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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

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

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 54, 55, 60, 61, 62, 66, 67, 68, 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, 101, 108, 109, 110, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178 }

B grade: { 25, 53, 72, 98, 99, 100, 102, 103, 104, 107, 111 }

C grade: { 51, 52, 56, 57, 58, 59, 63, 64, 65, 69, 70, 71, 105, 112, 113, 118, 126, 127, 128, 136, 137, 146, 155, 164 }

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

2.1.3 Maple

A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 11, 13, 14, 18, 22, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 46, 47, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 76, 79, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { 5, 10, 12, 15, 16, 17, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 44, 45, 48, 49, 50, 51, 52, 56, 70, 71, 72, 75, 77, 78, 88, 89, 105, 112, 113 }

C grade: { 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 114, 115, 116, 117 }

F grade: { 41, 68, 73, 74, 118, 119, 120, 126, 127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174, 175, 176 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 20, 29, 33, 34, 35, 39, 42, 43, 44, 45, 46, 47, 54, 61, 62, 67, 68, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { 15, 22 }

C grade: { }

F grade: { 8, 16, 18, 19, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 36, 37, 38, 40, 41, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 73, 74, 75, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 126, 127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174, 175, 176 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 29, 30, 31, 32, 33, 34, 35, 39, 40, 42, 43, 44, 45, 46, 54, 55, 61, 62, 67, 68, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 105, 118, 119, 120, 121, 122, 123, 124, 125, 128, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 144, 147, 148, 149, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { 7, 17, 47, 49, 50, 112, 113, 156, 157, 158 }

C grade: { }

F grade: { 8, 16, 18, 19, 24, 25, 26, 27, 28, 36, 37, 38, 41, 48, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 114, 115, 116, 117, 126, 127, 136, 137, 145, 146, 154, 155, 163, 164, 165, 166, 167, 174, 175, 176 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 33, 34, 35, 39, 40, 42, 43, 44, 45, 46, 47, 62, 68, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 121, 122, 123, 124, 125, 130, 131, 133, 134, 135, 141, 142, 143, 153, 168, 171, 172, 177, 178 }

B grade: { }

C grade: { }

F grade: { 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 38, 41, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 126, 127, 128, 129, 132, 136, 137, 138, 139, 140, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 169, 170, 173, 174, 175, 176 }

2.1.7 Giac

A grade: { 9, 10, 11, 12, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 54, 55, 61, 62, 67, 68, 73, 74, 80, 81, 92, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 17, 20, 21, 22, 23, 29, 30, 31, 32, 44, 45, 46, 47, 76, 77, 78, 79, 82, 83, 84, 85, 88, 89, 90, 91, 93, 94, 95 }

C grade: { }

F grade: { 8, 16, 18, 19, 24, 25, 26, 27, 28, 41, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 126, 127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174, 175, 176 }

