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acos
24-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.26
RMS Relative: -5.77 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    1   77 1376  582    6    0    0    0    0    0

53-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.78
RMS Relative: -5.48 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  152 1133  712   45    0    0    0    0    0

64-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.82
RMS Relative: -5.89 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    5  350 1487  197    3    0    0    0    0    0

113-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.94
RMS Relative: -5.65 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  177 1363  462   40    0    0    0    0    0


acosh
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -7.12 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   46 1937   47    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 0.96
RMS Relative: -7.63 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    1   25 1991   13    0    0    0    0    0    0

64-bit

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  Max Rel. ULP: 3 Max Rel. Bit: 0.95
RMS Relative: -7.77 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    1   19 1990   20    0    0    0    0    0    0

113-bit

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  Max Rel. ULP: 4 Max Rel. Bit: 1.46
RMS Relative: -7.67 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    1    1   21 1992   15    0    0    0    0    0    0


asin
24-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.12
RMS Relative: -5.78 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    2  331 1364  344    1    0    0    0    0    0

53-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.65
RMS Relative: -5.42 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   29  452 1079  444   38    0    0    0    0    0

64-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.91
RMS Relative: -5.49 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   27  419 1171  398   27    0    0    0    0    0

113-bit

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  Max Rel. ULP: 4 Max Rel. Bit: 2.47
RMS Relative: -5.08 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    1  103  426  982  436   94    0    0    0    0    0


asinh
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.98
RMS Relative: -7.34 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   38 1987   35    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 0.99
RMS Relative: -7.76 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    1   17 2030   12    0    0    0    0    0    0

64-bit

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  Max Rel. ULP: 3 Max Rel. Bit: 0.95
RMS Relative: -7.78 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    1   19 2018   22    0    0    0    0    0    0

113-bit

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  Max Rel. ULP: 4 Max Rel. Bit: 0.94
RMS Relative: -8.09 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    1    0    9 2037   13    0    0    0    0    0    0


assoc_laguerre
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -9.16 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   12 3088    0    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -9.24 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   16 3735    0    0    0    0    0    0    0

64-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.91
RMS Relative: -9.65 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   10 3741    0    0    0    0    0    0    0

113-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -9.59 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   10 3738    3    0    0    0    0    0    0


assoc_legendre
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -9.64 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    3 3457    5    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -9.77 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    4 4900   10    0    0    0    0    0    0

64-bit

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  Max Rel. ULP: 56621 Max Rel. Bit: 23.00
RMS Relative: 11.45 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    7    2    2    1    9    5   31 4811   17    8    9    1    2    2    7

113-bit

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  Max Rel. ULP: 57139 Max Rel. Bit: 32.33
RMS Relative: 20.57 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   10    2    2    1    7    4    9 4835   12   10    7    1    2    2   10


atan
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -6.53 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  106 1825  130    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -5.99 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  243 1558  260    0    0    0    0    0    0

64-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.90
RMS Relative: -5.83 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    9  310 1453  287    2    0    0    0    0    0

113-bit

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  Max Rel. ULP: 3 Max Rel. Bit: 2.32
RMS Relative: -5.15 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   77  534  846  545   59    0    0    0    0    0


atan2
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -6.14 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  375 2019  407    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.34
RMS Relative: -5.84 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   18  502 1726  535   20    0    0    0    0    0

64-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.93
RMS Relative: -6.21 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    6  339 2121  329    6    0    0    0    0    0

113-bit

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  Max Rel. ULP: 3 Max Rel. Bit: 2.44
RMS Relative: -5.83 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   30  436 1834  475   26    0    0    0    0    0


atanh
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -6.36 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  160 1734  146    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -6.35 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  150 1732  158    0    0    0    0    0    0

64-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.65
RMS Relative: -5.95 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    5  266 1527  240    2    0    0    0    0    0

