# Sorensen–Dice coefficient

Sorensen–Dice coefficient
You are encouraged to solve this task according to the task description, using any language you may know.

The Sørensen–Dice coefficient, also known as the Sørensen–Dice index (or sdi, or sometimes by one of the individual names: sorensen or dice) is a statistic used to gauge the similarity of two population samples.

The original use was in botany as a measure of similarity between populations of flora and fauna in different areas, but it has uses in other fields as well. It can be used as a text similarity function somewhat similar to the Levenshtein edit distance function, though its characteristics are quite different.

Levenshtein can be useful for spelling correction, but relies on the tested word or phrase being quite similar to the desired one, and can be very slow for long words or phrases.

Sørensen–Dice is more useful for 'fuzzy' matching partial and poorly spelled words or phrases, possibly in improper order.

There are several different methods to tokenize objects for Sørensen–Dice comparisons. The most typical tokenizing scheme for text is to break the words up into bi-grams: groups of two consecutive letters.

For instance, the word 'differ' would be tokenized to the group:

```   di if ff fe er
```

Different implementations may do slightly different transforms. For our purposes, fold case so that all characters are the same case, split words, and ignore white-space, but keep punctuation.

The phrase "Don't Panic!" will be tokenized to the bi-grams:

```   do on n' 't pa an ni ic c!

```

Sørensen–Dice measures the similarity of two groups by dividing twice the intersection token count by the total token count of both groups:

```   SDC = 2 × |A∩B| / (|A| + |B|)
```

where A, B and A∩B are to be understood as multisets, and that if an item, x, has multiplicity a in A and b in B, then it will have multiplicity min(a,b) in A∩B.

The Sørensen–Dice coefficient is thus a ratio between 0.0 and 1.0 giving the "percent similarity" between the two populations.

SDC can by used for spellchecking, but it's not really good at it, especially for short words. Where it really shines is for fuzzy matching of short phrases like book or movie titles. It may not return exactly what you are looking for, but often gets remarkably close with some pretty poor inputs.

• Use the list of Rosetta Code task and draft task names as your "dictionary" to search.
• Using that dictionary, search for the mangled task names: 'Primordial primes', 'Sunkist-Giuliani formula', 'Sieve of Euripides', 'Chowder numbers'.
• Show the search term and the coefficient / match for the five closest, most similar matches.

If there is a built-in or easily, freely available library implementation for Sørensen–Dice coefficient calculations, it is acceptable to use that with a pointer to where it may be obtained.

## C++

Translation of: Wren
```#include <algorithm>
#include <cctype>
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <iterator>
#include <set>
#include <sstream>
#include <string>
#include <vector>

using bigram = std::pair<char, char>;

std::multiset<bigram> bigrams(const std::string& phrase) {
std::multiset<bigram> result;
std::istringstream is(phrase);
std::string word;
while (is >> word) {
for (char& ch : word) {
ch = std::tolower(static_cast<unsigned char>(ch));
}
size_t length = word.size();
if (length == 1) {
result.emplace(word[0], '\0');
} else {
for (size_t i = 0; i + 1 < length; ++i) {
result.emplace(word[i], word[i + 1]);
}
}
}
return result;
}

double sorensen(const std::string& s1, const std::string& s2) {
auto a = bigrams(s1);
auto b = bigrams(s2);
std::multiset<bigram> c;
std::set_intersection(a.begin(), a.end(), b.begin(), b.end(),
std::inserter(c, c.begin()));
return (2.0 * c.size()) / (a.size() + b.size());
}

int main() {
if (!is) {
std::cerr << "Cannot open tasks file.\n";
return EXIT_FAILURE;
}
}
const std::string tests[] = {"Primordial primes",
"Sunkist-Giuliani formula",
"Sieve of Euripides", "Chowder numbers"};
std::vector<std::pair<double, size_t>> sdi(tc);
std::cout << std::fixed;
for (const std::string& test : tests) {
for (size_t i = 0; i != tc; ++i) {
}
std::partial_sort(sdi.begin(), sdi.begin() + 5, sdi.end(),
[](const std::pair<double, size_t>& a,
const std::pair<double, size_t>& b) {
return a.first > b.first;
});
std::cout << test << " >\n";
for (size_t i = 0; i < 5 && i < tc; ++i) {
std::cout << "  " << sdi[i].first << ' ' << tasks[sdi[i].second]
<< '\n';
}
std::cout << '\n';
}
return EXIT_SUCCESS;
}
```
Output:
```Primordial primes >
0.685714 Sequence of primorial primes
0.666667 Factorial primes
0.571429 Primorial numbers
0.545455 Prime words
0.521739 Almost prime

Sunkist-Giuliani formula >
0.565217 Almkvist-Giullera formula for pi
0.378378 Faulhaber's formula
0.342857 Haversine formula
0.333333 Check Machin-like formulas
0.307692 Resistance calculator

Sieve of Euripides >
0.461538 Four sides of square
0.461538 Sieve of Pritchard
0.413793 Sieve of Eratosthenes
0.400000 Piprimes
0.384615 Sierpinski curve

Chowder numbers >
0.782609 Chowla numbers
0.640000 Powerful numbers
0.608696 Rhonda numbers
0.608696 Fermat numbers
0.600000 Lah numbers