2.1.8 Mupad

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

B grade: { 6, 7, 8, 9, 10, 20, 29, 47, 79, 86, 87 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 36, 37, 38, 41, 44, 45, 46, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 126, 127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174, 175, 176 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 107 177 161 115 221 646 -1
normalized size 1 1.00 0.94 1.55 1.41 1.01 1.94 5.67 -0.01
time (sec) N/A 0.061 0.144 0.054 0.338 1.042 8.916 1.009 0.000
Problem 2 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 89 89 72 83 80 62 153 518 -1
normalized size 1 1.00 0.81 0.93 0.90 0.70 1.72 5.82 -0.01
time (sec) N/A 0.042 0.130 0.051 0.346 1.389 4.425 0.213 0.000
Problem 3 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 89 89 97 150 132 106 175 480 -1
normalized size 1 1.00 1.09 1.69 1.48 1.19 1.97 5.39 -0.01
time (sec) N/A 0.048 0.076 0.050 0.351 1.588 5.603 0.761 0.000
Problem 4 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 64 64 62 74 59 52 107 352 -1
normalized size 1 1.00 0.97 1.16 0.92 0.81 1.67 5.50 -0.02
time (sec) N/A 0.027 0.104 0.049 0.341 1.509 3.061 0.166 0.000
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 85 123 97 94 107 310 -1
normalized size 1 1.00 1.33 1.92 1.52 1.47 1.67 4.84 -0.02
time (sec) N/A 0.036 0.055 0.051 0.356 0.638 3.469 0.498 0.000
Problem 6 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 39 39 50 65 36 39 58 182 40
normalized size 1 1.00 1.28 1.67 0.92 1.00 1.49 4.67 1.03
time (sec) N/A 0.012 0.023 0.049 0.345 1.017 2.143 0.164 0.653
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 58 37 53 64 32 62 33
normalized size 1 1.00 1.87 1.19 1.71 2.06 1.03 2.00 1.06
time (sec) N/A 0.021 0.066 0.048 0.357 2.105 2.443 0.146 0.872
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 64 64 53 140 0 0 0 0 65
normalized size 1 1.00 0.83 2.19 0.00 0.00 0.00 0.00 1.02
time (sec) N/A 0.085 0.033 0.184 0.000 0.637 0.000 0.000 0.763
Problem 9 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 32 32 41 63 33 26 37 42 37
normalized size 1 1.00 1.28 1.97 1.03 0.81 1.16 1.31 1.16
time (sec) N/A 0.020 0.029 0.049 0.354 1.226 2.132 0.156 0.636
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 66 118 83 40 121 66 50
normalized size 1 1.00 1.29 2.31 1.63 0.78 2.37 1.29 0.98
time (sec) N/A 0.032 0.037 0.050 0.467 0.863 3.356 0.150 0.726
Problem 11 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 59 75 58 39 112 87 -1
normalized size 1 1.00 0.98 1.25 0.97 0.65 1.87 1.45 -0.02
time (sec) N/A 0.038 0.068 0.049 0.346 2.037 3.045 0.135 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 78 147 125 53 194 117 -1
normalized size 1 1.00 1.03 1.93 1.64 0.70 2.55 1.54 -0.01
time (sec) N/A 0.045 0.060 0.049 0.453 1.016 5.502 0.154 0.000
Problem 13 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 82 82 69 83 76 50 158 149 -1
normalized size 1 1.00 0.84 1.01 0.93 0.61 1.93 1.82 -0.01
time (sec) N/A 0.049 0.087 0.049 0.356 0.905 7.226 0.139 0.000
Problem 14 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 101 101 88 174 165 63 243 174 -1
normalized size 1 1.00 0.87 1.72 1.63 0.62 2.41 1.72 -0.01
time (sec) N/A 0.062 0.105 0.052 0.459 0.872 8.826 0.135 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 124 208 197 146 0 811 -1
normalized size 1 1.00 1.16 1.94 1.84 1.36 0.00 7.58 -0.01
time (sec) N/A 0.106 0.225 0.281 0.769 0.588 0.000 0.391 0.000
Problem 16 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 139 139 210 327 0 0 0 0 -1
normalized size 1 1.00 1.51 2.35 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.119 1.365 1.255 0.000 1.400 0.000 0.000 0.000
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 89 133 84 111 0 427 -1
normalized size 1 1.00 1.62 2.42 1.53 2.02 0.00 7.76 -0.02
time (sec) N/A 0.070 0.151 0.265 0.360 2.498 0.000 0.248 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 84 84 147 196 0 0 0 0 -1
normalized size 1 1.00 1.75 2.33 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.068 0.210 0.264 0.000 0.944 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 91 91 137 361 0 0 0 0 -1
normalized size 1 1.00 1.51 3.97 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.123 0.155 0.219 0.000 0.685 0.000 0.000 0.000
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 71 118 79 57 0 104 88
normalized size 1 1.00 1.42 2.36 1.58 1.14 0.00 2.08 1.76
time (sec) N/A 0.061 0.149 0.179 0.363 2.272 0.000 0.155 0.812
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 102 191 0 82 0 163 -1
normalized size 1 1.00 1.16 2.17 0.00 0.93 0.00 1.85 -0.01
time (sec) N/A 0.078 0.120 0.148 0.000 1.108 0.000 0.181 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 108 154 197 93 0 224 -1
normalized size 1 1.00 1.06 1.51 1.93 0.91 0.00 2.20 -0.01
time (sec) N/A 0.096 0.235 0.566 1.950 0.971 0.000 0.172 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 148 265 0 120 0 304 -1
normalized size 1 1.00 1.10 1.98 0.00 0.90 0.00 2.27 -0.01
time (sec) N/A 0.112 0.183 0.464 0.000 0.963 0.000 0.167 0.000
Problem 24 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 207 207 285 510 0 0 0 0 -1
normalized size 1 1.00 1.38 2.46 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.217 0.905 1.064 0.000 0.970 0.000 0.000 0.000
