Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5

Percentage Accurate: 70.7% → 84.0%

Time: 12.4s

Alternatives: 7

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (* 2.0 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))

C

double code(double x, double y, double z) {
	return 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt((((x * y) + (x * z)) + (y * z)))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 * Math.sqrt((((x * y) + (x * z)) + (y * z)));
}

Python

def code(x, y, z):
	return 2.0 * math.sqrt((((x * y) + (x * z)) + (y * z)))

Julia

function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(Float64(Float64(x * y) + Float64(x * z)) + Float64(y * z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
end

Wolfram

code[x_, y_, z_] := N[(2.0 * N[Sqrt[N[(N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 70.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (* 2.0 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))

C

double code(double x, double y, double z) {
	return 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt((((x * y) + (x * z)) + (y * z)))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 * Math.sqrt((((x * y) + (x * z)) + (y * z)));
}

Python

def code(x, y, z):
	return 2.0 * math.sqrt((((x * y) + (x * z)) + (y * z)))

Julia

function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(Float64(Float64(x * y) + Float64(x * z)) + Float64(y * z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
end

Wolfram

code[x_, y_, z_] := N[(2.0 * N[Sqrt[N[(N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 84.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 0.105:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y, x \cdot \left(y + z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(x, y \cdot \sqrt{\frac{1}{\left(y + x\right) \cdot \left(z \cdot \left(z \cdot z\right)\right)}}, 2 \cdot \sqrt{\frac{y + x}{z}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 0.105)
   (* 2.0 (sqrt (fma z y (* x (+ y z)))))
   (*
    z
    (fma
     x
     (* y (sqrt (/ 1.0 (* (+ y x) (* z (* z z))))))
     (* 2.0 (sqrt (/ (+ y x) z)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.105) {
		tmp = 2.0 * sqrt(fma(z, y, (x * (y + z))));
	} else {
		tmp = z * fma(x, (y * sqrt((1.0 / ((y + x) * (z * (z * z)))))), (2.0 * sqrt(((y + x) / z))));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 0.105)
		tmp = Float64(2.0 * sqrt(fma(z, y, Float64(x * Float64(y + z)))));
	else
		tmp = Float64(z * fma(x, Float64(y * sqrt(Float64(1.0 / Float64(Float64(y + x) * Float64(z * Float64(z * z)))))), Float64(2.0 * sqrt(Float64(Float64(y + x) / z)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 0.105], N[(2.0 * N[Sqrt[N[(z * y + N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y * N[Sqrt[N[(1.0 / N[(N[(y + x), $MachinePrecision] * N[(z * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[Sqrt[N[(N[(y + x), $MachinePrecision] / z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.104999999999999996

   1. Initial program 78.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot y + x \cdot z\right) + y \cdot z}} \]

      2. +-commutative N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot z + \left(x \cdot y + x \cdot z\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot z} + \left(x \cdot y + x \cdot z\right)} \]

      4. *-commutative N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y} + \left(x \cdot y + x \cdot z\right)} \]

      5. lower-fma.f64 78.1

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(z, y, x \cdot y + x \cdot z\right)}} \]

      6. lift-+.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, \color{blue}{x \cdot y + x \cdot z}\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, \color{blue}{x \cdot y} + x \cdot z\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, x \cdot y + \color{blue}{x \cdot z}\right)} \]

      9. distribute-lft-out N/A

         \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, \color{blue}{x \cdot \left(y + z\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, \color{blue}{x \cdot \left(y + z\right)}\right)} \]

      11. lower-+.f64 78.2

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, x \cdot \color{blue}{\left(y + z\right)}\right)} \]

   4. Applied rewrites 78.2%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(z, y, x \cdot \left(y + z\right)\right)}} \]

   if 0.104999999999999996 < y

   1. Initial program 55.4%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot y + x \cdot z\right)} + y \cdot z} \]

      2. lift-*.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\left(\color{blue}{x \cdot y} + x \cdot z\right) + y \cdot z} \]

      3. lift-*.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\left(x \cdot y + \color{blue}{x \cdot z}\right) + y \cdot z} \]

      4. distribute-lft-out N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)} + y \cdot z} \]