```

## J

Tentative implementation:

```TASKS=: fread '~/tasks.txt' NB. from Sorensen–Dice_coefficient/Tasks
sdtok=: [: (#~  ' '*/ .~:~])2]\ 7 u: tolower@rplc&(LF,' ')
sdinter=: {{
all=. ~.x,y
X=. <:#/.~all,x
Y=. <:#/.~all,y
+/X<.Y
}}
sdunion=: #@,
SDC=: (2 * sdinter % sdunion)&sdtok S:0
nearest=: {{ m{.\:~ x (] ;"0~ SDC) cutLF y }}
fmt=: ((8j6": 0{::]),' ',1{::])"1
```

The trick here is the concept of "intersection" which we must use. We can't use set intersection -- the current draft task description suggests that `SDI = 2 × (A ∩ B) / (A ⊎ B)` produces a number between 0 and 1. Because we're using division to produce this number, we must be using cardinality of the intersection rather than the intersection itself. But if A and B are sets, each containing the same tokens, the result here using cardinality of sets would be 2 rather than 1.

Instead, we treat A and B as sequences of tokens (so repeated copies of a token are distinct), for the cardinality of the intersection we count the number of times that each token appears in either A and in B and sum the minimum of the two counts. (So, tokens which only appear in A count 0 times, for example, where a token which appears 3 times in A and 2 times in B would contribute 2 to the sum.)

With this implementation, here's the task examples:

```   fmt 'Primordial prime' 5 nearest TASKS
0.647059 Sequence of primorial primes
0.615385 Factorial primes
0.592593 Primorial numbers
0.571429 Prime words
0.545455 Almost prime
fmt 'Sunkist-Giuliani formula' 5 nearest TASKS
0.565217 Almkvist-Giullera formula for pi
0.378378 Faulhaber's formula
0.342857 Haversine formula
0.333333 Check Machin-like formulas
0.307692 Resistance calculator
fmt 'Sieve of Euripides' 5 nearest TASKS
0.461538 Sieve of Pritchard
0.461538 Four sides of square
0.413793 Sieve of Eratosthenes
0.400000 Piprimes
0.384615 Sierpinski curve
fmt 'Chowder numbers' 5 nearest TASKS
0.782609 Chowla numbers
0.640000 Powerful numbers
0.608696 Rhonda numbers
0.608696 Fermat numbers
0.600000 Lah numbers     ```

## Java

```import java.io.IOException;
import java.nio.charset.StandardCharsets;
import java.nio.file.Files;
import java.nio.file.Path;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public final class SorensenDiceCoefficient {

public static void main(String[] args) throws IOException {

List<String> tests = List.of(
"Primordial primes", "Sunkist-Giuliani formula", "Sieve of Euripides", "Chowder numbers" );

for ( String test : tests ) {
Map<String, Integer> bigramsTest = createBigrams(test);
}

Collections.sort(taskValues, (one, two) -> Double.compare(two.value, one.value));

System.out.println(test + ":");
for ( int i = 0; i < 5; i++ ) {
System.out.println(String.format("%s%.4f%s%s",
}
System.out.println();
}
}

private static double sorensenDice(Map<String, Integer> bigramsOne, Map<String, Integer> bigramsTwo) {
int intersectionSize = 0;
for ( Map.Entry<String, Integer> entry : bigramsOne.entrySet() ) {
if ( bigramsTwo.keySet().contains(entry.getKey()) ) {
intersectionSize += Math.min(entry.getValue(), bigramsTwo.get(entry.getKey()));
}
}
return 2.0 * intersectionSize / ( size(bigramsOne) + size(bigramsTwo) );
}

private static Map<String, Integer> createBigrams(String text) {
Map<String, Integer> result = new HashMap<String, Integer>();
for ( String word : text.toLowerCase().split(" ") ) {
if ( word.length() == 1 ) {
result.merge(word, 1, Integer::sum);
} else {
for ( int i = 0; i < word.length() - 1; i++ ) {
result.merge(word.substring(i, i + 2), 1, Integer::sum);
}
}
}
return result;
}

private static int size(Map<String, Integer> map) {
return map.values().stream().mapToInt(Integer::intValue).sum();
}

