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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 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 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, 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, 79, 85, 91, 97, 98, 106, 112, 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, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 176, 177, 181, 182, 186, 187, 191, 192, 196, 197, 201, 202, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 157 }

C grade: { 11, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 173, 174, 175, 178, 179, 180, 183, 184, 185, 188, 189, 190, 193, 194, 195, 198, 199, 200, 203, 204, 205, 206, 207, 208 }

F grade: { 216}

2.1.3 Maple

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, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 179, 181, 182, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 201, 202, 203, 204, 205, 206, 207, 208, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 151, 156, 157, 178, 180, 183, 184, 185, 198, 199, 200 }

C grade: { 132, 133 }

F grade: { 121, 122, 130, 131, 209, 210, 211, 212, 213, 214 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 16, 19, 21, 22, 24, 26, 33, 35, 37, 49, 50, 65, 66, 72, 73, 123, 140, 141, 142, 143, 145, 146, 147, 148, 150, 153, 155, 161, 162, 171, 172, 176, 177, 181, 182, 186, 187, 191, 192, 196, 197, 201, 202, 220, 221, 222, 223, 224, 225, 226, 227

B grade: { }

C grade: { }

F grade: { 6, 13, 15, 17, 18, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 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, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 144, 149, 151, 152, 154, 156, 157, 158, 159, 160, 163, 164, 165, 166, 167, 168, 169, 170, 173, 174, 175, 178, 179, 180, 183, 184, 185, 188, 189, 190, 193, 194, 195, 198, 199, 200, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 21, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59, 65, 66, 72, 73, 119, 120, 123, 124, 129, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 153, 154, 155, 161, 162, 166, 167, 171, 172, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { }

C grade: { }

F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 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, 121, 122, 125, 126, 127, 128, 130, 131, 132, 133, 144, 151, 152, 156, 157, 158, 159, 160, 163, 164, 165, 168, 169, 170, 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 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 97, 98, 106, 112, 119, 120, 123, 124, 126, 127, 128, 129, 134, 135, 137, 138, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 153, 154, 155, 161, 162, 166, 167, 171, 172, 176, 177, 181, 182, 191, 192, 196, 197, 201, 204, 205, 216, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { }

C grade: { 7, 8 }

F grade: { 6, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 121, 122, 125, 130, 131, 132, 133, 136, 139, 144, 151, 152, 156, 157, 158, 159, 160, 163, 164, 165, 168, 169, 170, 173, 174, 175, 178, 179, 180, 183, 184, 185, 186, 187, 188, 189, 190, 193, 194, 195, 198, 199, 200, 202, 203, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 79, 85, 91, 97, 98, 106, 112, 118, 119, 120, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 150, 155, 158, 159, 160, 161, 162, 166, 167, 171, 172, 176, 177, 181, 182, 186, 187, 191, 192, 196, 197, 201, 202, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 8, 10, 19, 21, 51, 145, 146, 147, 148, 149, 153, 154, 163, 164, 165, 168, 169, 170 }

C grade: { 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 173, 174, 175, 178, 179, 180, 183, 184, 185, 188, 189, 190 }

F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 121, 122, 130, 131, 132, 133, 144, 151, 152, 156, 157, 193, 194, 195, 198, 199, 200, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214 }

