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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 26, 28, 29, 30, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 95, 96, 97, 104, 105, 106, 107, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 131, 132, 133, 134, 135, 136, 137, 138, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 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, 208, 209, 210, 211, 212, 213, 217, 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 }

B grade: { 22, 23, 62, 63, 64, 65, 66, 81, 82, 83, 84, 85, 86, 87, 88, 89, 111, 112, 113, 114, 128, 129, 130, 139, 140, 141, 147, 166 }

C grade: { 24, 25, 27, 31, 32, 33, 34, 35, 40, 41, 42, 43, 90, 91, 92, 93, 94, 98, 99, 100, 101, 102, 103, 108, 109, 110 }

F grade: { 207, 214, 215, 216, 218, 219}

2.1.3 Maple

A grade: { 68, 69, 138, 142, 143, 144, 145, 146, 148, 149, 198, 202, 203, 204, 220, 221, 222, 225, 226, 233, 246 }

B grade: { }

C grade: { 1, 2, 3, 4, 5, 7, 8, 9, 24, 25, 27, 64, 65, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 81, 82, 87, 88, 90, 91, 93, 94, 95, 96, 97, 98, 99, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 172, 173, 176, 177, 182, 186, 187, 190, 191, 192 }

F grade: { 6, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 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, 78, 79, 80, 83, 84, 85, 86, 89, 92, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 139, 140, 141, 147, 150, 151, 152, 153, 154, 155, 170, 171, 174, 175, 178, 179, 180, 181, 183, 184, 185, 188, 189, 193, 194, 195, 196, 197, 199, 200, 201, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 223, 224, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 247, 248, 249 }

2.1.4 Maxima

A grade: { 2, 3, 4, 5, 7, 8, 9, 68, 69, 70, 71, 72, 73, 75, 76, 77, 142, 143, 144, 145, 146, 148, 149, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 167, 168, 169, 173, 177, 193, 198, 202, 203, 204, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236

B grade: { 166 }

C grade: { 192 }

F grade: { 1, 6, 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, 74, 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, 147, 150, 151, 152, 153, 154, 155, 170, 171, 172, 174, 175, 176, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 194, 195, 196, 197, 199, 200, 201, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249 }

2.1.5 FriCAS

A grade: { 68, 69, 138, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 181, 186, 187, 190, 191, 198, 202, 203, 204, 208, 209, 210, 212, 213, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 234, 235, 236, 239, 240, 241, 245, 246 }

B grade: { 163, 164, 165, 166, 182, 230, 231, 232, 233, 237, 238 }

C grade: { 64, 65, 66, 67, 139, 140, 141, 147, 214, 215, 216, 218, 219 }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 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, 178, 179, 180, 183, 184, 185, 188, 189, 192, 193, 194, 195, 196, 197, 199, 200, 201, 205, 206, 207, 211, 217, 242, 243, 244, 247, 248, 249 }

2.1.6 Sympy

A grade: { 158, 177, 198, 202, 203, 204, 205, 210, 211, 217, 223, 224, 225, 226, 227, 228, 229, 233, 239, 246 }

B grade: { 156, 157, 160, 161, 162, 163, 164, 165, 167, 168, 169, 230, 231, 232, 234, 235, 236 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 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, 159, 166, 170, 171, 172, 173, 174, 175, 176, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 199, 200, 201, 206, 207, 208, 209, 212, 213, 214, 215, 216, 218, 219, 220, 221, 222, 237, 238, 240, 241, 242, 243, 244, 245, 247, 248, 249 }

2.1.7 Giac

A grade: { 68, 69, 138, 142, 143, 144, 145, 146, 148, 149, 158, 159, 160, 161, 162, 170, 171, 172, 173, 177, 198, 202, 203, 204, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 234, 240, 246 }

B grade: { 156, 157, 163, 164, 165, 166, 167, 168, 169, 176, 182, 230, 231, 232, 233, 235, 236, 237, 238, 239, 241 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 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, 139, 140, 141, 147, 150, 151, 152, 153, 154, 155, 174, 175, 178, 179, 180, 181, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 199, 200, 201, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 242, 243, 244, 245, 247, 248, 249 }

