Rosetta Stone Challenge: Find the rule for a series

Question

The goal of a Rosetta Stone Challenge is to write solutions in as many languages as possible. Show off your programming multilingualism!

The Challenge

Your challenge is to implement a program that will input a list of numbers and output the rule used to generate each successive number in the series, in as many programming languages as possible. You are allowed to use any sort of standard library function that your language has, since this is mostly a language showcase.

What is a "series?"

A series is an ordered list of integers. Each successive number in the series can be generated by applying a simple rule to the previous number in the series. In this challenge, the rule consists of multiplying the number by a constant, and then adding a second constant. Both of the constants can be any integer. The goal of this challenge is to output those two constants.

For the series 2 5 11, the rule can be written as 2 1. This means that each number is the previous number, times 2, plus 1. An important fact is that most series have exactly one rule. Some series have either an infinite number or none at all, but you will not have to deal with this.

Input

Input will be a list of three different integers which are the numbers in the sequence. The numbers can be either space, comma, or newline delimited, but please specify which. I am going to be flexible on this limitation because certain languages may have input restrictions. Here are four examples of input:

0 7 14
2 5 11
2 0 -4
5 -19  77

Output

Output will be two integers which represent the rule used to generate the series. The first number will be the multiplicative constant, while the second number will be the additive constant. The formatting of the output can be space, comma, or newline delimited. I am flexible on this limitation as well. Here are the corresponding examples of output:

1 7
2 1
2 -4
-4 1

The Objective Winning Criterion

As for an objective winning criterion, here it is: Each language is a separate competition as to who can write the shortest entry, but the overall winner would be the person who wins the most of these sub-competitions. This means that a person who answers in many uncommon languages can gain an advantage. Code-golf is mostly a tiebreaker for when there is more than one solution in a language: the person with the shortest program gets credit for that language.

Rules, Restrictions, and Notes

Your program can be written in any language that existed prior to April 9th, 2012. I will also have to rely on the community to validate some responses written in some of the more uncommon/esoteric languages, since I am unlikely to be able to test them.

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Current Leaderboard

This section will be periodically updated to show the number of languages and who is leading in each.

• AWK (32) - mellamokb
• bash (31) - Peter Taylor
• Befunge (29) - Howard
• bc (39) - kernigh
• brainfuck (174) - CMP
• C (78) - l0n3_shArk
• C++ (96) - leftaroundabout
• Common Lisp (88) - kernigh
• Cray Chapel (59) - Kyle Kanos
• csh (86) - kernigh
• Cuda (301) - leftaroundabout
• dc (30) - kernigh
• DOS BATCH (54) - mellamokb
• Element (27) - Howard
• es (95) - kernigh
• Factor (138) - kernigh
• Felix (86) - kirbyfan64sos
• Fortran (44) - Kyle Kanos
• Go (101) - Howard
• GolfScript (16) - Howard
• Golflua (44) - Kyle Kanos
• Haskell (35) - leftaroundabout
• J (23) - Gareth
• Java (141) - Howard
• JavaScript (47) - mellamokb
• Julia (71) - M L
• Lua (51) - Howard
• Mercury (319) - leftaroundabout
• MoonScript (48) - kirbyfan64sos
• Nimrod (146) - leftaroundabout
• Owl (22) - r.e.s.
• Pascal (88) - leftaroundabout
• Perl (57) - Gareth
• PHP (61) - mellamokb
• PicoLisp (72) - kernigh
• Piet (56) - M L
• PostScript (61) - Howard
• Python (40) - Howard
• Q (36) - tmartin
• QBasic (34) - mellamokb
• R (50) - r.e.s.
• Ruby (44) - Howard
• Scala (102) - Gareth
• SQL (57) - Aman ZeeK Verma
• TI-83 BASIC (25) - mellamokb
• Unlimited Register Machine (285) - Paxinum
• VBA (57) - Gaffi
• Whitespace (123) - r.e.s.
• zsh (62) - kernigh

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Current User Rankings

Equal ranks are sorted alphabetically.

