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Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

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

B grade: { }

C grade: { }

F grade: { }

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 }

F grade: { }

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