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 75 75 51 72 96 113 70 153
normalized size 1 1. 0.68 0.96 1.28 1.51 0.93 2.04
time (sec) N/A 0.049 0.032 0.032 1.686 2.134 7.083 1.222
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 69 69 50 60 99 109 61 113
normalized size 1 1. 0.72 0.87 1.43 1.58 0.88 1.64
time (sec) N/A 0.029 0.019 0.004 1.727 2.026 1.645 1.448
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 54 54 41 52 68 92 48 86
normalized size 1 1. 0.76 0.96 1.26 1.7 0.89 1.59
time (sec) N/A 0.035 0.025 0.003 1.709 2.138 0.82 1.303
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 45 45 40 40 70 86 37 62
normalized size 1 1. 0.89 0.89 1.56 1.91 0.82 1.38
time (sec) N/A 0.016 0.011 0.004 1.671 2.2 0.346 1.239
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 25 25 25 25 32 57 20 32
normalized size 1 1. 1. 1. 1.28 2.28 0.8 1.28
time (sec) N/A 0.008 0.008 0.001 1.689 2.106 0.619 1.331
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 46 111 0 0 0 0
normalized size 1 1. 0.9 2.18 0. 0. 0. 0.
time (sec) N/A 0.058 0.028 0.158 0. 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 28 31 53 124 32 65
normalized size 1 1. 1. 1.11 1.89 4.43 1.14 2.32
time (sec) N/A 0.022 0.002 0.003 1.624 2.235 4.859 1.475
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 29 38 38 66 51 92
normalized size 1 1. 0.85 1.12 1.12 1.94 1.5 2.71
time (sec) N/A 0.014 0.007 0.003 1.658 2.191 2.114 1.282
Problem 9 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 56 56 53 53 81 176 109 95
normalized size 1 1. 0.95 0.95 1.45 3.14 1.95 1.7
time (sec) N/A 0.033 0.014 0.003 1.731 2.743 7.035 1.315
Problem 10 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 58 58 41 58 68 89 100 176
normalized size 1 1. 0.71 1. 1.17 1.53 1.72 3.03
time (sec) N/A 0.022 0.019 0.003 1.656 2.535 3.911 1.354
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 80 80 51 73 111 204 182 120
normalized size 1 1. 0.64 0.91 1.39 2.55 2.28 1.5
time (sec) N/A 0.045 0.013 0.004 1.764 2.794 24.051 1.302
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 120 120 82 76 138 189 114 228
normalized size 1 1. 0.68 0.63 1.15 1.58 0.95 1.9
time (sec) N/A 0.194 0.034 0.126 1.67 2.428 7.614 1.344
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 74 93 0 162 90 180
normalized size 1 1. 0.76 0.95 0. 1.65 0.92 1.84
time (sec) N/A 0.163 0.029 0.063 0. 2.402 4.84 1.229
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 82 82 64 59 97 143 76 131
normalized size 1 1. 0.78 0.72 1.18 1.74 0.93 1.6
time (sec) N/A 0.121 0.028 0.059 1.735 2.415 2.594 1.312
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 55 65 0 123 51 99
normalized size 1 1. 0.92 1.08 0. 2.05 0.85 1.65
time (sec) N/A 0.093 0.017 0.025 0. 2.339 0.77 1.215
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 35 35 35 37 45 89 32 45
normalized size 1 1. 1. 1.06 1.29 2.54 0.91 1.29
time (sec) N/A 0.045 0.011 0.021 1.821 2.352 0.239 1.348
Problem 17 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 71 71 71 169 0 0 0 0
normalized size 1 1. 1. 2.38 0. 0. 0. 0.
time (sec) N/A 0.095 0.04 0.042 0. 0. 0. 0.
Problem 18 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 66 66 87 119 0 0 0 0
normalized size 1 1. 1.32 1.8 0. 0. 0. 0.
time (sec) N/A 0.103 0.162 0.092 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 44 43 54 112 0 116
normalized size 1 1. 1. 0.98 1.23 2.55 0. 2.64
time (sec) N/A 0.08 0.025 0.026 1.628 2.568 0. 1.382
Problem 20 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 116 116 139 157 0 0 0 0
normalized size 1 1. 1.2 1.35 0. 0. 0. 0.
time (sec) N/A 0.17 0.615 0.196 0. 0. 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 69 76 100 149 0 223
normalized size 1 1. 0.79 0.87 1.15 1.71 0. 2.56
time (sec) N/A 0.14 0.038 0.032 1.613 2.309 0. 1.457
Problem 22 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 201 201 122 159 231 265 196 336
normalized size 1 1. 0.61 0.79 1.15 1.32 0.98 1.67
time (sec) N/A 0.385 0.07 0.059 1.692 2.2 13.62 1.386
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 112 154 0 234 160 250
normalized size 1 1. 0.67 0.92 0. 1.4 0.96 1.5
time (sec) N/A 0.297 0.048 0.06 0. 2.05 6.943 1.302
Problem 24 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 136 136 95 106 162 189 128 192
normalized size 1 1. 0.7 0.78 1.19 1.39 0.94 1.41
time (sec) N/A 0.225 0.045 0.045 1.726 2.169 5.895 1.3
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 99 99 82 96 0 170 92 136
normalized size 1 1. 0.83 0.97 0. 1.72 0.93 1.37
time (sec) N/A 0.156 0.025 0.041 0. 2.035 1.609 1.305
Problem 26 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 60 60 60 57 77 116 54 76
normalized size 1 1. 1. 0.95 1.28 1.93 0.9 1.27
time (sec) N/A 0.08 0.011 0.024 1.681 2.047 0.832 1.36
Problem 27 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 97 97 97 229 0 0 0 0
normalized size 1 1. 1. 2.36 0. 0. 0. 0.
time (sec) N/A 0.109 0.056 0.046 0. 0. 0. 0.
Problem 28 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 108 108 133 179 0 0 0 0
normalized size 1 1. 1.23 1.66 0. 0. 0. 0.
time (sec) N/A 0.163 0.124 0.074 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 92 163 0 0 0 0
normalized size 1 1. 0.9 1.6 0. 0. 0. 0.
time (sec) N/A 0.169 0.253 0.098 0. 0. 0. 0.
Problem 30 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 179 179 284 250 0 0 0 0
normalized size 1 1. 1.59 1.4 0. 0. 0. 0.
time (sec) N/A 0.285 2.795 0.148 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 169 169 116 225 0 0 0 0
normalized size 1 1. 0.69 1.33 0. 0. 0. 0.
time (sec) N/A 0.292 0.679 0.156 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 282 282 167 320 0 383 269 489
normalized size 1 1. 0.59 1.13 0. 1.36 0.95 1.73
time (sec) N/A 0.869 0.098 0.1 0. 2.22 33.002 1.375
Problem 33 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 250 250 150 197 279 352 241 412