1. Howard (9): Befunge (29), Element (27), Go (101), GolfScript (16), Java (141), Lua (51), PostScript, (61) Python, (40) Ruby (44)

2. kernigh (8): bc (39), Common Lisp (88), csh (86), dc (30), es (95), Factor (138), PicoLisp (72), zsh (62)

3. leftroundabout (6): C++ (96), Cuda (301), Haskell (35), Mercury (319), Nimrod (146), Pascal (88)

4. mellamokb (6): AWK (32), DOS BATCH (54), JavaScript (47), PHP (61), QBasic (34), TI-83 BASIC (41)

5. Gareth (3): J (23), Perl (57), Scala (102)

6. Kyle Kanos (3): Cray Chapel (59), Fortran (44), Golflua (44)

7. r.e.s. (3): Owl (22), R (50), Whitespace (123)

8. kirbyfan64sos (2): Felix (86), MoonScript (48)

9. M L (2): Julia (71), Piet (56)

10. Aman Zeek verma (1): SQL (57)

11. CMP (1): brainfuck (174)

12. Gaffi (1): VBA (57)

13. l0n3_shArk (1): C (78)

14. Paxinum (1): Unlimited Register Machine (285)

15. Peter Taylor (1): bash (31)

16. tmartin (1): Q (36)

Answer 1

GolfScript, 16 characters

~1$- 1$3$-/.p@*-

Input is given as space-separated list.

JavaScript, 56 characters

p=prompt;x=alert;a=p();b=p();x(m=(p()-b)/(b-a));x(b-a*m)

Input is given on prompt.

Ruby, 44 characters

a,b,c=eval("[#{gets}]");m=c-b;p m/=b-a,b-m*a

Input is here given as comma-separated list.

Python, 40 characters

a,b,c=input();m=c-b;m/=b-a;print m,b-m*a

Input is again comma-separated.

Java, 141 characters

enum E{E;static int s(){return new java.util.Scanner(System.in).nextInt();}{int a=s(),b=s(),m=s()-b;m/=b-a;System.out.print(m+" "+(b-a*m));}}

Input separated by newline.

Lua, 51 characters

r=io.read
a,b=r(),r()
m=(r()-b)/(b-a)
print(m,b-m*a)

Input separated by newline.

Go, 101 characters

package main
import"fmt"
var a,b,c int
func main(){fmt.Scan(&a,&b,&c)
c-=b
c/=b-a
fmt.Print(c,b-a*c)}

Input separated by newline.

Fortran, 90 characters

      PROGRAM X
      READ(*,*)I,J,K
      K=(K-J)/(J-I)
      WRITE(*,*)K,J-I*K
      END

Input separated by newline.

Befunge, 29 characters

&01p&:11p:&-01g11g-/:.01g*-.@

PostScript, 61 characters

2 5 14
1 index sub 1 index 3 index sub idiv dup = 3 2 roll mul sub =

Owl, 23 characters

<%<%<$-1`4'-/%.32)2'*-.

Input separated by newline.

Element, 27 characters

_-a;_3:'-_+"a~+/2:`a~*+\ ``

Input separated by newline.

Answer 2

QBasic, 42

INPUT "",a,b,c
m=(c-b)/(b-a)
PRINT m;b-m*a

Requires input with commas, outputs with spaces (is this ok?)

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Mercury, 319

:-module r.
:-interface.
:-import_module io,list,int,char,string.
:-pred main(io::di,io::uo)is det.
:-implementation.
main(!IO):-io.read_line_as_string(J,!IO),(if J=ok(I),[A,B,C]=list.map(string.det_to_int,string.words_separator(char.is_whitespace,I)),M=(C-B)/(B-A)then io.format("%d %d",[i(M),i(B-M*A)],!IO)else true).

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Haskell, 85 81

f[a,b,c]|m<-(c-b)`div`(b-a)=[m,b-m*a]
main=getLine>>=mapM_ print.f.map read.words

Now inputs with spaces, outputs with newlines.

