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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 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, 280, 282, 283 }

B grade: { }

C grade: { }

F grade: { 169, 278, 279, 281, 284}

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 46, 47, 48, 49, 50, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 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, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 191, 192, 193, 194, 195, 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, 232, 233, 234, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 282, 283, 284 }

B grade: { 52, 81, 82, 108, 111, 120, 121, 190, 202, 235, 236, 256, 280 }

C grade: { 20, 44, 45, 51, 278, 279, 281 }

F grade: { 60}

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 46, 47, 48, 50, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 125, 127, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 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, 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, 238, 239, 240, 241, 243, 244, 245, 246, 247, 248, 249, 250, 252, 253, 254, 255, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 281, 283, 284 }

B grade: { 32, 44, 45, 60, 61, 110, 124, 126, 134, 135, 176, 204, 237, 242, 256, 257, 278, 280 }

C grade: { 49, 51, 203, 279, 282 }

F grade: { 86, 251 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 41, 46, 47, 48, 50, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 113, 114, 115, 116, 117, 118, 119, 120, 121, 124, 125, 126, 127, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 148, 149, 150, 151, 152, 153, 154, 155, 156, 158, 159, 162, 164, 165, 167, 169, 170, 171, 172, 173, 174, 177, 178, 179, 182, 183, 184, 188, 189, 190, 192, 193, 198, 199, 200, 201, 202, 209, 210, 215, 216, 217, 218, 219, 220, 221, 223, 227, 228, 229, 230, 231, 232, 233, 234, 237, 238, 240, 242, 243, 244, 245, 246, 247, 248, 249, 250, 252, 253, 254, 255, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 283

B grade: { 81, 82, 111, 112, 128, 129, 130, 146, 191, 194, 195, 204, 222, 225, 226, 241, 256, 280 }

C grade: { 102, 103, 104, 105, 166, 168, 197 }

F grade: { 8, 21, 35, 39, 40, 42, 43, 44, 45, 49, 51, 56, 64, 86, 122, 123, 147, 157, 160, 161, 163, 175, 176, 180, 181, 185, 186, 187, 196, 203, 205, 206, 207, 208, 211, 212, 213, 214, 224, 235, 236, 239, 251, 257, 278, 279, 281, 282, 284 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 38, 43, 46, 47, 48, 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, 83, 84, 85, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 196, 198, 200, 201, 202, 203, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 223, 224, 225, 226, 229, 230, 231, 232, 233, 234, 237, 238, 239, 240, 241, 242, 243, 248, 249, 250, 251, 252, 253, 255, 258, 259, 261, 262, 263, 264, 265, 266, 267, 270, 271, 272, 273, 274, 275, 276, 277, 279, 282, 283 }

B grade: { 36, 37, 39, 40, 41, 42, 44, 45, 49, 78, 79, 80, 81, 82, 90, 103, 110, 111, 112, 127, 133, 194, 195, 199, 204, 220, 222, 227, 228, 235, 236, 244, 245, 246, 247, 254, 256, 260, 268, 269, 278, 280, 284 }

C grade: { 128, 129, 197 }

F grade: { 86, 174, 257, 281 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 10, 11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 74, 75, 76, 77, 78, 79, 83, 84, 85, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 127, 130, 132, 134, 135, 136, 137, 144, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 161, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 177, 181, 182, 185, 186, 187, 188, 190, 191, 192, 193, 194, 195, 199, 200, 201, 202, 205, 206, 209, 210, 215, 216, 217, 218, 219, 221, 223, 225, 226, 227, 230, 231, 232, 240, 241, 243, 244, 245, 248, 250, 252, 253, 255, 258, 259, 260, 261, 262, 263, 264, 266, 267, 268, 269, 270, 271, 273, 274, 276, 277, 282, 283, 284 }

B grade: { 7, 8, 12, 13, 32, 41, 80, 81, 82, 90, 103, 104, 131, 133, 138, 139, 140, 141, 142, 143, 175, 178, 179, 180, 183, 184, 189, 204, 220, 222, 228, 229, 233, 234, 239, 246, 247, 254, 256, 272 }

C grade: { 9, 14, 31, 50, 70, 72, 73, 203, 224 }

F grade: { 56, 86, 123, 128, 129, 145, 146, 147, 160, 162, 163, 176, 196, 197, 198, 207, 208, 211, 212, 213, 214, 235, 236, 237, 238, 242, 249, 251, 257, 265, 275, 278, 279, 280, 281 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 35, 36, 37, 38, 39, 40, 41, 42, 43, 46, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 126, 130, 131, 132, 133, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 164, 165, 167, 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, 196, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 223, 224, 225, 226, 227, 229, 230, 231, 232, 233, 234, 239, 240, 241, 242, 243, 248, 249, 250, 251, 252, 253, 254, 255, 258, 261, 262, 263, 264, 265, 266, 267, 270, 271, 272, 273, 275, 276, 277, 282, 283, 284 }

B grade: { 11, 23, 32, 79, 81, 82, 110, 111, 112, 118, 127, 195, 199, 220, 222, 228, 244, 245, 246, 247, 256, 260, 268, 269, 280 }

