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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 }

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, 42, 43, 44, 45, 46, 47, 48, 49, 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, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 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, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174 }

B grade: { 50, 51, 83, 84, 105, 154 }

C grade: { 41, 98, 113, 175 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 18, 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, 49, 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, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 171, 173, 174, 175 }

B grade: { 14, 17, 48, 50, 51, 114, 139, 158, 169, 170 }

C grade: { }

F grade: { 19, 172 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 100, 101, 102, 103, 106, 107, 108, 109, 110, 111, 112, 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, 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, 170, 171, 172, 173 }

B grade: { 51, 83, 84, 113, 169 }

C grade: { }

F grade: { 19, 41, 98, 99, 104, 105, 141, 174, 175 }

2.1.5 FriCAS

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

B grade: { 16, 44, 45, 48, 50, 51, 61, 84, 88, 113, 114, 124, 131, 145, 146 }

C grade: { }

F grade: { 41, 156, 175 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 49, 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, 84, 85, 86, 87, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 102, 106, 107, 108, 109, 110, 111, 112, 113, 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, 147, 148, 149, 150, 152, 157, 158, 159, 160, 161, 166, 167, 168, 169, 170, 171, 172, 175 }

B grade: { 9, 17, 42, 47, 48, 50, 51, 90, 101, 114, 144 }

C grade: { 83, 89, 156 }

F grade: { 19, 88, 103, 104, 105, 145, 146, 151, 153, 154, 155, 162, 163, 164, 165, 173, 174 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 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, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 157, 158, 159, 160, 161, 162, 163, 165, 166, 167, 168, 169, 170, 171, 173, 174 }

B grade: { 44, 45, 51, 83, 84, 113, 136, 155, 164 }

C grade: { }

F grade: { 9, 41, 62, 156, 172, 175 }

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, 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, 100, 101, 102, 103, 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, 166, 167, 168, 169, 170, 171, 172, 173, 175 }

