1.289
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 178 178 166 2045 0 27774 0 609
normalized size 1 1. 0.93 11.49 0. 156.03 0. 3.42
time (sec) N/A 0.291 5.76 0.125 0. 3.825 0. 1.334
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 171 171 138 1020 1040 24520 0 656
normalized size 1 1. 0.81 5.96 6.08 143.39 0. 3.84
time (sec) N/A 0.262 1.719 0.128 1.401 7.58 0. 1.412
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 228 228 194 2139 0 0 0 683
normalized size 1 1. 0.85 9.38 0. 0. 0. 3.
time (sec) N/A 0.368 3.418 0.14 0. 0. 0. 1.458
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 201 201 203 608 0 0 0 1030
normalized size 1 1. 1.01 3.02 0. 0. 0. 5.12
time (sec) N/A 0.277 0.547 0.034 0. 0. 0. 1.315
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 3 3 19 4 7 39 0 7
normalized size 1 1. 6.33 1.33 2.33 13. 0. 2.33
time (sec) N/A 0.017 0.008 0.033 1.687 2.161 0. 1.169
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 21 15 7 4 0 23
normalized size 1 1. 1.31 0.94 0.44 0.25 0. 1.44
time (sec) N/A 0.021 0.007 0.036 1.678 2.234 0. 1.203
Problem 204 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 22 22 29 21 38 504 0 61
normalized size 1 1. 1.32 0.95 1.73 22.91 0. 2.77
time (sec) N/A 0.02 0.018 0.03 1.682 2.147 0. 1.297
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 28 28 43 4 0 84
normalized size 1 1. 0.8 0.8 1.23 0.11 0. 2.4
time (sec) N/A 0.024 0.019 0.035 1.724 2.355 0. 1.207
Problem 206 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 11 11 11 14 15 12 12 15
normalized size 1 1. 1. 1.27 1.36 1.09 1.09 1.36
time (sec) N/A 0.021 0.007 0.01 1.54 2.222 0.593 1.139
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 12 34 4 0 15
normalized size 1 1. 1. 0.92 2.62 0.31 0. 1.15
time (sec) N/A 0.021 0.007 0.014 1.56 2.29 0. 1.185
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 85 288 0 12513 97 0
normalized size 1 1. 0.98 3.31 0. 143.83 1.11 0.
time (sec) N/A 0.161 0.466 0.071 0. 6.511 7.927 0.
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 580 337 0 25867 0 0
normalized size 1 1. 4.79 2.79 0. 213.78 0. 0.
time (sec) N/A 0.2 6.167 0.049 0. 7.357 0. 0.
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 60 253 0 6839 71 0
normalized size 1 1. 0.95 4.02 0. 108.56 1.13 0.
time (sec) N/A 0.119 0.161 0.045 0. 3.917 4.425 0.
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 193 276 0 14340 0 0
normalized size 1 1. 2.27 3.25 0. 168.71 0. 0.
time (sec) N/A 0.125 3.262 0.042 0. 4.622 0. 0.
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 44 238 0 4456 51 0
normalized size 1 1. 1. 5.41 0. 101.27 1.16 0.
time (sec) N/A 0.077 0.027 0.049 0. 2.857 2.281 0.
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 137 238 0 9993 0 0
normalized size 1 1. 2.28 3.97 0. 166.55 0. 0.
time (sec) N/A 0.047 0.213 0.046 0. 3.689 0. 0.
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 56 0 0 9991 0 0
normalized size 1 1. 1. 0. 0. 178.41 0. 0.
time (sec) N/A 0.112 0.028 0.168 0. 3.595 0. 0.
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 42 0 0 4456 0 0
normalized size 1 1. 0.88 0. 0. 92.83 0. 0.
time (sec) N/A 0.093 0.105 0.153 0. 2.885 0. 0.
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 83 0 0 14338 0 0
normalized size 1 1. 1. 0. 0. 172.75 0. 0.
time (sec) N/A 0.155 0.206 0.155 0. 4.447 0. 0.
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 235 0 0 6839 0 0
normalized size 1 1. 3.01 0. 0. 87.68 0. 0.
time (sec) N/A 0.146 8.836 0.152 0. 3.914 0. 0.
