
letsberational_profiling	2097152	0 1e-14 1e-08 0.0001 0.001 0.01 0.05 0.1 0.25 0.5 1 2 4 8 16 32 64 128 256 512

Loaded letsberational_profiling revision 1520 [64 bit RELEASE running on 12th Gen Intel(R) Core(TM) i5-12500H] compiled with GCC 11.4.0 on Feb 15 2024 22:46:18 from ./Linux/. .

Average over 20 different values for x:  0.200746  microseconds per evaluation (41943040 successful evaluations in total).

Total average |(attained accuracy)/(theoretically attainable accuracy)| : 0.195557.
This means the method is on average 5.1 times more accurate than what one could
hope for on the basis of first order error propagation analysis.

Flat profile:

Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls  ns/call  ns/call  name    
 39.42      2.44     2.44 62914633    38.78    71.45  lets_be_rational
 15.02      3.37     0.93 103791926     8.96     8.96  asymptotic_expansion_of_scaled_normalised_black(double, double)
  8.56      3.90     0.53 56938203     9.31     9.31  inverse_norm_cdf
  7.43      4.36     0.46                             main
  4.20      4.62     0.26 103148829     2.52     2.52  erfc_cody(double)
  4.04      4.87     0.25 119110046     2.10    10.57  scaled_normalised_black_and_ln_vega(double, double)
  3.72      5.10     0.23 159469444     1.44     1.44  erfcx_cody_above_threshold(double)
  3.23      5.30     0.20                             _init
  2.75      5.47     0.17 160338615     1.06     2.49  erfcx_cody(double)
  2.42      5.62     0.15 62914633     2.38    73.83  ImpliedBlackVolatility
  1.62      5.72     0.10 19021759     5.26     5.26  convex_rational_cubic_control_parameter_to_fit_second_derivative_at_left_side(double, double, double, double, double, double, double, bool)
  1.45      5.81     0.09 11105267     8.10     9.20  small_t_expansion_of_scaled_normalised_black(double, double)
  1.13      5.88     0.07 58867679     1.19     1.19  rational_cubic_interpolation(double, double, double, double, double, double, double, double)
  1.13      5.95     0.07 49718270     1.41     6.42  normalised_black_with_optimal_use_of_codys_functions(double, double)
  0.97      6.01     0.06 41943072     1.43     9.63  Black
  0.97      6.07     0.06 41943040     1.43    11.47  BlackAccuracyFactor
  0.97      6.13     0.06 39845920     1.51     1.51  convex_rational_cubic_control_parameter_to_fit_second_derivative_at_right_side(double, double, double, double, double, double, double, bool)
  0.81      6.18     0.05 45505417     1.10     8.63  normalised_black(double, double)
  0.16      6.19     0.01 11105267     0.90     1.10  Yprime(double)
  0.00      6.19     0.00  3173185     0.00     0.00  erf_cody(double)
  0.00      6.19     0.00  3145733     0.00     0.00  erfinv(double)
  0.00      6.19     0.00       77     0.00     0.00  void std::vector<char const*, std::allocator<char const*> >::_M_realloc_insert<char const* const&>(__gnu_cxx::__normal_iterator<char const**, std::vector<char const*, std::allocator<char const*> > >, char const* const&)
  0.00      6.19     0.00       46     0.00     0.00  XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&)
  0.00      6.19     0.00       35     0.00     0.00  std::vector<char const*, std::allocator<char const*> >::vector(std::initializer_list<char const*>, std::allocator<char const*> const&)
  0.00      6.19     0.00       23     0.00     0.00  std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > std::operator+<char, std::char_traits<char>, std::allocator<char> >(char, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&)
  0.00      6.19     0.00       20     0.00     8.20  NormalisedBlack
  0.00      6.19     0.00       15     0.00     0.00  XLFunction::Declare(char const*, std::vector<char const*, std::allocator<char const*> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&)
  0.00      6.19     0.00       10     0.00     0.00  XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*)
  0.00      6.19     0.00        7     0.00     0.00  void std::vector<XLFunction, std::allocator<XLFunction> >::_M_realloc_insert<XLFunction>(__gnu_cxx::__normal_iterator<XLFunction*, std::vector<XLFunction, std::allocator<XLFunction> > >, XLFunction&&)
  0.00      6.19     0.00        5     0.00     0.00  std::vector<double, std::allocator<double> >::vector(unsigned long, std::allocator<double> const&)
  0.00      6.19     0.00        2     0.00     0.00  (anonymous namespace)::this_file_name()
  0.00      6.19     0.00        1     0.00     0.00  Bitness
  0.00      6.19     0.00        1     0.00     0.00  BuildConfiguration
  0.00      6.19     0.00        1     0.00     0.00  BuildDate
  0.00      6.19     0.00        1     0.00     0.00  CPUName
  0.00      6.19     0.00        1     0.00     0.00  CompilerVersion
  0.00      6.19     0.00        1     0.00     0.00  DLLDirectory
  0.00      6.19     0.00        1     0.00     0.00  DLLName
  0.00      6.19     0.00        1     0.00     0.00  Revision
  0.00      6.19     0.00        1     0.00     0.00  (anonymous namespace)::get_file_name()
  0.00      6.19     0.00        1     0.00     0.00  void (anonymous namespace)::free_xloper_content<XLOper12>(XLOper12*)
  0.00      6.19     0.00        1     0.00     0.00  (anonymous namespace)::skip_path(char const*)
  0.00      6.19     0.00        1     0.00     0.00  std::map<char, wchar_t, std::less<char>, std::allocator<std::pair<char const, wchar_t> > >::map(std::initializer_list<std::pair<char const, wchar_t> >, std::less<char> const&, std::allocator<std::pair<char const, wchar_t> > const&)
  0.00      6.19     0.00        1     0.00     0.00  std::_Rb_tree<char, std::pair<char const, wchar_t>, std::_Select1st<std::pair<char const, wchar_t> >, std::less<char>, std::allocator<std::pair<char const, wchar_t> > >::_M_get_insert_unique_pos(char const&)
  0.00      6.19     0.00        1     0.00     0.00  _sub_I_00100_0
  0.00      6.19     0.00        1     0.00     0.00  _sub_I_00100_0

