# There can be only 1!

Your task is, given a positive integer n, to generate an expression that equals the number n.

The catch is: you're only allowed the number 1 in the output.

The operators at your disposal are:

• +, -, * and /
• / is floating-point division (so 5/2 = 2.5).
• sqrt (as s)
• ceil and floor (as c and f respectively)
• ! (factorial)
• The factorial, in this case, only works for positive integers.

You are also allowed to stack 1's together, so something like 11 is acceptable in the output. However, they count as the same number of 1's that's in the number (so 11 counts as 2 1's).

You must also include brackets in the output, so that the expression in the output, when executed through the order of operations, will result in the input. They do not count as operations, though.

## Examples:

• Input = 24, one possible output = (1+1+1+1)!
• Input = 11, one possible output = 11
• Input = 5, one possible output = c(s((1+1+1+1)!))
• The ceiling of the square root of 24 is 5.

## Rules:

• You are guaranteed that the input is a positive integer from 1 to 2^31-1.
• Your program must work for any positive integer up to 2^31-1, even if they are not tested.
• Your program must finish processing all outputs for all numbers in the set in 1 hour.
• The results for every run of the program must be exactly the same - also, no seeds.
• You are only allowed to hardcode the expressions for a maximum of 10 numerical values.
• You are not allowed to have imaginary numbers anywhere in the output (so no s(some negative number)).
• You are also not allowed to have numbers larger than 2^31-1 or smaller than -2^31+1 anywhere in the output, even when they are sqrted or /ed (so no (((1+1+1)!)!)! or ((1+1+1+1)!)!).

## Set of Numbers:

945536, 16878234, 32608778, 42017515, 48950830, 51483452, 52970263, 54278649, 63636656, 78817406, 89918907, 90757642, 95364861, 102706605, 113965374, 122448605, 126594161, 148064959, 150735075, 154382918, 172057472, 192280850, 194713795, 207721209, 220946392, 225230299, 227043979, 241011012, 248906099, 249796314, 250546528, 258452706, 276862988, 277140688, 280158490, 286074562, 308946627, 310972897, 322612091, 324445400, 336060042, 346729632, 349428326, 352769482, 363039453, 363851029, 392168304, 401975104, 407890409, 407971913, 425780757, 459441559, 465592122, 475898732, 482826596, 484263150, 506235403, 548951531, 554295842, 580536366, 587051904, 588265985, 588298051, 590968352, 601194306, 607771869, 618578932, 626776380, 667919873, 681786366, 689854904, 692055400, 697665495, 711608194, 734027104, 750869335, 757710567, 759967747, 777616154, 830071127, 833809927, 835873060, 836438554, 836945593, 863728236, 864158514, 871273503, 881615667, 891619600, 897181691, 918159061, 920521050, 924502226, 929983535, 943162304, 950210939, 950214176, 962610357, 974842859, 988572832


(These are 100 random numbers from 1 to 1 billion.)

## Scoring System:

Your score is determined like so:

• Your program will be tested against the random numbers in the set.
• You must provide the output generated using the random numbers in the set (either inside your answer or as a pastebin link).
• Your then have two "scores": A primary score and a secondary score.
• Your primary score is (no. of 1's in output)*(no. of operators in output). If your primary score is the lowest, you win.
• Your secondary score is the time of your upload, in GMT, and in 24-hour time. So, if you upload your program on September 12th, 00:00 GMT, then your score is 12/09/2016, 00:00 (use DD/MM/YYYY HH:MM for your formatting).

(language name)
Primary Score = (primary score)
Secondary Score = (secondary score)
(no. of 1's) 1's, (no. of operators) operators


Replace all the things in the brackets with your language name, primary score and secondary score respectively.

## Current Winner:

### The current winner is @ChrisJefferson, who has a primary score of 3,810,660.

• Advice not a rule, but this is a pretty good argument for why golf as a tie breaker is problematic. Sorry I didn't spot this in the sandbox... Commented Sep 11, 2016 at 21:57
• Related math.SE question.
– xnor
Commented Sep 11, 2016 at 22:08
• I agree with trichoplax that the tiebreaker should be the answer to sooner reach its shortest score. Commented Sep 11, 2016 at 22:30
• @JonathanAllan Parentheses are not operations, but are required. Commented Sep 11, 2016 at 22:45
• You can look through the history of answers and see which one reached its final score first. Commented Sep 11, 2016 at 22:48

# C++11

Further small update: Do much less adding, and try all numbers of form A*B+C. I believe that, within the time limit, this is fairly close to optimal, assuming you only use +, * and !. I leave other operators to people with more time than me!