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 111 0 0 25865 0 0
normalized size 1 1. 0.92 0. 0. 213.76 0. 0.
time (sec) N/A 0.213 0.578 0.153 0. 8.328 0. 0.
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B B F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 86 593 0 13874 175 0
normalized size 1 1. 1.05 7.23 0. 169.2 2.13 0.
time (sec) N/A 0.152 0.412 0.027 0. 7.374 31.263 0.
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 584 633 0 0 0 0
normalized size 1 1. 4.75 5.15 0. 0. 0. 0.
time (sec) N/A 0.244 6.202 0.022 0. 0. 0. 0.
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B B F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 59 578 0 7218 128 0
normalized size 1 1. 0.94 9.17 0. 114.57 2.03 0.
time (sec) N/A 0.101 0.16 0.023 0. 3.241 16.326 0.
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 161 578 0 14453 0 0
normalized size 1 1. 1.83 6.57 0. 164.24 0. 0.
time (sec) N/A 0.085 0.338 0.023 0. 4.087 0. 0.
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 71 0 0 11954 0 0
normalized size 1 1. 1. 0. 0. 168.37 0. 0.
time (sec) N/A 0.136 0.06 0.116 0. 3.569 0. 0.
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 197 0 0 11507 0 0
normalized size 1 1. 2.56 0. 0. 149.44 0. 0.
time (sec) N/A 0.127 2.763 0.115 0. 3.639 0. 0.
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 51 97 0 2319 0 140
normalized size 1 1. 1.65 3.13 0. 74.81 0. 4.52
time (sec) N/A 0.027 0.058 0.059 0. 1.91 0. 1.216
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 53 142 0 710 0 136
normalized size 1 1. 1.18 3.16 0. 15.78 0. 3.02
time (sec) N/A 0.035 0.033 0.056 0. 1.878 0. 1.27
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 74 158 0 3526 0 273
normalized size 1 1. 1.48 3.16 0. 70.52 0. 5.46
time (sec) N/A 0.039 0.134 0.025 0. 2.044 0. 1.256
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 76 211 0 1103 0 273
normalized size 1 1. 1.13 3.15 0. 16.46 0. 4.07
time (sec) N/A 0.047 0.067 0.027 0. 1.841 0. 1.216
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 68 164 0 7692 0 0
normalized size 1 1. 0.97 2.34 0. 109.89 0. 0.
time (sec) N/A 0.136 0.482 0.053 0. 4.371 0. 0.
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 208 178 0 15340 0 0
normalized size 1 1. 2.36 2.02 0. 174.32 0. 0.
time (sec) N/A 0.123 4.434 0.048 0. 4.58 0. 0.
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 47 129 0 4629 0 0
normalized size 1 1. 1. 2.74 0. 98.49 0. 0.
time (sec) N/A 0.106 0.092 0.045 0. 2.686 0. 0.
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 101 137 0 9661 0 0
normalized size 1 1. 1.68 2.28 0. 161.02 0. 0.
time (sec) N/A 0.093 0.376 0.044 0. 3.38 0. 0.
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 29 114 0 3792 31 0
normalized size 1 1. 1. 3.93 0. 130.76 1.07 0.
time (sec) N/A 0.064 0.014 0.05 0. 2.146 1.035 0.
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 114 0 3568 0 0
normalized size 1 1. 1. 3.68 0. 115.1 0. 0.
time (sec) N/A 0.027 0.021 0.046 0. 2.23 0. 0.
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 56 0 0 10107 0 0
normalized size 1 1. 1. 0. 0. 180.48 0. 0.
time (sec) N/A 0.113 0.039 0.15 0. 3.477 0. 0.
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 51 51 123 0 0 4405 0 0
normalized size 1 1. 2.41 0. 0. 86.37 0. 0.
time (sec) N/A 0.095 5.579 0.151 0. 2.519 0. 0.
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 107 0 0 15786 0 0
normalized size 1 1. 1.22 0. 0. 179.39 0. 0.
time (sec) N/A 0.166 0.423 0.154 0. 4.626 0. 0.
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 67 322 0 9975 0 0
normalized size 1 1. 0.93 4.47 0. 138.54 0. 0.
time (sec) N/A 0.163 0.102 0.029 0. 5.041 0. 0.
