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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 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 6, 8, 9, 10, 11, 12, 15, 18, 20, 21, 23, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 71, 73, 74, 75, 76, 77, 78, 83, 84, 86, 88, 89, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 159, 161, 163, 165, 167, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 182, 183, 184, 185, 186, 187, 188, 190, 192, 193, 194, 195, 197, 201, 202, 203, 204, 208, 209, 210, 211, 212, 214, 216, 217, 219, 220 }

B grade: { 5, 7, 13, 14, 16, 17, 19, 22, 24, 25, 27, 30, 32, 35, 38, 40, 41, 43, 48, 70, 72, 79, 80, 81, 82, 85, 87, 90, 91, 92, 96, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 158, 160, 162, 164, 180, 181, 191, 196, 198, 199, 200, 205, 206, 207, 213, 215, 218 }

C grade: { 26, 28, 29, 31, 33, 34, 36, 37, 39, 42, 44, 45, 46, 47, 66, 68, 69, 108, 110, 166, 168, 169, 189 }

F grade: { }

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, 23, 28, 29, 31, 36, 44, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 103, 104, 105, 106, 107, 108, 109, 111, 115, 116, 117, 118, 119, 127, 128, 129, 130, 131, 136, 137, 142, 152, 163, 180, 189, 198, 207, 216 }

B grade: { 22, 24, 25, 26, 27, 30, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 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, 110, 112, 113, 114, 120, 121, 122, 123, 124, 125, 126, 132, 133, 134, 135, 138, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175 }

C grade: { }

F grade: { 176, 177, 178, 179, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 193, 194, 195, 196, 197, 199, 200, 201, 202, 203, 204, 205, 206, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220 }

2.1.4 Maxima

A grade: { 3, 4, 6, 12, 20, 49, 51, 52, 57, 59, 60, 65, 103, 104, 105, 106, 115, 118, 127, 138, 140, 170, 171, 172

B grade: { 1, 2, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 50, 53, 54, 55, 56, 58, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 102, 107, 108, 109, 110, 111, 112, 113, 114, 116, 117, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 142, 144, 146, 148, 150, 152, 154, 156, 159, 161, 163, 165, 167 }

C grade: { 173, 174, 175 }

F grade: { 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 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, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 158, 160, 162, 164, 166, 168, 169, 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 }

2.1.5 FriCAS

A grade: { 1, 3, 4, 49, 50, 51, 57, 59, 65, 171, 172, 173, 174, 175 }

B grade: { 2, 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, 52, 53, 54, 55, 56, 58, 60, 61, 62, 63, 64, 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, 170, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 212, 213, 214, 215, 216, 217, 219 }

C grade: { }

F grade: { 47, 48, 168, 169, 186, 193, 211, 218, 220 }

2.1.6 Sympy

A grade: { 51, 103, 105, 113, 115, 125, 127, 142, 207, 216 }

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, 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, 104, 106, 107, 108, 109, 110, 111, 112, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 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, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220 }

2.1.7 Giac

A grade: { 4, 6, 8, 12, 16, 17, 20, 30, 32, 33, 35, 52, 56, 57, 78, 80, 82, 89, 106, 107, 108, 118, 140, 143, 145, 151, 153 }

B grade: { 1, 2, 3, 5, 7, 9, 10, 11, 13, 14, 15, 18, 19, 21, 22, 23, 24, 25, 27, 38, 40, 41, 43, 46, 48, 49, 50, 51, 53, 54, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 84, 87, 91, 93, 96, 98, 100, 102, 103, 104, 105, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 144, 146, 147, 148, 149, 150, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172 }

C grade: { 173, 174, 175 }

F grade: { 26, 28, 29, 31, 34, 36, 37, 39, 42, 44, 45, 47, 74, 76, 77, 79, 81, 83, 85, 86, 88, 90, 92, 94, 95, 97, 99, 101, 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 }