Problem 25 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 220 220 580 648 0 0 0 0 -1
normalized size 1 1.00 2.64 2.95 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.188 7.818 1.547 0.000 1.917 0.000 0.000 0.000
Problem 26 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 126 126 182 349 0 0 0 0 -1
normalized size 1 1.00 1.44 2.77 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.147 0.486 0.875 0.000 0.578 0.000 0.000 0.000
Problem 27 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 144 144 265 437 0 0 0 0 -1
normalized size 1 1.00 1.84 3.03 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.112 0.297 0.763 0.000 2.194 0.000 0.000 0.000
Problem 28 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 124 124 242 666 0 0 0 0 -1
normalized size 1 1.00 1.95 5.37 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.143 0.232 0.265 0.000 1.995 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 135 199 147 98 0 195 155
normalized size 1 1.00 1.69 2.49 1.84 1.22 0.00 2.44 1.94
time (sec) N/A 0.086 0.211 0.219 0.686 1.111 0.000 0.191 0.792
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 186 315 0 150 0 302 -1
normalized size 1 1.00 1.49 2.52 0.00 1.20 0.00 2.42 -0.01
time (sec) N/A 0.105 0.220 0.383 0.000 1.555 0.000 0.179 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 170 170 204 299 0 173 0 428 -1
normalized size 1 1.00 1.20 1.76 0.00 1.02 0.00 2.52 -0.01
time (sec) N/A 0.150 0.326 0.594 0.000 0.716 0.000 0.182 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 208 208 283 472 0 225 0 576 -1
normalized size 1 1.00 1.36 2.27 0.00 1.08 0.00 2.77 -0.00
time (sec) N/A 0.176 0.360 0.757 0.000 0.932 0.000 0.181 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.015 2.913 2.294 0.000 1.837 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 13 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.006 3.489 0.901 0.000 1.075 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.024 0.299 1.046 0.000 0.446 0.000 0.000 0.000
Problem 36 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 47 47 43 48 0 0 0 54 -1
normalized size 1 1.00 0.91 1.02 0.00 0.00 0.00 1.15 -0.02
time (sec) N/A 0.106 0.079 0.178 0.000 0.411 0.000 0.123 0.000
Problem 37 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 95 -1
normalized size 1 1.00 0.89 0.92 0.00 0.00 0.00 1.51 -0.02
time (sec) N/A 0.134 0.079 0.098 0.000 0.435 0.000 0.163 0.000
Problem 38 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 117 117 91 102 0 0 0 200 -1
normalized size 1 1.00 0.78 0.87 0.00 0.00 0.00 1.71 -0.01
time (sec) N/A 0.229 0.176 0.099 0.000 0.415 0.000 0.148 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.024 7.352 4.296 0.000 0.449 0.000 0.000 0.000
Problem 40 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 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.024 4.863 3.973 0.000 0.455 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 83 0 0 0 0 0 -1
normalized size 1 1.00 1.26 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.043 0.187 3.873 0.000 0.434 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.026 0.878 2.826 0.000 0.408 0.000 0.000 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.026 1.775 2.918 0.000 0.422 0.000 0.000 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 165 485 269 290 362 1112 -1
normalized size 1 1.00 0.99 2.90 1.61 1.74 2.17 6.66 -0.01
time (sec) N/A 0.402 0.314 0.056 0.382 0.615 8.418 2.008 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 122 361 198 209 228 595 -1
normalized size 1 1.00 0.99 2.93 1.61 1.70 1.85 4.84 -0.01
time (sec) N/A 0.277 0.192 0.054 0.371 0.548 7.027 2.928 0.000
Problem 46 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 83 83 113 140 92 129 104 349 -1
normalized size 1 1.00 1.36 1.69 1.11 1.55 1.25 4.20 -0.01
time (sec) N/A 0.167 0.203 0.053 0.401 0.459 4.737 0.451 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 58 37 53 64 32 62 33
normalized size 1 1.00 1.87 1.19 1.71 2.06 1.03 2.00 1.06
time (sec) N/A 0.023 0.048 0.045 0.351 0.472 2.431 0.128 0.002
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 257 257 411 869 0 0 0 0 -1
normalized size 1 1.00 1.60 3.38 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.406 0.694 1.114 0.000 0.432 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 141 214 0 475 0 0 -1
normalized size 1 1.00 1.38 2.10 0.00 4.66 0.00 0.00 -0.01
time (sec) N/A 0.155 0.223 0.063 0.000 0.500 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 172 172 250 1007 0 1111 0 0 -1
normalized size 1 1.00 1.45 5.85 0.00 6.46 0.00 0.00 -0.01
time (sec) N/A 0.292 0.506 0.067 0.000 0.952 0.000 0.000 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 496 693 870 1222 0 0 0 0 -1
normalized size 1 1.40 1.75 2.46 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.827 13.934 0.086 0.000 1.432 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 404 502 368 836 0 0 0 0 -1
normalized size 1 1.24 0.91 2.07 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.195 1.655 0.075 0.000 0.000 0.000 0.000 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F(-2) F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 315 315 657 388 0 0 0 0 -1