113-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.79
RMS Relative: -5.95 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    3  242 1520  272    3    0    0    0    0    0


beta
24-bit

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  Max Rel. ULP: 487 Max Rel. Bit: 9.87
RMS Relative: -0.23 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   11   16   62   99  125  150  174  357  211   81  135  155   65   19    9

53-bit

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  Max Rel. ULP: 672 Max Rel. Bit: 9.87
RMS Relative: -0.18 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    7   24   80  112   61  105  200  415  200  113  116  137   71   19    9

64-bit

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  Max Rel. ULP: 673 Max Rel. Bit: 9.87
RMS Relative: 0.02 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   11   15   59   99  134  205  186  241  221  136  127  148   62   17    8

113-bit

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  Max Rel. ULP: 668 Max Rel. Bit: 9.88
RMS Relative: -0.17 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    7   23   82  117   87  150  207  262  205  181  116  131   72   20    9


cbrt
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.60
RMS Relative: -9.31 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    3 2042    5    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.08
RMS Relative: -5.99 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  313 1428  308    1    0    0    0    0    0

113-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -5.95 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  357 1389  304    0    0    0    0    0    0


ceil
24-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


comp_ellint_1
24-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.78
RMS Relative: -6.18 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   56  653 2836  414   41    0    0    0    0    0

53-bit

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  Max Rel. ULP: 3 Max Rel. Bit: 1.94
RMS Relative: -6.46 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   28  467 2975  485   45    0    0    0    0    0

64-bit

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  Max Rel. ULP: 3 Max Rel. Bit: 1.86
RMS Relative: -6.28 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   91  627 2803  426   53    0    0    0    0    0

113-bit

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  Max Rel. ULP: 3 Max Rel. Bit: 2.04
RMS Relative: -6.11 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0  100  563 2643  613   81    0    0    0    0    0


comp_ellint_2
24-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.99
RMS Relative: -6.01 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   49 1013 2616  319    3    0    0    0    0    0

53-bit

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  Max Rel. ULP: 5 Max Rel. Bit: 3.32
RMS Relative: -5.62 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    1  114 1029 2345  509    2    0    0    0    0    0

64-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 2.00
RMS Relative: -5.61 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0  111 1000 2077  752   60    0    0    0    0    0

113-bit

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  Max Rel. ULP: 91952 Max Rel. Bit: 34.47
RMS Relative: 22.82 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  111    4    7    5    6  137  888 1841  902   99    0    0    0    0    0


comp_ellint_3
24-bit

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  Max Rel. ULP: 6 Max Rel. Bit: 3.26
RMS Relative: -5.09 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    7  232  542 1509  617  271   17    0    0    0    0

53-bit

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  Max Rel. ULP: 6 Max Rel. Bit: 2.84
RMS Relative: -5.06 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0   15  293  570 1480  603  228    6    0    0    0    0

64-bit

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  Max Rel. ULP: 5 Max Rel. Bit: 2.93
RMS Relative: -5.07 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    6  268  515 1520  603  269   14    0    0    0    0

113-bit

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  Max Rel. ULP: 10 Max Rel. Bit: 3.67
RMS Relative: -4.35 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    1   43  236 1142  670  857  244    2    0    0    0


copysign
24-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


cos
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -6.01 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  317 1450  273    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -6.01 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  252 1483  305    0    0    0    0    0    0

64-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -6.30 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  134 1717  189    0    0    0    0    0    0

113-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -6.25 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  194 1679  167    0    0    0    0    0    0


cosh
24-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.44
RMS Relative: -5.91 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   12  295 1521  232    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.01
RMS Relative: -5.96 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    2  286 1561  211    0    0    0    0    0    0

64-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.78
RMS Relative: -5.52 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   19  437 1177  413   14    0    0    0    0    0

113-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.75
RMS Relative: -5.54 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   14  414 1187  421   24    0    0    0    0    0


cyl_bessel_i
24-bit

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  Max Rel. ULP: 19 Max Rel. Bit: 5.25
RMS Relative: -5.26 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    1    0    5   51  349 1843  227   40    2    2    0    0    0

