formatting pass, upkeep
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@ -15,8 +15,16 @@ int main()
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int n_dists = 4;
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// These are nested functions. They will not compile without gcc.
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double sample_0(uint64_t * seed) { UNUSED(seed); return 0; }
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double sample_1(uint64_t * seed) { UNUSED(seed); return 1; }
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double sample_0(uint64_t * seed)
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{
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UNUSED(seed);
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return 0;
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}
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double sample_1(uint64_t * seed)
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{
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UNUSED(seed);
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return 1;
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}
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double sample_few(uint64_t * seed) { return sample_to(1, 3, seed); }
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double sample_many(uint64_t * seed) { return sample_to(2, 10, seed); }
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BIN
examples/core/06_dissolving_fermi_paradox/example
Executable file
BIN
examples/core/06_dissolving_fermi_paradox/example
Executable file
Binary file not shown.
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@ -1,11 +1,11 @@
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#include "../squiggle.h"
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// #include "../squiggle_more.h"
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#include "../../../squiggle.h"
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#include <math.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <stdlib.h>
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double sample_loguniform(double a, double b, uint64_t* seed){
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double sample_loguniform(double a, double b, uint64_t* seed)
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{
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return exp(sample_uniform(log(a), log(b), seed));
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}
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@ -16,10 +16,11 @@ int main()
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// set randomness seed
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uint64_t* seed = malloc(sizeof(uint64_t));
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*seed = UINT64_MAX/64; // xorshift can't start with a seed of 0
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*seed = UINT64_MAX / 64; // xorshift can't start with a seed of 0
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double sample_fermi_naive(uint64_t* seed){
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double rate_of_star_formation = sample_loguniform(1,100, seed);
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double sample_fermi_naive(uint64_t * seed)
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{
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double rate_of_star_formation = sample_loguniform(1, 100, seed);
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double fraction_of_stars_with_planets = sample_loguniform(0.1, 1, seed);
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double number_of_habitable_planets_per_star_system = sample_loguniform(0.1, 1, seed);
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double rate_of_life_formation_in_habitable_planets = sample_lognormal(1, 50, seed);
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@ -41,34 +42,29 @@ int main()
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// Expected number of civilizations in the Milky way;
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// see footnote 3 (p. 5)
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double n = rate_of_star_formation *
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fraction_of_stars_with_planets *
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number_of_habitable_planets_per_star_system *
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fraction_of_habitable_planets_in_which_any_life_appears *
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fraction_of_planets_with_life_in_which_intelligent_life_appears *
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fraction_of_intelligent_planets_which_are_detectable_as_such *
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longevity_of_detectable_civilizations;
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double n = rate_of_star_formation * fraction_of_stars_with_planets * number_of_habitable_planets_per_star_system * fraction_of_habitable_planets_in_which_any_life_appears * fraction_of_planets_with_life_in_which_intelligent_life_appears * fraction_of_intelligent_planets_which_are_detectable_as_such * longevity_of_detectable_civilizations;
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return n;
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}
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double sample_fermi_paradox_naive(uint64_t* seed){
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double sample_fermi_paradox_naive(uint64_t * seed)
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{
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double n = sample_fermi_naive(seed);
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return ((n > 1) ? 1 : 0);
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}
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double n = 1000000;
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double naive_fermi_proportion = 0;
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for(int i=0; i<n; i++){
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for (int i = 0; i < n; i++) {
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double result = sample_fermi_paradox_naive(seed);
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// printf("result: %lf\n", result);
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naive_fermi_proportion+=result;
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naive_fermi_proportion += result;
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}
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printf("Naïve %% that we are not alone: %lf\n", naive_fermi_proportion/n);
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printf("Naïve %% that we are not alone: %lf\n", naive_fermi_proportion / n);
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// Thinking in log space
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double sample_fermi_logspace(uint64_t* seed){
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double sample_fermi_logspace(uint64_t * seed)
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{
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double log_rate_of_star_formation = sample_uniform(log(1), log(100), seed);
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double log_fraction_of_stars_with_planets = sample_uniform(log(0.1), log(1), seed);
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double log_number_of_habitable_planets_per_star_system = sample_uniform(log(0.1), log(1), seed);
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@ -83,13 +79,7 @@ int main()
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// printf(" log_fraction_of_intelligent_planets_which_are_detectable_as_such = %lf\n", log_fraction_of_intelligent_planets_which_are_detectable_as_such);
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// printf(" log_longevity_of_detectable_civilizations = %lf\n", log_longevity_of_detectable_civilizations);
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double log_n1 =
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log_rate_of_star_formation +
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log_fraction_of_stars_with_planets +
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log_number_of_habitable_planets_per_star_system +
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log_fraction_of_planets_with_life_in_which_intelligent_life_appears +
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log_fraction_of_intelligent_planets_which_are_detectable_as_such +
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log_longevity_of_detectable_civilizations;
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double log_n1 = log_rate_of_star_formation + log_fraction_of_stars_with_planets + log_number_of_habitable_planets_per_star_system + log_fraction_of_planets_with_life_in_which_intelligent_life_appears + log_fraction_of_intelligent_planets_which_are_detectable_as_such + log_longevity_of_detectable_civilizations;
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// printf("first part of calculation: %lf\n", log_n1);
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/* Consider fraction_of_habitable_planets_in_which_any_life_appears separately.
