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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, 16, 17, 18, 19, 20, 21, 22, 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, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 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 }

B grade: { 15, 23, 131, 142 }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 23, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 67, 69, 71, 73, 74, 75, 76, 78, 79, 80, 82, 87, 89, 90, 91, 92, 93, 95, 96, 97, 101, 106, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 120, 122, 123, 125, 126, 127, 128, 130, 133, 136, 137, 138, 140, 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, 170, 172, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 186, 187, 189, 190, 194, 195, 196, 197, 198, 201, 202, 204, 206, 208, 210, 212, 213, 214, 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, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 269, 270, 271, 272, 273, 274, 275, 277, 279, 281, 283, 285, 287, 288, 289, 291, 293, 294 }

B grade: { 6, 21, 24, 63, 66, 68, 70, 72, 81, 84, 85, 86, 88, 98, 99, 100, 103, 104, 105, 119, 121, 134, 143, 169, 171, 173, 179, 185, 188, 191, 192, 193, 199, 200, 203, 205, 207, 209, 211, 241, 242 }

C grade: { 8, 10, 16, 22, 25, 29, 50, 65, 77, 83, 94, 102, 112, 124, 129, 131, 132, 135, 139, 141, 142, 215, 264, 267, 268, 276, 278, 280, 282, 284, 286, 290, 292 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 26, 27, 28, 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, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 105, 106, 107, 108, 109, 111, 113, 114, 115, 116, 118, 120, 123, 124, 125, 126, 127, 128, 130, 131, 132, 134, 135, 136, 138, 140, 141, 143, 145, 147, 149, 150, 152, 153, 154, 155, 156, 158, 160, 162, 164, 165, 166, 167, 168, 169, 170, 172, 174, 175, 176, 177, 178, 179, 181, 182, 183, 185, 188, 189, 191, 192, 193, 194, 195, 196, 198, 199, 200, 201, 202, 204, 206, 207, 208, 210, 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, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 273, 275, 277, 278, 279, 281, 283, 284, 285, 286, 287, 289, 290, 291, 293, 294 }

B grade: { 8, 13, 21, 23, 24, 25, 67, 85, 103, 104, 110, 112, 117, 119, 121, 122, 129, 133, 137, 139, 142, 144, 146, 148, 151, 157, 159, 161, 163, 171, 173, 180, 184, 186, 190, 197, 203, 205, 209, 211, 249, 276, 280, 282, 288, 292 }

C grade: { }

F grade: { 29, 187, 271, 272, 274 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 16, 18, 20, 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, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 124, 126, 128, 130, 143, 145, 147, 149, 155, 167, 168, 170, 172, 174, 178, 179, 180, 181, 193, 198, 200, 201, 202, 206, 208, 212, 214, 217, 218, 219, 224, 225, 227, 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, 271, 284

B grade: { 8, 10, 12, 14, 22, 24, 26, 28, 67, 85, 104, 110, 112, 114, 116, 118, 120, 122, 132, 134, 136, 138, 140, 141, 156, 157, 158, 159, 160, 161, 162, 169, 171, 173, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 194, 195, 196, 197, 199, 203, 204, 205, 207, 209, 210, 211, 213, 215, 216, 220, 221, 222, 223, 226, 228, 264, 265, 266, 267, 268, 269, 270, 276, 278, 280, 282, 286, 288, 290, 292 }

C grade: { }

F grade: { 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 142, 144, 146, 148, 150, 151, 152, 153, 154, 163, 164, 165, 166, 175, 176, 177, 187, 257, 258, 259, 260, 261, 262, 263, 272, 273, 274, 275, 277, 279, 281, 283, 285, 287, 289, 291, 293, 294 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 7, 8, 10, 12, 30, 31, 32, 33, 34, 35, 36, 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, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 111, 112, 114, 116, 118, 119, 120, 121, 122, 126, 139, 150, 151, 152, 153, 154, 155, 156, 158, 160, 162, 163, 164, 165, 166, 167, 168, 169, 170, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 188, 189, 190, 193, 194, 195, 196, 197, 198, 200, 201, 202, 203, 204, 206, 207, 208, 209, 210, 212, 213, 214, 216, 217, 218, 219, 221, 222, 224, 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, 273, 276, 277, 278, 280, 281, 282, 283, 284, 286, 288, 290, 292 }

B grade: { 6, 9, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 37, 67, 85, 104, 113, 115, 117, 123, 124, 125, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 157, 159, 161, 171, 172, 173, 184, 185, 186, 191, 192, 199, 205, 211, 215, 220, 223, 225, 226, 264, 265, 266, 267, 268, 269, 270, 271, 275, 279, 285, 287, 289, 291, 293, 294 }

C grade: { }

F grade: { 29, 187, 272, 274 }

2.1.6 Sympy

A grade: { 2, 3, 4, 5, 6, 7, 18, 30, 31, 32, 33, 34, 35, 43, 44, 45, 46, 47, 48, 57, 58, 59, 60, 61, 62, 74, 75, 76, 77, 78, 79, 92, 93, 94, 95, 96, 97, 114, 150, 151, 152, 153, 154, 155, 163, 164, 165, 166, 167, 168, 175, 176, 177, 178, 179, 180, 202, 232 }

B grade: { 1, 188, 195 }

C grade: { }

F grade: { 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 36, 37, 38, 39, 40, 41, 42, 49, 50, 51, 52, 53, 54, 55, 56, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 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, 156, 157, 158, 159, 160, 161, 162, 169, 170, 171, 172, 173, 174, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 196, 197, 198, 199, 200, 201, 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, 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 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 14, 15, 17, 18, 19, 20, 21, 24, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 87, 89, 91, 92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 106, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 124, 125, 126, 127, 128, 129, 130, 131, 134, 136, 137, 138, 139, 140, 143, 145, 147, 148, 149, 150, 151, 152, 153, 154, 155, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 189, 191, 192, 193, 194, 196, 198, 199, 200, 201, 202, 204, 206, 207, 208, 210, 212, 213, 214, 216, 217, 218, 219, 221, 223, 225, 228, 232, 241, 242, 252, 253, 254, 255, 256, 258, 259, 260, 263, 275, 276, 277, 278, 279, 280, 281, 282, 285, 286, 287, 288, 290, 291, 294 }

B grade: { 5, 6, 13, 16, 22, 23, 25, 37, 39, 41, 53, 55, 67, 68, 70, 72, 84, 85, 86, 88, 90, 97, 104, 105, 107, 109, 121, 123, 132, 133, 135, 141, 142, 144, 146, 156, 157, 173, 179, 188, 190, 195, 197, 203, 205, 209, 211, 215, 220, 222, 224, 226, 227, 230, 231, 233, 234, 235, 237, 238, 239, 240, 247, 248, 249, 250, 251, 257, 261, 262, 264, 265, 266, 267, 268, 269, 270, 283, 284, 289, 292, 293 }