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 C F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 173 173 157 555 0 0 0 0
normalized size 1 1. 0.91 3.21 0. 0. 0. 0.
time (sec) N/A 0.18 0.169 0.216 0. 0. 0. 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 210 210 188 1014 350 0 0 0
normalized size 1 1. 0.9 4.83 1.67 0. 0. 0.
time (sec) N/A 0.119 0.09 0.102 1.365 0. 0. 0.
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 178 178 161 870 297 0 0 0
normalized size 1 1. 0.9 4.89 1.67 0. 0. 0.
time (sec) N/A 0.104 0.072 0.076 1.367 0. 0. 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 146 146 131 725 240 0 0 0
normalized size 1 1. 0.9 4.97 1.64 0. 0. 0.
time (sec) N/A 0.076 0.06 0.072 1.34 0. 0. 0.
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 90 557 170 0 0 0
normalized size 1 1. 1.22 7.53 2.3 0. 0. 0.
time (sec) N/A 0.089 0.031 0.064 1.319 0. 0. 0.
Problem 6 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 28 28 34 0 0 0 0 0
normalized size 1 1. 1.21 0. 0. 0. 0. 0.
time (sec) N/A 0.028 0.009 0.187 0. 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 69 481 173 0 0 0
normalized size 1 1. 0.64 4.5 1.62 0. 0. 0.
time (sec) N/A 0.07 0.053 0.078 1.351 0. 0. 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 215 647 262 0 0 0
normalized size 1 1. 1.32 3.97 1.61 0. 0. 0.
time (sec) N/A 0.091 0.07 0.095 1.342 0. 0. 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 195 206 796 313 0 0 0
normalized size 1 1. 1.06 4.08 1.61 0. 0. 0.
time (sec) N/A 0.107 0.08 0.103 1.306 0. 0. 0.
Problem 10 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 456 456 594 0 0 0 0 0
normalized size 1 1. 1.3 0. 0. 0. 0. 0.
time (sec) N/A 0.331 0.193 0.189 0. 0. 0. 0.
Problem 11 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 396 396 506 0 0 0 0 0
normalized size 1 1. 1.28 0. 0. 0. 0. 0.
time (sec) N/A 0.288 0.157 0.14 0. 0. 0. 0.
Problem 12 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 327 327 416 0 0 0 0 0
normalized size 1 1. 1.27 0. 0. 0. 0. 0.
time (sec) N/A 0.219 0.129 0.239 0. 0. 0. 0.
Problem 13 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 193 193 294 0 0 0 0 0
normalized size 1 1. 1.52 0. 0. 0. 0. 0.
time (sec) N/A 0.335 0.093 0.199 0. 0. 0. 0.
Problem 14 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 55 55 53 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.06 0.075 0.175 0. 0. 0. 0.
Problem 15 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 203 220 183 0 0 0 0 0
normalized size 1 1.08 0.9 0. 0. 0. 0. 0.
time (sec) N/A 0.343 0.206 0.134 0. 0. 0. 0.
Problem 16 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 287 310 513 0 0 0 0 0
normalized size 1 1.08 1.79 0. 0. 0. 0. 0.
time (sec) N/A 0.484 0.189 0.15 0. 0. 0. 0.
Problem 17 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 710 710 1144 0 0 0 0 0
normalized size 1 1. 1.61 0. 0. 0. 0. 0.
time (sec) N/A 0.777 0.339 0.154 0. 0. 0. 0.
Problem 18 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 615 615 975 0 0 0 0 0
normalized size 1 1. 1.59 0. 0. 0. 0. 0.
time (sec) N/A 0.638 0.279 0.131 0. 0. 0. 0.
Problem 19 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 530 530 806 0 0 0 0 0
normalized size 1 1. 1.52 0. 0. 0. 0. 0.
time (sec) N/A 0.493 0.248 0.129 0. 0. 0. 0.
Problem 20 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 327 327 584 0 0 0 0 0
normalized size 1 1. 1.79 0. 0. 0. 0. 0.
time (sec) N/A 0.763 0.177 0.246 0. 0. 0. 0.
Problem 21 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 81 81 77 0 0 0 0 0
normalized size 1 1. 0.95 0. 0. 0. 0. 0.
time (sec) N/A 0.098 0.115 0.107 0. 0. 0. 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 342 360 770 0 0 0 0 0
normalized size 1 1.05 2.25 0. 0. 0. 0. 0.
time (sec) N/A 0.601 0.302 0.141 0. 0. 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 470 499 1047 0 0 0 0 0
normalized size 1 1.06 2.23 0. 0. 0. 0. 0.
time (sec) N/A 0.82 0.377 0.155 0. 0. 0. 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 180 180 348 827 0 0 0 0
normalized size 1 1. 1.93 4.59 0. 0. 0. 0.
time (sec) N/A 0.166 0.1 0.095 0. 0. 0. 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 267 820 0 0 0 0
normalized size 1 1. 2.34 7.19 0. 0. 0. 0.
time (sec) N/A 0.177 0.048 0.079 0. 0. 0. 0.
Problem 26 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 39 39 50 0 0 0 0 0
normalized size 1 1. 1.28 0. 0. 0. 0. 0.
time (sec) N/A 0.032 0.01 0.156 0. 0. 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 241 619 0 0 0 0
normalized size 1 1. 1.71 4.39 0. 0. 0. 0.
time (sec) N/A 0.128 0.096 0.09 0. 0. 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 241 241 364 0 0 0 0 0
normalized size 1 1. 1.51 0. 0. 0. 0. 0.
time (sec) N/A 0.179 0.088 0.178 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 182 182 254 0 0 0 0 0
normalized size 1 1. 1.4 0. 0. 0. 0. 0.
time (sec) N/A 0.107 0.09 0.112 0. 0. 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 169 169 221 0 0 0 0 0
normalized size 1 1. 1.31 0. 0. 0. 0. 0.
time (sec) N/A 0.119 0.09 0.174 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 211 211 285 0 0 0 0 0
normalized size 1 1. 1.35 0. 0. 0. 0. 0.
time (sec) N/A 0.14 0.182 0.076 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 367 367 654 0 0 0 0 0
normalized size 1 1. 1.78 0. 0. 0. 0. 0.
time (sec) N/A 0.365 0.337 0.109 0. 0. 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 241 241 519 0 0 0 0 0
normalized size 1 1. 2.15 0. 0. 0. 0. 0.
time (sec) N/A 0.505 0.256 0.208 0. 0. 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 484 0 0 0 0 0
normalized size 1 1. 6.91 0. 0. 0. 0. 0.
time (sec) N/A 0.067 0.205 0.217 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 257 257 488 0 0 0 0 0
normalized size 1 1. 1.9 0. 0. 0. 0. 0.
time (sec) N/A 0.338 0.342 0.131 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 612 612 703 0 0 0 0 0
normalized size 1 1. 1.15 0. 0. 0. 0. 0.
time (sec) N/A 1.034 0.592 0.093 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 519 519 544 0 0 0 0 0
normalized size 1 1. 1.05 0. 0. 0. 0. 0.
time (sec) N/A 0.801 0.32 0.156 0. 0. 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 459 459 414 0 0 0 0 0
normalized size 1 1. 0.9 0. 0. 0. 0. 0.
time (sec) N/A 0.556 0.304 0.096 0. 0. 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 543 543 585 0 0 0 0 0
normalized size 1 1. 1.08 0. 0. 0. 0. 0.
time (sec) N/A 0.866 0.524 0.102 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 591 591 1234 0 0 0 0 0
normalized size 1 1. 2.09 0. 0. 0. 0. 0.
time (sec) N/A 0.734 1.041 0.153 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 411 411 1004 0 0 0 0 0
normalized size 1 1. 2.44 0. 0. 0. 0. 0.
time (sec) N/A 1.042 0.538 0.138 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 754 0 0 0 0 0
normalized size 1 1. 7.47 0. 0. 0. 0. 0.
time (sec) N/A 0.1 0.312 0.113 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 425 425 940 0 0 0 0 0
