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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 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, 79, 85, 91, 97, 98, 106, 112, 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, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 176, 177, 181, 182, 186, 187, 191, 192, 196, 197, 201, 202, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 157 }

C grade: { 11, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 173, 174, 175, 178, 179, 180, 183, 184, 185, 188, 189, 190, 193, 194, 195, 198, 199, 200, 203, 204, 205, 206, 207, 208 }

F grade: { 216 }

2.1.3 Maple

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, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 179, 181, 182, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 201, 202, 203, 204, 205, 206, 207, 208, 215, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 151, 156, 157, 178, 180, 183, 184, 185, 198, 199, 200 }

C grade: { 132, 133 }

F grade: { 121, 122, 130, 131, 209, 210, 211, 212, 213, 214, 217 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 16, 19, 21, 22, 24, 26, 33, 35, 37, 49, 50, 58, 65, 66, 72, 73, 123, 140, 141, 142, 143, 145, 146, 147, 148, 150, 153, 155, 161, 162, 171, 172, 176, 177, 181, 182, 186, 187, 191, 192, 196, 197, 201, 202, 215, 216, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { }

C grade: { }

F grade: { 6, 13, 15, 17, 18, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 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, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 144, 149, 151, 152, 154, 156, 157, 158, 159, 160, 163, 164, 165, 166, 167, 168, 169, 170, 173, 174, 175, 178, 179, 180, 183, 184, 185, 188, 189, 190, 193, 194, 195, 198, 199, 200, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 217, 218, 219 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 21, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59, 65, 66, 72, 73, 119, 120, 123, 124, 129, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 153, 154, 155, 161, 162, 166, 167, 171, 172, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { }

C grade: { }

F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 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, 121, 122, 125, 126, 127, 128, 130, 131, 132, 133, 144, 151, 152, 156, 157, 158, 159, 160, 163, 164, 165, 168, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 91, 97, 98, 106, 112, 118, 119, 120, 123, 124, 125, 126, 127, 128, 129, 134, 135, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 153, 154, 155, 161, 162, 166, 167, 171, 172, 176, 177, 181, 182, 186, 187, 191, 192, 196, 197, 201, 202, 203, 204, 205, 215, 216, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { }

C grade: { 7, 8 }

F grade: { 6, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 121, 122, 130, 131, 132, 133, 136, 144, 151, 152, 156, 157, 158, 159, 160, 163, 164, 165, 168, 169, 170, 173, 174, 175, 178, 179, 180, 183, 184, 185, 188, 189, 190, 193, 194, 195, 198, 199, 200, 206, 207, 208, 209, 210, 211, 212, 213, 214, 217, 218, 219 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 79, 85, 91, 97, 98, 106, 112, 118, 119, 120, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 150, 155, 158, 159, 160, 162, 166, 167, 171, 172, 176, 177, 181, 182, 186, 187, 191, 192, 197, 202, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 8, 10, 19, 21, 51, 145, 146, 147, 148, 149, 153, 154, 163, 164, 165, 168, 169, 170 }

C grade: { 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 173, 174, 175, 178, 179, 180, 183, 184, 185, 188, 189, 190 }

F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 121, 122, 130, 131, 132, 133, 144, 151, 152, 156, 157, 161, 193, 194, 195, 196, 198, 199, 200, 201, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216 }

2.1.8 Mupad

A grade: { 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 91, 97, 98, 106, 112, 118, 119, 120, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 161, 162, 166, 167, 171, 172, 176, 177, 181, 182, 186, 187, 191, 192, 196, 197, 201, 202, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 4, 5, 6, 7, 16, 26, 37, 142, 143, 144, 145, 150, 155 }

C grade: { }

F grade: { 1, 2, 3, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 121, 122, 130, 131, 132, 133, 140, 141, 146, 147, 148, 149, 151, 152, 153, 154, 156, 157, 158, 159, 160, 163, 164, 165, 168, 169, 170, 173, 174, 175, 178, 179, 180, 183, 184, 185, 188, 189, 190, 193, 194, 195, 198, 199, 200, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214 }