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 B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 54 78 174 300 0 193
normalized size 1 1. 0.77 1.11 2.49 4.29 0. 2.76
time (sec) N/A 0.081 0.314 0.032 1.016 2.553 0. 1.165
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 53 55 150 220 0 132
normalized size 1 1. 1.2 1.25 3.41 5. 0. 3.
time (sec) N/A 0.056 0.049 0.029 1.004 2.522 0. 1.186
Problem 3 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 43 43 57 45 84 177 0 130
normalized size 1 1. 1.33 1.05 1.95 4.12 0. 3.02
time (sec) N/A 0.056 0.186 0.028 1.035 2.445 0. 1.174
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 35 26 49 99 0 63
normalized size 1 1. 1.46 1.08 2.04 4.12 0. 2.62
time (sec) N/A 0.033 0.021 0.011 1.005 2.639 0. 1.144
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 67 36 108 541 0 104
normalized size 1 1. 2.48 1.33 4. 20.04 0. 3.85
time (sec) N/A 0.045 0.049 0.028 1.076 2.518 0. 1.145
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 37 44 53 246 0 46
normalized size 1 1. 1.37 1.63 1.96 9.11 0. 1.7
time (sec) N/A 0.046 0.07 0.027 1.036 2.416 0. 1.13
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 131 70 267 2469 0 198
normalized size 1 1. 2.43 1.3 4.94 45.72 0. 3.67
time (sec) N/A 0.071 0.047 0.036 1.027 2.712 0. 1.163
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 84 73 252 666 0 109
normalized size 1 1. 1.87 1.62 5.6 14.8 0. 2.42
time (sec) N/A 0.058 0.052 0.036 1.048 2.467 0. 1.159
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 153 109 285 880 0 328
normalized size 1 1. 1.34 0.96 2.5 7.72 0. 2.88
time (sec) N/A 0.138 1.621 0.04 1.052 2.705 0. 1.182
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 83 108 359 541 0 207
normalized size 1 1. 1.15 1.5 4.99 7.51 0. 2.88
time (sec) N/A 0.087 0.51 0.045 1.044 2.765 0. 1.179
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 126 90 216 641 0 204
normalized size 1 1. 1.73 1.23 2.96 8.78 0. 2.79
time (sec) N/A 0.107 0.934 0.036 1.042 2.901 0. 1.18
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 59 43 88 336 0 103
normalized size 1 1. 1.31 0.96 1.96 7.47 0. 2.29
time (sec) N/A 0.046 0.171 0.018 1.051 2.53 0. 1.202
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 108 72 266 3016 0 193
normalized size 1 1. 2.08 1.38 5.12 58. 0. 3.71
time (sec) N/A 0.077 0.553 0.036 1.055 2.678 0. 1.2
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 109 91 189 733 0 151
normalized size 1 1. 2.18 1.82 3.78 14.66 0. 3.02
time (sec) N/A 0.062 1.524 0.037 1.063 2.572 0. 1.222
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 144 126 478 7422 0 317
normalized size 1 1. 1.38 1.21 4.6 71.37 0. 3.05
time (sec) N/A 0.136 1.539 0.046 1.093 2.978 0. 1.224
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 151 138 385 1054 0 155
normalized size 1 1. 2.01 1.84 5.13 14.05 0. 2.07
time (sec) N/A 0.083 1.265 0.045 1.05 2.55 0. 1.169
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 182 182 651 182 570 1858 0 474
normalized size 1 1. 3.58 1. 3.13 10.21 0. 2.6
time (sec) N/A 0.232 2.424 0.046 1.079 2.647 0. 1.18
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 99 99 119 179 660 1029 0 277
normalized size 1 1. 1.2 1.81 6.67 10.39 0. 2.8
time (sec) N/A 0.111 1.21 0.043 1.077 2.655 0. 1.2
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 143 480 145 598 1508 0 385
normalized size 1 1.28 4.29 1.29 5.34 13.46 0. 3.44
time (sec) N/A 0.193 1.82 0.039 1.059 2.552 0. 1.19
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 93 58 127 702 0 138
normalized size 1 1. 1.45 0.91 1.98 10.97 0. 2.16
time (sec) N/A 0.059 0.247 0.019 1.059 2.522 0. 1.19
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 134 118 483 8645 0 313
normalized size 1 1. 1.61 1.42 5.82 104.16 0. 3.77
time (sec) N/A 0.1 1.22 0.04 1.1 3.092 0. 1.189
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 380 148 483 1580 0 338
normalized size 1 1. 5.43 2.11 6.9 22.57 0. 4.83
time (sec) N/A 0.073 2.736 0.043 1.057 2.549 0. 1.195
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 224 192 751 17022 0 470
normalized size 1 1. 1.56 1.33 5.22 118.21 0. 3.26
time (sec) N/A 0.178 3.734 0.05 1.07 3.63 0. 1.168
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 213 213 896 2480 0 481
normalized size 1 1. 2.05 2.05 8.62 23.85 0. 4.62
time (sec) N/A 0.105 2.303 0.051 1.096 2.558 0. 1.233
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 294 708 0 4338 0 312
normalized size 1 1. 2.51 6.05 0. 37.08 0. 2.67
time (sec) N/A 0.196 2.407 0.089 0. 2.969 0. 1.179
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 372 261 0 3343 0 0
normalized size 1 1. 5.24 3.68 0. 47.08 0. 0.
time (sec) N/A 0.105 2.146 0.061 0. 2.954 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 236 383 0 2132 0 186
normalized size 1 1. 3.15 5.11 0. 28.43 0. 2.48
time (sec) N/A 0.11 0.904 0.068 0. 2.856 0. 1.216
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 328 44 0 1643 0 0
normalized size 1 1. 6.98 0.94 0. 34.96 0. 0.
time (sec) N/A 0.048 1.045 0.023 0. 2.783 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 232 67 0 1461 0 0
normalized size 1 1. 4.22 1.22 0. 26.56 0. 0.
time (sec) N/A 0.082 0.849 0.051 0. 2.889 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 179 147 0 1589 0 107
normalized size 1 1. 3.38 2.77 0. 29.98 0. 2.02
time (sec) N/A 0.071 0.701 0.061 0. 2.809 0. 1.264
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 338 134 0 5080 0 0
normalized size 1 1. 3.89 1.54 0. 58.39 0. 0.
time (sec) N/A 0.118 1.954 0.058 0. 3.186 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 216 258 0 4602 0 173
normalized size 1 1. 2.88 3.44 0. 61.36 0. 2.31
time (sec) N/A 0.099 2.027 0.076 0. 3.003 0. 1.281
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 194 194 1330 1025 0 12945 0 454
normalized size 1 1. 6.86 5.28 0. 66.73 0. 2.34
time (sec) N/A 0.273 14.197 0.109 0. 3.926 0. 1.189
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 114 114 861 561 0 9646 0 0
normalized size 1 1. 7.55 4.92 0. 84.61 0. 0.
time (sec) N/A 0.144 4.678 0.082 0. 3.99 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 131 131 791 537 0 7262 0 325
normalized size 1 1. 6.04 4.1 0. 55.44 0. 2.48
time (sec) N/A 0.196 11.18 0.094 0. 2.886 0. 1.183
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 479 74 0 4732 0 0
normalized size 1 1. 5.7 0.88 0. 56.33 0. 0.