C grade: { }

F grade: { 29, 187, 229, 236, 243, 244, 245, 246, 271, 272, 273, 274 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 34 28 34 113 75 45
normalized size 1 1. 0.94 0.78 0.94 3.14 2.08 1.25
time (sec) N/A 0.049 0.006 0.023 1.204 0.491 0.759 1.141
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 26 20 27 77 27 34
normalized size 1 1. 1.08 0.83 1.12 3.21 1.12 1.42
time (sec) N/A 0.041 0.004 0.021 1.128 0.483 0.357 1.108
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 21 28 66 37 26
normalized size 1 1. 1. 0.84 1.12 2.64 1.48 1.04
time (sec) N/A 0.027 0.004 0.018 1.095 0.473 0.204 1.114
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 11 14 30 8 14
normalized size 1 1. 1. 1.1 1.4 3. 0.8 1.4
time (sec) N/A 0.006 0.002 0.01 1.002 0.46 0.059 1.137
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 9 9 9 10 12 34 8 32
normalized size 1 1. 1. 1.11 1.33 3.78 0.89 3.56
time (sec) N/A 0.019 0.005 0.037 1.167 0.489 1.557 1.095
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 25 19 32 116 24 45
normalized size 1 1. 2.08 1.58 2.67 9.67 2. 3.75
time (sec) N/A 0.033 0.007 0.037 1.104 0.49 3.856 1.143
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 14 20 59 17 18
normalized size 1 1. 1. 0.93 1.33 3.93 1.13 1.2
time (sec) N/A 0.043 0.008 0.041 1.189 0.459 13.241 1.115
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 94 173 282 223 0 200
normalized size 1 1. 1.03 1.9 3.1 2.45 0. 2.2
time (sec) N/A 0.107 0.178 0.091 1.751 0.519 0. 1.167
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 62 84 0 350 0 127
normalized size 1 1. 0.91 1.24 0. 5.15 0. 1.87
time (sec) N/A 0.078 0.155 0.081 0. 0.516 0. 1.252
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 47 54 119 112 0 74
normalized size 1 1. 1.34 1.54 3.4 3.2 0. 2.11
time (sec) N/A 0.057 0.055 0.058 1.718 0.501 0. 1.186
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 38 35 0 242 0 82
normalized size 1 1. 1.06 0.97 0. 6.72 0. 2.28
time (sec) N/A 0.018 0.025 0.072 0. 0.491 0. 1.208
Problem 12 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 23 23 20 21 65 123 0 30
normalized size 1 1. 0.87 0.91 2.83 5.35 0. 1.3
time (sec) N/A 0.07 0.045 0.076 1.143 0.504 0. 1.186
Problem 13 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 55 55 67 107 0 370 0 146
normalized size 1 1. 1.22 1.95 0. 6.73 0. 2.65
time (sec) N/A 0.068 0.123 0.105 0. 0.579 0. 1.261
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 55 55 48 64 161 281 0 105
normalized size 1 1. 0.87 1.16 2.93 5.11 0. 1.91
time (sec) N/A 0.121 0.152 0.09 1.109 0.533 0. 1.2
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 283 107 141 0 570 0 251
normalized size 1 2.64 1. 1.32 0. 5.33 0. 2.35
time (sec) N/A 1.169 0.425 0.107 0. 0.547 0. 1.204
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 121 99 158 305 0 188
normalized size 1 1. 1.89 1.55 2.47 4.77 0. 2.94
time (sec) N/A 0.118 0.247 0.087 1.693 0.509 0. 1.112
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 62 97 0 398 0 139
normalized size 1 1. 1.03 1.62 0. 6.63 0. 2.32
time (sec) N/A 0.046 0.154 0.092 0. 0.499 0. 1.195
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 14 19 95 75 18
normalized size 1 1. 1. 0.82 1.12 5.59 4.41 1.06
time (sec) N/A 0.013 0.021 0.08 1.129 0.464 99.08 1.102
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 72 106 0 563 0 147
normalized size 1 1. 1.14 1.68 0. 8.94 0. 2.33
time (sec) N/A 0.06 0.296 0.126 0. 0.596 0. 1.211
Problem 20 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 76 60 84 346 0 85
normalized size 1 1. 1.55 1.22 1.71 7.06 0. 1.73
time (sec) N/A 0.076 0.195 0.118 1.259 0.528 0. 1.116
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 270 224 0 859 0 290
normalized size 1 1. 2.29 1.9 0. 7.28 0. 2.46
time (sec) N/A 0.18 1.731 0.144 0. 0.709 0. 1.254
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 114 193 485 632 0 327
normalized size 1 1. 1.16 1.97 4.95 6.45 0. 3.34
time (sec) N/A 0.198 0.772 0.108 1.672 0.536 0. 1.182
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 300 92 212 0 656 0 266
normalized size 1 3.26 1. 2.3 0. 7.13 0. 2.89
time (sec) N/A 0.695 0.394 0.12 0. 0.529 0. 1.243
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 19 47 29 113 257 0 27
normalized size 1 1.27 3.13 1.93 7.53 17.13 0. 1.8
time (sec) N/A 0.026 0.087 0.097 1.142 0.478 0. 1.178
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 101 157 0 539 0 224
normalized size 1 1. 1.38 2.15 0. 7.38 0. 3.07
time (sec) N/A 0.035 0.154 0.117 0. 0.518 0. 1.2
Problem 26 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 59 59 96 73 232 524 0 104
normalized size 1 1. 1.63 1.24 3.93 8.88 0. 1.76
time (sec) N/A 0.082 0.197 0.12 1.243 0.554 0. 1.183
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 184 184 193 333 0 1084 0 286
normalized size 1 1. 1.05 1.81 0. 5.89 0. 1.55
time (sec) N/A 0.224 0.744 0.162 0. 0.721 0. 1.275
Problem 28 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 117 117 208 151 416 887 0 197
normalized size 1 1. 1.78 1.29 3.56 7.58 0. 1.68
time (sec) N/A 0.137 0.761 0.143 1.269 0.592 0. 1.195
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 66 66 367 0 0 0 0 0
normalized size 1 1. 5.56 0. 0. 0. 0. 0.
time (sec) N/A 0.063 3.452 0.631 0. 0. 0. 0.
Problem 30 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 87 87 57 62 84 161 219 128
normalized size 1 1. 0.66 0.71 0.97 1.85 2.52 1.47
time (sec) N/A 0.091 0.104 0.042 1.224 0.495 4.502 1.097
Problem 31 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 60 60 60 46 66 126 87 115
normalized size 1 1. 1. 0.77 1.1 2.1 1.45 1.92
time (sec) N/A 0.07 0.016 0.04 1.258 0.478 2.233 1.127
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 62 52 65 127 150 88
normalized size 1 1. 0.95 0.8 1. 1.95 2.31 1.35
time (sec) N/A 0.078 0.091 0.04 1.165 0.48 1.174 1.116
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 44 36 47 90 63 74
normalized size 1 1. 1. 0.82 1.07 2.05 1.43 1.68
time (sec) N/A 0.065 0.012 0.037 1.185 0.474 0.513 1.13
Problem 34 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 43 43 46 41 50 86 73 47
normalized size 1 1. 1.07 0.95 1.16 2. 1.7 1.09
time (sec) N/A 0.043 0.049 0.033 1.236 0.468 0.276 1.092
Problem 35 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 24 24 46 25 32 51 31 32
normalized size 1 1. 1.92 1.04 1.33 2.12 1.29 1.33
time (sec) N/A 0.013 0.012 0.017 1.062 0.468 0.159 1.093
Problem 36 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 17 17 17 24 41 46 0 36
normalized size 1 1. 1. 1.41 2.41 2.71 0. 2.12
time (sec) N/A 0.026 0.014 0.065 1.236 0.489 0. 1.123
Problem 37 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 24 24 24 34 54 144 0 73
normalized size 1 1. 1. 1.42 2.25 6. 0. 3.04
time (sec) N/A 0.045 0.013 0.066 1.121 0.493 0. 1.128
Problem 38 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 28 28 28 25 41 81 0 34
normalized size 1 1. 1. 0.89 1.46 2.89 0. 1.21
time (sec) N/A 0.058 0.013 0.072 1.057 0.456 0. 1.158
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 52 54 82 203 0 134
normalized size 1 1. 1. 1.04 1.58 3.9 0. 2.58
time (sec) N/A 0.067 0.017 0.075 1.096 0.498 0. 1.191
Problem 40 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 44 44 41 38 55 116 0 65
normalized size 1 1. 0.93 0.86 1.25 2.64 0. 1.48
time (sec) N/A 0.063 0.082 0.079 1.189 0.459 0. 1.138
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 68 74 116 242 0 190
normalized size 1 1. 0.92 1. 1.57 3.27 0. 2.57
time (sec) N/A 0.081 0.197 0.078 1.167 0.513 0. 1.199
Problem 42 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 60 60 53 48 72 147 0 95
normalized size 1 1. 0.88 0.8 1.2 2.45 0. 1.58
time (sec) N/A 0.071 0.148 0.078 1.143 0.472 0. 1.193
Problem 43 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 137 137 154 108 132 221 187 209
normalized size 1 1. 1.12 0.79 0.96 1.61 1.36 1.53
time (sec) N/A 0.138 0.378 0.064 1.144 0.5 7.901 1.167
Problem 44 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 174 174 147 118 138 223 384 178
normalized size 1 1. 0.84 0.68 0.79 1.28 2.21 1.02
time (sec) N/A 0.17 0.241 0.061 1.228 0.503 4.898 1.152
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 116 88 104 169 138 154
normalized size 1 1. 1.13 0.85 1.01 1.64 1.34 1.5
time (sec) N/A 0.122 0.171 0.059 1.094 0.486 2.353 1.162
Problem 46 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 126 126 98 97 101 170 260 115
normalized size 1 1. 0.78 0.77 0.8 1.35 2.06 0.91
time (sec) N/A 0.135 0.225 0.058 1.124 0.482 1.369 1.173
Problem 47 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 67 67 64 52 70 120 85 99
normalized size 1 1. 0.96 0.78 1.04 1.79 1.27 1.48
time (sec) N/A 0.091 0.388 0.051 1.124 0.472 0.545 1.154
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 52 70 92 120 128 68
normalized size 1 1. 0.95 1.27 1.67 2.18 2.33 1.24
time (sec) N/A 0.02 0.101 0.058 1.179 0.48 0.322 1.114
Problem 49 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 55 55 84 63 81 155 0 120
normalized size 1 1. 1.53 1.15 1.47 2.82 0. 2.18
time (sec) N/A 0.071 0.142 0.085 1.187 0.506 0. 1.173
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 69 57 66 146 0 59
