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

Percentage Accurate: 70.3% → 84.3%

Time: 10.6s

Alternatives: 9

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: 70.3% 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: 84.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 7.8 \cdot 10^{-302}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, z, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{z}\right) \cdot \sqrt{y + x}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 7.8e-302)
   (* 2.0 (sqrt (fma x z (* y x))))
   (* (* 2.0 (sqrt z)) (sqrt (+ y x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.8e-302) {
		tmp = 2.0 * sqrt(fma(x, z, (y * x)));
	} else {
		tmp = (2.0 * sqrt(z)) * sqrt((y + x));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 7.8e-302)
		tmp = Float64(2.0 * sqrt(fma(x, z, Float64(y * x))));
	else
		tmp = Float64(Float64(2.0 * sqrt(z)) * sqrt(Float64(y + x)));
	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, 7.8e-302], N[(2.0 * N[Sqrt[N[(x * z + N[(y * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[z], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(y + x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.7999999999999998e-302

   1. Initial program 71.1%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-out N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-lowering-+.f64 N/A

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

      7. *-lowering-*.f64 71.2

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

   4. Applied egg-rr 71.2%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 51.4%

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

   if 7.7999999999999998e-302 < y

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-lowering-+.f64 51.6

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

   5. Simplified 51.6%

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

      1. pow1/2 N/A

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

      2. unpow-prod-down N/A

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

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. pow1/2 N/A

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

      7. sqrt-lowering-sqrt.f64 N/A

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

      8. pow1/2 N/A

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

      9. sqrt-lowering-sqrt.f64 N/A

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

      10. +-lowering-+.f64 47.3

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

   7. Applied egg-rr 47.3%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.8 \cdot 10^{-302}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, z, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{z}\right) \cdot \sqrt{y + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.85 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(y + x, z, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2.85e+59)
   (* 2.0 (sqrt (fma (+ y x) z (* y x))))
   (* y (* 2.0 (sqrt (/ z y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.85e+59) {
		tmp = 2.0 * sqrt(fma((y + x), z, (y * x)));
	} else {
		tmp = y * (2.0 * sqrt((z / y)));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 2.85e+59)
		tmp = Float64(2.0 * sqrt(fma(Float64(y + x), z, Float64(y * x))));
	else
		tmp = Float64(y * Float64(2.0 * sqrt(Float64(z / 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, 2.85e+59], N[(2.0 * N[Sqrt[N[(N[(y + x), $MachinePrecision] * z + N[(y * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(y * N[(2.0 * N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.8500000000000001e59

   1. Initial program 76.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-out N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-lowering-+.f64 N/A

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

      7. *-lowering-*.f64 77.0

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

   4. Applied egg-rr 77.0%

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

   if 2.8500000000000001e59 < y

   1. Initial program 51.5%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-lowering-+.f64 24.6

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

   5. Simplified 24.6%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sqrt-lowering-sqrt.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. sqrt-lowering-sqrt.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. cube-mult N/A

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

      9. unpow2 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. unpow2 N/A

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

      12. *-lowering-*.f64 31.8

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

   8. Simplified 31.8%

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

   9. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

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

       2. sqrt-lowering-sqrt.f64 N/A

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

       3. /-lowering-/.f64 31.8

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

   11. Simplified 31.8%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.85 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(y + x, z, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.85 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(y + x, z, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{z}\right) \cdot \sqrt{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2.85e+59)
   (* 2.0 (sqrt (fma (+ y x) z (* y x))))
   (* (* 2.0 (sqrt z)) (sqrt y))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.85e+59) {
		tmp = 2.0 * sqrt(fma((y + x), z, (y * x)));
	} else {
		tmp = (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 <= 2.85e+59)
		tmp = Float64(2.0 * sqrt(fma(Float64(y + x), z, Float64(y * x))));
	else
		tmp = Float64(Float64(2.0 * 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, 2.85e+59], N[(2.0 * N[Sqrt[N[(N[(y + x), $MachinePrecision] * z + N[(y * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[z], $MachinePrecision]), $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.8500000000000001e59

   1. Initial program 76.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-out N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-lowering-+.f64 N/A

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

      7. *-lowering-*.f64 77.0

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

   4. Applied egg-rr 77.0%

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

   if 2.8500000000000001e59 < y

   1. Initial program 51.5%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-lowering-+.f64 24.6

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

   5. Simplified 24.6%

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

      1. pow1/2 N/A

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

      2. unpow-prod-down N/A

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

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. pow1/2 N/A

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

      7. sqrt-lowering-sqrt.f64 N/A

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

      8. pow1/2 N/A

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

      9. sqrt-lowering-sqrt.f64 N/A

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

      10. +-lowering-+.f64 40.9

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

   7. Applied egg-rr 40.9%

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

   8. Taylor expanded in x around 0

      \[\leadsto \left(2 \cdot \sqrt{z}\right) \cdot \color{blue}{\sqrt{y}} \]
   9. Step-by-step derivation