53-bit

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  Max Rel. ULP: 8 Max Rel. Bit: 3.42
RMS Relative: -5.59 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0   38  218  909 2766  873  218   17    1    0    0    0

64-bit

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  Max Rel. ULP: 18 Max Rel. Bit: 4.28
RMS Relative: -4.39 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    3   44  293  533  942 1862  700  419  204   40    0    0    0

113-bit

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  Max Rel. ULP: 26 Max Rel. Bit: 4.98
RMS Relative: -4.36 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    1   58  279  568  905 1861  702  420  208   37    1    0    0


cyl_bessel_j
24-bit

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  Max Rel. ULP: 1143 Max Rel. Bit: 10.19
RMS Relative: -0.83 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    3    5   10   22   31   85  495 1720  419   84   39   16    5    4    2

53-bit

Report Page
  Max Rel. ULP: 25 Max Rel. Bit: 5.13
RMS Relative: -4.69 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    5    7   32   18  352 1959  396  123   46    2    0    0    0

64-bit

Report Page
  Max Rel. ULP: 40 Max Rel. Bit: 5.91
RMS Relative: -3.85 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    1    5    1    6   15  269 2184  311   58   36   35   19    0    0

113-bit

Report Page
  Max Rel. ULP: 50 Max Rel. Bit: 6.27
RMS Relative: -3.29 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    3   44  112   43  212 2242  191   33    8    7   35   10    0


cyl_bessel_k
24-bit

Report Page
  Max Rel. ULP: 72819 Max Rel. Bit: 24.00
RMS Relative: 15.71 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  159   25   28   16   15   19  221 1619  291   20    5    1   10    4   51

53-bit

Report Page
  Max Rel. ULP: 4 Max Rel. Bit: 2.37
RMS Relative: -5.67 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    2   41  498 1742  525   89    1    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 2355 Max Rel. Bit: 11.78
RMS Relative: 1.53 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   10    1    0    0    0   49  552 1259  651  154   27   49   75   39   32

113-bit

Report Page
  Max Rel. ULP: 161806 Max Rel. Bit: 60.97
RMS Relative: 51.03 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    8    0    0    0    0   52  393 1299  729  162   44   15   63   18  115


cyl_neumann
24-bit

Report Page
  Max Rel. ULP: 693 Max Rel. Bit: 9.61
RMS Relative: -0.20 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    6    6   14   15   46   71  285 1064  315   71   28   16    8    8    7

53-bit

Report Page
  Max Rel. ULP: 479 Max Rel. Bit: 9.12
RMS Relative: -1.46 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    2    5    2    4   18   63  250 1201  315   68   16    7    5    2    2

64-bit

Report Page
  Max Rel. ULP: 337 Max Rel. Bit: 8.61
RMS Relative: -2.05 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    1    0    2    6   17   62  266 1267  239   63   24    7    2    2    2

113-bit

Report Page
  Max Rel. ULP: 95605 Max Rel. Bit: 51.76
RMS Relative: 40.95 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   33    2    4    2   17   52  274 1234  252   54   17   11    1    0    7


ellint_1
24-bit

Report Page
  Max Rel. ULP: 5 Max Rel. Bit: 2.89
RMS Relative: -6.51 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    2  585 3658  963   41    1    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 5 Max Rel. Bit: 2.89
RMS Relative: -6.35 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    1   21 1034 3376  795   21    2    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 4 Max Rel. Bit: 2.49
RMS Relative: -6.42 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    1   44 1040 3581  572   12    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 19 Max Rel. Bit: 4.91
RMS Relative: -5.91 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    2  232 1051 3087  848   26    1    2    1    0    0


ellint_2
24-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.41
RMS Relative: -5.78 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    2  164 1156  231    1    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.00
RMS Relative: -5.70 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    1  295 1092  166    0    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 3 Max Rel. Bit: 1.99
RMS Relative: -5.26 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   44  336  896  263   15    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 3 Max Rel. Bit: 2.31
RMS Relative: -5.03 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   76  357  798  298   25    0    0    0    0    0


ellint_3
24-bit

Report Page
  Max Rel. ULP: 12 Max Rel. Bit: 4.34
RMS Relative: -3.40 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    1   23   63  123  381  177   76   36    8    0    0    0

