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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

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

B grade: { 6, 99, 100, 101, 102, 104, 105, 106, 122, 123, 124, 125, 127, 129, 130, 131, 132, 134, 135, 149 }

C grade: { }

F grade: { 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 36, 37, 38, 39, 40, 42, 44, 46, 47, 48, 49, 50, 57, 58, 65, 66, 72, 73, 77, 97, 98, 103, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 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, 231, 232 }

2.1.8 Mupad

A grade: { 34, 35, 59, 60, 116, 117, 120, 121, 128, 147, 148, 151, 155, 156, 161, 165, 169, 174, 178, 182, 187, 191, 195, 199, 204, 208, 212, 216 }

B grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 16, 17, 20, 22, 37, 39, 41, 43, 45, 51, 52, 53, 54, 55, 56, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 93, 94, 95, 96, 99, 100, 101, 102, 104, 105, 106, 122, 123, 125, 129, 130, 131, 132, 134, 135, 138, 149, 150, 157, 170, 227, 228, 229, 230, 231, 232, 233, 234 }

C grade: { }

F grade: { 7, 13, 15, 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, 77, 88, 92, 97, 98, 103, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 124, 126, 127, 133, 136, 137, 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 Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 51 42 47 41 48 59 55
normalized size 1 1.00 1.00 0.82 0.92 0.80 0.94 1.16 1.08
time (sec) N/A 0.025 0.003 0.039 0.412 0.908 1.218 0.128 0.805
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 49 42 46 45 46 74 56
normalized size 1 1.00 1.00 0.86 0.94 0.92 0.94 1.51 1.14
time (sec) N/A 0.036 0.016 0.037 0.311 0.536 0.874 0.123 0.700
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 41 34 38 32 39 51 46
normalized size 1 1.00 1.00 0.83 0.93 0.78 0.95 1.24 1.12
time (sec) N/A 0.021 0.003 0.038 0.409 1.015 0.680 0.128 0.721
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 39 34 36 37 37 64 49
normalized size 1 1.00 1.00 0.87 0.92 0.95 0.95 1.64 1.26
time (sec) N/A 0.026 0.008 0.040 0.309 0.730 0.476 0.115 0.688
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 26 28 23 31 36 39
normalized size 1 1.00 1.00 0.84 0.90 0.74 1.00 1.16 1.26
time (sec) N/A 0.012 0.002 0.038 0.407 0.676 0.339 0.131 0.757
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 23 24 24 24 45 22
normalized size 1 1.00 1.00 0.96 1.00 1.00 1.00 1.88 0.92
time (sec) N/A 0.006 0.003 0.037 0.320 0.753 0.214 0.108 0.136
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 37 63 56 0 0 38 -1
normalized size 1 1.00 1.00 1.70 1.51 0.00 0.00 1.03 -0.03
time (sec) N/A 0.025 0.003 0.056 0.457 0.979 0.000 0.128 0.000
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 30 31 30 31 24 32 28
normalized size 1 1.00 1.00 1.03 1.00 1.03 0.80 1.07 0.93
time (sec) N/A 0.018 0.003 0.042 0.308 0.783 0.283 0.126 0.235
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 36 26 23 24 24 40 44
normalized size 1 1.00 1.16 0.84 0.74 0.77 0.77 1.29 1.42
time (sec) N/A 0.015 0.003 0.043 0.413 0.573 0.477 0.111 0.701
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 44 41 42 43 39 44 58
normalized size 1 1.00 0.96 0.89 0.91 0.93 0.85 0.96 1.26
time (sec) N/A 0.027 0.012 0.044 0.308 0.621 0.592 0.126 0.850
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 36 34 37 33 32 51 47
normalized size 1 1.00 0.88 0.83 0.90 0.80 0.78 1.24 1.15
time (sec) N/A 0.018 0.003 0.044 0.413 0.702 0.749 0.115 0.704
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 79 102 95 78 104 0 85
normalized size 1 1.00 0.76 0.98 0.91 0.75 1.00 0.00 0.82
time (sec) N/A 0.221 0.025 0.050 0.426 0.607 1.763 0.000 0.809
Problem 13 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 135 135 95 233 0 0 0 0 -1
normalized size 1 1.00 0.70 1.73 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.211 0.548 0.138 0.000 0.651 0.000 0.000 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 61 82 77 60 78 0 66
normalized size 1 1.00 0.76 1.02 0.96 0.75 0.98 0.00 0.82
time (sec) N/A 0.146 0.021 0.051 0.415 0.644 1.035 0.000 0.204
Problem 15 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 111 111 76 213 0 0 0 0 -1
normalized size 1 1.00 0.68 1.92 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.140 0.295 0.132 0.000 0.628 0.000 0.000 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 42 61 57 40 54 0 44
normalized size 1 1.00 0.79 1.15 1.08 0.75 1.02 0.00 0.83
time (sec) N/A 0.072 0.014 0.050 0.419 0.586 0.480 0.000 0.137
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 67 67 56 136 0 0 0 0 55
normalized size 1 1.00 0.84 2.03 0.00 0.00 0.00 0.00 0.82
time (sec) N/A 0.074 0.085 0.417 0.000 0.593 0.000 0.000 0.591
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 116 116 132 959 0 0 0 0 -1
normalized size 1 1.00 1.14 8.27 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.213 0.064 0.878 0.000 0.564 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 66 66 64 234 0 0 0 0 -1
normalized size 1 1.00 0.97 3.55 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.105 0.049 0.136 0.000 0.556 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 A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 56 68 56 57 53 60 50
normalized size 1 1.00 0.95 1.15 0.95 0.97 0.90 1.02 0.85
time (sec) N/A 0.088 0.018 0.054 0.424 0.714 0.502 0.122 0.660
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 113 113 96 290 0 0 0 0 -1
normalized size 1 1.00 0.85 2.57 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.161 0.250 0.143 0.000 0.678 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 A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 81 91 95 78 80 91 73
normalized size 1 1.00 0.91 1.02 1.07 0.88 0.90 1.02 0.82
time (sec) N/A 0.155 0.021 0.059 0.429 0.861 0.814 0.121 0.699
Problem 23 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 194 194 125 243 0 0 0 0 -1
normalized size 1 1.00 0.64 1.25 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.667 0.687 1.878 0.000 0.975 0.000 0.000 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 205 205 184 2731 0 0 0 0 -1
normalized size 1 1.00 0.90 13.32 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.517 0.642 6.145 0.000 1.133 0.000 0.000 0.000
Problem 25 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 148 148 96 209 0 0 0 0 -1
normalized size 1 1.00 0.65 1.41 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.386 0.380 1.553 0.000 0.549 0.000 0.000 0.000
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 157 157 149 1815 0 0 0 0 -1
normalized size 1 1.00 0.95 11.56 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.302 0.354 4.186 0.000 0.603 0.000 0.000 0.000
Problem 27 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 103 103 76 162 0 0 0 0 -1
normalized size 1 1.00 0.74 1.57 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.171 0.101 0.729 0.000 0.700 0.000 0.000 0.000
