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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 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 55, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 86, 87, 96, 97, 98, 99, 100, 102, 105, 108, 111, 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, 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, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 197, 198 }

B grade: { }

C grade: { 17, 18, 30, 31, 37, 38, 52, 53, 54, 56, 57, 58, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 103, 104, 106, 107, 109, 110, 112, 113 }

F grade: { 101, 181, 182, 183, 196}

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, 48, 55, 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, 96, 97, 98, 99, 100, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 134, 138, 139, 140, 142, 143, 153, 154, 155, 159, 160, 165, 173, 180 }

B grade: { 39, 40, 41, 42, 43, 44, 137, 144 }

C grade: { 45, 46, 47, 49, 50, 51, 52, 53, 54, 56, 57, 58, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113 }

F grade: { 101, 127, 131, 132, 133, 135, 136, 141, 145, 146, 147, 148, 149, 150, 151, 152, 156, 157, 158, 161, 162, 163, 164, 166, 167, 168, 169, 170, 171, 172, 174, 175, 176, 177, 178, 179, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 32, 33, 34, 36, 37, 38, 96, 97, 98, 99, 100, 114, 115, 117, 118, 119, 120, 122, 123, 124, 125, 126, 128, 129, 130, 131, 132, 133, 134, 137, 138, 139, 140, 142, 143, 145, 146, 147, 148, 153, 154, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 180, 184, 185, 186, 189, 190, 191, 192, 193, 197, 198

B grade: { 144, 155 }

C grade: { }

F grade: { 22, 26, 27, 28, 29, 30, 31, 35, 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, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 116, 121, 127, 135, 136, 141, 149, 150, 151, 152, 156, 157, 158, 159, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 182, 183, 187, 188, 194, 195, 196 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 48, 59, 60, 61, 62, 63, 64, 72, 73, 74, 96, 97, 98, 99, 100, 114, 115, 117, 118, 119, 120, 122, 123, 124, 125, 126, 134, 137, 138, 139, 140, 151, 152, 153, 154, 155, 160, 165, 180 }

B grade: { 75, 76, 77 }

C grade: { 11, 12, 13, 14, 16, 17, 18, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 55, 65, 66, 67, 68, 69, 70, 71, 78, 79, 80, 81, 82, 83, 84, 85, 131, 132, 133, 150 }

F grade: { 6, 15, 22, 35, 45, 46, 47, 49, 50, 51, 52, 53, 54, 56, 57, 58, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 116, 121, 127, 128, 129, 130, 135, 136, 141, 142, 143, 144, 145, 146, 147, 148, 149, 156, 157, 158, 159, 161, 162, 163, 164, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 19, 20, 21, 23, 24, 25, 27, 28, 29, 96, 97, 98, 99, 100, 114, 115, 116, 117, 118, 119, 120, 122, 123, 134, 160 }

B grade: { }

C grade: { }

F grade: { 11, 12, 13, 14, 16, 17, 18, 22, 26, 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, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198 }

2.1.7 Giac

A grade: { 96, 97, 98, 99, 100, 114, 115, 117, 118, 119, 120, 122, 123, 134, 160, 180 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 116, 121, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198 }