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C, 80

main(a,b,c,m){scanf("%d %d %d",&a,&b,&c);m=(c-b)/(b-a);printf("%d %d",m,b-m*a);}

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C++, 96

#include<iostream>
main(){int a,b,c,m;std::cin>>a>>b>>c;m=(c-b)/(b-a);std::cout<<m<<' '<<b-m*a;}

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Nimrod, 146

import strutils
var
 q:array[0..3,int]
 b,m:int
for i in 0..2:q[i]=ParseInt(readLine(stdin))
b=q[1]
m=(q[2]-b)div(b-q[0])
echo($m,",",$(b-m*q[0]))

Input w/ newlines, output comma.

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This one won't count, but I feel it still fits in in some way:

Mathematical theorem, 713 characters of LaTeX

\documentclass{article}\usepackage{amsmath}\usepackage{amsthm}\begin{document}Theorem: for a sequence $(a_i)_i$ of integers with $a_2\neq a_1$ where $a_3-a_2$ is divisible by $a_2-a_1$, $m:=\frac{a_3-a_2}{a_2-a_1},\ p:=a_2-m\cdot a_1$ give rise to a sequence\[b_i:=\begin{cases}a_1&\text{for }i=1\\b_{i-1}\cdot m+p&\text{else}\end{cases}\] such that $b_i=a_i\ \forall i\leq 3$.

Proof: $i=1$ is trivial,\[\begin{aligned}b_2=&b_1\cdot m+p=a_1\frac{a_3-a_2}{a_2-a_1}+a_2-\frac{a_1a_3-a_1a_2}{a_2-a_1}=a_2,\\b_3=&b_2\cdot m+p=\frac{a_2a_3-a_2^2}{a_2-a_1}+a_2-\frac{a_1a_3-a_2^2}{a_2-a_1}\\=&\frac{a_2a_3-a_1a_3+(a_2-a_1)a_2-a_2^2+a_1a_2}{a_2-a_1}\\=&\frac{a_2-a_1a_3+0}{a_2-a_1}=a_3.\end{aligned}\]\qed\end{document}

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While we're at writing := definitions...

Pascal, 90 88

program r;var a,b,c:integer;begin;read(a,b,c);c-=b;c:=c div(b-a);write(c,' ',b-c*a);end.

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Cuda, 301

#include<stdio.h>
__global__ void r(int*q){if(!(blockIdx.x|threadIdx.x)){q[1]-=*q;q[1]/=(*q-q[2]);*q-=q[1]*q[2];}}
main(){int p[3],*q;scanf("%d%d%d",p+2,p,p+1);cudaMalloc(&q,24);cudaMemcpy(q,p,24,cudaMemcpyHostToDevice);r<<<1,1>>>(q);cudaMemcpy(p,q,24,cudaMemcpyDeviceToHost);printf("%d %d",p[1],*p);}

Answer 3

Brainfuck - 174

,>,>,<[>->+>+<<<-]>>>[<<<+>>>-]<<<<[>>>->+<<<<-]>>>>[<<<<+>>>>-]<<[->-
[>+>>]>[+[-<+>]>+>>]<<<<<]>>>[<<<+>>>-]<[-]<[-]<.[>>+<<-]>>[<<<<[>>+>+
<<<-]>>>[<<<+>>>-]>-]<<[<->-]<.

Piet - 82?

Not sure how to measure competitive golf here. I'm gonna go with total image size (in codels) Mine is 41x2:

Befunge - 34

&00p&10p&10g-10g00g-/:.00g*10g\-.@

English - 278

The multiplier is the quotient of the difference of the second 
and third values and the second and first values. 
To generate a new term, multiply the current term by the multiplier
and add the difference of the first value and the product of the 
multiplier and the second value.

Not sure if this counts, but thought I'd give it a shot. It is remarkably difficult to describe even a simple algorithm accurately. Kinda wish English supported some kind of grouping symbol to establish precedence.

Answer 4

AWK (32)

{m=$3-$2;print m/=$2-$1,$2-$1*m}

Demo: http://ideone.com/kp0Dj

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bash (38)

awk '{m=$3-$2;print m/=$2-$1,$2-$1*m}'

Demo: http://ideone.com/tzFi8

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DOS/BATCH (54 55)

set/a m=(%3-%2)/(%2-%1)&set/a n=%2-%m%*%1&echo %m% %n%

Takes parameters as space-separated list of arguments.

