## 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, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263 }

#### 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, 27, 30, 32, 33, 35, 38, 40, 41, 43, 46, 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, 74, 76, 77, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 96, 97, 99, 100, 102, 103, 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, 134, 135, 136, 137, 138, 139, 141, 143, 145, 147, 148, 149, 151, 152, 153, 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, 203, 204, 205, 206, 207, 208, 210, 212, 214, 216, 218, 219, 221, 222, 223, 225, 226, 227, 228, 229, 231, 233, 234, 235, 237, 240, 248, 255, 256, 257, 258, 259, 260, 261, 262, 263 }

B grade: { 104, 144, 146, 202, 213, 241 }

C grade: { 26, 28, 29, 31, 34, 36, 37, 39, 42, 44, 45, 47, 73, 75, 78, 80, 93, 95, 98, 101, 133, 140, 142, 150, 154, 209, 211, 215, 217, 220, 224, 230, 232, 236, 238, 239, 242, 243, 244, 245, 246, 247, 249, 250, 251, 252, 253, 254 }

#### 2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 16, 17, 19, 23, 24, 29, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 71, 74, 76, 77, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 139, 140, 141, 142, 143, 149, 150, 151, 152, 153, 154, 155, 161, 162, 163, 164, 165, 166, 167, 170, 171, 172, 173, 174, 180, 182, 184, 202, 203, 204, 205, 206, 207, 257, 258, 260, 261 }

B grade: { 10, 12, 18, 20, 21, 22, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 62, 70, 72, 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, 144, 145, 146, 147, 148, 156, 157, 158, 159, 160, 168, 169, 175, 176, 177, 178, 179, 181, 183, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 208, 209, 210, 211, 212, 213, 219, 220, 221, 222, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 238, 239, 240, 241, 242, 243, 246, 247, 248, 249, 250, 251, 252, 255, 256 }

C grade: { 73, 75, 78, 80, 259, 262, 263 }

F grade: { 214, 215, 216, 217, 218, 223, 224, 235, 236, 237, 244, 245, 253, 254 }

#### 2.1.4 Maxima

A grade: { 5, 6, 49, 50, 51, 52, 53, 54, 66, 68, 74, 76, 77, 79, 81, 86, 94, 102, 138, 139, 140, 150, 172, 174, 176, 178, 202, 204, 206

B grade: { 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 69, 70, 71, 72, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99, 100, 101, 103, 104, 134, 135, 136, 137, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 180, 182, 184, 186, 188, 191, 193, 195, 197, 199, 207, 257, 258 }

C grade: { 203, 205 }

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, 75, 78, 80, 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, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 190, 192, 194, 196, 198, 200, 201, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 259, 260, 261, 262, 263 }

#### 2.1.5 FriCAS

A grade: { 1, 3, 4, 81, 82, 83, 89, 138, 203, 205, 206, 207 }

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, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 78, 84, 85, 86, 87, 88, 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, 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, 202, 204, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 224, 225, 227, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 247, 248, 249, 250, 251, 252, 254, 255, 257, 258, 260, 261, 262 }

C grade: { 75, 80, 226, 228, 256 }

F grade: { 41, 42, 47, 48, 65, 73, 74, 76, 77, 79, 200, 201, 220, 246, 253, 259, 263 }

#### 2.1.6 Sympy

A grade: { 77, 79, 134, 135, 136, 137, 138, 144, 145, 146, 147, 148, 156, 157, 158, 159, 160, 168, 169, 170, 171, 172, 173, 174, 175, 181, 183, 185, 206, 208, 210, 212, 233, 242, 251, 257 }

B grade: { 140, 219, 221, 258 }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 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, 139, 141, 142, 143, 149, 150, 151, 152, 153, 154, 155, 161, 162, 163, 164, 165, 166, 167, 176, 177, 178, 179, 180, 182, 184, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 207, 209, 211, 213, 214, 215, 216, 217, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 241, 243, 244, 245, 246, 247, 248, 249, 250, 252, 253, 254, 255, 256, 259, 260, 261, 262, 263 }

