## 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, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314 }

#### 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, 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, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 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, 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, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 277, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314 }

B grade: { 40, 41, 42, 43, 44, 45, 134, 189, 278, 279, 280, 281 }

C grade: { 108, 109, 110, 111, 112, 276 }

#### 2.1.3 Maple

A grade: { 1, 5, 6, 7, 8, 12, 13, 14, 15, 19, 25, 30, 34, 35, 36, 37, 39, 51, 55, 56, 58, 64, 75, 81, 86, 98, 104, 105, 113, 114, 115, 116, 117, 121, 122, 126, 127, 129, 130, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 153, 168, 171, 180, 181, 183, 184, 185, 186, 187, 188, 190, 195, 196, 197, 198, 199, 200, 207, 209, 210, 211, 213, 214, 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, 247, 248, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 294, 296, 298, 299, 308, 309, 313, 314 }

B grade: { 24, 91, 118, 119, 120, 123, 124, 125, 128, 131, 160, 161, 162, 164, 165, 167, 170, 173, 174, 176, 177, 191, 208, 212, 246, 249, 278 }

C grade: { 9, 10, 11, 17, 18, 20, 21, 22, 23, 26, 27, 28, 29, 38, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 87, 88, 89, 90, 94, 95, 150, 151, 154, 155, 156, 157, 158, 159, 169, 172, 179, 182, 189, 192, 194, 201, 202, 204, 205, 215, 216, 218, 219, 276, 277, 307, 312 }

F grade: { 2, 3, 4, 16, 31, 32, 33, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 92, 93, 96, 97, 99, 100, 101, 102, 103, 106, 107, 108, 109, 110, 111, 112, 149, 152, 163, 166, 175, 178, 193, 203, 206, 217, 220, 263, 264, 265, 279, 280, 281, 293, 295, 297, 300, 301, 302, 303, 304, 305, 306, 310, 311 }

#### 2.1.4 Maxima

A grade: { 6, 7, 8, 12, 13, 14, 15, 20, 21, 25, 27, 29, 35, 36, 37, 38, 39, 51, 55, 56, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 81, 96, 105, 113, 114, 115, 116, 117, 122, 127, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 151, 153, 160, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 179, 180, 181, 183, 184, 185, 186, 187, 188, 190, 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, 222, 223, 224, 225, 226, 227, 228, 229, 230, 235, 236, 238, 239, 240, 241, 242, 243, 244, 245, 247, 248, 250, 254, 259, 262, 267, 268, 270, 271, 272, 273, 274, 275, 276, 282, 284, 285, 286, 287, 288, 289, 290, 291, 292, 294, 295, 296, 297, 298, 299, 302, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314

B grade: { 22, 23, 24, 26, 28, 58, 161, 162, 163, 176, 177, 178, 182, 189, 191, 192, 193, 194, 221, 237, 246, 269, 301, 303, 304 }

C grade: { 154, 155, 156, 157, 158, 159 }

F grade: { 1, 2, 3, 4, 5, 9, 10, 11, 16, 17, 18, 19, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 57, 59, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 118, 119, 120, 121, 123, 124, 125, 126, 128, 149, 150, 152, 231, 232, 233, 234, 249, 251, 252, 253, 255, 256, 257, 258, 260, 261, 263, 264, 265, 266, 277, 278, 279, 280, 281, 283, 293, 300 }

#### 2.1.5 FriCAS

A grade: { 1, 5, 6, 7, 8, 12, 13, 14, 15, 16, 19, 20, 21, 25, 26, 27, 29, 30, 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, 60, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 116, 117, 121, 122, 126, 127, 129, 130, 132, 133, 134, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 194, 201, 203, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 268, 271, 272, 273, 274, 275, 276, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 308, 309, 313, 314 }

B grade: { 9, 10, 11, 17, 18, 22, 23, 24, 28, 89, 90, 128, 131, 135, 136, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 191, 195, 196, 197, 198, 199, 200, 202, 218, 219, 220, 221, 222, 225, 246, 307, 312 }

