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

Percentage Accurate: 93.4% → 97.2%

Time: 7.6s

Alternatives: 4

Speedup: 1.0×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x - \frac{y \cdot \left(z - t\right)}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- x (/ (* y (- z t)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y * (z - t)) / a);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y * (z - t)) / a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y * (z - t)) / a);
}

Python

def code(x, y, z, t, a):
	return x - ((y * (z - t)) / a)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y * Float64(z - t)) / a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y * (z - t)) / a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Initial Program: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y \cdot \left(z - t\right)}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- x (/ (* y (- z t)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y * (z - t)) / a);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y * (z - t)) / a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y * (z - t)) / a);
}

Python

def code(x, y, z, t, a):
	return x - ((y * (z - t)) / a)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y * Float64(z - t)) / a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y * (z - t)) / a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{a} \cdot \left(t - z\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y / a) * (t - z));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y / a) * (t - z))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y / a) * (t - z));
}

Python

def code(x, y, z, t, a):
	return x + ((y / a) * (t - z))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y / a) * Float64(t - z)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y / a) * (t - z));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.5%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
2. Step-by-step derivation

   1. associate-*l/ 97.7%

      \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

3. Simplified 97.7%

   \[\leadsto \color{blue}{x - \frac{y}{a} \cdot \left(z - t\right)} \]
4. Add Preprocessing

5. Final simplification 97.7%

   \[\leadsto x + \frac{y}{a} \cdot \left(t - z\right) \]
6. Add Preprocessing

Alternative 2: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+72} \lor \neg \left(z \leq 2.5 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.2e+72) (not (<= z 2.5e-33)))
   (- x (* (/ y a) z))
   (+ x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.2e+72) || !(z <= 2.5e-33)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.2d+72)) .or. (.not. (z <= 2.5d-33))) then
        tmp = x - ((y / a) * z)
    else
        tmp = x + ((y / a) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.2e+72) || !(z <= 2.5e-33)) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.2e+72) or not (z <= 2.5e-33):
		tmp = x - ((y / a) * z)
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.2e+72) || !(z <= 2.5e-33))
		tmp = Float64(x - Float64(Float64(y / a) * z));
	else
		tmp = Float64(x + Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.2e+72) || ~((z <= 2.5e-33)))
		tmp = x - ((y / a) * z);
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.2e+72], N[Not[LessEqual[z, 2.5e-33]], $MachinePrecision]], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999977e72 or 2.50000000000000014e-33 < z

   1. Initial program 96.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.2%

         \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x - \frac{y}{a} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 84.1%

      \[\leadsto x - \color{blue}{\frac{y \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*l/ 88.8%

         \[\leadsto x - \color{blue}{\frac{y}{a} \cdot z} \]

      2. *-commutative 88.8%

         \[\leadsto x - \color{blue}{z \cdot \frac{y}{a}} \]

   7. Simplified 88.8%

      \[\leadsto x - \color{blue}{z \cdot \frac{y}{a}} \]

   if -6.19999999999999977e72 < z < 2.50000000000000014e-33

   1. Initial program 95.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.5%

         \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{x - \frac{y}{a} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 86.7%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto x - -1 \cdot \frac{\color{blue}{y \cdot t}}{a} \]

      2. associate-*l/ 89.5%

         \[\leadsto x - -1 \cdot \color{blue}{\left(\frac{y}{a} \cdot t\right)} \]

      3. neg-mul-1 89.5%

         \[\leadsto x - \color{blue}{\left(-\frac{y}{a} \cdot t\right)} \]

      4. distribute-rgt-neg-out 89.5%

         \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]