Problem 28 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 96 96 90 199 0 0 0 0 -1
normalized size 1 1.00 0.94 2.07 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.150 0.116 0.447 0.000 0.540 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 178 178 180 1050 0 0 0 0 -1
normalized size 1 1.00 1.01 5.90 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.327 0.084 0.566 0.000 0.624 0.000 0.000 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-1) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 93 93 83 1576 0 0 0 0 -1
normalized size 1 1.00 0.89 16.95 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.188 0.083 1.585 0.000 0.857 0.000 0.000 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-1) F F A F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 105 105 90 109 0 0 0 29 -1
normalized size 1 1.00 0.86 1.04 0.00 0.00 0.00 0.28 -0.01
time (sec) N/A 0.199 0.177 0.763 0.000 0.768 0.000 0.146 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-1) F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 167 167 151 5029 0 0 0 0 -1
normalized size 1 1.00 0.90 30.11 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.337 0.259 5.041 0.000 0.529 0.000 0.000 0.000
Problem 33 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 152 152 126 158 0 0 0 0 -1
normalized size 1 1.00 0.83 1.04 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.420 0.283 1.591 0.000 0.726 0.000 0.000 0.000
Problem 34 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 0.013 0.935 1.836 0.000 0.546 0.000 0.000 0.000
Problem 35 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 0.013 0.931 1.351 0.000 0.578 0.000 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 52 0 0 0 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.020 0.024 1.655 0.000 0.622 0.000 0.000 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 32 38 35 31 34 0 32
normalized size 1 1.00 0.80 0.95 0.88 0.78 0.85 0.00 0.80
time (sec) N/A 0.097 0.029 0.050 0.424 0.607 0.506 0.000 0.734
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 67 67 241 128 0 0 0 0 -1
normalized size 1 1.00 3.60 1.91 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.093 0.066 0.179 0.000 0.394 0.000 0.000 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 26 24 19 19 0 19
normalized size 1 1.00 1.00 1.13 1.04 0.83 0.83 0.00 0.83
time (sec) N/A 0.048 0.016 0.049 0.433 0.559 0.296 0.000 0.636
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 48 48 221 114 0 0 0 0 -1
normalized size 1 1.00 4.60 2.38 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.054 0.051 0.131 0.000 0.633 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 7 6 6 7 8 6
normalized size 1 1.00 1.00 0.88 0.75 0.75 0.88 1.00 0.75
time (sec) N/A 0.012 0.003 0.038 0.310 0.645 0.877 0.110 0.617
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 49 49 251 163 0 0 0 0 -1
normalized size 1 1.00 5.12 3.33 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.073 0.061 0.138 0.000 0.396 0.000 0.000 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 30 33 29 29 22 26 26
normalized size 1 1.00 1.00 1.10 0.97 0.97 0.73 0.87 0.87
time (sec) N/A 0.056 0.015 0.054 0.420 1.018 0.433 0.113 0.092
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 72 72 280 180 0 0 0 0 -1
normalized size 1 1.00 3.89 2.50 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.115 0.067 0.109 0.000 1.505 0.000 0.000 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 47 43 55 47 42 39 35
normalized size 1 1.00 1.00 0.91 1.17 1.00 0.89 0.83 0.74
time (sec) N/A 0.109 0.021 0.059 0.417 0.662 0.848 0.116 0.097
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 206 206 626 265 189 0 0 0 -1
normalized size 1 1.00 3.04 1.29 0.92 0.00 0.00 0.00 -0.00
time (sec) N/A 0.580 1.766 0.736 0.451 0.551 0.000 0.000 0.000
Problem 47 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 188 188 343 284 0 0 0 0 -1
normalized size 1 1.00 1.82 1.51 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.184 0.092 0.316 0.000 2.915 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 183 183 319 304 187 0 0 0 -1
normalized size 1 1.00 1.74 1.66 1.02 0.00 0.00 0.00 -0.01
time (sec) N/A 0.465 0.089 0.684 0.440 0.599 0.000 0.000 0.000
Problem 49 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 223 223 379 345 0 0 0 0 -1
normalized size 1 1.00 1.70 1.55 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.247 0.103 0.257 0.000 1.462 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 212 212 348 271 183 0 0 0 -1
normalized size 1 1.00 1.64 1.28 0.86 0.00 0.00 0.00 -0.00
time (sec) N/A 0.503 0.104 0.077 0.446 0.489 0.000 0.000 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 5 5 5 6 5 5 5 8 5
normalized size 1 1.00 1.00 1.20 1.00 1.00 1.00 1.60 1.00
time (sec) N/A 0.020 0.025 0.036 0.324 0.464 0.243 0.123 0.589
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 14 13 13 17 15 13
normalized size 1 1.00 1.00 1.08 1.00 1.00 1.31 1.15 1.00
time (sec) N/A 0.024 0.008 0.041 0.319 0.462 1.447 0.124 0.606
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 244 244 212 279 226 237 367 347 234
normalized size 1 1.00 0.87 1.14 0.93 0.97 1.50 1.42 0.96
time (sec) N/A 0.176 0.190 0.041 0.321 0.491 4.359 0.146 0.217
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 168 168 149 191 159 167 243 252 190
normalized size 1 1.00 0.89 1.14 0.95 0.99 1.45 1.50 1.13
time (sec) N/A 0.120 0.118 0.043 0.330 1.434 2.501 0.141 1.016
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 97 119 103 108 151 171 116
normalized size 1 1.00 0.89 1.09 0.94 0.99 1.39 1.57 1.06
time (sec) N/A 0.127 0.076 0.041 0.314 1.523 1.361 0.143 0.844
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 67 60 53 57 73 99 62
normalized size 1 1.00 1.16 1.03 0.91 0.98 1.26 1.71 1.07
time (sec) N/A 0.061 0.011 0.041 0.319 0.974 0.617 0.117 0.786
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 403 403 523 826 528 0 0 0 -1
normalized size 1 1.00 1.30 2.05 1.31 0.00 0.00 0.00 -0.00
time (sec) N/A 0.919 0.326 0.722 0.645 0.586 0.000 0.000 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 801 801 806 2177 628 0 0 0 -1
normalized size 1 1.00 1.01 2.72 0.78 0.00 0.00 0.00 -0.00
time (sec) N/A 1.158 8.256 0.803 0.546 0.694 0.000 0.000 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) 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 0.019 6.844 1.395 0.000 0.590 0.000 0.000 0.000
Problem 60 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 0.022 4.234 1.294 0.000 0.957 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 169 0 0 349 0 59 -1
normalized size 1 1.00 2.56 0.00 0.00 5.29 0.00 0.89 -0.02
time (sec) N/A 0.094 0.266 1.201 0.000 1.467 0.000 0.170 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 262 0 0 712 0 126 -1