time (sec) N/A 0.065 2.702 0.031 0. 2.88 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 99 99 377 431 0 5986 0 0
normalized size 1 1. 3.81 4.35 0. 60.46 0. 0.
time (sec) N/A 0.13 1.121 0.07 0. 3.336 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 220 310 0 5806 0 328
normalized size 1 1. 2.39 3.37 0. 63.11 0. 3.57
time (sec) N/A 0.084 2.461 0.085 0. 2.47 0. 1.365
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 462 496 0 16629 0 0
normalized size 1 1. 3.14 3.37 0. 113.12 0. 0.
time (sec) N/A 0.206 2.154 0.083 0. 3.486 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 295 577 0 14893 0 358
normalized size 1 1. 2.4 4.69 0. 121.08 0. 2.91
time (sec) N/A 0.195 5.93 0.102 0. 2.992 0. 1.374
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 242 242 3080 1677 0 30538 0 714
normalized size 1 1. 12.73 6.93 0. 126.19 0. 2.95
time (sec) N/A 0.399 26.712 0.125 0. 3.981 0. 1.226
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 154 154 1217 1296 0 21811 0 0
normalized size 1 1. 7.9 8.42 0. 141.63 0. 0.
time (sec) N/A 0.218 10.78 0.098 0. 3.479 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 187 187 2544 1320 0 23448 0 517
normalized size 1 1. 13.6 7.06 0. 125.39 0. 2.76
time (sec) N/A 0.292 18.788 0.112 0. 4.003 0. 1.188
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 116 116 453 107 0 12176 0 0
normalized size 1 1. 3.91 0.92 0. 104.97 0. 0.
time (sec) N/A 0.084 9.168 0.035 0. 2.96 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 440 1476 0 20882 0 0
normalized size 1 1. 2.86 9.58 0. 135.6 0. 0.
time (sec) N/A 0.223 2.365 0.082 0. 4.276 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 126 126 981 819 0 17042 0 485
normalized size 1 1. 7.79 6.5 0. 135.25 0. 3.85
time (sec) N/A 0.1 6.802 0.102 0. 3.703 0. 1.417
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 213 213 524 1555 0 0 0 0
normalized size 1 1. 2.46 7.3 0. 0. 0. 0.
time (sec) N/A 0.342 3.737 0.101 0. 0. 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 165 165 985 1443 0 0 0 568
normalized size 1 1. 5.97 8.75 0. 0. 0. 3.44
time (sec) N/A 0.273 5.361 0.121 0. 0. 0. 1.523
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 45 66 131 163 0 157
normalized size 1 1. 0.74 1.08 2.15 2.67 0. 2.57
time (sec) N/A 0.046 0.092 0.04 1.136 2.066 0. 1.218
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 50 34 115 105 0 97
normalized size 1 1. 1.67 1.13 3.83 3.5 0. 3.23
time (sec) N/A 0.05 0.017 0.037 1.149 2.099 0. 1.167
Problem 51 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 31 31 33 37 51 74 60 89
normalized size 1 1. 1.06 1.19 1.65 2.39 1.94 2.87
time (sec) N/A 0.031 0.031 0.035 1.16 1.972 47.101 1.211
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 35 26 38 266 0 55
normalized size 1 1. 1.46 1.08 1.58 11.08 0. 2.29
time (sec) N/A 0.03 0.017 0.031 1.6 2.15 0. 1.194
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 48 45 109 882 0 115
normalized size 1 1. 1.2 1.12 2.72 22.05 0. 2.88
time (sec) N/A 0.027 0.021 0.02 1.723 2.094 0. 1.27
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 43 39 34 151 427 0 82
normalized size 1 1.43 1.3 1.13 5.03 14.23 0. 2.73
time (sec) N/A 0.04 0.012 0.019 1.043 1.924 0. 1.361
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 60 83 248 2931 0 213
normalized size 1 1. 0.86 1.19 3.54 41.87 0. 3.04
time (sec) N/A 0.05 0.104 0.021 1.685 2.155 0. 1.201
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 65 71 56 405 938 0 115
normalized size 1 1.3 1.42 1.12 8.1 18.76 0. 2.3
time (sec) N/A 0.046 0.013 0.02 1.058 2.063 0. 1.145
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 58 79 142 193 0 204
normalized size 1 1. 0.71 0.96 1.73 2.35 0. 2.49
time (sec) N/A 0.093 0.129 0.041 1.042 2.204 0. 1.158
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 72 66 142 1057 0 149
normalized size 1 1. 1.47 1.35 2.9 21.57 0. 3.04
time (sec) N/A 0.059 0.026 0.041 1.739 2.211 0. 1.202
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 52 51 85 196 0 180
normalized size 1 1. 1.11 1.09 1.81 4.17 0. 3.83
time (sec) N/A 0.078 0.142 0.036 1.137 2.149 0. 1.163
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 80 63 136 1678 0 157
normalized size 1 1. 1.43 1.12 2.43 29.96 0. 2.8
time (sec) N/A 0.068 0.04 0.041 1.6 2.23 0. 1.175
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 71 106 271 3445 0 232
normalized size 1 1. 0.79 1.18 3.01 38.28 0. 2.58
time (sec) N/A 0.084 0.131 0.027 1.735 2.218 0. 1.155
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 93 70 437 1054 0 211
normalized size 1 1. 1.75 1.32 8.25 19.89 0. 3.98
time (sec) N/A 0.066 0.03 0.023 1.12 2.074 0. 1.166
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 128 128 104 169 470 7609 0 397
normalized size 1 1. 0.81 1.32 3.67 59.45 0. 3.1
time (sec) N/A 0.149 0.238 0.026 1.7 2.491 0. 1.136
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 144 102 906 1828 0 266
normalized size 1 1. 1.8 1.27 11.32 22.85 0. 3.32
time (sec) N/A 0.076 0.03 0.026 1.154 2.055 0. 1.159
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 70 93 176 370 0 257
normalized size 1 1. 0.83 1.11 2.1 4.4 0. 3.06
time (sec) N/A 0.111 0.409 0.038 1.106 2.087 0. 1.192
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 81 81 483 103 242 3555 0 240
normalized size 1 1. 5.96 1.27 2.99 43.89 0. 2.96
time (sec) N/A 0.093 6.836 0.045 1.701 2.289 0. 1.192
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 64 77 216 670 0 215
normalized size 1 1. 0.89 1.07 3. 9.31 0. 2.99
time (sec) N/A 0.092 0.479 0.044 1.138 2.301 0. 1.19
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 93 93 575 125 298 4986 0 274
normalized size 1 1. 6.18 1.34 3.2 53.61 0. 2.95
time (sec) N/A 0.103 7.902 0.048 1.687 2.675 0. 1.183
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 147 147 1430 193 493 8805 0 420
normalized size 1 1. 9.73 1.31 3.35 59.9 0. 2.86
time (sec) N/A 0.143 9.735 0.03 1.716 2.49 0. 1.165
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 319 116 938 2103 0 408
normalized size 1 1. 4.31 1.57 12.68 28.42 0. 5.51
time (sec) N/A 0.08 1.415 0.026 1.233 2.055 0. 1.168
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 196 196 297 280 751 16578 0 656
normalized size 1 1. 1.52 1.43 3.83 84.58 0. 3.35
time (sec) N/A 0.232 9.324 0.03 1.704 2.733 0. 1.17
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 348 158 1681 3222 0 486
normalized size 1 1. 3.22 1.46 15.56 29.83 0. 4.5
time (sec) N/A 0.094 1.709 0.029 1.126 2.391 0. 1.178
