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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 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 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 }

B grade: { }

C grade: { }

F grade: { }

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, 45, 46, 47, 53, 69, 77, 85, 92, 98, 118, 125, 132, 139, 146, 171, 179, 187 }

B grade: { 54, 61 }

C grade: { 43, 44, 48, 49, 50, 51, 52, 55, 56, 57, 58, 59, 60, 62, 63, 64, 68, 76, 84, 89, 90, 91, 93, 94, 95, 96, 97, 99, 100, 110, 149, 150, 151, 152, 156, 157, 158 }

F grade: { 65, 66, 67, 70, 71, 72, 73, 74, 75, 78, 79, 80, 81, 82, 83, 86, 87, 88, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 147, 148, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193 }

2.1.4 Maxima

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, 69, 77, 85, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 118, 125, 132, 139, 146, 151, 152, 156, 157, 158, 171, 176, 177, 178, 179, 180, 181, 182, 184, 185, 186, 187, 188, 189, 190 }

B grade: { 149, 150 }

C grade: { }

F grade: { 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 147, 148, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 173, 174, 175, 183, 191, 192, 193 }

2.1.5 FriCAS

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, 53, 55, 56, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 118, 132, 139, 149, 152, 153, 154, 156, 157, 158, 159, 160, 161, 170, 171, 178, 179, 187 }

B grade: { 50, 51, 52, 54, 57, 58, 59, 60, 61, 62, 63, 64, 81, 82, 83, 84, 85, 86, 87, 88, 95, 125, 146, 150, 151, 155 }

C grade: { }

F grade: { 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 147, 148, 162, 163, 164, 165, 166, 167, 168, 169, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 25, 26, 32, 33, 39, 40, 43, 44, 45, 46, 47, 48, 49, 54, 69, 77, 85, 90, 91, 92, 93, 94, 118, 125, 132, 139, 149, 150, 151, 152, 156, 157, 158, 171, 179, 187 }

B grade: { 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 96, 97, 98, 99, 100 }

C grade: { }

F grade: { 22, 23, 24, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 41, 42, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 95, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193 }

2.1.7 Giac

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, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 49, 55, 56, 65, 66, 67, 68, 77, 85, 92, 93, 98, 105, 118, 132, 139, 146, 157, 158, 171, 179, 187 }

B grade: { 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62, 63, 64, 69, 73, 74, 75, 76, 81, 82, 83, 84, 94, 99, 100, 111, 125, 149, 150, 151, 152, 156 }

C grade: { 89, 90, 91, 95, 96, 97 }

F grade: { 27, 28, 34, 35, 41, 42, 70, 71, 72, 78, 79, 80, 86, 87, 88, 101, 102, 103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 147, 148, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193 }

2.1.8 Mupad

A grade: { }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 25, 26, 32, 33, 39, 40, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 69, 77, 85, 118, 125, 132, 139, 146, 171, 179, 187 }

C grade: { }

F grade: { 22, 23, 24, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 41, 42, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 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, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193 }

