
letsberational_profiling.exe	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.exe revision 1517 [64 bit RELEASE running on 12th Gen Intel(R) Core(TM) i5-12500H] compiled with MinGW-w64 10.0 (GCC 12.2.0) on Feb  9 2024 13:18:54 from ./x64 .

Average over 20 different values for x:  0.447392  microseconds per evaluation (41943040 successful evaluations in total).

Total average |(attained accuracy)/(theoretically attainable accuracy)| : 0.20433.
This means the method is on average 4.9 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    
 40.24      9.77     9.77                             exp
 12.11     12.71     2.94                             __logl_internal
  9.80     15.09     2.38 62914581    37.83    86.56  lets_be_rational
  5.07     16.32     1.23                             _mcount_private
  5.02     17.54     1.22 103783688    11.76    11.76  asymptotic_expansion_of_scaled_normalised_black(double, double)
  3.62     18.42     0.88                             log
  3.21     19.20     0.78                             __fentry__
  3.01     19.93     0.73                             cbrt
  2.92     20.64     0.71 103148745     6.88     6.88  erfc_cody(double)
  2.84     21.33     0.69 159475020     4.33     4.33  erfcx_cody_above_threshold(double)
  1.98     21.81     0.48 57781196     8.31     8.31  inverse_norm_cdf_for_low_probabilities(double)
  1.85     22.26     0.45                             ldexp
  1.28     22.57     0.31                             main
  1.19     22.86     0.29 62914581     4.61    91.17  ImpliedBlackVolatility
  0.91     23.08     0.22 119109776     1.85    14.53  scaled_normalised_black_and_ln_vega(double, double)
  0.91     23.30     0.22 49721098     4.42    16.23  normalised_black_with_optimal_use_of_codys_functions(double, double)
  0.66     23.46     0.16 39845872     4.02     4.02  convex_rational_cubic_control_parameter_to_fit_second_derivative_at_right_side(double, double, double, double, double, double, double, bool)
  0.62     23.61     0.15 58867631     2.55     2.55  rational_cubic_interpolation(double, double, double, double, double, double, double, double)
  0.49     23.73     0.12 160344260     0.75     5.05  erfcx_cody(double)
  0.45     23.84     0.11 41943040     2.62    16.75  BlackAccuracyFactor
  0.41     23.94     0.10 41943040     2.38    17.44  Black
  0.37     24.03     0.09 11110528     8.10    12.10  small_t_expansion_of_scaled_normalised_black(double, double)
  0.29     24.10     0.07 19021759     3.68     3.68  convex_rational_cubic_control_parameter_to_fit_second_derivative_at_left_side(double, double, double, double, double, double, double, bool)
  0.16     24.14     0.04 45505538     0.88    15.19  normalised_black(double, double)
  0.16     24.18     0.04 11110528     3.60     4.00  Yprime(double)
  0.16     24.22     0.04  3173166    12.61    12.61  erf_cody(double)
  0.08     24.24     0.02 56938067     0.35     0.35  inverse_norm_cdf
  0.08     24.26     0.02  3145729     6.36     8.79  implied_normalised_volatility_atm(double)
  0.08     24.28     0.02                             frexp
  0.00     24.28     0.00       65     0.00     0.00  printf(char const*, ...)