Small update: Try harder to make use of factorials and numbers like 11....111. Also fixed bug that I wasn't counting ! in my costing

New result:

Primary Score = 3,810,660

Secondary Score = 12/09/2016 20:00

2532 1s, 1505 operators.

Various tricks put together. My program starts by setting the shortest program for all factorials and numbers of the form 111..111 (I don't think this falls foul of the hard-wiring rule, as these are the shortest ways to make these numbers. I could rearrange my code so I check these patterns in my dynamic programming if you want). Then do a partial dynamic programming approach, trying various forms:

• A + B
• A*B + C
• A! + B
• 11....11 + B

Unfortunately I can't try all the ways of decomposing a number, so I choose for factorial and 11...11 to only try the nearest number, for A+B to try things near A/2, and for A*B+C to try only quite small As.

It would be easy to extend this to try some '-'s, by trying to overshoot slightly sometimes (particular in A*B - C), but I quite like only trying to grow.

Also, it is very hard to optimise the optimisation condition (I don't like it!) because in principle you can't come up with a 'best' value for each number in isolation, you have to consider your set of answers globally (which I don't intend to do).

Warning: This program needs a 64-bit machine, and around 10GB of memory (as I inefficiently make a giant array for all partially-computed results).

Program:

#include <algorithm>
#include <vector>
#include <string>
#include <assert.h>
#include <iostream>
#include <cmath>

std::vector<int> numints;
std::vector<int> numops;
std::vector<std::string> strings;

void fill_all_ones(long maxval)
{
int val = 1;
int len = 1;
std::string name = "1";
while(val < maxval) {
val = val * 10 + 1;
len++;
name = name + "1";
numints[val] = len;
strings[val] = name;
}
}

void get_best_for_next_full(long i);
// let's just assume this is the best way to make factorials
void fill_all_factorials(long maxval)
{
// skip 1 and 2
long result = 6;
long val = 3;
while(result < maxval) {
get_best_for_next_full(val);
strings[result] = "(" + strings[val] + ")!";
numints[result] = numints[val];
numops[result] = numops[val] + 1;
val++;
result = result * val;
}
}

long get_nearest_all_ones(long i)
{
int val = 11;
int prevval = 1;
while(val < i) {
prevval = val;
val = val * 10 + 1;
}
return prevval;
}

long get_nearest_factorial(long i)
{
int val = 6;
int prevval = 2;
int step = 3;
while(val < i) {
prevval = val;
step++;
val = val * step;
}
return prevval;
}

int getlen(long i);

void get_best_for_next_full(long i)
{
if(numints[i] > 0)
return;

int best = INT_MAX; // we'll do better than this
std::string beststring = "invalid2";
int ones = -1;
int ops = -1;
for(long loop = 1; loop <= i/2; loop++)
{
int new_val = getlen(loop) + getlen(i - loop);
if(new_val < best) {
best = new_val;
ones = numints[loop] + numints[i - loop];
beststring = "(" + strings[loop] + "+" + strings[i - loop] + ")";
ops = numops[loop] + numops[i - loop] + 1;
}
}

for(long loop = 2; loop * loop <= i; loop++)
{
long divisor = i / loop;
long rem = i - loop*divisor;
assert(rem >= 0);
int new_val;
if(rem == 0)
{
new_val = getlen(divisor) + getlen(loop);
}
else
{
new_val = getlen(divisor) + getlen(rem) + getlen(loop);
}

if(new_val < best) {
best = new_val;
if(rem == 0) {
ones = numints[divisor] + numints[loop];
beststring = "(" + strings[divisor] + "*" + strings[loop] + ")";
ops = numops[divisor] + numops[loop] + 1;
} else {
ones = numints[divisor] + numints[loop] + numints[rem];
beststring = "(" + strings[divisor] + "*" + strings[loop] + "+" + strings[rem] + ")";
ops = numops[divisor] + numops[loop] + numops[rem] + 2;
}
}
}

numints[i] = ones;
strings[i] = beststring;
numops[i] = ops;
}

void check_divising(const long i, const long loop, long& best, long& ones, std::string& beststring, long& ops);
void check_adding(const long i, const long loop, long& best, long& ones, std::string& beststring, long& ops);

void get_best_for_next_partial(long i)
{
if(numints[i] > 0)
return;

long best = INT_MAX; // we'll do better than this
long ones = 1;
std::string beststring = "invalid";
long ops = 1;