normalized size 1 1. 1.77 1.46 1.69 3.74 0. 1.51
time (sec) N/A 0.056 0.124 0.095 1.694 0.494 0. 1.16
Problem 51 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 67 67 67 98 120 234 0 165
normalized size 1 1. 1. 1.46 1.79 3.49 0. 2.46
time (sec) N/A 0.094 0.047 0.102 1.199 0.498 0. 1.19
Problem 52 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 30 30 46 48 61 131 0 55
normalized size 1 1. 1.53 1.6 2.03 4.37 0. 1.83
time (sec) N/A 0.046 0.04 0.103 1.048 0.463 0. 1.167
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 120 120 120 143 174 289 0 336
normalized size 1 1. 1. 1.19 1.45 2.41 0. 2.8
time (sec) N/A 0.142 0.076 0.105 1.093 0.525 0. 1.193
Problem 54 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 85 85 54 82 95 184 0 108
normalized size 1 1. 0.64 0.96 1.12 2.16 0. 1.27
time (sec) N/A 0.077 0.185 0.111 1.145 0.474 0. 1.152
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 168 168 104 189 243 343 0 463
normalized size 1 1. 0.62 1.12 1.45 2.04 0. 2.76
time (sec) N/A 0.17 0.555 0.11 1.094 0.526 0. 1.208
Problem 56 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 125 125 104 110 123 231 0 159
normalized size 1 1. 0.83 0.88 0.98 1.85 0. 1.27
time (sec) N/A 0.104 0.655 0.114 1.121 0.488 0. 1.177
Problem 57 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 265 265 235 175 220 350 508 294
normalized size 1 1. 0.89 0.66 0.83 1.32 1.92 1.11
time (sec) N/A 0.246 0.475 0.076 1.098 0.534 22.569 1.181
Problem 58 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 175 175 204 145 170 278 233 266
normalized size 1 1. 1.17 0.83 0.97 1.59 1.33 1.52
time (sec) N/A 0.184 0.412 0.081 1.121 0.506 8.98 1.179
Problem 59 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 216 216 171 155 177 292 454 212
normalized size 1 1. 0.79 0.72 0.82 1.35 2.1 0.98
time (sec) N/A 0.213 0.302 0.078 1.226 0.516 6.824 1.184
Problem 60 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 140 140 150 125 144 230 182 196
normalized size 1 1. 1.07 0.89 1.03 1.64 1.3 1.4
time (sec) N/A 0.163 0.289 0.07 1.24 0.494 2.782 1.148
Problem 61 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 78 78 94 114 123 228 299 140
normalized size 1 1. 1.21 1.46 1.58 2.92 3.83 1.79
time (sec) N/A 0.064 0.398 0.066 1.19 0.496 1.59 1.155
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 81 75 113 173 117 123
normalized size 1 1. 1.4 1.29 1.95 2.98 2.02 2.12
time (sec) N/A 0.023 0.333 0.066 1.207 0.48 0.753 1.13
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 401 123 123 181 0 126
normalized size 1 1. 4.41 1.35 1.35 1.99 0. 1.38
time (sec) N/A 0.119 0.734 0.109 1.246 0.516 0. 1.201
Problem 64 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 86 86 131 126 113 273 0 203
normalized size 1 1. 1.52 1.47 1.31 3.17 0. 2.36
time (sec) N/A 0.112 1.064 0.119 1.226 0.512 0. 1.198
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 79 93 115 215 0 96
normalized size 1 1. 1.1 1.29 1.6 2.99 0. 1.33
time (sec) N/A 0.093 0.268 0.122 1.755 0.506 0. 1.204
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 293 187 159 304 0 231
normalized size 1 1. 2.84 1.82 1.54 2.95 0. 2.24
time (sec) N/A 0.123 1.587 0.124 1.24 0.51 0. 1.208
Problem 67 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 30 30 57 72 117 181 0 77
normalized size 1 1. 1.9 2.4 3.9 6.03 0. 2.57
time (sec) N/A 0.047 0.169 0.121 1.185 0.467 0. 1.232
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 158 158 464 256 212 362 0 450
normalized size 1 1. 2.94 1.62 1.34 2.29 0. 2.85
time (sec) N/A 0.181 1.318 0.131 1.254 0.52 0. 1.238
Problem 69 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 120 120 54 127 165 246 0 151
normalized size 1 1. 0.45 1.06 1.38 2.05 0. 1.26
time (sec) N/A 0.098 0.373 0.13 1.187 0.51 0. 1.2
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 210 210 637 328 281 410 0 628
normalized size 1 1. 3.03 1.56 1.34 1.95 0. 2.99
time (sec) N/A 0.22 2.024 0.133 1.228 0.555 0. 1.201
Problem 71 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 174 174 115 173 208 304 0 224
normalized size 1 1. 0.66 0.99 1.2 1.75 0. 1.29
time (sec) N/A 0.14 0.598 0.128 1.289 0.513 0. 1.184
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 259 259 810 399 335 481 0 806
normalized size 1 1. 3.13 1.54 1.29 1.86 0. 3.11
time (sec) N/A 0.268 4.109 0.139 1.216 0.581 0. 1.215
Problem 73 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 213 213 177 219 248 344 0 297
normalized size 1 1. 0.83 1.03 1.16 1.62 0. 1.39
time (sec) N/A 0.179 1.989 0.129 1.291 0.553 0. 1.201
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 279 279 237 236 251 413 367 363
normalized size 1 1. 0.85 0.85 0.9 1.48 1.32 1.3
time (sec) N/A 0.258 0.718 0.084 1.561 0.551 21.754 1.212
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 381 381 222 250 269 424 736 331
normalized size 1 1. 0.58 0.66 0.71 1.11 1.93 0.87
time (sec) N/A 0.389 0.6 0.086 1.148 0.539 15.751 1.22
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 220 220 204 206 208 336 286 309
normalized size 1 1. 0.93 0.94 0.95 1.53 1.3 1.4
time (sec) N/A 0.234 0.52 0.081 1.146 0.526 8.205 1.212
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 301 301 178 219 230 342 614 252
normalized size 1 1. 0.59 0.73 0.76 1.14 2.04 0.84
time (sec) N/A 0.303 0.427 0.08 1.247 0.537 5.412 1.239
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 165 146 142 166 277 206 223
normalized size 1 1. 0.88 0.86 1.01 1.68 1.25 1.35
time (sec) N/A 0.181 0.379 0.069 1.154 0.517 2.458 1.194
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 107 153 184 273 381 165
normalized size 1 1. 0.99 1.42 1.7 2.53 3.53 1.53
time (sec) N/A 0.044 0.402 0.071 1.159 0.504 1.536 1.105
Problem 80 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 150 150 181 163 170 289 0 293
normalized size 1 1. 1.21 1.09 1.13 1.93 0. 1.95
time (sec) N/A 0.153 0.994 0.12 1.178 0.524 0. 1.229
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 477 210 182 312 0 173
normalized size 1 1. 4.01 1.76 1.53 2.62 0. 1.45
time (sec) N/A 0.183 6.263 0.133 1.785 0.524 0. 1.211
Problem 82 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 151 151 268 211 192 363 0 278
normalized size 1 1. 1.77 1.4 1.27 2.4 0. 1.84
time (sec) N/A 0.164 2.294 0.136 1.239 0.523 0. 1.273
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 105 145 157 282 0 140
normalized size 1 1. 1.02 1.41 1.52 2.74 0. 1.36
time (sec) N/A 0.156 0.392 0.14 1.837 0.515 0. 1.199
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 168 168 936 297 259 392 0 439
normalized size 1 1. 5.57 1.77 1.54 2.33 0. 2.61
time (sec) N/A 0.195 6.238 0.147 1.209 0.513 0. 1.255
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 73 96 139 250 0 99
normalized size 1 1. 2.43 3.2 4.63 8.33 0. 3.3
time (sec) N/A 0.048 0.309 0.146 1.232 0.485 0. 1.208
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 258 258 1342 394 339 458 0 724
normalized size 1 1. 5.2 1.53 1.31 1.78 0. 2.81
time (sec) N/A 0.294 6.258 0.146 1.194 0.544 0. 1.287
Problem 87 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 143 143 54 171 204 333 0 194
normalized size 1 1. 0.38 1.2 1.43 2.33 0. 1.36
time (sec) N/A 0.123 0.558 0.149 1.122 0.512 0. 1.176
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 330 330 1732 491 435 533 0 953
normalized size 1 1. 5.25 1.49 1.32 1.62 0. 2.89
time (sec) N/A 0.343 6.386 0.159 1.171 0.585 0. 1.288
Problem 89 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 201 201 115 236 261 400 0 289
normalized size 1 1. 0.57 1.17 1.3 1.99 0. 1.44
time (sec) N/A 0.171 0.848 0.147 1.244 0.54 0. 1.236
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 408 408 242 590 516 626 0 1188
normalized size 1 1. 0.59 1.45 1.26 1.53 0. 2.91
time (sec) N/A 0.398 1.33 0.143 1.238 0.628 0. 1.313
Problem 91 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 254 254 175 300 315 471 0 383
normalized size 1 1. 0.69 1.18 1.24 1.85 0. 1.51
time (sec) N/A 0.219 1.742 0.142 1.233 0.579 0. 1.215
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 515 515 307 335 392 595 979 462
normalized size 1 1. 0.6 0.65 0.76 1.16 1.9 0.9
time (sec) N/A 0.485 1.266 0.303 1.231 0.606 48.446 1.375
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 337 337 278 291 302 504 440 423
normalized size 1 1. 0.82 0.86 0.9 1.5 1.31 1.26
time (sec) N/A 0.3 1.026 0.213 1.203 0.562 32.26 1.434
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 426 426 259 305 308 509 821 375
normalized size 1 1. 0.61 0.72 0.72 1.19 1.93 0.88
time (sec) N/A 0.413 0.877 0.197 1.253 0.566 27.413 1.412
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 275 275 236 261 262 429 357 350
normalized size 1 1. 0.86 0.95 0.95 1.56 1.3 1.27
time (sec) N/A 0.281 0.768 0.201 1.09 0.538 10.632 1.395
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 126 188 236 252 417 663 285
normalized size 1 1. 1.49 1.87 2. 3.31 5.26 2.26
time (sec) N/A 0.09 0.617 0.18 1.094 0.537 9.868 1.324
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 156 175 232 354 267 252
normalized size 1 1. 1.66 1.86 2.47 3.77 2.84 2.68
time (sec) N/A 0.047 0.463 0.154 1.233 0.513 2.981 1.157
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 170 170 711 272 230 362 0 269
