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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

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

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, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 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, 76, 77, 79, 87, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 130, 131, 132, 133, 134, 135, 136, 137, 140, 141, 142, 143, 144, 145, 146, 147, 150, 151, 152, 153, 154, 155, 156, 159, 160, 161, 162, 163, 164, 165, 168, 169, 170, 171, 172, 173, 174, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190 }

B grade: { 45 }

C grade: { 19, 21, 23, 74, 75, 78, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 100, 101, 102, 103, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 138, 139, 148, 149, 157, 158, 166, 167, 175, 176 }

F grade: { 118, 126, 177, 178, 179 }

2.1.3 Maple

A grade: { 1, 2, 3, 5, 6, 7, 8, 9, 11, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 39, 40, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 69, 70, 72, 73, 74, 75, 76, 77, 79, 82, 83, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 133, 134, 135, 136, 137, 142, 143, 144, 145, 146, 153, 154, 155, 156, 162, 163, 164, 165, 171, 172, 173, 174, 180, 182, 183, 184, 185, 189 }

B grade: { 4, 33, 35, 38, 42, 44, 46, 47, 48, 49, 50, 61, 62, 66, 67, 68, 80, 81, 84, 85, 86, 117, 124, 125 }

C grade: { 78, 110, 111, 112, 113, 114, 115, 116, 118, 119, 120, 121, 122, 123, 126, 127, 128, 129 }

F grade: { 10, 12, 14, 43, 45, 71, 130, 131, 132, 138, 139, 140, 141, 147, 148, 149, 150, 151, 152, 157, 158, 159, 160, 161, 166, 167, 168, 169, 170, 175, 176, 177, 178, 179, 181, 186, 187, 188, 190 }

2.1.4 Maxima

A grade: { 4, 7, 16, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 35, 38, 47, 51, 52, 53, 57, 58, 59, 63, 64, 65, 69, 70, 72, 73, 74, 75, 76, 77, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 100, 101, 102, 103, 104, 105, 106, 107, 133, 134, 135, 136, 137, 142, 143, 144, 145, 146, 147, 153, 154, 155, 156, 162, 163, 164, 165, 171, 172, 173, 174, 180, 181, 182, 183, 184, 185, 189, 190 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 26, 33, 34, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 54, 55, 56, 60, 61, 62, 66, 67, 68, 71, 78, 79, 80, 81, 82, 83, 84, 85, 86, 98, 99, 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, 138, 139, 140, 141, 148, 149, 150, 151, 152, 157, 158, 159, 160, 161, 166, 167, 168, 169, 170, 175, 176, 177, 178, 179, 186, 187, 188 }

2.1.5 FriCAS

A grade: { 2, 8, 9, 16, 17, 18, 19, 20, 22, 27, 28, 29, 30, 31, 32, 39, 40, 41, 48, 49, 50, 51, 52, 53, 57, 58, 59, 63, 64, 65, 69, 70, 72, 73, 87, 88, 92, 93, 94, 95, 96, 97, 100, 104, 105, 106, 107, 130, 131, 133, 134, 135, 136, 137, 140, 142, 143, 144, 145, 146, 147, 150, 153, 154, 155, 156, 162, 163, 164, 165, 171, 172, 173, 174, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190 }

B grade: { 4, 7, 21, 23, 24, 25, 33, 35, 38, 47, 74, 75, 76, 77, 79, 80, 89, 90, 91, 101, 102, 103, 117, 124, 125, 132, 141, 151, 152, 159, 160, 161, 168, 169, 170, 188 }

C grade: { }

F grade: { 1, 3, 5, 6, 10, 11, 12, 13, 14, 15, 26, 34, 36, 37, 42, 43, 44, 45, 46, 54, 55, 56, 60, 61, 62, 66, 67, 68, 71, 78, 81, 82, 83, 84, 85, 86, 98, 99, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 119, 120, 121, 122, 123, 126, 127, 128, 129, 138, 139, 148, 149, 157, 158, 166, 167, 175, 176, 177, 178, 179 }

2.1.6 Sympy

A grade: { 4, 20, 22, 24, 35, 51, 52, 53, 57, 58, 59, 63, 64, 65, 69, 70, 72, 73, 87, 95, 96, 97, 106, 107, 133, 134, 135, 136, 137, 142, 143, 144, 145, 146, 147, 153, 154, 155, 156, 162, 164, 165, 180, 183, 184, 185, 189, 190 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 54, 55, 56, 60, 61, 62, 66, 67, 68, 71, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 93, 94, 98, 99, 100, 101, 102, 103, 104, 105, 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, 138, 139, 140, 141, 148, 149, 150, 151, 152, 157, 158, 159, 160, 161, 163, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 182, 186, 187, 188 }

2.1.7 Giac

A grade: { 51, 52, 53, 57, 58, 59, 63, 64, 65, 69, 70, 72, 73, 87, 133, 134, 135, 136, 137, 142, 143, 144, 145, 146, 147, 153, 154, 155, 156, 162, 163, 164, 165, 171, 172, 173, 174, 180, 181, 182, 183, 184, 185, 189, 190 }

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, 54, 55, 56, 60, 61, 62, 66, 67, 68, 71, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 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, 138, 139, 140, 141, 148, 149, 150, 151, 152, 157, 158, 159, 160, 161, 166, 167, 168, 169, 170, 175, 176, 177, 178, 179, 186, 187, 188 }

2.1.8 Mupad

A grade: { 51, 52, 53, 57, 58, 59, 63, 64, 65, 69, 70, 72, 73, 87, 133, 134, 135, 136, 137, 142, 143, 144, 145, 146, 147, 153, 154, 155, 156, 162, 163, 164, 165, 171, 172, 173, 174, 180, 181, 182, 183, 184, 185, 189, 190 }

