[next] [prev] [prev-tail] [tail] [up]

Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 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, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 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, 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, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 213, 214, 215, 216, 217, 218, 219, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 237, 238, 239, 240, 241, 242, 243, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 329, 330, 331, 332, 333, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 371, 372, 373, 374, 375, 376 }

B grade: { 80, 81, 100, 102, 103, 104, 113, 121, 152, 195, 211, 212, 221, 245, 246, 297, 328, 355, 370 }

C grade: { 220, 235, 236, 244, 316, 334 }

F grade: { }

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, 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, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 94, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 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, 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, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 321, 322, 324, 325, 326, 327, 328, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 371, 372, 373, 374, 375, 376 }

B grade: { 63, 74, 89, 92, 93, 95, 117, 226, 227, 256, 270, 296, 308, 314, 329, 341, 370 }

C grade: { 323, 363 }

F grade: { }

2.1.4 Maxima

A grade: { 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, 30, 31, 32, 33, 36, 37, 38, 39, 40, 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, 96, 98, 99, 100, 101, 102, 105, 106, 107, 108, 109, 110, 111, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 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, 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, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 239, 240, 242, 243, 247, 249, 251, 252, 254, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 272, 273, 274, 275, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 292, 293, 294, 295, 296, 297, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 331, 332, 333, 334, 335, 336, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 356, 357, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376

B grade: { 29, 34, 35, 41, 95, 97, 103, 104, 112, 113, 220, 221, 225, 235, 241, 244, 245, 246, 248, 253, 255, 271, 276, 291, 298, 313, 328, 329, 355, 363 }

C grade: { }

F grade: { 1, 133, 250, 330, 337 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 106, 107, 109, 110, 111, 112, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 144, 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, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 239, 240, 242, 243, 245, 247, 252, 253, 254, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 292, 293, 294, 296, 297, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 329, 330, 331, 332, 333, 335, 336, 338, 339, 340, 342, 343, 345, 346, 347, 348, 349, 350, 352, 353, 354, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 371, 372, 373, 374, 375, 376 }

B grade: { 7, 8, 13, 14, 29, 41, 67, 79, 86, 97, 98, 99, 100, 101, 102, 103, 104, 105, 108, 113, 115, 130, 139, 143, 145, 195, 220, 221, 225, 235, 241, 244, 246, 248, 249, 250, 251, 255, 270, 291, 295, 298, 311, 312, 313, 314, 328, 334, 337, 341, 344, 351, 355, 370 }

C grade: { }

F grade: { }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 77, 78, 79, 81, 83, 85, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 103, 105, 107, 109, 110, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 124, 125, 126, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 143, 148, 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, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 224, 225, 227, 228, 229, 231, 232, 233, 234, 236, 237, 239, 240, 242, 243, 245, 246, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 267, 268, 269, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 284, 285, 286, 287, 289, 290, 292, 293, 294, 299, 300, 302, 303, 304, 305, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 321, 323, 326, 327, 329, 331, 332, 333, 335, 336, 338, 339, 342, 343, 345, 346, 347, 348, 349, 350, 352, 354, 355, 356, 357, 358, 361, 362, 363, 364, 366, 367, 368, 369, 371, 373, 374, 375, 376 }

B grade: { 7, 8, 42, 67, 75, 76, 80, 82, 84, 86, 87, 100, 102, 104, 106, 108, 111, 113, 127, 139, 142, 181, 195, 226, 230, 235, 241, 266, 270, 283, 291, 296, 297, 298, 306, 320, 330, 334, 341, 344, 370, 372 }

C grade: { 324 }

F grade: { 29, 41, 74, 123, 144, 145, 146, 147, 149, 220, 238, 244, 247, 248, 249, 250, 288, 295, 301, 322, 325, 328, 337, 340, 351, 353, 359, 360, 365 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 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, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 105, 106, 107, 108, 109, 110, 111, 112, 114, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 131, 132, 134, 135, 136, 137, 139, 140, 141, 142, 143, 144, 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, 196, 197, 198, 199, 200, 201, 202, 203, 204, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 242, 243, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 256, 257, 258, 259, 260, 261, 262, 264, 265, 266, 267, 268, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 292, 294, 295, 296, 297, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 330, 331, 332, 333, 334, 335, 336, 338, 339, 340, 341, 342, 343, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 369, 370, 371, 372, 373, 374, 375, 376 }