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Java (143 185)

enum R{R;{int a=0,b=0,c,i=2;for(;(c=new java.util.Scanner(System.in).nextInt()+b*--i)+i>=c;b=c)a+=c*i;c/=b-a;System.out.print(c+" "+(b-a*c));}}

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JavaScript (48 61 67)

p=prompt;m=p(b=p(a=p()))-b;alert([m/=b-a,b-a*m])

​ Demo: http://jsfiddle.net/BT8bB/6/

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PHP (61 77)

<?list(,$a,$b,$c)=$argv;$c-=$b;echo($c/=$b-$a).' '.$b-=$c*$a;

Demo: http://ideone.com/CEgke

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QBasic (34)

INPUT a,b,c
m=(c-b)/(b-a)
?m;b-m*a

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TI-83 Basic (25 41)

:Prompt A,B,C
:(C-B)/(B-A
:Disp Ans,B-AAns

Yes, the missing right parenthesis is on purpose. It's a well-known optimization technique that closing the parentheses before a STO operation is not necessary in TI-83 Basic programming.

Answer 5

AWK, 35 characters

{m=($3-$2)/($2-$1);print m,$2-$1*m}

• Input format: 2 0 -4

bc, 39 characters

define f(a,b,c){
m=(c-b)/(b-a)
m
b-a*m}

• Input format: z=f(2, 0, -4)
• The input is a bc expression. After bc reads the source file, it reads the standard input. This is why the input must look like a function call.
• I use OpenBSD bc, which requires a newline after the {.

Common Lisp, 88 characters

(let*((a(read))(b(read))(c(read))(m(/(- c b)(- b a))))(format
t "~A ~A" m (- b(* a m))))

• Input format: 2 0 -4

csh, 86 characters

set i=(`cat`)
@ m=($i[3] - $i[2]) / ($i[2] - $i[1])
@ n=$i[2] - $i[1] * $m
echo $m $n

• Input format: 2 0 -4
• The 86th character is newline at end of file. csh is the only language for which I count newline at end of file. This is because csh never runs the last command unless newline is there.
• set i=($<) does not work, because $< has no word splitting.

dc, 30 characters

?scsbsalclb-lbla-/psmlblalm*-p

• Input format: 2 0 _4, where _ is the underscore.

es, 95 characters

i=(`cat)
b=$i(2)
m=`{expr \( $i(3) - $b \) / \( $b - $i(1) \)}
echo $m `{expr $b - $i(1) \* $m}

• Input format: 2 0 -4
• es is the extensible shell by Paul Haahr and Byron Rakitzis.

Factor, 138 characters

USING: eval formatting io kernel locals math ;
contents eval( -- a b c ) [let :> ( a b c )
c b - b a - / dup a * b swap - "%d %d" printf ]

• Input format: 2 0 -4

PicoLisp, 74 72 characters

(in()(let(r read a(r)b(r)c(r)m(/(- c b)(- b a)))(print
m (- b(* a m)))))

• Input format: 2 0 -4
• EDIT: Lost 2 characters by changing a(read)b(read)c(read) to r read a(r)b(r)c(r).

TI-83 BASIC, 63 61 characters

:Input A
:Input B
:Input C
:(C-B)/(B-A)→M
:Disp M
:Disp B-A*M

• Input format: 2 ENTER 0 ENTER ¯4 ENTER, where ¯ is the calculator's unary minus.
• I counted Unicode characters; → (the right arrow) counts as U+2192. For example, the calculator counts Input A as 2 characters, but I count Input A as 7 characters. I also count : as 1 character.
• EDIT: I miscounted: there are 61, not 63, characters.

zsh, 62 characters

i=(`cat`)
((b=i[2],m=(i[3]-b)/(b-i[1]),n=b-i[1]*m))
echo $m $n

• Input format: 2 0 -4

Answer 6

Whitespace, 123

I/O is newline-separated. (To obtain the source code, enter edit mode and copy the whitespace between the preformat tags; or, see the online example at Ideone.)