normalized size 1 1. 0.6 0.79 1.12 1.41 0.96 1.65
time (sec) N/A 0.663 0.075 0.059 1.853 2.149 18.648 1.29
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 198 198 135 209 0 292 190 316
normalized size 1 1. 0.68 1.06 0. 1.47 0.96 1.6
time (sec) N/A 0.516 0.059 0.059 0. 2.209 15.126 1.414
Problem 35 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 166 166 114 130 198 247 158 238
normalized size 1 1. 0.69 0.78 1.19 1.49 0.95 1.43
time (sec) N/A 0.353 0.048 0.048 1.687 2.01 5.592 1.404
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 96 117 0 205 104 171
normalized size 1 1. 0.86 1.05 0. 1.85 0.94 1.54
time (sec) N/A 0.238 0.029 0.039 0. 2.211 3.343 1.404
Problem 37 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 69 69 69 67 101 149 65 88
normalized size 1 1. 1. 0.97 1.46 2.16 0.94 1.28
time (sec) N/A 0.118 0.016 0.026 1.768 1.926 1.988 1.39
Problem 38 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 113 113 113 287 0 0 0 0
normalized size 1 1. 1. 2.54 0. 0. 0. 0.
time (sec) N/A 0.122 0.044 0.046 0. 0. 0. 0.
Problem 39 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 156 156 198 241 0 0 0 0
normalized size 1 1. 1.27 1.54 0. 0. 0. 0.
time (sec) N/A 0.194 0.267 0.077 0. 0. 0. 0.
Problem 40 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 119 119 124 227 0 0 0 0
normalized size 1 1. 1.04 1.91 0. 0. 0. 0.
time (sec) N/A 0.216 0.283 0.091 0. 0. 0. 0.
Problem 41 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 276 276 399 409 0 0 0 0
normalized size 1 1. 1.45 1.48 0. 0. 0. 0.
time (sec) N/A 0.41 4.27 0.145 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 40 40 0 0 0 63
normalized size 1 1. 0.73 0.73 0. 0. 0. 1.15
time (sec) N/A 0.097 0.016 0.039 0. 0. 0. 1.318
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 33 33 0 0 0 50
normalized size 1 1. 0.77 0.77 0. 0. 0. 1.16
time (sec) N/A 0.08 0.115 0.031 0. 0. 0. 1.275
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 31 31 0 0 0 47
normalized size 1 1. 0.76 0.76 0. 0. 0. 1.15
time (sec) N/A 0.081 0.009 0.023 0. 0. 0. 1.352
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 24 24 0 0 0 34
normalized size 1 1. 0.83 0.83 0. 0. 0. 1.17
time (sec) N/A 0.062 0.079 0.022 0. 0. 0. 1.339
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 22 22 0 0 0 31
normalized size 1 1. 0.81 0.81 0. 0. 0. 1.15
time (sec) N/A 0.063 0.006 0.021 0. 0. 0. 1.371
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 13 0 0 0 16
normalized size 1 1. 1. 0.93 0. 0. 0. 1.14
time (sec) N/A 0.035 0.023 0.025 0. 0. 0. 1.346
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 9 9 9 10 0 0 0 12
normalized size 1 1. 1. 1.11 0. 0. 0. 1.33
time (sec) N/A 0.017 0.009 0.017 0. 0. 0. 1.356
Problem 49 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.191 0.09 0. 0. 0. 0.
Problem 50 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 1.098 0.123 0. 0. 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 86 105 0 0 0 217
normalized size 1 1. 1.04 1.27 0. 0. 0. 2.61
time (sec) N/A 0.074 0.244 0.042 0. 0. 0. 1.287
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 78 78 0 0 0 162
normalized size 1 1. 1.1 1.1 0. 0. 0. 2.28
time (sec) N/A 0.063 0.045 0.033 0. 0. 0. 1.311
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 61 81 0 0 0 155
normalized size 1 1. 0.88 1.17 0. 0. 0. 2.25
time (sec) N/A 0.058 0.209 0.026 0. 0. 0. 1.305
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 56 54 0 0 0 97
normalized size 1 1. 0.98 0.95 0. 0. 0. 1.7
time (sec) N/A 0.049 0.017 0.021 0. 0. 0. 1.385
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 50 57 0 0 0 92
normalized size 1 1. 0.91 1.04 0. 0. 0. 1.67
time (sec) N/A 0.044 0.165 0.023 0. 0. 0. 1.36
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 32 28 0 0 0 49
normalized size 1 1. 0.84 0.74 0. 0. 0. 1.29
time (sec) N/A 0.025 0.003 0.024 0. 0. 0. 1.374
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 32 33 0 0 0 46
normalized size 1 1. 0.89 0.92 0. 0. 0. 1.28
time (sec) N/A 0.078 0.059 0.019 0. 0. 0. 1.33
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) 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 0.012 0.904 0.078 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) 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 0.014 9.711 0.141 0. 0. 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 103 121 0 0 0 230
normalized size 1 1. 1.05 1.23 0. 0. 0. 2.35
time (sec) N/A 0.343 0.185 0.042 0. 0. 0. 1.328
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 73 82 0 0 0 169
normalized size 1 1. 0.88 0.99 0. 0. 0. 2.04
time (sec) N/A 0.3 0.187 0.034 0. 0. 0. 1.362
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 68 82 0 0 0 138
normalized size 1 1. 0.83 1. 0. 0. 0. 1.68
time (sec) N/A 0.249 0.136 0.026 0. 0. 0. 1.371
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 61 45 0 0 0 90
normalized size 1 1. 0.95 0.7 0. 0. 0. 1.41
time (sec) N/A 0.168 0.06 0.026 0. 0. 0. 1.418
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 48 43 0 0 0 58
normalized size 1 1. 0.94 0.84 0. 0. 0. 1.14
time (sec) N/A 0.085 0.022 0.021 0. 0. 0. 1.339
Problem 65 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.012 0.541 0.078 0. 0. 0. 0.
Problem 66 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 6.431 0.122 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 158 158 159 171 0 0 0 338
normalized size 1 1. 1.01 1.08 0. 0. 0. 2.14
time (sec) N/A 0.314 0.338 0.04 0. 0. 0. 1.271
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 107 114 0 0 0 235
normalized size 1 1. 0.74 0.79 0. 0. 0. 1.63
time (sec) N/A 0.282 0.36 0.03 0. 0. 0. 1.377
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 102 117 0 0 0 200
normalized size 1 1. 0.72 0.83 0. 0. 0. 1.42
time (sec) N/A 0.303 0.259 0.028 0. 0. 0. 1.329
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 86 60 0 0 0 124
