Weapons of Math Instruction

Question

Last time when I tried to come up with something easy that wasn't a duplicate, it ended up being way too hard.. So hopefully this time it's indeed something newcomers can try as well.

Input:

An array/list with integers/decimals. (Or a string representing an array with integers/decimals.)

Output:

Loop through the numbers and apply the following five mathematical operands in this order:

• Addition (+);
• Subtraction (−);
• Multiplication (* or × or ·);
• Real / Calculator Division (/ or ÷);
• Exponentiation (^ or **).

(NOTE: The symbols between parenthesis are just added as clarification. If your programming language uses a completely different symbol for the mathematical operation than the examples, then that is of course completely acceptable.)

Keep continuing until you've reached the end of the list, and then give the result of the sum.

Challenge rules:

• Exponentiation by 0 (n ^ 0) should result in 1 (this also applies to 0 ^ 0 = 1).
• There are no test cases for division by 0 (n / 0), so you don't have to worry about that edge-case.
• If the array contains just a single number, we return that as the result.

General rules:

• This is code-golf, so shortest answer in bytes wins.
  Don't let code-golf languages discourage you from posting answers with non-codegolfing languages. Try to come up with an as short as possible answer for 'any' programming language.
• Standard rules apply for your answer, so you are allowed to use STDIN/STDOUT, functions/method with the proper parameters, full programs. Your call.
• Default Loopholes are forbidden.
• If possible, please add a link with a test for your code.

Test cases:

[1,2,3,4,5] -> 0
-> 1 + 2 = 3
  -> 3 - 3 = 0
    -> 0 * 4 = 0
      -> 0 / 5 = 0 

[5,12,23,2,4,4,2,6,7] -> 539
-> 5 + 12 = 17
  -> 17 - 23 = -6
    -> -6 * 2 = -12
      -> -12 / 4 = -3
        -> -3 ^ 4 = 81
          -> 81 + 2 = 83
            -> 83 - 6 = 77
              -> 77 * 7 -> 539

[-8,50,3,3,-123,4,17,99,13] -> -1055.356...
-> -8 + 50 = 42
  -> 42 - 3 = 39
    -> 39 * 3 = 117
      -> 117 / -123 = -0.9512...
        -> -0.9512... ^ 4 = 0.818...
          -> 0.818... + 17 = 17.818...
            -> 17.818... - 99 -> -81.181...
              -> -81.181... * 13 = -1055.356...

[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] -> 256
-> 2 + 2 = 4
  -> 4 - 2 = 2
    -> 2 * 2 = 4
      -> 4 / 2 = 2
        -> 2 ^ 2 = 4
          -> 4 + 2 = 6
            -> 6 - 2 = 4
              -> 4 * 2 = 8
                -> 8 / 2 = 4
                  -> 4 ^ 2 = 16
                    -> 16 + 2 = 18
                      -> 18 - 2 = 16
                        -> 16 * 2 = 32
                          -> 32 / 2 = 16
                            -> 16 ^ 2 = 256

[1,0,1,0,1,0] -> 1
-> 1 + 0 = 1
  -> 1 - 1 = 0
    -> 0 * 0 = 0
      -> 0 / 1 = 0
        -> 0 ^ 0 = 1

[-9,-8,-1] -> -16
  -> -9 + -8 = -17
    -> -17 - -1 = -16

[0,-3] -> -3
  -> 0 + -3 = -3

[-99] -> -99

Answer 1

Javascript ES7 49 bytes

a=>a.reduce((c,d,e)=>[c**d,c+d,c-d,c*d,c/d][e%5])

Saved 9 bytes thanks to Dom Hastings, saved another 6 thanks to Leaky Nun

Uses the new exponentiation operator.

Answer 2

Haskell, 76 65 64 62 bytes

Thanks to @Damien for removing another two bytes=)

f(u:v)=foldl(\x(f,y)->f x y)u(zip(v>>[(+),(-),(*),(/),(**)])v)

This uses the >> which here just appends the list [(+),...] to itself length v times. The rest still works still the same as the old versions.

Old versions:

These solutions make use of the infinite lists, as cycle[...] just repeats the given list infinitely. Then it basically gets ziped with the list of numbers, and we just fold (reduce in other languages) the zipped list via a lambda, that applies the operators to the accumulator/current list element.

f(u:v)=foldl(\x(f,y)->f x y)u(zip(cycle[(+),(-),(*),(/),(**)])v)

f(u:v)=foldl(\x(y,f)->f x y)u(zip v(cycle[(+),(-),(*),(/),(**)]))

f l=foldl(\x(y,f)->f x y)(head l)(zip(drop 1l)(cycle[(+),(-),(*),(/),(**)]))

Answer 3

Pyke, 22 21 bytes

lt5L%"+-*/^"L@\RJQ_XE

Try it here!

lt5L%                 -    map(len(input)-1, %5)
     "+-*/^"L@        -   map(^, "+-*/^"[<])
              \RJ     -  "R".join(^)
                    E - pyke_eval(^, V)
                 Q_X  -  splat(reversed(input))

Answer 4

Jelly, 13 bytes

“+_×÷*”ṁṖ⁸żFV

Try it online! or verify all test cases.

