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

Average Error: 19.8 → 3.0

Time: 13.9s

Precision: binary64

Cost: 26896

\[ \begin{array}{c}[x, y, z] = \mathsf{sort}([x, y, z])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_0 := 2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{3}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-181}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-293}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-172}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(y + x\right) - \log \left(\frac{1}{z}\right)\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+19}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          2.0
          (pow
           (exp (* 0.16666666666666666 (- (log (- (- y) z)) (log (/ -1.0 x)))))
           3.0))))
   (if (<= y -1.6e+45)
     t_0
     (if (<= y -1.5e-181)
       (* 2.0 (sqrt (* x (+ y z))))
       (if (<= y -1.9e-293)
         t_0
         (if (<= y 4.7e-172)
           (*
            2.0
            (pow
             (exp (* 0.16666666666666666 (- (log (+ y x)) (log (/ 1.0 z)))))
             3.0))
           (if (<= y 2.5e+19)
             (* 2.0 (sqrt (* z (+ y x))))
             (* 2.0 (* (sqrt z) (sqrt y))))))))))

C

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

↓

double code(double x, double y, double z) {
	double t_0 = 2.0 * pow(exp((0.16666666666666666 * (log((-y - z)) - log((-1.0 / x))))), 3.0);
	double tmp;
	if (y <= -1.6e+45) {
		tmp = t_0;
	} else if (y <= -1.5e-181) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else if (y <= -1.9e-293) {
		tmp = t_0;
	} else if (y <= 4.7e-172) {
		tmp = 2.0 * pow(exp((0.16666666666666666 * (log((y + x)) - log((1.0 / z))))), 3.0);
	} else if (y <= 2.5e+19) {
		tmp = 2.0 * sqrt((z * (y + x)));
	} else {
		tmp = 2.0 * (sqrt(z) * sqrt(y));
	}
	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
    code = 2.0d0 * sqrt((((x * y) + (x * z)) + (y * z)))
end 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) :: t_0
    real(8) :: tmp
    t_0 = 2.0d0 * (exp((0.16666666666666666d0 * (log((-y - z)) - log(((-1.0d0) / x))))) ** 3.0d0)
    if (y <= (-1.6d+45)) then
        tmp = t_0
    else if (y <= (-1.5d-181)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else if (y <= (-1.9d-293)) then
        tmp = t_0
    else if (y <= 4.7d-172) then
        tmp = 2.0d0 * (exp((0.16666666666666666d0 * (log((y + x)) - log((1.0d0 / z))))) ** 3.0d0)
    else if (y <= 2.5d+19) then
        tmp = 2.0d0 * sqrt((z * (y + x)))
    else
        tmp = 2.0d0 * (sqrt(z) * sqrt(y))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z) {
	double t_0 = 2.0 * Math.pow(Math.exp((0.16666666666666666 * (Math.log((-y - z)) - Math.log((-1.0 / x))))), 3.0);
	double tmp;
	if (y <= -1.6e+45) {
		tmp = t_0;
	} else if (y <= -1.5e-181) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else if (y <= -1.9e-293) {
		tmp = t_0;
	} else if (y <= 4.7e-172) {
		tmp = 2.0 * Math.pow(Math.exp((0.16666666666666666 * (Math.log((y + x)) - Math.log((1.0 / z))))), 3.0);
	} else if (y <= 2.5e+19) {
		tmp = 2.0 * Math.sqrt((z * (y + x)));
	} else {
		tmp = 2.0 * (Math.sqrt(z) * Math.sqrt(y));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = 2.0 * math.pow(math.exp((0.16666666666666666 * (math.log((-y - z)) - math.log((-1.0 / x))))), 3.0)
	tmp = 0
	if y <= -1.6e+45:
		tmp = t_0
	elif y <= -1.5e-181:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	elif y <= -1.9e-293:
		tmp = t_0
	elif y <= 4.7e-172:
		tmp = 2.0 * math.pow(math.exp((0.16666666666666666 * (math.log((y + x)) - math.log((1.0 / z))))), 3.0)
	elif y <= 2.5e+19:
		tmp = 2.0 * math.sqrt((z * (y + x)))
	else:
		tmp = 2.0 * (math.sqrt(z) * math.sqrt(y))
	return tmp