 %         the percentage of the total running time of the
time       program used by this function.

cumulative a running sum of the number of seconds accounted
 seconds   for by this function and those listed above it.

 self      the number of seconds accounted for by this
seconds    function alone.  This is the major sort for this
           listing.

calls      the number of times this function was invoked, if
           this function is profiled, else blank.

 self      the average number of milliseconds spent in this
ms/call    function per call, if this function is profiled,
	   else blank.

 total     the average number of milliseconds spent in this
ms/call    function and its descendents per call, if this
	   function is profiled, else blank.

name       the name of the function.  This is the minor sort
           for this listing. The index shows the location of
	   the function in the gprof listing. If the index is
	   in parenthesis it shows where it would appear in
	   the gprof listing if it were to be printed.

Copyright (C) 2012-2022 Free Software Foundation, Inc.

Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.

		     Call graph (explanation follows)


granularity: each sample hit covers 4 byte(s) for 0.16% of 6.19 seconds

index % time    self  children    called     name
                                                 <spontaneous>
[1]     96.8    0.46    5.53                 main [1]
                0.15    4.49 62914633/62914633     ImpliedBlackVolatility [2]
                0.06    0.42 41943040/41943040     BlackAccuracyFactor [7]
                0.06    0.34 41943072/41943072     Black [8]
                0.00    0.00      20/20          NormalisedBlack [20]
                0.00    0.00       5/5           std::vector<double, std::allocator<double> >::vector(unsigned long, std::allocator<double> const&) [67]
                0.00    0.00       1/1           (anonymous namespace)::skip_path(char const*) [71]
                0.00    0.00       1/1           DLLDirectory [26]
                0.00    0.00       1/1           BuildDate [23]
                0.00    0.00       1/1           CompilerVersion [25]
                0.00    0.00       1/1           CPUName [24]
                0.00    0.00       1/1           BuildConfiguration [22]
                0.00    0.00       1/1           Bitness [21]
                0.00    0.00       1/1           Revision [28]
                0.00    0.00       1/1           DLLName [27]
-----------------------------------------------
                0.15    4.49 62914633/62914633     main [1]
[2]     75.0    0.15    4.49 62914633         ImpliedBlackVolatility [2]
                2.44    2.05 62914633/62914633     lets_be_rational [3]
-----------------------------------------------
                2.44    2.05 62914633/62914633     ImpliedBlackVolatility [2]
[3]     72.6    2.44    2.05 62914633         lets_be_rational [3]
                0.17    0.67 79264158/119110046     scaled_normalised_black_and_ln_vega(double, double) [4]
                0.53    0.00 56938203/56938203     inverse_norm_cdf [6]
                0.11    0.15 106243530/160338615     erfcx_cody(double) [9]
                0.14    0.00 56938203/103148829     erfc_cody(double) [12]
                0.10    0.00 19021759/19021759     convex_rational_cubic_control_parameter_to_fit_second_derivative_at_left_side(double, double, double, double, double, double, double, bool) [16]
                0.07    0.00 58867679/58867679     rational_cubic_interpolation(double, double, double, double, double, double, double, double) [17]
                0.06    0.00 39845920/39845920     convex_rational_cubic_control_parameter_to_fit_second_derivative_at_right_side(double, double, double, double, double, double, double, bool) [18]
                0.01    0.04 5659482/45505417     normalised_black(double, double) [10]
                0.00    0.00 3145733/3145733     erfinv(double) [59]
-----------------------------------------------
                0.08    0.34 39845888/119110046     BlackAccuracyFactor [7]
                0.17    0.67 79264158/119110046     lets_be_rational [3]
[4]     20.3    0.25    1.01 119110046         scaled_normalised_black_and_ln_vega(double, double) [4]
                0.78    0.00 86520452/103791926     asymptotic_expansion_of_scaled_normalised_black(double, double) [5]
                0.03    0.12 23937858/49718270     normalised_black_with_optimal_use_of_codys_functions(double, double) [11]
                0.07    0.01 8651736/11105267     small_t_expansion_of_scaled_normalised_black(double, double) [15]
-----------------------------------------------
                0.15    0.00 17271474/103791926     normalised_black(double, double) [10]
                0.78    0.00 86520452/103791926     scaled_normalised_black_and_ln_vega(double, double) [4]
[5]     15.0    0.93    0.00 103791926         asymptotic_expansion_of_scaled_normalised_black(double, double) [5]
-----------------------------------------------
                0.53    0.00 56938203/56938203     lets_be_rational [3]
[6]      8.6    0.53    0.00 56938203         inverse_norm_cdf [6]
-----------------------------------------------