normalized size 1 1. 2.21 0. 0. 0. 0. 0.
time (sec) N/A 0.583 0.372 0.181 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 938 938 1027 0 0 0 0 0
normalized size 1 1. 1.09 0. 0. 0. 0. 0.
time (sec) N/A 1.546 0.697 0.25 0. 0. 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 849 849 794 0 0 0 0 0
normalized size 1 1. 0.94 0. 0. 0. 0. 0.
time (sec) N/A 1.04 0.345 0.145 0. 0. 0. 0.
Problem 46 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 350 350 263 0 0 0 0 0
normalized size 1 1. 0.75 0. 0. 0. 0. 0.
time (sec) N/A 0.277 0.298 0.023 0. 0. 0. 0.
Problem 47 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 268 268 191 0 0 0 0 0
normalized size 1 1. 0.71 0. 0. 0. 0. 0.
time (sec) N/A 0.192 0.211 0.02 0. 0. 0. 0.
Problem 48 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 172 172 117 0 0 0 0 0
normalized size 1 1. 0.68 0. 0. 0. 0. 0.
time (sec) N/A 0.105 0.158 0.017 0. 0. 0. 0.
Problem 49 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 39 39 50 0 0 0 0 0
normalized size 1 1. 1.28 0. 0. 0. 0. 0.
time (sec) N/A 0.032 0.007 0.02 0. 0. 0. 0.
Problem 50 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 196 196 124 0 0 0 0 0
normalized size 1 1. 0.63 0. 0. 0. 0. 0.
time (sec) N/A 0.151 0.191 0.022 0. 0. 0. 0.
Problem 51 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 289 289 207 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.205 0.25 0.027 0. 0. 0. 0.
Problem 52 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 372 372 288 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.252 0.361 0.029 0. 0. 0. 0.
Problem 53 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 708 708 995 0 0 0 0 0
normalized size 1 1. 1.41 0. 0. 0. 0. 0.
time (sec) N/A 0.638 0.563 0.019 0. 0. 0. 0.
Problem 54 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 557 557 769 0 0 0 0 0
normalized size 1 1. 1.38 0. 0. 0. 0. 0.
time (sec) N/A 0.465 0.398 0.02 0. 0. 0. 0.
Problem 55 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 374 374 527 0 0 0 0 0
normalized size 1 1. 1.41 0. 0. 0. 0. 0.
time (sec) N/A 0.269 0.32 0.019 0. 0. 0. 0.
Problem 56 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 70 70 70 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.067 0.14 0.02 0. 0. 0. 0.
Problem 57 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 389 389 627 0 0 0 0 0
normalized size 1 1. 1.61 0. 0. 0. 0. 0.
time (sec) N/A 0.409 0.401 0.02 0. 0. 0. 0.
Problem 58 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 555 555 881 0 0 0 0 0
normalized size 1 1. 1.59 0. 0. 0. 0. 0.
time (sec) N/A 0.55 0.523 0.02 0. 0. 0. 0.
Problem 59 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 858 858 1432 0 0 0 0 0
normalized size 1 1. 1.67 0. 0. 0. 0. 0.
time (sec) N/A 0.935 0.6 0.059 0. 0. 0. 0.
Problem 60 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 604 604 986 0 0 0 0 0
normalized size 1 1. 1.63 0. 0. 0. 0. 0.
time (sec) N/A 0.52 0.494 0.049 0. 0. 0. 0.
Problem 61 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 101 101 98 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.099 0.206 0.05 0. 0. 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 610 610 1455 0 0 0 0 0
normalized size 1 1. 2.39 0. 0. 0. 0. 0.
time (sec) N/A 0.778 0.858 0.063 0. 0. 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 849 849 2009 0 0 0 0 0
normalized size 1 1. 2.37 0. 0. 0. 0. 0.
time (sec) N/A 1.144 1.048 0.063 0. 0. 0. 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 1700 38574 0 1222 0 0
normalized size 1 1. 12.41 281.56 0. 8.92 0. 0.
time (sec) N/A 0.144 0.68 0.898 0. 1.452 0. 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 1035 11734 0 678 0 0
normalized size 1 1. 9.86 111.75 0. 6.46 0. 0.
time (sec) N/A 0.114 0.395 0.25 0. 1.426 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 526 2578 0 325 0 0
normalized size 1 1. 7.21 35.32 0. 4.45 0. 0.
time (sec) N/A 0.071 0.233 0.089 0. 1.384 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 52 308 0 113 0 0
normalized size 1 1. 1.3 7.7 0. 2.82 0. 0.
time (sec) N/A 0.048 0.009 0.043 0. 1.346 0. 0.
Problem 68 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 30 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.04 0.06 0.854 0. 0. 0. 0.
Problem 69 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 30 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.042 1.886 1.212 0. 0. 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 283 283 290 2403 514 0 0 0
normalized size 1 1. 1.02 8.49 1.82 0. 0. 0.
time (sec) N/A 0.206 0.223 0.394 1.866 0. 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 243 243 252 2222 443 0 0 0
normalized size 1 1. 1.04 9.14 1.82 0. 0. 0.
time (sec) N/A 0.166 0.153 0.318 1.693 0. 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 203 203 208 2041 363 0 0 0
normalized size 1 1. 1.02 10.05 1.79 0. 0. 0.
time (sec) N/A 0.126 0.122 0.319 1.824 0. 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 152 1762 254 0 0 0
normalized size 1 1. 1.3 15.06 2.17 0. 0. 0.
time (sec) N/A 0.145 0.069 0.274 1.72 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 147 1795 0 0 0 0
normalized size 1 1. 1.47 17.95 0. 0. 0. 0.
time (sec) N/A 0.093 0.066 0.16 0. 0. 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 164 164 117 1892 269 0 0 0
normalized size 1 1. 0.71 11.54 1.64 0. 0. 0.
time (sec) N/A 0.118 0.113 0.309 1.649 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 234 234 232 2100 385 0 0 0
normalized size 1 1. 0.99 8.97 1.65 0. 0. 0.
time (sec) N/A 0.163 0.148 0.348 1.692 0. 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 274 274 280 2282 462 0 0 0
normalized size 1 1. 1.02 8.33 1.69 0. 0. 0.
time (sec) N/A 0.184 0.176 0.384 1.663 0. 0. 0.
Problem 78 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 452 452 788 0 0 0 0 0
normalized size 1 1. 1.74 0. 0. 0. 0. 0.
time (sec) N/A 0.683 0.342 1.819 0. 0. 0. 0.
Problem 79 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 373 373 674 0 0 0 0 0
normalized size 1 1. 1.81 0. 0. 0. 0. 0.
time (sec) N/A 0.531 0.276 2.312 0. 0. 0. 0.
Problem 80 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 288 288 507 0 0 0 0 0
normalized size 1 1. 1.76 0. 0. 0. 0. 0.
time (sec) N/A 0.352 0.196 1.948 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 329 21792 0 0 0 0
normalized size 1 1. 2.51 166.35 0. 0. 0. 0.
time (sec) N/A 0.141 0.162 0.796 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 248 283 600 10991 0 0 0 0
normalized size 1 1.14 2.42 44.32 0. 0. 0. 0.
time (sec) N/A 0.399 0.34 0.635 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 344 385 796 0 0 0 0 0
normalized size 1 1.12 2.31 0. 0. 0. 0. 0.
time (sec) N/A 0.586 0.381 1.829 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 420 462 909 0 0 0 0 0
normalized size 1 1.1 2.16 0. 0. 0. 0. 0.
time (sec) N/A 0.724 0.429 1.957 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 603 603 1431 0 0 0 0 0