normalized size 1 1.00 1.96 0.00 0.00 5.31 0.00 0.94 -0.01
time (sec) N/A 0.326 0.731 1.201 0.000 1.157 0.000 0.156 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 208 208 345 0 0 1278 0 208 -1
normalized size 1 1.00 1.66 0.00 0.00 6.14 0.00 1.00 -0.00
time (sec) N/A 0.935 1.136 1.175 0.000 1.406 0.000 0.173 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F(-2) B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 293 293 450 0 0 1986 0 340 -1
normalized size 1 1.00 1.54 0.00 0.00 6.78 0.00 1.16 -0.00
time (sec) N/A 1.155 1.674 1.199 0.000 1.589 0.000 0.179 0.000
Problem 65 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 195 195 136 117 0 0 0 0 -1
normalized size 1 1.00 0.70 0.60 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.072 1.247 1.073 0.000 1.642 0.000 0.000 0.000
Problem 66 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 155 155 89 99 0 0 0 0 -1
normalized size 1 1.00 0.57 0.64 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.045 0.116 0.919 0.000 0.575 0.000 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 21 68 31 29 0 33 -1
normalized size 1 1.00 0.60 1.94 0.89 0.83 0.00 0.94 -0.03
time (sec) N/A 0.020 0.025 0.700 0.480 3.041 0.000 0.151 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 37 165 63 52 0 55 -1
normalized size 1 1.00 0.47 2.09 0.80 0.66 0.00 0.70 -0.01
time (sec) N/A 0.044 0.035 0.750 0.450 0.538 0.000 0.149 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 47 258 93 70 0 83 -1
normalized size 1 1.00 0.40 2.19 0.79 0.59 0.00 0.70 -0.01
time (sec) N/A 0.067 0.044 0.854 0.455 0.623 0.000 0.168 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 25 27 26 21 31 32 22
normalized size 1 1.00 0.78 0.84 0.81 0.66 0.97 1.00 0.69
time (sec) N/A 0.026 0.022 0.043 0.447 0.675 0.497 0.133 0.073
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 36 37 39 39 88 40 27
normalized size 1 1.00 0.82 0.84 0.89 0.89 2.00 0.91 0.61
time (sec) N/A 0.029 0.025 0.042 0.438 1.965 0.797 0.131 0.601
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-2) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 28 35 38 26 0 0 22
normalized size 1 1.00 0.82 1.03 1.12 0.76 0.00 0.00 0.65
time (sec) N/A 0.015 0.015 0.052 0.419 1.337 0.000 0.000 0.614
Problem 73 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 56 56 46 61 75 40 0 0 51
normalized size 1 1.00 0.82 1.09 1.34 0.71 0.00 0.00 0.91
time (sec) N/A 0.044 0.027 0.349 0.430 0.655 0.000 0.000 0.062
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 41 36 38 39 39 40 35
normalized size 1 1.00 1.00 0.88 0.93 0.95 0.95 0.98 0.85
time (sec) N/A 0.025 0.016 0.041 0.315 1.557 1.781 0.134 0.645
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 37 32 34 27 36 38 31
normalized size 1 1.00 1.00 0.86 0.92 0.73 0.97 1.03 0.84
time (sec) N/A 0.019 0.006 0.039 0.417 0.737 1.033 0.112 0.612
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 28 28 28 31 47 27
normalized size 1 1.00 1.00 0.90 0.90 0.90 1.00 1.52 0.87
time (sec) N/A 0.009 0.007 0.039 0.323 0.981 0.581 0.131 0.596
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 37 57 68 0 0 0 -1
normalized size 1 1.00 1.00 1.54 1.84 0.00 0.00 0.00 -0.03
time (sec) N/A 0.034 0.006 0.161 0.480 0.610 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 34 31 32 37 29 34 31
normalized size 1 1.00 1.00 0.91 0.94 1.09 0.85 1.00 0.91
time (sec) N/A 0.017 0.007 0.045 0.317 0.677 0.696 0.123 0.660
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 38 30 27 28 29 29 32
normalized size 1 1.00 1.09 0.86 0.77 0.80 0.83 0.83 0.91
time (sec) N/A 0.018 0.007 0.043 0.408 0.493 1.045 0.121 0.649
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 152 152 136 129 137 239 167 156 54
normalized size 1 1.00 0.89 0.85 0.90 1.57 1.10 1.03 0.36
time (sec) N/A 0.104 0.050 0.061 0.406 0.558 30.121 0.147 0.443
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 133 127 135 228 156 153 52
normalized size 1 1.00 0.89 0.85 0.90 1.52 1.04 1.02 0.35
time (sec) N/A 0.094 0.033 0.042 0.410 0.807 17.160 0.138 0.700
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 102 118 120 189 139 144 42
normalized size 1 1.00 0.77 0.89 0.91 1.43 1.05 1.09 0.32
time (sec) N/A 0.076 0.038 0.040 0.413 0.620 9.454 0.136 0.129
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 105 115 123 227 144 135 44
normalized size 1 1.00 0.78 0.85 0.91 1.68 1.07 1.00 0.33
time (sec) N/A 0.079 0.047 0.041 0.411 1.533 19.964 0.137 0.683
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 146 121 133 269 162 149 52
normalized size 1 1.00 0.97 0.81 0.89 1.79 1.08 0.99 0.35
time (sec) N/A 0.092 0.056 0.045 0.415 1.044 37.993 0.130 0.715
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 40 32 31 27 39 33 31
normalized size 1 1.00 0.78 0.63 0.61 0.53 0.76 0.65 0.61
time (sec) N/A 0.012 0.017 0.040 0.564 1.393 2.000 0.119 0.650
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 33 27 26 20 32 28 26
normalized size 1 1.00 0.79 0.64 0.62 0.48 0.76 0.67 0.62
time (sec) N/A 0.009 0.013 0.039 0.416 0.626 1.295 0.144 0.659
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 17 16 12 19 14 16
normalized size 1 1.00 1.00 0.77 0.73 0.55 0.86 0.64 0.73
time (sec) N/A 0.006 0.007 0.043 0.414 0.568 1.181 0.115 0.631
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 61 35 0 0 19 -1
normalized size 1 1.00 1.00 1.97 1.13 0.00 0.00 0.61 -0.03
time (sec) N/A 0.032 0.006 0.057 0.453 0.613 0.000 0.152 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 29 18 17 19 92 19 17
normalized size 1 1.00 1.26 0.78 0.74 0.83 4.00 0.83 0.74
time (sec) N/A 0.011 0.010 0.043 0.434 0.673 1.942 0.134 0.642
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 34 27 26 27 160 26 24
normalized size 1 1.00 0.81 0.64 0.62 0.64 3.81 0.62 0.57
time (sec) N/A 0.012 0.011 0.046 0.412 0.527 4.946 0.121 0.646
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 29 25 24 24 85 39 24
normalized size 1 1.00 0.81 0.69 0.67 0.67 2.36 1.08 0.67
time (sec) N/A 0.014 0.017 0.040 0.328 1.458 4.965 0.129 0.646
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 25 20 19 19 24 30 -1
normalized size 1 1.00 0.86 0.69 0.66 0.66 0.83 1.03 -0.03
time (sec) N/A 0.011 0.011 0.040 0.315 1.126 1.274 0.119 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 15 14 14 17 18 14
normalized size 1 1.00 1.00 0.83 0.78 0.78 0.94 1.00 0.78
time (sec) N/A 0.007 0.008 0.040 0.313 0.785 0.340 0.115 0.770
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 19 18 25 20 16 20
normalized size 1 1.00 1.00 0.86 0.82 1.14 0.91 0.73 0.91
time (sec) N/A 0.008 0.013 0.044 0.330 2.095 1.183 0.135 0.665
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 29 26 25 33 143 23 27
normalized size 1 1.00 0.78 0.70 0.68 0.89 3.86 0.62 0.73
time (sec) N/A 0.012 0.020 0.046 0.325 0.471 4.920 0.129 0.650
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 20 15 15 14 13 15