B grade: { 11, 12, 14, 29, 41, 79, 97, 98, 103, 104, 113, 115, 124, 130, 133, 138, 145, 195, 205, 225, 241, 244, 255, 263, 270, 291, 293, 298, 328, 329, 344, 368 }

C grade: { }

F grade: { 269, 337 }

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 F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 12 0 20 12 15
normalized size 1 1. 1. 1.09 0. 1.82 1.09 1.36
time (sec) N/A 0.002 0.001 0.003 0. 1.896 0.053 1.071
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 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. 0.917 1.798 0.039 1.059
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 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. 0.922 1.782 0.05 1.051
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 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. 0.922 1.9 0.083 1.041
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 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. 0.926 2.005 0.053 1.066
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 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 0.928 1.986 0.053 1.058
Problem 7 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 0.003 0.927 1.91 0.059 1.063
Problem 8 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 4 4 4 5 8 22 7 8
normalized size 1 1. 1. 1.25 2. 5.5 1.75 2.
time (sec) N/A 0.005 0.002 0.003 0.938 1.847 0.059 1.082
Problem 9 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 5 14 3 5
normalized size 1 1. 1. 1.5 2.5 7. 1.5 2.5
time (sec) N/A 0.007 0.001 0.006 0.928 1.855 0.061 1.064
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 4 4 4 5 8 15 5 8
normalized size 1 1. 1. 1.25 2. 3.75 1.25 2.
time (sec) N/A 0.008 0.002 0.005 0.919 1.866 0.063 1.06
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 2 2 2 3 3 12 2 15
normalized size 1 1. 1. 1.5 1.5 6. 1. 7.5
time (sec) N/A 0.003 0.001 0. 0.919 1.904 0.11 1.059
Problem 12 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 2 2 2 3 3 12 2 15
normalized size 1 1. 1. 1.5 1.5 6. 1. 7.5
time (sec) N/A 0.002 0.001 0.002 0.921 1.891 0.11 1.056
Problem 13 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. 0.929 2.006 0.058 1.06
Problem 14 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. 0.927 2.031 0.058 1.056
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 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 0.009 0.002 0. 0.933 1.91 0.167 1.049
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 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 0.001 0.922 1.828 0.076 1.059
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 19 19 12 12 15 28 10 15
normalized size 1 1. 0.63 0.63 0.79 1.47 0.53 0.79
time (sec) N/A 0.02 0.005 0.002 0.935 1.889 0.078 1.049
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 19 19 14 14 15 46 15 15
normalized size 1 1. 0.74 0.74 0.79 2.42 0.79 0.79
time (sec) N/A 0.007 0.005 0. 0.928 1.924 0.283 1.047
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 15 15 15 14 18 43 12 18
normalized size 1 1. 1. 0.93 1.2 2.87 0.8 1.2
time (sec) N/A 0.004 0.002 0.001 0.937 2.02 0.184 1.042
Problem 20 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 15 12 15 31 10 15
normalized size 1 1. 0.75 0.6 0.75 1.55 0.5 0.75
time (sec) N/A 0.008 0.004 0. 0.936 1.831 0.075 1.055
Problem 21 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. 0.938 1.901 0.164 1.041
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 18 18 18 15 19 45 14 19
normalized size 1 1. 1. 0.83 1.06 2.5 0.78 1.06
time (sec) N/A 0.01 0.011 0.008 0.949 1.947 0.167 1.05
Problem 23 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 0.003 0.001 0. 0.935 1.873 0.08 1.051
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 29 29 25 24 28 59 27 28
normalized size 1 1. 0.86 0.83 0.97 2.03 0.93 0.97
time (sec) N/A 0.025 0.027 0.008 0.941 2.028 0.304 1.04
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 29 29 25 24 28 59 24 28
normalized size 1 1. 0.86 0.83 0.97 2.03 0.83 0.97
time (sec) N/A 0.023 0.024 0.006 0.948 1.94 0.292 1.043
