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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 }

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, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 54, 55, 61, 62, 67, 68, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 119, 120, 121, 122, 123, 124, 125, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178 }

B grade: { 25, 27 }

C grade: { 48, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 118, 126, 127, 128, 136, 137, 146, 155, 164 }

F grade: { 106, 114, 165, 166, 167 }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 33, 34, 35, 39, 40, 42, 43, 44, 45, 46, 47, 54, 55, 61, 62, 67, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { 9, 10, 49, 50, 105, 112, 113 }

C grade: { 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75 }

F grade: { 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 38, 41, 48, 68, 73, 74, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 114, 115, 116, 117, 118, 119, 120, 126, 127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174, 175, 176 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 17, 20, 29, 33, 34, 35, 39, 40, 42, 43, 44, 45, 46, 47, 54, 55, 61, 62, 67, 68, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { 10, 12, 14 }

C grade: { }

F grade: { 8, 15, 16, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 36, 37, 38, 41, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75, 86, 87, 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, 126, 127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174, 175, 176 }

2.1.5 FriCAS

A grade: { 2, 4, 10, 11, 12, 13, 14, 23, 32, 33, 34, 35, 39, 40, 42, 43, 54, 55, 61, 62, 67, 68, 73, 74, 76, 77, 80, 81, 82, 83, 84, 85, 88, 92, 93, 94, 95, 118, 119, 120, 121, 122, 123, 124, 125, 128, 129, 130, 131, 132, 133, 134, 135, 138, 139, 141, 142, 143, 144, 147, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178 }

B grade: { 1, 3, 5, 6, 7, 9, 15, 17, 20, 21, 22, 29, 30, 31, 44, 45, 46, 47, 49, 50, 78, 79, 89, 90, 91, 105, 112, 113, 140, 148, 149, 156, 157, 158, 176 }

C grade: { }

F grade: { 8, 16, 18, 19, 24, 25, 26, 27, 28, 36, 37, 38, 41, 48, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 114, 115, 116, 117, 126, 127, 136, 137, 145, 146, 154, 155, 163, 164, 165, 166, 167 }

2.1.6 Sympy

A grade: { 9, 33, 34, 35, 39, 40, 42, 43, 61, 62, 67, 68, 121, 122, 123, 124, 125, 130, 131, 133, 134, 135, 141, 142, 143, 144, 153, 168, 171, 172, 177, 178 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 38, 41, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 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, 126, 127, 128, 129, 132, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 176 }

2.1.7 Giac

A grade: { 33, 34, 35, 39, 40, 42, 43, 54, 55, 61, 62, 67, 68, 73, 74, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 38, 41, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 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, 126, 127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174, 175, 176 }