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 B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 16 15 15 14 15 11
normalized size 1 1.00 1.00 0.84 0.79 0.79 0.74 0.79 0.58
time (sec) N/A 0.008 0.001 0.028 0.494 0.413 0.171 0.302 0.041
Problem 2 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 19 19 19 16 15 15 14 15 11
normalized size 1 1.00 1.00 0.84 0.79 0.79 0.74 0.79 0.58
time (sec) N/A 0.007 0.001 0.031 0.613 0.433 0.105 0.264 0.029
Problem 3 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 19 19 19 16 15 15 14 15 11
normalized size 1 1.00 1.00 0.84 0.79 0.79 0.74 0.79 0.58
time (sec) N/A 0.004 0.001 0.030 0.564 0.416 0.101 0.216 0.032
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 10 10 10 11 16 10 7 16 8
normalized size 1 1.00 1.00 1.10 1.60 1.00 0.70 1.60 0.80
time (sec) N/A 0.001 0.001 0.023 0.560 0.400 0.088 0.233 0.020
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 10 10 10 9 8 8 7 8 8
normalized size 1 1.00 1.00 0.90 0.80 0.80 0.70 0.80 0.80
time (sec) N/A 0.006 0.001 0.023 0.679 0.406 0.090 0.198 3.601
Problem 6 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 15 15 15 16 15 11 10 15 11
normalized size 1 1.00 1.00 1.07 1.00 0.73 0.67 1.00 0.73
time (sec) N/A 0.007 0.001 0.033 0.533 0.416 0.097 0.209 3.476
Problem 7 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 19 19 19 16 15 13 17 15 11
normalized size 1 1.00 1.00 0.84 0.79 0.68 0.89 0.79 0.58
time (sec) N/A 0.007 0.001 0.030 0.542 0.396 0.105 0.201 0.024
Problem 8 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 32 27 21 26 26 26 21
normalized size 1 1.00 1.00 0.84 0.66 0.81 0.81 0.81 0.66
time (sec) N/A 0.020 0.001 0.030 0.601 0.395 0.117 0.211 3.605
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 32 27 21 26 29 26 21
normalized size 1 1.00 1.00 0.84 0.66 0.81 0.91 0.81 0.66
time (sec) N/A 0.020 0.002 0.028 0.591 0.413 0.114 0.198 3.546
Problem 10 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 32 27 21 26 26 26 21
normalized size 1 1.00 1.00 0.84 0.66 0.81 0.81 0.81 0.66
time (sec) N/A 0.011 0.001 0.029 0.513 0.425 0.108 0.211 3.491
Problem 11 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 19 19 19 20 16 19 19 19 16
normalized size 1 1.00 1.00 1.05 0.84 1.00 1.00 1.00 0.84
time (sec) N/A 0.005 0.001 0.031 0.479 0.401 0.098 0.177 3.589
Problem 12 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 10 10 10 9 8 8 7 8 8
normalized size 1 1.00 1.00 0.90 0.80 0.80 0.70 0.80 0.80
time (sec) N/A 0.012 0.001 0.024 0.549 0.420 0.092 0.196 3.396
Problem 13 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 26 26 26 27 19 19 20 26 19
normalized size 1 1.00 1.00 1.04 0.73 0.73 0.77 1.00 0.73
time (sec) N/A 0.020 0.001 0.032 0.530 0.450 0.118 0.187 3.586
Problem 14 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 32 27 21 21 29 26 21
normalized size 1 1.00 1.00 0.84 0.66 0.66 0.91 0.81 0.66
time (sec) N/A 0.019 0.001 0.031 0.500 0.430 0.126 0.208 3.380
Problem 15 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 45 38 29 37 42 37 29
normalized size 1 1.00 1.00 0.84 0.64 0.82 0.93 0.82 0.64
time (sec) N/A 0.036 0.002 0.030 0.545 0.416 0.131 0.212 3.289
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 45 45 45 38 29 37 41 37 29
normalized size 1 1.00 1.00 0.84 0.64 0.82 0.91 0.82 0.64
time (sec) N/A 0.031 0.002 0.028 0.506 0.395 0.133 0.174 3.559
Problem 17 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 45 38 29 37 42 37 29
normalized size 1 1.00 1.00 0.84 0.64 0.82 0.93 0.82 0.64
time (sec) N/A 0.018 0.001 0.031 0.500 0.414 0.127 0.216 3.475
Problem 18 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 28 28 28 29 24 28 29 28 24
normalized size 1 1.00 1.00 1.04 0.86 1.00 1.04 1.00 0.86
time (sec) N/A 0.008 0.001 0.029 0.480 0.397 0.110 0.203 3.556
Problem 19 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 10 10 10 9 8 8 7 8 8
normalized size 1 1.00 1.00 0.90 0.80 0.80 0.70 0.80 0.80
time (sec) N/A 0.011 0.001 0.025 0.487 0.436 0.091 0.200 3.527
Problem 20 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 37 37 37 38 27 27 31 37 27
normalized size 1 1.00 1.00 1.03 0.73 0.73 0.84 1.00 0.73
time (sec) N/A 0.034 0.002 0.030 0.518 0.411 0.134 0.197 3.459
Problem 21 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 45 38 29 29 44 37 29
normalized size 1 1.00 1.00 0.84 0.64 0.64 0.98 0.82 0.64
time (sec) N/A 0.033 0.002 0.033 0.572 0.427 0.144 0.216 3.600
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 14 11 12 0 11 -1
normalized size 1 1.00 1.00 1.27 1.00 1.09 0.00 1.00 -0.09
time (sec) N/A 0.024 0.015 0.037 0.958 0.455 0.000 0.203 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 14 11 12 0 11 -1
normalized size 1 1.00 1.00 1.27 1.00 1.09 0.00 1.00 -0.09
time (sec) N/A 0.023 0.015 0.035 0.872 0.416 0.000 0.243 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 14 11 12 0 11 -1
normalized size 1 1.00 1.00 1.27 1.00 1.09 0.00 1.00 -0.09
time (sec) N/A 0.017 0.013 0.036 0.932 0.402 0.000 0.162 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 14 9 8 5 9 8
normalized size 1 1.00 1.00 1.75 1.12 1.00 0.62 1.12 1.00
time (sec) N/A 0.003 0.005 0.034 0.892 0.401 0.479 0.184 3.428
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 5 5 5 6 5 5 5 5 5
normalized size 1 1.00 1.00 1.20 1.00 1.00 1.00 1.00 1.00
time (sec) N/A 0.012 0.005 0.025 0.685 0.422 0.105 0.214 3.538
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 10 9 10 0 0 -1
normalized size 1 1.00 1.00 1.11 1.00 1.11 0.00 0.00 -0.11
time (sec) N/A 0.024 0.014 0.036 0.709 0.415 0.000 0.000 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 14 11 12 0 0 -1
normalized size 1 1.00 1.00 1.27 1.00 1.09 0.00 0.00 -0.09
time (sec) N/A 0.024 0.015 0.037 0.897 0.422 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 26 13 33 0 24 -1
normalized size 1 1.00 1.00 1.08 0.54 1.38 0.00 1.00 -0.04
time (sec) N/A 0.038 0.015 0.033 0.768 0.416 0.000 0.194 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 26 13 33 0 24 -1
normalized size 1 1.00 1.00 1.08 0.54 1.38 0.00 1.00 -0.04
time (sec) N/A 0.037 0.017 0.030 0.957 0.402 0.000 0.188 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 26 13 33 0 24 -1
normalized size 1 1.00 1.00 1.08 0.54 1.38 0.00 1.00 -0.04
time (sec) N/A 0.026 0.014 0.033 0.819 0.429 0.000 0.203 0.000
Problem 32 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 18 18 18 24 12 25 12 19 18
