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

Percentage Accurate: 93.6% → 97.2%

Time: 6.5s

Alternatives: 7

Speedup: 1.0×

• 24.6% 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: 93.6% 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 92.4%

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

   1. associate-*l/ 97.4%

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

3. Simplified 97.4%

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

4. Final simplification 97.4%

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

Alternative 2: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-25} \lor \neg \left(t \leq 1.55 \cdot 10^{+43}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))))
   (if (<= t -1.26e-37)
     t_1
     (if (<= t 1.1e-63)
       (- x (/ (* y z) a))
       (if (or (<= t 6.3e-25) (not (<= t 1.55e+43)))
         t_1
         (- x (* (/ y a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (t <= -1.26e-37) {
		tmp = t_1;
	} else if (t <= 1.1e-63) {
		tmp = x - ((y * z) / a);
	} else if ((t <= 6.3e-25) || !(t <= 1.55e+43)) {
		tmp = t_1;
	} else {
		tmp = x - ((y / a) * z);
	}
	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 = x + (y * (t / a))
    if (t <= (-1.26d-37)) then
        tmp = t_1
    else if (t <= 1.1d-63) then
        tmp = x - ((y * z) / a)
    else if ((t <= 6.3d-25) .or. (.not. (t <= 1.55d+43))) then
        tmp = t_1
    else
        tmp = x - ((y / a) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (t <= -1.26e-37) {
		tmp = t_1;
	} else if (t <= 1.1e-63) {
		tmp = x - ((y * z) / a);
	} else if ((t <= 6.3e-25) || !(t <= 1.55e+43)) {
		tmp = t_1;
	} else {
		tmp = x - ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	tmp = 0
	if t <= -1.26e-37:
		tmp = t_1
	elif t <= 1.1e-63:
		tmp = x - ((y * z) / a)
	elif (t <= 6.3e-25) or not (t <= 1.55e+43):
		tmp = t_1
	else:
		tmp = x - ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (t <= -1.26e-37)
		tmp = t_1;
	elseif (t <= 1.1e-63)
		tmp = Float64(x - Float64(Float64(y * z) / a));
	elseif ((t <= 6.3e-25) || !(t <= 1.55e+43))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y / a) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	tmp = 0.0;
	if (t <= -1.26e-37)
		tmp = t_1;
	elseif (t <= 1.1e-63)
		tmp = x - ((y * z) / a);
	elseif ((t <= 6.3e-25) || ~((t <= 1.55e+43)))
		tmp = t_1;
	else
		tmp = x - ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e-37], t$95$1, If[LessEqual[t, 1.1e-63], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 6.3e-25], N[Not[LessEqual[t, 1.55e+43]], $MachinePrecision]], t$95$1, N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25999999999999992e-37 or 1.1e-63 < t < 6.29999999999999961e-25 or 1.5500000000000001e43 < t

   1. Initial program 88.2%

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

      1. associate-*r/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around 0 83.5%

      \[\leadsto x - y \cdot \color{blue}{\left(-1 \cdot \frac{t}{a}\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 83.5%

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

      2. distribute-neg-frac 83.5%

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

   6. Simplified 83.5%

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

   if -1.25999999999999992e-37 < t < 1.1e-63

   1. Initial program 98.2%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 96.3%

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

   if 6.29999999999999961e-25 < t < 1.5500000000000001e43

   1. Initial program 86.1%

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

      1. associate-*r/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in z around inf 75.6%

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

      1. associate-*l/ 89.2%

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

      2. *-commutative 89.2%

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

   6. Simplified 89.2%

      \[\leadsto x - \color{blue}{z \cdot \frac{y}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-37}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-25} \lor \neg \left(t \leq 1.55 \cdot 10^{+43}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \end{array} \]