// Special: Try a nearby all ones
{
long loop = get_nearest_all_ones(i);
check_adding(i, loop, best, ones, beststring, ops);
}

// Special: Try nearest factorial
{
long loop = get_nearest_factorial(i);
check_adding(i, loop, best, ones, beststring, ops);
}

for(long loop = 2; loop * loop <= i; loop++)
{
check_divising(i, loop, best, ones, beststring, ops);
}

numints[i] = ones;
strings[i] = beststring;
numops[i] = ops;
}

void check_adding(const long i, const long loop, long& best, long& ones, std::string& beststring, long& ops)
{
int new_val = getlen(loop) + getlen(i - loop);
if(new_val < best) {
best = new_val;
ones = numints[loop] + numints[i - loop];
beststring = "(" + strings[loop] + "+" + strings[i - loop] + ")";
ops = numops[loop] + numops[i - loop] + 1;
}
}

void check_divising(const long i, const long loop, long& best, long& ones, std::string& beststring, long& ops)
{
long divisor = i / loop;
long rem = i - loop*divisor;
assert(rem >= 0);
int new_val;
if(rem == 0)
{
new_val = getlen(divisor) + getlen(loop);
}
else
{
new_val = getlen(divisor) + getlen(rem) + getlen(loop);
}

if(new_val < best) {
best = new_val;
if(rem == 0) {
ones = numints[divisor] + numints[loop];
beststring = "(" + strings[divisor] + "*" + strings[loop] + ")";
ops = numops[divisor] + numops[loop] + 1;
}
else {
ones = numints[divisor] + numints[loop] + numints[rem];
beststring = "(" + strings[divisor] + "*" + strings[loop] + "+" + strings[rem] + ")";
ops = numops[divisor] + numops[loop] + numops[rem] + 2;
}
}
}

long count = 0;
long countops = 0;

const int little_cutoff = 200000;

int getlen(long i)
{
if(numints[i] == 0) {
if(i < little_cutoff)
get_best_for_next_full(i);
else
get_best_for_next_partial(i);
}
if(numints[i] == 0) {
std::cout << i << " failure!" << numops[i] << ":" << strings[i] << std::endl;
exit(1);
}

return numints[i] + numops[i];
}

const std::vector<long> vals = {945536, 16878234, 32608778, 42017515, 48950830, 51483452, 52970263, 54278649, 63636656, 78817406, 89918907, 90757642, 95364861, 102706605, 113965374, 122448605, 126594161, 148064959, 150735075, 154382918, 172057472, 192280850, 194713795, 207721209, 220946392, 225230299, 227043979, 241011012, 248906099, 249796314, 250546528, 258452706, 276862988, 277140688, 280158490, 286074562, 308946627, 310972897, 322612091, 324445400, 336060042, 346729632, 349428326, 352769482, 363039453, 363851029, 392168304, 401975104, 407890409, 407971913, 425780757, 459441559, 465592122, 475898732, 482826596, 484263150, 506235403, 548951531, 554295842, 580536366, 587051904, 588265985, 588298051, 590968352, 601194306, 607771869, 618578932, 626776380, 667919873, 681786366, 689854904, 692055400, 697665495, 711608194, 734027104, 750869335, 757710567, 759967747, 777616154, 830071127, 833809927, 835873060, 836438554, 836945593, 863728236, 864158514, 871273503, 881615667, 891619600, 897181691, 918159061, 920521050, 924502226, 929983535, 943162304, 950210939, 950214176, 962610357, 974842859, 988572832};

const long biggest = 988572832;

int main(void)
{
numints.push_back(2);
strings.push_back("(1-1)");
numops.push_back(1);

numints.push_back(1);
strings.push_back("1");
numops.push_back(0);

numints.push_back(2);
strings.push_back("(1+1)");
numops.push_back(1);

numints.resize(biggest + 1);
strings.resize(biggest + 1);
numops.resize(biggest + 1);

fill_all_ones(biggest);
fill_all_factorials(biggest);

for(long i = 0; i < little_cutoff; ++i)
get_best_for_next_full(i);

for(long v : vals) {
get_best_for_next_partial(v);
std::cout << v << ":" << strings[v] << "\n";
count += numints[v];
countops += numops[v];

}

std::cout << count << ":" << countops << ":" << count * countops << "\n";

}


Results:

945536:((1111*(1+(11+11))+(1+1))*((1+11)*(1+(1+1))+1)+1)
16878234:(((1+(1+1111))*(1+(1+(1+111)))+(11+11))*((1+11)*11+1)+(1+1))
32608778:((((((1+(1+1)))!+(111+11111))*(11*11)+111)*(1+11)+1)*(1+1))
42017515:((11)!+((((1+111)*11)*11+1)*((1+11)*(1+11)+11)))
48950830:((((11+11)*(1+11))+(11111*(1+(1+1))))*((1+111)*(1+(1+11))+1)+1)
51483452:(((1+(1+1111))*(1+111)+1)*(11+(((1+11)*11+(1+1))*(1+(1+1))))+111)
52970263:((11+((1111*11+(1+(1+1)))*(1+(1+1))))*(111*(1+(1+11))+1)+11)
54278649:((11)!+(((1+(11+(11+(11+1111))))*111+1)*(1+(1+111))+1))
63636656:((((11+111)*(1+(1+1)))*(1+111)+11)*(1+(111+((((1+(1+1)))!)!*(1+1)))))
78817406:(((((111*(11+11)+1)*(1+1))*(1+111)+111)*(1+11)+1)*(1+11)+(1+1))
89918907:(((111+((1+(1+((1+(1+1)))!)))!)*(1+1))*(1+1111)+((11*11)*(1+(1+1))))
90757642:((1111+((11+11111)*(1+1)))*(111*(11+((1+(1+(1+1))))!)+1)+(1+111))
95364861:((11)!+(((((((11+11)*11)+11111)*111)*11+(1+1))*(1+1))*(1+1)+1))
102706605:(((11)!+(((111+((11*11)*11))*(1+(((1+(1+1)))!)!))*11))*(1+1)+1)
113965374:((((111*(1+(1+(1+11))))*1111+((1+(11+11))*11+1))*11+1)*((1+(1+1)))!)
122448605:(((((1+(1+1)))!)!+((111*11)*11))*((1+(((1+(1+1)))!)!)*(1+11)+1)+(1+1))
126594161:(((((11*11)+(((1+(1+1)))!)!)*(1+111))*(1+11)+1)*(1+111)+1)
148064959:((11)!+(((111*111+(1+11))*111+1)*((1+(1+11))*((1+(1+1)))!+1)+(1+(1+1))))
150735075:(((111*111+(1+1))*(1+1111)+(1+11))*11+(1+((1+(1+1)))!))
154382918:((1111*(1+11)+1)*(((1+(11+(111+111)))*(1+1))+11111)+111)
172057472:((((((1+11)*11)*11+1)*(1+(1+1)))+11111)*(11+11111)+((1+11)*11))
192280850:(((11111*(1+11)+11)*(1+(((1+(1+1)))!)!)+(11+111))*(1+1))
194713795:((11)!+((((111+11111)*(1+(1+(1+111)))+((1+(1+1)))!)*11)*11+1))
207721209:(((111*111)*(1+(11+11))+(1+1))*(1+(1+(11+(((1+(1+1)))!)!)))+(1+(1+(1+1))))
220946392:((11)!+((((1+(1+(1+1111)))*(11+111))*111+11)*(1+11)+(1+(1+(1+1)))))
225230299:((111111111+((111*111+(1+((1+(1+1)))!))*(11+111)+(11+11)))*(1+1)+1)
227043979:((((((11+11)*11)+11111)*(1+(1+1))+1)*1111+(1+(1+1)))*((1+(1+1)))!+1)
241011012:(((11)!+((11)!+((11)!+((11+1111)*((1+111)*((1+(1+1)))!+1)))))*(1+1))
248906099:(((11111+(((((1+(1+1)))!)!*111)*(1+1)))*(1+111)+111)*(1+(1+11)))
249796314:(((11)!+(((((1+(1+1)))!)!+((1+1111)*(1+11)))*(11+111)+111))*((1+(1+1)))!)
250546528:((11)!+(((111*111)*(1+(1+(1+11)))+11)*(111*11)+(1+(11+1111))))
258452706:(((11)!+(((((1+(1+1)))!)!*((1+(1+1)))!+1)*(11+(((1+(1+1)))!)!)))*((1+(1+1)))!)
276862988:(((11+(1111*(1+1)))*(((1+(1+1)))!+1111))*111+(((1+(1+1)))!+11))
277140688:(((111*111+(1+(1+(1+(1+11)))))*(1+1))*(11+(111+11111))+(1+111))