normalized size 1 1.00 1.00 1.33 0.67 1.39 0.67 1.06 1.00
time (sec) N/A 0.005 0.004 0.032 0.909 0.410 0.504 0.203 3.343
Problem 33 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 8 8 8 9 8 8 7 8 8
normalized size 1 1.00 1.00 1.12 1.00 1.00 0.88 1.00 1.00
time (sec) N/A 0.012 0.001 0.025 0.644 0.421 0.089 0.200 3.557
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 21 9 28 0 0 -1
normalized size 1 1.00 1.00 0.95 0.41 1.27 0.00 0.00 -0.05
time (sec) N/A 0.035 0.016 0.033 0.835 0.399 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 26 13 33 0 0 -1
normalized size 1 1.00 1.00 1.08 0.54 1.38 0.00 0.00 -0.04
time (sec) N/A 0.037 0.015 0.032 0.835 0.399 0.000 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 37 37 13 47 0 35 -1
normalized size 1 1.00 1.00 1.00 0.35 1.27 0.00 0.95 -0.03
time (sec) N/A 0.052 0.018 0.030 0.839 0.422 0.000 0.232 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 41 37 13 47 0 35 -1
normalized size 1 1.00 1.00 0.90 0.32 1.15 0.00 0.85 -0.02
time (sec) N/A 0.053 0.015 0.032 0.874 0.595 0.000 0.219 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 37 37 13 47 0 35 -1
normalized size 1 1.00 1.00 1.00 0.35 1.27 0.00 0.95 -0.03
time (sec) N/A 0.031 0.005 0.031 0.851 0.418 0.000 0.216 0.000
Problem 39 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 34 34 34 33 13 34 26 29 29
normalized size 1 1.00 1.00 0.97 0.38 1.00 0.76 0.85 0.85
time (sec) N/A 0.009 0.006 0.031 0.788 0.395 0.503 0.223 3.534
Problem 40 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 10 10 10 9 8 8 10 8 8
normalized size 1 1.00 1.00 0.90 0.80 0.80 1.00 0.80 0.80
time (sec) N/A 0.012 0.001 0.025 0.508 0.408 0.092 0.198 3.450
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 39 33 9 34 0 0 -1
normalized size 1 1.00 1.00 0.85 0.23 0.87 0.00 0.00 -0.03
time (sec) N/A 0.050 0.015 0.030 0.950 0.404 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 36 36 13 41 0 0 -1
normalized size 1 1.00 1.00 1.00 0.36 1.14 0.00 0.00 -0.03
time (sec) N/A 0.049 0.018 0.032 0.809 0.414 0.000 0.000 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 32 112 26 30 36 31 25
normalized size 1 1.00 1.19 4.15 0.96 1.11 1.33 1.15 0.93
time (sec) N/A 0.013 0.002 0.224 0.496 0.413 1.365 0.232 3.588
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 32 112 26 30 36 31 25
normalized size 1 1.00 1.19 4.15 0.96 1.11 1.33 1.15 0.93
time (sec) N/A 0.012 0.001 0.175 0.547 0.421 0.780 0.288 3.361
Problem 45 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 27 27 32 29 26 30 36 31 25
normalized size 1 1.00 1.19 1.07 0.96 1.11 1.33 1.15 0.93
time (sec) N/A 0.007 0.001 0.048 0.608 0.449 0.465 0.251 3.264
Problem 46 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 18 18 18 19 18 22 19 20 18
normalized size 1 1.00 1.00 1.06 1.00 1.22 1.06 1.11 1.00
time (sec) N/A 0.006 0.001 0.031 0.585 0.435 0.249 0.272 3.497
Problem 47 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 22 22 21 27 20 18 34 19 19
normalized size 1 1.00 0.95 1.23 0.91 0.82 1.55 0.86 0.86
time (sec) N/A 0.012 0.001 0.026 0.441 0.451 8.603 0.218 3.407
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 26 112 26 19 24 24 23
normalized size 1 1.00 1.13 4.87 1.13 0.83 1.04 1.04 1.00
time (sec) N/A 0.013 0.001 0.118 0.545 0.462 0.456 0.253 3.558
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 32 111 26 23 37 27 26
normalized size 1 1.00 1.19 4.11 0.96 0.85 1.37 1.00 0.96
time (sec) N/A 0.013 0.001 0.114 0.533 0.430 0.938 0.253 3.490
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 43 691 71 102 131 111 61
normalized size 1 1.00 0.83 13.29 1.37 1.96 2.52 2.13 1.17
time (sec) N/A 0.036 0.018 0.209 0.507 0.421 2.403 0.395 3.605
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 46 692 71 103 143 111 62
normalized size 1 1.00 0.88 13.31 1.37 1.98 2.75 2.13 1.19
time (sec) N/A 0.037 0.021 0.209 0.675 0.415 1.518 0.347 3.562
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 41 692 70 102 126 108 60
normalized size 1 1.00 0.79 13.31 1.35 1.96 2.42 2.08 1.15
time (sec) N/A 0.023 0.015 0.208 0.597 0.447 0.928 0.291 3.478
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 33 63 57 85 109 88 49
normalized size 1 1.00 0.77 1.47 1.33 1.98 2.53 2.05 1.14
time (sec) N/A 0.013 0.009 0.048 0.607 0.426 0.521 0.360 3.576
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 56 20 51 60 56 37
normalized size 1 1.00 1.00 2.55 0.91 2.32 2.73 2.55 1.68
time (sec) N/A 0.024 0.003 0.026 0.456 0.431 22.815 0.287 3.416
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 35 704 70 77 110 86 56
normalized size 1 1.00 0.76 15.30 1.52 1.67 2.39 1.87 1.22
time (sec) N/A 0.035 0.011 0.168 0.725 0.445 0.572 0.310 3.608
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 41 703 71 83 128 90 62
normalized size 1 1.00 0.79 13.52 1.37 1.60 2.46 1.73 1.19
time (sec) N/A 0.035 0.013 0.161 0.603 0.474 1.123 0.337 3.429
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 66 2649 135 222 338 262 110
normalized size 1 1.00 0.86 34.40 1.75 2.88 4.39 3.40 1.43
time (sec) N/A 0.063 0.032 0.315 0.621 0.418 4.396 0.289 3.664
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 67 2650 134 224 311 256 108
normalized size 1 1.00 0.87 34.42 1.74 2.91 4.04 3.32 1.40
time (sec) N/A 0.060 0.013 0.310 0.679 0.448 2.890 0.296 3.374
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 60 2650 135 222 337 262 110
normalized size 1 1.00 0.78 34.42 1.75 2.88 4.38 3.40 1.43
time (sec) N/A 0.039 0.030 0.318 0.688 0.443 1.777 0.375 3.440
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 50 2641 113 198 270 219 94
normalized size 1 1.00 0.76 40.02 1.71 3.00 4.09 3.32 1.42
time (sec) N/A 0.024 0.010 0.286 0.590 0.456 1.035 0.249 3.663
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 75 20 100 92 114 56
normalized size 1 1.00 1.00 3.41 0.91 4.55 4.18 5.18 2.55
time (sec) N/A 0.022 0.004 0.025 0.559 0.440 28.942 0.271 3.367
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 52 2674 133 180 272 197 104
normalized size 1 1.00 0.75 38.75 1.93 2.61 3.94 2.86 1.51
time (sec) N/A 0.060 0.019 0.285 0.613 0.412 1.034 0.280 3.375
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 60 2673 135 189 338 203 111
normalized size 1 1.00 0.78 34.71 1.75 2.45 4.39 2.64 1.44
time (sec) N/A 0.059 0.021 0.286 0.600 0.418 1.157 0.348 3.681
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 60 2674 136 191 313 204 110
