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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, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175 }

B grade: { }

C grade: { 160 }

F grade: { }

2.1.2 Mathematica

A grade: { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 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, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 111, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 135, 137, 138, 139, 141, 143, 145, 147, 149, 152, 153, 156, 157, 158, 160, 163, 164, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175 }

B grade: { 1, 24, 55, 67, 68, 69, 70, 73, 89, 91, 103, 110, 112, 159, 161, 162, 165 }

C grade: { 113, 115, 117, 132, 134, 136, 140, 142, 144, 146, 148, 150, 151, 154, 155 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 42, 43, 44, 45, 49, 50, 66, 67, 68, 69, 70, 71, 72, 73, 74, 79, 80, 81, 82, 83, 85, 87, 96, 97, 98, 100, 102, 104, 106, 107, 109, 114, 116, 117, 118, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175 }

B grade: { 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 46, 47, 48, 62, 63, 64, 65, 75, 76, 77, 78, 84, 86, 88, 89, 90, 91, 92, 93, 94, 95, 99, 101, 103, 105, 108, 110, 111, 112, 113, 115, 119, 120, 121, 122, 123, 124 }

C grade: { 160 }

F grade: { 13, 14, 15, 16, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 137, 139, 149, 153, 154, 155, 156, 157, 158, 159, 161, 162, 163, 164 }

2.1.4 Maxima

A grade: { 1, 2, 29, 30, 31, 32, 33, 34, 35, 45, 46, 47, 48, 49, 50, 62, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 84, 87, 93, 95, 97, 98, 105, 106, 107, 114, 115, 116, 117, 118, 119, 123, 126, 127, 128, 129, 130, 131, 133, 145, 162, 165, 166 }

B grade: { 3, 4, 5, 6, 42, 43, 44, 68, 69, 70, 76, 83, 85, 86, 88, 89, 90, 91, 92, 94, 96, 99, 100, 101, 102, 103, 104, 108, 109, 110, 111, 112, 113, 120, 121, 122, 124, 125, 141, 153, 160, 161, 167, 168, 169 }

C grade: { 22, 23, 24, 25, 26, 27, 28 }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 132, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 163, 164, 170, 171, 172, 173, 174, 175 }

2.1.5 FriCAS

A grade: { 49, 50, 62, 63, 66, 84, 97, 107, 108, 117, 118, 128, 129, 130, 131, 133, 135, 137, 139, 141, 143, 147, 149, 151, 153, 155, 161, 162 }

B grade: { 1, 2, 3, 4, 5, 6, 29, 30, 31, 32, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 109, 110, 111, 112, 113, 114, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 145, 160, 163, 164, 165, 166, 167, 168, 169 }

C grade: { 22, 23, 24, 25, 26, 27, 28 }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 157, 158, 159, 170, 171, 172, 173, 174, 175 }

2.1.6 Sympy

A grade: { }

B grade: { }

C grade: { }

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

2.1.7 Giac

A grade: { 2, 4, 6, 29, 30, 31, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 93, 94, 95, 96, 97, 98, 100, 102, 103, 105, 107, 108, 114, 116, 117, 118, 119, 123, 125, 126, 127, 128, 129, 130, 131, 161, 162, 166, 168 }

B grade: { 1, 3, 5, 32, 68, 85, 86, 87, 88, 89, 90, 91, 92, 99, 101, 104, 106, 109, 110, 111, 112, 113, 115, 120, 121, 122, 124, 160, 165, 167, 169 }

C grade: { 22, 23, 24, 25, 26, 27, 28 }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 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, 163, 164, 170, 171, 172, 173, 174, 175 }

2.1.8 Mupad

A grade: { }

B grade: { 1, 2, 3, 4, 5, 6, 25, 32, 42, 43, 44, 45, 49, 50, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 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, 133, 141, 145, 153, 160, 161, 162, 165, 166, 167, 168, 169 }

C grade: { }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 76, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 163, 164, 170, 171, 172, 173, 174, 175 }