      1. sqrt-lowering-sqrt.f64 39.2

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

   10. Simplified 39.2%

       \[\leadsto \left(2 \cdot \sqrt{z}\right) \cdot \color{blue}{\sqrt{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.85 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(y + x, z, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{z}\right) \cdot \sqrt{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, z, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.7e-233)
   (* 2.0 (sqrt (fma x z (* y x))))
   (* 2.0 (sqrt (* z (+ y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e-233) {
		tmp = 2.0 * sqrt(fma(x, z, (y * x)));
	} else {
		tmp = 2.0 * sqrt((z * (y + x)));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.7e-233)
		tmp = Float64(2.0 * sqrt(fma(x, z, Float64(y * x))));
	else
		tmp = Float64(2.0 * sqrt(Float64(z * Float64(y + x))));
	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, -1.7e-233], N[(2.0 * N[Sqrt[N[(x * z + N[(y * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7000000000000001e-233

   1. Initial program 72.6%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-out N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-lowering-+.f64 N/A

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

      7. *-lowering-*.f64 72.7

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

   4. Applied egg-rr 72.7%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 49.2%

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

   if -1.7000000000000001e-233 < y

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-lowering-+.f64 53.4

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

   5. Simplified 53.4%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, z, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.7e-233)
   (* 2.0 (sqrt (* x (+ y z))))
   (* 2.0 (sqrt (* z (+ y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e-233) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * sqrt((z * (y + x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.7d-233)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else
        tmp = 2.0d0 * sqrt((z * (y + x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e-233) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * Math.sqrt((z * (y + x)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.7e-233:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	else:
		tmp = 2.0 * math.sqrt((z * (y + x)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.7e-233)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	else
		tmp = Float64(2.0 * sqrt(Float64(z * Float64(y + x))));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.7e-233)
		tmp = 2.0 * sqrt((x * (y + z)));
	else
		tmp = 2.0 * sqrt((z * (y + x)));
	end
	tmp_2 = 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, -1.7e-233], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7000000000000001e-233

   1. Initial program 72.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-lowering-+.f64 49.2

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

   5. Simplified 49.2%

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

   if -1.7000000000000001e-233 < y

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-lowering-+.f64 53.4

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

   5. Simplified 53.4%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.7e-233) (* 2.0 (sqrt (* x (+ y z)))) (* 2.0 (sqrt (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e-233) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * sqrt((y * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.7d-233)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else
        tmp = 2.0d0 * sqrt((y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e-233) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * Math.sqrt((y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.7e-233:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	else:
		tmp = 2.0 * math.sqrt((y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.7e-233)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	else
		tmp = Float64(2.0 * sqrt(Float64(y * z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.7e-233)
		tmp = 2.0 * sqrt((x * (y + z)));
	else
		tmp = 2.0 * sqrt((y * z));
	end
	tmp_2 = 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, -1.7e-233], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7000000000000001e-233

   1. Initial program 72.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-lowering-+.f64 49.2

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

   5. Simplified 49.2%

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

   if -1.7000000000000001e-233 < y

   1. Initial program 73.4%

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

   3. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot z}} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 24.2

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot z}} \]

   5. Simplified 24.2%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 70.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(2.0 * sqrt(fma(Float64(y + x), z, Float64(y * x))))
end

Wolfram

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

Derivation

1. Initial program 73.1%

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

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. distribute-rgt-out N/A

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

   4. *-commutative N/A

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

   5. accelerator-lowering-fma.f64 N/A

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

   6. +-lowering-+.f64 N/A

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

   7. *-lowering-*.f64 73.2

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

4. Applied egg-rr 73.2%

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

5. Final simplification 73.2%

   \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(y + x, z, y \cdot x\right)} \]
6. Add Preprocessing

Alternative 8: 67.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.7e-233) (* 2.0 (sqrt (* y x))) (* 2.0 (sqrt (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e-233) {
		tmp = 2.0 * sqrt((y * x));
	} else {
		tmp = 2.0 * sqrt((y * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.7d-233)) then
        tmp = 2.0d0 * sqrt((y * x))
    else
        tmp = 2.0d0 * sqrt((y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e-233) {
		tmp = 2.0 * Math.sqrt((y * x));
	} else {
		tmp = 2.0 * Math.sqrt((y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.7e-233:
		tmp = 2.0 * math.sqrt((y * x))
	else:
		tmp = 2.0 * math.sqrt((y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.7e-233)
		tmp = Float64(2.0 * sqrt(Float64(y * x)));
	else
		tmp = Float64(2.0 * sqrt(Float64(y * z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.7e-233)
		tmp = 2.0 * sqrt((y * x));
	else
		tmp = 2.0 * sqrt((y * z));
	end
	tmp_2 = 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, -1.7e-233], N[(2.0 * N[Sqrt[N[(y * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7000000000000001e-233

   1. Initial program 72.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y}} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 22.1

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y}} \]

   5. Simplified 22.1%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y}} \]

   if -1.7000000000000001e-233 < y

   1. Initial program 73.4%

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

   3. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot z}} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 24.2

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot z}} \]

   5. Simplified 24.2%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-233}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ 2 \cdot \sqrt{y \cdot x} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* 2.0 (sqrt (* y x))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return 2.0 * sqrt((y * x));
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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((y * x))
end function

Java

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return 2.0 * math.sqrt((y * x))

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(y * x)))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = 2.0 * sqrt((y * x));
end

Wolfram

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

Derivation

1. Initial program 73.1%

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

3. Taylor expanded in z around 0

   \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y}} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 22.1

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y}} \]

5. Simplified 22.1%

   \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y}} \]

6. Final simplification 22.1%

   \[\leadsto 2 \cdot \sqrt{y \cdot x} \]
7. Add Preprocessing

Developer Target 1: 82.0% 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 2024195 
(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)))))