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

Percentage Accurate: 93.2% → 99.4%

Time: 10.9s

Alternatives: 7

Speedup: 0.6×

• 25.7% 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: 93.2% 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: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+23}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1e+23)
   (+ x (* y (/ (- z t) a)))
   (if (<= a 1.8e-5) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1e+23) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 1.8e-5) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / (a / (z - 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 (a <= (-1d+23)) then
        tmp = x + (y * ((z - t) / a))
    else if (a <= 1.8d-5) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y / (a / (z - 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 (a <= -1e+23) {
		tmp = x + (y * ((z - t) / a));
	} else if (a <= 1.8e-5) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1e+23:
		tmp = x + (y * ((z - t) / a))
	elif a <= 1.8e-5:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1e+23)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (a <= 1.8e-5)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1e+23)
		tmp = x + (y * ((z - t) / a));
	elseif (a <= 1.8e-5)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1e+23], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-5], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.9999999999999992e22

   1. Initial program 79.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -9.9999999999999992e22 < a < 1.80000000000000005e-5

   1. Initial program 99.9%

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

   if 1.80000000000000005e-5 < a

   1. Initial program 85.2%

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

      1. associate-/l* 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. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

Alternative 2: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+224} \lor \neg \left(t \leq 2.75 \cdot 10^{+116}\right):\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.25e+224) (not (<= t 2.75e+116)))
   (* t (/ y (- a)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.25e+224) || !(t <= 2.75e+116)) {
		tmp = t * (y / -a);
	} 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 <= (-2.25d+224)) .or. (.not. (t <= 2.75d+116))) then
        tmp = t * (y / -a)
    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 <= -2.25e+224) || !(t <= 2.75e+116)) {
		tmp = t * (y / -a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.25e+224) or not (t <= 2.75e+116):
		tmp = t * (y / -a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.25e+224) || !(t <= 2.75e+116))
		tmp = Float64(t * Float64(y / Float64(-a)));
	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 <= -2.25e+224) || ~((t <= 2.75e+116)))
		tmp = t * (y / -a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.25e+224], N[Not[LessEqual[t, 2.75e+116]], $MachinePrecision]], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2499999999999999e224 or 2.75000000000000017e116 < t

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-/l* 94.0%

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

   4. Applied egg-rr 94.0%

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

   5. Taylor expanded in z around 0 88.2%

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

      1. associate-*l/ 79.2%

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

      2. *-commutative 79.2%

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

      3. neg-mul-1 79.2%

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

      4. sub-neg 79.2%

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

      5. *-commutative 79.2%

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

      6. associate-*l/ 88.2%

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

      7. associate-*r/ 88.1%

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

   7. Simplified 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*l/ 88.2%

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

   9. Applied egg-rr 88.2%

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

   10. Taylor expanded in x around 0 77.7%

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

       1. mul-1-neg 77.7%

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

       2. associate-*r/ 76.9%

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

       3. distribute-rgt-neg-in 76.9%

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

       4. distribute-neg-frac2 76.9%

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

   12. Simplified 76.9%

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

   if -2.2499999999999999e224 < t < 2.75000000000000017e116

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      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 79.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+224} \lor \neg \left(t \leq 2.75 \cdot 10^{+116}\right):\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+85}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+81)
   (+ x (* z (/ y a)))
   (if (<= z 2.5e+85) (- x (* t (/ y a))) (+ x (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+81) {
		tmp = x + (z * (y / a));
	} else if (z <= 2.5e+85) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y * (z / 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 (z <= (-2.2d+81)) then
        tmp = x + (z * (y / a))
    else if (z <= 2.5d+85) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (y * (z / 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 (z <= -2.2e+81) {
		tmp = x + (z * (y / a));
	} else if (z <= 2.5e+85) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+81:
		tmp = x + (z * (y / a))
	elif z <= 2.5e+85:
		tmp = x - (t * (y / a))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+81)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	elseif (z <= 2.5e+85)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+81)
		tmp = x + (z * (y / a));
	elseif (z <= 2.5e+85)
		tmp = x - (t * (y / a));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+81], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+85], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.19999999999999987e81