normalized size 1 1. 4.18 1.6 1.35 2.13 0. 1.58
time (sec) N/A 0.222 6.441 0.236 1.097 0.55 0. 1.26
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 205 205 632 251 219 429 0 382
normalized size 1 1. 3.08 1.22 1.07 2.09 0. 1.86
time (sec) N/A 0.216 6.307 0.251 1.22 0.537 0. 1.275
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 169 169 571 291 242 414 0 234
normalized size 1 1. 3.38 1.72 1.43 2.45 0. 1.38
time (sec) N/A 0.231 6.378 0.253 1.785 0.536 0. 1.273
Problem 101 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 204 204 397 327 244 455 0 379
normalized size 1 1. 1.95 1.6 1.2 2.23 0. 1.86
time (sec) N/A 0.208 5.96 0.259 1.083 0.537 0. 1.294
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 126 202 235 367 0 194
normalized size 1 1. 0.86 1.37 1.6 2.5 0. 1.32
time (sec) N/A 0.23 0.754 0.264 1.743 0.534 0. 1.277
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 224 224 1219 440 311 478 0 554
normalized size 1 1. 5.44 1.96 1.39 2.13 0. 2.47
time (sec) N/A 0.233 6.322 0.26 1.134 0.571 0. 1.345
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 89 120 224 329 0 120
normalized size 1 1. 2.97 4. 7.47 10.97 0. 4.
time (sec) N/A 0.048 0.48 0.257 1.206 0.507 0. 1.313
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 318 318 1677 564 390 556 0 918
normalized size 1 1. 5.27 1.77 1.23 1.75 0. 2.89
time (sec) N/A 0.337 6.33 0.266 1.188 0.573 0. 1.318
Problem 106 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 177 177 54 217 301 408 0 238
normalized size 1 1. 0.31 1.23 1.7 2.31 0. 1.34
time (sec) N/A 0.152 0.443 0.267 1.286 0.546 0. 1.332
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 391 391 331 688 486 643 0 1199
normalized size 1 1. 0.85 1.76 1.24 1.64 0. 3.07
time (sec) N/A 0.389 2.215 0.266 1.223 0.629 0. 1.338
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 242 242 115 299 371 491 0 354
normalized size 1 1. 0.48 1.24 1.53 2.03 0. 1.46
time (sec) N/A 0.222 1.207 0.256 1.247 0.599 0. 1.322
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 472 472 374 814 567 720 0 1480
normalized size 1 1. 0.79 1.72 1.2 1.53 0. 3.14
time (sec) N/A 0.467 1.857 0.259 1.232 0.669 0. 1.324
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 227 227 218 524 761 471 0 435
normalized size 1 1. 0.96 2.31 3.35 2.07 0. 1.92
time (sec) N/A 0.214 0.41 0.123 1.815 0.563 0. 1.199
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 166 166 137 221 0 598 0 386
normalized size 1 1. 0.83 1.33 0. 3.6 0. 2.33
time (sec) N/A 0.175 1.015 0.135 0. 0.558 0. 1.319
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 143 236 383 278 0 246
normalized size 1 1. 1.2 1.98 3.22 2.34 0. 2.07
time (sec) N/A 0.129 0.221 0.122 1.736 0.525 0. 1.149
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 79 90 0 436 0 159
normalized size 1 1. 0.87 0.99 0. 4.79 0. 1.75
time (sec) N/A 0.082 0.18 0.132 0. 0.52 0. 1.288
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 41 74 167 144 299 100
normalized size 1 1. 0.91 1.64 3.71 3.2 6.64 2.22
time (sec) N/A 0.066 0.066 0.106 1.785 0.495 19.243 1.195
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 45 43 0 312 0 100
normalized size 1 1. 0.96 0.91 0. 6.64 0. 2.13
time (sec) N/A 0.023 0.033 0.116 0. 0.484 0. 1.253
Problem 116 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 41 41 18 19 139 144 0 26
normalized size 1 1. 0.44 0.46 3.39 3.51 0. 0.63
time (sec) N/A 0.082 0.017 0.138 1.091 0.513 0. 1.159
Problem 117 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 80 80 109 174 0 471 0 184
normalized size 1 1. 1.36 2.17 0. 5.89 0. 2.3
time (sec) N/A 0.084 0.138 0.174 0. 0.591 0. 1.333
Problem 118 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 88 88 52 72 321 294 0 73
normalized size 1 1. 0.59 0.82 3.65 3.34 0. 0.83
time (sec) N/A 0.141 0.141 0.16 1.105 0.525 0. 1.156
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 321 488 0 633 0 375
normalized size 1 1. 2.1 3.19 0. 4.14 0. 2.45
time (sec) N/A 0.157 1.99 0.202 0. 0.838 0. 1.35
Problem 120 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 158 158 99 162 624 439 0 162
normalized size 1 1. 0.63 1.03 3.95 2.78 0. 1.03
time (sec) N/A 0.222 1.209 0.158 1.094 0.568 0. 1.199
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 262 262 661 994 0 834 0 748
normalized size 1 1. 2.52 3.79 0. 3.18 0. 2.85
time (sec) N/A 0.256 5.248 0.201 0. 1.416 0. 1.388
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 149 292 381 614 0 338
normalized size 1 1. 1.03 2.01 2.63 4.23 0. 2.33
time (sec) N/A 0.293 0.896 0.161 1.761 0.565 0. 1.139
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 231 130 172 0 697 0 386
normalized size 1 1.67 0.94 1.25 0. 5.05 0. 2.8
time (sec) N/A 1.048 0.775 0.185 0. 0.554 0. 1.283
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 192 130 177 389 0 215
normalized size 1 1. 2.34 1.59 2.16 4.74 0. 2.62
time (sec) N/A 0.137 0.39 0.155 1.797 0.518 0. 1.14
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 79 118 0 502 0 186
normalized size 1 1. 0.95 1.42 0. 6.05 0. 2.24
time (sec) N/A 0.067 0.213 0.167 0. 0.507 0. 1.265
Problem 126 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 32 32 32 21 28 132 0 27
normalized size 1 1. 1. 0.66 0.88 4.12 0. 0.84
time (sec) N/A 0.017 0.032 0.142 1.067 0.497 0. 1.114
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 120 174 0 699 0 224
normalized size 1 1. 1.3 1.89 0. 7.6 0. 2.43
time (sec) N/A 0.079 0.735 0.22 0. 0.599 0. 1.288
Problem 128 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 75 75 51 78 81 440 0 96
normalized size 1 1. 0.68 1.04 1.08 5.87 0. 1.28
time (sec) N/A 0.096 0.26 0.204 1.192 0.536 0. 1.138
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 179 179 709 440 0 860 0 378
normalized size 1 1. 3.96 2.46 0. 4.8 0. 2.11
time (sec) N/A 0.24 6.112 0.247 0. 0.697 0. 1.322
Problem 130 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 141 141 122 174 155 656 0 201
normalized size 1 1. 0.87 1.23 1.1 4.65 0. 1.43
time (sec) N/A 0.15 2.815 0.216 1.136 0.582 0. 1.146
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B C A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 216 492 211 283 0 1073 0 539
normalized size 1 2.28 0.98 1.31 0. 4.97 0. 2.5
time (sec) N/A 1.742 1.035 0.213 0. 0.609 0. 1.378
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 122 122 154 219 649 748 0 358
normalized size 1 1. 1.26 1.8 5.32 6.13 0. 2.93
time (sec) N/A 0.212 1.16 0.184 1.655 0.547 0. 1.263
Problem 133 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 119 225 119 280 0 795 0 396
normalized size 1 1.89 1. 2.35 0. 6.68 0. 3.33
time (sec) N/A 0.588 0.655 0.206 0. 0.587 0. 1.358
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 30 57 21 231 313 0 27
normalized size 1 1.36 2.59 0.95 10.5 14.23 0. 1.23
time (sec) N/A 0.031 0.118 0.168 1.139 0.483 0. 1.231
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 132 191 0 679 0 298
normalized size 1 1. 1.28 1.85 0. 6.59 0. 2.89
time (sec) N/A 0.049 0.262 0.184 0. 0.517 0. 1.263
Problem 136 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 86 86 57 84 425 647 0 84
normalized size 1 1. 0.66 0.98 4.94 7.52 0. 0.98
time (sec) N/A 0.103 0.525 0.234 1.2 0.563 0. 1.27
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 260 260 396 611 0 1175 0 424
normalized size 1 1. 1.52 2.35 0. 4.52 0. 1.63
time (sec) N/A 0.286 2.445 0.29 0. 0.719 0. 1.61
Problem 138 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 161 161 140 184 880 814 0 189
normalized size 1 1. 0.87 1.14 5.47 5.06 0. 1.17
time (sec) N/A 0.168 3.105 0.267 1.33 0.598 0. 1.343
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 383 383 688 1125 0 1299 0 689
normalized size 1 1. 1.8 2.94 0. 3.39 0. 1.8
time (sec) N/A 0.785 2.295 0.308 0. 0.856 0. 1.416
Problem 140 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 232 232 272 321 1422 1076 0 328
normalized size 1 1. 1.17 1.38 6.13 4.64 0. 1.41
time (sec) N/A 0.244 1.331 0.269 1.45 0.69 0. 1.311
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 165 419 304 520 1256 0 500
normalized size 1 1. 2.54 1.84 3.15 7.61 0. 3.03
time (sec) N/A 0.303 6.211 0.212 1.825 0.611 0. 1.176
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B C B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 157 362 165 494 0 1173 0 707
normalized size 1 2.31 1.05 3.15 0. 7.47 0. 4.5
time (sec) N/A 1.173 1.055 0.234 0. 0.596 0. 1.277
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 124 21 72 552 0 27
normalized size 1 1. 4.13 0.7 2.4 18.4 0. 0.9
time (sec) N/A 0.053 0.662 0.2 1.178 0.526 0. 1.116
Problem 144 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 141 141 128 383 0 945 0 575
normalized size 1 1. 0.91 2.72 0. 6.7 0. 4.08
time (sec) N/A 0.111 0.699 0.233 0. 0.567 0. 1.302
Problem 145 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 85 64 115 470 0 68
normalized size 1 1. 0.87 0.65 1.17 4.8 0. 0.69
time (sec) N/A 0.04 0.29 0.202 1.188 0.502 0. 1.153
Problem 146 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 231 231 290 1367 0 1655 0 711
normalized size 1 1. 1.26 5.92 0. 7.16 0. 3.08
time (sec) N/A 0.17 3.257 0.316 0. 1.035 0. 1.34