normalized size 1 1. 2.37 0. 0. 0. 0. 0.
time (sec) N/A 0.974 0.554 36.276 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 473 473 1122 0 0 0 0 0
normalized size 1 1. 2.37 0. 0. 0. 0. 0.
time (sec) N/A 0.652 0.408 5.89 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 161 602 60520 0 0 0 0
normalized size 1 1. 3.74 375.9 0. 0. 0. 0.
time (sec) N/A 0.19 0.254 2.217 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 411 459 1347 42181 0 0 0 0
normalized size 1 1.12 3.28 102.63 0. 0. 0. 0.
time (sec) N/A 0.696 0.665 1.706 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 555 614 1736 0 0 0 0 0
normalized size 1 1.11 3.13 0. 0. 0. 0. 0.
time (sec) N/A 1.015 0.763 6.108 0. 0. 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 221 221 324 2259 0 0 0 0
normalized size 1 1. 1.47 10.22 0. 0. 0. 0.
time (sec) N/A 0.224 0.159 0.354 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 148 148 266 2068 0 0 0 0
normalized size 1 1. 1.8 13.97 0. 0. 0. 0.
time (sec) N/A 0.218 0.082 0.286 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 297 0 0 0 0 0
normalized size 1 1. 2.63 0. 0. 0. 0. 0.
time (sec) N/A 0.126 0.087 0.792 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 195 298 2101 0 0 0 0
normalized size 1 1. 1.53 10.77 0. 0. 0. 0.
time (sec) N/A 0.182 0.126 0.314 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 248 248 363 2313 0 0 0 0
normalized size 1 1. 1.46 9.33 0. 0. 0. 0.
time (sec) N/A 0.226 0.145 0.368 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 251 251 389 2321 0 0 0 0
normalized size 1 1. 1.55 9.25 0. 0. 0. 0.
time (sec) N/A 0.185 0.128 0.168 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 194 194 332 2001 0 0 0 0
normalized size 1 1. 1.71 10.31 0. 0. 0. 0.
time (sec) N/A 0.116 0.077 0.158 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 179 179 305 1972 0 0 0 0
normalized size 1 1. 1.7 11.02 0. 0. 0. 0.
time (sec) N/A 0.133 0.083 0.167 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 227 227 362 2204 0 0 0 0
normalized size 1 1. 1.59 9.71 0. 0. 0. 0.
time (sec) N/A 0.163 0.108 0.181 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 267 267 399 2385 0 0 0 0
normalized size 1 1. 1.49 8.93 0. 0. 0. 0.
time (sec) N/A 0.189 0.164 0.194 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 310 310 814 0 0 0 0 0
normalized size 1 1. 2.63 0. 0. 0. 0. 0.
time (sec) N/A 0.536 0.252 2.338 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 736 0 0 0 0 0
normalized size 1 1. 5.01 0. 0. 0. 0. 0.
time (sec) N/A 0.175 0.233 1.58 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 276 276 946 0 0 0 0 0
normalized size 1 1. 3.43 0. 0. 0. 0. 0.
time (sec) N/A 0.33 0.463 1.664 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 356 408 1111 0 0 0 0 0
normalized size 1 1.15 3.12 0. 0. 0. 0. 0.
time (sec) N/A 0.672 0.462 1.876 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 630 630 1128 0 0 0 0 0
normalized size 1 1. 1.79 0. 0. 0. 0. 0.
time (sec) N/A 1.065 0.43 13.078 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 546 546 993 0 0 0 0 0
normalized size 1 1. 1.82 0. 0. 0. 0. 0.
time (sec) N/A 0.806 0.314 5.022 0. 0. 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 478 478 917 0 0 0 0 0
normalized size 1 1. 1.92 0. 0. 0. 0. 0.
time (sec) N/A 0.515 0.318 7.095 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 571 571 1083 0 0 0 0 0
normalized size 1 1. 1.9 0. 0. 0. 0. 0.
time (sec) N/A 0.931 0.446 9.602 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 514 514 1911 0 0 0 0 0
normalized size 1 1. 3.72 0. 0. 0. 0. 0.
time (sec) N/A 0.924 0.515 4.701 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 181 181 1348 0 0 0 0 0
normalized size 1 1. 7.45 0. 0. 0. 0. 0.
time (sec) N/A 0.215 0.365 2.873 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 451 451 2248 0 0 0 0 0
normalized size 1 1. 4.98 0. 0. 0. 0. 0.
time (sec) N/A 0.569 0.863 5.322 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 1092 1092 2544 0 0 0 0 0
normalized size 1 1. 2.33 0. 0. 0. 0. 0.
time (sec) N/A 1.807 0.925 103.929 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 977 977 2302 0 0 0 0 0
normalized size 1 1. 2.36 0. 0. 0. 0. 0.
time (sec) N/A 1.499 0.698 28.803 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 879 879 2166 0 0 0 0 0
normalized size 1 1. 2.46 0. 0. 0. 0. 0.
time (sec) N/A 1.106 0.683 27.737 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 1007 1007 2488 0 0 0 0 0
normalized size 1 1. 2.47 0. 0. 0. 0. 0.
time (sec) N/A 1.702 0.839 44.451 0. 0. 0. 0.
Problem 115 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 403 403 434 0 0 0 0 0
normalized size 1 1. 1.08 0. 0. 0. 0. 0.
time (sec) N/A 0.345 0.463 0.043 0. 0. 0. 0.
Problem 116 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 313 313 336 0 0 0 0 0
normalized size 1 1. 1.07 0. 0. 0. 0. 0.
time (sec) N/A 0.244 0.349 0.02 0. 0. 0. 0.
Problem 117 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 209 209 218 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.15 0.232 0.046 0. 0. 0. 0.
Problem 118 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 117 117 186 0 0 0 0 0
normalized size 1 1. 1.59 0. 0. 0. 0. 0.
time (sec) N/A 0.146 0.166 0.023 0. 0. 0. 0.
Problem 119 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 248 248 250 0 0 0 0 0
normalized size 1 1. 1.01 0. 0. 0. 0. 0.
time (sec) N/A 0.21 0.308 0.022 0. 0. 0. 0.
Problem 120 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 346 346 359 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.28 0.41 0.02 0. 0. 0. 0.
Problem 121 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 434 434 457 0 0 0 0 0
normalized size 1 1. 1.05 0. 0. 0. 0. 0.
time (sec) N/A 0.35 0.497 0.02 0. 0. 0. 0.
Problem 122 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 750 750 1319 0 0 0 0 0
normalized size 1 1. 1.76 0. 0. 0. 0. 0.
time (sec) N/A 0.846 0.873 0.033 0. 0. 0. 0.
Problem 123 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 598 598 960 0 0 0 0 0
normalized size 1 1. 1.61 0. 0. 0. 0. 0.
time (sec) N/A 0.656 0.488 0.025 0. 0. 0. 0.
Problem 124 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 405 405 718 0 0 0 0 0
normalized size 1 1. 1.77 0. 0. 0. 0. 0.
time (sec) N/A 0.441 0.384 0.022 0. 0. 0. 0.
Problem 125 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 145 145 263 0 0 0 0 0
normalized size 1 1. 1.81 0. 0. 0. 0. 0.
time (sec) N/A 0.194 0.24 0.031 0. 0. 0. 0.
Problem 126 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 441 441 821 0 0 0 0 0
normalized size 1 1. 1.86 0. 0. 0. 0. 0.
time (sec) N/A 0.633 0.5 0.036 0. 0. 0. 0.
Problem 127 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 608 608 1078 0 0 0 0 0
normalized size 1 1. 1.77 0. 0. 0. 0. 0.
time (sec) N/A 0.784 0.58 0.038 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 907 907 1968 0 0 0 0 0
normalized size 1 1. 2.17 0. 0. 0. 0. 0.