}
```
Output:
```Primordial primes:
0.6857 Sequence of primorial primes
0.6667 Factorial primes
0.5714 Primorial numbers
0.5455 Prime words
0.5217 Almost prime

Sunkist-Giuliani formula:
0.5652 Almkvist-Giullera formula for pi
0.3784 Faulhaber's formula
0.3429 Haversine formula
0.3333 Check Machin-like formulas
0.3077 Resistance calculator

Sieve of Euripides:
0.4615 Four sides of square
0.4615 Sieve of Pritchard
0.4138 Sieve of Eratosthenes
0.4000 Piprimes
0.3846 Sierpinski curve

Chowder numbers:
0.7826 Chowla numbers
0.6400 Powerful numbers
0.6087 Fermat numbers
0.6087 Rhonda numbers
0.6000 Lah numbers
```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

Works with jaq, the Rust implementation of jq

```### Generic preliminaries

def count(s): reduce s as \$x (0; .+1);

def lpad(\$len): tostring | (\$len - length) as \$l | (" " * \$l) + .;

# Emit the count of the common items in the two given sorted arrays
# viewed as multisets
def count_commonality_of_multisets(\$A; \$B):
# Returns a stream of the common elements
def pop:
.[0] as \$i
| .[1] as \$j
| if \$i == (\$A|length) or \$j == (\$B|length) then empty
elif \$A[\$i] == \$B[\$j] then 1, ([\$i+1, \$j+1] | pop)
elif \$A[\$i] <  \$B[\$j] then [\$i+1, \$j] | pop
else [\$i, \$j+1] | pop
end;
count([0,0] | pop);

# Emit an array of the normalized bigrams of the input string
def bigrams:
# Emit a stream of the bigrams of the input string blindly
def bg: . as \$in | range(0;length-1 ) | \$in[.:.+2];
ascii_downcase | [splits("  *") | bg];

### The Sorensen-Dice coefficient

def sorensen(\$a; \$b):
(\$a | bigrams | sort) as \$A
| (\$b | bigrams | sort) as \$B
| 2 * count_commonality_of_multisets(\$A; \$B) / ((\$A|length) + (\$B|length));

### Exercises

def exercises:
"Primordial primes",
"Sunkist-Giuliani formula",
"Sieve of Euripides",
"Chowder numbers"
;

[inputs] as \$phrases
| exercises as \$test
| [ range(0; \$phrases|length) as \$i
| [sorensen(\$phrases[\$i]; \$test), \$phrases[\$i] ] ]
| sort_by(first)
| .[-5:]
| reverse
| "\(\$test) >",
""```
Output:

Invocation: jq -nrR -f sorensen-dice-coefficient.jq rc_tasks_2022_09_24.txt

```Primordial primes >
0.68  Sequence of primorial primes
0.66  Factorial primes
0.57  Primorial numbers
0.54  Prime words
0.52  Almost prime

Sunkist-Giuliani formula >
0.56  Almkvist-Giullera formula for pi
0.37  Faulhaber's formula
0.34  Haversine formula
0.33  Check Machin-like formulas
0.30  Resistance calculator

Sieve of Euripides >
0.46  Sieve of Pritchard
0.46  Four sides of square
0.41  Sieve of Eratosthenes
0.4  Piprimes
0.38  Sierpinski curve

Chowder numbers >
0.78  Chowla numbers
0.64  Powerful numbers
0.60  Rhonda numbers
0.60  Fermat numbers
0.6  Lah numbers
```