How it works

“+_×÷*”ṁṖ⁸żFV  Main link. Argument: A (list of integers)

“+_×÷*”        Yield the list of operations as a string.
        Ṗ      Yield A popped, i.e., with its last element removed.
       ṁ       Mold; reshape the string as popped A.
               This repeats the characters of the string until it contains
               length(A)-1 characters.
         ⁸ż    Zipwith; pairs the integers of A with the corresponding characters.
           F   Flatten the result.
            V  Eval the resulting Jelly code.
               Jelly always evaluates left-to-right (with blatant disregard towards
               the order of operations), so this returns the desired result.

Answer 5

Haskell, 61 Bytes

foldl(flip id)0.zipWith flip((+):cycle[(+),(-),(*),(/),(**)])

Creates a series of transformations in a list, as in [add 1, add 2, subtract 3, ...], starting with 2 additions because we start with 0 in the fold. Next, we do what I call the List Application Fold, or foldl (flip id), which applies a list of homomorphisms in series. This starts with zero, adds the initial value, then does all of the above computed transformations to get a final result.

Note that (flip id) is the same as (\x y->y x), just shorter.

Sample usage:

f = foldl(flip id)0.zipWith flip((+):cycle[(+),(-),(*),(/),(**)])
f [1,2,3,4,5] -- Is 0.0

Answer 6

TSQL 116 115 88 bytes

Thanks to Ross Presser suggestion I was able to golf this down to 88 characters

-- In Try-it code, this must be DECLARE @y TABLE 
CREATE TABLE T(a real, i int identity)
INSERT T values(5),(12),(23),(2),(4),(4),(2),(6),(7)

DECLARE @ REAL SELECT @=CHOOSE(i%5+1,@/a,ISNULL(POWER(@,a),a),@+a,@-a,@*a)FROM T
PRINT @

Try it online

Answer 7

Pyth, 27 26 25 bytes

.v+>tlQ*lQ"^c*-+":jdQ\-\_

Test suite.

Pyth uses prefix notation: 1+2 is written as +1 2 (space needed to separate numbers).

Therefore, for the first testcase, the expression would be (((1+2)-3)*4)/5, which in prefix notation, would be written as /*-+ 1 2 3 4 5.

In Pyth, float division is c instead of /, so it becomes c*-+ 1 2 3 4 5.

Also, in Pyth, -100 is written as _100 instead.

Therefore, for the third test case, which is ((((((((-8+50)-3)*3)/-123)^4)+17)-99)*13), it becomes: *-+^c*-+ _8 50 3 3 _123 4 17 99 13.

.v+>tlQ*lQ"^c*-+":jdQ\-\_
                  jdQ       Join input by space.
                 :   \-\_   Replace "-" with "_".
   >tlQ*lQ"^c*-+"           Generate the string "...^c*-+" of suitable length.
  +                         Join the two strings above.
.v                          Evaluate as a Pyth expression.

History

• 33 bytes: v:P+*lQ\(ssV+R\)Q*"+-*/p"lQ\p"**"
• 27 bytes: .vs+_XUtQUQ"+-*c^"m:+;d\-\_
• 26 bytes: .vs+_XUtQUQ"+-*c^":jdQ\-\_

Answer 8

Actually, 23 bytes

;l"+-*/ⁿ"*@R':j':+'?o+ƒ

Try it online!

Actually uses postfix notation for mathematics, and operators that only ever take two arguments (such as the operators for addition, subtraction, multiplication, division, and exponentiation) do nothing when there is only one element on the stack. Thus, turning the input into Actually code is as simple as reversing the input, formatting it as numerics, and appending the operations. Then, the resultant code can be executed, giving the desired output.

Explanation:

;l"+-*/ⁿ"*@R':j':+'?o+ƒ
;l"+-*/ⁿ"*               repeat the operations a number of times equal to the length of the input
                            (since extraneous operations will be NOPs, there's no harm in overshooting)
          @R             reverse the input
            ':j          join on ":" (make a string, inserting ":" between every pair of elements in the list)
               ':+       prepend a ":" (for the first numeric literal)
                  '?o    append a "?"
                           (this keeps the poor numeric parsing from trying to gobble up the first + as part of the numeric literal, since ? isn't interpreted as part of the literal, and is a NOP)
                     +   append the operations string
                      ƒ  cast as a function and call it

Example of translated code for input 1,2,3,4,5:

:5:4:3:2:1?+-*/ⁿ+-*/ⁿ+-*/ⁿ+-*/ⁿ+-*/ⁿ

Answer 9

Julia, 53 50 bytes

!x=(i=0;foldl((a,b)->(+,-,*,/,^)[i=i%5+1](a,b),x))

Try it online!