normalized size 1 1.00 0.78 34.73 1.77 2.48 4.06 2.65 1.43
time (sec) N/A 0.061 0.026 0.289 0.591 0.423 1.811 0.301 3.590
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 51 0 0 42 0 48 -1
normalized size 1 1.00 1.00 0.00 0.00 0.82 0.00 0.94 -0.02
time (sec) N/A 0.056 0.062 0.297 0.000 0.437 0.000 0.337 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 51 0 0 42 0 48 -1
normalized size 1 1.00 1.00 0.00 0.00 0.82 0.00 0.94 -0.02
time (sec) N/A 0.055 0.060 0.276 0.000 0.410 0.000 0.256 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 51 0 0 42 0 48 -1
normalized size 1 1.00 1.00 0.00 0.00 0.82 0.00 0.94 -0.02
time (sec) N/A 0.045 0.052 0.280 0.000 0.430 0.000 0.306 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 48 240 0 39 0 42 -1
normalized size 1 1.00 1.00 5.00 0.00 0.81 0.00 0.88 -0.02
time (sec) N/A 0.036 0.044 0.499 0.000 0.416 0.000 0.286 0.000
Problem 69 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 18 18 18 19 18 19 34 45 18
normalized size 1 1.00 1.00 1.06 1.00 1.06 1.89 2.50 1.00
time (sec) N/A 0.025 0.017 0.026 0.799 0.436 1.090 0.306 3.560
Problem 70 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 48 48 48 0 0 41 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.85 0.00 0.00 -0.02
time (sec) N/A 0.051 0.051 0.284 0.000 0.421 0.000 0.000 0.000
Problem 71 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 51 51 51 0 0 42 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.82 0.00 0.00 -0.02
time (sec) N/A 0.051 0.053 0.294 0.000 0.596 0.000 0.000 0.000
Problem 72 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 51 51 51 0 0 42 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.82 0.00 0.00 -0.02
time (sec) N/A 0.052 0.063 0.312 0.000 0.528 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 70 0 0 101 0 261 -1
normalized size 1 1.00 0.92 0.00 0.00 1.33 0.00 3.43 -0.01
time (sec) N/A 0.079 0.148 1.000 0.000 0.616 0.000 0.498 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 70 0 0 101 0 261 -1
normalized size 1 1.00 0.92 0.00 0.00 1.33 0.00 3.43 -0.01
time (sec) N/A 0.079 0.143 0.935 0.000 0.638 0.000 0.442 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 70 0 0 101 0 261 -1
normalized size 1 1.00 0.92 0.00 0.00 1.33 0.00 3.43 -0.01
time (sec) N/A 0.059 0.124 0.894 0.000 0.422 0.000 0.424 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 66 350 0 95 0 238 -1
normalized size 1 1.00 0.94 5.00 0.00 1.36 0.00 3.40 -0.01
time (sec) N/A 0.040 0.124 0.493 0.000 0.404 0.000 0.315 0.000
Problem 77 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 20 20 20 21 20 25 70 21 20
normalized size 1 1.00 1.00 1.05 1.00 1.25 3.50 1.05 1.00
time (sec) N/A 0.024 0.004 0.025 0.497 0.401 22.744 0.252 3.269
Problem 78 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 73 73 76 0 0 88 0 0 -1
normalized size 1 1.00 1.04 0.00 0.00 1.21 0.00 0.00 -0.01
time (sec) N/A 0.075 0.120 0.917 0.000 0.421 0.000 0.000 0.000
Problem 79 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 76 76 80 0 0 102 0 0 -1
normalized size 1 1.00 1.05 0.00 0.00 1.34 0.00 0.00 -0.01
time (sec) N/A 0.078 0.092 0.978 0.000 0.457 0.000 0.000 0.000
Problem 80 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 76 76 80 0 0 102 0 0 -1
normalized size 1 1.00 1.05 0.00 0.00 1.34 0.00 0.00 -0.01
time (sec) N/A 0.075 0.099 1.025 0.000 0.420 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 89 0 0 211 0 1029 -1
normalized size 1 1.00 0.88 0.00 0.00 2.09 0.00 10.19 -0.01
time (sec) N/A 0.108 0.136 0.982 0.000 0.436 0.000 0.550 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 89 0 0 211 0 1029 -1
normalized size 1 1.00 0.85 0.00 0.00 2.01 0.00 9.80 -0.01
time (sec) N/A 0.108 0.131 0.927 0.000 0.445 0.000 0.556 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 89 0 0 211 0 1029 -1
normalized size 1 1.00 0.88 0.00 0.00 2.09 0.00 10.19 -0.01
time (sec) N/A 0.080 0.131 0.897 0.000 0.459 0.000 0.565 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 82 459 0 198 0 982 -1
normalized size 1 1.00 0.84 4.68 0.00 2.02 0.00 10.02 -0.01
time (sec) N/A 0.052 0.118 0.497 0.000 0.445 0.000 0.361 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 21 20 62 121 21 39
normalized size 1 1.00 1.00 0.95 0.91 2.82 5.50 0.95 1.77
time (sec) N/A 0.024 0.004 0.025 0.576 0.427 93.787 0.326 3.534
Problem 86 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 102 102 94 0 0 192 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 1.88 0.00 0.00 -0.01
time (sec) N/A 0.106 0.096 0.949 0.000 0.441 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 89 0 0 221 0 0 -1
normalized size 1 1.00 0.89 0.00 0.00 2.21 0.00 0.00 -0.01
time (sec) N/A 0.108 0.119 0.981 0.000 0.464 0.000 0.000 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 89 0 0 221 0 0 -1
normalized size 1 1.00 0.85 0.00 0.00 2.10 0.00 0.00 -0.01
time (sec) N/A 0.107 0.117 1.024 0.000 0.466 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-1) C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 29 128 41 50 0 117 -1
normalized size 1 1.00 0.71 3.12 1.00 1.22 0.00 2.85 -0.02
time (sec) N/A 0.016 0.015 0.148 0.533 0.485 0.000 0.517 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 29 128 41 42 70 108 -1
normalized size 1 1.00 0.71 3.12 1.00 1.02 1.71 2.63 -0.02
time (sec) N/A 0.016 0.010 0.123 0.556 0.447 25.449 0.533 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 29 124 41 32 70 105 -1
normalized size 1 1.00 0.71 3.02 1.00 0.78 1.71 2.56 -0.02
time (sec) N/A 0.014 0.007 0.125 0.534 0.470 1.065 0.538 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 37 37 24 42 41 25 63 41 -1
normalized size 1 1.00 0.65 1.14 1.11 0.68 1.70 1.11 -0.03
time (sec) N/A 0.015 0.006 0.040 0.560 0.467 0.769 0.289 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 24 122 41 28 65 43 -1
normalized size 1 1.00 0.65 3.30 1.11 0.76 1.76 1.16 -0.03
time (sec) N/A 0.016 0.007 0.130 0.552 0.467 2.861 0.376 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 29 128 41 32 71 67 -1
normalized size 1 1.00 0.71 3.12 1.00 0.78 1.73 1.63 -0.02
time (sec) N/A 0.015 0.009 0.134 0.630 0.478 28.214 0.353 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F(-1) C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 61 716 102 141 0 425 -1
normalized size 1 1.00 0.84 9.81 1.40 1.93 0.00 5.82 -0.01
time (sec) N/A 0.045 0.021 0.174 0.594 0.460 0.000 1.309 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A B C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 61 716 102 121 216 386 -1