#### 2.1.7 Giac

A grade: { 5, 6, 8, 14, 23, 30, 49, 50, 51, 52, 53, 54, 58, 60, 61, 63, 66, 68, 73, 74, 75, 76, 77, 78, 79, 80, 81, 85, 93, 110, 112, 138, 139, 140, 153, 171, 173, 174, 175, 176, 177, 178, 202, 206, 257, 258 }

B grade: { 1, 2, 3, 4, 7, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 27, 32, 33, 35, 38, 40, 41, 43, 46, 48, 55, 56, 57, 59, 62, 64, 65, 67, 69, 70, 71, 72, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 114, 116, 119, 121, 123, 125, 128, 130, 132, 134, 135, 136, 137, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 204, 225, 227, 255 }

C grade: { 26, 28, 29, 31, 34, 36, 37, 39, 42, 44, 45, 47, 106, 108, 109, 111, 113, 115, 117, 118, 120, 122, 124, 126, 127, 129, 131, 133, 203, 205, 207, 226, 228, 256 }

F grade: { 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 259, 260, 261, 262, 263 }

### 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 B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 73 73 56 96 208 327 0 196 normalized size 1 1. 0.77 1.32 2.85 4.48 0. 2.68 time (sec) N/A 0.076 0.341 0.041 1.202 1.85 0. 1.323
 Problem 2 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 47 47 73 73 184 246 0 162 normalized size 1 1. 1.55 1.55 3.91 5.23 0. 3.45 time (sec) N/A 0.055 0.05 0.034 1.152 1.999 0. 1.302
 Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B A F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 44 44 41 66 136 193 0 147 normalized size 1 1. 0.93 1.5 3.09 4.39 0. 3.34 time (sec) N/A 0.051 0.189 0.033 1.126 1.959 0. 1.27
 Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B A F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 25 25 45 43 90 115 0 107 normalized size 1 1. 1.8 1.72 3.6 4.6 0. 4.28 time (sec) N/A 0.032 0.045 0.033 1.108 1.905 0. 1.206
 Problem 5 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 26 26 52 44 54 483 0 70 normalized size 1 1. 2. 1.69 2.08 18.58 0. 2.69 time (sec) N/A 0.033 0.027 0.037 1.08 2.084 0. 1.33
 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 24 24 24 23 53 238 0 61 normalized size 1 1. 1. 0.96 2.21 9.92 0. 2.54 time (sec) N/A 0.033 0.02 0.036 1.141 1.886 0. 1.264
 Problem 7 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 51 51 87 50 205 2480 0 153 normalized size 1 1. 1.71 0.98 4.02 48.63 0. 3. time (sec) N/A 0.059 0.046 0.044 1.101 2.219 0. 1.208
 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 44 44 61 55 153 657 0 108 normalized size 1 1. 1.39 1.25 3.48 14.93 0. 2.45 time (sec) N/A 0.043 0.068 0.046 1.164 2.04 0. 1.215
 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 118 118 94 166 398 1021 0 398 normalized size 1 1. 0.8 1.41 3.37 8.65 0. 3.37 time (sec) N/A 0.133 1.374 0.049 1.118 2.068 0. 1.726
 Problem 10 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 71 162 358 664 0 392 normalized size 1 1. 0.92 2.1 4.65 8.62 0. 5.09 time (sec) N/A 0.098 0.517 0.052 1.192 2.055 0. 1.646
 Problem 11 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 79 79 70 118 293 747 0 290 normalized size 1 1. 0.89 1.49 3.71 9.46 0. 3.67 time (sec) N/A 0.111 0.85 0.05 1.243 2.059 0. 1.465
 Problem 12 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 49 49 46 113 231 424 0 219 normalized size 1 1. 0.94 2.31 4.71 8.65 0. 4.47 time (sec) N/A 0.053 0.308 0.046 1.137 2.058 0. 1.371
 Problem 13 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 51 51 50 97 265 2331 0 170 normalized size 1 1. 0.98 1.9 5.2 45.71 0. 3.33 time (sec) N/A 0.065 0.155 0.05 1.042 2.003 0. 1.335
 Problem 14 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 46 46 43 68 184 683 0 116 normalized size 1 1. 0.93 1.48 4. 14.85 0. 2.52 time (sec) N/A 0.057 0.449 0.048 1.054 1.859 0. 1.35