280158490:((11)!+(((1+(111+111111))*(((1+(1+1)))!)!+(1+(1+1)))*(1+(1+1))+1))
286074562:(((11)!+((((11+1111)*(11+11))*(1+1)+1)*(1+(11+1111))))*(1+(1+1))+1)
308946627:((11)!+((((1+1111)*(((1+(1+1)))!)!+((11+11)*(1+1)))*(1+111)+1)*(1+(1+1))))
310972897:((11111*(1+(1+1))+1)*(((1111+(111*11))*(1+1))*(1+1)+1)+11)
322612091:((((((1+11)*(1+11))*(1+11)+(1+1))*111+1)*(1+111))*(1+(1+(1+(1+11))))+11)
324445400:(((1111111+(1+(1+1)))*(1+1))*((1+11)*(1+11)+(1+1))+(1+111))
336060042:(((1+1111)*(1+(11+111))+(1+111))*(11+((111*11+1)*(1+1)))+(1+1))
346729632:(((1+(1+(11111+(111*111))))*((1+111)*11+1)+(1+(1+(1+11))))*(1+11))
349428326:(((((11+11)*11)*11+1)*(1+1111)+1)*(1+(((1+(1+1)))!+111)))
352769482:(((1+11111)*(111*(11+11))+((11+111)*((1+1)*(1+1)+1)))*(1+(1+11)))
363039453:(((((1+111)*(1+111)+1)*(1+1))*(1+(1+11))+11)*(1+(1+1111)))
363851029:((((111*11+1)*1111+11)*((1+11)*11+(1+1))+(1+11))*(1+1)+1)
392168304:(((((1+(1+1111))*(1+111))*11+1)*(1+(1+11))+11)*(11+11))
401975104:(((((1+11)*(1+11)+1)*111)*111+11)*((1+111)*(1+1)+1)+(1+(1+(1+1))))
407890409:(((1+11111)*11)*((1+1111)*(1+(1+1))+1)+((1+1111)*(1+1)+1))
407971913:((11)!+((11)!+(((1+(1+11111))*(1+1)+1)*(((11+111)*11)*11+1)+(1+1111))))
425780757:(((1111+((((1+11)*11)+11111)*(1+(1+1))))*11+1)*1111+((1+(1+1)))!)
459441559:(((11111+(((1+(1+111))*(1+1)+1)*111))*111+1)*(1+(1+(1+111)))+(1+(1+11)))
465592122:(((11)!+((((1111*(11*(1+(1+1))+1)+1)*(1+(11+11)))*(1+1)+1)*111))*(1+1))
475898732:(((11)!+(((((1+111)*11+(1+1))*(1+11))*(1+1)+1)*(1+(1+111))))*11+1)
482826596:(((1+(((111*11)*11)+(11111*(1+1))))*111+1)*(11+111)+((1+(1+1)))!)
484263150:(((111*111+(1+(1+1)))*111+11)*(1+(111+((11+11)*11))))
506235403:(((1+11))!+((((1+(1+1111))*(1+1111)+((11+111)*(1+1)))*11+1)*(1+1)+1))
548951531:((((111+111)*(1+1)+1)*111+11)*11111+((11+111)*(1+11)+1))
554295842:(((1+11))!+((((1+1111)*111+1)*((1+1)*(1+1)+1))*(11+111)+(1+111)))
580536366:(((1+(111+((111*111+11)*(1+11))))*(1+111)+1)*(11+((1+(1+(1+1))))!)+11)
587051904:(((((1+1111)*(1+11))*(1+(1+1))+1)*(111*11+1)+(111*((1+(1+1)))!))*(1+11))
588265985:(((1+11))!+((1+(111+(1111*(1+(1+11)))))*((1+111)*(11*((1+(1+1)))!+1)+(1+(1+1)))))
588298051:((((((11+111)*11)*11)+(11111*(1+(1+1))))*(1+1111)+1)*11)
590968352:(((((((1+(1+1)))!)!+11111)*111+(11+11))*((1+111)*(1+1)+1)+1)*(1+1))
601194306:((((1111*(1+(1+(1+(11+111))))+1)*111+(1+1))*(1+(1+1))+1)*(1+(1+11))+11)
607771869:(((1+11))!+(((11)!+(((1111*11+1)*(1+1))*(1+(11+111))+11))*(1+(1+1))))
618578932:(((((1111*111)*11+1)*(1+1)+1)*(1+1))*(1+(1+(1+111)))+(1+111))
626776380:((((1+(1+(1+1))))!+((((1+(1+1)))!)!+(1111*111)))*(1+(11+((1+((1+(1+1)))!))!)))