normalized size 1 1.00 0.84 9.81 1.40 1.66 2.96 5.29 -0.01
time (sec) N/A 0.046 0.018 0.173 0.622 0.472 50.356 1.425 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A B C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 61 710 102 99 216 383 -1
normalized size 1 1.00 0.84 9.73 1.40 1.36 2.96 5.25 -0.01
time (sec) N/A 0.041 0.017 0.181 0.523 0.477 2.462 1.283 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 54 107 102 87 199 118 -1
normalized size 1 1.00 0.81 1.60 1.52 1.30 2.97 1.76 -0.01
time (sec) N/A 0.041 0.014 0.056 0.534 0.438 1.457 0.427 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A B B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 54 707 101 87 201 149 -1
normalized size 1 1.00 0.81 10.55 1.51 1.30 3.00 2.22 -0.01
time (sec) N/A 0.047 0.013 0.174 0.634 0.438 2.899 0.409 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A B B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 61 716 102 94 218 213 -1
normalized size 1 1.00 0.84 9.81 1.40 1.29 2.99 2.92 -0.01
time (sec) N/A 0.046 0.016 0.176 0.657 0.462 26.711 0.407 0.000
Problem 101 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 64 64 62 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.064 0.084 0.141 0.000 0.433 0.000 0.000 0.000
Problem 102 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 64 64 62 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.064 0.075 0.139 0.000 0.460 0.000 0.000 0.000
Problem 103 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 64 64 62 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.060 0.075 0.141 0.000 0.458 0.000 0.000 0.000
Problem 104 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 64 64 62 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.061 0.066 0.143 0.000 0.485 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 64 62 0 0 0 0 49 -1
normalized size 1 0.96 0.93 0.00 0.00 0.00 0.00 0.73 -0.01
time (sec) N/A 0.061 0.079 0.142 0.000 0.478 0.000 0.389 0.000
Problem 106 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 64 64 62 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.059 0.078 0.144 0.000 0.436 0.000 0.000 0.000
Problem 107 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 98 98 84 0 0 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.091 0.164 5.100 0.000 0.437 0.000 0.000 0.000
Problem 108 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 98 98 84 0 0 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.096 0.175 5.217 0.000 0.430 0.000 0.000 0.000
Problem 109 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 98 98 84 0 0 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.087 0.168 4.997 0.000 0.414 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 F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 83 427 0 0 0 0 -1
normalized size 1 1.00 0.85 4.36 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.088 0.198 2.000 0.000 0.406 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 98 93 0 0 0 0 293 -1
normalized size 1 0.97 0.92 0.00 0.00 0.00 0.00 2.90 -0.01
time (sec) N/A 0.093 0.163 4.995 0.000 0.417 0.000 0.428 0.000
Problem 112 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 98 98 94 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.092 0.149 5.159 0.000 0.418 0.000 0.000 0.000
Problem 113 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 85 85 85 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.072 0.045 0.731 0.000 0.000 0.000 0.000 0.000
Problem 114 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 64 64 61 0 0 0 0 0 -1
normalized size 1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.054 0.023 0.647 0.000 0.000 0.000 0.000 0.000
Problem 115 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 72 72 67 0 0 0 0 0 -1
normalized size 1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.065 0.035 0.296 0.000 0.000 0.000 0.000 0.000
Problem 116 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 72 72 67 0 0 0 0 0 -1
normalized size 1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.054 0.034 0.294 0.000 0.000 0.000 0.000 0.000
Problem 117 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 56 56 56 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.028 0.018 0.288 0.000 0.000 0.000 0.000 0.000
Problem 118 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 17 17 17 14 13 14 29 14 13
normalized size 1 1.00 1.00 0.82 0.76 0.82 1.71 0.82 0.76
time (sec) N/A 0.014 0.002 0.028 0.638 0.454 1.174 0.363 3.541
Problem 119 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 59 59 65 0 0 0 0 0 -1
normalized size 1 1.00 1.10 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.050 0.051 0.289 0.000 0.000 0.000 0.000 0.000
Problem 120 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 72 72 73 0 0 0 0 0 -1
normalized size 1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.056 0.048 0.289 0.000 0.000 0.000 0.000 0.000
Problem 121 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 82 82 73 0 0 0 0 0 -1
normalized size 1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.068 0.044 0.293 0.000 0.000 0.000 0.000 0.000
Problem 122 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 90 90 76 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 0.074 0.054 0.305 0.000 0.000 0.000 0.000 0.000
Problem 123 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 90 90 79 0 0 0 0 0 -1
normalized size 1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.057 0.058 0.303 0.000 0.000 0.000 0.000 0.000
Problem 124 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 72 72 72 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.035 0.040 0.276 0.000 0.000 0.000 0.000 0.000
Problem 125 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 17 17 17 14 13 34 75 72 13
normalized size 1 1.00 1.00 0.82 0.76 2.00 4.41 4.24 0.76
time (sec) N/A 0.014 0.002 0.028 0.612 0.459 21.925 0.405 3.527
Problem 126 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 77 77 79 0 0 0 0 0 -1
normalized size 1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.067 0.058 0.297 0.000 0.000 0.000 0.000 0.000
Problem 127 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 90 90 88 0 0 0 0 0 -1
normalized size 1 1.00 0.98 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.073 0.066 0.283 0.000 0.000 0.000 0.000 0.000