normalized size 1 1.00 2.09 1.23 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.485 13.196 0.073 0.000 0.000 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.071 18.518 8.853 0.000 1.268 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.076 8.307 10.087 0.000 1.798 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 372 372 333 810 0 0 0 0 -1
normalized size 1 1.00 0.90 2.18 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.755 1.498 0.073 0.000 0.000 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 714 714 873 1248 0 0 0 0 -1
normalized size 1 1.00 1.22 1.75 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.589 13.848 0.083 0.000 0.000 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 530 530 784 862 0 0 0 0 -1
normalized size 1 1.00 1.48 1.63 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.907 13.671 0.076 0.000 0.000 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 344 344 289 412 0 0 0 0 -1
normalized size 1 1.00 0.84 1.20 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.600 1.509 0.073 0.000 0.000 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 212 212 243 254 0 0 0 0 -1
normalized size 1 1.00 1.15 1.20 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.319 3.690 0.069 0.000 0.000 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.072 6.640 4.565 0.000 0.837 0.000 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.079 9.214 7.832 0.000 2.940 0.000 0.000 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 551 551 814 890 0 0 0 0 -1
normalized size 1 1.00 1.48 1.62 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.474 14.016 0.082 0.000 0.000 0.000 0.000 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 369 369 750 441 0 0 0 0 -1
normalized size 1 1.00 2.03 1.20 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.814 13.839 0.076 0.000 0.000 0.000 0.000 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 238 238 226 277 0 0 0 0 -1
normalized size 1 1.00 0.95 1.16 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.575 1.883 0.074 0.000 0.000 0.000 0.000 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 124 217 0 0 0 0 -1
normalized size 1 1.00 1.04 1.82 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.225 0.216 0.063 0.000 2.914 0.000 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.089 11.783 7.378 0.000 1.462 0.000 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.094 14.909 180.000 0.000 0.977 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 602 602 887 1077 0 0 0 0 -1
normalized size 1 1.00 1.47 1.79 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.896 14.101 0.086 0.000 1.488 0.000 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 440 440 856 1040 0 0 0 0 -1
normalized size 1 1.00 1.95 2.36 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.185 13.952 0.080 0.000 0.984 0.000 0.000 0.000
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 314 314 345 913 0 0 0 0 -1
normalized size 1 1.00 1.10 2.91 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.001 1.750 0.079 0.000 1.032 0.000 0.000 0.000
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 298 298 725 886 0 0 0 0 -1
normalized size 1 1.00 2.43 2.97 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.409 13.636 0.079 0.000 0.000 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) F(-1) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.088 29.957 180.000 0.000 1.457 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) F(-1) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.101 26.677 180.000 0.000 2.498 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 540 637 1002 1640 0 0 0 0 -1
normalized size 1 1.18 1.86 3.04 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.752 13.985 0.081 0.000 0.000 0.000 0.000 0.000
Problem 76 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 206 206 140 338 296 191 408 1190 -1
normalized size 1 1.00 0.68 1.64 1.44 0.93 1.98 5.78 -0.00
time (sec) N/A 0.125 0.230 0.056 0.343 1.771 12.254 2.124 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 121 282 232 170 294 840 -1
normalized size 1 1.00 0.75 1.75 1.44 1.06 1.83 5.22 -0.01
time (sec) N/A 0.108 0.176 0.055 0.326 1.610 7.471 1.444 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 149 194 153 141 153 485 -1
normalized size 1 1.00 1.37 1.78 1.40 1.29 1.40 4.45 -0.01
time (sec) N/A 0.051 0.276 0.055 0.322 0.707 6.027 1.232 0.000
Problem 79 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 87 87 104 136 89 125 73 1062 75
normalized size 1 1.00 1.20 1.56 1.02 1.44 0.84 12.21 0.86
time (sec) N/A 0.065 0.124 0.060 0.320 0.548 5.433 0.458 0.833
Problem 80 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 105 105 69 121 94 66 151 139 -1
normalized size 1 1.00 0.66 1.15 0.90 0.63 1.44 1.32 -0.01
time (sec) N/A 0.078 0.115 0.062 0.331 0.937 4.728 0.145 0.000
Problem 81 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 152 152 94 140 137 88 280 250 -1
normalized size 1 1.00 0.62 0.92 0.90 0.58 1.84 1.64 -0.01
time (sec) N/A 0.092 0.170 0.062 0.336 0.535 9.748 0.171 0.000
Problem 82 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 197 197 110 158 172 109 372 374 -1
normalized size 1 1.00 0.56 0.80 0.87 0.55 1.89 1.90 -0.01
time (sec) N/A 0.118 0.173 0.064 0.336 0.605 56.150 0.158 0.000
Problem 83 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 196 196 115 152 183 127 364 1270 -1
normalized size 1 1.00 0.59 0.78 0.93 0.65 1.86 6.48 -0.01
