٭٭٭٭٭ Report ٭٭٭٭٭

٭ User input
# 2021.12.16
# AmirHosein Sadeghimanesh
# 
# The goal is to apply Lemma 5.2 of the superlevel set paper to conclude
# that with probability one, the rectangle [2, 2.5] * [2.5, 3] in Figure
# 3c of the Kac-Rice paper (the arXiv version) which has average number
# of solutions equal to 2 is not a rectangle that almost all of it is
# inside the region with 2 solutions, but instead has non-zero measure 
# intersections with regions of different number of solutions.
#
Task: MCKR integrate
Save_location: ./
Save_name: File_20211216_testing_Lemma_5_2_output_3
MCKR_file_name: Kac_Rice_Example_2_3_normal
Box: [2,2.5,2.25,0.1],[2,3,2.5,0.1]
MC_method: Antithetic
Sample_size: 10^9
Include standard error
Include integration time
Include cpu information
Include memory information
٭ End of input.

٭ Main computations.

Consider the Antithetic Monte Carlo integration for the Kac_Rice_Example_2_3_normal example on the box
[[2.0, 2.5, 2.25, 0.1], [2.0, 3.0, 2.5, 0.1]]
and N=1000000000.

I-hat = 2.97879402559404, e-hat = 0.004560553725957775, integration time = 296.4538743 seconds

٭ End of computations.

٭ Information of cpus of the computing system.
This system has 12 cpus.
Base.Sys.CPUinfo[Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    1540312            0      3453531    140274015      1463296  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz     990046            0       807453    143470140        51281  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    4912984            0      2991781    137362906        33703  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    1760796            0       851640    142655218         9921  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    3157515            0      2460046    139650093        27421  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    1060656            0       623750    143583250         6218  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    2058828            0      1347203    141861625        21484  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    1320140            0       915218    143032296        10828  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    1485312            0      1035515    142746828        14921  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    1590531            0       976921    142700187        15718  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    1650625            0      1100328    142516703        19859  ticks, Intel(R) Core(TM) i7-10850H CPU @ 2.70GHz: 
        speed         user         nice          sys         idle          irq
     2712 MHz    1125546            0       592937    143549156        11343  ticks]

٭ Information about the memory.
The total memory is 63.60728454589844 GB.
The free memory before compiling the task was 53.498435974121094 GB.