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-/l* 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in z around inf 89.5%

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

   if -2.19999999999999987e81 < z < 2.5e85

   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* 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in z around 0 88.1%

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

      1. associate-*l/ 83.8%

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

      2. *-commutative 83.8%

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

      3. neg-mul-1 83.8%

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

      4. sub-neg 83.8%

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

      5. *-commutative 83.8%

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

      6. associate-*l/ 88.1%

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

      7. associate-*r/ 89.4%

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

   7. Simplified 89.4%

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

   if 2.5e85 < z

   1. Initial program 85.8%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+85}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1150000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1150000000.0) x (if (<= a 2.4e-82) (* t (/ y (- a))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1150000000.0) {
		tmp = x;
	} else if (a <= 2.4e-82) {
		tmp = t * (y / -a);
	} 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 (a <= (-1150000000.0d0)) then
        tmp = x
    else if (a <= 2.4d-82) then
        tmp = t * (y / -a)
    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 (a <= -1150000000.0) {
		tmp = x;
	} else if (a <= 2.4e-82) {
		tmp = t * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1150000000.0:
		tmp = x
	elif a <= 2.4e-82:
		tmp = t * (y / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1150000000.0)
		tmp = x;
	elseif (a <= 2.4e-82)
		tmp = Float64(t * Float64(y / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1150000000.0)
		tmp = x;
	elseif (a <= 2.4e-82)
		tmp = t * (y / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1150000000.0], x, If[LessEqual[a, 2.4e-82], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.15e9 or 2.40000000000000008e-82 < a

   1. Initial program 84.8%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 54.7%

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

   if -1.15e9 < a < 2.40000000000000008e-82

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in z around 0 69.1%

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

      1. associate-*l/ 58.1%

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

      2. *-commutative 58.1%

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

      3. neg-mul-1 58.1%

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

      4. sub-neg 58.1%

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

      5. *-commutative 58.1%

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

      6. associate-*l/ 69.1%

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

      7. associate-*r/ 72.3%

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

   7. Simplified 72.3%

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

      1. *-commutative 72.3%

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

      2. associate-*l/ 69.1%

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

   9. Applied egg-rr 69.1%

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

   10. Taylor expanded in x around 0 56.9%

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

       1. mul-1-neg 56.9%

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

       2. associate-*r/ 60.1%

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

       3. distribute-rgt-neg-in 60.1%

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

       4. distribute-neg-frac2 60.1%

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

   12. Simplified 60.1%

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

Alternative 5: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e+21) (+ x (* y (/ (- z t) a))) (+ x (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e+21) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + ((z - t) * (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 (a <= (-5d+21)) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = x + ((z - t) * (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 (a <= -5e+21) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e+21:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e+21)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5e+21)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + ((z - t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e+21], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5e21

   1. Initial program 79.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -5e21 < a

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

      2. associate-/l* 97.6%

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

   4. Applied egg-rr 97.6%

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

Alternative 6: 93.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{+213}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.28e+213) (- x (* t (/ y a))) (+ x (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.28e+213) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y * ((z - t) / 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 <= (-1.28d+213)) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (y * ((z - t) / 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 <= -1.28e+213) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.28e+213:
		tmp = x - (t * (y / a))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.28e+213)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.28e+213)
		tmp = x - (t * (y / a));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.28e+213], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2799999999999999e213

   1. Initial program 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 85.2%

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

      1. associate-*l/ 75.1%

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

      2. *-commutative 75.1%

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

      3. neg-mul-1 75.1%

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

      4. sub-neg 75.1%

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

      5. *-commutative 75.1%

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

      6. associate-*l/ 85.2%

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

      7. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   if -1.2799999999999999e213 < t

   1. Initial program 92.3%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

Alternative 7: 39.6% 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 91.8%

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

   1. associate-/l* 92.2%

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

3. Simplified 92.2%

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

5. Taylor expanded in x around inf 36.1%

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

Developer Target 1: 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 2024116 
(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)))