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 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 0.003 0.001 0. 0.936 1.751 0.087 1.046
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 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. 1.402 2.025 0.117 1.065
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 23 23 18 18 19 61 24 19
normalized size 1 1. 0.78 0.78 0.83 2.65 1.04 0.83
time (sec) N/A 0.013 0.003 0.001 0.938 1.956 0.313 1.051
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 8 8 8 9 100 55 0 139
normalized size 1 1. 1. 1.12 12.5 6.88 0. 17.38
time (sec) N/A 0.018 0.005 0.004 1.426 2.087 0. 1.102
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 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 0.007 0.001 0.001 0.936 1.834 0.083 1.059
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 17 17 22 39 15 22
normalized size 1 1. 0.63 0.63 0.81 1.44 0.56 0.81
time (sec) N/A 0.031 0.006 0.002 0.934 1.831 0.08 1.05
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 22 22 26 65 26 26
normalized size 1 1. 0.81 0.81 0.96 2.41 0.96 0.96
time (sec) N/A 0.011 0.032 0.004 0.926 1.925 0.293 1.059
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 20 22 23 62 20 23
normalized size 1 1. 0.74 0.81 0.85 2.3 0.74 0.85
time (sec) N/A 0.011 0.027 0.007 0.937 1.879 0.458 1.052
Problem 34 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 0.012 0.003 0.001 0.948 1.781 0.171 1.049
Problem 35 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 19 19 19 19 77 45 20 41
normalized size 1 1. 1. 1. 4.05 2.37 1.05 2.16
time (sec) N/A 0.016 0.013 0.009 0.95 1.771 0.212 1.053
Problem 36 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 11 10 12 23 7 12
normalized size 1 1. 0.69 0.62 0.75 1.44 0.44 0.75
time (sec) N/A 0.009 0.004 0.001 0.925 1.991 0.073 1.048
Problem 37 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 15 14 18 43 66 18
normalized size 1 1. 0.71 0.67 0.86 2.05 3.14 0.86
time (sec) N/A 0.008 0.003 0.003 0.934 2.175 2.037 1.049
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 18 18 18 15 19 42 14 19
normalized size 1 1. 1. 0.83 1.06 2.33 0.78 1.06
time (sec) N/A 0.012 0.009 0.005 0.936 2.375 0.162 1.041
Problem 39 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 16 15 19 34 12 19
normalized size 1 1. 0.62 0.58 0.73 1.31 0.46 0.73
time (sec) N/A 0.018 0.006 0.001 0.938 2.061 0.079 1.054
Problem 40 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 41 12 22
normalized size 1 1. 1. 0.94 1.22 2.28 0.67 1.22
time (sec) N/A 0.004 0.002 0.001 1.406 2.39 0.118 1.048
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 9 9 9 10 140 61 0 70
normalized size 1 1. 1. 1.11 15.56 6.78 0. 7.78
time (sec) N/A 0.016 0.015 0.003 0.945 2.618 0. 1.095
Problem 42 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 17 17 17 14 18 76 26 18
normalized size 1 1. 1. 0.82 1.06 4.47 1.53 1.06
time (sec) N/A 0.009 0.007 0.074 0.934 2.692 0.513 1.059
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 9 18 43 22 18
normalized size 1 1. 1. 0.53 1.06 2.53 1.29 1.06
time (sec) N/A 0.008 0.006 0.01 0.933 2.415 0.558 1.101
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 12 15 39 10 15
normalized size 1 1. 1. 1.09 1.36 3.55 0.91 1.36
time (sec) N/A 0.01 0.002 0.004 0.926 2.28 0.876 1.058
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 14 12 15 31 10 15
normalized size 1 1. 0.64 0.55 0.68 1.41 0.45 0.68
time (sec) N/A 0.019 0.002 0.002 0.941 2.326 0.078 1.06
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 15 15 9 9 16 20 7 11
normalized size 1 1. 0.6 0.6 1.07 1.33 0.47 0.73
time (sec) N/A 0.008 0.009 0. 0.944 2.242 0.074 1.055
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 14 15 19 39 14 19
normalized size 1 1. 0.74 0.79 1. 2.05 0.74 1.
time (sec) N/A 0.009 0.003 0.004 1.425 2.24 0.091 1.049
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 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. 0.937 2.374 0.376 1.052
Problem 49 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 16 17 15 36 20 15