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@ -125,9 +115,9 @@ int main()
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// printf("log_rate_of_life_formation_in_habitable_planets: %lf\n", log_rate_of_life_formation_in_habitable_planets);
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double log_fraction_of_habitable_planets_in_which_any_life_appears;
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if(log_rate_of_life_formation_in_habitable_planets < -32){
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if (log_rate_of_life_formation_in_habitable_planets < -32) {
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log_fraction_of_habitable_planets_in_which_any_life_appears = log_rate_of_life_formation_in_habitable_planets;
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} else{
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} else {
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double rate_of_life_formation_in_habitable_planets = exp(log_rate_of_life_formation_in_habitable_planets);
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double fraction_of_habitable_planets_in_which_any_life_appears = -expm1(-rate_of_life_formation_in_habitable_planets);
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log_fraction_of_habitable_planets_in_which_any_life_appears = log(fraction_of_habitable_planets_in_which_any_life_appears);
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@ -139,19 +129,19 @@ int main()
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return log_n;
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}
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double sample_fermi_paradox_logspace(uint64_t* seed){
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double sample_fermi_paradox_logspace(uint64_t * seed)
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{
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double n = sample_fermi_logspace(seed);
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return ((n > 0) ? 1 : 0);
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}
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double logspace_fermi_proportion = 0;
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for(int i=0; i<n; i++){
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for (int i = 0; i < n; i++) {
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double result = sample_fermi_paradox_logspace(seed);
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// printf("result: %lf\n", result);
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logspace_fermi_proportion+=result;
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logspace_fermi_proportion += result;
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}
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printf("Using more accurate logspace computations, %% that we are not alone: %lf\n", logspace_fermi_proportion/n);
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double result2;
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printf("Using more accurate logspace computations, %% that we are not alone: %lf\n", logspace_fermi_proportion / n);
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free(seed);
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}
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Binary file not shown.
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@ -1,5 +1,5 @@
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#include "../squiggle.h"
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#include "../squiggle_more.h"
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// #include "../squiggle_more.h"
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#include <math.h>
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#include <stdint.h>
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#include <stdio.h>
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@ -7,16 +7,18 @@
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double sample_loguniform(double a, double b, uint64_t* seed){
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return exp(sample_uniform(log(a), log(b), seed));
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}
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int main()
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{
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// Replicate <https://arxiv.org/pdf/1806.02404.pdf>, and in particular the red line in page 11.
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// Could also be interesting to just produce and save many samples.