normalized size 1 1. 0.89 0.62 0. 0. 0. 1.28
time (sec) N/A 0.164 0.138 0.027 0. 0. 0. 1.257
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 70 63 0 0 0 89
normalized size 1 1. 0.9 0.81 0. 0. 0. 1.14
time (sec) N/A 0.153 0.062 0.023 0. 0. 0. 1.245
Problem 72 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.012 2.34 0.075 0. 0. 0. 0.
Problem 73 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 17.869 0.118 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 121 121 204 143 0 0 0 333
normalized size 1 1. 1.69 1.18 0. 0. 0. 2.75
time (sec) N/A 0.242 0.099 0.074 0. 0. 0. 1.345
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 95 95 138 91 0 0 0 207
normalized size 1 1. 1.45 0.96 0. 0. 0. 2.18
time (sec) N/A 0.189 0.061 0.049 0. 0. 0. 1.432
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 86 86 126 96 0 0 0 223
normalized size 1 1. 1.47 1.12 0. 0. 0. 2.59
time (sec) N/A 0.181 0.05 0.044 0. 0. 0. 1.488
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 59 59 81 42 0 0 0 96
normalized size 1 1. 1.37 0.71 0. 0. 0. 1.63
time (sec) N/A 0.151 0.021 0.033 0. 0. 0. 1.378
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 44 44 66 49 0 0 0 112
normalized size 1 1. 1.5 1.11 0. 0. 0. 2.55
time (sec) N/A 0.09 0.031 0.032 0. 0. 0. 1.361
Problem 79 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.399 0.078 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 214 282 202 193 0 0 0 479
normalized size 1 1.32 0.94 0.9 0. 0. 0. 2.24
time (sec) N/A 0.533 0.065 0.079 0. 0. 0. 1.401
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 157 157 130 121 0 0 0 304
normalized size 1 1. 0.83 0.77 0. 0. 0. 1.94
time (sec) N/A 0.379 0.033 0.053 0. 0. 0. 1.398
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 147 147 136 131 0 0 0 320
normalized size 1 1. 0.93 0.89 0. 0. 0. 2.18
time (sec) N/A 0.303 0.059 0.05 0. 0. 0. 1.392
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 89 89 71 64 0 0 0 144
normalized size 1 1. 0.8 0.72 0. 0. 0. 1.62
time (sec) N/A 0.183 0.015 0.036 0. 0. 0. 1.342
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 75 75 76 72 0 0 0 161
normalized size 1 1. 1.01 0.96 0. 0. 0. 2.15
time (sec) N/A 0.099 0.043 0.036 0. 0. 0. 1.469
Problem 85 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.372 0.063 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 263 298 204 233 0 0 0 625
normalized size 1 1.13 0.78 0.89 0. 0. 0. 2.38
time (sec) N/A 0.803 0.071 0.077 0. 0. 0. 1.475
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 205 205 140 154 0 0 0 401
normalized size 1 1. 0.68 0.75 0. 0. 0. 1.96
time (sec) N/A 0.6 0.041 0.056 0. 0. 0. 1.494
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 178 178 125 156 0 0 0 417
normalized size 1 1. 0.7 0.88 0. 0. 0. 2.34
time (sec) N/A 0.469 0.047 0.055 0. 0. 0. 1.436
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 119 119 81 79 0 0 0 193
normalized size 1 1. 0.68 0.66 0. 0. 0. 1.62
time (sec) N/A 0.313 0.02 0.036 0. 0. 0. 1.463
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 88 88 68 88 0 0 0 209
normalized size 1 1. 0.77 1. 0. 0. 0. 2.38
time (sec) N/A 0.165 0.035 0.037 0. 0. 0. 1.514
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.373 0.063 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 106 106 193 72 0 0 0 188
normalized size 1 1. 1.82 0.68 0. 0. 0. 1.77
time (sec) N/A 0.112 0.057 0.055 0. 0. 0. 1.452
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 65 65 128 44 0 0 0 109
normalized size 1 1. 1.97 0.68 0. 0. 0. 1.68
time (sec) N/A 0.083 0.032 0.039 0. 0. 0. 1.476
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 71 71 128 51 0 0 0 126
normalized size 1 1. 1.8 0.72 0. 0. 0. 1.77
time (sec) N/A 0.089 0.051 0.039 0. 0. 0. 1.434
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 28 28 71 21 0 0 0 47
normalized size 1 1. 2.54 0.75 0. 0. 0. 1.68
time (sec) N/A 0.045 0.017 0.029 0. 0. 0. 1.479
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 30 30 69 25 0 0 0 63
normalized size 1 1. 2.3 0.83 0. 0. 0. 2.1
time (sec) N/A 0.024 0.026 0.028 0. 0. 0. 1.369
Problem 97 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.356 0.069 0. 0. 0. 0.
Problem 98 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 2.993 0.122 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 171 171 427 184 0 0 0 0
normalized size 1 1. 2.5 1.08 0. 0. 0. 0.
time (sec) N/A 0.144 0.234 0.077 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 127 127 231 121 0 0 0 0
normalized size 1 1. 1.82 0.95 0. 0. 0. 0.
time (sec) N/A 0.107 0.135 0.067 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 136 136 319 138 0 0 0 0
normalized size 1 1. 2.35 1.01 0. 0. 0. 0.
time (sec) N/A 0.098 0.152 0.051 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 90 90 154 83 0 0 0 0
normalized size 1 1. 1.71 0.92 0. 0. 0. 0.
time (sec) N/A 0.07 0.046 0.042 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 96 96 211 95 0 0 0 0
normalized size 1 1. 2.2 0.99 0. 0. 0. 0.
time (sec) N/A 0.069 0.072 0.046 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 55 55 91 43 0 0 0 0
normalized size 1 1. 1.65 0.78 0. 0. 0. 0.
time (sec) N/A 0.032 0.033 0.031 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 59 59 87 65 0 0 0 0
normalized size 1 1. 1.47 1.1 0. 0. 0. 0.
time (sec) N/A 0.09 0.095 0.035 0. 0. 0. 0.
Problem 106 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.455 0.063 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 171 235 418 175 0 0 0 0
normalized size 1 1.37 2.44 1.02 0. 0. 0. 0.
time (sec) N/A 0.434 0.329 0.07 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 126 126 200 109 0 0 0 0
normalized size 1 1. 1.59 0.87 0. 0. 0. 0.
time (sec) N/A 0.338 0.394 0.057 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 125 125 277 117 0 0 0 0
normalized size 1 1. 2.22 0.94 0. 0. 0. 0.
