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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
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 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, 39, 41, 43, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 97, 98, 102, 107, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 128, 132, 133, 136, 137, 138, 140, 142, 143, 146, 147, 148, 149, 150, 151, 154, 155, 156, 157, 158, 159, 161, 162, 163, 165, 166, 167, 169, 170, 171, 172, 174, 175, 176, 178, 179, 180, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 234 }

B grade: { 38, 40, 42, 46, 103, 108, 110, 141, 160, 164, 168, 173, 177, 181, 183, 200 }

C grade: { 9, 11, 44, 61, 62, 63, 64, 79, 89, 90, 99, 100, 101, 104, 105, 106, 123, 129, 130, 131, 134, 135, 217, 230, 231, 232, 233 }

F grade: { 139, 144, 145, 152, 153}

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 16, 20, 22, 23, 25, 27, 31, 33, 34, 35, 37, 39, 41, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 59, 60, 65, 66, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 105, 106, 108, 109, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 125, 128, 131, 132, 133, 134, 135, 145, 147, 148, 149, 151, 155, 156, 157, 161, 165, 169, 174, 178, 182, 187, 191, 195, 199, 204, 208, 212, 216, 219, 220, 224, 227, 228 }

B grade: { 7, 13, 15, 17, 19, 21, 28, 38, 40, 42, 44, 57, 58, 88, 97, 107, 113, 124, 126, 127, 129, 130, 136, 137, 138, 140, 141, 142, 143, 152, 153, 154, 160, 164, 168, 170, 173, 177, 181, 186, 190, 194, 198, 203, 207, 211, 215, 218, 221, 222, 223, 225, 226 }

C grade: { 18, 24, 26, 29, 30, 32, 67, 68, 69, 77, 98, 110, 111, 112, 139, 144, 150, 158, 159, 162, 163, 166, 167, 171, 172, 175, 176, 179, 180, 183, 184, 185, 188, 189, 192, 193, 196, 197, 200, 201, 202, 205, 206, 209, 210, 213, 214, 217, 229, 230, 231, 232, 233, 234 }

F grade: { 36, 61, 62, 63, 64, 146 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 16, 20, 22, 37, 39, 41, 43, 45, 46, 48, 50, 51, 53, 54, 55, 56, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 105, 106, 109, 116, 117, 120, 121, 123, 125, 129, 130, 131, 132, 134, 135, 149, 150, 151, 155, 156, 157, 170, 187, 191, 192, 193, 194, 195, 196, 197, 198, 199, 204, 208, 209, 210, 211, 212, 213, 214, 215, 216, 218, 221, 224, 227, 228, 229, 230, 231, 232, 233, 234

B grade: { 7, 77, 80, 81, 82, 83, 84, 88, 98, 108, 122, 124, 126, 127, 160, 162, 163, 164, 166, 167, 168, 173 }

C grade: { }

F grade: { 13, 15, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 40, 42, 44, 47, 49, 52, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 97, 107, 110, 111, 112, 113, 114, 115, 118, 119, 128, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 152, 153, 154, 158, 159, 161, 165, 169, 171, 172, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 200, 201, 202, 203, 205, 206, 207, 217, 219, 220, 222, 223, 225, 226 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 16, 20, 22, 34, 35, 37, 39, 41, 43, 45, 51, 52, 53, 54, 55, 56, 59, 60, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 82, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 104, 105, 106, 116, 117, 120, 121, 122, 123, 125, 129, 130, 131, 132, 134, 147, 148, 149, 150, 151, 155, 156, 157, 161, 165, 169, 170, 174, 177, 178, 181, 182, 187, 191, 195, 199, 204, 208, 212, 216, 224, 227, 228, 234 }

B grade: { 61, 62, 63, 64, 80, 81, 83, 84, 135, 160, 164, 168, 173, 186, 190, 194, 198, 203, 207, 211, 215, 218, 221, 229, 230, 231, 232, 233 }

C grade: { 158, 159, 162, 163, 166, 167, 171, 172, 175, 176, 179, 180, 183, 184, 185, 188, 189, 192, 193, 196, 197, 200, 201, 202, 205, 206, 209, 210, 213, 214, 217, 219, 220, 222, 223, 225, 226 }

F grade: { 7, 13, 15, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36, 38, 40, 42, 44, 46, 47, 48, 49, 50, 57, 58, 65, 66, 77, 88, 98, 103, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 124, 126, 127, 128, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 152, 153, 154 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 16, 20, 22, 34, 35, 37, 39, 41, 43, 45, 51, 52, 53, 54, 55, 56, 59, 60, 70, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 92, 93, 94, 96, 99, 100, 101, 102, 116, 117, 120, 122, 123, 125, 128, 129, 130, 131, 132, 149, 151, 155, 156, 170, 187, 204, 227, 228 }

B grade: { 71, 89, 90, 91, 95, 104, 105, 106, 157 }

C grade: { }

F grade: { 7, 13, 15, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36, 38, 40, 42, 44, 46, 47, 48, 49, 50, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 77, 85, 86, 87, 88, 97, 98, 103, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 121, 124, 126, 127, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 152, 153, 154, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 229, 230, 231, 232, 233, 234 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 16, 34, 35, 41, 51, 52, 53, 54, 55, 56, 59, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 104, 105, 106, 116, 117, 120, 121, 122, 123, 125, 128, 132, 134, 147, 148, 149, 150, 151, 155, 156, 157, 161, 165, 169, 170, 174, 178, 182, 187, 191, 195, 199, 204, 208, 212, 216, 227, 228, 229, 230, 231, 232, 233, 234 }

B grade: { 37, 39, 129, 130, 131, 135 }

C grade: { }

F grade: { 7, 13, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36, 38, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 57, 58, 65, 66, 72, 73, 77, 88, 97, 98, 103, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 124, 126, 127, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 152, 153, 154, 158, 159, 160, 162, 163, 164, 166, 167, 168, 171, 172, 173, 175, 176, 177, 179, 180, 181, 183, 184, 185, 186, 188, 189, 190, 192, 193, 194, 196, 197, 198, 200, 201, 202, 203, 205, 206, 207, 209, 210, 211, 213, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226 }