time (sec) N/A 0.150 0.249 0.053 0.342 0.710 8.357 0.322 0.000
Problem 84 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 153 153 97 134 142 106 272 920 -1
normalized size 1 1.00 0.63 0.88 0.93 0.69 1.78 6.01 -0.01
time (sec) N/A 0.122 0.219 0.053 0.332 0.597 5.549 0.264 0.000
Problem 85 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 138 138 78 115 98 85 177 570 -1
normalized size 1 1.00 0.57 0.83 0.71 0.62 1.28 4.13 -0.01
time (sec) N/A 0.096 0.104 0.053 0.335 0.891 3.779 0.223 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 124 124 108 198 0 0 0 0 111
normalized size 1 1.00 0.87 1.60 0.00 0.00 0.00 0.00 0.90
time (sec) N/A 0.286 0.088 3.304 0.000 1.007 0.000 0.000 0.925
Problem 87 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 137 137 125 185 0 0 0 0 124
normalized size 1 1.00 0.91 1.35 0.00 0.00 0.00 0.00 0.91
time (sec) N/A 0.302 0.101 0.776 0.000 0.610 0.000 0.000 0.991
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 252 252 184 494 404 273 542 1573 -1
normalized size 1 1.00 0.73 1.96 1.60 1.08 2.15 6.24 -0.00
time (sec) N/A 0.237 0.373 0.056 0.338 1.186 14.163 4.954 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 191 191 151 371 296 237 355 1027 -1
normalized size 1 1.00 0.79 1.94 1.55 1.24 1.86 5.38 -0.01
time (sec) N/A 0.114 0.257 0.056 0.336 2.602 10.120 3.200 0.000
Problem 90 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 163 163 134 286 197 232 207 2494 -1
normalized size 1 1.00 0.82 1.75 1.21 1.42 1.27 15.30 -0.01
time (sec) N/A 0.130 0.210 0.061 0.347 1.158 8.825 2.154 0.000
Problem 91 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 157 157 125 254 158 222 211 4280 -1
normalized size 1 1.00 0.80 1.62 1.01 1.41 1.34 27.26 -0.01
time (sec) N/A 0.132 0.290 0.067 0.327 0.513 8.426 14.422 0.000
Problem 92 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 183 183 127 191 181 126 335 316 -1
normalized size 1 1.00 0.69 1.04 0.99 0.69 1.83 1.73 -0.01
time (sec) N/A 0.160 0.278 0.064 0.350 0.694 10.894 0.158 0.000
Problem 93 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 241 241 153 223 241 158 510 493 -1
normalized size 1 1.00 0.63 0.93 1.00 0.66 2.12 2.05 -0.00
time (sec) N/A 0.197 0.278 0.066 0.339 0.694 59.500 0.174 0.000
Problem 94 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 242 242 159 214 253 186 493 1700 -1
normalized size 1 1.00 0.66 0.88 1.05 0.77 2.04 7.02 -0.00
time (sec) N/A 0.223 0.338 0.056 0.348 0.748 9.219 0.446 0.000
Problem 95 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 195 195 124 182 189 152 352 1154 -1
normalized size 1 1.00 0.64 0.93 0.97 0.78 1.81 5.92 -0.01
time (sec) N/A 0.144 0.294 0.056 0.344 0.476 6.382 0.321 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 186 186 157 301 0 0 0 0 -1
normalized size 1 1.00 0.84 1.62 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.422 0.387 6.183 0.000 0.531 0.000 0.000 0.000
Problem 97 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 189 189 187 276 0 0 0 0 -1
normalized size 1 1.00 0.99 1.46 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.430 0.678 4.297 0.000 0.561 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 565 565 1260 407 0 0 0 0 -1
normalized size 1 1.00 2.23 0.72 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.257 1.819 4.272 0.000 0.611 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 507 507 1123 401 0 0 0 0 -1
normalized size 1 1.00 2.21 0.79 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.139 0.427 1.124 0.000 0.669 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 529 529 1068 272 0 0 0 0 -1
normalized size 1 1.00 2.02 0.51 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.870 0.438 2.036 0.000 0.478 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 479 479 407 2875 0 0 0 0 -1
normalized size 1 1.00 0.85 6.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.900 0.940 1.073 0.000 0.452 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F(-1) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 572 572 1241 332 0 0 0 0 -1
normalized size 1 1.00 2.17 0.58 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.100 1.750 3.983 0.000 0.000 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 628 628 1480 729 0 0 0 0 -1
normalized size 1 1.00 2.36 1.16 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.321 6.236 1.828 0.000 1.122 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 593 590 1442 541 0 0 0 0 -1
normalized size 1 0.99 2.43 0.91 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.238 2.255 1.364 0.000 0.642 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 131 286 354 0 385 0 0 -1
normalized size 1 0.98 2.13 2.64 0.00 2.87 0.00 0.00 -0.01
time (sec) N/A 0.121 0.783 0.081 0.000 0.613 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F C F F F(-1) F(-2) F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 566 566 0 3036 0 0 0 0 -1
normalized size 1 1.00 0.00 5.36 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.161 43.452 2.613 0.000 0.627 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 803 803 1634 1888 0 0 0 0 -1
normalized size 1 1.00 2.03 2.35 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.400 6.165 19.149 0.000 0.615 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 765 765 1482 1722 0 0 0 0 -1