Problem 147 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 138 138 133 188 194 1191 0 186
normalized size 1 1. 0.96 1.36 1.41 8.63 0. 1.35
time (sec) N/A 0.16 2.205 0.285 1.27 0.703 0. 1.199
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 400 400 538 1255 0 1843 0 740
normalized size 1 1. 1.34 3.14 0. 4.61 0. 1.85
time (sec) N/A 0.796 3.206 0.344 0. 0.917 0. 1.357
Problem 149 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 232 232 295 330 293 1251 0 336
normalized size 1 1. 1.27 1.42 1.26 5.39 0. 1.45
time (sec) N/A 0.249 2.013 0.306 1.195 0.703 0. 1.136
Problem 150 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 99 99 82 137 0 242 221 157
normalized size 1 1. 0.83 1.38 0. 2.44 2.23 1.59
time (sec) N/A 0.151 0.136 0.119 0. 0.473 0.861 1.135
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 111 141 0 200 197 161
normalized size 1 1. 1.59 2.01 0. 2.86 2.81 2.3
time (sec) N/A 0.128 0.068 0.112 0. 0.467 0.761 1.109
Problem 152 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 75 75 60 98 0 159 153 134
normalized size 1 1. 0.8 1.31 0. 2.12 2.04 1.79
time (sec) N/A 0.128 0.101 0.115 0. 0.467 0.439 1.125
Problem 153 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 52 52 73 75 0 122 128 90
normalized size 1 1. 1.4 1.44 0. 2.35 2.46 1.73
time (sec) N/A 0.12 0.071 0.11 0. 0.466 0.442 1.125
Problem 154 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 46 46 38 59 0 86 61 81
normalized size 1 1. 0.83 1.28 0. 1.87 1.33 1.76
time (sec) N/A 0.029 0.068 0.098 0. 0.46 0.544 1.144
Problem 155 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 29 29 29 23 39 35 31 28
normalized size 1 1. 1. 0.79 1.34 1.21 1.07 0.97
time (sec) N/A 0.016 0.034 0.09 1.187 0.457 0.152 1.093
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 22 136 65 0 80
normalized size 1 1. 1. 0.96 5.91 2.83 0. 3.48
time (sec) N/A 0.07 0.065 0.121 1.168 0.493 0. 1.145
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 35 85 112 217 0 81
normalized size 1 1. 1.13 2.74 3.61 7. 0. 2.61
time (sec) N/A 0.094 0.194 0.145 1.176 0.474 0. 1.152
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 35 26 146 88 0 36
normalized size 1 1. 1.03 0.76 4.29 2.59 0. 1.06
time (sec) N/A 0.107 0.184 0.135 1.187 0.438 0. 1.165
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 54 258 251 505 0 136
normalized size 1 1. 0.9 4.3 4.18 8.42 0. 2.27
time (sec) N/A 0.117 0.24 0.163 1.174 0.482 0. 1.175
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 53 47 285 208 0 63
normalized size 1 1. 1.02 0.9 5.48 4. 0. 1.21
time (sec) N/A 0.116 0.272 0.148 1.213 0.452 0. 1.179
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 66 430 390 810 0 189
normalized size 1 1. 0.79 5.12 4.64 9.64 0. 2.25
time (sec) N/A 0.133 0.477 0.169 1.277 0.497 0. 1.178
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 67 68 423 333 0 90
normalized size 1 1. 0.96 0.97 6.04 4.76 0. 1.29
time (sec) N/A 0.122 0.35 0.153 1.283 0.461 0. 1.156
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 149 174 0 244 233 196
normalized size 1 1. 1.75 2.05 0. 2.87 2.74 2.31
time (sec) N/A 0.186 0.104 0.138 0. 0.469 1.815 1.114
Problem 164 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 101 101 82 117 0 198 190 139
normalized size 1 1. 0.81 1.16 0. 1.96 1.88 1.38
time (sec) N/A 0.101 0.127 0.134 0. 0.47 0.582 1.145
Problem 165 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 68 68 111 108 0 161 165 126
normalized size 1 1. 1.63 1.59 0. 2.37 2.43 1.85
time (sec) N/A 0.176 0.085 0.127 0. 0.473 0.882 1.164
Problem 166 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 89 89 60 79 0 126 119 97
normalized size 1 1. 0.67 0.89 0. 1.42 1.34 1.09
time (sec) N/A 0.082 0.105 0.127 0. 0.467 0.407 1.151
Problem 167 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 52 52 73 57 61 86 94 63
normalized size 1 1. 1.4 1.1 1.17 1.65 1.81 1.21
time (sec) N/A 0.114 0.057 0.112 1.048 0.464 0.417 1.113
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 23 30 49 46 41
normalized size 1 1. 1. 0.74 0.97 1.58 1.48 1.32
time (sec) N/A 0.016 0.043 0.099 1.014 0.46 0.238 1.143
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 184 63 158 161 0 80
normalized size 1 1. 4. 1.37 3.43 3.5 0. 1.74
time (sec) N/A 0.115 0.231 0.154 1.683 0.483 0. 1.176
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 71 35 41 192 0 138
normalized size 1 1. 1.29 0.64 0.75 3.49 0. 2.51
time (sec) N/A 0.071 0.414 0.161 1.115 0.486 0. 1.205
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 146 170 225 375 0 131
normalized size 1 1. 2.61 3.04 4.02 6.7 0. 2.34
time (sec) N/A 0.146 0.395 0.184 1.051 0.481 0. 1.199
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 68 36 47 139 0 47
normalized size 1 1. 2. 1.06 1.38 4.09 0. 1.38
time (sec) N/A 0.064 0.251 0.172 1.003 0.448 0. 1.103
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 215 342 398 667 0 207
normalized size 1 1. 2.56 4.07 4.74 7.94 0. 2.46
time (sec) N/A 0.192 0.948 0.197 1.1 0.487 0. 1.206
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 77 47 63 267 0 63
normalized size 1 1. 1.1 0.67 0.9 3.81 0. 0.9
time (sec) N/A 0.078 0.407 0.175 0.999 0.457 0. 1.132
Problem 175 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 125 125 106 137 0 247 226 161
normalized size 1 1. 0.85 1.1 0. 1.98 1.81 1.29
time (sec) N/A 0.111 0.19 0.202 0. 0.472 0.925 1.157
Problem 176 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 106 106 149 141 0 205 199 161
normalized size 1 1. 1.41 1.33 0. 1.93 1.88 1.52
time (sec) N/A 0.234 0.089 0.149 0. 0.471 1.169 1.195
Problem 177 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 131 131 84 98 0 166 156 108
normalized size 1 1. 0.64 0.75 0. 1.27 1.19 0.82
time (sec) N/A 0.141 0.117 0.142 0. 0.464 0.639 1.159
Problem 178 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 90 90 111 90 93 128 133 99
normalized size 1 1. 1.23 1. 1.03 1.42 1.48 1.1
time (sec) N/A 0.221 0.079 0.137 1.136 0.461 0.643 1.193
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 77 23 69 86 97 77
normalized size 1 1. 2.41 0.72 2.16 2.69 3.03 2.41
time (sec) N/A 0.032 0.059 0.115 1.154 0.463 0.419 1.121
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 57 39 49 46 49
normalized size 1 1. 1. 1.84 1.26 1.58 1.48 1.58
time (sec) N/A 0.016 0.04 0.128 1.018 0.458 0.199 1.106
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 91 40 134 157 0 138
normalized size 1 1. 1.49 0.66 2.2 2.57 0. 2.26
time (sec) N/A 0.064 0.262 0.185 1.617 0.48 0. 1.145
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 109 108 444 302 0 151
normalized size 1 1. 1.76 1.74 7.16 4.87 0. 2.44
time (sec) N/A 0.162 0.315 0.196 1.633 0.493 0. 1.204
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 110 52 404 317 0 176
normalized size 1 1. 1.47 0.69 5.39 4.23 0. 2.35
time (sec) N/A 0.081 0.599 0.196 1.648 0.484 0. 1.189
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 64 258 290 521 0 154
normalized size 1 1. 0.84 3.39 3.82 6.86 0. 2.03
time (sec) N/A 0.182 0.471 0.215 1.085 0.487 0. 1.174
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 90 47 324 177 0 63
normalized size 1 1. 2.65 1.38 9.53 5.21 0. 1.85
time (sec) N/A 0.063 0.465 0.197 1.089 0.449 0. 1.22
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 115 430 460 836 0 224
normalized size 1 1. 1.11 4.13 4.42 8.04 0. 2.15
time (sec) N/A 0.23 0.444 0.224 1.106 0.501 0. 1.212
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 90 0 0 0 0 0
normalized size 1 1. 1.36 0. 0. 0. 0. 0.
time (sec) N/A 0.061 2.073 0.586 0. 0. 0. 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 5 5 16 6 42 23 17 30
normalized size 1 1. 3.2 1.2 8.4 4.6 3.4 6.
time (sec) N/A 0.023 0.018 0.068 0.997 0.479 0.173 1.133
Problem 189 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 10 10 19 11 73 36 0 14
normalized size 1 1. 1.9 1.1 7.3 3.6 0. 1.4
time (sec) N/A 0.068 0.021 0.089 1.577 0.471 0. 1.095
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 4 4 4 15 41 16 0 19
normalized size 1 1. 1. 3.75 10.25 4. 0. 4.75
time (sec) N/A 0.06 0.018 0.091 1.644 0.468 0. 1.125
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 25 13 38 88 0 16
normalized size 1 1. 2.27 1.18 3.45 8. 0. 1.45
time (sec) N/A 0.053 0.034 0.065 1.662 0.464 0. 1.125
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 9 9 20 10 31 82 0 14
normalized size 1 1. 2.22 1.11 3.44 9.11 0. 1.56
time (sec) N/A 0.078 0.023 0.099 1.628 0.491 0. 1.134
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 23 11 20 62 0 14
normalized size 1 1. 2.3 1.1 2. 6.2 0. 1.4
time (sec) N/A 0.024 0.017 0.061 1.07 0.461 0. 1.121
Problem 194 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 11 11 20 8 34 47 0 16
normalized size 1 1. 1.82 0.73 3.09 4.27 0. 1.45
time (sec) N/A 0.055 0.022 0.089 1.116 0.486 0. 1.12
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 9 9 18 8 39 26 17 27
normalized size 1 1. 2. 0.89 4.33 2.89 1.89 3.
time (sec) N/A 0.027 0.02 0.067 1.097 0.483 0.233 1.115
Problem 196 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 14 14 23 13 73 38 0 19
normalized size 1 1. 1.64 0.93 5.21 2.71 0. 1.36
time (sec) N/A 0.082 0.022 0.083 1.664 0.482 0. 1.109