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
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 51 42 63 100 48 74
normalized size 1 1. 1. 0.82 1.24 1.96 0.94 1.45
time (sec) N/A 0.025 0.003 0.039 1.468 1.846 1.593 1.143
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 49 42 62 104 46 68
normalized size 1 1. 1. 0.86 1.27 2.12 0.94 1.39
time (sec) N/A 0.036 0.012 0.04 0.975 1.856 1.196 1.081
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 41 34 51 78 39 61
normalized size 1 1. 1. 0.83 1.24 1.9 0.95 1.49
time (sec) N/A 0.021 0.002 0.042 1.454 1.858 0.884 1.113
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 39 34 49 84 37 54
normalized size 1 1. 1. 0.87 1.26 2.15 0.95 1.38
time (sec) N/A 0.026 0.01 0.039 0.989 1.922 0.638 1.137
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 26 38 58 31 43
normalized size 1 1. 1. 0.84 1.23 1.87 1. 1.39
time (sec) N/A 0.012 0.002 0.039 1.49 1.905 0.413 1.115
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 24 23 32 62 24 35
normalized size 1 1. 1. 0.96 1.33 2.58 1. 1.46
time (sec) N/A 0.006 0.003 0.036 0.972 2.026 0.258 1.122
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 37 63 89 0 0 0
normalized size 1 1. 1. 1.7 2.41 0. 0. 0.
time (sec) N/A 0.025 0.003 0.049 1.626 0. 0. 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 30 31 41 82 24 46
normalized size 1 1. 1. 1.03 1.37 2.73 0.8 1.53
time (sec) N/A 0.018 0.002 0.043 0.967 1.913 0.345 1.093
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 36 26 31 58 24 36
normalized size 1 1. 1.16 0.84 1. 1.87 0.77 1.16
time (sec) N/A 0.015 0.002 0.043 1.501 1.875 0.631 1.11
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 44 41 57 105 39 73
normalized size 1 1. 0.96 0.89 1.24 2.28 0.85 1.59
time (sec) N/A 0.027 0.011 0.044 0.981 1.995 0.87 1.125
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 36 34 50 80 32 55
normalized size 1 1. 0.88 0.83 1.22 1.95 0.78 1.34
time (sec) N/A 0.018 0.003 0.046 1.484 1.864 1.018 1.123
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 79 102 128 189 104 190
normalized size 1 1. 0.76 0.98 1.23 1.82 1. 1.83
time (sec) N/A 0.221 0.023 0.049 1.523 1.989 2.48 1.119
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 135 135 95 233 0 0 0 0
normalized size 1 1. 0.7 1.73 0. 0. 0. 0.
time (sec) N/A 0.211 0.501 0.121 0. 0. 0. 0.
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 61 82 104 144 78 146
normalized size 1 1. 0.76 1.02 1.3 1.8 0.98 1.82
time (sec) N/A 0.146 0.02 0.051 1.543 1.917 1.327 1.137
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 111 111 76 213 0 0 0 0
normalized size 1 1. 0.68 1.92 0. 0. 0. 0.
time (sec) N/A 0.14 0.263 0.112 0. 0. 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 42 61 77 105 54 101
normalized size 1 1. 0.79 1.15 1.45 1.98 1.02 1.91
time (sec) N/A 0.072 0.013 0.048 1.537 1.749 0.646 1.122
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 67 67 56 136 0 0 0 0
normalized size 1 1. 0.84 2.03 0. 0. 0. 0.
time (sec) N/A 0.074 0.076 0.164 0. 0. 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 116 116 132 959 0 0 0 0
normalized size 1 1. 1.14 8.27 0. 0. 0. 0.
time (sec) N/A 0.213 0.06 0.601 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 66 66 64 234 0 0 0 0
normalized size 1 1. 0.97 3.55 0. 0. 0. 0.
time (sec) N/A 0.105 0.044 0.138 0. 0. 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 56 68 76 143 53 0
normalized size 1 1. 0.95 1.15 1.29 2.42 0.9 0.
time (sec) N/A 0.088 0.017 0.052 1.473 2.027 0.695 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 113 113 96 290 0 0 0 0
normalized size 1 1. 0.85 2.57 0. 0. 0. 0.
time (sec) N/A 0.161 0.232 0.133 0. 0. 0. 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 81 91 128 181 80 0
normalized size 1 1. 0.91 1.02 1.44 2.03 0.9 0.
time (sec) N/A 0.155 0.02 0.058 1.526 1.88 1.197 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 194 194 125 243 0 0 0 0
normalized size 1 1. 0.64 1.25 0. 0. 0. 0.
time (sec) N/A 0.667 0.601 0.531 0. 0. 0. 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 205 205 184 2731 0 0 0 0
normalized size 1 1. 0.9 13.32 0. 0. 0. 0.
time (sec) N/A 0.517 0.586 3.753 0. 0. 0. 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 148 148 96 209 0 0 0 0
normalized size 1 1. 0.65 1.41 0. 0. 0. 0.
time (sec) N/A 0.386 0.333 0.451 0. 0. 0. 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 157 157 149 1815 0 0 0 0
normalized size 1 1. 0.95 11.56 0. 0. 0. 0.
time (sec) N/A 0.302 0.324 1.355 0. 0. 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 103 103 76 162 0 0 0 0
normalized size 1 1. 0.74 1.57 0. 0. 0. 0.
time (sec) N/A 0.171 0.086 0.316 0. 0. 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 96 96 90 199 0 0 0 0
normalized size 1 1. 0.94 2.07 0. 0. 0. 0.
time (sec) N/A 0.15 0.104 0.163 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 178 178 180 1050 0 0 0 0
normalized size 1 1. 1.01 5.9 0. 0. 0. 0.
time (sec) N/A 0.327 0.076 0.412 0. 0. 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 93 93 83 1576 0 0 0 0
normalized size 1 1. 0.89 16.95 0. 0. 0. 0.
time (sec) N/A 0.188 0.072 0.574 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 105 105 90 109 0 0 0 0
normalized size 1 1. 0.86 1.04 0. 0. 0. 0.
time (sec) N/A 0.199 0.16 0.322 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 167 167 151 5029 0 0 0 0
normalized size 1 1. 0.9 30.11 0. 0. 0. 0.
time (sec) N/A 0.337 0.244 1.627 0. 0. 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 152 152 126 158 0 0 0 0
normalized size 1 1. 0.83 1.04 0. 0. 0. 0.
time (sec) N/A 0.42 0.258 0.485 0. 0. 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.828 1.293 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.815 0.956 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 52 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.02 0.02 1.026 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 32 38 47 100 34 90
normalized size 1 1. 0.8 0.95 1.18 2.5 0.85 2.25
time (sec) N/A 0.097 0.027 0.029 1.479 1.999 0.711 1.137
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 67 67 241 128 0 0 0 0
normalized size 1 1. 3.6 1.91 0. 0. 0. 0.
time (sec) N/A 0.093 0.059 0.114 0. 0. 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 26 32 68 19 58
normalized size 1 1. 1. 1.13 1.39 2.96 0.83 2.52
time (sec) N/A 0.048 0.013 0.03 1.541 1.867 0.389 1.124