Alternative 3: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{a} \cdot t\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y a) t))))
   (if (<= t -1.22e-42)
     t_1
     (if (<= t 1.12e-63)
       (- x (/ (* y z) a))
       (if (<= t 3.1e-25)
         (+ x (* y (/ t a)))
         (if (<= t 5.5e+42) (- x (* (/ y a) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * t);
	double tmp;
	if (t <= -1.22e-42) {
		tmp = t_1;
	} else if (t <= 1.12e-63) {
		tmp = x - ((y * z) / a);
	} else if (t <= 3.1e-25) {
		tmp = x + (y * (t / a));
	} else if (t <= 5.5e+42) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = 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 = x + ((y / a) * t)
    if (t <= (-1.22d-42)) then
        tmp = t_1
    else if (t <= 1.12d-63) then
        tmp = x - ((y * z) / a)
    else if (t <= 3.1d-25) then
        tmp = x + (y * (t / a))
    else if (t <= 5.5d+42) then
        tmp = x - ((y / a) * z)
    else
        tmp = 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 = x + ((y / a) * t);
	double tmp;
	if (t <= -1.22e-42) {
		tmp = t_1;
	} else if (t <= 1.12e-63) {
		tmp = x - ((y * z) / a);
	} else if (t <= 3.1e-25) {
		tmp = x + (y * (t / a));
	} else if (t <= 5.5e+42) {
		tmp = x - ((y / a) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y / a) * t)
	tmp = 0
	if t <= -1.22e-42:
		tmp = t_1
	elif t <= 1.12e-63:
		tmp = x - ((y * z) / a)
	elif t <= 3.1e-25:
		tmp = x + (y * (t / a))
	elif t <= 5.5e+42:
		tmp = x - ((y / a) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y / a) * t))
	tmp = 0.0
	if (t <= -1.22e-42)
		tmp = t_1;
	elseif (t <= 1.12e-63)
		tmp = Float64(x - Float64(Float64(y * z) / a));
	elseif (t <= 3.1e-25)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t <= 5.5e+42)
		tmp = Float64(x - Float64(Float64(y / a) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y / a) * t);
	tmp = 0.0;
	if (t <= -1.22e-42)
		tmp = t_1;
	elseif (t <= 1.12e-63)
		tmp = x - ((y * z) / a);
	elseif (t <= 3.1e-25)
		tmp = x + (y * (t / a));
	elseif (t <= 5.5e+42)
		tmp = x - ((y / a) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.22e-42], t$95$1, If[LessEqual[t, 1.12e-63], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-25], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+42], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.22000000000000007e-42 or 5.50000000000000001e42 < t

   1. Initial program 87.4%

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

      1. associate-*r/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in z around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. associate-*l/ 87.2%

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

      3. distribute-rgt-neg-out 87.2%

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

   6. Simplified 87.2%

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

   if -1.22000000000000007e-42 < t < 1.12000000000000002e-63

   1. Initial program 98.2%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 96.3%

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

   if 1.12000000000000002e-63 < t < 3.09999999999999995e-25

   1. Initial program 99.8%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

      \[\leadsto x - y \cdot \color{blue}{\left(-1 \cdot \frac{t}{a}\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 99.8%

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

      2. distribute-neg-frac 99.8%

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

   6. Simplified 99.8%

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

   if 3.09999999999999995e-25 < t < 5.50000000000000001e42

   1. Initial program 86.1%

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

      1. associate-*r/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in z around inf 75.6%

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

      1. associate-*l/ 89.2%

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

      2. *-commutative 89.2%

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

   6. Simplified 89.2%

      \[\leadsto x - \color{blue}{z \cdot \frac{y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-42}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 4: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-34}:\\ \;\;\;\;x - \frac{t}{\frac{-a}{y}}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e-34)
   (- x (/ t (/ (- a) y)))
   (if (<= t 1.12e-63)
     (- x (/ (* y z) a))
     (if (<= t 3.1e-25)
       (+ x (* y (/ t a)))
       (if (<= t 9.5e+42) (- 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 <= -4e-34) {
		tmp = x - (t / (-a / y));
	} else if (t <= 1.12e-63) {
		tmp = x - ((y * z) / a);
	} else if (t <= 3.1e-25) {
		tmp = x + (y * (t / a));
	} else if (t <= 9.5e+42) {
		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 <= (-4d-34)) then
        tmp = x - (t / (-a / y))
    else if (t <= 1.12d-63) then
        tmp = x - ((y * z) / a)
    else if (t <= 3.1d-25) then
        tmp = x + (y * (t / a))
    else if (t <= 9.5d+42) 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 <= -4e-34) {
		tmp = x - (t / (-a / y));
	} else if (t <= 1.12e-63) {
		tmp = x - ((y * z) / a);
	} else if (t <= 3.1e-25) {
		tmp = x + (y * (t / a));
	} else if (t <= 9.5e+42) {
		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 <= -4e-34:
		tmp = x - (t / (-a / y))
	elif t <= 1.12e-63:
		tmp = x - ((y * z) / a)
	elif t <= 3.1e-25:
		tmp = x + (y * (t / a))
	elif t <= 9.5e+42:
		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 <= -4e-34)
		tmp = Float64(x - Float64(t / Float64(Float64(-a) / y)));
	elseif (t <= 1.12e-63)
		tmp = Float64(x - Float64(Float64(y * z) / a));
	elseif (t <= 3.1e-25)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t <= 9.5e+42)
		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 <= -4e-34)
		tmp = x - (t / (-a / y));
	elseif (t <= 1.12e-63)
		tmp = x - ((y * z) / a);
	elseif (t <= 3.1e-25)
		tmp = x + (y * (t / a));
	elseif (t <= 9.5e+42)
		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, -4e-34], N[(x - N[(t / N[((-a) / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e-63], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-25], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+42], 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 5 regimes