Julia

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

↓

function code(x, y, z)
	t_0 = Float64(2.0 * (exp(Float64(0.16666666666666666 * Float64(log(Float64(Float64(-y) - z)) - log(Float64(-1.0 / x))))) ^ 3.0))
	tmp = 0.0
	if (y <= -1.6e+45)
		tmp = t_0;
	elseif (y <= -1.5e-181)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	elseif (y <= -1.9e-293)
		tmp = t_0;
	elseif (y <= 4.7e-172)
		tmp = Float64(2.0 * (exp(Float64(0.16666666666666666 * Float64(log(Float64(y + x)) - log(Float64(1.0 / z))))) ^ 3.0));
	elseif (y <= 2.5e+19)
		tmp = Float64(2.0 * sqrt(Float64(z * Float64(y + x))));
	else
		tmp = Float64(2.0 * Float64(sqrt(z) * sqrt(y)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	t_0 = 2.0 * (exp((0.16666666666666666 * (log((-y - z)) - log((-1.0 / x))))) ^ 3.0);
	tmp = 0.0;
	if (y <= -1.6e+45)
		tmp = t_0;
	elseif (y <= -1.5e-181)
		tmp = 2.0 * sqrt((x * (y + z)));
	elseif (y <= -1.9e-293)
		tmp = t_0;
	elseif (y <= 4.7e-172)
		tmp = 2.0 * (exp((0.16666666666666666 * (log((y + x)) - log((1.0 / z))))) ^ 3.0);
	elseif (y <= 2.5e+19)
		tmp = 2.0 * sqrt((z * (y + x)));
	else
		tmp = 2.0 * (sqrt(z) * sqrt(y));
	end
	tmp_2 = tmp;
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]

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(2.0 * N[Power[N[Exp[N[(0.16666666666666666 * N[(N[Log[N[((-y) - z), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+45], t$95$0, If[LessEqual[y, -1.5e-181], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-293], t$95$0, If[LessEqual[y, 4.7e-172], N[(2.0 * N[Power[N[Exp[N[(0.16666666666666666 * N[(N[Log[N[(y + x), $MachinePrecision]], $MachinePrecision] - N[Log[N[(1.0 / z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+19], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	19.8
Target	11.4
Herbie	3.0

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

Derivation

1. Split input into 5 regimes

2. if y < -1.6000000000000001e45 or -1.49999999999999987e-181 < y < -1.9e-293

   1. Initial program 38.5

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

   2. Simplified 38.5

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

      [Start] 38.5	\[ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
      distribute-lft-out [=>] 38.5	\[ 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)} + y \cdot z} \]

   3. Applied egg-rr 39.0

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

   4. Taylor expanded in x around -inf 6.9

      \[\leadsto 2 \cdot \color{blue}{{\left(e^{0.16666666666666666 \cdot \left(-1 \cdot \log \left(\frac{-1}{x}\right) + \log \left(-1 \cdot \left(y + z\right)\right)\right)}\right)}^{3}} \]

   if -1.6000000000000001e45 < y < -1.49999999999999987e-181

   1. Initial program 1.4

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

   2. Simplified 1.4

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

      [Start] 1.4	\[ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
      distribute-lft-out [=>] 1.4	\[ 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)} + y \cdot z} \]

   3. Taylor expanded in x around inf 1.5

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

   if -1.9e-293 < y < 4.69999999999999976e-172

   1. Initial program 13.8

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

   2. Simplified 13.8

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

      [Start] 13.8	\[ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
      distribute-lft-out [=>] 13.8	\[ 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)} + y \cdot z} \]

   3. Applied egg-rr 14.8

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

   4. Taylor expanded in z around inf 7.4

      \[\leadsto 2 \cdot \color{blue}{{\left(e^{0.16666666666666666 \cdot \left(-1 \cdot \log \left(\frac{1}{z}\right) + \log \left(y + x\right)\right)}\right)}^{3}} \]

   if 4.69999999999999976e-172 < y < 2.5e19

   1. Initial program 0.5

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

   2. Simplified 0.5

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

      [Start] 0.5	\[ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
      distribute-lft-out [=>] 0.5	\[ 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)} + y \cdot z} \]

   3. Taylor expanded in z around inf 0.6

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

   if 2.5e19 < y

   1. Initial program 39.3

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

   2. Simplified 39.3

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

      [Start] 39.3	\[ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
      associate-+l+ [=>] 39.3	\[ 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]
      fma-def [=>] 39.3	\[ 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(x, y, x \cdot z + y \cdot z\right)}} \]
      distribute-rgt-out [=>] 39.3	\[ 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(x + y\right)}\right)} \]