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 95 493 0 4313 0 296
normalized size 1 1. 0.81 4.21 0. 36.86 0. 2.53
time (sec) N/A 0.189 0.522 0.084 0. 2.752 0. 1.185
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 79 256 0 3991 0 0
normalized size 1 1. 1.04 3.37 0. 52.51 0. 0.
time (sec) N/A 0.09 0.287 0.083 0. 2.792 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 67 278 0 2188 0 178
normalized size 1 1. 0.89 3.71 0. 29.17 0. 2.37
time (sec) N/A 0.116 0.228 0.079 0. 2.423 0. 1.186
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 52 128 0 1891 0 0
normalized size 1 1. 1. 2.46 0. 36.37 0. 0.
time (sec) N/A 0.061 0.121 0.069 0. 2.375 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 36 82 0 1291 0 0
normalized size 1 1. 1. 2.28 0. 35.86 0. 0.
time (sec) N/A 0.042 0.065 0.047 0. 2.313 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 36 107 0 1065 0 63
normalized size 1 1. 1. 2.97 0. 29.58 0. 1.75
time (sec) N/A 0.061 0.079 0.043 0. 2.187 0. 1.151
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 194 107 0 1431 0 0
normalized size 1 1. 3.53 1.95 0. 26.02 0. 0.
time (sec) N/A 0.069 0.682 0.048 0. 2.302 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 182 141 0 1661 0 100
normalized size 1 1. 3.5 2.71 0. 31.94 0. 1.92
time (sec) N/A 0.07 0.68 0.045 0. 2.271 0. 1.167
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 213 189 0 3997 0 0
normalized size 1 1. 2.48 2.2 0. 46.48 0. 0.
time (sec) N/A 0.103 1.865 0.047 0. 2.524 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 214 313 0 4709 0 159
normalized size 1 1. 2.78 4.06 0. 61.16 0. 2.06
time (sec) N/A 0.089 2.233 0.051 0. 2.382 0. 1.251
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 113 517 0 13824 0 0
normalized size 1 1. 0.9 4.14 0. 110.59 0. 0.
time (sec) N/A 0.154 0.863 0.101 0. 2.905 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 103 551 0 8946 0 446
normalized size 1 1. 0.72 3.83 0. 62.12 0. 3.1
time (sec) N/A 0.235 1.318 0.102 0. 2.783 0. 1.158
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 234 385 0 7525 0 0
normalized size 1 1. 2.34 3.85 0. 75.25 0. 0.
time (sec) N/A 0.132 1.832 0.091 0. 2.621 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 124 332 0 4533 0 0
normalized size 1 1. 1.51 4.05 0. 55.28 0. 0.
time (sec) N/A 0.066 0.302 0.068 0. 2.395 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 187 260 0 3563 0 180
normalized size 1 1. 2.53 3.51 0. 48.15 0. 2.43
time (sec) N/A 0.074 1.001 0.059 0. 2.345 0. 1.267
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 108 241 0 3996 0 0
normalized size 1 1. 1.48 3.3 0. 54.74 0. 0.
time (sec) N/A 0.071 0.217 0.059 0. 2.425 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 88 380 0 3765 0 189
normalized size 1 1. 1.06 4.58 0. 45.36 0. 2.28
time (sec) N/A 0.09 0.207 0.058 0. 2.322 0. 1.174
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 282 361 0 5195 0 0
normalized size 1 1. 2.79 3.57 0. 51.44 0. 0.
time (sec) N/A 0.117 2.47 0.064 0. 2.675 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 229 413 0 6961 0 306
normalized size 1 1. 2.27 4.09 0. 68.92 0. 3.03
time (sec) N/A 0.142 3.79 0.063 0. 2.498 0. 1.274
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 489 448 0 15336 0 0
normalized size 1 1. 3.2 2.93 0. 100.24 0. 0.
time (sec) N/A 0.2 5.048 0.067 0. 3.426 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 204 204 156 1435 0 27738 0 552
normalized size 1 1. 0.76 7.03 0. 135.97 0. 2.71
time (sec) N/A 0.377 4.004 0.128 0. 3.766 0. 1.213
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 292 1238 0 23050 0 0
normalized size 1 1. 1.9 8.04 0. 149.68 0. 0.
time (sec) N/A 0.185 3.652 0.118 0. 3.495 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 214 1174 0 15863 0 0
normalized size 1 1. 1.51 8.27 0. 111.71 0. 0.
time (sec) N/A 0.137 2.857 0.082 0. 3.137 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 258 612 0 11784 0 386
normalized size 1 1. 2.39 5.67 0. 109.11 0. 3.57
time (sec) N/A 0.09 2.078 0.073 0. 2.794 0. 1.353
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 159 1038 0 14071 0 0
normalized size 1 1. 1.29 8.44 0. 114.4 0. 0.
time (sec) N/A 0.108 0.812 0.079 0. 2.931 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 250 1084 0 12354 0 374
normalized size 1 1. 2. 8.67 0. 98.83 0. 2.99
time (sec) N/A 0.107 3.421 0.092 0. 2.874 0. 1.355
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 125 592 0 12078 0 0
normalized size 1 1. 1.18 5.58 0. 113.94 0. 0.
time (sec) N/A 0.092 0.282 0.077 0. 2.767 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 125 1236 0 13508 0 413
normalized size 1 1. 0.87 8.58 0. 93.81 0. 2.87
time (sec) N/A 0.142 0.961 0.078 0. 2.868 0. 1.341
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 247 1202 0 18826 0 0
normalized size 1 1. 1.61 7.86 0. 123.05 0. 0.
time (sec) N/A 0.205 4.601 0.084 0. 3.8 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 57 98 124 876 0 142
normalized size 1 1. 1.19 2.04 2.58 18.25 0. 2.96
time (sec) N/A 0.064 0.024 0.034 1.194 2.077 0. 1.317
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 45 72 105 2871 80 157
normalized size 1 1. 0.92 1.47 2.14 58.59 1.63 3.2
time (sec) N/A 0.056 0.023 0.035 1.708 2.395 2.732 1.251
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 41 60 57 396 0 93
normalized size 1 1. 1.28 1.88 1.78 12.38 0. 2.91
time (sec) N/A 0.057 0.016 0.028 1.172 2.23 0. 1.249
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 29 29 36 973 42 108
normalized size 1 1. 1. 1. 1.24 33.55 1.45 3.72
time (sec) N/A 0.028 0.022 0.013 1.15 2.085 0.726 1.195
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 16 31 88 0 31
normalized size 1 1. 1. 1.07 2.07 5.87 0. 2.07
time (sec) N/A 0.013 0.003 0.007 1.153 1.998 0. 1.146
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 44 26 88 178 0 76
normalized size 1 1. 1.57 0.93 3.14 6.36 0. 2.71
time (sec) N/A 0.051 0.038 0.033 1.733 2.097 0. 1.177
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 41 30 63 103 0 36
normalized size 1 1. 2.28 1.67 3.5 5.72 0. 2.
time (sec) N/A 0.059 0.031 0.032 1.159 2.025 0. 1.192
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 52 50 146 990 0 109
normalized size 1 1. 1.68 1.61 4.71 31.94 0. 3.52
time (sec) N/A 0.057 0.168 0.04 1.184 2.149 0. 1.227
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 49 70 230 370 0 90
normalized size 1 1. 1.44 2.06 6.76 10.88 0. 2.65
