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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183 }

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, 26, 27, 29, 30, 31, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 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, 113, 114, 115, 116, 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, 175, 176, 177, 178, 179, 180, 181, 182, 183 }

B grade: { 28, 52, 54, 60, 62, 71, 173, 174 }

C grade: { 32, 74, 112, 117 }

F grade: { 39, 40 }

2.1.3 Maple

A grade: { 4, 5, 6, 12, 13, 19, 20, 21, 24, 25, 29, 30, 33, 34, 35, 39, 40, 68, 69, 75, 79, 80, 102, 103, 107, 108, 109, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 127, 128, 129, 142, 143, 147, 148, 149, 150, 154, 155, 159, 160, 164, 165, 166, 171, 172, 176, 177, 178, 182, 183 }

B grade: { 1, 2, 3, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 22, 23, 28, 31, 32, 38, 99, 100, 101, 104, 105, 106, 110, 111, 112, 116, 156, 157, 158, 161, 162, 163, 167, 170, 175 }

C grade: { 63, 64, 65, 66, 67, 81, 82, 83, 84, 85, 86, 87 }

F grade: { 26, 27, 36, 37, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 70, 71, 72, 73, 74, 76, 77, 78, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 124, 125, 126, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 151, 152, 153, 168, 169, 173, 174, 179, 180, 181 }

2.1.4 Maxima

A grade: { 5, 6, 7, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 29, 30, 34, 35, 39, 40, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 66, 67, 68, 69, 70, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 101, 102, 103, 104, 107, 108, 109, 110, 113, 114, 115, 119, 120, 121, 122, 123, 127, 128, 129, 133, 134, 135, 142, 143, 147, 148, 149, 150, 151, 152, 153, 154, 155, 158, 159, 160, 161, 163, 164, 165, 166, 167, 171, 172, 176, 177, 178, 179, 180, 181, 182, 183 }

B grade: { 1, 2, 3, 4, 8, 9, 16, 17, 18, 19, 31, 33, 41, 42, 43, 44, 63, 64, 65, 99, 100, 105, 106, 111, 116, 118, 156, 157, 162 }

C grade: { }

F grade: { 26, 27, 28, 32, 36, 37, 38, 71, 72, 73, 74, 93, 94, 95, 96, 97, 98, 112, 117, 124, 125, 126, 130, 131, 132, 136, 137, 138, 139, 140, 141, 144, 145, 146, 168, 169, 170, 173, 174, 175 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 9, 10, 11, 12, 18, 19, 20, 23, 24, 25, 29, 30, 34, 35, 39, 40, 44, 51, 59, 65, 68, 69, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 99, 100, 101, 102, 103, 105, 106, 107, 108, 114, 115, 119, 120, 142, 143, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 162, 163, 164, 165, 166, 171, 172, 176, 177, 178, 179, 180, 181, 182, 183 }

B grade: { 6, 7, 8, 13, 14, 15, 16, 17, 21, 22, 28, 33, 38, 41, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 72, 104, 109, 110, 112, 113, 117, 118, 161, 167, 170, 175 }

C grade: { 26, 27, 31, 32, 36, 37, 111, 116, 168, 169, 173, 174 }

F grade: { 70, 71, 73, 74, 95, 96, 97, 98, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 149 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 23, 24, 25, 29, 30, 34, 35, 39, 40, 68, 69, 70, 75, 79, 80, 99, 100, 101, 105, 106, 107, 113, 114, 115, 118, 119, 120, 142, 143, 147, 148, 149, 154, 155, 156, 157, 158, 162, 163, 164, 171, 172, 182, 183 }

B grade: { }

C grade: { 63, 64, 65, 66, 67 }

F grade: { 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 26, 27, 28, 31, 32, 33, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 71, 72, 73, 74, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 102, 103, 104, 108, 109, 110, 111, 112, 116, 117, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 150, 151, 152, 153, 159, 160, 161, 165, 166, 167, 168, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181 }

2.1.7 Giac

A grade: { 4, 5, 10, 11, 12, 19, 20, 23, 24, 25, 29, 30, 34, 35, 39, 40, 41, 42, 43, 44, 51, 63, 64, 65, 68, 69, 70, 75, 79, 80, 101, 102, 107, 108, 113, 114, 115, 119, 120, 121, 122, 123, 124, 125, 126, 133, 134, 135, 136, 137, 142, 143, 147, 148, 149, 150, 154, 155, 158, 159, 164, 165, 171, 172, 176, 177, 178, 182, 183 }

B grade: { 1, 2, 3, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 21, 22, 33, 99, 100, 103, 104, 105, 106, 109, 110, 118, 138, 156, 157, 160, 161, 162, 163, 166, 167 }

C grade: { }

F grade: { 26, 27, 28, 31, 32, 36, 37, 38, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 66, 67, 71, 72, 73, 74, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 111, 112, 116, 117, 127, 128, 129, 130, 131, 132, 139, 140, 141, 144, 145, 146, 151, 152, 153, 168, 169, 170, 173, 174, 175, 179, 180, 181 }

2.1.8 Mupad

A grade: { 29, 30, 34, 35, 39, 40, 68, 69, 70, 75, 79, 80, 114, 115, 119, 120, 142, 143, 147, 148, 149, 150, 154, 155, 171, 172, 176, 177, 178, 182, 183 }

B grade: { 1, 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 23, 24, 25, 33, 71, 72, 73, 99, 100, 101, 105, 106, 107, 113, 118, 121, 122, 123, 127, 128, 129, 156, 157, 158, 162, 163, 164 }

C grade: { }

F grade: { 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 26, 27, 28, 31, 32, 36, 37, 38, 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, 74, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 102, 103, 104, 108, 109, 110, 111, 112, 116, 117, 124, 125, 126, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 151, 152, 153, 159, 160, 161, 165, 166, 167, 168, 169, 170, 173, 174, 175, 179, 180, 181 }