Answer 10

J, 40 bytes

^~`(%~)`*`(-~)`+/@(|.@,7#:~#&2)(5-5|4+#)

Finds the number of values needed to use a multiple of 5 operators, than pads with the identity values of those operators. In order, + is 0, - is 0, * is 1, % is 1, and ^ is 1, which can be a bit value 00111, or 7 in base 10. Then operates on that list while cycling through operators.

Usage

   f =: ^~`(%~)`*`(-~)`+/@(|.@,7#:~#&2)(5-5|4+#)
   f 1 2 3 4 5
0
   f 5 12 23 2 4 4 2 6 7
539
   f _8 50 3 3 _123 4 17 99 13
_1055.36
   f 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
256
   f 1 0 1 0 1 0
1
   f _9 _8 _1
_16
   f 0 _3
_3
   f _99
_99

Explanation

^~`(%~)`*`(-~)`+/@(|.@,7#:~#&2)(5-5|4+#) Input: A
                                      #  Get length of A
                                    4+   Add four to it
                                  5|     Take it mod 5
                                5-       Find 5 minus its value, call it x
                           #&2           Create x copies of 2
                       7#:~              Convert 7 to base 2 and take the last x digits
                      ,                  Append those x digits to the end of A
                   |.@                   Reverse it, call it A'
^~                                       Power, reversed operators
    %~                                   Division, reversed operators
       *                                 Multiplication
         -~                              Subtraction, reversed operators
            +                            Addition
             /@                          Insert the previous operations, separated by `,
                                         into A' in order and cycle until the end
                                         Then evaluate the equation from right-to-left
                                         and return

Answer 11

Python 2, 81 67 64 bytes

i=10
for n in input():exec'r%s=n'%'*+-*/*'[i::5];i=-~i%5
print r

Input is an array of floats. Test it on Ideone.

How it works

'*+-*/*'[i::5] selects every fifth character of the string, starting with the one at index i, so this yields ** if i = 0, + if i = 1, - if i = 2, * if i = 3 and / if i = 4. Since the string has length 6, the expression will yield an empty string if i > 5.

We initialize the variable i to 10. For each number n in the input array, we construct the string r<op>=n, which exec executes.

Initially, i = 10, so <op> is the empty string, and it initializes r with r+=n. After each step, we increment i modulo 5 with i=-~i%5, so the next step will retrieve the proper operator.

When all input numbers has been processed, and we print r, which holds the desired output.

Answer 12

Matlab - 95 91 85 bytes / Octave - 81 bytes

Input is in such form: a = ['1' '2' '3' '4' '5'];, I hope this is covered by "string representing an array with integers/decimals", else there are 2 num2str needed additionally.

Every intermediate result gets printed to console because that saves me some semicolons. a(1) is executed so its value is then saved to ans. Also of course using ans in code is bad practice.

b='+-*/^'
a(1)
for i=2:length(a)
  ['(',ans,')',b(mod(i-2,5)+1),a(i)]
end
eval(ans)

In Octave, '+-*/^'(mod(i+2,5)+1) also works, which saves another 4 bytes, thanks Adám and Luis Mendo:

a(1)
for i=2:length(a)
  strcat('(',ans,')','+-*/^'(mod(i-2,5)+1),a(i))
end
eval(ans)

Changelog:

• Removed spaces where possible
• added Octave solution
• replaced strcat() with []

Answer 13

Mathematica, 67 66 65 bytes

Fold[{+##,#-#2,#2#,#/#2,If[#2==0,1,#^#2]}[[i++~Mod~5+1]]&,i=0;#]&

Simple Fold with a variable i holding the index.

Answer 14

CJam, 18 bytes

q~{"+-*/#"W):W=~}*

Input is an array of floats. Try it online!

How it works

q~                  Read and evaluate all input.
  {             }*  Reduce:
   "+-*/#"            Push the string of operators.
          W           Push W (initially -1).
           ):W        Increment and save in W.
              =       Retrieve the character at that index.
               ~      Evaluate.

Answer 15

R, 87 78 70 bytes

i=0
Reduce(function(a,j)get(substr("+-*/^",i<<-i%%5+1,i))(a,j),scan())

Try it online!

Answer 16

Haskell - 74

f(x:xs)=foldl(\x(o,y)->o x y)x(zip(cycle[(+),(-),(*),(/),flip(^).floor])xs)

Test cases:

λ> f[1,2,3,4,5] -> 0.0
λ> f[5,12,23,2,4,4,2,6,7] -> 539.0
λ> f[-8,50,3,3,-123,4,17,99,13] -> -1055.356943846277
λ> f [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] -> 256.0

It could probably be shorter; Haskell's support for infinite lists and higher order functions make the direct solution quite pleasant, though. A version of ^ :: Double -> Double -> Double would be nicer for golfing, but I couldn't find one. Thankfully, I didn't need a full lambda, so pointless style shaved off a few bytes.