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 6 6 6 15 41 16 0 19
normalized size 1 1. 1. 2.5 6.83 2.67 0. 3.17
time (sec) N/A 0.06 0.021 0.099 1.483 0.47 0. 1.121
Problem 198 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 15 15 29 15 38 89 0 19
normalized size 1 1. 1.93 1. 2.53 5.93 0. 1.27
time (sec) N/A 0.06 0.036 0.067 1.496 0.468 0. 1.142
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 7 7 18 8 31 81 0 11
normalized size 1 1. 2.57 1.14 4.43 11.57 0. 1.57
time (sec) N/A 0.089 0.022 0.105 1.505 0.49 0. 1.156
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 25 11 20 61 0 14
normalized size 1 1. 2.27 1. 1.82 5.55 0. 1.27
time (sec) N/A 0.029 0.016 0.059 0.982 0.457 0. 1.159
Problem 201 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 13 13 22 8 34 49 0 19
normalized size 1 1. 1.69 0.62 2.62 3.77 0. 1.46
time (sec) N/A 0.062 0.022 0.09 1.015 0.488 0. 1.126
Problem 202 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 23 23 15 24 30 51 27 22
normalized size 1 1. 0.65 1.04 1.3 2.22 1.17 0.96
time (sec) N/A 0.094 0.014 0.027 1.044 0.458 6.244 1.125
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 6 6 14 19 51 16 0 24
normalized size 1 1. 2.33 3.17 8.5 2.67 0. 4.
time (sec) N/A 0.07 0.007 0.083 1.666 0.465 0. 1.096
Problem 204 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 10 10 20 11 46 45 0 14
normalized size 1 1. 2. 1.1 4.6 4.5 0. 1.4
time (sec) N/A 0.067 0.007 0.082 1.6 0.485 0. 1.122
Problem 205 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 7 7 36 21 53 66 0 30
normalized size 1 1. 5.14 3. 7.57 9.43 0. 4.29
time (sec) N/A 0.085 0.027 0.086 1.641 0.49 0. 1.139
Problem 206 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 12 12 10 9 31 51 0 11
normalized size 1 1. 0.83 0.75 2.58 4.25 0. 0.92
time (sec) N/A 0.054 0.018 0.057 1.666 0.487 0. 1.132
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 25 6 39 53 0 16
normalized size 1 1. 2.27 0.55 3.55 4.82 0. 1.45
time (sec) N/A 0.06 0.009 0.078 1.108 0.485 0. 1.141
Problem 208 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 9 9 6 5 12 28 0 5
normalized size 1 1. 0.67 0.56 1.33 3.11 0. 0.56
time (sec) N/A 0.026 0.019 0.05 1.076 0.458 0. 1.171
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 4 4 14 19 51 16 0 24
normalized size 1 1. 3.5 4.75 12.75 4. 0. 6.
time (sec) N/A 0.07 0.007 0.079 1.532 0.47 0. 1.121
Problem 210 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 10 10 20 9 62 45 0 14
normalized size 1 1. 2. 0.9 6.2 4.5 0. 1.4
time (sec) N/A 0.068 0.01 0.078 1.662 0.481 0. 1.092
Problem 211 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 5 5 46 19 53 65 0 27
normalized size 1 1. 9.2 3.8 10.6 13. 0. 5.4
time (sec) N/A 0.094 0.016 0.095 1.672 0.488 0. 1.134
Problem 212 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 16 16 16 13 31 45 0 16
normalized size 1 1. 1. 0.81 1.94 2.81 0. 1.
time (sec) N/A 0.06 0.015 0.063 1.642 0.465 0. 1.093
Problem 213 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 13 13 25 6 55 54 0 19
normalized size 1 1. 1.92 0.46 4.23 4.15 0. 1.46
time (sec) N/A 0.061 0.01 0.081 1.093 0.48 0. 1.104
Problem 214 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 12 12 8 9 14 30 0 11
normalized size 1 1. 0.67 0.75 1.17 2.5 0. 0.92
time (sec) N/A 0.03 0.007 0.054 1.118 0.455 0. 1.131
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 61 21 238 119 0 92
normalized size 1 1. 2.65 0.91 10.35 5.17 0. 4.
time (sec) N/A 0.039 0.185 0.077 1.663 0.485 0. 1.247
Problem 216 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 51 51 30 30 340 140 0 111
normalized size 1 1. 0.59 0.59 6.67 2.75 0. 2.18
time (sec) N/A 0.172 0.072 0.087 1.692 0.494 0. 1.199
Problem 217 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 18 18 20 17 22 43 0 22
normalized size 1 1. 1.11 0.94 1.22 2.39 0. 1.22
time (sec) N/A 0.031 0.107 0.042 1.674 0.493 0. 1.152
Problem 218 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 29 29 24 42 47 111 0 50
normalized size 1 1. 0.83 1.45 1.62 3.83 0. 1.72
time (sec) N/A 0.038 0.035 0.102 1.61 0.519 0. 1.197
Problem 219 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 11 11 11 13 15 32 0 15
normalized size 1 1. 1. 1.18 1.36 2.91 0. 1.36
time (sec) N/A 0.025 0.036 0.045 1.665 0.486 0. 1.14
Problem 220 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 16 16 30 19 53 77 0 107
normalized size 1 1. 1.88 1.19 3.31 4.81 0. 6.69
time (sec) N/A 0.032 0.048 0.05 1.577 0.497 0. 1.231
Problem 221 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 48 48 22 20 331 128 0 97
normalized size 1 1. 0.46 0.42 6.9 2.67 0. 2.02
time (sec) N/A 0.108 0.025 0.07 1.835 0.485 0. 1.18
Problem 222 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 10 10 10 13 38 27 0 38
normalized size 1 1. 1. 1.3 3.8 2.7 0. 3.8
time (sec) N/A 0.025 0.009 0.076 1.048 0.449 0. 1.101
Problem 223 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 14 14 23 24 86 72 0 24
normalized size 1 1. 1.64 1.71 6.14 5.14 0. 1.71
time (sec) N/A 0.147 0.008 0.079 1.623 0.47 0. 1.12
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 12 13 32 31 0 35
normalized size 1 1. 1. 1.08 2.67 2.58 0. 2.92
time (sec) N/A 0.031 0.007 0.041 1.11 0.487 0. 1.154
Problem 225 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 34 34 34 60 62 163 0 65
normalized size 1 1. 1. 1.76 1.82 4.79 0. 1.91
time (sec) N/A 0.039 0.016 0.103 1.119 0.498 0. 1.195
Problem 226 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 11 11 11 12 35 76 0 38
normalized size 1 1. 1. 1.09 3.18 6.91 0. 3.45
time (sec) N/A 0.026 0.002 0.075 1.073 0.489 0. 1.185
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 14 23 32 0 62
normalized size 1 1. 1. 0.93 1.53 2.13 0. 4.13
time (sec) N/A 0.032 0.012 0.046 1.098 0.48 0. 1.144
Problem 228 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 10 10 10 11 59 42 0 14
normalized size 1 1. 1. 1.1 5.9 4.2 0. 1.4
time (sec) N/A 0.086 0.004 0.067 1.058 0.448 0. 1.144
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 33 29 38 69 0 0
normalized size 1 1. 1. 0.88 1.15 2.09 0. 0.
time (sec) N/A 0.062 0.012 0.032 1.1 0.487 0. 0.
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 38 29 38 68 0 134
normalized size 1 1. 1.15 0.88 1.15 2.06 0. 4.06
time (sec) N/A 0.054 0.115 0.03 1.066 0.486 0. 1.211
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 29 40 26 34 62 0 138
normalized size 1 1.32 1.82 1.18 1.55 2.82 0. 6.27
time (sec) N/A 0.03 0.011 0.023 1.107 0.477 0. 1.191
Problem 232 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 26 26 37 31 34 59 37 36
normalized size 1 1. 1.42 1.19 1.31 2.27 1.42 1.38
time (sec) N/A 0.013 0.018 0.014 1.065 0.501 0.56 1.126
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 25 43 80 0 144
normalized size 1 1. 1. 1. 1.72 3.2 0. 5.76
time (sec) N/A 0.028 0.013 0.028 1.116 0.501 0. 1.167
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 28 25 36 63 0 96
normalized size 1 1. 1. 0.89 1.29 2.25 0. 3.43
time (sec) N/A 0.05 0.02 0.03 1.025 0.468 0. 1.158
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 33 28 43 66 0 131
normalized size 1 1. 1. 0.85 1.3 2. 0. 3.97
time (sec) N/A 0.057 0.023 0.033 1.054 0.472 0. 1.167
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 77 100 92 211 0 0
normalized size 1 1. 0.73 0.94 0.87 1.99 0. 0.
time (sec) N/A 0.349 0.396 0.063 1.119 0.5 0. 0.
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 82 86 89 178 0 6967
normalized size 1 1. 0.95 1. 1.03 2.07 0. 81.01
time (sec) N/A 0.19 0.223 0.059 1.017 0.499 0. 7.746
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 117 83 103 207 0 7713
normalized size 1 1. 1.34 0.95 1.18 2.38 0. 88.66
time (sec) N/A 0.321 0.152 0.052 1.113 0.529 0. 5.721
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 116 99 113 279 0 3715
normalized size 1 1. 1.51 1.29 1.47 3.62 0. 48.25
time (sec) N/A 0.116 0.605 0.045 1.571 0.525 0. 2.314
Problem 240 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 75 123 138 305 0 231
normalized size 1 1. 0.83 1.37 1.53 3.39 0. 2.57
time (sec) N/A 0.426 0.193 0.063 1.717 0.545 0. 2.759
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 99 99 201 109 111 294 0 213
normalized size 1 1. 2.03 1.1 1.12 2.97 0. 2.15
time (sec) N/A 0.467 1.146 0.073 1.699 0.523 0. 2.905
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 336 169 174 325 0 305
normalized size 1 1. 2.69 1.35 1.39 2.6 0. 2.44
time (sec) N/A 0.44 0.636 0.08 1.13 0.525 0. 2.9
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 114 109 128 240 0 0
normalized size 1 1. 1.48 1.42 1.66 3.12 0. 0.
time (sec) N/A 0.189 0.249 0.078 1.161 0.508 0. 0.
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 120 120 106 128 127 247 0 0
normalized size 1 1. 0.88 1.07 1.06 2.06 0. 0.
time (sec) N/A 0.194 0.186 0.076 1.165 0.53 0. 0.
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 98 147 117 311 0 0
normalized size 1 1. 0.88 1.31 1.04 2.78 0. 0.
time (sec) N/A 0.177 0.272 0.06 1.12 0.538 0. 0.
Problem 246 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 102 164 153 300 0 0
normalized size 1 1. 0.88 1.41 1.32 2.59 0. 0.
time (sec) N/A 0.104 0.31 0.056 1.046 0.536 0. 0.
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 100 213 147 297 0 691