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 188 328 0 18425 0 0
normalized size 1 1. 2.24 3.9 0. 219.35 0. 0.
time (sec) N/A 0.13 2.253 0.027 0. 5.325 0. 0.
Problem 240 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 52 287 0 6730 0 0
normalized size 1 1. 1. 5.52 0. 129.42 0. 0.
time (sec) N/A 0.123 0.119 0.023 0. 3.074 0. 0.
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 112 289 0 6395 0 0
normalized size 1 1. 2.11 5.45 0. 120.66 0. 0.
time (sec) N/A 0.099 1.456 0.021 0. 3.099 0. 0.
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 41 273 0 6395 51 0
normalized size 1 1. 0.84 5.57 0. 130.51 1.04 0.
time (sec) N/A 0.086 0.035 0.02 0. 2.989 12.259 0.
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 56 56 223 272 0 6730 0 0
normalized size 1 1. 3.98 4.86 0. 120.18 0. 0.
time (sec) N/A 0.043 4.215 0.026 0. 3.097 0. 0.
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 70 0 0 18423 0 0
normalized size 1 1. 0.9 0. 0. 236.19 0. 0.
time (sec) N/A 0.146 0.077 0.115 0. 5.605 0. 0.
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 230 0 0 9975 0 0
normalized size 1 1. 2.71 0. 0. 117.35 0. 0.
time (sec) N/A 0.161 7.811 0.121 0. 4.994 0. 0.
Problem 246 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 231 549 0 0 0 0
normalized size 1 1. 1.96 4.65 0. 0. 0. 0.
time (sec) N/A 0.22 1.862 0.032 0. 0. 0. 0.
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 68 469 0 16629 0 0
normalized size 1 1. 0.81 5.58 0. 197.96 0. 0.
time (sec) N/A 0.181 0.111 0.027 0. 9.055 0. 0.
Problem 248 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 132 491 0 14436 0 0
normalized size 1 1. 1.47 5.46 0. 160.4 0. 0.
time (sec) N/A 0.138 2.556 0.025 0. 8.557 0. 0.
Problem 249 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 63 435 0 15965 0 0
normalized size 1 1. 0.85 5.88 0. 215.74 0. 0.
time (sec) N/A 0.144 0.087 0.021 0. 8.759 0. 0.
Problem 250 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 88 88 193 454 0 15741 0 0
normalized size 1 1. 2.19 5.16 0. 178.88 0. 0.
time (sec) N/A 0.132 7.519 0.02 0. 8.763 0. 0.
Problem 251 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 43 420 0 14660 73 0
normalized size 1 1. 0.61 6. 0. 209.43 1.04 0.
time (sec) N/A 0.103 0.041 0.02 0. 8.4 20.681 0.
Problem 252 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 93 93 976 420 0 16405 0 0
normalized size 1 1. 10.49 4.52 0. 176.4 0. 0.
time (sec) N/A 0.085 7.488 0.024 0. 8.35 0. 0.
Problem 253 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 73 0 0 0 0 0
normalized size 1 1. 0.68 0. 0. 0. 0. 0.
time (sec) N/A 0.208 0.072 0.122 0. 0. 0. 0.
Problem 254 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 246 0 0 25307 0 0
normalized size 1 1. 1.88 0. 0. 193.18 0. 0.
time (sec) N/A 0.242 7.456 0.119 0. 18.786 0. 0.
Problem 255 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 35 62 0 1831 0 78
normalized size 1 1. 1.4 2.48 0. 73.24 0. 3.12
time (sec) N/A 0.019 0.025 0.047 0. 2.546 0. 1.308
Problem 256 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 37 66 0 551 0 96
normalized size 1 1. 1.37 2.44 0. 20.41 0. 3.56
time (sec) N/A 0.02 0.021 0.049 0. 2.325 0. 1.33
Problem 257 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 112 95 163 262 5516 100 196
normalized size 1 1.26 1.07 1.83 2.94 61.98 1.12 2.2
time (sec) N/A 0.075 0.673 0.006 1.522 2.676 0.773 1.348
Problem 258 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 40 41 99 340 102 34
normalized size 1 1. 1.05 1.08 2.61 8.95 2.68 0.89
time (sec) N/A 0.066 0.065 0.024 1.507 2.461 0.822 1.298
Problem 259 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 166 620 0 0 0 0
normalized size 1 1. 1.34 5. 0. 0. 0. 0.
time (sec) N/A 0.242 4.395 0.082 0. 0. 0. 0.