C grade: { }

F grade: { 98, 99, 104, 105, 165, 174 }

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 13 13 13 10 9 9 8 9 9
normalized size 1 1.00 1.00 0.77 0.69 0.69 0.62 0.69 0.69
time (sec) N/A 0.001 0.004 0.034 0.556 0.393 0.103 0.005 0.321
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 27 27 18 15 19 19 39 19 14
normalized size 1 1.00 0.67 0.56 0.70 0.70 1.44 0.70 0.52
time (sec) N/A 0.004 0.007 0.003 0.461 0.403 1.043 0.008 0.085
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 34 34 21 18 22 22 48 22 19
normalized size 1 1.00 0.62 0.53 0.65 0.65 1.41 0.65 0.56
time (sec) N/A 0.005 0.007 0.004 0.546 0.393 1.388 0.008 0.069
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 27 27 18 15 19 14 61 19 14
normalized size 1 1.00 0.67 0.56 0.70 0.52 2.26 0.70 0.52
time (sec) N/A 0.005 0.006 0.003 0.501 0.409 0.952 0.009 0.057
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 14 14 14 13 12 22 22 12 12
normalized size 1 1.00 1.00 0.93 0.86 1.57 1.57 0.86 0.86
time (sec) N/A 0.003 0.005 0.007 0.439 0.390 0.117 0.010 0.065
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 13 13 15 11 11 11 8 11 10
normalized size 1 1.00 1.15 0.85 0.85 0.85 0.62 0.85 0.77
time (sec) N/A 0.006 0.002 0.145 0.497 0.429 0.068 0.006 0.158
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 23 23 16 13 15 17 92 15 12
normalized size 1 1.00 0.70 0.57 0.65 0.74 4.00 0.65 0.52
time (sec) N/A 0.004 0.006 0.004 0.708 0.394 0.988 0.008 0.031
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 8 8 8 7 6 10 8 6 6
normalized size 1 1.00 1.00 0.88 0.75 1.25 1.00 0.75 0.75
time (sec) N/A 0.013 0.005 0.019 0.489 0.413 0.067 0.009 0.418
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 13 12 18 29 0 12
normalized size 1 1.00 1.00 0.81 0.75 1.12 1.81 0.00 0.75
time (sec) N/A 0.023 0.014 0.026 0.567 0.423 0.337 0.000 0.171
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 6 6 6 7 6 6 5 6 6
normalized size 1 1.00 1.00 1.17 1.00 1.00 0.83 1.00 1.00
time (sec) N/A 0.018 0.015 0.066 0.698 0.408 0.415 0.006 0.043
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 12 12 12 11 10 12 12 6 9
normalized size 1 1.00 1.00 0.92 0.83 1.00 1.00 0.50 0.75
time (sec) N/A 0.028 0.010 0.073 0.636 0.429 0.649 0.006 0.199
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 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 0.016 0.022 0.009 0.520 0.408 0.331 0.007 0.171
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 9 9 9 10 9 9 7 9 9
normalized size 1 1.00 1.00 1.11 1.00 1.00 0.78 1.00 1.00
time (sec) N/A 0.011 0.018 0.018 0.791 0.423 6.727 0.010 0.207
Problem 14 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 15 15 15 32 11 11 10 11 11
normalized size 1 1.00 1.00 2.13 0.73 0.73 0.67 0.73 0.73
time (sec) N/A 0.003 0.004 0.010 0.457 0.396 0.274 0.008 0.354
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 23 23 16 13 15 15 34 15 12
normalized size 1 1.00 0.70 0.57 0.65 0.65 1.48 0.65 0.52
time (sec) N/A 0.004 0.006 0.003 0.499 0.385 1.013 0.008 0.034
Problem 16 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 11 11 11 10 9 22 8 9 9
normalized size 1 1.00 1.00 0.91 0.82 2.00 0.73 0.82 0.82
time (sec) N/A 0.001 0.003 0.004 0.467 0.402 0.734 0.019 0.072
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 27 11 11 27 11 11
normalized size 1 1.00 1.00 1.80 0.73 0.73 1.80 0.73 0.73
time (sec) N/A 0.003 0.005 0.006 0.533 0.388 0.377 0.008 0.185
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 15 15 15 12 11 11 12 11 15
normalized size 1 1.00 1.00 0.80 0.73 0.73 0.80 0.73 1.00
time (sec) N/A 0.026 0.059 0.031 0.717 0.414 0.350 0.031 0.239
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 37 0 0 23 0 15 47
normalized size 1 1.00 1.16 0.00 0.00 0.72 0.00 0.47 1.47
time (sec) N/A 0.101 0.058 0.144 0.000 0.460 0.000 0.061 0.589
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 17 17 17 14 13 13 14 13 13
normalized size 1 1.00 1.00 0.82 0.76 0.76 0.82 0.76 0.76
time (sec) N/A 0.111 0.016 0.010 0.589 0.438 0.370 0.009 0.210
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 16 16 13 13 7 12 15 12 9
normalized size 1 1.00 0.81 0.81 0.44 0.75 0.94 0.75 0.56
time (sec) N/A 0.008 0.008 0.003 0.549 0.408 1.751 0.009 0.156
Problem 22 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 0.009 0.002 0.015 0.524 0.409 0.183 0.007 0.064
Problem 23 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 15 18 15 15 17 15 15
normalized size 1 1.00 0.88 1.06 0.88 0.88 1.00 0.88 0.88
time (sec) N/A 0.021 0.017 0.011 0.562 0.414 0.337 0.007 0.033
Problem 24 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 23 23 19 24 20 20 26 20 24
normalized size 1 1.00 0.83 1.04 0.87 0.87 1.13 0.87 1.04
time (sec) N/A 0.036 0.016 0.017 0.641 0.402 0.644 0.007 0.030
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 24 24 20 25 21 21 26 21 23
normalized size 1 1.00 0.83 1.04 0.88 0.88 1.08 0.88 0.96
time (sec) N/A 0.036 0.015 0.016 0.536 0.405 0.641 0.007 0.030
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 8 8 8 7 6 6 5 6 6
normalized size 1 1.00 1.00 0.88 0.75 0.75 0.62 0.75 0.75
time (sec) N/A 0.007 0.001 0.003 0.627 0.403 0.063 0.006 0.019
Problem 27 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 23 23 18 18 14 17 24 14 18
normalized size 1 1.00 0.78 0.78 0.61 0.74 1.04 0.61 0.78
time (sec) N/A 0.013 0.003 0.005 0.513 0.419 0.343 0.009 0.095
Problem 28 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 14 14 14 11 10 10 10 10 10
normalized size 1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 0.71
time (sec) N/A 0.005 0.002 0.016 0.571 0.420 0.068 0.008 0.032
Problem 29 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 13 13 15 11 11 11 8 11 10
normalized size 1 1.00 1.15 0.85 0.85 0.85 0.62 0.85 0.77
time (sec) N/A 0.006 0.002 0.000 0.582 0.411 0.073 0.006 0.002
Problem 30 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 24 24 22 18 16 19 24 16 16
normalized size 1 1.00 0.92 0.75 0.67 0.79 1.00 0.67 0.67