Answer 17

PowerShell v2+, 124 bytes

param($n)$o=$n[0];if($y=$n.count-1){1..$y|%{$o=if(($x=$i++%5)-4){"$o"+'+-*/'[$x]+$n[$_]|iex}else{[math]::pow($o,$n[$_])}}}$o

Long because PowerShell doesn't have a ^ or ** operator, so we have to account for a separate case and use a .NET call.

Takes input $n as an array, sets our output $o to be the first digit. We then check the .count of the array, and so long as it's greater than one we enter the if. Otherwise, we skip the if.

Inside the if we loop through the array 1..$y|%{...} and each iteration we re-set $o to a new value, the result of another if/else statement. So long as our counter $i++ isn't modulo-5 equal to 4 (i.e., we're not at the ^ operator), we simply take $o and concatenate it with the appropriate symbol '+-*/'[$x] and the next number in the input array $n[$_]. We pipe that to iex (alias for Invoke-Expression and similar to eval), and that gets re-saved to $o. If we're on the ^ operator, we're in the else, so we execute a [math]::Pow() call, and that result gets re-saved back into $o.

In either case, we simply output $o to the pipeline and exit, with output implicit.

Answer 18

Rust, 123, 117 bytes

Original answer:

fn a(v:&[f32])->f32{v.iter().skip(1).enumerate().fold(v[0],|s,(i,&x)|match i%5{0=>s+x,1=>s-x,2=>s*x,3=>s/x,_=>s.powf(x)})}

stupid long method names ^^ ahh much better

fn f(v:&[f32])->f32{v[1..].iter().zip(0..).fold(v[0],|s,(&x,i)|match i%5{0=>s+x,1=>s-x,2=>s*x,3=>s/x,_=>s.powf(x)})}

ungolfed

fn f(values : &[f32]) -> f32 {
    values[1..].iter().zip(0..)
    .fold(values[0], |state,(&x,i)|
        match i%5 {
            0=>state+x,
            1=>state-x,
            2=>state*x,
            3=>state/x,
            _=>state.powf(x)
        }
    )
}

Answer 19

Perl 6,  70 68 65  62 bytes

{$/=[(|(&[+],&[-],&[*],&[/],&[**])xx*)];.reduce: {$/.shift.($^a,$^b)}}
{(@_ Z |(&[+],&[-],&[*],&[/],&[**])xx*).flat.reduce: {&^b($^a,$^c)}}
{(@_ Z |(*+*,*-*,&[*],*/*,&[**])xx*).flat.reduce: {&^b($^a,$^c)}}
{reduce {&^b($^a,$^c)},flat @_ Z |(*+*,*-*,&[*],*/*,&[**])xx*}

Explanation:

-> *@_ {
  reduce
    -> $a, &b, $c { b($a,$c) },

    flat       # flatten list produced from zip
      zip
        @_,    # input

        slip(  # causes the list of operators to flatten into the xx list

          # list of 5 infix operators
          &infix:<+>, &infix:<->, &infix:<*>, &infix:</>, &infix:<**>

        ) xx * # repeat the list of operators infinitely
}

Technically * + * is a Whatever lambda, but is effectively the same as &[+] which is short for &infix:<+> the set of subroutines that handle infix numeric addition.
I didn't use that for multiplication or exponentiation as the ways to write them like that is at least as long as what I have (*×* or * * * and * ** *)

Test:

Test it on ideone.com
(after they upgrade to a Rakudo version that isn't from a year and a half before the official release of the Perl 6 spectests)

#! /usr/bin/env perl6

use v6.c;
use Test;

my @tests = (
  [1,2,3,4,5] => 0,
  [5,12,23,2,4,4,2,6,7] => 539,
  [-8,50,3,3,-123,4,17,99,13] => -1055.35694385, # -2982186493/2825761
  [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 256,
  [1,0,1,0,1,0] => 1,
  [-9,-8,-1] => -16,
  [0,-3] => -3,
  [-99] => -99,
);

plan +@tests;

my &code = {reduce {&^b($^a,$^c)},flat @_ Z |(*+*,*-*,&[*],&[/],&[**])xx*}

for @tests -> $_ ( :key(@input), :value($expected) ) {
  is code(@input), $expected, .gist
}

1..8
ok 1 - [1 2 3 4 5] => 0
ok 2 - [5 12 23 2 4 4 2 6 7] => 539
ok 3 - [-8 50 3 3 -123 4 17 99 13] => -1055.35694385
ok 4 - [2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2] => 256
ok 5 - [1 0 1 0 1 0] => 1
ok 6 - [-9 -8 -1] => -16
ok 7 - [0 -3] => -3
ok 8 - [-99] => -99

Answer 20

Python 3, 88 93 bytes

f=lambda x:eval('('*(len(x)-1)+'){}'.join(map(str,x)).format(*['+','-','*','/','**']*len(x)))

It started off being much shorter but then operator precedence defeated me and I had to include lots of parenthesis...