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// set randomness seed
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uint64_t* seed = malloc(sizeof(uint64_t));
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*seed = UINT64_MAX/64; // xorshift can't start with a seed of 0
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double fermi_naive(uint64_t* seed){
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double sample_fermi_naive(uint64_t* seed){
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double rate_of_star_formation = sample_loguniform(1,100, seed);
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double fraction_of_stars_with_planets = sample_loguniform(0.1, 1, seed);
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double number_of_habitable_planets_per_star_system = sample_loguniform(0.1, 1, seed);
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return n;
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}
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double fermi_paradox_naive(uint64_t* seed){
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double n = fermi_naive(seed);
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return (n > 1 ? 1 : 0);
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double sample_fermi_paradox_naive(uint64_t* seed){
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double n = sample_fermi_naive(seed);
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return ((n > 1) ? 1 : 0);
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}
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double result;
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for(int i=0; i<1000; i++){
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result = fermi_naive(seed);
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printf("result from fermi_naive: %lf\n", result);
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printf("\n\n");
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double n = 1000000;
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double naive_fermi_proportion = 0;
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for(int i=0; i<n; i++){
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double result = sample_fermi_paradox_naive(seed);
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// printf("result: %lf\n", result);
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naive_fermi_proportion+=result;
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}
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printf("result from naïve implementation: %lf\n", result);
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printf("Naïve %% that we are not alone: %lf\n", naive_fermi_proportion/n);
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// Thinking in log space
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double fermi_logspace(uint64_t* seed){
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double sample_fermi_logspace(uint64_t* seed){
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double log_rate_of_star_formation = sample_uniform(log(1), log(100), seed);
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double log_fraction_of_stars_with_planets = sample_uniform(log(0.1), log(1), seed);
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double log_number_of_habitable_planets_per_star_system = sample_uniform(log(0.1), log(1), seed);
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log_fraction_of_planets_with_life_in_which_intelligent_life_appears +
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log_fraction_of_intelligent_planets_which_are_detectable_as_such +
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log_longevity_of_detectable_civilizations;
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printf("first part of calculation: %lf\n", log_n1);
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// printf("first part of calculation: %lf\n", log_n1);
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/* Consider fraction_of_habitable_planets_in_which_any_life_appears separately.
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Imprecisely, we could do:
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@ -110,14 +114,15 @@ int main()
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Turns out there is!
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Looking at the Taylor expansion for c = 1 - exp(-b), it's b - b^2/2 + b^3/6 - x^b/24, etc.
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When b ~ 0 (as it is), this is close to b.
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// https://www.wolframalpha.com/input?i=1-exp%28-x%29
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When b ~ 0 (as is often the case), this is close to b.
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But now, if b ~ 0
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c ~ b
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and d = log(c) ~ log(b) = log(exp(a)) = a
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*/
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double log_rate_of_life_formation_in_habitable_planets = sample_normal(1, 50, seed);
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printf("log_rate_of_life_formation_in_habitable_planets: %lf\n", log_rate_of_life_formation_in_habitable_planets);
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// printf("log_rate_of_life_formation_in_habitable_planets: %lf\n", log_rate_of_life_formation_in_habitable_planets);
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double log_fraction_of_habitable_planets_in_which_any_life_appears;
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if(log_rate_of_life_formation_in_habitable_planets < -32){
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double fraction_of_habitable_planets_in_which_any_life_appears = -expm1(-rate_of_life_formation_in_habitable_planets);
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log_fraction_of_habitable_planets_in_which_any_life_appears = log(fraction_of_habitable_planets_in_which_any_life_appears);
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}
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printf(" log_fraction_of_habitable_planets_in_which_any_life_appears: %lf\n", log_fraction_of_habitable_planets_in_which_any_life_appears);
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// printf(" log_fraction_of_habitable_planets_in_which_any_life_appears: %lf\n", log_fraction_of_habitable_planets_in_which_any_life_appears);
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double log_n = log_n1 + log_fraction_of_habitable_planets_in_which_any_life_appears;
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return log_n;
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}
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double result2;
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/*
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for(int i=0; i<1000; i++){
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result2 = fermi_logspace(seed);
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printf("result from logspace implementation: %lf.2\n", result2);
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printf("\n\n");
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double sample_fermi_paradox_logspace(uint64_t* seed){
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double n = sample_fermi_logspace(seed);
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return ((n > 0) ? 1 : 0);
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}
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*/
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double logspace_fermi_proportion = 0;
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for(int i=0; i<n; i++){
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double result = sample_fermi_paradox_logspace(seed);
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// printf("result: %lf\n", result);
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logspace_fermi_proportion+=result;
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}
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printf("Using more accurate logspace computations, %% that we are not alone: %lf\n", logspace_fermi_proportion/n);
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double result2;
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free(seed);
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}
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