time (sec) N/A 0.301 0.208 0.055 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 89 89 112 56 0 0 0 0
normalized size 1 1. 1.26 0.63 0. 0. 0. 0.
time (sec) N/A 0.18 0.225 0.039 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 76 76 138 83 0 0 0 0
normalized size 1 1. 1.82 1.09 0. 0. 0. 0.
time (sec) N/A 0.099 0.127 0.042 0. 0. 0. 0.
Problem 112 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.462 0.069 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 264 264 417 225 0 0 0 0
normalized size 1 1. 1.58 0.85 0. 0. 0. 0.
time (sec) N/A 0.396 0.772 0.083 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 190 190 272 139 0 0 0 0
normalized size 1 1. 1.43 0.73 0. 0. 0. 0.
time (sec) N/A 0.319 1.187 0.055 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 191 191 280 154 0 0 0 0
normalized size 1 1. 1.47 0.81 0. 0. 0. 0.
time (sec) N/A 0.348 0.476 0.055 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 119 119 146 73 0 0 0 0
normalized size 1 1. 1.23 0.61 0. 0. 0. 0.
time (sec) N/A 0.172 0.412 0.038 0. 0. 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 105 105 143 110 0 0 0 0
normalized size 1 1. 1.36 1.05 0. 0. 0. 0.
time (sec) N/A 0.166 0.26 0.04 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.462 0.066 0. 0. 0. 0.
Problem 119 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 64 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.122 1.064 0.828 0. 0. 0. 0.
Problem 120 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 64 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.118 0.941 0.548 0. 0. 0. 0.
Problem 121 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 150 150 122 0 0 0 0 0
normalized size 1 1. 0.81 0. 0. 0. 0. 0.
time (sec) N/A 0.114 0.043 0.525 0. 0. 0. 0.
Problem 122 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 69 69 56 0 0 0 0 0
normalized size 1 1. 0.81 0. 0. 0. 0. 0.
time (sec) N/A 0.025 0.02 0.531 0. 0. 0. 0.
Problem 123 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.017 0.561 0.434 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 0.576 0.434 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 2.626 0.07 0. 0. 0. 0.
Problem 126 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 2.929 0.062 0. 0. 0. 0.
Problem 127 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 2.204 0.066 0. 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 2.192 0.059 0. 0. 0. 0.
Problem 129 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 0.798 0.758 0. 0. 0. 0.
Problem 130 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 167 167 132 0 0 0 0 0
normalized size 1 1. 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.177 0.088 0.144 0. 0. 0. 0.
Problem 131 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 171 171 137 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.166 0.072 0.154 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 75 138 0 0 0 0
normalized size 1 1. 0.88 1.62 0. 0. 0. 0.
time (sec) N/A 0.082 0.019 0.117 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 73 240 0 0 0 0
normalized size 1 1. 0.92 3.04 0. 0. 0. 0.
time (sec) N/A 0.055 0.035 0.082 0. 0. 0. 0.
Problem 134 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 0.015 0.278 0.102 0. 0. 0. 0.
Problem 135 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 0.016 0.525 0.072 0. 0. 0. 0.
Problem 136 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.021 3.571 0.089 0. 0. 0. 0.
Problem 137 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.017 4.269 0.07 0. 0. 0. 0.
Problem 138 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.018 1.552 0.069 0. 0. 0. 0.
Problem 139 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.021 1.9 0.069 0. 0. 0. 0.
Problem 140 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 76 76 81 72 111 139 80 163
normalized size 1 1. 1.07 0.95 1.46 1.83 1.05 2.14
time (sec) N/A 0.035 0.03 0.005 1.591 1.436 2.371 1.37
Problem 141 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 60 60 49 64 80 119 65 100
normalized size 1 1. 0.82 1.07 1.33 1.98 1.08 1.67
time (sec) N/A 0.039 0.039 0.003 1.686 1.53 0.922 1.347
Problem 142 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 56 52 82 111 54 86
normalized size 1 1. 1.1 1.02 1.61 2.18 1.06 1.69
time (sec) N/A 0.019 0.019 0.003 1.598 1.484 0.435 1.316
Problem 143 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 30 39 73 26 39
normalized size 1 1. 1. 1. 1.3 2.43 0.87 1.3
time (sec) N/A 0.014 0.012 0.003 1.517 1.459 0.17 1.286
Problem 144 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 63 63 52 122 0 0 0 0
normalized size 1 1. 0.83 1.94 0. 0. 0. 0.
time (sec) N/A 0.07 0.032 0.03 0. 0. 0. 0.
Problem 145 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 33 33 36 43 63 140 39 439
normalized size 1 1. 1.09 1.3 1.91 4.24 1.18 13.3
time (sec) N/A 0.027 0.003 0.004 1.505 1.552 3.323 1.583
Problem 146 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 39 39 44 50 49 88 61 220
normalized size 1 1. 1.13 1.28 1.26 2.26 1.56 5.64
time (sec) N/A 0.019 0.013 0.004 1.538 1.489 2.896 1.402
Problem 147 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 62 62 67 65 93 194 119 383
normalized size 1 1. 1.08 1.05 1.5 3.13 1.92 6.18
time (sec) N/A 0.038 0.018 0.003 1.55 1.663 5.744 2.034
Problem 148 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 102 102 95 126 192 255 170 262
normalized size 1 1. 0.93 1.24 1.88 2.5 1.67 2.57
time (sec) N/A 0.154 0.189 0.025 1.549 1.436 2.059 1.347
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 73 120 0 221 126 209
normalized size 1 1. 0.96 1.58 0. 2.91 1.66 2.75
time (sec) N/A 0.119 0.073 0.023 0. 1.482 1.174 1.3
Problem 150 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 47 72 97 159 82 101
normalized size 1 1. 1. 1.53 2.06 3.38 1.74 2.15
time (sec) N/A 0.06 0.04 0.023 1.566 1.555 0.528 1.351
Problem 151 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 90 90 143 319 0 0 0 0