## Julia

```using Multisets

""" convert a phrase into a count of bigram tokens of its words """
function tokenizetext(txt)
tokens = Multiset{String}()
words = split(lowercase(txt), r"\s+")
for w in words
a = collect(w)
if length(a) < 3
push!(tokens, w)
else
for i in 1:length(a)-1
push!(tokens, String(a[i:i+1]))
end
end
end
end

""" Sorenson-Dice similarity of multisets """
function sorenson_dice(text1, text2)
bc1, bc2 = tokenizetext(text1), tokenizetext(text2)
return 2 * length(bc1 ∩ bc2) / (length(bc1) + length(bc2))
end

# run tests
for test in ["Primordial primes", "Sunkist-Giuliani formula",
"Sieve of Euripides", "Chowder numbers"]
taskvalues = sort!([(sorenson_dice(test, t), t) for t in alltasks], rev = true)
println("\n\$test:")
end
end
```
Output:
```Primordial primes:
0.6855  Sequence of primorial primes
0.6665  Factorial primes
0.5713  Primorial numbers
0.5454  Prime words
0.522  Almost prime

Sunkist-Giuliani formula:
0.5654  Almkvist-Giullera formula for pi
0.3784  Faulhaber's formula
0.3428  Haversine formula
0.3333  Check Machin-like formulas
0.3076  Resistance calculator

Sieve of Euripides:
0.4614  Sieve of Pritchard
0.4614  Four sides of square
0.4138  Sieve of Eratosthenes
0.4  Piprimes
0.3845  Sierpinski curve

Chowder numbers:
0.7827  Chowla numbers
0.64  Powerful numbers
0.609  Rhonda numbers
0.609  Fermat numbers
0.6  Lah numbers
```

## Nim

```import std/[algorithm, strutils, sugar, tables]

func bigrams(text: string): CountTable[string] =
## Extract the bigrams from a text.
for word in text.toLower.split(' '):
if word.len == 1:
result.inc(word)
else:
for i in 0..(word.len - 2):
result.inc(word[i..(i+1)])

func intersectionCount(a, b: CountTable[string]): int =
## Compute the cardinal of the intersection of two
## count tables.
for key, count in a:
if key in b:
inc result, min(count, b[key])

func card(a: CountTable[string]): int =
## Return the cardinal of a count table (i.e. the sum of counts).
for count in a.values:
inc result, count

func sorensenDice(text1, text2: string): float =
## Compute the Sorensen-dice coefficient of "text1" and "text2".
let ct1 = text1.bigrams
let ct2 = text2.bigrams
result = 2 * intersectionCount(ct1, ct2) / (ct1.card + ct2.card)

# Build the list of tasks.
for line in lines("Sorensen-Dice.txt"):
line

const Tests = ["Primordial primes", "Sunkist-Giuliani formula",
"Sieve of Euripides", "Chowder numbers"]

for test in Tests:
echo test
var scores: seq[(float, string)]
scores.sort(Descending)
for i in 0..4:
echo "  ", scores[i][0].formatFloat(ffDecimal, 6), ' ', scores[i][1]
echo()
```
Output:
```Primordial primes
0.685714 Sequence of primorial primes
0.666667 Factorial primes
0.571429 Primorial numbers
0.545455 Prime words
0.521739 Almost prime

Sunkist-Giuliani formula
0.565217 Almkvist-Giullera formula for pi
0.378378 Faulhaber's formula
0.342857 Haversine formula
0.333333 Check Machin-like formulas
0.307692 Resistance calculator

Sieve of Euripides
0.461538 Sieve of Pritchard
0.461538 Four sides of square
0.413793 Sieve of Eratosthenes
0.400000 Piprimes
0.384615 Sierpinski curve

Chowder numbers
0.782609 Chowla numbers
0.640000 Powerful numbers
0.608696 Rhonda numbers
0.608696 Fermat numbers
0.600000 Lah numbers
```

