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

Percentage Accurate: 71.0% → 95.0%

Time: 11.7s

Alternatives: 8

Speedup: 1.0×

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: 71.0% 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: 95.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+38}:\\ \;\;\;\;2 \cdot e^{\left(\log \left(\left(-z\right) - y\right) + \log \left(-x\right)\right) \cdot 0.5}\\ \mathbf{elif}\;y \leq 380000:\\ \;\;\;\;2 \cdot \sqrt{\left(y \cdot x + z \cdot x\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(x, y \cdot \sqrt{\frac{1}{\left(z \cdot \left(z \cdot z\right)\right) \cdot \left(y + x\right)}}, 2 \cdot \sqrt{\frac{y + x}{z}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -4e+38)
   (* 2.0 (exp (* (+ (log (- (- z) y)) (log (- x))) 0.5)))
   (if (<= y 380000.0)
     (* 2.0 (sqrt (+ (+ (* y x) (* z x)) (* y z))))
     (*
      z
      (fma
       x
       (* y (sqrt (/ 1.0 (* (* z (* z z)) (+ y x)))))
       (* 2.0 (sqrt (/ (+ y x) z))))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+38) {
		tmp = 2.0 * exp(((log((-z - y)) + log(-x)) * 0.5));
	} else if (y <= 380000.0) {
		tmp = 2.0 * sqrt((((y * x) + (z * x)) + (y * z)));
	} else {
		tmp = z * fma(x, (y * sqrt((1.0 / ((z * (z * z)) * (y + x))))), (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 <= -4e+38)
		tmp = Float64(2.0 * exp(Float64(Float64(log(Float64(Float64(-z) - y)) + log(Float64(-x))) * 0.5)));
	elseif (y <= 380000.0)
		tmp = Float64(2.0 * sqrt(Float64(Float64(Float64(y * x) + Float64(z * x)) + Float64(y * z))));
	else
		tmp = Float64(z * fma(x, Float64(y * sqrt(Float64(1.0 / Float64(Float64(z * Float64(z * z)) * Float64(y + x))))), 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, -4e+38], N[(2.0 * N[Exp[N[(N[(N[Log[N[((-z) - y), $MachinePrecision]], $MachinePrecision] + N[Log[(-x)], $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 380000.0], N[(2.0 * N[Sqrt[N[(N[(N[(y * x), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y * N[Sqrt[N[(1.0 / N[(N[(z * N[(z * z), $MachinePrecision]), $MachinePrecision] * N[(y + x), $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 3 regimes

2. if y < -3.99999999999999991e38

   1. Initial program 36.5%

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

   3. Taylor expanded in z around inf

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

      1. distribute-rgt-in N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l* N/A

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

      5. distribute-lft-out N/A

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

      6. lower-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 31.7

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

   5. Applied rewrites 31.7%

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

      1. lift-sqrt.f64 N/A

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

      2. pow1/2 N/A

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

      3. pow-to-exp N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-*.f64 N/A

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

   7. Applied rewrites 34.3%

      \[\leadsto 2 \cdot \color{blue}{e^{\log \left(\mathsf{fma}\left(y, z, x \cdot \left(y + z\right)\right)\right) \cdot 0.5}} \]

   8. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-log.f64 N/A

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

      12. lower-/.f64 89.7

          \[\leadsto 2 \cdot e^{\left(\log \left(\left(-z\right) - y\right) - \log \color{blue}{\left(\frac{-1}{x}\right)}\right) \cdot 0.5} \]

   10. Applied rewrites 89.7%

       \[\leadsto 2 \cdot e^{\color{blue}{\left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)} \cdot 0.5} \]
   11. Step-by-step derivation

   12. Applied rewrites 89.7%

       \[\leadsto 2 \cdot e^{\left(\log \left(\left(-z\right) - y\right) + \color{blue}{\log \left(-x\right)}\right) \cdot 0.5} \]

   if -3.99999999999999991e38 < y < 3.8e5

   1. Initial program 94.9%

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

   if 3.8e5 < y

   1. Initial program 39.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   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 39.6

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

   5. Applied rewrites 39.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(2 \cdot \sqrt{\frac{x + y}{z}} + \left(x \cdot y\right) \cdot \sqrt{\frac{1}{{z}^{3} \cdot \left(x + y\right)}}\right)} \]
   7. 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

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

   8. Applied rewrites 99.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+38}:\\ \;\;\;\;2 \cdot e^{\left(\log \left(\left(-z\right) - y\right) + \log \left(-x\right)\right) \cdot 0.5}\\ \mathbf{elif}\;y \leq 380000:\\ \;\;\;\;2 \cdot \sqrt{\left(y \cdot x + z \cdot x\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(x, y \cdot \sqrt{\frac{1}{\left(z \cdot \left(z \cdot z\right)\right) \cdot \left(y + x\right)}}, 2 \cdot \sqrt{\frac{y + x}{z}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 380000:\\ \;\;\;\;2 \cdot \sqrt{\left(y \cdot x + z \cdot x\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(x, y \cdot \sqrt{\frac{1}{\left(z \cdot \left(z \cdot z\right)\right) \cdot \left(y + x\right)}}, 2 \cdot \sqrt{\frac{y + x}{z}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 380000.0)
   (* 2.0 (sqrt (+ (+ (* y x) (* z x)) (* y z))))
   (*
    z
    (fma
     x
     (* y (sqrt (/ 1.0 (* (* z (* z z)) (+ y x)))))
     (* 2.0 (sqrt (/ (+ y x) z)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 380000.0) {
		tmp = 2.0 * sqrt((((y * x) + (z * x)) + (y * z)));
	} else {
		tmp = z * fma(x, (y * sqrt((1.0 / ((z * (z * z)) * (y + x))))), (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 <= 380000.0)
		tmp = Float64(2.0 * sqrt(Float64(Float64(Float64(y * x) + Float64(z * x)) + Float64(y * z))));
	else
		tmp = Float64(z * fma(x, Float64(y * sqrt(Float64(1.0 / Float64(Float64(z * Float64(z * z)) * Float64(y + x))))), 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, 380000.0], N[(2.0 * N[Sqrt[N[(N[(N[(y * x), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y * N[Sqrt[N[(1.0 / N[(N[(z * N[(z * z), $MachinePrecision]), $MachinePrecision] * N[(y + x), $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 < 3.8e5

   1. Initial program 79.0%

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

   if 3.8e5 < y

   1. Initial program 46.7%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   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 46.6

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

   5. Applied rewrites 46.6%

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

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(2 \cdot \sqrt{\frac{x + y}{z}} + \left(x \cdot y\right) \cdot \sqrt{\frac{1}{{z}^{3} \cdot \left(x + y\right)}}\right)} \]
   7. 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

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

   8. Applied rewrites 99.6%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 380000:\\ \;\;\;\;2 \cdot \sqrt{\left(y \cdot x + z \cdot x\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(x, y \cdot \sqrt{\frac{1}{\left(z \cdot \left(z \cdot z\right)\right) \cdot \left(y + x\right)}}, 2 \cdot \sqrt{\frac{y + x}{z}}\right)\\ \end{array} \]
5. Add Preprocessing

Developer Target 1: 83.3% 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 2024227 
(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)))))