Answer 21

Oracle PL/SQL, 275 254 Bytes

declare r number;begin for x in (select n,mod(rownum,5)r from t) loop if r is null then r:=x.n;elsif x.r=2then r:=r+x.n;elsif x.r=3then r:=r-x.n;elsif x.r=4then r:=r*x.n;elsif x.r=0then r:=r/x.n;else r:=r**x.n;end if;end loop;DBMS_OUTPUT.PUT_LINE(r);end;

The data must be inserted in a table called T with a column N of type NUMBER

Usage:

drop table t;
create table t (n number);
insert into t values (-8);
insert into t values (50);
insert into t values (3);
insert into t values (3);
insert into t values (-123);
insert into t values (4);
insert into t values (17);
insert into t values (99);
insert into t values (13);

declare r number;begin for x in (select n,mod(rownum,5)r from t) loop if r is null then r:=x.n;elsif x.r=2then r:=r+x.n;elsif x.r=3then r:=r-x.n;elsif x.r=4then r:=r*x.n;elsif x.r=0then r:=r/x.n;else r:=r**x.n;end if;end loop;DBMS_OUTPUT.PUT_LINE(r);end;

Output:

-1055,356943846277162152071601242992595623

275 Bytes version:

declare r number;cursor c is select n,mod(rownum,5) r from t;begin for x in c loop if r is null then r:=x.n;else case x.r when 2 then r:=r+x.n;when 3 then r:=r-x.n;when 4 then r:=r*x.n;when 0 then r:=r/x.n;else r:=r**x.n; end case;end if;end loop;DBMS_OUTPUT.PUT_LINE(r);end;

Answer 22

Java 8, 173 172 167 138 137 118 113 bytes

a->{double r=a[0],t;for(int i=1;i<a.length;r=new double[]{Math.pow(r,t),r+t,r-t,r*t,r/t}[i++%5])t=a[i];return r;}

Explanation:

Try it here.

a->{                     // Method with double-array parameter and double return-type
  double r=a[0],         //  Result-double, starting at the first item of the input
         t;              //  Temp double
  for(int i=1;           //  Index-integer, starting at the second item
      i<a.length;        //  Loop over the input-array
      r=new double[]{    //    After every iteration, change `r` to:
         Math.pow(r,t),  //      If `i%5` is 0: `r^t`
         r+t,            //      Else-if `i%5` is 1: `r+t`
         r-t,            //      Else-if `i%5` is 2: `r-t`
         r*t,            //      Else-if `i%5` is 3: `r*t`
         r/t}[i++%5])    //      Else-if `i%5` is 4: `r/t`
                         //      And increase `i` by 1 afterwards with `i++`
    t=a[i];              //   Change `t` to the next item in the array
  return r;}             //  Return result-double

Answer 23

A few tricks can reduce @Willmore´s approach by 23 to 174 bytes (requires php 5.6 or later). The most saving part is removing unneccessary parentheses (-10 bytes).

function f($a){while(count($a)>1){$l=array_shift($a);$r=array_shift($a);array_unshift($a,($j=$i++%5)?($j==1?$l-$r:($j==2?$l*$r:($j==3?$l/$r:$l**$r))):$l+$r);}return end($a);}

But using the ** operator instead of pow() also allows to use eval with an array for the operations; and with a few more tricks ...

PHP >= 5.6, 82 bytes

while(--$argc)eval('$x'.['/','**','+','-','*'][$i++?$i%5:2]."=$argv[$i];");echo$x;

takes list from command line parameters. Run with php -nr '<code>' or try it online.

old version, 161 157 151 145 144 140 137 117 bytes

function f($a){while(count($a)>1)eval('$a[0]=array_shift($a)'.['+','-','*','/','**'][$i++%5].'$a[0];');return$a[0];}

The most effective golfing came from writing the intermediate result directly to the first element - after shifting the previous result from the array.

breakdown

function f($a)
{
    while(count($a)>1)  // while array has more than one element ...
        eval('$a[0]='                           // future first element :=
            . 'array_shift($a)'                 // = old first element (removed)
            . ['+','-','*','/','**'][$i++%5]    // (operation)
            .'$a[0];'                           // new first element (after shift)
        );
    return$a[0];        // return last remaining element
}

test suite

$cases = array (
    0=>[1,2,3,4,5],
    539=>[5,12,23,2,4,4,2,6,7],
    '-1055.356...' => [-8,50,3,3,-123,4,17,99,13],
    256 => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2],
    1 => [1,0,1,0,1,0],
    -16 => [-9,-8,-1],
    -3 => [0, -3],
    -99 => [-99]
);
echo '<table border=1><tr><th>values</th><th>expected</th><th>actual result</th></tr>';
foreach ($cases as $expect=>$a)
{
    $result=f($a);
    echo "<tr><td>[", implode(',',$a),"]</td><td>$expect</td><td>$result</td></tr>";
}
echo '</table>';