B grade: { 24, 25, 27, 28, 76, 77, 91 }

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, 26, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 54, 55, 56, 60, 61, 62, 66, 67, 68, 71, 74, 75, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 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, 138, 139, 140, 141, 148, 149, 150, 151, 152, 157, 158, 159, 160, 161, 166, 167, 168, 169, 170, 175, 176, 177, 178, 179, 186, 187, 188 }

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 F(-1) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 164 164 182 289 0 0 0 0 -1
normalized size 1 1.00 1.11 1.76 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.124 0.464 0.946 0.000 0.583 0.000 0.000 0.000
Problem 2 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 104 104 77 151 0 125 0 0 -1
normalized size 1 1.00 0.74 1.45 0.00 1.20 0.00 0.00 -0.01
time (sec) N/A 0.088 0.118 0.798 0.000 0.608 0.000 0.000 0.000
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 117 117 138 240 0 0 0 0 -1
normalized size 1 1.00 1.18 2.05 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.097 0.254 0.715 0.000 0.689 0.000 0.000 0.000
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 53 101 40 106 42 0 -1
normalized size 1 1.00 1.00 1.91 0.75 2.00 0.79 0.00 -0.02
time (sec) N/A 0.057 0.065 0.612 0.329 0.625 0.993 0.000 0.000
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 63 63 90 190 0 0 0 0 -1
normalized size 1 1.00 1.43 3.02 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.055 0.200 0.336 0.000 0.527 0.000 0.000 0.000
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 64 64 63 136 0 0 0 0 -1
normalized size 1 1.00 0.98 2.12 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.092 0.036 0.141 0.000 0.678 0.000 0.000 0.000
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 42 61 35 97 0 0 -1
normalized size 1 1.00 0.86 1.24 0.71 1.98 0.00 0.00 -0.02
time (sec) N/A 0.048 0.100 0.119 0.328 0.474 0.000 0.000 0.000
Problem 8 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 90 90 54 77 0 106 0 0 -1
normalized size 1 1.00 0.60 0.86 0.00 1.18 0.00 0.00 -0.01
time (sec) N/A 0.059 0.044 0.123 0.000 0.562 0.000 0.000 0.000
Problem 9 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 102 102 73 112 0 116 0 0 -1
normalized size 1 1.00 0.72 1.10 0.00 1.14 0.00 0.00 -0.01
time (sec) N/A 0.084 0.109 0.421 0.000 0.953 0.000 0.000 0.000
Problem 10 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 297 297 281 0 0 0 0 0 -1
normalized size 1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.203 0.639 1.342 0.000 0.636 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 NO TBD TBD TBD TBD TBD TBD
size 184 184 188 246 0 0 0 0 -1
normalized size 1 1.00 1.02 1.34 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.177 0.636 0.857 0.000 0.709 0.000 0.000 0.000
Problem 12 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 198 198 199 0 0 0 0 0 -1
normalized size 1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.141 0.502 0.916 0.000 0.672 0.000 0.000 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 102 102 101 152 0 0 0 0 -1
normalized size 1 1.00 0.99 1.49 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.122 0.397 0.645 0.000 0.696 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 NO TBD TBD TBD TBD TBD TBD
size 111 111 128 0 0 0 0 0 -1
normalized size 1 1.00 1.15 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.088 0.130 0.398 0.000 0.568 0.000 0.000 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 88 88 84 181 0 0 0 0 -1
normalized size 1 1.00 0.95 2.06 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.108 0.053 0.148 0.000 0.627 0.000 0.000 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 75 98 55 155 0 0 -1
normalized size 1 1.00 0.90 1.18 0.66 1.87 0.00 0.00 -0.01
time (sec) N/A 0.071 0.088 0.127 0.322 0.710 0.000 0.000 0.000
Problem 17 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 137 137 147 126 0 174 0 0 -1
normalized size 1 1.00 1.07 0.92 0.00 1.27 0.00 0.00 -0.01
time (sec) N/A 0.086 0.153 0.129 0.000 0.629 0.000 0.000 0.000
Problem 18 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 179 179 120 192 0 186 0 0 -1
normalized size 1 1.00 0.67 1.07 0.00 1.04 0.00 0.00 -0.01
time (sec) N/A 0.125 0.128 0.427 0.000 0.678 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 143 138 135 183 0 0 -1
normalized size 1 1.00 1.01 0.97 0.95 1.29 0.00 0.00 -0.01
time (sec) N/A 0.061 0.222 0.087 0.412 0.587 0.000 0.000 0.000
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 97 81 78 100 94 0 -1
normalized size 1 1.00 0.89 0.74 0.72 0.92 0.86 0.00 -0.01
time (sec) N/A 0.047 0.110 0.065 0.311 0.510 5.567 0.000 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 123 118 106 174 0 0 -1
normalized size 1 1.00 1.12 1.07 0.96 1.58 0.00 0.00 -0.01
time (sec) N/A 0.040 0.136 0.064 0.410 0.553 0.000 0.000 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 77 72 57 90 68 0 -1
normalized size 1 1.00 1.00 0.94 0.74 1.17 0.88 0.00 -0.01
time (sec) N/A 0.031 0.079 0.060 0.305 0.470 1.973 0.000 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 103 96 73 162 0 0 -1
normalized size 1 1.00 1.32 1.23 0.94 2.08 0.00 0.00 -0.01
time (sec) N/A 0.027 0.090 0.062 0.404 0.640 0.000 0.000 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 57 63 36 73 46 0 50
normalized size 1 1.00 1.27 1.40 0.80 1.62 1.02 0.00 1.11
time (sec) N/A 0.014 0.054 0.061 0.302 0.583 0.526 0.000 1.391
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 60 42 31 119 0 0 44
normalized size 1 1.00 1.50 1.05 0.78 2.98 0.00 0.00 1.10
time (sec) N/A 0.015 0.107 0.042 0.301 0.543 0.000 0.000 1.344