normalized size 1 1. 0.67 0.71 0.62 1.5 0.83 0.62
time (sec) N/A 0.008 0.006 0. 0.946 2.218 0.178 1.067
Problem 50 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 12 10 12 30 8 12
normalized size 1 1. 0.86 0.71 0.86 2.14 0.57 0.86
time (sec) N/A 0.001 0.001 0. 0.937 2.215 0.079 1.05
Problem 51 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 0.002 0.001 0.938 2.36 0.375 1.048
Problem 52 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 0.012 0. 0.935 2.258 0.294 1.049
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 20 20 20 17 22 45 15 22
normalized size 1 1. 1. 0.85 1.1 2.25 0.75 1.1
time (sec) N/A 0.016 0.009 0.004 0.939 2.307 1.852 1.065
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 28 28 19 17 22 42 15 22
normalized size 1 1. 0.68 0.61 0.79 1.5 0.54 0.79
time (sec) N/A 0.034 0.002 0.001 0.943 2.288 0.085 1.066
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 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 0.009 0.003 0. 1.42 2.278 0.334 1.056
Problem 56 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 47 15 24
normalized size 1 1. 1. 0.94 1.22 2.61 0.83 1.33
time (sec) N/A 0.013 0.015 0.005 0.935 2.561 0.217 1.052
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 21 21 15 14 18 43 66 18
normalized size 1 1. 0.71 0.67 0.86 2.05 3.14 0.86
time (sec) N/A 0.006 0.002 0.002 0.94 2.51 2.123 1.061
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 18 18 14 15 14 43 14 14
normalized size 1 1. 0.78 0.83 0.78 2.39 0.78 0.78
time (sec) N/A 0.006 0.006 0.007 0.936 2.583 0.061 1.073
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 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 0.005 0.94 2.218 0.058 1.05
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 22 18 22 59 24 22
normalized size 1 1. 0.92 0.75 0.92 2.46 1. 0.92
time (sec) N/A 0.013 0.002 0.001 0.953 2.089 0.059 1.058
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 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. 0.928 1.971 0.064 1.077
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 17 17 31 18 18 39 12 18
normalized size 1 1. 1.82 1.06 1.06 2.29 0.71 1.06
time (sec) N/A 0.023 0.01 0.006 0.957 2.219 0.062 1.06
Problem 63 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 17 17 31 30 18 73 12 18
normalized size 1 1. 1.82 1.76 1.06 4.29 0.71 1.06
time (sec) N/A 0.022 0.009 0.004 0.928 2.132 0.063 1.046
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 30 29 24 81 31 30
normalized size 1 1. 0.83 0.81 0.67 2.25 0.86 0.83
time (sec) N/A 0.045 0.007 0.006 0.937 2.018 0.061 1.065
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 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. 0.925 2.039 0.066 1.051
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 22 22 18 19 19 58 37 19
normalized size 1 1. 0.82 0.86 0.86 2.64 1.68 0.86
time (sec) N/A 0.009 0.008 0.023 0.936 1.976 0.177 1.056
Problem 67 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 20 20 20 15 19 105 37 19
normalized size 1 1. 1. 0.75 0.95 5.25 1.85 0.95
time (sec) N/A 0.014 0.011 0.029 0.933 1.983 0.545 1.06
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 25 25 25 28 26 63 19 26
normalized size 1 1. 1. 1.12 1.04 2.52 0.76 1.04
time (sec) N/A 0.03 0.01 0.007 0.928 2.003 0.068 1.051
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 34 34 30 24 32 84 36 30
normalized size 1 1. 0.88 0.71 0.94 2.47 1.06 0.88
time (sec) N/A 0.017 0.002 0. 0.924 1.998 0.061 1.053
Problem 70 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 34 34 30 24 32 82 36 30
normalized size 1 1. 0.88 0.71 0.94 2.41 1.06 0.88
time (sec) N/A 0.017 0.002 0.029 0.927 2.051 0.057 1.047
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 46 46 30 36 24 92 41 30
normalized size 1 1. 0.65 0.78 0.52 2. 0.89 0.65
time (sec) N/A 0.036 0.014 0.011 0.939 1.995 0.062 1.052
Problem 72 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 23 17 23 53 17 23
normalized size 1 1. 1.1 0.81 1.1 2.52 0.81 1.1
time (sec) N/A 0.007 0.002 0.004 0.929 1.977 0.063 1.045