## Perl

```use v5.036;
use Path::Tiny;

sub bi_gram {
my \$line = lc shift;
uniq map { substr \$line,\$_,2 } 0..length(\$line)-2;
}

sub score {
my(\$phrase, \$word) = @_;
my %count;
my @match = bi_gram \$phrase;
\$count{\$_}++ for @match, @\$word;
2 * (grep { \$count{\$_} > 1 } keys %count) / (@match + @\$word);
}

sub sorensen {
my(\$dict,\$word,\$cutoff) = @_; \$cutoff //= 0.00;
my(%matches,\$s);
(\$s = score(\$word, \$\$dict{\$_})) > \$cutoff and \$matches{\$_} = \$s for keys %\$dict;
%matches;
}

my %dict = map { \$_ => [ bi_gram(\$_) ] } path('ref/Sorensen-Dice-Tasks.txt')->slurp =~ /.{10,}/gm;

for my \$word ( ('Primordial primes', 'Sunkist-Giuliani formula', 'Sieve of Euripides', 'Chowder numbers') ) {
my(%scored,@ranked);
%scored = sorensen(\%dict,\$word);
push @ranked, sprintf "%.3f \$_", \$scored{\$_} for sort { \$scored{\$b} <=> \$scored{\$a} || \$a cmp \$b } keys %scored;
say "\n\$word:\n" . join("\n", head 5, @ranked);
}
```
Output:
```Primordial primes:
0.741 Factorial primes
0.629 Sequence of primorial primes
0.583 Almost prime
0.581 Next special primes
0.571 Pandigital prime

Sunkist-Giuliani formula:
0.542 Almkvist-Giullera formula for pi
0.368 Haversine formula
0.359 Faulhaber's formula
0.348 Check Machin-like formulas
0.303 FASTA format

Sieve of Euripides:
0.541 Sieve of Eratosthenes
0.529 Sieve of Pritchard
0.457 Four sides of square
0.457 The sieve of Sundaram
0.387 Sum of a series

Chowder numbers:
0.769 Chowla numbers
0.615 Rhonda numbers
0.609 Bell numbers
0.609 Lah numbers
0.593 Kaprekar numbers```

## Phix

```with javascript_semantics
function bigram(string s)
sequence words = split(lower(s)),
res = {}
for word in words do
for i=1 to length(word)-1 do
res = append(res,word[i..i+1])
end for
end for
res = sort(res)
return res
end function

function intrasect(sequence s1, s2)
integer l1 = length(s1),
l2 = length(s2),
i1 = 1, i2 = 1,
res = 0
while i1<=l1 and i2<=l2 do
integer c = compare(s1[i1],s2[i2])
res += (c=0)
i1 += (c<=0)
i2 += (c>=0)
end while
return res
end function

procedure test(string s, sequence dictionary)
sequence scores = {},
s1 = bigram(s)
for phrase in dictionary do
sequence s2 = bigram(phrase)
scores &= 2*intrasect(s1,s2)/(length(s1)+length(s2))
end for
printf(1,"%s >\n",s)
sequence tags = reverse(custom_sort(scores,tagset(length(scores)))[-5..-1])
for t in tags do
printf(1,"%f %s\n",{scores[t],dictionary[t]})
end for
printf(1,"\n")
end procedure

constant tests = split("""
Primordial primes
Sunkist-Giuliani formula
Sieve of Euripides
Chowder numbers
""",'\n'),
Almkvist-Giullera formula for pi
Almost prime
Check Machin-like formulas
Chowla numbers
Factorial primes
Faulhaber's formula
Fermat numbers
Four sides of square
Haversine formula
Lah numbers
Piprimes
Powerful numbers
Prime words
Primorial numbers
Resistance calculator
Rhonda numbers
Sequence of primorial primes
Sierpinski curve
Sieve of Eratosthenes
Sieve of Pritchard
""",'\n')
```
Output:

Extending the task list to the full 1577 entries changes nothing.

```Primordial primes >
0.685714 Sequence of primorial primes
0.666667 Factorial primes
0.571429 Primorial numbers
0.545455 Prime words
0.521739 Almost prime

Sunkist-Giuliani formula >
0.565217 Almkvist-Giullera formula for pi
0.378378 Faulhaber's formula
0.342857 Haversine formula
0.333333 Check Machin-like formulas
0.307692 Resistance calculator

Sieve of Euripides >
0.461538 Sieve of Pritchard
0.461538 Four sides of square
0.413793 Sieve of Eratosthenes
0.400000 Piprimes
0.384615 Sierpinski curve

Chowder numbers >
0.782609 Chowla numbers
0.640000 Powerful numbers
0.608696 Rhonda numbers
0.608696 Fermat numbers
0.600000 Lah numbers
```

## Python

Of the several Python string similarity libraries implementing Sorenson-Dice similarity, none give the same results as the original example's Raku library, so this was imitated using Multisets, as per the C++ and Wren examples.

