Inputs                   Output

  1      1      1         1
  3      4      5         1.25
 42     42   3.14         ≈ 6.9476
 14      6     12         1.575
  6     12     14         1.575
0.5    0.6    0.7         ≈ 1.09375

S_Ḥ⁸÷P

Implicit argument [a, b, c].
S          Take the sum, a+b+c or 2*s
  Ḥ        Take the double, [2*a, 2*b, 2*c].
 _         Vectorized subtract, giving us [2*(s-a), 2*(s-b), 2*(s-c)].
   ⁸÷      Vectorized divide the initial left argument, the input [a, b, c],
             by [2*(s-a), 2*(s-b), 2*(s-c)].
     P     Take the product giving us the aspect ratio, abc/8(s-a)(s-b)(s-c).

SH_÷@HP

S÷_2Pİ

S÷_2Pİ  Main link. Argument: [a, b, c]

S       Sum; compute 2s := a + b + c.
 ÷      Divide; yield [2s ÷ a, 2s ÷ b, 2s ÷ c].
  _2    Subtract 2; yield [2s ÷ a - 2, 2s ÷ b - 2, 2s ÷ c - 2].
    P   Product; yield (2s ÷ a - 2)(2s ÷ b - 2)(2s ÷ c - 2).
     İ  Invert; yield 1 ÷ (2s ÷ a - 2)(2s ÷ b - 2)(2s ÷ c - 2).

a=>b=>c=>a*b*c/(b+c-a)/(a+c-b)/(a+b-c)

tsGE-/p

t    % Take input implicitly. Duplicate
     % STACK: [3 4 5], [3 4 5]
s    % Sum of array
     % STACK: [3 4 5], 12
G    % Push input again
     % STACK: [3 4 5], 12, [3 4 5]
E    % Multiply by 2, element-wise
     % STACK: [3 4 5], 12, [6 8 10]
-    % Subtract, element-wise
     % STACK: [3 4 5], [6 4 2]
/    % Divide, element-wise
     % STACK: [0.5 1 2.5]
p    % Product of array. Implicitly display
     % STACK: 1.25

O¹·-¹/P

O         # sum input
 ¹        # push input again
  ·       # multiply by 2
   -      # subtract from sum
    ¹/    # divide by input
      P   # product

x=scan();prod(x/(sum(x)-2*x))

(a#b)c=a*b*c/(b+c-a)/(a+c-b)/(a+b-c)

p=product
f v=p v/p((sum v-).(2*)<$>v)

@(v)prod(v./(sum(v)-2*v))

sum(v)        = 3+4+5 = 12
             sum(v)-2*v    = 12 - 2*[3,4,5] = 12 - [6,8,10] = [6,4,2]
         v./(sum(v)-2*v))  = [3,4,5] ./ [6,4,2] = [0.5,1,2.5]
    prod(v./(sum(v)-2*v))  = 0.5 * 1 * 2.5 = 1.25

1##&@@(#/(Tr@#-2#))&

fun a b c->a*.b*.c/.(b+.c-.a)/.(a+.c-.b)/.(a+.b-.c)

@@@prod[#0#1#2/1- +#1#0#2/1- +#2#0#1/1- +#2#1#0]

(((@@@prod[#0#1#2/1* * - +#1#0#2- +#2#0#1- +#2#1#0])3)4)5

(a,b,c)=>product([a,b,c,1/(b+c-a),1/(a+c-b),1/(a+b-c)])

;Σ♀/♂¬πì

Implicit input [a, b, c].
;    Duplicate [a, b, c].
Σ    sum() to get twice the semiperimeter, 2*s.
♀/   Vectorized divide 2*s by [a, b, c] to get [2*s/a, 2*s/b, 2*s/c].
♂¬   Vectorized subtract 2 to get [2*s/a-2, 2*s/b-2, 2*s/c-2].
π    Get the product of the above to get 8*(s/a-1)*(s/b-1)*(s/c-1).
     This is the same as 8(s-a)(s-b)(s-c)/abc.
ì    Invert to get the aspect ratio, abc/8(s-a)(s-b)(s-c).
     Implicit return.