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 B A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 38 15 14 38 0 27 27
normalized size 1 1.00 3.17 1.25 1.17 3.17 0.00 2.25 2.25
time (sec) N/A 0.006 0.016 0.017 0.309 0.505 0.000 0.128 0.111
Problem 2 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 11 11 11 12 18 43 0 18 18
normalized size 1 1.00 1.00 1.09 1.64 3.91 0.00 1.64 1.64
time (sec) N/A 0.010 0.011 0.313 0.361 0.644 0.000 0.131 0.073
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 57 27 84 387 0 84 86
normalized size 1 1.00 1.68 0.79 2.47 11.38 0.00 2.47 2.53
time (sec) N/A 0.022 0.013 0.322 0.332 0.585 0.000 0.120 1.403
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 35 23 90 164 0 31 31
normalized size 1 1.00 1.35 0.88 3.46 6.31 0.00 1.19 1.19
time (sec) N/A 0.012 0.013 0.323 0.463 0.570 0.000 0.120 1.455
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 95 41 133 1114 0 110 193
normalized size 1 1.00 1.73 0.75 2.42 20.25 0.00 2.00 3.51
time (sec) N/A 0.043 0.016 0.313 0.425 0.622 0.000 0.135 0.062
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 56 33 205 344 0 42 42
normalized size 1 1.00 1.33 0.79 4.88 8.19 0.00 1.00 1.00
time (sec) N/A 0.015 0.017 0.291 0.319 1.200 0.000 0.142 0.077
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 61 101 0 0 0 0 -1
normalized size 1 1.00 0.76 1.26 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.037 0.126 0.418 0.000 0.521 0.000 0.000 0.000
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 57 154 0 0 0 0 -1
normalized size 1 1.00 0.75 2.03 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.030 0.222 0.375 0.000 1.105 0.000 0.000 0.000
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 48 87 0 0 0 0 -1
normalized size 1 1.00 0.89 1.61 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.020 0.193 0.239 0.000 1.093 0.000 0.000 0.000
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 50 108 0 0 0 0 -1
normalized size 1 1.00 0.93 2.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.020 0.037 0.362 0.000 1.604 0.000 0.000 0.000
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 63 100 0 0 0 0 -1
normalized size 1 1.00 0.79 1.25 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.032 0.068 0.407 0.000 0.941 0.000 0.000 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 67 164 0 0 0 0 -1
normalized size 1 1.00 0.84 2.05 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.032 0.130 0.389 0.000 0.470 0.000 0.000 0.000
Problem 13 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 116 116 79 0 0 0 0 0 -1
normalized size 1 1.00 0.68 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.061 0.160 0.299 0.000 0.565 0.000 0.000 0.000
Problem 14 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 88 88 66 0 0 0 0 0 -1
normalized size 1 1.00 0.75 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.039 0.112 0.291 0.000 0.934 0.000 0.000 0.000
Problem 15 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 84 84 60 0 0 0 0 0 -1
normalized size 1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.038 0.061 0.245 0.000 2.145 0.000 0.000 0.000
Problem 16 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 56 56 54 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.022 0.036 0.351 0.000 0.505 0.000 0.000 0.000
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 52 227 0 0 0 0 -1
normalized size 1 1.00 0.93 4.05 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.023 0.046 0.329 0.000 1.400 0.000 0.000 0.000
Problem 18 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 90 90 73 0 0 0 0 0 -1
normalized size 1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.039 0.091 0.208 0.000 0.613 0.000 0.000 0.000
Problem 19 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 90 90 68 0 0 0 0 0 -1
normalized size 1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.038 0.136 0.211 0.000 0.447 0.000 0.000 0.000
Problem 20 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 118 118 80 0 0 0 0 0 -1
normalized size 1 1.00 0.68 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.056 0.162 0.208 0.000 0.591 0.000 0.000 0.000
Problem 21 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 74 74 67 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 0.035 0.104 0.447 0.000 0.731 0.000 0.000 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 41 114 74 115 0 72 -1
normalized size 1 1.00 1.02 2.85 1.85 2.88 0.00 1.80 -0.02
time (sec) N/A 0.017 0.124 0.220 0.523 0.502 0.000 0.143 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 41 99 49 67 0 57 -1
normalized size 1 1.00 1.71 4.12 2.04 2.79 0.00 2.38 -0.04
time (sec) N/A 0.012 0.063 0.189 0.633 0.563 0.000 0.140 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 20 67 19 15 0 27 -1
normalized size 1 1.00 6.67 22.33 6.33 5.00 0.00 9.00 -0.33
time (sec) N/A 0.008 0.005 0.205 0.564 0.977 0.000 0.139 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C C F C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 58 11 14 0 25 31
normalized size 1 1.00 1.00 4.46 0.85 1.08 0.00 1.92 2.38
time (sec) N/A 0.010 0.005 0.195 0.495 1.047 0.000 0.126 1.715
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 27 118 23 26 0 50 -1
normalized size 1 1.00 0.82 3.58 0.70 0.79 0.00 1.52 -0.03
time (sec) N/A 0.015 0.015 0.185 0.436 2.466 0.000 0.159 0.000
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 33 178 35 38 0 64 -1
normalized size 1 1.00 0.67 3.63 0.71 0.78 0.00 1.31 -0.02
time (sec) N/A 0.020 0.025 0.184 0.459 1.452 0.000 0.168 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B C C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 39 238 47 50 0 76 -1
normalized size 1 1.00 0.60 3.66 0.72 0.77 0.00 1.17 -0.02
time (sec) N/A 0.024 0.037 0.206 1.032 1.130 0.000 0.167 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 41 123 92 1128 0 75 -1
normalized size 1 1.00 0.63 1.89 1.42 17.35 0.00 1.15 -0.02