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 F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 73 76 97 177 66 0
normalized size 1 1. 0.85 0.88 1.13 2.06 0.77 0.
time (sec) N/A 0.053 0.042 0.046 0.964 2.689 15.264 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 65 68 86 153 58 0
normalized size 1 1. 0.86 0.89 1.13 2.01 0.76 0.
time (sec) N/A 0.045 0.033 0.046 0.983 2.662 8.741 0.
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 57 60 76 132 49 0
normalized size 1 1. 0.86 0.91 1.15 2. 0.74 0.
time (sec) N/A 0.04 0.029 0.047 0.973 2.599 4.428 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 48 52 65 111 41 0
normalized size 1 1. 0.86 0.93 1.16 1.98 0.73 0.
time (sec) N/A 0.028 0.024 0.046 0.965 2.582 2.437 0.
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 26 36 39 70 22 0
normalized size 1 1. 0.9 1.24 1.34 2.41 0.76 0.
time (sec) N/A 0.009 0.012 0.045 0.981 2.635 1.209 0.
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 5 5 5 6 7 0 3 0
normalized size 1 1. 1. 1.2 1.4 0. 0.6 0.
time (sec) N/A 0.009 0.001 0.043 0.975 0. 1.712 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 36 40 38 88 24 0
normalized size 1 1. 1. 1.11 1.06 2.44 0.67 0.
time (sec) N/A 0.022 0.01 0.119 1.009 2.782 1.563 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 50 52 54 117 42 0
normalized size 1 1. 0.86 0.9 0.93 2.02 0.72 0.
time (sec) N/A 0.033 0.022 0.118 0.981 2.629 2.965 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 52 60 66 143 51 0
normalized size 1 1. 0.76 0.88 0.97 2.1 0.75 0.
time (sec) N/A 0.036 0.037 0.119 0.99 2.688 5.569 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 60 68 78 163 60 0
normalized size 1 1. 0.77 0.87 1. 2.09 0.77 0.
time (sec) N/A 0.039 0.035 0.128 0.986 2.786 11.28 0.
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 86 78 104 244 0 0
normalized size 1 1. 0.98 0.89 1.18 2.77 0. 0.
time (sec) N/A 0.057 0.012 0.161 0.999 2.549 0. 0.
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 78 69 93 224 0 0
normalized size 1 1. 1. 0.88 1.19 2.87 0. 0.
time (sec) N/A 0.051 0.011 0.164 0.996 2.676 0. 0.
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 69 62 82 201 0 0
normalized size 1 1. 1.01 0.91 1.21 2.96 0. 0.
time (sec) N/A 0.035 0.009 0.155 1.014 2.616 0. 0.
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 39 41 53 151 0 0
normalized size 1 1. 1.15 1.21 1.56 4.44 0. 0.
time (sec) N/A 0.011 0.012 0.092 0.991 2.598 0. 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 5 5 5 6 7 0 3 0
normalized size 1 1. 1. 1.2 1.4 0. 0.6 0.
time (sec) N/A 0.009 0.001 0.04 0.984 0. 0.552 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 44 57 45 162 0 0
normalized size 1 1. 0.96 1.24 0.98 3.52 0. 0.
time (sec) N/A 0.03 0.032 0.08 0.995 2.662 0. 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A C F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 70 70 25 90 63 194 0 0
normalized size 1 1. 0.36 1.29 0.9 2.77 0. 0.
time (sec) N/A 0.043 0.009 0.165 0.993 2.718 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A C F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 80 80 25 106 76 221 0 0
normalized size 1 1. 0.31 1.32 0.95 2.76 0. 0.
time (sec) N/A 0.048 0.009 0.168 0.988 2.814 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 65 62 84 142 56 0
normalized size 1 1. 0.88 0.84 1.14 1.92 0.76 0.
time (sec) N/A 0.061 0.022 0.044 1.008 2.527 42.518 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 56 54 73 120 48 0
normalized size 1 1. 0.88 0.84 1.14 1.88 0.75 0.
time (sec) N/A 0.05 0.017 0.045 0.969 2.584 13.184 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 43 52 54 89 39 0
normalized size 1 1. 0.93 1.13 1.17 1.93 0.85 0.
time (sec) N/A 0.025 0.009 0.045 0.985 2.57 4.027 0.
Problem 22 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 11 11 11 10 0 0 0 0
normalized size 1 1. 1. 0.91 0. 0. 0. 0.
time (sec) N/A 0.009 0.001 0.115 0. 0. 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 49 43 46 112 37 0
normalized size 1 1. 1. 0.88 0.94 2.29 0.76 0.
time (sec) N/A 0.041 0.012 0.05 0.96 2.68 4.88 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 51 54 62 131 49 0
normalized size 1 1. 0.8 0.84 0.97 2.05 0.77 0.
time (sec) N/A 0.05 0.028 0.05 0.988 2.649 14.997 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 60 62 74 154 58 0
normalized size 1 1. 0.81 0.84 1. 2.08 0.78 0.
time (sec) N/A 0.054 0.031 0.05 0.981 2.657 43.062 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 65 58 0 398 0 0
normalized size 1 1. 0.89 0.79 0. 5.45 0. 0.
time (sec) N/A 0.045 0.072 0.046 0. 2.698 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 57 50 0 351 83 0
normalized size 1 1. 0.9 0.79 0. 5.57 1.32 0.
time (sec) N/A 0.039 0.051 0.046 0. 2.639 119.376 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 39 37 0 269 60 0
normalized size 1 1. 0.98 0.92 0. 6.72 1.5 0.
time (sec) N/A 0.017 0.028 0.046 0. 2.631 23.224 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 41 39 0 232 184 0
normalized size 1 1. 0.98 0.93 0. 5.52 4.38 0.
time (sec) N/A 0.026 0.018 0.049 0. 2.792 84.144 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 47 45 0 289 0 0
normalized size 1 1. 0.84 0.8 0. 5.16 0. 0.
time (sec) N/A 0.032 0.014 0.053 0. 2.746 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 47 53 0 333 0 0
normalized size 1 1. 0.71 0.8 0. 5.05 0. 0.