C grade: { 134, 135, 136, 137, 138, 139, 140, 141, 160, 161, 166, 197 }

F grade: { 33, 34, 44, 45, 47, 48, 56, 63, 86, 128, 129, 162, 163, 168, 169, 198, 200, 201, 203, 235, 236, 237, 238, 257, 259, 274, 278, 279, 281 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 13 16 31 10 16
normalized size 1 1. 1. 0.81 1. 1.94 0.62 1.
time (sec) N/A 0.002 0. 0.001 0.941 1.573 0.051 1.091
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 22 22 22 17 22 39 17 22
normalized size 1 1. 1. 0.77 1. 1.77 0.77 1.
time (sec) N/A 0.01 0.001 0. 0.95 1.605 0.053 1.101
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 22 22 22 17 22 39 15 22
normalized size 1 1. 1. 0.77 1. 1.77 0.68 1.
time (sec) N/A 0.004 0.001 0.001 0.948 1.781 0.052 1.093
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 2 2 2 3 3 11 2 4
normalized size 1 1. 1. 1.5 1.5 5.5 1. 2.
time (sec) N/A 0. 0. 0. 1.017 1.89 0.051 1.077
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 24 27 43 120 29 31
normalized size 1 1. 0.67 0.75 1.19 3.33 0.81 0.86
time (sec) N/A 0.013 0.011 0.006 0.949 1.84 0.109 1.067
Problem 6 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 32 32 28 25 32 108 24 46
normalized size 1 1. 0.88 0.78 1. 3.38 0.75 1.44
time (sec) N/A 0.012 0.011 0.008 0.948 1.772 0.134 1.082
Problem 7 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 40 40 34 66 54 77 144 57
normalized size 1 1. 0.85 1.65 1.35 1.92 3.6 1.42
time (sec) N/A 0.027 0.017 0.007 0.937 1.941 0.655 1.068
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 38 35 0 277 124 46
normalized size 1 1. 1.12 1.03 0. 8.15 3.65 1.35
time (sec) N/A 0.03 0.011 0.006 0. 2.004 0.198 1.082
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 15 19 46 26 19
normalized size 1 1. 1. 0.94 1.19 2.88 1.62 1.19
time (sec) N/A 0.006 0.006 0.002 1.42 1.989 0.154 1.075
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 16 17 19 55 22 19
normalized size 1 1. 0.84 0.89 1. 2.89 1.16 1.
time (sec) N/A 0.01 0.005 0.003 1.411 1.95 0.099 1.063
Problem 11 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 49 49 35 36 53 186 39 108
normalized size 1 1. 0.71 0.73 1.08 3.8 0.8 2.2
time (sec) N/A 0.029 0.02 0.011 1.433 1.932 0.161 1.119
Problem 12 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 68 68 62 69 105 166 4216 109
normalized size 1 1. 0.91 1.01 1.54 2.44 62. 1.6
time (sec) N/A 0.052 0.03 0.008 0.961 2.762 85.206 1.063
Problem 13 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 47 47 34 44 58 70 121 88
normalized size 1 1. 0.72 0.94 1.23 1.49 2.57 1.87
time (sec) N/A 0.02 0.011 0.007 0.948 2.019 0.54 1.141
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 30 41 54 61 393 54
normalized size 1 1. 0.75 1.02 1.35 1.52 9.82 1.35
time (sec) N/A 0.019 0.014 0.007 1.419 2.073 0.944 1.075
Problem 15 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 27 27 27 20 26 69 19 27
normalized size 1 1. 1. 0.74 0.96 2.56 0.7 1.
time (sec) N/A 0.018 0.004 0.004 1.424 2.015 0.114 1.088
Problem 16 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 41 41 40 35 46 112 41 47
normalized size 1 1. 0.98 0.85 1.12 2.73 1. 1.15
time (sec) N/A 0.02 0.008 0.006 1.417 1.829 0.121 1.104
Problem 17 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 34 32 42 124 31 49
normalized size 1 1. 0.79 0.74 0.98 2.88 0.72 1.14
time (sec) N/A 0.13 0.019 0.006 1.41 1.845 0.131 1.104
Problem 18 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 85 85 64 58 97 302 73 97
normalized size 1 1. 0.75 0.68 1.14 3.55 0.86 1.14
time (sec) N/A 0.041 0.018 0. 1.44 1.865 0.137 1.073
Problem 19 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 85 85 64 58 97 302 73 97
normalized size 1 1. 0.75 0.68 1.14 3.55 0.86 1.14
time (sec) N/A 0.041 0.01 0.001 1.45 1.951 0.137 1.102
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 67 67 73 54 72 180 70 72
normalized size 1 1. 1.09 0.81 1.07 2.69 1.04 1.07
time (sec) N/A 0.036 0.055 0.003 1.425 1.968 0.169 1.091
Problem 21 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 18 18 17 19 0 45 20 24
normalized size 1 1. 0.94 1.06 0. 2.5 1.11 1.33
time (sec) N/A 0.004 0.01 0.002 0. 2.082 0.057 1.089
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 33 36 57 104 201 103
normalized size 1 1. 0.85 0.92 1.46 2.67 5.15 2.64
time (sec) N/A 0.013 0.019 0.002 0.965 1.991 0.605 1.077
Problem 23 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 60 60 57 73 92 188 597 189
normalized size 1 1. 0.95 1.22 1.53 3.13 9.95 3.15
time (sec) N/A 0.021 0.027 0.005 0.954 2.109 1.185 1.071
Problem 24 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 22 7 15
normalized size 1 1. 1. 1.1 1.4 2.2 0.7 1.5
time (sec) N/A 0.001 0.001 0.002 0.95 1.927 0.057 1.078
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 12 13 16 24 10 16
normalized size 1 1. 1. 1.08 1.33 2. 0.83 1.33
time (sec) N/A 0.002 0.003 0.002 0.931 1.997 0.284 1.084
Problem 26 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 18 18 18 19 24 38 14 26
normalized size 1 1. 1. 1.06 1.33 2.11 0.78 1.44
time (sec) N/A 0.01 0.002 0.002 0.951 1.882 0.261 1.081
Problem 27 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 30 39 68 26 41
normalized size 1 1. 1. 0.97 1.26 2.19 0.84 1.32
time (sec) N/A 0.016 0.003 0.002 0.943 2.017 0.267 1.072
Problem 28 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 18 18 18 19 24 38 10 27
normalized size 1 1. 1. 1.06 1.33 2.11 0.56 1.5
time (sec) N/A 0.004 0.004 0.005 0.95 1.995 0.132 1.097
Problem 29 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 28 28 28 29 38 61 19 41
normalized size 1 1. 1. 1.04 1.36 2.18 0.68 1.46
time (sec) N/A 0.013 0.004 0.009 0.959 1.995 0.325 1.079
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 42 42 35 43 61 138 36 70
normalized size 1 1. 0.83 1.02 1.45 3.29 0.86 1.67
time (sec) N/A 0.023 0.038 0.01 0.931 1.845 0.404 1.064
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 11 14 20 20 14
normalized size 1 1. 1. 1.1 1.4 2. 2. 1.4
time (sec) N/A 0.002 0.002 0.005 1.431 1.878 0.104 1.066
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 22 28 46 15 31
normalized size 1 1. 1. 2.2 2.8 4.6 1.5 3.1
time (sec) N/A 0.003 0.003 0.004 0.946 1.905 0.112 1.072
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 66 58 89 209 78 0
normalized size 1 1. 0.85 0.74 1.14 2.68 1. 0.
time (sec) N/A 0.044 0.022 0.003 1.451 1.931 0.309 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 65 54 76 221 71 0
normalized size 1 1. 0.88 0.73 1.03 2.99 0.96 0.
time (sec) N/A 0.034 0.018 0.004 1.435 2.007 0.308 0.
Problem 35 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 115 115 89 92 0 751 20 140
normalized size 1 1. 0.77 0.8 0. 6.53 0.17 1.22
time (sec) N/A 0.066 0.029 0.003 0. 1.937 0.145 1.107
Problem 36 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 35 35 43 35 46 201 46 53
normalized size 1 1. 1.23 1. 1.31 5.74 1.31 1.51
time (sec) N/A 0.011 0.018 0.002 1.448 2.071 0.317 1.119
Problem 37 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 35 35 43 36 55 182 48 53
normalized size 1 1. 1.23 1.03 1.57 5.2 1.37 1.51
time (sec) N/A 0.014 0.015 0.003 1.439 1.927 0.323 1.111
Problem 38 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 171 171 120 111 204 621 151 128
normalized size 1 1. 0.7 0.65 1.19 3.63 0.88 0.75
time (sec) N/A 0.108 0.048 0.005 1.464 1.984 0.397 1.114
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 68 56 0 475 24 100
normalized size 1 1. 0.93 0.77 0. 6.51 0.33 1.37
time (sec) N/A 0.074 0.053 0.033 0. 1.983 0.35 1.148
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 68 56 0 475 24 100
normalized size 1 1. 0.93 0.77 0. 6.51 0.33 1.37
time (sec) N/A 0.017 0.025 0.025 0. 2.165 0.359 1.137
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 83 54 101 255 158 109
normalized size 1 1. 1.15 0.75 1.4 3.54 2.19 1.51
time (sec) N/A 0.065 0.035 0.006 1.446 1.893 0.414 1.086
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 67 60 0 408 24 136
normalized size 1 1. 1. 0.9 0. 6.09 0.36 2.03
time (sec) N/A 0.052 0.031 0.03 0. 1.995 0.423 1.123
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 67 60 0 266 92 69
normalized size 1 1. 1. 0.9 0. 3.97 1.37 1.03
time (sec) N/A 0.012 0.02 0.025 0. 2.084 0.189 1.082
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 196 196 91 386 0 988 24 0
normalized size 1 1. 0.46 1.97 0. 5.04 0.12 0.
time (sec) N/A 0.148 0.062 0.064 0. 2.085 0.47 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 196 196 91 386 0 932 24 0
normalized size 1 1. 0.46 1.97 0. 4.76 0.12 0.
time (sec) N/A 0.139 0.082 0.054 0. 2.159 0.487 0.
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 73 73 75 66 88 230 83 90
normalized size 1 1. 1.03 0.9 1.21 3.15 1.14 1.23
time (sec) N/A 0.1 0.016 0.008 1.432 1.965 0.229 1.079