time (sec) N/A 0.034 0.100 0.250 0.539 0.631 0.000 0.122 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 30 103 60 340 0 58 -1
normalized size 1 1.00 0.65 2.24 1.30 7.39 0.00 1.26 -0.02
time (sec) N/A 0.025 0.068 0.206 0.474 0.567 0.000 0.118 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 20 67 24 97 0 29 -1
normalized size 1 1.00 0.77 2.58 0.92 3.73 0.00 1.12 -0.04
time (sec) N/A 0.018 0.005 0.230 0.454 1.133 0.000 0.129 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 58 17 83 0 24 33
normalized size 1 1.00 1.00 4.46 1.31 6.38 0.00 1.85 2.54
time (sec) N/A 0.014 0.006 0.213 0.446 2.481 0.000 0.131 1.603
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 27 130 35 285 0 54 -1
normalized size 1 1.00 0.75 3.61 0.97 7.92 0.00 1.50 -0.03
time (sec) N/A 0.022 0.023 0.194 0.688 1.308 0.000 0.146 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 36 196 53 590 0 67 -1
normalized size 1 1.00 0.65 3.56 0.96 10.73 0.00 1.22 -0.02
time (sec) N/A 0.030 0.028 0.202 0.534 0.598 0.000 0.163 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 42 262 71 984 0 80 -1
normalized size 1 1.00 0.57 3.54 0.96 13.30 0.00 1.08 -0.01
time (sec) N/A 0.040 0.056 0.207 0.496 1.287 0.000 0.170 0.000
Problem 36 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 135 135 68 0 0 0 0 0 -1
normalized size 1 1.00 0.50 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.070 0.177 0.241 0.000 0.611 0.000 0.000 0.000
Problem 37 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 81 81 56 0 0 0 0 0 -1
normalized size 1 1.00 0.69 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.045 0.121 0.206 0.000 0.475 0.000 0.000 0.000
Problem 38 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 56 60 42 0 0 0 0 0 -1
normalized size 1 1.07 0.75 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.034 0.031 0.225 0.000 0.515 0.000 0.000 0.000
Problem 39 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 62 62 43 0 0 0 0 0 -1
normalized size 1 1.00 0.69 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.034 0.077 0.227 0.000 0.591 0.000 0.000 0.000
Problem 40 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 89 89 57 0 0 0 0 0 -1
normalized size 1 1.00 0.64 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.048 0.078 0.202 0.000 0.597 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 71 0 0 0 0 0 -1
normalized size 1 1.00 0.53 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.071 0.128 0.199 0.000 1.529 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 164 164 59 72 620 2825 0 51 498
normalized size 1 1.00 0.36 0.44 3.78 17.23 0.00 0.31 3.04
time (sec) N/A 0.042 0.052 0.276 0.434 0.652 0.000 0.135 1.485
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 47 60 322 1493 0 39 356
normalized size 1 1.00 0.40 0.51 2.73 12.65 0.00 0.33 3.02
time (sec) N/A 0.032 0.032 0.221 0.487 0.779 0.000 0.116 1.440
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 33 46 120 529 0 27 46
normalized size 1 1.00 0.53 0.74 1.94 8.53 0.00 0.44 0.74
time (sec) N/A 0.023 0.019 0.204 0.511 1.571 0.000 0.130 1.457
Problem 45 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 16 16 16 29 13 81 0 13 71
normalized size 1 1.00 1.00 1.81 0.81 5.06 0.00 0.81 4.44
time (sec) N/A 0.017 0.006 0.228 0.499 0.669 0.000 0.109 1.456
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 24 89 22 253 0 26 -1
normalized size 1 1.00 0.67 2.47 0.61 7.03 0.00 0.72 -0.03
time (sec) N/A 0.016 0.025 0.249 0.440 0.651 0.000 0.111 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 38 230 46 1141 0 50 -1
normalized size 1 1.00 0.44 2.67 0.53 13.27 0.00 0.58 -0.01
time (sec) N/A 0.033 0.040 0.209 0.465 0.811 0.000 0.110 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 55 362 72 2600 0 76 -1
normalized size 1 1.00 0.42 2.74 0.55 19.70 0.00 0.58 -0.01
time (sec) N/A 0.051 0.116 0.219 0.581 0.742 0.000 0.131 0.000
Problem 49 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 32 32 54 63 35 32 0 29 26
normalized size 1 1.00 1.69 1.97 1.09 1.00 0.00 0.91 0.81
time (sec) N/A 0.015 0.122 0.254 0.362 1.426 0.000 0.131 1.553
Problem 50 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 32 32 54 63 35 32 0 29 26
normalized size 1 1.00 1.69 1.97 1.09 1.00 0.00 0.91 0.81
time (sec) N/A 0.015 0.108 0.260 0.343 0.753 0.000 0.140 1.501
Problem 51 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 107 107 136 0 0 569 0 0 -1
normalized size 1 1.00 1.27 0.00 0.00 5.32 0.00 0.00 -0.01
time (sec) N/A 0.127 1.481 0.949 0.000 0.616 0.000 0.000 0.000
Problem 52 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 72 72 100 0 0 467 0 0 -1
normalized size 1 1.00 1.39 0.00 0.00 6.49 0.00 0.00 -0.01
time (sec) N/A 0.042 1.247 0.698 0.000 0.579 0.000 0.000 0.000
Problem 53 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 40 40 80 0 0 386 0 0 -1
normalized size 1 1.00 2.00 0.00 0.00 9.65 0.00 0.00 -0.02
time (sec) N/A 0.020 0.935 2.389 0.000 0.945 0.000 0.000 0.000
Problem 54 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 91 91 118 0 0 561 0 0 -1
normalized size 1 1.00 1.30 0.00 0.00 6.16 0.00 0.00 -0.01
time (sec) N/A 0.087 1.120 0.821 0.000 1.497 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 327 0 0 886 0 0 -1
normalized size 1 1.00 2.66 0.00 0.00 7.20 0.00 0.00 -0.01
time (sec) N/A 0.146 2.450 0.630 0.000 2.454 0.000 0.000 0.000
Problem 56 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 40 40 80 0 0 386 0 0 -1
normalized size 1 1.00 2.00 0.00 0.00 9.65 0.00 0.00 -0.02
time (sec) N/A 0.023 1.009 2.784 0.000 0.582 0.000 0.000 0.000
Problem 57 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 91 91 117 0 0 561 0 0 -1
normalized size 1 1.00 1.29 0.00 0.00 6.16 0.00 0.00 -0.01
time (sec) N/A 0.084 1.098 0.876 0.000 1.281 0.000 0.000 0.000
Problem 58 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 23 23 46 0 0 218 0 0 -1
normalized size 1 1.00 2.00 0.00 0.00 9.48 0.00 0.00 -0.04