time (sec) N/A 0.063 0.023 0.04 1.155 2.044 0. 1.242
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 62 86 339 2898 0 158
normalized size 1 1. 1.22 1.69 6.65 56.82 0. 3.1
time (sec) N/A 0.078 0.262 0.041 1.208 2.242 0. 1.28
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 395 181 876 1868 0 371
normalized size 1 1. 5.13 2.35 11.38 24.26 0. 4.82
time (sec) N/A 0.105 1.166 0.046 1.221 2.085 0. 1.322
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 107 150 450 6669 129 325
normalized size 1 1. 1.39 1.95 5.84 86.61 1.68 4.22
time (sec) N/A 0.095 0.307 0.043 2.359 2.435 8.809 1.283
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 281 115 439 1099 0 261
normalized size 1 1. 4.76 1.95 7.44 18.63 0. 4.42
time (sec) N/A 0.098 0.9 0.037 1.188 2.076 0. 1.239
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 81 48 74 3012 63 215
normalized size 1 1. 1.69 1. 1.54 62.75 1.31 4.48
time (sec) N/A 0.05 0.132 0.011 1.116 2.184 2.919 1.162
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 106 47 162 447 0 107
normalized size 1 1. 2.65 1.18 4.05 11.18 0. 2.68
time (sec) N/A 0.034 0.42 0.022 1.111 2.007 0. 1.139
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 84 60 217 1709 0 231
normalized size 1 1. 1.58 1.13 4.09 32.25 0. 4.36
time (sec) N/A 0.08 0.243 0.041 1.862 2.213 0. 1.184
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 82 64 96 265 0 88
normalized size 1 1. 2.28 1.78 2.67 7.36 0. 2.44
time (sec) N/A 0.085 0.7 0.033 1.202 2.11 0. 1.261
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 82 86 278 1553 0 217
normalized size 1 1. 1.49 1.56 5.05 28.24 0. 3.95
time (sec) N/A 0.089 0.209 0.044 1.79 2.279 0. 1.318
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 160 96 362 478 0 131
normalized size 1 1. 3.48 2.09 7.87 10.39 0. 2.85
time (sec) N/A 0.092 0.818 0.04 1.161 2.067 0. 1.324
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 77 142 381 3093 0 198
normalized size 1 1. 1.48 2.73 7.33 59.48 0. 3.81
time (sec) N/A 0.094 0.232 0.046 1.152 2.232 0. 1.436
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 256 163 828 1050 0 225
normalized size 1 1. 4. 2.55 12.94 16.41 0. 3.52
time (sec) N/A 0.097 1.101 0.049 1.193 2.165 0. 1.458
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 107 228 940 6593 0 292
normalized size 1 1. 1.24 2.65 10.93 76.66 0. 3.4
time (sec) N/A 0.125 0.508 0.053 1.218 2.467 0. 1.653
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 301 274 1962 3414 0 637
normalized size 1 1. 2.74 2.49 17.84 31.04 0. 5.79
time (sec) N/A 0.118 6.144 0.049 1.182 2.219 0. 1.586
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 128 253 880 12142 178 518
normalized size 1 1. 1.24 2.46 8.54 117.88 1.73 5.03
time (sec) N/A 0.098 0.886 0.051 1.568 2.699 22.626 1.355
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 479 180 1064 2249 0 481
normalized size 1 1. 5.21 1.96 11.57 24.45 0. 5.23
time (sec) N/A 0.11 1.803 0.042 1.24 2.181 0. 1.309
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 100 67 115 6511 87 362
normalized size 1 1. 1.41 0.94 1.62 91.7 1.23 5.1
time (sec) N/A 0.058 0.292 0.013 1.127 2.754 8.921 1.238
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 268 83 448 1173 0 246
normalized size 1 1. 3.67 1.14 6.14 16.07 0. 3.37
time (sec) N/A 0.047 0.914 0.026 1.034 2.497 0. 1.163
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 114 111 405 5819 0 439
normalized size 1 1. 1.36 1.32 4.82 69.27 0. 5.23
time (sec) N/A 0.107 0.62 0.048 1.627 2.722 0. 1.209
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 126 111 232 863 0 178
normalized size 1 1. 2.07 1.82 3.8 14.15 0. 2.92
time (sec) N/A 0.103 1.76 0.043 1.172 2.456 0. 1.267
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 110 145 424 4127 0 394
normalized size 1 1. 1.36 1.79 5.23 50.95 0. 4.86
time (sec) N/A 0.116 1.226 0.053 1.787 2.722 0. 1.402
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 343 149 494 837 0 209
normalized size 1 1. 5.72 2.48 8.23 13.95 0. 3.48
time (sec) N/A 0.101 1.707 0.043 1.228 2.374 0. 1.423
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 101 194 570 4574 0 335
normalized size 1 1. 1.25 2.4 7.04 56.47 0. 4.14
time (sec) N/A 0.121 0.858 0.047 1.701 2.749 0. 1.581
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 303 199 1115 1249 0 284
normalized size 1 1. 4.39 2.88 16.16 18.1 0. 4.12
time (sec) N/A 0.109 1.098 0.046 1.254 2.371 0. 1.607
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 98 310 981 6665 0 323
normalized size 1 1. 1.27 4.03 12.74 86.56 0. 4.19
time (sec) N/A 0.121 0.773 0.05 1.269 2.478 0. 1.734
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 455 129 949 2410 0 451
normalized size 1 1. 4.1 1.16 8.55 21.71 0. 4.06
time (sec) N/A 0.07 1.599 0.032 1.461 2.17 0. 1.159
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 724 185 1724 4396 0 725
normalized size 1 1. 4.44 1.13 10.58 26.97 0. 4.45
time (sec) N/A 0.095 6.542 0.039 1.212 2.155 0. 1.189
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 98 331 177 1895 0 240
normalized size 1 1. 1.4 4.73 2.53 27.07 0. 3.43
time (sec) N/A 0.112 0.29 0.062 1.767 2.665 0. 2.243
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 196 386 0 1854 0 147
normalized size 1 1. 3.32 6.54 0. 31.42 0. 2.49
time (sec) N/A 0.178 1.107 0.067 0. 2.316 0. 1.915
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 41 196 104 294 0 107
normalized size 1 1. 0.91 4.36 2.31 6.53 0. 2.38
time (sec) N/A 0.088 0.106 0.054 1.752 2.33 0. 1.791
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 174 257 0 1087 0 104
normalized size 1 1. 3.78 5.59 0. 23.63 0. 2.26
time (sec) N/A 0.14 0.299 0.059 0. 2.187 0. 1.49
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 26 38 69 198 124 76
normalized size 1 1. 1.13 1.65 3. 8.61 5.39 3.3
time (sec) N/A 0.035 0.175 0.017 1.133 2.189 9.338 1.398
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 172 152 0 1122 0 88
normalized size 1 1. 3.74 3.3 0. 24.39 0. 1.91
time (sec) N/A 0.046 0.247 0.052 0. 2.308 0. 1.171
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 42 133 135 305 0 131
normalized size 1 1. 0.91 2.89 2.93 6.63 0. 2.85
time (sec) N/A 0.087 0.089 0.059 1.043 2.79 0. 1.47
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 193 189 0 1980 0 120
normalized size 1 1. 3.11 3.05 0. 31.94 0. 1.94
time (sec) N/A 0.18 1.112 0.072 0. 2.662 0. 1.613
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 100 199 252 2144 0 288