normalized size 1 1.00 1.94 2.25 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.255 2.801 4.792 0.000 0.698 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 762 759 1477 1716 0 0 0 0 -1
normalized size 1 1.00 1.94 2.25 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.288 2.873 5.046 0.000 0.504 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 806 806 1525 1784 0 0 0 0 -1
normalized size 1 1.00 1.89 2.21 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.364 2.713 19.918 0.000 0.647 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 727 727 2053 1498 0 0 0 0 -1
normalized size 1 1.00 2.82 2.06 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.442 7.763 2.030 0.000 0.799 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 390 1870 0 1015 0 0 -1
normalized size 1 1.00 2.48 11.91 0.00 6.46 0.00 0.00 -0.01
time (sec) N/A 0.182 1.117 0.087 0.000 1.389 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 385 1840 0 890 0 0 -1
normalized size 1 1.00 1.99 9.53 0.00 4.61 0.00 0.00 -0.01
time (sec) N/A 0.191 0.942 0.076 0.000 1.084 0.000 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F C F F F(-1) F(-2) F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 704 704 0 5294 0 0 0 0 -1
normalized size 1 1.00 0.00 7.52 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.318 64.962 7.102 0.000 0.503 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1144 1144 2067 3175 0 0 0 0 -1
normalized size 1 1.00 1.81 2.78 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.600 6.199 5.009 0.000 0.493 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1144 1144 2075 2329 0 0 0 0 -1
normalized size 1 1.00 1.81 2.04 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.069 6.143 7.794 0.000 0.771 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1134 1134 2060 3166 0 0 0 0 -1
normalized size 1 1.00 1.82 2.79 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 4.049 6.064 10.036 0.000 1.967 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F A F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 403 403 365 0 0 1699 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 4.22 0.00 0.00 -0.00
time (sec) N/A 1.312 0.637 7.372 0.000 7.328 0.000 0.000 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 294 294 326 0 0 1379 0 0 -1
normalized size 1 1.00 1.11 0.00 0.00 4.69 0.00 0.00 -0.00
time (sec) N/A 0.409 0.745 6.635 0.000 2.216 0.000 0.000 0.000
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 195 265 0 0 1098 0 0 -1
normalized size 1 1.00 1.36 0.00 0.00 5.63 0.00 0.00 -0.01
time (sec) N/A 0.212 0.483 5.056 0.000 2.837 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.102 5.216 4.387 0.000 0.758 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.107 4.815 1.296 0.000 0.705 0.000 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.096 9.571 6.372 0.000 0.853 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.034 6.674 4.379 0.000 0.432 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.087 1.741 3.382 0.000 0.434 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 328 328 247 0 0 0 0 0 -1
normalized size 1 1.00 0.75 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.432 0.651 6.424 0.000 0.510 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 453 453 325 0 0 0 0 0 -1
normalized size 1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.620 0.721 8.948 0.000 0.730 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F A F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 374 374 339 0 0 1697 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 4.54 0.00 0.00 -0.00
time (sec) N/A 0.538 0.617 6.428 0.000 9.246 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 304 0 0 1375 0 0 -1
normalized size 1 1.00 1.16 0.00 0.00 5.25 0.00 0.00 -0.00
time (sec) N/A 0.288 0.758 4.740 0.000 4.496 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.116 6.085 3.975 0.000 0.880 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.122 6.056 1.069 0.000 2.942 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.124 9.914 5.865 0.000 0.859 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.045 8.473 4.244 0.000 1.636 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.106 13.649 3.707 0.000 1.238 0.000 0.000 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.107 6.488 6.641 0.000 1.467 0.000 0.000 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 416 416 303 0 0 0 0 0 -1
normalized size 1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.573 0.687 9.023 0.000 2.034 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 554 554 383 0 0 0 0 0 -1
normalized size 1 1.00 0.69 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.891 0.875 7.491 0.000 0.991 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 321 321 328 0 0 1383 0 0 -1
normalized size 1 1.00 1.02 0.00 0.00 4.31 0.00 0.00 -0.00
time (sec) N/A 1.048 0.748 7.873 0.000 4.800 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 271 0 0 1107 0 0 -1
normalized size 1 1.00 1.20 0.00 0.00 4.92 0.00 0.00 -0.00
time (sec) N/A 0.327 0.528 7.302 0.000 2.401 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 210 0 0 870 0 0 -1
normalized size 1 1.00 1.59 0.00 0.00 6.59 0.00 0.00 -0.01