time (sec) N/A 0.017 0.736 0.829 0.000 0.460 0.000 0.000 0.000
Problem 59 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 23 23 46 0 0 218 0 0 -1
normalized size 1 1.00 2.00 0.00 0.00 9.48 0.00 0.00 -0.04
time (sec) N/A 0.018 0.716 1.010 0.000 0.464 0.000 0.000 0.000
Problem 60 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 23 23 46 0 0 215 0 0 -1
normalized size 1 1.00 2.00 0.00 0.00 9.35 0.00 0.00 -0.04
time (sec) N/A 0.016 0.689 0.565 0.000 0.432 0.000 0.000 0.000
Problem 61 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 23 23 46 0 0 215 0 0 -1
normalized size 1 1.00 2.00 0.00 0.00 9.35 0.00 0.00 -0.04
time (sec) N/A 0.017 0.685 0.484 0.000 0.436 0.000 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 63 182 71 79 0 66 64
normalized size 1 1.00 1.09 3.14 1.22 1.36 0.00 1.14 1.10
time (sec) N/A 0.071 0.150 0.210 0.313 0.468 0.000 0.143 1.589
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 56 137 59 67 0 50 52
normalized size 1 1.00 1.22 2.98 1.28 1.46 0.00 1.09 1.13
time (sec) N/A 0.071 0.135 0.206 0.315 0.442 0.000 0.141 0.176
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 46 96 47 55 0 40 38
normalized size 1 1.00 1.28 2.67 1.31 1.53 0.00 1.11 1.06
time (sec) N/A 0.060 0.127 0.212 0.309 0.411 0.000 0.126 1.474
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 35 51 31 40 0 26 24
normalized size 1 1.00 1.75 2.55 1.55 2.00 0.00 1.30 1.20
time (sec) N/A 0.047 0.053 0.201 0.316 0.409 0.000 0.127 1.460
Problem 66 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 14 14 27 12 12 8 0 8 10
normalized size 1 1.00 1.93 0.86 0.86 0.57 0.00 0.57 0.71
time (sec) N/A 0.021 0.019 0.116 0.312 0.394 0.000 0.129 0.066
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 37 19 29 31 0 22 26
normalized size 1 1.00 2.18 1.12 1.71 1.82 0.00 1.29 1.53
time (sec) N/A 0.054 0.035 0.098 0.312 0.473 0.000 0.120 0.219
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 70 35 55 77 0 46 60
normalized size 1 1.00 2.69 1.35 2.12 2.96 0.00 1.77 2.31
time (sec) N/A 0.084 0.115 0.110 0.316 0.420 0.000 0.122 1.645
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 81 53 81 130 0 50 63
normalized size 1 1.00 2.19 1.43 2.19 3.51 0.00 1.35 1.70
time (sec) N/A 0.064 0.328 0.128 0.320 0.417 0.000 0.125 1.685
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 508 92 234 1440 0 169 239
normalized size 1 1.00 4.66 0.84 2.15 13.21 0.00 1.55 2.19
time (sec) N/A 0.128 6.244 0.493 0.325 0.436 0.000 0.125 0.210
Problem 71 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 75 75 118 66 136 769 0 122 170
normalized size 1 1.00 1.57 0.88 1.81 10.25 0.00 1.63 2.27
time (sec) N/A 0.051 0.872 0.414 0.327 0.422 0.000 0.139 0.150
Problem 72 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 34 34 61 37 44 222 0 59 74
normalized size 1 1.00 1.79 1.09 1.29 6.53 0.00 1.74 2.18
time (sec) N/A 0.031 0.222 0.317 0.315 0.418 0.000 0.121 1.480
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 43 20 19 44 0 32 42
normalized size 1 1.00 2.53 1.18 1.12 2.59 0.00 1.88 2.47
time (sec) N/A 0.010 0.011 0.023 0.312 0.406 0.000 0.112 0.066
Problem 74 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 54 54 64 87 85 186 0 84 121
normalized size 1 1.00 1.19 1.61 1.57 3.44 0.00 1.56 2.24
time (sec) N/A 0.059 0.109 0.202 0.415 0.415 0.000 0.144 0.328
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 142 238 187 645 0 161 269
normalized size 1 1.00 1.41 2.36 1.85 6.39 0.00 1.59 2.66
time (sec) N/A 0.158 0.394 0.321 0.408 0.422 0.000 0.155 1.948
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 213 822 373 2094 0 293 -1
normalized size 1 1.00 1.31 5.04 2.29 12.85 0.00 1.80 -0.01
time (sec) N/A 0.316 0.930 0.342 0.419 0.459 0.000 0.161 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 104 262 157 807 0 155 199
normalized size 1 1.00 0.97 2.45 1.47 7.54 0.00 1.45 1.86
time (sec) N/A 0.458 0.430 0.161 0.408 0.427 0.000 0.139 1.826
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 82 174 116 456 0 115 157
normalized size 1 1.00 1.02 2.18 1.45 5.70 0.00 1.44 1.96
time (sec) N/A 0.288 0.132 0.171 0.405 0.422 0.000 0.135 1.668
Problem 79 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 57 57 61 92 84 238 0 86 129
normalized size 1 1.00 1.07 1.61 1.47 4.18 0.00 1.51 2.26
time (sec) N/A 0.107 0.106 0.165 0.401 0.420 0.000 0.133 1.579
Problem 80 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 37 37 45 35 54 111 0 56 49
normalized size 1 1.00 1.22 0.95 1.46 3.00 0.00 1.51 1.32
time (sec) N/A 0.066 0.026 0.084 0.403 0.396 0.000 0.136 1.516
Problem 81 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 50 50 58 49 83 156 0 82 287
normalized size 1 1.00 1.16 0.98 1.66 3.12 0.00 1.64 5.74
time (sec) N/A 0.115 0.051 0.094 0.406 0.440 0.000 0.147 1.685
Problem 82 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 59 59 71 73 100 345 0 98 292
normalized size 1 1.00 1.20 1.24 1.69 5.85 0.00 1.66 4.95
time (sec) N/A 0.160 0.289 0.098 0.422 0.434 0.000 0.150 1.728
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 124 108 158 947 0 141 617
normalized size 1 1.00 1.49 1.30 1.90 11.41 0.00 1.70 7.43
time (sec) N/A 0.292 0.481 0.105 0.415 0.526 0.000 0.156 2.094
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 32 170 42 43 0 38 41
normalized size 1 1.00 0.84 4.47 1.11 1.13 0.00 1.00 1.08
time (sec) N/A 0.128 0.034 0.165 0.304 0.410 0.000 0.138 1.551
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 15 39 36 0 35 39
normalized size 1 1.00 1.00 0.79 2.05 1.89 0.00 1.84 2.05
time (sec) N/A 0.106 0.010 0.107 0.302 0.404 0.000 0.140 0.142
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 84 30 31 0 26 29
normalized size 1 1.00 1.00 4.20 1.50 1.55 0.00 1.30 1.45
time (sec) N/A 0.092 0.031 0.120 0.301 0.464 0.000 0.142 1.463
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 20 21 28 0 25 12
normalized size 1 1.00 1.00 1.25 1.31 1.75 0.00 1.56 0.75