time (sec) N/A 0.009 0.002 0.125 0.494 0.417 0.068 0.006 0.036
Problem 31 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 23 17 17 17 17 17 17
normalized size 1 1.00 1.10 0.81 0.81 0.81 0.81 0.81 0.81
time (sec) N/A 0.007 0.002 0.104 0.511 0.429 0.074 0.007 0.043
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 34 34 30 24 24 25 36 22 22
normalized size 1 1.00 0.88 0.71 0.71 0.74 1.06 0.65 0.65
time (sec) N/A 0.016 0.002 0.103 0.624 0.414 0.067 0.007 0.039
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 25 25 25 25 19 19 36 19 19
normalized size 1 1.00 1.00 1.00 0.76 0.76 1.44 0.76 0.76
time (sec) N/A 0.014 0.011 0.014 0.500 0.428 0.358 0.007 0.093
Problem 34 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 33 33 31 23 23 23 39 23 25
normalized size 1 1.00 0.94 0.70 0.70 0.70 1.18 0.70 0.76
time (sec) N/A 0.022 0.009 0.057 0.567 0.419 0.646 0.007 0.119
Problem 35 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 41 41 29 37 26 29 56 26 28
normalized size 1 1.00 0.71 0.90 0.63 0.71 1.37 0.63 0.68
time (sec) N/A 0.031 0.039 0.036 0.498 0.435 0.653 0.007 0.063
Problem 36 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 14 14 14 11 10 10 10 10 10
normalized size 1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 0.71
time (sec) N/A 0.006 0.002 0.016 0.517 0.430 0.064 0.006 0.026
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 15 11 9 10 8 9 9
normalized size 1 1.00 1.36 1.00 0.82 0.91 0.73 0.82 0.82
time (sec) N/A 0.006 0.002 0.094 0.578 0.412 0.067 0.006 0.033
Problem 38 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 24 24 22 18 16 19 24 16 16
normalized size 1 1.00 0.92 0.75 0.67 0.79 1.00 0.67 0.67
time (sec) N/A 0.011 0.002 0.109 0.539 0.426 0.065 0.006 0.029
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 84 84 62 69 60 60 180 50 37
normalized size 1 1.00 0.74 0.82 0.71 0.71 2.14 0.60 0.44
time (sec) N/A 0.015 0.077 0.008 1.309 0.423 3.709 0.047 0.215
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 38 38 25 22 34 21 39 28 20
normalized size 1 1.00 0.66 0.58 0.89 0.55 1.03 0.74 0.53
time (sec) N/A 0.013 0.008 0.006 1.427 0.416 1.242 0.007 0.029
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 172 172 34 168 0 0 31 0 301
normalized size 1 1.00 0.20 0.98 0.00 0.00 0.18 0.00 1.75
time (sec) N/A 0.029 0.006 0.184 0.000 0.435 0.719 0.000 0.075
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 6 6 6 7 6 6 7 6 6
normalized size 1 1.00 1.00 1.17 1.00 1.00 1.17 1.00 1.00
time (sec) N/A 0.004 0.004 0.005 1.220 0.408 0.065 0.009 0.070
Problem 43 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 14 14 18 13 12 12 19 12 12
normalized size 1 1.00 1.29 0.93 0.86 0.86 1.36 0.86 0.86
time (sec) N/A 0.009 0.003 0.004 1.274 0.412 0.070 0.009 0.034
Problem 44 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 8 8 8 12 10 20 8 18 8
normalized size 1 1.00 1.00 1.50 1.25 2.50 1.00 2.25 1.00
time (sec) N/A 0.005 0.002 0.004 1.272 0.414 0.069 0.018 0.057
Problem 45 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 12 12 18 14 16 48 19 34 10
normalized size 1 1.00 1.50 1.17 1.33 4.00 1.58 2.83 0.83
time (sec) N/A 0.010 0.003 0.003 1.277 0.421 0.078 0.019 0.022
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 22 22 26 21 20 18 26 18 20
normalized size 1 1.00 1.18 0.95 0.91 0.82 1.18 0.82 0.91
time (sec) N/A 0.011 0.014 0.021 0.536 0.417 0.197 0.013 0.103
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 10 9 9 22 9 9
normalized size 1 1.00 1.00 0.77 0.69 0.69 1.69 0.69 0.69
time (sec) N/A 0.002 0.002 0.003 0.438 0.390 0.196 0.007 0.025
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 11 52 9 51 58 9 9
normalized size 1 1.00 0.85 4.00 0.69 3.92 4.46 0.69 0.69
time (sec) N/A 0.001 0.002 0.002 0.464 0.350 0.063 0.008 0.097
Problem 49 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 16 20 19 19 15 14 14
normalized size 1 1.00 0.89 1.11 1.06 1.06 0.83 0.78 0.78
time (sec) N/A 0.002 0.004 0.006 0.576 0.380 0.102 0.009 0.042
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 43 32 9 31 31 9 31
normalized size 1 1.00 3.91 2.91 0.82 2.82 2.82 0.82 2.82
time (sec) N/A 0.002 0.002 0.001 0.524 0.351 0.058 0.008 0.025
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 140 107 106 106 131 106 106
normalized size 1 1.00 2.50 1.91 1.89 1.89 2.34 1.89 1.89
time (sec) N/A 0.025 0.002 0.003 0.610 0.345 0.080 0.008 0.464
Problem 52 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 4 4 4 5 4 4 3 4 4
normalized size 1 1.00 1.00 1.25 1.00 1.00 0.75 1.00 1.00
time (sec) N/A 0.008 0.009 0.005 0.608 0.407 0.646 0.008 0.096
Problem 53 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 62 62 46 49 37 37 60 37 41
normalized size 1 1.00 0.74 0.79 0.60 0.60 0.97 0.60 0.66
time (sec) N/A 0.043 0.035 0.007 0.528 0.422 2.031 0.011 0.226
Problem 54 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 8 8 8
normalized size 1 1.00 1.00 0.90 0.80 0.80 0.80 0.80 0.80
time (sec) N/A 0.007 0.003 0.003 0.531 0.418 0.325 0.006 0.050
Problem 55 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 16 16 16 13 12 12 15 12 12
normalized size 1 1.00 1.00 0.81 0.75 0.75 0.94 0.75 0.75
time (sec) N/A 0.031 0.014 0.071 0.478 0.440 2.059 0.008 0.193
Problem 56 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 9 6
normalized size 1 1.00 1.00 0.90 0.80 0.80 0.70 0.90 0.60
time (sec) N/A 0.001 0.001 0.000 0.543 0.390 0.059 0.005 0.074
Problem 57 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 12 15 15 15 12
normalized size 1 1.00 1.00 1.07 0.80 1.00 1.00 1.00 0.80
time (sec) N/A 0.004 0.001 0.009 0.518 0.413 0.094 0.006 0.079
Problem 58 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 13 12 13 9
normalized size 1 1.00 1.00 0.82 0.76 0.76 0.71 0.76 0.53
time (sec) N/A 0.003 0.001 0.003 0.502 0.389 0.090 0.007 0.032
Problem 59 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 23 17 22 22 22 17
normalized size 1 1.00 1.00 0.82 0.61 0.79 0.79 0.79 0.61
time (sec) N/A 0.009 0.001 0.003 0.538 0.404 0.108 0.008 0.030
