Chapter 2detailed summary tables of results

2.1.1 Rubi
2.1.2 Mathematica
2.1.3 Maple
2.1.4 Maxima
2.1.5 FriCAS
2.1.6 Sympy
2.1.7 Giac

2.1 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 }

2.1.2 Mathematica

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, 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, 125, 126, 127, 128, 129, 130, 131, 137, 138, 139, 140, 141, 142, 143, 144, 145 }

B grade: { 135, 136 }

C grade: { 40, 41, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 132, 133, 134 }

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, 51, 64, 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, 131, 132, 133, 134, 143, 144, 145 }

B grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130 }

C grade: { 135, 136, 137, 138, 139, 140, 141, 142 }

F grade: { 30, 40, 41 }

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, 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, 131, 132, 133, 134, 139, 140

F grade: { 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, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 135, 136, 137, 138, 141, 142, 143, 144, 145 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 47, 48, 49, 50, 51, 52, 53, 54, 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, 125, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145 }

B grade: { 37, 38, 39, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124 }

F grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 46, 68, 73, 126, 127, 128, 129, 130 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 39, 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 }

B grade: { 47, 48, 49, 50, 57, 58, 63, 64, 125 }

C grade: { 134, 135, 136, 137, 139, 140, 141, 142 }

F grade: { 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 73, 126, 127, 128, 129, 130, 131, 132, 133, 138, 143, 144, 145 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 47, 48, 49, 50, 51, 52, 53, 54, 61, 62, 63, 64, 65, 66, 67, 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, 125, 132, 133, 134, 139, 140 }

B grade: { 37, 38, 39, 131, 143, 144, 145 }

C grade: { 24, 25, 26, 27 }

F grade: { 21, 22, 23, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 46, 55, 56, 57, 58, 59, 60, 68, 69, 70, 71, 72, 73, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 135, 136, 137, 138, 141, 142 }

2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column normalized size is deﬁned as $$\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}$$

 Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 74 74 74 61 81 169 68 86 normalized size 1 1. 1. 0.82 1.09 2.28 0.92 1.16 time (sec) N/A 0.082 0.015 0.001 0.932 1.052 0.087 1.093
 Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 74 74 74 61 81 169 68 86 normalized size 1 1. 1. 0.82 1.09 2.28 0.92 1.16 time (sec) N/A 0.057 0.012 0.001 0.961 1.124 0.074 1.085
 Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 69 69 69 58 77 161 65 82 normalized size 1 1. 1. 0.84 1.12 2.33 0.94 1.19 time (sec) N/A 0.036 0.013 0. 0.946 1.122 0.11 1.093
 Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 65 65 65 60 74 143 63 81 normalized size 1 1. 1. 0.92 1.14 2.2 0.97 1.25 time (sec) N/A 0.04 0.015 0.003 0.941 1.271 0.45 1.095
 Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 63 63 63 57 74 157 58 77 normalized size 1 1. 1. 0.9 1.17 2.49 0.92 1.22 time (sec) N/A 0.051 0.023 0.007 0.965 1.289 0.492 1.095
 Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 63 63 58 58 74 154 60 78 normalized size 1 1. 0.92 0.92 1.17 2.44 0.95 1.24 time (sec) N/A 0.048 0.04 0.006 0.945 1.211 0.67 1.083
 Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 63 63 60 57 76 149 61 76 normalized size 1 1. 0.95 0.9 1.21 2.37 0.97 1.21 time (sec) N/A 0.051 0.047 0.006 0.959 1.263 1.013 1.106
 Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 63 63 62 58 76 154 61 77 normalized size 1 1. 0.98 0.92 1.21 2.44 0.97 1.22 time (sec) N/A 0.051 0.03 0.007 0.969 1.291 2.982 1.097
 Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 63 63 63 60 76 159 63 77 normalized size 1 1. 1. 0.95 1.21 2.52 1. 1.22 time (sec) N/A 0.052 0.058 0.007 0.952 1.208 8.345 1.091
 Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 68 68 68 63 80 159 66 81 normalized size 1 1. 1. 0.93 1.18 2.34 0.97 1.19 time (sec) N/A 0.048 0.048 0.006 0.968 1.272 16.138 1.096
 Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 159 159 159 142 193 400 168 208 normalized size 1 1. 1. 0.89 1.21 2.52 1.06 1.31 time (sec) N/A 0.214 0.047 0.002 0.943 1.113 0.094 1.115
 Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 159 159 159 142 193 397 163 208 normalized size 1 1. 1. 0.89 1.21 2.5 1.03 1.31 time (sec) N/A 0.143 0.036 0.001 0.949 1.13 0.095 1.1
 Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 154 154 154 139 189 385 165 204 normalized size 1 1. 1. 0.9 1.23 2.5 1.07 1.32 time (sec) N/A 0.111 0.031 0.001 0.973 1.103 0.095 1.091
 Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 150 150 150 149 186 335 156 201 normalized size 1 1. 1. 0.99 1.24 2.23 1.04 1.34 time (sec) N/A 0.107 0.04 0.003 0.955 1.247 0.5 1.095
 Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 145 145 145 147 185 365 156 198 normalized size 1 1. 1. 1.01 1.28 2.52 1.08 1.37 time (sec) N/A 0.121 0.097 0.007 0.931 1.251 0.503 1.088
 Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 149 149 139 148 188 362 151 200 normalized size 1 1. 0.93 0.99 1.26 2.43 1.01 1.34 time (sec) N/A 0.123 0.109 0.008 0.944 1.3 0.641 1.136
 Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 149 149 151 146 189 354 158 197 normalized size 1 1. 1.01 0.98 1.27 2.38 1.06 1.32 time (sec) N/A 0.137 0.082 0.006 0.956 1.288 0.886 1.088
 Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 148 148 130 144 188 346 151 192 normalized size 1 1. 0.88 0.97 1.27 2.34 1.02 1.3 time (sec) N/A 0.142 0.083 0.008 0.984 1.237 2.622 1.114
 Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 143 143 142 144 186 344 151 189 normalized size 1 1. 0.99 1.01 1.3 2.41 1.06 1.32 time (sec) N/A 0.147 0.082 0.007 0.97 1.204 8.278 1.121
 Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 149 149 144 148 189 346 153 190 normalized size 1 1. 0.97 0.99 1.27 2.32 1.03 1.28 time (sec) N/A 0.143 0.101 0.009 0.953 1.217 29.718 1.129
 Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 339 339 460 1622 0 0 0 0 normalized size 1 1. 1.36 4.78 0. 0. 0. 0. time (sec) N/A 1.856 0.644 0.046 0. 0. 0. 0.
 Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 278 278 377 1171 0 0 0 0 normalized size 1 1. 1.36 4.21 0. 0. 0. 0. time (sec) N/A 0.466 0.451 0.033 0. 0. 0. 0.
 Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 270 270 360 1327 0 0 0 0 normalized size 1 1. 1.33 4.91 0. 0. 0. 0. time (sec) N/A 0.835 0.396 0.036 0. 0. 0. 0.
 Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 223 223 240 728 0 0 0 7461 normalized size 1 1. 1.08 3.26 0. 0. 0. 33.46 time (sec) N/A 0.213 0.396 0.023 0. 0. 0. 3.237
 Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 211 211 234 616 0 0 0 9080 normalized size 1 1. 1.11 2.92 0. 0. 0. 43.03 time (sec) N/A 0.266 0.223 0.017 0. 0. 0. 2.946
 Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 229 229 285 488 0 0 0 4740 normalized size 1 1. 1.24 2.13 0. 0. 0. 20.7 time (sec) N/A 0.259 0.468 0.027 0. 0. 0. 2.447
 Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 260 260 315 811 0 0 0 7089 normalized size 1 1. 1.21 3.12 0. 0. 0. 27.27 time (sec) N/A 0.471 1.135 0.027 0. 0. 0. 3.037
 Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 288 288 377 1054 0 0 0 0 normalized size 1 1. 1.31 3.66 0. 0. 0. 0. time (sec) N/A 0.474 0.984 0.037 0. 0. 0. 0.
 Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 412 412 444 1429 0 0 0 0 normalized size 1 1. 1.08 3.47 0. 0. 0. 0. time (sec) N/A 1.334 1.561 0.042 0. 0. 0. 0.
 Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 347 347 358 0 0 0 0 0 normalized size 1 1. 1.03 0. 0. 0. 0. 0. time (sec) N/A 0.618 0.995 180. 0. 0. 0. 0.
 Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 0 normalized size 1 1. 1.06 3.14 0. 0. 0. 0. time (sec) N/A 0.902 1.161 0.036 0. 0. 0. 0.
 Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-1) F(-1) F(-1) F(-1) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 317 317 335 1344 0 0 0 0 normalized size 1 1. 1.06 4.24 0. 0. 0. 0. time (sec) N/A 0.415 1.411 0.117 0. 0. 0. 0.
 Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 368 368 393 1813 0 0 0 0 normalized size 1 1. 1.07 4.93 0. 0. 0. 0. time (sec) N/A 0.867 1.456 0.105 0. 0. 0. 0.
 Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 403 403 458 1603 0 0 0 0 normalized size 1 1. 1.14 3.98 0. 0. 0. 0. time (sec) N/A 0.932 1.676 0.042 0. 0. 0. 0.
 Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 514 514 559 2398 0 0 0 0 normalized size 1 1. 1.09 4.67 0. 0. 0. 0. time (sec) N/A 1.486 2.278 0.057 0. 0. 0. 0.
 Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 534 534 655 2512 0 0 0 0 normalized size 1 1. 1.23 4.7 0. 0. 0. 0. time (sec) N/A 1.992 2.761 0.062 0. 0. 0. 0.
 Problem 37 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 399 399 296 5520 0 11187 0 10541 normalized size 1 1. 0.74 13.83 0. 28.04 0. 26.42 time (sec) N/A 0.425 1.271 0.016 0. 2.672 0. 1.338
 Problem 38 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 260 260 185 2187 0 4469 0 4324 normalized size 1 1. 0.71 8.41 0. 17.19 0. 16.63 time (sec) N/A 0.223 0.383 0.01 0. 1.825 0. 1.195
 Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 137 137 90 585 0 1181 3735 1234 normalized size 1 1. 0.66 4.27 0. 8.62 27.26 9.01 time (sec) N/A 0.088 0.122 0.004 0. 1.577 2.79 1.123
 Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C F F F F F veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 368 368 168 0 0 0 0 0 normalized size 1 1. 0.46 0. 0. 0. 0. 0. time (sec) N/A 0.622 0.22 0.043 0. 0. 0. 0.
 Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C F F F F(-1) F veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 685 670 242 0 0 0 0 0 normalized size 1 0.98 0.35 0. 0. 0. 0. 0. time (sec) N/A 2.378 0.345 0.029 0. 0. 0. 0.
 Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 0 normalized size 1 1. 1.06 3.14 0. 0. 0. 0. time (sec) N/A 0.924 1.187 0. 0. 0. 0. 0.
 Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 0 normalized size 1 1. 1.06 3.14 0. 0. 0. 0. time (sec) N/A 0.371 0.793 0.025 0. 0. 0. 0.
 Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 0 normalized size 1 1. 1.06 3.14 0. 0. 0. 0. time (sec) N/A 0.37 0.171 0.022 0. 0. 0. 0.
 Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 0 normalized size 1 1. 1.06 3.14 0. 0. 0. 0. time (sec) N/A 0.356 0.165 0.021 0. 0. 0. 0.
 Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 356 356 378 1119 0 0 0 0 normalized size 1 1. 1.06 3.14 0. 0. 0. 0. time (sec) N/A 0.359 0.16 0.024 0. 0. 0. 0.
 Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 273 273 260 622 0 1854 1392 413 normalized size 1 1. 0.95 2.28 0. 6.79 5.1 1.51 time (sec) N/A 0.854 0.208 0.007 0. 4.168 49.741 1.15
 Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 203 203 193 474 0 1404 1044 289 normalized size 1 1. 0.95 2.33 0. 6.92 5.14 1.42 time (sec) N/A 0.424 0.143 0.006 0. 2.823 35.705 1.162
 Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 144 144 136 321 0 994 721 190 normalized size 1 1. 0.94 2.23 0. 6.9 5.01 1.32 time (sec) N/A 0.272 0.107 0.005 0. 1.966 19.719 1.15
 Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 103 103 100 211 0 691 498 134 normalized size 1 1. 0.97 2.05 0. 6.71 4.83 1.3 time (sec) N/A 0.179 0.069 0.005 0. 1.747 11.093 1.147
 Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 97 97 178 165 0 683 0 131 normalized size 1 1. 1.84 1.7 0. 7.04 0. 1.35 time (sec) N/A 0.2 0.143 0.008 0. 2.633 0. 1.174
 Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 118 118 203 227 0 873 0 182 normalized size 1 1. 1.72 1.92 0. 7.4 0. 1.54 time (sec) N/A 0.285 0.162 0.009 0. 2.991 0. 1.129
 Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 174 174 314 356 0 1283 0 286 normalized size 1 1. 1.8 2.05 0. 7.37 0. 1.64 time (sec) N/A 0.407 0.353 0.011 0. 5.267 0. 1.137
 Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 244 244 416 523 0 1747 0 423 normalized size 1 1. 1.7 2.14 0. 7.16 0. 1.73 time (sec) N/A 0.573 0.352 0.014 0. 13.701 0. 1.146
 Problem 55 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 369 369 456 1450 0 31190 0 0 normalized size 1 1. 1.24 3.93 0. 84.53 0. 0. time (sec) N/A 4.577 0.546 0.036 0. 100.239 0. 0.
 Problem 56 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 282 282 365 1035 0 18515 0 0 normalized size 1 1. 1.29 3.67 0. 65.66 0. 0. time (sec) N/A 3.59 0.538 0.031 0. 22.088 0. 0.
 Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F B B F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 219 219 258 676 0 11135 1151 0 normalized size 1 1. 1.18 3.09 0. 50.84 5.26 0. time (sec) N/A 0.637 0.347 0.025 0. 11.18 90.156 0.
 Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F B B F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 213 213 253 563 0 11429 1192 0 normalized size 1 1. 1.19 2.64 0. 53.66 5.6 0. time (sec) N/A 0.839 0.328 0.025 0. 5.209 96.593 0.
 Problem 59 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 267 267 284 727 0 19478 0 0 normalized size 1 1. 1.06 2.72 0. 72.95 0. 0. time (sec) N/A 1.065 0.373 0.029 0. 27.674 0. 0.
 Problem 60 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 329 329 394 1121 0 31905 0 0 normalized size 1 1. 1.2 3.41 0. 96.98 0. 0. time (sec) N/A 1.942 0.604 0.036 0. 102.526 0. 0.
 Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 320 320 309 1167 0 4393 0 572 normalized size 1 1. 0.97 3.65 0. 13.73 0. 1.79 time (sec) N/A 1.233 0.551 0.018 0. 3.462 0. 19.825
 Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 236 236 236 832 0 3043 0 377 normalized size 1 1. 1. 3.53 0. 12.89 0. 1.6 time (sec) N/A 0.44 0.385 0.017 0. 2.305 0. 19.206
 Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 165 165 175 336 0 2033 1030 263 normalized size 1 1. 1.06 2.04 0. 12.32 6.24 1.59 time (sec) N/A 0.287 0.288 0.013 0. 1.7 145.522 19.602
 Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 123 123 130 205 0 1374 474 189 normalized size 1 1. 1.06 1.67 0. 11.17 3.85 1.54 time (sec) N/A 0.184 0.122 0.011 0. 1.446 40.153 19.251
 Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 166 166 268 462 0 2333 0 306 normalized size 1 1. 1.61 2.78 0. 14.05 0. 1.84 time (sec) N/A 0.394 0.469 0.018 0. 7.603 0. 19.512
 Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 234 234 403 722 0 3637 0 387 normalized size 1 1. 1.72 3.09 0. 15.54 0. 1.65 time (sec) N/A 0.725 0.692 0.023 0. 16.641 0. 21.974
 Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 329 329 592 1078 0 5341 0 722 normalized size 1 1. 1.8 3.28 0. 16.23 0. 2.19 time (sec) N/A 1.157 1.219 0.028 0. 39.111 0. 19.648
 Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 550 550 648 2558 0 0 0 0 normalized size 1 1. 1.18 4.65 0. 0. 0. 0. time (sec) N/A 13.227 2.313 0.053 0. 0. 0. 0.
 Problem 69 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 436 436 511 1977 0 26999 0 0 normalized size 1 1. 1.17 4.53 0. 61.92 0. 0. time (sec) N/A 5.541 1.74 0.042 0. 75.811 0. 0.
 Problem 70 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 362 362 414 1300 0 18090 0 0 normalized size 1 1. 1.14 3.59 0. 49.97 0. 0. time (sec) N/A 2.498 1.235 0.035 0. 37.949 0. 0.
 Problem 71 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 346 346 382 1182 0 18375 0 0 normalized size 1 1. 1.1 3.42 0. 53.11 0. 0. time (sec) N/A 1.896 1.196 0.033 0. 35.917 0. 0.
 Problem 72 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 399 399 444 1575 0 28044 0 0 normalized size 1 1. 1.11 3.95 0. 70.29 0. 0. time (sec) N/A 2.203 1.473 0.045 0. 79.06 0. 0.
 Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 575 575 548 2180 0 0 0 0 normalized size 1 1. 0.95 3.79 0. 0. 0. 0. time (sec) N/A 9.906 1.96 0.048 0. 0. 0. 0.
 Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 68 68 62 56 78 220 61 85 normalized size 1 1. 0.91 0.82 1.15 3.24 0.9 1.25 time (sec) N/A 0.126 0.035 0.015 0.972 1.962 0.163 1.119
 Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 61 61 61 51 72 208 54 78 normalized size 1 1. 1. 0.84 1.18 3.41 0.89 1.28 time (sec) N/A 0.118 0.027 0.016 1.016 1.949 0.156 1.111
 Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 54 54 54 46 65 186 48 72 normalized size 1 1. 1. 0.85 1.2 3.44 0.89 1.33 time (sec) N/A 0.108 0.024 0.014 0.996 1.964 0.155 1.131
 Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 49 49 49 41 58 169 42 61 normalized size 1 1. 1. 0.84 1.18 3.45 0.86 1.24 time (sec) N/A 0.086 0.022 0.013 1.027 1.975 0.156 1.093
 Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 42 42 42 36 51 144 36 54 normalized size 1 1. 1. 0.86 1.21 3.43 0.86 1.29 time (sec) N/A 0.049 0.017 0.015 0.965 2.003 0.15 1.121
 Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 44 44 44 38 59 185 39 63 normalized size 1 1. 1. 0.86 1.34 4.2 0.89 1.43 time (sec) N/A 0.077 0.022 0.017 1.019 1.749 0.164 1.084
 Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 55 55 50 45 72 219 51 72 normalized size 1 1. 0.91 0.82 1.31 3.98 0.93 1.31 time (sec) N/A 0.104 0.025 0.017 1.001 1.859 0.19 1.11
 Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 64 64 56 50 76 231 56 89 normalized size 1 1. 0.88 0.78 1.19 3.61 0.88 1.39 time (sec) N/A 0.111 0.029 0.018 0.953 1.727 0.204 1.094
 Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 70 70 71 56 78 247 66 78 normalized size 1 1. 1.01 0.8 1.11 3.53 0.94 1.11 time (sec) N/A 0.085 0.046 0.013 1.468 1.843 0.186 1.083
 Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 57 57 58 49 69 209 54 69 normalized size 1 1. 1.02 0.86 1.21 3.67 0.95 1.21 time (sec) N/A 0.082 0.048 0.013 1.486 1.756 0.185 1.084
 Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 56 56 57 46 65 198 53 65 normalized size 1 1. 1.02 0.82 1.16 3.54 0.95 1.16 time (sec) N/A 0.073 0.043 0.01 1.488 1.903 0.19 1.147
 Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 49 49 50 41 58 180 48 58 normalized size 1 1. 1.02 0.84 1.18 3.67 0.98 1.18 time (sec) N/A 0.066 0.039 0.01 1.487 2.14 0.186 1.101
 Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 48 48 46 38 54 170 44 54 normalized size 1 1. 0.96 0.79 1.12 3.54 0.92 1.12 time (sec) N/A 0.028 0.041 0.011 1.499 2.06 0.182 1.081
 Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 53 53 51 43 61 185 49 61 normalized size 1 1. 0.96 0.81 1.15 3.49 0.92 1.15 time (sec) N/A 0.073 0.049 0.012 1.458 2.18 0.201 1.123
 Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 62 62 56 48 70 213 56 70 normalized size 1 1. 0.9 0.77 1.13 3.44 0.9 1.13 time (sec) N/A 0.084 0.053 0.014 1.471 1.587 0.225 1.115
 Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 69 69 61 53 77 239 61 77 normalized size 1 1. 0.88 0.77 1.12 3.46 0.88 1.12 time (sec) N/A 0.09 0.06 0.016 1.466 1.53 0.243 1.142
 Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 76 76 77 58 84 271 66 84 normalized size 1 1. 1.01 0.76 1.11 3.57 0.87 1.11 time (sec) N/A 0.1 0.057 0.013 1.531 1.565 0.263 1.077
 Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 81 81 71 64 96 325 75 82 normalized size 1 1. 0.88 0.79 1.19 4.01 0.93 1.01 time (sec) N/A 0.112 0.06 0.013 1.494 1.585 0.241 1.096
 Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 80 80 66 62 92 313 75 78 normalized size 1 1. 0.82 0.78 1.15 3.91 0.94 0.98 time (sec) N/A 0.1 0.055 0.011 1.495 1.538 0.238 1.113
 Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 75 75 60 56 85 285 68 72 normalized size 1 1. 0.8 0.75 1.13 3.8 0.91 0.96 time (sec) N/A 0.091 0.061 0.011 1.496 1.626 0.241 1.085
 Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 72 72 55 54 81 274 65 68 normalized size 1 1. 0.76 0.75 1.12 3.81 0.9 0.94 time (sec) N/A 0.068 0.061 0.012 1.49 1.64 0.237 1.1
 Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 72 72 56 53 81 279 65 68 normalized size 1 1. 0.78 0.74 1.12 3.88 0.9 0.94 time (sec) N/A 0.066 0.063 0.012 1.497 1.521 0.236 1.105
 Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 72 72 56 53 81 281 65 68 normalized size 1 1. 0.78 0.74 1.12 3.9 0.9 0.94 time (sec) N/A 0.037 0.06 0.013 1.515 1.573 0.231 1.106
 Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 79 79 63 58 88 302 70 74 normalized size 1 1. 0.8 0.73 1.11 3.82 0.89 0.94 time (sec) N/A 0.103 0.068 0.014 1.486 1.567 0.26 1.127
 Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 86 86 78 64 97 336 76 84 normalized size 1 1. 0.91 0.74 1.13 3.91 0.88 0.98 time (sec) N/A 0.119 0.06 0.016 1.548 1.544 0.278 1.11
 Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 93 93 73 68 104 370 82 90 normalized size 1 1. 0.78 0.73 1.12 3.98 0.88 0.97 time (sec) N/A 0.134 0.079 0.015 1.474 1.569 0.301 1.121
 Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 86 86 78 74 96 270 85 103 normalized size 1 1. 0.91 0.86 1.12 3.14 0.99 1.2 time (sec) N/A 0.135 0.047 0.011 1.472 1.5 0.172 1.131
 Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 81 81 73 69 89 255 80 96 normalized size 1 1. 0.9 0.85 1.1 3.15 0.99 1.19 time (sec) N/A 0.127 0.031 0.01 1.499 1.545 0.168 1.121
 Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 74 74 66 64 80 235 73 89 normalized size 1 1. 0.89 0.86 1.08 3.18 0.99 1.2 time (sec) N/A 0.121 0.03 0.008 1.469 1.557 0.164 1.08
 Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 65 65 61 59 73 219 66 73 normalized size 1 1. 0.94 0.91 1.12 3.37 1.02 1.12 time (sec) N/A 0.105 0.027 0.008 1.471 1.503 0.168 1.112
 Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 58 58 58 54 66 194 60 66 normalized size 1 1. 1. 0.93 1.14 3.34 1.03 1.14 time (sec) N/A 0.067 0.022 0.01 1.47 1.527 0.162 1.109
 Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 66 66 93 58 74 238 65 84 normalized size 1 1. 1.41 0.88 1.12 3.61 0.98 1.27 time (sec) N/A 0.108 0.06 0.01 1.479 1.481 0.174 1.08
 Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 71 71 97 63 89 275 75 89 normalized size 1 1. 1.37 0.89 1.25 3.87 1.06 1.25 time (sec) N/A 0.134 0.051 0.014 1.458 1.615 0.201 1.098
 Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 80 80 105 68 96 289 80 107 normalized size 1 1. 1.31 0.85 1.2 3.61 1. 1.34 time (sec) N/A 0.137 0.061 0.012 1.475 1.49 0.214 1.083
 Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 87 87 110 73 103 317 85 113 normalized size 1 1. 1.26 0.84 1.18 3.64 0.98 1.3 time (sec) N/A 0.149 0.069 0.013 1.499 1.527 0.237 1.094
 Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 248 248 145 427 0 2484 71 0 normalized size 1 1. 0.58 1.72 0. 10.02 0.29 0. time (sec) N/A 0.345 0.178 0.105 0. 1.747 0.537 0.
 Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 237 237 132 419 0 2055 63 0 normalized size 1 1. 0.56 1.77 0. 8.67 0.27 0. time (sec) N/A 0.293 0.165 0.026 0. 1.665 0.541 0.
 Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 232 232 129 416 0 2102 58 0 normalized size 1 1. 0.56 1.79 0. 9.06 0.25 0. time (sec) N/A 0.292 0.162 0.022 0. 1.775 0.533 0.
 Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 225 225 121 412 0 2072 51 0 normalized size 1 1. 0.54 1.83 0. 9.21 0.23 0. time (sec) N/A 0.297 0.17 0.018 0. 1.756 0.535 0.
 Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 224 224 115 408 0 1993 48 0 normalized size 1 1. 0.51 1.82 0. 8.9 0.21 0. time (sec) N/A 0.215 0.274 0.02 0. 1.724 0.522 0.
 Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 229 229 126 414 0 1871 53 0 normalized size 1 1. 0.55 1.81 0. 8.17 0.23 0. time (sec) N/A 0.31 0.185 0.023 0. 1.706 0.551 0.
 Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 238 238 131 419 0 2205 60 0 normalized size 1 1. 0.55 1.76 0. 9.26 0.25 0. time (sec) N/A 0.335 0.31 0.023 0. 1.723 0.575 0.
 Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 245 245 140 424 0 2392 65 0 normalized size 1 1. 0.57 1.73 0. 9.76 0.27 0. time (sec) N/A 0.329 0.303 0.023 0. 1.741 0.59 0.
 Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 243 243 156 429 0 2853 82 0 normalized size 1 1. 0.64 1.77 0. 11.74 0.34 0. time (sec) N/A 0.36 0.222 0.02 0. 1.794 0.591 0.
 Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 242 242 155 426 0 2421 80 0 normalized size 1 1. 0.64 1.76 0. 10. 0.33 0. time (sec) N/A 0.31 0.211 0.022 0. 1.81 0.607 0.
 Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 235 235 138 422 0 2670 71 0 normalized size 1 1. 0.59 1.8 0. 11.36 0.3 0. time (sec) N/A 0.3 0.33 0.022 0. 1.773 0.587 0.
 Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 238 238 129 418 0 2402 68 0 normalized size 1 1. 0.54 1.76 0. 10.09 0.29 0. time (sec) N/A 0.29 0.304 0.019 0. 1.835 0.592 0.
 Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 246 246 133 418 0 2074 68 0 normalized size 1 1. 0.54 1.7 0. 8.43 0.28 0. time (sec) N/A 0.284 0.299 0.022 0. 1.734 0.592 0.
 Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 248 248 129 418 0 2261 68 0 normalized size 1 1. 0.52 1.69 0. 9.12 0.27 0. time (sec) N/A 0.254 0.302 0.022 0. 1.68 0.571 0.
 Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 253 253 140 424 0 2529 73 0 normalized size 1 1. 0.55 1.68 0. 10. 0.29 0. time (sec) N/A 0.343 0.379 0.023 0. 1.733 0.607 0.
 Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size