time (sec) N/A 0.058 0.010 0.120 0.302 0.596 0.000 0.119 0.093
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 20 43 41 53 0 53 46
normalized size 1 1.00 0.71 1.54 1.46 1.89 0.00 1.89 1.64
time (sec) N/A 0.080 0.029 0.182 0.303 0.405 0.000 0.137 0.229
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 64 49 81 33 0 27 31
normalized size 1 1.00 3.37 2.58 4.26 1.74 0.00 1.42 1.63
time (sec) N/A 0.111 0.056 0.202 0.308 0.392 0.000 0.139 1.573
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 32 89 92 145 0 94 122
normalized size 1 1.00 0.80 2.22 2.30 3.62 0.00 2.35 3.05
time (sec) N/A 0.130 0.062 0.205 0.307 0.412 0.000 0.125 1.950
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 96 93 257 69 0 55 207
normalized size 1 1.00 3.31 3.21 8.86 2.38 0.00 1.90 7.14
time (sec) N/A 0.121 0.111 0.203 0.307 0.524 0.000 0.130 1.924
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 97 600 242 1398 0 194 228
normalized size 1 1.00 0.95 5.88 2.37 13.71 0.00 1.90 2.24
time (sec) N/A 0.198 0.287 0.141 0.317 0.555 0.000 0.129 2.067
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 125 125 180 486 217 924 0 221 247
normalized size 1 1.00 1.44 3.89 1.74 7.39 0.00 1.77 1.98
time (sec) N/A 0.378 1.207 0.149 0.409 0.590 0.000 0.136 2.024
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 56 274 127 476 0 97 121
normalized size 1 1.00 0.98 4.81 2.23 8.35 0.00 1.70 2.12
time (sec) N/A 0.160 0.111 0.144 0.316 0.665 0.000 0.125 1.684
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 80 172 122 304 0 121 159
normalized size 1 1.00 1.04 2.23 1.58 3.95 0.00 1.57 2.06
time (sec) N/A 0.206 0.223 0.136 0.403 0.764 0.000 0.135 1.693
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 19 31 48 80 0 39 20
normalized size 1 1.00 0.95 1.55 2.40 4.00 0.00 1.95 1.00
time (sec) N/A 0.080 0.013 0.124 0.308 0.634 0.000 0.141 0.084
Problem 97 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 64 64 36 84 66 57 0 89 93
normalized size 1 1.00 0.56 1.31 1.03 0.89 0.00 1.39 1.45
time (sec) N/A 0.111 0.059 0.149 0.404 0.565 0.000 0.145 2.357
Problem 98 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 60 60 67 81 91 256 0 85 133
normalized size 1 1.00 1.12 1.35 1.52 4.27 0.00 1.42 2.22
time (sec) N/A 0.142 0.184 0.171 0.408 1.331 0.000 0.154 1.659
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 78 275 161 675 0 218 256
normalized size 1 1.00 0.82 2.89 1.69 7.11 0.00 2.29 2.69
time (sec) N/A 0.220 0.156 0.194 0.411 0.640 0.000 0.138 2.994
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 114 170 226 1155 0 174 269
normalized size 1 1.00 1.10 1.63 2.17 11.11 0.00 1.67 2.59
time (sec) N/A 0.270 0.629 0.180 0.418 1.555 0.000 0.176 1.793
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 138 1168 348 2778 0 374 513
normalized size 1 1.00 0.93 7.84 2.34 18.64 0.00 2.51 3.44
time (sec) N/A 0.341 0.284 0.195 0.428 1.578 0.000 0.141 5.507
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 75 155 144 299 0 120 274
normalized size 1 1.00 0.69 1.42 1.32 2.74 0.00 1.10 2.51
time (sec) N/A 0.086 0.203 0.251 0.328 1.372 0.000 0.148 4.105
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 126 99 96 123 0 62 237
normalized size 1 1.00 2.42 1.90 1.85 2.37 0.00 1.19 4.56
time (sec) N/A 0.093 0.135 0.253 0.317 1.017 0.000 0.128 2.218
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 61 109 96 185 0 98 140
normalized size 1 1.00 0.79 1.42 1.25 2.40 0.00 1.27 1.82
time (sec) N/A 0.067 0.124 0.250 0.317 1.974 0.000 0.124 0.577
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 71 67 42 51 0 38 85
normalized size 1 1.00 1.97 1.86 1.17 1.42 0.00 1.06 2.36
time (sec) N/A 0.073 0.087 0.211 0.314 1.458 0.000 0.126 1.634
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 39 65 45 71 0 55 50
normalized size 1 1.00 0.87 1.44 1.00 1.58 0.00 1.22 1.11
time (sec) N/A 0.048 0.040 0.209 0.311 1.217 0.000 0.123 0.225
Problem 107 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 17 15 11 0 13 14
normalized size 1 1.00 1.00 1.31 1.15 0.85 0.00 1.00 1.08
time (sec) N/A 0.023 0.008 0.118 0.303 1.307 0.000 0.144 1.463
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 13 27 20 16 0 17 21
normalized size 1 1.00 1.18 2.45 1.82 1.45 0.00 1.55 1.91
time (sec) N/A 0.038 0.036 0.116 0.310 1.970 0.000 0.122 0.178
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 12 36 40 0 38 27
normalized size 1 1.00 1.00 1.00 3.00 3.33 0.00 3.17 2.25
time (sec) N/A 0.039 0.011 0.092 0.307 0.732 0.000 0.128 1.571
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 65 61 55 85 0 48 56
normalized size 1 1.00 2.41 2.26 2.04 3.15 0.00 1.78 2.07
time (sec) N/A 0.056 0.037 0.182 0.309 1.062 0.000 0.130 1.640
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 30 78 75 97 0 68 81
normalized size 1 1.00 1.00 2.60 2.50 3.23 0.00 2.27 2.70
time (sec) N/A 0.046 0.015 0.233 0.310 2.108 0.000 0.144 1.682
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 129 95 96 154 0 77 106
normalized size 1 1.00 3.00 2.21 2.23 3.58 0.00 1.79 2.47
time (sec) N/A 0.075 0.042 0.247 0.309 0.572 0.000 0.126 1.862
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 194 194 253 1323 383 4025 0 432 611
normalized size 1 1.00 1.30 6.82 1.97 20.75 0.00 2.23 3.15
time (sec) N/A 0.255 0.506 0.227 0.432 3.045 0.000 0.163 7.041
Problem 114 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 183 183 141 207 261 1746 0 215 707
normalized size 1 1.00 0.77 1.13 1.43 9.54 0.00 1.17 3.86
time (sec) N/A 0.384 0.744 0.203 0.409 0.637 0.000 0.149 3.429
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 191 324 172 965 0 234 335
normalized size 1 1.00 1.69 2.87 1.52 8.54 0.00 2.07 2.96
time (sec) N/A 0.163 0.201 0.189 0.419 0.867 0.000 0.130 4.011
Problem 116 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 100 100 82 95 108 349 0 102 376
normalized size 1 1.00 0.82 0.95 1.08 3.49 0.00 1.02 3.76
time (sec) N/A 0.221 0.332 0.178 0.416 0.688 0.000 0.162 2.471