time (sec) N/A 0.038 0.015 0.052 0. 2.661 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 88 80 104 240 0 0
normalized size 1 1. 1. 0.91 1.18 2.73 0. 0.
time (sec) N/A 0.075 0.018 0.058 0.98 2.717 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 79 72 93 217 0 0
normalized size 1 1. 1.01 0.92 1.19 2.78 0. 0.
time (sec) N/A 0.061 0.014 0.054 0.968 2.706 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 52 56 72 181 0 0
normalized size 1 1. 0.87 0.93 1.2 3.02 0. 0.
time (sec) N/A 0.03 0.011 0.055 1.001 2.664 0. 0.
Problem 35 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 11 11 11 10 0 0 0 0
normalized size 1 1. 1. 0.91 0. 0. 0. 0.
time (sec) N/A 0.009 0.001 0.154 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 60 68 55 194 0 0
normalized size 1 1. 0.95 1.08 0.87 3.08 0. 0.
time (sec) N/A 0.047 0.027 0.061 0.99 2.719 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A C F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 78 78 30 98 74 217 0 0
normalized size 1 1. 0.38 1.26 0.95 2.78 0. 0.
time (sec) N/A 0.064 0.012 0.065 1.003 2.718 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A C F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 88 88 30 115 86 242 0 0
normalized size 1 1. 0.34 1.31 0.98 2.75 0. 0.
time (sec) N/A 0.065 0.012 0.066 0.998 2.797 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 77 144 0 608 0 0
normalized size 1 1. 0.89 1.66 0. 6.99 0. 0.
time (sec) N/A 0.053 0.161 0.178 0. 2.777 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 69 136 0 555 0 0
normalized size 1 1. 0.9 1.77 0. 7.21 0. 0.
time (sec) N/A 0.049 0.138 0.175 0. 2.743 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 50 119 0 452 0 0
normalized size 1 1. 1. 2.38 0. 9.04 0. 0.
time (sec) N/A 0.023 0.088 0.173 0. 2.694 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 50 112 0 402 0 0
normalized size 1 1. 0.93 2.07 0. 7.44 0. 0.
time (sec) N/A 0.036 0.081 0.172 0. 2.871 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 61 125 0 462 0 0
normalized size 1 1. 0.87 1.79 0. 6.6 0. 0.
time (sec) N/A 0.041 0.089 0.177 0. 3.227 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 69 138 0 513 0 0
normalized size 1 1. 0.86 1.72 0. 6.41 0. 0.
time (sec) N/A 0.047 0.101 0.18 0. 3.241 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 69 108 0 0 0 0
normalized size 1 1. 0.97 1.52 0. 0. 0. 0.
time (sec) N/A 0.037 0.044 0.26 0. 0. 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 69 108 0 0 0 0
normalized size 1 1. 0.97 1.52 0. 0. 0. 0.
time (sec) N/A 0.032 0.036 0.207 0. 0. 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 51 88 0 0 0 0
normalized size 1 1. 0.94 1.63 0. 0. 0. 0.
time (sec) N/A 0.023 0.045 0.207 0. 0. 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 12 0 28 0 0
normalized size 1 1. 1. 1.09 0. 2.55 0. 0.
time (sec) N/A 0.01 0.002 0.044 0. 2.839 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 60 106 0 0 0 0
normalized size 1 1. 0.87 1.54 0. 0. 0. 0.
time (sec) N/A 0.039 0.053 0.208 0. 0. 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 61 108 0 0 0 0
normalized size 1 1. 0.78 1.38 0. 0. 0. 0.
time (sec) N/A 0.042 0.052 0.209 0. 0. 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 61 108 0 0 0 0
normalized size 1 1. 0.8 1.42 0. 0. 0. 0.
time (sec) N/A 0.04 0.052 0.205 0. 0. 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 88 88 41 132 0 0 0 0
normalized size 1 1. 0.47 1.5 0. 0. 0. 0.
time (sec) N/A 0.052 0.009 0.345 0. 0. 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 88 88 41 132 0 0 0 0
normalized size 1 1. 0.47 1.5 0. 0. 0. 0.
time (sec) N/A 0.043 0.008 0.338 0. 0. 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 69 69 39 105 0 0 0 0
normalized size 1 1. 0.57 1.52 0. 0. 0. 0.
time (sec) N/A 0.028 0.006 0.334 0. 0. 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 12 0 209 0 0
normalized size 1 1. 1. 1.09 0. 19. 0. 0.
time (sec) N/A 0.01 0.001 0.041 0. 2.724 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 84 84 37 129 0 0 0 0
normalized size 1 1. 0.44 1.54 0. 0. 0. 0.
time (sec) N/A 0.05 0.009 0.333 0. 0. 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 95 95 41 132 0 0 0 0
normalized size 1 1. 0.43 1.39 0. 0. 0. 0.
time (sec) N/A 0.05 0.009 0.343 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 93 93 41 132 0 0 0 0
normalized size 1 1. 0.44 1.42 0. 0. 0. 0.
time (sec) N/A 0.051 0.01 0.34 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 90 96 0 470 0 0
normalized size 1 1. 0.77 0.82 0. 4.02 0. 0.
time (sec) N/A 0.072 0.102 0.194 0. 2.82 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 75 83 0 362 0 0
normalized size 1 1. 0.74 0.81 0. 3.55 0. 0.
time (sec) N/A 0.053 0.082 0.05 0. 2.569 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 63 69 0 331 0 0
normalized size 1 1. 0.79 0.86 0. 4.14 0. 0.
time (sec) N/A 0.046 0.079 0.05 0. 2.615 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 51 63 0 316 0 0
normalized size 1 1. 0.75 0.93 0. 4.65 0. 0.
time (sec) N/A 0.043 0.071 0.053 0. 2.712 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 57 76 0 365 0 0
normalized size 1 1. 0.64 0.85 0. 4.1 0. 0.
time (sec) N/A 0.05 0.074 0.055 0. 2.665 0. 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 65 89 0 412 0 0
normalized size 1 1. 0.61 0.84 0. 3.89 0. 0.
time (sec) N/A 0.057 0.095 0.054 0. 2.593 0. 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 98 149 0 822 0 0
