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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

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

B grade: { }

C grade: { 186 }

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, 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, 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, 133, 134, 140, 142, 143, 144, 151, 152, 153, 154, 155, 156, 157, 159, 161, 163, 164, 165, 167, 169, 171, 173, 175, 178, 179, 182, 183, 184, 186, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201 }

B grade: { 27, 85, 86, 129, 132, 135, 136, 137, 145, 146, 185, 187, 188 }

C grade: { 158, 160, 162, 166, 168, 170, 172, 174, 176, 177, 180, 181 }

F grade: { 130, 131, 138, 139, 141, 147, 148, 149, 150}

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 45, 46, 47, 55, 56, 57, 58, 59, 63, 64, 65, 66, 67, 72, 73, 74, 75, 76, 77, 87, 88, 89, 90, 91, 98, 99, 100, 101, 102, 104, 108, 109, 110, 111, 112, 119, 120, 121, 122, 123, 124, 127, 135, 144, 151, 152, 153, 154, 155, 156, 157, 159, 161, 167, 169, 171, 173, 177, 178, 191, 192, 193, 194, 195, 197, 200 }

B grade: { 9, 11, 12, 13, 14, 19, 28, 29, 30, 31, 35, 36, 37, 38, 48, 49, 50, 51, 52, 53, 54, 60, 61, 62, 68, 69, 70, 71, 92, 93, 95, 96, 97, 103, 105, 106, 107, 113, 114, 115, 116, 117, 118, 164, 196, 198, 199, 201 }

C grade: { 24, 25, 26, 27, 32, 33, 34, 158, 160, 162, 166, 168, 170, 172, 174, 176, 186 }

F grade: { 15, 16, 17, 18, 20, 21, 22, 23, 39, 40, 41, 42, 43, 44, 78, 79, 80, 81, 82, 83, 84, 85, 86, 94, 125, 126, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 163, 165, 175, 179, 180, 181, 182, 183, 184, 185, 187, 188, 189, 190 }

2.1.4 Maxima

A grade: { 1, 2, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 48, 49, 50, 51, 52, 54, 56, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 88, 89, 90, 107, 108, 109, 110, 111, 117, 119, 120, 122, 152, 153, 154, 155, 156, 157, 159, 171, 179, 191, 192

B grade: { 3, 4, 5, 6, 7, 8, 24, 25, 45, 46, 47, 53, 55, 57, 58, 59, 61, 63, 87, 103, 104, 105, 106, 112, 113, 115, 124, 151, 167, 186, 187, 188, 194 }

C grade: { }

F grade: { 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 39, 40, 41, 42, 43, 44, 60, 62, 65, 67, 78, 79, 80, 81, 82, 83, 84, 85, 86, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 114, 116, 118, 121, 123, 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, 158, 160, 161, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 189, 190, 193, 195, 196, 197, 198, 199, 200, 201 }

2.1.5 FriCAS

A grade: { 1, 27, 28, 29, 30, 31, 34, 52, 53, 54, 64, 70, 71, 72, 73, 76, 77, 90, 91, 99, 100, 107, 108, 110, 118, 119, 120, 154, 155, 156, 157, 161, 165, 167, 169, 173, 175, 177, 179, 181, 191 }

B grade: { 2, 3, 4, 5, 6, 7, 8, 24, 25, 26, 32, 33, 35, 36, 37, 38, 45, 46, 47, 48, 49, 50, 51, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 74, 75, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 109, 111, 112, 113, 114, 115, 116, 117, 121, 122, 123, 124, 125, 126, 127, 128, 133, 134, 135, 136, 142, 143, 144, 151, 152, 153, 159, 163, 171, 186, 187, 188, 189, 190, 192, 193, 194, 195 }

C grade: { }

F grade: { 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 39, 40, 41, 42, 43, 44, 94, 129, 130, 131, 132, 137, 138, 139, 140, 141, 145, 146, 147, 148, 149, 150, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 183, 184, 185, 196, 197, 198, 199, 200, 201 }

2.1.6 Sympy

A grade: { 28, 29, 30, 35, 36, 37, 119 }

B grade: { 108 }

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, 31, 32, 33, 34, 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, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201 }

2.1.7 Giac

A grade: { 1, 2, 4, 6, 7, 8, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 114, 116, 118, 119, 120, 121, 122, 123, 151, 152, 153, 154, 155, 156, 157, 187, 188, 191, 192, 194, 195 }

B grade: { 3, 5, 26, 58, 59, 66, 79, 80, 83, 85, 86, 106, 113, 115, 117, 124, 193 }