Problem 60 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 4 4 4 5 4 4 3 5 4
normalized size 1 1.00 1.00 1.25 1.00 1.00 0.75 1.25 1.00
time (sec) N/A 0.000 0.001 0.001 0.529 0.389 0.058 0.005 0.015
Problem 61 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 3 3 3 4 3 11 3 4 3
normalized size 1 1.00 1.00 1.33 1.00 3.67 1.00 1.33 1.00
time (sec) N/A 0.003 0.002 0.002 0.483 0.417 0.068 0.010 0.023
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 21 36 28 32 94 0 38
normalized size 1 1.00 0.75 1.29 1.00 1.14 3.36 0.00 1.36
time (sec) N/A 0.010 0.007 0.026 0.584 0.418 0.768 0.000 0.205
Problem 63 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 23 17 22 26 22 17
normalized size 1 1.00 1.00 0.82 0.61 0.79 0.93 0.79 0.61
time (sec) N/A 0.017 0.001 0.003 0.522 0.397 0.107 0.008 0.029
Problem 64 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 3 3 3 4 3 3 3 4 3
normalized size 1 1.00 1.00 1.33 1.00 1.00 1.00 1.33 1.00
time (sec) N/A 0.012 0.005 0.003 0.458 0.405 0.097 0.005 0.070
Problem 65 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 12 12 12 11 10 10 8 10 10
normalized size 1 1.00 1.00 0.92 0.83 0.83 0.67 0.83 0.83
time (sec) N/A 0.015 0.002 0.001 0.556 0.412 0.096 0.008 0.346
Problem 66 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 23 23 16 18 17 12 20 17 13
normalized size 1 1.00 0.70 0.78 0.74 0.52 0.87 0.74 0.57
time (sec) N/A 0.038 0.018 0.007 0.596 0.403 5.068 0.006 0.168
Problem 67 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 39 39 39 32 23 31 37 31 23
normalized size 1 1.00 1.00 0.82 0.59 0.79 0.95 0.79 0.59
time (sec) N/A 0.030 0.002 0.004 0.510 0.391 0.126 0.009 0.036
Problem 68 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 9 9 9 7 6 6 5 6 6
normalized size 1 1.00 1.00 0.78 0.67 0.67 0.56 0.67 0.67
time (sec) N/A 0.012 0.002 0.005 0.488 0.407 0.089 0.005 0.076
Problem 69 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 14 14 14 12 12 11 10 11 11
normalized size 1 1.00 1.00 0.86 0.86 0.79 0.71 0.79 0.79
time (sec) N/A 0.009 0.004 0.004 0.581 0.409 0.185 0.006 0.105
Problem 70 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 8 7 7 7 7 7
normalized size 1 1.00 1.00 0.80 0.70 0.70 0.70 0.70 0.70
time (sec) N/A 0.009 0.008 0.014 0.635 0.413 0.357 0.006 0.101
Problem 71 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 14 14 11 13 15 11 11
normalized size 1 1.00 0.74 0.74 0.58 0.68 0.79 0.58 0.58
time (sec) N/A 0.007 0.015 0.013 0.528 0.413 0.310 0.006 0.018
Problem 72 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 12 14 9 13 15 9 9
normalized size 1 1.00 0.63 0.74 0.47 0.68 0.79 0.47 0.47
time (sec) N/A 0.007 0.010 0.015 0.505 0.401 0.323 0.006 0.019
Problem 73 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 12 9 9 7 9 9
normalized size 1 1.00 1.00 1.20 0.90 0.90 0.70 0.90 0.90
time (sec) N/A 0.006 0.003 0.008 0.567 0.408 0.084 0.006 0.045
Problem 74 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 11 11 7 7 6 6 5 6 6
normalized size 1 1.00 0.64 0.64 0.55 0.55 0.45 0.55 0.55
time (sec) N/A 0.005 0.001 0.002 0.570 0.399 0.085 0.005 0.018
Problem 75 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 16 16 11 10 9 9 7 9 9
normalized size 1 1.00 0.69 0.62 0.56 0.56 0.44 0.56 0.56
time (sec) N/A 0.007 0.005 0.002 0.515 0.387 0.085 0.019 0.021
Problem 76 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 12 12 11 11 10 11 11
normalized size 1 1.00 0.63 0.63 0.58 0.58 0.53 0.58 0.58
time (sec) N/A 0.015 0.005 0.003 0.532 0.401 0.088 0.006 0.022
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 32 32 19 19 16 16 17 16 16
normalized size 1 1.00 0.59 0.59 0.50 0.50 0.53 0.50 0.50
time (sec) N/A 0.018 0.008 0.003 0.655 0.383 0.090 0.007 0.075
Problem 78 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 24 24 16 17 11 11 20 11 11
normalized size 1 1.00 0.67 0.71 0.46 0.46 0.83 0.46 0.46
time (sec) N/A 0.008 0.007 0.009 0.543 0.403 0.201 0.006 0.024
Problem 79 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 16 14 13 13 12 13 13
normalized size 1 1.00 0.62 0.54 0.50 0.50 0.46 0.50 0.50
time (sec) N/A 0.020 0.003 0.004 0.512 0.384 0.091 0.007 0.109
Problem 80 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 41 41 28 40 27 31 136 36 27
normalized size 1 1.00 0.68 0.98 0.66 0.76 3.32 0.88 0.66
time (sec) N/A 0.011 0.032 0.023 0.478 0.400 1.112 0.008 0.032
Problem 81 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 42 42 29 41 29 33 139 38 29
normalized size 1 1.00 0.69 0.98 0.69 0.79 3.31 0.90 0.69
time (sec) N/A 0.011 0.031 0.007 0.531 0.414 1.100 0.009 0.021
Problem 82 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 13 12 21 13
normalized size 1 1.00 1.00 0.93 0.87 0.87 0.80 1.40 0.87
time (sec) N/A 0.003 0.002 0.004 0.540 0.417 0.212 0.012 0.105
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B A C B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 64 22 35 33 17 37 21
normalized size 1 1.00 3.37 1.16 1.84 1.74 0.89 1.95 1.11
time (sec) N/A 0.009 0.074 0.007 0.473 0.445 2.182 0.030 0.609
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 64 20 35 35 17 37 20
normalized size 1 1.00 3.76 1.18 2.06 2.06 1.00 2.18 1.18
time (sec) N/A 0.009 0.048 0.006 0.600 0.444 2.243 0.029 0.209
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 24 23 23 22 23 22
normalized size 1 1.00 1.00 0.96 0.92 0.92 0.88 0.92 0.88
time (sec) N/A 0.034 0.008 0.074 1.130 0.424 0.204 0.017 0.032
Problem 86 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 22 21 33 39 22 38 20
normalized size 1 1.00 1.00 0.95 1.50 1.77 1.00 1.73 0.91
time (sec) N/A 0.016 0.002 0.005 1.225 0.453 2.021 0.021 0.021
Problem 87 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 16 16 16 15 6 23 19 9 14
normalized size 1 1.00 1.00 0.94 0.38 1.44 1.19 0.56 0.88
time (sec) N/A 0.002 0.004 0.004 1.225 0.404 1.146 0.039 0.163
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 14 10 11 21 0 9 11
normalized size 1 1.00 1.40 1.00 1.10 2.10 0.00 0.90 1.10
time (sec) N/A 0.009 0.006 0.005 1.361 0.393 0.000 0.034 0.090