  0.00     24.28     0.00       20     0.00    15.06  NormalisedBlack
  0.00     24.28     0.00        6     0.00     0.00  XLOper::isUndefined() const
  0.00     24.28     0.00        4     0.00     0.00  NormalisedImpliedBlackVolatilityForExcel
  0.00     24.28     0.00        1     0.00     0.00  Bitness
  0.00     24.28     0.00        1     0.00     0.00  BuildConfiguration
  0.00     24.28     0.00        1     0.00     0.00  BuildDate
  0.00     24.28     0.00        1     0.00     0.00  CPUName
  0.00     24.28     0.00        1     0.00     0.00  CompilerVersion
  0.00     24.28     0.00        1     0.00     0.00  DLLDirectory
  0.00     24.28     0.00        1     0.00     0.00  DLLName
  0.00     24.28     0.00        1     0.00     0.00  Revision

 %         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 0.04% of 24.28 seconds

index % time    self  children    called     name
                                                 <spontaneous>
[1]     40.2    9.77    0.00                 exp [1]
-----------------------------------------------
                                                 <spontaneous>
[2]     30.8    0.31    7.17                 main [2]
                0.29    5.45 62914581/62914581     ImpliedBlackVolatility [3]
                0.10    0.63 41943040/41943040     Black [13]
                0.11    0.59 41943040/41943040     BlackAccuracyFactor [16]
                0.00    0.00      20/20          NormalisedBlack [30]
                0.00    0.00      65/65          printf(char const*, ...) [262]
                0.00    0.00       6/6           XLOper::isUndefined() const [263]
                0.00    0.00       1/1           DLLDirectory [37]
                0.00    0.00       1/1           BuildDate [34]
                0.00    0.00       1/1           CompilerVersion [36]
                0.00    0.00       1/1           CPUName [35]
                0.00    0.00       1/1           BuildConfiguration [33]
                0.00    0.00       1/1           Bitness [32]
                0.00    0.00       1/1           Revision [39]
                0.00    0.00       1/1           DLLName [38]
-----------------------------------------------
                0.29    5.45 62914581/62914581     main [2]
[3]     23.6    0.29    5.45 62914581         ImpliedBlackVolatility [3]
                2.38    3.07 62914581/62914581     lets_be_rational [4]
-----------------------------------------------
                2.38    3.07 62914581/62914581     ImpliedBlackVolatility [3]
[4]     22.4    2.38    3.07 62914581         lets_be_rational [4]
                0.15    1.01 79263888/119109776     scaled_normalised_black_and_ln_vega(double, double) [6]
                0.08    0.46 106243502/160344260     erfcx_cody(double) [10]
                0.47    0.00 56860345/57781196     inverse_norm_cdf_for_low_probabilities(double) [19]
                0.39    0.00 56938067/103148745     erfc_cody(double) [15]
                0.16    0.00 39845872/39845872     convex_rational_cubic_control_parameter_to_fit_second_derivative_at_right_side(double, double, double, double, double, double, double, bool) [21]
                0.15    0.00 58867631/58867631     rational_cubic_interpolation(double, double, double, double, double, double, double, double) [22]
                0.00    0.08 5659631/45505538     normalised_black(double, double) [17]
                0.07    0.00 19021759/19021759     convex_rational_cubic_control_parameter_to_fit_second_derivative_at_left_side(double, double, double, double, double, double, double, bool) [24]
                0.02    0.01 3145729/3145729     implied_normalised_volatility_atm(double) [27]
                0.02    0.00 56938067/56938067     inverse_norm_cdf [28]
-----------------------------------------------
                                                 <spontaneous>
[5]     12.1    2.94    0.00                 __logl_internal [5]
-----------------------------------------------
                0.07    0.51 39845888/119109776     BlackAccuracyFactor [16]
                0.15    1.01 79263888/119109776     lets_be_rational [4]
[6]      7.1    0.22    1.51 119109776         scaled_normalised_black_and_ln_vega(double, double) [6]
                1.02    0.00 86513612/103783688     asymptotic_expansion_of_scaled_normalised_black(double, double) [8]
                0.11    0.28 23940130/49721098     normalised_black_with_optimal_use_of_codys_functions(double, double) [11]
                0.07    0.03 8656034/11110528     small_t_expansion_of_scaled_normalised_black(double, double) [23]
-----------------------------------------------
                                                 <spontaneous>
[7]      5.1    1.23    0.00                 _mcount_private [7]
-----------------------------------------------
                0.20    0.00 17270076/103783688     normalised_black(double, double) [17]
                1.02    0.00 86513612/103783688     scaled_normalised_black_and_ln_vega(double, double) [6]
[8]      5.0    1.22    0.00 103783688         asymptotic_expansion_of_scaled_normalised_black(double, double) [8]
-----------------------------------------------
                                                 <spontaneous>
[9]      3.6    0.88    0.00                 log [9]