53-bit

Report Page
  Max Rel. ULP: 30 Max Rel. Bit: 5.66
RMS Relative: -3.01 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    1   14   50  103  397  216   78   20    3    6    0    0

64-bit

Report Page
  Max Rel. ULP: 22 Max Rel. Bit: 5.21
RMS Relative: -3.14 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    1   10   33   81  159  399  114   60   27    4    0    0    0

113-bit

Report Page
  Max Rel. ULP: 26 Max Rel. Bit: 5.45
RMS Relative: -2.74 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    8   16   55   72  107  346  162   94   23    5    0    0    0


erf
24-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -6.31 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  199 1668  194    0    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 0.99
RMS Relative: -7.85 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   29 1999   20   13    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 3 Max Rel. Bit: 1.83
RMS Relative: -6.21 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   24  142 1746  111   38    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 4 Max Rel. Bit: 2.05
RMS Relative: -6.42 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   14  116 1816   94   15    6    0    0    0    0


erfc
24-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 2.00
RMS Relative: -5.96 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   21  231 1685  268   16    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.85
RMS Relative: -6.06 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   19  224 1765  194   19    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 4 Max Rel. Bit: 2.35
RMS Relative: -5.36 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    1   65  403 1230  413  107    2    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 6 Max Rel. Bit: 2.86
RMS Relative: -5.07 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    3  103  390 1179  397  124   25    0    0    0    0


exp
24-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -8.40 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    5 2044   11    0    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.87
RMS Relative: -7.39 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   42 1985   33    0    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.54
RMS Relative: -5.67 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    3  405 1283  363    6    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.52
RMS Relative: -5.68 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    3  404 1284  365    4    0    0    0    0    0


exp2
24-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.94
RMS Relative: -7.70 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   92 3870   98    0    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.91
RMS Relative: -7.70 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   98 3869   93    0    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.61
RMS Relative: -6.13 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   14  845 2439  754    8    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.56
RMS Relative: -6.14 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   12  793 2488  755   12    0    0    0    0    0


expint
24-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.82
RMS Relative: -5.79 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   10  376 1424  271    5    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.62
RMS Relative: -5.76 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   11  486 1375  214    0    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 4 Max Rel. Bit: 2.54
RMS Relative: -5.03 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0  129  488  914  435  117    3    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 4 Max Rel. Bit: 2.55
RMS Relative: -4.96 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    6  161  520  868  421  109    1    0    0    0    0


expm1
24-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -5.99 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  224 1629  248    0    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -6.06 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  201 1667  233    0    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 3 Max Rel. Bit: 2.52
RMS Relative: -5.32 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   64  404 1170  410   53    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 3 Max Rel. Bit: 2.31
RMS Relative: -5.29 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   77  474 1149  344   57    0    0    0    0    0


fabs
24-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


fdim
24-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.75
RMS Relative: -8.81 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   26 3017    0    0    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.93
RMS Relative: -8.58 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   32 3011    0    0    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.88
RMS Relative: -8.92 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   16 3027    0    0    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.97
RMS Relative: -8.58 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   22 3014    7    0    0    0    0    0    0


floor
24-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


fma
24-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -6.95 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   14 1292   24    0    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.00
RMS Relative: -6.99 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   14 1292   23    1    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.00
RMS Relative: -6.98 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   14 1292   23    1    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 4 Max Rel. Bit: 1.00
RMS Relative: -6.96 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   14 1292   23    0    1    0    0    0    0