C grade: { }

F grade: { 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 39, 40, 41, 42, 43, 44, 81, 82, 84, 94, 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, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 189, 190, 196, 197, 198, 199, 200, 201 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 12 15 58 0 16
normalized size 1 1. 1. 1.09 1.36 5.27 0. 1.45
time (sec) N/A 0.005 0.002 0.004 1.004 2.007 0. 1.097
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 11 24 111 0 24
normalized size 1 1. 1. 1.1 2.4 11.1 0. 2.4
time (sec) N/A 0.01 0.003 0.005 0.991 2.071 0. 1.139
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 34 30 88 757 0 107
normalized size 1 1. 1. 0.88 2.59 22.26 0. 3.15
time (sec) N/A 0.016 0.009 0.01 1.497 1.996 0. 1.132
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 26 23 122 448 0 42
normalized size 1 1. 1. 0.88 4.69 17.23 0. 1.62
time (sec) N/A 0.012 0.006 0.012 1.018 1.963 0. 1.154
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 47 50 151 2263 0 140
normalized size 1 1. 0.85 0.91 2.75 41.15 0. 2.55
time (sec) N/A 0.028 0.041 0.01 1.512 2.149 0. 1.144
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 41 33 277 954 0 57
normalized size 1 1. 1. 0.8 6.76 23.27 0. 1.39
time (sec) N/A 0.015 0.011 0.013 1.018 2.092 0. 1.124
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 17 66 331 0 24
normalized size 1 1. 1. 0.89 3.47 17.42 0. 1.26
time (sec) N/A 0.01 0.004 0.007 1.045 2.11 0. 1.134
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 27 185 859 0 41
normalized size 1 1. 1. 0.77 5.29 24.54 0. 1.17
time (sec) N/A 0.014 0.004 0.009 1.028 2.129 0. 1.143
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 51 217 0 0 0 0
normalized size 1 1. 0.77 3.29 0. 0. 0. 0.
time (sec) N/A 0.032 0.075 0.276 0. 0. 0. 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 49 103 0 0 0 0
normalized size 1 1. 0.79 1.66 0. 0. 0. 0.
time (sec) N/A 0.03 0.043 0.287 0. 0. 0. 0.
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 40 135 0 0 0 0
normalized size 1 1. 1. 3.38 0. 0. 0. 0.
time (sec) N/A 0.02 0.029 0.241 0. 0. 0. 0.
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 40 135 0 0 0 0
normalized size 1 1. 1. 3.38 0. 0. 0. 0.
time (sec) N/A 0.02 0.034 0.245 0. 0. 0. 0.
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 53 174 0 0 0 0
normalized size 1 1. 0.8 2.64 0. 0. 0. 0.
time (sec) N/A 0.032 0.045 0.277 0. 0. 0. 0.
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 59 188 0 0 0 0
normalized size 1 1. 0.89 2.85 0. 0. 0. 0.
time (sec) N/A 0.033 0.07 0.309 0. 0. 0. 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 68 0 0 0 0 0
normalized size 1 1. 0.67 0. 0. 0. 0. 0.
time (sec) N/A 0.06 0.197 0.099 0. 0. 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 56 0 0 0 0 0
normalized size 1 1. 0.76 0. 0. 0. 0. 0.
time (sec) N/A 0.038 0.07 0.079 0. 0. 0. 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 52 0 0 0 0 0
normalized size 1 1. 0.74 0. 0. 0. 0. 0.
time (sec) N/A 0.038 0.039 0.079 0. 0. 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 42 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.022 0.021 0.138 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 42 244 0 0 0 0
normalized size 1 1. 1. 5.81 0. 0. 0. 0.
time (sec) N/A 0.022 0.03 0.141 0. 0. 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 63 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.039 0.063 0.083 0. 0. 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 64 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.039 0.081 0.082 0. 0. 0. 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 70 0 0 0 0 0
normalized size 1 1. 0.67 0. 0. 0. 0. 0.
time (sec) N/A 0.058 0.127 0.082 0. 0. 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 60 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.037 0.062 0.191 0. 0. 0. 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 81 230 211 4601 0 170
normalized size 1 1. 0.9 2.56 2.34 51.12 0. 1.89
time (sec) N/A 0.03 0.101 0.177 1.525 2.334 0. 1.106
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 55 208 151 2263 0 140
normalized size 1 1. 0.85 3.2 2.32 34.82 0. 2.15
time (sec) N/A 0.022 0.115 0.129 1.51 2.208 0. 1.14
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 46 183 88 757 0 107
normalized size 1 1. 1.15 4.58 2.2 18.92 0. 2.68
time (sec) N/A 0.017 0.041 0.12 1.541 2.152 0. 1.122
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 29 130 15 58 0 16
normalized size 1 1. 2.64 11.82 1.36 5.27 0. 1.45
time (sec) N/A 0.011 0.016 0.132 0.996 2.002 0. 1.141
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 97 35 23 29 31
normalized size 1 1. 1. 4.41 1.59 1.05 1.32 1.41
time (sec) N/A 0.016 0.026 0.106 0.977 1.973 16.08 1.15
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 44 201 73 89 54 65
normalized size 1 1. 0.86 3.94 1.43 1.75 1.06 1.27
time (sec) N/A 0.02 0.066 0.104 1.012 2.047 20.335 1.138
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 47 305 111 182 80 95
normalized size 1 1. 0.62 4.01 1.46 2.39 1.05 1.25
time (sec) N/A 0.027 0.082 0.098 1.031 2.125 54.543 1.128
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 57 409 135 302 0 124
normalized size 1 1. 0.56 4.05 1.34 2.99 0. 1.23
time (sec) N/A 0.035 0.131 0.102 1.018 2.073 0. 1.12
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 42 127 97 3067 0 88
normalized size 1 1. 0.65 1.95 1.49 47.18 0. 1.35
time (sec) N/A 0.034 0.034 0.08 1.686 2.238 0. 1.136
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 29 106 53 952 0 65
normalized size 1 1. 0.63 2.3 1.15 20.7 0. 1.41