C grade: { 113, 114, 115, 118, 119, 120, 123, 124, 125, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 305, 306, 310, 311 }

F grade: { 2, 3, 4, 31, 32, 33, 59, 65, 70, 76, 87, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 193, 263, 264, 265, 266, 267, 269, 270, 277, 278, 279, 301, 302, 303, 304 }

#### 2.1.6 Sympy

A grade: { 11, 12, 13, 14, 19, 23, 24, 25, 26, 34, 55, 60, 61, 62, 63, 64, 66, 67, 68, 69, 75, 81, 86, 117, 129, 130, 132, 137, 138, 139, 141, 142, 144, 145, 146, 147, 148, 153, 160, 182, 184, 187, 188, 190, 194, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 235, 236, 237, 239, 241, 242, 243, 244, 245, 247, 248, 250, 251, 252, 253, 258, 259, 260, 261, 262, 272, 273, 274, 275, 276, 282, 283, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 308, 309 }

B grade: { 131, 133, 140, 189, 192, 238, 240, 246 }

C grade: { 268, 270 }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 16, 17, 18, 20, 21, 22, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 65, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 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, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 134, 135, 136, 143, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 183, 185, 186, 191, 193, 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, 225, 234, 249, 254, 255, 256, 257, 263, 264, 265, 266, 267, 269, 271, 277, 278, 279, 280, 281, 284, 300, 301, 302, 303, 304, 305, 306, 307, 310, 311, 312, 313, 314 }

#### 2.1.7 Giac

A grade: { 5, 6, 7, 8, 11, 12, 13, 14, 15, 19, 25, 26, 27, 34, 35, 36, 37, 39, 46, 47, 48, 49, 50, 51, 55, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 85, 86, 88, 101, 102, 103, 104, 105, 106, 107, 117, 122, 127, 130, 132, 133, 135, 138, 139, 140, 142, 143, 144, 145, 146, 148, 150, 151, 152, 153, 160, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 194, 195, 196, 197, 198, 199, 200, 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, 251, 253, 254, 255, 257, 258, 259, 260, 261, 262, 265, 272, 273, 274, 275, 276, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 296, 301, 302, 304 }

B grade: { 9, 10, 23, 24, 28, 82, 83, 84, 89, 90, 91, 129, 131, 136, 141, 149, 221, 222, 250, 252, 256, 294, 298, 303 }

C grade: { 154, 155, 156, 157, 158, 159 }

F grade: { 1, 2, 3, 4, 16, 17, 18, 20, 21, 22, 29, 30, 31, 32, 33, 38, 40, 41, 42, 43, 44, 45, 52, 53, 54, 59, 65, 70, 76, 87, 92, 93, 94, 95, 96, 97, 98, 99, 100, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 119, 120, 121, 123, 124, 125, 126, 128, 134, 137, 147, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 191, 193, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 249, 263, 264, 266, 267, 268, 269, 270, 271, 277, 278, 279, 280, 281, 293, 295, 297, 299, 300, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314 }