fmax
24-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


fmin
24-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


fmod
24-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


gsl_sf_bessel_Inu
53-bit

Report Page
  Max Rel. ULP: 91317 Max Rel. Bit: 52.00
RMS Relative: 39.80
Note: 350 special function values gave 15 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   55    9    8    7   69  615 1025 1754  839  513   42    3    3   12   71


gsl_sf_bessel_Jnu
53-bit

Report Page
  Max Rel. ULP: 127965 Max Rel. Bit: 46.98
RMS Relative: 35.91 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  877   61   74   57   44   57  101  338   98   37   33   53   89   96  925


gsl_sf_bessel_Knu
53-bit

Report Page
  Max Rel. ULP: 425 Max Rel. Bit: 8.99
RMS Relative: 0.04 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   53   16    8    5   38  289  466  955  608  325   39    5    6   20   65


gsl_sf_bessel_sphJnu
53-bit

Report Page
  Max Rel. ULP: 207514 Max Rel. Bit: 56.72
RMS Relative: 47.53
Note: 31 special function values gave 31 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  745   15   13   19   43   77  104  151   82   64   29   28   26   26  777


gsl_sf_bessel_sphYnu
53-bit

Report Page
  Max Rel. ULP: 219405 Max Rel. Bit: 56.42
RMS Relative: 47.13
Note: 57 special function values gave 45 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  377   22   22   40   51  117  308  580  314  110   49   37   25   28  441


gsl_sf_bessel_Ynu
53-bit

Report Page
  Max Rel. ULP: 65186 Max Rel. Bit: 24.12
RMS Relative: 13.38
Note: 65 special function values gave 59 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  528   71   68   32   28   39   84  114   44   21   30   46   65   74  657


gsl_sf_beta
53-bit

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  Max Rel. ULP: 674 Max Rel. Bit: 9.88
RMS Relative: -0.11
Note: 45 special function values gave 15 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    7   26   75  112  147  117  121  103  100  176  175  309  153   24    9


gsl_sf_cos
53-bit

Report Page
  Max Rel. ULP: 195371 Max Rel. Bit: 3.69
RMS Relative: -7.00
Note: 15 special function values gave 14 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   12    0    0    1    1    0    3 2040    5    0    0    0    0    0    0


gsl_sf_ellint_Ecomp
53-bit

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  Max Rel. ULP: 12710 Max Rel. Bit: 14.63
RMS Relative: 5.69
Note: 1 special function values gave 1 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  185    0    0   25  117  451  721 1462  630  287  107   14    0    0    0


gsl_sf_ellint_Ex
53-bit

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  Max Rel. ULP: 7 Max Rel. Bit: 2.81
RMS Relative: -5.25
Note: 7 special function values gave 6 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    2   15  298  866  345   22    0    0    0    0    0


gsl_sf_ellint_Fx
53-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.82
RMS Relative: -6.32
Note: 4 special function values gave 3 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   21  844 3148 1192   42    0    0    0    0    0


gsl_sf_ellint_Kcomp
53-bit

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  Max Rel. ULP: 184728 Max Rel. Bit: 52.88
RMS Relative: 45.26
Note: 1 special function values gave 1 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  459    0    2    1    4    8  493 2487  491   14    2    1    2    2   33


gsl_sf_ellint_Pcomp
53-bit

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  Max Rel. ULP: 35 Max Rel. Bit: 5.76
RMS Relative: -2.37
Note: 71 special function values gave 71 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    3   69  344  357  291  184  532  284  303  324  334   96    3    0


gsl_sf_ellint_Px
53-bit

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  Max Rel. ULP: 27 Max Rel. Bit: 5.12
RMS Relative: -2.38 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    4   31   68   90  135  306  104   57   64   23    6    0    0


gsl_sf_erf
53-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -6.50
Note: 1 special function values gave 1 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  233 1582  245    0    0    0    0    0    0