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 63 108 74 75 0 89 132
normalized size 1 1.00 1.03 1.77 1.21 1.23 0.00 1.46 2.16
time (sec) N/A 0.099 0.062 0.180 0.409 1.261 0.000 0.128 2.526
Problem 118 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 19 19 11 21 28 27 0 22 25
normalized size 1 1.00 0.58 1.11 1.47 1.42 0.00 1.16 1.32
time (sec) N/A 0.032 0.008 0.114 0.317 0.602 0.000 0.126 0.099
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 65 110 90 141 0 89 316
normalized size 1 1.00 1.14 1.93 1.58 2.47 0.00 1.56 5.54
time (sec) N/A 0.178 0.085 0.126 0.415 0.629 0.000 0.158 0.344
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 37 106 82 199 0 80 261
normalized size 1 1.00 1.16 3.31 2.56 6.22 0.00 2.50 8.16
time (sec) N/A 0.072 0.053 0.144 0.316 0.614 0.000 0.126 1.840
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 151 207 178 831 0 161 378
normalized size 1 1.00 1.72 2.35 2.02 9.44 0.00 1.83 4.30
time (sec) N/A 0.332 0.588 0.148 0.428 1.719 0.000 0.151 2.623
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 83 219 190 1288 0 170 155
normalized size 1 1.00 1.19 3.13 2.71 18.40 0.00 2.43 2.21
time (sec) N/A 0.094 0.135 0.153 0.327 0.887 0.000 0.128 1.975
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 269 360 330 3160 0 305 543
normalized size 1 1.00 1.47 1.97 1.80 17.27 0.00 1.67 2.97
time (sec) N/A 0.337 1.579 0.167 0.418 2.180 0.000 0.142 2.898
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 130 388 364 4024 0 295 317
normalized size 1 1.00 1.09 3.26 3.06 33.82 0.00 2.48 2.66
time (sec) N/A 0.141 0.259 0.161 0.334 0.714 0.000 0.153 2.182
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 199 199 84 91 386 592 0 90 413
normalized size 1 1.00 0.42 0.46 1.94 2.97 0.00 0.45 2.08
time (sec) N/A 0.303 0.082 0.636 0.420 0.635 0.000 0.154 1.595
Problem 126 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 147 147 72 80 209 315 0 77 91
normalized size 1 1.00 0.49 0.54 1.42 2.14 0.00 0.52 0.62
time (sec) N/A 0.171 0.067 0.607 0.416 1.977 0.000 0.149 1.530
Problem 127 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 58 58 56 69 84 121 0 64 78
normalized size 1 1.00 0.97 1.19 1.45 2.09 0.00 1.10 1.34
time (sec) N/A 0.118 0.045 0.601 0.422 1.060 0.000 0.130 1.549
Problem 128 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 46 46 44 68 39 42 0 48 -1
normalized size 1 1.00 0.96 1.48 0.85 0.91 0.00 1.04 -0.02
time (sec) N/A 0.091 0.037 0.704 0.415 0.451 0.000 0.156 0.000
Problem 129 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 74 74 48 106 36 66 0 71 -1
normalized size 1 1.00 0.65 1.43 0.49 0.89 0.00 0.96 -0.01
time (sec) N/A 0.115 0.051 0.542 0.415 0.594 0.000 0.127 0.000
Problem 130 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 162 162 76 216 62 126 0 204 -1
normalized size 1 1.00 0.47 1.33 0.38 0.78 0.00 1.26 -0.01
time (sec) N/A 0.153 0.066 0.540 0.419 0.609 0.000 0.146 0.000
Problem 131 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 250 250 106 326 90 218 0 278 -1
normalized size 1 1.00 0.42 1.30 0.36 0.87 0.00 1.11 -0.00
time (sec) N/A 0.200 0.104 0.544 0.423 2.046 0.000 0.174 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 80 125 0 0 0 0 -1
normalized size 1 1.00 0.99 1.54 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.068 0.179 0.209 0.000 2.017 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 44 39 46 48 0 0 42
normalized size 1 1.00 1.47 1.30 1.53 1.60 0.00 0.00 1.40
time (sec) N/A 0.045 0.050 0.145 0.475 1.213 0.000 0.000 2.153
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 60 127 0 0 0 0 -1
normalized size 1 1.00 0.50 1.07 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.086 0.116 0.158 0.000 1.990 0.000 0.000 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 74 97 0 92 0 0 -1
normalized size 1 1.00 1.07 1.41 0.00 1.33 0.00 0.00 -0.01
time (sec) N/A 0.058 0.144 0.186 0.000 1.664 0.000 0.000 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 57 109 0 0 0 0 -1
normalized size 1 1.00 0.95 1.82 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.041 0.109 0.147 0.000 0.971 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 77 0 0 86 0 0 -1
normalized size 1 1.00 1.28 0.00 0.00 1.43 0.00 0.00 -0.02
time (sec) N/A 0.035 0.090 0.143 0.000 0.709 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 43 90 0 0 0 0 -1
normalized size 1 1.00 0.93 1.96 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.032 0.075 0.287 0.000 0.607 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 54 0 0 43 0 0 -1
normalized size 1 1.00 1.32 0.00 0.00 1.05 0.00 0.00 -0.02
time (sec) N/A 0.046 0.118 0.140 0.000 0.465 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 58 126 0 0 0 0 -1
normalized size 1 1.00 0.78 1.70 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.066 0.096 0.161 0.000 0.457 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 33 38 89 37 0 0 58
normalized size 1 1.00 1.32 1.52 3.56 1.48 0.00 0.00 2.32
time (sec) N/A 0.041 0.040 0.136 0.428 0.461 0.000 0.000 1.471
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 60 112 0 0 0 0 -1
normalized size 1 1.00 0.94 1.75 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.055 0.099 0.137 0.000 0.593 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 128 128 95 121 0 110 0 0 -1
normalized size 1 1.00 0.74 0.95 0.00 0.86 0.00 0.00 -0.01
time (sec) N/A 0.080 0.208 0.214 0.000 0.426 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 80 133 0 0 0 0 -1
normalized size 1 1.00 0.68 1.13 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.078 0.176 0.155 0.000 0.459 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 44 47 46 56 0 0 42
normalized size 1 1.00 1.47 1.57 1.53 1.87 0.00 0.00 1.40
time (sec) N/A 0.041 0.052 0.136 0.467 1.028 0.000 0.000 1.555
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 63 140 0 0 0 0 -1