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 A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 51 72 71 49 70 113 -1
normalized size 1 1.00 0.68 0.96 0.95 0.65 0.93 1.51 -0.01
time (sec) N/A 0.049 0.075 0.069 0.827 1.541 1.725 0.370 0.000
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 50 60 61 47 61 84 -1
normalized size 1 1.00 0.72 0.87 0.88 0.68 0.88 1.22 -0.01
time (sec) N/A 0.029 0.030 0.007 0.466 0.570 0.862 0.170 0.000
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 41 52 50 40 48 64 -1
normalized size 1 1.00 0.76 0.96 0.93 0.74 0.89 1.19 -0.02
time (sec) N/A 0.035 0.025 0.005 0.479 1.053 0.440 0.169 0.000
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 40 40 40 36 37 46 38
normalized size 1 1.00 0.89 0.89 0.89 0.80 0.82 1.02 0.84
time (sec) N/A 0.016 0.015 0.005 0.421 0.595 0.190 0.124 0.083
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 25 24 24 20 24 23
normalized size 1 1.00 1.00 1.00 0.96 0.96 0.80 0.96 0.92
time (sec) N/A 0.008 0.009 0.003 0.417 0.650 0.121 0.131 0.108
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 46 111 0 0 0 0 41
normalized size 1 1.00 0.90 2.18 0.00 0.00 0.00 0.00 0.80
time (sec) N/A 0.058 0.088 0.395 0.000 0.652 0.000 0.000 0.079
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 31 39 49 32 48 26
normalized size 1 1.00 1.00 1.11 1.39 1.75 1.14 1.71 0.93
time (sec) N/A 0.022 0.002 0.005 0.401 0.844 1.443 0.151 0.023
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 29 38 28 25 51 68 -1
normalized size 1 1.00 0.85 1.12 0.82 0.74 1.50 2.00 -0.03
time (sec) N/A 0.014 0.008 0.005 0.405 0.774 1.141 0.205 0.000
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 53 53 60 73 109 77 -1
normalized size 1 1.00 0.95 0.95 1.07 1.30 1.95 1.38 -0.02
time (sec) N/A 0.033 0.018 0.004 0.416 0.719 2.328 0.148 0.000
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 41 58 50 37 100 130 -1
normalized size 1 1.00 0.71 1.00 0.86 0.64 1.72 2.24 -0.02
time (sec) N/A 0.022 0.020 0.005 0.435 0.846 1.728 0.181 0.000
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 51 73 82 85 182 101 -1
normalized size 1 1.00 0.64 0.91 1.02 1.06 2.28 1.26 -0.01
time (sec) N/A 0.045 0.014 0.005 0.417 0.578 4.235 0.142 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 120 120 82 76 102 76 114 169 -1
normalized size 1 1.00 0.68 0.63 0.85 0.63 0.95 1.41 -0.01
time (sec) N/A 0.194 0.033 0.191 0.569 0.744 3.140 0.189 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 74 93 0 70 90 133 -1
normalized size 1 1.00 0.76 0.95 0.00 0.71 0.92 1.36 -0.01
time (sec) N/A 0.163 0.028 0.141 0.000 0.753 1.847 0.158 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 64 59 72 59 76 97 -1
normalized size 1 1.00 0.78 0.72 0.88 0.72 0.93 1.18 -0.01
time (sec) N/A 0.121 0.026 0.122 0.794 0.562 0.888 0.142 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 55 65 0 51 51 73 -1
normalized size 1 1.00 0.92 1.08 0.00 0.85 0.85 1.22 -0.02
time (sec) N/A 0.093 0.016 0.041 0.000 0.697 0.446 0.152 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 35 37 33 36 32 33 32
normalized size 1 1.00 1.00 1.06 0.94 1.03 0.91 0.94 0.91
time (sec) N/A 0.045 0.011 0.034 0.706 0.504 0.182 0.123 0.137
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 71 71 71 169 0 0 0 0 -1
normalized size 1 1.00 1.00 2.38 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.095 0.039 0.061 0.000 0.736 0.000 0.000 0.000
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 66 66 87 119 0 0 0 0 -1
normalized size 1 1.00 1.32 1.80 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.103 0.166 0.041 0.000 0.631 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 44 43 40 44 0 82 -1
normalized size 1 1.00 1.00 0.98 0.91 1.00 0.00 1.86 -0.02
time (sec) N/A 0.080 0.023 0.043 0.532 1.309 0.000 0.179 0.000
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 116 116 139 157 0 0 0 0 -1
normalized size 1 1.00 1.20 1.35 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.170 0.600 0.322 0.000 0.830 0.000 0.000 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 69 76 74 62 0 185 -1
normalized size 1 1.00 0.79 0.87 0.85 0.71 0.00 2.13 -0.01
time (sec) N/A 0.140 0.035 0.053 0.493 0.756 0.000 0.775 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 201 201 122 159 171 105 196 249 -1
normalized size 1 1.00 0.61 0.79 0.85 0.52 0.98 1.24 -0.00
time (sec) N/A 0.385 0.069 0.081 0.518 0.695 5.683 0.184 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 112 154 0 96 160 185 -1
normalized size 1 1.00 0.67 0.92 0.00 0.57 0.96 1.11 -0.01
time (sec) N/A 0.297 0.045 0.088 0.000 0.528 3.341 0.196 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 95 106 120 79 128 142 -1
normalized size 1 1.00 0.70 0.78 0.88 0.58 0.94 1.04 -0.01
time (sec) N/A 0.225 0.041 0.062 0.520 1.844 1.867 0.225 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 82 96 0 69 92 101 -1
normalized size 1 1.00 0.83 0.97 0.00 0.70 0.93 1.02 -0.01
time (sec) N/A 0.156 0.029 0.059 0.000 0.742 0.902 0.141 0.000
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 60 57 57 44 54 56 40
normalized size 1 1.00 1.00 0.95 0.95 0.73 0.90 0.93 0.67
time (sec) N/A 0.080 0.011 0.040 0.540 0.649 0.447 0.143 0.144
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 97 97 97 229 0 0 0 0 -1
normalized size 1 1.00 1.00 2.36 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.109 0.055 0.065 0.000 0.484 0.000 0.000 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 108 108 133 179 0 0 0 0 -1
normalized size 1 1.00 1.23 1.66 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.163 0.120 0.113 0.000 1.282 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 92 163 0 0 0 0 -1
normalized size 1 1.00 0.90 1.60 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.169 0.260 0.143 0.000 1.401 0.000 0.000 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 179 179 284 250 0 0 0 0 -1
normalized size 1 1.00 1.59 1.40 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.285 2.734 0.224 0.000 0.494 0.000 0.000 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 169 169 116 225 0 0 0 0 -1
normalized size 1 1.00 0.69 1.33 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.292 0.633 0.215 0.000 0.921 0.000 0.000 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 282 282 167 320 0 153 269 362 -1
normalized size 1 1.00 0.59 1.13 0.00 0.54 0.95 1.28 -0.00
time (sec) N/A 0.869 0.082 0.182 0.000 0.474 15.746 0.152 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 250 250 150 197 207 134 241 305 -1
normalized size 1 1.00 0.60 0.79 0.83 0.54 0.96 1.22 -0.00
time (sec) N/A 0.663 0.072 0.081 0.457 0.415 9.506 0.148 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 198 198 135 209 0 121 190 234 -1
normalized size 1 1.00 0.68 1.06 0.00 0.61 0.96 1.18 -0.01
time (sec) N/A 0.516 0.058 0.092 0.000 1.292 6.098 0.164 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 114 130 147 99 158 176 -1