(a,b,c)->a*b*c/(b+c-a)/(a-b+c)/(a+b-c)

public class Pcg101234 {
  interface F {
    double f(double a, double b, double c);
  }
  public static void main(String[] args) {
    F f = (a,b,c)->a*b*c/(b+c-a)/(a-b+c)/(a+b-c);

    System.out.println(f.f(1,1,1));
    System.out.println(f.f(3,4,5));
    System.out.println(f.f(42,42,3.14));
    System.out.println(f.f(14,6,12));
    System.out.println(f.f(6,12,14));
    System.out.println(f.f(0.5,0.6,0.7));
  }
}

1.0
1.25
6.947606226693615
1.575
1.575
1.09375

p%/*-)/+i
    2%

print(
  1 / fold(
    multiply,
    fold(add, i) / i - 2
  )
)

print(1 / product(sum(i) / i - 2))

Os/ÍPz

5k?dsa?dsb?dsc++2/sslalblc**lsla-lslb-lslc-8***/p

5k                                                # Set the output precision to 5 digits after the decimal
  ?dsa                                            # Prompt for first input value on first line, duplicate it, and then store it in register `a`
      ?dsb                                        # Prompt for second input, duplicate it, and store it in register `b`
          ?dsc                                    # Prompt for third input, duplicate it, and store it in register `c`
              ++2/ss                              # Sum up the 3 values on the main stack, then divide sum by 2 and store the result in register `s`
                    lalblc**                      # Copy all three values from registers `a`,`b`,`c` onto the main stack, find their product, and push result to top of main stack
                            lsla-                 # Copy value from register `s` onto main stack, subtract register `a`'s value from it, and push result to main stack
                                 lslb-            # Copy value from register `s` onto main stack, subtract register `b`'s value from it, and push result to main stack
                                      lslc-       # Copy value from register `s` onto main stack, subtract register `c`'s value from it, and push result to main stack
                                           8***   # Find the product of the top three values and 8 and then push the result to main stack
                                               /p # Divide the second to top value (a*b*c) by the top of stack value (8*(s-a)*(s-b)*(s-c)), push the result to the main stack, and then output the result to STDOUT

prod(Ans)/prod(sum(Ans)-2Ans

->a,b,c{a*b*c/(b+c -a)/(a+c -b)/(a+b -c)}

def f(x,y,z):s=x+y+z;return 1/((s/x-2)*(s/y-2)*(s/z-2))

: p 3 fpick ;
: T p p p ;
: f 0 s>f T f- f+ f- T f+ f- f* T f- f- f* 1/f f* f* f* ;

 3 fpick takes the 3rd element (0-indexed) and pushes a copy
 Used to copy parameters on the stack over another number 'x' ( a b c x -> a b c x a b c )
: f3p 3 fpick 3 fpick 3 fpick ;

: f                      define a function f
0 s>f f3p f- f+ f-       push a zero, copy params, compute 0-(a+b-c)
                         the zero allows me to copy (I need an 'x' to jump over)
f3p f+ f- f*             copy params and compute -(b+c-a), multiply by previous result
                         the negatives miraculously cancel
f3p f- f- f*             copy and compute (a+c-b), multiply by previous result
1/f f* f* f* ;           take the reciprocal and multiply by a*b*c
                         the result is left on the floating point stack

@*$1/@*{@+$1-2.*$1}

Π$1/Π{Σ$1-2.*$1}

Function r(a,b,c)
s=(a+b+c)/2:r=(a*b*c)/(8*(s-a)*(s-b)*(s-c))
End Function

void ar(double a,double b,double c)=>Console.Write(a*b*c/(b+c-a)/(a+c-b)/(a+b-c));

ar(42, 42, 3.14);

1QFQsR/tt)B/

{(*/x)%8*/-x-+/x%2}

a,b,c=...print(a*b*c/(b+c-a)/(a+c-b)/(a+b-c))