Answer 24

PHP, 135 130 bytes

Thanks @titus, -5 bytes, plus 0 case fix!

function f($z){return array_reduce($z,function($c,$x)use(&$i){eval('$c'.['/','**','+','-','*'][$i++?$i%5:5].'=$x;');return$c;});};

Try it online!

Less golfy:

function f( $t ) {
    return array_reduce( $t,
        function( $c, $x ) use( &$i ) {
            eval('$c'.['/','**','+','-','*'][$i++?$i%5:5].'=$x;');
            return $c;
        }
    );
};

Was really rooting for array_reduce() to work for this, but requires too many chars to beat the current lowest PHP score.

Posting it anyway in case anyone has any suggestions!

Answer 25

Brachylog, 68 bytes

hI,?bL,1:+:-:*:/:^b:L:I{bhv?t.|[O:L:I]h$(P,LbM,OhA,Lh:Ir:A&:M:Pr&.}.

That's long… but it uses no evaluation predicate.

Explanation

• Main predicate

  hI,                                  Unify I with the first element of the input
     ?bL,                              L is the input minus the first element
         1:+:-:*:/:^b                  Construct the list of predicates [+:-:*:/:^]
                     :L:I{...}.        Call predicate 1 with [[+:-:*:/:^]:L:I] as input
  

• Predicate 1

  bhv?t.                               If the second element of Input is empty (i.e. L),
                                       unify Output with the last element of Input
  |                                    Or
  [O:L:I]                              Input = [O:L:I]
         h$(P,                         P is O circularly permutated to the left
              LbM,                     M is L minus the first element
                  OhA,                 A is the first element of O
                      Lh:Ir:A&         Call predicate A on [I:First element of L]
                              :M:Pr&.  Call predicate 1 recursively with P:M:
  

Answer 26

IBM PC 8087 FPU, 66 82 bytes

Uses only the IBM PC's Intel 8087 math-coprocessor for calculations.

Try it offline! (in DOSBox or whatever). Give your old PC's bored 8087 chip something do to, other than all of those Lotus 1-2-3 spreadsheets you used to do in the 80's.

9bdf 0783 c302 499b de07 83c3 0249 e342 9bde 2783 c302 49e3 399b de0f 83c3 0249 
e330 9bde 3783 c302 49e3 2751 8b0f 9bd9 e883 f900 7413 9c7f 02f7 d99b d8c9 e2fb 
9d7d 069b d9e8 9bd8 f159 83c3 0249 e302 ebb5 c3

Ungolfed (unassembled):

START: 
    ; RUN TESTS  
    MOV  BX, OFFSET TST     ; 5, 12, 23, 2, 4, 4, 2, 6, 7
    MOV  CX, CTST           ; input array length
    CALL WOMI               ; calculate sequence
    CALL PRINT_FLT          ; output to console

    MOV  BX, OFFSET TST1    ; 5, 12, 23, 2, 4, -4, 2, 6, 7
    MOV  CX, CTST1
    CALL WOMI
    CALL PRINT_FLT

    MOV  BX, OFFSET TST2    ; -8, 50, 3, 3, -123, 4, 17, 99, 13
    MOV  CX, CTST2
    CALL WOMI
    CALL PRINT_FLT

    MOV  BX, OFFSET TST3    ; 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
    MOV  CX, CTST3
    CALL WOMI
    CALL PRINT_FLT

    MOV  BX, OFFSET TST4    ; 1,0,1,0,1,0
    MOV  CX, CTST4
    CALL WOMI
    CALL PRINT_FLT

    MOV  BX, OFFSET TST5    ; -9, -8, -1
    MOV  CX, CTST5
    CALL WOMI
    CALL PRINT_FLT

    MOV  BX, OFFSET TST6    ; 0, -3
    MOV  CX, CTST6
    CALL WOMI
    CALL PRINT_FLT

    MOV  AX, 4C00H          ; exit to DOS
    INT  21H

;  TEST DATA

TST   DW  5, 12, 23, 2, 4, 4, 2, 6, 7
CTST  EQU ($-TST)/(SIZE TST)    ; count of items on list

TST1  DW  5, 12, 23, 2, 4, -4, 2, 6, 7
CTST1 EQU ($-TST1)/(SIZE TST1)  ; count of items on list

TST2  DW -8, 50, 3, 3, -123, 4, 17, 99, 13
CTST2 EQU ($-TST2)/(SIZE TST2)  ; count of items on list