normalized size 1 1. 1.59 3.54 0. 0. 0. 0.
time (sec) N/A 0.123 0.156 0.03 0. 0. 0. 0.
Problem 152 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 81 81 126 171 0 0 0 0
normalized size 1 1. 1.56 2.11 0. 0. 0. 0.
time (sec) N/A 0.128 0.225 0.056 0. 0. 0. 0.
Problem 153 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 178 178 163 235 369 441 328 497
normalized size 1 1. 0.92 1.32 2.07 2.48 1.84 2.79
time (sec) N/A 0.297 0.409 0.029 1.888 1.804 3.745 1.458
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 114 219 0 378 264 385
normalized size 1 1. 0.91 1.75 0. 3.02 2.11 3.08
time (sec) N/A 0.205 0.148 0.027 0. 1.681 1.893 1.478
Problem 155 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 82 82 77 132 190 262 160 203
normalized size 1 1. 0.94 1.61 2.32 3.2 1.95 2.48
time (sec) N/A 0.109 0.088 0.024 1.869 1.793 1.209 1.374
Problem 156 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 123 123 244 592 0 0 0 0
normalized size 1 1. 1.98 4.81 0. 0. 0. 0.
time (sec) N/A 0.147 0.239 0.026 0. 0. 0. 0.
Problem 157 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 137 137 283 378 0 0 0 0
normalized size 1 1. 2.07 2.76 0. 0. 0. 0.
time (sec) N/A 0.213 0.314 0.042 0. 0. 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 117 91 102 0 0 0 234
normalized size 1 0.97 0.75 0.84 0. 0. 0. 1.93
time (sec) N/A 0.254 0.2 0.025 0. 0. 0. 1.302
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 56 58 0 0 0 116
normalized size 1 1. 0.89 0.92 0. 0. 0. 1.84
time (sec) N/A 0.132 0.079 0.023 0. 0. 0. 1.288
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 44 48 0 0 0 66
normalized size 1 1. 0.83 0.91 0. 0. 0. 1.25
time (sec) N/A 0.067 0.065 0.023 0. 0. 0. 1.412
Problem 161 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 0.245 0.145 0. 0. 0. 0.
Problem 162 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 2.167 0.243 0. 0. 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 152 125 149 0 0 0 872
normalized size 1 0.97 0.8 0.96 0. 0. 0. 5.59
time (sec) N/A 0.182 0.531 0.037 0. 0. 0. 1.403
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 79 77 0 0 0 440
normalized size 1 1. 0.88 0.86 0. 0. 0. 4.89
time (sec) N/A 0.1 0.266 0.027 0. 0. 0. 1.413
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 82 72 76 0 0 0 259
normalized size 1 0.95 0.84 0.88 0. 0. 0. 3.01
time (sec) N/A 0.169 0.156 0.03 0. 0. 0. 1.359
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 3.985 0.184 0. 0. 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 33.323 0.339 0. 0. 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 197 245 168 290 0 0 0 2078
normalized size 1 1.24 0.85 1.47 0. 0. 0. 10.55
time (sec) N/A 0.542 0.861 0.034 0. 0. 0. 1.705
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 108 157 0 0 0 1166
normalized size 1 1. 0.83 1.21 0. 0. 0. 8.97
time (sec) N/A 0.323 0.33 0.027 0. 0. 0. 1.687
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 93 138 0 0 0 651
normalized size 1 1. 0.84 1.24 0. 0. 0. 5.86
time (sec) N/A 0.172 0.418 0.03 0. 0. 0. 1.426
Problem 171 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 2.128 0.276 0. 0. 0. 0.
Problem 172 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 17.855 0.5 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 242 242 246 356 0 0 0 531
normalized size 1 1. 1.02 1.47 0. 0. 0. 2.19
time (sec) N/A 0.756 0.304 0.083 0. 0. 0. 2.105
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 137 137 141 173 0 0 0 236
normalized size 1 1. 1.03 1.26 0. 0. 0. 1.72
time (sec) N/A 0.453 0.072 0.052 0. 0. 0. 1.805
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 120 120 119 178 0 0 0 266
normalized size 1 1. 0.99 1.48 0. 0. 0. 2.22
time (sec) N/A 0.331 0.089 0.043 0. 0. 0. 1.687
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) 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 0.046 3.254 0.128 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) 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 0.037 11.4 0.165 0. 0. 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 313 313 245 540 0 0 0 1740
normalized size 1 1. 0.78 1.73 0. 0. 0. 5.56
time (sec) N/A 1.046 0.285 0.105 0. 0. 0. 3.5
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 172 172 126 267 0 0 0 757
normalized size 1 1. 0.73 1.55 0. 0. 0. 4.4
time (sec) N/A 0.525 0.059 0.092 0. 0. 0. 2.23
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 159 159 291 270 0 0 0 879
normalized size 1 1. 1.83 1.7 0. 0. 0. 5.53
time (sec) N/A 0.281 2.796 0.056 0. 0. 0. 2.469
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) 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 0.045 2.901 0.11 0. 0. 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) 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 0.042 10.143 0.169 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F(-1) C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 358 358 228 792 0 0 0 3357
normalized size 1 1. 0.64 2.21 0. 0. 0. 9.38
time (sec) N/A 1.409 0.273 0.118 0. 0. 0. 5.104
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F(-1) C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 216 216 141 394 0 0 0 1570
normalized size 1 1. 0.65 1.82 0. 0. 0. 7.27
time (sec) N/A 0.743 0.095 0.068 0. 0. 0. 2.798
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F(-1) C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 179 179 379 393 0 0 0 1578
normalized size 1 1. 2.12 2.2 0. 0. 0. 8.82
time (sec) N/A 0.502 2.899 0.067 0. 0. 0. 3.193
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) 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 0.044 3.06 0.101 0. 0. 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) 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 0.043 10.216 0.161 0. 0. 0. 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 223 223 228 168 0 0 0 428