 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 82 82 96 103 244 6384 0 227 normalized size 1 1. 1.17 1.26 2.98 77.85 0. 2.77 time (sec) N/A 0.119 1.54 0.062 1.057 2.32 0. 1.373
 Problem 16 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 72 72 59 81 284 1011 0 193 normalized size 1 1. 0.82 1.12 3.94 14.04 0. 2.68 time (sec) N/A 0.079 0.48 0.059 1.051 1.932 0. 1.417
 Problem 17 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 182 182 125 246 648 2273 0 684 normalized size 1 1. 0.69 1.35 3.56 12.49 0. 3.76 time (sec) N/A 0.222 3.978 0.053 1.077 2.075 0. 2.748
 Problem 18 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 105 105 91 287 593 1388 0 597 normalized size 1 1. 0.87 2.73 5.65 13.22 0. 5.69 time (sec) N/A 0.123 0.291 0.052 1.101 1.967 0. 2.437
 Problem 19 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 122 139 95 180 509 1854 0 533 normalized size 1 1.14 0.78 1.48 4.17 15.2 0. 4.37 time (sec) N/A 0.185 2.159 0.053 1.1 2.102 0. 2.176
 Problem 20 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 70 70 63 219 433 959 0 435 normalized size 1 1. 0.9 3.13 6.19 13.7 0. 6.21 time (sec) N/A 0.068 0.829 0.049 1.092 1.984 0. 1.774
 Problem 21 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 84 84 79 186 756 5895 0 354 normalized size 1 1. 0.94 2.21 9. 70.18 0. 4.21 time (sec) N/A 0.084 0.302 0.052 1.05 2.251 0. 1.643
 Problem 22 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 64 64 70 141 470 1449 0 273 normalized size 1 1. 1.09 2.2 7.34 22.64 0. 4.27 time (sec) N/A 0.064 0.679 0.053 1.113 1.875 0. 1.713
 Problem 23 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 152 152 127 174 544 12984 0 379 normalized size 1 1. 0.84 1.14 3.58 85.42 0. 2.49 time (sec) N/A 0.225 6.175 0.063 1.093 2.476 0. 1.77
 Problem 24 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 98 98 87 136 666 2385 0 347 normalized size 1 1. 0.89 1.39 6.8 24.34 0. 3.54 time (sec) N/A 0.097 1.218 0.058 1.158 2.14 0. 1.783
 Problem 25 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 118 118 93 865 0 5158 0 406 normalized size 1 1. 0.79 7.33 0. 43.71 0. 3.44 time (sec) N/A 0.172 0.254 0.108 0. 2.314 0. 2.395
 Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 75 75 135 202 0 3729 0 5603 normalized size 1 1. 1.8 2.69 0. 49.72 0. 74.71 time (sec) N/A 0.128 0.539 0.069 0. 2.451 0. 1.888
 Problem 27 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 78 78 67 605 0 2475 0 238 normalized size 1 1. 0.86 7.76 0. 31.73 0. 3.05 time (sec) N/A 0.104 0.142 0.076 0. 2.441 0. 1.658
 Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 53 53 107 104 0 1906 0 6017 normalized size 1 1. 2.02 1.96 0. 35.96 0. 113.53 time (sec) N/A 0.063 0.242 0.055 0. 2.201 0. 1.559
 Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C A F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 55 55 123 69 0 1673 0 5242 normalized size 1 1. 2.24 1.25 0. 30.42 0. 95.31 time (sec) N/A 0.078 0.199 0.063 0. 2.395 0. 1.526
 Problem 30 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 48 48 48 413 0 1636 0 93 normalized size 1 1. 1. 8.6 0. 34.08 0. 1.94 time (sec) N/A 0.063 0.115 0.076 0. 2.204 0. 1.42
 Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 85 85 170 181 0 4872 0 7173 normalized size 1 1. 2. 2.13 0. 57.32 0. 84.39 time (sec) N/A 0.119 0.638 0.077 0. 2.651 0. 1.822
 Problem 32 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 70 70 71 750 0 4307 0 178 normalized size 1 1. 1.01 10.71 0. 61.53 0. 2.54 time (sec) N/A 0.088 0.289 0.089 0. 2.386 0. 1.419