TST3  DW 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
CTST3 EQU ($-TST3)/(SIZE TST3)  ; count of items on list

TST4  DW 1,0,1,0,1,0
CTST4 EQU ($-TST4)/(SIZE TST4)  ; count of items on list

TST5  DW -9, -8, -1
CTST5 EQU ($-TST5)/(SIZE TST5)  ; count of items on list

TST6  DW 0, -3
CTST6 EQU ($-TST6)/(SIZE TST6)  ; count of items on list

; 8087 exponent: ST(0) = ST(0) ^ EXP
FIEXP   MACRO   EXP
        LOCAL   REPEAT, DONE
        PUSH CX
        MOV  CX, EXP        ; Exponent is count for loop
        FLD1                ; load 1 into ST
        CMP  CX, 0          ; is exponent pos, neg or 0?
        JZ   DONE           ; exit (with value 1) if exponent is 0
        PUSHF               ; save result flags for later
        JG   REPEAT         ; if exp > 1 start calculation
        NEG  CX             ; make exponent positive for loop
REPEAT:
        FMUL ST(0), ST(1)   ; multiply ST0 = ST0 * ST1
        LOOP REPEAT
        POPF                ; retrieve flags from earlier
        JGE  DONE           ; if exponent was negative, divide 1 by result
        FLD1                ; push 1 into numerator
        FDIV ST(0), ST(1)   ; ST0 = 1 / ST1
DONE:
        POP  CX
        ENDM

; Function WOMI: (Weapons of Math Instruction)
; input: BX - address of start of input array
;       CX - length of input array
; output: ST - result on top of 8087 register stack
WOMI PROC
    FILD WORD PTR [BX]      ; load first item
    ADD  BX, 2              ; move to next
    DEC  CX
CALC:
    FIADD WORD PTR [BX]     ; add
    ADD  BX, 2              ; move to next
    DEC  CX                 ; decrement counter
    JCXZ OUTPUT             ; check if done

    FISUB WORD PTR [BX]     ; subtract
    ADD  BX, 2
    DEC  CX
    JCXZ OUTPUT

    FIMUL WORD PTR [BX]     ; multiply
    ADD  BX, 2
    DEC  CX
    JCXZ OUTPUT

    FIDIV WORD PTR [BX]     ; divide
    ADD  BX, 2
    DEC  CX
    JCXZ OUTPUT

    FIEXP [BX]              ; exponent
    ADD  BX, 2
    DEC  CX
    JCXZ OUTPUT
    JMP CALC                ; start again

OUTPUT:
    RET 
WOMI ENDP

PRINT_FLT PROC
; print top of 8087 stack
; scaling: 14 digits, 4 decimal places
; input: BX = address of a TBYTE (BCD) output buffer
;       ST = value to display on top of 8087 stack  
    LEA   BX, BUFF                  ; set BX to BCD output buffer
    MOV   AH, 2
    MOV   WORD  PTR[BX], 10000      ; ten thousand (scale factor)
    FIMUL WORD  PTR[BX]             ; scale up by 10000
    FBSTP TBYTE PTR[BX]             ; store as BCD
    FWAIT                           ; sync 8088 and 8087
    TEST  BYTE  PTR[BX+9], 80H      ; check sign bit
    JE    PF_1                      ; 0, goto PF_1
    MOV   DL, '-'                   ; output '-'
    INT   21H
PF_1:
    ADD   BX, 8                     ; point to high byte
    MOV   CH, 7                     ; 14 digits before decimal point
    MOV   CL, 4                     ; 4 shifts (8 bytes / 2 = 4 = 1 nibble)
    MOV   DH, 2                     ; 2 times (8 bytes / 4)
PF_LOOP:
    MOV   DL, [BX]                  ; get BCD digits
    SHR   DL, CL                    ; move high digit to low nibble
    OR    DL, 30H                   ; convert to ASCII
    INT   21H
    MOV   DL, [BX]                  ; get byte again
    AND   DL, 0FH                   ; mask out high digit
    OR    DL, 30H                   ; convert to ASCII
    INT   21H                       ; output
    DEC   BX                        ; next byte
    DEC   CH                        ; decrement byte
    JG    PF_LOOP                   ; repeat if more bytes
    DEC   DH                        ; second time?
    JE    PF_DONE                   ; yes, done
    MOV   DL, '.'                   ; no, output decimal point
    INT   21H
    MOV   CH, 2                     ; 4 more digits after decimal point
    JMP   PF_LOOP                   ; go print digits
PF_DONE:
    MOV  DL, 0DH                    ; display newline CRLF
    MOV  AH, 2
    INT  21H
    MOV  DL, 0AH
    INT  21H
    RET 
PRINT_FLT ENDP

BUFF DT 0   ; output buffer for floating point digit string

_TEXT ENDS
END START

Output:

A>WOMI.COM
00000000000539.0000
-00000000000027.9136
-00000000001055.3569
00000000000256.0000
00000000000001.0000
-00000000000016.0000
-00000000000003.0000

Input is via a PROC (x86 most equivalent to a function), with BX being a pointer to an array of WORDs in memory, and CX being the number of items in it and returns the result in ST.