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 48 48 221 114 0 0 0 0
normalized size 1 1. 4.6 2.38 0. 0. 0. 0.
time (sec) N/A 0.054 0.047 0.104 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 8 8 8 7 8 24 7 11
normalized size 1 1. 1. 0.88 1. 3. 0.88 1.38
time (sec) N/A 0.012 0.003 0.02 0.978 1.922 0.695 1.108
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 49 49 251 163 0 0 0 0
normalized size 1 1. 5.12 3.33 0. 0. 0. 0.
time (sec) N/A 0.073 0.06 0.115 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 30 33 39 90 22 0
normalized size 1 1. 1. 1.1 1.3 3. 0.73 0.
time (sec) N/A 0.056 0.016 0.033 1.507 1.944 0.654 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 72 72 280 180 0 0 0 0
normalized size 1 1. 3.89 2.5 0. 0. 0. 0.
time (sec) N/A 0.115 0.063 0.115 0. 0. 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 47 43 74 130 42 0
normalized size 1 1. 1. 0.91 1.57 2.77 0.89 0.
time (sec) N/A 0.109 0.02 0.039 1.479 1.957 1.875 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 206 206 626 265 269 0 0 0
normalized size 1 1. 3.04 1.29 1.31 0. 0. 0.
time (sec) N/A 0.58 1.585 0.247 1.588 0. 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 188 188 343 284 0 0 0 0
normalized size 1 1. 1.82 1.51 0. 0. 0. 0.
time (sec) N/A 0.184 0.083 0.174 0. 0. 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 183 183 319 304 266 0 0 0
normalized size 1 1. 1.74 1.66 1.45 0. 0. 0.
time (sec) N/A 0.465 0.078 0.184 1.596 0. 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 223 223 379 345 0 0 0 0
normalized size 1 1. 1.7 1.55 0. 0. 0. 0.
time (sec) N/A 0.247 0.091 0.149 0. 0. 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 212 212 348 271 261 0 0 0
normalized size 1 1. 1.64 1.28 1.23 0. 0. 0.
time (sec) N/A 0.503 0.085 0.207 1.549 0. 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 5 5 5 6 7 23 5 11
normalized size 1 1. 1. 1.2 1.4 4.6 1. 2.2
time (sec) N/A 0.02 0.023 0.019 0.947 1.769 0.345 1.095
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 14 0 43 17 20
normalized size 1 1. 1. 1.08 0. 3.31 1.31 1.54
time (sec) N/A 0.024 0.007 0.038 0. 1.999 4.601 1.09
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 244 244 212 279 305 540 367 320
normalized size 1 1. 0.87 1.14 1.25 2.21 1.5 1.31
time (sec) N/A 0.176 0.162 0.044 1.003 1.91 6.184 1.12
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 168 168 149 191 215 366 243 221
normalized size 1 1. 0.89 1.14 1.28 2.18 1.45 1.32
time (sec) N/A 0.12 0.104 0.043 0.972 1.838 3.536 1.131
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 97 119 139 240 151 142
normalized size 1 1. 0.89 1.09 1.28 2.2 1.39 1.3
time (sec) N/A 0.127 0.066 0.042 1.013 1.923 1.935 1.116
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 67 60 72 127 73 74
normalized size 1 1. 1.16 1.03 1.24 2.19 1.26 1.28
time (sec) N/A 0.061 0.009 0.04 0.953 2.147 0.836 1.104
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 403 403 523 826 0 0 0 0
normalized size 1 1. 1.3 2.05 0. 0. 0. 0.
time (sec) N/A 0.919 0.293 0.264 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 801 801 802 2177 0 0 0 0
normalized size 1 1. 1. 2.72 0. 0. 0. 0.
time (sec) N/A 1.158 7.306 0.447 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.019 5.408 0.954 0. 0. 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.022 3.74 0.858 0. 0. 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 169 0 0 729 0 80
normalized size 1 1. 2.56 0. 0. 11.05 0. 1.21
time (sec) N/A 0.094 0.227 0.644 0. 2.329 0. 1.144
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 262 0 0 1450 0 170
normalized size 1 1. 1.96 0. 0. 10.82 0. 1.27
time (sec) N/A 0.326 0.607 0.665 0. 2.82 0. 1.175
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 208 208 345 0 0 2569 0 281
normalized size 1 1. 1.66 0. 0. 12.35 0. 1.35
time (sec) N/A 0.935 0.938 0.891 0. 3.581 0. 1.217
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 293 293 450 0 0 4097 0 459
normalized size 1 1. 1.54 0. 0. 13.98 0. 1.57
time (sec) N/A 1.155 1.395 0.725 0. 7.702 0. 1.23
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 195 195 136 117 0 0 0 0
normalized size 1 1. 0.7 0.6 0. 0. 0. 0.
time (sec) N/A 0.072 1.114 0.7 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 155 155 89 99 0 0 0 0
normalized size 1 1. 0.57 0.64 0. 0. 0. 0.
time (sec) N/A 0.045 0.103 0.57 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 21 68 42 69 0 45
normalized size 1 1. 0.6 1.94 1.2 1.97 0. 1.29
time (sec) N/A 0.02 0.023 0.381 1.469 2.118 0. 1.144
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 37 165 85 122 0 74
normalized size 1 1. 0.47 2.09 1.08 1.54 0. 0.94
time (sec) N/A 0.044 0.031 0.386 1.456 2.203 0. 1.148
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 47 289 126 174 0 112
normalized size 1 1. 0.4 2.45 1.07 1.47 0. 0.95
time (sec) N/A 0.067 0.038 0.455 1.539 2.192 0. 1.145
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 25 27 35 55 31 38
normalized size 1 1. 0.78 0.84 1.09 1.72 0.97 1.19
time (sec) N/A 0.026 0.018 0.026 1.487 2.145 0.707 1.102
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 36 37 53 96 88 49
normalized size 1 1. 0.82 0.84 1.2 2.18 2. 1.11
time (sec) N/A 0.029 0.021 0.025 1.472 2.102 1.204 1.112
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 28 35 51 81 0 0
normalized size 1 1. 0.82 1.03 1.5 2.38 0. 0.
time (sec) N/A 0.015 0.013 0.034 1.464 2.151 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 46 61 101 123 0 0
normalized size 1 1. 0.82 1.09 1.8 2.2 0. 0.
time (sec) N/A 0.044 0.024 0.169 1.525 2.082 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 41 36 51 88 39 54
normalized size 1 1. 1. 0.88 1.24 2.15 0.95 1.32
time (sec) N/A 0.025 0.014 0.045 0.975 2.16 2.94 1.106
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 37 32 46 63 36 49
normalized size 1 1. 1. 0.86 1.24 1.7 0.97 1.32
time (sec) N/A 0.019 0.006 0.04 1.443 2.108 1.485 1.126
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 28 38 68 31 39
normalized size 1 1. 1. 0.9 1.23 2.19 1. 1.26
time (sec) N/A 0.009 0.006 0.039 0.994 2.21 0.839 1.091
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 37 57 108 0 0 0
normalized size 1 1. 1. 1.54 2.92 0. 0. 0.
time (sec) N/A 0.034 0.006 0.117 1.614 0. 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 34 31 43 93 29 46