time (sec) N/A 0.024 0.019 0.066 1.832 2.263 0. 1.125
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 21 72 11 444 0 11
normalized size 1 1. 0.84 2.88 0.44 17.76 0. 0.44
time (sec) N/A 0.016 0.006 0.082 1.771 2.234 0. 1.132
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 58 23 247 15 19
normalized size 1 1. 1. 4.46 1.77 19. 1.15 1.46
time (sec) N/A 0.029 0.006 0.072 1.873 2.03 0.695 1.141
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 27 130 47 856 37 39
normalized size 1 1. 0.75 3.61 1.31 23.78 1.03 1.08
time (sec) N/A 0.02 0.021 0.059 1.705 2.199 1.532 1.138
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 36 196 72 1885 60 55
normalized size 1 1. 0.65 3.56 1.31 34.27 1.09 1.
time (sec) N/A 0.029 0.039 0.054 1.829 2.149 15.078 1.135
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 42 262 96 3340 0 72
normalized size 1 1. 0.57 3.54 1.3 45.14 0. 0.97
time (sec) N/A 0.04 0.049 0.057 1.655 2.299 0. 1.114
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 63 0 0 0 0 0
normalized size 1 1. 0.52 0. 0. 0. 0. 0.
time (sec) N/A 0.06 0.096 0.059 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 47 0 0 0 0 0
normalized size 1 1. 0.68 0. 0. 0. 0. 0.
time (sec) N/A 0.04 0.036 0.054 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 36 0 0 0 0 0
normalized size 1 1. 0.78 0. 0. 0. 0. 0.
time (sec) N/A 0.034 0.019 0.073 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 38 0 0 0 0 0
normalized size 1 1. 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.031 0.04 0.079 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 47 0 0 0 0 0
normalized size 1 1. 0.61 0. 0. 0. 0. 0.
time (sec) N/A 0.044 0.089 0.058 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 63 0 0 0 0 0
normalized size 1 1. 0.52 0. 0. 0. 0. 0.
time (sec) N/A 0.064 0.091 0.053 0. 0. 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 54 72 837 9415 0 69
normalized size 1 1. 0.33 0.44 5.13 57.76 0. 0.42
time (sec) N/A 0.045 0.172 0.089 1.657 3.054 0. 1.2
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 42 60 435 4632 0 53
normalized size 1 1. 0.36 0.51 3.72 39.59 0. 0.45
time (sec) N/A 0.035 0.093 0.07 1.769 2.43 0. 1.172
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 30 46 162 1623 0 36
normalized size 1 1. 0.49 0.75 2.66 26.61 0. 0.59
time (sec) N/A 0.023 0.054 0.06 1.723 2.04 0. 1.174
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 29 18 230 0 18
normalized size 1 1. 1. 1.93 1.2 15.33 0. 1.2
time (sec) N/A 0.017 0.005 0.075 1.576 2.108 0. 1.176
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 23 89 41 771 0 38
normalized size 1 1. 0.64 2.47 1.14 21.42 0. 1.06
time (sec) N/A 0.016 0.022 0.085 1.725 2.331 0. 1.132
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 38 230 88 3687 0 70
normalized size 1 1. 0.44 2.67 1.02 42.87 0. 0.81
time (sec) N/A 0.036 0.036 0.058 1.689 2.647 0. 1.139
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 55 362 139 9443 0 103
normalized size 1 1. 0.42 2.74 1.05 71.54 0. 0.78
time (sec) N/A 0.056 0.076 0.069 1.745 2.761 0. 1.124
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 28 130 73 113 0 57
normalized size 1 1. 0.64 2.95 1.66 2.57 0. 1.3
time (sec) N/A 0.139 0.102 0.029 1.108 2.387 0. 1.09
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 67 62 100 0 50
normalized size 1 1. 1. 2.91 2.7 4.35 0. 2.17
time (sec) N/A 0.122 0.045 0.024 1.163 2.302 0. 1.129
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 16 78 57 47 0 38
normalized size 1 1. 0.59 2.89 2.11 1.74 0. 1.41
time (sec) N/A 0.101 0.06 0.023 1.083 2.484 0. 1.158
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 16 27 47 200 0 43
normalized size 1 1. 0.94 1.59 2.76 11.76 0. 2.53
time (sec) N/A 0.073 0.018 0.017 1.127 2.408 0. 1.15
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 44 23 65 397 0 70
normalized size 1 1. 1.33 0.7 1.97 12.03 0. 2.12
time (sec) N/A 0.098 0.049 0.02 1.112 2.416 0. 1.113
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 25 23 122 230 0 42
normalized size 1 1. 1.09 1. 5.3 10. 0. 1.83
time (sec) N/A 0.139 0.038 0.022 1.143 2.292 0. 1.152
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 59 45 134 2060 0 122
normalized size 1 1. 1.28 0.98 2.91 44.78 0. 2.65
time (sec) N/A 0.195 0.154 0.027 1.126 2.536 0. 1.194
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 39 39 394 695 0 80
normalized size 1 1. 1.15 1.15 11.59 20.44 0. 2.35
time (sec) N/A 0.146 0.06 0.026 1.174 2.365 0. 1.182
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 219 488 0 4609 0 266
normalized size 1 1. 1.66 3.7 0. 34.92 0. 2.02
time (sec) N/A 0.37 0.705 0.036 0. 2.742 0. 1.171
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 66 361 173 1251 0 117
normalized size 1 1. 1.08 5.92 2.84 20.51 0. 1.92
time (sec) N/A 0.18 0.127 0.031 1.131 2.763 0. 1.172
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 76 213 0 1500 0 135
normalized size 1 1. 0.93 2.6 0. 18.29 0. 1.65
time (sec) N/A 0.212 0.153 0.027 0. 2.759 0. 1.148
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 19 31 62 246 0 46
normalized size 1 1. 0.95 1.55 3.1 12.3 0. 2.3
time (sec) N/A 0.088 0.01 0.02 1.134 2.574 0. 1.124
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 37 48 80 181 0 88
normalized size 1 1. 0.7 0.91 1.51 3.42 0. 1.66
time (sec) N/A 0.118 0.073 0.022 1.107 2.475 0. 1.125
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 75 77 0 1156 0 86
normalized size 1 1. 1.14 1.17 0. 17.52 0. 1.3
time (sec) N/A 0.133 0.252 0.023 0. 2.588 0. 1.134
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 86 82 200 2097 0 235