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 122 111 151 603 14 0
normalized size 1 1. 0.88 0.8 1.09 4.37 0.1 0.
time (sec) N/A 0.192 0.04 0.071 1.441 2.022 0.572 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 115 95 144 593 14 0
normalized size 1 1. 0.83 0.69 1.04 4.3 0.1 0.
time (sec) N/A 0.281 0.027 0.098 1.435 2.133 0.256 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 339 339 209 22 0 3183 14 323
normalized size 1 1. 0.62 0.06 0. 9.39 0.04 0.95
time (sec) N/A 0.235 0.006 0.005 0. 2.206 1.155 1.095
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 98 66 119 371 44 122
normalized size 1 1. 1.01 0.68 1.23 3.82 0.45 1.26
time (sec) N/A 0.052 0.026 0. 1.433 2.119 128.354 1.086
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 275 275 42 30 0 608 165 277
normalized size 1 1. 0.15 0.11 0. 2.21 0.6 1.01
time (sec) N/A 0.262 0.012 0.007 0. 2.138 0.203 1.098
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 260 41 54 124 46 54
normalized size 1 1. 5.31 0.84 1.1 2.53 0.94 1.1
time (sec) N/A 0.037 0.11 0.005 1.446 2.041 0.167 1.098
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 8 8 8 9 11 19 5 11
normalized size 1 1. 1. 1.12 1.38 2.38 0.62 1.38
time (sec) N/A 0.001 0.001 0. 0.965 1.889 0.08 1.066
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 14 18 35 12 18
normalized size 1 1. 1. 0.82 1.06 2.06 0.71 1.06
time (sec) N/A 0.004 0.001 0. 0.94 1.895 0.084 1.092
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 14 18 35 12 18
normalized size 1 1. 1. 0.82 1.06 2.06 0.71 1.06
time (sec) N/A 0.006 0.001 0.002 0.946 1.923 0.086 1.089
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 19 34 0 59 0 0
normalized size 1 1. 0.73 1.31 0. 2.27 0. 0.
time (sec) N/A 0.01 0.007 0.007 0. 1.916 0. 0.
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 15 15 15 16 16 42 15 20
normalized size 1 1. 1. 1.07 1.07 2.8 1. 1.33
time (sec) N/A 0.004 0.001 0. 0.943 2.065 0.091 1.095
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 127 127 127 104 96 410 133 139
normalized size 1 1. 1. 0.82 0.76 3.23 1.05 1.09
time (sec) N/A 0.141 0.003 0.002 0.937 2.053 0.263 1.075
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 8 8 8 7 8 19 5 8
normalized size 1 1. 1. 0.88 1. 2.38 0.62 1.
time (sec) N/A 0.012 0.001 0. 0.94 2.004 0.082 1.094
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F B A A A A
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 2 2 0 9 4 23 2 4
normalized size 1 1. 0. 4.5 2. 11.5 1. 2.
time (sec) N/A 0.002 0.002 0.003 1.033 1.804 0.447 1.081
Problem 61 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 4 4 5 11 7 28 3 7
normalized size 1 1. 1.25 2.75 1.75 7. 0.75 1.75
time (sec) N/A 0.004 0.01 0.002 1.035 1.854 0.471 1.08
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 3 3 3 4 4 18 3 5
normalized size 1 1. 1. 1.33 1.33 6. 1. 1.67
time (sec) N/A 0.012 0.004 0. 0.955 2.004 0.086 1.074
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 15 8 62 14 0
normalized size 1 1. 1. 0.88 0.47 3.65 0.82 0.
time (sec) N/A 0.035 0.016 0.003 1.027 1.937 0.636 0.
Problem 64 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 12 12 12 13 0 34 15 16
normalized size 1 1. 1. 1.08 0. 2.83 1.25 1.33
time (sec) N/A 0.016 0.002 0.001 0. 2.048 0.917 1.089
Problem 65 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 28 29 28 25 34 63 22 32
normalized size 1 1.04 1. 0.89 1.21 2.25 0.79 1.14
time (sec) N/A 0.011 0.001 0.003 0.95 1.965 0.103 1.083
Problem 66 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 54 54 53 48 63 109 44 63
normalized size 1 1. 0.98 0.89 1.17 2.02 0.81 1.17
time (sec) N/A 0.028 0.01 0.001 0.959 1.982 0.12 1.081
Problem 67 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 27 30 51 77 24 49
normalized size 1 1. 0.93 1.03 1.76 2.66 0.83 1.69
time (sec) N/A 0.013 0.013 0.007 0.93 1.992 0.363 1.109
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 46 47 59 85 42 78
normalized size 1 1. 1. 1.02 1.28 1.85 0.91 1.7
time (sec) N/A 0.023 0.015 0.003 0.956 1.979 0.321 1.076
Problem 69 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 59 59 59 58 77 111 54 127
normalized size 1 1. 1. 0.98 1.31 1.88 0.92 2.15
time (sec) N/A 0.032 0.017 0.003 0.945 1.968 0.33 1.072
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 24 31 57 36 31
normalized size 1 1. 1. 1.04 1.35 2.48 1.57 1.35
time (sec) N/A 0.007 0.002 0.003 1.443 2.056 0.305 1.181
Problem 71 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 27 27 26 29 38 58 31 38
normalized size 1 1. 0.96 1.07 1.41 2.15 1.15 1.41
time (sec) N/A 0.02 0.003 0.001 0.966 2.021 0.307 1.084
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 44 37 49 93 53 49
normalized size 1 1. 1. 0.84 1.11 2.11 1.2 1.11
time (sec) N/A 0.023 0.002 0.004 1.416 2.023 0.335 1.078
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 54 45 59 113 63 59
normalized size 1 1. 1. 0.83 1.09 2.09 1.17 1.09
time (sec) N/A 0.025 0.003 0.003 1.429 2.049 0.349 1.089
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 25 25 25 32 42 76 29 45
normalized size 1 1. 1. 1.28 1.68 3.04 1.16 1.8
time (sec) N/A 0.01 0.002 0.007 0.939 2.101 0.306 1.08
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 7 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.006 0.036 0.014 0. 0. 0. 0.
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 4 4 4 5 5 12 3 5
normalized size 1 1. 1. 1.25 1.25 3. 0.75 1.25
time (sec) N/A 0.002 0.001 0.001 0.947 2.057 0.059 1.077
Problem 77 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 2 2 2 3 3 11 2 3
normalized size 1 1. 1. 1.5 1.5 5.5 1. 1.5
time (sec) N/A 0.002 0.001 0.001 0.939 2.194 0.054 1.068
Problem 78 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 5 5 5 6 4 38 5 8
normalized size 1 1. 1. 1.2 0.8 7.6 1. 1.6
time (sec) N/A 0.002 0.002 0. 0.931 2.127 0.061 1.097
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 3 3 3 4 4 46 3 23
normalized size 1 1. 1. 1.33 1.33 15.33 1. 7.67
time (sec) N/A 0.002 0.002 0.002 0.935 1.977 0.066 1.081
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 27 26 34 124 75 35
normalized size 1 1. 1.29 1.24 1.62 5.9 3.57 1.67
time (sec) N/A 0.026 0.04 0.014 1.426 2.061 0.365 1.1
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 3 3 33 7 20 59 15 23
normalized size 1 1. 11. 2.33 6.67 19.67 5. 7.67
time (sec) N/A 0.003 0.003 0.004 0.942 2.098 0.098 1.088
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 5 5 17 9 20 77 15 23
normalized size 1 1. 3.4 1.8 4. 15.4 3. 4.6
time (sec) N/A 0.002 0.003 0.005 0.942 2.082 0.097 1.102
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 11 14 38 10 14
normalized size 1 1. 1. 0.79 1. 2.71 0.71 1.
time (sec) N/A 0.005 0.002 0. 0.935 1.982 0.058 1.075
Problem 84 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 20 20 20 17 22 46 15 22
normalized size 1 1. 1. 0.85 1.1 2.3 0.75 1.1
time (sec) N/A 0.016 0.002 0.005 0.945 1.816 0.563 1.071
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 15 11 15 31 8 15
normalized size 1 1. 1.15 0.85 1.15 2.38 0.62 1.15
time (sec) N/A 0.005 0.002 0.001 0.947 1.791 0.061 1.076
Problem 86 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 44 44 44 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.008 0.04 0.385 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 16 20 61 17 20
normalized size 1 1. 1. 0.84 1.05 3.21 0.89 1.05
time (sec) N/A 0.019 0.004 0.01 0.956 1.635 1.094 1.069
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 11 14 36 10 14
normalized size 1 1. 1. 0.79 1. 2.57 0.71 1.
time (sec) N/A 0.006 0.002 0. 0.94 1.719 0.059 1.098
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 15 11 12 36 8 12
normalized size 1 1. 1.36 1. 1.09 3.27 0.73 1.09
time (sec) N/A 0.006 0.002 0. 0.939 1.684 0.062 1.102
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 2 2 2 3 3 20 5 3
normalized size 1 1. 1. 1.5 1.5 10. 2.5 1.5
time (sec) N/A 0.006 0.002 0.029 0.941 1.601 0.058 1.082
Problem 91 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 7 15 38 20 15
normalized size 1 1. 1. 0.47 1. 2.53 1.33 1.
time (sec) N/A 0.007 0.005 0.01 0.93 1.758 0.603 1.087
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 8 8 8 9 11 27 7 11
normalized size 1 1. 1. 1.12 1.38 3.38 0.88 1.38
time (sec) N/A 0.008 0.002 0. 0.957 1.735 0.175 1.101
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 17 17 15 18 20 43 17 20
normalized size 1 1. 0.88 1.06 1.18 2.53 1. 1.18
time (sec) N/A 0.02 0.015 0. 0.93 1.89 0.317 1.088
Problem 94 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 25 26 63 36 26
normalized size 1 1. 1. 1. 1.04 2.52 1.44 1.04
time (sec) N/A 0.013 0.008 0. 0.957 1.662 0.333 1.094
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 41 41 29 37 35 89 56 35
normalized size 1 1. 0.71 0.9 0.85 2.17 1.37 0.85
time (sec) N/A 0.03 0.037 0. 0.941 1.815 0.625 1.084