normalized size 1 1. 0.87 1.85 1.28 2.58 0. 6.01
time (sec) N/A 0.242 0.544 0.078 1.117 0.55 0. 100.792
Problem 248 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 97 204 130 258 0 567
normalized size 1 1. 0.87 1.84 1.17 2.32 0. 5.11
time (sec) N/A 0.254 1.978 0.09 1.086 0.542 0. 105.274
Problem 249 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 99 252 173 270 0 579
normalized size 1 1. 0.83 2.12 1.45 2.27 0. 4.87
time (sec) N/A 0.22 0.316 0.096 1.124 0.536 0. 104.493
Problem 250 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 100 111 254 288 0 409
normalized size 1 1. 0.88 0.98 2.25 2.55 0. 3.62
time (sec) N/A 0.341 0.376 0.124 1.642 0.633 0. 1.259
Problem 251 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 80 93 174 239 0 257
normalized size 1 1. 0.87 1.01 1.89 2.6 0. 2.79
time (sec) N/A 0.279 0.225 0.12 1.659 0.589 0. 1.247
Problem 252 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 80 80 70 80 138 190 0 180
normalized size 1 1. 0.88 1. 1.72 2.38 0. 2.25
time (sec) N/A 0.237 0.1 0.101 1.563 0.564 0. 1.216
Problem 253 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 74 74 63 75 96 173 0 135
normalized size 1 1. 0.85 1.01 1.3 2.34 0. 1.82
time (sec) N/A 0.08 0.085 0.099 1.136 0.534 0. 1.213
Problem 254 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 75 75 64 75 99 174 0 136
normalized size 1 1. 0.85 1. 1.32 2.32 0. 1.81
time (sec) N/A 0.186 0.062 0.123 1.06 0.539 0. 1.205
Problem 255 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 94 94 103 95 169 236 0 180
normalized size 1 1. 1.1 1.01 1.8 2.51 0. 1.91
time (sec) N/A 0.27 0.151 0.137 1.16 0.77 0. 1.268
Problem 256 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 108 108 92 110 213 360 0 257
normalized size 1 1. 0.85 1.02 1.97 3.33 0. 2.38
time (sec) N/A 0.284 0.292 0.132 1.075 0.912 0. 1.264
Problem 257 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 243 243 164 291 0 1839 0 639
normalized size 1 1. 0.67 1.2 0. 7.57 0. 2.63
time (sec) N/A 0.611 3.06 0.186 0. 0.701 0. 1.29
Problem 258 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 227 227 151 255 0 1507 0 447
normalized size 1 1. 0.67 1.12 0. 6.64 0. 1.97
time (sec) N/A 0.491 2.166 0.171 0. 0.635 0. 1.228
Problem 259 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 219 219 131 155 0 1134 0 381
normalized size 1 1. 0.6 0.71 0. 5.18 0. 1.74
time (sec) N/A 0.385 1.294 0.145 0. 0.596 0. 1.212
Problem 260 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 203 203 128 162 0 1164 0 390
normalized size 1 1. 0.63 0.8 0. 5.73 0. 1.92
time (sec) N/A 0.399 1.246 0.148 0. 0.591 0. 1.13
Problem 261 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 127 162 0 1164 0 389
normalized size 1 1. 0.93 1.19 0. 8.56 0. 2.86
time (sec) N/A 0.318 1.137 0.17 0. 0.599 0. 1.214
Problem 262 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 121 155 0 1131 0 383
normalized size 1 1. 0.92 1.18 0. 8.63 0. 2.92
time (sec) N/A 0.334 0.763 0.188 0. 0.584 0. 1.205
Problem 263 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 231 231 196 276 0 1906 0 478
normalized size 1 1. 0.85 1.19 0. 8.25 0. 2.07
time (sec) N/A 0.437 2.002 0.186 0. 2.544 0. 1.294
Problem 264 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 248 248 713 333 923 2583 0 1145
normalized size 1 1. 2.88 1.34 3.72 10.42 0. 4.62
time (sec) N/A 0.902 6.347 0.18 1.897 1.802 0. 1.489
Problem 265 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 232 232 204 295 795 2279 0 913
normalized size 1 1. 0.88 1.27 3.43 9.82 0. 3.94
time (sec) N/A 0.762 6.179 0.174 1.207 1.194 0. 1.378
Problem 266 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 211 211 184 220 801 2115 0 932
normalized size 1 1. 0.87 1.04 3.8 10.02 0. 4.42
time (sec) N/A 0.668 5.478 0.142 1.309 1.108 0. 1.366
Problem 267 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 229 229 696 322 811 2344 0 1080
normalized size 1 1. 3.04 1.41 3.54 10.24 0. 4.72
time (sec) N/A 0.48 6.311 0.151 1.213 1.226 0. 1.23
Problem 268 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 231 231 703 324 813 2338 0 1081
normalized size 1 1. 3.04 1.4 3.52 10.12 0. 4.68
time (sec) N/A 0.621 6.313 0.177 1.194 1.174 0. 1.386
Problem 269 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 212 212 217 251 805 2021 0 930
normalized size 1 1. 1.02 1.18 3.8 9.53 0. 4.39
time (sec) N/A 0.364 6.273 0.194 1.267 1.112 0. 1.396
Problem 270 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 228 228 217 256 798 2142 0 911
normalized size 1 1. 0.95 1.12 3.5 9.39 0. 4.
time (sec) N/A 0.408 6.262 0.183 1.238 1.161 0. 1.393
Problem 271 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 246 0 243 876 0 0
normalized size 1 1. 1.59 0. 1.57 5.65 0. 0.
time (sec) N/A 0.385 1.512 3.616 1.129 0.612 0. 0.
Problem 272 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 264 264 401 0 0 0 0 0
normalized size 1 1. 1.52 0. 0. 0. 0. 0.
time (sec) N/A 0.764 12.386 1.85 0. 0. 0. 0.
Problem 273 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 35 40 0 81 0 0
normalized size 1 1. 0.9 1.03 0. 2.08 0. 0.
time (sec) N/A 0.073 0.079 0.056 0. 0.495 0. 0.
Problem 274 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 106 0 0 0 0 0
normalized size 1 1. 0.74 0. 0. 0. 0. 0.
time (sec) N/A 0.432 0.39 0.547 0. 0. 0. 0.
Problem 275 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 61 81 0 348 0 127
normalized size 1 1. 0.94 1.25 0. 5.35 0. 1.95
time (sec) N/A 0.065 0.13 0.079 0. 0.523 0. 1.261
Problem 276 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 153 174 285 221 0 205
normalized size 1 1. 1.66 1.89 3.1 2.4 0. 2.23
time (sec) N/A 0.139 0.324 0.069 1.642 0.514 0. 1.139
Problem 277 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 122 122 113 166 0 494 0 257
normalized size 1 1. 0.93 1.36 0. 4.05 0. 2.11
time (sec) N/A 0.166 1.007 0.092 0. 0.539 0. 1.208
Problem 278 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 93 93 82 175 286 223 0 211
normalized size 1 1. 0.88 1.88 3.08 2.4 0. 2.27
time (sec) N/A 0.133 0.303 0.069 1.645 0.514 0. 1.143
Problem 279 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 115 168 0 498 0 259
normalized size 1 1. 1.03 1.5 0. 4.45 0. 2.31
time (sec) N/A 0.196 0.655 0.091 0. 0.535 0. 1.229
Problem 280 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 176 176 178 363 582 396 0 371
normalized size 1 1. 1.01 2.06 3.31 2.25 0. 2.11
time (sec) N/A 0.278 0.507 0.075 1.789 0.555 0. 1.121
Problem 281 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 112 170 0 494 0 271
normalized size 1 1. 0.91 1.38 0. 4.02 0. 2.2
time (sec) N/A 0.158 1.069 0.091 0. 0.537 0. 1.218
Problem 282 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 175 175 287 363 572 397 0 369
normalized size 1 1. 1.64 2.07 3.27 2.27 0. 2.11
time (sec) N/A 0.278 0.758 0.078 1.654 0.558 0. 1.173
Problem 283 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 193 193 223 305 0 706 0 487
normalized size 1 1. 1.16 1.58 0. 3.66 0. 2.52
time (sec) N/A 0.359 1.552 0.111 0. 0.584 0. 1.236
Problem 284 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 87 144 120 159 323 0 194
normalized size 1 1.24 2.06 1.71 2.27 4.61 0. 2.77
time (sec) N/A 0.166 0.239 0.089 1.711 0.506 0. 1.091
Problem 285 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 152 111 142 0 597 0 282
normalized size 1 1.38 1.01 1.29 0. 5.43 0. 2.56
time (sec) N/A 0.239 0.589 0.114 0. 0.544 0. 1.206
Problem 286 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 129 198 226 243 350 531 0 301
normalized size 1 1.53 1.75 1.88 2.71 4.12 0. 2.33
time (sec) N/A 0.506 1.438 0.101 1.704 0.56 0. 1.12
Problem 287 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 151 110 144 0 586 0 275
normalized size 1 1.39 1.01 1.32 0. 5.38 0. 2.52
time (sec) N/A 0.259 0.682 0.121 0. 0.543 0. 1.24
Problem 288 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 186 145 260 347 540 0 296
normalized size 1 1.42 1.11 1.98 2.65 4.12 0. 2.26
time (sec) N/A 0.545 1.585 0.105 1.697 0.566 0. 1.091
Problem 289 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 172 238 200 269 0 818 0 462
normalized size 1 1.38 1.16 1.56 0. 4.76 0. 2.69
time (sec) N/A 0.677 1.217 0.133 0. 0.6 0. 1.214
Problem 290 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 128 196 221 241 346 562 0 289
normalized size 1 1.53 1.73 1.88 2.7 4.39 0. 2.26
time (sec) N/A 0.408 1.285 0.098 1.7 0.56 0. 1.132
Problem 291 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 176 238 198 261 0 838 0 452
normalized size 1 1.35 1.12 1.48 0. 4.76 0. 2.57
time (sec) N/A 0.697 1.223 0.131 0. 0.604 0. 1.216
Problem 292 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 210 289 409 515 616 822 0 587
normalized size 1 1.38 1.95 2.45 2.93 3.91 0. 2.8
time (sec) N/A 1.251 2.758 0.108 1.653 0.65 0. 1.116
Problem 293 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 76 63 0 347 0 122
normalized size 1 1. 1.62 1.34 0. 7.38 0. 2.6
time (sec) N/A 0.079 0.117 0.101 0. 0.591 0. 1.245
Problem 294 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 60 49 0 363 0 101
normalized size 1 1. 1.25 1.02 0. 7.56 0. 2.1
time (sec) N/A 0.078 0.083 0.106 0. 0.574 0. 1.193