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 11 10 10 20 10 10
normalized size 1 1.00 1.00 1.10 1.00 1.00 2.00 1.00 1.00
time (sec) N/A 0.002 0.002 0.005 1.374 0.402 0.117 0.007 0.036
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 16 15 67 53 15 16
normalized size 1 1.00 1.00 0.67 0.62 2.79 2.21 0.62 0.67
time (sec) N/A 0.004 0.005 0.007 1.490 0.393 0.139 0.007 0.101
Problem 91 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 17 16 16 26 16 16
normalized size 1 1.00 1.00 0.89 0.84 0.84 1.37 0.84 0.84
time (sec) N/A 0.009 0.006 0.002 1.422 0.402 0.117 0.007 0.076
Problem 92 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 16 15 13 15 15 14
normalized size 1 1.00 1.00 0.76 0.71 0.62 0.71 0.71 0.67
time (sec) N/A 0.008 0.003 0.003 1.299 0.423 0.251 0.010 0.023
Problem 93 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 40 40 30 34 33 24 32 33 24
normalized size 1 1.00 0.75 0.85 0.82 0.60 0.80 0.82 0.60
time (sec) N/A 0.022 0.013 0.007 1.268 0.429 0.367 0.022 0.029
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 26 30 34 25 29 29 29
normalized size 1 1.00 0.74 0.86 0.97 0.71 0.83 0.83 0.83
time (sec) N/A 0.056 0.009 0.014 1.261 0.432 0.358 0.021 0.124
Problem 95 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 18 17 16 14 19 16 16
normalized size 1 1.00 0.82 0.77 0.73 0.64 0.86 0.73 0.73
time (sec) N/A 0.005 0.007 0.003 1.130 0.438 1.520 0.016 0.057
Problem 96 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 7 6 6 7 6 6
normalized size 1 1.00 1.00 0.88 0.75 0.75 0.88 0.75 0.75
time (sec) N/A 0.030 0.007 0.005 0.535 0.419 1.403 0.011 0.661
Problem 97 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 23 23 20 18 17 31 15 17 17
normalized size 1 1.00 0.87 0.78 0.74 1.35 0.65 0.74 0.74
time (sec) N/A 0.003 0.006 0.003 1.344 0.397 0.208 0.015 0.078
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F A A A F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 22 22 37 16 0 15 31 24 -1
normalized size 1 1.00 1.68 0.73 0.00 0.68 1.41 1.09 -0.05
time (sec) N/A 0.041 0.011 0.006 0.000 0.426 18.839 0.013 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 16 0 15 31 22 -1
normalized size 1 1.00 1.00 0.80 0.00 0.75 1.55 1.10 -0.05
time (sec) N/A 0.023 0.007 0.004 0.000 0.436 17.375 0.012 0.000
Problem 100 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 21 12 15 17
normalized size 1 1.00 1.00 0.84 0.79 1.11 0.63 0.79 0.89
time (sec) N/A 0.004 0.009 0.008 1.124 0.387 0.102 0.009 0.028
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 4 4 4 4 3 3 15 3 3
normalized size 1 1.00 1.00 1.00 0.75 0.75 3.75 0.75 0.75
time (sec) N/A 0.016 0.003 0.011 1.114 0.418 0.112 0.006 0.100
Problem 102 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 27 25 19 28 19 21 22
normalized size 1 1.00 1.00 0.93 0.70 1.04 0.70 0.78 0.81
time (sec) N/A 0.018 0.020 0.009 0.508 0.428 7.745 0.010 0.136
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 83 64 49 38 0 36 49
normalized size 1 1.00 1.98 1.52 1.17 0.90 0.00 0.86 1.17
time (sec) N/A 0.013 0.055 0.022 1.181 0.423 0.000 0.040 0.070
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 106 122 0 80 0 61 -1
normalized size 1 1.00 1.49 1.72 0.00 1.13 0.00 0.86 -0.01
time (sec) N/A 0.022 0.167 0.017 0.000 0.422 0.000 0.030 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F(-2) A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 72 28 0 43 0 22 -1
normalized size 1 1.00 2.25 0.88 0.00 1.34 0.00 0.69 -0.03
time (sec) N/A 0.012 0.030 0.004 0.000 0.390 0.000 0.117 0.000
Problem 106 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 13 12 15 13
normalized size 1 1.00 1.00 0.93 0.87 0.87 0.80 1.00 0.87
time (sec) N/A 0.004 0.004 0.006 0.434 0.381 0.105 0.007 0.051
Problem 107 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 14 13 13 14 15 13
normalized size 1 1.00 1.00 0.74 0.68 0.68 0.74 0.79 0.68
time (sec) N/A 0.004 0.004 0.007 0.471 0.391 0.104 0.007 0.038
Problem 108 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 23 23 23 20 19 19 19 21 19
normalized size 1 1.00 1.00 0.87 0.83 0.83 0.83 0.91 0.83
time (sec) N/A 0.027 0.005 0.007 0.481 0.396 0.109 0.008 0.041
Problem 109 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 23 23 23 18 17 17 17 20 19
normalized size 1 1.00 1.00 0.78 0.74 0.74 0.74 0.87 0.83
time (sec) N/A 0.033 0.006 0.010 0.507 0.407 0.140 0.008 0.189
Problem 110 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 24 24 22 19 18 26 19 24 18
normalized size 1 1.00 0.92 0.79 0.75 1.08 0.79 1.00 0.75
time (sec) N/A 0.014 0.011 0.010 0.454 0.407 0.118 0.009 0.050
Problem 111 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 28 28 3 29 57
normalized size 1 1.00 1.00 1.04 1.00 1.00 0.11 1.04 2.04
time (sec) N/A 0.028 0.012 0.009 1.172 0.404 0.132 0.010 0.186
Problem 112 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 49 49 61 37 36 51 14 37 53
normalized size 1 1.00 1.24 0.76 0.73 1.04 0.29 0.76 1.08
time (sec) N/A 0.067 0.032 0.013 1.296 0.399 0.170 0.011 0.101
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 24 19 39 38 39 37 21
normalized size 1 1.00 1.14 0.90 1.86 1.81 1.86 1.76 1.00
time (sec) N/A 0.009 0.023 0.046 1.239 0.413 0.514 0.035 0.326
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 266 14 55 44 14 87
normalized size 1 1.00 1.00 16.62 0.88 3.44 2.75 0.88 5.44
time (sec) N/A 0.045 0.031 0.105 0.621 0.400 5.396 0.009 0.157
Problem 115 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 11 11 9 9 9 9 8 11 9
normalized size 1 1.00 0.82 0.82 0.82 0.82 0.73 1.00 0.82
time (sec) N/A 0.004 0.004 0.001 0.574 0.396 0.091 0.007 0.047
Problem 116 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 23 23 23 20 19 19 20 22 19
normalized size 1 1.00 1.00 0.87 0.83 0.83 0.87 0.96 0.83
time (sec) N/A 0.008 0.007 0.009 0.471 0.388 0.132 0.008 0.111
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 28 21 20 27 22 22 18
normalized size 1 1.00 0.93 0.70 0.67 0.90 0.73 0.73 0.60
