Golf the xᵗʰ root of x

Question

While bored in high-school (when I was half my current age...), I found that \$f(x) = x^{x^{-1}}\$ had some interesting properties, including e.g. that the maximum \$f\$ for \$0 ≤ x\$ is \$f(e)\$, and that the binding energy per nucleon of an isotope can be approximated as \$6 × f(x ÷ 21)\$...

Anyway, write the shortest function or program that calculates the x^th root of x for any number in your language's domain.

Examples cases

For all languages

     -1   >       -1
   ¯0.2   >    -3125
   ¯0.5   >        4
    0.5   >     0.25
      1   >        1
      2   >    1.414
      e   >    1.444 
      3   >    1.442
    100   >    1.047
  10000   >    1.001

For languages that handle complex numbers

   -2   >        -0.7071i
    i   >            4.81         
   2i   >    2.063-0.745i
 1+2i   >   1.820-0.1834i
 2+2i   >   1.575-0.1003i

For languages that handle infinities

-1/∞   >   0    (or ∞ or ̃∞)
   0   >   0    (or 1 or ∞)
 1/∞   >   0
   ∞   >   1
  -∞   >   1

For languages that handle both infinities and complex numbers

 -∞-2i   >   1      (or ̃∞)

---

^{̃∞ denotes directed infinity.}

Answer 1

Awk, 8 bytes

$1^$1^-1

A shell command to check it

awk '{print $1^$1^-1}'

---

Longer version (+1) with

$1^(1/$1)

Answer 2

MATLAB, 11bytes

@(x)x^(1/x)

Creates an anonymous function. This will work with all test cases including complex numbers and infinities.

This also works with Octave. You can try online here. Simply enter something like:

f=@(x)x^(1/x)

At the command line of the online interpreter, then do:

f(-1)

To test.

Answer 3

C#, 25 bytes, type: double

Bare form of a lambda expression:

x=>System.Math.Pow(x,1/x)

The expression can be assigned to a function variable, e.g. (Func<double, double>), ...

System. can be omitted, if using System; is used (but more bytes).

Complete test program (143 bytes) with the input of the question:

using System;class P{static void Main(){Array.ForEach(new double[]{-.2,-.5,.5,1,2,Math.E,3,100,10000},x=>Console.WriteLine(Math.Pow(x,1/x)));}}

Result:

-3125
4
0,25
1
1,4142135623731
1,44466786100977
1,44224957030741
1,0471285480509
1,0009214583193

C#, 37 bytes, type: Complex

x=>System.Numerics.Complex.Pow(x,1/x)

Also the assembly for System.Numerics needs to be referenced. The division operator is overloaded for complex arguments.

Test program (189 bytes) with the input of the question for complex numbers:

using System;using C=System.Numerics.Complex;class P{static void Main(){Array.ForEach(new C[]{new C(-2,0),new C(0,1),new C(0,2),new C(1,2),new C(2,2)},x=>Console.WriteLine(C.Pow(x,1/x)));}}

Result:

(4,32963728535968E-17, -0,707106781186548)
(4,81047738096535, 0)
(2,0628722350809, -0,745007062179724)
(1,81984053615444, -0,183434723804562)
(1,57500291115344, -0,100274868564155)

Test program (264 bytes) with infinity:

using System;using C=System.Numerics.Complex;class P{static void Main(){var p=double.PositiveInfinity;var n=double.NegativeInfinity;Array.ForEach(new C[]{new C(-1/p,0),new C(0,0),new C(1/p,0),new C(p,0),new C(n,0),new C(n,2) },x=>Console.WriteLine(C.Pow(x,1/x)));}}

Result:

(0, 0)
(0, 0)
(0, 0)
(1, 0)
(1, 0)
(1, 0)

Answer 4

Vitsy, 4 + 1 (function declaration) = 5 bytes

Hey, look, my language actually does this. Go figure.

Di^^
D    Duplicate the top item (input)
 i   Push -1.
  ^  Pop top (-1), put the second to top to the power of the popped item (x^-1)
   ^ Same as above, except we now have the desired number.

This is a function that leaves the value requested on the stack. For view-ability, I have also made the program output on the Try it Online! link.

Try it Online!

Answer 5

PARI/GP, 9 bytes

x->x^x^-1

This is shorter than the alternatives x->x^(1/x) and x->sqrtn(x,x). It uses the right-associativity of ^ and the strong binding of the unary -. GP isn't quite functional enough to curry (a,b)->sqrtn(a,b) into (x)->sqrtn(x,x); the best it can manage is x->call(sqrtn,[x,x]) which is far too long.

Answer 6

Bean, 11 bytes

Hexdump:

00000000 26 4c a0 43 95 4c a5 3a 8e 20 43  &L C.L¥:. C
0000000b

Equivalent JavaScript:

A**(1/A)

Implicitly converts first line of input to number as A and implicitly outputs the result of the expression.