Problem 260 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 86 116 0 15323 0 0
normalized size 1 1. 0.97 1.3 0. 172.17 0. 0.
time (sec) N/A 0.128 0.057 0.052 0. 4.128 0. 0.
Problem 261 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 40 37 0 3553 0 0
normalized size 1 1. 1. 0.92 0. 88.82 0. 0.
time (sec) N/A 0.078 0.016 0.054 0. 4.294 0. 0.
Problem 262 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 73 431 0 10031 0 0
normalized size 1 1. 0.99 5.82 0. 135.55 0. 0.
time (sec) N/A 0.123 0.524 0.041 0. 5.86 0. 0.
Problem 263 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 113 637 0 0 0 0
normalized size 1 1. 0.96 5.4 0. 0. 0. 0.
time (sec) N/A 0.199 0.786 0.053 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 [258] had the largest ratio of [ 0.625 ]

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 5 5 1. 21 0.238
2 A 3 2 1. 21 0.095
3 A 4 4 1. 21 0.19
4 A 3 2 1. 19 0.105
5 A 3 3 1. 19 0.158
6 A 3 2 1. 21 0.095
7 A 4 4 1. 21 0.19
8 A 3 2 1. 21 0.095
9 A 6 5 1. 23 0.217
10 A 3 2 1. 23 0.087
11 A 5 5 1. 23 0.217
12 A 3 2 1. 21 0.095
13 A 4 3 1. 21 0.143
14 A 3 2 1. 23 0.087
15 A 5 5 1. 23 0.217
16 A 3 2 1. 23 0.087
17 A 6 5 1. 23 0.217
18 A 3 2 1. 23 0.087
19 A 6 5 1.14 23 0.217
20 A 3 2 1. 21 0.095
21 A 4 3 1. 21 0.143
22 A 3 2 1. 23 0.087
23 A 6 5 1. 23 0.217
24 A 3 2 1. 23 0.087
25 A 6 6 1. 23 0.261
26 A 4 4 1. 23 0.174
27 A 5 5 1. 23 0.217
28 A 3 3 1. 21 0.143
29 A 4 4 1. 21 0.19
30 A 3 3 1. 23 0.13
31 A 5 5 1. 23 0.217
32 A 4 4 1. 23 0.174
33 A 7 6 1. 23 0.261
34 A 5 4 1. 23 0.174
35 A 6 6 1. 23 0.261
36 A 4 4 1. 21 0.19
37 A 5 5 1. 21 0.238
38 A 4 4 1. 23 0.174
39 A 6 6 1. 23 0.261
40 A 5 4 1. 23 0.174
41 A 8 6 1. 23 0.261
42 A 6 5 1. 23 0.217
43 A 7 6 1. 23 0.261
44 A 5 4 1. 21 0.19
45 A 6 6 1. 21 0.286
46 A 5 4 1. 23 0.174
47 A 7 6 1. 23 0.261
48 A 6 5 1. 23 0.217
49 A 8 5 1. 21 0.238
50 A 9 6 1. 21 0.286
51 A 7 5 1. 21 0.238
52 A 7 6 1. 19 0.316
53 A 5 3 1. 19 0.158
54 A 3 2 1. 21 0.095
55 A 6 3 1. 21 0.143
56 A 3 2 1. 21 0.095
57 A 8 5 1.21 23 0.217
58 A 12 8 1. 23 0.348
59 A 7 5 1.23 23 0.217
60 A 10 8 1. 21 0.381
61 A 8 5 1. 21 0.238
62 A 3 2 1. 23 0.087
63 A 9 5 1. 23 0.217
64 A 3 2 1. 23 0.087