   7. Simplified 89.5%

      \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+72} \lor \neg \left(z \leq 2.5 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+82}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.45e+25)
   (- x (/ y (/ (- a) t)))
   (if (<= t 9.8e+82) (- x (* (/ y a) z)) (+ x (* (/ y a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+25) {
		tmp = x - (y / (-a / t));
	} else if (t <= 9.8e+82) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.45d+25)) then
        tmp = x - (y / (-a / t))
    else if (t <= 9.8d+82) then
        tmp = x - ((y / a) * z)
    else
        tmp = x + ((y / a) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+25) {
		tmp = x - (y / (-a / t));
	} else if (t <= 9.8e+82) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.45e+25:
		tmp = x - (y / (-a / t))
	elif t <= 9.8e+82:
		tmp = x - ((y / a) * z)
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.45e+25)
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	elseif (t <= 9.8e+82)
		tmp = Float64(x - Float64(Float64(y / a) * z));
	else
		tmp = Float64(x + Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.45e+25)
		tmp = x - (y / (-a / t));
	elseif (t <= 9.8e+82)
		tmp = x - ((y / a) * z);
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.45e+25], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e+82], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.44999999999999995e25

   1. Initial program 94.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-/l* 95.6%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 85.2%

      \[\leadsto x - \frac{y}{\color{blue}{-1 \cdot \frac{a}{t}}} \]
   6. Step-by-step derivation

      1. associate-*r/ 85.2%

         \[\leadsto x - \frac{y}{\color{blue}{\frac{-1 \cdot a}{t}}} \]

      2. neg-mul-1 85.2%

         \[\leadsto x - \frac{y}{\frac{\color{blue}{-a}}{t}} \]

   7. Simplified 85.2%

      \[\leadsto x - \frac{y}{\color{blue}{\frac{-a}{t}}} \]

   if -1.44999999999999995e25 < t < 9.8000000000000001e82

   1. Initial program 96.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 98.0%

         \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{x - \frac{y}{a} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 85.5%

      \[\leadsto x - \color{blue}{\frac{y \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*l/ 89.4%

         \[\leadsto x - \color{blue}{\frac{y}{a} \cdot z} \]

      2. *-commutative 89.4%

         \[\leadsto x - \color{blue}{z \cdot \frac{y}{a}} \]

   7. Simplified 89.4%

      \[\leadsto x - \color{blue}{z \cdot \frac{y}{a}} \]

   if 9.8000000000000001e82 < t

   1. Initial program 95.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.5%

         \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x - \frac{y}{a} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 95.7%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 95.7%

         \[\leadsto x - -1 \cdot \frac{\color{blue}{y \cdot t}}{a} \]

      2. associate-*l/ 99.5%

         \[\leadsto x - -1 \cdot \color{blue}{\left(\frac{y}{a} \cdot t\right)} \]

      3. neg-mul-1 99.5%

         \[\leadsto x - \color{blue}{\left(-\frac{y}{a} \cdot t\right)} \]

      4. distribute-rgt-neg-out 99.5%

         \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]

   7. Simplified 99.5%

      \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+82}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{a} \cdot z \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (- x (* (/ y a) z)))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y / a) * z);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y / a) * z)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y / a) * z);
}

Python

def code(x, y, z, t, a):
	return x - ((y / a) * z)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y / a) * z))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y / a) * z);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.5%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
2. Step-by-step derivation

   1. associate-*l/ 97.7%

      \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

3. Simplified 97.7%

   \[\leadsto \color{blue}{x - \frac{y}{a} \cdot \left(z - t\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 69.0%

   \[\leadsto x - \color{blue}{\frac{y \cdot z}{a}} \]
6. Step-by-step derivation

   1. associate-*l/ 72.8%

      \[\leadsto x - \color{blue}{\frac{y}{a} \cdot z} \]

   2. *-commutative 72.8%

      \[\leadsto x - \color{blue}{z \cdot \frac{y}{a}} \]

7. Simplified 72.8%

   \[\leadsto x - \color{blue}{z \cdot \frac{y}{a}} \]

8. Final simplification 72.8%

   \[\leadsto x - \frac{y}{a} \cdot z \]
9. Add Preprocessing

Developer target: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{t_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (- x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (- x (/ (* y (- z t)) a))
       (- x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x - (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x - ((y * (z - t)) / a)
    else
        tmp = x - (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x - (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x - ((y * (z - t)) / a)
	else:
		tmp = x - (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x - Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x - Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x - Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x - (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x - ((y * (z - t)) / a);
	else
		tmp = x - (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x - N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))