Try the demo here.

Try the test suite here.

Answer 7

Codename Dragon, 16 bytes

a=<>;dispa^(1/a)

I'm abusing the lack of a syntax error.

Ungolfed:

disp((a=<>)^(1/a))

This is a simple program that takes input through <>.

You can find an interpreter here, no github site yet.

Answer 8

Jolf, 5 bytes

Try it here!

^j/1j
 j    input
^ /1j to the 1/j pow.

Answer 9

Gnuplot, 13 bytes

f(x)=x**(1/x)

or

f(x)=x**x**-1

Answer 10

Brachylog, 8 7 bytes

Thanks to Fatalize for saving a byte.

^?^-1=.

Explanation

^?^-1=.
     =.   unify output with
^?^-1     input raised to the 1/input power

Answer 11

Lua, 20

n=(...)print(n^n^-1)

How it works:

n=(...)              Take input and store at n
       print(
             n^n^-1  n^(n^(-1))
                   )

Answer 12

dc, 8 6 chars

Outputs to the top of the stack:

?d1r/^

Or if I can expect the input at the top of the stack, this 5 char solution works too:

d1r/^

Explanation:

?        take input from STDIN and execute it (numbers are executed by pushing to the stack)
 d1r     duplicate top of stack, push 1 and swap them
    /^   divide and exponentiate

Alas, dc does not allow for fractional exponents so this answer does not actually work for any given inputs above 1, and gives the wrong answer for 0 < input < 1. It does the same thing as many of the other programs though.

Answer 13

Factor, 14 10 bytes

1 over / ^

Expects input on top of the stack.

Answer 14

Convex, 3 bytes

Convex is a new language that I am developing that is heavily based on CJam and Golfscript. The interpreter and IDE can be found here. Input is an integer into the command line arguments. Indexes are one-based. Uses the CP-1252 encoding. This answer in non-competing as it was created after this challenge.

_¹#

Explanation:

    Implied input
_   Duplicate top of stack
 ¹  Find reciprocal
  # Power
    Implied output

Answer 15

Racket, 28 22 bytes

(λ(n)(expt n(/ 1 n)))

@cat gets credit for the 6 byte save. Thanks!

Seriously, Racket is impossible to golf with :). Nothing to see here, move along!

Answer 16

Python 3: 34

n=complex(input());print(n**(1/n))

Unless I'm missing something this would do nicely. I like that Python normally uses spaces, but this solution doesn't need them.

Answer 17

05AB1E, 3 bytes

Dzm

Explanation:

D    # Duplicate the input
 z   # Inverse, 1 ÷ input
  m  # Power, calculating input ** (1 ÷ input)

Try it online!.

Answer 18

Quetzalcoatl, 4 bytes

c.I?

Explanation:

c    # Input
 .   # Duplicate
  I  # Inverse
   ? # Power

Answer 19

TI-Basic, 4 bytes

Ans^Ansֿ ¹

Since TI-Basic is tokenized, this code is a mere four bytes.

Answer 20

Mouse-2002, 13 bytes

x:x.b/x.&ROOT

Other programs assume the number's on the top of the stack and so shall I.

x:    ~ put TOS in x
x.    ~ push x
b /   ~ divide by 1
x.    ~ push x again
&ROOT ~ y to the x root

Answer 21

Scala, 33 bytes

def f=(x:Double)=>Math.pow(x,1/x)

Answer 22

Perl, 11 bytes

Added 2 bytes for -pn.

$_**=1/$_

Try it here !

Answer 23

Mumps, 14 Bytes

R I W I**(1/I)

R reads from input into variable I, and the W (write) statement does the mathematical calculations.

I will warn you: the output will be ugly as there are no implied newlines in Mumps, and at least the way I read the challenge, the OP didn't require them. If you did want cleaner output, add 2 bytes and add a newline:

R I W !,I**(1/I)

Answer 24

SQL (MySQL), 60 bytes

CREATE FUNCTION G(X REAL) RETURNS REAL RETURN POWER(X,1./X);

Caps lock is cruise control for cool golf.

Answer 25

Desmos, 14 bytes

a=1
\sqrt[a]{a}

Demonstration

Answer 26

tcl, 23

I post two approaches which occupy the exact same number of bytes.

puts [expr $n**(1./$n)]

—

puts [expr $n**$n**-1.]

Available to test on http://rextester.com/EMW19680

Answer 27

QBIC, 9 bytes

:?a^(1/a)

Gets a numeric input from the command line and does the math...

Answer 28

SmileBASIC, 18 bytes

INPUT X?POW(X,1/X)

Answer 29

Common Lisp, 24 bytes

(lambda(x)(expt x(/ x)))

Try it online!

Answer 30

Excel, 10 bytes

=A1^(1/A1)

Self explanatory.