2.1.8 Mupad

A grade: { 33, 34, 35, 39, 40, 42, 43, 54, 55, 61, 62, 67, 68, 73, 74, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { 6, 9, 10 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 38, 41, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 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, 126, 127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174, 175, 176 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 107 127 158 208 0 0 -1
normalized size 1 1.00 0.97 1.15 1.44 1.89 0.00 0.00 -0.01
time (sec) N/A 0.061 0.143 0.085 0.358 0.801 0.000 0.000 0.000
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 72 83 77 97 0 0 -1
normalized size 1 1.00 0.84 0.97 0.90 1.13 0.00 0.00 -0.01
time (sec) N/A 0.044 0.135 0.051 0.309 2.011 0.000 0.000 0.000
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 97 108 128 199 0 0 -1
normalized size 1 1.00 1.13 1.26 1.49 2.31 0.00 0.00 -0.01
time (sec) N/A 0.048 0.048 0.049 0.369 0.733 0.000 0.000 0.000
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 62 74 57 87 0 0 -1
normalized size 1 1.00 1.00 1.19 0.92 1.40 0.00 0.00 -0.02
time (sec) N/A 0.027 0.102 0.045 0.316 3.314 0.000 0.000 0.000
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 85 88 96 186 0 0 -1
normalized size 1 1.00 1.37 1.42 1.55 3.00 0.00 0.00 -0.02
time (sec) N/A 0.035 0.052 0.050 0.344 1.575 0.000 0.000 0.000
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 50 65 35 70 0 0 39
normalized size 1 1.00 1.32 1.71 0.92 1.84 0.00 0.00 1.03
time (sec) N/A 0.013 0.025 0.045 0.375 0.736 0.000 0.000 2.217
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 44 36 49 143 0 0 -1
normalized size 1 1.00 1.47 1.20 1.63 4.77 0.00 0.00 -0.03
time (sec) N/A 0.021 0.060 0.043 0.328 0.725 0.000 0.000 0.000
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 56 56 47 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.090 0.045 0.068 0.000 2.073 0.000 0.000 0.000
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 40 62 32 64 36 0 35
normalized size 1 1.00 1.33 2.07 1.07 2.13 1.20 0.00 1.17
time (sec) N/A 0.024 0.031 0.046 0.351 0.775 1.823 0.000 2.323
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 66 100 105 76 0 0 51
normalized size 1 1.00 1.32 2.00 2.10 1.52 0.00 0.00 1.02
time (sec) N/A 0.037 0.036 0.048 0.389 0.980 0.000 0.000 2.265
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 59 75 56 77 0 0 -1
normalized size 1 1.00 1.02 1.29 0.97 1.33 0.00 0.00 -0.02
time (sec) N/A 0.043 0.047 0.049 0.370 1.004 0.000 0.000 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 78 120 147 89 0 0 -1
normalized size 1 1.00 1.05 1.62 1.99 1.20 0.00 0.00 -0.01
time (sec) N/A 0.048 0.043 0.046 0.329 1.025 0.000 0.000 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 69 83 73 87 0 0 -1
normalized size 1 1.00 0.87 1.05 0.92 1.10 0.00 0.00 -0.01
time (sec) N/A 0.051 0.063 0.046 0.312 0.484 0.000 0.000 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 88 139 185 99 0 0 -1
normalized size 1 1.00 0.90 1.42 1.89 1.01 0.00 0.00 -0.01
time (sec) N/A 0.064 0.074 0.056 0.307 1.122 0.000 0.000 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 122 0 0 272 0 0 -1
normalized size 1 1.00 1.16 0.00 0.00 2.59 0.00 0.00 -0.01
time (sec) N/A 0.119 0.211 0.052 0.000 1.337 0.000 0.000 0.000
Problem 16 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 122 122 211 0 0 0 0 0 -1
normalized size 1 1.00 1.73 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.132 1.427 0.052 0.000 1.370 0.000 0.000 0.000
Problem 17 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 54 54 87 0 82 234 0 0 -1
normalized size 1 1.00 1.61 0.00 1.52 4.33 0.00 0.00 -0.02
time (sec) N/A 0.076 0.143 0.055 0.360 0.783 0.000 0.000 0.000
Problem 18 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 68 68 121 0 0 0 0 0 -1
normalized size 1 1.00 1.78 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.068 0.236 0.050 0.000 2.257 0.000 0.000 0.000
Problem 19 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 81 81 115 0 0 0 0 0 -1
normalized size 1 1.00 1.42 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.138 0.133 0.053 0.000 0.529 0.000 0.000 0.000
Problem 20 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 49 49 70 0 78 139 0 0 -1
normalized size 1 1.00 1.43 0.00 1.59 2.84 0.00 0.00 -0.02
time (sec) N/A 0.070 0.168 0.066 0.334 1.075 0.000 0.000 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 100 0 0 163 0 0 -1
normalized size 1 1.00 1.15 0.00 0.00 1.87 0.00 0.00 -0.01
time (sec) N/A 0.082 0.143 0.056 0.000 0.668 0.000 0.000 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 106 0 0 178 0 0 -1
normalized size 1 1.00 1.06 0.00 0.00 1.78 0.00 0.00 -0.01
time (sec) N/A 0.108 0.194 0.047 0.000 0.819 0.000 0.000 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 147 0 0 202 0 0 -1
normalized size 1 1.00 1.11 0.00 0.00 1.53 0.00 0.00 -0.01
time (sec) N/A 0.117 0.181 0.051 0.000 0.829 0.000 0.000 0.000
Problem 24 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 195 195 271 0 0 0 0 0 -1
normalized size 1 1.00 1.39 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.232 1.019 0.050 0.000 0.627 0.000 0.000 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 194 194 548 0 0 0 0 0 -1
normalized size 1 1.00 2.82 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.208 7.520 0.049 0.000 1.124 0.000 0.000 0.000