gsl_sf_erfc
53-bit

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  Max Rel. ULP: 308 Max Rel. Bit: 8.95
RMS Relative: -0.48
Note: 1 special function values gave 1 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   32   16   35   70  107  125  197 1149  106  130  111   73   28   12   29


gsl_sf_exp
53-bit

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  Max Rel. ULP: 415 Max Rel. Bit: 51.00
RMS Relative: 40.49 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    1    0    1    0    0    0    1 2055    2    0    0    0    0    0    0


gsl_sf_expint_Ei
53-bit

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  Max Rel. ULP: 167241 Max Rel. Bit: 52.38
RMS Relative: 41.43
Note: 7 special function values gave 7 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   10    0    1    3    3    9  125 1232  537  143   11    2    2    0    8


gsl_sf_expm1
53-bit

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  Max Rel. ULP: 215 Max Rel. Bit: 7.51
RMS Relative: -2.35
Note: 5 special function values gave 1 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    3    1   10   20   36   95  415  949  398  104   35   20    9    3    3


gsl_sf_gamma
53-bit

Report Page
  Max Rel. ULP: 89572 Max Rel. Bit: 45.34
RMS Relative: 34.80
Note: 30 special function values gave 6 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    2    0   16   87  111  238  303  358  260  269  290  181   18    1    1


gsl_sf_hyperg_1F1
53-bit

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  Max Rel. ULP: 225075 Max Rel. Bit: 499.26
RMS Relative: 486.87
Note: 2093 special function values gave 582 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  974  124  111   83   96  137  207 2535  285  161  135  120  138  117  924


gsl_sf_hyperg_2F1
53-bit

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  Max Rel. ULP: 207723 Max Rel. Bit: 224.81
RMS Relative: 211.35
Note: 1579 special function values gave 381 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
 3203  251  331  355  276  414  572 2098  502  439  298  409  398  237 1585


gsl_sf_laguerre
53-bit

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  Max Rel. ULP: 211981 Max Rel. Bit: 185.86
RMS Relative: 175.46 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  554    3    3   60    9    5   58  689   51    5   89  140    9   58  188


gsl_sf_laguerre_n
53-bit

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  Max Rel. ULP: 212913 Max Rel. Bit: 184.84
RMS Relative: 172.97 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  904   84   79   55   17   14  100 1966   83   36   45   76   41   58  193


gsl_sf_legendre_Pl
53-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.74
RMS Relative: -8.93 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    7 3178   14    0    0    0    0    0    0


gsl_sf_legendre_Plm
53-bit

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  Max Rel. ULP: 9 Max Rel. Bit: 3.57
RMS Relative: -8.33 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    1    1    0   14 4882   16    0    0    0    0    0    0


gsl_sf_legendre_sphPlmx
53-bit

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  Max Rel. ULP: 187233 Max Rel. Bit: 53.00
RMS Relative: 43.81
Note: 6 special function values gave 1 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  873  332  400  434  473  545  408 1759  580  910  582  489  417  318  677


gsl_sf_lngamma
53-bit

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  Max Rel. ULP: 173576 Max Rel. Bit: 56.62
RMS Relative: 46.37
Note: 549 special function values gave 546 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
  576    0    0    1    1   27  276 1006  250   28    6    0    0    0   90


gsl_sf_log
53-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.18
RMS Relative: -10.40 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    1 2048    1    0    0    0    0    0    0


gsl_sf_log_1plusx
53-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.26
RMS Relative: -5.89 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0   13  276 1519  220   12    0    0    0    0    0


gsl_sf_sin
53-bit

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  Max Rel. ULP: 7 Max Rel. Bit: 3.67
RMS Relative: -6.79 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    1    0    3 2031    4    0    1    0    0    0    0