normalized size 1 1.00 1.00 1.18 0.88 0.88 0.82 0.76 0.88
time (sec) N/A 0.006 0.002 0.068 0.332 0.482 0.152 0.122 0.056
Problem 97 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 47 47 40 94 0 63 0 0 -1
normalized size 1 1.00 0.85 2.00 0.00 1.34 0.00 0.00 -0.02
time (sec) N/A 0.035 0.018 0.060 0.000 2.580 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 37 57 68 0 0 0 -1
normalized size 1 1.00 1.00 1.54 1.84 0.00 0.00 0.00 -0.03
time (sec) N/A 0.034 0.007 0.156 0.562 1.070 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 95 132 104 92 155 617 133
normalized size 1 1.00 0.90 1.25 0.98 0.87 1.46 5.82 1.25
time (sec) N/A 0.107 0.077 0.044 0.431 0.700 1.453 0.981 0.775
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 114 94 85 73 117 423 101
normalized size 1 1.00 1.42 1.18 1.06 0.91 1.46 5.29 1.26
time (sec) N/A 0.078 0.047 0.044 0.444 2.253 0.996 0.847 1.335
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 90 66 68 55 78 210 61
normalized size 1 1.00 1.50 1.10 1.13 0.92 1.30 3.50 1.02
time (sec) N/A 0.055 0.038 0.041 0.429 1.055 0.613 0.272 0.973
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 44 36 29 43 46 111 42
normalized size 1 1.00 1.33 1.09 0.88 1.30 1.39 3.36 1.27
time (sec) N/A 0.012 0.015 0.037 0.373 0.585 0.383 0.192 1.197
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 120 120 251 103 133 0 0 0 -1
normalized size 1 1.00 2.09 0.86 1.11 0.00 0.00 0.00 -0.01
time (sec) N/A 0.108 0.029 0.062 0.483 0.534 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 66 63 77 64 167 498 62
normalized size 1 1.00 1.06 1.02 1.24 1.03 2.69 8.03 1.00
time (sec) N/A 0.039 0.067 0.048 0.425 0.520 1.771 0.367 1.222
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 92 104 112 99 381 1309 230
normalized size 1 1.00 0.97 1.09 1.18 1.04 4.01 13.78 2.42
time (sec) N/A 0.082 0.112 0.049 0.422 0.744 2.831 0.712 1.386
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 126 164 165 142 760 3449 285
normalized size 1 1.00 0.98 1.27 1.28 1.10 5.89 26.74 2.21
time (sec) N/A 0.112 0.155 0.053 0.417 0.587 4.506 2.612 1.240
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F F(-1) F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 642 655 563 2082 8519 0 0 0 -1
normalized size 1 1.02 0.88 3.24 13.27 0.00 0.00 0.00 -0.00
time (sec) N/A 0.998 0.602 1.390 5.978 1.500 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 152 152 345 198 283 0 0 0 -1
normalized size 1 1.00 2.27 1.30 1.86 0.00 0.00 0.00 -0.01
time (sec) N/A 0.142 0.047 0.064 0.550 2.520 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A F F(-1) F F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 338 422 602 317 280 0 0 0 -1
normalized size 1 1.25 1.78 0.94 0.83 0.00 0.00 0.00 -0.00
time (sec) N/A 0.498 11.124 0.069 0.554 1.686 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C B F F(-1) F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 735 818 5764 52954 8518 0 0 0 -1
normalized size 1 1.11 7.84 72.05 11.59 0.00 0.00 0.00 -0.00
time (sec) N/A 1.518 36.559 2.640 1.364 0.659 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 693 693 618 343 0 0 0 0 -1
normalized size 1 1.00 0.89 0.49 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.065 0.807 0.286 0.000 0.565 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 830 830 809 376 0 0 0 0 -1
normalized size 1 1.00 0.97 0.45 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.322 0.740 0.291 0.000 0.648 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 367 367 629 4601 0 0 0 0 -1
normalized size 1 1.00 1.71 12.54 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.686 0.495 1.602 0.000 0.642 0.000 0.000 0.000
Problem 114 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 132 132 127 125 0 0 0 0 -1
normalized size 1 1.00 0.96 0.95 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.096 0.160 0.691 0.000 0.626 0.000 0.000 0.000
Problem 115 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 216 216 138 156 0 0 0 0 -1
normalized size 1 1.00 0.64 0.72 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.168 0.092 1.022 0.000 0.607 0.000 0.000 0.000
Problem 116 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 NO TBD TBD TBD TBD TBD TBD
size 23 0 177 0 0 0 0 0 -1
normalized size 1 0.00 7.70 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.040 0.410 1.375 0.000 1.413 0.000 0.000 0.000
Problem 117 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 NO TBD TBD TBD TBD TBD TBD
size 25 0 180 0 0 0 0 0 -1
normalized size 1 0.00 7.20 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.053 0.112 1.296 0.000 2.422 0.000 0.000 0.000
Problem 118 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 187 187 202 167 0 0 0 0 -1
normalized size 1 1.00 1.08 0.89 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.223 1.546 2.629 0.000 2.103 0.000 0.000 0.000
Problem 119 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 281 281 207 202 0 0 0 0 -1
normalized size 1 1.00 0.74 0.72 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.349 0.928 3.993 0.000 1.095 0.000 0.000 0.000
Problem 120 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 NO TBD TBD TBD TBD TBD TBD
size 30 0 198 0 0 0 0 0 -1
normalized size 1 0.00 6.60 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.137 1.003 3.488 0.000 0.572 0.000 0.000 0.000
Problem 121 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 NO TBD TBD TBD TBD TBD TBD
size 32 0 200 0 0 0 0 0 -1
normalized size 1 0.00 6.25 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.190 0.225 3.471 0.000 0.673 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 42 86 93 81 99 203 85
normalized size 1 1.00 0.81 1.65 1.79 1.56 1.90 3.90 1.63
time (sec) N/A 0.039 0.015 0.043 0.432 0.554 2.910 0.308 0.153
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 141 57 52 33 56 100 49
normalized size 1 1.00 3.62 1.46 1.33 0.85 1.44 2.56 1.26
time (sec) N/A 0.021 0.059 0.041 0.425 0.518 1.774 0.179 1.510
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 38 98 112 0 0 100 -1
normalized size 1 1.00 0.84 2.18 2.49 0.00 0.00 2.22 -0.02
time (sec) N/A 0.041 0.008 0.061 0.480 0.615 0.000 0.550 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 40 46 53 59 151 238 57
normalized size 1 1.00 0.85 0.98 1.13 1.26 3.21 5.06 1.21
time (sec) N/A 0.032 0.021 0.047 0.320 0.558 6.137 0.173 0.774
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 35 68 64 0 0 26 -1
normalized size 1 1.00 1.00 1.94 1.83 0.00 0.00 0.74 -0.03
time (sec) N/A 0.037 0.005 0.059 0.458 2.081 0.000 0.159 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 38 98 122 0 0 103 -1
normalized size 1 1.00 0.84 2.18 2.71 0.00 0.00 2.29 -0.02
time (sec) N/A 0.046 0.008 0.059 0.480 1.729 0.000 0.688 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 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 0.018 9.258 3.411 0.000 0.000 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 233 233 157 526 341 325 654 2272 783