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 56 56 47 100 0 0 0 0 -1
normalized size 1 1.00 0.84 1.79 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.088 0.048 0.155 0.000 0.543 0.000 0.000 0.000
Problem 27 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 40 40 42 58 32 66 0 0 46
normalized size 1 1.00 1.05 1.45 0.80 1.65 0.00 0.00 1.15
time (sec) N/A 0.020 0.057 0.061 0.307 0.486 0.000 0.000 1.476
Problem 28 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 94 94 117 112 105 77 0 0 61
normalized size 1 1.00 1.24 1.19 1.12 0.82 0.00 0.00 0.65
time (sec) N/A 0.040 0.077 0.072 0.307 0.431 0.000 0.000 1.464
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 74 77 56 79 0 0 -1
normalized size 1 1.00 0.96 1.00 0.73 1.03 0.00 0.00 -0.01
time (sec) N/A 0.033 0.069 0.065 0.303 0.579 0.000 0.000 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 137 135 147 90 0 0 -1
normalized size 1 1.00 1.09 1.07 1.17 0.71 0.00 0.00 -0.01
time (sec) N/A 0.055 0.113 0.066 0.306 0.599 0.000 0.000 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 94 85 73 89 0 0 -1
normalized size 1 1.00 0.86 0.78 0.67 0.82 0.00 0.00 -0.01
time (sec) N/A 0.050 0.093 0.066 0.305 0.634 0.000 0.000 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 158 158 157 155 185 100 0 0 -1
normalized size 1 1.00 0.99 0.98 1.17 0.63 0.00 0.00 -0.01
time (sec) N/A 0.073 0.158 0.074 0.318 0.591 0.000 0.000 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 212 264 0 244 0 0 -1
normalized size 1 1.00 1.71 2.13 0.00 1.97 0.00 0.00 -0.01
time (sec) N/A 0.119 0.349 0.721 0.000 0.535 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 140 140 224 372 0 0 0 0 -1
normalized size 1 1.00 1.60 2.66 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.123 1.275 0.642 0.000 0.496 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 112 168 84 205 99 0 -1
normalized size 1 1.00 1.72 2.58 1.29 3.15 1.52 0.00 -0.02
time (sec) N/A 0.075 0.253 0.579 0.320 0.702 1.167 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 78 78 126 250 0 0 0 0 -1
normalized size 1 1.00 1.62 3.21 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.070 0.266 0.297 0.000 0.699 0.000 0.000 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 83 83 116 250 0 0 0 0 -1
normalized size 1 1.00 1.40 3.01 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.125 0.174 0.128 0.000 0.620 0.000 0.000 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 87 124 78 143 0 0 -1
normalized size 1 1.00 1.43 2.03 1.28 2.34 0.00 0.00 -0.02
time (sec) N/A 0.070 0.243 0.139 0.318 0.587 0.000 0.000 0.000
Problem 39 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 118 118 183 192 0 165 0 0 -1
normalized size 1 1.00 1.55 1.63 0.00 1.40 0.00 0.00 -0.01
time (sec) N/A 0.085 0.179 0.141 0.000 0.580 0.000 0.000 0.000
Problem 40 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 122 122 134 192 0 181 0 0 -1
normalized size 1 1.00 1.10 1.57 0.00 1.48 0.00 0.00 -0.01
time (sec) N/A 0.102 0.290 0.440 0.000 0.524 0.000 0.000 0.000
Problem 41 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 151 151 268 264 0 204 0 0 -1
normalized size 1 1.00 1.77 1.75 0.00 1.35 0.00 0.00 -0.01
time (sec) N/A 0.120 0.282 0.473 0.000 0.616 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 223 223 337 546 0 0 0 0 -1
normalized size 1 1.00 1.51 2.45 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.239 2.146 0.955 0.000 0.615 0.000 0.000 0.000
Problem 43 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 242 242 440 0 0 0 0 0 -1
normalized size 1 1.00 1.82 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.195 1.113 1.017 0.000 0.539 0.000 0.000 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 126 126 219 343 0 0 0 0 -1
normalized size 1 1.00 1.74 2.72 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.157 0.954 0.715 0.000 0.606 0.000 0.000 0.000
Problem 45 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 140 140 282 0 0 0 0 0 -1
normalized size 1 1.00 2.01 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.111 0.442 0.417 0.000 0.521 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 114 114 182 454 0 0 0 0 -1
normalized size 1 1.00 1.60 3.98 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.145 0.249 0.151 0.000 0.475 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 165 227 144 228 0 0 -1
normalized size 1 1.00 1.62 2.23 1.41 2.24 0.00 0.00 -0.01
time (sec) N/A 0.103 0.359 0.171 0.329 0.542 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 245 321 0 271 0 0 -1
normalized size 1 1.00 1.50 1.97 0.00 1.66 0.00 0.00 -0.01
time (sec) N/A 0.116 0.478 0.174 0.000 0.480 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 213 213 256 387 0 305 0 0 -1
normalized size 1 1.00 1.20 1.82 0.00 1.43 0.00 0.00 -0.00
time (sec) N/A 0.166 0.420 0.506 0.000 0.719 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 242 242 332 485 0 351 0 0 -1
normalized size 1 1.00 1.37 2.00 0.00 1.45 0.00 0.00 -0.00
time (sec) N/A 0.196 0.787 0.481 0.000 0.605 0.000 0.000 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.017 2.375 1.069 0.000 0.573 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 13 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.007 0.034 0.486 0.000 0.441 0.000 0.000 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.027 0.325 0.257 0.000 0.559 0.000 0.000 0.000
Problem 54 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 46 46 43 54 0 0 0 0 -1
normalized size 1 1.00 0.93 1.17 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.110 0.081 0.132 0.000 0.542 0.000 0.000 0.000
Problem 55 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 63 63 56 60 0 0 0 0 -1