                0.06    0.42 41943040/41943040     main [1]
[7]      7.8    0.06    0.42 41943040         BlackAccuracyFactor [7]
                0.08    0.34 39845888/119110046     scaled_normalised_black_and_ln_vega(double, double) [4]
                0.00    0.00 1076029/3173185     erf_cody(double) [58]
-----------------------------------------------
                0.06    0.34 41943072/41943072     main [1]
[8]      6.5    0.06    0.34 41943072         Black [8]
                0.04    0.30 39845916/45505417     normalised_black(double, double) [10]
                0.00    0.00 2097155/3173185     erf_cody(double) [58]
-----------------------------------------------
                0.00    0.00  869171/160338615     Yprime(double) [19]
                0.06    0.08 53225914/160338615     normalised_black_with_optimal_use_of_codys_functions(double, double) [11]
                0.11    0.15 106243530/160338615     lets_be_rational [3]
[9]      6.5    0.17    0.23 160338615         erfcx_cody(double) [9]
                0.23    0.00 159469444/159469444     erfcx_cody_above_threshold(double) [13]
-----------------------------------------------
                0.00    0.00      19/45505417     NormalisedBlack [20]
                0.01    0.04 5659482/45505417     lets_be_rational [3]
                0.04    0.30 39845916/45505417     Black [8]
[10]     6.3    0.05    0.34 45505417         normalised_black(double, double) [10]
                0.04    0.13 25780412/49718270     normalised_black_with_optimal_use_of_codys_functions(double, double) [11]
                0.15    0.00 17271474/103791926     asymptotic_expansion_of_scaled_normalised_black(double, double) [5]
                0.02    0.00 2453531/11105267     small_t_expansion_of_scaled_normalised_black(double, double) [15]
-----------------------------------------------
                0.03    0.12 23937858/49718270     scaled_normalised_black_and_ln_vega(double, double) [4]
                0.04    0.13 25780412/49718270     normalised_black(double, double) [10]
[11]     5.2    0.07    0.25 49718270         normalised_black_with_optimal_use_of_codys_functions(double, double) [11]
                0.06    0.08 53225914/160338615     erfcx_cody(double) [9]
                0.12    0.00 46210626/103148829     erfc_cody(double) [12]
-----------------------------------------------
                0.12    0.00 46210626/103148829     normalised_black_with_optimal_use_of_codys_functions(double, double) [11]
                0.14    0.00 56938203/103148829     lets_be_rational [3]
[12]     4.2    0.26    0.00 103148829         erfc_cody(double) [12]
-----------------------------------------------
                0.23    0.00 159469444/159469444     erfcx_cody(double) [9]
[13]     3.7    0.23    0.00 159469444         erfcx_cody_above_threshold(double) [13]
-----------------------------------------------
                                                 <spontaneous>
[14]     3.2    0.20    0.00                 _init [14]
-----------------------------------------------
                0.02    0.00 2453531/11105267     normalised_black(double, double) [10]
                0.07    0.01 8651736/11105267     scaled_normalised_black_and_ln_vega(double, double) [4]
[15]     1.7    0.09    0.01 11105267         small_t_expansion_of_scaled_normalised_black(double, double) [15]
                0.01    0.00 11105267/11105267     Yprime(double) [19]
-----------------------------------------------
                0.10    0.00 19021759/19021759     lets_be_rational [3]
[16]     1.6    0.10    0.00 19021759         convex_rational_cubic_control_parameter_to_fit_second_derivative_at_left_side(double, double, double, double, double, double, double, bool) [16]
-----------------------------------------------
                0.07    0.00 58867679/58867679     lets_be_rational [3]
[17]     1.1    0.07    0.00 58867679         rational_cubic_interpolation(double, double, double, double, double, double, double, double) [17]
-----------------------------------------------
                0.06    0.00 39845920/39845920     lets_be_rational [3]
[18]     1.0    0.06    0.00 39845920         convex_rational_cubic_control_parameter_to_fit_second_derivative_at_right_side(double, double, double, double, double, double, double, bool) [18]
-----------------------------------------------
                0.01    0.00 11105267/11105267     small_t_expansion_of_scaled_normalised_black(double, double) [15]
[19]     0.2    0.01    0.00 11105267         Yprime(double) [19]
                0.00    0.00  869171/160338615     erfcx_cody(double) [9]
-----------------------------------------------
                0.00    0.00      20/20          main [1]
[20]     0.0    0.00    0.00      20         NormalisedBlack [20]
                0.00    0.00      19/45505417     normalised_black(double, double) [10]