normalized size 1 1. 0.64 0.97 0. 5.37 0. 0.
time (sec) N/A 0.098 0.26 0.182 0. 2.975 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 88 141 0 721 0 0
normalized size 1 1. 0.65 1.04 0. 5.3 0. 0.
time (sec) N/A 0.083 0.218 0.061 0. 2.874 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 73 133 0 593 0 0
normalized size 1 1. 0.6 1.1 0. 4.9 0. 0.
time (sec) N/A 0.067 0.188 0.058 0. 2.848 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 57 127 0 547 0 0
normalized size 1 1. 0.59 1.31 0. 5.64 0. 0.
time (sec) N/A 0.062 0.139 0.057 0. 2.726 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 58 111 0 518 0 0
normalized size 1 1. 0.68 1.31 0. 6.09 0. 0.
time (sec) N/A 0.059 0.102 0.056 0. 2.589 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 64 122 0 575 0 0
normalized size 1 1. 0.59 1.13 0. 5.32 0. 0.
time (sec) N/A 0.066 0.096 0.06 0. 2.789 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 72 135 0 629 0 0
normalized size 1 1. 0.58 1.08 0. 5.03 0. 0.
time (sec) N/A 0.076 0.13 0.062 0. 2.86 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 101 150 0 471 0 0
normalized size 1 1. 0.72 1.07 0. 3.36 0. 0.
time (sec) N/A 0.107 0.104 0.214 0. 2.846 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 91 139 0 440 0 0
normalized size 1 1. 0.73 1.11 0. 3.52 0. 0.
time (sec) N/A 0.086 0.07 0.052 0. 2.703 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 115 115 57 137 0 408 0 0
normalized size 1 1. 0.5 1.19 0. 3.55 0. 0.
time (sec) N/A 0.08 0.074 0.053 0. 2.882 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 103 103 62 127 0 425 0 0
normalized size 1 1. 0.6 1.23 0. 4.13 0. 0.
time (sec) N/A 0.074 0.07 0.052 0. 2.664 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 111 111 62 129 0 470 0 0
normalized size 1 1. 0.56 1.16 0. 4.23 0. 0.
time (sec) N/A 0.072 0.067 0.054 0. 2.735 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 126 126 70 140 0 512 0 0
normalized size 1 1. 0.56 1.11 0. 4.06 0. 0.
time (sec) N/A 0.086 0.077 0.056 0. 2.755 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) C F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 161 161 89 155 0 682 0 0
normalized size 1 1. 0.55 0.96 0. 4.24 0. 0.
time (sec) N/A 0.127 0.103 0.193 0. 3.106 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) C F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 161 161 89 155 0 606 0 0
normalized size 1 1. 0.55 0.96 0. 3.76 0. 0.
time (sec) N/A 0.116 0.1 0.208 0. 2.915 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) C F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 146 146 68 147 0 579 0 0
normalized size 1 1. 0.47 1.01 0. 3.97 0. 0.
time (sec) N/A 0.097 0.092 0.224 0. 2.852 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) C F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 134 134 68 147 0 521 0 0
normalized size 1 1. 0.51 1.1 0. 3.89 0. 0.
time (sec) N/A 0.101 0.086 0.191 0. 2.862 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) C F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 122 122 71 131 0 549 0 0
normalized size 1 1. 0.58 1.07 0. 4.5 0. 0.
time (sec) N/A 0.093 0.09 0.191 0. 3.007 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) C F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 132 132 71 131 0 591 0 0
normalized size 1 1. 0.54 0.99 0. 4.48 0. 0.
time (sec) N/A 0.091 0.094 0.194 0. 2.818 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) C F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 147 147 79 142 0 641 0 0
normalized size 1 1. 0.54 0.97 0. 4.36 0. 0.
time (sec) N/A 0.107 0.099 0.206 0. 3.003 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) C F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 147 147 84 142 0 629 0 0
normalized size 1 1. 0.57 0.97 0. 4.28 0. 0.
time (sec) N/A 0.106 0.096 0.191 0. 3.057 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 82 121 0 0 0 0
normalized size 1 1. 0.81 1.2 0. 0. 0. 0.
time (sec) N/A 0.059 0.124 0.255 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 82 121 0 0 0 0
normalized size 1 1. 0.82 1.21 0. 0. 0. 0.
time (sec) N/A 0.055 0.106 0.229 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 93 93 48 109 0 0 0 0
normalized size 1 1. 0.52 1.17 0. 0. 0. 0.
time (sec) N/A 0.054 0.021 0.232 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 97 97 48 121 0 0 0 0
normalized size 1 1. 0.49 1.25 0. 0. 0. 0.
time (sec) N/A 0.06 0.029 0.224 0. 0. 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 105 105 48 121 0 0 0 0
normalized size 1 1. 0.46 1.15 0. 0. 0. 0.
time (sec) N/A 0.061 0.026 0.23 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 125 125 50 145 0 0 0 0
normalized size 1 1. 0.4 1.16 0. 0. 0. 0.
time (sec) N/A 0.075 0.03 0.379 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 124 124 50 145 0 0 0 0
normalized size 1 1. 0.4 1.17 0. 0. 0. 0.
time (sec) N/A 0.07 0.026 0.381 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 115 115 50 133 0 0 0 0
normalized size 1 1. 0.43 1.16 0. 0. 0. 0.
time (sec) N/A 0.069 0.02 0.372 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 119 119 50 145 0 0 0 0
normalized size 1 1. 0.42 1.22 0. 0. 0. 0.
time (sec) N/A 0.078 0.025 0.372 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 129 129 50 145 0 0 0 0
normalized size 1 1. 0.39 1.12 0. 0. 0. 0.