normalized size 1 1.00 0.89 0.95 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.142 0.085 0.242 0.000 0.526 0.000 0.000 0.000
Problem 56 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 117 117 91 110 0 0 0 0 -1
normalized size 1 1.00 0.78 0.94 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.236 0.166 0.402 0.000 0.507 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.016 17.757 1.076 0.000 0.510 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 13 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.007 9.714 0.474 0.000 0.609 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.025 5.431 0.263 0.000 0.678 0.000 0.000 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 82 164 0 0 0 0 -1
normalized size 1 1.00 0.95 1.91 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.145 0.325 0.194 0.000 0.500 0.000 0.000 0.000
Problem 61 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 85 85 92 186 0 0 0 0 -1
normalized size 1 1.00 1.08 2.19 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.165 0.362 0.260 0.000 0.640 0.000 0.000 0.000
Problem 62 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 190 190 250 420 0 0 0 0 -1
normalized size 1 1.00 1.32 2.21 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.295 0.543 0.435 0.000 0.842 0.000 0.000 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.016 6.282 1.030 0.000 1.046 0.000 0.000 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 13 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.006 3.919 0.678 0.000 0.614 0.000 0.000 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.025 2.691 0.237 0.000 0.646 0.000 0.000 0.000
Problem 66 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 114 114 103 244 0 0 0 0 -1
normalized size 1 1.00 0.90 2.14 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.176 0.307 0.171 0.000 0.547 0.000 0.000 0.000
Problem 67 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 112 112 122 277 0 0 0 0 -1
normalized size 1 1.00 1.09 2.47 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.206 0.431 0.287 0.000 0.959 0.000 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 240 240 204 628 0 0 0 0 -1
normalized size 1 1.00 0.85 2.62 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.371 0.628 0.469 0.000 0.613 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.024 5.607 2.891 0.000 0.697 0.000 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.026 3.613 2.683 0.000 0.721 0.000 0.000 0.000
Problem 71 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 87 87 97 0 0 0 0 0 -1
normalized size 1 1.00 1.11 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.037 0.149 2.598 0.000 1.232 0.000 0.000 0.000
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.028 0.415 1.846 0.000 0.645 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.027 0.824 1.718 0.000 0.558 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 264 264 190 283 221 358 0 0 -1
normalized size 1 1.00 0.72 1.07 0.84 1.36 0.00 0.00 -0.00
time (sec) N/A 0.362 0.425 0.069 0.424 0.762 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 201 201 147 215 152 280 0 0 -1
normalized size 1 1.00 0.73 1.07 0.76 1.39 0.00 0.00 -0.00
time (sec) N/A 0.217 0.246 0.066 0.421 0.695 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 122 125 70 177 0 0 99
normalized size 1 1.00 0.86 0.88 0.49 1.25 0.00 0.00 0.70
time (sec) N/A 0.118 0.377 0.063 0.319 0.679 0.000 0.000 1.527
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 60 42 31 119 0 0 44
normalized size 1 1.00 1.50 1.05 0.78 2.98 0.00 0.00 1.10
time (sec) N/A 0.015 0.077 0.040 0.313 0.682 0.000 0.000 1.392
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 229 229 393 514 0 0 0 0 -1
normalized size 1 1.00 1.72 2.24 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.933 0.580 0.679 0.000 0.690 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 147 147 222 231 0 578 0 0 -1
normalized size 1 1.00 1.51 1.57 0.00 3.93 0.00 0.00 -0.01
time (sec) N/A 0.119 0.243 0.122 0.000 1.081 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 306 306 342 1090 0 1212 0 0 -1
normalized size 1 1.00 1.12 3.56 0.00 3.96 0.00 0.00 -0.00
time (sec) N/A 0.193 0.695 0.087 0.000 0.878 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 343 343 2653 830 0 0 0 0 -1
normalized size 1 1.00 7.73 2.42 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.621 10.779 0.228 0.000 173.840 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 279 279 2938 415 0 0 0 0 -1
normalized size 1 1.00 10.53 1.49 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.372 13.559 0.100 0.000 9.079 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 187 187 1707 288 0 0 0 0 -1
normalized size 1 1.00 9.13 1.54 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.247 11.748 0.100 0.000 0.000 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 105 105 1675 253 0 0 0 0 -1
normalized size 1 1.00 15.95 2.41 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.178 11.339 0.094 0.000 7.574 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 278 278 4527 902 0 0 0 0 -1
normalized size 1 1.00 16.28 3.24 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.313 13.741 0.117 0.000 5.007 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F(-1) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 609 609 8675 1632 0 0 0 0 -1
normalized size 1 1.00 14.24 2.68 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.594 14.965 0.129 0.000 0.000 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 87 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.048 1.955 2.095 0.000 1.190 0.000 0.000 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 162 224 244 259 0 0 -1