                0.00    0.00       1/3173185     erf_cody(double) [58]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[21]     0.0    0.00    0.00       1         Bitness [21]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[22]     0.0    0.00    0.00       1         BuildConfiguration [22]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[23]     0.0    0.00    0.00       1         BuildDate [23]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[24]     0.0    0.00    0.00       1         CPUName [24]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[25]     0.0    0.00    0.00       1         CompilerVersion [25]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[26]     0.0    0.00    0.00       1         DLLDirectory [26]
                0.00    0.00       1/2           (anonymous namespace)::this_file_name() [68]
                0.00    0.00       1/35          std::vector<char const*, std::allocator<char const*> >::vector(std::initializer_list<char const*>, std::allocator<char const*> const&) [62]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[27]     0.0    0.00    0.00       1         DLLName [27]
                0.00    0.00       1/2           (anonymous namespace)::this_file_name() [68]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[28]     0.0    0.00    0.00       1         Revision [28]
-----------------------------------------------
                0.00    0.00       1/3173185     NormalisedBlack [20]
                0.00    0.00 1076029/3173185     BlackAccuracyFactor [7]
                0.00    0.00 2097155/3173185     Black [8]
[58]     0.0    0.00    0.00 3173185         erf_cody(double) [58]
-----------------------------------------------
                0.00    0.00 3145733/3145733     lets_be_rational [3]
[59]     0.0    0.00    0.00 3145733         erfinv(double) [59]
-----------------------------------------------
                0.00    0.00      77/77          XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [61]
[60]     0.0    0.00    0.00      77         void std::vector<char const*, std::allocator<char const*> >::_M_realloc_insert<char const* const&>(__gnu_cxx::__normal_iterator<char const**, std::vector<char const*, std::allocator<char const*> > >, char const* const&) [60]
-----------------------------------------------
                0.00    0.00       2/46          _sub_I_00100_0 [74]
                0.00    0.00      10/46          XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*) [65]
                0.00    0.00      34/46          XLFunction::Declare(char const*, std::vector<char const*, std::allocator<char const*> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [64]
[61]     0.0    0.00    0.00      46         XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [61]
                0.00    0.00      77/77          void std::vector<char const*, std::allocator<char const*> >::_M_realloc_insert<char const* const&>(__gnu_cxx::__normal_iterator<char const**, std::vector<char const*, std::allocator<char const*> > >, char const* const&) [60]
                0.00    0.00      23/23          std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > std::operator+<char, std::char_traits<char>, std::allocator<char> >(char, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&) [63]
                0.00    0.00       7/7           void std::vector<XLFunction, std::allocator<XLFunction> >::_M_realloc_insert<XLFunction>(__gnu_cxx::__normal_iterator<XLFunction*, std::vector<XLFunction, std::allocator<XLFunction> > >, XLFunction&&) [66]
-----------------------------------------------
                0.00    0.00       1/35          _sub_I_00100_0 [75]
                0.00    0.00       1/35          DLLDirectory [26]
                0.00    0.00       2/35          (anonymous namespace)::get_file_name() [69]
                0.00    0.00       4/35          std::map<char, wchar_t, std::less<char>, std::allocator<std::pair<char const, wchar_t> > >::~map() [212]
                0.00    0.00      27/35          _sub_I_00100_0 [74]
[62]     0.0    0.00    0.00      35         std::vector<char const*, std::allocator<char const*> >::vector(std::initializer_list<char const*>, std::allocator<char const*> const&) [62]
-----------------------------------------------
                0.00    0.00      23/23          XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [61]
[63]     0.0    0.00    0.00      23         std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > std::operator+<char, std::char_traits<char>, std::allocator<char> >(char, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&) [63]
-----------------------------------------------
                0.00    0.00       1/15          _sub_I_00100_0 [75]
                0.00    0.00      14/15          _sub_I_00100_0 [74]
[64]     0.0    0.00    0.00      15         XLFunction::Declare(char const*, std::vector<char const*, std::allocator<char const*> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [64]
                0.00    0.00      34/46          XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [61]
-----------------------------------------------
                0.00    0.00       2/10          _sub_I_00100_0 [74]
                0.00    0.00       8/10          _sub_I_00100_0 [75]
[65]     0.0    0.00    0.00      10         XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*) [65]
                0.00    0.00      10/46          XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [61]
-----------------------------------------------