Problem 128 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 46 46 46 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.035 0.006 0.293 0.000 0.000 0.000 0.000 0.000
Problem 129 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 51 51 51 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.036 0.009 0.296 0.000 0.000 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 51 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.033 0.009 0.291 0.000 0.000 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.022 0.004 0.276 0.000 0.000 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 14 13 14 24 14 13
normalized size 1 1.00 1.00 0.93 0.87 0.93 1.60 0.93 0.87
time (sec) N/A 0.013 0.002 0.029 0.550 0.409 2.078 0.209 3.576
Problem 133 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 40 40 52 0 0 0 0 0 -1
normalized size 1 1.00 1.30 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.033 0.036 0.282 0.000 0.000 0.000 0.000 0.000
Problem 134 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 51 51 60 0 0 0 0 0 -1
normalized size 1 1.00 1.18 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.039 0.036 0.292 0.000 0.000 0.000 0.000 0.000
Problem 135 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 63 63 73 0 0 0 0 0 -1
normalized size 1 1.00 1.16 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.053 0.047 0.298 0.000 0.000 0.000 0.000 0.000
Problem 136 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 69 69 78 0 0 0 0 0 -1
normalized size 1 1.00 1.13 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.058 0.053 0.301 0.000 0.000 0.000 0.000 0.000
Problem 137 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 69 69 78 0 0 0 0 0 -1
normalized size 1 1.00 1.13 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.049 0.050 0.286 0.000 0.000 0.000 0.000 0.000
Problem 138 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 58 58 69 0 0 0 0 0 -1
normalized size 1 1.00 1.19 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.029 0.036 0.296 0.000 0.000 0.000 0.000 0.000
Problem 139 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 15 15 15 14 13 24 41 14 13
normalized size 1 1.00 1.00 0.93 0.87 1.60 2.73 0.93 0.87
time (sec) N/A 0.014 0.002 0.031 0.697 0.461 93.977 0.271 3.450
Problem 140 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 60 60 58 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.050 0.050 0.283 0.000 0.000 0.000 0.000 0.000
Problem 141 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 69 69 66 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.057 0.049 0.290 0.000 0.000 0.000 0.000 0.000
Problem 142 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 87 87 87 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.073 0.066 0.281 0.000 0.000 0.000 0.000 0.000
Problem 143 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 89 89 92 0 0 0 0 0 -1
normalized size 1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.073 0.069 0.277 0.000 0.000 0.000 0.000 0.000
Problem 144 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 93 93 92 0 0 0 0 0 -1
normalized size 1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.058 0.066 0.294 0.000 0.000 0.000 0.000 0.000
Problem 145 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 80 80 83 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 0.037 0.060 0.295 0.000 0.000 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 14 13 37 0 14 13
normalized size 1 1.00 1.00 0.82 0.76 2.18 0.00 0.82 0.76
time (sec) N/A 0.014 0.002 0.030 0.806 0.452 0.000 0.254 3.434
Problem 147 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 84 84 70 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 0.069 0.072 0.299 0.000 0.000 0.000 0.000 0.000
Problem 148 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 93 93 78 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 0.076 0.064 0.286 0.000 0.000 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 17 260 102 26 27 214 -1
normalized size 1 1.00 0.81 12.38 4.86 1.24 1.29 10.19 -0.05
time (sec) N/A 0.020 0.012 0.173 0.610 0.467 0.984 0.460 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B B A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 76 9684 247 574 2778 1133 -1
normalized size 1 1.00 0.66 83.48 2.13 4.95 23.95 9.77 -0.01
time (sec) N/A 0.091 0.048 0.777 0.696 0.450 43.508 0.847 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 76 2126 132 208 891 402 -1
normalized size 1 1.00 0.94 26.25 1.63 2.57 11.00 4.96 -0.01
time (sec) N/A 0.046 0.037 0.254 0.713 0.448 27.731 0.408 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 32 371 57 52 192 95 -1
normalized size 1 1.00 0.70 8.07 1.24 1.13 4.17 2.07 -0.02
time (sec) N/A 0.015 0.013 0.168 0.567 0.510 10.453 0.324 0.000
Problem 153 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 66 66 67 0 0 68 0 0 -1
normalized size 1 1.00 1.02 0.00 0.00 1.03 0.00 0.00 -0.02
time (sec) N/A 0.074 0.120 0.515 0.000 0.440 0.000 0.000 0.000
Problem 154 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 100 100 89 0 0 131 0 0 -1
normalized size 1 1.00 0.89 0.00 0.00 1.31 0.00 0.00 -0.01
time (sec) N/A 0.093 0.242 1.962 0.000 0.451 0.000 0.000 0.000
Problem 155 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 142 142 113 0 0 322 0 0 -1
normalized size 1 1.00 0.80 0.00 0.00 2.27 0.00 0.00 -0.01
time (sec) N/A 0.139 0.369 1.842 0.000 0.468 0.000 0.000 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 40 2008 75 73 292 170 -1
normalized size 1 1.00 0.54 27.14 1.01 0.99 3.95 2.30 -0.01
time (sec) N/A 0.053 0.008 0.302 0.586 0.439 123.181 0.533 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 30 750 53 42 163 99 -1
normalized size 1 1.00 0.57 14.15 1.00 0.79 3.08 1.87 -0.02
time (sec) N/A 0.032 0.006 0.178 0.741 0.448 43.863 0.350 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 20 263 32 20 68 50 -1
normalized size 1 1.00 0.62 8.22 1.00 0.62 2.12 1.56 -0.03
time (sec) N/A 0.011 0.004 0.141 0.666 0.484 13.721 0.356 0.000
Problem 159 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 27 27 27 0 0 20 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.74 0.00 0.00 -0.04
time (sec) N/A 0.037 0.008 0.486 0.000 0.458 0.000 0.000 0.000
Problem 160 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 49 49 49 0 0 50 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 1.02 0.00 0.00 -0.02
time (sec) N/A 0.053 0.017 1.836 0.000 0.441 0.000 0.000 0.000