normalized size 1 1. 1.37 2.73 3.45 29.37 0. 3.95
time (sec) N/A 0.122 0.222 0.07 1.21 3.021 0. 2.076
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 380 301 0 6730 0 217
normalized size 1 1. 4.37 3.46 0. 77.36 0. 2.49
time (sec) N/A 0.286 3.269 0.085 0. 2.621 0. 2.265
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 109 351 208 2044 0 281
normalized size 1 1. 1.43 4.62 2.74 26.89 0. 3.7
time (sec) N/A 0.117 0.444 0.083 1.634 2.703 0. 2.997
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 228 667 0 3748 0 252
normalized size 1 1. 2.51 7.33 0. 41.19 0. 2.77
time (sec) N/A 0.194 2.108 0.086 0. 2.389 0. 2.521
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 81 186 146 1260 0 163
normalized size 1 1. 1.59 3.65 2.86 24.71 0. 3.2
time (sec) N/A 0.09 0.711 0.076 1.23 2.205 0. 2.136
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 85 85 326 417 0 4431 0 198
normalized size 1 1. 3.84 4.91 0. 52.13 0. 2.33
time (sec) N/A 0.169 4.489 0.081 0. 2.506 0. 1.923
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 79 60 143 1243 0 163
normalized size 1 1. 1.61 1.22 2.92 25.37 0. 3.33
time (sec) N/A 0.062 0.572 0.025 1.269 2.284 0. 1.591
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 93 93 221 423 0 4199 0 224
normalized size 1 1. 2.38 4.55 0. 45.15 0. 2.41
time (sec) N/A 0.096 2.029 0.073 0. 2.539 0. 1.143
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 115 292 282 2457 0 332
normalized size 1 1. 1.39 3.52 3.4 29.6 0. 4.
time (sec) N/A 0.129 0.288 0.084 1.374 3.305 0. 1.694
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 121 121 268 481 0 8483 0 381
normalized size 1 1. 2.21 3.98 0. 70.11 0. 3.15
time (sec) N/A 0.284 2.847 0.099 0. 2.823 0. 2.168
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 130 367 518 8284 0 517
normalized size 1 1. 1.18 3.34 4.71 75.31 0. 4.7
time (sec) N/A 0.175 1.295 0.096 1.268 4.779 0. 2.692
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 161 161 350 634 0 22652 0 408
normalized size 1 1. 2.17 3.94 0. 140.7 0. 2.53
time (sec) N/A 0.411 5.227 0.109 0. 3.605 0. 3.034
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 148 148 515 1713 0 12740 0 501
normalized size 1 1. 3.48 11.57 0. 86.08 0. 3.39
time (sec) N/A 0.32 6.055 0.106 0. 2.895 0. 4.319
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 136 579 278 4238 0 252
normalized size 1 1. 1.77 7.52 3.61 55.04 0. 3.27
time (sec) N/A 0.12 2.074 0.093 1.221 2.398 0. 3.532
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 139 139 1317 1306 0 14841 0 398
normalized size 1 1. 9.47 9.4 0. 106.77 0. 2.86
time (sec) N/A 0.294 14.278 0.104 0. 3.121 0. 3.189
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 131 672 282 4297 0 236
normalized size 1 1. 1.62 8.3 3.48 53.05 0. 2.91
time (sec) N/A 0.126 1.39 0.093 1.299 2.499 0. 2.753
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 139 139 1317 1173 0 16496 0 417
normalized size 1 1. 9.47 8.44 0. 118.68 0. 3.
time (sec) N/A 0.246 14.552 0.104 0. 3.311 0. 2.405
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 129 82 261 4103 0 252
normalized size 1 1. 1.77 1.12 3.58 56.21 0. 3.45
time (sec) N/A 0.082 1.896 0.027 1.214 2.466 0. 1.818
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 146 146 301 1292 0 15505 0 450
normalized size 1 1. 2.06 8.85 0. 106.2 0. 3.08
time (sec) N/A 0.181 6.113 0.093 0. 3.329 0. 1.177
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 155 1046 566 9400 0 641
normalized size 1 1. 1.19 8.05 4.35 72.31 0. 4.93
time (sec) N/A 0.186 1.073 0.101 1.375 5.792 0. 1.932
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 182 182 2083 1442 0 27173 0 543
normalized size 1 1. 11.45 7.92 0. 149.3 0. 2.98
time (sec) N/A 0.403 7.031 0.12 0. 3.812 0. 2.58
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 152 152 172 1128 934 23458 0 1034
normalized size 1 1. 1.13 7.42 6.14 154.33 0. 6.8
time (sec) N/A 0.243 1.937 0.123 1.468 9.424 0. 3.535
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F(-1) F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 232 232 3334 1610 0 0 0 651
normalized size 1 1. 14.37 6.94 0. 0. 0. 2.81
time (sec) N/A 0.514 7.528 0.134 0. 0. 0. 3.926
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F(-1) F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 207 207 1405 2892 0 0 0 811
normalized size 1 1. 6.79 13.97 0. 0. 0. 3.92
time (sec) N/A 0.346 6.859 0.119 0. 0. 0. 1.181
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 25 120 45 620 0 97
normalized size 1 1. 0.86 4.14 1.55 21.38 0. 3.34
time (sec) N/A 0.031 0.023 0.108 1.65 1.953 0. 1.127
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 79 18 55 0 35
normalized size 1 1. 1. 5.64 1.29 3.93 0. 2.5
time (sec) N/A 0.022 0.006 0.116 1.676 1.876 0. 1.126
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 79 30 55 0 42
normalized size 1 1. 1. 5.64 2.14 3.93 0. 3.
time (sec) N/A 0.024 0.011 0.099 1.682 1.858 0. 1.137
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 27 123 45 4 0 112
normalized size 1 1. 0.79 3.62 1.32 0.12 0. 3.29
time (sec) N/A 0.029 0.015 0.102 1.66 2.054 0. 1.137
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 81 18 4 0 42
normalized size 1 1. 1. 5.06 1.12 0.25 0. 2.62
time (sec) N/A 0.02 0.006 0.122 1.708 1.976 0. 1.123
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 81 30 4 0 50
normalized size 1 1. 1. 5.06 1.88 0.25 0. 3.12
time (sec) N/A 0.022 0.009 0.101 1.704 1.97 0. 1.14
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 114 0 0 12714 0 0
normalized size 1 1. 1.37 0. 0. 153.18 0. 0.
time (sec) N/A 0.147 0.708 0.156 0. 5.889 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 192 0 0 24571 0 0
normalized size 1 1. 1.54 0. 0. 196.57 0. 0.
time (sec) N/A 0.313 0.44 0.125 0. 5.808 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 90 0 0 7024 0 0
normalized size 1 1. 1.53 0. 0. 119.05 0. 0.
time (sec) N/A 0.107 0.373 0.112 0. 3.266 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 150 0 0 12953 0 0
normalized size 1 1. 1.72 0. 0. 148.89 0. 0.
time (sec) N/A 0.218 0.265 0.109 0. 3.548 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 90 43 0 4658 0 0
normalized size 1 1. 2.25 1.08 0. 116.45 0. 0.
time (sec) N/A 0.063 0.257 0.034 0. 2.288 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 134 0 0 8756 0 0
normalized size 1 1. 2.27 0. 0. 148.41 0. 0.
time (sec) N/A 0.045 0.679 0.102 0. 2.77 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 111 0 0 10376 0 0