 Problem 33 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 192 192 132 1246 0 17565 0 709 normalized size 1 1. 0.69 6.49 0. 91.48 0. 3.69 time (sec) N/A 0.252 0.933 0.119 0. 3.304 0. 3.392
 Problem 34 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 124 124 160 267 0 12417 0 8694 normalized size 1 1. 1.29 2.15 0. 100.14 0. 70.11 time (sec) N/A 0.218 1.22 0.095 0. 3.063 0. 2.472
 Problem 35 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 132 132 105 1128 0 9441 0 540 normalized size 1 1. 0.8 8.55 0. 71.52 0. 4.09 time (sec) N/A 0.165 0.65 0.099 0. 2.677 0. 2.253
 Problem 36 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 92 92 133 167 0 5933 0 6742 normalized size 1 1. 1.45 1.82 0. 64.49 0. 73.28 time (sec) N/A 0.075 0.684 0.079 0. 2.585 0. 1.698
 Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 103 103 175 331 0 6604 0 7329 normalized size 1 1. 1.7 3.21 0. 64.12 0. 71.16 time (sec) N/A 0.144 0.663 0.092 0. 3.284 0. 1.704
 Problem 38 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 82 82 86 552 0 6218 0 306 normalized size 1 1. 1.05 6.73 0. 75.83 0. 3.73 time (sec) N/A 0.076 0.42 0.102 0. 2.409 0. 1.653
 Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 141 141 203 367 0 15776 0 5650 normalized size 1 1. 1.44 2.6 0. 111.89 0. 40.07 time (sec) N/A 0.209 4.089 0.108 0. 3.304 0. 1.973
 Problem 40 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 113 113 114 1012 0 12585 0 298 normalized size 1 1. 1.01 8.96 0. 111.37 0. 2.64 time (sec) N/A 0.154 0.775 0.119 0. 2.786 0. 1.61
 Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 240 240 184 2366 0 0 0 1246 normalized size 1 1. 0.77 9.86 0. 0. 0. 5.19 time (sec) N/A 0.345 0.763 0.128 0. 0. 0. 4.662
 Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F(-2) F(-1) F(-1) C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 166 166 227 341 0 0 0 8107 normalized size 1 1. 1.37 2.05 0. 0. 0. 48.84 time (sec) N/A 0.286 1.812 0.109 0. 0. 0. 3.143
 Problem 43 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 185 185 158 2110 0 29831 0 788 normalized size 1 1. 0.85 11.41 0. 161.25 0. 4.26 time (sec) N/A 0.251 1.209 0.115 0. 3.844 0. 3.103
 Problem 44 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 126 126 157 252 0 17194 0 8412 normalized size 1 1. 1.25 2. 0. 136.46 0. 66.76 time (sec) N/A 0.097 1.737 0.089 0. 3.084 0. 2.003
 Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 156 156 236 1132 0 25141 0 9281 normalized size 1 1. 1.51 7.26 0. 161.16 0. 59.49 time (sec) N/A 0.254 1.288 0.104 0. 4.358 0. 1.981
 Problem 46 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 112 112 109 816 0 19301 0 474 normalized size 1 1. 0.97 7.29 0. 172.33 0. 4.23 time (sec) N/A 0.087 0.882 0.116 0. 3.142 0. 1.916
 Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B F F(-1) F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 196 196 269 1083 0 0 0 8479 normalized size 1 1. 1.37 5.53 0. 0. 0. 43.26 time (sec) N/A 0.334 4.095 0.118 0. 0. 0. 2.445
 Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F(-2) F(-1) F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 151 151 149 1416 0 0 0 549 normalized size 1 1. 0.99 9.38 0. 0. 0. 3.64 time (sec) N/A 0.201 1.244 0.135 0. 0. 0. 1.918
 Problem 49 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 132 132 92 122 262 4209 0 278 normalized size 1 1. 0.7 0.92 1.98 31.89 0. 2.11 time (sec) N/A 0.172 0.19 0.047 1.608 2.49 0. 1.374
 Problem 50 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 98 98 104 129 235 2942 0 192 normalized size 1 1. 1.06 1.32 2.4 30.02 0. 1.96 time (sec) N/A 0.12 0.257 0.043 1.541 2.334 0. 1.3