Problem 26 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 117 117 171 0 0 0 0 0 -1
normalized size 1 1.00 1.46 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.160 0.471 0.049 0.000 1.391 0.000 0.000 0.000
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 120 120 246 0 0 0 0 0 -1
normalized size 1 1.00 2.05 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.117 0.341 0.049 0.000 2.955 0.000 0.000 0.000
Problem 28 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 110 110 198 0 0 0 0 0 -1
normalized size 1 1.00 1.80 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.154 0.227 0.055 0.000 0.410 0.000 0.000 0.000
Problem 29 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 78 78 132 0 144 222 0 0 -1
normalized size 1 1.00 1.69 0.00 1.85 2.85 0.00 0.00 -0.01
time (sec) N/A 0.099 0.249 0.052 0.353 0.826 0.000 0.000 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 182 0 0 267 0 0 -1
normalized size 1 1.00 1.48 0.00 0.00 2.17 0.00 0.00 -0.01
time (sec) N/A 0.106 0.326 0.052 0.000 0.404 0.000 0.000 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 200 0 0 301 0 0 -1
normalized size 1 1.00 1.20 0.00 0.00 1.81 0.00 0.00 -0.01
time (sec) N/A 0.171 0.314 0.053 0.000 0.768 0.000 0.000 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 204 204 277 0 0 346 0 0 -1
normalized size 1 1.00 1.36 0.00 0.00 1.70 0.00 0.00 -0.00
time (sec) N/A 0.181 0.368 0.053 0.000 0.982 0.000 0.000 0.000
Problem 33 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 15 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 -0.07
time (sec) N/A 0.015 2.931 0.053 0.000 0.878 0.000 0.000 0.000
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 13 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 -0.08
time (sec) N/A 0.006 2.821 0.054 0.000 0.975 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 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 0.026 0.307 0.062 0.000 0.901 0.000 0.000 0.000
Problem 36 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 46 46 44 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 0.076 0.049 0.000 1.590 0.000 0.000 0.000
Problem 37 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 63 63 56 0 0 0 0 0 -1
normalized size 1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.141 0.076 0.048 0.000 2.149 0.000 0.000 0.000
Problem 38 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 117 117 91 0 0 0 0 0 -1
normalized size 1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.240 0.165 0.052 0.000 2.138 0.000 0.000 0.000
Problem 39 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 0.024 6.870 0.049 0.000 2.686 0.000 0.000 0.000
Problem 40 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 0.025 4.489 0.050 0.000 0.782 0.000 0.000 0.000
Problem 41 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 67 67 81 0 0 0 0 0 -1
normalized size 1 1.00 1.21 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.045 0.243 0.049 0.000 0.830 0.000 0.000 0.000
Problem 42 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 0.931 0.048 0.000 2.983 0.000 0.000 0.000
Problem 43 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 0.027 1.899 0.049 0.000 1.359 0.000 0.000 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 165 269 261 419 0 0 -1
normalized size 1 1.00 0.99 1.61 1.56 2.51 0.00 0.00 -0.01
time (sec) N/A 0.384 0.294 0.059 0.322 1.161 0.000 0.000 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 122 204 192 328 0 0 -1
normalized size 1 1.00 1.00 1.67 1.57 2.69 0.00 0.00 -0.01
time (sec) N/A 0.259 0.191 0.053 0.340 0.996 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 99 115 87 207 0 0 -1
normalized size 1 1.00 1.22 1.42 1.07 2.56 0.00 0.00 -0.01
time (sec) N/A 0.161 0.203 0.051 0.390 1.696 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 44 36 49 143 0 0 -1
normalized size 1 1.00 1.47 1.20 1.63 4.77 0.00 0.00 -0.03
time (sec) N/A 0.022 0.050 0.046 0.307 0.783 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 215 215 506 0 0 0 0 0 -1
normalized size 1 1.00 2.35 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.390 0.664 0.492 0.000 0.682 0.000 0.000 0.000
Problem 49 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 98 98 134 208 0 354 0 0 -1
normalized size 1 1.00 1.37 2.12 0.00 3.61 0.00 0.00 -0.01
time (sec) N/A 0.154 0.219 0.087 0.000 0.610 0.000 0.000 0.000
Problem 50 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 163 163 204 963 0 745 0 0 -1
normalized size 1 1.00 1.25 5.91 0.00 4.57 0.00 0.00 -0.01
time (sec) N/A 0.292 0.478 0.070 0.000 1.337 0.000 0.000 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 918 918 1094 2515 0 0 0 0 -1
normalized size 1 1.00 1.19 2.74 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.253 14.395 0.357 0.000 0.000 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 679 679 418 1964 0 0 0 0 -1
normalized size 1 1.00 0.62 2.89 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.519 1.678 0.085 0.000 0.000 0.000 0.000 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 429 429 926 840 0 0 0 0 -1
normalized size 1 1.00 2.16 1.96 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.708 14.077 0.079 0.000 0.000 0.000 0.000 0.000
Problem 54 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 24 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 0.076 19.511 6.871 0.000 0.573 0.000 0.000 0.000