2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 76 547 326 171 311 324 215
normalized size 1 1.00 0.84 6.01 3.58 1.88 3.42 3.56 2.36
time (sec) N/A 0.119 0.313 0.052 0.542 0.445 2.602 0.139 0.185
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 61 308 222 111 202 204 143
normalized size 1 1.00 0.87 4.40 3.17 1.59 2.89 2.91 2.04
time (sec) N/A 0.079 0.203 0.058 0.411 0.660 1.262 0.140 0.935
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 44 147 135 64 112 112 82
normalized size 1 1.00 0.90 3.00 2.76 1.31 2.29 2.29 1.67
time (sec) N/A 0.047 0.152 0.050 0.577 0.656 0.559 0.134 0.905
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 27 53 68 30 46 46 35
normalized size 1 1.00 0.96 1.89 2.43 1.07 1.64 1.64 1.25
time (sec) N/A 0.020 0.057 0.048 0.374 0.630 0.227 0.120 0.073
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 49 82 57 94 0 56 -1
normalized size 1 1.00 0.96 1.61 1.12 1.84 0.00 1.10 -0.02
time (sec) N/A 0.101 0.078 0.075 0.545 0.481 0.000 0.116 0.000
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 65 133 81 150 0 615 -1
normalized size 1 1.00 0.92 1.87 1.14 2.11 0.00 8.66 -0.01
time (sec) N/A 0.119 0.247 0.090 0.654 0.743 0.000 0.168 0.000
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 88 277 95 254 0 298 -1
normalized size 1 1.00 0.85 2.66 0.91 2.44 0.00 2.87 -0.01
time (sec) N/A 0.163 0.555 0.099 0.477 0.533 0.000 0.141 0.000
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 132 910 382 312 660 372 332
normalized size 1 1.00 0.81 5.62 2.36 1.93 4.07 2.30 2.05
time (sec) N/A 0.101 0.656 0.069 0.491 0.431 4.710 0.142 1.502
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 104 523 263 209 456 243 229
normalized size 1 1.00 0.78 3.90 1.96 1.56 3.40 1.81 1.71
time (sec) N/A 0.073 0.432 0.059 0.477 0.498 2.578 0.125 1.178
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 75 262 165 123 264 136 127
normalized size 1 1.00 0.79 2.76 1.74 1.29 2.78 1.43 1.34
time (sec) N/A 0.053 0.302 0.052 0.378 0.719 1.222 0.122 0.983
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 51 103 88 66 126 63 58
normalized size 1 1.00 0.93 1.87 1.60 1.20 2.29 1.15 1.05
time (sec) N/A 0.025 0.161 0.053 0.438 0.545 0.526 0.140 0.099
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 64 97 72 104 0 68 -1
normalized size 1 1.00 0.82 1.24 0.92 1.33 0.00 0.87 -0.01
time (sec) N/A 0.154 0.114 0.254 0.532 0.468 0.000 0.120 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 75 152 88 164 0 574 -1
normalized size 1 1.00 0.93 1.88 1.09 2.02 0.00 7.09 -0.01
time (sec) N/A 0.146 0.413 0.238 0.381 0.447 0.000 0.188 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 102 299 99 278 0 330 -1
normalized size 1 1.00 0.91 2.67 0.88 2.48 0.00 2.95 -0.01
time (sec) N/A 0.187 0.877 0.249 0.601 0.540 0.000 0.129 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 121 555 110 409 0 537 -1
normalized size 1 1.00 0.75 3.43 0.68 2.52 0.00 3.31 -0.01
time (sec) N/A 0.181 0.856 0.250 0.472 0.838 0.000 0.132 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 385 1139 644 528 772 654 532
normalized size 1 1.00 1.71 5.06 2.86 2.35 3.43 2.91 2.36
time (sec) N/A 0.282 0.965 0.173 0.401 0.516 7.947 0.134 1.350
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 175 175 122 634 439 343 495 414 364
normalized size 1 1.00 0.70 3.62 2.51 1.96 2.83 2.37 2.08
time (sec) N/A 0.176 0.962 0.157 0.467 0.568 4.217 0.128 1.140
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 93 302 272 199 284 230 183
normalized size 1 1.00 0.76 2.46 2.21 1.62 2.31 1.87 1.49
time (sec) N/A 0.103 0.555 0.157 0.415 0.536 2.248 0.156 1.218
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 52 109 143 95 126 98 77
normalized size 1 1.00 0.69 1.45 1.91 1.27 1.68 1.31 1.03
time (sec) N/A 0.044 0.241 0.154 0.384 0.471 0.939 0.120 0.217
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 102 166 117 186 0 112 -1
normalized size 1 1.00 0.84 1.37 0.97 1.54 0.00 0.93 -0.01
time (sec) N/A 0.240 0.232 0.300 0.411 0.797 0.000 0.135 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 196 271 145 305 0 1075 -1
normalized size 1 1.00 1.35 1.87 1.00 2.10 0.00 7.41 -0.01
time (sec) N/A 0.237 0.533 0.303 0.461 0.530 0.000 0.211 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 184 184 218 562 145 527 0 602 -1
normalized size 1 1.00 1.18 3.05 0.79 2.86 0.00 3.27 -0.01
time (sec) N/A 0.340 0.886 0.323 0.450 0.553 0.000 0.134 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 172 172 100 400 176 195 253 150 129
normalized size 1 1.00 0.58 2.33 1.02 1.13 1.47 0.87 0.75
time (sec) N/A 0.146 0.415 0.170 0.363 0.562 5.700 0.120 0.368
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 90 237 132 147 209 118 94
normalized size 1 1.00 0.67 1.77 0.99 1.10 1.56 0.88 0.70
time (sec) N/A 0.107 0.163 0.164 0.380 0.787 3.272 0.121 0.249
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 53 112 96 114 138 86 68
normalized size 1 1.00 0.66 1.40 1.20 1.42 1.72 1.08 0.85
time (sec) N/A 0.044 0.182 0.157 0.389 1.188 1.834 0.123 0.146
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 179 179 343 0 0 493 0 0 -1
normalized size 1 1.00 1.92 0.00 0.00 2.75 0.00 0.00 -0.01
time (sec) N/A 0.123 2.650 0.461 0.000 0.653 0.000 0.000 0.000
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 199 0 0 303 0 0 -1
normalized size 1 1.00 1.67 0.00 0.00 2.55 0.00 0.00 -0.01
time (sec) N/A 0.081 1.518 0.399 0.000 0.976 0.000 0.000 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 127 147 0 157 0 0 -1