Explanation, where S,T,L represents Space,Tab,Linefeed:

Pseudocode     Whitespace
----------     ----------
push 0         SS SSL
readn          TLTT
push 1         SS STL
readn          TLTT
push 2         SS STSL
dup            SLS
readn          TLTT
retr           TTT
push 1         SS STL
retr           TTT
-              TSST
push 1         SS STL
retr           TTT
push 0         SS SSL
retr           TTT
-              TSST
/              TSTS
dup            SLS
outn           TLST
push 10        SS STSTSL
outc           TLSS
push 0         SS SSL
retr           TTT
*              TSSL
push 1         SS STL
retr           TTT
swap           SLT
-              TSST
outn           TLST
exit           LLL

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R, 50

x=scan(n=3);y=diff(x);z=y[2]/y[1];c(z,x[2]-x[1]*z)

I/O is space-separated.

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Owl

---22---

< <%<-2`2`-/%.10)2'*-.

I/O is newline-separated.

---19--- (if this version is allowed; but I think it's cheating, since the \ is executable code):

1`-1`3`-/%.32)2'*-.

I/O is space-separated. Command-line usage: owl prog 5 19\ 77 (the \ acts as a postfix unary minus in Owl).

Answer 7

J, 23 characters

(],1{x-0{x*])%~/2-/\x=:

Usage:

   (],1{x-0{x*])%~/2-/\x=: 5 _19 77
_4 1

Negative numbers are represented by underscores in J.

PHP, 88 characters

<?php
list($x,$y,$z)=split(' ',fgets(STDIN));
$a=($z-$y)/($y-$x);
echo$a." ".($y-$a*$x);

Scala, 102 characters

val x=readLine.split(" ").toList.map(_.toInt)
val a=(x(2)-x(1))/(x(1)-x(0))
print(a+" "+(x(1)-x(0)*a))

Perl, 57 characters

s!(.+) (.+) (.+)!$a=($3-$2)/($2-$1);$a." ".($2-$1*$a)!e

Requires the '-p' option, for which I have added 2 characters. Assumes that the input is valid to save some characters.

All my answers take space separated numbers.

Answer 8

PHP, 74,72,69

<?fscanf(STDIN,'%d%d%d',$a,$b,$c);echo($d=($c-$b)/($b-$a)).' '.($b-$d*$a);

When input is passed as arguments:

<?echo($d=($argv[3]-$argv[2])/($b=$argv[2]-$a=$argv[1])).' '.($b-$d*$a);

Now, as @mellamokb suggested, using $n=$argv:

<?$n=$argv;echo($d=($n[3]-$n[2])/($b=$n[2]-$a=$n[1])).' '.($b-$d*$a);

C, 77,78

main(a,b,c,d){printf("%d %d",d=(c-b)/(b-a),b-d*a,scanf("%d%d%d",&a,&b,&c));}

^ doesn't work so, here's the stuff: [thanks to @ugoren for bringing it to notice]

main(a,b,c,d){printf("%d %d",d,b-a*(d=(c-b)/(b-a)),scanf("%d%d%d",&a,&b,&c));}

Answer 9

DOS-BATCH, 98

@ECHO OFF&SET/P p=&SET/P q=&SET/P r=&SET/A m=(%r%-%q%)/(%q%-%p%)&SET/A n=%q%-%p%*%m%&ECHO %m% %n%

Input in separate lines

Bash, 51

m=$((($3 - $2)/($2 - $1)))
echo $m $(($2 - $m*$1))

Example : sh prog.sh 2 0 -4 (space separated arguments)

Perl, 84

@s=split(/ /,<STDIN>);$m=($s[2]-$s[1])/($s[1]-$s[0]);print $m." ".($s[1]-$s[0]*$m);

Java, 297

import java.util.*;public class A{public static void main(String a[]){StringTokenizer s=new StringTokenizer(new Scanner(System.in).nextLine());int i=4;int[] p=new int[i];while(i-->1)p[3-i]=Integer.parseInt(s.nextToken());p[3]=(p[2]-p[1])/(p[1]-p[0]);System.out.print(p[3]+" "+(p[1]-p[0]*p[3]));}}

Space separated input, space separated output.

