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

Percentage Accurate: 70.1% → 94.0%

Time: 11.3s

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: 70.1% 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: 94.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \sqrt{\left(y \cdot x + x \cdot z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot \sqrt{y}, \sqrt{z}, x \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -7.3e+49)
   (* 2.0 (pow (exp (* 0.25 (- (log (- (- z) y)) (log (/ -1.0 x))))) 2.0))
   (if (<= y 5e+62)
     (* 2.0 (sqrt (+ (+ (* y x) (* x z)) (* y z))))
     (fma (* 2.0 (sqrt y)) (sqrt z) (* x (sqrt (/ z y)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.3e+49) {
		tmp = 2.0 * pow(exp((0.25 * (log((-z - y)) - log((-1.0 / x))))), 2.0);
	} else if (y <= 5e+62) {
		tmp = 2.0 * sqrt((((y * x) + (x * z)) + (y * z)));
	} else {
		tmp = fma((2.0 * sqrt(y)), sqrt(z), (x * sqrt((z / y))));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -7.3e+49)
		tmp = Float64(2.0 * (exp(Float64(0.25 * Float64(log(Float64(Float64(-z) - y)) - log(Float64(-1.0 / x))))) ^ 2.0));
	elseif (y <= 5e+62)
		tmp = Float64(2.0 * sqrt(Float64(Float64(Float64(y * x) + Float64(x * z)) + Float64(y * z))));
	else
		tmp = fma(Float64(2.0 * sqrt(y)), sqrt(z), Float64(x * 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, -7.3e+49], N[(2.0 * N[Power[N[Exp[N[(0.25 * N[(N[Log[N[((-z) - y), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+62], N[(2.0 * N[Sqrt[N[(N[(N[(y * x), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[y], $MachinePrecision]), $MachinePrecision] * N[Sqrt[z], $MachinePrecision] + N[(x * N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.30000000000000014e49

   1. Initial program 58.9%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. sqr-pow N/A

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

      4. pow2 N/A

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

      5. lower-pow.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. distribute-lft-out N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. metadata-eval 59.0

          \[\leadsto 2 \cdot {\left({\left(\mathsf{fma}\left(x, y + z, y \cdot z\right)\right)}^{\color{blue}{0.25}}\right)}^{2} \]

   4. Applied rewrites 59.0%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(x, y + z, y \cdot z\right)\right)}^{0.25}\right)}^{2}} \]

   5. Taylor expanded in x around -inf

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

      1. lower-exp.f64 N/A

         \[\leadsto 2 \cdot {\color{blue}{\left(e^{\frac{1}{4} \cdot \left(\log \left(-1 \cdot \left(y + z\right)\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}}^{2} \]

      2. lower-*.f64 N/A

         \[\leadsto 2 \cdot {\left(e^{\color{blue}{\frac{1}{4} \cdot \left(\log \left(-1 \cdot \left(y + z\right)\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}}\right)}^{2} \]

      3. mul-1-neg N/A

         \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \left(\log \left(-1 \cdot \left(y + z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\log \left(\frac{-1}{x}\right)\right)\right)}\right)}\right)}^{2} \]

      4. unsub-neg N/A

         \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \color{blue}{\left(\log \left(-1 \cdot \left(y + z\right)\right) - \log \left(\frac{-1}{x}\right)\right)}}\right)}^{2} \]

      5. lower--.f64 N/A

         \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \color{blue}{\left(\log \left(-1 \cdot \left(y + z\right)\right) - \log \left(\frac{-1}{x}\right)\right)}}\right)}^{2} \]

      6. distribute-lft-in N/A

         \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \left(\log \color{blue}{\left(-1 \cdot y + -1 \cdot z\right)} - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2} \]

      7. lower-log.f64 N/A

         \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \left(\color{blue}{\log \left(-1 \cdot y + -1 \cdot z\right)} - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2} \]

      8. +-commutative N/A

         \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \left(\log \color{blue}{\left(-1 \cdot z + -1 \cdot y\right)} - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2} \]

      9. mul-1-neg N/A

         \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \left(\log \left(-1 \cdot z + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2} \]

      10. unsub-neg N/A

          \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \left(\log \color{blue}{\left(-1 \cdot z - y\right)} - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2} \]

      11. lower--.f64 N/A

          \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \left(\log \color{blue}{\left(-1 \cdot z - y\right)} - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2} \]

      12. mul-1-neg N/A

          \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \left(\log \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2} \]

      13. lower-neg.f64 N/A

          \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \left(\log \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2} \]

      14. lower-log.f64 N/A

          \[\leadsto 2 \cdot {\left(e^{\frac{1}{4} \cdot \left(\log \left(\left(\mathsf{neg}\left(z\right)\right) - y\right) - \color{blue}{\log \left(\frac{-1}{x}\right)}\right)}\right)}^{2} \]

      15. lower-/.f64 44.4

          \[\leadsto 2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \color{blue}{\left(\frac{-1}{x}\right)}\right)}\right)}^{2} \]

   7. Applied rewrites 44.4%

      \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}}^{2} \]

   if -7.30000000000000014e49 < y < 5.00000000000000029e62

   1. Initial program 83.8%

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

   if 5.00000000000000029e62 < y

   1. Initial program 62.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   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 25.7

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

   5. Applied rewrites 25.7%

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

   7. Applied rewrites 30.2%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 33.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \sqrt{\left(y \cdot x + x \cdot z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot \sqrt{y}, \sqrt{z}, x \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \sqrt{\left(y \cdot x + x \cdot z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot \sqrt{y}, \sqrt{z}, x \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 5e+62)
   (* 2.0 (sqrt (+ (+ (* y x) (* x z)) (* y z))))
   (fma (* 2.0 (sqrt y)) (sqrt z) (* x (sqrt (/ z y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 5e+62) {
		tmp = 2.0 * sqrt((((y * x) + (x * z)) + (y * z)));
	} else {
		tmp = fma((2.0 * sqrt(y)), sqrt(z), (x * sqrt((z / y))));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 5e+62)
		tmp = Float64(2.0 * sqrt(Float64(Float64(Float64(y * x) + Float64(x * z)) + Float64(y * z))));
	else
		tmp = fma(Float64(2.0 * sqrt(y)), sqrt(z), Float64(x * 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, 5e+62], N[(2.0 * N[Sqrt[N[(N[(N[(y * x), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[y], $MachinePrecision]), $MachinePrecision] * N[Sqrt[z], $MachinePrecision] + N[(x * N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.00000000000000029e62

   1. Initial program 77.2%

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

   if 5.00000000000000029e62 < y

   1. Initial program 62.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   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 25.7

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

   5. Applied rewrites 25.7%

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

   7. Applied rewrites 30.2%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 33.2%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \sqrt{\left(y \cdot x + x \cdot z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2 \cdot \sqrt{y}, \sqrt{z}, x \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.1% accurate, 1.0× speedup

Math

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

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) (* x z)) (* y z)))))

C

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

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) + (x * z)) + (y * z)))
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) + (x * z)) + (y * z)));
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 75.0%

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

3. Final simplification 75.0%

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

Alternative 4: 70.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -4e-303) (* 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 <= -4e-303) {
		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 <= (-4d-303)) 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 <= -4e-303) {
		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 <= -4e-303:
		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 <= -4e-303)
		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 <= -4e-303)
		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, -4e-303], 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 < -3.99999999999999972e-303

   1. Initial program 74.0%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   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. lower-*.f64 N/A

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

      2. lower-+.f64 46.1

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

   5. Applied rewrites 46.1%

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

   if -3.99999999999999972e-303 < y

   1. Initial program 75.9%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   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. lower-*.f64 N/A

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

      2. lower-+.f64 49.0

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

   5. Applied rewrites 49.0%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{-273}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2.6e-273) (* 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 <= 2.6e-273) {
		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 <= 2.6d-273) 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 <= 2.6e-273) {
		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 <= 2.6e-273:
		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 <= 2.6e-273)
		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 <= 2.6e-273)
		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, 2.6e-273], 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 < 2.59999999999999983e-273

   1. Initial program 75.7%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   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. lower-*.f64 N/A

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

      2. lower-+.f64 49.7

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

   5. Applied rewrites 49.7%

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

   if 2.59999999999999983e-273 < y

   1. Initial program 74.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   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. lower-*.f64 25.5

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

   5. Applied rewrites 25.5%

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

Alternative 6: 68.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-310}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-310) (* 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 <= -1e-310) {
		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 <= (-1d-310)) 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 <= -1e-310) {
		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 <= -1e-310:
		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 <= -1e-310)
		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 <= -1e-310)
		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, -1e-310], 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 < -9.999999999999969e-311

   1. Initial program 74.2%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   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. lower-*.f64 25.2

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

   5. Applied rewrites 25.2%

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

   if -9.999999999999969e-311 < y

   1. Initial program 75.7%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   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. lower-*.f64 23.9

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

   5. Applied rewrites 23.9%

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

4. Final simplification 24.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-310}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.2% 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 75.0%

   \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
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. lower-*.f64 27.4

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

5. Applied rewrites 27.4%

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

6. Final simplification 27.4%

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

Developer Target 1: 82.3% 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 2024233 
(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)))))