time (sec) N/A 0.075 0.024 0.381 0. 0. 0. 0.
Problem 96 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 29 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.008 0.007 0.043 0. 0. 0. 0.
Problem 97 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 21 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.005 0.006 0.046 0. 0. 0. 0.
Problem 98 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 9 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.002 0.007 0.048 0. 0. 0. 0.
Problem 99 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 21 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.005 0.006 0.062 0. 0. 0. 0.
Problem 100 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 29 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.008 0.007 0.047 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 9 9 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.008 0.007 0.056 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 53 144 0 0 0 0
normalized size 1 1. 0.68 1.85 0. 0. 0. 0.
time (sec) N/A 0.049 0.039 0.227 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 102 102 88 173 0 0 0 0
normalized size 1 1. 0.86 1.7 0. 0. 0. 0.
time (sec) N/A 0.064 0.06 0.388 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 121 121 119 198 0 0 0 0
normalized size 1 1. 0.98 1.64 0. 0. 0. 0.
time (sec) N/A 0.086 0.073 0.794 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 72 177 0 0 0 0
normalized size 1 1. 0.77 1.88 0. 0. 0. 0.
time (sec) N/A 0.055 0.045 0.236 0. 0. 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 118 118 126 218 0 0 0 0
normalized size 1 1. 1.07 1.85 0. 0. 0. 0.
time (sec) N/A 0.071 0.079 0.41 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 142 142 166 259 0 0 0 0
normalized size 1 1. 1.17 1.82 0. 0. 0. 0.
time (sec) N/A 0.093 0.1 0.792 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 72 177 0 0 0 0
normalized size 1 1. 0.77 1.88 0. 0. 0. 0.
time (sec) N/A 0.055 0.045 0.277 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 118 118 126 218 0 0 0 0
normalized size 1 1. 1.07 1.85 0. 0. 0. 0.
time (sec) N/A 0.071 0.08 0.414 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 142 142 166 259 0 0 0 0
normalized size 1 1. 1.17 1.82 0. 0. 0. 0.
time (sec) N/A 0.094 0.097 0.856 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 80 148 0 0 0 0
normalized size 1 1. 0.79 1.47 0. 0. 0. 0.
time (sec) N/A 0.06 0.064 0.293 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 130 130 50 180 0 0 0 0
normalized size 1 1. 0.38 1.38 0. 0. 0. 0.
time (sec) N/A 0.076 0.025 0.529 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 154 154 52 217 0 0 0 0
normalized size 1 1. 0.34 1.41 0. 0. 0. 0.
time (sec) N/A 0.102 0.02 3.379 0. 0. 0. 0.
Problem 114 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 9 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.005 0.022 0.05 0. 0. 0. 0.
Problem 115 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 7 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.002 0.001 0.047 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 7 7 7 8 0 0 5 0
normalized size 1 1. 1. 1.14 0. 0. 0.71 0.
time (sec) N/A 0.009 0.001 0.044 0. 0. 0.528 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 11 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.009 0.021 0.05 0. 0. 0. 0.
Problem 118 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 11 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.009 0.021 0.049 0. 0. 0. 0.
Problem 119 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 11 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.006 0.023 0.046 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 9 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.003 0.004 0.049 0. 0. 0. 0.
Problem 121 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 13 13 13 14 0 0 0 0
normalized size 1 1. 1. 1.08 0. 0. 0. 0.
time (sec) N/A 0.01 0.001 0.046 0. 0. 0. 0.
Problem 122 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 13 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.009 0.021 0.046 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 13 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.009 0.022 0.046 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 260 260 144 269 270 366 0 0
normalized size 1 1. 0.55 1.03 1.04 1.41 0. 0.
time (sec) N/A 0.321 0.208 0.008 0.995 2.393 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 152 152 96 177 196 242 0 0
normalized size 1 1. 0.63 1.16 1.29 1.59 0. 0.
time (sec) N/A 0.169 0.101 0.004 0.993 2.348 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 53 96 122 126 0 0
normalized size 1 1. 0.88 1.6 2.03 2.1 0. 0.
time (sec) N/A 0.049 0.018 0.003 0.983 2.416 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 401 401 422 0 0 0 0 0
normalized size 1 1. 1.05 0. 0. 0. 0. 0.
time (sec) N/A 0.355 0.146 0.01 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 73 85 154 0 0 0
normalized size 1 1. 0.87 1.01 1.83 0. 0. 0.
time (sec) N/A 0.117 0.052 0.13 0.982 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 173 173 131 195 261 0 0 0
normalized size 1 1. 0.76 1.13 1.51 0. 0. 0.
time (sec) N/A 0.178 0.18 0.227 0.994 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 276 276 210 376 408 0 0 0
normalized size 1 1. 0.76 1.36 1.48 0. 0. 0.
time (sec) N/A 0.273 0.304 0.214 1.027 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 347 347 296 0 356 675 0 0