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 33 33 31 23 31 74 39 31
normalized size 1 1. 0.94 0.7 0.94 2.24 1.18 0.94
time (sec) N/A 0.022 0.009 0. 0.962 1.821 0.603 1.085
Problem 97 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 7 7 7 8 9 26 7 9
normalized size 1 1. 1. 1.14 1.29 3.71 1. 1.29
time (sec) N/A 0.009 0.002 0.004 0.932 1.698 0.169 1.077
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 14 17 19 42 17 19
normalized size 1 1. 0.88 1.06 1.19 2.62 1.06 1.19
time (sec) N/A 0.021 0.013 0.001 0.947 1.682 0.319 1.087
Problem 99 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 25 26 62 36 26
normalized size 1 1. 1. 1. 1.04 2.48 1.44 1.04
time (sec) N/A 0.014 0.011 0.005 0.952 1.664 0.336 1.072
Problem 100 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 41 41 29 37 35 89 56 35
normalized size 1 1. 0.71 0.9 0.85 2.17 1.37 0.85
time (sec) N/A 0.032 0.036 0.017 0.952 1.778 0.641 1.094
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 31 23 31 80 39 31
normalized size 1 1. 0.94 0.7 0.94 2.42 1.18 0.94
time (sec) N/A 0.023 0.008 0.011 0.952 1.775 0.602 1.065
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 2 2 2 3 18 23 2 3
normalized size 1 1. 1. 1.5 9. 11.5 1. 1.5
time (sec) N/A 0.011 0.01 0. 1.054 1.822 0.576 1.073
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 2 2 2 3 18 59 12 3
normalized size 1 1. 1. 1.5 9. 29.5 6. 1.5
time (sec) N/A 0.012 0.001 0.005 1.056 1.693 1.164 1.092
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 11 20 80 17 18
normalized size 1 1. 1. 1.1 2. 8. 1.7 1.8
time (sec) N/A 0.025 0.002 0.004 1.068 1.816 1.602 1.072
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 12 23 84 10 15
normalized size 1 1. 1. 0.8 1.53 5.6 0.67 1.
time (sec) N/A 0.038 0.012 0.007 1.062 1.861 1.086 1.082
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 12 17 27 57 12 22
normalized size 1 1. 1. 1.42 2.25 4.75 1. 1.83
time (sec) N/A 0.006 0.003 0.002 0.95 1.859 0.087 1.092
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 22 12 15 23 14 15
normalized size 1 1. 2. 1.09 1.36 2.09 1.27 1.36
time (sec) N/A 0.004 0.009 0.003 0.94 1.757 0.126 1.07
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 21 11 14 22 12 14
normalized size 1 1. 2.1 1.1 1.4 2.2 1.2 1.4
time (sec) N/A 0.004 0.009 0.005 0.956 1.751 0.129 1.089
Problem 109 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 12 12 12 17 15 49 19 18
normalized size 1 1. 1. 1.42 1.25 4.08 1.58 1.5
time (sec) N/A 0.004 0.009 0.002 0.936 1.809 0.123 1.071
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 19 29 15 65 29 76
normalized size 1 1. 1.73 2.64 1.36 5.91 2.64 6.91
time (sec) N/A 0.004 0.01 0.004 0.964 1.765 0.338 1.134
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 38 21 35 93 17 69
normalized size 1 1. 3.17 1.75 2.92 7.75 1.42 5.75
time (sec) N/A 0.004 0.017 0.006 0.964 1.89 0.538 1.085
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 19 35 76 34 38
normalized size 1 1. 1. 1.73 3.18 6.91 3.09 3.45
time (sec) N/A 0.004 0.002 0.006 0.94 1.801 0.613 1.112
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 23 27 32 55 46 24
normalized size 1 1. 0.92 1.08 1.28 2.2 1.84 0.96
time (sec) N/A 0.009 0.026 0.005 0.946 1.693 0.227 1.065
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 29 22 30 55 37 34
normalized size 1 1. 1.07 0.81 1.11 2.04 1.37 1.26
time (sec) N/A 0.01 0.01 0.005 0.952 1.524 0.496 1.1
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 23 27 30 55 46 24
normalized size 1 1. 0.92 1.08 1.2 2.2 1.84 0.96
time (sec) N/A 0.009 0.017 0.008 0.957 1.807 0.229 1.096
Problem 116 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 26 22 30 55 36 30
normalized size 1 1. 1. 0.85 1.15 2.12 1.38 1.15
time (sec) N/A 0.011 0.007 0.009 0.943 1.613 0.467 1.073
Problem 117 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 42 58 14
normalized size 1 1. 1. 1.1 1.4 4.2 5.8 1.4
time (sec) N/A 0.008 0.003 0.006 0.934 1.725 1.276 1.088
Problem 118 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 6 5 12 28 3 41
normalized size 1 1. 0.67 0.56 1.33 3.11 0.33 4.56
time (sec) N/A 0.007 0.004 0.003 0.938 1.677 0.177 1.073
Problem 119 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 12 12 8 9 14 30 7 11
normalized size 1 1. 0.67 0.75 1.17 2.5 0.58 0.92
time (sec) N/A 0.008 0.009 0.007 0.949 1.754 0.353 1.102
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 23 11 20 62 8 14
normalized size 1 1. 2.3 1.1 2. 6.2 0.8 1.4
time (sec) N/A 0.006 0.01 0.006 0.939 1.666 0.376 1.073
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 25 11 20 61 8 14
normalized size 1 1. 2.27 1. 1.82 5.55 0.73 1.27
time (sec) N/A 0.008 0.011 0.016 0.957 1.691 0.38 1.089
Problem 122 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 40 40 40 39 0 344 114 65
normalized size 1 1. 1. 0.98 0. 8.6 2.85 1.62
time (sec) N/A 0.04 0.037 0.014 0. 1.846 8.443 1.096
Problem 123 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 47 47 44 43 0 707 0 81
normalized size 1 1. 0.94 0.91 0. 15.04 0. 1.72
time (sec) N/A 0.056 0.06 0.039 0. 1.971 0. 1.093
Problem 124 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 73 73 47 158 158 134 105 61
normalized size 1 1. 0.64 2.16 2.16 1.84 1.44 0.84
time (sec) N/A 0.043 0.128 0.005 0.966 1.777 1.102 1.101
Problem 125 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 12 15 39 20 15
normalized size 1 1. 1. 0.8 1. 2.6 1.33 1.
time (sec) N/A 0.007 0.005 0.019 0.947 1.761 0.594 1.077
Problem 126 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 73 73 47 158 153 134 105 61
normalized size 1 1. 0.64 2.16 2.1 1.84 1.44 0.84
time (sec) N/A 0.043 0.122 0.01 0.963 1.773 1.109 1.081
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 22 19 95 14 39
normalized size 1 1. 1. 1.57 1.36 6.79 1. 2.79
time (sec) N/A 0.008 0.003 0.006 0.93 1.665 0.091 1.127
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 101 138 655 548 0 0
normalized size 1 1. 0.97 1.33 6.3 5.27 0. 0.
time (sec) N/A 0.227 0.144 0.056 1.721 1.926 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 133 237 1034 683 0 0
normalized size 1 1. 0.87 1.55 6.76 4.46 0. 0.
time (sec) N/A 0.407 0.311 0.069 3.097 1.842 0. 0.
Problem 130 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 15 15 15 20 144 66 19 31
normalized size 1 1. 1. 1.33 9.6 4.4 1.27 2.07
time (sec) N/A 0.014 0.014 0.008 1.422 1.855 0.159 1.12
Problem 131 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 15 15 15 12 15 38 26 15
normalized size 1 1. 1. 0.8 1. 2.53 1.73 1.
time (sec) N/A 0.008 0.006 0.036 0.931 1.905 0.525 1.092
Problem 132 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 14 19 14 58 14 14
normalized size 1 1. 0.58 0.79 0.58 2.42 0.58 0.58
time (sec) N/A 0.025 0.004 0.005 0.948 1.742 0.065 1.08
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 7 7 6 15 12 47 12 12
normalized size 1 1. 0.86 2.14 1.71 6.71 1.71 1.71
time (sec) N/A 0.021 0.007 0.03 0.946 1.675 0.069 1.068
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 22 69 34 61 104 443
normalized size 1 1. 0.69 2.16 1.06 1.91 3.25 13.84
time (sec) N/A 0.011 0.018 0.018 0.976 1.829 1.095 1.131
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 20 71 32 61 107 444
normalized size 1 1. 0.65 2.29 1.03 1.97 3.45 14.32
time (sec) N/A 0.008 0.016 0.016 0.959 1.879 1.08 1.123
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 50 137 81 177 308 1574
normalized size 1 1. 0.6 1.63 0.96 2.11 3.67 18.74
time (sec) N/A 0.049 0.053 0.02 0.979 1.862 3.5 1.137
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 49 142 78 182 304 1573
normalized size 1 1. 0.59 1.71 0.94 2.19 3.66 18.95
time (sec) N/A 0.046 0.045 0.02 0.978 1.775 3.552 1.156
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 162 94 225 144 333 668 3552
normalized size 1 1. 0.58 1.39 0.89 2.06 4.12 21.93
time (sec) N/A 0.176 0.083 0.032 1.018 1.847 9.894 1.245
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 161 93 231 142 329 665 3552
normalized size 1 1. 0.58 1.43 0.88 2.04 4.13 22.06
time (sec) N/A 0.171 0.074 0.028 1.02 1.783 9.793 1.209
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 261 261 169 431 251 570 1352 6857
normalized size 1 1. 0.65 1.65 0.96 2.18 5.18 26.27
time (sec) N/A 0.435 0.146 0.039 1.088 1.883 27.707 1.275
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 260 260 168 441 248 578 1355 6851
normalized size 1 1. 0.65 1.7 0.95 2.22 5.21 26.35
time (sec) N/A 0.416 0.122 0.039 1.097 1.788 27.026 1.316
Problem 142 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 25 25 25 20 26 54 114 18
normalized size 1 1. 1. 0.8 1.04 2.16 4.56 0.72
time (sec) N/A 0.031 0.01 0.047 0.943 1.82 15.248 1.086
Problem 143 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 30 30 30 23 30 81 112 30