*Note: The actual code for the function is 66 82 bytes. Of course, the code just to write a floating point number to the console (cookbook code) is 83 bytes. The testing program and data is 183 215 bytes, making the .COM executable 305 380 bytes in total.

Answer 27

APL (Dyalog Unicode), 29 27 bytes^SBCS

Anomymous tacit prefix function. Note that * is exponentiation in APL.

≢{⍎3↓⍕⌽⍵,¨⍨⍺⍴'+-×÷*',¨'⍨'}⊢

Try it online!

Because APL executes right to left, we can just reverse the order of arguments of the inserted operations and reverse the entire expression. Postfix ⍨ reverses arguments. After doing a perfect shuffle of numbers and operations, we only just need to reverse, flatten, and evaluate:

≢{…}⊢ call the following function with count of and actual numbers as ⍺ and ⍵:

 '⍨' this character

 '+-×÷*',¨ prepend each of these characters to that; ["+⍨","-⍨","×⍨","÷⍨","*⍨"]

 ⍺⍴ use the left argument (count of numbers) to cyclically reshape that

 ⌽ reverse

 ⍕ format as flat string

 3↓ drop leading 3 characters (a space and a symbol and ⍨)

 ⍎ execute as APL code

Answer 28

Japt, 16 bytes

r@[XY]r"p+-*/"gZ

Try it online!

Explanation:

r@                  #Reduce the input list:
       "p+-*/"      # The list of functions to apply (offset by one due to the behavior of Z)
              gZ    # Choose the one at the current index, wrapping
  [  ]r             # Apply that function to:
   X                #  The result of the previous step
    Y               #  and the current number
                    #Implicitly return the result of the final step

Answer 29

c#, 238, 202 bytes

double d(double[]a){Array.Reverse(a);var s=new Stack<double>(a);int i=0,j;while(s.Count>1){double l=s.Pop(),r=s.Pop();j=i++%5;s.Push(j==0?l+r:j==1?l-r:j==2?l*r:j==3?l/r:Math.Pow(l,r));}return s.Peek();}

I didn't see any c# solution so I will give one. This is my first codegolf. I started writing in c# "two months ago" (though I know Java to some extent).

It uses Stack

Ungolfed and test cases

using System;
using System.Collections.Generic;

class M 
{
    double d(double[]a) {
        Array.Reverse(a);
        var s = new Stack<double>(a);
        int i=0,j;
        while (s.Count>1)
        {
            double l=s.Pop(),r=s.Pop();
            j=i++%5;
            s.Push(j==0?l+r:j==1?l-r:j==2?l*r:j==3?l/r:Math.Pow(l, r));
        }
        return s.Peek();
    }

    public static void Main()
    {
        int[][] a = new int[][]{
            new int[]{1,2,3,4,5},
            new int[]{5,12,23,2,4,4,2,6,7},
            new int[]{-8,50,3,3,-123,4,17,99,13},
            new int[]{2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
            new int[]{1,0,1,0,1,0},
            new int[]{-9,-8,-1},
            new int[]{0,-3},
            new int[]{-99}
        };

        for (int i = 0; i < a.Length; i++)
        {
            Console.WriteLine(new M().d(Array.ConvertAll(a[i], e => Convert.ToDouble(e))));
        }
        Console.ReadKey();
    }
}

Output:

0
539
-1055,35694384628
256
1
-16
-3
-99

Answer 30

PHP, 206,198,197 bytes

function f($a){while(count($a)>1){$l=array_shift($a);$r=array_shift($a);array_unshift($a,($j=$i++%5)==0?($l+$r):($j==1?($l-$r):($j==2?($l*$r):($j==3?($l/$r):(pow($l,$r))))));}return array_pop($a);}

Ungolfed

<?php
 
function f($a)
{
    while(count($a)>1)
    {
        $l = array_shift($a); $r = array_shift($a);
        array_unshift($a,($j=$i++%5)==0?($l+$r):($j==1?($l-$r):($j==2?($l*$r):($j==3?($l/$r):(pow($l,$r))))));
    }
    return array_pop($a);
}
 
echo f([1,2,3,4,5])."\n";
echo f([5,12,23,2,4,4,2,6,7])."\n";
echo f([-8,50,3,3,-123,4,17,99,13])."\n";
echo f([2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2])."\n";
echo f([1,0,1,0,1,0])."\n";
echo f([-9,-8,-1])."\n";
echo f([0,-3])."\n";
echo f([-99])."\n";

In PHP, logic similar to my c# answer (202 bytes) :) .