normalized size 1 1. 0.85 0. 1.03 1.95 0. 0.
time (sec) N/A 0.638 0.068 0.005 1.03 2.345 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 198 198 198 0 261 510 0 0
normalized size 1 1. 1. 0. 1.32 2.58 0. 0.
time (sec) N/A 0.287 0.047 0.006 1.011 2.511 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 66 0 162 355 0 0
normalized size 1 1. 0.79 0. 1.93 4.23 0. 0.
time (sec) N/A 0.069 0.023 0.005 1.03 2.355 0. 0.
Problem 134 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 0.038 0.037 0.004 0. 0. 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 486 486 477 0 0 0 0 0
normalized size 1 1. 0.98 0. 0. 0. 0. 0.
time (sec) N/A 0.56 0.742 0.005 0. 0. 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 629 629 573 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.664 1.931 0.004 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 605 605 485 1177 919 1339 0 0
normalized size 1 1. 0.8 1.95 1.52 2.21 0. 0.
time (sec) N/A 0.587 0.562 0.064 1.043 2.378 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 385 385 274 687 548 779 0 0
normalized size 1 1. 0.71 1.78 1.42 2.02 0. 0.
time (sec) N/A 0.339 0.183 0.058 1.034 2.321 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 210 210 161 292 286 377 0 0
normalized size 1 1. 0.77 1.39 1.36 1.8 0. 0.
time (sec) N/A 0.197 0.09 0.049 1.019 2.491 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 53 96 122 126 0 0
normalized size 1 1. 0.88 1.6 2.03 2.1 0. 0.
time (sec) N/A 0.052 0.016 0.006 1.003 2.436 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 591 591 622 0 0 0 0 0
normalized size 1 1. 1.05 0. 0. 0. 0. 0.
time (sec) N/A 0.518 0.308 0.401 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 108 189 224 0 0 0
normalized size 1 1. 0.78 1.37 1.62 0. 0. 0.
time (sec) N/A 0.184 0.141 0.38 1.031 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 278 278 190 437 512 0 0 0
normalized size 1 1. 0.68 1.57 1.84 0. 0. 0.
time (sec) N/A 0.27 0.421 0.462 1.008 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 448 448 313 1075 1928 0 0 0
normalized size 1 1. 0.7 2.4 4.3 0. 0. 0.
time (sec) N/A 0.426 0.632 0.394 1.224 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 46 0 59 0 0 0
normalized size 1 1. 1. 0. 1.28 0. 0. 0.
time (sec) N/A 0.066 0.039 0.322 1.022 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 46 0 59 0 0 0
normalized size 1 1. 1. 0. 1.28 0. 0. 0.
time (sec) N/A 0.067 0.007 0.281 0.957 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 51 0 66 0 0 0
normalized size 1 1. 1. 0. 1.29 0. 0. 0.
time (sec) N/A 0.133 0.039 0.302 0.965 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 51 0 66 0 0 0
normalized size 1 1. 1. 0. 1.29 0. 0. 0.
time (sec) N/A 0.134 0.015 0.282 0.978 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 34 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.071 0.02 0.891 0. 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 32 0 0 782 0 0
normalized size 1 1. 0.97 0. 0. 23.7 0. 0.
time (sec) N/A 0.061 0.007 0.703 0. 3.456 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 32 0 0 74 0 0
normalized size 1 1. 0.97 0. 0. 2.24 0. 0.
time (sec) N/A 0.061 0.007 0.805 0. 2.71 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 40 0 0 68 0 0
normalized size 1 1. 1.21 0. 0. 2.06 0. 0.
time (sec) N/A 0.058 1.823 0.702 0. 2.445 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 38 37 78 72 0 0
normalized size 1 1. 1.06 1.03 2.17 2. 0. 0.
time (sec) N/A 0.317 0.091 0.121 1.014 2.34 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 35 56 70 84 0 0
normalized size 1 1. 0.97 1.56 1.94 2.33 0. 0.
time (sec) N/A 0.367 0.103 0.171 1.045 2.478 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 52 57 285 182 0 0
normalized size 1 1. 1. 1.1 5.48 3.5 0. 0.
time (sec) N/A 2.025 0.265 0.276 1.179 2.276 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 135 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.088 0.012 0.185 0. 0. 0. 0.
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 100 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.058 0.006 0.053 0. 0. 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 65 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.033 0.005 0.055 0. 0. 0. 0.
Problem 159 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 31 31 31 32 0 0 0 0
normalized size 1 1. 1. 1.03 0. 0. 0. 0.
time (sec) N/A 0.018 0.005 0.061 0. 0. 0. 0.
Problem 160 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 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.068 0.051 0.088 0. 0. 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 300 300 223 0 508 0 0 0
normalized size 1 1. 0.74 0. 1.69 0. 0. 0.
time (sec) N/A 0.523 0.573 0.052 1.129 0. 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 258 258 192 0 400 0 0 0
normalized size 1 1. 0.74 0. 1.55 0. 0. 0.
time (sec) N/A 0.405 0.357 0.051 1.119 0. 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 262 262 160 0 300 0 0 0
normalized size 1 1. 0.61 0. 1.15 0. 0. 0.
time (sec) N/A 0.255 0.3 0.049 1.152 0. 0. 0.
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 119 0 190 0 0 0
normalized size 1 1. 0.9 0. 1.44 0. 0. 0.
time (sec) N/A 0.212 0.023 0.049 1.102 0. 0. 0.
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 10 11 26 0 0
normalized size 1 1. 1. 0.91 1. 2.36 0. 0.