 Problem 51 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 100 100 69 79 190 2453 0 192 normalized size 1 1. 0.69 0.79 1.9 24.53 0. 1.92 time (sec) N/A 0.117 0.107 0.041 1.584 2.351 0. 1.266
 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 63 63 72 85 142 1473 0 128 normalized size 1 1. 1.14 1.35 2.25 23.38 0. 2.03 time (sec) N/A 0.076 0.121 0.04 1.611 2.361 0. 1.217
 Problem 53 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 49 49 75 65 112 1453 0 100 normalized size 1 1. 1.53 1.33 2.29 29.65 0. 2.04 time (sec) N/A 0.074 0.031 0.049 1.516 2.634 0. 1.217
 Problem 54 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 29 29 29 34 59 375 0 61 normalized size 1 1. 1. 1.17 2.03 12.93 0. 2.1 time (sec) N/A 0.034 0.025 0.05 1.043 2.445 0. 1.212
 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 71 71 95 62 211 3216 0 193 normalized size 1 1. 1.34 0.87 2.97 45.3 0. 2.72 time (sec) N/A 0.09 0.026 0.059 1.531 2.795 0. 1.222
 Problem 56 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 56 56 74 60 248 4702 0 201 normalized size 1 1. 1.32 1.07 4.43 83.96 0. 3.59 time (sec) N/A 0.058 0.197 0.061 1.577 2.454 0. 1.236
 Problem 57 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 170 206 156 243 512 13666 0 508 normalized size 1 1.21 0.92 1.43 3.01 80.39 0. 2.99 time (sec) N/A 0.297 2.809 0.058 1.586 2.942 0. 2.273
 Problem 58 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 182 182 121 296 470 9211 0 405 normalized size 1 1. 0.66 1.63 2.58 50.61 0. 2.23 time (sec) N/A 0.225 0.72 0.058 1.555 2.777 0. 2.041
 Problem 59 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 129 159 137 173 406 9671 0 402 normalized size 1 1.23 1.06 1.34 3.15 74.97 0. 3.12 time (sec) N/A 0.205 1.55 0.056 1.578 2.871 0. 1.836
 Problem 60 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 123 123 90 225 342 5998 0 289 normalized size 1 1. 0.73 1.83 2.78 48.76 0. 2.35 time (sec) N/A 0.147 0.393 0.054 1.584 2.512 0. 1.617
 Problem 61 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 98 98 106 180 603 6643 0 240 normalized size 1 1. 1.08 1.84 6.15 67.79 0. 2.45 time (sec) N/A 0.136 0.157 0.072 1.535 2.673 0. 1.511
 Problem 62 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 47 47 94 105 346 1334 0 165 normalized size 1 1. 2. 2.23 7.36 28.38 0. 3.51 time (sec) N/A 0.058 0.221 0.067 1.055 2.178 0. 1.613
 Problem 63 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 107 107 138 154 510 12523 0 259 normalized size 1 1. 1.29 1.44 4.77 117.04 0. 2.42 time (sec) N/A 0.16 0.151 0.085 1.561 2.992 0. 1.593
 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 97 97 147 146 632 11420 0 336 normalized size 1 1. 1.52 1.51 6.52 117.73 0. 3.46 time (sec) N/A 0.098 0.186 0.083 1.582 2.815 0. 1.693
 Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B F(-1) F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 275 306 294 385 873 0 0 956 normalized size 1 1.11 1.07 1.4 3.17 0. 0. 3.48 time (sec) N/A 0.494 6.239 0.076 1.807 0. 0. 4.874
 Problem 66 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 351 351 291 554 815 23883 0 811 normalized size 1 1. 0.83 1.58 2.32 68.04 0. 2.31 time (sec) N/A 0.35 6.545 0.13 1.787 3.607 0. 3.952
 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 220 241 244 289 734 25608 0 799 normalized size 1 1.1 1.11 1.31 3.34 116.4 0. 3.63 time (sec) N/A 0.315 6.22 0.073 1.751 4.052 0. 3.473
 Problem 68 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 269 269 233 458 653 17484 0 655 normalized size 1 1. 0.87 1.7 2.43 65. 0. 2.43 time (sec) N/A 0.249 6.289 0.067 1.747 3.985 0. 2.633