normalized size 1 1. 1.01 0.96 2.35 24.67 0. 2.76
time (sec) N/A 0.238 0.33 0.029 1.112 2.743 0. 1.147
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 156 154 0 5416 0 201
normalized size 1 1. 1.41 1.39 0. 48.79 0. 1.81
time (sec) N/A 0.304 0.577 0.032 0. 2.872 0. 1.136
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 63 139 108 491 0 116
normalized size 1 1. 0.94 2.07 1.61 7.33 0. 1.73
time (sec) N/A 0.096 0.086 0.032 1.079 2.548 0. 1.181
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 53 111 89 346 0 95
normalized size 1 1. 0.98 2.06 1.65 6.41 0. 1.76
time (sec) N/A 0.086 0.073 0.029 1.168 2.43 0. 1.148
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 45 87 76 242 0 69
normalized size 1 1. 1.1 2.12 1.85 5.9 0. 1.68
time (sec) N/A 0.08 0.048 0.029 1.151 2.171 0. 1.123
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 32 59 55 151 0 47
normalized size 1 1. 1.23 2.27 2.12 5.81 0. 1.81
time (sec) N/A 0.057 0.06 0.027 1.121 2.43 0. 1.166
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 10 9 16 43 0 15
normalized size 1 1. 0.91 0.82 1.45 3.91 0. 1.36
time (sec) N/A 0.024 0.007 0.012 1.137 2.271 0. 1.148
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 22 21 31 117 0 27
normalized size 1 1. 1.1 1.05 1.55 5.85 0. 1.35
time (sec) N/A 0.066 0.029 0.01 1.753 2.392 0. 1.119
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 45 39 61 467 0 49
normalized size 1 1. 1.73 1.5 2.35 17.96 0. 1.88
time (sec) N/A 0.101 0.085 0.015 1.67 2.299 0. 1.114
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 51 61 99 1099 0 65
normalized size 1 1. 1.13 1.36 2.2 24.42 0. 1.44
time (sec) N/A 0.085 0.084 0.017 1.695 2.436 0. 1.152
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 58 58 45 131 0 42
normalized size 1 1. 2. 2. 1.55 4.52 0. 1.45
time (sec) N/A 0.015 0.139 0.036 1.144 2.385 0. 1.149
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 59 60 47 131 0 42
normalized size 1 1. 1.97 2. 1.57 4.37 0. 1.4
time (sec) N/A 0.015 0.14 0.032 1.115 2.42 0. 1.169
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 99 0 0 2558 0 216
normalized size 1 1. 1.01 0. 0. 26.1 0. 2.2
time (sec) N/A 0.12 0.328 0.178 0. 2.776 0. 1.363
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 75 0 0 1975 0 159
normalized size 1 1. 1.14 0. 0. 29.92 0. 2.41
time (sec) N/A 0.042 0.195 0.131 0. 2.438 0. 1.228
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 60 0 0 1808 0 112
normalized size 1 1. 1.62 0. 0. 48.86 0. 3.03
time (sec) N/A 0.019 0.089 0.217 0. 2.558 0. 1.178
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 118 0 0 2480 0 0
normalized size 1 1. 1.39 0. 0. 29.18 0. 0.
time (sec) N/A 0.074 1.124 0.172 0. 2.877 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 177 0 0 3401 0 0
normalized size 1 1. 1.55 0. 0. 29.83 0. 0.
time (sec) N/A 0.128 4.627 0.13 0. 2.915 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 70 0 0 1808 0 136
normalized size 1 1. 1.84 0. 0. 47.58 0. 3.58
time (sec) N/A 0.023 2.266 0.227 0. 2.567 0. 1.185
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 118 0 0 2480 0 0
normalized size 1 1. 1.36 0. 0. 28.51 0. 0.
time (sec) N/A 0.079 2.164 0.161 0. 2.811 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 39 0 0 833 0 70
normalized size 1 1. 2.05 0. 0. 43.84 0. 3.68
time (sec) N/A 0.017 0.038 0.116 0. 2.496 0. 1.148
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 51 0 0 833 0 93
normalized size 1 1. 2.43 0. 0. 39.67 0. 4.43
time (sec) N/A 0.019 0.526 0.111 0. 2.476 0. 1.121
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 78 121 285 2547 0 194
normalized size 1 1. 0.73 1.13 2.66 23.8 0. 1.81
time (sec) N/A 0.124 0.237 0.033 1.817 2.488 0. 1.165
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 55 80 154 1319 0 131
normalized size 1 1. 0.75 1.1 2.11 18.07 0. 1.79
time (sec) N/A 0.052 0.13 0.023 1.828 2.361 0. 1.133
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 32 42 55 428 0 65
normalized size 1 1. 0.97 1.27 1.67 12.97 0. 1.97
time (sec) N/A 0.028 0.063 0.01 1.084 2.435 0. 1.166
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 17 22 74 0 23
normalized size 1 1. 1. 1.06 1.38 4.62 0. 1.44
time (sec) N/A 0.009 0.002 0.003 1.219 2.312 0. 1.132
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 60 88 0 648 0 76
normalized size 1 1. 1.02 1.49 0. 10.98 0. 1.29
time (sec) N/A 0.055 0.105 0.014 0. 2.519 0. 1.141
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 203 221 0 2708 0 185
normalized size 1 1. 1.86 2.03 0. 24.84 0. 1.7
time (sec) N/A 0.159 0.402 0.046 0. 2.612 0. 1.124
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 173 173 205 660 0 8986 0 362
normalized size 1 1. 1.18 3.82 0. 51.94 0. 2.09
time (sec) N/A 0.308 0.727 0.05 0. 3.172 0. 1.179
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 168 0 0 0 0 0
normalized size 1 1. 1.58 0. 0. 0. 0. 0.
time (sec) N/A 0.029 2.345 0.235 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 146 146 126 406 0 5667 0 246
normalized size 1 1. 0.86 2.78 0. 38.82 0. 1.68
time (sec) N/A 0.657 0.275 0.037 0. 2.813 0. 1.147
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 99 264 0 3675 0 180
normalized size 1 1. 0.88 2.36 0. 32.81 0. 1.61
time (sec) N/A 0.423 0.16 0.036 0. 2.695 0. 1.148
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 78 174 0 2067 0 124
normalized size 1 1. 0.92 2.05 0. 24.32 0. 1.46
time (sec) N/A 0.265 0.124 0.031 0. 2.6 0. 1.133
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 57 94 0 1064 0 84
normalized size 1 1. 0.92 1.52 0. 17.16 0. 1.35
time (sec) N/A 0.092 0.113 0.031 0. 2.63 0. 1.161