time (sec) N/A 0.026 0.009 0.046 0.966 2.534 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 115 0 153 0 0 0
normalized size 1 1. 1.04 0. 1.38 0. 0. 0.
time (sec) N/A 0.164 0.136 0.049 1.166 0. 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 191 191 185 0 219 0 0 0
normalized size 1 1. 0.97 0. 1.15 0. 0. 0.
time (sec) N/A 0.282 0.275 0.05 1.664 0. 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 245 245 246 0 254 0 0 0
normalized size 1 1. 1. 0. 1.04 0. 0. 0.
time (sec) N/A 0.355 0.235 0.05 1.653 0. 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 287 287 277 0 289 0 0 0
normalized size 1 1. 0.97 0. 1.01 0. 0. 0.
time (sec) N/A 0.449 0.236 0.05 1.74 0. 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 423 366 252 0 0 0 0 0
normalized size 1 0.87 0.6 0. 0. 0. 0. 0.
time (sec) N/A 0.611 0.461 0.23 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 330 287 211 0 0 0 0 0
normalized size 1 0.87 0.64 0. 0. 0. 0. 0.
time (sec) N/A 0.449 0.339 0.227 0. 0. 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 149 0 0 0 0 0
normalized size 1 1. 0.89 0. 0. 0. 0. 0.
time (sec) N/A 0.211 0.068 0.199 0. 0. 0. 0.
Problem 173 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 20 20 20 19 0 0 0 0
normalized size 1 1. 1. 0.95 0. 0. 0. 0.
time (sec) N/A 0.058 0.011 0.155 0. 0. 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 165 150 0 0 0 0 0
normalized size 1 1.06 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.355 0.172 0.276 0. 0. 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 266 278 238 0 0 0 0 0
normalized size 1 1.05 0.89 0. 0. 0. 0. 0.
time (sec) N/A 0.496 0.256 0.333 0. 0. 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 340 351 301 0 0 0 0 0
normalized size 1 1.03 0.89 0. 0. 0. 0. 0.
time (sec) N/A 0.651 0.201 0.349 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 2995 2995 2610 0 0 0 0 0
normalized size 1 1. 0.87 0. 0. 0. 0. 0.
time (sec) N/A 4.6 11.481 0.493 0. 0. 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 2252 2252 1996 0 0 0 0 0
normalized size 1 1. 0.89 0. 0. 0. 0. 0.
time (sec) N/A 2.904 8.832 0.289 0. 0. 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 1653 1653 1546 0 0 0 0 0
normalized size 1 1. 0.94 0. 0. 0. 0. 0.
time (sec) N/A 3.186 4.922 0.285 0. 0. 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 29 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 0.553 0.302 0. 0. 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 2498 2498 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.667 10.192 0.428 0. 0. 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 3119 3119 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 3.238 10.412 0.521 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 3733 3733 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 4.308 10.519 0.537 0. 0. 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 661 661 425 0 560 0 0 0
normalized size 1 1. 0.64 0. 0.85 0. 0. 0.
time (sec) N/A 0.982 0.755 0.007 1.04 0. 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 546 546 362 0 466 0 0 0
normalized size 1 1. 0.66 0. 0.85 0. 0. 0.
time (sec) N/A 0.718 0.611 0.007 1.038 0. 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 390 390 285 0 348 0 0 0
normalized size 1 1. 0.73 0. 0.89 0. 0. 0.
time (sec) N/A 0.449 0.49 0.005 1.007 0. 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 137 0 0 0 0 0
normalized size 1 1. 0.9 0. 0. 0. 0. 0.
time (sec) N/A 0.338 0.235 0.005 0. 0. 0. 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 135 0 0 0 0 0
normalized size 1 1. 1.03 0. 0. 0. 0. 0.
time (sec) N/A 0.314 0.714 0.008 0. 0. 0. 0.
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 331 331 285 0 288 0 0 0
normalized size 1 1. 0.86 0. 0.87 0. 0. 0.
time (sec) N/A 0.541 1.188 0.007 1.164 0. 0. 0.
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 460 460 389 0 387 0 0 0
normalized size 1 1. 0.85 0. 0.84 0. 0. 0.
time (sec) N/A 0.672 1.304 0.006 1.201 0. 0. 0.
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 584 584 505 0 460 0 0 0
normalized size 1 1. 0.86 0. 0.79 0. 0. 0.
time (sec) N/A 0.845 1.518 0.007 1.189 0. 0. 0.
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 900 900 583 0 699 0 0 0
normalized size 1 1. 0.65 0. 0.78 0. 0. 0.
time (sec) N/A 1.185 1.28 0.047 1.054 0. 0. 0.
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 645 645 472 0 556 0 0 0
normalized size 1 1. 0.73 0. 0.86 0. 0. 0.
time (sec) N/A 0.818 1.033 0.05 1.05 0. 0. 0.
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 402 402 298 0 0 0 0 0
normalized size 1 1. 0.74 0. 0. 0. 0. 0.
time (sec) N/A 0.619 0.356 0.049 0. 0. 0. 0.
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 218 218 280 0 0 0 0 0
normalized size 1 1. 1.28 0. 0. 0. 0. 0.
time (sec) N/A 0.508 0.834 0.049 0. 0. 0. 0.
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 343 343 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.74 1.986 0.049 0. 0. 0. 0.
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 515 515 488 0 431 0 0 0
normalized size 1 1. 0.95 0. 0.84 0. 0. 0.
time (sec) N/A 0.823 1.632 0.048 1.218 0. 0. 0.
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 767 767 621 0 544 0 0 0
normalized size 1 1. 0.81 0. 0.71 0. 0. 0.
time (sec) N/A 1.125 1.953 0.052 1.234 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 [163] had the largest ratio of [ 1.214 ]