Problem 55 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 24 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 0.079 7.967 5.921 0.000 0.924 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 486 486 380 1939 0 0 0 0 -1
normalized size 1 1.00 0.78 3.99 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.023 1.607 0.068 0.000 11.811 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 939 939 1098 2543 0 0 0 0 -1
normalized size 1 1.00 1.17 2.71 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.871 14.302 0.078 0.000 15.322 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 707 707 1012 1991 0 0 0 0 -1
normalized size 1 1.00 1.43 2.82 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.142 14.426 0.073 0.000 0.000 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 474 474 343 868 0 0 0 0 -1
normalized size 1 1.00 0.72 1.83 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.751 1.335 0.071 0.000 0.000 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 284 284 307 395 0 0 0 0 -1
normalized size 1 1.00 1.08 1.39 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.414 5.224 0.066 0.000 0.000 0.000 0.000 0.000
Problem 61 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 24 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 0.077 6.551 1.532 0.000 1.122 0.000 0.000 0.000
Problem 62 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 24 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 0.082 9.214 5.263 0.000 0.833 0.000 0.000 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 731 731 1042 2019 0 0 0 0 -1
normalized size 1 1.00 1.43 2.76 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.636 14.699 0.075 0.000 16.601 0.000 0.000 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 499 499 979 896 0 0 0 0 -1
normalized size 1 1.00 1.96 1.80 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.010 14.494 0.073 0.000 0.000 0.000 0.000 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 318 318 264 418 0 0 0 0 -1
normalized size 1 1.00 0.83 1.31 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.691 1.585 0.071 0.000 0.000 0.000 0.000 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 166 328 0 0 0 0 -1
normalized size 1 1.00 1.11 2.20 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.284 0.682 0.072 0.000 9.003 0.000 0.000 0.000
Problem 67 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 24 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 0.090 12.169 6.987 0.000 0.809 0.000 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 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 0.099 15.678 180.000 0.000 1.347 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 777 777 1108 2726 0 0 0 0 -1
normalized size 1 1.00 1.43 3.51 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.186 14.487 0.089 0.000 16.418 0.000 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 569 569 1076 2497 0 0 0 0 -1
normalized size 1 1.00 1.89 4.39 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.497 14.383 0.084 0.000 0.000 0.000 0.000 0.000
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 393 393 390 2107 0 0 0 0 -1
normalized size 1 1.00 0.99 5.36 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.191 2.514 0.075 0.000 8.178 0.000 0.000 0.000
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 369 369 892 2079 0 0 0 0 -1
normalized size 1 1.00 2.42 5.63 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.567 14.102 0.073 0.000 0.000 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 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 0.094 28.845 180.000 0.000 3.642 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 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 0.106 28.471 180.000 0.000 2.038 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 648 785 1217 3782 0 0 0 0 -1
normalized size 1 1.21 1.88 5.84 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.035 14.494 0.107 0.000 9.390 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 214 214 138 211 289 295 0 0 -1
normalized size 1 1.00 0.64 0.99 1.35 1.38 0.00 0.00 -0.00
time (sec) N/A 0.132 0.235 0.051 0.372 1.951 0.000 0.000 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 119 171 227 273 0 0 -1
normalized size 1 1.00 0.71 1.02 1.36 1.63 0.00 0.00 -0.01
time (sec) N/A 0.109 0.170 0.051 0.380 3.015 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 135 126 148 245 0 0 -1
normalized size 1 1.00 1.17 1.10 1.29 2.13 0.00 0.00 -0.01
time (sec) N/A 0.056 0.261 0.056 0.348 1.012 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 89 107 84 222 0 0 -1
normalized size 1 1.00 0.98 1.18 0.92 2.44 0.00 0.00 -0.01
time (sec) N/A 0.068 0.132 0.066 0.369 0.799 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 68 122 91 105 0 0 -1
normalized size 1 1.00 0.62 1.12 0.83 0.96 0.00 0.00 -0.01
time (sec) N/A 0.079 0.084 0.069 0.350 0.946 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 158 158 93 140 132 127 0 0 -1
normalized size 1 1.00 0.59 0.89 0.84 0.80 0.00 0.00 -0.01
time (sec) N/A 0.103 0.124 0.065 0.315 0.950 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 109 158 165 146 0 0 -1
normalized size 1 1.00 0.53 0.77 0.80 0.71 0.00 0.00 -0.00
time (sec) N/A 0.122 0.146 0.058 0.326 1.045 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 204 204 114 152 176 165 0 0 -1
normalized size 1 1.00 0.56 0.75 0.86 0.81 0.00 0.00 -0.00