      5. *-commutative N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y + z\right) \cdot x} + y \cdot z} \]

      6. flip-+ N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\frac{y \cdot y - z \cdot z}{y - z}} \cdot x + y \cdot z} \]

      7. associate-*l/ N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\frac{\left(y \cdot y - z \cdot z\right) \cdot x}{y - z}} + y \cdot z} \]

      8. lower-/.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\frac{\left(y \cdot y - z \cdot z\right) \cdot x}{y - z}} + y \cdot z} \]

      9. lower-*.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\frac{\color{blue}{\left(y \cdot y - z \cdot z\right) \cdot x}}{y - z} + y \cdot z} \]

      10. difference-of-squares N/A

          \[\leadsto 2 \cdot \sqrt{\frac{\color{blue}{\left(\left(y + z\right) \cdot \left(y - z\right)\right)} \cdot x}{y - z} + y \cdot z} \]

      11. lower-*.f64 N/A

          \[\leadsto 2 \cdot \sqrt{\frac{\color{blue}{\left(\left(y + z\right) \cdot \left(y - z\right)\right)} \cdot x}{y - z} + y \cdot z} \]

      12. lower-+.f64 N/A

          \[\leadsto 2 \cdot \sqrt{\frac{\left(\color{blue}{\left(y + z\right)} \cdot \left(y - z\right)\right) \cdot x}{y - z} + y \cdot z} \]

      13. lower--.f64 N/A

          \[\leadsto 2 \cdot \sqrt{\frac{\left(\left(y + z\right) \cdot \color{blue}{\left(y - z\right)}\right) \cdot x}{y - z} + y \cdot z} \]

      14. lower--.f64 31.7

          \[\leadsto 2 \cdot \sqrt{\frac{\left(\left(y + z\right) \cdot \left(y - z\right)\right) \cdot x}{\color{blue}{y - z}} + y \cdot z} \]

   4. Applied rewrites 31.7%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\frac{\left(\left(y + z\right) \cdot \left(y - z\right)\right) \cdot x}{y - z}} + y \cdot z} \]

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(2 \cdot \sqrt{\frac{x + y}{z}} + \left(x \cdot y\right) \cdot \sqrt{\frac{1}{{z}^{3} \cdot \left(x + y\right)}}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(2 \cdot \sqrt{\frac{x + y}{z}} + \left(x \cdot y\right) \cdot \sqrt{\frac{1}{{z}^{3} \cdot \left(x + y\right)}}\right)} \]

      2. +-commutative N/A

         \[\leadsto z \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot \sqrt{\frac{1}{{z}^{3} \cdot \left(x + y\right)}} + 2 \cdot \sqrt{\frac{x + y}{z}}\right)} \]

      3. associate-*l* N/A

         \[\leadsto z \cdot \left(\color{blue}{x \cdot \left(y \cdot \sqrt{\frac{1}{{z}^{3} \cdot \left(x + y\right)}}\right)} + 2 \cdot \sqrt{\frac{x + y}{z}}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(x, y \cdot \sqrt{\frac{1}{{z}^{3} \cdot \left(x + y\right)}}, 2 \cdot \sqrt{\frac{x + y}{z}}\right)} \]

   7. Applied rewrites 99.7%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(x, y \cdot \sqrt{\frac{1}{\left(x + y\right) \cdot \left(z \cdot \left(z \cdot z\right)\right)}}, 2 \cdot \sqrt{\frac{x + y}{z}}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.105:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y, x \cdot \left(y + z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(x, y \cdot \sqrt{\frac{1}{\left(y + x\right) \cdot \left(z \cdot \left(z \cdot z\right)\right)}}, 2 \cdot \sqrt{\frac{y + x}{z}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{+18}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y, x \cdot \left(y + z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \sqrt{\frac{z}{y}}, 2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2.7e+18)
   (* 2.0 (sqrt (fma z y (* x (+ y z)))))
   (fma x (sqrt (/ z y)) (* 2.0 (* (sqrt z) (sqrt y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.7e+18) {
		tmp = 2.0 * sqrt(fma(z, y, (x * (y + z))));
	} else {
		tmp = fma(x, sqrt((z / y)), (2.0 * (sqrt(z) * sqrt(y))));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 2.7e+18)
		tmp = Float64(2.0 * sqrt(fma(z, y, Float64(x * Float64(y + z)))));
	else
		tmp = fma(x, sqrt(Float64(z / y)), Float64(2.0 * Float64(sqrt(z) * sqrt(y))));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 2.7e+18], N[(2.0 * N[Sqrt[N[(z * y + N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision] + N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.7e18