normalized size 1 1. 1. 0.91 1.26 2.74 0.85 1.35
time (sec) N/A 0.017 0.006 0.048 0.966 2.291 1.054 1.143
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 38 30 36 63 29 39
normalized size 1 1. 1.09 0.86 1.03 1.8 0.83 1.11
time (sec) N/A 0.018 0.006 0.044 1.463 2.127 1.733 1.122
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 152 152 136 129 362 757 1086 211
normalized size 1 1. 0.89 0.85 2.38 4.98 7.14 1.39
time (sec) N/A 0.104 0.041 0.061 1.455 2.369 58.118 1.14
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 150 150 133 127 342 713 1081 207
normalized size 1 1. 0.89 0.85 2.28 4.75 7.21 1.38
time (sec) N/A 0.094 0.027 0.043 1.502 2.301 30.421 1.12
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 102 118 339 647 440 194
normalized size 1 1. 0.77 0.89 2.57 4.9 3.33 1.47
time (sec) N/A 0.076 0.034 0.041 1.511 2.25 14.902 1.097
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 105 115 327 633 462 182
normalized size 1 1. 0.78 0.85 2.42 4.69 3.42 1.35
time (sec) N/A 0.079 0.04 0.042 1.492 2.313 30.065 1.129
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 150 150 146 121 356 706 1074 189
normalized size 1 1. 0.97 0.81 2.37 4.71 7.16 1.26
time (sec) N/A 0.092 0.051 0.043 1.476 2.34 55.366 1.109
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 40 32 42 88 0 42
normalized size 1 1. 0.78 0.63 0.82 1.73 0. 0.82
time (sec) N/A 0.012 0.015 0.023 1.456 2.229 0. 1.105
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 33 27 35 72 0 35
normalized size 1 1. 0.79 0.64 0.83 1.71 0. 0.83
time (sec) N/A 0.009 0.011 0.022 1.424 2.28 0. 1.091
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 17 22 47 0 22
normalized size 1 1. 1. 0.77 1. 2.14 0. 1.
time (sec) N/A 0.006 0.006 0.023 1.454 2.212 0. 1.108
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 61 47 0 0 0
normalized size 1 1. 1. 1.97 1.52 0. 0. 0.
time (sec) N/A 0.032 0.005 0.033 1.583 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 29 18 23 54 92 26
normalized size 1 1. 1.26 0.78 1. 2.35 4. 1.13
time (sec) N/A 0.011 0.009 0.024 1.466 2.269 3.079 1.101
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 34 27 35 80 160 35
normalized size 1 1. 0.81 0.64 0.83 1.9 3.81 0.83
time (sec) N/A 0.012 0.01 0.029 1.463 2.188 8.744 1.108
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 29 25 32 88 85 32
normalized size 1 1. 0.81 0.69 0.89 2.44 2.36 0.89
time (sec) N/A 0.014 0.016 0.023 0.974 2.209 7.887 1.096
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 25 20 26 73 24 26
normalized size 1 1. 0.86 0.69 0.9 2.52 0.83 0.9
time (sec) N/A 0.011 0.011 0.023 0.973 2.189 1.332 1.107
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 18 15 19 54 17 19
normalized size 1 1. 1. 0.83 1.06 3. 0.94 1.06
time (sec) N/A 0.007 0.007 0.023 0.955 2.208 0.45 1.093
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 19 24 77 20 22
normalized size 1 1. 1. 0.86 1.09 3.5 0.91 1.
time (sec) N/A 0.008 0.012 0.027 0.979 2.136 1.766 1.128
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 29 26 34 97 143 38
normalized size 1 1. 0.78 0.7 0.92 2.62 3.86 1.03
time (sec) N/A 0.012 0.018 0.029 1.006 2.262 8.517 1.129
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 20 20 46 14 18
normalized size 1 1. 1. 1.18 1.18 2.71 0.82 1.06
time (sec) N/A 0.006 0.002 0.049 0.992 2.075 0.191 1.099
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 40 94 0 181 0 0
normalized size 1 1. 0.85 2. 0. 3.85 0. 0.
time (sec) N/A 0.035 0.015 0.052 0. 2.321 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 37 57 108 0 0 0
normalized size 1 1. 1. 1.54 2.92 0. 0. 0.
time (sec) N/A 0.034 0.007 0.116 1.629 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 95 132 140 225 155 142
normalized size 1 1. 0.9 1.25 1.32 2.12 1.46 1.34
time (sec) N/A 0.107 0.067 0.052 1.445 2.227 4.025 1.127
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 114 94 115 184 117 113
normalized size 1 1. 1.42 1.18 1.44 2.3 1.46 1.41
time (sec) N/A 0.078 0.042 0.041 1.475 2.208 1.309 1.12
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 90 66 92 143 78 84
normalized size 1 1. 1.5 1.1 1.53 2.38 1.3 1.4
time (sec) N/A 0.055 0.033 0.044 1.474 2.273 0.833 1.093
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 44 36 39 119 46 68
normalized size 1 1. 1.33 1.09 1.18 3.61 1.39 2.06
time (sec) N/A 0.012 0.013 0.039 0.956 2.146 0.488 1.118
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 120 120 251 103 180 0 0 0
normalized size 1 1. 2.09 0.86 1.5 0. 0. 0.
time (sec) N/A 0.108 0.025 0.056 1.65 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 66 63 104 174 330 97
normalized size 1 1. 1.06 1.02 1.68 2.81 5.32 1.56
time (sec) N/A 0.039 0.052 0.049 1.478 2.316 9.504 1.111
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 92 104 151 248 675 158
normalized size 1 1. 0.97 1.09 1.59 2.61 7.11 1.66
time (sec) N/A 0.082 0.093 0.048 1.474 2.305 15.208 1.114
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 129 129 126 164 223 344 1125 242
normalized size 1 1. 0.98 1.27 1.73 2.67 8.72 1.88
time (sec) N/A 0.112 0.132 0.053 1.489 2.403 33.039 1.134
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 642 655 563 2082 0 0 0 0
normalized size 1 1.02 0.88 3.24 0. 0. 0. 0.
time (sec) N/A 0.998 0.549 0.814 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 152 152 345 198 382 0 0 0
normalized size 1 1. 2.27 1.3 2.51 0. 0. 0.
time (sec) N/A 0.142 0.04 0.057 1.896 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 338 422 602 317 378 0 0 0
normalized size 1 1.25 1.78 0.94 1.12 0. 0. 0.
time (sec) N/A 0.498 9.245 0.066 1.879 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F(-2) F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 735 818 5117 52954 0 0 0 0
normalized size 1 1.11 6.96 72.05 0. 0. 0. 0.
time (sec) N/A 1.518 33.893 1.987 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 693 693 618 343 0 0 0 0
normalized size 1 1. 0.89 0.49 0. 0. 0. 0.
time (sec) N/A 2.065 0.736 0.231 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 830 830 809 376 0 0 0 0
normalized size 1 1. 0.97 0.45 0. 0. 0. 0.
time (sec) N/A 2.322 0.686 0.214 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 367 367 629 4601 0 0 0 0
normalized size 1 1. 1.71 12.54 0. 0. 0. 0.
time (sec) N/A 0.686 0.455 1.072 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 132 132 127 123 0 0 0 0