                0.00    0.00       7/7           XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [61]
[66]     0.0    0.00    0.00       7         void std::vector<XLFunction, std::allocator<XLFunction> >::_M_realloc_insert<XLFunction>(__gnu_cxx::__normal_iterator<XLFunction*, std::vector<XLFunction, std::allocator<XLFunction> > >, XLFunction&&) [66]
-----------------------------------------------
                0.00    0.00       5/5           main [1]
[67]     0.0    0.00    0.00       5         std::vector<double, std::allocator<double> >::vector(unsigned long, std::allocator<double> const&) [67]
-----------------------------------------------
                0.00    0.00       1/2           DLLName [27]
                0.00    0.00       1/2           DLLDirectory [26]
[68]     0.0    0.00    0.00       2         (anonymous namespace)::this_file_name() [68]
                0.00    0.00       1/1           (anonymous namespace)::get_file_name() [69]
-----------------------------------------------
                0.00    0.00       1/1           (anonymous namespace)::this_file_name() [68]
[69]     0.0    0.00    0.00       1         (anonymous namespace)::get_file_name() [69]
                0.00    0.00       2/35          std::vector<char const*, std::allocator<char const*> >::vector(std::initializer_list<char const*>, std::allocator<char const*> const&) [62]
-----------------------------------------------
                0.00    0.00       1/1           XLOper::~XLOper() [115]
[70]     0.0    0.00    0.00       1         void (anonymous namespace)::free_xloper_content<XLOper12>(XLOper12*) [70]
-----------------------------------------------
                0.00    0.00       1/1           main [1]
[71]     0.0    0.00    0.00       1         (anonymous namespace)::skip_path(char const*) [71]
-----------------------------------------------
                0.00    0.00       1/1           _sub_I_00100_0 [75]
[72]     0.0    0.00    0.00       1         std::map<char, wchar_t, std::less<char>, std::allocator<std::pair<char const, wchar_t> > >::map(std::initializer_list<std::pair<char const, wchar_t> >, std::less<char> const&, std::allocator<std::pair<char const, wchar_t> > const&) [72]
                0.00    0.00       1/1           std::_Rb_tree<char, std::pair<char const, wchar_t>, std::_Select1st<std::pair<char const, wchar_t> >, std::less<char>, std::allocator<std::pair<char const, wchar_t> > >::_M_get_insert_unique_pos(char const&) [73]
-----------------------------------------------
                0.00    0.00       1/1           std::map<char, wchar_t, std::less<char>, std::allocator<std::pair<char const, wchar_t> > >::map(std::initializer_list<std::pair<char const, wchar_t> >, std::less<char> const&, std::allocator<std::pair<char const, wchar_t> > const&) [72]
[73]     0.0    0.00    0.00       1         std::_Rb_tree<char, std::pair<char const, wchar_t>, std::_Select1st<std::pair<char const, wchar_t> >, std::less<char>, std::allocator<std::pair<char const, wchar_t> > >::_M_get_insert_unique_pos(char const&) [73]
-----------------------------------------------
                                  54             _sub_I_00100_0 [74]
                0.00    0.00       1/1           _GLOBAL__sub_I__Z47asymptotic_expansion_of_scaled_normalised_blackdd [76]
[74]     0.0    0.00    0.00       1+54      _sub_I_00100_0 [74]
                0.00    0.00      27/35          std::vector<char const*, std::allocator<char const*> >::vector(std::initializer_list<char const*>, std::allocator<char const*> const&) [62]
                0.00    0.00      14/15          XLFunction::Declare(char const*, std::vector<char const*, std::allocator<char const*> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [64]
                0.00    0.00       2/46          XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [61]
                0.00    0.00       2/10          XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*) [65]
                                  54             _sub_I_00100_0 [74]
-----------------------------------------------
                                  28             _sub_I_00100_0 [75]
                0.00    0.00       1/1           _GLOBAL__sub_I__Z9to_stringB5cxx11PKwm [77]
[75]     0.0    0.00    0.00       1+28      _sub_I_00100_0 [75]
                0.00    0.00       8/10          XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*) [65]
                0.00    0.00       1/1           std::map<char, wchar_t, std::less<char>, std::allocator<std::pair<char const, wchar_t> > >::map(std::initializer_list<std::pair<char const, wchar_t> >, std::less<char> const&, std::allocator<std::pair<char const, wchar_t> > const&) [72]
                0.00    0.00       1/35          std::vector<char const*, std::allocator<char const*> >::vector(std::initializer_list<char const*>, std::allocator<char const*> const&) [62]
                0.00    0.00       1/15          XLFunction::Declare(char const*, std::vector<char const*, std::allocator<char const*> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [64]
                                  28             _sub_I_00100_0 [75]
-----------------------------------------------