time (sec) N/A 0.161 0.249 0.055 0.336 0.822 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 159 159 97 134 137 144 0 0 -1
normalized size 1 1.00 0.61 0.84 0.86 0.91 0.00 0.00 -0.01
time (sec) N/A 0.134 0.211 0.050 0.315 0.888 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 146 146 77 115 95 123 0 0 -1
normalized size 1 1.00 0.53 0.79 0.65 0.84 0.00 0.00 -0.01
time (sec) N/A 0.106 0.101 0.049 0.343 1.126 0.000 0.000 0.000
Problem 86 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 115 115 93 0 0 0 0 0 -1
normalized size 1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.291 0.141 0.106 0.000 0.952 0.000 0.000 0.000
Problem 87 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 128 128 138 0 0 0 0 0 -1
normalized size 1 1.00 1.08 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.300 0.567 0.107 0.000 2.671 0.000 0.000 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 260 260 182 286 396 388 0 0 -1
normalized size 1 1.00 0.70 1.10 1.52 1.49 0.00 0.00 -0.00
time (sec) N/A 0.258 0.357 0.060 0.334 1.327 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 197 197 149 217 287 353 0 0 -1
normalized size 1 1.00 0.76 1.10 1.46 1.79 0.00 0.00 -0.01
time (sec) N/A 0.128 0.228 0.049 0.356 1.152 0.000 0.000 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 170 170 134 189 191 347 0 0 -1
normalized size 1 1.00 0.79 1.11 1.12 2.04 0.00 0.00 -0.01
time (sec) N/A 0.139 0.218 0.064 0.408 1.216 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 164 164 123 190 152 334 0 0 -1
normalized size 1 1.00 0.75 1.16 0.93 2.04 0.00 0.00 -0.01
time (sec) N/A 0.143 0.270 0.065 0.327 0.919 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 126 191 175 165 0 0 -1
normalized size 1 1.00 0.67 1.01 0.93 0.87 0.00 0.00 -0.01
time (sec) N/A 0.160 0.225 0.060 0.359 0.634 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 249 249 152 223 232 197 0 0 -1
normalized size 1 1.00 0.61 0.90 0.93 0.79 0.00 0.00 -0.00
time (sec) N/A 0.197 0.262 0.062 0.450 1.008 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 250 250 159 214 244 224 0 0 -1
normalized size 1 1.00 0.64 0.86 0.98 0.90 0.00 0.00 -0.00
time (sec) N/A 0.235 0.388 0.053 0.375 1.249 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 123 182 183 189 0 0 -1
normalized size 1 1.00 0.61 0.90 0.90 0.93 0.00 0.00 -0.00
time (sec) N/A 0.156 0.311 0.050 0.368 1.163 0.000 0.000 0.000
Problem 96 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 178 178 148 0 0 0 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.421 0.423 0.427 0.000 0.947 0.000 0.000 0.000
Problem 97 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 178 178 187 0 0 0 0 0 -1
normalized size 1 1.00 1.05 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.424 0.907 0.457 0.000 0.663 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 512 512 1221 0 0 0 0 0 -1
normalized size 1 1.00 2.38 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.198 1.666 3.395 0.000 0.614 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 467 449 1103 0 0 0 0 0 -1
normalized size 1 0.96 2.36 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.106 0.351 0.462 0.000 0.945 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 477 477 1055 0 0 0 0 0 -1
normalized size 1 1.00 2.21 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.849 0.508 1.453 0.000 0.805 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 425 425 387 0 0 0 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.862 0.978 0.444 0.000 0.715 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 518 518 1211 0 0 0 0 0 -1
normalized size 1 1.00 2.34 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.060 1.687 2.759 0.000 1.042 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 591 571 1447 0 0 0 0 0 -1
normalized size 1 0.97 2.45 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.282 6.365 0.444 0.000 0.565 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 553 535 1410 0 0 0 0 0 -1
normalized size 1 0.97 2.55 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.249 2.414 0.440 0.000 1.947 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 139 139 271 360 0 615 0 0 -1
normalized size 1 1.00 1.95 2.59 0.00 4.42 0.00 0.00 -0.01
time (sec) N/A 0.150 0.792 0.074 0.000 0.943 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 515 515 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.153 44.155 0.482 0.000 1.670 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 756 756 1583 0 0 0 0 0 -1
normalized size 1 1.00 2.09 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.468 6.172 15.131 0.000 0.854 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 719 719 1442 0 0 0 0 0 -1
normalized size 1 1.00 2.01 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.242 2.736 3.510 0.000 0.572 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 713 713 1437 0 0 0 0 0 -1
normalized size 1 1.00 2.02 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.187 3.648 4.649 0.000 0.814 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 758 758 1487 0 0 0 0 0 -1
normalized size 1 1.00 1.96 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.246 3.119 14.660 0.000 2.023 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 694 676 2023 0 0 0 0 0 -1