normalized size 1 1.00 0.39 0.86 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.100 0.127 0.150 0.000 0.539 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 87 113 0 102 0 0 -1
normalized size 1 1.00 0.91 1.18 0.00 1.06 0.00 0.00 -0.01
time (sec) N/A 0.067 0.184 0.186 0.000 0.622 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 65 124 0 0 0 0 -1
normalized size 1 1.00 0.76 1.44 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.063 0.128 0.148 0.000 0.565 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 88 0 0 94 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 1.03 0.00 0.00 -0.01
time (sec) N/A 0.073 0.162 0.149 0.000 0.658 0.000 0.000 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 60 152 0 0 0 0 -1
normalized size 1 1.00 0.46 1.17 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.073 0.115 0.159 0.000 0.429 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 63 130 0 106 0 0 -1
normalized size 1 1.00 0.66 1.35 0.00 1.10 0.00 0.00 -0.01
time (sec) N/A 0.046 0.096 0.191 0.000 0.492 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 54 163 0 0 0 0 -1
normalized size 1 1.00 0.81 2.43 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.037 0.098 0.414 0.000 1.306 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F B A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 33 0 87 29 0 0 29
normalized size 1 1.00 1.22 0.00 3.22 1.07 0.00 0.00 1.07
time (sec) N/A 0.039 0.035 0.152 0.464 0.473 0.000 0.000 1.474
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F(-1) 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 0.054 0.108 0.138 0.000 0.491 0.000 0.000 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 53 0 0 78 0 0 -1
normalized size 1 1.00 0.77 0.00 0.00 1.13 0.00 0.00 -0.01
time (sec) N/A 0.061 0.107 0.147 0.000 0.730 0.000 0.000 0.000
Problem 156 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 62 62 62 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 0.055 1.201 0.369 0.000 0.463 0.000 0.000 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 68 68 126 0 0 0 0 0 -1
normalized size 1 1.00 1.85 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.065 4.320 1.782 0.000 0.493 0.000 0.000 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 69 69 101 0 0 0 0 0 -1
normalized size 1 1.00 1.46 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.069 5.097 2.109 0.000 0.716 0.000 0.000 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 68 68 200 0 0 0 0 0 -1
normalized size 1 1.00 2.94 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.069 9.024 1.813 0.000 0.478 0.000 0.000 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A C B B F B B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 42 137 30 509 95 187 0 215 65
normalized size 1 3.26 0.71 12.12 2.26 4.45 0.00 5.12 1.55
time (sec) N/A 0.135 0.424 1.109 0.706 1.576 0.000 0.548 1.520
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F B A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 62 0 76 48 0 38 48
normalized size 1 1.00 2.38 0.00 2.92 1.85 0.00 1.46 1.85
time (sec) N/A 0.039 0.127 0.529 0.315 0.585 0.000 0.145 1.647
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 65 0 49 49 0 39 36
normalized size 1 1.00 2.50 0.00 1.88 1.88 0.00 1.50 1.38
time (sec) N/A 0.046 0.112 0.728 0.354 0.409 0.000 0.111 1.592
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 90 90 115 0 0 475 0 0 -1
normalized size 1 1.00 1.28 0.00 0.00 5.28 0.00 0.00 -0.01
time (sec) N/A 0.087 6.756 0.513 0.000 0.487 0.000 0.000 0.000
Problem 164 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 66 66 64 0 0 539 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 8.17 0.00 0.00 -0.02
time (sec) N/A 0.075 0.918 0.513 0.000 1.133 0.000 0.000 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 54 23 22 65 0 145 43
normalized size 1 1.00 2.70 1.15 1.10 3.25 0.00 7.25 2.15
time (sec) N/A 0.018 0.062 0.087 0.307 0.603 0.000 0.579 1.620
Problem 166 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 19 19 19 20 29 71 0 28 25
normalized size 1 1.00 1.00 1.05 1.53 3.74 0.00 1.47 1.32
time (sec) N/A 0.027 0.072 0.327 0.326 0.677 0.000 0.155 1.438
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 81 51 150 643 0 210 140
normalized size 1 1.00 1.47 0.93 2.73 11.69 0.00 3.82 2.55
time (sec) N/A 0.045 0.063 0.329 0.362 1.349 0.000 0.190 1.489
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 56 36 92 272 0 47 55
normalized size 1 1.00 1.33 0.86 2.19 6.48 0.00 1.12 1.31
time (sec) N/A 0.033 0.068 0.302 0.335 0.441 0.000 0.161 1.454
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 135 84 232 1806 0 248 318
normalized size 1 1.00 1.52 0.94 2.61 20.29 0.00 2.79 3.57
time (sec) N/A 0.070 0.063 0.313 0.353 0.513 0.000 0.223 1.477
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 84 144 0 0 0 0 -1
normalized size 1 1.00 0.76 1.30 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.068 0.223 0.485 0.000 0.408 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 80 212 0 0 0 0 -1
normalized size 1 1.00 0.75 1.98 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.063 0.115 0.550 0.000 0.478 0.000 0.000 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 66 120 0 0 0 0 -1
normalized size 1 1.00 0.92 1.67 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.043 0.097 0.344 0.000 0.432 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 68 146 0 0 0 0 -1
normalized size 1 1.00 0.94 2.03 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.044 0.082 0.587 0.000 0.460 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 86 143 0 0 0 0 -1
normalized size 1 1.00 0.77 1.29 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.060 0.135 0.452 0.000 0.448 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 95 227 0 0 0 0 -1
normalized size 1 1.00 0.86 2.05 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.061 0.190 0.688 0.000 0.453 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 [114] had the largest ratio of [.6923]