normalized size 1 1. 0.96 0.93 0. 0. 0. 0.
time (sec) N/A 0.096 0.144 0.429 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 216 216 138 156 0 0 0 0
normalized size 1 1. 0.64 0.72 0. 0. 0. 0.
time (sec) N/A 0.168 0.077 0.518 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 22 0 177 0 0 0 0 0
normalized size 1 0. 8.05 0. 0. 0. 0. 0.
time (sec) N/A 0.04 0.379 1.135 0. 0. 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 24 0 180 0 0 0 0 0
normalized size 1 0. 7.5 0. 0. 0. 0. 0.
time (sec) N/A 0.053 0.085 1.108 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 187 187 202 167 0 0 0 0
normalized size 1 1. 1.08 0.89 0. 0. 0. 0.
time (sec) N/A 0.223 1.444 0.642 0. 0. 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 281 281 207 202 0 0 0 0
normalized size 1 1. 0.74 0.72 0. 0. 0. 0.
time (sec) N/A 0.349 0.901 1.1 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 29 0 198 0 0 0 0 0
normalized size 1 0. 6.83 0. 0. 0. 0. 0.
time (sec) N/A 0.137 0.92 1.473 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 31 0 200 0 0 0 0 0
normalized size 1 0. 6.45 0. 0. 0. 0. 0.
time (sec) N/A 0.19 0.205 1.456 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 42 86 126 192 100 86
normalized size 1 1. 0.81 1.65 2.42 3.69 1.92 1.65
time (sec) N/A 0.039 0.014 0.042 1.472 2.186 1.671 1.1
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 141 57 70 82 56 54
normalized size 1 1. 3.62 1.46 1.79 2.1 1.44 1.38
time (sec) N/A 0.021 0.055 0.043 1.452 2.108 1.071 1.111
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 38 98 151 0 0 0
normalized size 1 1. 0.84 2.18 3.36 0. 0. 0.
time (sec) N/A 0.041 0.007 0.052 1.632 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 40 46 72 150 150 49
normalized size 1 1. 0.85 0.98 1.53 3.19 3.19 1.04
time (sec) N/A 0.032 0.017 0.046 1.007 2.222 1.962 1.109
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 68 86 0 0 0
normalized size 1 1. 1. 1.94 2.46 0. 0. 0.
time (sec) N/A 0.037 0.004 0.036 1.597 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 38 98 165 0 0 0
normalized size 1 1. 0.84 2.18 3.67 0. 0. 0.
time (sec) N/A 0.046 0.006 0.054 1.646 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.018 8.545 0.55 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 233 233 157 526 460 694 627 1045
normalized size 1 1. 0.67 2.26 1.97 2.98 2.69 4.48
time (sec) N/A 0.357 0.266 0.052 1.496 2.469 8.921 3.224
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 118 312 292 459 357 641
normalized size 1 1. 0.77 2.03 1.9 2.98 2.32 4.16
time (sec) N/A 0.186 0.145 0.048 1.497 2.388 4.351 1.494
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 163 146 153 257 177 340
normalized size 1 1. 1.68 1.51 1.58 2.65 1.82 3.51
time (sec) N/A 0.114 0.082 0.045 1.472 2.301 2.026 1.234
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 49 42 46 140 51 77
normalized size 1 1. 1.29 1.11 1.21 3.68 1.34 2.03
time (sec) N/A 0.02 0.012 0.041 0.986 2.147 0.49 1.095
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 162 162 304 224 0 0 0 0
normalized size 1 1. 1.88 1.38 0. 0. 0. 0.
time (sec) N/A 0.149 0.095 0.06 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 118 206 239 513 0 396
normalized size 1 1. 0.77 1.35 1.56 3.35 0. 2.59
time (sec) N/A 0.111 0.164 0.051 1.497 5.349 0. 1.108
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 228 228 180 437 554 1531 0 1550
normalized size 1 1. 0.79 1.92 2.43 6.71 0. 6.8
time (sec) N/A 0.278 0.502 0.059 1.521 20.437 0. 6.614
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 382 382 665 1832 0 0 0 0
normalized size 1 1. 1.74 4.8 0. 0. 0. 0.
time (sec) N/A 0.582 4.98 0.153 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 220 220 286 766 0 0 0 0
normalized size 1 1. 1.3 3.48 0. 0. 0. 0.
time (sec) N/A 0.384 0.561 0.135 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 102 102 118 236 0 0 0 0
normalized size 1 1. 1.16 2.31 0. 0. 0. 0.
time (sec) N/A 0.116 0.161 0.143 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F C F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 261 261 0 2201 0 0 0 0
normalized size 1 1. 0. 8.43 0. 0. 0. 0.
time (sec) N/A 0.177 6.452 1.504 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 567 567 454 1180 0 0 0 0
normalized size 1 1. 0.8 2.08 0. 0. 0. 0.
time (sec) N/A 1.386 8.941 0.114 0. 0. 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 565 565 2336 3693 0 0 0 0
normalized size 1 1. 4.13 6.54 0. 0. 0. 0.
time (sec) N/A 0.963 10.451 0.552 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 337 337 630 1570 0 0 0 0
normalized size 1 1. 1.87 4.66 0. 0. 0. 0.
time (sec) N/A 0.664 1.221 0.517 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 143 143 228 507 0 0 0 0
normalized size 1 1. 1.59 3.55 0. 0. 0. 0.
time (sec) N/A 0.217 0.312 0.324 0. 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F C F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 372 372 0 4521 0 0 0 0
normalized size 1 1. 0. 12.15 0. 0. 0. 0.
time (sec) N/A 0.216 55.631 0.865 0. 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F A F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1233 1233 0 1579 0 0 0 0
normalized size 1 1. 0. 1.28 0. 0. 0. 0.
time (sec) N/A 2.254 60.416 0.522 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 177 177 162 0 0 0 0 0
normalized size 1 1. 0.92 0. 0. 0. 0. 0.
time (sec) N/A 0.244 0.327 1.395 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.061 5.214 1.3 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.06 0.473 1.349 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 37 46 47 130 60 80
normalized size 1 1. 0.88 1.1 1.12 3.1 1.43 1.9
time (sec) N/A 0.044 0.016 0.039 0.974 2.52 5.628 1.096
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 40 149 51 140 0 88
normalized size 1 1. 0.89 3.31 1.13 3.11 0. 1.96
time (sec) N/A 0.044 0.035 0.215 0.963 2.718 0. 1.107
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 42 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.046 0.093 1.185 0. 0. 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F B F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 488 488 0 1717 0 0 0 0
normalized size 1 1. 0. 3.52 0. 0. 0. 0.
time (sec) N/A 0.523 0.293 2.868 0. 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F B F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 321 321 0 931 0 0 0 0