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. 9 0.333
2 A 4 3 1. 9 0.333
3 A 4 3 1. 9 0.333
4 A 4 3 1. 7 0.429
5 A 3 3 1. 5 0.6
6 A 1 1 1. 9 0.111
7 A 5 5 1. 9 0.556
8 A 4 3 1. 9 0.333
9 A 4 3 1. 9 0.333
10 A 4 3 1. 9 0.333
11 A 5 3 1. 9 0.333
12 A 5 3 1. 9 0.333
13 A 5 3 1. 7 0.429
14 A 4 3 1. 5 0.6
15 A 1 1 1. 9 0.111
16 A 6 5 1. 9 0.556
17 A 5 3 1. 9 0.333
18 A 5 3 1. 9 0.333
19 A 5 4 1. 11 0.364
20 A 5 4 1. 11 0.364
21 A 4 4 1. 9 0.444
22 A 1 1 1. 11 0.091
23 A 6 6 1. 11 0.546
24 A 5 4 1. 11 0.364
25 A 5 4 1. 11 0.364
26 A 5 4 1. 11 0.364
27 A 5 4 1. 11 0.364
28 A 4 4 1. 7 0.571
29 A 3 3 1. 11 0.273
30 A 4 4 1. 11 0.364
31 A 5 4 1. 11 0.364
32 A 6 4 1. 11 0.364
33 A 6 4 1. 11 0.364
34 A 5 4 1. 9 0.444
35 A 1 1 1. 11 0.091
36 A 7 6 1. 11 0.546
37 A 6 4 1. 11 0.364
38 A 6 4 1. 11 0.364
39 A 6 4 1. 11 0.364
40 A 6 4 1. 11 0.364
41 A 5 4 1. 7 0.571
42 A 4 3 1. 11 0.273
43 A 5 4 1. 11 0.364
44 A 6 4 1. 11 0.364
45 A 3 3 1. 11 0.273
46 A 3 3 1. 9 0.333
47 A 3 3 1. 7 0.429
48 A 1 1 1. 11 0.091
49 A 3 3 1. 11 0.273
50 A 3 3 1. 11 0.273
51 A 3 3 1. 11 0.273
52 A 4 3 1. 11 0.273
53 A 4 3 1. 9 0.333
54 A 4 3 1. 7 0.429
55 A 1 1 1. 11 0.091
56 A 4 3 1. 11 0.273
57 A 4 3 1. 11 0.273
58 A 4 3 1. 11 0.273
59 A 7 5 1. 13 0.385
60 A 6 5 1. 13 0.385
61 A 5 5 1. 13 0.385
62 A 4 4 1. 13 0.308
63 A 5 5 1. 13 0.385
64 A 6 5 1. 13 0.385
65 A 9 5 1. 13 0.385
66 A 8 5 1. 13 0.385
67 A 7 5 1. 13 0.385
68 A 6 5 1. 13 0.385
69 A 5 4 1. 13 0.308
70 A 6 5 1. 13 0.385
71 A 7 5 1. 13 0.385
72 A 9 8 1. 15 0.533
73 A 8 8 1. 15 0.533
74 A 8 8 1. 15 0.533
75 A 7 7 1. 15 0.467
76 A 7 7 1. 15 0.467
77 A 8 8 1. 15 0.533
78 A 10 8 1. 15 0.533
79 A 10 8 1. 15 0.533
80 A 9 8 1. 15 0.533
81 A 9 8 1. 15 0.533
82 A 8 7 1. 15 0.467
83 A 8 7 1. 15 0.467
84 A 9 8 1. 15 0.533
85 A 9 8 1. 15 0.533
86 A 4 4 1. 15 0.267
87 A 4 4 1. 15 0.267
88 A 4 4 1. 15 0.267
89 A 4 4 1. 15 0.267
90 A 4 4 1. 15 0.267
91 A 5 4 1. 15 0.267
92 A 5 4 1. 15 0.267
93 A 5 4 1. 15 0.267
94 A 5 4 1. 15 0.267
95 A 5 4 1. 15 0.267
96 A 0 0 0. 0 0.
97 A 0 0 0. 0 0.
98 A 0 0 0. 0 0.
99 A 0 0 0. 0 0.
100 A 0 0 0. 0 0.
101 A 2 1 1. 15 0.067
102 A 3 3 1. 11 0.273
103 A 4 3 1. 11 0.273
104 A 5 3 1. 11 0.273
105 A 4 4 1. 13 0.308
106 A 5 4 1. 13 0.308
107 A 6 4 1. 13 0.308
108 A 4 4 1. 13 0.308
109 A 5 4 1. 13 0.308
110 A 6 4 1. 13 0.308
111 A 4 4 1. 13 0.308
112 A 5 4 1. 13 0.308
113 A 6 4 1. 13 0.308
114 A 0 0 0. 0 0.
115 A 0 0 0. 0 0.
116 A 1 1 1. 9 0.111
117 A 0 0 0. 0 0.
118 A 0 0 0. 0 0.
119 A 0 0 0. 0 0.
120 A 0 0 0. 0 0.
121 A 1 1 1. 11 0.091
122 A 0 0 0. 0 0.
123 A 0 0 0. 0 0.
124 A 13 8 1. 13 0.615
125 A 10 8 1. 11 0.727
126 A 7 7 1. 9 0.778
127 A 3 3 1. 13 0.231
128 A 7 9 1. 13 0.692
129 A 11 11 1. 13 0.846
130 A 14 11 1. 13 0.846
131 A 33 13 1. 13 1.
132 A 19 12 1. 11 1.091
133 A 9 8 1. 9 0.889
134 A 0 0 0. 0 0.
135 A 6 5 1. 13 0.385
136 A 12 13 1. 13 1.
137 A 16 8 1. 17 0.471
138 A 13 8 1. 17 0.471
139 A 10 8 1. 15 0.533
140 A 7 7 1. 9 0.778
141 A 3 3 1. 17 0.176
142 A 8 5 1. 17 0.294
143 A 12 8 1. 17 0.471
144 A 15 9 1. 17 0.529
145 A 5 5 1. 9 0.556
146 A 5 5 1. 12 0.417
147 A 8 6 1. 12 0.5
148 A 8 6 1. 15 0.4
149 A 1 1 1. 34 0.029
150 A 1 1 1. 34 0.029
151 A 1 1 1. 34 0.029
152 A 1 1 1. 37 0.027
153 A 2 2 1. 53 0.038
154 A 2 2 1. 53 0.038
155 A 4 4 1. 76 0.053
156 A 5 3 1. 19 0.158
157 A 4 3 1. 19 0.158
158 A 3 3 1. 17 0.176
159 A 2 2 1. 15 0.133
160 A 0 0 0. 0 0.
161 A 38 16 1. 16 1.
162 A 31 16 1. 16 1.
163 A 22 17 1. 14 1.214
164 A 15 12 1. 13 0.923
165 A 1 2 1. 16 0.125
166 A 10 13 1. 16 0.812
167 A 23 17 1. 16 1.062
168 A 30 17 1. 16 1.062
169 A 37 17 1. 16 1.062
170 A 37 20 0.87 20 1.
171 A 30 20 0.87 18 1.111
172 A 18 14 1. 17 0.824
173 A 3 3 1. 20 0.15
174 A 19 15 1.06 20 0.75
175 A 31 22 1.05 20 1.1
176 A 42 24 1.03 20 1.2
177 A 108 20 1. 27 0.741
178 A 67 20 1. 25 0.8
179 A 42 17 1. 24 0.708
180 A 0 0 0. 0 0.
181 A 22 9 1. 27 0.333
182 A 44 16 1. 27 0.593
183 A 78 18 1. 27 0.667
184 A 52 17 1. 21 0.81
185 A 40 21 1. 19 1.105
186 A 26 20 1. 18 1.111
187 A 18 15 1. 21 0.714
188 A 13 17 1. 21 0.81
189 A 30 20 1. 21 0.952
190 A 41 19 1. 21 0.905
191 A 51 19 1. 21 0.905
192 A 60 22 1. 24 0.917
193 A 43 21 1. 23 0.913
194 A 29 24 1. 26 0.923
195 A 19 21 1. 26 0.808
196 A 32 22 1. 26 0.846
197 A 43 20 1. 26 0.769
198 A 61 19 1. 26 0.731

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