normalized size 1 1.00 0.71 0.98 1.07 1.13 0.00 0.00 -0.00
time (sec) N/A 0.127 0.344 0.067 0.419 1.007 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 144 182 182 238 0 0 -1
normalized size 1 1.00 0.83 1.05 1.05 1.37 0.00 0.00 -0.01
time (sec) N/A 0.103 0.224 0.065 0.420 1.020 0.000 0.000 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 169 135 107 209 0 0 -1
normalized size 1 1.00 1.51 1.21 0.96 1.87 0.00 0.00 -0.01
time (sec) N/A 0.051 0.370 0.065 0.415 0.981 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 107 114 66 182 0 0 98
normalized size 1 1.00 1.11 1.19 0.69 1.90 0.00 0.00 1.02
time (sec) N/A 0.066 0.263 0.067 0.316 0.531 0.000 0.000 1.809
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 76 123 91 106 0 0 -1
normalized size 1 1.00 0.60 0.98 0.72 0.84 0.00 0.00 -0.01
time (sec) N/A 0.079 0.119 0.068 0.315 0.612 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 101 142 132 128 0 0 -1
normalized size 1 1.00 0.55 0.78 0.72 0.70 0.00 0.00 -0.01
time (sec) N/A 0.099 0.176 0.072 0.316 0.630 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 238 238 117 160 165 149 0 0 -1
normalized size 1 1.00 0.49 0.67 0.69 0.63 0.00 0.00 -0.00
time (sec) N/A 0.122 0.222 0.076 0.318 0.580 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 232 232 126 150 177 168 228 0 -1
normalized size 1 1.00 0.54 0.65 0.76 0.72 0.98 0.00 -0.00
time (sec) N/A 0.164 0.218 0.069 0.323 0.663 15.657 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 180 180 106 132 138 147 177 0 -1
normalized size 1 1.00 0.59 0.73 0.77 0.82 0.98 0.00 -0.01
time (sec) N/A 0.135 0.188 0.063 0.316 0.498 5.809 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 164 164 85 113 96 125 126 0 -1
normalized size 1 1.00 0.52 0.69 0.59 0.76 0.77 0.00 -0.01
time (sec) N/A 0.193 0.135 0.066 0.318 0.689 2.186 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 296 296 98 166 0 0 0 0 -1
normalized size 1 1.00 0.33 0.56 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.875 0.314 1.493 0.000 0.521 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 309 309 149 170 0 0 0 0 -1
normalized size 1 1.00 0.48 0.55 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.780 0.614 0.786 0.000 0.704 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 275 275 207 300 328 341 0 0 -1
normalized size 1 1.00 0.75 1.09 1.19 1.24 0.00 0.00 -0.00
time (sec) N/A 0.235 0.499 0.069 0.422 1.823 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 204 204 174 228 224 305 0 0 -1
normalized size 1 1.00 0.85 1.12 1.10 1.50 0.00 0.00 -0.00
time (sec) N/A 0.127 0.345 0.069 0.427 0.809 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 177 177 158 197 152 287 0 0 -1
normalized size 1 1.00 0.89 1.11 0.86 1.62 0.00 0.00 -0.01
time (sec) N/A 0.132 0.315 0.075 0.414 1.840 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 176 176 149 205 134 267 0 0 -1
normalized size 1 1.00 0.85 1.16 0.76 1.52 0.00 0.00 -0.01
time (sec) N/A 0.139 0.308 0.073 0.311 0.701 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 213 213 134 193 175 167 0 0 -1
normalized size 1 1.00 0.63 0.91 0.82 0.78 0.00 0.00 -0.00
time (sec) N/A 0.167 0.290 0.076 0.326 1.075 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 281 281 160 225 232 199 0 0 -1
normalized size 1 1.00 0.57 0.80 0.83 0.71 0.00 0.00 -0.00
time (sec) N/A 0.201 0.398 0.084 0.324 0.547 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 278 278 168 212 245 227 332 0 -1
normalized size 1 1.00 0.60 0.76 0.88 0.82 1.19 0.00 -0.00
time (sec) N/A 0.237 0.310 0.071 0.329 1.084 16.463 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 230 230 139 180 185 192 252 0 -1
normalized size 1 1.00 0.60 0.78 0.80 0.83 1.10 0.00 -0.00
time (sec) N/A 0.252 0.324 0.069 0.327 0.999 6.165 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 370 370 176 286 0 0 0 0 -1
normalized size 1 1.00 0.48 0.77 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.098 0.444 1.818 0.000 1.904 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 373 373 212 252 0 0 0 0 -1
normalized size 1 1.00 0.57 0.68 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.047 0.839 1.602 0.000 0.509 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 519 519 921 411 0 0 0 0 -1
normalized size 1 1.00 1.77 0.79 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.273 1.755 6.534 0.000 1.580 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 459 441 860 513 0 0 0 0 -1
normalized size 1 0.96 1.87 1.12 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.229 0.406 0.893 0.000 0.717 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 469 469 849 302 0 0 0 0 -1
normalized size 1 1.00 1.81 0.64 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.966 0.391 2.693 0.000 0.667 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 417 417 386 3157 0 0 0 0 -1
normalized size 1 1.00 0.93 7.57 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.989 0.935 0.892 0.000 0.641 0.000 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 523 523 933 372 0 0 0 0 -1
normalized size 1 1.00 1.78 0.71 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.261 1.862 6.503 0.000 0.715 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 631 611 1278 870 0 0 0 0 -1
normalized size 1 0.97 2.03 1.38 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.548 5.618 1.628 0.000 0.789 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 580 562 1208 661 0 0 0 0 -1
normalized size 1 0.97 2.08 1.14 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.463 1.290 1.107 0.000 0.855 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 147 147 345 840 0 602 0 0 -1