normalized size 1 1. 0. 2.9 0. 0. 0. 0.
time (sec) N/A 0.32 0.536 1.422 0. 0. 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 93 364 0 0 0 0
normalized size 1 1. 0.95 3.71 0. 0. 0. 0.
time (sec) N/A 0.069 0.036 0.773 0. 0. 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 42 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.046 0.093 1.186 0. 0. 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 42 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.042 0.825 1.228 0. 0. 0. 0.
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 18 20 23 42 48 41
normalized size 1 1. 1.12 1.25 1.44 2.62 3. 2.56
time (sec) N/A 0.008 0.005 0.042 0.976 2.353 0.167 1.123
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 403 403 363 8034 0 5146 0 0
normalized size 1 1. 0.9 19.94 0. 12.77 0. 0.
time (sec) N/A 0.512 0.81 8.365 0. 3.626 0. 0.
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 305 305 272 7678 0 4035 0 0
normalized size 1 1. 0.89 25.17 0. 13.23 0. 0.
time (sec) N/A 0.406 0.589 31.149 0. 3.491 0. 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 198 198 555 1142 585 2894 0 0
normalized size 1 1. 2.8 5.77 2.95 14.62 0. 0.
time (sec) N/A 0.243 1.664 0.314 1.871 3.429 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.075 0.32 0.385 0. 0. 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 136 1526 417 902 0 0
normalized size 1 1. 0.88 9.91 2.71 5.86 0. 0.
time (sec) N/A 0.253 0.203 23.174 1.132 2.68 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 110 1491 294 749 0 0
normalized size 1 1. 0.89 12.12 2.39 6.09 0. 0.
time (sec) N/A 0.22 0.112 12.351 1.065 2.442 0. 0.
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 85 85 967 1489 614 541 0 0
normalized size 1 1. 11.38 17.52 7.22 6.36 0. 0.
time (sec) N/A 0.132 2.709 0.11 1.623 2.554 0. 0.
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.104 0.32 0.415 0. 0. 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 141 1527 421 918 0 0
normalized size 1 1. 0.91 9.85 2.72 5.92 0. 0.
time (sec) N/A 0.261 0.224 22.292 1.131 2.62 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 111 1492 298 763 0 0
normalized size 1 1. 0.9 12.03 2.4 6.15 0. 0.
time (sec) N/A 0.239 0.092 10.865 1.101 2.58 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 86 86 847 1681 608 552 0 0
normalized size 1 1. 9.85 19.55 7.07 6.42 0. 0.
time (sec) N/A 0.142 3.02 0.112 1.602 2.596 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.164 0.771 0.407 0. 0. 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 18 45 14 23 15 14
normalized size 1 1. 1.12 2.81 0.88 1.44 0.94 0.88
time (sec) N/A 0.013 0.006 0.049 0.946 1.963 0.18 1.105
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 399 399 359 7900 0 4058 0 0
normalized size 1 1. 0.9 19.8 0. 10.17 0. 0.
time (sec) N/A 0.508 0.766 8.084 0. 3.996 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 303 303 270 7550 0 3298 0 0
normalized size 1 1. 0.89 24.92 0. 10.88 0. 0.
time (sec) N/A 0.417 0.584 28.744 0. 3.973 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 198 198 1649 1160 710 2508 0 0
normalized size 1 1. 8.33 5.86 3.59 12.67 0. 0.
time (sec) N/A 0.254 12.984 0.316 1.909 3.9 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.118 0.366 0.405 0. 0. 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 140 1526 0 482 0 0
normalized size 1 1. 0.91 9.91 0. 3.13 0. 0.
time (sec) N/A 0.266 0.197 22.095 0. 2.501 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 110 1491 0 419 0 0
normalized size 1 1. 0.89 12.12 0. 3.41 0. 0.
time (sec) N/A 0.224 0.101 11.927 0. 2.527 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 85 85 929 1498 0 327 0 0
normalized size 1 1. 10.93 17.62 0. 3.85 0. 0.
time (sec) N/A 0.136 5.243 0.116 0. 2.509 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.114 0.365 0.418 0. 0. 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 136 1527 0 481 0 0
normalized size 1 1. 0.88 9.85 0. 3.1 0. 0.
time (sec) N/A 0.257 0.201 22.102 0. 2.674 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 110 1492 0 416 0 0
normalized size 1 1. 0.89 12.03 0. 3.35 0. 0.
time (sec) N/A 0.219 0.123 12.221 0. 2.748 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 86 86 872 1756 0 323 0 0
normalized size 1 1. 10.14 20.42 0. 3.76 0. 0.
time (sec) N/A 0.132 2.616 0.116 0. 2.366 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.117 0.379 0.434 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 299 299 600 7275 0 4072 0 0
normalized size 1 1. 2.01 24.33 0. 13.62 0. 0.
time (sec) N/A 0.208 0.333 4.991 0. 3.884 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 229 229 375 5425 0 2901 0 0
normalized size 1 1. 1.64 23.69 0. 12.67 0. 0.
time (sec) N/A 0.154 0.189 10.434 0. 3.561 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 159 159 278 2688 0 1894 0 0
normalized size 1 1. 1.75 16.91 0. 11.91 0. 0.
time (sec) N/A 0.102 0.223 8.715 0. 3.34 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 132 196 0 1098 0 0
normalized size 1 1. 1.81 2.68 0. 15.04 0. 0.
time (sec) N/A 0.041 0.049 0.17 0. 2.736 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.04 0.75 0.936 0. 0. 0. 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 355 355 305 6930 0 3641 0 0
normalized size 1 1. 0.86 19.52 0. 10.26 0. 0.
time (sec) N/A 0.455 5.115 10.428 0. 3.269 0. 0.
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 267 267 229 6580 0 2985 0 0
normalized size 1 1. 0.86 24.64 0. 11.18 0. 0.
time (sec) N/A 0.376 3.93 21.403 0. 3.011 0. 0.
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 288 350 0 2288 0 0
normalized size 1 1. 1.66 2.01 0. 13.15 0. 0.
time (sec) N/A 0.222 1.347 0.097 0. 6.682 0. 0.
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.081 5.104 0.447 0. 0. 0. 0.
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 128 1549 174 869 0 0
normalized size 1 1. 0.9 10.91 1.23 6.12 0. 0.
time (sec) N/A 0.228 0.177 17.627 5.767 2.245 0. 0.
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 102 1513 144 720 0 0
normalized size 1 1. 0.9 13.39 1.27 6.37 0. 0.
time (sec) N/A 0.197 0.086 8.242 5.787 2.175 0. 0.
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 71 1381 108 520 0 0
normalized size 1 1. 0.9 17.48 1.37 6.58 0. 0.
time (sec) N/A 0.12 0.793 0.118 5.849 2.24 0. 0.
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.093 3.183 0.414 0. 0. 0. 0.
