## 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, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

#### 2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 32, 44, 46, 53, 55, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 86, 87, 88, 89, 96, 100, 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, 141, 144, 149, 152, 153, 154, 155, 156 }

B grade: { 93, 94, 95, 97, 98, 99, 101, 102, 103, 142, 143 }

C grade: { 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 54, 56, 57, 58, 59, 60, 79, 80, 81, 82, 83, 84, 85, 138, 139, 140 }

F grade: { 90, 91, 92, 145, 146, 147, 148, 150, 151}

#### 2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 20, 21, 22, 23, 24, 32, 33, 34, 44, 48, 53, 55, 57, 59, 64, 65, 66, 67, 74, 86, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 144, 155, 156 }

B grade: { 6, 9, 35, 36, 37, 38, 39, 40, 41, 42, 46, 50, 61, 62, 63, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 125, 126, 127, 128 }

C grade: { 14, 15, 16, 17, 18, 19, 25, 26, 27, 28, 29, 30, 31, 43, 45, 47, 49, 51, 52, 54, 56, 58, 60, 140 }

F grade: { 87, 88, 89, 90, 91, 92, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154 }

#### 2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 20, 21, 22, 23, 24, 32, 33, 53, 57, 86, 93, 97, 101, 105, 106, 107, 108, 109, 113, 114, 115, 116, 117, 121, 122, 123, 125, 130, 131, 132, 134, 135, 136, 138, 139, 140, 144, 155, 156

B grade: { 94, 95, 98, 99, 102, 103, 110, 111, 112, 118, 119, 120, 124, 126, 127, 128 }

F grade: { 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 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, 87, 88, 89, 90, 91, 92, 96, 100, 104, 129, 133, 137, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154 }

#### 2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 20, 21, 22, 23, 24, 32, 33, 34, 44, 48, 52, 53, 55, 57, 58, 61, 62, 63, 64, 65, 66, 86, 105, 106, 107, 108, 113, 114, 115, 116, 121, 122, 123, 124, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 144, 155, 156 }

B grade: { 8, 17, 25, 26, 27, 28, 29, 30, 31, 45, 46, 47, 50, 54, 56, 59, 60, 72, 73, 74, 75, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 109, 110, 111, 112, 117, 118, 119, 120, 125, 126, 127, 128 }

F grade: { 14, 15, 16, 18, 19, 35, 36, 37, 38, 39, 40, 41, 42, 43, 49, 51, 67, 68, 69, 70, 71, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154 }

#### 2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 16, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 52, 53, 54, 55, 56, 57, 58, 59, 60, 105, 106, 107, 113, 114, 115, 121, 122, 123, 124, 137 }

B grade: { 9, 10, 11, 44, 93, 94, 95, 97, 98, 99, 101, 102, 103, 109, 117, 125, 129, 133, 138 }

F grade: { 12, 13, 14, 15, 17, 18, 19, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 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, 96, 100, 104, 108, 110, 111, 112, 116, 118, 119, 120, 126, 127, 128, 130, 131, 132, 134, 135, 136, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

#### 2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 22, 23, 24, 32, 33, 34, 44, 48, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 86, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 132, 136, 137, 138, 139, 140, 144, 155, 156 }

B grade: { 25, 26, 27, 28, 29, 30, 31, 59, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 129, 130, 131, 133, 134, 135 }

C grade: { 46, 50 }

F grade: { 14, 15, 16, 17, 18, 19, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 47, 49, 51, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 111, 119, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154 }