normalized size 1 1.00 2.08 2.41 0.00 2.57 0.00 0.00 -0.02
time (sec) N/A 0.037 0.147 0.020 0.000 0.670 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.021 3.711 0.158 0.000 0.592 0.000 0.000 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.020 7.282 0.161 0.000 0.680 0.000 0.000 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 145 298 238 1332 0 0 -1
normalized size 1 1.00 1.41 2.89 2.31 12.93 0.00 0.00 -0.01
time (sec) N/A 0.206 2.074 0.291 0.856 0.756 0.000 0.000 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F C F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 73 73 277 159 0 715 0 0 -1
normalized size 1 1.00 3.79 2.18 0.00 9.79 0.00 0.00 -0.01
time (sec) N/A 0.133 6.303 0.261 0.000 0.614 0.000 0.000 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 51 57 72 161 0 78 50
normalized size 1 1.00 1.76 1.97 2.48 5.55 0.00 2.69 1.72
time (sec) N/A 0.029 0.092 0.184 0.585 0.764 0.000 0.141 0.089
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.037 17.783 0.196 0.000 0.692 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.035 17.960 0.192 0.000 2.443 0.000 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 296 296 455 0 0 4735 0 0 -1
normalized size 1 1.00 1.54 0.00 0.00 16.00 0.00 0.00 -0.00
time (sec) N/A 0.217 29.522 0.675 0.000 1.216 0.000 0.000 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 175 175 270 0 0 2613 0 0 -1
normalized size 1 1.00 1.54 0.00 0.00 14.93 0.00 0.00 -0.01
time (sec) N/A 0.133 5.519 0.571 0.000 1.267 0.000 0.000 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 178 216 0 1243 0 0 -1
normalized size 1 1.00 1.75 2.12 0.00 12.19 0.00 0.00 -0.01
time (sec) N/A 0.063 3.017 0.279 0.000 1.205 0.000 0.000 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A F(-1) A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.037 180.008 0.523 0.000 0.858 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A F(-1) A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.034 180.017 0.676 0.000 2.020 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 171 171 107 0 308 523 0 232 -1
normalized size 1 1.00 0.63 0.00 1.80 3.06 0.00 1.36 -0.01
time (sec) N/A 0.330 0.051 0.148 0.452 0.910 0.000 0.220 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 146 146 107 0 268 387 0 202 -1
normalized size 1 1.00 0.73 0.00 1.84 2.65 0.00 1.38 -0.01
time (sec) N/A 0.243 0.103 0.155 0.356 2.983 0.000 0.181 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 105 0 230 302 0 169 -1
normalized size 1 1.00 0.85 0.00 1.87 2.46 0.00 1.37 -0.01
time (sec) N/A 0.178 0.091 0.147 0.338 1.019 0.000 0.162 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F B A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 105 0 180 123 0 89 -1
normalized size 1 1.00 1.01 0.00 1.73 1.18 0.00 0.86 -0.01
time (sec) N/A 0.130 0.044 0.146 0.329 0.558 0.000 0.131 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 118 0 104 338 0 0 -1
normalized size 1 1.00 0.99 0.00 0.87 2.84 0.00 0.00 -0.01
time (sec) N/A 0.183 0.365 0.139 0.329 1.047 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 150 0 115 534 0 0 -1
normalized size 1 1.00 1.01 0.00 0.77 3.58 0.00 0.00 -0.01
time (sec) N/A 0.248 0.730 0.139 0.540 0.908 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 191 0 115 853 0 0 -1
normalized size 1 1.00 1.10 0.00 0.66 4.90 0.00 0.00 -0.01
time (sec) N/A 0.312 0.416 0.146 0.409 0.511 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 239 239 189 0 281 1001 0 0 -1
normalized size 1 1.00 0.79 0.00 1.18 4.19 0.00 0.00 -0.00
time (sec) N/A 0.400 1.201 0.298 0.463 0.465 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 211 211 163 0 239 755 0 0 -1
normalized size 1 1.00 0.77 0.00 1.13 3.58 0.00 0.00 -0.00
time (sec) N/A 0.303 0.602 0.292 0.587 0.491 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 129 0 189 590 0 0 -1
normalized size 1 1.00 0.78 0.00 1.14 3.55 0.00 0.00 -0.01
time (sec) N/A 0.269 0.448 0.280 0.416 0.538 0.000 0.000 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 141 0 107 155 0 115 -1
normalized size 1 1.00 1.02 0.00 0.78 1.12 0.00 0.83 -0.01
time (sec) N/A 0.214 0.127 0.278 0.496 0.511 0.000 0.172 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 570 0 116 569 0 0 -1
normalized size 1 1.00 4.01 0.00 0.82 4.01 0.00 0.00 -0.01
time (sec) N/A 0.230 2.973 0.273 1.285 0.538 0.000 0.000 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 156 0 118 861 0 0 -1
normalized size 1 1.00 0.90 0.00 0.68 4.95 0.00 0.00 -0.01
time (sec) N/A 0.309 1.383 0.286 0.405 0.551 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 220 220 825 0 116 1350 0 0 -1
normalized size 1 1.00 3.75 0.00 0.53 6.14 0.00 0.00 -0.00
time (sec) N/A 0.311 3.171 0.291 0.446 0.633 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 251 251 222 0 116 1825 0 0 -1
normalized size 1 1.00 0.88 0.00 0.46 7.27 0.00 0.00 -0.00
time (sec) N/A 0.379 0.854 0.281 1.037 0.715 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 381 381 243 0 513 2092 0 0 -1
normalized size 1 1.00 0.64 0.00 1.35 5.49 0.00 0.00 -0.00
time (sec) N/A 0.906 4.000 0.506 1.540 0.645 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 326 326 243 0 429 1545 0 0 -1
normalized size 1 1.00 0.75 0.00 1.32 4.74 0.00 0.00 -0.00
time (sec) N/A 0.712 2.005 0.497 0.439 0.672 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 275 275 210 0 334 1217 0 0 -1
normalized size 1 1.00 0.76 0.00 1.21 4.43 0.00 0.00 -0.00