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 128 1570 174 853 0 0
normalized size 1 1. 0.88 10.83 1.2 5.88 0. 0.
time (sec) N/A 0.227 0.184 15.757 5.878 2.261 0. 0.
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 102 1534 143 706 0 0
normalized size 1 1. 0.88 13.22 1.23 6.09 0. 0.
time (sec) N/A 0.194 0.098 5.872 5.817 2.142 0. 0.
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 71 1351 108 509 0 0
normalized size 1 1. 0.87 16.48 1.32 6.21 0. 0.
time (sec) N/A 0.119 0.711 0.116 5.773 2.246 0. 0.
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.089 3.216 0.446 0. 0. 0. 0.
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 299 299 600 7275 0 4070 0 0
normalized size 1 1. 2.01 24.33 0. 13.61 0. 0.
time (sec) N/A 0.208 0.336 7.395 0. 3.03 0. 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 229 229 375 5425 0 2903 0 0
normalized size 1 1. 1.64 23.69 0. 12.68 0. 0.
time (sec) N/A 0.154 0.202 9.65 0. 2.585 0. 0.
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 159 159 278 2688 0 1894 0 0
normalized size 1 1. 1.75 16.91 0. 11.91 0. 0.
time (sec) N/A 0.099 0.245 8.72 0. 2.374 0. 0.
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 132 196 0 1098 0 0
normalized size 1 1. 1.78 2.65 0. 14.84 0. 0.
time (sec) N/A 0.043 0.041 0.143 0. 2.011 0. 0.
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.037 0.773 0.937 0. 0. 0. 0.
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 351 351 299 6912 0 3614 0 0
normalized size 1 1. 0.85 19.69 0. 10.3 0. 0.
time (sec) N/A 0.463 5.398 12.255 0. 2.85 0. 0.
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 265 265 225 6514 0 2963 0 0
normalized size 1 1. 0.85 24.58 0. 11.18 0. 0.
time (sec) N/A 0.376 4.036 20.174 0. 2.561 0. 0.
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 287 350 0 2272 0 0
normalized size 1 1. 1.65 2.01 0. 13.06 0. 0.
time (sec) N/A 0.232 1.218 0.095 0. 5.706 0. 0.
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.079 5.209 0.382 0. 0. 0. 0.
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 128 1548 174 856 0 0
normalized size 1 1. 0.9 10.9 1.23 6.03 0. 0.
time (sec) N/A 0.231 0.172 14.447 5.841 2.069 0. 0.
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 102 1512 144 709 0 0
normalized size 1 1. 0.9 13.38 1.27 6.27 0. 0.
time (sec) N/A 0.203 0.091 6.462 5.886 2.168 0. 0.
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 71 1381 108 512 0 0
normalized size 1 1. 0.9 17.48 1.37 6.48 0. 0.
time (sec) N/A 0.124 0.623 0.121 5.901 2.219 0. 0.
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.083 3.162 0.441 0. 0. 0. 0.
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 128 1571 174 867 0 0
normalized size 1 1. 0.88 10.83 1.2 5.98 0. 0.
time (sec) N/A 0.232 0.196 16.543 6.041 2.192 0. 0.
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 102 1535 143 717 0 0
normalized size 1 1. 0.88 13.23 1.23 6.18 0. 0.
time (sec) N/A 0.205 0.116 8.506 5.902 2.27 0. 0.
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 71 1351 108 517 0 0
normalized size 1 1. 0.87 16.48 1.32 6.3 0. 0.
time (sec) N/A 0.124 0.644 0.12 5.903 2.172 0. 0.
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.108 3.089 0.424 0. 0. 0. 0.
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 187 187 132 1058 0 711 0 0
normalized size 1 1. 0.71 5.66 0. 3.8 0. 0.
time (sec) N/A 0.608 0.336 0.371 0. 2.409 0. 0.
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 59 59 46 147 0 0
normalized size 1 1. 1.69 1.69 1.31 4.2 0. 0.
time (sec) N/A 0.028 0.033 0.033 1.61 2.158 0. 0.
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 58 50 0 238 0 0
normalized size 1 1. 0.82 0.7 0. 3.35 0. 0.
time (sec) N/A 0.047 0.01 0.185 0. 2.193 0. 0.
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 103 76 0 298 0 0
normalized size 1 1. 1. 0.74 0. 2.89 0. 0.
time (sec) N/A 0.07 0.008 0.154 0. 2.236 0. 0.
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 83 106 85 297 0 0
normalized size 1 1. 1.63 2.08 1.67 5.82 0. 0.
time (sec) N/A 0.03 0.079 0.058 1.635 2.382 0. 0.
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 83 355 0 431 0 0
normalized size 1 1. 0.81 3.45 0. 4.18 0. 0.
time (sec) N/A 0.062 0.014 0.25 0. 2.455 0. 0.
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 151 413 0 540 0 0
normalized size 1 1. 1. 2.74 0. 3.58 0. 0.
time (sec) N/A 0.098 0.008 0.253 0. 2.696 0. 0.
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 196 196 167 186 302 554 0 0
normalized size 1 1. 0.85 0.95 1.54 2.83 0. 0.
time (sec) N/A 0.154 0.182 0.057 1.712 2.691 0. 0.
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 250 250 250 678 0 778 0 0
normalized size 1 1. 1. 2.71 0. 3.11 0. 0.
time (sec) N/A 2.654 0.284 0.414 0. 2.818 0. 0.
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 313 313 313 764 0 967 0 0
normalized size 1 1. 1. 2.44 0. 3.09 0. 0.
time (sec) N/A 2.448 0.229 0.408 0. 2.806 0. 0.
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 25 26 84 19 28
normalized size 1 1. 1. 0.93 0.96 3.11 0.7 1.04
time (sec) N/A 0.02 0.021 0.027 0.987 2.4 12.894 1.095
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 19 23 43 12 24
normalized size 1 1. 1. 1.12 1.35 2.53 0.71 1.41
time (sec) N/A 0.04 0.045 0.128 1.014 2.35 0.74 1.146
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 47 47 61 1281 63 343 0 89
normalized size 1 1. 1.3 27.26 1.34 7.3 0. 1.89
time (sec) N/A 0.074 0.104 0.337 1.525 2.494 0. 1.143
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 103 103 146 1358 177 741 0 208
normalized size 1 1. 1.42 13.18 1.72 7.19 0. 2.02
time (sec) N/A 0.139 0.139 0.394 1.541 2.715 0. 1.134
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 180 180 89 1323 225 1153 0 344
normalized size 1 1. 0.49 7.35 1.25 6.41 0. 1.91
time (sec) N/A 0.178 0.109 0.403 1.54 2.788 0. 1.485
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 180 180 89 1323 225 1152 0 344
normalized size 1 1. 0.49 7.35 1.25 6.4 0. 1.91
time (sec) N/A 0.18 0.109 0.377 1.543 2.642 0. 1.53
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 103 103 145 859 228 591 0 208
normalized size 1 1. 1.41 8.34 2.21 5.74 0. 2.02
time (sec) N/A 0.151 0.147 0.356 1.577 2.754 0. 1.14
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 48 48 59 903 65 192 0 88
normalized size 1 1. 1.23 18.81 1.35 4. 0. 1.83
time (sec) N/A 0.077 0.093 0.307 1.521 2.487 0. 1.132