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 6 0.167
2 A 2 2 1.00 8 0.250
3 A 2 2 1.00 8 0.250
4 A 2 1 1.00 8 0.125
5 A 3 2 1.00 8 0.250
6 A 2 1 1.00 8 0.125
7 A 3 3 1.00 10 0.300
8 A 3 3 1.00 10 0.300
9 A 2 2 1.00 10 0.200
10 A 2 2 1.00 10 0.200
11 A 3 3 1.00 10 0.300
12 A 3 3 1.00 10 0.300
13 A 4 3 1.00 12 0.250
14 A 3 3 1.00 12 0.250
15 A 3 3 1.00 12 0.250
16 A 2 2 1.00 12 0.167
17 A 2 2 1.00 12 0.167
18 A 3 3 1.00 12 0.250
19 A 3 3 1.00 12 0.250
20 A 4 3 1.00 12 0.250
21 A 2 2 1.00 10 0.200
22 A 4 3 1.00 10 0.300
23 A 3 3 1.00 10 0.300
24 A 2 2 1.00 10 0.200
25 A 2 2 1.00 10 0.200
26 A 3 3 1.00 10 0.300
27 A 4 3 1.00 10 0.300
28 A 5 3 1.00 10 0.300
29 A 5 4 1.00 10 0.400
30 A 4 4 1.00 10 0.400
31 A 3 3 1.00 10 0.300
32 A 2 2 1.00 10 0.200
33 A 3 3 1.00 10 0.300
34 A 4 3 1.00 10 0.300
35 A 5 3 1.00 10 0.300
36 A 7 4 1.00 10 0.400
37 A 5 4 1.00 10 0.400
38 A 4 4 1.07 10 0.400
39 A 4 4 1.00 10 0.400
40 A 5 4 1.00 10 0.400
41 A 7 4 1.00 10 0.400
42 A 3 2 1.00 10 0.200
43 A 3 2 1.00 10 0.200
44 A 3 2 1.00 10 0.200
45 A 3 3 1.00 10 0.300
46 A 3 3 1.00 10 0.300
47 A 5 3 1.00 10 0.300
48 A 7 3 1.00 10 0.300
49 A 2 2 1.00 15 0.133
50 A 2 2 1.00 15 0.133
51 A 5 5 1.00 17 0.294
52 A 4 4 1.00 17 0.235
53 A 2 2 1.00 17 0.118
54 A 5 4 1.00 17 0.235
55 A 6 5 1.00 17 0.294
56 A 2 2 1.00 17 0.118
57 A 5 4 1.00 17 0.235
58 A 2 2 1.00 12 0.167
59 A 2 2 1.00 12 0.167
60 A 2 2 1.00 12 0.167
61 A 2 2 1.00 12 0.167
62 A 7 5 1.00 13 0.385
63 A 6 5 1.00 13 0.385
64 A 5 5 1.00 13 0.385
65 A 4 4 1.00 11 0.364
66 A 1 1 1.00 11 0.091
67 A 3 3 1.00 13 0.231
68 A 4 4 1.00 13 0.308
69 A 6 6 1.00 13 0.462
70 A 6 5 1.00 12 0.417
71 A 5 4 1.00 12 0.333
72 A 4 4 1.00 12 0.333
73 A 2 1 1.00 10 0.100
74 A 4 4 1.00 12 0.333
75 A 6 6 1.00 12 0.500
76 A 7 7 1.00 12 0.583
77 A 8 7 1.00 13 0.538
78 A 7 7 1.00 13 0.538
79 A 6 6 1.00 11 0.546
80 A 4 4 1.00 11 0.364
81 A 6 6 1.00 13 0.462
82 A 7 7 1.00 13 0.538
83 A 8 8 1.00 13 0.615
84 A 7 7 1.00 13 0.538
85 A 6 4 1.00 13 0.308
86 A 5 5 1.00 13 0.385
87 A 4 3 1.00 11 0.273
88 A 6 6 1.00 11 0.546
89 A 6 5 1.00 13 0.385
90 A 7 7 1.00 13 0.538
91 A 7 6 1.00 13 0.462
92 A 5 4 1.00 13 0.308
93 A 7 6 1.00 13 0.462
94 A 5 4 1.00 13 0.308
95 A 6 6 1.00 13 0.462
96 A 5 4 1.00 11 0.364
97 A 4 3 1.00 11 0.273
98 A 6 6 1.00 13 0.462
99 A 6 5 1.00 13 0.385
100 A 7 6 1.00 13 0.462
101 A 7 5 1.00 13 0.385
102 A 3 2 1.00 13 0.154
103 A 5 3 1.00 13 0.231
104 A 3 2 1.00 13 0.154
105 A 4 3 1.00 13 0.231
106 A 3 2 1.00 11 0.182
107 A 2 2 1.00 11 0.182
108 A 3 2 1.00 13 0.154
109 A 3 2 1.00 13 0.154
110 A 4 3 1.00 13 0.231
111 A 3 2 1.00 13 0.154
112 A 5 3 1.00 13 0.231
113 A 11 7 1.00 13 0.538
114 A 16 9 1.00 13 0.692
115 A 8 6 1.00 13 0.462
116 A 10 9 1.00 13 0.692
117 A 6 5 1.00 11 0.454
118 A 4 4 1.00 11 0.364
119 A 8 8 1.00 13 0.615
120 A 3 2 1.00 13 0.154
121 A 7 7 1.00 13 0.538
122 A 3 2 1.00 13 0.154
123 A 16 9 1.00 13 0.692
124 A 3 2 1.00 13 0.154
125 A 6 5 1.00 25 0.200
126 A 6 5 1.00 25 0.200
127 A 4 4 1.00 25 0.160
128 A 4 4 1.00 25 0.160
129 A 5 4 1.00 25 0.160
130 A 6 5 1.00 25 0.200
131 A 6 5 1.00 25 0.200
132 A 6 6 1.00 15 0.400
133 A 3 3 1.00 15 0.200
134 A 9 9 1.00 15 0.600
135 A 6 6 1.00 15 0.400
136 A 5 5 1.00 13 0.385
137 A 6 6 1.00 11 0.546
138 A 3 2 1.00 15 0.133
139 A 5 5 1.00 15 0.333
140 A 7 7 1.00 15 0.467
141 A 3 3 1.00 15 0.200
142 A 5 5 1.00 15 0.333
143 A 8 7 1.00 15 0.467
144 A 7 6 1.00 15 0.400
145 A 3 3 1.00 15 0.200
146 A 10 9 1.00 15 0.600
147 A 7 6 1.00 15 0.400
148 A 6 5 1.00 15 0.333
149 A 7 6 1.00 15 0.400
150 A 9 8 1.00 13 0.615
151 A 7 7 1.00 11 0.636
152 A 4 3 1.00 15 0.200
153 A 3 3 1.00 15 0.200
154 A 5 5 1.00 15 0.333
155 A 6 6 1.00 15 0.400
156 A 4 4 1.00 11 0.364
157 A 4 4 1.00 13 0.308
158 A 4 4 1.00 13 0.308
159 A 4 4 1.00 13 0.308
160 C 9 4 3.26 45 0.089
161 A 3 3 1.00 15 0.200
162 A 4 4 1.00 15 0.267
163 A 3 3 1.00 20 0.150
164 A 3 3 1.00 21 0.143
165 A 2 1 1.00 15 0.067
166 A 3 2 1.00 17 0.118
167 A 3 2 1.00 17 0.118
168 A 3 1 1.00 17 0.059
169 A 4 2 1.00 17 0.118
170 A 4 3 1.00 19 0.158
171 A 4 3 1.00 19 0.158
172 A 3 2 1.00 19 0.105
173 A 3 2 1.00 19 0.105
174 A 4 3 1.00 19 0.158
175 A 4 3 1.00 19 0.158

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