```''' Rosetta Code task rosettacode.org/wiki/Sorensenâ€“Dice_coefficient '''

from multiset import Multiset

def tokenizetext(txt):
''' convert a phrase into a count of bigram tokens of its words '''
arr = []
for wrd in txt.lower().split(' '):
arr += ([wrd] if len(wrd) == 1 else [wrd[i:i+2]
for i in range(len(wrd)-1)])
return Multiset(arr)

def sorenson_dice(text1, text2):
''' Sorenson-Dice similarity of Multisets '''
bc1, bc2 = tokenizetext(text1), tokenizetext(text2)
return 2 * len(bc1 & bc2) / (len(bc1) + len(bc2))

for testtext in ['Primordial primes', 'Sunkist-Giuliani formula',
'Sieve of Euripides', 'Chowder numbers']:
print(f'\n{testtext}:')
```
Output:
```Primordial primes:
0.685714  Sequence of primorial primes
0.666667  Factorial primes
0.571429  Primorial numbers
0.545455  Prime words
0.521739  Almost prime

Sunkist-Giuliani formula:
0.565217  Almkvist-Giullera formula for pi
0.378378  Faulhaber's formula
0.342857  Haversine formula
0.333333  Check Machin-like formulas
0.307692  Resistance calculator

Sieve of Euripides:
0.461538  Sieve of Pritchard
0.461538  Four sides of square
0.413793  Sieve of Eratosthenes
0.400000  Piprimes
0.384615  Sierpinski curve

Chowder numbers:
0.782609  Chowla numbers
0.640000  Powerful numbers
0.608696  Rhonda numbers
0.608696  Fermat numbers
0.600000  Lah numbers
```

## Raku

Using the library Text::Sorensen from the Raku ecosystem.

See the Raku entry for Text completion for a bespoke implementation of Sorenson-Dice. (Which is very similar to the library implementation.)

```use Text::Sorensen :sdi;

say "\n\$_ >\n" ~ .&fuzzy-search for
'Primordial primes',
'Sunkist-Giuliani formula',
'Sieve of Euripides',
'Chowder numbers';
```
Output:
```Primordial primes >
0.685714 Sequence of primorial primes
0.666667 Factorial primes
0.571429 Primorial numbers
0.545455 Prime words
0.521739 Almost prime

Sunkist-Giuliani formula >
0.565217 Almkvist-Giullera formula for pi
0.378378 Faulhaber's formula
0.342857 Haversine formula
0.333333 Check Machin-like formulas
0.307692 Resistance calculator

Sieve of Euripides >
0.461538 Four sides of square
0.461538 Sieve of Pritchard
0.413793 Sieve of Eratosthenes
0.4 Piprimes
0.384615 Sierpinski curve

Chowder numbers >
0.782609 Chowla numbers
0.64 Powerful numbers
0.608696 Fermat numbers
0.608696 Rhonda numbers
0.6 Lah numbers```

## Wren

Library: Wren-str
Library: Wren-set
Library: Wren-fmt

This assumes that a one letter word is treated as a bigram. It also assumes that all bigrams are matched whether duplicates or not.

The results on this basis are the same as the Raku example.

```import "io" for File
import "./str" for Str
import "./set" for Bag
import "./fmt" for Fmt

var bigrams = Fn.new { |phrase|
var words = Str.splitNoEmpty(phrase, " ")
var res = []
for (word in words) {
var chars = Str.lower(word).toList
if (chars.count == 1) {
} else {
for (i in 0...chars.count-1) {
}
}
}
return res
}

var sorensen = Fn.new { |a, b|
var abi = Bag.new(bigrams.call(a))
var bbi = Bag.new(bigrams.call(b))
var common = abi.intersect(bbi)
return 2 * common.count / (abi.count + bbi.count)
}

var fileName = "rc_tasks_2022_09_24.txt"  // local copy
var tests = [
"Primordial primes", "Sunkist-Giuliani formula", "Sieve of Euripides", "Chowder numbers"
]
var sdis = List.filled(tc, null)
for (test in tests) {
var top5 = sdis.sort { |e1, e2| e1[1] >= e2[1] }.take(5).toList
System.print("%(test) >")
for (e in top5) Fmt.print("  \$f \$s", e[1], e[0])
System.print()
}
```
Output:
```Primordial primes >
0.685714 Sequence of primorial primes
0.666667 Factorial primes
0.571429 Primorial numbers
0.545455 Prime words
0.521739 Almost prime

Sunkist-Giuliani formula >
0.565217 Almkvist-Giullera formula for pi
0.378378 Faulhaber's formula
0.342857 Haversine formula
0.333333 Check Machin-like formulas
0.307692 Resistance calculator

Sieve of Euripides >
0.461538 Four sides of square
0.461538 Sieve of Pritchard
0.413793 Sieve of Eratosthenes
0.400000 Piprimes
0.384615 Sierpinski curve

Chowder numbers >
0.782609 Chowla numbers
0.640000 Powerful numbers
0.608696 Fermat numbers
0.608696 Rhonda numbers
0.600000 Lah numbers
```