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [286] had the largest ratio of [ 0.7222 ]

Table 2.1Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\)
1 A 7 5 1. 14 0.357
2 A 6 4 1. 14 0.286
3 A 6 5 1. 12 0.417
4 A 3 2 1. 9 0.222
5 A 3 2 1. 12 0.167
6 A 5 4 1. 14 0.286
7 A 6 5 1. 14 0.357
8 A 5 5 1. 16 0.312
9 A 4 4 1. 16 0.25
10 A 2 2 1. 14 0.143
11 A 2 2 1. 11 0.182
12 A 3 3 1. 14 0.214
13 A 4 4 1. 16 0.25
14 A 6 6 1. 16 0.375
15 B 19 11 2.64 16 0.688
16 A 4 4 1. 16 0.25
17 A 3 3 1. 14 0.214
18 A 1 1 1. 11 0.091
19 A 4 4 1. 14 0.286
20 A 3 2 1. 16 0.125
21 A 11 7 1. 16 0.438
22 A 5 5 1. 16 0.312
23 B 13 7 3.26 16 0.438
24 A 2 2 1.27 14 0.143
25 A 3 3 1. 11 0.273
26 A 3 2 1. 14 0.143
27 A 12 7 1. 16 0.438
28 A 3 2 1. 16 0.125
29 A 1 1 1. 33 0.03
30 A 8 5 1. 26 0.192
31 A 6 4 1. 26 0.154
32 A 7 5 1. 26 0.192
33 A 6 4 1. 26 0.154
34 A 6 5 1. 24 0.208
35 A 3 2 1. 17 0.118
36 A 3 2 1. 24 0.083
37 A 5 4 1. 26 0.154
38 A 6 5 1. 26 0.192
39 A 6 5 1. 26 0.192
40 A 6 4 1. 26 0.154
41 A 7 5 1. 26 0.192
42 A 6 4 1. 26 0.154
43 A 9 6 1. 28 0.214
44 A 12 6 1. 28 0.214
45 A 9 6 1. 28 0.214
46 A 10 6 1. 28 0.214
47 A 8 5 1. 26 0.192
48 A 2 2 1. 19 0.105
49 A 7 6 1. 26 0.231
50 A 3 3 1. 28 0.107
51 A 7 5 1. 28 0.179
52 A 2 2 1. 28 0.071
53 A 9 6 1. 28 0.214
54 A 3 2 1. 28 0.071
55 A 11 6 1. 28 0.214
56 A 3 2 1. 28 0.071
57 A 17 7 1. 28 0.25
58 A 12 7 1. 28 0.25
59 A 15 8 1. 28 0.286
60 A 12 6 1. 28 0.214
61 A 4 4 1. 26 0.154
62 A 2 1 1. 19 0.053
63 A 7 6 1. 26 0.231
64 A 10 8 1. 28 0.286
65 A 4 4 1. 28 0.143
66 A 9 5 1. 28 0.179
67 A 2 2 1. 28 0.071
68 A 12 7 1. 28 0.25
69 A 3 2 1. 28 0.071
70 A 14 7 1. 28 0.25
71 A 3 2 1. 28 0.071
72 A 16 7 1. 28 0.25
73 A 3 2 1. 28 0.071
74 A 15 7 1. 28 0.25
75 A 22 7 1. 28 0.25
76 A 15 7 1. 28 0.25
77 A 19 8 1. 28 0.286
78 A 14 6 1. 26 0.231
79 A 3 2 1. 19 0.105
80 A 14 8 1. 26 0.308
81 A 7 6 1. 28 0.214
82 A 14 9 1. 28 0.321
83 A 5 5 1. 28 0.179
84 A 12 5 1. 28 0.179
85 A 2 2 1. 28 0.071
86 A 16 7 1. 28 0.25
87 A 3 2 1. 28 0.071
88 A 19 7 1. 28 0.25
89 A 3 2 1. 28 0.071
90 A 22 7 1. 28 0.25
91 A 3 2 1. 28 0.071
92 A 29 10 1. 28 0.357
93 A 18 7 1. 28 0.25
94 A 25 8 1. 28 0.286
95 A 18 7 1. 28 0.25
96 A 5 4 1. 26 0.154
97 A 3 2 1. 19 0.105
98 A 8 6 1. 26 0.231
99 A 17 10 1. 28 0.357
100 A 7 6 1. 28 0.214
101 A 17 10 1. 28 0.357
102 A 6 5 1. 28 0.179
103 A 15 6 1. 28 0.214
104 A 2 2 1. 28 0.071
105 A 19 8 1. 28 0.286
106 A 3 2 1. 28 0.071
107 A 22 8 1. 28 0.286
108 A 3 2 1. 28 0.071
109 A 25 8 1. 28 0.286
110 A 9 5 1. 28 0.179
111 A 7 5 1. 28 0.179
112 A 5 5 1. 28 0.179
113 A 4 4 1. 28 0.143
114 A 2 2 1. 26 0.077
115 A 2 2 1. 19 0.105
116 A 3 3 1. 26 0.115
117 A 4 4 1. 28 0.143
118 A 6 6 1. 28 0.214
119 A 7 5 1. 28 0.179
120 A 9 6 1. 28 0.214
121 A 11 5 1. 28 0.179
122 A 7 6 1. 28 0.214
123 A 11 6 1.67 28 0.214
124 A 4 4 1. 28 0.143
125 A 3 3 1. 26 0.115
126 A 1 1 1. 19 0.053
127 A 4 4 1. 26 0.154
128 A 3 2 1. 28 0.071
129 A 11 7 1. 28 0.25
130 A 3 2 1. 28 0.071
131 B 15 7 2.28 28 0.25
132 A 5 5 1. 28 0.179
133 A 6 4 1.89 28 0.143
134 A 2 2 1.36 26 0.077
135 A 3 3 1. 19 0.158
136 A 3 2 1. 26 0.077
137 A 12 7 1. 28 0.25
138 A 3 2 1. 28 0.071
139 A 31 8 1. 28 0.286
140 A 3 2 1. 28 0.071
141 A 6 5 1. 28 0.179
142 B 7 4 2.31 28 0.143
143 A 2 2 1. 28 0.071
144 A 5 5 1. 26 0.192
145 A 2 2 1. 19 0.105
146 A 8 5 1. 26 0.192
147 A 3 2 1. 28 0.071
148 A 32 8 1. 28 0.286
149 A 3 2 1. 28 0.071
150 A 9 6 1. 31 0.194
151 A 7 5 1. 31 0.161
152 A 8 6 1. 31 0.194
153 A 7 5 1. 31 0.161
154 A 2 2 1. 29 0.069
155 A 1 1 1. 22 0.045
156 A 4 3 1. 29 0.103
157 A 6 5 1. 31 0.161
158 A 7 6 1. 31 0.194
159 A 7 6 1. 31 0.194
160 A 7 5 1. 31 0.161
161 A 8 6 1. 31 0.194
162 A 7 5 1. 31 0.161
163 A 10 7 1. 31 0.226
164 A 5 4 1. 31 0.129
165 A 10 7 1. 31 0.226
166 A 3 2 1. 31 0.065
167 A 9 6 1. 29 0.207
168 A 1 1 1. 22 0.045
169 A 8 7 1. 29 0.241
170 A 4 3 1. 31 0.097
171 A 8 6 1. 31 0.194
172 A 3 3 1. 31 0.097
173 A 10 7 1. 31 0.226
174 A 4 3 1. 31 0.097
175 A 5 4 1. 31 0.129
176 A 13 8 1. 31 0.258
177 A 4 2 1. 31 0.065
178 A 13 7 1. 31 0.226
179 A 2 2 1. 29 0.069
180 A 1 1 1. 22 0.045
181 A 4 3 1. 29 0.103
182 A 11 9 1. 31 0.29
183 A 4 3 1. 31 0.097
184 A 10 6 1. 31 0.194
185 A 3 3 1. 31 0.097
186 A 13 8 1. 31 0.258
187 A 1 1 1. 33 0.03
188 A 3 3 1. 7 0.429
189 A 4 3 1. 10 0.3
190 A 3 3 1. 10 0.3
191 A 3 3 1. 10 0.3
192 A 4 4 1. 10 0.4
193 A 2 2 1. 10 0.2
194 A 5 5 1. 10 0.5
195 A 3 3 1. 9 0.333
196 A 4 3 1. 12 0.25
197 A 3 3 1. 12 0.25
198 A 3 3 1. 12 0.25
199 A 4 4 1. 12 0.333
200 A 2 2 1. 12 0.167
201 A 5 5 1. 12 0.417
202 A 4 4 1. 20 0.2
203 A 3 3 1. 10 0.3
204 A 4 3 1. 10 0.3
205 A 4 4 1. 10 0.4
206 A 3 3 1. 10 0.3
207 A 5 5 1. 10 0.5
208 A 2 2 1. 10 0.2
209 A 3 3 1. 12 0.25
210 A 4 3 1. 12 0.25
211 A 4 4 1. 12 0.333
212 A 3 3 1. 12 0.25
213 A 5 5 1. 12 0.417
214 A 2 2 1. 12 0.167
215 A 3 3 1. 15 0.2
216 A 4 2 1. 22 0.091
217 A 2 2 1. 22 0.091
218 A 4 3 1. 22 0.136
219 A 2 2 1. 22 0.091
220 A 3 2 1. 22 0.091
221 A 2 1 1. 22 0.045
222 A 3 3 1. 17 0.176
223 A 3 2 1. 24 0.083
224 A 2 2 1. 24 0.083
225 A 3 2 1. 24 0.083
226 A 2 2 1. 24 0.083
227 A 2 1 1. 24 0.042
228 A 2 1 1. 24 0.042
229 A 6 4 1. 26 0.154
230 A 6 5 1. 26 0.192
231 A 5 5 1.32 24 0.208
232 A 3 2 1. 17 0.118
233 A 5 5 1. 24 0.208
234 A 6 5 1. 26 0.192
235 A 6 4 1. 26 0.154
236 A 6 5 1. 28 0.179
237 A 5 5 1. 28 0.179
238 A 7 7 1. 26 0.269
239 A 10 8 1. 19 0.421
240 A 7 7 1. 26 0.269
241 A 7 7 1. 28 0.25
242 A 9 9 1. 28 0.321
243 A 4 3 1. 28 0.107
244 A 5 4 1. 28 0.143
245 A 5 4 1. 26 0.154
246 A 4 3 1. 19 0.158
247 A 5 4 1. 26 0.154
248 A 5 4 1. 28 0.143
249 A 5 4 1. 28 0.143
250 A 5 4 1. 28 0.143
251 A 5 4 1. 28 0.143
252 A 5 4 1. 26 0.154
253 A 4 3 1. 19 0.158
254 A 7 5 1. 26 0.192
255 A 5 4 1. 28 0.143
256 A 5 4 1. 28 0.143
257 A 12 8 1. 28 0.286
258 A 11 7 1. 28 0.25
259 A 11 7 1. 26 0.269
260 A 11 7 1. 19 0.368
261 A 6 6 1. 26 0.231
262 A 6 6 1. 28 0.214
263 A 12 8 1. 28 0.286
264 A 6 5 1. 28 0.179
265 A 6 5 1. 28 0.179
266 A 6 5 1. 26 0.192
267 A 5 4 1. 19 0.21
268 A 6 5 1. 26 0.192
269 A 6 5 1. 28 0.179
270 A 5 4 1. 28 0.143
271 A 4 3 1. 28 0.107
272 A 8 7 1. 28 0.25
273 A 6 4 1. 26 0.154
274 A 7 4 1. 28 0.143
275 A 5 5 1. 16 0.312
276 A 7 7 1. 18 0.389
277 A 9 8 1. 18 0.444
278 A 7 7 1. 18 0.389
279 A 10 8 1. 20 0.4
280 A 13 8 1. 20 0.4
281 A 9 8 1. 18 0.444
282 A 13 9 1. 20 0.45
283 A 17 9 1. 20 0.45
284 A 6 5 1.24 16 0.312
285 A 13 8 1.38 18 0.444
286 A 17 13 1.53 18 0.722
287 A 13 8 1.39 18 0.444
288 A 21 10 1.42 20 0.5
289 A 33 12 1.38 20 0.6
290 A 17 13 1.53 18 0.722
291 A 33 12 1.35 20 0.6
292 A 48 12 1.38 20 0.6
293 A 5 4 1. 14 0.286
294 A 5 4 1. 14 0.286

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