Problem 161 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 77 77 61 0 0 84 0 0 -1
normalized size 1 1.00 0.79 0.00 0.00 1.09 0.00 0.00 -0.01
time (sec) N/A 0.076 0.024 1.751 0.000 0.436 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 101 0 0 0 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.126 0.189 0.291 0.000 0.502 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 F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 86 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.067 0.052 0.316 0.000 0.475 0.000 0.000 0.000
Problem 164 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 61 61 61 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.047 0.011 0.297 0.000 0.445 0.000 0.000 0.000
Problem 165 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 83 83 86 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 0.068 0.198 0.291 0.000 0.485 0.000 0.000 0.000
Problem 166 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 112 112 103 0 0 0 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.092 0.422 0.285 0.000 0.509 0.000 0.000 0.000
Problem 167 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 106 106 107 0 0 0 0 0 -1
normalized size 1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.069 0.142 1.685 0.000 0.466 0.000 0.000 0.000
Problem 168 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 89 89 89 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.064 0.097 1.367 0.000 0.418 0.000 0.000 0.000
Problem 169 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 89 89 89 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.052 0.084 1.266 0.000 0.421 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 80 0 0 52 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.65 0.00 0.00 -0.01
time (sec) N/A 0.038 0.073 0.933 0.000 0.453 0.000 0.000 0.000
Problem 171 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 26 26 26 27 26 35 56 27 26
normalized size 1 1.00 1.00 1.04 1.00 1.35 2.15 1.04 1.00
time (sec) N/A 0.032 0.008 0.030 0.708 0.424 1.865 0.253 3.671
Problem 172 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 78 78 78 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.054 0.083 1.115 0.000 0.469 0.000 0.000 0.000
Problem 173 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 89 89 89 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.058 0.086 0.714 0.000 0.469 0.000 0.000 0.000
Problem 174 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 89 89 89 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.059 0.089 0.733 0.000 0.475 0.000 0.000 0.000
Problem 175 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 86 86 82 0 0 0 0 0 -1
normalized size 1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.072 0.115 0.625 0.000 0.454 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 63 0 44 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.70 0.00 0.00 0.00 -0.02
time (sec) N/A 0.059 0.066 0.057 0.826 0.454 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 63 0 44 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.70 0.00 0.00 0.00 -0.02
time (sec) N/A 0.047 0.033 0.051 0.814 0.468 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 56 0 44 38 0 0 -1
normalized size 1 1.00 1.00 0.00 0.79 0.68 0.00 0.00 -0.02
time (sec) N/A 0.033 0.028 0.048 0.835 0.422 0.000 0.000 0.000
Problem 179 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 21 21 21 22 21 26 39 21 21
normalized size 1 1.00 1.00 1.05 1.00 1.24 1.86 1.00 1.00
time (sec) N/A 0.028 0.006 0.027 0.529 0.418 1.307 0.394 3.704
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 48 0 40 0 0 0 -1
normalized size 1 1.00 0.92 0.00 0.77 0.00 0.00 0.00 -0.02
time (sec) N/A 0.049 0.035 0.057 0.632 0.455 0.000 0.000 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 63 0 44 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.70 0.00 0.00 0.00 -0.02
time (sec) N/A 0.055 0.037 0.043 0.696 0.432 0.000 0.000 0.000
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 63 0 44 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.70 0.00 0.00 0.00 -0.02
time (sec) N/A 0.054 0.036 0.043 0.691 0.456 0.000 0.000 0.000
Problem 183 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 107 107 103 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.084 0.195 0.071 0.000 0.475 0.000 0.000 0.000
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 80 0 48 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.60 0.00 0.00 0.00 -0.01
time (sec) N/A 0.062 0.106 0.039 0.644 0.446 0.000 0.000 0.000
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 75 0 48 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.64 0.00 0.00 0.00 -0.01
time (sec) N/A 0.055 0.066 0.039 0.676 0.482 0.000 0.000 0.000
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 73 0 48 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.66 0.00 0.00 0.00 -0.01
time (sec) N/A 0.035 0.031 0.037 0.802 0.470 0.000 0.000 0.000
Problem 187 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 26 26 26 25 24 31 48 25 24
normalized size 1 1.00 1.00 0.96 0.92 1.19 1.85 0.96 0.92
time (sec) N/A 0.028 0.010 0.028 0.557 0.433 4.758 0.310 3.716
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 73 0 48 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.66 0.00 0.00 0.00 -0.01
time (sec) N/A 0.052 0.056 0.037 0.970 0.467 0.000 0.000 0.000
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 75 0 48 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.64 0.00 0.00 0.00 -0.01
time (sec) N/A 0.058 0.051 0.041 0.785 0.463 0.000 0.000 0.000
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 80 0 48 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.60 0.00 0.00 0.00 -0.01
time (sec) N/A 0.058 0.050 0.040 0.769 0.454 0.000 0.000 0.000
Problem 191 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 65 65 65 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.051 0.052 4.261 0.000 0.494 0.000 0.000 0.000
Problem 192 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 114 114 118 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 0.107 0.234 2.127 0.000 0.434 0.000 0.000 0.000
Problem 193 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 136 136 142 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 0.168 0.244 24.092 0.000 0.445 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 [117] had the largest ratio of [.4000]