### 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 163 163 164 169 224 448 187 234 normalized size 1 1. 1.01 1.04 1.37 2.75 1.15 1.44 time (sec) N/A 0.185 0.048 0.001 1.006 1.139 0.096 1.133
 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 135 135 135 136 182 360 151 190 normalized size 1 1. 1. 1.01 1.35 2.67 1.12 1.41 time (sec) N/A 0.125 0.036 0.001 0.983 1.164 0.089 1.114
 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 103 103 104 103 138 282 117 147 normalized size 1 1. 1.01 1. 1.34 2.74 1.14 1.43 time (sec) N/A 0.097 0.029 0.002 1.053 1.157 0.082 1.077
 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 73 73 73 70 93 192 75 103 normalized size 1 1. 1. 0.96 1.27 2.63 1.03 1.41 time (sec) N/A 0.062 0.022 0. 0.962 1.097 0.075 1.162
 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 42 42 42 37 49 107 39 58 normalized size 1 1. 1. 0.88 1.17 2.55 0.93 1.38 time (sec) N/A 0.028 0.009 0. 1.058 1.128 0.063 1.099
 Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 188 188 176 313 0 1096 175 279 normalized size 1 1. 0.94 1.66 0. 5.83 0.93 1.48 time (sec) N/A 0.211 0.155 0.004 0. 1.433 1.07 1.103
 Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 213 213 199 345 0 1548 206 306 normalized size 1 1. 0.93 1.62 0. 7.27 0.97 1.44 time (sec) N/A 0.226 0.199 0.008 0. 1.389 1.984 1.122
 Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 242 242 209 362 0 2067 246 340 normalized size 1 1. 0.86 1.5 0. 8.54 1.02 1.4 time (sec) N/A 0.262 0.271 0.01 0. 1.398 7.551 1.145
 Problem 9 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 132 132 126 260 0 902 619 177 normalized size 1 1. 0.95 1.97 0. 6.83 4.69 1.34 time (sec) N/A 0.218 0.065 0.004 0. 3.254 15.002 1.361
 Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 97 97 93 175 0 664 434 128 normalized size 1 1. 0.96 1.8 0. 6.85 4.47 1.32 time (sec) N/A 0.12 0.07 0.003 0. 1.928 9.096 1.35
 Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 72 72 71 99 0 481 287 95 normalized size 1 1. 0.99 1.38 0. 6.68 3.99 1.32 time (sec) N/A 0.073 0.05 0.002 0. 1.445 4.389 1.375
 Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C A F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 78 78 80 106 0 556 0 103 normalized size 1 1. 1.03 1.36 0. 7.13 0. 1.32 time (sec) N/A 0.128 0.034 0.006 0. 2.198 0. 1.384
 Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C A F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 112 112 130 191 0 845 0 173 normalized size 1 1. 1.16 1.71 0. 7.54 0. 1.54 time (sec) N/A 0.197 0.052 0.009 0. 4.111 0. 1.366
 Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 723 723 88 70 0 0 0 0 normalized size 1 1. 0.12 0.1 0. 0. 0. 0. time (sec) N/A 1.813 0.049 0.007 0. 0. 0. 0.
 Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 718 718 88 67 0 0 0 0 normalized size 1 1. 0.12 0.09 0. 0. 0. 0. time (sec) N/A 1.457 0.052 0.006 0. 0. 0. 0.
 Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F F(-1) A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 634 634 59 49 0 0 920 0 normalized size 1 1. 0.09 0.08 0. 0. 1.45 0. time (sec) N/A 0.728 0.031 0.002 0. 0. 133.311 0.
 Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 634 634 61 47 0 28045 0 0 normalized size 1 1. 0.1 0.07 0. 44.24 0. 0. time (sec) N/A 0.654 0.031 0.003 0. 108.462 0. 0.
 Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 653 653 85 70 0 0 0 0 normalized size 1 1. 0.13 0.11 0. 0. 0. 0. time (sec) N/A 1.175 0.049 0.006 0. 0. 0. 0.
 Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 655 655 89 68 0 0 0 0 normalized size 1 1. 0.14 0.1 0. 0. 0. 0. time (sec) N/A 1.11 0.048 0.006 0. 0. 0. 0.
 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 46 46 46 38 50 109 42 50 normalized size 1 1. 1. 0.83 1.09 2.37 0.91 1.09 time (sec) N/A 0.058 0.016 0.003 1.491 1.778 0.15 1.11
 Problem 21 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 31 31 31 25 32 76 32 32 normalized size 1 1. 1. 0.81 1.03 2.45 1.03 1.03 time (sec) N/A 0.035 0.008 0.003 1.457 1.8 0.126 1.167
 Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 39 39 39 33 43 95 37 43 normalized size 1 1. 1. 0.85 1.1 2.44 0.95 1.1 time (sec) N/A 0.04 0.009 0.002 1.507 1.681 0.14 1.146
 Problem 23 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 41 41 44 35 51 108 41 47 normalized size 1 1. 1.07 0.85 1.24 2.63 1. 1.15 time (sec) N/A 0.055 0.013 0.005 1.458 1.766 0.154 1.11
 Problem 24 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 31 31 45 25 32 84 36 32 normalized size 1 1. 1.45 0.81 1.03 2.71 1.16 1.03 time (sec) N/A 0.045 0.013 0.004 1.526 1.352 0.158 1.106
 Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 418 418 47 46 0 3918 31 867 normalized size 1 1. 0.11 0.11 0. 9.37 0.07 2.07 time (sec) N/A 0.538 0.011 0.006 0. 1.607 0.177 1.168
 Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 382 382 48 44 0 5949 32 1103 normalized size 1 1. 0.13 0.12 0. 15.57 0.08 2.89 time (sec) N/A 0.328 0.014 0.004 0. 1.942 0.193 1.16
 Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 378 378 46 41 0 3906 24 853 normalized size 1 1. 0.12 0.11 0. 10.33 0.06 2.26 time (sec) N/A 0.259 0.013 0.004 0. 1.673 0.179 1.178
 Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 411 411 55 44 0 5936 22 1108 normalized size 1 1. 0.13 0.11 0. 14.44 0.05 2.7 time (sec) N/A 0.276 0.012 0.006 0. 2.013 0.183 1.196
 Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 411 411 57 44 0 3903 26 860 normalized size 1 1. 0.14 0.11 0. 9.5 0.06 2.09 time (sec) N/A 0.277 0.012 0.004 0. 1.639 0.185 1.195
 Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 416 416 47 46 0 5952 31 1119 normalized size 1 1. 0.11 0.11 0. 14.31 0.07 2.69 time (sec) N/A 0.275 0.014 0.006 0. 1.937 0.19 1.157
 Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 418 418 47 46 0 3945 32 867 normalized size 1 1. 0.11 0.11 0. 9.44 0.08 2.07 time (sec) N/A 0.359 0.012 0.006 0. 1.626 0.2 1.164
 Problem 32 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 36 36 37 33 43 96 37 43 normalized size 1 1. 1.03 0.92 1.19 2.67 1.03 1.19 time (sec) N/A 0.039 0.01 0.003 1.5 1.276 0.136 1.171
 Problem 33 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 39 39 55 35 51 107 41 47 normalized size 1 1. 1.41 0.9 1.31 2.74 1.05 1.21 time (sec) N/A 0.056 0.014 0.006 1.486 1.476 0.143 1.128
 Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C A F A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 39 39 55 35 0 107 41 47 normalized size 1 1. 1.41 0.9 0. 2.74 1.05 1.21 time (sec) N/A 0.063 0.01 0.004 0. 1.498 0.148 1.094
 Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 396 396 103 1070 0 0 400 0 normalized size 1 1. 0.26 2.7 0. 0. 1.01 0. time (sec) N/A 0.416 0.179 0.161 0. 0. 10.083 0.
 Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 356 356 101 1010 0 0 257 0 normalized size 1 1. 0.28 2.84 0. 0. 0.72 0. time (sec) N/A 0.311 0.153 0.029 0. 0. 5.848 0.
 Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 316 316 98 956 0 0 124 0 normalized size 1 1. 0.31 3.03 0. 0. 0.39 0. time (sec) N/A 0.246 0.134 0.027 0. 0. 3.115 0.
 Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 278 278 98 907 0 0 119 0 normalized size 1 1. 0.35 3.26 0. 0. 0.43 0. time (sec) N/A 0.182 0.091 0.028 0. 0. 2.629 0.
 Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F A F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 289 289 102 934 0 0 119 0 normalized size 1 1. 0.35 3.23 0. 0. 0.41 0. time (sec) N/A 0.189 0.106 0.038 0. 0. 18.698 0.
 Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 309 309 129 1005 0 0 0 0 normalized size 1 1. 0.42 3.25 0. 0. 0. 0. time (sec) N/A 0.211 0.139 0.042 0. 0. 0. 0.
 Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 349 349 166 1095 0 0 0 0 normalized size 1 1. 0.48 3.14 0. 0. 0. 0. time (sec) N/A 0.324 0.191 0.043 0. 0. 0. 0.
 Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 389 389 200 1182 0 0 0 0 normalized size 1 1. 0.51 3.04 0. 0. 0. 0. time (sec) N/A 0.395 0.243 0.048 0. 0. 0. 0.
 Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 433 433 88 67 0 0 0 0 normalized size 1 1. 0.2 0.15 0. 0. 0. 0. time (sec) N/A 1.132 0.075 0.004 0. 0. 0. 0.
 Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 72 72 71 99 0 481 287 95 normalized size 1 1. 0.99 1.38 0. 6.68 3.99 1.32 time (sec) N/A 0.072 0.056 0.003 0. 2.224 7.519 6.167
 Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 375 375 59 51 0 26996 0 0 normalized size 1 1. 0.16 0.14 0. 71.99 0. 0. time (sec) N/A 0.456 0.047 0.003 0. 97.806 0. 0.
 Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F B F(-1) C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 184 184 179 340 0 3077 0 6484 normalized size 1 1. 0.97 1.85 0. 16.72 0. 35.24 time (sec) N/A 0.213 0.156 0.022 0. 2.278 0. 7.939
 Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 375 375 61 47 0 26437 0 0 normalized size 1 1. 0.16 0.13 0. 70.5 0. 0. time (sec) N/A 0.351 0.048 0.003 0. 20.939 0. 0.
 Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C A F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 78 78 80 106 0 556 0 105 normalized size 1 1. 1.03 1.36 0. 7.13 0. 1.35 time (sec) N/A 0.126 0.034 0.007 0. 4.899 0. 6.592
 Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F(-1) F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 392 392 85 72 0 0 0 0 normalized size 1 1. 0.22 0.18 0. 0. 0. 0. time (sec) N/A 0.683 0.065 0.006 0. 0. 0. 0.
 Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B F(-1) C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 199 199 89 365 0 5485 0 2365 normalized size 1 1. 0.45 1.83 0. 27.56 0. 11.88 time (sec) N/A 0.311 0.049 0.02 0. 5.412 0. 7.081
 Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F F(-1) F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 394 394 86 68 0 0 0 0 normalized size 1 1. 0.22 0.17 0. 0. 0. 0. time (sec) N/A 0.625 0.074 0.007 0. 0. 0. 0.
 Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 278 278 46 34 0 613 170 281 normalized size 1 1. 0.17 0.12 0. 2.21 0.61 1.01 time (sec) N/A 0.3 0.016 0.006 0. 1.832 0.328 1.151
 Problem 53 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 39 39 39 33 43 96 37 43 normalized size 1 1. 1. 0.85 1.1 2.46 0.95 1.1 time (sec) N/A 0.042 0.013 0.004 1.487 1.752 0.182 1.119
 Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 355 355 55 46 0 2313 27 342 normalized size 1 1. 0.15 0.13 0. 6.52 0.08 0.96 time (sec) N/A 0.289 0.016 0.007 0. 2.07 1.35 1.14
 Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 50 50 44 39 0 104 42 42 normalized size 1 1. 0.88 0.78 0. 2.08 0.84 0.84 time (sec) N/A 0.04 0.016 0.012 0. 1.726 0.162 1.112
 Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 355 355 57 44 0 2313 26 342 normalized size 1 1. 0.16 0.12 0. 6.52 0.07 0.96 time (sec) N/A 0.216 0.013 0. 0. 1.868 1.542 1.127
 Problem 57 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 41 41 44 35 51 109 41 51 normalized size 1 1. 1.07 0.85 1.24 2.66 1. 1.24 time (sec) N/A 0.053 0.013 0.006 1.545 1.466 0.201 1.108
 Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 280 280 47 38 0 617 168 284 normalized size 1 1. 0.17 0.14 0. 2.2 0.6 1.01 time (sec) N/A 0.208 0.016 0.007 0. 1.629 0.306 1.135
 Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C A F B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 89 89 49 70 0 566 76 348 normalized size 1 1. 0.55 0.79 0. 6.36 0.85 3.91 time (sec) N/A 0.09 0.016 0.01 0. 1.569 0.263 1.263
 Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 370 370 47 46 0 1962 32 348 normalized size 1 1. 0.13 0.12 0. 5.3 0.09 0.94 time (sec) N/A 0.269 0.015 0.01 0. 1.798 1.599 1.17
 Problem 61 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 280 280 283 662 0 2079 0 398 normalized size 1 1. 1.01 2.36 0. 7.42 0. 1.42 time (sec) N/A 0.597 0.241 0.014 0. 137.062 0. 1.108
 Problem 62 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 218 218 218 512 0 1623 0 302 normalized size 1 1. 1. 2.35 0. 7.44 0. 1.39 time (sec) N/A 0.395 0.181 0.006 0. 84.083 0. 1.115
 Problem 63 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 176 176 178 388 0 1237 0 250 normalized size 1 1. 1.01 2.2 0. 7.03 0. 1.42 time (sec) N/A 0.285 0.187 0.007 0. 30.694 0. 1.096
 Problem 64 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 149 149 132 275 0 872 0 201 normalized size 1 1. 0.89 1.85 0. 5.85 0. 1.35 time (sec) N/A 0.21 0.128 0.007 0. 9.367 0. 1.117
 Problem 65 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 124 124 107 169 0 694 0 171 normalized size 1 1. 0.86 1.36 0. 5.6 0. 1.38 time (sec) N/A 0.145 0.079 0.003 0. 3.256 0. 1.109
 Problem 66 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 123 123 105 168 0 697 0 170 normalized size 1 1. 0.85 1.37 0. 5.67 0. 1.38 time (sec) N/A 0.107 0.077 0.006 0. 3.293 0. 1.096
 Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 158 159 152 285 0 0 0 221 normalized size 1 1.01 0.96 1.8 0. 0. 0. 1.4 time (sec) N/A 0.271 0.189 0.008 0. 0. 0. 1.104
 Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 193 193 194 412 0 0 0 284 normalized size 1 1. 1.01 2.13 0. 0. 0. 1.47 time (sec) N/A 0.343 0.178 0.011 0. 0. 0. 1.108
 Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 252 252 252 562 0 0 0 377 normalized size 1 1. 1. 2.23 0. 0. 0. 1.5 time (sec) N/A 0.428 0.234 0.012 0. 0. 0. 1.099
 Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 343 343 338 943 0 0 0 763 normalized size 1 1. 0.99 2.75 0. 0. 0. 2.22 time (sec) N/A 0.907 0.38 0.012 0. 0. 0. 1.134
 Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 274 274 269 765 0 0 0 643 normalized size 1 1. 0.98 2.79 0. 0. 0. 2.35 time (sec) N/A 0.563 0.316 0.012 0. 0. 0. 1.131
 Problem 72 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 246 246 207 580 0 3005 0 556 normalized size 1 1. 0.84 2.36 0. 12.22 0. 2.26 time (sec) N/A 0.395 0.248 0.007 0. 110.084 0. 1.117
 Problem 73 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 194 194 159 389 0 2365 0 455 normalized size 1 1. 0.82 2.01 0. 12.19 0. 2.35 time (sec) N/A 0.306 0.24 0.008 0. 36.977 0. 1.122
 Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 183 183 148 328 0 2217 0 441 normalized size 1 1. 0.81 1.79 0. 12.11 0. 2.41 time (sec) N/A 0.236 0.262 0.007 0. 31.559 0. 1.136
 Problem 75 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 189 189 151 386 0 2295 0 447 normalized size 1 1. 0.8 2.04 0. 12.14 0. 2.37 time (sec) N/A 0.305 0.226 0.009 0. 17.499 0. 1.112
 Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 248 249 246 589 0 0 0 528 normalized size 1 1. 0.99 2.38 0. 0. 0. 2.13 time (sec) N/A 0.409 0.285 0.013 0. 0. 0. 1.136
 Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 291 291 287 791 0 0 0 657 normalized size 1 1. 0.99 2.72 0. 0. 0. 2.26 time (sec) N/A 0.563 0.381 0.016 0. 0. 0. 1.109
 Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 372 372 370 993 0 0 0 792 normalized size 1 1. 0.99 2.67 0. 0. 0. 2.13 time (sec) N/A 0.851 0.468 0.019 0. 0. 0. 1.119
 Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F F(-1) F(-1) veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 981 981 10904 11938 0 0 0 0 normalized size 1 1. 11.12 12.17 0. 0. 0. 0. time (sec) N/A 6.172 14.328 0.148 0. 0. 0. 0.
 Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F F(-1) F(-1) veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 778 778 7531 9182 0 0 0 0 normalized size 1 1. 9.68 11.8 0. 0. 0. 0. time (sec) N/A 2.349 13.756 0.062 0. 0. 0. 0.
 Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F F(-1) F(-1) veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 636 636 5350 6302 0 0 0 0 normalized size 1 1. 8.41 9.91 0. 0. 0. 0. time (sec) N/A 0.993 13.094 0.049 0. 0. 0. 0.
 Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F F(-1) F(-1) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 550 550 693 4361 0 0 0 0 normalized size 1 1. 1.26 7.93 0. 0. 0. 0. time (sec) N/A 0.655 12.161 0.045 0. 0. 0. 0.
 Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F(-1) F(-1) F(-1) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 955 955 1258 3023 0 0 0 0 normalized size 1 1. 1.32 3.17 0. 0. 0. 0. time (sec) N/A 3.313 10.681 0.048 0. 0. 0. 0.
 Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F(-1) F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 929 929 1372 3553 0 0 0 0 normalized size 1 1. 1.48 3.82 0. 0. 0. 0. time (sec) N/A 2.725 11.486 0.045 0. 0. 0. 0.
 Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F(-1) F(-1) F(-1) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 1287 1287 811 4957 0 0 0 0 normalized size 1 1. 0.63 3.85 0. 0. 0. 0. time (sec) N/A 5.302 12.653 0.051 0. 0. 0. 0.
 Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade N/A A A A A A F(-1) A veriﬁed N/A N/A N/A TBD TBD TBD TBD TBD size 28 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.019 0.191 0.424 0. 0. 0. 0.
 Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F F F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 358 358 249 0 0 0 0 0 normalized size 1 1. 0.7 0. 0. 0. 0. 0. time (sec) N/A 0.237 0.314 0.074 0. 0. 0. 0.
 Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F F F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 262 262 189 0 0 0 0 0 normalized size 1 1. 0.72 0. 0. 0. 0. 0. time (sec) N/A 0.16 0.168 0.075 0. 0. 0. 0.
 Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 166 166 136 0 0 0 0 0 normalized size 1 1. 0.82 0. 0. 0. 0. 0. time (sec) N/A 0.095 0.076 0.073 0. 0. 0. 0.
 Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A F F F F F(-1) F veriﬁed N/A Yes N/A TBD TBD TBD TBD TBD size 194 194 0 0 0 0 0 0 normalized size 1 1. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.224 0.116 0.094 0. 0. 0. 0.
 Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A F F F F F(-1) F veriﬁed N/A Yes N/A TBD TBD TBD TBD TBD size 302 302 0 0 0 0 0 0 normalized size 1 1. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.333 0.163 0.094 0. 0. 0. 0.
 Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A F F F F F(-1) F veriﬁed N/A Yes N/A TBD TBD TBD TBD TBD size 412 412 0 0 0 0 0 0 normalized size 1 1. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.449 0.607 0.092 0. 0. 0. 0.
 Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B A B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 16 16 201 46548 19 3474 1326 1952 normalized size 1 1. 12.56 2909.25 1.19 217.12 82.88 122. time (sec) N/A 0.06 0.169 0.004 1.036 0.936 0.305 1.113
 Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 233 46552 1674 3578 1384 1963 normalized size 1 1. 12.94 2586.22 93. 198.78 76.89 109.06 time (sec) N/A 0.329 0.174 0.003 1.037 0.893 0.307 1.15
 Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 233 46552 1674 3594 1394 1963 normalized size 1 1. 12.94 2586.22 93. 199.67 77.44 109.06 time (sec) N/A 0.302 0.179 0.003 1.07 0.927 0.305 1.147
 Problem 96 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 23 23 22 2042 0 2969 0 2286 normalized size 1 1. 0.96 88.78 0. 129.09 0. 99.39 time (sec) N/A 0.056 0.068 0.062 0. 1.298 0. 1.291
 Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B A B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 201 47685 22 3474 1326 1958 normalized size 1 1. 11.17 2649.17 1.22 193. 73.67 108.78 time (sec) N/A 0.069 0.173 0.006 1.23 0.808 0.313 1.11
 Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 233 47688 1677 3578 1384 1963 normalized size 1 1. 11.65 2384.4 83.85 178.9 69.2 98.15 time (sec) N/A 0.322 0.168 0.002 1.054 0.86 0.311 1.146
 Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 233 47688 1677 3594 1394 1963 normalized size 1 1. 11.65 2384.4 83.85 179.7 69.7 98.15 time (sec) N/A 0.31 0.165 0.001 1.062 0.968 0.321 1.14
 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 25 25 24 2046 0 2969 0 2286 normalized size 1 1. 0.96 81.84 0. 118.76 0. 91.44 time (sec) N/A 0.06 0.056 0.06 0. 1.358 0. 1.287
 Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B A B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 15 15 172 155 18 387 175 208 normalized size 1 1. 11.47 10.33 1.2 25.8 11.67 13.87 time (sec) N/A 0.014 0.005 0.003 1.002 0.937 0.118 1.088
 Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 16 16 182 157 211 402 182 211 normalized size 1 1. 11.38 9.81 13.19 25.12 11.38 13.19 time (sec) N/A 0.054 0.006 0.004 1.134 0.897 0.157 1.089
 Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B B B B B B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 16 16 186 157 211 408 185 211 normalized size 1 1. 11.62 9.81 13.19 25.5 11.56 13.19 time (sec) N/A 0.056 0.006 0.004 1.17 0.818 0.121 1.094
 Problem 104 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 21 21 21 230 0 467 0 255 normalized size 1 1. 1. 10.95 0. 22.24 0. 12.14 time (sec) N/A 0.033 0.118 0.033 0. 1.103 0. 1.132
 Problem 105 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 11 11 10 12 15 30 10 15 normalized size 1 1. 0.91 1.09 1.36 2.73 0.91 1.36 time (sec) N/A 0.004 0.003 0.001 1.138 0.979 0.297 1.096
 Problem 106 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 17 17 17 16 20 38 14 20 normalized size 1 1. 1. 0.94 1.18 2.24 0.82 1.18 time (sec) N/A 0.019 0.006 0. 1.139 0.995 0.418 1.137