normalized size 1 0.97 2.91 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.408 7.854 0.490 0.000 2.920 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(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 375 1922 0 1381 0 0 -1
normalized size 1 1.00 2.25 11.51 0.00 8.27 0.00 0.00 -0.01
time (sec) N/A 0.215 1.476 0.094 0.000 3.046 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 368 1892 0 1256 0 0 -1
normalized size 1 1.00 1.80 9.23 0.00 6.13 0.00 0.00 -0.00
time (sec) N/A 0.205 0.957 0.079 0.000 1.430 0.000 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 657 657 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.322 70.345 0.444 0.000 0.841 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1106 1106 2045 0 0 0 0 0 -1
normalized size 1 1.00 1.85 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.741 6.214 3.803 0.000 0.956 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1106 1106 2053 0 0 0 0 0 -1
normalized size 1 1.00 1.86 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.046 6.148 5.009 0.000 0.657 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1096 1096 2038 0 0 0 0 0 -1
normalized size 1 1.00 1.86 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.743 6.066 3.774 0.000 0.876 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F A F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 413 413 345 0 0 1951 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 4.72 0.00 0.00 -0.00
time (sec) N/A 1.412 0.705 0.434 0.000 5.103 0.000 0.000 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 302 302 337 0 0 1625 0 0 -1
normalized size 1 1.00 1.12 0.00 0.00 5.38 0.00 0.00 -0.00
time (sec) N/A 0.434 0.752 0.440 0.000 1.798 0.000 0.000 0.000
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 278 0 0 1342 0 0 -1
normalized size 1 1.00 1.37 0.00 0.00 6.61 0.00 0.00 -0.00
time (sec) N/A 0.206 0.511 0.479 0.000 1.105 0.000 0.000 0.000
Problem 121 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.100 5.625 0.449 0.000 0.524 0.000 0.000 0.000
Problem 122 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.106 5.399 0.450 0.000 0.644 0.000 0.000 0.000
Problem 123 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.101 9.309 0.426 0.000 0.656 0.000 0.000 0.000
Problem 124 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 0.037 2.656 0.422 0.000 0.426 0.000 0.000 0.000
Problem 125 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.090 1.779 0.455 0.000 0.531 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 389 389 237 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 0.427 0.619 0.438 0.000 0.656 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 527 527 314 0 0 0 0 0 -1
normalized size 1 1.00 0.60 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.638 0.696 0.434 0.000 0.714 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F A F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 384 384 318 0 0 1943 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 5.06 0.00 0.00 -0.00
time (sec) N/A 0.514 0.769 0.479 0.000 3.407 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 270 270 314 0 0 1625 0 0 -1
normalized size 1 1.00 1.16 0.00 0.00 6.02 0.00 0.00 -0.00
time (sec) N/A 0.281 0.798 0.431 0.000 2.007 0.000 0.000 0.000
Problem 130 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.117 6.559 0.433 0.000 0.653 0.000 0.000 0.000
Problem 131 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.123 5.860 0.420 0.000 0.727 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.120 9.669 0.613 0.000 0.704 0.000 0.000 0.000
Problem 133 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 0.044 3.523 0.440 0.000 0.426 0.000 0.000 0.000
Problem 134 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.106 5.794 0.447 0.000 0.651 0.000 0.000 0.000
Problem 135 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.108 15.969 0.446 0.000 0.594 0.000 0.000 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 492 492 291 0 0 0 0 0 -1
normalized size 1 1.00 0.59 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.575 0.703 0.427 0.000 0.580 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 643 643 372 0 0 0 0 0 -1
normalized size 1 1.00 0.58 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.866 0.828 0.463 0.000 0.630 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 329 329 339 0 0 1633 0 0 -1
normalized size 1 1.00 1.03 0.00 0.00 4.96 0.00 0.00 -0.00
time (sec) N/A 1.179 0.789 0.449 0.000 1.824 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 280 0 0 1341 0 0 -1
normalized size 1 1.00 1.22 0.00 0.00 5.86 0.00 0.00 -0.00
time (sec) N/A 0.318 0.565 0.441 0.000 1.023 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 223 0 0 1064 0 0 -1
normalized size 1 1.00 1.65 0.00 0.00 7.88 0.00 0.00 -0.01
time (sec) N/A 0.154 0.240 0.433 0.000 0.689 0.000 0.000 0.000
Problem 141 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.096 1.745 0.422 0.000 0.665 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.108 23.255 0.463 0.000 0.440 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.092 6.333 0.437 0.000 0.497 0.000 0.000 0.000
Problem 144 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 0.031 1.046 0.433 0.000 0.657 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 Yes TBD TBD TBD TBD TBD TBD
size 294 294 139 0 0 0 0 0 -1