time (sec) N/A 1.309 0.761 0.043 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 639 639 1522 0 0 0 0 0
normalized size 1 1. 2.38 0. 0. 0. 0. 0.
time (sec) N/A 0.856 0.654 0.026 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 178 178 403 0 0 0 0 0
normalized size 1 1. 2.26 0. 0. 0. 0. 0.
time (sec) N/A 0.232 0.406 0.041 0. 0. 0. 0.
Problem 131 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 673 673 976 0 0 0 0 0
normalized size 1 1. 1.45 0. 0. 0. 0. 0.
time (sec) N/A 1.182 1.093 0.05 0. 0. 0. 0.
Problem 132 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 914 914 1549 0 0 0 0 0
normalized size 1 1. 1.69 0. 0. 0. 0. 0.
time (sec) N/A 1.52 2.226 0.059 0. 0. 0. 0.
Problem 133 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 367 367 394 0 0 0 0 0
normalized size 1 1. 1.07 0. 0. 0. 0. 0.
time (sec) N/A 0.298 0.418 0.032 0. 0. 0. 0.
Problem 134 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 283 283 296 0 0 0 0 0
normalized size 1 1. 1.05 0. 0. 0. 0. 0.
time (sec) N/A 0.228 0.306 0.02 0. 0. 0. 0.
Problem 135 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 199 199 145 0 0 0 0 0
normalized size 1 1. 0.73 0. 0. 0. 0. 0.
time (sec) N/A 0.17 0.396 0.021 0. 0. 0. 0.
Problem 136 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 310 310 326 0 0 0 0 0
normalized size 1 1. 1.05 0. 0. 0. 0. 0.
time (sec) N/A 0.242 0.396 0.02 0. 0. 0. 0.
Problem 137 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 394 394 422 0 0 0 0 0
normalized size 1 1. 1.07 0. 0. 0. 0. 0.
time (sec) N/A 0.305 0.452 0.023 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 30 0 304 0 0 0 0 0
normalized size 1 0. 10.13 0. 0. 0. 0. 0.
time (sec) N/A 0.02 0.33 0.25 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 185 185 1395 0 0 1824 0 0
normalized size 1 1. 7.54 0. 0. 9.86 0. 0.
time (sec) N/A 0.299 0.618 0.109 0. 1.16 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 150 150 741 0 0 995 0 0
normalized size 1 1. 4.94 0. 0. 6.63 0. 0.
time (sec) N/A 0.249 0.36 0.086 0. 1.108 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 277 0 0 450 0 0
normalized size 1 1. 2.43 0. 0. 3.95 0. 0.
time (sec) N/A 0.193 0.165 0.085 0. 1.098 0. 0.
Problem 142 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 30 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.034 0.159 0.074 0. 0. 0. 0.
Problem 143 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 30 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.034 1.777 0.076 0. 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 28 0 292 0 0 0 0 0
normalized size 1 0. 10.43 0. 0. 0. 0. 0.
time (sec) N/A 0.019 0.178 0.088 0. 0. 0. 0.
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 NO TBD TBD TBD TBD TBD
size 26 0 292 0 0 0 0 0
normalized size 1 0. 11.23 0. 0. 0. 0. 0.
time (sec) N/A 0.011 0.171 0.084 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 25 0 165 0 0 0 0 0
normalized size 1 0. 6.6 0. 0. 0. 0. 0.
time (sec) N/A 0.005 0.169 0.086 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 277 0 0 450 0 0
normalized size 1 1. 2.43 0. 0. 3.95 0. 0.
time (sec) N/A 0.188 0.177 0.089 0. 1.421 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 28 0 282 0 0 0 0 0
normalized size 1 0. 10.07 0. 0. 0. 0. 0.
time (sec) N/A 0.02 0.165 0.087 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 28 0 292 0 0 0 0 0
normalized size 1 0. 10.43 0. 0. 0. 0. 0.
time (sec) N/A 0.019 0.153 0.088 0. 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 433 433 410 0 0 910 0 0
normalized size 1 1. 0.95 0. 0. 2.1 0. 0.
time (sec) N/A 0.603 0.427 0.238 0. 0.991 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 363 363 352 0 0 730 0 0
normalized size 1 1. 0.97 0. 0. 2.01 0. 0.
time (sec) N/A 0.418 0.379 0.24 0. 0.987 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 255 255 268 0 0 505 0 0
normalized size 1 1. 1.05 0. 0. 1.98 0. 0.
time (sec) N/A 0.245 0.227 0.234 0. 0.868 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 304 304 162 0 0 595 0 0
normalized size 1 1. 0.53 0. 0. 1.96 0. 0.
time (sec) N/A 0.305 0.34 0.23 0. 0.955 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 414 414 302 0 0 828 0 0
normalized size 1 1. 0.73 0. 0. 2. 0. 0.
time (sec) N/A 0.521 0.356 0.237 0. 0.9 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 484 484 358 0 0 999 0 0
normalized size 1 1. 0.74 0. 0. 2.06 0. 0.
time (sec) N/A 0.701 0.406 0.239 0. 1.018 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 71 1640 140 347 202 217
normalized size 1 1. 0.85 19.52 1.67 4.13 2.4 2.58
time (sec) N/A 0.075 0.072 0.188 1.191 0.872 34.727 1.295
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 68 1640 138 324 199 217
normalized size 1 1. 0.81 19.52 1.64 3.86 2.37 2.58
time (sec) N/A 0.052 0.062 0.18 1.18 0.802 12.293 1.401
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 58 1503 111 270 151 165
normalized size 1 1. 0.75 19.52 1.44 3.51 1.96 2.14
time (sec) N/A 0.036 0.021 0.154 1.222 0.904 3.358 1.316
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 72 1597 99 188 0 115
normalized size 1 1. 1.26 28.02 1.74 3.3 0. 2.02
time (sec) N/A 0.072 0.062 0.26 1.155 0.81 0. 1.297
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 57 1443 127 247 153 146
normalized size 1 1. 0.79 20.04 1.76 3.43 2.12 2.03
time (sec) N/A 0.071 0.064 0.187 1.169 0.905 3.161 1.25
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 64 1442 126 266 201 157
normalized size 1 1. 0.77 17.37 1.52 3.2 2.42 1.89
time (sec) N/A 0.073 0.07 0.19 1.173 0.769 11.437 1.214
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 69 1451 134 294 204 163
normalized size 1 1. 0.83 17.48 1.61 3.54 2.46 1.96
time (sec) N/A 0.074 0.074 0.204 1.175 0.974 32.193 1.186
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 207 207 157 9271 338 907 654 683
normalized size 1 1. 0.76 44.79 1.63 4.38 3.16 3.3
time (sec) N/A 0.203 0.143 0.522 1.24 0.932 110.905 1.301
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 206 206 154 9262 333 892 600 671
normalized size 1 1. 0.75 44.96 1.62 4.33 2.91 3.26
time (sec) N/A 0.166 0.131 0.52 1.214 0.832 36.678 1.334
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 141 8701 288 790 534 574
normalized size 1 1. 0.96 59.19 1.96 5.37 3.63 3.9
time (sec) N/A 0.088 0.104 0.5 1.198 0.835 13.149 1.33
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 129 9164 220 451 0 301
normalized size 1 1. 2.26 160.77 3.86 7.91 0. 5.28
time (sec) N/A 0.095 0.133 0.886 1.2 0.883 0. 1.328
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 181 181 138 8407 298 743 536 529
normalized size 1 1. 0.76 46.45 1.65 4.1 2.96 2.92
time (sec) N/A 0.193 0.148 0.657 1.212 0.831 12.499 1.336
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 204 204 151 8407 302 791 602 544
normalized size 1 1. 0.74 41.21 1.48 3.88 2.95 2.67
time (sec) N/A 0.206 0.155 0.671 1.216 0.968 12.468 1.264