Problem 73 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 22 36 22 103 31 22
normalized size 1 1. 0.48 0.78 0.48 2.24 0.67 0.48
time (sec) N/A 0.052 0.007 0.005 0.929 2.105 0.067 1.048
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 34 39 18 58 0 18
normalized size 1 1. 1.62 1.86 0.86 2.76 0. 0.86
time (sec) N/A 0.022 0.063 0.033 0.93 2.062 0. 1.053
Problem 75 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 21 21 18 14 18 49 167 18
normalized size 1 1. 0.86 0.67 0.86 2.33 7.95 0.86
time (sec) N/A 0.022 0.011 0.02 0.933 2.066 42.137 1.05
Problem 76 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 19 19 18 14 16 50 39 16
normalized size 1 1. 0.95 0.74 0.84 2.63 2.05 0.84
time (sec) N/A 0.02 0.027 0.009 0.927 1.879 0.321 1.048
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 19 19 19 15 20 42 22 20
normalized size 1 1. 1. 0.79 1.05 2.21 1.16 1.05
time (sec) N/A 0.014 0.015 0.006 0.931 2.066 0.572 1.056
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 13 22 39 10 19
normalized size 1 1. 1. 0.93 1.57 2.79 0.71 1.36
time (sec) N/A 0.013 0.005 0.011 0.93 2.115 0.08 1.071
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 22 22 20 29 27 116 20 49
normalized size 1 1. 0.91 1.32 1.23 5.27 0.91 2.23
time (sec) N/A 0.029 0.023 0.013 0.931 2.069 0.095 1.07
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 5 5 36 6 7 23 19 7
normalized size 1 1. 7.2 1.2 1.4 4.6 3.8 1.4
time (sec) N/A 0.013 0.007 0.021 0.935 2.076 0.318 1.054
Problem 81 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 0.012 0. 0.932 1.942 0.381 1.056
Problem 82 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 6 6 6 7 8 18 7 8
normalized size 1 1. 1. 1.17 1.33 3. 1.17 1.33
time (sec) N/A 0.004 0.002 0.002 1.407 1.977 0.062 1.064
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 18 13 16 36 19 16
normalized size 1 1. 1.29 0.93 1.14 2.57 1.36 1.14
time (sec) N/A 0.008 0.004 0.001 1.41 1.91 0.066 1.055
Problem 84 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 11 11 17 13 12 51 19 12
normalized size 1 1. 1.55 1.18 1.09 4.64 1.73 1.09
time (sec) N/A 0.007 0.002 0.027 0.924 1.965 0.061 1.079
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 19 19 27 19 20 70 31 20
normalized size 1 1. 1.42 1. 1.05 3.68 1.63 1.05
time (sec) N/A 0.009 0.003 0.027 0.926 1.948 0.062 1.056
Problem 86 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 8 8 8 11 8 66 29 8
normalized size 1 1. 1. 1.38 1. 8.25 3.62 1.
time (sec) N/A 0.02 0.002 0.011 0.924 1.977 0.063 1.056
Problem 87 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 17 17 27 22 18 69 29 18
normalized size 1 1. 1.59 1.29 1.06 4.06 1.71 1.06
time (sec) N/A 0.022 0.019 0.012 0.924 1.975 0.065 1.07
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 8 8 8 7 8 19 7 8
normalized size 1 1. 1. 0.88 1. 2.38 0.88 1.
time (sec) N/A 0.012 0.005 0.006 0.927 1.972 0.065 1.054
Problem 89 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 17 17 17 42 19 45 15 19
normalized size 1 1. 1. 2.47 1.12 2.65 0.88 1.12
time (sec) N/A 0.023 0.023 0.011 0.925 2.237 0.097 1.051
Problem 90 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 20 23 46 77 20 30
normalized size 1 1. 0.91 1.05 2.09 3.5 0.91 1.36
time (sec) N/A 0.01 0.003 0.002 0.925 2.259 0.104 1.059
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 22 22 30 19 24 57 31 24
normalized size 1 1. 1.36 0.86 1.09 2.59 1.41 1.09
time (sec) N/A 0.013 0.004 0.002 1.411 2.036 0.067 1.058
Problem 92 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 19 19 19 48 27 63 20 27
normalized size 1 1. 1. 2.53 1.42 3.32 1.05 1.42
time (sec) N/A 0.016 0.01 0.008 0.938 2.028 0.104 1.059
Problem 93 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 25 25 25 58 27 66 20 27
normalized size 1 1. 1. 2.32 1.08 2.64 0.8 1.08
time (sec) N/A 0.029 0.012 0.012 0.926 2.058 0.115 1.065
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 8 8 8 7 14 19 7 8
normalized size 1 1. 1. 0.88 1.75 2.38 0.88 1.
time (sec) N/A 0.013 0.004 0.007 0.925 2.003 0.068 1.058
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 32 49 45 15 19