-----------------------------------------------
                0.00    0.00  869240/160344260     Yprime(double) [25]
                0.04    0.23 53231518/160344260     normalised_black_with_optimal_use_of_codys_functions(double, double) [11]
                0.08    0.46 106243502/160344260     lets_be_rational [4]
[10]     3.3    0.12    0.69 160344260         erfcx_cody(double) [10]
                0.69    0.00 159475020/159475020     erfcx_cody_above_threshold(double) [18]
-----------------------------------------------
                0.11    0.28 23940130/49721098     scaled_normalised_black_and_ln_vega(double, double) [6]
                0.11    0.30 25780968/49721098     normalised_black(double, double) [17]
[11]     3.3    0.22    0.59 49721098         normalised_black_with_optimal_use_of_codys_functions(double, double) [11]
                0.32    0.00 46210678/103148745     erfc_cody(double) [15]
                0.04    0.23 53231518/160344260     erfcx_cody(double) [10]
-----------------------------------------------
                                                 <spontaneous>
[12]     3.2    0.78    0.00                 __fentry__ [12]
-----------------------------------------------
                0.10    0.63 41943040/41943040     main [2]
[13]     3.0    0.10    0.63 41943040         Black [13]
                0.04    0.57 39845888/45505538     normalised_black(double, double) [17]
                0.03    0.00 2097152/3173166     erf_cody(double) [26]
-----------------------------------------------
                                                 <spontaneous>
[14]     3.0    0.73    0.00                 cbrt [14]
-----------------------------------------------
                0.32    0.00 46210678/103148745     normalised_black_with_optimal_use_of_codys_functions(double, double) [11]
                0.39    0.00 56938067/103148745     lets_be_rational [4]
[15]     2.9    0.71    0.00 103148745         erfc_cody(double) [15]
-----------------------------------------------
                0.11    0.59 41943040/41943040     main [2]
[16]     2.9    0.11    0.59 41943040         BlackAccuracyFactor [16]
                0.07    0.51 39845888/119109776     scaled_normalised_black_and_ln_vega(double, double) [6]
                0.01    0.00 1076013/3173166     erf_cody(double) [26]
-----------------------------------------------
                0.00    0.00      19/45505538     NormalisedBlack [30]
                0.00    0.08 5659631/45505538     lets_be_rational [4]
                0.04    0.57 39845888/45505538     Black [13]
[17]     2.8    0.04    0.65 45505538         normalised_black(double, double) [17]
                0.11    0.30 25780968/49721098     normalised_black_with_optimal_use_of_codys_functions(double, double) [11]
                0.20    0.00 17270076/103783688     asymptotic_expansion_of_scaled_normalised_black(double, double) [8]
                0.02    0.01 2454494/11110528     small_t_expansion_of_scaled_normalised_black(double, double) [23]
-----------------------------------------------
                0.69    0.00 159475020/159475020     erfcx_cody(double) [10]
[18]     2.8    0.69    0.00 159475020         erfcx_cody_above_threshold(double) [18]
-----------------------------------------------
                0.01    0.00  920851/57781196     implied_normalised_volatility_atm(double) [27]
                0.47    0.00 56860345/57781196     lets_be_rational [4]
[19]     2.0    0.48    0.00 57781196         inverse_norm_cdf_for_low_probabilities(double) [19]
-----------------------------------------------
                                                 <spontaneous>
[20]     1.9    0.45    0.00                 ldexp [20]
-----------------------------------------------
                0.16    0.00 39845872/39845872     lets_be_rational [4]
[21]     0.7    0.16    0.00 39845872         convex_rational_cubic_control_parameter_to_fit_second_derivative_at_right_side(double, double, double, double, double, double, double, bool) [21]
-----------------------------------------------
                0.15    0.00 58867631/58867631     lets_be_rational [4]
[22]     0.6    0.15    0.00 58867631         rational_cubic_interpolation(double, double, double, double, double, double, double, double) [22]
-----------------------------------------------
                0.02    0.01 2454494/11110528     normalised_black(double, double) [17]
                0.07    0.03 8656034/11110528     scaled_normalised_black_and_ln_vega(double, double) [6]
[23]     0.6    0.09    0.04 11110528         small_t_expansion_of_scaled_normalised_black(double, double) [23]
                0.04    0.00 11110528/11110528     Yprime(double) [25]
-----------------------------------------------
                0.07    0.00 19021759/19021759     lets_be_rational [4]
[24]     0.3    0.07    0.00 19021759         convex_rational_cubic_control_parameter_to_fit_second_derivative_at_left_side(double, double, double, double, double, double, double, bool) [24]
-----------------------------------------------
                0.04    0.00 11110528/11110528     small_t_expansion_of_scaled_normalised_black(double, double) [23]
[25]     0.2    0.04    0.00 11110528         Yprime(double) [25]