time (sec) N/A 0.484 0.295 0.491 0.437 0.508 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 228 228 192 0 177 253 0 0 -1
normalized size 1 1.00 0.84 0.00 0.78 1.11 0.00 0.00 -0.00
time (sec) N/A 0.374 0.204 0.471 0.437 0.556 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 246 246 717 0 196 1344 0 0 -1
normalized size 1 1.00 2.91 0.00 0.80 5.46 0.00 0.00 -0.00
time (sec) N/A 0.421 2.886 0.469 0.474 0.549 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 277 277 253 0 194 2058 0 0 -1
normalized size 1 1.00 0.91 0.00 0.70 7.43 0.00 0.00 -0.00
time (sec) N/A 0.605 2.909 0.473 0.470 0.713 0.000 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 331 331 3211 0 196 3280 0 0 -1
normalized size 1 1.00 9.70 0.00 0.59 9.91 0.00 0.00 -0.00
time (sec) N/A 0.680 6.347 0.458 0.732 0.625 0.000 0.000 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B B C A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 51 133 174 191 131 145 -1
normalized size 1 1.00 0.46 1.20 1.57 1.72 1.18 1.31 -0.01
time (sec) N/A 0.155 0.014 0.087 0.324 0.453 18.030 0.150 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B B C A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 48 121 148 138 100 108 -1
normalized size 1 1.00 0.52 1.32 1.61 1.50 1.09 1.17 -0.01
time (sec) N/A 0.106 0.013 0.082 0.553 0.628 1.404 0.150 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B A C A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 48 72 117 59 66 60 -1
normalized size 1 1.00 0.62 0.94 1.52 0.77 0.86 0.78 -0.01
time (sec) N/A 0.077 0.008 0.088 0.500 0.458 0.962 0.119 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 67 115 76 136 99 0 -1
normalized size 1 1.00 0.76 1.31 0.86 1.55 1.12 0.00 -0.01
time (sec) N/A 0.113 0.037 0.083 1.001 0.480 2.788 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 78 126 58 179 124 0 -1
normalized size 1 1.00 0.68 1.11 0.51 1.57 1.09 0.00 -0.01
time (sec) N/A 0.148 0.099 0.085 3.610 0.540 19.881 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.028 11.384 0.163 0.000 0.451 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.030 9.888 0.163 0.000 0.459 0.000 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 63 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.085 4.091 180.000 0.000 0.000 0.000 0.000 0.000
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F(-2) F F(-2) F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 20 20 46 0 0 0 0 0 39
normalized size 1 1.00 2.30 0.00 0.00 0.00 0.00 0.00 1.95
time (sec) N/A 0.048 0.388 180.000 0.000 0.000 0.000 0.000 0.968
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 16 0 0 109 0 0 42
normalized size 1 1.00 0.67 0.00 0.00 4.54 0.00 0.00 1.75
time (sec) N/A 0.050 0.079 0.245 0.000 0.526 0.000 0.000 0.936
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F F(-2) F(-1) F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 47 47 64 0 0 0 0 0 110
normalized size 1 1.00 1.36 0.00 0.00 0.00 0.00 0.00 2.34
time (sec) N/A 0.066 0.638 180.000 0.000 0.000 0.000 0.000 1.082
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-2) F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 76 0 0 0 0 0 -1
normalized size 1 1.00 2.11 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.092 1.027 180.000 0.000 0.000 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.046 3.191 0.141 0.000 0.525 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 237 237 205 0 161 340 0 0 -1
normalized size 1 1.00 0.86 0.00 0.68 1.43 0.00 0.00 -0.00
time (sec) N/A 0.284 0.196 0.316 0.564 0.555 0.000 0.000 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 132 0 102 241 0 0 -1
normalized size 1 1.00 0.92 0.00 0.71 1.67 0.00 0.00 -0.01
time (sec) N/A 0.184 0.216 0.217 1.173 0.548 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 102 0 79 168 0 0 -1
normalized size 1 1.00 0.93 0.00 0.72 1.53 0.00 0.00 -0.01
time (sec) N/A 0.091 0.058 0.147 2.574 0.455 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.020 5.931 0.140 0.000 0.627 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.036 3.490 0.143 0.000 0.500 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 54 73 55 86 0 0 -1
normalized size 1 1.00 0.92 1.24 0.93 1.46 0.00 0.00 -0.02
time (sec) N/A 0.074 0.039 0.102 1.378 0.456 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 54 73 55 86 0 0 -1
normalized size 1 1.00 0.92 1.24 0.93 1.46 0.00 0.00 -0.02
time (sec) N/A 0.072 0.021 0.129 1.226 0.449 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 54 73 55 86 0 0 -1
normalized size 1 1.00 0.92 1.24 0.93 1.46 0.00 0.00 -0.02
time (sec) N/A 0.071 0.033 0.120 0.745 0.438 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 54 73 55 78 0 0 -1
normalized size 1 1.00 0.92 1.24 0.93 1.32 0.00 0.00 -0.02
time (sec) N/A 0.069 0.018 0.107 1.214 0.459 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 49 67 43 78 0 0 -1
normalized size 1 1.00 1.00 1.37 0.88 1.59 0.00 0.00 -0.02
time (sec) N/A 0.069 0.021 0.119 0.768 0.439 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 52 67 55 86 0 0 -1
normalized size 1 1.00 0.95 1.22 1.00 1.56 0.00 0.00 -0.02
time (sec) N/A 0.069 0.020 0.129 1.194 0.506 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 55 71 55 86 0 0 -1
normalized size 1 1.00 0.93 1.20 0.93 1.46 0.00 0.00 -0.02
time (sec) N/A 0.070 0.022 0.097 2.311 0.423 0.000 0.000 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 79 0 71 136 0 0 -1
normalized size 1 1.00 0.92 0.00 0.83 1.58 0.00 0.00 -0.01