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 41 36 0 446 0 43
normalized size 1 1. 0.98 0.86 0. 10.62 0. 1.02
time (sec) N/A 0.055 0.026 0.013 0. 2.337 0. 1.174
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 54 51 0 587 0 61
normalized size 1 1. 1. 0.94 0. 10.87 0. 1.13
time (sec) N/A 0.1 0.05 0.014 0. 2.605 0. 1.158
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 63 73 0 1285 0 82
normalized size 1 1. 0.98 1.14 0. 20.08 0. 1.28
time (sec) N/A 0.14 0.105 0.024 0. 2.704 0. 1.169
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 82 146 0 3321 0 120
normalized size 1 1. 0.94 1.68 0. 38.17 0. 1.38
time (sec) N/A 0.242 0.2 0.021 0. 3.544 0. 1.137
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 60 117 126 2288 0 93
normalized size 1 1. 1.25 2.44 2.62 47.67 0. 1.94
time (sec) N/A 0.097 0.118 0.059 1.702 2.609 0. 1.15
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 38 34 100 1403 0 82
normalized size 1 1. 1.06 0.94 2.78 38.97 0. 2.28
time (sec) N/A 0.059 0.071 0.037 1.501 2.563 0. 1.153
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 41 75 69 711 0 57
normalized size 1 1. 1.32 2.42 2.23 22.94 0. 1.84
time (sec) N/A 0.07 0.058 0.033 1.665 2.511 0. 1.143
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 10 54 45 288 0 47
normalized size 1 1. 0.71 3.86 3.21 20.57 0. 3.36
time (sec) N/A 0.048 0.034 0.027 1.655 2.525 0. 1.224
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 15 35 22 50 0 19
normalized size 1 1. 1.07 2.5 1.57 3.57 0. 1.36
time (sec) N/A 0.046 0.03 0.019 1.659 2.428 0. 1.15
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 9 9 12 19 24 53 19 23
normalized size 1 1. 1.33 2.11 2.67 5.89 2.11 2.56
time (sec) N/A 0.027 0.007 0.016 1.132 2.419 0.205 1.152
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 44 47 70 497 0 76
normalized size 1 1. 1.1 1.18 1.75 12.42 0. 1.9
time (sec) N/A 0.058 0.048 0.029 1.155 2.464 0. 1.167
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 33 56 63 149 0 54
normalized size 1 1. 0.87 1.47 1.66 3.92 0. 1.42
time (sec) N/A 0.089 0.072 0.03 1.096 2.238 0. 1.173
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 66 69 146 2475 0 127
normalized size 1 1. 0.97 1.01 2.15 36.4 0. 1.87
time (sec) N/A 0.086 0.147 0.036 1.145 2.475 0. 1.16
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 69 78 142 502 0 86
normalized size 1 1. 1.25 1.42 2.58 9.13 0. 1.56
time (sec) N/A 0.12 0.102 0.037 1.198 2.443 0. 1.113
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 132 415 448 9682 0 360
normalized size 1 1. 1.09 3.43 3.7 80.02 0. 2.98
time (sec) N/A 0.149 0.325 0.047 1.727 3.278 0. 1.161
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 187 187 185 575 0 12166 0 338
normalized size 1 1. 0.99 3.07 0. 65.06 0. 1.81
time (sec) N/A 0.293 0.589 0.043 0. 5.44 0. 1.136
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 85 233 221 3216 0 205
normalized size 1 1. 1.18 3.24 3.07 44.67 0. 2.85
time (sec) N/A 0.097 0.171 0.04 1.667 3.192 0. 1.151
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 113 248 0 3224 0 150
normalized size 1 1. 1.2 2.64 0. 34.3 0. 1.6
time (sec) N/A 0.319 0.403 0.033 0. 3.971 0. 1.142
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 37 107 90 543 0 99
normalized size 1 1. 1.06 3.06 2.57 15.51 0. 2.83
time (sec) N/A 0.075 0.084 0.03 1.565 2.572 0. 1.138
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 62 113 0 551 0 70
normalized size 1 1. 1. 1.82 0. 8.89 0. 1.13
time (sec) N/A 0.171 0.081 0.026 0. 2.812 0. 1.172
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 11 21 35 72 41 26
normalized size 1 1. 0.58 1.11 1.84 3.79 2.16 1.37
time (sec) N/A 0.032 0.017 0.014 1.132 2.437 0.586 1.134
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 44 78 90 220 0 90
normalized size 1 1. 0.67 1.18 1.36 3.33 0. 1.36
time (sec) N/A 0.106 0.085 0.029 1.072 2.33 0. 1.117
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 81 104 0 1582 0 111
normalized size 1 1. 0.71 0.91 0. 13.88 0. 0.97
time (sec) N/A 0.205 0.335 0.03 0. 2.36 0. 1.151
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 112 119 221 2885 0 261
normalized size 1 1. 0.99 1.05 1.96 25.53 0. 2.31
time (sec) N/A 0.19 0.3 0.043 1.183 2.718 0. 1.141
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 207 207 166 179 0 8041 0 257
normalized size 1 1. 0.8 0.86 0. 38.85 0. 1.24
time (sec) N/A 0.329 0.762 0.042 0. 2.621 0. 1.158
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 178 178 167 215 494 11934 0 513
normalized size 1 1. 0.94 1.21 2.78 67.04 0. 2.88
time (sec) N/A 0.32 0.998 0.041 1.141 3.652 0. 1.189
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 169 169 160 0 0 10971 0 0
normalized size 1 1. 0.95 0. 0. 64.92 0. 0.
time (sec) N/A 0.194 4.835 0.221 0. 9.438 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 108 0 0 4070 0 0
normalized size 1 1. 1.08 0. 0. 40.7 0. 0.
time (sec) N/A 0.122 0.962 0.201 0. 9.05 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 90 43 0 1613 0 0
normalized size 1 1. 1.76 0.84 0. 31.63 0. 0.
time (sec) N/A 0.054 0.141 0.03 0. 8.722 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 195 0 0 22756 0 0
normalized size 1 1. 1.84 0. 0. 214.68 0. 0.
time (sec) N/A 0.175 2.22 0.181 0. 7.566 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 217 217 518 0 0 0 0 0
normalized size 1 1. 2.39 0. 0. 0. 0. 0.
time (sec) N/A 0.327 20.391 0.201 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 344 344 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.392 180.002 0.195 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 125 125 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 7.717 0.194 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 246 246 539 0 0 0 0 0