normalized size 1 1.00 0.69 0.78 0.89 0.60 0.95 1.06 -0.01
time (sec) N/A 0.353 0.048 0.067 0.509 0.630 3.313 0.176 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 96 117 0 82 104 127 -1
normalized size 1 1.00 0.86 1.05 0.00 0.74 0.94 1.14 -0.01
time (sec) N/A 0.238 0.026 0.059 0.000 0.483 1.895 0.152 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 69 67 75 55 65 65 48
normalized size 1 1.00 1.00 0.97 1.09 0.80 0.94 0.94 0.70
time (sec) N/A 0.118 0.021 0.041 0.540 0.409 0.859 0.124 0.139
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 113 113 113 287 0 0 0 0 -1
normalized size 1 1.00 1.00 2.54 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.122 0.046 0.062 0.000 0.483 0.000 0.000 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 156 156 198 241 0 0 0 0 -1
normalized size 1 1.00 1.27 1.54 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.194 0.260 0.114 0.000 0.560 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 119 119 124 227 0 0 0 0 -1
normalized size 1 1.00 1.04 1.91 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.216 0.265 0.161 0.000 0.642 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 276 276 399 409 0 0 0 0 -1
normalized size 1 1.00 1.45 1.48 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.410 3.974 0.225 0.000 1.057 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 40 40 0 0 0 47 -1
normalized size 1 1.00 0.73 0.73 0.00 0.00 0.00 0.85 -0.02
time (sec) N/A 0.097 0.015 0.061 0.000 0.428 0.000 0.151 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 33 33 0 0 0 37 -1
normalized size 1 1.00 0.77 0.77 0.00 0.00 0.00 0.86 -0.02
time (sec) N/A 0.080 0.120 0.056 0.000 0.515 0.000 0.139 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 31 31 0 0 0 35 -1
normalized size 1 1.00 0.76 0.76 0.00 0.00 0.00 0.85 -0.02
time (sec) N/A 0.081 0.008 0.030 0.000 0.532 0.000 0.130 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 24 24 0 0 0 25 -1
normalized size 1 1.00 0.83 0.83 0.00 0.00 0.00 0.86 -0.03
time (sec) N/A 0.062 0.076 0.030 0.000 0.540 0.000 0.146 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 22 22 0 0 0 23 -1
normalized size 1 1.00 0.81 0.81 0.00 0.00 0.00 0.85 -0.04
time (sec) N/A 0.063 0.007 0.030 0.000 0.540 0.000 0.159 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 13 0 0 0 12 -1
normalized size 1 1.00 1.00 0.93 0.00 0.00 0.00 0.86 -0.07
time (sec) N/A 0.035 0.020 0.043 0.000 0.457 0.000 0.148 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 10 0 0 0 9 -1
normalized size 1 1.00 1.00 1.11 0.00 0.00 0.00 1.00 -0.11
time (sec) N/A 0.017 0.009 0.023 0.000 0.548 0.000 0.181 0.000
Problem 49 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 0.013 0.196 0.145 0.000 0.595 0.000 0.000 0.000
Problem 50 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 0.014 1.025 0.181 0.000 0.543 0.000 0.000 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-1) F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 86 105 0 0 0 161 -1
normalized size 1 1.00 1.04 1.27 0.00 0.00 0.00 1.94 -0.01
time (sec) N/A 0.074 0.248 0.066 0.000 0.490 0.000 0.150 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-1) F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 78 78 0 0 0 120 -1
normalized size 1 1.00 1.10 1.10 0.00 0.00 0.00 1.69 -0.01
time (sec) N/A 0.063 0.043 0.056 0.000 0.634 0.000 0.142 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-1) F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 61 81 0 0 0 115 -1
normalized size 1 1.00 0.88 1.17 0.00 0.00 0.00 1.67 -0.01
time (sec) N/A 0.058 0.184 0.034 0.000 0.474 0.000 0.155 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-1) F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 56 54 0 0 0 72 -1
normalized size 1 1.00 0.98 0.95 0.00 0.00 0.00 1.26 -0.02
time (sec) N/A 0.049 0.016 0.032 0.000 0.480 0.000 0.206 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-1) F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 50 57 0 0 0 68 -1
normalized size 1 1.00 0.91 1.04 0.00 0.00 0.00 1.24 -0.02
time (sec) N/A 0.044 0.159 0.031 0.000 0.492 0.000 0.206 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 32 28 0 0 0 36 -1
normalized size 1 1.00 0.84 0.74 0.00 0.00 0.00 0.95 -0.03
time (sec) N/A 0.025 0.003 0.038 0.000 0.507 0.000 0.259 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 32 33 0 0 0 34 -1
normalized size 1 1.00 0.89 0.92 0.00 0.00 0.00 0.94 -0.03
time (sec) N/A 0.078 0.066 0.025 0.000 0.457 0.000 0.226 0.000
Problem 58 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 0.012 0.861 0.100 0.000 0.494 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) 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 0.014 9.009 0.162 0.000 0.770 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 103 121 0 0 0 170 -1
normalized size 1 1.00 1.05 1.23 0.00 0.00 0.00 1.73 -0.01
time (sec) N/A 0.343 0.162 0.059 0.000 0.753 0.000 0.278 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 73 82 0 0 0 125 -1
normalized size 1 1.00 0.88 0.99 0.00 0.00 0.00 1.51 -0.01
time (sec) N/A 0.300 0.186 0.050 0.000 0.553 0.000 0.269 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 68 82 0 0 0 102 -1
normalized size 1 1.00 0.83 1.00 0.00 0.00 0.00 1.24 -0.01
time (sec) N/A 0.249 0.112 0.033 0.000 0.564 0.000 0.208 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 61 45 0 0 0 67 -1
normalized size 1 1.00 0.95 0.70 0.00 0.00 0.00 1.05 -0.02
time (sec) N/A 0.168 0.068 0.041 0.000 0.519 0.000 0.210 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 48 43 0 0 0 43 -1
normalized size 1 1.00 0.94 0.84 0.00 0.00 0.00 0.84 -0.02
time (sec) N/A 0.085 0.022 0.026 0.000 0.512 0.000 0.205 0.000
Problem 65 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 0.012 0.502 0.105 0.000 0.431 0.000 0.000 0.000
Problem 66 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 0.013 6.370 0.170 0.000 0.446 0.000 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 158 158 159 171 0 0 0 250 -1
normalized size 1 1.00 1.01 1.08 0.00 0.00 0.00 1.58 -0.01
time (sec) N/A 0.314 0.293 0.064 0.000 0.416 0.000 0.277 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 107 114 0 0 0 174 -1
normalized size 1 1.00 0.74 0.79 0.00 0.00 0.00 1.21 -0.01
time (sec) N/A 0.282 0.355 0.055 0.000 0.485 0.000 0.232 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 102 117 0 0 0 148 -1
normalized size 1 1.00 0.72 0.83 0.00 0.00 0.00 1.05 -0.01
time (sec) N/A 0.303 0.227 0.036 0.000 0.441 0.000 0.212 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 86 60 0 0 0 92 -1
normalized size 1 1.00 0.89 0.62 0.00 0.00 0.00 0.95 -0.01
time (sec) N/A 0.164 0.118 0.043 0.000 0.433 0.000 0.380 0.000
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 70 63 0 0 0 66 -1
normalized size 1 1.00 0.90 0.81 0.00 0.00 0.00 0.85 -0.01