time (sec) N/A 0.017 0.010 0.008 0.606 0.394 0.102 0.007 0.041
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 27 27 27 24 23 23 20 26 30
normalized size 1 1.00 1.00 0.89 0.85 0.85 0.74 0.96 1.11
time (sec) N/A 0.031 0.006 0.009 0.504 0.382 0.133 0.008 0.095
Problem 119 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 23 23 24 24 20 32 17 16 15
normalized size 1 1.00 1.04 1.04 0.87 1.39 0.74 0.70 0.65
time (sec) N/A 0.026 0.013 0.009 0.601 0.389 0.115 0.007 0.086
Problem 120 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 16 16 16 15 14 14 14 15 14
normalized size 1 1.00 1.00 0.94 0.88 0.88 0.88 0.94 0.88
time (sec) N/A 0.017 0.005 0.006 1.121 0.383 0.097 0.008 0.044
Problem 121 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 13 12 12 14 12 12
normalized size 1 1.00 1.00 0.72 0.67 0.67 0.78 0.67 0.67
time (sec) N/A 0.012 0.008 0.010 1.136 0.389 0.148 0.010 0.038
Problem 122 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 11 11 11 12 11 11 8 13 11
normalized size 1 1.00 1.00 1.09 1.00 1.00 0.73 1.18 1.00
time (sec) N/A 0.005 0.002 0.006 0.489 0.392 0.101 0.006 0.103
Problem 123 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 24 24 24 21 24 32 19 29 20
normalized size 1 1.00 1.00 0.88 1.00 1.33 0.79 1.21 0.83
time (sec) N/A 0.010 0.010 0.013 0.565 0.388 0.106 0.008 0.035
Problem 124 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 46 46 44 39 46 83 46 52 45
normalized size 1 1.00 0.96 0.85 1.00 1.80 1.00 1.13 0.98
time (sec) N/A 0.013 0.021 0.012 0.521 0.404 0.200 0.009 0.088
Problem 125 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 10 16 8 11 10
normalized size 1 1.00 1.00 1.10 1.00 1.60 0.80 1.10 1.00
time (sec) N/A 0.004 0.003 0.007 0.473 0.395 0.079 0.006 0.028
Problem 126 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 18 17 13 10 16 13
normalized size 1 1.00 1.00 1.06 1.00 0.76 0.59 0.94 0.76
time (sec) N/A 0.007 0.003 0.009 0.518 0.382 0.096 0.007 0.110
Problem 127 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 15 14 14 17 16 14
normalized size 1 1.00 1.00 0.75 0.70 0.70 0.85 0.80 0.70
time (sec) N/A 0.008 0.003 0.007 0.508 0.376 0.106 0.007 0.045
Problem 128 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 16 16 12 13 12 16 8 13 12
normalized size 1 1.00 0.75 0.81 0.75 1.00 0.50 0.81 0.75
time (sec) N/A 0.005 0.004 0.005 0.491 0.376 0.083 0.007 0.037
Problem 129 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 14 14 14 15 14 17 10 14 14
normalized size 1 1.00 1.00 1.07 1.00 1.21 0.71 1.00 1.00
time (sec) N/A 0.010 0.008 0.008 1.267 0.395 0.140 0.009 0.082
Problem 130 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 18 17 17 20 20 17
normalized size 1 1.00 1.00 0.86 0.81 0.81 0.95 0.95 0.81
time (sec) N/A 0.018 0.005 0.007 0.626 0.401 0.135 0.008 0.063
Problem 131 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 21 21 27 28 23 34 20 25 17
normalized size 1 1.00 1.29 1.33 1.10 1.62 0.95 1.19 0.81
time (sec) N/A 0.003 0.008 0.009 0.528 0.387 0.111 0.007 0.087
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 22 22 22 17 16 16 17 17 16
normalized size 1 1.00 1.00 0.77 0.73 0.73 0.77 0.77 0.73
time (sec) N/A 0.011 0.003 0.005 1.233 0.383 0.095 0.008 0.159
Problem 133 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 14 18 8 14 10
normalized size 1 1.00 1.00 1.10 1.40 1.80 0.80 1.40 1.00
time (sec) N/A 0.015 0.005 0.008 0.576 0.387 0.101 0.009 0.030
Problem 134 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 31 31 31 22 19 25 19 21 16
normalized size 1 1.00 1.00 0.71 0.61 0.81 0.61 0.68 0.52
time (sec) N/A 0.009 0.002 0.009 0.488 0.376 0.110 0.006 0.040
Problem 135 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 17 16 16 15 17 24
normalized size 1 1.00 1.00 0.94 0.89 0.89 0.83 0.94 1.33
time (sec) N/A 0.025 0.005 0.006 1.435 0.416 0.127 0.009 0.039
Problem 136 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 13 13 25 10 17 17 17 19 9
normalized size 1 1.00 1.92 0.77 1.31 1.31 1.31 1.46 0.69
time (sec) N/A 0.003 0.004 0.002 1.370 0.397 0.127 0.007 0.029
Problem 137 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 85 85 64 58 72 95 73 72 33
normalized size 1 1.00 0.75 0.68 0.85 1.12 0.86 0.85 0.39
time (sec) N/A 0.039 0.020 0.003 1.413 0.394 0.152 0.009 0.115
Problem 138 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 23 23 15 16 15 26 14 15 15
normalized size 1 1.00 0.65 0.70 0.65 1.13 0.61 0.65 0.65
time (sec) N/A 0.007 0.009 0.006 1.222 0.403 0.108 0.010 0.081
Problem 139 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 11 11 11 41 11 11 8 11 11
normalized size 1 1.00 1.00 3.73 1.00 1.00 0.73 1.00 1.00
time (sec) N/A 0.006 0.007 0.010 0.517 0.373 0.117 0.020 0.062
Problem 140 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 23 20 23 36 39 47 21
normalized size 1 1.00 0.51 0.44 0.51 0.80 0.87 1.04 0.47
time (sec) N/A 0.024 0.030 0.060 1.272 0.417 0.486 0.010 0.100
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 31 30 0 111 110 53 28
normalized size 1 1.00 0.84 0.81 0.00 3.00 2.97 1.43 0.76
time (sec) N/A 0.018 0.026 0.025 0.000 0.460 3.193 0.014 0.319
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 20 16 37 50 36 35 15
normalized size 1 1.00 0.36 0.29 0.66 0.89 0.64 0.62 0.27
time (sec) N/A 0.015 0.015 0.017 1.348 0.408 0.343 0.032 0.239
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 20 16 19 23 32 40 32
normalized size 1 1.00 0.65 0.52 0.61 0.74 1.03 1.29 1.03
time (sec) N/A 0.011 0.013 0.028 1.302 0.430 0.292 0.009 0.219
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 18 15 14 33 248 48 26
normalized size 1 1.00 0.50 0.42 0.39 0.92 6.89 1.33 0.72
time (sec) N/A 0.038 0.035 0.037 1.228 0.441 57.584 0.015 0.208
Problem 145 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 15 15 15 16 15 43 0 26 15
normalized size 1 1.00 1.00 1.07 1.00 2.87 0.00 1.73 1.00
time (sec) N/A 0.023 0.050 0.069 1.143 0.446 0.000 0.017 0.455
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 14 14 39 0 13 29
normalized size 1 1.00 1.00 0.82 0.82 2.29 0.00 0.76 1.71