normalized size 1 1. 2.19 0. 0. 0. 0. 0.
time (sec) N/A 0.215 18.313 0.196 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 148 148 167 0 0 7063 0 0
normalized size 1 1. 1.13 0. 0. 47.72 0. 0.
time (sec) N/A 0.165 4.432 0.22 0. 10.507 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 111 0 0 2434 0 0
normalized size 1 1. 1.41 0. 0. 30.81 0. 0.
time (sec) N/A 0.108 0.624 0.305 0. 9.95 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 73 26 0 1492 0 0
normalized size 1 1. 2.35 0.84 0. 48.13 0. 0.
time (sec) N/A 0.047 0.13 0.034 0. 9.529 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 230 0 0 23317 0 0
normalized size 1 1. 2.17 0. 0. 219.97 0. 0.
time (sec) N/A 0.148 3.011 0.199 0. 12.038 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 262 262 902 0 0 0 0 0
normalized size 1 1. 3.44 0. 0. 0. 0. 0.
time (sec) N/A 0.297 7.281 0.404 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 610 610 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.791 180.001 0.342 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 310 310 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.258 180.001 0.199 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 168 0 0 0 0 0
normalized size 1 1. 1.58 0. 0. 0. 0. 0.
time (sec) N/A 0.021 0.626 0. 0. 0. 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 362 362 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.436 86.492 0.215 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 148 148 155 0 0 9172 0 0
normalized size 1 1. 1.05 0. 0. 61.97 0. 0.
time (sec) N/A 0.191 3.077 0.174 0. 12.53 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 103 0 0 2801 0 0
normalized size 1 1. 1.17 0. 0. 31.83 0. 0.
time (sec) N/A 0.141 0.65 0.167 0. 11.793 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 79 46 0 2456 0 0
normalized size 1 1. 1.46 0.85 0. 45.48 0. 0.
time (sec) N/A 0.062 0.243 0.018 0. 10.067 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 904 0 0 0 0 0
normalized size 1 1. 6.37 0. 0. 0. 0. 0.
time (sec) N/A 0.217 7.319 0.154 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 316 316 996 0 0 0 0 0
normalized size 1 1. 3.15 0. 0. 0. 0. 0.
time (sec) N/A 0.427 7.523 0.167 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 907 907 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.366 180.004 0.171 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 344 344 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.42 180.003 0.148 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 347 347 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.337 81.578 0.142 0. 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 665 665 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.983 104.747 0.166 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 191 191 84 91 521 1516 0 86
normalized size 1 1. 0.44 0.48 2.73 7.94 0. 0.45
time (sec) N/A 0.282 0.088 0.228 1.132 3.883 0. 1.138
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 72 80 282 797 0 69
normalized size 1 1. 0.51 0.57 2. 5.65 0. 0.49
time (sec) N/A 0.167 0.066 0.174 1.151 3.124 0. 1.126
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 44 69 113 302 0 51
normalized size 1 1. 0.79 1.23 2.02 5.39 0. 0.91
time (sec) N/A 0.113 0.056 0.174 1.092 3.51 0. 1.122
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 42 66 28 97 0 27
normalized size 1 1. 0.95 1.5 0.64 2.2 0. 0.61
time (sec) N/A 0.087 0.037 0.207 1.679 3.225 0. 1.138
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 48 106 39 163 0 45
normalized size 1 1. 0.65 1.43 0.53 2.2 0. 0.61
time (sec) N/A 0.113 0.049 0.188 1.121 2.956 0. 1.127
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 162 78 216 100 323 0 111
normalized size 1 1. 0.48 1.33 0.62 1.99 0. 0.69
time (sec) N/A 0.155 0.064 0.19 1.152 3.32 0. 1.127
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 250 250 106 326 151 562 0 149
normalized size 1 1. 0.42 1.3 0.6 2.25 0. 0.6
time (sec) N/A 0.196 0.103 0.204 1.179 3.181 0. 1.122
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 77 130 0 0 0 0
normalized size 1 1. 0.71 1.2 0. 0. 0. 0.
time (sec) N/A 0.087 0.17 0.075 0. 0. 0. 0.
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 44 39 41 103 0 0
normalized size 1 1. 1.57 1.39 1.46 3.68 0. 0.
time (sec) N/A 0.042 0.047 0.035 1.811 3.024 0. 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 203 203 65 134 0 0 0 0
normalized size 1 1. 0.32 0.66 0. 0. 0. 0.
time (sec) N/A 0.13 0.112 0.041 0. 0. 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 77 97 0 194 0 0
normalized size 1 1. 1.15 1.45 0. 2.9 0. 0.
time (sec) N/A 0.055 0.138 0.053 0. 3.01 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 58 114 0 0 0 0
normalized size 1 1. 0.67 1.31 0. 0. 0. 0.
time (sec) N/A 0.06 0.096 0.035 0. 0. 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 77 0 0 213 0 0
normalized size 1 1. 1.31 0. 0. 3.61 0. 0.
time (sec) N/A 0.033 0.089 0.033 0. 3.004 0. 0.
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 36 167 0 0 0 0
normalized size 1 1. 1. 4.64 0. 0. 0. 0.
time (sec) N/A 0.029 0.055 0.417 0. 0. 0. 0.
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 55 0 0 124 0 0
normalized size 1 1. 1.38 0. 0. 3.1 0. 0.
time (sec) N/A 0.045 0.118 0.04 0. 3.041 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 59 134 0 0 0 0
normalized size 1 1. 0.43 0.98 0. 0. 0. 0.
time (sec) N/A 0.099 0.118 0.04 0. 0. 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 33 38 57 81 0 0