   1. Initial program 79.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot y + x \cdot z\right) + y \cdot z}} \]

      2. +-commutative N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot z + \left(x \cdot y + x \cdot z\right)}} \]

      3. lift-*.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot z} + \left(x \cdot y + x \cdot z\right)} \]

      4. *-commutative N/A

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y} + \left(x \cdot y + x \cdot z\right)} \]

      5. lower-fma.f64 79.1

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(z, y, x \cdot y + x \cdot z\right)}} \]

      6. lift-+.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, \color{blue}{x \cdot y + x \cdot z}\right)} \]

      7. lift-*.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, \color{blue}{x \cdot y} + x \cdot z\right)} \]

      8. lift-*.f64 N/A

         \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, x \cdot y + \color{blue}{x \cdot z}\right)} \]

      9. distribute-lft-out N/A

         \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, \color{blue}{x \cdot \left(y + z\right)}\right)} \]

      10. lower-*.f64 N/A

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, \color{blue}{x \cdot \left(y + z\right)}\right)} \]

      11. lower-+.f64 79.3

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(z, y, x \cdot \color{blue}{\left(y + z\right)}\right)} \]

   4. Applied rewrites 79.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(z, y, x \cdot \left(y + z\right)\right)}} \]

   if 2.7e18 < y

   1. Initial program 42.2%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \sqrt{y \cdot z} + \left(x \cdot \left(y + z\right)\right) \cdot \sqrt{\frac{1}{y \cdot z}}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(y + z\right)\right) \cdot \sqrt{\frac{1}{y \cdot z}} + 2 \cdot \sqrt{y \cdot z}} \]

      2. associate-*l* N/A

         \[\leadsto \color{blue}{x \cdot \left(\left(y + z\right) \cdot \sqrt{\frac{1}{y \cdot z}}\right)} + 2 \cdot \sqrt{y \cdot z} \]

      3. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\left(\sqrt{\frac{1}{y \cdot z}} \cdot \left(y + z\right)\right)} + 2 \cdot \sqrt{y \cdot z} \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, \sqrt{\frac{1}{y \cdot z}} \cdot \left(y + z\right), 2 \cdot \sqrt{y \cdot z}\right)} \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(y + z\right) \cdot \sqrt{\frac{1}{y \cdot z}}}, 2 \cdot \sqrt{y \cdot z}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(y + z\right) \cdot \sqrt{\frac{1}{y \cdot z}}}, 2 \cdot \sqrt{y \cdot z}\right) \]

      7. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(y + z\right)} \cdot \sqrt{\frac{1}{y \cdot z}}, 2 \cdot \sqrt{y \cdot z}\right) \]

      8. lower-sqrt.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \left(y + z\right) \cdot \color{blue}{\sqrt{\frac{1}{y \cdot z}}}, 2 \cdot \sqrt{y \cdot z}\right) \]

      9. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(x, \left(y + z\right) \cdot \sqrt{\color{blue}{\frac{1}{y \cdot z}}}, 2 \cdot \sqrt{y \cdot z}\right) \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, \left(y + z\right) \cdot \sqrt{\frac{1}{\color{blue}{y \cdot z}}}, 2 \cdot \sqrt{y \cdot z}\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, \left(y + z\right) \cdot \sqrt{\frac{1}{y \cdot z}}, \color{blue}{2 \cdot \sqrt{y \cdot z}}\right) \]

      12. lower-sqrt.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, \left(y + z\right) \cdot \sqrt{\frac{1}{y \cdot z}}, 2 \cdot \color{blue}{\sqrt{y \cdot z}}\right) \]

      13. lower-*.f64 42.4

          \[\leadsto \mathsf{fma}\left(x, \left(y + z\right) \cdot \sqrt{\frac{1}{y \cdot z}}, 2 \cdot \sqrt{\color{blue}{y \cdot z}}\right) \]