 This table describes the call tree of the program, and was sorted by
 the total amount of time spent in each function and its children.

 Each entry in this table consists of several lines.  The line with the
 index number at the left hand margin lists the current function.
 The lines above it list the functions that called this function,
 and the lines below it list the functions this one called.
 This line lists:
     index	A unique number given to each element of the table.
		Index numbers are sorted numerically.
		The index number is printed next to every function name so
		it is easier to look up where the function is in the table.

     % time	This is the percentage of the `total' time that was spent
		in this function and its children.  Note that due to
		different viewpoints, functions excluded by options, etc,
		these numbers will NOT add up to 100%.

     self	This is the total amount of time spent in this function.

     children	This is the total amount of time propagated into this
		function by its children.

     called	This is the number of times the function was called.
		If the function called itself recursively, the number
		only includes non-recursive calls, and is followed by
		a `+' and the number of recursive calls.

     name	The name of the current function.  The index number is
		printed after it.  If the function is a member of a
		cycle, the cycle number is printed between the
		function's name and the index number.


 For the function's parents, the fields have the following meanings:

     self	This is the amount of time that was propagated directly
		from the function into this parent.

     children	This is the amount of time that was propagated from
		the function's children into this parent.

     called	This is the number of times this parent called the
		function `/' the total number of times the function
		was called.  Recursive calls to the function are not
		included in the number after the `/'.

     name	This is the name of the parent.  The parent's index
		number is printed after it.  If the parent is a
		member of a cycle, the cycle number is printed between
		the name and the index number.

 If the parents of the function cannot be determined, the word
 `<spontaneous>' is printed in the `name' field, and all the other
 fields are blank.

