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

Percentage Accurate: 93.0% → 93.4%

Time: 11.9s

Alternatives: 7

Speedup: 1.0×

• 24.3% 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: 93.0% 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: 93.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-289}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-154}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) a)))))
   (if (<= y -5e-195)
     t_1
     (if (<= y 8.2e-289)
       (+ x (/ (* z y) a))
       (if (<= y 3.6e-154) (- x (/ (* t y) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / a));
	double tmp;
	if (y <= -5e-195) {
		tmp = t_1;
	} else if (y <= 8.2e-289) {
		tmp = x + ((z * y) / a);
	} else if (y <= 3.6e-154) {
		tmp = x - ((t * y) / a);
	} 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 * ((z - t) / a))
    if (y <= (-5d-195)) then
        tmp = t_1
    else if (y <= 8.2d-289) then
        tmp = x + ((z * y) / a)
    else if (y <= 3.6d-154) then
        tmp = x - ((t * y) / a)
    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 * ((z - t) / a));
	double tmp;
	if (y <= -5e-195) {
		tmp = t_1;
	} else if (y <= 8.2e-289) {
		tmp = x + ((z * y) / a);
	} else if (y <= 3.6e-154) {
		tmp = x - ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / a))
	tmp = 0
	if y <= -5e-195:
		tmp = t_1
	elif y <= 8.2e-289:
		tmp = x + ((z * y) / a)
	elif y <= 3.6e-154:
		tmp = x - ((t * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (y <= -5e-195)
		tmp = t_1;
	elseif (y <= 8.2e-289)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	elseif (y <= 3.6e-154)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / a));
	tmp = 0.0;
	if (y <= -5e-195)
		tmp = t_1;
	elseif (y <= 8.2e-289)
		tmp = x + ((z * y) / a);
	elseif (y <= 3.6e-154)
		tmp = x - ((t * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e-195], t$95$1, If[LessEqual[y, 8.2e-289], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-154], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000009e-195 or 3.6000000000000003e-154 < y

   1. Initial program 92.4%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   if -5.00000000000000009e-195 < y < 8.1999999999999996e-289

   1. Initial program 100.0%

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

      1. associate-/l* 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in z around inf 90.7%

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

   if 8.1999999999999996e-289 < y < 3.6000000000000003e-154

   1. Initial program 99.8%

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

      1. associate-/l* 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in z around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-/l* 75.6%

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

   7. Simplified 75.6%

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

      1. associate-*r/ 99.8%

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

   9. Applied egg-rr 99.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-195}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-289}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-154}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.76 \cdot 10^{+37} \lor \neg \left(t \leq 5.4 \cdot 10^{+40}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.76e+37) (not (<= t 5.4e+40)))
   (- x (* t (/ y a)))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.76e+37) || !(t <= 5.4e+40)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	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 <= (-1.76d+37)) .or. (.not. (t <= 5.4d+40))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (z / (a / y))
    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 <= -1.76e+37) || !(t <= 5.4e+40)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.76e+37) or not (t <= 5.4e+40):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.76e+37) || !(t <= 5.4e+40))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.76e+37) || ~((t <= 5.4e+40)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.76e+37], N[Not[LessEqual[t, 5.4e+40]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.76e37 or 5.40000000000000019e40 < t

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-/l* 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in z around 0 81.1%

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

      1. associate-*l/ 78.1%

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

      2. *-commutative 78.1%

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

      3. neg-mul-1 78.1%

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

      4. sub-neg 78.1%

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

      5. *-commutative 78.1%

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

      6. associate-*l/ 81.1%

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

      7. associate-*r/ 88.5%

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

   7. Simplified 88.5%

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

   if -1.76e37 < t < 5.40000000000000019e40

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in z around inf 91.2%

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

      1. clear-num 91.2%

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

      2. un-div-inv 91.6%

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

   7. Applied egg-rr 91.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.76 \cdot 10^{+37} \lor \neg \left(t \leq 5.4 \cdot 10^{+40}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+194} \lor \neg \left(t \leq 7.5 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.42e+194) (not (<= t 7.5e+86)))
   (/ t (/ a (- y)))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.42e+194) || !(t <= 7.5e+86)) {
		tmp = t / (a / -y);
	} else {
		tmp = x + (z / (a / y));
	}
	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 <= (-1.42d+194)) .or. (.not. (t <= 7.5d+86))) then
        tmp = t / (a / -y)
    else
        tmp = x + (z / (a / y))
    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 <= -1.42e+194) || !(t <= 7.5e+86)) {
		tmp = t / (a / -y);
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.42e+194) or not (t <= 7.5e+86):
		tmp = t / (a / -y)
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.42e+194) || !(t <= 7.5e+86))
		tmp = Float64(t / Float64(a / Float64(-y)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.42e+194) || ~((t <= 7.5e+86)))
		tmp = t / (a / -y);
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.42e+194], N[Not[LessEqual[t, 7.5e+86]], $MachinePrecision]], N[(t / N[(a / (-y)), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4199999999999999e194 or 7.4999999999999997e86 < t