normalized size 1 1.00 2.35 5.71 0.00 4.10 0.00 0.00 -0.01
time (sec) N/A 0.245 1.053 0.101 0.000 0.663 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F C F(-2) F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 542 542 0 3326 0 0 0 0 -1
normalized size 1 1.00 0.00 6.14 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.363 42.089 2.174 0.000 1.180 0.000 0.000 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 840 840 1270 2016 0 0 0 0 -1
normalized size 1 1.00 1.51 2.40 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.088 1.772 18.231 0.000 0.465 0.000 0.000 0.000
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 786 786 1226 1880 0 0 0 0 -1
normalized size 1 1.00 1.56 2.39 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.574 1.747 5.842 0.000 0.659 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 786 786 1216 1870 0 0 0 0 -1
normalized size 1 1.00 1.55 2.38 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.836 1.790 6.059 0.000 1.304 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 844 844 1305 1952 0 0 0 0 -1
normalized size 1 1.00 1.55 2.31 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.953 1.393 12.207 0.000 1.069 0.000 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 778 760 2000 1779 0 0 0 0 -1
normalized size 1 0.98 2.57 2.29 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.709 7.740 1.580 0.000 0.653 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 486 3331 0 1346 0 0 -1
normalized size 1 1.00 2.81 19.25 0.00 7.78 0.00 0.00 -0.01
time (sec) N/A 0.189 1.593 0.112 0.000 0.900 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 217 217 486 3289 0 1232 0 0 -1
normalized size 1 1.00 2.24 15.16 0.00 5.68 0.00 0.00 -0.00
time (sec) N/A 0.293 1.099 0.103 0.000 0.715 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F C F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 741 741 0 5713 0 0 0 0 -1
normalized size 1 1.00 0.00 7.71 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.542 63.224 2.779 0.000 0.574 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1272 1272 2022 3455 0 0 0 0 -1
normalized size 1 1.00 1.59 2.72 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.263 6.217 9.406 0.000 0.731 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1276 1276 2030 2537 0 0 0 0 -1
normalized size 1 1.00 1.59 1.99 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 4.040 6.143 9.280 0.000 1.123 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F(-1) F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1272 1272 2015 3446 0 0 0 0 -1
normalized size 1 1.00 1.58 2.71 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 4.910 6.073 10.821 0.000 0.507 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 447 447 409 0 0 1995 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 4.46 0.00 0.00 -0.00
time (sec) N/A 1.395 3.102 3.720 0.000 3.531 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 329 329 365 0 0 1669 0 0 -1
normalized size 1 1.00 1.11 0.00 0.00 5.07 0.00 0.00 -0.00
time (sec) N/A 0.427 1.495 3.394 0.000 1.993 0.000 0.000 0.000
Problem 132 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 221 221 307 0 0 1382 0 0 -1
normalized size 1 1.00 1.39 0.00 0.00 6.25 0.00 0.00 -0.00
time (sec) N/A 0.357 1.278 2.553 0.000 2.023 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.099 5.525 1.622 0.000 0.564 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.104 6.341 0.870 0.000 0.612 0.000 0.000 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.098 13.897 2.839 0.000 0.638 0.000 0.000 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.036 3.171 1.624 0.000 0.687 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.087 1.927 1.326 0.000 0.625 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-2) F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 312 312 576 0 0 0 0 0 -1
normalized size 1 1.00 1.85 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.380 4.215 180.000 0.000 0.646 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-2) F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 446 446 641 0 0 0 0 0 -1
normalized size 1 1.00 1.44 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.561 6.379 180.000 0.000 0.753 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 418 418 382 0 0 1989 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 4.76 0.00 0.00 -0.00
time (sec) N/A 0.530 2.986 3.371 0.000 3.980 0.000 0.000 0.000
Problem 141 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 297 297 342 0 0 1667 0 0 -1
normalized size 1 1.00 1.15 0.00 0.00 5.61 0.00 0.00 -0.00
time (sec) N/A 0.432 1.544 2.426 0.000 1.568 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.120 6.375 1.500 0.000 0.662 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.125 6.222 0.710 0.000 0.795 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.122 13.649 2.730 0.000 0.600 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.044 4.475 1.438 0.000 0.592 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.104 6.870 1.137 0.000 0.562 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.128 16.579 180.000 0.000 0.528 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-2) F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 409 409 620 0 0 0 0 0 -1
normalized size 1 1.00 1.52 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.533 6.371 180.000 0.000 0.599 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-2) F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 556 556 728 0 0 0 0 0 -1
