Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 6

Speedup: 1.0×

• 21.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(z + 1\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))

C

double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (z + 1.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

Python

def code(x, y, z):
	return (x + y) * (z + 1.0)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(z + 1.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (z + 1.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(z + 1\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))

C

double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (z + 1.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

Python

def code(x, y, z):
	return (x + y) * (z + 1.0)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(z + 1.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (z + 1.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(z + 1\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))

C

double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (z + 1.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}

Python

def code(x, y, z):
	return (x + y) * (z + 1.0)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(z + 1.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (z + 1.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(z + 1\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+185}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 54:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.8e+185)
   (* y z)
   (if (<= z -1.0) (* x z) (if (<= z 54.0) (+ y x) (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.8e+185) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 54.0) {
		tmp = y + x;
	} else {
		tmp = y * z;
	}
	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) :: tmp
    if (z <= (-6.8d+185)) then
        tmp = y * z
    else if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 54.0d0) then
        tmp = y + x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.8e+185) {
		tmp = y * z;
	} else if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 54.0) {
		tmp = y + x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.8e+185:
		tmp = y * z
	elif z <= -1.0:
		tmp = x * z
	elif z <= 54.0:
		tmp = y + x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.8e+185)
		tmp = Float64(y * z);
	elseif (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 54.0)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.8e+185)
		tmp = y * z;
	elseif (z <= -1.0)
		tmp = x * z;
	elseif (z <= 54.0)
		tmp = y + x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.8e+185], N[(y * z), $MachinePrecision], If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 54.0], N[(y + x), $MachinePrecision], N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.80000000000000034e185 or 54 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 99.5

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 51.2%

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

   if -6.80000000000000034e185 < z < -1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 95.6

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

   5. Applied rewrites 95.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 46.1%

      \[\leadsto x \cdot \color{blue}{z} \]

   if -1 < z < 54

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 3.8

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

   5. Applied rewrites 3.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 3.7%

      \[\leadsto x \cdot \color{blue}{z} \]

   9. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{y + x} \]

       2. lower-+.f64 97.5

          \[\leadsto \color{blue}{y + x} \]

   11. Applied rewrites 97.5%

       \[\leadsto \color{blue}{y + x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 74.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.25 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.25e+22))) (* x z) (+ y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.25e+22)) {
		tmp = x * z;
	} else {
		tmp = y + x;
	}
	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) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.25d+22))) then
        tmp = x * z
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.25e+22)) {
		tmp = x * z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.25e+22):
		tmp = x * z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.25e+22))
		tmp = Float64(x * z);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.25e+22)))
		tmp = x * z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.25e+22]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.2499999999999999e22 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 98.6

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.7%

      \[\leadsto x \cdot \color{blue}{z} \]

   if -1 < z < 1.2499999999999999e22

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 5.0

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

   5. Applied rewrites 5.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 3.8%

      \[\leadsto x \cdot \color{blue}{z} \]

   9. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{y + x} \]

       2. lower-+.f64 96.0

          \[\leadsto \color{blue}{y + x} \]

   11. Applied rewrites 96.0%

       \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.25 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-262}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-262) (fma z x x) (fma z y y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-262) {
		tmp = fma(z, x, x);
	} else {
		tmp = fma(z, y, y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-262)
		tmp = fma(z, x, x);
	else
		tmp = fma(z, y, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-262], N[(z * x + x), $MachinePrecision], N[(z * y + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000001e-262

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{z \cdot x + 1 \cdot x} \]

      3. *-lft-identity N/A

         \[\leadsto z \cdot x + \color{blue}{x} \]

      4. lower-fma.f64 57.3

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

   5. Applied rewrites 57.3%

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

   if -1.00000000000000001e-262 < (+.f64 x y)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{z \cdot y + 1 \cdot y} \]

      3. *-lft-identity N/A

         \[\leadsto z \cdot y + \color{blue}{y} \]

      4. lower-fma.f64 47.1

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

   5. Applied rewrites 47.1%

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

Alternative 5: 39.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-262}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x y) -1e-262) (fma z x x) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + y) <= -1e-262) {
		tmp = fma(z, x, x);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + y) <= -1e-262)
		tmp = fma(z, x, x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-262], N[(z * x + x), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000001e-262

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. distribute-rgt-in N/A

         \[\leadsto \color{blue}{z \cdot x + 1 \cdot x} \]

      3. *-lft-identity N/A

         \[\leadsto z \cdot x + \color{blue}{x} \]

      4. lower-fma.f64 57.3

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

   5. Applied rewrites 57.3%

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

   if -1.00000000000000001e-262 < (+.f64 x y)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(z + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 56.1

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

   5. Applied rewrites 56.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 29.0%

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

Alternative 6: 51.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ y + x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ y x))

C

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

Fortran

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

Java

public static double code(double x, double y, double z) {
	return y + x;
}

Python

def code(x, y, z):
	return y + x

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(z + 1\right) \]
2. Add Preprocessing

3. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. +-commutative N/A

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

   4. lower-+.f64 54.0

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

5. Applied rewrites 54.0%

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

6. Taylor expanded in x around inf

   \[\leadsto x \cdot \color{blue}{z} \]
7. Step-by-step derivation

8. Applied rewrites 28.9%

   \[\leadsto x \cdot \color{blue}{z} \]

9. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x + y} \]
10. Step-by-step derivation

    1. +-commutative N/A

       \[\leadsto \color{blue}{y + x} \]

    2. lower-+.f64 47.3

       \[\leadsto \color{blue}{y + x} \]

11. Applied rewrites 47.3%

    \[\leadsto \color{blue}{y + x} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024338 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))