normalized size 1 1. 1. 0.77 1. 2.7 3.73 1.
time (sec) N/A 0.032 0.008 0.041 0.937 1.878 14.623 1.078
Problem 144 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 85 85 55 64 74 144 100 81
normalized size 1 1. 0.65 0.75 0.87 1.69 1.18 0.95
time (sec) N/A 0.066 0.079 0.026 0.973 1.802 2.194 1.103
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 13 0 0 0 324 0 0 0
normalized size 1 0. 0. 0. 24.92 0. 0. 0.
time (sec) N/A 0.435 0.88 0.789 0.983 0. 0. 0.
Problem 146 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 12 12 12 11 55 43 0 24
normalized size 1 1. 1. 0.92 4.58 3.58 0. 2.
time (sec) N/A 0.03 0.013 0.044 0.951 1.703 0. 1.112
Problem 147 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 77 77 76 143 0 684 0 132
normalized size 1 1. 0.99 1.86 0. 8.88 0. 1.71
time (sec) N/A 0.098 0.247 0.041 0. 1.925 0. 1.104
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 14 16 54 15 18
normalized size 1 1. 1. 0.82 0.94 3.18 0.88 1.06
time (sec) N/A 0.003 0.003 0.001 0.938 1.754 0.414 1.075
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 14 14 53 15 18
normalized size 1 1. 1. 0.82 0.82 3.12 0.88 1.06
time (sec) N/A 0.003 0.003 0.001 0.942 1.893 0.403 1.064
Problem 150 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 3 3 3 3 3 7 2 3
normalized size 1 1. 1. 1. 1. 2.33 0.67 1.
time (sec) N/A 0.001 0. 0. 0.952 1.577 0.041 1.08
Problem 151 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 8 8 8 9 11 16 8 11
normalized size 1 1. 1. 1.12 1.38 2. 1. 1.38
time (sec) N/A 0.003 0.001 0.003 0.931 1.69 0.084 1.079
Problem 152 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 9 9 9 9 11 15 7 11
normalized size 1 1. 1. 1. 1.22 1.67 0.78 1.22
time (sec) N/A 0.002 0.001 0.001 0.956 1.561 0.055 1.071
Problem 153 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 4 4 4 9 5 12 3 5
normalized size 1 1. 1. 2.25 1.25 3. 0.75 1.25
time (sec) N/A 0.011 0.005 0.003 1.049 1.655 0.964 1.074
Problem 154 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 24 31 31 46 15 32
normalized size 1 1. 1. 1.29 1.29 1.92 0.62 1.33
time (sec) N/A 0.015 0.005 0.004 0.928 1.528 0.169 1.074
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 12 12 12 11 14 27 8 14
normalized size 1 1. 1. 0.92 1.17 2.25 0.67 1.17
time (sec) N/A 0.021 0.009 0.002 0.95 1.819 0.098 1.072
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 15 19 31 14 19
normalized size 1 1. 1. 1.15 1.46 2.38 1.08 1.46
time (sec) N/A 0.008 0.003 0.002 0.934 1.704 0.103 1.081
Problem 157 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 31 31 31 22 0 192 26 28
normalized size 1 1. 1. 0.71 0. 6.19 0.84 0.9
time (sec) N/A 0.029 0.009 0.005 0. 1.73 0.177 1.093
Problem 158 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 21 21 14 14 18 31 19 18
normalized size 1 1. 0.67 0.67 0.86 1.48 0.9 0.86
time (sec) N/A 0.009 0.006 0.002 0.942 1.68 0.101 1.095
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 102 102 136 535 102 136
normalized size 1 1. 0.63 0.63 0.83 3.28 0.63 0.83
time (sec) N/A 0.242 0.01 0.003 0.949 1.584 0.128 1.083
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-2) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 18 19 0 39 0 292
normalized size 1 1. 1. 1.06 0. 2.17 0. 16.22
time (sec) N/A 0.021 0.013 0.004 0. 1.557 0. 1.134
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 15 0 36 24 320
normalized size 1 1. 1. 1.07 0. 2.57 1.71 22.86
time (sec) N/A 0.015 0.007 0.003 0. 1.673 0.651 1.163
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 21 14 45 0 0
normalized size 1 1. 1. 1.24 0.82 2.65 0. 0.
time (sec) N/A 0.019 0.011 0.02 1.038 1.675 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 43 79 0 117 0 0
normalized size 1 1. 0.67 1.23 0. 1.83 0. 0.
time (sec) N/A 0.097 0.127 0.032 0. 1.767 0. 0.
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 16 22 31 12 38
normalized size 1 1. 1. 1. 1.38 1.94 0.75 2.38
time (sec) N/A 0.032 0.045 0.003 0.951 1.557 0.116 1.108
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 12 15 27 17 15
normalized size 1 1. 1. 0.92 1.15 2.08 1.31 1.15
time (sec) N/A 0.007 0.002 0.003 0.941 1.733 0.095 1.081
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 8 12 30 8 12
normalized size 1 1. 1. 0.73 1.09 2.73 0.73 1.09
time (sec) N/A 0.003 0.001 0.003 0.942 1.608 0.242 1.107
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 9 9 9 7 8 18 5 8
normalized size 1 1. 1. 0.78 0.89 2. 0.56 0.89
time (sec) N/A 0.007 0.001 0.002 0.936 1.665 0.081 1.081
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 17 18 23 38 14 0
normalized size 1 1. 0.63 0.67 0.85 1.41 0.52 0.
time (sec) N/A 0.105 0.012 0.002 1.025 1.504 0.096 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A A A A A F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 25 0 25 23 30 73 31 0
normalized size 1 0. 1. 0.92 1.2 2.92 1.24 0.
time (sec) N/A 0.982 0.165 0.06 1.271 1.792 0.407 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 11 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.046 0.019 0.016 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 12 14 27 8 14
normalized size 1 1. 1. 1.09 1.27 2.45 0.73 1.27
time (sec) N/A 0.016 0.006 0.01 1.03 1.765 1.989 1.071
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 17 21 20 46 17 20
normalized size 1 1. 0.77 0.95 0.91 2.09 0.77 0.91
time (sec) N/A 0.052 0.011 0.013 1.029 1.854 3.196 1.078
Problem 173 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 17 28 15 31 10 15
normalized size 1 1. 0.74 1.22 0.65 1.35 0.43 0.65
time (sec) N/A 0.013 0.005 0.001 0.951 1.912 0.089 1.074
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 13 16 0 12 16
normalized size 1 1. 1. 0.81 1. 0. 0.75 1.
time (sec) N/A 0.002 0. 0.001 1.417 0. 0.053 1.098
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 43 48 0 234 930 65
normalized size 1 1. 0.75 0.84 0. 4.11 16.32 1.14
time (sec) N/A 0.03 0.023 0.009 0. 1.883 4.279 1.103
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 118 305 0 699 0 189
normalized size 1 1. 1.02 2.63 0. 6.03 0. 1.63
time (sec) N/A 0.068 0.292 0.011 0. 1.932 0. 1.131
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 13 16 31 12 16
normalized size 1 1. 1. 0.81 1. 1.94 0.75 1.
time (sec) N/A 0.001 0.004 0.002 0.943 1.559 0.055 1.061
Problem 178 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 34 34 24 21 35 70 202 34
normalized size 1 1. 0.71 0.62 1.03 2.06 5.94 1.
time (sec) N/A 0.009 0.011 0.003 0.954 1.605 1.048 1.056
Problem 179 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 53 53 35 32 55 97 666 50
normalized size 1 1. 0.66 0.6 1.04 1.83 12.57 0.94
time (sec) N/A 0.014 0.015 0.003 0.94 1.605 1.636 1.102
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 28 0 188 68 43
normalized size 1 1. 1. 0.8 0. 5.37 1.94 1.23
time (sec) N/A 0.012 0.009 0.004 0. 1.658 1.437 1.068
Problem 181 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 39 39 47 37 0 225 44 55
normalized size 1 1. 1.21 0.95 0. 5.77 1.13 1.41
time (sec) N/A 0.011 0.027 0.008 0. 1.607 1.905 1.075
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 13 16 26 10 16
normalized size 1 1. 1. 0.93 1.14 1.86 0.71 1.14
time (sec) N/A 0.001 0.003 0.002 0.94 1.611 0.055 1.066
Problem 183 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 32 32 23 21 35 47 162 31
normalized size 1 1. 0.72 0.66 1.09 1.47 5.06 0.97
time (sec) N/A 0.008 0.01 0.002 0.933 1.505 1.038 1.072
Problem 184 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 51 51 35 32 55 73 600 50
normalized size 1 1. 0.69 0.63 1.08 1.43 11.76 0.98
time (sec) N/A 0.013 0.014 0.004 0.966 1.612 1.569 1.068
Problem 185 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 23 23 23 18 0 142 24 28
normalized size 1 1. 1. 0.78 0. 6.17 1.04 1.22
time (sec) N/A 0.007 0.003 0.006 0. 1.733 1.094 1.11
Problem 186 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 41 41 47 40 0 232 44 63
normalized size 1 1. 1.15 0.98 0. 5.66 1.07 1.54
time (sec) N/A 0.012 0.063 0.007 0. 1.756 2.185 1.106
Problem 187 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 23 23 24 25 0 55 26 28
normalized size 1 1. 1.04 1.09 0. 2.39 1.13 1.22
time (sec) N/A 0.004 0.012 0.001 0. 1.701 0.058 1.076
Problem 188 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 48 48 38 43 61 117 216 116
normalized size 1 1. 0.79 0.9 1.27 2.44 4.5 2.42
time (sec) N/A 0.014 0.02 0.002 0.968 1.819 0.655 1.063
Problem 189 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 55 55 48 42 70 111 230 70
normalized size 1 1. 0.87 0.76 1.27 2.02 4.18 1.27
time (sec) N/A 0.028 0.034 0.003 1.426 1.91 1.301 1.075
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 38 11 19 35 2 20
normalized size 1 1. 3.17 0.92 1.58 2.92 0.17 1.67
time (sec) N/A 0.002 0.003 0.002 0.955 1.609 0.125 1.093