normalized size 1 1.00 1.31 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.758 7.811 180.000 0.000 0.664 0.000 0.000 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 356 356 366 0 0 1679 0 0 -1
normalized size 1 1.00 1.03 0.00 0.00 4.72 0.00 0.00 -0.00
time (sec) N/A 1.160 1.602 4.740 0.000 1.847 0.000 0.000 0.000
Problem 151 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 251 251 406 0 0 1389 0 0 -1
normalized size 1 1.00 1.62 0.00 0.00 5.53 0.00 0.00 -0.00
time (sec) N/A 0.330 1.317 4.609 0.000 1.005 0.000 0.000 0.000
Problem 152 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 153 153 239 0 0 1102 0 0 -1
normalized size 1 1.00 1.56 0.00 0.00 7.20 0.00 0.00 -0.01
time (sec) N/A 0.295 0.564 2.728 0.000 0.821 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.095 3.254 1.605 0.000 0.786 0.000 0.000 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.111 23.958 1.147 0.000 0.532 0.000 0.000 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.098 7.181 3.518 0.000 0.667 0.000 0.000 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.035 1.066 2.061 0.000 0.689 0.000 0.000 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 221 221 501 0 0 0 0 0 -1
normalized size 1 1.00 2.27 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.258 4.378 1.540 0.000 0.576 0.000 0.000 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-2) F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 346 346 612 0 0 0 0 0 -1
normalized size 1 1.00 1.77 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.485 5.030 180.000 0.000 0.654 0.000 0.000 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 278 278 436 0 0 1771 0 0 -1
normalized size 1 1.00 1.57 0.00 0.00 6.37 0.00 0.00 -0.00
time (sec) N/A 1.117 1.498 4.654 0.000 2.588 0.000 0.000 0.000
Problem 160 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 177 177 249 0 0 1311 0 0 -1
normalized size 1 1.00 1.41 0.00 0.00 7.41 0.00 0.00 -0.01
time (sec) N/A 0.272 1.776 4.328 0.000 1.801 0.000 0.000 0.000
Problem 161 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 87 87 135 0 0 379 0 0 -1
normalized size 1 1.00 1.55 0.00 0.00 4.36 0.00 0.00 -0.01
time (sec) N/A 0.245 0.635 2.418 0.000 0.609 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.116 32.022 1.406 0.000 1.039 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.133 37.542 1.102 0.000 0.667 0.000 0.000 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.111 9.907 3.915 0.000 0.563 0.000 0.000 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.106 4.712 3.768 0.000 0.506 0.000 0.000 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 334 0 0 0 0 0 -1
normalized size 1 1.00 3.63 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.079 1.391 2.171 0.000 0.716 0.000 0.000 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 249 249 501 0 0 0 0 0 -1
normalized size 1 1.00 2.01 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.287 4.490 1.510 0.000 0.519 0.000 0.000 0.000
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 272 272 348 0 0 2415 0 0 -1
normalized size 1 1.00 1.28 0.00 0.00 8.88 0.00 0.00 -0.00
time (sec) N/A 1.281 1.971 4.575 0.000 1.186 0.000 0.000 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 179 179 218 0 0 786 0 0 -1
normalized size 1 1.00 1.22 0.00 0.00 4.39 0.00 0.00 -0.01
time (sec) N/A 0.264 0.377 4.483 0.000 0.779 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 204 0 0 692 0 0 -1
normalized size 1 1.00 1.32 0.00 0.00 4.49 0.00 0.00 -0.01
time (sec) N/A 0.291 0.316 2.580 0.000 1.407 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.123 43.676 1.476 0.000 0.553 0.000 0.000 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.142 54.748 1.234 0.000 0.617 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.122 14.891 4.402 0.000 1.649 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.111 13.536 3.947 0.000 0.620 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 246 246 488 0 0 0 0 0 -1
normalized size 1 1.00 1.98 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.246 2.656 3.603 0.000 0.716 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 266 266 517 0 0 0 0 0 -1
normalized size 1 1.00 1.94 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.206 5.505 2.023 0.000 0.731 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F(-2) F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 596 576 0 0 0 0 0 0 -1
normalized size 1 0.97 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.545 0.246 180.000 0.000 1.511 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F(-2) F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 372 352 0 0 0 0 0 0 -1
normalized size 1 0.95 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.432 0.161 180.000 0.000 0.710 0.000 0.000 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F(-2) F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 206 192 0 0 0 0 0 0 -1
normalized size 1 0.93 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.179 0.126 180.000 0.000 0.489 0.000 0.000 0.000
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.076 2.483 2.377 0.000 0.722 0.000 0.000 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.075 7.550 180.000 0.000 1.046 0.000 0.000 0.000
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.110 1.077 1.794 0.000 0.611 0.000 0.000 0.000
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.099 0.122 1.724 0.000 0.614 0.000 0.000 0.000
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.100 1.420 2.583 0.000 1.650 0.000 0.000 0.000
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.110 1.729 2.456 0.000 0.664 0.000 0.000 0.000
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 473 473 213 0 0 393 0 0 -1