time (sec) N/A 0.150 0.111 0.191 1.341 0.505 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 78 0 71 136 0 0 -1
normalized size 1 1.00 0.92 0.00 0.84 1.60 0.00 0.00 -0.01
time (sec) N/A 0.133 0.101 0.195 1.413 0.515 0.000 0.000 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 79 0 71 136 0 0 -1
normalized size 1 1.00 0.92 0.00 0.83 1.58 0.00 0.00 -0.01
time (sec) N/A 0.133 0.110 0.230 2.771 0.542 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 76 0 71 122 0 0 -1
normalized size 1 1.00 0.89 0.00 0.84 1.44 0.00 0.00 -0.01
time (sec) N/A 0.127 0.090 0.206 0.903 0.489 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 64 0 55 117 0 0 -1
normalized size 1 1.00 0.89 0.00 0.76 1.62 0.00 0.00 -0.01
time (sec) N/A 0.125 0.060 0.251 0.644 0.479 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 73 0 0 136 0 0 -1
normalized size 1 1.00 0.88 0.00 0.00 1.64 0.00 0.00 -0.01
time (sec) N/A 0.130 0.100 0.202 0.000 0.457 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 84 0 0 136 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 1.62 0.00 0.00 -0.01
time (sec) N/A 0.140 0.114 0.204 0.000 0.444 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 17 0 0 0 0 0 -1
normalized size 1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.091 0.097 0.230 0.000 0.000 0.000 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 17 0 0 0 0 0 -1
normalized size 1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.088 0.151 0.216 0.000 0.000 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 45 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.104 0.109 0.229 0.000 0.000 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 55 0 0 0 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.169 0.110 0.223 0.000 0.000 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 122 482 237 168 264 260 187
normalized size 1 1.00 1.37 5.42 2.66 1.89 2.97 2.92 2.10
time (sec) N/A 0.132 0.564 0.064 2.312 0.645 1.380 0.125 1.019
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 80 240 141 102 151 148 112
normalized size 1 1.00 1.19 3.58 2.10 1.52 2.25 2.21 1.67
time (sec) N/A 0.091 0.331 0.069 1.048 0.615 0.636 0.116 0.135
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 52 91 66 51 68 66 53
normalized size 1 1.00 1.16 2.02 1.47 1.13 1.51 1.47 1.18
time (sec) N/A 0.045 0.221 0.069 0.441 0.520 0.277 0.116 0.079
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 54 94 70 111 0 69 -1
normalized size 1 1.00 0.84 1.47 1.09 1.73 0.00 1.08 -0.02
time (sec) N/A 0.138 0.111 0.139 0.446 0.442 0.000 0.137 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 68 149 87 162 0 683 -1
normalized size 1 1.00 0.78 1.71 1.00 1.86 0.00 7.85 -0.01
time (sec) N/A 0.172 0.317 0.141 0.420 0.589 0.000 0.162 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 90 296 98 274 0 328 -1
normalized size 1 1.00 0.73 2.41 0.80 2.23 0.00 2.67 -0.01
time (sec) N/A 0.216 0.458 0.147 0.572 0.562 0.000 0.123 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 237 237 217 1071 527 395 779 581 452
normalized size 1 1.00 0.92 4.52 2.22 1.67 3.29 2.45 1.91
time (sec) N/A 0.265 1.493 0.077 0.388 0.533 4.075 0.131 2.252
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 168 168 192 541 327 227 456 333 257
normalized size 1 1.00 1.14 3.22 1.95 1.35 2.71 1.98 1.53
time (sec) N/A 0.188 0.536 0.079 0.354 0.511 1.704 0.129 1.288
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 81 211 167 113 219 155 123
normalized size 1 1.00 0.69 1.79 1.42 0.96 1.86 1.31 1.04
time (sec) N/A 0.099 0.542 0.074 0.488 0.608 0.669 0.135 0.135
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 113 191 149 228 0 139 -1
normalized size 1 1.00 0.78 1.32 1.03 1.57 0.00 0.96 -0.01
time (sec) N/A 0.342 0.210 0.367 0.525 0.432 0.000 0.150 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 207 308 182 359 0 1226 -1
normalized size 1 1.00 1.32 1.96 1.16 2.29 0.00 7.81 -0.01
time (sec) N/A 0.333 0.743 0.375 0.581 0.568 0.000 0.244 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 207 207 353 618 202 596 0 706 -1
normalized size 1 1.00 1.71 2.99 0.98 2.88 0.00 3.41 -0.00
time (sec) N/A 0.505 1.217 0.391 0.517 0.500 0.000 0.138 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 154 325 228 438 0 0 -1
normalized size 1 1.00 1.32 2.78 1.95 3.74 0.00 0.00 -0.01
time (sec) N/A 0.273 2.299 0.244 0.695 0.642 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 88 88 472 174 0 243 0 0 -1
normalized size 1 1.00 5.36 1.98 0.00 2.76 0.00 0.00 -0.01
time (sec) N/A 0.201 6.379 0.213 0.000 0.406 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 70 63 71 92 76 71 53
normalized size 1 1.00 1.43 1.29 1.45 1.88 1.55 1.45 1.08
time (sec) N/A 0.068 0.275 0.129 0.367 0.541 0.725 0.123 0.903
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.060 9.246 0.201 0.000 0.540 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.057 9.608 0.221 0.000 1.191 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 255 255 462 600 610 1863 0 0 -1
normalized size 1 1.00 1.81 2.35 2.39 7.31 0.00 0.00 -0.00
time (sec) N/A 0.364 3.486 0.295 0.617 0.583 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 200 200 637 313 0 963 0 0 -1
normalized size 1 1.00 3.18 1.56 0.00 4.82 0.00 0.00 -0.00
time (sec) N/A 0.252 6.478 0.236 0.000 0.690 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 114 108 239 385 156 207 138
normalized size 1 1.00 0.93 0.88 1.94 3.13 1.27 1.68 1.12
time (sec) N/A 0.096 0.457 0.205 0.366 0.532 1.263 0.126 0.893