Problem 191 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 43 43 31 50 96 105 119 42
normalized size 1 1. 0.72 1.16 2.23 2.44 2.77 0.98
time (sec) N/A 0.005 0.012 0.003 0.947 1.716 2.596 1.148
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 17 22 57 20 22
normalized size 1 1. 1. 0.77 1. 2.59 0.91 1.
time (sec) N/A 0.011 0.013 0.004 0.938 1.666 0.295 1.087
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 18 15 42 8 15
normalized size 1 1. 1. 1.38 1.15 3.23 0.62 1.15
time (sec) N/A 0.002 0.002 0.002 0.957 1.521 1.073 1.086
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 8 8 8 7 22 47 19 8
normalized size 1 1. 1. 0.88 2.75 5.88 2.38 1.
time (sec) N/A 0.003 0.002 0.008 1.421 1.554 0.964 1.113
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 11 34 78 8 34
normalized size 1 1. 1. 0.79 2.43 5.57 0.57 2.43
time (sec) N/A 0.006 0.003 0.009 0.936 1.565 0.938 1.07
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 18 14 0 62 0 30
normalized size 1 1. 1. 0.78 0. 3.44 0. 1.67
time (sec) N/A 0.016 0.003 0.011 0. 1.606 0. 1.105
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 28 23 23 155 0 20
normalized size 1 1. 0.93 0.77 0.77 5.17 0. 0.67
time (sec) N/A 0.021 0.004 0.011 1.441 1.71 0. 1.126
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 16 15 19 46 0 0
normalized size 1 1. 0.94 0.88 1.12 2.71 0. 0.
time (sec) N/A 0.009 0.007 0.003 1.42 1.635 0. 0.
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 2 2 2 3 3 35 2 19
normalized size 1 1. 1. 1.5 1.5 17.5 1. 9.5
time (sec) N/A 0.001 0.003 0.002 1.415 1.616 0.126 1.076
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 30 15 19 50 17 0
normalized size 1 1. 1.5 0.75 0.95 2.5 0.85 0.
time (sec) N/A 0.913 0.018 0.002 0.947 1.512 1.213 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 24 21 41 50 19 0
normalized size 1 1. 1. 0.88 1.71 2.08 0.79 0.
time (sec) N/A 0.324 0.167 0.005 1.6 1.62 1.63 0.
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 71 24 42 74 8 42
normalized size 1 1. 2.63 0.89 1.56 2.74 0.3 1.56
time (sec) N/A 0.008 0.009 0.003 0.952 1.555 0.199 1.096
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 127 25 0 552 51 0
normalized size 1 1. 1.55 0.3 0. 6.73 0.62 0.
time (sec) N/A 0.074 0.179 0.037 0. 1.682 1.492 0.
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 12 39 54 95 48 14
normalized size 1 1. 1. 3.25 4.5 7.92 4. 1.17
time (sec) N/A 0.053 0.021 0.009 1.46 1.636 1.726 1.105
Problem 205 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 40 40 40 33 0 235 68 46
normalized size 1 1. 1. 0.82 0. 5.88 1.7 1.15
time (sec) N/A 0.011 0.01 0.003 0. 1.605 1.191 1.089
Problem 206 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 46 66 0 132 42 51
normalized size 1 1. 1. 1.43 0. 2.87 0.91 1.11
time (sec) N/A 0.034 0.011 0.009 0. 1.642 1.268 1.081
Problem 207 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 37 37 39 52 0 140 0 54
normalized size 1 1. 1.05 1.41 0. 3.78 0. 1.46
time (sec) N/A 0.018 0.018 0.007 0. 1.7 0. 1.119
Problem 208 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 61 61 65 74 0 325 0 69
normalized size 1 1. 1.07 1.21 0. 5.33 0. 1.13
time (sec) N/A 0.024 0.029 0.005 0. 1.727 0. 1.19
Problem 209 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 23 20 26 42 29 26
normalized size 1 1. 1. 0.87 1.13 1.83 1.26 1.13
time (sec) N/A 0.004 0.004 0.003 0.948 1.649 0.438 1.089
Problem 210 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 28 28 28 25 32 58 36 22
normalized size 1 1. 1. 0.89 1.14 2.07 1.29 0.79
time (sec) N/A 0.005 0.005 0.004 0.95 1.68 0.543 1.089
Problem 211 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 56 56 56 47 0 381 0 81
normalized size 1 1. 1. 0.84 0. 6.8 0. 1.45
time (sec) N/A 0.04 0.023 0.012 0. 1.697 0. 1.239
Problem 212 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 81 81 82 70 0 481 0 97
normalized size 1 1. 1.01 0.86 0. 5.94 0. 1.2
time (sec) N/A 0.028 0.101 0.005 0. 1.654 0. 1.243
Problem 213 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 44 44 49 56 0 155 0 42
normalized size 1 1. 1.11 1.27 0. 3.52 0. 0.95
time (sec) N/A 0.039 0.008 0.01 0. 1.62 0. 1.227
Problem 214 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 68 68 71 78 0 339 0 42
normalized size 1 1. 1.04 1.15 0. 4.99 0. 0.62
time (sec) N/A 0.049 0.025 0.012 0. 1.899 0. 1.26
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 12 15 57 10 15
normalized size 1 1. 1. 0.92 1.15 4.38 0.77 1.15
time (sec) N/A 0.017 0.007 0.006 0.944 1.65 0.304 1.107
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 16 20 34 17 20
normalized size 1 1. 1. 0.84 1.05 1.79 0.89 1.05
time (sec) N/A 0.006 0.001 0.005 0.944 1.582 0.094 1.09
Problem 217 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 12 12 12 21 27 38 10 16
normalized size 1 1. 1. 1.75 2.25 3.17 0.83 1.33
time (sec) N/A 0.009 0.024 0.005 0.944 1.684 0.169 1.093
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 11 14 23 7 14
normalized size 1 1. 1. 1. 1.27 2.09 0.64 1.27
time (sec) N/A 0.025 0.008 0.013 1.09 1.577 0.283 1.079
Problem 219 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 27 27 27 24 31 49 20 32
normalized size 1 1. 1. 0.89 1.15 1.81 0.74 1.19
time (sec) N/A 0.018 0.004 0.002 0.938 1.562 0.294 1.097
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 21 16 27 124 165 89
normalized size 1 1. 0.64 0.48 0.82 3.76 5. 2.7
time (sec) N/A 0.003 0.006 0.003 0.944 1.61 9.954 1.119
Problem 221 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 9 9 9 10 12 30 7 15
normalized size 1 1. 1. 1.11 1.33 3.33 0.78 1.67
time (sec) N/A 0.001 0.002 0.003 0.95 1.559 0.086 1.077
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 14 38 80 39 43
normalized size 1 1. 1. 0.74 2. 4.21 2.05 2.26
time (sec) N/A 0.005 0.003 0.003 1.418 1.618 0.324 1.081
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 16 13 15 38 15 15
normalized size 1 1. 0.84 0.68 0.79 2. 0.79 0.79
time (sec) N/A 0.003 0.003 0.002 0.931 1.581 0.963 1.074
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 112 85 0 309 153 139
normalized size 1 1. 1.27 0.97 0. 3.51 1.74 1.58
time (sec) N/A 0.039 0.04 0.007 0. 1.607 1.745 1.839
Problem 225 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 9 9 9 10 46 28 7 23
normalized size 1 1. 1. 1.11 5.11 3.11 0.78 2.56
time (sec) N/A 0.011 0.002 0.005 0.952 1.562 0.172 1.085
Problem 226 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 9 9 9 10 46 28 7 23
normalized size 1 1. 1. 1.11 5.11 3.11 0.78 2.56
time (sec) N/A 0.011 0.002 0.003 0.96 1.591 0.185 1.077
Problem 227 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 9 9 9 8 9 69 7 18
normalized size 1 1. 1. 0.89 1. 7.67 0.78 2.
time (sec) N/A 0.004 0.003 0.005 0.943 1.732 0.13 1.094
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 12 16 18 74 22 31
normalized size 1 1. 1. 1.33 1.5 6.17 1.83 2.58
time (sec) N/A 0.033 0.083 0.011 0.967 1.722 1.331 1.087
Problem 229 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 28 28 28 23 30 116 75 30
normalized size 1 1. 1. 0.82 1.07 4.14 2.68 1.07
time (sec) N/A 0.023 0.015 0.011 0.951 1.869 2.261 1.078
Problem 230 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 21 21 21 16 20 45 15 20
normalized size 1 1. 1. 0.76 0.95 2.14 0.71 0.95
time (sec) N/A 0.008 0.003 0.001 1.431 1.713 0.247 1.076
Problem 231 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 21 21 21 16 20 45 15 23
normalized size 1 1. 1. 0.76 0.95 2.14 0.71 1.1
time (sec) N/A 0.008 0.002 0.002 1.446 1.649 0.248 1.081
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 23 23 22 23 30 53 26 30
normalized size 1 1. 0.96 1. 1.3 2.3 1.13 1.3
time (sec) N/A 0.019 0.003 0.002 0.965 1.603 0.297 1.059
Problem 233 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 18 18 18 15 19 103 32 19
normalized size 1 1. 1. 0.83 1.06 5.72 1.78 1.06
time (sec) N/A 0.016 0.019 0.018 0.955 1.746 0.548 1.088
Problem 234 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 18 18 18 15 19 103 32 19
normalized size 1 1. 1. 0.83 1.06 5.72 1.78 1.06
time (sec) N/A 0.013 0.012 0.015 0.948 1.788 0.544 1.069
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 40 17 0 88 0 0
normalized size 1 1. 3.33 1.42 0. 7.33 0. 0.
time (sec) N/A 0.006 0.012 0.027 0. 1.659 0. 0.
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 42 23 0 88 0 0
normalized size 1 1. 3. 1.64 0. 6.29 0. 0.
time (sec) N/A 0.009 0.011 0.035 0. 1.608 0. 0.
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 16 22 12 36 0 0
normalized size 1 1. 1.33 1.83 1. 3. 0. 0.
time (sec) N/A 0.007 0.006 0.027 1.589 1.498 0. 0.
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 18 22 27 57 0 0
normalized size 1 1. 1.29 1.57 1.93 4.07 0. 0.
time (sec) N/A 0.009 0.008 0.03 1.464 1.622 0. 0.
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 17 14 0 45 63 18