time (sec) N/A 0.153 0.055 0.032 0.000 0.521 0.000 0.249 0.000
Problem 72 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 0.012 2.330 0.105 0.000 0.623 0.000 0.000 0.000
Problem 73 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 0.014 17.403 0.169 0.000 0.452 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 121 121 204 143 0 0 0 247 -1
normalized size 1 1.00 1.69 1.18 0.00 0.00 0.00 2.04 -0.01
time (sec) N/A 0.242 0.100 0.129 0.000 0.000 0.000 0.297 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 95 95 138 90 0 0 0 153 -1
normalized size 1 1.00 1.45 0.95 0.00 0.00 0.00 1.61 -0.01
time (sec) N/A 0.189 0.059 0.083 0.000 0.000 0.000 0.531 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 86 86 126 96 0 0 0 165 -1
normalized size 1 1.00 1.47 1.12 0.00 0.00 0.00 1.92 -0.01
time (sec) N/A 0.181 0.045 0.076 0.000 0.000 0.000 0.268 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 59 59 81 42 0 0 0 71 -1
normalized size 1 1.00 1.37 0.71 0.00 0.00 0.00 1.20 -0.02
time (sec) N/A 0.151 0.019 0.056 0.000 0.000 0.000 0.571 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 44 44 66 49 0 0 0 83 -1
normalized size 1 1.00 1.50 1.11 0.00 0.00 0.00 1.89 -0.02
time (sec) N/A 0.090 0.026 0.050 0.000 0.000 0.000 0.224 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.013 0.462 0.124 0.000 0.000 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 214 282 202 193 0 0 0 355 -1
normalized size 1 1.32 0.94 0.90 0.00 0.00 0.00 1.66 -0.00
time (sec) N/A 0.533 0.065 0.122 0.000 0.000 0.000 0.371 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 157 157 130 121 0 0 0 225 -1
normalized size 1 1.00 0.83 0.77 0.00 0.00 0.00 1.43 -0.01
time (sec) N/A 0.379 0.033 0.089 0.000 0.000 0.000 0.310 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 147 147 136 131 0 0 0 237 -1
normalized size 1 1.00 0.93 0.89 0.00 0.00 0.00 1.61 -0.01
time (sec) N/A 0.303 0.050 0.080 0.000 0.000 0.000 0.471 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 89 89 71 64 0 0 0 107 -1
normalized size 1 1.00 0.80 0.72 0.00 0.00 0.00 1.20 -0.01
time (sec) N/A 0.183 0.014 0.076 0.000 0.000 0.000 0.273 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 75 75 76 72 0 0 0 119 -1
normalized size 1 1.00 1.01 0.96 0.00 0.00 0.00 1.59 -0.01
time (sec) N/A 0.099 0.038 0.053 0.000 0.000 0.000 0.333 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.013 0.373 0.118 0.000 0.000 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F(-1) C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 263 298 204 233 0 0 0 463 -1
normalized size 1 1.13 0.78 0.89 0.00 0.00 0.00 1.76 -0.00
time (sec) N/A 0.803 0.067 0.140 0.000 0.000 0.000 0.321 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 205 205 140 154 0 0 0 297 -1
normalized size 1 1.00 0.68 0.75 0.00 0.00 0.00 1.45 -0.00
time (sec) N/A 0.600 0.039 0.095 0.000 0.000 0.000 0.311 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 178 178 125 156 0 0 0 309 -1
normalized size 1 1.00 0.70 0.88 0.00 0.00 0.00 1.74 -0.01
time (sec) N/A 0.469 0.058 0.091 0.000 0.000 0.000 0.536 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 119 119 81 79 0 0 0 143 -1
normalized size 1 1.00 0.68 0.66 0.00 0.00 0.00 1.20 -0.01
time (sec) N/A 0.313 0.015 0.067 0.000 0.000 0.000 0.283 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 88 88 68 88 0 0 0 155 -1
normalized size 1 1.00 0.77 1.00 0.00 0.00 0.00 1.76 -0.01
time (sec) N/A 0.165 0.036 0.061 0.000 0.000 0.000 0.347 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.013 0.381 0.115 0.000 0.000 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 106 106 193 72 0 0 0 139 -1
normalized size 1 1.00 1.82 0.68 0.00 0.00 0.00 1.31 -0.01
time (sec) N/A 0.112 0.051 0.101 0.000 0.000 0.000 0.559 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 65 65 128 44 0 0 0 81 -1
normalized size 1 1.00 1.97 0.68 0.00 0.00 0.00 1.25 -0.02
time (sec) N/A 0.083 0.036 0.066 0.000 0.000 0.000 0.312 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 71 71 128 51 0 0 0 93 -1
normalized size 1 1.00 1.80 0.72 0.00 0.00 0.00 1.31 -0.01
time (sec) N/A 0.089 0.047 0.068 0.000 0.000 0.000 0.370 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 28 28 71 21 0 0 0 35 -1
normalized size 1 1.00 2.54 0.75 0.00 0.00 0.00 1.25 -0.04
time (sec) N/A 0.045 0.017 0.052 0.000 0.000 0.000 0.310 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 30 30 69 25 0 0 0 47 -1
normalized size 1 1.00 2.30 0.83 0.00 0.00 0.00 1.57 -0.03
time (sec) N/A 0.024 0.025 0.047 0.000 0.000 0.000 0.590 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.014 0.354 0.108 0.000 0.000 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.013 2.973 0.213 0.000 0.000 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 171 171 427 184 0 0 0 0 -1
normalized size 1 1.00 2.50 1.08 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.144 0.219 0.142 0.000 0.000 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 127 127 231 121 0 0 0 0 -1
normalized size 1 1.00 1.82 0.95 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.107 0.142 0.112 0.000 0.000 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 136 136 319 141 0 0 0 0 -1
normalized size 1 1.00 2.35 1.04 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.098 0.115 0.079 0.000 0.000 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 90 90 154 83 0 0 0 0 -1
normalized size 1 1.00 1.71 0.92 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.070 0.043 0.063 0.000 0.000 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 96 96 211 95 0 0 0 0 -1
normalized size 1 1.00 2.20 0.99 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.069 0.067 0.065 0.000 0.000 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 55 55 91 43 0 0 0 0 -1
normalized size 1 1.00 1.65 0.78 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.032 0.029 0.052 0.000 0.000 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 59 59 87 65 0 0 0 0 -1
normalized size 1 1.00 1.47 1.10 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.090 0.092 0.055 0.000 0.000 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.014 0.449 0.109 0.000 0.000 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 171 235 418 173 0 0 0 0 -1
normalized size 1 1.37 2.44 1.01 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.434 0.295 0.117 0.000 0.000 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 126 126 200 109 0 0 0 0 -1
normalized size 1 1.00 1.59 0.87 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.338 0.380 0.081 0.000 0.000 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 125 125 277 117 0 0 0 0 -1
normalized size 1 1.00 2.22 0.94 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.301 0.150 0.069 0.000 0.000 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 89 89 112 56 0 0 0 0 -1