SQL, 57

select (&3-&2)/(&2-&1),&2-((&3-&2)/(&2-&1)*&1) from dual

This is a sad entry, but 'just' solves the purpose. The query binds input at runtime 1,2,3 are variables in order of input.

Answer 10

bash (42 chars)

Pure bash:

((m=($3-$2)/($2-$1),c=$2-m*$1));echo $m $c

bash (31 chars)

Shelling out to something else:

owl -p"<%<%<$-1`4'-/%.32)2'*-."

(Based on Howard's OWL implementation)

Answer 11

VBA, 57 characters

Sub x(a,b,c)
y=(c-b)/(b-a)
MsgBox y & " " & b-a*y
End Sub

(This is basically the same as the other 'BASIC' functions, but I didn't see any VBA submissions out there already.)

Answer 12

This is (non-optimized) code for the unimited register machine, described here: http://www.proofwiki.org/wiki/Definition:Unlimited_Register_Machine

The input should be in register 1,2 and 3, and the output will be in register 1, 2 after the program is done. Non-negative and non-integer numbers are not handled, but inputs 0,7,14 and 2,5,11 are handled correctly.

Zero[8] Trans[2,11] Jump[3,11,7] Succ[11] Succ[8] Jump[11,11,3] Zero[5] Trans[1,12] Jump[2,12,13] Succ[12] Succ[5] Jump[12,12,9] Zero[17] Trans[8,13] Jump[13,17,25] Zero[16] Trans[5,14] Jump[13,14,22] Succ[14] Succ[16] Jump[14,14,18] Succ[9] Trans[16,13] Jump[17,17,15] Zero[6] Zero[20] Jump[9,6,40] Zero[7] Trans[1,21] Jump[20,7,36] Succ[21] Trans[21,19] Trans[19,21] Succ[7] Jump[7,7,30] Trans[21,18] Trans[18,20] Succ[6] Jump[6,6,27] Trans[20,4] Zero[10] Trans[4,15] Jump[2,15,47] Succ[15] Succ[10] Jump[15,15,43] Trans[9,1] Trans[10,2]

EDIT: by removing brackes, and shortening instruction names:

URM 285

Z8 T2,11 J3,11,7 S11 S8 J11,11,3 Z5 T1,12 J2,12,13 S12 S5 J12,12,9 Z17 T8,13 J13,17,25 Z16 T5,14 J13,14,22 S14 S16 J14,14,18 S9 T16,13 J17,17,15 Z6 Z20 J9,6,40 Z7 T1,21 J20,7,36 S21 T21,19 T19,21 S7 J7,7,30 T21,18 T18,20 S6 J6,6,27 T20,4 Z10 T4,15 J2,15,47 S15 S10 J15,15,43 T9,1 T10,2

Answer 13

Fortran 44

read*,i,j,k;k=(k-j)/(j-i);print*,k,j-i*k;end

Input will be in a single line (comma or space separated)

Cray Chapel 59

var i,j,k:int;read(i,j,k);k=(k-j)/(j-i);write(k," ",j-i*k);

Input will be on single line, no newline (add 2 chars for that by using writeln in place of write).

Golflua 44

r=I.r;a,b=r(),r();m=(r()-b)/(b-a);w(m,b-m*a)

Newline delimited input, space delimited output

Answer 14

Julia, 71 characters

Space delimited input and output.

i,j,k=int(split(readline(STDIN)));println("$(l=div(k-j,j-i)) $(j-i*l)")

Example input and output:

julia> i,j,k=int(split(readline(STDIN)));println("$(l=div(k-j,j-i)) $(j-i*l)")
5 -19 77
-4 1

Piet, 86 60 56 codels (14x4), codel size 10 for better visibility

I could actually shrink down the amount of codels by a whopping 35%. I didn’t expect such a good outcome. Coding this program backwards was, as I expected, quite successful. I doubt it can be shorter than this, but I would be really interested if anyone could find a smaller solution.