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.054 30.764 0.655 0.000 0.506 0.000 0.000 0.000
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.052 32.277 0.808 0.000 1.130 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 53 108 120 0 0 147 117
normalized size 1 1.00 0.48 0.98 1.09 0.00 0.00 1.34 1.06
time (sec) N/A 0.148 0.227 0.139 0.450 0.000 0.000 0.125 0.207
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 44 86 90 0 0 107 95
normalized size 1 1.00 0.50 0.98 1.02 0.00 0.00 1.22 1.08
time (sec) N/A 0.113 0.159 0.094 0.452 0.000 0.000 0.141 0.934
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 34 64 60 0 0 67 56
normalized size 1 1.00 0.64 1.21 1.13 0.00 0.00 1.26 1.06
time (sec) N/A 0.062 0.129 0.097 0.445 0.000 0.000 0.134 0.907
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 54 0 0 0 0 32 -1
normalized size 1 1.00 0.65 0.00 0.00 0.00 0.00 0.39 -0.01
time (sec) N/A 0.132 0.075 0.126 0.000 0.000 0.000 0.117 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 75 0 0 0 0 68 -1
normalized size 1 1.00 0.68 0.00 0.00 0.00 0.00 0.62 -0.01
time (sec) N/A 0.140 0.141 0.138 0.000 0.000 0.000 0.137 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 97 0 0 0 0 107 -1
normalized size 1 1.00 0.64 0.00 0.00 0.00 0.00 0.71 -0.01
time (sec) N/A 0.170 0.213 0.099 0.000 0.000 0.000 0.131 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 33 62 88 0 0 0 63
normalized size 1 1.00 0.49 0.91 1.29 0.00 0.00 0.00 0.93
time (sec) N/A 0.117 0.056 0.098 0.409 0.000 0.000 0.000 0.911
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 31 50 66 0 0 0 51
normalized size 1 1.00 0.58 0.94 1.25 0.00 0.00 0.00 0.96
time (sec) N/A 0.097 0.044 0.085 0.424 0.000 0.000 0.000 0.071
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F(-2) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 22 38 44 0 0 0 39
normalized size 1 1.00 0.69 1.19 1.38 0.00 0.00 0.00 1.22
time (sec) N/A 0.051 0.022 0.084 0.408 0.000 0.000 0.000 0.880
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.083 0.008 0.108 0.000 0.000 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 33 0 0 0 0 0 -1
normalized size 1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.090 0.054 0.088 0.000 0.000 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 44 0 0 0 0 0 -1
normalized size 1 1.00 0.66 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.106 0.073 0.092 0.000 0.000 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F(-2) F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 185 185 70 0 180 0 0 192 -1
normalized size 1 1.00 0.38 0.00 0.97 0.00 0.00 1.04 -0.01
time (sec) N/A 0.195 0.289 0.069 0.446 0.000 0.000 0.135 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 54 0 136 0 0 144 -1
normalized size 1 1.00 0.37 0.00 0.94 0.00 0.00 0.99 -0.01
time (sec) N/A 0.149 0.219 0.069 0.414 0.000 0.000 0.130 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 56 0 92 0 0 96 -1
normalized size 1 1.00 0.63 0.00 1.03 0.00 0.00 1.08 -0.01
time (sec) N/A 0.075 0.085 0.069 0.418 0.000 0.000 0.142 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 36 0 0 0 0 40 -1
normalized size 1 1.00 0.65 0.00 0.00 0.00 0.00 0.73 -0.02
time (sec) N/A 0.128 0.021 0.072 0.000 0.000 0.000 0.149 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 53 0 0 0 0 112 -1
normalized size 1 1.00 0.67 0.00 0.00 0.00 0.00 1.42 -0.01
time (sec) N/A 0.131 0.086 0.068 0.000 0.000 0.000 0.151 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 69 0 0 0 0 170 -1
normalized size 1 1.00 0.63 0.00 0.00 0.00 0.00 1.56 -0.01
time (sec) N/A 0.173 0.065 0.076 0.000 0.000 0.000 0.150 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 383 383 213 0 0 0 0 0 -1
normalized size 1 1.00 0.56 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.208 1.783 0.100 0.000 0.831 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 269 269 163 0 0 0 0 0 -1
normalized size 1 1.00 0.61 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.163 1.751 0.099 0.000 0.644 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 157 157 117 0 0 0 0 0 -1
normalized size 1 1.00 0.75 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.082 0.707 0.093 0.000 0.506 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.068 2.992 0.093 0.000 0.427 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.066 1.756 0.096 0.000 0.628 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 402 402 716 0 0 0 0 0 -1
normalized size 1 1.00 1.78 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.257 2.973 0.069 0.000 0.498 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 248 248 214 0 0 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.191 0.911 0.072 0.000 0.436 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 137 0 0 0 0 0 -1
normalized size 1 1.00 0.98 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.101 0.107 0.069 0.000 0.945 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.077 8.938 0.072 0.000 0.934 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.074 10.676 0.070 0.000 0.480 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.063 2.798 0.105 0.000 0.000 0.000 0.000 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.045 6.524 0.171 0.000 0.808 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 402 402 429 0 373 713 0 0 -1
normalized size 1 1.00 1.07 0.00 0.93 1.77 0.00 0.00 -0.00
time (sec) N/A 0.553 2.420 0.287 0.477 0.708 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 263 263 302 0 209 493 0 0 -1