normalized size 1 1.00 0.47 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.251 0.207 0.506 0.000 0.613 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 425 425 239 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 0.486 0.636 0.493 0.000 0.900 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 256 256 311 0 0 1719 0 0 -1
normalized size 1 1.00 1.21 0.00 0.00 6.71 0.00 0.00 -0.00
time (sec) N/A 1.135 0.644 0.470 0.000 1.034 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 160 160 233 0 0 1274 0 0 -1
normalized size 1 1.00 1.46 0.00 0.00 7.96 0.00 0.00 -0.01
time (sec) N/A 0.275 0.375 0.437 0.000 0.840 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 122 0 0 368 0 0 -1
normalized size 1 1.00 1.49 0.00 0.00 4.49 0.00 0.00 -0.01
time (sec) N/A 0.111 0.165 0.443 0.000 0.690 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.121 32.960 0.443 0.000 0.676 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.133 38.594 0.457 0.000 0.563 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.111 8.805 0.439 0.000 0.614 0.000 0.000 0.000
Problem 153 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.107 5.019 0.429 0.000 0.500 0.000 0.000 0.000
Problem 154 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 111 111 113 0 0 0 0 0 -1
normalized size 1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.075 0.197 0.459 0.000 0.993 0.000 0.000 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 321 321 201 0 0 0 0 0 -1
normalized size 1 1.00 0.63 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.320 0.457 0.448 0.000 0.612 0.000 0.000 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 251 251 327 0 0 2421 0 0 -1
normalized size 1 1.00 1.30 0.00 0.00 9.65 0.00 0.00 -0.00
time (sec) N/A 1.229 0.562 0.440 0.000 1.106 0.000 0.000 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 169 169 201 0 0 786 0 0 -1
normalized size 1 1.00 1.19 0.00 0.00 4.65 0.00 0.00 -0.01
time (sec) N/A 0.268 0.298 0.452 0.000 0.938 0.000 0.000 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 185 0 0 698 0 0 -1
normalized size 1 1.00 1.28 0.00 0.00 4.85 0.00 0.00 -0.01
time (sec) N/A 0.144 0.234 0.430 0.000 0.658 0.000 0.000 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.124 45.844 0.502 0.000 0.694 0.000 0.000 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.152 59.836 0.509 0.000 0.761 0.000 0.000 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.132 13.403 0.477 0.000 0.789 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.110 12.602 0.442 0.000 0.615 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 359 359 189 0 0 0 0 0 -1
normalized size 1 1.00 0.53 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.308 0.296 0.428 0.000 0.507 0.000 0.000 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 278 278 248 0 0 0 0 0 -1
normalized size 1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.177 0.560 0.436 0.000 0.522 0.000 0.000 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 596 577 0 0 0 0 0 0 -1
normalized size 1 0.97 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.575 0.228 0.425 0.000 0.776 0.000 0.000 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 379 360 0 0 0 0 0 0 -1
normalized size 1 0.95 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.491 0.156 0.409 0.000 0.493 0.000 0.000 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 220 208 0 0 0 0 0 0 -1
normalized size 1 0.95 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.220 0.114 0.059 0.000 0.565 0.000 0.000 0.000
Problem 168 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 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.079 1.867 0.445 0.000 0.634 0.000 0.000 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.076 6.956 0.430 0.000 0.884 0.000 0.000 0.000
Problem 170 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 28 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 0.116 1.145 0.450 0.000 0.559 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 28 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 0.104 0.117 0.464 0.000 0.607 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 28 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 0.103 1.459 0.443 0.000 0.711 0.000 0.000 0.000
Problem 173 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 28 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 0.115 1.872 0.516 0.000 0.549 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 395 395 214 0 0 382 0 0 -1
normalized size 1 1.00 0.54 0.00 0.00 0.97 0.00 0.00 -0.00
time (sec) N/A 2.344 0.314 0.547 0.000 0.609 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 264 264 180 0 0 324 0 0 -1
normalized size 1 1.00 0.68 0.00 0.00 1.23 0.00 0.00 -0.00
time (sec) N/A 1.916 0.418 0.477 0.000 0.590 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 133 141 0 0 265 0 0 -1
normalized size 1 1.02 1.08 0.00 0.00 2.04 0.00 0.00 -0.01
time (sec) N/A 0.214 0.337 0.464 0.000 0.680 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 A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 29 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 -0.03
time (sec) N/A 0.091 0.411 0.446 0.000 0.455 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 A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 29 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 -0.03
time (sec) N/A 0.104 3.487 0.456 0.000 0.747 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 [69] had the largest ratio of [.8571]