normalized size 1 1.00 0.67 2.26 1.46 1.39 2.81 9.75 3.36
time (sec) N/A 0.357 0.291 0.051 0.449 1.937 26.449 2.762 1.194
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 118 312 216 206 376 1169 409
normalized size 1 1.00 0.77 2.03 1.40 1.34 2.44 7.59 2.66
time (sec) N/A 0.186 0.158 0.049 0.426 0.735 11.141 1.880 0.956
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 163 146 113 110 177 452 136
normalized size 1 1.00 1.68 1.51 1.16 1.13 1.82 4.66 1.40
time (sec) N/A 0.114 0.094 0.045 0.426 0.520 4.758 0.342 1.453
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 49 42 34 52 51 116 48
normalized size 1 1.00 1.29 1.11 0.89 1.37 1.34 3.05 1.26
time (sec) N/A 0.020 0.014 0.039 0.310 0.694 0.387 0.215 1.285
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 162 162 304 224 0 0 0 0 -1
normalized size 1 1.00 1.88 1.38 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.149 0.109 0.067 0.000 0.525 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 118 206 177 223 0 1278 128
normalized size 1 1.00 0.77 1.35 1.16 1.46 0.00 8.35 0.84
time (sec) N/A 0.111 0.199 0.050 0.441 1.125 0.000 0.867 2.084
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 228 228 180 437 410 728 0 6190 399
normalized size 1 1.00 0.79 1.92 1.80 3.19 0.00 27.15 1.75
time (sec) N/A 0.278 0.619 0.053 0.452 3.215 0.000 4.698 7.329
Problem 136 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 382 382 665 1832 0 0 0 0 -1
normalized size 1 1.00 1.74 4.80 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.582 5.370 0.196 0.000 0.623 0.000 0.000 0.000
Problem 137 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 220 220 286 766 0 0 0 0 -1
normalized size 1 1.00 1.30 3.48 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.384 0.585 0.147 0.000 0.541 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 102 102 118 236 0 0 0 0 123
normalized size 1 1.00 1.16 2.31 0.00 0.00 0.00 0.00 1.21
time (sec) N/A 0.116 0.170 0.334 0.000 0.624 0.000 0.000 0.966
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F C F F F(-1) F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 261 261 0 2201 0 0 0 0 -1
normalized size 1 1.00 0.00 8.43 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.177 7.037 2.530 0.000 0.667 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 567 567 454 1180 0 0 0 0 -1
normalized size 1 1.00 0.80 2.08 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.386 9.504 0.126 0.000 0.833 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 565 565 2336 3693 0 0 0 0 -1
normalized size 1 1.00 4.13 6.54 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.963 11.429 0.577 0.000 0.588 0.000 0.000 0.000
Problem 142 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 337 337 630 1570 0 0 0 0 -1
normalized size 1 1.00 1.87 4.66 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.664 1.270 1.201 0.000 0.591 0.000 0.000 0.000
Problem 143 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 143 143 228 507 0 0 0 0 -1
normalized size 1 1.00 1.59 3.55 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.217 0.352 0.453 0.000 0.727 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F C F F F(-1) F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 372 372 0 4521 0 0 0 0 -1
normalized size 1 1.00 0.00 12.15 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.216 45.863 1.049 0.000 0.477 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1233 1233 1584 1579 0 0 0 0 -1
normalized size 1 1.00 1.28 1.28 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.254 38.759 0.873 0.000 0.726 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 177 177 162 0 0 0 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.244 0.360 2.106 0.000 0.581 0.000 0.000 0.000
Problem 147 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 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 0.061 5.441 1.886 0.000 0.774 0.000 0.000 0.000
Problem 148 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 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 0.060 0.485 2.039 0.000 0.540 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 37 46 35 51 60 127 230
normalized size 1 1.00 0.88 1.10 0.83 1.21 1.43 3.02 5.48
time (sec) N/A 0.044 0.016 0.041 0.319 0.679 3.339 0.230 0.763
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 40 149 38 56 0 60 58
normalized size 1 1.00 0.89 3.31 0.84 1.24 0.00 1.33 1.29
time (sec) N/A 0.044 0.036 0.439 0.317 0.608 0.000 0.377 1.377
Problem 151 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 43 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 -0.02
time (sec) N/A 0.046 0.091 1.835 0.000 0.621 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F B F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 488 488 0 1605 0 0 0 0 -1
normalized size 1 1.00 0.00 3.29 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.523 0.296 2.361 0.000 0.544 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F B F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 321 321 0 823 0 0 0 0 -1
normalized size 1 1.00 0.00 2.56 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.320 0.521 1.647 0.000 0.608 0.000 0.000 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 93 259 0 0 0 0 -1
normalized size 1 1.00 0.95 2.64 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.069 0.035 0.972 0.000 0.603 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 43 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 -0.02
time (sec) N/A 0.046 0.091 1.382 0.000 0.734 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 43 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 -0.02
time (sec) N/A 0.042 0.818 1.347 0.000 0.737 0.000 0.000 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 18 20 17 15 48 30 21
normalized size 1 1.00 1.12 1.25 1.06 0.94 3.00 1.88 1.31
time (sec) N/A 0.008 0.009 0.039 0.315 0.683 0.137 0.207 0.077
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 403 403 363 8034 0 1973 0 0 -1
normalized size 1 1.00 0.90 19.94 0.00 4.90 0.00 0.00 -0.00
time (sec) N/A 0.512 0.891 64.667 0.000 0.806 0.000 0.000 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 305 305 272 7654 0 1557 0 0 -1
normalized size 1 1.00 0.89 25.10 0.00 5.10 0.00 0.00 -0.00
time (sec) N/A 0.406 0.617 6.339 0.000 0.851 0.000 0.000 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 198 198 555 1142 433 1117 0 0 -1
normalized size 1 1.00 2.80 5.77 2.19 5.64 0.00 0.00 -0.01
time (sec) N/A 0.243 1.763 1.018 0.537 1.113 0.000 0.000 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 18 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 0.075 0.413 1.189 0.000 0.496 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 136 1526 309 319 0 0 -1
normalized size 1 1.00 0.88 9.91 2.01 2.07 0.00 0.00 -0.01