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

      2. associate-/l* 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around 0 84.6%

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

      1. associate-*l/ 80.0%

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

      2. *-commutative 80.0%

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

      3. neg-mul-1 80.0%

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

      4. sub-neg 80.0%

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

      5. *-commutative 80.0%

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

      6. associate-*l/ 84.6%

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

      7. associate-*r/ 93.8%

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

   7. Simplified 93.8%

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

   8. Taylor expanded in x around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*l/ 65.7%

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

      3. associate-/r/ 77.7%

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

   10. Simplified 77.7%

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

   if -1.4199999999999999e194 < t < 7.4999999999999997e86

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-/l* 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in z around inf 87.6%

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

      1. clear-num 87.5%

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

      2. un-div-inv 87.9%

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

   7. Applied egg-rr 87.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+194} \lor \neg \left(t \leq 7.5 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+198} \lor \neg \left(t \leq 5.4 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.5e+198) (not (<= t 5.4e+85)))
   (/ t (/ a (- y)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e+198) || !(t <= 5.4e+85)) {
		tmp = t / (a / -y);
	} else {
		tmp = x + (z * (y / a));
	}
	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 <= (-9.5d+198)) .or. (.not. (t <= 5.4d+85))) then
        tmp = t / (a / -y)
    else
        tmp = x + (z * (y / a))
    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 <= -9.5e+198) || !(t <= 5.4e+85)) {
		tmp = t / (a / -y);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.5e+198) or not (t <= 5.4e+85):
		tmp = t / (a / -y)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.5e+198) || !(t <= 5.4e+85))
		tmp = Float64(t / Float64(a / Float64(-y)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.5e+198) || ~((t <= 5.4e+85)))
		tmp = t / (a / -y);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.5e+198], N[Not[LessEqual[t, 5.4e+85]], $MachinePrecision]], N[(t / N[(a / (-y)), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.5e198 or 5.39999999999999966e85 < t

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

      2. associate-/l* 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around 0 84.6%

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

      1. associate-*l/ 80.0%

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

      2. *-commutative 80.0%

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

      3. neg-mul-1 80.0%

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

      4. sub-neg 80.0%

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

      5. *-commutative 80.0%

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

      6. associate-*l/ 84.6%

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

      7. associate-*r/ 93.8%

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

   7. Simplified 93.8%

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

   8. Taylor expanded in x around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*l/ 65.7%

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

      3. associate-/r/ 77.7%

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

   10. Simplified 77.7%

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

   if -9.5e198 < t < 5.39999999999999966e85

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-/l* 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in z around inf 87.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+198} \lor \neg \left(t \leq 5.4 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+143} \lor \neg \left(t \leq 1.5 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.6e+143) (not (<= t 1.5e+83))) (/ t (/ a (- y))) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.6e+143) || !(t <= 1.5e+83)) {
		tmp = t / (a / -y);
	} else {
		tmp = x;
	}
	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 <= (-1.6d+143)) .or. (.not. (t <= 1.5d+83))) then
        tmp = t / (a / -y)
    else
        tmp = x
    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 <= -1.6e+143) || !(t <= 1.5e+83)) {
		tmp = t / (a / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.6e+143) or not (t <= 1.5e+83):
		tmp = t / (a / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.6e+143) || !(t <= 1.5e+83))
		tmp = Float64(t / Float64(a / Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.6e+143) || ~((t <= 1.5e+83)))
		tmp = t / (a / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.6e+143], N[Not[LessEqual[t, 1.5e+83]], $MachinePrecision]], N[(t / N[(a / (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.60000000000000008e143 or 1.5e83 < t

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-/l* 97.1%

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

   4. Applied egg-rr 97.1%

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

   5. Taylor expanded in z around 0 81.1%

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

      1. associate-*l/ 77.3%

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

      2. *-commutative 77.3%

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

      3. neg-mul-1 77.3%

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

      4. sub-neg 77.3%

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

      5. *-commutative 77.3%

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

      6. associate-*l/ 81.1%

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

      7. associate-*r/ 89.9%

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

   7. Simplified 89.9%

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

   8. Taylor expanded in x around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. associate-*l/ 63.7%

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

      3. associate-/r/ 74.8%

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

   10. Simplified 74.8%

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

   if -1.60000000000000008e143 < t < 1.5e83

   1. Initial program 95.9%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in x around inf 46.1%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+143} \lor \neg \left(t \leq 1.5 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. *-commutative 94.1%

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

   2. associate-/l* 96.9%

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

4. Applied egg-rr 96.9%

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

Alternative 7: 40.4% accurate, 9.0× speedup

Math

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

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 94.1%

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

   1. associate-/l* 92.1%

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

3. Simplified 92.1%

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

5. Taylor expanded in x around inf 37.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.2% 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 2024135 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t)))))))

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