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 [50] had the largest ratio of [ 1.267 ]

Table 2.1Rubi 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 4 3 1. 8 0.375
2 A 4 3 1. 8 0.375
3 A 4 3 1. 8 0.375
4 A 4 3 1. 8 0.375
5 A 3 3 1. 6 0.5
6 A 2 2 1. 4 0.5
7 A 3 2 1. 8 0.25
8 A 5 5 1. 8 0.625
9 A 3 3 1. 8 0.375
10 A 4 3 1. 8 0.375
11 A 4 3 1. 8 0.375
12 A 15 7 1. 10 0.7
13 A 14 9 1. 10 0.9
14 A 10 7 1. 10 0.7
15 A 9 8 1. 10 0.8
16 A 5 5 1. 8 0.625
17 A 5 5 1. 6 0.833
18 A 6 5 1. 10 0.5
19 A 4 4 1. 10 0.4
20 A 8 7 1. 10 0.7
21 A 8 7 1. 10 0.7
22 A 13 8 1. 10 0.8
23 A 33 11 1. 10 1.1
24 A 22 11 1. 10 1.1
25 A 18 10 1. 10 1.
26 A 11 9 1. 10 0.9
27 A 8 8 1. 8 1.
28 A 5 6 1. 6 1.
29 A 8 6 1. 10 0.6
30 A 5 6 1. 10 0.6
31 A 7 6 1. 10 0.6
32 A 14 11 1. 10 1.1
33 A 16 8 1. 10 0.8
34 A 0 0 0. 0 0.
35 A 0 0 0. 0 0.
36 A 2 2 1. 8 0.25
37 A 9 7 1. 13 0.538
38 A 8 8 1. 13 0.615
39 A 4 4 1. 13 0.308
40 A 4 4 1. 11 0.364
41 A 1 1 1. 10 0.1
42 A 3 3 1. 13 0.231
43 A 7 7 1. 13 0.538
44 A 7 7 1. 13 0.538
45 A 12 8 1. 13 0.615
46 A 28 15 1. 15 1.
47 A 10 5 1. 13 0.385
48 A 25 13 1. 12 1.083
49 A 15 7 1. 15 0.467
50 A 31 19 1. 15 1.267
51 A 1 1 1. 12 0.083
52 A 1 1 1. 12 0.083
53 A 4 4 1. 14 0.286
54 A 4 4 1. 14 0.286
55 A 5 5 1. 14 0.357
56 A 5 4 1. 12 0.333
57 A 27 13 1. 14 0.929
58 A 24 12 1. 14 0.857
59 A 0 0 0. 0 0.
60 A 0 0 0. 0 0.
61 A 5 6 1. 16 0.375
62 A 7 9 1. 16 0.562
63 A 8 9 1. 16 0.562
64 A 8 9 1. 16 0.562
65 A 3 3 1. 14 0.214
66 A 2 2 1. 14 0.143
67 A 1 1 1. 14 0.071
68 A 2 2 1. 14 0.143
69 A 3 2 1. 14 0.143
70 A 3 3 1. 11 0.273
71 A 4 3 1. 11 0.273
72 A 2 2 1. 10 0.2
73 A 4 4 1. 12 0.333
74 A 4 3 1. 10 0.3
75 A 4 4 1. 10 0.4
76 A 2 2 1. 8 0.25
77 A 4 3 1. 10 0.3
78 A 5 5 1. 10 0.5
79 A 4 4 1. 10 0.4
80 A 11 8 1. 10 0.8
81 A 11 8 1. 10 0.8
82 A 10 7 1. 6 1.167
83 A 10 7 1. 10 0.7
84 A 11 8 1. 10 0.8
85 A 6 4 1. 10 0.4
86 A 5 4 1. 8 0.5
87 A 4 4 1. 6 0.667
88 A 4 3 1. 10 0.3
89 A 4 4 1. 10 0.4
90 A 5 4 1. 10 0.4
91 A 3 2 1. 12 0.167
92 A 3 2 1. 12 0.167
93 A 2 2 1. 12 0.167
94 A 4 4 1. 12 0.333
95 A 3 2 1. 12 0.167
96 A 3 3 1. 4 0.75
97 A 4 3 1. 10 0.3
98 A 4 3 1. 10 0.3
99 A 7 6 1. 10 0.6
100 A 7 6 1. 10 0.6
101 A 7 6 1. 8 0.75
102 A 3 3 1. 6 0.5
103 A 5 5 1. 10 0.5
104 A 7 7 1. 10 0.7
105 A 8 7 1. 10 0.7
106 A 8 7 1. 10 0.7
107 A 37 7 1.02 16 0.438
108 A 5 5 1. 14 0.357
109 A 37 10 1.25 16 0.625
110 A 57 11 1.11 16 0.688
111 A 55 16 1. 18 0.889
112 A 65 19 1. 18 1.056
113 A 12 8 1. 19 0.421
114 A 2 2 1. 28 0.071
115 A 3 3 1. 33 0.091
116 A 0 0 0. 0 0.
117 A 0 0 0. 0 0.
118 A 4 4 1. 35 0.114
119 A 5 5 1. 40 0.125
120 A 0 0 0. 0 0.
121 A 0 0 0. 0 0.
122 A 5 4 1. 14 0.286
123 A 4 4 1. 12 0.333
124 A 4 3 1. 14 0.214
125 A 6 6 1. 14 0.429
126 A 5 4 1. 12 0.333
127 A 5 4 1. 19 0.21
128 A 0 0 0. 0 0.
129 A 7 6 1. 18 0.333
130 A 7 6 1. 18 0.333
131 A 7 6 1. 16 0.375
132 A 4 3 1. 10 0.3
133 A 5 5 1. 18 0.278
134 A 8 8 1. 18 0.444
135 A 9 8 1. 18 0.444
136 A 16 13 1. 20 0.65
137 A 13 10 1. 18 0.556
138 A 6 6 1. 12 0.5
139 A 2 2 1. 20 0.1
140 A 25 25 1. 20 1.25
141 A 21 14 1. 20 0.7
142 A 15 11 1. 18 0.611
143 A 6 7 1. 12 0.583
144 A 2 2 1. 20 0.1
145 A 35 22 1. 20 1.1
146 A 6 4 1. 18 0.222
147 A 0 0 0. 0 0.
148 A 0 0 0. 0 0.
149 A 4 4 1. 12 0.333
150 A 4 4 1. 14 0.286
151 A 0 0 0. 0 0.
152 A 9 7 1. 40 0.175
153 A 7 6 1. 40 0.15
154 A 4 4 1. 38 0.105
155 A 0 0 0. 0 0.
156 A 0 0 0. 0 0.
157 A 2 2 1. 7 0.286
158 A 11 6 1. 15 0.4
159 A 9 5 1. 13 0.385
160 A 7 4 1. 11 0.364
161 A 0 0 0. 0 0.
162 A 7 7 1. 21 0.333
163 A 6 6 1. 19 0.316
164 A 5 5 1. 17 0.294
165 A 0 0 0. 0 0.
166 A 7 7 1. 22 0.318
167 A 6 6 1. 20 0.3
168 A 5 5 1. 18 0.278
169 A 0 0 0. 0 0.
170 A 2 2 1. 7 0.286
171 A 11 6 1. 15 0.4
172 A 9 5 1. 13 0.385
173 A 7 4 1. 11 0.364
174 A 0 0 0. 0 0.
175 A 7 7 1. 21 0.333
176 A 6 6 1. 19 0.316
177 A 5 5 1. 17 0.294
178 A 0 0 0. 0 0.
179 A 7 7 1. 22 0.318
180 A 6 6 1. 20 0.3
181 A 5 5 1. 18 0.278
182 A 0 0 0. 0 0.
183 A 12 6 1. 15 0.4
184 A 10 6 1. 15 0.4
185 A 8 5 1. 13 0.385
186 A 6 4 1. 7 0.571
187 A 0 0 0. 0 0.
188 A 11 6 1. 15 0.4
189 A 9 5 1. 13 0.385
190 A 7 4 1. 11 0.364
191 A 0 0 0. 0 0.
192 A 7 7 1. 19 0.368
193 A 6 6 1. 17 0.353
194 A 5 5 1. 15 0.333
195 A 0 0 0. 0 0.
196 A 7 7 1. 22 0.318
197 A 6 6 1. 20 0.3
198 A 5 5 1. 18 0.278
199 A 0 0 0. 0 0.
200 A 12 6 1. 15 0.4
201 A 10 6 1. 15 0.4
202 A 8 5 1. 13 0.385
203 A 6 4 1. 7 0.571
204 A 0 0 0. 0 0.
205 A 11 6 1. 15 0.4
206 A 9 5 1. 13 0.385
207 A 7 4 1. 11 0.364
208 A 0 0 0. 0 0.
209 A 7 7 1. 19 0.368
210 A 6 6 1. 17 0.353
211 A 5 5 1. 15 0.333
212 A 0 0 0. 0 0.
213 A 7 7 1. 22 0.318
214 A 6 6 1. 20 0.3
215 A 5 5 1. 18 0.278
216 A 0 0 0. 0 0.
217 A 13 9 1. 24 0.375
218 A 4 3 1. 4 0.75
219 A 7 4 1. 6 0.667
220 A 9 5 1. 8 0.625
221 A 4 3 1. 8 0.375
222 A 7 4 1. 10 0.4
223 A 9 5 1. 12 0.417
224 A 6 6 1. 12 0.5
225 A 25 8 1. 14 0.571
226 A 29 9 1. 16 0.562
227 A 5 6 1. 10 0.6
228 A 1 1 1. 19 0.053
229 A 5 5 1. 20 0.25
230 A 8 7 1. 20 0.35
231 A 13 10 1. 20 0.5
232 A 13 10 1. 20 0.5
233 A 8 7 1. 20 0.35
234 A 5 5 1. 20 0.25

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