2. if t < -3.99999999999999971e-34

   1. Initial program 89.5%

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

      1. associate-*r/ 94.7%

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

   3. Simplified 94.7%

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

      1. div-sub 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in z around 0 78.5%

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

      1. associate-*r/ 82.4%

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

      2. *-commutative 82.4%

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

      3. associate-*r* 82.4%

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

      4. *-commutative 82.4%

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

      5. associate-*l/ 82.4%

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

      6. associate-*r/ 82.4%

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

      7. metadata-eval 82.4%

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

      8. associate-/r* 82.4%

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

      9. neg-mul-1 82.4%

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

      10. associate-*r/ 82.4%

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

      11. *-commutative 82.4%

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

      12. *-lft-identity 82.4%

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

      13. /-rgt-identity 82.4%

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

      14. times-frac 78.5%

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

      15. *-rgt-identity 78.5%

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

      16. associate-/l* 82.5%

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

      17. distribute-frac-neg 82.5%

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

   8. Simplified 82.5%

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

   if -3.99999999999999971e-34 < t < 1.12000000000000002e-63

   1. Initial program 98.2%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 96.3%

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

   if 1.12000000000000002e-63 < t < 3.09999999999999995e-25

   1. Initial program 99.8%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 99.8%

      \[\leadsto x - y \cdot \color{blue}{\left(-1 \cdot \frac{t}{a}\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 99.8%

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

      2. distribute-neg-frac 99.8%

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

   6. Simplified 99.8%

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

   if 3.09999999999999995e-25 < t < 9.50000000000000019e42

   1. Initial program 86.1%

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

      1. associate-*r/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in z around inf 75.6%

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

      1. associate-*l/ 89.2%

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

      2. *-commutative 89.2%

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

   6. Simplified 89.2%

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

   if 9.50000000000000019e42 < t

   1. Initial program 84.5%

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

      1. associate-*r/ 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in z around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. associate-*l/ 93.9%

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

      3. distribute-rgt-neg-out 93.9%

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

   6. Simplified 93.9%

      \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-34}:\\ \;\;\;\;x - \frac{t}{\frac{-a}{y}}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-25}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 5: 92.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.15 \cdot 10^{+73}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 4.15e+73) (+ x (* y (/ (- t z) a))) (+ x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.15e+73) {
		tmp = x + (y * ((t - z) / a));
	} 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 <= 4.15d+73) then
        tmp = x + (y * ((t - z) / a))
    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 <= 4.15e+73) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 4.15e+73:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 4.15e+73)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	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 <= 4.15e+73)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 4.15e+73], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.15000000000000003e73

   1. Initial program 94.0%

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

      1. associate-*r/ 95.4%

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

   3. Simplified 95.4%

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

   if 4.15000000000000003e73 < t

   1. Initial program 84.7%

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

      1. associate-*r/ 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around 0 80.1%

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

      1. mul-1-neg 80.1%

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

      2. associate-*l/ 95.3%

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

      3. distribute-rgt-neg-out 95.3%

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

   6. Simplified 95.3%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.15 \cdot 10^{+73}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 6: 68.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. associate-*r/ 93.5%

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

3. Simplified 93.5%

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

4. Taylor expanded in z around inf 67.7%

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

5. Final simplification 67.7%

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

Alternative 7: 71.0% 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 92.4%

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

   1. associate-*r/ 93.5%

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

3. Simplified 93.5%

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

4. Taylor expanded in z around inf 68.0%

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

   1. associate-*l/ 71.1%

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

   2. *-commutative 71.1%

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

6. Simplified 71.1%

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

7. Final simplification 71.1%

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

Developer target: 99.2% accurate, 0.7× 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 2023238 
(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)))