65 A 8 5 1.11 23 0.217
66 A 20 8 1. 23 0.348
67 A 7 5 1.1 23 0.217
68 A 17 8 1. 21 0.381
69 A 13 5 1. 21 0.238
70 A 3 2 1. 23 0.087
71 A 14 6 1. 23 0.261
72 A 3 2 1. 23 0.087
73 A 11 10 1. 23 0.435
74 A 0 0 0. 0 0.
75 A 11 10 1. 23 0.435
76 A 0 0 0. 0 0.
77 A 0 0 0. 0 0.
78 A 8 8 1. 23 0.348
79 A 0 0 0. 0 0.
80 A 12 11 1. 23 0.478
81 A 4 4 1. 21 0.19
82 A 2 1 1. 21 0.048
83 A 3 3 1. 21 0.143
84 A 3 3 1. 19 0.158
85 A 3 3 1. 19 0.158
86 A 2 1 1. 21 0.048
87 A 4 4 1. 21 0.19
88 A 3 2 1. 21 0.095
89 A 4 4 1. 23 0.174
90 A 4 3 1. 23 0.13
91 A 5 4 1. 23 0.174
92 A 5 4 1. 21 0.19
93 A 4 4 1. 21 0.19
94 A 3 2 1. 23 0.087
95 A 5 5 1. 23 0.217
96 A 3 2 1. 23 0.087
97 A 6 5 1. 23 0.217
98 A 5 4 1. 23 0.174
99 A 5 4 1. 23 0.174
100 A 6 5 1. 21 0.238
101 A 5 5 1. 21 0.238
102 A 3 2 1. 23 0.087
103 A 6 6 1. 23 0.261
104 A 3 2 1. 23 0.087
105 A 6 6 1. 23 0.261
106 A 4 3 1. 23 0.13
107 A 5 5 1. 23 0.217
108 A 3 3 1. 21 0.143
109 A 2 2 1. 21 0.095
110 A 2 2 1. 23 0.087
111 A 4 4 1. 23 0.174
112 A 3 3 1. 23 0.13
113 A 5 5 1. 23 0.217
114 A 4 3 1. 23 0.13
115 A 5 4 1. 23 0.174
116 A 6 6 1. 23 0.261
117 A 5 4 1. 21 0.19
118 A 3 3 1. 21 0.143
119 A 3 3 1. 23 0.13
120 A 3 3 1. 23 0.13
121 A 3 3 1. 23 0.13
122 A 5 5 1. 23 0.217
123 A 5 4 1. 23 0.174
124 A 6 6 1. 23 0.261
125 A 7 6 1. 23 0.261
126 A 6 5 1. 21 0.238
127 A 4 4 1. 21 0.19
128 A 4 3 1. 23 0.13
129 A 4 4 1. 23 0.174
130 A 4 4 1. 23 0.174
131 A 4 3 1. 23 0.13
132 A 4 4 1. 23 0.174
133 A 6 6 1. 23 0.261
134 A 4 3 1. 21 0.143
135 A 3 3 1. 21 0.143
136 A 3 3 1. 21 0.143
137 A 2 2 1. 19 0.105
138 A 3 2 1. 12 0.167
139 A 3 2 1. 19 0.105
140 A 2 2 1. 21 0.095
141 A 3 3 1. 21 0.143
142 A 4 4 1. 21 0.19
143 A 4 4 1. 21 0.19
144 A 4 3 1. 23 0.13
145 A 4 3 1. 23 0.13
146 A 4 3 1. 23 0.13
147 A 4 3 1. 21 0.143
148 A 4 3 1. 14 0.214
149 A 4 3 1. 21 0.143
150 A 4 3 1. 23 0.13
151 A 4 3 1. 23 0.13
152 A 4 3 1. 23 0.13
153 A 4 3 1. 23 0.13
154 A 4 3 1. 23 0.13
155 A 4 3 1. 23 0.13
156 A 4 3 1. 23 0.13
157 A 4 3 1. 23 0.13
158 A 4 3 1. 23 0.13
159 A 4 3 1. 21 0.143
160 A 4 3 1. 14 0.214
161 A 4 3 1. 21 0.143
162 A 4 3 1. 23 0.13
163 A 4 3 1. 23 0.13
164 A 4 3 1. 23 0.13
165 A 4 3 1. 23 0.13