time (sec) N/A 0.012 0.034 0.154 0.572 0.411 0.000 0.017 0.634
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 22 25 41 11 22 25 34
normalized size 1 1.00 0.73 0.83 1.37 0.37 0.73 0.83 1.13
time (sec) N/A 0.029 0.043 0.075 1.148 0.421 0.316 0.022 0.314
Problem 148 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 29 29 29 23 22 29 24 22 22
normalized size 1 1.00 1.00 0.79 0.76 1.00 0.83 0.76 0.76
time (sec) N/A 0.004 0.009 0.003 1.137 0.408 0.213 0.014 0.037
Problem 149 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 13 13 13 12 11 11 8 11 11
normalized size 1 1.00 1.00 0.92 0.85 0.85 0.62 0.85 0.85
time (sec) N/A 0.002 0.002 0.004 0.482 0.414 0.153 0.007 0.169
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 33 30 41 40 88 47 35
normalized size 1 1.00 0.89 0.81 1.11 1.08 2.38 1.27 0.95
time (sec) N/A 0.020 0.009 0.005 1.198 0.397 1.381 0.012 0.209
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 31 22 25 25 0 26 21
normalized size 1 1.00 1.41 1.00 1.14 1.14 0.00 1.18 0.95
time (sec) N/A 0.007 0.016 0.006 0.511 0.399 0.000 0.018 0.085
Problem 152 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 27 21 20 25 24 25 20
normalized size 1 1.00 1.00 0.78 0.74 0.93 0.89 0.93 0.74
time (sec) N/A 0.003 0.009 0.005 1.274 0.391 0.212 0.009 0.088
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 21 22 27 0 27 23
normalized size 1 1.00 1.00 0.78 0.81 1.00 0.00 1.00 0.85
time (sec) N/A 0.011 0.005 0.006 1.197 0.394 0.000 0.028 0.053
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 29 12 15 17 0 18 11
normalized size 1 1.00 2.07 0.86 1.07 1.21 0.00 1.29 0.79
time (sec) N/A 0.003 0.006 0.003 0.554 0.395 0.000 0.024 0.171
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 68 88 59 92 0 168 73
normalized size 1 1.00 1.00 1.29 0.87 1.35 0.00 2.47 1.07
time (sec) N/A 0.037 0.033 0.009 1.185 0.433 0.000 0.037 0.085
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F C F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 13 12 0 58 0 13
normalized size 1 1.00 1.00 1.00 0.92 0.00 4.46 0.00 1.00
time (sec) N/A 0.015 0.002 0.004 0.592 0.421 2.439 0.000 0.031
Problem 157 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 15 2 2 2 2 2
normalized size 1 1.00 1.00 1.00 0.13 0.13 0.13 0.13 0.13
time (sec) N/A 0.010 0.011 0.023 0.633 0.404 0.200 0.003 0.099
Problem 158 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 2 2 2 8 2 2 2 2 2
normalized size 1 1.00 1.00 4.00 1.00 1.00 1.00 1.00 1.00
time (sec) N/A 0.010 0.005 0.006 0.660 0.398 0.737 0.004 0.007
Problem 159 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 4 4 4 9 4 4 3 4 4
normalized size 1 1.00 1.00 2.25 1.00 1.00 0.75 1.00 1.00
time (sec) N/A 0.012 0.008 0.003 0.823 0.385 0.782 0.005 0.014
Problem 160 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 11 11 11 16 5 13 7 13 14
normalized size 1 1.00 1.00 1.45 0.45 1.18 0.64 1.18 1.27
time (sec) N/A 0.020 0.009 0.005 0.694 0.396 0.976 0.007 0.024
Problem 161 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 14 14 14 15 9 13 10 18 9
normalized size 1 1.00 1.00 1.07 0.64 0.93 0.71 1.29 0.64
time (sec) N/A 0.012 0.002 0.003 0.645 0.399 1.054 0.009 0.017
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 17 16 14 0 14 14
normalized size 1 1.00 1.00 1.13 1.07 0.93 0.00 0.93 0.93
time (sec) N/A 0.015 0.014 0.010 0.872 0.400 0.000 0.009 0.028
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 14 13 10 0 10 10
normalized size 1 1.00 1.00 1.08 1.00 0.77 0.00 0.77 0.77
time (sec) N/A 0.065 0.021 0.009 0.790 0.395 0.000 0.007 0.118
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 22 16 23 0 80 17
normalized size 1 1.00 1.00 1.16 0.84 1.21 0.00 4.21 0.89
time (sec) N/A 0.023 0.023 0.007 0.796 0.405 0.000 0.012 0.126
Problem 165 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 18 18 18 19 18 19 0 16 -1
normalized size 1 1.00 1.00 1.06 1.00 1.06 0.00 0.89 -0.06
time (sec) N/A 0.020 0.010 0.043 0.766 0.406 0.000 0.007 0.000
Problem 166 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 16 16 11 10 9 9 7 9 9
normalized size 1 1.00 0.69 0.62 0.56 0.56 0.44 0.56 0.56
time (sec) N/A 0.009 0.005 0.002 0.476 0.398 0.081 0.006 0.017
Problem 167 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 16 15 14 14 12 14 14
normalized size 1 1.00 0.62 0.58 0.54 0.54 0.46 0.54 0.54
time (sec) N/A 0.021 0.006 0.002 0.511 0.400 0.087 0.007 0.030
Problem 168 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 36 36 21 20 19 19 17 19 19
normalized size 1 1.00 0.58 0.56 0.53 0.53 0.47 0.53 0.53
time (sec) N/A 0.034 0.006 0.003 0.484 0.393 0.089 0.007 0.023
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 39 111 181 60 360 77 2034
normalized size 1 1.00 0.81 2.31 3.77 1.25 7.50 1.60 42.38
time (sec) N/A 0.034 0.134 0.130 1.296 0.439 1.000 0.046 10.613
Problem 170 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 2 2 2 9 3 2 2 3 2
normalized size 1 1.00 1.00 4.50 1.50 1.00 1.00 1.50 1.00
time (sec) N/A 0.002 0.002 0.007 0.632 0.402 0.458 0.006 0.009
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 10 10 10 17 6 14 7 11 10
normalized size 1 1.00 1.00 1.70 0.60 1.40 0.70 1.10 1.00
time (sec) N/A 0.004 0.001 0.001 0.692 0.385 0.465 0.006 0.034
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 0 22 15 24 0 22
normalized size 1 1.00 1.00 0.00 1.00 0.68 1.09 0.00 1.00
time (sec) N/A 0.017 0.013 0.040 0.653 0.442 2.743 0.000 0.062
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 10 12 11 9 0 9 9
normalized size 1 1.00 0.83 1.00 0.92 0.75 0.00 0.75 0.75
time (sec) N/A 0.015 0.016 0.006 0.668 0.380 0.000 0.008 0.015
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 23 0 20 0 20 -1
normalized size 1 1.00 1.00 1.05 0.00 0.91 0.00 0.91 -0.05
time (sec) N/A 0.056 0.038 0.013 0.000 0.406 0.000 0.010 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 17 116 0 0 27 0 155
normalized size 1 1.00 0.17 1.13 0.00 0.00 0.26 0.00 1.50
time (sec) N/A 0.008 0.002 0.133 0.000 0.415 0.625 0.000 0.285