normalized size 1 1.00 1.26 0.63 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.180 0.212 0.057 0.000 0.000 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 76 76 138 83 0 0 0 0 -1
normalized size 1 1.00 1.82 1.09 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.099 0.174 0.059 0.000 0.000 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.013 0.520 0.099 0.000 0.000 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 264 264 417 225 0 0 0 0 -1
normalized size 1 1.00 1.58 0.85 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.396 0.741 0.126 0.000 0.000 0.000 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 190 190 272 139 0 0 0 0 -1
normalized size 1 1.00 1.43 0.73 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.319 1.107 0.090 0.000 0.000 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 191 191 280 154 0 0 0 0 -1
normalized size 1 1.00 1.47 0.81 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.348 0.344 0.082 0.000 0.000 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 119 119 146 73 0 0 0 0 -1
normalized size 1 1.00 1.23 0.61 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.172 0.368 0.059 0.000 0.000 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 105 105 143 110 0 0 0 0 -1
normalized size 1 1.00 1.36 1.05 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.166 0.242 0.062 0.000 0.000 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.013 0.469 0.100 0.000 0.000 0.000 0.000 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 65 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.122 1.063 1.172 0.000 0.475 0.000 0.000 0.000
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 65 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.118 0.977 0.810 0.000 0.548 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 122 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 0.114 0.039 0.768 0.000 0.529 0.000 0.000 0.000
Problem 122 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 69 69 56 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 0.025 0.019 0.797 0.000 0.529 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 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 0.017 0.558 0.653 0.000 0.433 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) 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 0.585 0.700 0.000 0.532 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.016 2.693 0.106 0.000 0.000 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.015 2.975 0.091 0.000 0.000 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.015 2.252 0.090 0.000 0.000 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) 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 0.015 2.279 0.088 0.000 0.000 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) 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 0.016 0.850 0.984 0.000 0.550 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 132 0 0 0 0 0 -1
normalized size 1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.177 0.100 0.256 0.000 0.449 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 171 171 137 0 0 0 0 0 -1
normalized size 1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.166 0.074 0.229 0.000 0.527 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-2) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 75 138 0 0 0 0 -1
normalized size 1 1.00 0.88 1.62 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.082 0.020 0.166 0.000 0.538 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-2) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 73 240 0 0 0 0 -1
normalized size 1 1.00 0.92 3.04 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.055 0.036 0.114 0.000 0.539 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) 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 0.015 0.308 0.145 0.000 0.476 0.000 0.000 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) 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 0.016 0.673 0.120 0.000 0.521 0.000 0.000 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.021 3.580 0.127 0.000 0.534 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) 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 0.017 4.282 0.107 0.000 0.458 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) 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 0.018 1.599 0.104 0.000 0.460 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.021 1.927 0.097 0.000 0.454 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 81 72 70 61 80 95 -1
normalized size 1 1.00 1.07 0.95 0.92 0.80 1.05 1.25 -0.01
time (sec) N/A 0.035 0.030 0.008 0.449 0.427 1.162 0.298 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 49 64 59 53 65 74 -1
normalized size 1 1.00 0.82 1.07 0.98 0.88 1.08 1.23 -0.02
time (sec) N/A 0.039 0.041 0.005 0.449 0.472 0.493 0.354 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 56 52 49 49 54 64 45
normalized size 1 1.00 1.10 1.02 0.96 0.96 1.06 1.25 0.88
time (sec) N/A 0.019 0.020 0.007 0.434 0.452 0.256 0.518 0.147
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 30 30 29 31 26 29 28
normalized size 1 1.00 1.00 1.00 0.97 1.03 0.87 0.97 0.93
time (sec) N/A 0.014 0.014 0.003 0.434 0.448 0.136 0.463 0.167
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 63 63 52 122 0 0 0 0 48
normalized size 1 1.00 0.83 1.94 0.00 0.00 0.00 0.00 0.76
time (sec) N/A 0.070 0.032 0.049 0.000 0.610 0.000 0.000 0.150
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 36 43 47 55 39 325 34
normalized size 1 1.00 1.09 1.30 1.42 1.67 1.18 9.85 1.03
time (sec) N/A 0.027 0.003 0.004 0.423 0.560 1.711 0.370 0.129
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 44 50 36 35 61 163 -1
normalized size 1 1.00 1.13 1.28 0.92 0.90 1.56 4.18 -0.03
time (sec) N/A 0.019 0.012 0.006 0.471 0.544 1.448 0.285 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 67 65 69 80 119 284 -1
normalized size 1 1.00 1.08 1.05 1.11 1.29 1.92 4.58 -0.02
time (sec) N/A 0.038 0.018 0.005 0.440 0.573 2.606 0.918 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 95 126 142 111 170 194 -1
normalized size 1 1.00 0.93 1.24 1.39 1.09 1.67 1.90 -0.01
time (sec) N/A 0.154 0.178 0.034 0.458 0.446 1.063 0.387 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 73 120 0 99 126 155 -1
normalized size 1 1.00 0.96 1.58 0.00 1.30 1.66 2.04 -0.01
time (sec) N/A 0.119 0.075 0.035 0.000 1.093 0.554 0.264 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 47 72 72 65 82 75 142
normalized size 1 1.00 1.00 1.53 1.53 1.38 1.74 1.60 3.02
time (sec) N/A 0.060 0.044 0.038 0.466 0.400 0.267 0.400 0.347
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 90 90 143 319 0 0 0 0 -1
normalized size 1 1.00 1.59 3.54 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.123 0.152 0.046 0.000 0.480 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 81 81 126 171 0 0 0 0 -1