The challenge does not state if the program has to stop after showing the result, so my smallest (56 codel) program should be valid. It just loops back to the beginning after showing the result, asking for a new triplet of integers. Due to the tight packing there is no place for the output of two newline characters, but that is no problem with the npiet interpreter, because it always prints a ‘?’ if it awaits input.

There are two possible sizes to build a looped version, but a version that runs only once is only possible in a program that’s at least 64 codels (16x4) big. The versions below show the reason. Maybe it’s also interesting for those who are familiar with Piet.

The final, most tightly packed 56 codel version, with a loop:

Second version (60 codels), with a loop

If the 56 codel version is against the rules, here is the final 64 codel version, running only once:

My first version (86 codels)

Input and output are newline delimited.

Example input and output:

D:\codegolf\npiet-1.3a-win32>npiet ml_series.png
? 5
? -19
? 77
-4
1

For looped versions, looking a bit uglier:

D:\codegolf\npiet-1.3a-win32>npiet ml_series_56_codels.png"
? 5
? -19
? 77
-4
1? 5
? -19
? 77
-4
1? 5
? -19
? 77
-4
1?

I chose newline as delimiter because coding ASCII 10 (\n) obviously needs only 7 codels, compared to ASCII 32 ( ) which needs 8 codels or even ASCII 40 (,) which needs 9 codels.

Coding backwards from the result to the first input is a great way to reduce the codel use for ROL operations. The stack order at the beginning and at the end are known, the rest is easily done by hand.

Here is a text version of the 64 codel program (with stack), in my made-up shorthand. The shorter programs just don’t terminate but loop back to the beginning.

NOP ADD DIV GRT DUP INC END
 0   +   /   >   =   c   ~
PSH SUB MOD PTR ROL OUN
 X   -   %   #   @   N
POP MUL NOT SWI INN OUC
 ?   *   !   $   n   C

                   1
        1    1   2 2     1                   a,b,c: input for series
      5 5  3 3 c c cb  3 3                       D: c-b
    b b bb b bbb b bcD D Da                      E: b-a
   bb b bb b baa a aaa a abE F                   F: D/E, (c-b)/(b-a), mul. const.
  bbb b ba a abb b bbb b bDDFFF    5             G: a*F, a(c-b)/(b-a)
 aaaa a aa a aaa a aaa a aaaaaaG  55 10          H: b-G, b-a*F, add. const.
aaaaa a ab b bbb b bbb b bbbbbbbH HH  H H
n=n==5X1X@3X1X@n2X1X@-3X1X@-/=N*-5X=  + CN~
| |            |     |     || |||\____/ ||
| |            |     |     || |||  |    |+———— output add. const.
| |            |     |     || |||  |    +————— output newline character
| |            |     |     || |||  +—————————— 5 DUP + =10, ASCII for \n
| |            |     |     || ||+————————————— H, add. const.
| |            |     |     || |+—————————————— G
| |            |     |     || +——————————————— output mul. const.
| |            |     |     |+————————————————— F, mul. const.
| |            |     |     +—————————————————— E
| |            |     +———————————————————————— D
| |            +—————————————————————————————— input c
| +——————————————————————————————————————————— input b
+————————————————————————————————————————————— input a

Answer 15

Q, 36

{a,x[2]-x[1]*a:%[x[2]-x 1;x[1]-x 0]}

usage

q){a,x[2]-x[1]*a:%[x[2]-x 1;x[1]-x 0]}each(0 7 14;2 5 11;2 0 -4;5 -19 77)
1  7 
2  1 
2  -4
-4 1

Answer 16

MoonScript(48 chars, newline delimited input, space delimited output)

r=io.read
a,b=r!,r!
m=(r!-b)/(b-a)
print m,b-m*a

Felix(86 chars, newline delimited input, comma delimited output)

gen r()=>int $ readln stdin;
var a,b=r(),r();
var m=(r()-b)/(b- a);
println(m,b- m*a);

Julia(84 chars, space delimited input, space delimited output)

a,b,c=tuple(map(int,split(readline(STDIN)))...)
m=(c-b)/(b-a)
println("$m $(b-m*a)")