normalized size 1 1. 1.02 0.75 0. 0. 0. 1.92
time (sec) N/A 0.421 0.266 0.058 0. 0. 0. 2.271
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 99 99 123 80 0 0 0 178
normalized size 1 1. 1.24 0.81 0. 0. 0. 1.8
time (sec) N/A 0.176 0.061 0.038 0. 0. 0. 1.992
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F C
verified N/A Yes NO TBD TBD TBD TBD TBD
size 101 101 121 83 0 0 0 215
normalized size 1 1. 1.2 0.82 0. 0. 0. 2.13
time (sec) N/A 0.091 0.087 0.029 0. 0. 0. 1.912
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) 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 0.037 2.866 0.082 0. 0. 0. 0.
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) 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 0.037 11.63 0.137 0. 0. 0. 0.
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 250 250 343 295 0 0 0 0
normalized size 1 1. 1.37 1.18 0. 0. 0. 0.
time (sec) N/A 0.418 0.443 0.066 0. 0. 0. 0.
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 130 130 155 143 0 0 0 0
normalized size 1 1. 1.19 1.1 0. 0. 0. 0.
time (sec) N/A 0.163 0.145 0.045 0. 0. 0. 0.
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 137 137 167 149 0 0 0 0
normalized size 1 1. 1.22 1.09 0. 0. 0. 0.
time (sec) N/A 0.294 0.298 0.042 0. 0. 0. 0.
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) 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 0.044 3.458 0.079 0. 0. 0. 0.
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) 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 0.043 11.405 0.158 0. 0. 0. 0.
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 291 291 370 660 0 0 0 0
normalized size 1 1. 1.27 2.27 0. 0. 0. 0.
time (sec) N/A 1.007 1.855 0.088 0. 0. 0. 0.
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 180 180 173 311 0 0 0 0
normalized size 1 1. 0.96 1.73 0. 0. 0. 0.
time (sec) N/A 0.506 1.231 0.059 0. 0. 0. 0.
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 163 163 214 325 0 0 0 0
normalized size 1 1. 1.31 1.99 0. 0. 0. 0.
time (sec) N/A 0.276 0.852 0.053 0. 0. 0. 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) 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 0.045 3.613 0.073 0. 0. 0. 0.
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) 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 0.045 11.448 0.161 0. 0. 0. 0.
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 120 120 100 144 0 0 0 0
normalized size 1 1. 0.83 1.2 0. 0. 0. 0.
time (sec) N/A 0.076 0.039 0.036 0. 0. 0. 0.
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 66 138 0 0 82 0
normalized size 1 1. 0.53 1.11 0. 0. 0.66 0.
time (sec) N/A 0.098 0.025 0.01 0. 0. 163.098 0.
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 66 119 0 0 76 0
normalized size 1 1. 0.75 1.35 0. 0. 0.86 0.
time (sec) N/A 0.045 0.017 0.008 0. 0. 4.419 0.
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 45 98 0 0 0 0
normalized size 1 1. 0.51 1.1 0. 0. 0. 0.
time (sec) N/A 0.078 0.015 0.009 0. 0. 0. 0.
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 40 85 0 0 0 0
normalized size 1 1. 0.73 1.55 0. 0. 0. 0.
time (sec) N/A 0.038 0.013 0.009 0. 0. 0. 0.
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 42 129 0 0 0 0
normalized size 1 1. 0.34 1.03 0. 0. 0. 0.
time (sec) N/A 0.097 0.015 0.013 0. 0. 0. 0.
Problem 209 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 109 109 90 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.141 0.061 0.158 0. 0. 0. 0.
Problem 210 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 109 109 90 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.141 0.056 0.143 0. 0. 0. 0.
Problem 211 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 109 109 90 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.143 0.052 0.184 0. 0. 0. 0.
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 90 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.13 0.049 0.358 0. 0. 0. 0.
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 87 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.135 0.047 0.154 0. 0. 0. 0.
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 87 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.145 0.054 0.144 0. 0. 0. 0.
Problem 215 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 68 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.17 36.379 0.144 0. 0. 0. 0.
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A F A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 66 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.168 180.002 0.142 0. 0. 0. 0.
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-2) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 64 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.16 8.126 0.199 0. 0. 0. 0.
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-2) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 64 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.159 7.576 0.145 0. 0. 0. 0.
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-2) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 66 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.173 13.129 0.139 0. 0. 0. 0.
Problem 220 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.03 2.676 0.093 0. 0. 0. 0.
Problem 221 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 2.565 0.092 0. 0. 0. 0.
Problem 222 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.029 0.769 0.1 0. 0. 0. 0.
Problem 223 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.032 3.841 0.099 0. 0. 0. 0.
Problem 224 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.029 5.683 0.098 0. 0. 0. 0.
Problem 225 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 4.897 0.095 0. 0. 0. 0.
Problem 226 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 8.376 0.102 0. 0. 0. 0.
Problem 227 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 13.561 0.092 0. 0. 0. 0.