time (sec) N/A 0.151 0.225 5.435 0.000 1.653 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.097 1.710 4.178 0.000 0.558 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.111 12.333 1.440 0.000 0.589 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.092 16.601 7.451 0.000 0.589 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.031 1.024 4.686 0.000 0.636 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 247 247 140 0 0 0 0 0 -1
normalized size 1 1.00 0.57 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.266 0.199 4.445 0.000 0.662 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 362 362 249 0 0 0 0 0 -1
normalized size 1 1.00 0.69 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.569 0.664 8.422 0.000 0.816 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 252 252 302 0 0 1480 0 0 -1
normalized size 1 1.00 1.20 0.00 0.00 5.87 0.00 0.00 -0.00
time (sec) N/A 1.074 0.637 7.404 0.000 1.678 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 156 220 0 0 1072 0 0 -1
normalized size 1 1.00 1.41 0.00 0.00 6.87 0.00 0.00 -0.01
time (sec) N/A 0.321 0.361 6.681 0.000 0.957 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 96 0 0 283 0 0 -1
normalized size 1 1.00 1.22 0.00 0.00 3.58 0.00 0.00 -0.01
time (sec) N/A 0.117 0.155 4.786 0.000 0.706 0.000 0.000 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.125 19.369 3.842 0.000 0.678 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.136 25.009 1.339 0.000 0.763 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.113 9.537 6.200 0.000 0.753 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.102 4.828 6.918 0.000 0.603 0.000 0.000 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 112 0 0 0 0 0 -1
normalized size 1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.091 0.207 4.350 0.000 0.761 0.000 0.000 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-1) F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 275 275 213 0 0 0 0 0 -1
normalized size 1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.318 0.492 4.026 0.000 0.778 0.000 0.000 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 243 243 311 0 0 2119 0 0 -1
normalized size 1 1.00 1.28 0.00 0.00 8.72 0.00 0.00 -0.00
time (sec) N/A 1.057 0.538 7.342 0.000 1.378 0.000 0.000 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 173 0 0 663 0 0 -1
normalized size 1 1.00 1.06 0.00 0.00 4.07 0.00 0.00 -0.01
time (sec) N/A 0.246 0.268 6.727 0.000 1.095 0.000 0.000 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 157 0 0 573 0 0 -1
normalized size 1 1.00 1.14 0.00 0.00 4.15 0.00 0.00 -0.01
time (sec) N/A 0.135 0.208 4.939 0.000 1.056 0.000 0.000 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.123 37.842 3.726 0.000 0.818 0.000 0.000 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.140 46.557 1.347 0.000 0.797 0.000 0.000 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.121 14.827 8.811 0.000 0.802 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.110 12.520 6.298 0.000 0.807 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 276 276 185 0 0 0 0 0 -1
normalized size 1 1.00 0.67 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.283 0.286 6.914 0.000 0.657 0.000 0.000 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 296 296 249 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.238 0.560 4.315 0.000 0.731 0.000 0.000 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 585 566 0 0 0 0 0 0 -1
normalized size 1 0.97 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.405 0.223 12.128 0.000 0.761 0.000 0.000 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 371 352 0 0 0 0 0 0 -1
normalized size 1 0.95 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.432 0.145 9.316 0.000 0.624 0.000 0.000 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F(-1) F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 215 202 0 0 0 0 0 0 -1
normalized size 1 0.94 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.194 0.107 7.525 0.000 0.639 0.000 0.000 0.000
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.075 1.990 3.590 0.000 0.605 0.000 0.000 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.074 6.445 6.050 0.000 0.626 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.115 1.156 4.785 0.000 0.684 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.097 0.115 4.877 0.000 0.636 0.000 0.000 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.100 1.485 6.561 0.000 0.777 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.117 1.671 6.271 0.000 0.858 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 401 401 194 0 0 0 0 0 -1
normalized size 1 1.00 0.48 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.527 0.295 13.067 0.000 0.000 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 268 268 159 0 0 0 0 0 -1
normalized size 1 1.00 0.59 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.027 0.408 9.292 0.000 0.000 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 135 138 0 0 0 0 0 -1
normalized size 1 1.07 1.10 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.212 0.179 6.284 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 A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 29 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.089 0.411 6.198 0.000 0.610 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 29 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.101 3.582 4.244 0.000 0.766 0.000 0.000 0.000