normalized size 1 1.00 1.56 2.11 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.128 0.225 0.028 0.000 0.537 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 178 178 163 235 273 194 328 368 -1
normalized size 1 1.00 0.92 1.32 1.53 1.09 1.84 2.07 -0.01
time (sec) N/A 0.297 0.381 0.034 0.485 1.774 2.489 0.595 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 114 219 0 169 264 285 -1
normalized size 1 1.00 0.91 1.75 0.00 1.35 2.11 2.28 -0.01
time (sec) N/A 0.205 0.140 0.039 0.000 0.545 1.296 0.420 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 77 132 141 108 160 150 242
normalized size 1 1.00 0.94 1.61 1.72 1.32 1.95 1.83 2.95
time (sec) N/A 0.109 0.082 0.040 0.441 2.030 0.596 0.625 0.407
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 123 123 244 592 0 0 0 0 -1
normalized size 1 1.00 1.98 4.81 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.147 0.234 0.032 0.000 0.433 0.000 0.000 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 137 137 283 378 0 0 0 0 -1
normalized size 1 1.00 2.07 2.76 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.213 0.316 0.102 0.000 0.746 0.000 0.000 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 117 91 102 0 0 0 173 -1
normalized size 1 0.97 0.75 0.84 0.00 0.00 0.00 1.43 -0.01
time (sec) N/A 0.254 0.201 0.033 0.000 0.523 0.000 0.448 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 56 58 0 0 0 86 -1
normalized size 1 1.00 0.89 0.92 0.00 0.00 0.00 1.37 -0.02
time (sec) N/A 0.132 0.079 0.034 0.000 0.480 0.000 0.316 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 44 48 0 0 0 49 -1
normalized size 1 1.00 0.83 0.91 0.00 0.00 0.00 0.92 -0.02
time (sec) N/A 0.067 0.073 0.037 0.000 0.647 0.000 0.644 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A F(-2) 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 0.024 0.251 0.214 0.000 0.974 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 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 0.025 2.179 0.345 0.000 1.377 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-1) F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 152 125 149 0 0 0 646 -1
normalized size 1 0.97 0.80 0.96 0.00 0.00 0.00 4.14 -0.01
time (sec) N/A 0.182 0.561 0.037 0.000 0.499 0.000 0.613 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-1) F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 79 77 0 0 0 326 -1
normalized size 1 1.00 0.88 0.86 0.00 0.00 0.00 3.62 -0.01
time (sec) N/A 0.100 0.294 0.030 0.000 0.566 0.000 0.658 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-1) F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 82 72 76 0 0 0 192 -1
normalized size 1 0.95 0.84 0.88 0.00 0.00 0.00 2.23 -0.01
time (sec) N/A 0.169 0.151 0.042 0.000 0.674 0.000 0.493 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) 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 0.023 4.117 0.228 0.000 0.584 0.000 0.000 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) 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 0.023 34.250 0.447 0.000 0.657 0.000 0.000 0.000
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 197 245 168 290 0 0 0 1539 -1
normalized size 1 1.24 0.85 1.47 0.00 0.00 0.00 7.81 -0.01
time (sec) N/A 0.542 0.874 0.045 0.000 1.182 0.000 0.822 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 108 157 0 0 0 864 -1
normalized size 1 1.00 0.83 1.21 0.00 0.00 0.00 6.65 -0.01
time (sec) N/A 0.323 0.386 0.033 0.000 0.542 0.000 1.515 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 93 138 0 0 0 482 -1
normalized size 1 1.00 0.84 1.24 0.00 0.00 0.00 4.34 -0.01
time (sec) N/A 0.172 0.464 0.043 0.000 0.484 0.000 1.073 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 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 0.023 2.405 0.352 0.000 0.513 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 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 0.023 19.117 0.613 0.000 0.522 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 242 242 246 356 0 0 0 1057 -1
normalized size 1 1.00 1.02 1.47 0.00 0.00 0.00 4.37 -0.00
time (sec) N/A 0.756 0.320 0.147 0.000 0.000 0.000 2.133 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 137 137 141 173 0 0 0 448 -1
normalized size 1 1.00 1.03 1.26 0.00 0.00 0.00 3.27 -0.01
time (sec) N/A 0.453 0.076 0.080 0.000 0.000 0.000 1.460 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 120 120 119 178 0 0 0 531 -1
normalized size 1 1.00 0.99 1.48 0.00 0.00 0.00 4.42 -0.01
time (sec) N/A 0.331 0.099 0.069 0.000 0.000 0.000 2.051 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 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 0.046 3.487 0.140 0.000 0.000 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.037 11.904 0.269 0.000 0.000 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 313 313 245 542 0 0 0 1967 -1
normalized size 1 1.00 0.78 1.73 0.00 0.00 0.00 6.28 -0.00
time (sec) N/A 1.046 0.306 0.170 0.000 0.000 0.000 4.168 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 172 172 126 267 0 0 0 845 -1
normalized size 1 1.00 0.73 1.55 0.00 0.00 0.00 4.91 -0.01
time (sec) N/A 0.525 0.066 0.095 0.000 0.000 0.000 2.090 0.000
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 159 159 291 270 0 0 0 993 -1
normalized size 1 1.00 1.83 1.70 0.00 0.00 0.00 6.25 -0.01
time (sec) N/A 0.281 2.976 0.089 0.000 0.000 0.000 2.792 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 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 0.045 3.123 0.159 0.000 0.000 0.000 0.000 0.000
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 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 0.042 10.575 0.282 0.000 0.000 0.000 0.000 0.000
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 358 358 228 792 0 0 0 2667 -1
normalized size 1 1.00 0.64 2.21 0.00 0.00 0.00 7.45 -0.00
time (sec) N/A 1.409 0.284 0.191 0.000 0.000 0.000 6.680 0.000
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 216 216 141 394 0 0 0 1307 -1
normalized size 1 1.00 0.65 1.82 0.00 0.00 0.00 6.05 -0.00
time (sec) N/A 0.743 0.100 0.111 0.000 0.000 0.000 2.729 0.000
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 179 179 379 393 0 0 0 1179 -1
normalized size 1 1.00 2.12 2.20 0.00 0.00 0.00 6.59 -0.01
time (sec) N/A 0.502 3.190 0.105 0.000 0.000 0.000 4.075 0.000
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 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 0.044 3.248 0.146 0.000 0.000 0.000 0.000 0.000
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 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 0.043 10.601 0.280 0.000 0.000 0.000 0.000 0.000
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 223 223 228 168 0 0 0 317 -1
normalized size 1 1.00 1.02 0.75 0.00 0.00 0.00 1.42 -0.00
time (sec) N/A 0.421 0.289 0.112 0.000 0.000 0.000 1.862 0.000