166 A 4 3 1. 23 0.13
167 A 4 3 1. 23 0.13
168 A 4 3 1. 14 0.214
169 A 4 3 1. 14 0.214
170 A 4 3 1. 23 0.13
171 A 5 5 1. 23 0.217
172 A 4 3 1. 23 0.13
173 A 4 4 1. 23 0.174
174 A 5 4 1. 21 0.19
175 A 3 3 1. 14 0.214
176 A 4 3 1. 21 0.143
177 A 5 5 1. 23 0.217
178 A 4 3 1. 23 0.13
179 A 6 6 1. 23 0.261
180 A 4 3 1. 23 0.13
181 A 5 5 1. 23 0.217
182 A 4 3 1. 23 0.13
183 A 5 5 1. 23 0.217
184 A 4 3 1. 21 0.143
185 A 5 5 1. 14 0.357
186 A 4 3 1. 21 0.143
187 A 6 6 1. 23 0.261
188 A 4 3 1. 23 0.13
189 A 7 6 1. 23 0.261
190 A 6 6 1. 23 0.261
191 A 4 3 1. 23 0.13
192 A 6 6 1. 23 0.261
193 A 4 3 1. 23 0.13
194 A 6 6 1. 23 0.261
195 A 4 3 1. 21 0.143
196 A 6 6 1. 14 0.429
197 A 4 3 1. 21 0.143
198 A 7 7 1. 23 0.304
199 A 4 3 1. 23 0.13
200 A 8 7 1. 23 0.304
201 A 7 6 1. 14 0.429
202 A 3 3 1. 12 0.25
203 A 4 4 1. 10 0.4
204 A 4 4 1. 12 0.333
205 A 5 5 1. 10 0.5
206 A 3 3 1. 12 0.25
207 A 3 3 1. 10 0.3
208 A 7 6 1. 17 0.353
209 A 8 7 1. 17 0.412
210 A 6 6 1. 17 0.353
211 A 7 6 1. 17 0.353
212 A 5 5 1. 15 0.333
213 A 6 5 1. 12 0.417
214 A 7 5 1. 15 0.333
215 A 5 5 1. 17 0.294
216 A 8 6 1. 17 0.353
217 A 6 6 1. 17 0.353
218 A 9 7 1. 17 0.412
219 A 7 6 1. 17 0.353
220 A 8 7 1. 17 0.412
221 A 6 5 1. 15 0.333
222 A 7 6 1. 12 0.5
223 A 8 6 1. 15 0.4
224 A 7 6 1. 17 0.353
225 A 5 5 1. 10 0.5
226 A 6 5 1. 12 0.417
227 A 6 6 1. 10 0.6
228 A 7 6 1. 12 0.5
229 A 6 5 1. 17 0.294
230 A 7 6 1. 17 0.353
231 A 5 5 1. 17 0.294
232 A 6 5 1. 17 0.294
233 A 4 4 1. 15 0.267
234 A 3 3 1. 12 0.25
235 A 7 5 1. 15 0.333
236 A 5 5 1. 17 0.294
237 A 8 6 1. 17 0.353
238 A 6 5 1. 17 0.294
239 A 7 6 1. 17 0.353
240 A 5 5 1. 17 0.294
241 A 4 4 1. 17 0.235
242 A 5 5 1. 15 0.333
243 A 4 4 1. 12 0.333
244 A 8 6 1. 15 0.4
245 A 6 6 1. 17 0.353
246 A 8 7 1. 17 0.412
247 A 6 5 1. 17 0.294
248 A 6 6 1. 17 0.353
249 A 6 6 1. 17 0.353
250 A 6 6 1. 17 0.353
251 A 6 5 1. 15 0.333
252 A 6 6 1. 12 0.5
253 A 9 7 1. 15 0.467
254 A 7 7 1. 17 0.412
255 A 3 3 1. 10 0.3
256 A 3 3 1. 12 0.25
257 A 6 4 1.26 14 0.286
258 A 6 5 1. 8 0.625
259 A 9 8 1. 15 0.533
260 A 8 7 1. 15 0.467
261 A 4 4 1. 15 0.267
262 A 6 6 1. 15 0.4
263 A 7 7 1. 15 0.467

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