normalized size 1 1. 1.43 1.65 2.48 3.52 0. 0.
time (sec) N/A 0.04 0.038 0.037 1.602 2.966 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 65 117 0 0 0 0
normalized size 1 1. 0.81 1.46 0. 0. 0. 0.
time (sec) N/A 0.07 0.098 0.042 0. 0. 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 122 122 98 121 0 242 0 0
normalized size 1 1. 0.8 0.99 0. 1.98 0. 0.
time (sec) N/A 0.075 0.185 0.039 0. 3.251 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 77 138 0 0 0 0
normalized size 1 1. 0.55 0.98 0. 0. 0. 0.
time (sec) N/A 0.098 0.177 0.036 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 44 47 41 122 0 0
normalized size 1 1. 1.57 1.68 1.46 4.36 0. 0.
time (sec) N/A 0.043 0.054 0.033 1.907 2.926 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 251 251 65 147 0 0 0 0
normalized size 1 1. 0.26 0.59 0. 0. 0. 0.
time (sec) N/A 0.149 0.118 0.037 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 90 113 0 220 0 0
normalized size 1 1. 0.98 1.23 0. 2.39 0. 0.
time (sec) N/A 0.066 0.167 0.036 0. 3.104 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 61 129 0 0 0 0
normalized size 1 1. 0.55 1.16 0. 0. 0. 0.
time (sec) N/A 0.083 0.106 0.033 0. 0. 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 88 0 0 234 0 0
normalized size 1 1. 1. 0. 0. 2.66 0. 0.
time (sec) N/A 0.067 0.168 0.033 0. 3.1 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 214 214 65 159 0 0 0 0
normalized size 1 1. 0.3 0.74 0. 0. 0. 0.
time (sec) N/A 0.116 0.115 0.039 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 64 131 0 227 0 0
normalized size 1 1. 0.7 1.42 0. 2.47 0. 0.
time (sec) N/A 0.039 0.086 0.037 0. 3.321 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 45 127 0 0 0 0
normalized size 1 1. 0.8 2.27 0. 0. 0. 0.
time (sec) N/A 0.036 0.101 0.314 0. 0. 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 32 0 53 58 0 0
normalized size 1 1. 1.28 0. 2.12 2.32 0. 0.
time (sec) N/A 0.04 0.035 0.036 1.51 3.135 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 65 0 0 0 0 0
normalized size 1 1. 0.71 0. 0. 0. 0. 0.
time (sec) N/A 0.077 0.108 0.03 0. 0. 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 51 0 0 194 0 0
normalized size 1 1. 0.77 0. 0. 2.94 0. 0.
time (sec) N/A 0.057 0.105 0.036 0. 3.066 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 64 0 0 0 0 0
normalized size 1 1. 1.02 0. 0. 0. 0. 0.
time (sec) N/A 0.059 0.147 0.084 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 69 69 126 0 0 0 0 0
normalized size 1 1. 1.83 0. 0. 0. 0. 0.
time (sec) N/A 0.07 5.41 1.099 0. 0. 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 70 70 101 0 0 0 0 0
normalized size 1 1. 1.44 0. 0. 0. 0. 0.
time (sec) N/A 0.071 0.886 1.303 0. 0. 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 69 69 192 0 0 0 0 0
normalized size 1 1. 2.78 0. 0. 0. 0. 0.
time (sec) N/A 0.073 13.402 0.105 0. 0. 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A C B B F F
verified N/A NO Yes TBD TBD TBD TBD TBD
size 40 139 29 509 130 603 0 0
normalized size 1 3.48 0.72 12.72 3.25 15.08 0. 0.
time (sec) N/A 0.135 0.287 0.275 2.132 2.927 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 62 0 100 104 0 51
normalized size 1 1. 2.48 0. 4. 4.16 0. 2.04
time (sec) N/A 0.039 0.116 0.051 1.104 2.876 0. 1.134
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 64 0 66 107 0 50
normalized size 1 1. 2.56 0. 2.64 4.28 0. 2.
time (sec) N/A 0.046 0.096 0.066 1.06 2.851 0. 1.112
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 57 0 0 1322 0 0
normalized size 1 1. 0.64 0. 0. 14.85 0. 0.
time (sec) N/A 0.089 0.715 0.165 0. 3.206 0. 0.
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 62 0 0 1343 0 0
normalized size 1 1. 0.95 0. 0. 20.66 0. 0.
time (sec) N/A 0.076 0.817 0.119 0. 3.123 0. 0.
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 20 26 112 0 36
normalized size 1 1. 1. 1.05 1.37 5.89 0. 1.89
time (sec) N/A 0.016 0.048 0.005 1.07 3.132 0. 1.129
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 18 19 38 219 0 38
normalized size 1 1. 1. 1.06 2.11 12.17 0. 2.11
time (sec) N/A 0.028 0.059 0.013 1.202 3.036 0. 1.153
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 55 51 0 1486 0 155
normalized size 1 1. 1. 0.93 0. 27.02 0. 2.82
time (sec) N/A 0.04 0.055 0.02 0. 3.192 0. 1.172
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 42 36 123 869 0 63
normalized size 1 1. 1. 0.86 2.93 20.69 0. 1.5
time (sec) N/A 0.034 0.048 0.017 1.202 3.059 0. 1.17
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 75 84 0 4298 0 205
normalized size 1 1. 0.84 0.94 0. 48.29 0. 2.3
time (sec) N/A 0.057 0.089 0.022 0. 3.311 0. 1.18
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 74 295 0 0 0 0
normalized size 1 1. 0.76 3.04 0. 0. 0. 0.
time (sec) N/A 0.061 0.162 0.47 0. 0. 0. 0.
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 93 93 72 141 0 0 0 0
normalized size 1 1. 0.77 1.52 0. 0. 0. 0.
time (sec) N/A 0.072 0.088 0.414 0. 0. 0. 0.
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 58 183 0 0 0 0
normalized size 1 1. 1. 3.16 0. 0. 0. 0.
time (sec) N/A 0.069 0.066 0.268 0. 0. 0. 0.
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 58 183 0 0 0 0
normalized size 1 1. 1. 3.16 0. 0. 0. 0.
time (sec) N/A 0.056 0.07 0.297 0. 0. 0. 0.
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 76 237 0 0 0 0
normalized size 1 1. 0.78 2.44 0. 0. 0. 0.
time (sec) N/A 0.073 0.111 0.287 0. 0. 0. 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 87 256 0 0 0 0
normalized size 1 1. 0.9 2.64 0. 0. 0. 0.
time (sec) N/A 0.07 0.129 0.345 0. 0. 0. 0.