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 99 99 123 80 0 0 0 132 -1
normalized size 1 1.00 1.24 0.81 0.00 0.00 0.00 1.33 -0.01
time (sec) N/A 0.176 0.077 0.056 0.000 0.000 0.000 2.057 0.000
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-2) F C F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 101 101 121 83 0 0 0 159 -1
normalized size 1 1.00 1.20 0.82 0.00 0.00 0.00 1.57 -0.01
time (sec) N/A 0.091 0.088 0.042 0.000 0.000 0.000 1.456 0.000
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.037 3.119 0.132 0.000 0.000 0.000 0.000 0.000
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.037 11.747 0.244 0.000 0.000 0.000 0.000 0.000
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 250 250 343 295 0 0 0 0 -1
normalized size 1 1.00 1.37 1.18 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.418 0.472 0.118 0.000 0.000 0.000 0.000 0.000
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 130 130 155 143 0 0 0 0 -1
normalized size 1 1.00 1.19 1.10 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.163 0.150 0.073 0.000 0.000 0.000 0.000 0.000
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 137 137 167 149 0 0 0 0 -1
normalized size 1 1.00 1.22 1.09 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.294 0.329 0.072 0.000 0.000 0.000 0.000 0.000
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A F(-2) 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 0.044 3.812 0.118 0.000 0.000 0.000 0.000 0.000
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 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 0.043 11.525 0.270 0.000 0.000 0.000 0.000 0.000
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 291 291 370 660 0 0 0 0 -1
normalized size 1 1.00 1.27 2.27 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.007 1.877 0.153 0.000 0.000 0.000 0.000 0.000
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 180 180 173 311 0 0 0 0 -1
normalized size 1 1.00 0.96 1.73 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.506 1.359 0.090 0.000 0.000 0.000 0.000 0.000
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 163 163 214 325 0 0 0 0 -1
normalized size 1 1.00 1.31 1.99 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.276 0.978 0.090 0.000 0.000 0.000 0.000 0.000
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A F(-2) 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 0.045 3.950 0.118 0.000 0.000 0.000 0.000 0.000
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 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 0.045 11.565 0.271 0.000 0.000 0.000 0.000 0.000
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 120 120 100 144 0 0 82 0 -1
normalized size 1 1.00 0.83 1.20 0.00 0.00 0.68 0.00 -0.01
time (sec) N/A 0.076 0.039 0.045 0.000 1.305 104.624 0.000 0.000
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 66 138 0 0 82 0 -1
normalized size 1 1.00 0.53 1.11 0.00 0.00 0.66 0.00 -0.01
time (sec) N/A 0.098 0.032 0.011 0.000 2.005 17.699 0.000 0.000
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 66 119 0 0 76 0 -1
normalized size 1 1.00 0.75 1.35 0.00 0.00 0.86 0.00 -0.01
time (sec) N/A 0.045 0.017 0.011 0.000 0.566 2.638 0.000 0.000
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 45 98 0 0 0 0 -1
normalized size 1 1.00 0.51 1.10 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.078 0.012 0.010 0.000 0.469 0.000 0.000 0.000
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 40 85 0 0 0 0 -1
normalized size 1 1.00 0.73 1.55 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.038 0.014 0.011 0.000 0.611 0.000 0.000 0.000
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 42 129 0 0 0 0 -1
normalized size 1 1.00 0.34 1.03 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.097 0.016 0.014 0.000 0.539 0.000 0.000 0.000
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 90 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 0.141 0.062 0.180 0.000 0.446 0.000 0.000 0.000
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 90 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 0.141 0.075 0.171 0.000 1.933 0.000 0.000 0.000
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 90 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 0.143 0.052 0.174 0.000 1.565 0.000 0.000 0.000
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-2) F(-1) F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 90 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.130 0.051 180.000 0.000 0.486 0.000 0.000 0.000
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 87 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 0.135 0.051 0.184 0.000 0.445 0.000 0.000 0.000
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 87 0 0 0 0 0 -1
normalized size 1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.145 0.060 0.175 0.000 0.503 0.000 0.000 0.000
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A F(-2) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 69 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 -0.01
time (sec) N/A 0.170 39.368 0.180 0.000 0.417 0.000 0.000 0.000
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A F(-1) A A A A F(-2) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 67 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 -0.01
time (sec) N/A 0.168 180.003 0.172 0.000 0.484 0.000 0.000 0.000
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) F(-1) A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 65 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.160 9.011 180.000 0.000 0.470 0.000 0.000 0.000
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 65 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.159 8.443 0.178 0.000 0.449 0.000 0.000 0.000
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 67 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 -0.01
time (sec) N/A 0.173 14.411 0.178 0.000 0.456 0.000 0.000 0.000
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.030 3.069 0.116 0.000 0.388 0.000 0.000 0.000
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.026 2.897 0.122 0.000 0.386 0.000 0.000 0.000
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.029 0.858 0.126 0.000 0.388 0.000 0.000 0.000
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.032 4.211 0.122 0.000 0.424 0.000 0.000 0.000
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.029 6.205 0.122 0.000 0.481 0.000 0.000 0.000
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.026 5.287 0.122 0.000 0.503 0.000 0.000 0.000
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.025 9.361 0.132 0.000 0.398 0.000 0.000 0.000
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.028 14.813 0.125 0.000 0.395 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 [30] had the largest ratio of [1.000]