### 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 N/A A A A F(-2) A F(-1) F(-2) veriﬁed N/A N/A N/A TBD TBD TBD TBD TBD size 75 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.247 1.18 0.48 0. 0. 0. 0.
 Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 231 231 223 0 0 0 0 0 normalized size 1 1. 0.97 0. 0. 0. 0. 0. time (sec) N/A 0.348 0.739 2.418 0. 0. 0. 0.
 Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 156 156 149 0 0 0 0 0 normalized size 1 1. 0.96 0. 0. 0. 0. 0. time (sec) N/A 0.274 0.414 4.449 0. 0. 0. 0.
 Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 81 81 77 0 0 0 0 0 normalized size 1 1. 0.95 0. 0. 0. 0. 0. time (sec) N/A 0.157 0.156 3.949 0. 0. 0. 0.
 Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F(-2) A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 15 15 15 16 0 74 0 22 normalized size 1 1. 1. 1.07 0. 4.93 0. 1.47 time (sec) N/A 0.022 0.002 0.003 0. 1.947 0. 1.301
 Problem 6 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 67 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.245 0.126 8.273 0. 0. 0. 0.
 Problem 7 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 69 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.289 0.665 6.506 0. 0. 0. 0.
 Problem 8 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 71 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.245 1.472 49.67 0. 0. 0. 0.
 Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) B F(-2) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 272 272 230 61910 0 1558 0 1034 normalized size 1 1. 0.85 227.61 0. 5.73 0. 3.8 time (sec) N/A 0.305 0.224 5.05 0. 2.162 0. 1.341
 Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) B F(-2) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 125 125 115 14983 0 659 0 386 normalized size 1 1. 0.92 119.86 0. 5.27 0. 3.09 time (sec) N/A 0.166 0.105 1.375 0. 1.856 0. 1.657
 Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) B A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 41 41 41 2146 0 213 68 99 normalized size 1 1. 1. 52.34 0. 5.2 1.66 2.41 time (sec) N/A 0.077 0.033 0.303 0. 1.956 10.166 1.278
 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 15 15 15 14 18 43 51 18 normalized size 1 1. 1. 0.93 1.2 2.87 3.4 1.2 time (sec) N/A 0.007 0.001 0.003 1.003 1.839 1.689 1.303
 Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade N/A A A A A A A A veriﬁed N/A N/A N/A TBD TBD TBD TBD TBD size 66 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.192 1.409 1.777 0. 0. 0. 0.
 Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade N/A A A A A A A A veriﬁed N/A N/A N/A TBD TBD TBD TBD TBD size 67 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.196 1.567 51.749 0. 0. 0. 0.
 Problem 15 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 67 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.177 2.872 56.374 0. 0. 0. 0.
 Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) A F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 26 26 26 0 0 107 0 0 normalized size 1 1. 1. 0. 0. 4.12 0. 0. time (sec) N/A 0.171 0.089 0.5 0. 1.992 0. 0.
 Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) B F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 22 22 22 204 0 174 0 0 normalized size 1 1. 1. 9.27 0. 7.91 0. 0. time (sec) N/A 0.173 0.038 0.197 0. 2.052 0. 0.
 Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) B F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 22 22 22 135 0 115 0 0 normalized size 1 1. 1. 6.14 0. 5.23 0. 0. time (sec) N/A 0.109 0.033 0.162 0. 1.959 0. 0.
 Problem 19 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 16 16 16 17 0 82 58 23 normalized size 1 1. 1. 1.06 0. 5.12 3.62 1.44 time (sec) N/A 0.035 0.015 0.003 0. 1.999 61.902 1.315
 Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C A A F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 17 17 17 213 30 51 0 0 normalized size 1 1. 1. 12.53 1.76 3. 0. 0. time (sec) N/A 0.185 0.233 0.164 1.56 1.824 0. 0.
 Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C A A F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 20 68 28 51 0 0 normalized size 1 1. 1. 3.4 1.4 2.55 0. 0. time (sec) N/A 0.182 0.04 0.129 1.716 1.99 0. 0.
 Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C B B F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 22 22 22 68 66 116 0 0 normalized size 1 1. 1. 3.09 3. 5.27 0. 0. time (sec) N/A 0.18 0.04 0.184 2.132 2.049 0. 0.
 Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C B B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 20 16321 285 478 221 267 normalized size 1 1. 1. 816.05 14.25 23.9 11.05 13.35 time (sec) N/A 0.152 0.018 1.223 1.027 1.845 13.441 1.291
 Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B B B A B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 38 63 100 230 117 122 normalized size 1 1. 1.9 3.15 5. 11.5 5.85 6.1 time (sec) N/A 0.093 0.004 0.018 1.05 1.962 6.32 1.231
 Problem 25 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 14 14 14 15 19 59 60 27 normalized size 1 1. 1. 1.07 1.36 4.21 4.29 1.93 time (sec) N/A 0.009 0.002 0.003 1.015 1.882 1.676 1.241
 Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C B A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 15 15 15 428 43 84 48 38 normalized size 1 1. 1. 28.53 2.87 5.6 3.2 2.53 time (sec) N/A 0.082 0.095 0.066 1.185 1.812 2.393 1.149
 Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C A A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 18 18 18 451 42 84 0 42 normalized size 1 1. 1. 25.06 2.33 4.67 0. 2.33 time (sec) N/A 0.133 0.013 0.072 1.217 1.861 0. 1.451
 Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C B B F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 20 451 128 254 0 413 normalized size 1 1. 1. 22.55 6.4 12.7 0. 20.65 time (sec) N/A 0.16 0.014 0.085 1.425 2.028 0. 1.278
 Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C A A F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 19 19 23 216 35 59 0 0 normalized size 1 1. 1.21 11.37 1.84 3.11 0. 0. time (sec) N/A 0.321 0.46 0.191 1.543 1.926 0. 0.
 Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade N/A A A A F(-2) A F(-1) F(-2) veriﬁed N/A N/A N/A TBD TBD TBD TBD TBD size 80 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.231 1.801 0.487 0. 0. 0. 0.
 Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 331 331 445 0 0 0 0 0 normalized size 1 1. 1.34 0. 0. 0. 0. 0. time (sec) N/A 0.504 1.551 7.961 0. 0. 0. 0.
 Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 235 235 298 0 0 0 0 0 normalized size 1 1. 1.27 0. 0. 0. 0. 0. time (sec) N/A 0.395 0.927 17.253 0. 0. 0. 0.
 Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 139 139 157 0 0 0 0 0 normalized size 1 1. 1.13 0. 0. 0. 0. 0. time (sec) N/A 0.171 0.386 10.297 0. 0. 0. 0.
 Problem 34 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 25 25 25 26 0 107 53 36 normalized size 1 1. 1. 1.04 0. 4.28 2.12 1.44 time (sec) N/A 0.034 0.02 0.007 0. 1.862 60.999 1.313
 Problem 35 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 72 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.267 4.747 35.223 0. 0. 0. 0.
 Problem 36 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 74 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.282 7.308 7.905 0. 0. 0. 0.
 Problem 37 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 76 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.249 66.919 91.029 0. 0. 0. 0.
 Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C A A F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 26 26 26 158 42 80 0 0 normalized size 1 1. 1. 6.08 1.62 3.08 0. 0. time (sec) N/A 0.245 0.357 0.128 1.674 1.935 0. 0.
 Problem 39 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 60 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.153 76.601 0.368 0. 0. 0. 0.
 Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B F F(-2) A F(-1) F(-2) veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 49 49 625 0 0 95 0 0 normalized size 1 1. 12.76 0. 0. 1.94 0. 0. time (sec) N/A 0.099 0.433 180. 0. 1.948 0. 0.
 Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B F F(-2) A F(-1) F(-2) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 50 50 642 0 0 93 0 0 normalized size 1 1. 12.84 0. 0. 1.86 0. 0. time (sec) N/A 0.087 0.366 180. 0. 1.951 0. 0.
 Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B F F(-2) A F(-2) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 53 53 320 0 0 109 0 0 normalized size 1 1. 6.04 0. 0. 2.06 0. 0. time (sec) N/A 0.096 0.209 180. 0. 1.946 0. 0.
 Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B F F(-2) A F(-2) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 52 52 316 0 0 111 0 0 normalized size 1 1. 6.08 0. 0. 2.13 0. 0. time (sec) N/A 0.073 0.188 180. 0. 1.843 0. 0.
 Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B F F(-2) A F(-2) F(-1) veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 49 49 641 0 0 111 0 0 normalized size 1 1. 13.08 0. 0. 2.27 0. 0. time (sec) N/A 0.102 0.311 180. 0. 1.929 0. 0.
 Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A B F F(-2) A F(-2) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 50 50 645 0 0 109 0 0 normalized size 1 1. 12.9 0. 0. 2.18 0. 0. time (sec) N/A 0.078 0.251 180. 0. 1.848 0. 0.
 Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 67 67 56 0 0 204 0 112 normalized size 1 1. 0.84 0. 0. 3.04 0. 1.67 time (sec) N/A 0.057 0.131 180. 0. 2.052 0. 1.31
 Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 79 79 59 0 0 261 0 150 normalized size 1 1. 0.75 0. 0. 3.3 0. 1.9 time (sec) N/A 0.061 0.157 0.185 0. 1.978 0. 1.427
 Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 55 55 49 0 0 161 0 76 normalized size 1 1. 0.89 0. 0. 2.93 0. 1.38 time (sec) N/A 0.049 0.059 0.063 0. 1.879 0. 1.377
 Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 55 55 49 0 0 161 0 76 normalized size 1 1. 0.89 0. 0. 2.93 0. 1.38 time (sec) N/A 0.035 0.057 0.061 0. 1.855 0. 1.319
 Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 45 45 43 0 0 144 0 57 normalized size 1 1. 0.96 0. 0. 3.2 0. 1.27 time (sec) N/A 0.03 0.048 0.066 0. 1.975 0. 1.324
 Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 32 32 40 48 86 124 0 73 normalized size 1 1. 1.25 1.5 2.69 3.88 0. 2.28 time (sec) N/A 0.017 0.011 0.01 1.028 1.874 0. 1.3
 Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 48 48 45 0 0 123 0 0 normalized size 1 1. 0.94 0. 0. 2.56 0. 0. time (sec) N/A 0.047 0.041 0.066 0. 1.895 0. 0.
 Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 55 55 49 0 0 136 0 0 normalized size 1 1. 0.89 0. 0. 2.47 0. 0. time (sec) N/A 0.046 0.042 0.053 0. 1.712 0. 0.
 Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 55 55 49 0 0 136 0 0 normalized size 1 1. 0.89 0. 0. 2.47 0. 0. time (sec) N/A 0.047 0.043 0.061 0. 1.539 0. 0.
 Problem 55 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 22 22 22 26 31 81 19 35 normalized size 1 1. 1. 1.18 1.41 3.68 0.86 1.59 time (sec) N/A 0.007 0.014 0.009 1.142 1.646 1.314 1.205
 Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 20 20 22 23 30 68 0 43 normalized size 1 1. 1.1 1.15 1.5 3.4 0. 2.15 time (sec) N/A 0.02 0.007 0.006 0.994 1.639 0. 1.303
 Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 40 40 39 0 0 126 0 49 normalized size 1 1. 0.98 0. 0. 3.15 0. 1.22 time (sec) N/A 0.022 0.02 0.056 0. 1.633 0. 1.214
 Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A B A F A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 27 27 34 35 74 105 0 58 normalized size 1 1. 1.26 1.3 2.74 3.89 0. 2.15 time (sec) N/A 0.021 0.01 0.006 1.017 1.524 0. 1.367
 Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 66 66 48 0 0 0 0 0 normalized size 1 1. 0.73 0. 0. 0. 0. 0. time (sec) N/A 0.059 0.021 180. 0. 0. 0. 0.
 Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 99 99 85 0 117 232 134 120 normalized size 1 1. 0.86 0. 1.18 2.34 1.35 1.21 time (sec) N/A 0.073 0.048 0.038 1.043 1.612 14.224 1.3
 Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 85 85 74 0 101 196 119 101 normalized size 1 1. 0.87 0. 1.19 2.31 1.4 1.19 time (sec) N/A 0.062 0.036 0.023 1.093 1.569 7.437 1.228
 Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 71 71 63 0 88 171 107 88 normalized size 1 1. 0.89 0. 1.24 2.41 1.51 1.24 time (sec) N/A 0.053 0.029 0.023 1.083 1.505 4.219 1.142
 Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 57 57 49 0 69 132 92 69 normalized size 1 1. 0.86 0. 1.21 2.32 1.61 1.21 time (sec) N/A 0.041 0.02 0.03 1.012 1.552 2.343 1.214
 Problem 64 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 33 33 31 34 49 95 56 50 normalized size 1 1. 0.94 1.03 1.48 2.88 1.7 1.52 time (sec) N/A 0.016 0.007 0.006 1.157 1.523 1.216 1.229
 Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F A F F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 53 53 50 0 108 0 0 0 normalized size 1 1. 0.94 0. 2.04 0. 0. 0. time (sec) N/A 0.126 0.02 0.036 1.055 0. 0. 0.
 Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 47 47 45 0 62 113 76 63 normalized size 1 1. 0.96 0. 1.32 2.4 1.62 1.34 time (sec) N/A 0.044 0.012 0.016 1.005 1.922 2.679 1.305
 Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 72 72 65 0 84 169 110 88 normalized size 1 1. 0.9 0. 1.17 2.35 1.53 1.22 time (sec) N/A 0.05 0.032 0.023 1.031 1.843 4.976 1.27
 Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 86 86 77 0 101 198 133 108 normalized size 1 1. 0.9 0. 1.17 2.3 1.55 1.26 time (sec) N/A 0.057 0.035 0.024 1.017 1.875 8.755 1.16
 Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F A A A A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 100 100 87 0 116 228 141 124 normalized size 1 1. 0.87 0. 1.16 2.28 1.41 1.24 time (sec) N/A 0.063 0.046 0.024 1.026 1.921 16.643 1.167
 Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 157 157 137 0 0 0 0 0 normalized size 1 1. 0.87 0. 0. 0. 0. 0. time (sec) N/A 0.221 0.186 0.306 0. 0. 0. 0.
 Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 207 207 190 1621 0 1013 0 298 normalized size 1 1. 0.92 7.83 0. 4.89 0. 1.44 time (sec) N/A 0.229 0.207 0.123 0. 1.975 0. 1.234
 Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 167 167 151 1146 0 826 0 238 normalized size 1 1. 0.9 6.86 0. 4.95 0. 1.43 time (sec) N/A 0.189 0.148 0.1 0. 1.965 0. 1.271
 Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 136 136 122 870 0 691 0 197 normalized size 1 1. 0.9 6.4 0. 5.08 0. 1.45 time (sec) N/A 0.149 0.109 0.089 0. 1.996 0. 1.293
 Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 109 109 94 510 0 567 0 153 normalized size 1 1. 0.86 4.68 0. 5.2 0. 1.4 time (sec) N/A 0.112 0.087 0.093 0. 1.94 0. 1.34
 Problem 75 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 79 79 78 118 0 459 275 124 normalized size 1 1. 0.99 1.49 0. 5.81 3.48 1.57 time (sec) N/A 0.061 0.061 0.013 0. 1.825 102.018 1.313
 Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F F F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 129 129 156 315 0 0 0 0 normalized size 1 1. 1.21 2.44 0. 0. 0. 0. time (sec) N/A 0.176 0.156 0.063 0. 0. 0. 0.
 Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 86 86 87 261 0 486 0 134 normalized size 1 1. 1.01 3.03 0. 5.65 0. 1.56 time (sec) N/A 0.113 0.105 0.069 0. 2.352 0. 1.21
 Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 121 121 105 1178 0 628 0 174 normalized size 1 1. 0.87 9.74 0. 5.19 0. 1.44 time (sec) N/A 0.154 0.238 0.089 0. 2.354 0. 1.269
 Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 149 149 132 423 0 741 0 221 normalized size 1 1. 0.89 2.84 0. 4.97 0. 1.48 time (sec) N/A 0.2 0.366 0.085 0. 2.747 0. 1.208
 Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 190 190 172 3583 0 932 0 284 normalized size 1 1. 0.91 18.86 0. 4.91 0. 1.49 time (sec) N/A 0.223 0.45 0.114 0. 2.803 0. 1.235