667919873:((((((1+(11+111))*11+1)*111+(1+(1+1)))*1111+1)*(1+1))*(1+1)+1)
681786366:(((1+11))!+((11)!+(((11)!+((11)!+((1+(1+11111))*((1+11)*(1+11))+111)))*(1+1))))
689854904:(((11+((11111+((1+1111)*11))*(1+1)))*((11+111)*11+1)+11)*11+(1+1))
692055400:(((1+11))!+(((((1+(1+111))*(1+(1+(1+11))))*11)*11+1)*(1+(1+1111))+1))
697665495:(((1+11))!+(((((((1+(1+1)))!)!*(1+(1+(1+111)))+1)*(1+11))*(1+1)+1)*111))
711608194:(((11)!+(((1+(1+(1+(1+1111))))*(11+((11+111)*(1+1)))+(1+1))*1111))*(1+1))
734027104:(((111*(11+((1+(1+(1+1))))!)+1)*(((1+(1+1)))!+11)+1)*11111+1111)
750869335:((11111111+((1+(((1+(1+1)))!)!)*((1+11)*11+1)+1))*(11*((1+(1+1)))!+1))
757710567:((((((11+111)*11)+111111)*(1+(1+1))+1)*(1+(11+1111))+(1+(1+1)))*(1+1)+1)
759967747:(((11)!+(((1+(1+(111+11111)))*(1+(1+111)))*(1+(11+11))+1))*11)
777616154:((11111*(111+(((111*11+1)*(1+1))*(1+1)))+(11+111))*(1+(1+(1+11))))
830071127:((((1+111)*111)*((1+(1+1)))!+1)*(((1+(1+1)))!+(11+11111))+(111*(1+1)+1))
833809927:((((11+1111)*(1+1)+1)*111+1)*(1+(1+(11+(1111*(1+(1+1))))))+111)
835873060:(((((11+(111+111))*111+1)*(1+(1+111))+1)*(1+(1+11))+1)*(11+11))
836438554:(((1+11))!+(((11111*(1+1)+1)*((11+(((1+(1+1)))!)!)*11+1)+1111)*(1+1)))
836945593:(((1111*1111+(1+111))*(1+(1+111))+(1+(1+1)))*((1+(1+1)))!+1)
863728236:(((1+(1111+((11+11111)*(1+1))))*(111*111+((1+(1+1)))!))*(1+(1+1)))
864158514:(((1+11))!+(((1111*(1+(1+(1+11)))+((1+(1+1)))!)*111+1)*(111*(1+1)+1)+11))
871273503:((((1+11111)*(11+11)+1)*((1+(1+11))*(1+1)+1)+1)*((1+11)*11)+111)
881615667:((11111+((111*111+11)*(1+1)))*((111*111)*(1+1)+1)+((11+1111)*11))
891619600:(((11)!+((11)!+((((1+(11+11))*(1+1))+111111)*11)))*11+(1+(1+1)))
897181691:((11+(11+(11+((1+(1+((1+(1+1)))!)))!)))*(11+(11111*(1+1)))+((111*11+1)*11))
918159061:(((11)!+(((11+11)*11+1)*(1+(1+11))))*(1+(11+11))+(1+(1+(1+1))))
920521050:(((11)!+((((1+(11+1111))*(1+(1+(1+1111))))*(1+111)+111)*(1+(1+1))))*(1+1))
924502226:((((1111*(1+11))*(1+1)+1)*((111*(1+11)+1)*(1+1)+1))*(1+(1+11))+11)
929983535:(((11)!+((((11+111)*111+1)*111)*((1+11)*(1+1)+1)+(1+1)))*(1+11)+11)
943162304:(((11)!+((((((1+((1+(1+1)))!))!+(111*111))*111+(1+1))*(1+111))*(1+1)))*(1+1))
950210939:(((11+(111+11111))*(1+(1+(1+(((1+(1+1)))!)!)))+(1+1))*(((1+(1+1)))!+111)+(1+1))
950214176:(((11)!+((((111*111)*(1+(1+11)))*11+1)*((1+(11+111))*(1+1)+1)))*(1+1))
962610357:((((1+11))!+((1+((((1+(1+1)))!)!+(111*(1+11))))*(11+1111)+(1+111)))*(1+1)+1)
974842859:((((((11*(1+((1+(1+1)))!))+1111)*11+1)*(1+111))*((1+(1+1)))!)*111+11)
988572832:(((111111111+((11111*(1+(1+1111))+11)*11+(1+(1+1))))*(1+1))*(1+1))