time (sec) N/A 0.253 0.261 6.488 0.368 0.592 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 110 1491 218 268 0 0 -1
normalized size 1 1.00 0.89 12.12 1.77 2.18 0.00 0.00 -0.01
time (sec) N/A 0.220 0.109 5.678 0.345 0.721 0.000 0.000 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 85 85 967 1489 455 199 0 0 -1
normalized size 1 1.00 11.38 17.52 5.35 2.34 0.00 0.00 -0.01
time (sec) N/A 0.132 5.584 0.611 0.454 0.682 0.000 0.000 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 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 0.357 1.857 0.000 0.772 0.000 0.000 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 141 1527 312 321 0 0 -1
normalized size 1 1.00 0.91 9.85 2.01 2.07 0.00 0.00 -0.01
time (sec) N/A 0.261 0.255 6.513 0.367 0.724 0.000 0.000 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 111 1492 221 270 0 0 -1
normalized size 1 1.00 0.90 12.03 1.78 2.18 0.00 0.00 -0.01
time (sec) N/A 0.239 0.097 6.079 0.368 0.619 0.000 0.000 0.000
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 86 86 847 1681 450 201 0 0 -1
normalized size 1 1.00 9.85 19.55 5.23 2.34 0.00 0.00 -0.01
time (sec) N/A 0.142 2.978 0.613 0.466 0.578 0.000 0.000 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 25 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 0.164 0.835 1.828 0.000 0.581 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 18 45 10 10 19 10 16
normalized size 1 1.00 1.12 2.81 0.62 0.62 1.19 0.62 1.00
time (sec) N/A 0.013 0.009 0.049 0.322 0.631 0.124 0.123 0.637
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 399 399 359 7900 0 1585 0 0 -1
normalized size 1 1.00 0.90 19.80 0.00 3.97 0.00 0.00 -0.00
time (sec) N/A 0.508 0.909 75.343 0.000 0.888 0.000 0.000 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 303 303 270 7532 0 1285 0 0 -1
normalized size 1 1.00 0.89 24.86 0.00 4.24 0.00 0.00 -0.00
time (sec) N/A 0.417 0.596 6.576 0.000 1.076 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 198 198 1649 1160 532 961 0 0 -1
normalized size 1 1.00 8.33 5.86 2.69 4.85 0.00 0.00 -0.01
time (sec) N/A 0.254 13.048 1.216 0.541 0.978 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 18 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 0.118 0.422 1.529 0.000 0.518 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-2) C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 140 1526 0 174 0 0 -1
normalized size 1 1.00 0.91 9.91 0.00 1.13 0.00 0.00 -0.01
time (sec) N/A 0.266 0.233 7.077 0.000 0.723 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-2) C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 110 1491 0 152 0 0 -1
normalized size 1 1.00 0.89 12.12 0.00 1.24 0.00 0.00 -0.01
time (sec) N/A 0.224 0.113 6.119 0.000 0.426 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) A F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 85 85 929 1498 0 116 0 0 -1
normalized size 1 1.00 10.93 17.62 0.00 1.36 0.00 0.00 -0.01
time (sec) N/A 0.136 6.883 0.752 0.000 0.412 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 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 0.114 0.414 2.070 0.000 0.527 0.000 0.000 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-2) C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 136 1527 0 173 0 0 -1
normalized size 1 1.00 0.88 9.85 0.00 1.12 0.00 0.00 -0.01
time (sec) N/A 0.257 0.230 6.796 0.000 0.812 0.000 0.000 0.000
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F(-2) C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 110 1492 0 151 0 0 -1
normalized size 1 1.00 0.89 12.03 0.00 1.22 0.00 0.00 -0.01
time (sec) N/A 0.219 0.134 6.073 0.000 0.690 0.000 0.000 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) A F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 86 86 872 1756 0 115 0 0 -1
normalized size 1 1.00 10.14 20.42 0.00 1.34 0.00 0.00 -0.01
time (sec) N/A 0.132 2.844 0.762 0.000 0.819 0.000 0.000 0.000
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-2) A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 25 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 0.117 0.413 2.306 0.000 0.508 0.000 0.000 0.000
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 299 299 600 7275 0 1448 0 0 -1
normalized size 1 1.00 2.01 24.33 0.00 4.84 0.00 0.00 -0.00
time (sec) N/A 0.208 0.362 48.500 0.000 0.971 0.000 0.000 0.000
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 375 5425 0 994 0 0 -1
normalized size 1 1.00 1.64 23.69 0.00 4.34 0.00 0.00 -0.00
time (sec) N/A 0.154 0.208 40.635 0.000 0.780 0.000 0.000 0.000
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 159 159 278 2688 0 596 0 0 -1
normalized size 1 1.00 1.75 16.91 0.00 3.75 0.00 0.00 -0.01
time (sec) N/A 0.102 0.240 5.128 0.000 0.835 0.000 0.000 0.000
Problem 186 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 73 73 132 198 0 334 0 0 -1
normalized size 1 1.00 1.81 2.71 0.00 4.58 0.00 0.00 -0.01
time (sec) N/A 0.041 0.057 0.621 0.000 0.599 0.000 0.000 0.000
Problem 187 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 18 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 0.040 4.307 2.679 0.000 0.773 0.000 0.000 0.000
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 355 355 305 6930 0 1335 0 0 -1
normalized size 1 1.00 0.86 19.52 0.00 3.76 0.00 0.00 -0.00
time (sec) N/A 0.455 5.456 60.451 0.000 0.723 0.000 0.000 0.000
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 267 267 229 6580 0 1103 0 0 -1
normalized size 1 1.00 0.86 24.64 0.00 4.13 0.00 0.00 -0.00
time (sec) N/A 0.376 4.196 6.450 0.000 0.710 0.000 0.000 0.000
Problem 190 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 174 174 288 350 0 851 0 0 -1
normalized size 1 1.00 1.66 2.01 0.00 4.89 0.00 0.00 -0.01
time (sec) N/A 0.222 1.511 0.384 0.000 1.651 0.000 0.000 0.000
Problem 191 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 18 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 0.081 9.511 1.366 0.000 0.585 0.000 0.000 0.000
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 128 1549 129 290 0 0 -1
normalized size 1 1.00 0.90 10.91 0.91 2.04 0.00 0.00 -0.01
time (sec) N/A 0.228 0.221 6.272 2.100 0.840 0.000 0.000 0.000
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 102 1513 107 244 0 0 -1
normalized size 1 1.00 0.90 13.39 0.95 2.16 0.00 0.00 -0.01
time (sec) N/A 0.197 0.089 5.457 2.019 0.425 0.000 0.000 0.000
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 71 1381 80 186 0 0 -1
normalized size 1 1.00 0.90 17.48 1.01 2.35 0.00 0.00 -0.01
time (sec) N/A 0.120 0.874 0.673 1.989 0.582 0.000 0.000 0.000
Problem 195 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 22 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 0.093 3.481 1.854 0.000 0.648 0.000 0.000 0.000
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 128 1570 129 290 0 0 -1
normalized size 1 1.00 0.88 10.83 0.89 2.00 0.00 0.00 -0.01