normalized size 1 1. 1.98 0. 0. 185.29 0. 0.
time (sec) N/A 0.108 0.121 0.116 0. 2.914 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 75 0 0 3892 0 0
normalized size 1 1. 1.56 0. 0. 81.08 0. 0.
time (sec) N/A 0.178 0.525 0.119 0. 2.529 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 156 0 0 15598 0 0
normalized size 1 1. 1.88 0. 0. 187.93 0. 0.
time (sec) N/A 0.143 0.514 0.122 0. 4.281 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 149 0 0 7036 0 0
normalized size 1 1. 1.77 0. 0. 83.76 0. 0.
time (sec) N/A 0.248 0.587 0.126 0. 3.424 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 191 0 0 0 0 0
normalized size 1 1. 1.53 0. 0. 0. 0. 0.
time (sec) N/A 0.221 0.91 0.128 0. 0. 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 129 0 0 12290 0 0
normalized size 1 1. 1.7 0. 0. 161.71 0. 0.
time (sec) N/A 0.128 0.971 0.095 0. 6.048 0. 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 197 0 0 23956 0 0
normalized size 1 1. 1.58 0. 0. 191.65 0. 0.
time (sec) N/A 0.361 0.808 0.09 0. 5.828 0. 0.
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 65 56 0 6842 0 0
normalized size 1 1. 1.14 0.98 0. 120.04 0. 0.
time (sec) N/A 0.084 0.114 0.014 0. 3.284 0. 0.
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 152 0 0 12542 0 0
normalized size 1 1. 1.73 0. 0. 142.52 0. 0.
time (sec) N/A 0.091 0.26 0.082 0. 3.591 0. 0.
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 159 0 0 12166 0 0
normalized size 1 1. 2.27 0. 0. 173.8 0. 0.
time (sec) N/A 0.132 0.491 0.095 0. 3.584 0. 0.
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 144 0 0 10029 0 0
normalized size 1 1. 1.78 0. 0. 123.81 0. 0.
time (sec) N/A 0.232 0.327 0.102 0. 3.452 0. 0.
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 170 170 280 0 0 0 0 0
normalized size 1 1. 1.65 0. 0. 0. 0. 0.
time (sec) N/A 0.194 9.017 0.193 0. 0. 0. 0.
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 109 0 0 7483 0 0
normalized size 1 1. 1.65 0. 0. 113.38 0. 0.
time (sec) N/A 0.131 0.491 0.125 0. 3.496 0. 0.
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 169 0 0 13245 0 0
normalized size 1 1. 1.88 0. 0. 147.17 0. 0.
time (sec) N/A 0.228 0.495 0.125 0. 3.841 0. 0.
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 105 0 0 4733 0 0
normalized size 1 1. 2.5 0. 0. 112.69 0. 0.
time (sec) N/A 0.093 0.212 0.121 0. 2.62 0. 0.
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 107 0 0 8377 0 0
normalized size 1 1. 1.78 0. 0. 139.62 0. 0.
time (sec) N/A 0.193 0.168 0.115 0. 3.041 0. 0.
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 70 30 0 4004 0 0
normalized size 1 1. 2.8 1.2 0. 160.16 0. 0.
time (sec) N/A 0.053 0.081 0.035 0. 2.179 0. 0.
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 62 0 0 3023 0 0
normalized size 1 1. 2.14 0. 0. 104.24 0. 0.
time (sec) N/A 0.025 0.04 0.149 0. 2.165 0. 0.
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 124 0 0 10525 0 0
normalized size 1 1. 2.21 0. 0. 187.95 0. 0.
time (sec) N/A 0.103 0.259 0.12 0. 3.028 0. 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 94 0 0 3951 0 0
normalized size 1 1. 1.77 0. 0. 74.55 0. 0.
time (sec) N/A 0.188 0.114 0.124 0. 2.484 0. 0.
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 159 0 0 17920 0 0
normalized size 1 1. 1.77 0. 0. 199.11 0. 0.
time (sec) N/A 0.161 0.826 0.13 0. 4.514 0. 0.
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 129 0 0 8805 0 0
normalized size 1 1. 1.9 0. 0. 129.49 0. 0.
time (sec) N/A 0.147 0.577 0.104 0. 4.185 0. 0.
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 169 0 0 14456 0 0
normalized size 1 1. 1.97 0. 0. 168.09 0. 0.
time (sec) N/A 0.252 0.381 0.099 0. 4.313 0. 0.
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 103 0 0 6137 0 0
normalized size 1 1. 2.1 0. 0. 125.24 0. 0.
time (sec) N/A 0.115 0.229 0.098 0. 2.748 0. 0.
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 128 0 0 5075 0 0
normalized size 1 1. 2.51 0. 0. 99.51 0. 0.
time (sec) N/A 0.218 0.713 0.095 0. 2.648 0. 0.
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 98 46 0 5840 44 0
normalized size 1 1. 2.28 1.07 0. 135.81 1.02 0.
time (sec) N/A 0.073 0.396 0.015 0. 2.617 6.611 0.
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 107 0 0 5858 0 0
normalized size 1 1. 1.88 0. 0. 102.77 0. 0.
time (sec) N/A 0.045 0.81 0.085 0. 2.815 0. 0.
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 155 0 0 18668 0 0
normalized size 1 1. 1.96 0. 0. 236.3 0. 0.
time (sec) N/A 0.14 0.651 0.101 0. 4.71 0. 0.
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 120 0 0 10016 0 0
normalized size 1 1. 1.36 0. 0. 113.82 0. 0.
time (sec) N/A 0.274 0.42 0.103 0. 4.428 0. 0.
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 178 0 0 0 0 0
normalized size 1 1. 1.51 0. 0. 0. 0. 0.
time (sec) N/A 0.339 0.692 0.106 0. 0. 0. 0.
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 126 0 0 12878 0 0
normalized size 1 1. 1.66 0. 0. 169.45 0. 0.
time (sec) N/A 0.158 0.521 0.108 0. 4.855 0. 0.
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 290 0 0 9694 0 0
normalized size 1 1. 3.22 0. 0. 107.71 0. 0.
time (sec) N/A 0.262 2.016 0.102 0. 4.469 0. 0.
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 124 0 0 12041 0 0
normalized size 1 1. 1.82 0. 0. 177.07 0. 0.
time (sec) N/A 0.124 0.915 0.098 0. 4.456 0. 0.
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 290 0 0 12787 0 0
normalized size 1 1. 3.3 0. 0. 145.31 0. 0.
time (sec) N/A 0.248 1.158 0.093 0. 4.722 0. 0.
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 112 61 0 10838 65 0
normalized size 1 1. 1.81 0.98 0. 174.81 1.05 0.
time (sec) N/A 0.087 0.773 0.014 0. 4.478 52.206 0.
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 130 0 0 15431 0 0
normalized size 1 1. 1.37 0. 0. 162.43 0. 0.
time (sec) N/A 0.09 0.423 0.086 0. 5.245 0. 0.
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 242 0 0 0 0 0
normalized size 1 1. 2.22 0. 0. 0. 0. 0.
time (sec) N/A 0.2 1.042 0.1 0. 0. 0. 0.
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 133 133 155 0 0 26619 0 0
normalized size 1 1. 1.17 0. 0. 200.14 0. 0.
time (sec) N/A 0.376 0.782 0.103 0. 10.539 0. 0.
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 183 183 330 0 0 0 0 0
normalized size 1 1. 1.8 0. 0. 0. 0. 0.
time (sec) N/A 0.191 7.458 0.152 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 [190] had the largest ratio of [ 0.5833 ]