 Problem 69 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 219 219 154 387 883 19499 0 570 normalized size 1 1. 0.7 1.77 4.03 89.04 0. 2.6 time (sec) N/A 0.264 2.886 0.096 1.72 3.6 0. 2.286
 Problem 70 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 71 71 113 223 917 3071 0 420 normalized size 1 1. 1.59 3.14 12.92 43.25 0. 5.92 time (sec) N/A 0.065 0.687 0.086 1.195 2.234 0. 2.492
 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 232 232 243 334 791 30318 0 586 normalized size 1 1. 1.05 1.44 3.41 130.68 0. 2.53 time (sec) N/A 0.316 6.316 0.099 1.778 3.905 0. 2.564
 Problem 72 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 138 138 213 275 1346 25978 0 590 normalized size 1 1. 1.54 1.99 9.75 188.25 0. 4.28 time (sec) N/A 0.115 0.169 0.106 1.81 3.63 0. 2.877
 Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F F(-1) F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 491 491 645 603 0 0 0 489 normalized size 1 1. 1.31 1.23 0. 0. 0. 1. time (sec) N/A 0.892 4.377 0.128 0. 0. 0. 2.33
 Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade N/A A A A A F(-1) F(-1) A veriﬁed N/A N/A Yes TBD TBD TBD TBD TBD size 32 0 826 346 0 0 0 473 normalized size 1 0. 25.81 10.81 0. 0. 0. 14.78 time (sec) N/A 0.046 0.484 0.11 0. 0. 0. 2.058
 Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F C F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 384 384 423 356 0 22579 0 301 normalized size 1 1. 1.1 0.93 0. 58.8 0. 0.78 time (sec) N/A 0.629 3.391 0.109 0. 16.062 0. 1.784
 Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade N/A A A A A F(-1) F(-1) A veriﬁed N/A N/A Yes TBD TBD TBD TBD TBD size 30 0 409 164 0 0 0 263 normalized size 1 0. 13.63 5.47 0. 0. 0. 8.77 time (sec) N/A 0.028 0.226 0.108 0. 0. 0. 1.621
 Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade N/A A A A A F(-1) A A veriﬁed N/A N/A Yes TBD TBD TBD TBD TBD size 30 0 319 98 0 0 0 207 normalized size 1 0. 10.63 3.27 0. 0. 0. 6.9 time (sec) N/A 0.041 0.158 0.105 0. 0. 0. 1.453
 Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F B F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 157 157 190 121 0 1801 0 28 normalized size 1 1. 1.21 0.77 0. 11.47 0. 0.18 time (sec) N/A 0.14 0.135 0.112 0. 2.665 0. 1.33
 Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade N/A A A A A F(-1) A A veriﬁed N/A N/A Yes TBD TBD TBD TBD TBD size 32 0 201 144 0 0 0 0 normalized size 1 0. 6.28 4.5 0. 0. 0. 0. time (sec) N/A 0.047 0.362 0.125 0. 0. 0. 0.
 Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C C F C F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 215 215 322 187 0 4415 0 243 normalized size 1 1. 1.5 0.87 0. 20.53 0. 1.13 time (sec) N/A 0.239 3.157 0.131 0. 17.102 0. 1.423
 Problem 81 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 63 63 44 82 140 169 0 144 normalized size 1 1. 0.7 1.3 2.22 2.68 0. 2.29 time (sec) N/A 0.05 0.163 0.039 1.144 1.825 0. 1.279
 Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B A F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 30 30 44 53 112 119 0 127 normalized size 1 1. 1.47 1.77 3.73 3.97 0. 4.23 time (sec) N/A 0.036 0.016 0.036 1.097 1.813 0. 1.246
 Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B A F B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 33 33 32 54 93 80 0 109 normalized size 1 1. 0.97 1.64 2.82 2.42 0. 3.3 time (sec) N/A 0.039 0.057 0.033 1.11 1.861 0. 1.219
 Problem 84 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 27 27 47 37 74 296 0 76 normalized size 1 1. 1.74 1.37 2.74 10.96 0. 2.81 time (sec) N/A 0.032 0.029 0.034 1.61 1.865 0. 1.265