normalized size 1 1. 0.81 0.67 0. 2.14 3. 0.86
time (sec) N/A 0.008 0.021 0.003 0. 1.628 0.386 1.075
Problem 240 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 24 31 24 55 20 26
normalized size 1 1. 1. 1.29 1. 2.29 0.83 1.08
time (sec) N/A 0.01 0.01 0.005 0.933 1.652 0.118 1.12
Problem 241 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 12 12 12 9 45 45 7 22
normalized size 1 1. 1. 0.75 3.75 3.75 0.58 1.83
time (sec) N/A 0.004 0.002 0.009 0.943 1.552 0.922 1.082
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 32 92 32 76 0 32
normalized size 1 1. 1. 2.88 1. 2.38 0. 1.
time (sec) N/A 0.012 0.011 0.026 0.944 1.548 0. 1.086
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 33 27 35 103 31 35
normalized size 1 1. 1. 0.82 1.06 3.12 0.94 1.06
time (sec) N/A 0.009 0.012 0.005 1.438 1.599 0.128 1.077
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 3 3 3 4 4 41 3 15
normalized size 1 1. 1. 1.33 1.33 13.67 1. 5.
time (sec) N/A 0.002 0.002 0. 0.959 1.619 0.059 1.116
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 18 14 22 126 19 46
normalized size 1 1. 1.5 1.17 1.83 10.5 1.58 3.83
time (sec) N/A 0.01 0.003 0. 1.431 1.634 0.066 1.097
Problem 246 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 3 3 3 4 4 55 7 15
normalized size 1 1. 1. 1.33 1.33 18.33 2.33 5.
time (sec) N/A 0.003 0.002 0.001 0.931 1.539 0.123 1.094
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 3 3 3 4 4 55 12 16
normalized size 1 1. 1. 1.33 1.33 18.33 4. 5.33
time (sec) N/A 0.003 0.002 0.001 0.955 1.536 0.294 1.079
Problem 248 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 8 8 8 9 11 16 8 11
normalized size 1 1. 1. 1.12 1.38 2. 1. 1.38
time (sec) N/A 0.002 0.001 0.003 0.941 1.621 0.083 1.086
Problem 249 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 49 49 29 32 14 23 0 15
normalized size 1 1. 0.59 0.65 0.29 0.47 0. 0.31
time (sec) N/A 0.015 0.009 0.004 1.433 1.438 0. 1.096
Problem 250 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 17 13 16 35 12 18
normalized size 1 1. 1.06 0.81 1. 2.19 0.75 1.12
time (sec) N/A 0.006 0.003 0.001 0.947 1.511 0.069 1.079
Problem 251 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 36 0 0 84 0 54
normalized size 1 1. 0.9 0. 0. 2.1 0. 1.35
time (sec) N/A 0.016 0.009 0.003 0. 1.639 0. 1.108
Problem 252 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 128 128 67 63 78 162 109 77
normalized size 1 1. 0.52 0.49 0.61 1.27 0.85 0.6
time (sec) N/A 0.19 0.165 0.009 0.974 1.673 5.386 1.108
Problem 253 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 30 30 18 20 23 58 27 20
normalized size 1 1. 0.6 0.67 0.77 1.93 0.9 0.67
time (sec) N/A 0.037 0.026 0.004 0.951 1.625 0.788 1.072
Problem 254 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 9 8 9 43 17 9
normalized size 1 1. 0.82 0.73 0.82 3.91 1.55 0.82
time (sec) N/A 0.001 0.001 0. 0.974 1.499 0.095 1.075
Problem 255 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 40 40 40 33 43 112 41 45
normalized size 1 1. 1. 0.82 1.08 2.8 1.02 1.12
time (sec) N/A 0.021 0.008 0.002 1.432 1.619 0.128 1.091
Problem 256 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 8 8 23 22 23 51 15 24
normalized size 1 1. 2.88 2.75 2.88 6.38 1.88 3.
time (sec) N/A 0.003 0.003 0.003 0.941 1.579 0.089 1.085
Problem 257 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 227 227 194 1210 0 0 0 0
normalized size 1 1. 0.85 5.33 0. 0. 0. 0.
time (sec) N/A 0.197 0.252 0.014 0. 0. 0. 0.
Problem 258 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 30 26 34 78 32 34
normalized size 1 1. 1.25 1.08 1.42 3.25 1.33 1.42
time (sec) N/A 0.009 0.003 0.003 0.946 1.579 1.443 1.081
Problem 259 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 71 54 77 242 73 0
normalized size 1 1. 0.91 0.69 0.99 3.1 0.94 0.
time (sec) N/A 0.046 0.023 0.004 1.423 1.662 0.304 0.
Problem 260 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 2 2 2 3 3 35 2 19
normalized size 1 1. 1. 1.5 1.5 17.5 1. 9.5
time (sec) N/A 0.001 0.003 0. 1.435 1.608 0.122 1.108
Problem 261 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 27 27 27 21 27 69 24 34
normalized size 1 1. 1. 0.78 1. 2.56 0.89 1.26
time (sec) N/A 0.004 0.006 0.003 1.417 1.727 0.188 1.072
Problem 262 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 46 8 15
normalized size 1 1. 1. 1.1 1.4 4.6 0.8 1.5
time (sec) N/A 0.004 0.003 0. 0.928 1.636 0.074 1.097
Problem 263 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 15 19 41 12 19
normalized size 1 1. 1. 0.94 1.19 2.56 0.75 1.19
time (sec) N/A 0.004 0.002 0. 1.41 1.71 0.117 1.084
Problem 264 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 40 40 29 34 45 68 32 51
normalized size 1 1. 0.72 0.85 1.12 1.7 0.8 1.27
time (sec) N/A 0.023 0.011 0.002 1.412 1.726 0.321 1.098
Problem 265 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 21 21 29 14 18 104 0 20
normalized size 1 1. 1.38 0.67 0.86 4.95 0. 0.95
time (sec) N/A 0.115 0.028 0.053 0.924 1.81 0. 1.122
Problem 266 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 11 14 36 10 22
normalized size 1 1. 1. 0.79 1. 2.57 0.71 1.57
time (sec) N/A 0.006 0.002 0.007 0.926 1.615 0.061 1.104
Problem 267 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 18 18 18 17 22 50 14 24
normalized size 1 1. 1. 0.94 1.22 2.78 0.78 1.33
time (sec) N/A 0.014 0.004 0.007 0.938 1.558 0.104 1.063
Problem 268 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 7 8 46 7 22
normalized size 1 1. 1. 0.7 0.8 4.6 0.7 2.2
time (sec) N/A 0.001 0.004 0.003 1.401 1.612 0.141 1.072
Problem 269 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 6 6 6 5 5 35 3 19
normalized size 1 1. 1. 0.83 0.83 5.83 0.5 3.17
time (sec) N/A 0.001 0.003 0.003 1.409 1.538 0.128 1.091
Problem 270 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 21 21 21 17 22 59 22 22
normalized size 1 1. 1. 0.81 1.05 2.81 1.05 1.05
time (sec) N/A 0.017 0.008 0.003 1.411 1.831 0.104 1.082
Problem 271 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 53 53 51 42 63 173 46 62
normalized size 1 1. 0.96 0.79 1.19 3.26 0.87 1.17
time (sec) N/A 0.031 0.02 0.01 1.416 1.796 0.161 1.083
Problem 272 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 49 49 49 66 55 127 762 59
normalized size 1 1. 1. 1.35 1.12 2.59 15.55 1.2
time (sec) N/A 0.078 0.026 0.006 0.937 1.976 25.138 1.082
Problem 273 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.004 2.811 0.028 0. 0. 0. 0.
Problem 274 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 28 28 36 128 26 0
normalized size 1 1. 1. 1. 1.29 4.57 0.93 0.
time (sec) N/A 0.211 10.248 0.031 1.059 1.873 0.443 0.
Problem 275 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 199 199 136 127 216 342 0 154
normalized size 1 1. 0.68 0.64 1.09 1.72 0. 0.77
time (sec) N/A 0.101 0.208 0.035 1.029 2.175 0. 1.09
Problem 276 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 18 18 18 16 20 51 15 20
normalized size 1 1. 1. 0.89 1.11 2.83 0.83 1.11
time (sec) N/A 0.005 0.007 0.006 0.929 1.803 0.308 1.077
Problem 277 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 24 22 28 88 36 50
normalized size 1 1. 1. 0.92 1.17 3.67 1.5 2.08
time (sec) N/A 0.008 0.028 0.001 0.931 1.876 0.497 1.072
Problem 278 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C B F B F F
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 94 0 5137 1197351 0 464 0 0
normalized size 1 0. 54.65 12737.8 0. 4.94 0. 0.
time (sec) N/A 1.84 6.419 0.914 0. 2.691 0. 0.
Problem 279 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C C F A F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 142 0 630 354 0 572 0 0
normalized size 1 0. 4.44 2.49 0. 4.03 0. 0.
time (sec) N/A 3.324 1.524 0.213 0. 2.814 0. 0.
Problem 280 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 21 21 97 1088 231 452 0 105
normalized size 1 1. 4.62 51.81 11. 21.52 0. 5.
time (sec) N/A 0.285 1.235 0.136 1.207 1.924 0. 1.388
Problem 281 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C A F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 4030 0 3168 4640 0 0 0 0
normalized size 1 0. 0.79 1.15 0. 0. 0. 0.
time (sec) N/A 0.025 6.048 0.73 0. 0. 0. 0.
Problem 282 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 330 330 181 1356 0 590 330 637
normalized size 1 1. 0.55 4.11 0. 1.79 1. 1.93
time (sec) N/A 0.872 0.14 0.144 0. 1.984 16.283 1.141
Problem 283 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 4 4 4 5 5 15 5 5
normalized size 1 1. 1. 1.25 1.25 3.75 1.25 1.25
time (sec) N/A 0.012 0.001 0.009 0.927 1.812 0.707 1.098
Problem 284 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A A F B A A
verified N/A N/A Yes TBD TBD TBD TBD TBD
size 71 0 71 102 0 319 76 132
normalized size 1 0. 1. 1.44 0. 4.49 1.07 1.86
time (sec) N/A 0.754 0.036 0.022 0. 1.614 0.205 1.135