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 205 205 155 8407 311 801 656 544
normalized size 1 1. 0.76 41.01 1.52 3.91 3.2 2.65
time (sec) N/A 0.211 0.156 0.71 1.235 0.833 34.708 1.28
Problem 170 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 141 141 93 0 0 242 0 262
normalized size 1 1. 0.66 0. 0. 1.72 0. 1.86
time (sec) N/A 0.18 0.164 0.338 0. 0.924 0. 1.401
Problem 171 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 141 141 93 0 0 242 0 262
normalized size 1 1. 0.66 0. 0. 1.72 0. 1.86
time (sec) N/A 0.154 0.145 1.092 0. 0.889 0. 1.356
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 86 2356 0 220 0 230
normalized size 1 1. 0.66 18.12 0. 1.69 0. 1.77
time (sec) N/A 0.122 0.128 0.281 0. 0.785 0. 1.448
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 58 1744 159 144 0 115
normalized size 1 1. 0.82 24.56 2.24 2.03 0. 1.62
time (sec) N/A 0.106 0.069 0.152 1.243 0.88 0. 1.281
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 133 133 87 0 0 198 0 0
normalized size 1 1. 0.65 0. 0. 1.49 0. 0.
time (sec) N/A 0.172 0.125 0.312 0. 0.826 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 94 0 0 225 0 0
normalized size 1 1. 0.67 0. 0. 1.6 0. 0.
time (sec) N/A 0.169 0.13 0.352 0. 0.809 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 135 87 371 0 358 0 892
normalized size 1 1.52 0.98 4.17 0. 4.02 0. 10.02
time (sec) N/A 0.138 0.144 0.115 0. 0.848 0. 1.473
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 28 131 43 55 32 23
normalized size 1 1. 0.97 4.52 1.48 1.9 1.1 0.79
time (sec) N/A 0.053 0.017 0.04 1.143 0.818 9.622 1.304
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 347 347 179 0 0 0 0 0
normalized size 1 1. 0.52 0. 0. 0. 0. 0.
time (sec) N/A 0.358 0.611 0.827 0. 0. 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 298 298 156 0 0 0 0 0
normalized size 1 1. 0.52 0. 0. 0. 0. 0.
time (sec) N/A 0.245 0.378 0.506 0. 0. 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 298 298 156 0 0 0 0 0
normalized size 1 1. 0.52 0. 0. 0. 0. 0.
time (sec) N/A 0.22 0.367 0.618 0. 0. 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 271 271 146 0 0 339 0 0
normalized size 1 1. 0.54 0. 0. 1.25 0. 0.
time (sec) N/A 0.166 0.304 0.438 0. 0.904 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 71 854 0 518 0 332
normalized size 1 1. 1. 12.03 0. 7.3 0. 4.68
time (sec) N/A 0.155 0.139 0.277 0. 0.824 0. 1.34
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 260 260 141 0 0 0 0 0
normalized size 1 1. 0.54 0. 0. 0. 0. 0.
time (sec) N/A 0.227 0.317 0.5 0. 0. 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 295 295 154 0 0 0 0 0
normalized size 1 1. 0.52 0. 0. 0. 0. 0.
time (sec) N/A 0.234 0.375 0.215 0. 0. 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 295 295 154 0 0 0 0 0
normalized size 1 1. 0.52 0. 0. 0. 0. 0.
time (sec) N/A 0.24 0.377 0.208 0. 0. 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 246 246 248 10458 0 537 0 0
normalized size 1 1. 1.01 42.51 0. 2.18 0. 0.
time (sec) N/A 0.233 0.166 2.663 0. 1.802 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 245 245 248 8281 0 726 0 0
normalized size 1 1. 1.01 33.8 0. 2.96 0. 0.
time (sec) N/A 0.227 0.175 2.079 0. 1.762 0. 0.
Problem 188 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 182 182 165 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.164 0.117 11.802 0. 0. 0. 0.
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 182 182 178 0 0 0 0 0
normalized size 1 1. 0.98 0. 0. 0. 0. 0.
time (sec) N/A 0.148 0.121 11.066 0. 0. 0. 0.
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 244 244 240 4077 0 707 0 0
normalized size 1 1. 0.98 16.71 0. 2.9 0. 0.
time (sec) N/A 0.219 0.15 1.861 0. 1.325 0. 0.
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 312 312 145 4732 0 630 0 0
normalized size 1 1. 0.46 15.17 0. 2.02 0. 0.
time (sec) N/A 0.21 0.224 1.968 0. 1.369 0. 0.
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C C F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 180 180 167 90875 478 0 0 0
normalized size 1 1. 0.93 504.86 2.66 0. 0. 0.
time (sec) N/A 0.162 0.136 5.25 1.448 0. 0. 0.
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 180 180 178 0 431 0 0 0
normalized size 1 1. 0.99 0. 2.39 0. 0. 0.
time (sec) N/A 0.156 0.13 5.356 1.461 0. 0. 0.
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 482 482 456 0 0 0 0 0
normalized size 1 1. 0.95 0. 0. 0. 0. 0.
time (sec) N/A 0.734 0.828 2.362 0. 0. 0. 0.
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 490 490 564 0 0 0 0 0
normalized size 1 1. 1.15 0. 0. 0. 0. 0.
time (sec) N/A 0.702 0.801 2.036 0. 0. 0. 0.
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 458 458 516 0 0 0 0 0
normalized size 1 1. 1.13 0. 0. 0. 0. 0.
time (sec) N/A 0.702 0.706 0.892 0. 0. 0. 0.
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 508 508 770 0 0 0 0 0
normalized size 1 1. 1.52 0. 0. 0. 0. 0.
time (sec) N/A 1.546 3.564 0.849 0. 0. 0. 0.
Problem 198 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.033 0.048 0.033 0. 0. 0. 0.
Problem 199 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 104 104 99 0 0 0 0 0
normalized size 1 1. 0.95 0. 0. 0. 0. 0.
time (sec) N/A 0.112 0.049 0.027 0. 0. 0. 0.
Problem 200 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 72 72 69 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.069 0.017 0.027 0. 0. 0. 0.
Problem 201 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 40 40 51 0 0 0 0 0
normalized size 1 1. 1.27 0. 0. 0. 0. 0.
time (sec) N/A 0.033 0.004 0.024 0. 0. 0. 0.
Problem 202 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.032 0.041 0.023 0. 0. 0. 0.
Problem 203 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 63 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.071 0.044 0.025 0. 0. 0. 0.
Problem 204 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 102 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.112 0.047 0.026 0. 0. 0. 0.
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 20 0 0 0 15 0
normalized size 1 1. 1. 0. 0. 0. 0.75 0.
time (sec) N/A 0.024 0.002 0.007 0. 0. 2.213 0.
Problem 206 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 33 33 33 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.044 0.003 0.018 0. 0. 0. 0.
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 26 26 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.11 0.147 0.055 0. 0. 0. 0.
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 217 217 196 0 0 576 0 0
normalized size 1 1. 0.9 0. 0. 2.65 0. 0.
time (sec) N/A 0.181 0.529 0.193 0. 0.889 0. 0.
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 185 185 168 0 0 477 0 0
normalized size 1 1. 0.91 0. 0. 2.58 0. 0.
time (sec) N/A 0.132 0.324 0.181 0. 0.982 0. 0.
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 113 0 0 329 172 0
normalized size 1 1. 1.07 0. 0. 3.1 1.62 0.
time (sec) N/A 0.114 0.074 0.151 0. 0.897 99.244 0.