 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 42 42 35 38 50 105 46 50 normalized size 1 1. 0.83 0.9 1.19 2.5 1.1 1.19 time (sec) N/A 0.026 0.013 0.007 1.776 2.034 0.141 1.164
 Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 485 485 468 31895 0 2700 0 1338 normalized size 1 1. 0.96 65.76 0. 5.57 0. 2.76 time (sec) N/A 2.058 1.905 0.23 0. 2.992 0. 1.385
 Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 338 338 324 16059 0 1858 0 923 normalized size 1 1. 0.96 47.51 0. 5.5 0. 2.73 time (sec) N/A 0.516 0.504 0.196 0. 2.435 0. 1.392
 Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 226 226 204 7155 0 1242 0 591 normalized size 1 1. 0.9 31.66 0. 5.5 0. 2.62 time (sec) N/A 0.319 0.378 0.148 0. 2.25 0. 1.347
 Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 154 154 123 1706 0 767 0 315 normalized size 1 1. 0.8 11.08 0. 4.98 0. 2.05 time (sec) N/A 0.186 0.186 0.145 0. 2.266 0. 1.362
 Problem 86 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 79 79 78 118 0 459 275 124 normalized size 1 1. 0.99 1.49 0. 5.81 3.48 1.57 time (sec) N/A 0.062 0.059 0.015 0. 2.147 106.601 1.313
 Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 228 228 226 493 0 0 0 0 normalized size 1 1. 0.99 2.16 0. 0. 0. 0. time (sec) N/A 0.412 0.293 0.089 0. 0. 0. 0.
 Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 165 165 166 6540 0 950 0 383 normalized size 1 1. 1.01 39.64 0. 5.76 0. 2.32 time (sec) N/A 0.245 0.333 0.148 0. 3.223 0. 1.395
 Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) B F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 259 259 215 55216 0 2867 0 1197 normalized size 1 1. 0.83 213.19 0. 11.07 0. 4.62 time (sec) N/A 0.406 0.595 0.237 0. 17.134 0. 1.328
 Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) B F(-1) B veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 356 356 310 306209 0 6159 0 2650 normalized size 1 1. 0.87 860.14 0. 17.3 0. 7.44 time (sec) N/A 0.621 1.198 0.303 0. 125.094 0. 1.518
 Problem 91 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 519 519 469 1137077 0 0 0 5075 normalized size 1 1. 0.9 2190.9 0. 0. 0. 9.78 time (sec) N/A 1.006 2.065 0.443 0. 0. 0. 2.584
 Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 175 175 131 0 0 0 0 0 normalized size 1 1. 0.75 0. 0. 0. 0. 0. time (sec) N/A 0.158 0.043 0.101 0. 0. 0. 0.
 Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 258 258 339 0 0 0 0 0 normalized size 1 1. 1.31 0. 0. 0. 0. 0. time (sec) N/A 0.346 0.162 0.229 0. 0. 0. 0.
 Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 762 762 626 610 0 0 0 0 normalized size 1 1. 0.82 0.8 0. 0. 0. 0. time (sec) N/A 1.452 0.941 0.135 0. 0. 0. 0.
 Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A C F(-2) F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 782 782 663 764 0 0 0 0 normalized size 1 1. 0.85 0.98 0. 0. 0. 0. time (sec) N/A 1.514 0.813 0.11 0. 0. 0. 0.
 Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F A F F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 144 144 111 0 166 0 0 0 normalized size 1 1. 0.77 0. 1.15 0. 0. 0. time (sec) N/A 0.284 0.064 0.037 1.232 0. 0. 0.
 Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F(-2) F F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 587 587 478 0 0 0 0 0 normalized size 1 1. 0.81 0. 0. 0. 0. 0. time (sec) N/A 0.949 0.824 0.205 0. 0. 0. 0.
 Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F F F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 311 311 290 279 0 0 0 0 normalized size 1 1. 0.93 0.9 0. 0. 0. 0. time (sec) N/A 0.478 0.16 0.021 0. 0. 0. 0.
 Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F F F(-2) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 371 371 323 0 0 0 0 0 normalized size 1 1. 0.87 0. 0. 0. 0. 0. time (sec) N/A 0.541 0.146 0.027 0. 0. 0. 0.
 Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F F F(-1) F veriﬁed N/A Yes NO TBD TBD TBD TBD TBD size 443 443 826 0 0 0 0 0 normalized size 1 1. 1.86 0. 0. 0. 0. 0. time (sec) N/A 0.684 0.745 0.022 0. 0. 0. 0.
 Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 172 172 117 0 0 424 0 181 normalized size 1 1. 0.68 0. 0. 2.47 0. 1.05 time (sec) N/A 0.381 0.496 0.01 0. 2.515 0. 1.357
 Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 149 149 107 0 0 375 0 167 normalized size 1 1. 0.72 0. 0. 2.52 0. 1.12 time (sec) N/A 0.292 0.335 0.007 0. 2.616 0. 1.36
 Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 127 127 102 0 0 327 0 154 normalized size 1 1. 0.8 0. 0. 2.57 0. 1.21 time (sec) N/A 0.245 0.269 0.004 0. 2.575 0. 1.297
 Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A F A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 95 95 85 80 0 278 0 136 normalized size 1 1. 0.89 0.84 0. 2.93 0. 1.43 time (sec) N/A 0.162 0.028 0.031 0. 2.61 0. 1.323
 Problem 105 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 25 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.076 0.454 0.005 0. 0. 0. 0.
 Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 76 76 68 0 0 296 0 124 normalized size 1 1. 0.89 0. 0. 3.89 0. 1.63 time (sec) N/A 0.262 0.214 0.008 0. 2.487 0. 1.35
 Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A F F A F(-1) A veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 101 101 82 0 0 358 0 176 normalized size 1 1. 0.81 0. 0. 3.54 0. 1.74 time (sec) N/A 0.291 0.275 0.006 0. 2.333 0. 1.404
 Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C F F A F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 187 187 232 0 0 327 0 0 normalized size 1 1. 1.24 0. 0. 1.75 0. 0. time (sec) N/A 0.541 0.829 0.006 0. 2.25 0. 0.
 Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C F F A F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 158 158 209 0 0 286 0 0 normalized size 1 1. 1.32 0. 0. 1.81 0. 0. time (sec) N/A 0.431 0.641 0.007 0. 2.347 0. 0.
 Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C F F A F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 118 118 186 0 0 243 0 0 normalized size 1 1. 1.58 0. 0. 2.06 0. 0. time (sec) N/A 0.385 0.545 0.009 0. 2.182 0. 0.
 Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C F F A F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 114 114 177 0 0 240 0 0 normalized size 1 1. 1.55 0. 0. 2.11 0. 0. time (sec) N/A 0.309 0.434 0.006 0. 2.29 0. 0.
 Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A C F F A F(-1) F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 151 151 204 0 0 311 0 0 normalized size 1 1. 1.35 0. 0. 2.06 0. 0. time (sec) N/A 0.478 0.605 0.006 0. 2.19 0. 0.
 Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A C F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 93 93 93 84 111 224 0 0 normalized size 1 1. 1. 0.9 1.19 2.41 0. 0. time (sec) N/A 0.073 0.007 0.007 1.207 2.048 0. 0.
 Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A C F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 77 77 77 69 90 185 0 0 normalized size 1 1. 1. 0.9 1.17 2.4 0. 0. time (sec) N/A 0.058 0.005 0.006 1.129 2.057 0. 0.
 Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A C F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 59 59 59 52 68 143 0 0 normalized size 1 1. 1. 0.88 1.15 2.42 0. 0. time (sec) N/A 0.037 0.005 0.007 1.124 2.135 0. 0.
 Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A A A A F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 38 38 38 28 46 93 0 0 normalized size 1 1. 1. 0.74 1.21 2.45 0. 0. time (sec) N/A 0.048 0.002 0.013 1.081 2.091 0. 0.
 Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade N/A A A A A A A A veriﬁed N/A N/A N/A TBD TBD TBD TBD TBD size 14 0 0 0 0 0 0 0 normalized size 1 0. 0. 0. 0. 0. 0. 0. time (sec) N/A 0.032 0.051 0.026 0. 0. 0. 0.
 Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A B F C F F veriﬁed N/A Yes Yes TBD TBD TBD TBD TBD size 132 132 132 645 0 323 0 0 normalized size 1 1. 1. 4.89 0. 2.45 0. 0. time (sec) N/A 0.097 0.013 0.069 0. 2.195 0. 0.
 Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac grade A A A