gsl_sf_zeta
53-bit

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  Max Rel. ULP: 217278 Max Rel. Bit: 16.51
RMS Relative: 6.12
Note: 103 special function values gave 79 mismatches 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
   61   36   61   93   67   60   58  723   62   76   73   70   52   48  139


hermite
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -6.94 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   86 4654   84    0    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.92
RMS Relative: -10.99 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    3 8036    1    0    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -7.47 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  304 7394  342    0    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.97
RMS Relative: -5.65 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   58  889   58    0    0    0    0    0    0


hypot
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.93
RMS Relative: -8.43 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   19 2141    0    0    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.61
RMS Relative: -8.55 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   17 2143    0    0    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.63
RMS Relative: -8.40 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   10 2139   11    0    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.50
RMS Relative: -8.39 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   17 2139    4    0    0    0    0    0    0


ilogb
24-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


jn
24-bit

Report Page
  Max Rel. ULP: 900 Max Rel. Bit: 9.96
RMS Relative: -1.56 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    5    4   16    9   37  117  728 2144  680  107   39   19    9    2    4

53-bit

Report Page
  Max Rel. ULP: 43 Max Rel. Bit: 6.33
RMS Relative: -5.16 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    1   24   19  536 2704  538   71   26    0    0    1    0


laguerre
24-bit

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  Max Rel. ULP: 4978 Max Rel. Bit: 13.13
RMS Relative: 2.92 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    2    0    0    0    1    0    1 1917    0    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -9.70 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    2 1919    0    0    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.19
RMS Relative: -10.71 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    1 1920    0    0    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.19
RMS Relative: -10.71 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    1 1920    0    0    0    0    0    0    0


ldexp
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -7.26 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    3  783    3    0    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.00
RMS Relative: -7.27 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    3  783    0    3    0    0    0    0    0

64-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


legendre
24-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.95
RMS Relative: -9.59 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    2 3192    5    0    0    0    0    0    0

64-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.83
RMS Relative: -8.50 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    2    8 3180    8    1    0    0    0    0    0

113-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.79
RMS Relative: -9.02 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    5 3188    5    1    0    0    0    0    0


lgamma
24-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.77
RMS Relative: -5.72 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    5  294 1689  272    2    0    0    0    0    0

53-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.86
RMS Relative: -5.75 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    2  262 1747  250    1    0    0    0    0    0

64-bit

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  Max Rel. ULP: 2 Max Rel. Bit: 1.80
RMS Relative: -5.73 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    4  269 1729  259    1    0    0    0    0    0

113-bit

Report Page
  Max Rel. ULP: 2 Max Rel. Bit: 1.78
RMS Relative: -5.70 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    4  286 1714  257    1    0    0    0    0    0


llrint
24-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


llround
24-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

53-bit

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  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

64-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00

113-bit

Report Page
  Max Rel. ULP: 0 Max Rel. Bit: 0.00
RMS Relative: 0.00


log
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.75
RMS Relative: -9.13 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    5 2043    2    0    0    0    0    0    0

53-bit

Report Page
  Max Rel. ULP: 1 Max Rel. Bit: 0.88
RMS Relative: -8.97 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    5 2042    3    0    0    0    0    0    0

64-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -6.69 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   87 1865   98    0    0    0    0    0    0

113-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -6.74 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   87 1879   84    0    0    0    0    0    0


log10
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -8.04 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0   29 2021    0    0    0    0    0    0    0

53-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.99
RMS Relative: -8.85 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    0 2039   11    0    0    0    0    0    0

64-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -6.28 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  147 1710  193    0    0    0    0    0    0

113-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 1.00
RMS Relative: -6.38 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0  132 1736  182    0    0    0    0    0    0


log1p
24-bit

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  Max Rel. ULP: 1 Max Rel. Bit: 0.87
RMS Relative: -8.92 
  64+  32+  16+   8+   4+   2+    1    0    1   2+   4+   8+  16+  32+  64+
    0    0    0    0    0    0    4 2033    3    0    0    0    0    0    0

53-bit

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