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [177] had the largest ratio of [ 0.6364 ]

Table 2.1Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\)
1 A 1 1 1. 6 0.167
2 A 2 2 1. 8 0.25
3 A 2 2 1. 8 0.25
4 A 2 1 1. 8 0.125
5 A 3 2 1. 8 0.25
6 A 2 1 1. 8 0.125
7 A 2 1 1. 6 0.167
8 A 2 1 1. 6 0.167
9 A 3 3 1. 10 0.3
10 A 3 3 1. 10 0.3
11 A 2 2 1. 10 0.2
12 A 2 2 1. 10 0.2
13 A 3 3 1. 10 0.3
14 A 3 3 1. 10 0.3
15 A 4 3 1. 12 0.25
16 A 3 3 1. 12 0.25
17 A 3 3 1. 12 0.25
18 A 2 2 1. 12 0.167
19 A 2 2 1. 12 0.167
20 A 3 3 1. 12 0.25
21 A 3 3 1. 12 0.25
22 A 4 3 1. 12 0.25
23 A 2 2 1. 10 0.2
24 A 5 3 1. 12 0.25
25 A 4 3 1. 12 0.25
26 A 3 3 1. 12 0.25
27 A 2 2 1. 12 0.167
28 A 2 2 1. 12 0.167
29 A 3 3 1. 12 0.25
30 A 4 3 1. 12 0.25
31 A 5 3 1. 12 0.25
32 A 5 4 1. 10 0.4
33 A 4 4 1. 10 0.4
34 A 3 3 1. 10 0.3
35 A 2 2 1. 10 0.2
36 A 3 3 1. 10 0.3
37 A 4 3 1. 10 0.3
38 A 5 3 1. 10 0.3
39 A 7 4 1. 10 0.4
40 A 5 4 1. 10 0.4
41 A 4 4 1. 10 0.4
42 A 4 4 1. 10 0.4
43 A 5 4 1. 10 0.4
44 A 7 4 1. 10 0.4
45 A 3 2 1. 10 0.2
46 A 3 2 1. 10 0.2
47 A 3 2 1. 10 0.2
48 A 3 3 1. 10 0.3
49 A 3 3 1. 10 0.3
50 A 5 3 1. 10 0.3
51 A 7 3 1. 10 0.3
52 A 7 7 1. 13 0.538
53 A 6 5 1. 13 0.385
54 A 5 5 1. 13 0.385
55 A 5 4 1. 11 0.364
56 A 6 6 1. 11 0.546
57 A 6 5 1. 13 0.385
58 A 7 7 1. 13 0.538
59 A 7 6 1. 13 0.462
60 A 6 5 1. 13 0.385
61 A 5 4 1. 13 0.308
62 A 5 5 1. 13 0.385
63 A 5 4 1. 11 0.364
64 A 4 3 1. 11 0.273
65 A 5 5 1. 13 0.385
66 A 6 5 1. 13 0.385
67 A 6 5 1. 13 0.385
68 A 7 5 1. 13 0.385
69 A 6 5 1. 13 0.385
70 A 5 5 1. 13 0.385
71 A 4 4 1. 11 0.364
72 A 1 1 1. 11 0.091
73 A 3 3 1. 13 0.231
74 A 4 4 1. 13 0.308
75 A 6 6 1. 13 0.462
76 A 2 2 1. 12 0.167
77 A 2 2 1. 13 0.154
78 A 5 5 1. 14 0.357
79 A 4 4 1. 14 0.286
80 A 2 2 1. 14 0.143
81 A 5 4 1. 14 0.286
82 A 6 5 1. 14 0.357
83 A 2 2 1. 15 0.133
84 A 5 4 1. 15 0.267
85 A 2 2 1. 10 0.2
86 A 2 2 1. 10 0.2
87 A 6 5 1. 12 0.417
88 A 5 4 1. 12 0.333
89 A 4 4 1. 12 0.333
90 A 2 1 1. 10 0.1
91 A 3 3 1. 12 0.25
92 A 5 5 1. 12 0.417
93 A 6 6 1. 12 0.5
94 A 1 1 1. 14 0.071
95 A 8 6 1. 13 0.462
96 A 7 6 1. 13 0.462
97 A 6 6 1. 13 0.462
98 A 5 5 1. 11 0.454
99 A 3 3 1. 11 0.273
100 A 5 5 1. 13 0.385
101 A 6 6 1. 13 0.462
102 A 7 7 1. 13 0.538
103 A 5 3 1. 13 0.231
104 A 3 2 1. 13 0.154
105 A 4 3 1. 13 0.231
106 A 3 2 1. 13 0.154
107 A 3 2 1. 13 0.154
108 A 2 2 1. 11 0.182
109 A 3 2 1. 11 0.182
110 A 4 3 1. 13 0.231
111 A 3 2 1. 13 0.154
112 A 5 3 1. 13 0.231
113 A 3 2 1. 13 0.154
114 A 15 8 1. 13 0.615
115 A 3 2 1. 13 0.154
116 A 6 6 1. 13 0.462
117 A 3 2 1. 13 0.154
118 A 7 7 1. 13 0.538
119 A 4 4 1. 11 0.364
120 A 3 2 1. 11 0.182
121 A 9 8 1. 13 0.615
122 A 3 2 1. 13 0.154
123 A 15 8 1. 13 0.615
124 A 3 2 1. 13 0.154
125 A 5 4 1. 23 0.174
126 A 5 4 1. 23 0.174
127 A 4 4 1. 21 0.19
128 A 7 5 1. 21 0.238
129 A 13 9 1. 23 0.391
130 A 7 7 1. 23 0.304
131 A 1 1 1. 14 0.071
132 A 5 4 1. 23 0.174
133 A 5 4 1. 23 0.174
134 A 5 4 1. 23 0.174
135 A 3 3 1. 21 0.143
136 A 7 5 1. 21 0.238
137 A 11 6 1. 23 0.261
138 A 11 8 1. 23 0.348
139 A 6 6 1. 23 0.261
140 A 1 1 1. 14 0.071
141 A 9 8 1. 23 0.348
142 A 5 4 1. 23 0.174
143 A 5 4 1. 23 0.174
144 A 4 4 1. 21 0.19
145 A 7 4 1. 21 0.19
146 A 11 5 1. 23 0.217
147 A 17 11 1. 23 0.478
148 A 7 7 1. 23 0.304
149 A 6 6 1. 14 0.429
150 A 14 11 1. 23 0.478
151 A 6 5 1. 25 0.2
152 A 6 5 1. 25 0.2
153 A 4 4 1. 25 0.16
154 A 4 4 1. 25 0.16
155 A 5 4 1. 25 0.16
156 A 6 5 1. 25 0.2
157 A 6 5 1. 25 0.2
158 A 6 6 1. 15 0.4
159 A 3 3 1. 15 0.2
160 A 8 8 1. 15 0.533
161 A 6 6 1. 15 0.4
162 A 5 5 1. 13 0.385
163 A 6 6 1. 11 0.546
164 A 3 2 1. 15 0.133
165 A 5 5 1. 15 0.333
166 A 6 6 1. 15 0.4
167 A 3 3 1. 15 0.2
168 A 5 5 1. 15 0.333
169 A 8 7 1. 15 0.467
170 A 7 6 1. 15 0.4
171 A 3 3 1. 15 0.2
172 A 9 8 1. 15 0.533
173 A 7 6 1. 15 0.4
174 A 6 5 1. 15 0.333
175 A 7 6 1. 15 0.4
176 A 8 7 1. 13 0.538
177 A 7 7 1. 11 0.636
178 A 4 3 1. 15 0.2
179 A 3 3 1. 15 0.2
180 A 5 5 1. 15 0.333
181 A 6 6 1. 15 0.4
182 A 4 4 1. 11 0.364
183 A 4 4 1. 13 0.308
184 A 4 4 1. 13 0.308
185 A 4 4 1. 13 0.308
186 C 9 4 3.48 44 0.091
187 A 3 3 1. 15 0.2
188 A 4 4 1. 15 0.267
189 A 3 3 1. 20 0.15
190 A 3 3 1. 21 0.143
191 A 2 1 1. 15 0.067
192 A 3 2 1. 17 0.118
193 A 3 2 1. 17 0.118
194 A 3 1 1. 17 0.059
195 A 4 2 1. 17 0.118
196 A 4 3 1. 19 0.158
197 A 4 3 1. 19 0.158
198 A 3 2 1. 19 0.105
199 A 3 2 1. 19 0.105
200 A 4 3 1. 19 0.158
201 A 4 3 1. 19 0.158

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