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 5 5 1. 21 0.238
2 A 3 2 1. 21 0.095
3 A 4 4 1. 21 0.19
4 A 3 2 1. 19 0.105
5 A 3 3 1. 19 0.158
6 A 3 2 1. 21 0.095
7 A 4 4 1. 21 0.19
8 A 3 2 1. 21 0.095
9 A 6 5 1. 23 0.217
10 A 3 2 1. 23 0.087
11 A 5 5 1. 23 0.217
12 A 3 2 1. 21 0.095
13 A 4 3 1. 21 0.143
14 A 3 2 1. 23 0.087
15 A 5 5 1. 23 0.217
16 A 3 2 1. 23 0.087
17 A 6 5 1. 23 0.217
18 A 3 2 1. 23 0.087
19 A 6 5 1.28 23 0.217
20 A 3 2 1. 21 0.095
21 A 4 3 1. 21 0.143
22 A 3 2 1. 23 0.087
23 A 5 4 1. 23 0.174
24 A 3 2 1. 23 0.087
25 A 6 6 1. 23 0.261
26 A 4 4 1. 23 0.174
27 A 5 5 1. 23 0.217
28 A 3 3 1. 21 0.143
29 A 4 4 1. 21 0.19
30 A 3 3 1. 23 0.13
31 A 5 5 1. 23 0.217
32 A 4 4 1. 23 0.174
33 A 7 6 1. 23 0.261
34 A 5 4 1. 23 0.174
35 A 6 6 1. 23 0.261
36 A 4 4 1. 21 0.19
37 A 5 5 1. 21 0.238
38 A 4 4 1. 23 0.174
39 A 6 6 1. 23 0.261
40 A 5 4 1. 23 0.174
41 A 8 6 1. 23 0.261
42 A 6 5 1. 23 0.217
43 A 7 6 1. 23 0.261
44 A 5 4 1. 21 0.19
45 A 6 6 1. 21 0.286
46 A 5 4 1. 23 0.174
47 A 7 7 1. 23 0.304
48 A 6 5 1. 23 0.217
49 A 3 3 1. 21 0.143
50 A 3 2 1. 21 0.095
51 A 2 2 1. 21 0.095
52 A 2 2 1. 19 0.105
53 A 2 2 1. 19 0.105
54 A 3 3 1.43 21 0.143
55 A 3 3 1. 21 0.143
56 A 3 2 1.3 21 0.095
57 A 4 4 1. 23 0.174
58 A 4 3 1. 23 0.13
59 A 5 4 1. 23 0.174
60 A 5 4 1. 21 0.19
61 A 4 4 1. 21 0.19
62 A 3 2 1. 23 0.087
63 A 5 5 1. 23 0.217
64 A 3 2 1. 23 0.087
65 A 6 5 1. 23 0.217
66 A 5 4 1. 23 0.174
67 A 5 4 1. 23 0.174
68 A 6 5 1. 21 0.238
69 A 5 5 1. 21 0.238
70 A 3 2 1. 23 0.087
71 A 6 6 1. 23 0.261
72 A 3 2 1. 23 0.087
73 A 6 6 1. 23 0.261
74 A 4 3 1. 23 0.13
75 A 5 5 1. 23 0.217
76 A 3 3 1. 21 0.143
77 A 2 2 1. 21 0.095
78 A 2 2 1. 23 0.087
79 A 4 4 1. 23 0.174
80 A 3 3 1. 23 0.13
81 A 5 5 1. 23 0.217
82 A 4 3 1. 23 0.13
83 A 5 4 1. 23 0.174
84 A 6 6 1. 23 0.261
85 A 5 4 1. 21 0.19
86 A 3 3 1. 21 0.143
87 A 3 3 1. 23 0.13
88 A 3 3 1. 23 0.13
89 A 3 3 1. 23 0.13
90 A 5 5 1. 23 0.217
91 A 5 4 1. 23 0.174
92 A 6 6 1. 23 0.261
93 A 7 6 1. 23 0.261
94 A 6 5 1. 21 0.238
95 A 4 4 1. 21 0.19
96 A 4 3 1. 23 0.13
97 A 4 4 1. 23 0.174
98 A 4 4 1. 23 0.174
99 A 4 3 1. 23 0.13
100 A 4 4 1. 23 0.174
101 A 6 6 1. 23 0.261
102 A 4 3 1. 21 0.143
103 A 4 3 1. 21 0.143
104 A 4 3 1. 21 0.143
105 A 3 2 1. 19 0.105
106 A 3 2 1. 12 0.167
107 A 4 3 1. 19 0.158
108 A 4 3 1. 21 0.143
109 A 4 3 1. 21 0.143
110 A 4 3 1. 21 0.143
111 A 4 3 1. 21 0.143
112 A 4 3 1. 23 0.13
113 A 4 3 1. 23 0.13
114 A 4 3 1. 23 0.13
115 A 4 3 1. 21 0.143
116 A 4 3 1. 14 0.214
117 A 4 3 1. 21 0.143
118 A 4 3 1. 23 0.13
119 A 4 3 1. 23 0.13
120 A 4 3 1. 23 0.13
121 A 4 3 1. 23 0.13
122 A 4 3 1. 23 0.13
123 A 5 4 1. 23 0.174
124 A 4 3 1. 23 0.13
125 A 5 4 1. 23 0.174
126 A 4 3 1. 23 0.13
127 A 4 3 1. 21 0.143
128 A 4 3 1. 14 0.214
129 A 4 3 1. 21 0.143
130 A 4 3 1. 23 0.13
131 A 4 3 1. 23 0.13
132 A 4 3 1. 23 0.13
133 A 4 3 1. 23 0.13
134 A 4 3 1. 23 0.13
135 A 4 3 1. 23 0.13
136 A 4 3 1. 14 0.214
137 A 4 3 1. 14 0.214
138 A 4 3 1. 23 0.13
139 A 6 6 1. 23 0.261
140 A 4 3 1. 23 0.13
141 A 5 5 1. 23 0.217
142 A 2 2 1. 21 0.095
143 A 3 3 1. 14 0.214
144 A 4 3 1. 21 0.143
145 A 6 6 1. 23 0.261
146 A 4 3 1. 23 0.13
147 A 7 7 1. 23 0.304
148 A 4 3 1. 23 0.13
149 A 6 6 1. 23 0.261
150 A 4 3 1. 23 0.13
151 A 6 6 1. 23 0.261
152 A 4 3 1. 21 0.143
153 A 5 5 1. 14 0.357
154 A 4 3 1. 21 0.143
155 A 7 7 1. 23 0.304
156 A 4 3 1. 23 0.13
157 A 8 7 1. 23 0.304
158 A 7 7 1. 23 0.304
159 A 4 3 1. 23 0.13
160 A 7 7 1. 23 0.304
161 A 4 3 1. 23 0.13
162 A 7 7 1. 23 0.304
163 A 4 3 1. 21 0.143
164 A 6 6 1. 14 0.429
165 A 4 3 1. 21 0.143
166 A 8 8 1. 23 0.348
167 A 4 3 1. 23 0.13
168 A 9 8 1. 23 0.348
169 A 7 6 1. 14 0.429
170 A 4 4 1. 12 0.333
171 A 3 3 1. 12 0.25
172 A 3 3 1. 12 0.25
173 A 4 4 1. 10 0.4
174 A 3 3 1. 10 0.3
175 A 3 3 1. 10 0.3
176 A 7 6 1. 17 0.353
177 A 9 9 1. 17 0.529
178 A 6 6 1. 17 0.353
179 A 8 8 1. 17 0.471
180 A 5 5 1. 15 0.333
181 A 6 6 1. 12 0.5
182 A 7 5 1. 15 0.333
183 A 6 6 1. 17 0.353
184 A 8 6 1. 17 0.353
185 A 7 7 1. 17 0.412
186 A 9 7 1. 17 0.412
187 A 7 6 1. 17 0.353
188 A 9 9 1. 17 0.529
189 A 6 5 1. 15 0.333
190 A 7 7 1. 12 0.583
191 A 8 6 1. 15 0.4
192 A 8 8 1. 17 0.471
193 A 8 8 1. 16 0.5
194 A 6 5 1. 17 0.294
195 A 8 8 1. 17 0.471
196 A 5 5 1. 17 0.294
197 A 7 7 1. 17 0.412
198 A 4 4 1. 15 0.267
199 A 3 3 1. 12 0.25
200 A 7 5 1. 15 0.333
201 A 6 6 1. 17 0.353
202 A 8 6 1. 17 0.353
203 A 6 5 1. 17 0.294
204 A 8 8 1. 17 0.471
205 A 5 5 1. 17 0.294
206 A 5 5 1. 17 0.294
207 A 5 5 1. 15 0.333
208 A 4 4 1. 12 0.333
209 A 8 6 1. 15 0.4
210 A 7 7 1. 17 0.412
211 A 9 9 1. 17 0.529
212 A 6 5 1. 17 0.294
213 A 7 7 1. 17 0.412
214 A 6 6 1. 17 0.353
215 A 7 7 1. 17 0.412
216 A 6 5 1. 15 0.333
217 A 6 6 1. 12 0.5
218 A 9 7 1. 15 0.467
219 A 8 8 1. 17 0.471
220 A 7 6 1. 16 0.375

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