   5. Applied rewrites 42.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(y + z\right) \cdot \sqrt{\frac{1}{y \cdot z}}, 2 \cdot \sqrt{y \cdot z}\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 98.4%

      \[\leadsto \mathsf{fma}\left(x, \left(y + z\right) \cdot \sqrt{\frac{1}{y \cdot z}}, 2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\right) \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(x, \sqrt{\frac{z}{y}}, 2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 98.7%

       \[\leadsto \mathsf{fma}\left(x, \sqrt{\frac{z}{y}}, 2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Developer Target 1: 83.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\\ \mathbf{if}\;z < 7.636950090573675 \cdot 10^{+176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(t\_0 \cdot t\_0\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z)))
          (* (pow z 0.25) (pow y 0.25)))))
   (if (< z 7.636950090573675e+176)
     (* 2.0 (sqrt (+ (* (+ x y) z) (* x y))))
     (* (* t_0 t_0) 2.0))))

C

double code(double x, double y, double z) {
	double t_0 = (0.25 * ((pow(y, -0.75) * (pow(z, -0.75) * x)) * (y + z))) + (pow(z, 0.25) * pow(y, 0.25));
	double tmp;
	if (z < 7.636950090573675e+176) {
		tmp = 2.0 * sqrt((((x + y) * z) + (x * y)));
	} else {
		tmp = (t_0 * t_0) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (0.25d0 * (((y ** (-0.75d0)) * ((z ** (-0.75d0)) * x)) * (y + z))) + ((z ** 0.25d0) * (y ** 0.25d0))
    if (z < 7.636950090573675d+176) then
        tmp = 2.0d0 * sqrt((((x + y) * z) + (x * y)))
    else
        tmp = (t_0 * t_0) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (0.25 * ((Math.pow(y, -0.75) * (Math.pow(z, -0.75) * x)) * (y + z))) + (Math.pow(z, 0.25) * Math.pow(y, 0.25));
	double tmp;
	if (z < 7.636950090573675e+176) {
		tmp = 2.0 * Math.sqrt((((x + y) * z) + (x * y)));
	} else {
		tmp = (t_0 * t_0) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.25 * ((math.pow(y, -0.75) * (math.pow(z, -0.75) * x)) * (y + z))) + (math.pow(z, 0.25) * math.pow(y, 0.25))
	tmp = 0
	if z < 7.636950090573675e+176:
		tmp = 2.0 * math.sqrt((((x + y) * z) + (x * y)))
	else:
		tmp = (t_0 * t_0) * 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.25 * Float64(Float64((y ^ -0.75) * Float64((z ^ -0.75) * x)) * Float64(y + z))) + Float64((z ^ 0.25) * (y ^ 0.25)))
	tmp = 0.0
	if (z < 7.636950090573675e+176)
		tmp = Float64(2.0 * sqrt(Float64(Float64(Float64(x + y) * z) + Float64(x * y))));
	else
		tmp = Float64(Float64(t_0 * t_0) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.25 * (((y ^ -0.75) * ((z ^ -0.75) * x)) * (y + z))) + ((z ^ 0.25) * (y ^ 0.25));
	tmp = 0.0;
	if (z < 7.636950090573675e+176)
		tmp = 2.0 * sqrt((((x + y) * z) + (x * y)));
	else
		tmp = (t_0 * t_0) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.25 * N[(N[(N[Power[y, -0.75], $MachinePrecision] * N[(N[Power[z, -0.75], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Power[z, 0.25], $MachinePrecision] * N[Power[y, 0.25], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, 7.636950090573675e+176], N[(2.0 * N[Sqrt[N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 * t$95$0), $MachinePrecision] * 2.0), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 763695009057367500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* 2 (sqrt (+ (* (+ x y) z) (* x y)))) (* (* (+ (* 1/4 (* (* (pow y -3/4) (* (pow z -3/4) x)) (+ y z))) (* (pow z 1/4) (pow y 1/4))) (+ (* 1/4 (* (* (pow y -3/4) (* (pow z -3/4) x)) (+ y z))) (* (pow z 1/4) (pow y 1/4)))) 2)))

  (* 2.0 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))