normalized size 1 1.00 0.45 0.00 0.00 0.83 0.00 0.00 -0.00
time (sec) N/A 1.579 0.443 6.404 0.000 0.671 0.000 0.000 0.000
Problem 187 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 316 316 178 0 0 336 0 0 -1
normalized size 1 1.00 0.56 0.00 0.00 1.06 0.00 0.00 -0.00
time (sec) N/A 1.383 0.383 5.727 0.000 0.579 0.000 0.000 0.000
Problem 188 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 159 159 140 0 0 279 0 0 -1
normalized size 1 1.00 0.88 0.00 0.00 1.75 0.00 0.00 -0.01
time (sec) N/A 0.164 0.353 3.326 0.000 0.670 0.000 0.000 0.000
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 29 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.091 0.414 3.198 0.000 1.083 0.000 0.000 0.000
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A F(-2) A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 29 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.102 3.539 180.000 0.000 1.244 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 [11] had the largest ratio of [1.000]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 9 6 1.00 10 0.600
2 A 5 5 1.00 10 0.500
3 A 8 6 1.00 10 0.600
4 A 4 4 1.00 8 0.500
5 A 7 5 1.00 6 0.833
6 A 6 6 1.00 10 0.600
7 A 4 3 1.00 10 0.300
8 A 4 4 1.00 10 0.400
9 A 5 5 1.00 10 0.500
10 A 14 9 1.00 10 0.900
11 A 10 10 1.00 10 1.000
12 A 11 8 1.00 10 0.800
13 A 7 7 1.00 8 0.875
14 A 9 6 1.00 6 1.000
15 A 7 7 1.00 10 0.700
16 A 5 3 1.00 10 0.300
17 A 6 6 1.00 10 0.600
18 A 8 6 1.00 10 0.600
19 A 8 6 1.00 12 0.500
20 A 6 4 1.00 12 0.333
21 A 6 6 1.00 12 0.500
22 A 4 4 1.00 12 0.333
23 A 4 4 1.00 12 0.333
24 A 2 2 1.00 10 0.200
25 A 3 2 1.00 8 0.250
26 A 6 6 1.00 12 0.500
27 A 2 2 1.00 12 0.167
28 A 5 5 1.00 12 0.417
29 A 4 4 1.00 12 0.333
30 A 7 5 1.00 12 0.417
31 A 6 4 1.00 12 0.333
32 A 9 5 1.00 12 0.417
33 A 5 5 1.00 14 0.357
34 A 8 6 1.00 14 0.429
35 A 4 4 1.00 12 0.333
36 A 7 5 1.00 10 0.500
37 A 6 6 1.00 14 0.429
38 A 4 3 1.00 14 0.214
39 A 4 3 1.00 14 0.214
40 A 5 5 1.00 14 0.357
41 A 5 3 1.00 14 0.214
42 A 10 10 1.00 14 0.714
43 A 11 8 1.00 14 0.571
44 A 7 7 1.00 12 0.583
45 A 9 6 1.00 10 0.600
46 A 7 7 1.00 14 0.500
47 A 5 3 1.00 14 0.214
48 A 6 6 1.00 14 0.429
49 A 8 6 1.00 14 0.429
50 A 10 6 1.00 14 0.429
51 A 0 0 0.00 0 0.000
52 A 0 0 0.00 0 0.000
53 A 0 0 0.00 0 0.000
54 A 4 4 1.00 14 0.286
55 A 6 6 1.00 14 0.429
56 A 9 5 1.00 14 0.357
57 A 0 0 0.00 0 0.000
58 A 0 0 0.00 0 0.000
59 A 0 0 0.00 0 0.000
60 A 5 5 1.00 14 0.357
61 A 7 7 1.00 14 0.500
62 A 11 6 1.00 14 0.429
63 A 0 0 0.00 0 0.000
64 A 0 0 0.00 0 0.000
65 A 0 0 0.00 0 0.000
66 A 6 5 1.00 14 0.357
67 A 8 7 1.00 14 0.500
68 A 13 6 1.00 14 0.429
69 A 0 0 0.00 0 0.000
70 A 0 0 0.00 0 0.000
71 A 3 3 1.00 14 0.214
72 A 0 0 0.00 0 0.000
73 A 0 0 0.00 0 0.000
74 A 9 7 1.00 16 0.438
75 A 8 7 1.00 16 0.438
76 A 7 7 1.00 14 0.500
77 A 3 2 1.00 8 0.250
78 A 4 2 1.00 16 0.125
79 A 8 7 1.00 16 0.438
80 A 11 8 1.00 16 0.500
81 A 21 12 1.00 18 0.667
82 A 14 10 1.00 18 0.556
83 A 8 8 1.00 18 0.444
84 A 5 5 1.00 18 0.278
85 A 11 10 1.00 18 0.556
86 A 18 13 1.00 18 0.722
87 A 0 0 0.00 0 0.000
88 A 6 6 1.00 19 0.316
89 A 5 6 1.00 19 0.316
90 A 4 4 1.00 16 0.250
91 A 3 4 1.00 19 0.210
92 A 4 5 1.00 19 0.263
93 A 5 6 1.00 19 0.316
94 A 6 6 1.00 19 0.316
95 A 5 5 1.00 19 0.263
96 A 5 5 1.00 19 0.263
97 A 7 6 1.00 17 0.353
98 A 12 12 1.00 19 0.632
99 A 14 14 1.00 19 0.737
100 A 6 7 1.00 21 0.333
101 A 5 6 1.00 18 0.333
102 A 5 6 1.00 21 0.286
103 A 5 6 1.00 21 0.286
104 A 5 6 1.00 21 0.286
105 A 6 7 1.00 21 0.333
106 A 5 6 1.00 21 0.286
107 A 7 6 1.00 19 0.316
108 A 13 14 1.00 21 0.667
109 A 15 16 1.00 21 0.762
110 A 24 11 1.00 21 0.524
111 A 26 9 0.96 19 0.474
112 A 19 7 1.00 18 0.389
113 A 19 7 1.00 21 0.333
114 A 24 10 1.00 21 0.476
115 A 32 15 0.97 21 0.714
116 A 30 13 0.97 21 0.619
117 A 8 6 1.00 19 0.316
118 A 25 11 1.00 21 0.524
119 A 50 13 1.00 21 0.619
120 A 27 10 1.00 21 0.476
121 A 47 11 1.00 18 0.611
122 A 50 13 1.00 21 0.619
123 A 35 14 0.98 21 0.667
124 A 6 7 1.00 21 0.333
125 A 9 7 1.00 19 0.368
126 A 30 12 1.00 21 0.571
127 A 35 11 1.00 21 0.524
128 A 63 12 1.00 21 0.571
129 A 81 12 1.00 18 0.667
130 A 12 12 1.00 23 0.522
131 A 11 12 1.00 23 0.522
132 A 10 10 1.00 21 0.476
133 A 0 0 0.00 0 0.000
134 A 0 0 0.00 0 0.000
135 A 0 0 0.00 0 0.000
136 A 0 0 0.00 0 0.000
137 A 0 0 0.00 0 0.000
138 A 9 10 1.00 23 0.435
139 A 10 11 1.00 23 0.478
140 A 12 12 1.00 23 0.522
141 A 11 11 1.00 21 0.524
142 A 0 0 0.00 0 0.000
143 A 0 0 0.00 0 0.000
144 A 0 0 0.00 0 0.000
145 A 0 0 0.00 0 0.000
146 A 0 0 0.00 0 0.000
147 A 0 0 0.00 0 0.000
148 A 10 11 1.00 23 0.478
149 A 11 11 1.00 23 0.478
150 A 11 12 1.00 23 0.522
151 A 10 12 1.00 23 0.522
152 A 9 9 1.00 21 0.429
153 A 0 0 0.00 0 0.000
154 A 0 0 0.00 0 0.000
155 A 0 0 0.00 0 0.000
156 A 0 0 0.00 0 0.000
157 A 9 10 1.00 23 0.435
158 A 9 11 1.00 23 0.478
159 A 10 11 1.00 23 0.478
160 A 9 11 1.00 23 0.478
161 A 5 5 1.00 21 0.238
162 A 0 0 0.00 0 0.000
163 A 0 0 0.00 0 0.000
164 A 0 0 0.00 0 0.000
165 A 0 0 0.00 0 0.000
166 A 4 5 1.00 20 0.250
167 A 8 10 1.00 23 0.435
168 A 10 11 1.00 23 0.478
169 A 7 8 1.00 23 0.348
170 A 6 6 1.00 21 0.286
171 A 0 0 0.00 0 0.000
172 A 0 0 0.00 0 0.000
173 A 0 0 0.00 0 0.000
174 A 0 0 0.00 0 0.000
175 A 8 9 1.00 23 0.391
176 A 8 10 1.00 20 0.500
177 A 5 6 0.97 23 0.261
178 A 5 6 0.95 23 0.261
179 A 4 5 0.93 21 0.238
180 A 0 0 0.00 0 0.000
181 A 0 0 0.00 0 0.000
182 A 0 0 0.00 0 0.000
183 A 0 0 0.00 0 0.000
184 A 0 0 0.00 0 0.000
185 A 0 0 0.00 0 0.000
186 A 15 10 1.00 26 0.385
187 A 12 10 1.00 26 0.385
188 A 7 8 1.00 26 0.308
189 A 0 0 0.00 0 0.000
190 A 0 0 0.00 0 0.000

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