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 1 1 1.00 8 0.125
2 A 1 1 1.00 8 0.125
3 A 1 1 1.00 6 0.167
4 A 1 1 1.00 4 0.250
5 A 1 1 1.00 8 0.125
6 A 1 1 1.00 8 0.125
7 A 1 1 1.00 8 0.125
8 A 2 2 1.00 10 0.200
9 A 2 2 1.00 10 0.200
10 A 2 2 1.00 8 0.250
11 A 2 2 1.00 6 0.333
12 A 2 2 1.00 10 0.200
13 A 2 2 1.00 10 0.200
14 A 2 2 1.00 10 0.200
15 A 3 2 1.00 10 0.200
16 A 3 2 1.00 10 0.200
17 A 3 2 1.00 8 0.250
18 A 3 2 1.00 6 0.333
19 A 2 2 1.00 10 0.200
20 A 3 2 1.00 10 0.200
21 A 3 2 1.00 10 0.200
22 A 2 2 1.00 10 0.200
23 A 2 2 1.00 10 0.200
24 A 2 2 1.00 8 0.250
25 A 1 1 1.00 6 0.167
26 A 2 2 1.00 10 0.200
27 A 2 2 1.00 10 0.200
28 A 2 2 1.00 10 0.200
29 A 3 3 1.00 10 0.300
30 A 3 3 1.00 10 0.300
31 A 3 3 1.00 8 0.375
32 A 2 2 1.00 6 0.333
33 A 2 2 1.00 10 0.200
34 A 3 3 1.00 10 0.300
35 A 3 3 1.00 10 0.300
36 A 4 3 1.00 10 0.300
37 A 4 3 1.00 10 0.300
38 A 4 3 1.00 8 0.375
39 A 3 2 1.00 6 0.333
40 A 2 2 1.00 10 0.200
41 A 4 3 1.00 10 0.300
42 A 4 3 1.00 10 0.300
43 A 1 1 1.00 14 0.071
44 A 1 1 1.00 14 0.071
45 A 1 1 1.00 12 0.083
46 A 2 1 1.00 10 0.100
47 A 1 1 1.00 14 0.071
48 A 1 1 1.00 14 0.071
49 A 1 1 1.00 14 0.071
50 A 2 2 1.00 16 0.125
51 A 2 2 1.00 16 0.125
52 A 2 2 1.00 14 0.143
53 A 3 2 1.00 12 0.167
54 A 2 2 1.00 16 0.125
55 A 2 2 1.00 16 0.125
56 A 2 2 1.00 16 0.125
57 A 3 2 1.00 16 0.125
58 A 3 2 1.00 16 0.125
59 A 3 2 1.00 14 0.143
60 A 4 2 1.00 12 0.167
61 A 2 2 1.00 16 0.125
62 A 3 2 1.00 16 0.125
63 A 3 2 1.00 16 0.125
64 A 3 2 1.00 16 0.125
65 A 2 2 1.00 16 0.125
66 A 2 2 1.00 16 0.125
67 A 2 2 1.00 14 0.143
68 A 2 2 1.00 12 0.167
69 A 2 2 1.00 16 0.125
70 A 2 2 1.00 16 0.125
71 A 2 2 1.00 16 0.125
72 A 2 2 1.00 16 0.125
73 A 3 3 1.00 16 0.188
74 A 3 3 1.00 16 0.188
75 A 3 3 1.00 14 0.214
76 A 3 3 1.00 12 0.250
77 A 2 2 1.00 16 0.125
78 A 3 3 1.00 16 0.188
79 A 3 3 1.00 16 0.188
80 A 3 3 1.00 16 0.188
81 A 4 3 1.00 16 0.188
82 A 4 3 1.00 16 0.188
83 A 4 3 1.00 14 0.214
84 A 4 3 1.00 12 0.250
85 A 2 2 1.00 16 0.125
86 A 4 3 1.00 16 0.188
87 A 4 3 1.00 16 0.188
88 A 4 3 1.00 16 0.188
89 A 1 1 1.00 18 0.056
90 A 1 1 1.00 18 0.056
91 A 1 1 1.00 18 0.056
92 A 1 1 1.00 18 0.056
93 A 1 1 1.00 18 0.056
94 A 1 1 1.00 18 0.056
95 A 2 2 1.00 20 0.100
96 A 2 2 1.00 20 0.100
97 A 2 2 1.00 20 0.100
98 A 2 2 1.00 20 0.100
99 A 2 2 1.00 20 0.100
100 A 2 2 1.00 20 0.100
101 A 2 2 1.00 20 0.100
102 A 2 2 1.00 20 0.100
103 A 2 2 1.00 20 0.100
104 A 2 2 1.00 20 0.100
105 A 2 2 0.96 20 0.100
106 A 2 2 1.00 20 0.100
107 A 3 3 1.00 20 0.150
108 A 3 3 1.00 20 0.150
109 A 3 3 1.00 20 0.150
110 A 3 3 1.00 20 0.150
111 A 3 3 0.97 20 0.150
112 A 3 3 1.00 20 0.150
113 A 4 4 1.00 14 0.286
114 A 4 4 1.00 14 0.286
115 A 4 4 1.00 14 0.286
116 A 4 4 1.00 12 0.333
117 A 4 4 1.00 10 0.400
118 A 2 2 1.00 14 0.143
119 A 4 4 1.00 14 0.286
120 A 4 4 1.00 14 0.286
121 A 5 4 1.00 14 0.286
122 A 5 4 1.00 14 0.286
123 A 5 4 1.00 12 0.333
124 A 5 4 1.00 10 0.400
125 A 2 2 1.00 14 0.143
126 A 5 4 1.00 14 0.286
127 A 5 4 1.00 14 0.286
128 A 3 3 1.00 14 0.214
129 A 3 3 1.00 14 0.214
130 A 3 3 1.00 12 0.250
131 A 3 3 1.00 10 0.300
132 A 2 2 1.00 14 0.143
133 A 3 3 1.00 14 0.214
134 A 3 3 1.00 14 0.214
135 A 4 4 1.00 14 0.286
136 A 4 4 1.00 14 0.286
137 A 4 4 1.00 12 0.333
138 A 4 4 1.00 10 0.400
139 A 2 2 1.00 14 0.143
140 A 4 4 1.00 14 0.286
141 A 4 4 1.00 14 0.286
142 A 5 4 1.00 14 0.286
143 A 5 4 1.00 14 0.286
144 A 5 4 1.00 12 0.333
145 A 5 4 1.00 10 0.400
146 A 2 2 1.00 14 0.143
147 A 5 4 1.00 14 0.286
148 A 5 4 1.00 14 0.286
149 A 1 1 1.00 22 0.045
150 A 3 2 1.00 18 0.111
151 A 2 2 1.00 18 0.111
152 A 1 1 1.00 16 0.062
153 A 2 2 1.00 18 0.111
154 A 3 3 1.00 18 0.167
155 A 4 3 1.00 18 0.167
156 A 3 2 1.00 16 0.125
157 A 2 2 1.00 16 0.125
158 A 1 1 1.00 14 0.071
159 A 3 3 1.00 16 0.188
160 A 4 4 1.00 16 0.250
161 A 5 4 1.00 16 0.250
162 A 5 4 1.00 14 0.286
163 A 4 4 1.00 14 0.286
164 A 3 3 1.00 14 0.214
165 A 4 4 1.00 14 0.286
166 A 5 4 1.00 14 0.286
167 A 2 2 1.00 18 0.111
168 A 2 2 1.00 16 0.125
169 A 2 2 1.00 14 0.143
170 A 2 2 1.00 12 0.167
171 A 2 2 1.00 16 0.125
172 A 2 2 1.00 16 0.125
173 A 2 2 1.00 16 0.125
174 A 2 2 1.00 16 0.125
175 A 2 2 1.00 16 0.125
176 A 2 2 1.00 14 0.143
177 A 2 2 1.00 12 0.167
178 A 2 2 1.00 10 0.200
179 A 2 2 1.00 14 0.143
180 A 2 2 1.00 14 0.143
181 A 2 2 1.00 14 0.143
182 A 2 2 1.00 14 0.143
183 A 2 2 1.00 20 0.100
184 A 2 2 1.00 18 0.111
185 A 2 2 1.00 16 0.125
186 A 2 2 1.00 14 0.143
187 A 2 2 1.00 18 0.111
188 A 2 2 1.00 18 0.111
189 A 2 2 1.00 18 0.111
190 A 2 2 1.00 18 0.111
191 A 2 2 1.00 18 0.111
192 A 3 3 1.00 20 0.150
193 A 4 3 1.00 27 0.111

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