normalized size 1 1.00 1.15 0.00 0.79 1.87 0.00 0.00 -0.00
time (sec) N/A 0.342 1.093 0.317 0.426 0.796 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 189 0 100 249 0 0 -1
normalized size 1 1.00 1.44 0.00 0.76 1.90 0.00 0.00 -0.01
time (sec) N/A 0.147 0.335 0.148 0.411 0.594 0.000 0.000 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.054 5.253 0.147 0.000 0.649 0.000 0.000 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.052 9.872 0.189 0.000 0.585 0.000 0.000 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 123 482 237 168 264 260 187
normalized size 1 1.00 1.38 5.42 2.66 1.89 2.97 2.92 2.10
time (sec) N/A 0.132 0.511 0.066 0.350 0.579 1.409 0.119 0.988
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 83 240 141 102 151 148 110
normalized size 1 1.00 1.24 3.58 2.10 1.52 2.25 2.21 1.64
time (sec) N/A 0.090 0.346 0.059 0.334 0.588 0.637 0.141 0.946
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 46 91 66 51 68 66 49
normalized size 1 1.00 1.02 2.02 1.47 1.13 1.51 1.47 1.09
time (sec) N/A 0.046 0.115 0.054 0.352 0.772 0.286 0.118 0.084
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 57 94 70 111 0 69 -1
normalized size 1 1.00 0.89 1.47 1.09 1.73 0.00 1.08 -0.02
time (sec) N/A 0.121 0.147 0.101 0.389 0.556 0.000 0.120 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 71 149 87 162 0 683 -1
normalized size 1 1.00 0.82 1.71 1.00 1.86 0.00 7.85 -0.01
time (sec) N/A 0.152 0.419 0.114 0.395 0.490 0.000 0.160 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 95 296 98 274 0 328 -1
normalized size 1 1.00 0.77 2.41 0.80 2.23 0.00 2.67 -0.01
time (sec) N/A 0.197 0.635 0.119 0.414 0.543 0.000 0.127 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 250 250 232 1061 523 409 779 603 481
normalized size 1 1.00 0.93 4.24 2.09 1.64 3.12 2.41 1.92
time (sec) N/A 0.285 1.525 0.081 0.386 1.020 3.607 0.146 2.636
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 182 182 252 535 324 240 456 349 281
normalized size 1 1.00 1.38 2.94 1.78 1.32 2.51 1.92 1.54
time (sec) N/A 0.194 1.045 0.073 0.369 0.526 1.650 0.153 1.335
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 96 208 165 122 219 164 135
normalized size 1 1.00 0.83 1.79 1.42 1.05 1.89 1.41 1.16
time (sec) N/A 0.101 0.893 0.071 0.366 0.564 0.660 0.145 0.149
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 156 133 202 148 230 0 148 -1
normalized size 1 1.00 0.85 1.29 0.95 1.47 0.00 0.95 -0.01
time (sec) N/A 0.310 0.310 0.328 0.434 0.506 0.000 0.133 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 233 319 181 355 0 1227 -1
normalized size 1 1.00 1.27 1.74 0.99 1.94 0.00 6.70 -0.01
time (sec) N/A 0.345 0.796 0.358 0.440 0.497 0.000 0.253 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 242 242 394 626 201 586 0 702 -1
normalized size 1 1.00 1.63 2.59 0.83 2.42 0.00 2.90 -0.00
time (sec) N/A 0.428 1.320 0.380 0.453 0.519 0.000 0.149 0.000
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 436 436 384 0 0 1042 0 0 -1
normalized size 1 1.00 0.88 0.00 0.00 2.39 0.00 0.00 -0.00
time (sec) N/A 0.821 1.617 0.482 0.000 0.617 0.000 0.000 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 320 320 247 0 0 736 0 0 -1
normalized size 1 1.00 0.77 0.00 0.00 2.30 0.00 0.00 -0.00
time (sec) N/A 0.670 1.054 0.442 0.000 0.494 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 152 437 0 473 0 0 -1
normalized size 1 1.00 0.75 2.15 0.00 2.33 0.00 0.00 -0.00
time (sec) N/A 0.376 0.964 0.216 0.000 0.494 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.061 0.973 0.171 0.000 1.436 0.000 0.000 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.059 1.023 0.167 0.000 0.539 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F(-2) C F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 823 823 11178 0 0 7116 0 0 -1
normalized size 1 1.00 13.58 0.00 0.00 8.65 0.00 0.00 -0.00
time (sec) N/A 1.353 27.196 0.816 0.000 0.771 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F(-2) C F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 593 593 6018 0 0 4105 0 0 -1
normalized size 1 1.00 10.15 0.00 0.00 6.92 0.00 0.00 -0.00
time (sec) N/A 1.025 22.803 0.700 0.000 0.545 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 274 274 509 585 0 1765 0 0 -1
normalized size 1 1.00 1.86 2.14 0.00 6.44 0.00 0.00 -0.00
time (sec) N/A 0.457 5.038 0.297 0.000 0.861 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.056 51.534 0.587 0.000 0.616 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.054 54.958 0.785 0.000 0.779 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.050 4.531 0.148 0.000 0.591 0.000 0.000 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 543 543 447 0 375 813 0 0 -1
normalized size 1 1.00 0.82 0.00 0.69 1.50 0.00 0.00 -0.00
time (sec) N/A 0.743 1.738 0.364 0.510 0.624 0.000 0.000 0.000
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 282 282 254 0 208 509 0 0 -1
normalized size 1 1.00 0.90 0.00 0.74 1.80 0.00 0.00 -0.00
time (sec) N/A 0.363 0.805 0.281 0.420 0.802 0.000 0.000 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 119 0 100 249 0 0 -1
normalized size 1 1.00 0.91 0.00 0.76 1.90 0.00 0.00 -0.01
time (sec) N/A 0.145 0.184 0.154 0.411 0.558 0.000 0.000 0.000
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.056 1.203 0.146 0.000 0.663 0.000 0.000 0.000
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.055 5.575 0.175 0.000 0.474 0.000 0.000 0.000