time (sec) N/A 0.227 0.231 6.237 2.003 0.654 0.000 0.000 0.000
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 102 1534 106 244 0 0 -1
normalized size 1 1.00 0.88 13.22 0.91 2.10 0.00 0.00 -0.01
time (sec) N/A 0.194 0.118 5.437 2.015 0.658 0.000 0.000 0.000
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 71 1351 80 186 0 0 -1
normalized size 1 1.00 0.87 16.48 0.98 2.27 0.00 0.00 -0.01
time (sec) N/A 0.119 0.776 0.551 2.006 0.739 0.000 0.000 0.000
Problem 199 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 25 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 0.089 3.470 1.938 0.000 0.745 0.000 0.000 0.000
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 299 299 600 7275 0 1448 0 0 -1
normalized size 1 1.00 2.01 24.33 0.00 4.84 0.00 0.00 -0.00
time (sec) N/A 0.208 0.371 51.065 0.000 0.753 0.000 0.000 0.000
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 375 5425 0 994 0 0 -1
normalized size 1 1.00 1.64 23.69 0.00 4.34 0.00 0.00 -0.00
time (sec) N/A 0.154 0.218 41.302 0.000 0.837 0.000 0.000 0.000
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 159 159 278 2688 0 596 0 0 -1
normalized size 1 1.00 1.75 16.91 0.00 3.75 0.00 0.00 -0.01
time (sec) N/A 0.099 0.278 5.092 0.000 0.822 0.000 0.000 0.000
Problem 203 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 74 74 132 198 0 334 0 0 -1
normalized size 1 1.00 1.78 2.68 0.00 4.51 0.00 0.00 -0.01
time (sec) N/A 0.043 0.050 0.589 0.000 0.829 0.000 0.000 0.000
Problem 204 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 18 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 0.037 0.845 2.661 0.000 0.625 0.000 0.000 0.000
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 351 351 299 6858 0 1315 0 0 -1
normalized size 1 1.00 0.85 19.54 0.00 3.75 0.00 0.00 -0.00
time (sec) N/A 0.463 5.770 60.217 0.000 1.179 0.000 0.000 0.000
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 265 265 225 6508 0 1087 0 0 -1
normalized size 1 1.00 0.85 24.56 0.00 4.10 0.00 0.00 -0.00
time (sec) N/A 0.376 4.513 6.464 0.000 1.082 0.000 0.000 0.000
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 287 350 0 839 0 0 -1
normalized size 1 1.00 1.65 2.01 0.00 4.82 0.00 0.00 -0.01
time (sec) N/A 0.232 1.310 0.583 0.000 1.414 0.000 0.000 0.000
Problem 208 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 18 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 0.079 9.316 1.577 0.000 0.580 0.000 0.000 0.000
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 128 1548 129 290 0 0 -1
normalized size 1 1.00 0.90 10.90 0.91 2.04 0.00 0.00 -0.01
time (sec) N/A 0.231 0.219 5.939 2.010 0.807 0.000 0.000 0.000
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 102 1512 107 244 0 0 -1
normalized size 1 1.00 0.90 13.38 0.95 2.16 0.00 0.00 -0.01
time (sec) N/A 0.203 0.096 5.653 1.977 0.845 0.000 0.000 0.000
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 71 1381 80 186 0 0 -1
normalized size 1 1.00 0.90 17.48 1.01 2.35 0.00 0.00 -0.01
time (sec) N/A 0.124 0.714 0.753 2.008 0.698 0.000 0.000 0.000
Problem 212 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 22 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 0.083 3.416 2.151 0.000 0.672 0.000 0.000 0.000
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 128 1571 129 290 0 0 -1
normalized size 1 1.00 0.88 10.83 0.89 2.00 0.00 0.00 -0.01
time (sec) N/A 0.232 0.235 6.096 2.012 0.608 0.000 0.000 0.000
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 102 1535 106 244 0 0 -1
normalized size 1 1.00 0.88 13.23 0.91 2.10 0.00 0.00 -0.01
time (sec) N/A 0.205 0.122 5.786 2.006 0.671 0.000 0.000 0.000
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 71 1351 80 186 0 0 -1
normalized size 1 1.00 0.87 16.48 0.98 2.27 0.00 0.00 -0.01
time (sec) N/A 0.124 0.716 0.617 2.032 0.722 0.000 0.000 0.000
Problem 216 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 25 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 0.108 3.563 2.087 0.000 0.717 0.000 0.000 0.000
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 187 187 132 1058 0 246 0 0 -1
normalized size 1 1.00 0.71 5.66 0.00 1.32 0.00 0.00 -0.01
time (sec) N/A 0.608 0.364 0.574 0.000 0.821 0.000 0.000 0.000
Problem 218 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 35 35 59 59 34 40 0 0 -1
normalized size 1 1.00 1.69 1.69 0.97 1.14 0.00 0.00 -0.03
time (sec) N/A 0.028 0.081 0.059 0.455 0.494 0.000 0.000 0.000
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 58 50 0 65 0 0 -1
normalized size 1 1.00 0.82 0.70 0.00 0.92 0.00 0.00 -0.01
time (sec) N/A 0.047 0.012 0.269 0.000 0.674 0.000 0.000 0.000
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 103 76 0 87 0 0 -1
normalized size 1 1.00 1.00 0.74 0.00 0.84 0.00 0.00 -0.01
time (sec) N/A 0.070 0.009 0.235 0.000 0.575 0.000 0.000 0.000
Problem 221 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 51 51 83 106 63 103 0 0 -1
normalized size 1 1.00 1.63 2.08 1.24 2.02 0.00 0.00 -0.02
time (sec) N/A 0.030 0.180 0.059 0.463 0.749 0.000 0.000 0.000
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 83 355 0 151 0 0 -1
normalized size 1 1.00 0.81 3.45 0.00 1.47 0.00 0.00 -0.01
time (sec) N/A 0.062 0.016 0.345 0.000 0.659 0.000 0.000 0.000
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 151 413 0 187 0 0 -1
normalized size 1 1.00 1.00 2.74 0.00 1.24 0.00 0.00 -0.01
time (sec) N/A 0.098 0.010 0.341 0.000 0.816 0.000 0.000 0.000
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 196 196 167 186 189 212 0 0 -1
normalized size 1 1.00 0.85 0.95 0.96 1.08 0.00 0.00 -0.01
time (sec) N/A 0.154 0.187 0.063 0.514 1.526 0.000 0.000 0.000
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 250 250 250 678 0 304 0 0 -1
normalized size 1 1.00 1.00 2.71 0.00 1.22 0.00 0.00 -0.00
time (sec) N/A 2.654 0.307 0.484 0.000 0.695 0.000 0.000 0.000
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 313 313 313 764 0 378 0 0 -1
normalized size 1 1.00 1.00 2.44 0.00 1.21 0.00 0.00 -0.00
time (sec) N/A 2.448 0.238 0.482 0.000 0.794 0.000 0.000 0.000
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 25 19 28 19 21 22
normalized size 1 1.00 1.00 0.93 0.70 1.04 0.70 0.78 0.81
time (sec) N/A 0.020 0.023 0.044 0.337 0.521 6.092 0.123 0.093
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 19 17 15 12 18 15
normalized size 1 1.00 1.00 1.12 1.00 0.88 0.71 1.06 0.88
time (sec) N/A 0.040 0.049 0.101 0.356 0.643 0.527 0.108 0.127
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F(-1) A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 47 47 61 1281 47 131 0 66 65
normalized size 1 1.00 1.30 27.26 1.00 2.79 0.00 1.40 1.38
time (sec) N/A 0.074 0.112 0.516 0.441 0.625 0.000 0.127 0.730
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F(-1) A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 103 103 146 1358 131 276 0 154 133