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 7 5 1.00 12 0.417
2 A 4 3 1.00 12 0.250
3 A 6 5 1.00 12 0.417
4 A 3 3 1.00 12 0.250
5 A 5 5 1.00 12 0.417
6 A 2 2 1.00 10 0.200
7 A 5 4 1.00 8 0.500
8 A 6 6 1.00 12 0.500
9 A 2 2 1.00 12 0.167
10 A 4 4 1.00 12 0.333
11 A 4 3 1.00 12 0.250
12 A 5 4 1.00 12 0.333
13 A 4 3 1.00 12 0.250
14 A 6 4 1.00 12 0.333
15 A 5 5 1.00 14 0.357
16 A 8 6 1.00 14 0.429
17 A 4 4 1.00 12 0.333
18 A 7 5 1.00 10 0.500
19 A 6 6 1.00 14 0.429
20 A 4 3 1.00 14 0.214
21 A 4 3 1.00 14 0.214
22 A 5 5 1.00 14 0.357
23 A 5 3 1.00 14 0.214
24 A 10 10 1.00 14 0.714
25 A 11 8 1.00 14 0.571
26 A 7 7 1.00 12 0.583
27 A 9 6 1.00 10 0.600
28 A 7 7 1.00 14 0.500
29 A 5 3 1.00 14 0.214
30 A 6 6 1.00 14 0.429
31 A 8 6 1.00 14 0.429
32 A 10 6 1.00 14 0.429
33 A 0 0 0.00 0 0.000
34 A 0 0 0.00 0 0.000
35 A 0 0 0.00 0 0.000
36 A 4 4 1.00 14 0.286
37 A 6 6 1.00 14 0.429
38 A 9 5 1.00 14 0.357
39 A 0 0 0.00 0 0.000
40 A 0 0 0.00 0 0.000
41 A 3 3 1.00 14 0.214
42 A 0 0 0.00 0 0.000
43 A 0 0 0.00 0 0.000
44 A 11 9 1.00 16 0.562
45 A 10 9 1.00 16 0.562
46 A 9 9 1.00 14 0.643
47 A 5 4 1.00 8 0.500
48 A 4 2 1.00 16 0.125
49 A 7 7 1.00 16 0.438
50 A 8 8 1.00 16 0.500
51 A 31 16 1.00 21 0.762
52 A 24 15 1.00 19 0.790
53 A 15 11 1.00 18 0.611
54 A 0 0 0.00 0 0.000
55 A 0 0 0.00 0 0.000
56 A 22 13 1.00 18 0.722
57 A 27 17 1.00 21 0.810
58 A 20 15 1.00 21 0.714
59 A 14 13 1.00 19 0.684
60 A 9 9 1.00 18 0.500
61 A 0 0 0.00 0 0.000
62 A 0 0 0.00 0 0.000
63 A 23 15 1.00 21 0.714
64 A 16 13 1.00 21 0.619
65 A 11 11 1.00 19 0.579
66 A 6 6 1.00 18 0.333
67 A 0 0 0.00 0 0.000
68 A 0 0 0.00 0 0.000
69 A 31 18 1.00 21 0.857
70 A 25 17 1.00 21 0.810
71 A 19 14 1.00 19 0.737
72 A 12 11 1.00 18 0.611
73 A 0 0 0.00 0 0.000
74 A 0 0 0.00 0 0.000
75 A 19 14 1.21 18 0.778
76 A 7 7 1.00 19 0.368
77 A 6 7 1.00 19 0.368
78 A 5 5 1.00 16 0.312
79 A 4 5 1.00 19 0.263
80 A 4 5 1.00 19 0.263
81 A 5 6 1.00 19 0.316
82 A 6 6 1.00 19 0.316
83 A 5 5 1.00 19 0.263
84 A 5 5 1.00 19 0.263
85 A 6 5 1.00 17 0.294
86 A 11 11 1.00 19 0.579
87 A 13 13 1.00 19 0.684
88 A 7 8 1.00 21 0.381
89 A 6 7 1.00 18 0.389
90 A 6 7 1.00 21 0.333
91 A 6 7 1.00 21 0.333
92 A 5 6 1.00 21 0.286
93 A 6 7 1.00 21 0.333
94 A 5 6 1.00 21 0.286
95 A 6 5 1.00 19 0.263
96 A 12 13 1.00 21 0.619
97 A 14 15 1.00 21 0.714
98 A 25 12 1.00 21 0.571
99 A 26 9 0.96 19 0.474
100 A 19 7 1.00 18 0.389
101 A 19 7 1.00 21 0.333
102 A 24 10 1.00 21 0.476
103 A 31 14 0.97 21 0.667
104 A 29 12 0.97 21 0.571
105 A 7 6 1.00 19 0.316
106 A 24 10 1.00 21 0.476
107 A 51 15 1.00 21 0.714
108 A 27 10 1.00 21 0.476
109 A 47 11 1.00 18 0.611
110 A 50 13 1.00 21 0.619
111 A 33 13 0.97 21 0.619
112 A 6 7 1.00 21 0.333
113 A 8 7 1.00 19 0.368
114 A 28 11 1.00 21 0.524
115 A 35 11 1.00 21 0.524
116 A 63 12 1.00 21 0.571
117 A 81 12 1.00 18 0.667
118 A 12 12 1.00 23 0.522
119 A 11 12 1.00 23 0.522
120 A 9 9 1.00 21 0.429
121 A 0 0 0.00 0 0.000
122 A 0 0 0.00 0 0.000
123 A 0 0 0.00 0 0.000
124 A 0 0 0.00 0 0.000
125 A 0 0 0.00 0 0.000
126 A 8 9 1.00 23 0.391
127 A 9 10 1.00 23 0.435
128 A 12 12 1.00 23 0.522
129 A 10 10 1.00 21 0.476
130 A 0 0 0.00 0 0.000
131 A 0 0 0.00 0 0.000
132 A 0 0 0.00 0 0.000
133 A 0 0 0.00 0 0.000
134 A 0 0 0.00 0 0.000
135 A 0 0 0.00 0 0.000
136 A 9 10 1.00 23 0.435
137 A 10 10 1.00 23 0.435
138 A 11 12 1.00 23 0.522
139 A 10 12 1.00 23 0.522
140 A 8 8 1.00 21 0.381
141 A 0 0 0.00 0 0.000
142 A 0 0 0.00 0 0.000
143 A 0 0 0.00 0 0.000
144 A 0 0 0.00 0 0.000
145 A 8 9 1.00 23 0.391
146 A 8 10 1.00 23 0.435
147 A 10 11 1.00 23 0.478
148 A 9 11 1.00 23 0.478
149 A 4 4 1.00 21 0.190
150 A 0 0 0.00 0 0.000
151 A 0 0 0.00 0 0.000
152 A 0 0 0.00 0 0.000
153 A 0 0 0.00 0 0.000
154 A 3 4 1.00 20 0.200
155 A 7 9 1.00 23 0.391
156 A 10 11 1.00 23 0.478
157 A 7 8 1.00 23 0.348
158 A 5 5 1.00 21 0.238
159 A 0 0 0.00 0 0.000
160 A 0 0 0.00 0 0.000
161 A 0 0 0.00 0 0.000
162 A 0 0 0.00 0 0.000
163 A 7 8 1.00 23 0.348
164 A 5 7 1.00 20 0.350
165 A 6 7 0.97 23 0.304
166 A 6 7 0.95 23 0.304
167 A 5 6 0.95 21 0.286
168 A 0 0 0.00 0 0.000
169 A 0 0 0.00 0 0.000
170 A 0 0 0.00 0 0.000
171 A 0 0 0.00 0 0.000
172 A 0 0 0.00 0 0.000
173 A 0 0 0.00 0 0.000
174 A 16 11 1.00 26 0.423
175 A 13 11 1.00 26 0.423
176 A 8 9 1.02 26 0.346
177 A 0 0 0.00 0 0.000
178 A 0 0 0.00 0 0.000

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