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [144] had the largest ratio of [.6429]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 5 2 1.00 14 0.143
2 A 4 2 1.00 14 0.143
3 A 3 2 1.00 14 0.143
4 A 2 2 1.00 12 0.167
5 A 3 3 1.00 14 0.214
6 A 4 4 1.00 14 0.286
7 A 5 4 1.00 14 0.286
8 A 6 4 1.00 16 0.250
9 A 4 3 1.00 16 0.188
10 A 4 4 1.00 16 0.250
11 A 2 1 1.00 14 0.071
12 A 5 4 1.00 16 0.250
13 A 5 5 1.00 16 0.312
14 A 7 6 1.00 16 0.375
15 A 7 7 1.00 16 0.438
16 A 12 4 1.00 16 0.250
17 A 8 4 1.00 16 0.250
18 A 6 4 1.00 16 0.250
19 A 3 3 1.00 14 0.214
20 A 8 4 1.00 16 0.250
21 A 8 4 1.00 16 0.250
22 A 12 5 1.00 16 0.312
23 A 8 3 1.00 12 0.250
24 A 8 4 1.00 12 0.333
25 A 3 2 1.00 10 0.200
26 A 9 5 1.00 14 0.357
27 A 7 4 1.00 14 0.286
28 A 5 3 1.00 12 0.250
29 A 0 0 0.00 0 0.000
30 A 0 0 0.00 0 0.000
31 A 6 6 1.00 16 0.375
32 A 5 5 1.00 16 0.312
33 A 2 2 1.00 14 0.143
34 A 0 0 0.00 0 0.000
35 A 0 0 0.00 0 0.000
36 A 15 8 1.00 16 0.500
37 A 9 6 1.00 16 0.375
38 A 6 4 1.00 14 0.286
39 A 0 0 0.00 0 0.000
40 A 0 0 0.00 0 0.000
41 A 8 5 1.00 16 0.312
42 A 7 5 1.00 16 0.312
43 A 6 5 1.00 16 0.312
44 A 5 4 1.00 16 0.250
45 A 6 5 1.00 16 0.312
46 A 7 5 1.00 16 0.312
47 A 8 5 1.00 16 0.312
48 A 10 8 1.00 18 0.444
49 A 9 7 1.00 18 0.389
50 A 8 6 1.00 18 0.333
51 A 7 5 1.00 18 0.278
52 A 7 6 1.00 18 0.333
53 A 9 7 1.00 18 0.389
54 A 9 8 1.00 18 0.444
55 A 11 7 1.00 18 0.389
56 A 23 7 1.00 18 0.389
57 A 20 7 1.00 18 0.389
58 A 14 6 1.00 18 0.333
59 A 12 5 1.00 18 0.278
60 A 12 5 1.00 18 0.278
61 A 18 6 1.00 18 0.333
62 A 19 7 1.00 18 0.389
63 A 7 5 1.00 12 0.417
64 A 6 5 1.00 12 0.417
65 A 5 4 1.00 12 0.333
66 A 6 5 1.00 12 0.417
67 A 7 5 1.00 12 0.417
68 A 0 0 0.00 0 0.000
69 A 0 0 0.00 0 0.000
70 A 0 0 0.00 0 0.000
71 A 2 1 1.00 17 0.059
72 A 2 1 1.00 20 0.050
73 A 3 1 1.00 20 0.050
74 A 3 2 1.00 21 0.095
75 A 0 0 0.00 0 0.000
76 A 8 3 1.00 16 0.188
77 A 5 3 1.00 16 0.188
78 A 3 2 1.00 14 0.143
79 A 0 0 0.00 0 0.000
80 A 0 0 0.00 0 0.000
81 A 3 2 1.00 12 0.167
82 A 3 2 1.00 12 0.167
83 A 3 2 1.00 12 0.167
84 A 3 2 1.00 10 0.200
85 A 3 2 1.00 12 0.167
86 A 3 2 1.00 12 0.167
87 A 3 2 1.00 12 0.167
88 A 5 3 1.00 14 0.214
89 A 5 3 1.00 14 0.214
90 A 5 3 1.00 14 0.214
91 A 5 3 1.00 12 0.250
92 A 5 3 1.00 14 0.214
93 A 5 3 1.00 14 0.214
94 A 5 3 1.00 14 0.214
95 A 4 2 1.00 20 0.100
96 A 4 2 1.00 20 0.100
97 A 5 2 1.00 20 0.100
98 A 7 5 1.00 24 0.208
99 A 6 3 1.00 18 0.167
100 A 5 3 1.00 18 0.167
101 A 4 3 1.00 16 0.188
102 A 5 4 1.00 18 0.222
103 A 6 5 1.00 18 0.278
104 A 7 5 1.00 18 0.278
105 A 10 6 1.00 20 0.300
106 A 9 7 1.00 20 0.350
107 A 6 4 1.00 18 0.222
108 A 9 5 1.00 20 0.250
109 A 9 5 1.00 20 0.250
110 A 15 6 1.00 20 0.300
111 A 7 7 1.00 20 0.350
112 A 6 6 1.00 20 0.300
113 A 3 3 1.00 18 0.167
114 A 0 0 0.00 0 0.000
115 A 0 0 0.00 0 0.000
116 A 10 9 1.00 20 0.450
117 A 9 9 1.00 20 0.450
118 A 4 4 1.00 18 0.222
119 A 0 0 0.00 0 0.000
120 A 0 0 0.00 0 0.000
121 A 5 3 1.00 18 0.167
122 A 4 3 1.00 18 0.167
123 A 3 3 1.00 16 0.188
124 A 4 4 1.00 18 0.222
125 A 5 5 1.00 18 0.278
126 A 6 5 1.00 18 0.278
127 A 5 3 1.00 14 0.214
128 A 4 3 1.00 14 0.214
129 A 3 3 1.00 12 0.250
130 A 2 2 1.00 14 0.143
131 A 3 3 1.00 14 0.214
132 A 4 3 1.00 14 0.214
133 A 9 5 1.00 14 0.357
134 A 7 5 1.00 14 0.357
135 A 4 4 1.00 12 0.333
136 A 5 3 1.00 14 0.214
137 A 5 3 1.00 14 0.214
138 A 7 4 1.00 14 0.286
139 A 10 6 1.00 18 0.333
140 A 8 5 1.00 18 0.278
141 A 6 4 1.00 16 0.250
142 A 0 0 0.00 0 0.000
143 A 0 0 0.00 0 0.000
144 A 16 9 1.00 14 0.643
145 A 10 7 1.00 14 0.500
146 A 7 5 1.00 12 0.417
147 A 0 0 0.00 0 0.000
148 A 0 0 0.00 0 0.000
149 A 0 0 0.00 0 0.000
150 A 0 0 0.00 0 0.000
151 A 12 4 1.00 20 0.200
152 A 9 4 1.00 20 0.200
153 A 5 3 1.00 18 0.167
154 A 0 0 0.00 0 0.000
155 A 0 0 0.00 0 0.000
156 A 6 3 1.00 18 0.167
157 A 5 3 1.00 18 0.167
158 A 4 3 1.00 16 0.188
159 A 5 4 1.00 18 0.222
160 A 6 5 1.00 18 0.278
161 A 7 5 1.00 18 0.278
162 A 10 6 1.00 20 0.300
163 A 9 7 1.00 20 0.350
164 A 6 4 1.00 18 0.222
165 A 10 5 1.00 20 0.250
166 A 11 7 1.00 20 0.350
167 A 14 8 1.00 20 0.400
168 A 12 7 1.00 20 0.350
169 A 10 6 1.00 20 0.300
170 A 8 5 1.00 18 0.278
171 A 0 0 0.00 0 0.000
172 A 0 0 0.00 0 0.000
173 A 22 9 1.00 20 0.450
174 A 18 10 1.00 20 0.500
175 A 11 8 1.00 18 0.444
176 A 0 0 0.00 0 0.000
177 A 0 0 0.00 0 0.000
178 A 0 0 0.00 0 0.000
179 A 18 4 1.00 20 0.200
180 A 10 4 1.00 20 0.200
181 A 5 3 1.00 18 0.167
182 A 0 0 0.00 0 0.000
183 A 0 0 0.00 0 0.000

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