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 4 3 1.00 8 0.375
2 A 4 3 1.00 8 0.375
3 A 4 3 1.00 8 0.375
4 A 3 3 1.00 6 0.500
5 A 2 2 1.00 4 0.500
6 A 5 5 1.00 8 0.625
7 A 4 4 1.00 8 0.500
8 A 2 2 1.00 8 0.250
9 A 5 5 1.00 8 0.625
10 A 3 3 1.00 8 0.375
11 A 6 5 1.00 8 0.625
12 A 7 5 1.00 10 0.500
13 A 6 4 1.00 10 0.400
14 A 5 5 1.00 10 0.500
15 A 4 4 1.00 8 0.500
16 A 3 3 1.00 6 0.500
17 A 6 6 1.00 10 0.600
18 A 7 5 1.00 10 0.500
19 A 3 3 1.00 10 0.300
20 A 9 7 1.00 10 0.700
21 A 5 5 1.00 10 0.500
22 A 14 7 1.00 10 0.700
23 A 11 5 1.00 10 0.500
24 A 9 7 1.00 10 0.700
25 A 6 5 1.00 8 0.625
26 A 4 3 1.00 6 0.500
27 A 7 7 1.00 10 0.700
28 A 9 6 1.00 10 0.600
29 A 7 7 1.00 10 0.700
30 A 14 10 1.00 10 1.000
31 A 10 9 1.00 10 0.900
32 A 23 4 1.00 10 0.400
33 A 19 6 1.00 10 0.600
34 A 14 4 1.00 10 0.400
35 A 11 6 1.00 10 0.600
36 A 7 4 1.00 8 0.500
37 A 5 3 1.00 6 0.500
38 A 8 7 1.00 10 0.700
39 A 11 7 1.00 10 0.700
40 A 8 8 1.00 10 0.800
41 A 19 10 1.00 10 1.000
42 A 7 3 1.00 10 0.300
43 A 6 3 1.00 10 0.300
44 A 6 3 1.00 10 0.300
45 A 5 3 1.00 10 0.300
46 A 5 3 1.00 10 0.300
47 A 4 4 1.00 8 0.500
48 A 2 2 1.00 6 0.333
49 A 0 0 0.00 0 0.000
50 A 0 0 0.00 0 0.000
51 A 6 2 1.00 10 0.200
52 A 5 2 1.00 10 0.200
53 A 5 2 1.00 10 0.200
54 A 4 2 1.00 10 0.200
55 A 4 2 1.00 10 0.200
56 A 2 2 1.00 8 0.250
57 A 3 3 1.00 6 0.500
58 A 0 0 0.00 0 0.000
59 A 0 0 0.00 0 0.000
60 A 14 5 1.00 10 0.500
61 A 12 6 1.00 10 0.600
62 A 10 6 1.00 10 0.600
63 A 7 7 1.00 8 0.875
64 A 4 4 1.00 6 0.667
65 A 0 0 0.00 0 0.000
66 A 0 0 0.00 0 0.000
67 A 12 4 1.00 10 0.400
68 A 9 4 1.00 10 0.400
69 A 10 6 1.00 10 0.600
70 A 5 5 1.00 8 0.625
71 A 5 4 1.00 6 0.667
72 A 0 0 0.00 0 0.000
73 A 0 0 0.00 0 0.000
74 A 10 5 1.00 12 0.417
75 A 8 5 1.00 12 0.417
76 A 8 5 1.00 12 0.417
77 A 6 5 1.00 10 0.500
78 A 4 4 1.00 8 0.500
79 A 0 0 0.00 0 0.000
80 A 23 8 1.32 12 0.667
81 A 16 8 1.00 12 0.667
82 A 13 8 1.00 12 0.667
83 A 8 8 1.00 10 0.800
84 A 5 5 1.00 8 0.625
85 A 0 0 0.00 0 0.000
86 A 26 8 1.13 12 0.667
87 A 18 7 1.00 12 0.583
88 A 15 8 1.00 12 0.667
89 A 9 7 1.00 10 0.700
90 A 6 5 1.00 8 0.625
91 A 0 0 0.00 0 0.000
92 A 9 4 1.00 12 0.333
93 A 7 4 1.00 12 0.333
94 A 7 4 1.00 12 0.333
95 A 5 5 1.00 10 0.500
96 A 3 3 1.00 8 0.375
97 A 0 0 0.00 0 0.000
98 A 0 0 0.00 0 0.000
99 A 10 3 1.00 12 0.250
100 A 8 3 1.00 12 0.250
101 A 8 3 1.00 12 0.250
102 A 6 3 1.00 12 0.250
103 A 6 3 1.00 12 0.250
104 A 3 3 1.00 10 0.300
105 A 4 4 1.00 8 0.500
106 A 0 0 0.00 0 0.000
107 A 19 6 1.37 12 0.500
108 A 15 7 1.00 12 0.583
109 A 13 7 1.00 12 0.583
110 A 8 8 1.00 10 0.800
111 A 5 5 1.00 8 0.625
112 A 0 0 0.00 0 0.000
113 A 17 5 1.00 12 0.417
114 A 12 5 1.00 12 0.417
115 A 13 7 1.00 12 0.583
116 A 6 6 1.00 10 0.600
117 A 6 5 1.00 8 0.625
118 A 0 0 0.00 0 0.000
119 A 0 0 0.00 0 0.000
120 A 0 0 0.00 0 0.000
121 A 2 2 1.00 12 0.167
122 A 2 2 1.00 10 0.200
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 0 0 0.00 0 0.000
127 A 0 0 0.00 0 0.000
128 A 0 0 0.00 0 0.000
129 A 0 0 0.00 0 0.000
130 A 9 4 1.00 10 0.400
131 A 9 4 1.00 10 0.400
132 A 6 5 1.00 8 0.625
133 A 4 3 1.00 6 0.500
134 A 0 0 0.00 0 0.000
135 A 0 0 0.00 0 0.000
136 A 0 0 0.00 0 0.000
137 A 0 0 0.00 0 0.000
138 A 0 0 0.00 0 0.000
139 A 0 0 0.00 0 0.000
140 A 4 3 1.00 12 0.250
141 A 4 3 1.00 12 0.250
142 A 3 3 1.00 10 0.300
143 A 3 2 1.00 8 0.250
144 A 5 5 1.00 12 0.417
145 A 4 4 1.00 12 0.333
146 A 2 2 1.00 12 0.167
147 A 5 5 1.00 12 0.417
148 A 5 5 1.00 14 0.357
149 A 4 4 1.00 12 0.333
150 A 3 3 1.00 10 0.300
151 A 6 6 1.00 14 0.429
152 A 7 5 1.00 14 0.357
153 A 10 7 1.00 14 0.500
154 A 6 5 1.00 12 0.417
155 A 5 3 1.00 10 0.300
156 A 7 7 1.00 14 0.500
157 A 9 6 1.00 14 0.429
158 A 9 5 0.97 14 0.357
159 A 6 6 1.00 12 0.500
160 A 4 4 1.00 10 0.400
161 A 0 0 0.00 0 0.000
162 A 0 0 0.00 0 0.000
163 A 8 4 0.97 14 0.286
164 A 4 4 1.00 12 0.333
165 A 5 5 0.95 10 0.500
166 A 0 0 0.00 0 0.000
167 A 0 0 0.00 0 0.000
168 A 16 8 1.24 14 0.571
169 A 9 9 1.00 12 0.750
170 A 6 6 1.00 10 0.600
171 A 0 0 0.00 0 0.000
172 A 0 0 0.00 0 0.000
173 A 14 8 1.00 16 0.500
174 A 9 8 1.00 14 0.571
175 A 7 7 1.00 12 0.583
176 A 0 0 0.00 0 0.000
177 A 0 0 0.00 0 0.000
178 A 22 11 1.00 16 0.688
179 A 11 11 1.00 14 0.786
180 A 8 8 1.00 12 0.667
181 A 0 0 0.00 0 0.000
182 A 0 0 0.00 0 0.000
183 A 24 11 1.00 16 0.688
184 A 12 10 1.00 14 0.714
185 A 9 8 1.00 12 0.667
186 A 0 0 0.00 0 0.000
187 A 0 0 0.00 0 0.000
188 A 13 7 1.00 16 0.438
189 A 8 8 1.00 14 0.571
190 A 6 6 1.00 12 0.500
191 A 0 0 0.00 0 0.000
192 A 0 0 0.00 0 0.000
193 A 12 6 1.00 16 0.375
194 A 6 6 1.00 14 0.429
195 A 7 7 1.00 12 0.583
196 A 0 0 0.00 0 0.000
197 A 0 0 0.00 0 0.000
198 A 22 10 1.00 16 0.625
199 A 11 11 1.00 14 0.786
200 A 8 8 1.00 12 0.667
201 A 0 0 0.00 0 0.000
202 A 0 0 0.00 0 0.000
203 A 5 4 1.00 16 0.250
204 A 7 7 1.00 16 0.438
205 A 4 4 1.00 16 0.250
206 A 6 6 1.00 16 0.375
207 A 3 3 1.00 16 0.188
208 A 7 7 1.00 16 0.438
209 A 2 2 1.00 18 0.111
210 A 2 2 1.00 18 0.111
211 A 2 2 1.00 18 0.111
212 A 2 2 1.00 18 0.111
213 A 2 2 1.00 18 0.111
214 A 2 2 1.00 18 0.111
215 A 0 0 0.00 0 0.000
216 A 0 0 0.00 0 0.000
217 A 0 0 0.00 0 0.000
218 A 0 0 0.00 0 0.000
219 A 0 0 0.00 0 0.000
220 A 0 0 0.00 0 0.000
221 A 0 0 0.00 0 0.000
222 A 0 0 0.00 0 0.000
223 A 0 0 0.00 0 0.000
224 A 0 0 0.00 0 0.000
225 A 0 0 0.00 0 0.000
226 A 0 0 0.00 0 0.000
227 A 0 0 0.00 0 0.000

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