normalized size 1 1.00 1.42 13.18 1.27 2.68 0.00 1.50 1.29
time (sec) N/A 0.139 0.152 0.725 0.451 0.673 0.000 0.136 0.855
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F(-1) F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 180 180 89 1323 167 431 0 0 164
normalized size 1 1.00 0.49 7.35 0.93 2.39 0.00 0.00 0.91
time (sec) N/A 0.178 0.120 1.737 0.432 0.710 0.000 0.000 2.564
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F F B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 180 180 89 1323 167 431 0 0 164
normalized size 1 1.00 0.49 7.35 0.93 2.39 0.00 0.00 0.91
time (sec) N/A 0.180 0.120 1.475 0.445 0.680 0.000 0.000 2.372
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C A B F(-1) A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 103 103 145 859 169 221 0 154 135
normalized size 1 1.00 1.41 8.34 1.64 2.15 0.00 1.50 1.31
time (sec) N/A 0.151 0.156 0.762 0.483 0.445 0.000 0.127 0.835
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 48 48 59 903 48 75 0 65 68
normalized size 1 1.00 1.23 18.81 1.00 1.56 0.00 1.35 1.42
time (sec) N/A 0.077 0.102 0.595 0.436 0.625 0.000 0.128 0.706

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 2.1: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 4 3 1.00 8 0.375
2 A 4 3 1.00 8 0.375
3 A 4 3 1.00 8 0.375
4 A 4 3 1.00 8 0.375
5 A 3 3 1.00 6 0.500
6 A 2 2 1.00 4 0.500
7 A 3 2 1.00 8 0.250
8 A 5 5 1.00 8 0.625
9 A 3 3 1.00 8 0.375
10 A 4 3 1.00 8 0.375
11 A 4 3 1.00 8 0.375
12 A 15 7 1.00 10 0.700
13 A 14 9 1.00 10 0.900
14 A 10 7 1.00 10 0.700
15 A 9 8 1.00 10 0.800
16 A 5 5 1.00 8 0.625
17 A 5 5 1.00 6 0.833
18 A 6 5 1.00 10 0.500
19 A 4 4 1.00 10 0.400
20 A 8 7 1.00 10 0.700
21 A 8 7 1.00 10 0.700
22 A 13 8 1.00 10 0.800
23 A 33 11 1.00 10 1.100
24 A 22 11 1.00 10 1.100
25 A 18 10 1.00 10 1.000
26 A 11 9 1.00 10 0.900
27 A 8 8 1.00 8 1.000
28 A 5 6 1.00 6 1.000
29 A 8 6 1.00 10 0.600
30 A 5 6 1.00 10 0.600
31 A 7 6 1.00 10 0.600
32 A 14 11 1.00 10 1.100
33 A 16 8 1.00 10 0.800
34 A 0 0 0.00 0 0.000
35 A 0 0 0.00 0 0.000
36 A 2 2 1.00 8 0.250
37 A 9 7 1.00 13 0.538
38 A 8 8 1.00 13 0.615
39 A 4 4 1.00 13 0.308
40 A 4 4 1.00 11 0.364
41 A 1 1 1.00 10 0.100
42 A 3 3 1.00 13 0.231
43 A 7 7 1.00 13 0.538
44 A 7 7 1.00 13 0.538
45 A 12 8 1.00 13 0.615
46 A 28 15 1.00 15 1.000
47 A 10 5 1.00 13 0.385
48 A 25 13 1.00 12 1.083
49 A 15 7 1.00 15 0.467
50 A 31 19 1.00 15 1.267
51 A 1 1 1.00 12 0.083
52 A 1 1 1.00 12 0.083
53 A 4 4 1.00 14 0.286
54 A 4 4 1.00 14 0.286
55 A 5 5 1.00 14 0.357
56 A 5 4 1.00 12 0.333
57 A 27 13 1.00 14 0.929
58 A 24 12 1.00 14 0.857
59 A 0 0 0.00 0 0.000
60 A 0 0 0.00 0 0.000
61 A 5 6 1.00 16 0.375
62 A 7 9 1.00 16 0.562
63 A 8 9 1.00 16 0.562
64 A 8 9 1.00 16 0.562
65 A 3 3 1.00 14 0.214
66 A 2 2 1.00 14 0.143
67 A 1 1 1.00 14 0.071
68 A 2 2 1.00 14 0.143
69 A 3 2 1.00 14 0.143
70 A 3 3 1.00 11 0.273
71 A 4 3 1.00 11 0.273
72 A 2 2 1.00 10 0.200
73 A 4 4 1.00 12 0.333
74 A 4 3 1.00 10 0.300
75 A 4 4 1.00 10 0.400
76 A 2 2 1.00 8 0.250
77 A 4 3 1.00 10 0.300
78 A 5 5 1.00 10 0.500
79 A 4 4 1.00 10 0.400
80 A 11 8 1.00 10 0.800
81 A 11 8 1.00 10 0.800
82 A 10 7 1.00 6 1.167
83 A 10 7 1.00 10 0.700
84 A 11 8 1.00 10 0.800
85 A 6 4 1.00 10 0.400
86 A 5 4 1.00 8 0.500
87 A 4 4 1.00 6 0.667
88 A 4 3 1.00 10 0.300
89 A 4 4 1.00 10 0.400
90 A 5 4 1.00 10 0.400
91 A 3 2 1.00 12 0.167
92 A 3 2 1.00 12 0.167
93 A 2 2 1.00 12 0.167
94 A 4 4 1.00 12 0.333
95 A 3 2 1.00 12 0.167
96 A 3 3 1.00 4 0.750
97 A 4 3 1.00 10 0.300
98 A 4 3 1.00 10 0.300
99 A 7 6 1.00 10 0.600
100 A 7 6 1.00 10 0.600
101 A 7 6 1.00 8 0.750
102 A 3 3 1.00 6 0.500
103 A 5 5 1.00 10 0.500
104 A 7 7 1.00 10 0.700
105 A 8 7 1.00 10 0.700
106 A 8 7 1.00 10 0.700
107 A 37 7 1.02 16 0.438
108 A 5 5 1.00 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 1.00 18 0.889
112 A 65 19 1.00 18 1.056
113 A 12 8 1.00 19 0.421
114 A 2 2 1.00 28 0.071
115 A 3 3 1.00 33 0.091
116 A 0 0 0.00 0 0.000
117 A 0 0 0.00 0 0.000
118 A 4 4 1.00 35 0.114
119 A 5 5 1.00 40 0.125
120 A 0 0 0.00 0 0.000
121 A 0 0 0.00 0 0.000
122 A 5 4 1.00 14 0.286
123 A 4 4 1.00 12 0.333
124 A 4 3 1.00 14 0.214
125 A 6 6 1.00 14 0.429
126 A 5 4 1.00 12 0.333
127 A 5 4 1.00 19 0.210
128 A 0 0 0.00 0 0.000
129 A 7 6 1.00 18 0.333
130 A 7 6 1.00 18 0.333
131 A 7 6 1.00 16 0.375
132 A 4 3 1.00 10 0.300
133 A 5 5 1.00 18 0.278
134 A 8 8 1.00 18 0.444
135 A 9 8 1.00 18 0.444
136 A 16 13 1.00 20 0.650
137 A 13 10 1.00 18 0.556
138 A 6 6 1.00 12 0.500
139 A 2 2 1.00 20 0.100
140 A 25 25 1.00 20 1.250
141 A 21 14 1.00 20 0.700
142 A 15 11 1.00 18 0.611
143 A 6 7 1.00 12 0.583
144 A 2 2 1.00 20 0.100
145 A 35 22 1.00 20 1.100
146 A 6 4 1.00 18 0.222
147 A 0 0 0.00 0 0.000
148 A 0 0 0.00 0 0.000
149 A 4 4 1.00 12 0.333
150 A 4 4 1.00 14 0.286
151 A 0 0 0.00 0 0.000
152 A 9 7 1.00 40 0.175
153 A 7 6 1.00 40 0.150
154 A 4 4 1.00 38 0.105
155 A 0 0 0.00 0 0.000
156 A 0 0 0.00 0 0.000
157 A 2 2 1.00 7 0.286
158 A 11 6 1.00 15 0.400
159 A 9 5 1.00 13 0.385
160 A 7 4 1.00 11 0.364
161 A 0 0 0.00 0 0.000
162 A 7 7 1.00 21 0.333
163 A 6 6 1.00 19 0.316
164 A 5 5 1.00 17 0.294
165 A 0 0 0.00 0 0.000
166 A 7 7 1.00 22 0.318
167 A 6 6 1.00 20 0.300
168 A 5 5 1.00 18 0.278
169 A 0 0 0.00 0 0.000
170 A 2 2 1.00 7 0.286
171 A 11 6 1.00 15 0.400
172 A 9 5 1.00 13 0.385
173 A 7 4 1.00 11 0.364
174 A 0 0 0.00 0 0.000
175 A 7 7 1.00 21 0.333
176 A 6 6 1.00 19 0.316
177 A 5 5 1.00 17 0.294
178 A 0 0 0.00 0 0.000
179 A 7 7 1.00 22 0.318
180 A 6 6 1.00 20 0.300
181 A 5 5 1.00 18 0.278
182 A 0 0 0.00 0 0.000
183 A 12 6 1.00 15 0.400
184 A 10 6 1.00 15 0.400
185 A 8 5 1.00 13 0.385
186 A 6 4 1.00 7 0.571
187 A 0 0 0.00 0 0.000
188 A 11 6 1.00 15 0.400
189 A 9 5 1.00 13 0.385
190 A 7 4 1.00 11 0.364
191 A 0 0 0.00 0 0.000
192 A 7 7 1.00 19 0.368
193 A 6 6 1.00 17 0.353
194 A 5 5 1.00 15 0.333
195 A 0 0 0.00 0 0.000
196 A 7 7 1.00 22 0.318
197 A 6 6 1.00 20 0.300
198 A 5 5 1.00 18 0.278
199 A 0 0 0.00 0 0.000
200 A 12 6 1.00 15 0.400
201 A 10 6 1.00 15 0.400
202 A 8 5 1.00 13 0.385
203 A 6 4 1.00 7 0.571
204 A 0 0 0.00 0 0.000
205 A 11 6 1.00 15 0.400
206 A 9 5 1.00 13 0.385
207 A 7 4 1.00 11 0.364
208 A 0 0 0.00 0 0.000
209 A 7 7 1.00 19 0.368
210 A 6 6 1.00 17 0.353
211 A 5 5 1.00 15 0.333
212 A 0 0 0.00 0 0.000
213 A 7 7 1.00 22 0.318
214 A 6 6 1.00 20 0.300
215 A 5 5 1.00 18 0.278
216 A 0 0 0.00 0 0.000
217 A 13 9 1.00 24 0.375
218 A 4 3 1.00 4 0.750
219 A 7 4 1.00 6 0.667
220 A 9 5 1.00 8 0.625
221 A 4 3 1.00 8 0.375
222 A 7 4 1.00 10 0.400
223 A 9 5 1.00 12 0.417
224 A 6 6 1.00 12 0.500
225 A 25 8 1.00 14 0.571
226 A 29 9 1.00 16 0.562
227 A 5 6 1.00 10 0.600
228 A 1 1 1.00 19 0.053
229 A 5 5 1.00 20 0.250
230 A 8 7 1.00 20 0.350
231 A 13 10 1.00 20 0.500
232 A 13 10 1.00 20 0.500
233 A 8 7 1.00 20 0.350
234 A 5 5 1.00 20 0.250

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