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 30 0 0 0 26 0
normalized size 1 1. 1.15 0. 0. 0. 1. 0.
time (sec) N/A 0.029 0.003 0.167 0. 0. 123.353 0.
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 115 0 0 351 0 0
normalized size 1 1. 0.81 0. 0. 2.47 0. 0.
time (sec) N/A 0.114 0.154 0.145 0. 0.974 0. 0.
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 202 202 163 0 0 451 0 0
normalized size 1 1. 0.81 0. 0. 2.23 0. 0.
time (sec) N/A 0.157 0.189 0.194 0. 0.962 0. 0.
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F C F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 253 253 0 0 0 738 0 0
normalized size 1 1. 0. 0. 0. 2.92 0. 0.
time (sec) N/A 0.254 0.135 0.349 0. 0.975 0. 0.
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F C F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 221 221 0 0 0 639 0 0
normalized size 1 1. 0. 0. 0. 2.89 0. 0.
time (sec) N/A 0.19 0.117 0.336 0. 0.866 0. 0.
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F C F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 131 131 0 0 0 464 0 0
normalized size 1 1. 0. 0. 0. 3.54 0. 0.
time (sec) N/A 0.127 0.08 0.273 0. 0.983 0. 0.
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 30 0 0 0 26 0
normalized size 1 1. 1.15 0. 0. 0. 1. 0.
time (sec) N/A 0.028 0.003 0.306 0. 0. 9.213 0.
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F C F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 174 174 0 0 0 463 0 0
normalized size 1 1. 0. 0. 0. 2.66 0. 0.
time (sec) N/A 0.156 0.128 0.238 0. 0.872 0. 0.
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F C F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 238 238 0 0 0 594 0 0
normalized size 1 1. 0. 0. 0. 2.5 0. 0.
time (sec) N/A 0.218 0.123 0.309 0. 0.958 0. 0.
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A NO TBD TBD TBD TBD TBD
size 29 0 266 844 0 0 0 0
normalized size 1 0. 9.17 29.1 0. 0. 0. 0.
time (sec) N/A 0.022 0.233 0.468 0. 0. 0. 0.
Problem 221 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 177 0 0 867 0 0 0 0
normalized size 1 0. 0. 4.9 0. 0. 0. 0.
time (sec) N/A 0.104 0.108 0.267 0. 0. 0. 0.
Problem 222 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 244 0 0 1065 0 0 0 0
normalized size 1 0. 0. 4.36 0. 0. 0. 0.
time (sec) N/A 0.217 0.061 1.089 0. 0. 0. 0.
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 0 31 95 37 43
normalized size 1 1. 1. 0. 1.15 3.52 1.37 1.59
time (sec) N/A 0.031 0.003 0.071 1.141 0.885 2.715 1.352
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 0 31 95 37 43
normalized size 1 1. 1. 0. 1.15 3.52 1.37 1.59
time (sec) N/A 0.017 0.001 0.026 1.165 0.825 1.058 1.31
Problem 225 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 62 24 28
normalized size 1 1. 1. 1.06 1.33 3.44 1.33 1.56
time (sec) N/A 0.007 0.001 0.004 1.148 0.872 0.43 1.276
Problem 226 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 21 27 63 37 27
normalized size 1 1. 1. 0.95 1.23 2.86 1.68 1.23
time (sec) N/A 0.03 0.001 0.004 1.144 0.968 1.995 1.293
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 0 31 58 26 34
normalized size 1 1. 1. 0. 1.35 2.52 1.13 1.48
time (sec) N/A 0.031 0.001 0.028 1.177 0.889 1.196 1.32
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 0 31 74 39 38
normalized size 1 1. 1. 0. 1.15 2.74 1.44 1.41
time (sec) N/A 0.029 0.001 0.026 1.132 0.882 3.048 1.311
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 0 31 74 39 38
normalized size 1 1. 1. 0. 1.15 2.74 1.44 1.41
time (sec) N/A 0.03 0.001 0.028 1.159 0.879 7.924 1.311
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 52 0 62 293 150 155
normalized size 1 1. 1. 0. 1.19 5.63 2.88 2.98
time (sec) N/A 0.071 0.003 0.028 1.163 0.734 8.069 1.303
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 43 0 62 292 133 151
normalized size 1 1. 0.83 0. 1.19 5.62 2.56 2.9
time (sec) N/A 0.045 0.006 0.027 1.19 0.943 2.819 1.26
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 37 0 53 230 116 124
normalized size 1 1. 0.95 0. 1.36 5.9 2.97 3.18
time (sec) N/A 0.022 0.003 0.027 1.205 0.926 1.176 1.322
Problem 233 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 22 22 22 21 27 157 41 80
normalized size 1 1. 1. 0.95 1.23 7.14 1.86 3.64
time (sec) N/A 0.05 0.001 0.005 1.117 0.832 1.856 1.32
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 40 0 62 209 117 122
normalized size 1 1. 0.87 0. 1.35 4.54 2.54 2.65
time (sec) N/A 0.07 0.004 0.028 1.138 0.766 1.205 1.27
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 43 0 62 231 134 127
normalized size 1 1. 0.83 0. 1.19 4.44 2.58 2.44
time (sec) N/A 0.07 0.004 0.026 1.158 0.836 3.138 1.322
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 52 0 62 235 151 128
normalized size 1 1. 1. 0. 1.19 4.52 2.9 2.46
time (sec) N/A 0.07 0.002 0.026 1.104 0.774 7.737 1.313
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 91 0 0 2808 0 2445
normalized size 1 1. 0.67 0. 0. 20.8 0. 18.11
time (sec) N/A 0.221 0.055 0.126 0. 1.01 0. 1.399
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 93 93 90 0 0 859 0 757
normalized size 1 1. 0.97 0. 0. 9.24 0. 8.14
time (sec) N/A 0.126 0.037 0.087 0. 0.869 0. 1.373
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 37 0 0 186 112 150
normalized size 1 1. 0.73 0. 0. 3.65 2.2 2.94
time (sec) N/A 0.046 0.012 0.086 0. 0.929 9.992 1.341
Problem 240 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 86 86 85 0 0 244 0 189
normalized size 1 1. 0.99 0. 0. 2.84 0. 2.2
time (sec) N/A 0.184 0.156 0.053 0. 0.908 0. 1.32
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 112 0 0 497 0 2079
normalized size 1 1. 0.88 0. 0. 3.91 0. 16.37
time (sec) N/A 0.242 0.297 0.053 0. 0.92 0. 1.687
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 133 0 0 0 0 0
normalized size 1 1. 0.99 0. 0. 0. 0. 0.
time (sec) N/A 0.19 0.194 0.213 0. 0. 0. 0.
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 117 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.168 0.147 0.05 0. 0. 0. 0.
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 117 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.133 0.141 0.05 0. 0. 0. 0.
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 108 0 0 181 0 0
normalized size 1 1. 1. 0. 0. 1.68 0. 0.
time (sec) N/A 0.099 0.121 0.049 0. 0.827 0. 0.
Problem 246 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 33 33 33 34 0 144 80 49
normalized size 1 1. 1. 1.03 0. 4.36 2.42 1.48
time (sec) N/A 0.094 0.009 0.006 0. 0.896 5.961 1.311
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 107 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.16 0.128 0.048 0. 0. 0. 0.
Problem 248 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 117 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.163 0.133 0.049 0. 0. 0. 0.
Problem 249 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 113 0 0 0 0 0
normalized size 1 1. 1.02 0. 0. 0. 0. 0.
time (sec) N/A 0.162 0.084 0.065 0. 0. 0. 0.