 For the function's children, the fields have the following meanings:

     self	This is the amount of time that was propagated directly
		from the child into the function.

     children	This is the amount of time that was propagated from the
		child's children to the function.

     called	This is the number of times the function called
		this child `/' the total number of times the child
		was called.  Recursive calls by the child are not
		listed in the number after the `/'.

     name	This is the name of the child.  The child's index
		number is printed after it.  If the child is a
		member of a cycle, the cycle number is printed
		between the name and the index number.

 If there are any cycles (circles) in the call graph, there is an
 entry for the cycle-as-a-whole.  This entry shows who called the
 cycle (as parents) and the members of the cycle (as children.)
 The `+' recursive calls entry shows the number of function calls that
 were internal to the cycle, and the calls entry for each member shows,
 for that member, how many times it was called from other members of
 the cycle.

Copyright (C) 2012-2022 Free Software Foundation, Inc.

Copying and distribution of this file, with or without modification,
are permitted in any medium without royalty provided the copyright
notice and this notice are preserved.

Index by function name

  [21] Bitness                 [4] scaled_normalised_black_and_ln_vega(double, double) [71] (anonymous namespace)::skip_path(char const*) (lets_be_rational_timing.cpp)
   [8] Black                  [15] small_t_expansion_of_scaled_normalised_black(double, double) [72] std::map<char, wchar_t, std::less<char>, std::allocator<std::pair<char const, wchar_t> > >::map(std::initializer_list<std::pair<char const, wchar_t> >, std::less<char> const&, std::allocator<std::pair<char const, wchar_t> > const&)
   [7] BlackAccuracyFactor     [5] asymptotic_expansion_of_scaled_normalised_black(double, double) [66] void std::vector<XLFunction, std::allocator<XLFunction> >::_M_realloc_insert<XLFunction>(__gnu_cxx::__normal_iterator<XLFunction*, std::vector<XLFunction, std::allocator<XLFunction> > >, XLFunction&&)
  [22] BuildConfiguration     [11] normalised_black_with_optimal_use_of_codys_functions(double, double) [60] void std::vector<char const*, std::allocator<char const*> >::_M_realloc_insert<char const* const&>(__gnu_cxx::__normal_iterator<char const**, std::vector<char const*, std::allocator<char const*> > >, char const* const&)
  [23] BuildDate              [19] Yprime(double)         [62] std::vector<char const*, std::allocator<char const*> >::vector(std::initializer_list<char const*>, std::allocator<char const*> const&)
  [24] CPUName                [59] erfinv(double)         [67] std::vector<double, std::allocator<double> >::vector(unsigned long, std::allocator<double> const&)
  [25] CompilerVersion        [16] convex_rational_cubic_control_parameter_to_fit_second_derivative_at_left_side(double, double, double, double, double, double, double, bool) [73] std::_Rb_tree<char, std::pair<char const, wchar_t>, std::_Select1st<std::pair<char const, wchar_t> >, std::less<char>, std::allocator<std::pair<char const, wchar_t> > >::_M_get_insert_unique_pos(char const&)
  [26] DLLDirectory           [18] convex_rational_cubic_control_parameter_to_fit_second_derivative_at_right_side(double, double, double, double, double, double, double, bool) [63] std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > std::operator+<char, std::char_traits<char>, std::allocator<char> >(char, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&)
  [27] DLLName                [58] erf_cody(double)       [14] _init
   [2] ImpliedBlackVolatility [12] erfc_cody(double)      [74] _sub_I_00100_0
  [20] NormalisedBlack        [64] XLFunction::Declare(char const*, std::vector<char const*, std::allocator<char const*> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [75] _sub_I_00100_0 (lets_be_rational.cpp)
  [28] Revision               [61] XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::vector<char const*, std::allocator<char const*> > const&) [6] inverse_norm_cdf
   [9] erfcx_cody(double)     [65] XLFunction::Declare(char const*, char const*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char> > const&, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*, char const*) [3] lets_be_rational
  [10] normalised_black(double, double) [69] (anonymous namespace)::get_file_name() (dllmain.cpp) [1] main
  [13] erfcx_cody_above_threshold(double) [68] (anonymous namespace)::this_file_name() (dllmain.cpp)
  [17] rational_cubic_interpolation(double, double, double, double, double, double, double, double) [70] void (anonymous namespace)::free_xloper_content<XLOper12>(XLOper12*) (XLOper.cpp)