   3. Applied egg-rr 55.7

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)\right)}^{1.5}\right)}^{0.3333333333333333}} \]

   4. Simplified 54.9

      \[\leadsto 2 \cdot \color{blue}{\sqrt[3]{{\left(\mathsf{fma}\left(y + z, x, y \cdot z\right)\right)}^{1.5}}} \]
      Proof

      [Start] 55.7	\[ 2 \cdot {\left({\left(\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)\right)}^{1.5}\right)}^{0.3333333333333333} \]
      unpow1/3 [=>] 54.9	\[ 2 \cdot \color{blue}{\sqrt[3]{{\left(\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)\right)}^{1.5}}} \]
      fma-def [<=] 54.9	\[ 2 \cdot \sqrt[3]{{\color{blue}{\left(x \cdot y + z \cdot \left(x + y\right)\right)}}^{1.5}} \]
      distribute-lft-in [=>] 54.9	\[ 2 \cdot \sqrt[3]{{\left(x \cdot y + \color{blue}{\left(z \cdot x + z \cdot y\right)}\right)}^{1.5}} \]
      *-commutative [<=] 54.9	\[ 2 \cdot \sqrt[3]{{\left(x \cdot y + \left(z \cdot x + \color{blue}{y \cdot z}\right)\right)}^{1.5}} \]
      associate-+r+ [=>] 54.9	\[ 2 \cdot \sqrt[3]{{\color{blue}{\left(\left(x \cdot y + z \cdot x\right) + y \cdot z\right)}}^{1.5}} \]
      *-commutative [<=] 54.9	\[ 2 \cdot \sqrt[3]{{\left(\left(x \cdot y + \color{blue}{x \cdot z}\right) + y \cdot z\right)}^{1.5}} \]
      distribute-lft-in [<=] 54.9	\[ 2 \cdot \sqrt[3]{{\left(\color{blue}{x \cdot \left(y + z\right)} + y \cdot z\right)}^{1.5}} \]
      *-commutative [<=] 54.9	\[ 2 \cdot \sqrt[3]{{\left(\color{blue}{\left(y + z\right) \cdot x} + y \cdot z\right)}^{1.5}} \]
      fma-def [=>] 54.9	\[ 2 \cdot \sqrt[3]{{\color{blue}{\left(\mathsf{fma}\left(y + z, x, y \cdot z\right)\right)}}^{1.5}} \]

   5. Taylor expanded in x around 0 39.7

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

   6. Simplified 39.7

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

      [Start] 39.7	\[ 2 \cdot \sqrt{y \cdot z} \]
      *-commutative [=>] 39.7	\[ 2 \cdot \sqrt{\color{blue}{z \cdot y}} \]

   7. Applied egg-rr 1.4

      \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{y}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 3.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-181}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-293}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-172}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(y + x\right) - \log \left(\frac{1}{z}\right)\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+19}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	4.1
Cost	19972

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+69}:\\ \;\;\;\;2 \cdot e^{\left(\log \left(-x\right) - \log \left(\frac{-1}{y}\right)\right) \cdot 0.5}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+18}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(y + x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternative 2
Error	11.4
Cost	14148

\[\begin{array}{l} \mathbf{if}\;\left(y \cdot x + x \cdot z\right) + y \cdot z \leq 5 \cdot 10^{+298}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(y + x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternative 3
Error	11.4
Cost	13892

\[\begin{array}{l} \mathbf{if}\;\left(y \cdot x + x \cdot z\right) + y \cdot z \leq 5 \cdot 10^{+298}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z + x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternative 4
Error	19.8
Cost	7104

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

Alternative 5
Error	20.7
Cost	6980

\[\begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]

Alternative 6
Error	20.0
Cost	6980

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-269}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]

Alternative 7
Error	21.3
Cost	6852

\[\begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]

Alternative 8
Error	42.3
Cost	6720

\[2 \cdot \sqrt{y \cdot x} \]

Alternative 9
Error	62.2
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2023073 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< z 7.636950090573675e+176) (* 2.0 (sqrt (+ (* (+ x y) z) (* x y)))) (* (* (+ (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z))) (* (pow z 0.25) (pow y 0.25))) (+ (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z))) (* (pow z 0.25) (pow y 0.25)))) 2.0))

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