• Seems like you didn't count the 225 !. I think that's 1632 operators, not 1407. (Which still leads to a great score, though.) Commented Sep 12, 2016 at 18:47
• Woops, indeed, I missed a '1' in the costing of factorial functions. Suprisingly (to me) fixing that makes almost no difference to the expressions I generate, I suppose because factorials are generally so great, that if they cost one more they are still the best choice. Commented Sep 12, 2016 at 18:59
• long maxval grumble grumble Commented Mar 13, 2018 at 19:34

Primary score: 27242281

Secondary score: 12/09/2016 09:01

11891 1's, 2291 operators

import Data.List

nums = iterate (\x -> x*10+1) 1

g n | n > a = show a ++ "+(" ++ g (n-a) ++ ")"
| n < a = show a ++ "-(" ++ g (a-n) ++ ")"
| otherwise = show a
where a = minimumBy (\x y -> compare (abs$x-n) (abs$y-n))
. take 2 . reverse
b=and($0, 1) b for(chall=""; length(b=substr(b,2)); ) { if(chall!="") chall=chall"*" chall=chall"(1+1)" if(substr(b, 1, 1)=="1") { chall=chall"+1" if(length(b)>1) chall="("chall")" } } print chall }  Simply prints the binary representation calculated from left to right. For example 19 is 10011 which is (((((1)*2+0)*2+0)*2+1)*2+1). I just leave out the +0 and write the 2 as (1+1). I was just curious about how this method would be scoring. Output: 945536: (((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1) 16878234: (((((((((1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1) 32608778: (((((((((((1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1) 42017515: ((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1 48950830: ((((((((((((((((1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1) 51483452: ((((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1) 52970263: ((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1 54278649: (((((((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1 63636656: (((((((((((1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1) 78817406: ((((((((((((((1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1) 89918907: ((((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1 90757642: ((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1) 95364861: (((((((((((((((((1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1 102706605: (((((((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1 113965374: (((((((((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1) 122448605: (((((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1 126594161: ((((((((((((((1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1 148064959: (((((((((((((((1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1 150735075: ((((((((((((1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1 154382918: (((((((((((((1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1) 172057472: (((((((((1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1) 192280850: ((((((((((((((((1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1) 194713795: (((((((((((((1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1 207721209: (((((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1 220946392: (((((((((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1) 225230299: ((((((((((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1 227043979: ((((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1 241011012: (((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1) 248906099: (((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1 249796314: (((((((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1) 250546528: ((((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1) 258452706: (((((((((((((((((1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1) 276862988: (((((((1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1) 277140688: ((((((((((1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1) 280158490: ((((((((((((1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1) 286074562: (((((((((((1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1) 308946627: ((((((((((((1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1 310972897: ((((((((((1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1 322612091: (((((((((((((((((1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1 324445400: ((((((((((((((1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1) 336060042: ((((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1) 346729632: ((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1) 349428326: ((((((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1) 352769482: ((((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1) 363039453: (((((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1 363851029: 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((((((((1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1 588298051: ((((((((((((1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1 590968352: (((((((((((((1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1) 601194306: (((((((((((((((((1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1) 607771869: ((((((((((((((((1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1 618578932: (((((((((((((((((1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1) 626776380: (((((((((((((((((1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1) 667919873: ((((((((((((((1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1 681786366: ((((((((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1) 689854904: (((((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1) 692055400: ((((((((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1) 697665495: ((((((((((((((((1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1 711608194: 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(((((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1) 836438554: ((((((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1) 836945593: (((((((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1 863728236: ((((((((((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1) 864158514: (((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1) 871273503: (((((((((((((((((1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1 881615667: (((((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1 891619600: ((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1) 897181691: (((((((((((((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1 918159061: ((((((((((((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1 920521050: ((((((((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1) 924502226: (((((((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1) 929983535: ((((((((((((((((((1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1 943162304: (((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1) 950210939: ((((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1 950214176: ((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1) 962610357: ((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1 974842859: ((((((((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1 988572832: (((((((((((((((1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)+1)*(1+1)*(1+1)*(1+1)*(1+1)*(1+1)  # Python 3 Primary Score: 69720516 Secondary Score: 09:30 14/09/2016 def genNum(num): dic = { 6: "(1+1+1)!", 24: "(1+1+1+1)!", 120: "((1+1+1)!-1)!", 720: "((1+1+1)!)!", 5040: "((1+1+1)!+1)!", 40320: "((1+1+1)!+1+1)!", 362880: "(11-1-1)!", 39916800: "(11)!", 479001600: "(11+1)!", 6227020800: "(11+1+1)!" } lis = [6227020800,479001600,39916800,362880,40320,5040,720,120,24,6] out = "" for i in lis: if num/i >= 1: st = dic[i] + "*(" + genNum(num // i) + ")" out += st if num%i != 0: out += "+" + genNum(num%i) return out else: st = "1+"*num return st[:-1]  Edit: Now uses multiplication to greatly reduce the score. This makes great use of factorials and recursion. In total, the program uses: • 5958 ones • 11702 operators Ideone it! # JAVA Primary Score 1045978739 Secondary score 12/09/2016 16:05 37193 1s 28123 operators  void main() { int arr[]={945536, 16878234, 32608778, 42017515, 48950830, 51483452, 52970263, 54278649, 63636656, 78817406, 89918907, 90757642, 95364861, 102706605, 113965374, 122448605, 126594161, 148064959, 150735075, 154382918, 172057472, 192280850, 194713795, 207721209, 220946392, 225230299, 227043979, 241011012, 248906099, 249796314, 250546528, 258452706, 276862988, 277140688, 280158490, 286074562, 308946627, 310972897, 322612091, 324445400, 336060042, 346729632, 349428326, 352769482, 363039453, 363851029, 392168304, 401975104, 407890409, 407971913, 425780757, 459441559, 465592122, 475898732, 482826596, 484263150, 506235403, 548951531, 554295842, 580536366, 587051904, 588265985, 588298051, 590968352, 601194306, 607771869, 618578932, 626776380, 667919873, 681786366, 689854904, 692055400, 697665495, 711608194, 734027104, 750869335, 757710567, 759967747, 777616154, 830071127, 833809927, 835873060, 836438554, 836945593, 863728236, 864158514, 871273503, 881615667, 891619600, 897181691, 918159061, 920521050, 924502226, 929983535, 943162304, 950210939, 950214176, 962610357, 974842859, 988572832 }; int sum=1; for(int i=0;i<arr.length;i++){ System.out.print(arr[i]+":"); while(arr[i]>11){ System.out.print("("+"1"); sum=11; while(sum<=arr[i]){ if(sum<=arr[i]) System.out.print("*11"); sum*=11; } arr[i]=arr[i]-sum/11; System.out.print(")"); if(arr[i]!=0) System.out.print("+"); } while(arr[i]--!=0){ System.out.print(1); if(arr[i]!=0) System.out.print("+"); } System.out.println(); } }  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Commented Sep 14, 2016 at 8:43 # Emacs Lisp Primary score: 81638725 Secondary score: 12/09/2016 09:35 (defun 1s (n) (let((x 1)r) (while (> (/ n x) 11) (setq x (1+ (* x 10)))) (while (> n 0) (while (>= n x) (push x r) (push '+ r) (setq n (- n x))) (setq x (/ x 10))) r))  Basically builds a sum over the domain (1, 11, 111, ...) which is equivalent to n. • From what I understand, in your program, when it gets an input like 124, it outputs 111+11+1+1, right? (Correct me if I'm wrong.) Commented Sep 12, 2016 at 8:38 • (Also, the time is in GMT.) Commented Sep 12, 2016 at 8:44 • How can this have a score of < 1million? Have you added up all the 1s across the whole 100 number output and multiplied that by the total number of + operations across the whole output? Commented Sep 12, 2016 at 8:47 • This has a score of 81638725 Commented Sep 12, 2016 at 9:24 • I don't see why this is downvoted. is there something wrong? – user56309 Commented Sep 12, 2016 at 14:30 # AWK, 15642720 Secondary Score=30/05/2017, 21:11 BEGIN{RS="[,\n]"} func f2(x) { div=int(x/11) mod=x%11 } func trans(z){ r="" if (z > 6) { r="11" for (i=11;i>z;i--){ r=r"-1" } } else if (z>0){ r=r 1 for (i=1;i<z;i++){ r=r"+1" } } } {n=$1
do {f2(n)
trans(mod)
if (r) s=s"(" r  ")"
if(div){
if (r)s=s"+"
s=s"11*("
count++
}
n=div
} while(div >10)
trans(div)
s = s r
for (i=0;i<count;i++)s = s")"
print \$1": " s
slength+=length(s)
ones+=gsub("1","",s);
parens+=gsub("[()]","",s);
ops+=length(s);
s=""
count=0;
}
END {
print "Total string length: " slength
print "Ones: " ones
print "Ops: " ops
print "Parens: " parens
print "Primary Score="ones*ops
}



Try it online!

Ones: 4590

Ops: 3408 Primary Score=15642720 Secondary Score=30/05/2017 21:11