 Problem 85 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 40 40 48 65 108 883 0 85 normalized size 1 1. 1.2 1.62 2.7 22.08 0. 2.12 time (sec) N/A 0.031 0.023 0.026 1.65 1.96 0. 1.211
 Problem 86 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 28 28 28 53 46 424 0 80 normalized size 1 1. 1. 1.89 1.64 15.14 0. 2.86 time (sec) N/A 0.029 0.011 0.036 1.133 1.818 0. 1.189
 Problem 87 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 66 66 93 103 244 2826 0 178 normalized size 1 1. 1.41 1.56 3.7 42.82 0. 2.7 time (sec) N/A 0.046 0.029 0.044 1.616 2.012 0. 1.226
 Problem 88 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 48 48 86 75 501 934 0 128 normalized size 1 1. 1.79 1.56 10.44 19.46 0. 2.67 time (sec) N/A 0.04 0.048 0.044 1.108 1.92 0. 1.343
 Problem 89 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 85 85 63 124 231 234 0 255 normalized size 1 1. 0.74 1.46 2.72 2.75 0. 3. time (sec) N/A 0.087 0.293 0.04 1.035 1.96 0. 1.933
 Problem 90 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 54 54 71 117 217 1314 0 221 normalized size 1 1. 1.31 2.17 4.02 24.33 0. 4.09 time (sec) N/A 0.06 0.443 0.043 1.674 1.926 0. 1.791
 Problem 91 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 51 51 54 96 189 261 0 230 normalized size 1 1. 1.06 1.88 3.71 5.12 0. 4.51 time (sec) N/A 0.076 0.371 0.04 1.205 2.008 0. 1.689
 Problem 92 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 60 60 54 122 205 1967 0 185 normalized size 1 1. 0.9 2.03 3.42 32.78 0. 3.08 time (sec) N/A 0.082 0.179 0.043 1.749 1.993 0. 1.666
 Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B B B F A veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 91 91 427 173 269 3433 0 212 normalized size 1 1. 4.69 1.9 2.96 37.73 0. 2.33 time (sec) N/A 0.085 7.22 0.036 1.615 2.191 0. 1.396
 Problem 94 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 49 49 49 126 72 1023 0 228 normalized size 1 1. 1. 2.57 1.47 20.88 0. 4.65 time (sec) N/A 0.053 0.18 0.052 1.165 1.862 0. 1.411
 Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B B B F B veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 125 125 792 236 466 7337 0 393 normalized size 1 1. 6.34 1.89 3.73 58.7 0. 3.14 time (sec) N/A 0.152 8.641 0.056 1.72 2.294 0. 1.489
 Problem 96 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 83 158 1253 1829 0 321 normalized size 1 1. 1.09 2.08 16.49 24.07 0. 4.22 time (sec) N/A 0.07 0.515 0.057 1.211 1.904 0. 1.456
 Problem 97 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 91 91 81 184 360 539 0 385 normalized size 1 1. 0.89 2.02 3.96 5.92 0. 4.23 time (sec) N/A 0.13 0.668 0.042 1.167 2.04 0. 2.677
 Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B B B F(-1) B veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 87 87 494 227 383 4523 0 377 normalized size 1 1. 5.68 2.61 4.4 51.99 0. 4.33 time (sec) N/A 0.105 6.901 0.044 1.665 2.207 0. 2.42
 Problem 99 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 78 78 69 148 346 903 0 360 normalized size 1 1. 0.88 1.9 4.44 11.58 0. 4.62 time (sec) N/A 0.09 0.85 0.047 1.155 2.042 0. 2.061
 Problem 100 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 99 99 89 257 398 5933 0 347 normalized size 1 1. 0.9 2.6 4.02 59.93 0. 3.51 time (sec) N/A 0.116 0.363 0.048 1.701 2.189 0. 1.832
 Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C B B B F B veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 149 149 1341 334 489 8768 0 433 normalized size 1 1. 9. 2.24 3.28 58.85 0. 2.91 time (sec) N/A 0.154 17.289 0.041 1.687 2.322 0. 1.589