normalized size 1 1. 1. 1.88 2.88 2.65 0.88 1.12
time (sec) N/A 0.028 0.013 0.013 0.928 1.945 0.127 1.049
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 8 8 8 7 14 19 7 8
normalized size 1 1. 1. 0.88 1.75 2.38 0.88 1.
time (sec) N/A 0.012 0.004 0.01 0.925 2.04 0.067 1.054
Problem 97 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 16 16 16 24 36 109 27 39
normalized size 1 1. 1. 1.5 2.25 6.81 1.69 2.44
time (sec) N/A 0.015 0.006 0.008 0.929 2.172 0.109 1.059
Problem 98 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 8 8 8 12 14 53 8 24
normalized size 1 1. 1. 1.5 1.75 6.62 1. 3.
time (sec) N/A 0.005 0.002 0.003 1.409 2.098 0.059 1.068
Problem 99 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 14 14 14 17 19 90 14 30
normalized size 1 1. 1. 1.21 1.36 6.43 1. 2.14
time (sec) N/A 0.007 0.003 0.002 0.93 1.972 0.088 1.061
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 37 22 19 112 41 19
normalized size 1 1. 2.18 1.29 1.12 6.59 2.41 1.12
time (sec) N/A 0.026 0.027 0.013 0.934 1.958 0.067 1.077
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 22 19 86 14 24
normalized size 1 1. 1. 1.29 1.12 5.06 0.82 1.41
time (sec) N/A 0.026 0.007 0.013 0.94 2.018 0.103 1.053
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 5 5 17 9 11 77 15 8
normalized size 1 1. 3.4 1.8 2.2 15.4 3. 1.6
time (sec) N/A 0.002 0.003 0.002 0.931 2.151 0.093 1.073
Problem 103 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 16 16 47 18 36 150 27 73
normalized size 1 1. 2.94 1.12 2.25 9.38 1.69 4.56
time (sec) N/A 0.007 0.005 0.031 0.932 2.044 0.112 1.065
Problem 104 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 8 8 19 12 23 88 19 26
normalized size 1 1. 2.38 1.5 2.88 11. 2.38 3.25
time (sec) N/A 0.011 0.004 0.007 0.924 2.153 0.093 1.055
Problem 105 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 13 13 17 12 19 73 20 19
normalized size 1 1. 1.31 0.92 1.46 5.62 1.54 1.46
time (sec) N/A 0.007 0.002 0.026 0.93 1.962 0.057 1.058
Problem 106 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 17 17 17 14 18 81 26 18
normalized size 1 1. 1. 0.82 1.06 4.76 1.53 1.06
time (sec) N/A 0.008 0.007 0.046 0.933 2.082 0.503 1.046
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 17 17 17 14 18 35 22 18
normalized size 1 1. 1. 0.82 1.06 2.06 1.29 1.06
time (sec) N/A 0.008 0.005 0.029 0.93 1.934 0.512 1.072
Problem 108 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 15 15 15 12 15 78 26 15
normalized size 1 1. 1. 0.8 1. 5.2 1.73 1.
time (sec) N/A 0.008 0.006 0.049 0.925 2.13 0.493 1.054
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 17 17 17 9 18 43 24 18
normalized size 1 1. 1. 0.53 1.06 2.53 1.41 1.06
time (sec) N/A 0.008 0.006 0.01 0.939 2.103 0.533 1.052
Problem 110 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 20 7 8
normalized size 1 1. 1. 0.88 1. 2.5 0.88 1.
time (sec) N/A 0.013 0.001 0.001 0.928 1.951 0.056 1.053
Problem 111 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 0.031 0.008 0. 0.931 1.97 14.487 1.067
Problem 112 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 5 5 8 6 15 20 7 12
normalized size 1 1. 1.6 1.2 3. 4. 1.4 2.4
time (sec) N/A 0.022 0.002 0.016 0.93 2.124 0.414 1.063
Problem 113 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 15 15 61 20 93 149 32 39
normalized size 1 1. 4.07 1.33 6.2 9.93 2.13 2.6
time (sec) N/A 0.053 0.009 0.049 1.438 2.096 1.051 1.101
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 14 14 14 13 22 39 10 24
normalized size 1 1. 1. 0.93 1.57 2.79 0.71 1.71
time (sec) N/A 0.015 0.005 0.011 0.927 2.167 0.077 1.081
Problem 115 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 20 29 27 116 20 49
normalized size 1 1. 0.91 1.32 1.23 5.27 0.91 2.23
time (sec) N/A 0.052 0.012 0.013 0.926 2.074 0.095 1.06
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 8 8 8 7 8 19 7 8
normalized size 1 1. 1. 0.88 1. 2.38 0.88 1.
time (sec) N/A 0.015 0.003 0. 0.935 1.996 0.062 1.049
Problem 117 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