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [69] had the largest ratio of [.8571]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 7 5 1.00 12 0.417
2 A 4 3 1.00 12 0.250
3 A 6 5 1.00 12 0.417
4 A 3 3 1.00 12 0.250
5 A 5 5 1.00 12 0.417
6 A 2 2 1.00 10 0.200
7 A 5 4 1.00 8 0.500
8 A 6 6 1.00 12 0.500
9 A 2 2 1.00 12 0.167
10 A 4 4 1.00 12 0.333
11 A 4 3 1.00 12 0.250
12 A 5 4 1.00 12 0.333
13 A 4 3 1.00 12 0.250
14 A 6 4 1.00 12 0.333
15 A 5 5 1.00 14 0.357
16 A 8 6 1.00 14 0.429
17 A 4 4 1.00 12 0.333
18 A 7 5 1.00 10 0.500
19 A 6 6 1.00 14 0.429
20 A 4 3 1.00 14 0.214
21 A 4 3 1.00 14 0.214
22 A 5 5 1.00 14 0.357
23 A 5 3 1.00 14 0.214
24 A 10 10 1.00 14 0.714
25 A 11 8 1.00 14 0.571
26 A 7 7 1.00 12 0.583
27 A 9 6 1.00 10 0.600
28 A 7 7 1.00 14 0.500
29 A 5 3 1.00 14 0.214
30 A 6 6 1.00 14 0.429
31 A 8 6 1.00 14 0.429
32 A 10 6 1.00 14 0.429
33 A 0 0 0.00 0 0.000
34 A 0 0 0.00 0 0.000
35 A 0 0 0.00 0 0.000
36 A 4 4 1.00 14 0.286
37 A 6 6 1.00 14 0.429
38 A 9 5 1.00 14 0.357
39 A 0 0 0.00 0 0.000
40 A 0 0 0.00 0 0.000
41 A 3 3 1.00 14 0.214
42 A 0 0 0.00 0 0.000
43 A 0 0 0.00 0 0.000
44 A 11 9 1.00 16 0.562
45 A 10 9 1.00 16 0.562
46 A 9 9 1.00 14 0.643
47 A 5 4 1.00 8 0.500
48 A 4 2 1.00 16 0.125
49 A 7 7 1.00 16 0.438
50 A 8 8 1.00 16 0.500
51 A 31 16 1.40 21 0.762
52 A 24 15 1.24 19 0.790
53 A 15 11 1.00 18 0.611
54 A 0 0 0.00 0 0.000
55 A 0 0 0.00 0 0.000
56 A 22 13 1.00 18 0.722
57 A 27 17 1.00 21 0.810
58 A 20 15 1.00 21 0.714
59 A 14 13 1.00 19 0.684
60 A 9 9 1.00 18 0.500
61 A 0 0 0.00 0 0.000
62 A 0 0 0.00 0 0.000
63 A 23 15 1.00 21 0.714
64 A 16 13 1.00 21 0.619
65 A 11 11 1.00 19 0.579
66 A 6 6 1.00 18 0.333
67 A 0 0 0.00 0 0.000
68 A 0 0 0.00 0 0.000
69 A 31 18 1.00 21 0.857
70 A 25 17 1.00 21 0.810
71 A 19 14 1.00 19 0.737
72 A 12 11 1.00 18 0.611
73 A 0 0 0.00 0 0.000
74 A 0 0 0.00 0 0.000
75 A 19 14 1.18 18 0.778
76 A 7 7 1.00 19 0.368
77 A 6 7 1.00 19 0.368
78 A 5 5 1.00 16 0.312
79 A 4 5 1.00 19 0.263
80 A 4 5 1.00 19 0.263
81 A 5 6 1.00 19 0.316
82 A 6 6 1.00 19 0.316
83 A 5 5 1.00 19 0.263
84 A 5 5 1.00 19 0.263
85 A 6 5 1.00 17 0.294
86 A 11 11 1.00 19 0.579
87 A 13 13 1.00 19 0.684
88 A 7 8 1.00 21 0.381
89 A 6 7 1.00 18 0.389
90 A 6 7 1.00 21 0.333
91 A 6 7 1.00 21 0.333
92 A 5 6 1.00 21 0.286
93 A 6 7 1.00 21 0.333
94 A 5 6 1.00 21 0.286
95 A 6 5 1.00 19 0.263
96 A 12 13 1.00 21 0.619
97 A 14 15 1.00 21 0.714
98 A 25 12 1.00 21 0.571
99 A 26 9 1.00 19 0.474
100 A 19 7 1.00 18 0.389
101 A 19 7 1.00 21 0.333
102 A 24 10 1.00 21 0.476
103 A 31 14 1.00 21 0.667
104 A 29 12 0.99 21 0.571
105 A 7 5 0.98 19 0.263
106 A 24 10 1.00 21 0.476
107 A 51 15 1.00 21 0.714
108 A 27 10 1.00 21 0.476
109 A 47 11 1.00 18 0.611
110 A 50 13 1.00 21 0.619
111 A 33 13 1.00 21 0.619
112 A 6 7 1.00 21 0.333
113 A 8 6 1.00 19 0.316
114 A 28 11 1.00 21 0.524
115 A 35 11 1.00 21 0.524
116 A 63 12 1.00 21 0.571
117 A 81 12 1.00 18 0.667
118 A 12 12 1.00 23 0.522
119 A 11 12 1.00 23 0.522
120 A 9 9 1.00 21 0.429
121 A 0 0 0.00 0 0.000
122 A 0 0 0.00 0 0.000
123 A 0 0 0.00 0 0.000
124 A 0 0 0.00 0 0.000
125 A 0 0 0.00 0 0.000
126 A 11 11 1.00 23 0.478
127 A 12 12 1.00 23 0.522
128 A 12 12 1.00 23 0.522
129 A 10 10 1.00 21 0.476
130 A 0 0 0.00 0 0.000
131 A 0 0 0.00 0 0.000
132 A 0 0 0.00 0 0.000
133 A 0 0 0.00 0 0.000
134 A 0 0 0.00 0 0.000
135 A 0 0 0.00 0 0.000
136 A 12 12 1.00 23 0.522
137 A 13 12 1.00 23 0.522
138 A 11 12 1.00 23 0.522
139 A 10 12 1.00 23 0.522
140 A 8 8 1.00 21 0.381
141 A 0 0 0.00 0 0.000
142 A 0 0 0.00 0 0.000
143 A 0 0 0.00 0 0.000
144 A 0 0 0.00 0 0.000
145 A 11 11 1.00 23 0.478
146 A 11 12 1.00 23 0.522
147 A 10 11 1.00 23 0.478
148 A 9 11 1.00 23 0.478
149 A 4 4 1.00 21 0.190
150 A 0 0 0.00 0 0.000
151 A 0 0 0.00 0 0.000
152 A 0 0 0.00 0 0.000
153 A 0 0 0.00 0 0.000
154 A 5 5 1.00 20 0.250
155 A 10 11 1.00 23 0.478
156 A 10 11 1.00 23 0.478
157 A 7 8 1.00 23 0.348
158 A 5 5 1.00 21 0.238
159 A 0 0 0.00 0 0.000
160 A 0 0 0.00 0 0.000
161 A 0 0 0.00 0 0.000
162 A 0 0 0.00 0 0.000
163 A 10 10 1.00 23 0.435
164 A 10 11 1.00 20 0.550
165 A 6 7 0.97 23 0.304
166 A 6 7 0.95 23 0.304
167 A 5 6 0.94 21 0.286
168 A 0 0 0.00 0 0.000
169 A 0 0 0.00 0 0.000
170 A 0 0 0.00 0 0.000
171 A 0 0 0.00 0 0.000
172 A 0 0 0.00 0 0.000
173 A 0 0 0.00 0 0.000
174 A 16 11 1.00 26 0.423
175 A 13 11 1.00 26 0.423
176 A 8 9 1.07 26 0.346
177 A 0 0 0.00 0 0.000
178 A 0 0 0.00 0 0.000

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