 Problem 102 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 67 67 67 227 96 2034 0 468 normalized size 1 1. 1. 3.39 1.43 30.36 0. 6.99 time (sec) N/A 0.061 0.167 0.065 1.054 1.99 0. 1.705
 Problem 103 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 198 198 158 421 747 16058 0 698 normalized size 1 1. 0.8 2.13 3.77 81.1 0. 3.53 time (sec) N/A 0.239 11.677 0.071 1.668 2.568 0. 1.704
 Problem 104 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 102 102 218 269 2493 3218 0 603 normalized size 1 1. 2.14 2.64 24.44 31.55 0. 5.91 time (sec) N/A 0.089 0.826 0.124 1.172 2.014 0. 1.827
 Problem 105 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 120 120 115 857 0 5515 0 440 normalized size 1 1. 0.96 7.14 0. 45.96 0. 3.67 time (sec) N/A 0.168 0.275 0.088 0. 2.574 0. 2.795
 Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 80 80 79 468 0 4604 0 6807 normalized size 1 1. 0.99 5.85 0. 57.55 0. 85.09 time (sec) N/A 0.109 0.396 0.087 0. 2.374 0. 2.115
 Problem 107 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 77 77 77 608 0 2520 0 232 normalized size 1 1. 1. 7.9 0. 32.73 0. 3.01 time (sec) N/A 0.103 0.148 0.083 0. 2.285 0. 1.853
 Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 53 53 53 315 0 2040 0 6017 normalized size 1 1. 1. 5.94 0. 38.49 0. 113.53 time (sec) N/A 0.07 0.092 0.071 0. 2.462 0. 1.584
 Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 36 36 36 235 0 1385 0 6607 normalized size 1 1. 1. 6.53 0. 38.47 0. 183.53 time (sec) N/A 0.044 0.037 0.059 0. 2.398 0. 1.57
 Problem 110 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 32 32 32 363 0 1199 0 59 normalized size 1 1. 1. 11.34 0. 37.47 0. 1.84 time (sec) N/A 0.056 0.053 0.07 0. 2.396 0. 1.401
 Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 55 55 55 494 0 1494 0 4938 normalized size 1 1. 1. 8.98 0. 27.16 0. 89.78 time (sec) N/A 0.073 0.195 0.073 0. 2.584 0. 1.793
 Problem 112 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 50 50 50 648 0 1750 0 113 normalized size 1 1. 1. 12.96 0. 35. 0. 2.26 time (sec) N/A 0.07 0.133 0.068 0. 2.422 0. 1.38
 Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 86 86 79 836 0 4316 0 5747 normalized size 1 1. 0.92 9.72 0. 50.19 0. 66.83 time (sec) N/A 0.12 0.557 0.076 0. 2.825 0. 1.844
 Problem 114 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 71 1077 0 5189 0 207 normalized size 1 1. 0.95 14.36 0. 69.19 0. 2.76 time (sec) N/A 0.092 0.341 0.078 0. 2.65 0. 1.449
 Problem 115 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 128 128 111 875 0 16069 0 9686 normalized size 1 1. 0.87 6.84 0. 125.54 0. 75.67 time (sec) N/A 0.182 1.053 0.105 0. 3.215 0. 2.513
 Problem 116 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 140 140 110 1146 0 10118 0 606 normalized size 1 1. 0.79 8.19 0. 72.27 0. 4.33 time (sec) N/A 0.194 0.748 0.107 0. 2.861 0. 2.307
 Problem 117 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 101 101 84 729 0 8197 0 8317 normalized size 1 1. 0.83 7.22 0. 81.16 0. 82.35 time (sec) N/A 0.139 0.697 0.096 0. 2.532 0. 1.88
 Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 83 83 78 666 0 4917 0 6892 normalized size 1 1. 0.94 8.02 0. 59.24 0. 83.04 time (sec) N/A 0.071 0.275 0.082 0. 2.302 0. 1.681
 Problem 119 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 66 66 63 498 0 3663 0 186 normalized size 1 1. 0.95 7.55 0. 55.5 0. 2.82 time (sec) N/A 0.066 0.239 0.096 0. 2.308 0. 1.618
 Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F B F C veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 72 72 69 375 0 4026 0 4585 normalized size 1 1. 0.96 5.21 0. 55.92 0. 63.68 time (sec) N/A 0.077 0.138 0.101 0. 2.274 0. 1.938