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 [30] had the largest ratio of [ 1. ]

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 3 3 1. 6 0.5
5 A 2 2 1. 4 0.5
6 A 5 5 1. 8 0.625
7 A 4 4 1. 8 0.5
8 A 2 2 1. 8 0.25
9 A 5 5 1. 8 0.625
10 A 3 3 1. 8 0.375
11 A 6 5 1. 8 0.625
12 A 7 5 1. 10 0.5
13 A 6 4 1. 10 0.4
14 A 5 5 1. 10 0.5
15 A 4 4 1. 8 0.5
16 A 3 3 1. 6 0.5
17 A 6 6 1. 10 0.6
18 A 7 5 1. 10 0.5
19 A 3 3 1. 10 0.3
20 A 9 7 1. 10 0.7
21 A 5 5 1. 10 0.5
22 A 14 7 1. 10 0.7
23 A 11 5 1. 10 0.5
24 A 9 7 1. 10 0.7
25 A 6 5 1. 8 0.625
26 A 4 3 1. 6 0.5
27 A 7 7 1. 10 0.7
28 A 9 6 1. 10 0.6
29 A 7 7 1. 10 0.7
30 A 14 10 1. 10 1.
31 A 10 9 1. 10 0.9
32 A 23 4 1. 10 0.4
33 A 19 6 1. 10 0.6
34 A 14 4 1. 10 0.4
35 A 11 6 1. 10 0.6
36 A 7 4 1. 8 0.5
37 A 5 3 1. 6 0.5
38 A 8 7 1. 10 0.7
39 A 11 7 1. 10 0.7
40 A 8 8 1. 10 0.8
41 A 19 10 1. 10 1.
42 A 7 3 1. 10 0.3
43 A 6 3 1. 10 0.3
44 A 6 3 1. 10 0.3
45 A 5 3 1. 10 0.3
46 A 5 3 1. 10 0.3
47 A 4 4 1. 8 0.5
48 A 2 2 1. 6 0.333
49 A 0 0 0. 0 0.
50 A 0 0 0. 0 0.
51 A 6 2 1. 10 0.2
52 A 5 2 1. 10 0.2
53 A 5 2 1. 10 0.2
54 A 4 2 1. 10 0.2
55 A 4 2 1. 10 0.2
56 A 2 2 1. 8 0.25
57 A 3 3 1. 6 0.5
58 A 0 0 0. 0 0.
59 A 0 0 0. 0 0.
60 A 14 5 1. 10 0.5
61 A 12 6 1. 10 0.6
62 A 10 6 1. 10 0.6
63 A 7 7 1. 8 0.875
64 A 4 4 1. 6 0.667
65 A 0 0 0. 0 0.
66 A 0 0 0. 0 0.
67 A 12 4 1. 10 0.4
68 A 9 4 1. 10 0.4
69 A 10 6 1. 10 0.6
70 A 5 5 1. 8 0.625
71 A 5 4 1. 6 0.667
72 A 0 0 0. 0 0.
73 A 0 0 0. 0 0.
74 A 10 5 1. 12 0.417
75 A 8 5 1. 12 0.417
76 A 8 5 1. 12 0.417
77 A 6 5 1. 10 0.5
78 A 4 4 1. 8 0.5
79 A 0 0 0. 0 0.
80 A 23 8 1.32 12 0.667
81 A 16 8 1. 12 0.667
82 A 13 8 1. 12 0.667
83 A 8 8 1. 10 0.8
84 A 5 5 1. 8 0.625
85 A 0 0 0. 0 0.
86 A 26 8 1.13 12 0.667
87 A 18 7 1. 12 0.583
88 A 15 8 1. 12 0.667
89 A 9 7 1. 10 0.7
90 A 6 5 1. 8 0.625
91 A 0 0 0. 0 0.
92 A 9 4 1. 12 0.333
93 A 7 4 1. 12 0.333
94 A 7 4 1. 12 0.333
95 A 5 5 1. 10 0.5
96 A 3 3 1. 8 0.375
97 A 0 0 0. 0 0.
98 A 0 0 0. 0 0.
99 A 10 3 1. 12 0.25
100 A 8 3 1. 12 0.25
101 A 8 3 1. 12 0.25
102 A 6 3 1. 12 0.25
103 A 6 3 1. 12 0.25
104 A 3 3 1. 10 0.3
105 A 4 4 1. 8 0.5
106 A 0 0 0. 0 0.
107 A 19 6 1.37 12 0.5
108 A 15 7 1. 12 0.583
109 A 13 7 1. 12 0.583
110 A 8 8 1. 10 0.8
111 A 5 5 1. 8 0.625
112 A 0 0 0. 0 0.
113 A 17 5 1. 12 0.417
114 A 12 5 1. 12 0.417
115 A 13 7 1. 12 0.583
116 A 6 6 1. 10 0.6
117 A 6 5 1. 8 0.625
118 A 0 0 0. 0 0.
119 A 0 0 0. 0 0.
120 A 0 0 0. 0 0.
121 A 2 2 1. 12 0.167
122 A 2 2 1. 10 0.2
123 A 0 0 0. 0 0.
124 A 0 0 0. 0 0.
125 A 0 0 0. 0 0.
126 A 0 0 0. 0 0.
127 A 0 0 0. 0 0.
128 A 0 0 0. 0 0.
129 A 0 0 0. 0 0.
130 A 9 4 1. 10 0.4
131 A 9 4 1. 10 0.4
132 A 6 5 1. 8 0.625
133 A 4 3 1. 6 0.5
134 A 0 0 0. 0 0.
135 A 0 0 0. 0 0.
136 A 0 0 0. 0 0.
137 A 0 0 0. 0 0.
138 A 0 0 0. 0 0.
139 A 0 0 0. 0 0.
140 A 4 3 1. 12 0.25
141 A 4 3 1. 12 0.25
142 A 3 3 1. 10 0.3
143 A 3 2 1. 8 0.25
144 A 5 5 1. 12 0.417
145 A 4 4 1. 12 0.333
146 A 2 2 1. 12 0.167
147 A 5 5 1. 12 0.417
148 A 5 5 1. 14 0.357
149 A 4 4 1. 12 0.333
150 A 3 3 1. 10 0.3
151 A 6 6 1. 14 0.429
152 A 7 5 1. 14 0.357
153 A 10 7 1. 14 0.5
154 A 6 5 1. 12 0.417
155 A 5 3 1. 10 0.3
156 A 7 7 1. 14 0.5
157 A 9 6 1. 14 0.429
158 A 9 5 0.97 14 0.357
159 A 6 6 1. 12 0.5
160 A 4 4 1. 10 0.4
161 A 0 0 0. 0 0.
162 A 0 0 0. 0 0.
163 A 8 4 0.97 14 0.286
164 A 4 4 1. 12 0.333
165 A 5 5 0.95 10 0.5
166 A 0 0 0. 0 0.
167 A 0 0 0. 0 0.
168 A 16 8 1.24 14 0.571
169 A 9 9 1. 12 0.75
170 A 6 6 1. 10 0.6
171 A 0 0 0. 0 0.
172 A 0 0 0. 0 0.
173 A 14 8 1. 16 0.5
174 A 9 8 1. 14 0.571
175 A 7 7 1. 12 0.583
176 A 0 0 0. 0 0.
177 A 0 0 0. 0 0.
178 A 22 11 1. 16 0.688
179 A 11 11 1. 14 0.786
180 A 8 8 1. 12 0.667
181 A 0 0 0. 0 0.
182 A 0 0 0. 0 0.
183 A 24 11 1. 16 0.688
184 A 12 10 1. 14 0.714
185 A 9 8 1. 12 0.667
186 A 0 0 0. 0 0.
187 A 0 0 0. 0 0.
188 A 13 7 1. 16 0.438
189 A 8 8 1. 14 0.571
190 A 6 6 1. 12 0.5
191 A 0 0 0. 0 0.
192 A 0 0 0. 0 0.
193 A 12 6 1. 16 0.375
194 A 6 6 1. 14 0.429
195 A 7 7 1. 12 0.583
196 A 0 0 0. 0 0.
197 A 0 0 0. 0 0.
198 A 22 10 1. 16 0.625
199 A 11 11 1. 14 0.786
200 A 8 8 1. 12 0.667
201 A 0 0 0. 0 0.
202 A 0 0 0. 0 0.
203 A 5 4 1. 16 0.25
204 A 7 7 1. 16 0.438
205 A 4 4 1. 16 0.25
206 A 6 6 1. 16 0.375
207 A 3 3 1. 16 0.188
208 A 7 7 1. 16 0.438
209 A 2 2 1. 18 0.111
210 A 2 2 1. 18 0.111
211 A 2 2 1. 18 0.111
212 A 2 2 1. 18 0.111
213 A 2 2 1. 18 0.111
214 A 2 2 1. 18 0.111
215 A 0 0 0. 0 0.
216 A 0 0 0. 0 0.
217 A 0 0 0. 0 0.
218 A 0 0 0. 0 0.
219 A 0 0 0. 0 0.
220 A 0 0 0. 0 0.
221 A 0 0 0. 0 0.
222 A 0 0 0. 0 0.
223 A 0 0 0. 0 0.
224 A 0 0 0. 0 0.
225 A 0 0 0. 0 0.
226 A 0 0 0. 0 0.
227 A 0 0 0. 0 0.

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