                0.00    0.00  869240/160344260     erfcx_cody(double) [10]
-----------------------------------------------
                0.00    0.00       1/3173166     NormalisedBlack [30]
                0.01    0.00 1076013/3173166     BlackAccuracyFactor [16]
                0.03    0.00 2097152/3173166     Black [13]
[26]     0.2    0.04    0.00 3173166         erf_cody(double) [26]
-----------------------------------------------
                0.02    0.01 3145729/3145729     lets_be_rational [4]
[27]     0.1    0.02    0.01 3145729         implied_normalised_volatility_atm(double) [27]
                0.01    0.00  920851/57781196     inverse_norm_cdf_for_low_probabilities(double) [19]
-----------------------------------------------
                0.02    0.00 56938067/56938067     lets_be_rational [4]
[28]     0.1    0.02    0.00 56938067         inverse_norm_cdf [28]
-----------------------------------------------
                                                 <spontaneous>
[29]     0.1    0.02    0.00                 frexp [29]
-----------------------------------------------
                0.00    0.00      20/20          main [2]
[30]     0.0    0.00    0.00      20         NormalisedBlack [30]
                0.00    0.00      19/45505538     normalised_black(double, double) [17]
                0.00    0.00       1/3173166     erf_cody(double) [26]
-----------------------------------------------
                0.00    0.00       1/4           (anonymous namespace)::this_file_name() [341]
                0.00    0.00       1/4           DLLName [38]
                0.00    0.00       2/4           DLLDirectory [37]
[31]     0.0    0.00    0.00       4         NormalisedImpliedBlackVolatilityForExcel [31]
-----------------------------------------------
                0.00    0.00       1/1           main [2]
[32]     0.0    0.00    0.00       1         Bitness [32]
-----------------------------------------------
                0.00    0.00       1/1           main [2]
[33]     0.0    0.00    0.00       1         BuildConfiguration [33]
-----------------------------------------------
                0.00    0.00       1/1           main [2]
[34]     0.0    0.00    0.00       1         BuildDate [34]
-----------------------------------------------
                0.00    0.00       1/1           main [2]
[35]     0.0    0.00    0.00       1         CPUName [35]
-----------------------------------------------
                0.00    0.00       1/1           main [2]
[36]     0.0    0.00    0.00       1         CompilerVersion [36]
-----------------------------------------------
                0.00    0.00       1/1           main [2]
[37]     0.0    0.00    0.00       1         DLLDirectory [37]
                0.00    0.00       2/4           NormalisedImpliedBlackVolatilityForExcel [31]
-----------------------------------------------
                0.00    0.00       1/1           main [2]
[38]     0.0    0.00    0.00       1         DLLName [38]
                0.00    0.00       1/4           NormalisedImpliedBlackVolatilityForExcel [31]
-----------------------------------------------
                0.00    0.00       1/1           main [2]
[39]     0.0    0.00    0.00       1         Revision [39]
-----------------------------------------------
                0.00    0.00      65/65          main [2]
[262]    0.0    0.00    0.00      65         printf(char const*, ...) [262]
-----------------------------------------------
                0.00    0.00       6/6           main [2]
[263]    0.0    0.00    0.00       6         XLOper::isUndefined() const [263]
-----------------------------------------------

 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

  [32] Bitness                [17] normalised_black(double, double) [15] erfc_cody(double)
  [13] Black                  [18] erfcx_cody_above_threshold(double) [263] XLOper::isUndefined() const
  [16] BlackAccuracyFactor    [22] rational_cubic_interpolation(double, double, double, double, double, double, double, double) [12] __fentry__
  [33] BuildConfiguration     [27] implied_normalised_volatility_atm(double) [5] __logl_internal
  [34] BuildDate               [6] scaled_normalised_black_and_ln_vega(double, double) [7] _mcount_private
  [35] CPUName                [19] inverse_norm_cdf_for_low_probabilities(double) [14] cbrt
  [36] CompilerVersion        [23] small_t_expansion_of_scaled_normalised_black(double, double) [1] exp
  [37] DLLDirectory            [8] asymptotic_expansion_of_scaled_normalised_black(double, double) [29] frexp
  [38] DLLName                [11] normalised_black_with_optimal_use_of_codys_functions(double, double) [28] inverse_norm_cdf
   [3] ImpliedBlackVolatility [25] Yprime(double)         [20] ldexp
  [30] NormalisedBlack       [262] printf(char const*, ...) [4] lets_be_rational
  [31] NormalisedImpliedBlackVolatilityForExcel [24] convex_rational_cubic_control_parameter_to_fit_second_derivative_at_left_side(double, double, double, double, double, double, double, bool) [9] log
  [39] Revision               [21] convex_rational_cubic_control_parameter_to_fit_second_derivative_at_right_side(double, double, double, double, double, double, double, bool) [2] main
  [10] erfcx_cody(double)     [26] erf_cody(double)