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 [50] had the largest ratio of [ 1.429 ]

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 1 0 1. 6 0.
2 A 3 2 1. 13 0.154
3 A 2 1 1. 10 0.1
4 A 1 1 1. 3 0.333
5 A 2 1 1. 11 0.091
6 A 2 1 1. 14 0.071
7 A 2 1 1. 20 0.05
8 A 2 2 1. 12 0.167
9 A 3 3 1. 13 0.231
10 A 2 2 1. 10 0.2
11 A 6 5 1. 13 0.385
12 A 2 1 1. 23 0.043
13 A 4 3 1. 20 0.15
14 A 3 2 1. 22 0.091
15 A 5 4 1. 14 0.286
16 A 6 6 1. 9 0.667
17 A 3 2 1. 16 0.125
18 A 9 6 1. 7 0.857
19 A 9 6 1. 11 0.546
20 A 9 5 1. 10 0.5
21 A 1 1 1. 7 0.143
22 A 2 1 1. 9 0.111
23 A 2 1 1. 11 0.091
24 A 1 1 1. 7 0.143
25 A 1 1 1. 7 0.143
26 A 2 1 1. 9 0.111
27 A 2 1 1. 11 0.091
28 A 3 3 1. 11 0.273
29 A 2 1 1. 11 0.091
30 A 2 1 1. 11 0.091
31 A 1 1 1. 9 0.111
32 A 1 1 1. 11 0.091
33 A 6 6 1. 9 0.667
34 A 6 6 1. 7 0.857
35 A 6 6 1. 11 0.546
36 A 3 3 1. 7 0.429
37 A 3 3 1. 9 0.333
38 A 9 6 1. 9 0.667
39 A 3 3 1. 12 0.25
40 A 3 3 1. 12 0.25
41 A 3 2 1. 12 0.167
42 A 3 2 1. 12 0.167
43 A 3 2 1. 12 0.167
44 A 9 5 1. 10 0.5
45 A 9 5 1. 12 0.417
46 A 10 6 1. 7 0.857
47 A 10 6 1. 7 0.857
48 A 10 6 1. 7 0.857
49 A 19 6 1. 7 0.857
50 A 13 10 1. 7 1.429
51 A 19 6 1. 12 0.5
52 A 7 7 1. 11 0.636
53 A 1 1 1. 2 0.5
54 A 1 1 1. 4 0.25
55 A 1 1 1. 6 0.167
56 A 1 1 1. 6 0.167
57 A 2 2 1. 4 0.5
58 A 11 2 1. 8 0.25
59 A 2 2 1. 8 0.25
60 A 1 1 1. 4 0.25
61 A 2 2 1. 6 0.333
62 A 2 2 1. 8 0.25
63 A 3 3 1. 8 0.375
64 A 2 2 1. 8 0.25
65 A 2 1 1.04 8 0.125
66 A 4 4 1. 10 0.4
67 A 2 2 1. 10 0.2
68 A 3 2 1. 8 0.25
69 A 3 2 1. 10 0.2
70 A 3 3 1. 8 0.375
71 A 3 3 1. 10 0.3
72 A 4 3 1. 12 0.25
73 A 4 3 1. 12 0.25
74 A 3 3 1. 10 0.3
75 A 0 0 0. 0 0.
76 A 1 1 1. 2 0.5
77 A 1 1 1. 2 0.5
78 A 1 1 1. 2 0.5
79 A 1 1 1. 2 0.5
80 A 2 2 1. 6 0.333
81 A 1 1 1. 2 0.5
82 A 1 1 1. 2 0.5
83 A 2 2 1. 4 0.5
84 A 3 3 1. 8 0.375
85 A 2 1 1. 4 0.25
86 A 1 1 1. 4 0.25
87 A 3 2 1. 11 0.182
88 A 2 2 1. 4 0.5
89 A 2 1 1. 4 0.25
90 A 2 2 1. 4 0.5
91 A 1 1 1. 7 0.143
92 A 2 2 1. 4 0.5
93 A 3 2 1. 6 0.333
94 A 2 2 1. 6 0.333
95 A 4 4 1. 8 0.5
96 A 3 3 1. 6 0.5
97 A 2 2 1. 4 0.5
98 A 3 2 1. 6 0.333
99 A 2 2 1. 6 0.333
100 A 4 4 1. 8 0.5
101 A 3 3 1. 6 0.5
102 A 1 1 1. 6 0.167
103 A 1 1 1. 6 0.167
104 A 2 2 1. 6 0.333
105 A 3 2 1. 8 0.25
106 A 2 2 1. 4 0.5
107 A 1 1 1. 6 0.167
108 A 1 1 1. 6 0.167
109 A 1 1 1. 6 0.167
110 A 1 1 1. 6 0.167
111 A 1 1 1. 6 0.167
112 A 1 1 1. 6 0.167
113 A 2 2 1. 8 0.25
114 A 2 1 1. 8 0.125
115 A 2 2 1. 8 0.25
116 A 2 1 1. 8 0.125
117 A 2 2 1. 8 0.25
118 A 1 1 1. 6 0.167
119 A 1 1 1. 8 0.125
120 A 1 1 1. 6 0.167
121 A 1 1 1. 8 0.125
122 A 3 3 1. 8 0.375
123 A 3 3 1. 10 0.3
124 A 4 4 1. 12 0.333
125 A 1 1 1. 7 0.143
126 A 4 4 1. 12 0.333
127 A 2 2 1. 4 0.5
128 A 17 8 1. 8 1.
129 A 34 9 1. 8 1.125
130 A 3 3 1. 6 0.5
131 A 1 1 1. 9 0.111
132 A 3 3 1. 9 0.333
133 A 3 2 1. 9 0.222
134 A 1 1 1. 6 0.167
135 A 1 1 1. 6 0.167
136 A 4 3 1. 7 0.429
137 A 4 3 1. 7 0.429
138 A 11 5 1. 9 0.556
139 A 11 5 1. 9 0.556
140 A 25 5 1. 9 0.556
141 A 25 5 1. 9 0.556
142 A 5 2 1. 11 0.182
143 A 5 2 1. 11 0.182
144 A 6 4 1. 10 0.4
145 A 0 0 0. 0 0.
146 A 4 3 1. 9 0.333
147 A 5 5 1. 15 0.333
148 A 1 1 1. 3 0.333
149 A 1 1 1. 3 0.333
150 A 1 1 1. 3 0.333
151 A 1 1 1. 3 0.333
152 A 1 1 1. 5 0.2
153 A 1 1 1. 9 0.111
154 A 4 4 1. 11 0.364
155 A 3 2 1. 13 0.154
156 A 2 2 1. 9 0.222
157 A 2 2 1. 18 0.111
158 A 2 2 1. 7 0.286
159 A 21 2 1. 7 0.286
160 A 2 2 1. 9 0.222
161 A 2 2 1. 7 0.286
162 A 2 2 1. 7 0.286
163 A 5 3 1. 12 0.25
164 A 1 1 1. 14 0.071
165 A 1 1 1. 7 0.143
166 A 1 1 1. 5 0.2
167 A 1 1 1. 7 0.143
168 A 7 3 1. 12 0.25
169 F 0 0 N/A 0 N/A
170 A 0 0 0. 0 0.
171 A 2 3 1. 6 0.5
172 A 5 5 1. 7 0.714
173 A 3 3 1. 10 0.3
174 A 1 0 1. 13 0.
175 A 4 4 1. 12 0.333
176 A 5 4 1. 19 0.21
177 A 1 1 1. 9 0.111
178 A 2 1 1. 11 0.091
179 A 2 1 1. 13 0.077
180 A 3 3 1. 13 0.231
181 A 3 3 1. 13 0.231
182 A 1 1 1. 9 0.111
183 A 2 1 1. 11 0.091
184 A 2 1 1. 13 0.077
185 A 2 2 1. 13 0.154
186 A 3 3 1. 13 0.231
187 A 1 1 1. 11 0.091
188 A 2 1 1. 13 0.077
189 A 6 6 1. 18 0.333
190 A 2 2 1. 9 0.222
191 A 4 3 1. 13 0.231
192 A 3 3 1. 6 0.5
193 A 1 1 1. 13 0.077
194 A 2 2 1. 13 0.154
195 A 3 3 1. 13 0.231
196 A 3 3 1. 14 0.214
197 A 3 3 1. 18 0.167
198 A 1 1 1. 20 0.05
199 A 1 1 1. 9 0.111
200 A 3 2 1. 65 0.031
201 A 5 4 1. 68 0.059
202 A 5 2 1. 21 0.095
203 A 6 6 1. 21 0.286
204 A 4 3 1. 23 0.13
205 A 2 2 1. 16 0.125
206 A 3 3 1. 25 0.12
207 A 2 2 1. 24 0.083
208 A 2 2 1. 29 0.069
209 A 1 1 1. 18 0.056
210 A 1 1 1. 23 0.043
211 A 3 3 1. 24 0.125
212 A 3 3 1. 22 0.136
213 A 3 3 1. 26 0.115
214 A 3 3 1. 31 0.097
215 A 3 3 1. 16 0.188
216 A 1 1 1. 8 0.125
217 A 2 2 1. 6 0.333
218 A 1 1 1. 20 0.05
219 A 3 2 1. 13 0.154
220 A 2 2 1. 13 0.154
221 A 3 3 1. 9 0.333
222 A 2 2 1. 13 0.154
223 A 2 1 1. 11 0.091
224 A 5 5 1. 13 0.385
225 A 2 2 1. 4 0.5
226 A 2 2 1. 4 0.5
227 A 1 1 1. 4 0.25
228 A 1 1 1. 28 0.036
229 A 4 2 1. 11 0.182
230 A 3 3 1. 4 0.75
231 A 3 3 1. 4 0.75
232 A 3 3 1. 8 0.375
233 A 3 2 1. 7 0.286
234 A 3 2 1. 7 0.286
235 A 1 1 1. 8 0.125
236 A 1 1 1. 10 0.1
237 A 1 1 1. 8 0.125
238 A 1 1 1. 10 0.1
239 A 3 3 1. 17 0.176
240 A 4 3 1. 13 0.231
241 A 2 2 1. 11 0.182
242 A 4 3 1. 13 0.231
243 A 3 3 1. 8 0.375
244 A 1 1 1. 2 0.5
245 A 3 2 1. 4 0.5
246 A 1 1 1. 2 0.5
247 A 1 1 1. 2 0.5
248 A 1 1 1. 3 0.333
249 A 4 3 1. 12 0.25
250 A 2 1 1. 13 0.077
251 A 3 3 1. 14 0.214
252 A 14 8 1. 12 0.667
253 A 4 3 1. 7 0.429
254 A 1 1 1. 5 0.2
255 A 6 6 1. 9 0.667
256 A 2 2 1. 9 0.222
257 A 10 3 1. 15 0.2
258 A 6 2 1. 11 0.182
259 A 6 6 1. 7 0.857
260 A 1 1 1. 9 0.111
261 A 2 2 1. 9 0.222
262 A 2 1 1. 7 0.143
263 A 2 2 1. 2 1.
264 A 4 3 1. 6 0.5
265 A 4 2 1. 17 0.118
266 A 2 2 1. 4 0.5
267 A 2 1 1. 19 0.053
268 A 1 1 1. 11 0.091
269 A 1 1 1. 9 0.111
270 A 2 2 1. 12 0.167
271 A 3 2 1. 24 0.083
272 A 2 1 1. 29 0.034
273 A 0 0 0. 0 0.
274 A 9 7 1. 54 0.13
275 A 4 3 1. 21 0.143
276 A 1 1 1. 2 0.5
277 A 1 1 1. 4 0.25
278 F 0 0 N/A 0 N/A
279 F 0 0 N/A 0 N/A
280 A 1 1 1. 85 0.012
281 F 0 0 N/A 0 N/A
282 A 20 8 1. 107 0.075
283 A 2 2 1. 7 0.286
284 F 0 0 N/A 0 N/A

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