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 [83] had the largest ratio of [2.000]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 1 1 1.00 9 0.111
2 A 2 1 1.00 11 0.091
3 A 2 1 1.00 11 0.091
4 A 2 1 1.00 11 0.091
5 A 1 1 1.00 14 0.071
6 A 2 1 1.00 4 0.250
7 A 2 1 1.00 9 0.111
8 A 2 2 1.00 7 0.286
9 A 2 2 1.00 17 0.118
10 A 2 2 1.00 9 0.222
11 A 3 3 1.00 11 0.273
12 A 3 3 1.00 16 0.188
13 A 2 2 1.00 10 0.200
14 A 1 1 1.00 15 0.067
15 A 2 1 1.00 9 0.111
16 A 1 1 1.00 9 0.111
17 A 1 1 1.00 15 0.067
18 A 1 1 1.00 17 0.059
19 A 3 2 1.00 20 0.100
20 A 1 1 1.00 26 0.038
21 A 2 2 1.00 20 0.100
22 A 2 2 1.00 4 0.500
23 A 3 2 1.00 6 0.333
24 A 4 2 1.00 6 0.333
25 A 4 2 1.00 6 0.333
26 A 2 2 1.00 5 0.400
27 A 3 3 1.00 6 0.500
28 A 2 2 1.00 4 0.500
29 A 2 1 1.00 4 0.250
30 A 3 2 1.00 4 0.500
31 A 2 1 1.00 4 0.250
32 A 4 2 1.00 4 0.500
33 A 2 2 1.00 6 0.333
34 A 3 3 1.00 6 0.500
35 A 4 4 1.00 8 0.500
36 A 2 2 1.00 4 0.500
37 A 2 1 1.00 4 0.250
38 A 3 2 1.00 4 0.500
39 A 5 3 1.00 13 0.231
40 A 3 2 1.00 13 0.154
41 A 2 2 1.00 13 0.154
42 A 2 2 1.00 4 0.500
43 A 3 2 1.00 4 0.500
44 A 2 2 1.00 4 0.500
45 A 3 2 1.00 4 0.500
46 A 2 2 1.00 10 0.200
47 A 1 1 1.00 11 0.091
48 A 1 1 1.00 9 0.111
49 A 1 1 1.00 13 0.077
50 A 1 1 1.00 11 0.091
51 A 2 1 1.00 11 0.091
52 A 2 2 1.00 8 0.250
53 A 5 3 1.00 8 0.375
54 A 1 1 1.00 10 0.100
55 A 3 2 1.00 17 0.118
56 A 1 1 1.00 7 0.143
57 A 2 2 1.00 4 0.500
58 A 1 1 1.00 4 0.250
59 A 2 2 1.00 6 0.333
60 A 1 1 1.00 5 0.200
61 A 1 1 1.00 2 0.500
62 A 1 1 1.00 8 0.125
63 A 2 2 1.00 8 0.250
64 A 2 2 1.00 8 0.250
65 A 2 2 1.00 14 0.143
66 A 3 2 1.00 14 0.143
67 A 3 2 1.00 8 0.250
68 A 1 1 1.00 9 0.111
69 A 1 1 1.00 13 0.077
70 A 2 2 1.00 9 0.222
71 A 1 1 1.00 6 0.167
72 A 1 1 1.00 6 0.167
73 A 4 4 1.00 7 0.571
74 A 2 2 1.00 5 0.400
75 A 2 2 1.00 7 0.286
76 A 3 2 1.00 7 0.286
77 A 3 2 1.00 9 0.222
78 A 3 3 1.00 7 0.429
79 A 2 2 1.00 11 0.182
80 A 1 1 1.00 10 0.100
81 A 1 1 1.00 10 0.100
82 A 2 2 1.00 2 1.000
83 A 4 4 1.00 2 2.000
84 A 4 4 1.00 2 2.000
85 A 3 3 1.00 4 0.750
86 A 4 4 1.00 6 0.667
87 A 2 2 1.00 13 0.154
88 A 2 2 1.00 14 0.143
89 A 1 1 1.00 9 0.111
90 A 1 1 1.00 9 0.111
91 A 2 2 1.00 10 0.200
92 A 3 3 1.00 4 0.750
93 A 4 3 1.00 6 0.500
94 A 5 5 1.00 6 0.833
95 A 4 4 1.00 6 0.667
96 A 1 3 1.00 17 0.176
97 A 2 2 1.00 11 0.182
98 A 1 1 1.00 15 0.067
99 A 1 1 1.00 14 0.071
100 A 2 2 1.00 11 0.182
101 A 2 2 1.00 13 0.154
102 A 5 6 1.00 10 0.600
103 A 3 3 1.00 15 0.200
104 A 4 4 1.00 15 0.267
105 A 3 3 1.00 15 0.200
106 A 3 2 1.00 16 0.125
107 A 3 2 1.00 16 0.125
108 A 6 4 1.00 18 0.222
109 A 3 2 1.00 23 0.087
110 A 2 1 1.00 19 0.053
111 A 5 5 1.00 18 0.278
112 A 6 5 1.00 31 0.161
113 A 2 2 1.00 7 0.286
114 A 3 2 1.00 22 0.091
115 A 2 1 1.00 16 0.062
116 A 2 1 1.00 17 0.059
117 A 2 1 1.00 12 0.083
118 A 3 2 1.00 21 0.095
119 A 2 1 1.00 20 0.050
120 A 3 3 1.00 16 0.188
121 A 4 3 1.00 16 0.188
122 A 2 1 1.00 11 0.091
123 A 3 2 1.00 11 0.182
124 A 2 1 1.00 16 0.062
125 A 2 1 1.00 7 0.143
126 A 5 5 1.00 9 0.556
127 A 4 3 1.00 12 0.250
128 A 3 2 1.00 14 0.143
129 A 4 4 1.00 21 0.190
130 A 3 2 1.00 18 0.111
131 A 2 2 1.00 7 0.286
132 A 3 3 1.00 11 0.273
133 A 3 2 1.00 16 0.125
134 A 3 2 1.00 11 0.182
135 A 5 4 1.00 18 0.222
136 A 3 3 1.00 7 0.429
137 A 9 6 1.00 7 0.857
138 A 3 3 1.00 14 0.214
139 A 1 1 1.00 16 0.062
140 A 3 3 1.00 12 0.250
141 A 2 2 1.00 8 0.250
142 A 2 2 1.00 8 0.250
143 A 1 1 1.00 10 0.100
144 A 3 3 1.00 13 0.231
145 A 2 1 1.00 19 0.053
146 A 1 1 1.00 11 0.091
147 A 3 3 1.00 11 0.273
148 A 2 2 1.00 11 0.182
149 A 1 1 1.00 13 0.077
150 A 4 4 1.00 15 0.267
151 A 3 3 1.00 13 0.231
152 A 2 2 1.00 9 0.222
153 A 3 3 1.00 12 0.250
154 A 2 2 1.00 9 0.222
155 A 6 6 1.00 18 0.333
156 A 2 2 1.00 8 0.250
157 A 3 3 1.00 5 0.600
158 A 1 1 1.00 7 0.143
159 A 1 1 1.00 9 0.111
160 A 2 2 1.00 7 0.286
161 A 2 2 1.00 5 0.400
162 A 1 1 1.00 14 0.071
163 A 2 2 1.00 14 0.143
164 A 2 2 1.00 9 0.222
165 A 2 3 1.00 8 0.375
166 A 2 2 1.00 7 0.286
167 A 3 2 1.00 9 0.222
168 A 4 2 1.00 9 0.222
169 A 1 1 1.00 21 0.048
170 A 1 1 1.00 4 0.250
171 A 2 2 1.00 4 0.500
172 A 2 2 1.00 8 0.250
173 A 1 1 1.00 11 0.091
174 A 4 2 1.00 16 0.125
175 A 1 1 1.00 9 0.111

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