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 [20] had the largest ratio of [ 0.8421 ]

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 6 3 1. 23 0.13
2 A 6 4 1. 20 0.2
3 A 6 4 1. 20 0.2
4 A 6 4 1. 18 0.222
5 A 7 7 1. 17 0.412
6 A 2 2 1. 20 0.1
7 A 8 7 1. 20 0.35
8 A 7 5 1. 20 0.25
9 A 7 5 1. 20 0.25
10 A 15 9 1. 22 0.409
11 A 14 9 1. 22 0.409
12 A 13 9 1. 20 0.45
13 A 14 12 1. 19 0.632
14 A 3 3 1. 22 0.136
15 A 15 14 1.08 22 0.636
16 A 19 13 1.08 22 0.591
17 A 29 12 1. 22 0.546
18 A 26 12 1. 22 0.546
19 A 23 12 1. 20 0.6
20 A 24 16 1. 19 0.842
21 A 4 3 1. 22 0.136
22 A 22 15 1.05 22 0.682
23 A 30 14 1.06 22 0.636
24 A 7 5 1. 26 0.192
25 A 8 9 1. 24 0.375
26 A 2 2 1. 26 0.077
27 A 9 8 1. 26 0.308
28 A 9 7 1. 26 0.269
29 A 8 7 1. 23 0.304
30 A 7 6 1. 26 0.231
31 A 8 7 1. 26 0.269
32 A 13 9 1. 28 0.321
33 A 15 16 1. 26 0.615
34 A 3 3 1. 28 0.107
35 A 11 11 1. 28 0.393
36 A 30 17 1. 28 0.607
37 A 26 16 1. 25 0.64
38 A 16 12 1. 28 0.429
39 A 24 15 1. 28 0.536
40 A 22 11 1. 28 0.393
41 A 24 21 1. 26 0.808
42 A 4 3 1. 28 0.107
43 A 15 12 1. 28 0.429
44 A 42 17 1. 25 0.68
45 A 26 13 1. 28 0.464
46 A 7 5 1. 28 0.179
47 A 7 5 1. 26 0.192
48 A 7 5 1. 25 0.2
49 A 2 2 1. 28 0.071
50 A 8 6 1. 28 0.214
51 A 8 6 1. 28 0.214
52 A 8 6 1. 28 0.214
53 A 18 10 1. 30 0.333
54 A 16 10 1. 28 0.357
55 A 14 9 1. 27 0.333
56 A 3 3 1. 30 0.1
57 A 17 14 1. 30 0.467
58 A 19 14 1. 30 0.467
59 A 30 13 1. 28 0.464
60 A 24 12 1. 27 0.444
61 A 4 3 1. 30 0.1
62 A 28 16 1. 30 0.533
63 A 34 16 1. 30 0.533
64 A 5 3 1. 28 0.107
65 A 4 3 1. 28 0.107
66 A 3 3 1. 28 0.107
67 A 2 2 1. 26 0.077
68 A 0 0 0. 0 0.
69 A 0 0 0. 0 0.
70 A 7 5 1. 24 0.208
71 A 7 5 1. 24 0.208
72 A 7 5 1. 22 0.227
73 A 8 8 1. 21 0.381
74 A 4 4 1. 24 0.167
75 A 9 8 1. 24 0.333
76 A 8 6 1. 24 0.25
77 A 8 6 1. 24 0.25
78 A 24 12 1. 26 0.462
79 A 21 12 1. 24 0.5
80 A 18 11 1. 23 0.478
81 A 5 5 1. 26 0.192
82 A 15 14 1.14 26 0.538
83 A 19 13 1.12 26 0.5
84 A 22 13 1.1 26 0.5
85 A 34 13 1. 24 0.542
86 A 28 12 1. 23 0.522
87 A 6 5 1. 26 0.192
88 A 22 15 1.12 26 0.577
89 A 30 14 1.11 26 0.538
90 A 9 6 1. 26 0.231
91 A 9 10 1. 24 0.417
92 A 4 4 1. 26 0.154
93 A 11 9 1. 26 0.346
94 A 10 7 1. 26 0.269
95 A 9 6 1. 26 0.231
96 A 8 6 1. 23 0.261
97 A 7 5 1. 26 0.192
98 A 8 6 1. 26 0.231
99 A 9 6 1. 26 0.231
100 A 17 11 1. 26 0.423
101 A 5 5 1. 28 0.179
102 A 11 11 1. 28 0.393
103 A 20 14 1.15 28 0.5
104 A 30 17 1. 28 0.607
105 A 26 16 1. 25 0.64
106 A 16 12 1. 28 0.429
107 A 24 15 1. 28 0.536
108 A 26 12 1. 26 0.462
109 A 6 5 1. 28 0.179
110 A 15 12 1. 28 0.429
111 A 49 18 1. 28 0.643
112 A 42 17 1. 25 0.68
113 A 26 13 1. 28 0.464
114 A 39 16 1. 28 0.571
115 A 9 6 1. 28 0.214
116 A 9 6 1. 26 0.231
117 A 9 7 1. 25 0.28
118 A 4 4 1. 28 0.143
119 A 10 7 1. 28 0.25
120 A 10 7 1. 28 0.25
121 A 10 7 1. 28 0.25
122 A 22 13 1. 28 0.464
123 A 20 13 1. 26 0.5
124 A 18 13 1. 25 0.52
125 A 5 5 1. 28 0.179
126 A 21 17 1. 28 0.607
127 A 23 17 1. 28 0.607
128 A 36 16 1. 26 0.615
129 A 30 16 1. 25 0.64
130 A 6 5 1. 28 0.179
131 A 34 19 1. 28 0.679
132 A 40 19 1. 28 0.679
133 A 9 6 1. 30 0.2
134 A 9 6 1. 30 0.2
135 A 11 9 1. 30 0.3
136 A 10 7 1. 30 0.233
137 A 10 7 1. 30 0.233
138 A 0 0 0. 0 0.
139 A 6 5 1. 28 0.179
140 A 5 5 1. 28 0.179
141 A 4 4 1. 26 0.154
142 A 0 0 0. 0 0.
143 A 0 0 0. 0 0.
144 A 0 0 0. 0 0.
145 A 0 0 0. 0 0.
146 A 0 0 0. 0 0.
147 A 4 4 1. 26 0.154
148 A 0 0 0. 0 0.
149 A 0 0 0. 0 0.
150 A 18 12 1. 32 0.375
151 A 16 12 1. 32 0.375
152 A 14 11 1. 30 0.367
153 A 15 12 1. 32 0.375
154 A 16 12 1. 32 0.375
155 A 18 12 1. 32 0.375
156 A 3 3 1. 24 0.125
157 A 3 3 1. 22 0.136
158 A 3 2 1. 21 0.095
159 A 4 5 1. 24 0.208
160 A 2 2 1. 24 0.083
161 A 3 3 1. 24 0.125
162 A 3 3 1. 24 0.125
163 A 7 5 1. 26 0.192
164 A 7 5 1. 24 0.208
165 A 6 3 1. 23 0.13
166 A 4 4 1. 26 0.154
167 A 6 4 1. 26 0.154
168 A 7 5 1. 26 0.192
169 A 7 5 1. 26 0.192
170 A 6 6 1. 26 0.231
171 A 6 6 1. 24 0.25
172 A 6 6 1. 23 0.261
173 A 5 6 1. 26 0.231
174 A 6 6 1. 26 0.231
175 A 6 6 1. 26 0.231
176 A 7 4 1.52 23 0.174
177 A 2 4 1. 18 0.222
178 A 8 7 1. 28 0.25
179 A 7 7 1. 26 0.269
180 A 7 7 1. 24 0.292
181 A 7 7 1. 23 0.304
182 A 4 4 1. 26 0.154
183 A 7 7 1. 26 0.269
184 A 7 7 1. 26 0.269
185 A 7 7 1. 26 0.269
186 A 17 11 1. 18 0.611
187 A 17 11 1. 18 0.611
188 A 9 10 1. 18 0.556
189 A 9 10 1. 18 0.556
190 A 17 11 1. 18 0.611
191 A 12 11 1. 18 0.611
192 A 9 10 1. 18 0.556
193 A 9 10 1. 18 0.556
194 A 21 14 1. 20 0.7
195 A 21 14 1. 20 0.7
196 A 21 14 1. 20 0.7
197 A 21 14 1. 20 0.7
198 A 0 0 0. 0 0.
199 A 4 2 1. 23 0.087
200 A 3 2 1. 23 0.087
201 A 2 2 1. 21 0.095
202 A 0 0 0. 0 0.
203 A 0 0 0. 0 0.
204 A 0 0 0. 0 0.
205 A 2 2 1. 11 0.182
206 A 3 2 1. 13 0.154
207 A 2 1 1. 57 0.018
208 A 10 5 1. 19 0.263
209 A 10 5 1. 17 0.294
210 A 10 8 1. 16 0.5
211 A 2 2 1. 19 0.105
212 A 13 8 1. 19 0.421
213 A 11 6 1. 19 0.316
214 A 15 6 1. 19 0.316
215 A 15 6 1. 17 0.353
216 A 14 9 1. 16 0.562
217 A 2 2 1. 19 0.105
218 A 19 9 1. 19 0.474
219 A 16 7 1. 19 0.368
220 A 0 0 0. 0 0.
221 A 0 0 0. 0 0.
222 A 0 0 0. 0 0.
223 A 2 2 1. 14 0.143
224 A 2 2 1. 12 0.167
225 A 2 2 1. 10 0.2
226 A 2 2 1. 14 0.143
227 A 2 2 1. 14 0.143
228 A 2 2 1. 14 0.143
229 A 2 2 1. 14 0.143
230 A 3 3 1. 16 0.188
231 A 3 3 1. 14 0.214
232 A 3 3 1. 12 0.25
233 A 3 3 1. 16 0.188
234 A 3 3 1. 16 0.188
235 A 3 3 1. 16 0.188
236 A 3 3 1. 16 0.188
237 A 4 3 1. 22 0.136
238 A 3 3 1. 22 0.136
239 A 2 2 1. 20 0.1
240 A 3 3 1. 22 0.136
241 A 4 4 1. 22 0.182
242 A 3 3 1. 22 0.136
243 A 3 3 1. 20 0.15
244 A 3 3 1. 18 0.167
245 A 3 3 1. 16 0.188
246 A 3 3 1. 20 0.15
247 A 3 3 1. 20 0.15
248 A 3 3 1. 20 0.15
249 A 6 6 1. 24 0.25

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