 Problem 107 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 17 17 17 16 20 38 14 20 normalized size 1 1. 1. 0.94 1.18 2.24 0.82 1.18 time (sec) N/A 0.024 0.007 0.002 1.03 0.988 0.53 1.368
 Problem 108 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 19 19 19 24 31 41 0 26 normalized size 1 1. 1. 1.26 1.63 2.16 0. 1.37 time (sec) N/A 0.027 0.109 0.019 1.161 1.109 0. 1.082
 Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 16 16 15 15 19 737 359 19 normalized size 1 1. 0.94 0.94 1.19 46.06 22.44 1.19 time (sec) N/A 0.005 0.011 0. 1.031 1.236 51.451 1.141
 Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 18 17 475 748 0 22 normalized size 1 1. 1. 0.94 26.39 41.56 0. 1.22 time (sec) N/A 0.02 0.014 0.002 1.673 1.244 0. 50.318
 Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B B F(-1) F(-1) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 18 17 475 749 0 0 normalized size 1 1. 1. 0.94 26.39 41.61 0. 0. time (sec) N/A 0.023 0.013 0.001 1.705 1.268 0. 0.
 Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 23 23 22 22 562 851 0 28 normalized size 1 1. 0.96 0.96 24.43 37. 0. 1.22 time (sec) N/A 0.027 0.062 0.059 3.203 1.356 0. 1.183
 Problem 113 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 13 13 12 14 18 30 10 18 normalized size 1 1. 0.92 1.08 1.38 2.31 0.77 1.38 time (sec) N/A 0.005 0.005 0. 1.186 0.95 0.393 1.121
 Problem 114 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 19 19 19 18 23 38 14 23 normalized size 1 1. 1. 0.95 1.21 2. 0.74 1.21 time (sec) N/A 0.019 0.007 0.003 1.014 1.038 0.418 1.158
 Problem 115 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 19 19 19 18 23 38 14 23 normalized size 1 1. 1. 0.95 1.21 2. 0.74 1.21 time (sec) N/A 0.024 0.006 0. 0.979 1.016 0.512 1.332
 Problem 116 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 21 21 21 26 34 41 0 28 normalized size 1 1. 1. 1.24 1.62 1.95 0. 1.33 time (sec) N/A 0.029 0.114 0.02 1.148 1.208 0. 1.095
 Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A B B A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 16 17 22 737 359 22 normalized size 1 1. 0.89 0.94 1.22 40.94 19.94 1.22 time (sec) N/A 0.004 0.013 0.002 1.006 1.318 55.204 1.109
 Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 20 19 481 748 0 24 normalized size 1 1. 1. 0.95 24.05 37.4 0. 1.2 time (sec) N/A 0.02 0.017 0.001 1.481 1.324 0. 55.488
 Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B B F(-1) F(-1) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 20 19 481 749 0 0 normalized size 1 1. 1. 0.95 24.05 37.45 0. 0. time (sec) N/A 0.024 0.017 0. 1.531 1.327 0. 0.
 Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B B F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 25 25 23 24 566 851 0 31 normalized size 1 1. 0.92 0.96 22.64 34.04 0. 1.24 time (sec) N/A 0.029 0.068 0.059 2.891 1.513 0. 1.238
 Problem 121 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 10 10 9 9 14 24 8 15 normalized size 1 1. 0.9 0.9 1.4 2.4 0.8 1.5 time (sec) N/A 0.004 0.004 0.002 1.026 1.096 0.353 1.096
 Problem 122 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 16 15 15 14 23 39 12 20 normalized size 1 0.94 0.94 0.88 1.44 2.44 0.75 1.25 time (sec) N/A 0.024 0.006 0.004 0.997 1.021 0.324 1.097
 Problem 123 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 16 15 15 14 23 39 12 20 normalized size 1 0.94 0.94 0.88 1.44 2.44 0.75 1.25 time (sec) N/A 0.03 0.007 0.006 1.202 1.168 0.348 1.121
 Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac