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

Percentage Accurate: 92.9% → 97.3%

Time: 7.9s

Alternatives: 7

Speedup: 1.0×

• 24.0% 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: 92.9% 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: 97.3% 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 89.2%

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

   1. associate-*l/ 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 2: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot t\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-215}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) t)))
   (if (<= t -7.2e+133)
     t_1
     (if (<= t -6.5e-140)
       x
       (if (<= t -4.1e-215) (* (/ z a) (- y)) (if (<= t 9.8e+107) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * t;
	double tmp;
	if (t <= -7.2e+133) {
		tmp = t_1;
	} else if (t <= -6.5e-140) {
		tmp = x;
	} else if (t <= -4.1e-215) {
		tmp = (z / a) * -y;
	} else if (t <= 9.8e+107) {
		tmp = x;
	} 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 = (y / a) * t
    if (t <= (-7.2d+133)) then
        tmp = t_1
    else if (t <= (-6.5d-140)) then
        tmp = x
    else if (t <= (-4.1d-215)) then
        tmp = (z / a) * -y
    else if (t <= 9.8d+107) then
        tmp = x
    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 = (y / a) * t;
	double tmp;
	if (t <= -7.2e+133) {
		tmp = t_1;
	} else if (t <= -6.5e-140) {
		tmp = x;
	} else if (t <= -4.1e-215) {
		tmp = (z / a) * -y;
	} else if (t <= 9.8e+107) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * t
	tmp = 0
	if t <= -7.2e+133:
		tmp = t_1
	elif t <= -6.5e-140:
		tmp = x
	elif t <= -4.1e-215:
		tmp = (z / a) * -y
	elif t <= 9.8e+107:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * t)
	tmp = 0.0
	if (t <= -7.2e+133)
		tmp = t_1;
	elseif (t <= -6.5e-140)
		tmp = x;
	elseif (t <= -4.1e-215)
		tmp = Float64(Float64(z / a) * Float64(-y));
	elseif (t <= 9.8e+107)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * t;
	tmp = 0.0;
	if (t <= -7.2e+133)
		tmp = t_1;
	elseif (t <= -6.5e-140)
		tmp = x;
	elseif (t <= -4.1e-215)
		tmp = (z / a) * -y;
	elseif (t <= 9.8e+107)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -7.2e+133], t$95$1, If[LessEqual[t, -6.5e-140], x, If[LessEqual[t, -4.1e-215], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t, 9.8e+107], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.19999999999999956e133 or 9.8000000000000003e107 < t

   1. Initial program 84.9%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-*r/ 76.0%

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

   6. Simplified 76.0%

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

   if -7.19999999999999956e133 < t < -6.4999999999999995e-140 or -4.09999999999999985e-215 < t < 9.8000000000000003e107

   1. Initial program 91.8%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in x around inf 55.6%

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

   if -6.4999999999999995e-140 < t < -4.09999999999999985e-215

   1. Initial program 91.0%

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

      1. associate-*l/ 82.9%

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

   3. Simplified 82.9%

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

      1. *-commutative 82.9%

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

      2. clear-num 82.9%

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

      3. un-div-inv 82.6%

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

   5. Applied egg-rr 82.6%

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

   6. Taylor expanded in z around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. associate-*r/ 64.5%

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

      3. distribute-rgt-neg-in 64.5%

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

      4. distribute-neg-frac 64.5%

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

   8. Simplified 64.5%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+133}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-215}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \]

Alternative 3: 68.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-5} \lor \neg \left(y \leq 5.3 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.8e-5) (not (<= y 5.3e+17))) (* y (/ (- t z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.8e-5) || !(y <= 5.3e+17)) {
		tmp = y * ((t - z) / 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 ((y <= (-2.8d-5)) .or. (.not. (y <= 5.3d+17))) then
        tmp = y * ((t - z) / 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 ((y <= -2.8e-5) || !(y <= 5.3e+17)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.8e-5) or not (y <= 5.3e+17):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.8e-5) || !(y <= 5.3e+17))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.8e-5) || ~((y <= 5.3e+17)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.8e-5], N[Not[LessEqual[y, 5.3e+17]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.79999999999999996e-5 or 5.3e17 < y

   1. Initial program 81.0%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

      1. *-commutative 96.4%

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

      2. clear-num 96.3%

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

      3. un-div-inv 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in x around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-*l/ 83.0%

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

      3. *-commutative 83.0%

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

      4. distribute-rgt-neg-in 83.0%

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

      5. neg-sub0 83.0%

         \[\leadsto y \cdot \color{blue}{\left(0 - \frac{z - t}{a}\right)} \]

      6. div-sub 81.5%

         \[\leadsto y \cdot \left(0 - \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)}\right) \]

      7. associate--r- 81.5%

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - \frac{z}{a}\right) + \frac{t}{a}\right)} \]

      8. neg-sub0 81.5%

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

      9. mul-1-neg 81.5%

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

      10. +-commutative 81.5%

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

      11. mul-1-neg 81.5%

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

      12. sub-neg 81.5%

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

      13. div-sub 83.0%

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

   8. Simplified 83.0%

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

   if -2.79999999999999996e-5 < y < 5.3e17

   1. Initial program 98.3%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around inf 65.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-5} \lor \neg \left(y \leq 5.3 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 78.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+32} \lor \neg \left(y \leq 7.2 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7e+32) (not (<= y 7.2e+53)))
   (* y (/ (- t z) a))
   (+ x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7e+32) || !(y <= 7.2e+53)) {
		tmp = 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 ((y <= (-7d+32)) .or. (.not. (y <= 7.2d+53))) then
        tmp = 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 ((y <= -7e+32) || !(y <= 7.2e+53)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7e+32) or not (y <= 7.2e+53):
		tmp = y * ((t - z) / a)
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7e+32) || !(y <= 7.2e+53))
		tmp = 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 ((y <= -7e+32) || ~((y <= 7.2e+53)))
		tmp = y * ((t - z) / a);
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7e+32], N[Not[LessEqual[y, 7.2e+53]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000002e32 or 7.2e53 < y

   1. Initial program 78.9%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

      1. *-commutative 96.0%

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

      2. clear-num 96.0%

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

      3. un-div-inv 96.3%

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

   5. Applied egg-rr 96.3%

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

   6. Taylor expanded in x around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-*l/ 84.6%

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

      3. *-commutative 84.6%

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

      4. distribute-rgt-neg-in 84.6%

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

      5. neg-sub0 84.6%

         \[\leadsto y \cdot \color{blue}{\left(0 - \frac{z - t}{a}\right)} \]

      6. div-sub 83.0%

         \[\leadsto y \cdot \left(0 - \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)}\right) \]

      7. associate--r- 83.0%

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - \frac{z}{a}\right) + \frac{t}{a}\right)} \]

      8. neg-sub0 83.0%

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

      9. mul-1-neg 83.0%

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

      10. +-commutative 83.0%

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

      11. mul-1-neg 83.0%

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

      12. sub-neg 83.0%

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

      13. div-sub 84.6%

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

   8. Simplified 84.6%

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

   if -7.0000000000000002e32 < y < 7.2e53

   1. Initial program 98.5%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in z around 0 85.5%

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

      1. cancel-sign-sub-inv 85.5%

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

      2. metadata-eval 85.5%

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

      3. *-lft-identity 85.5%

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

      4. +-commutative 85.5%

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

      5. *-commutative 85.5%

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

      6. associate-*r/ 86.0%

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

   6. Simplified 86.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+32} \lor \neg \left(y \leq 7.2 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 5: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+128} \lor \neg \left(t \leq 5.8 \cdot 10^{-42}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+128) (not (<= t 5.8e-42)))
   (+ x (* (/ y a) t))
   (- x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+128) || !(t <= 5.8e-42)) {
		tmp = x + ((y / a) * t);
	} 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 ((t <= (-2.4d+128)) .or. (.not. (t <= 5.8d-42))) then
        tmp = x + ((y / a) * t)
    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 ((t <= -2.4e+128) || !(t <= 5.8e-42)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+128) or not (t <= 5.8e-42):
		tmp = x + ((y / a) * t)
	else:
		tmp = x - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+128) || !(t <= 5.8e-42))
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(x - Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e+128) || ~((t <= 5.8e-42)))
		tmp = x + ((y / a) * t);
	else
		tmp = x - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+128], N[Not[LessEqual[t, 5.8e-42]], $MachinePrecision]], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4000000000000002e128 or 5.8000000000000006e-42 < t

   1. Initial program 86.8%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around 0 80.9%

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

      1. cancel-sign-sub-inv 80.9%

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

      2. metadata-eval 80.9%

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

      3. *-lft-identity 80.9%

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

      4. +-commutative 80.9%

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

      5. *-commutative 80.9%

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

      6. associate-*r/ 90.7%

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

   6. Simplified 90.7%

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

   if -2.4000000000000002e128 < t < 5.8000000000000006e-42

   1. Initial program 91.5%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around inf 82.2%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+128} \lor \neg \left(t \leq 5.8 \cdot 10^{-42}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 6: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+133} \lor \neg \left(t \leq 5.5 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.2e+133) (not (<= t 5.5e+108))) (* (/ y a) t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.2e+133) || !(t <= 5.5e+108)) {
		tmp = (y / a) * t;
	} 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 <= (-7.2d+133)) .or. (.not. (t <= 5.5d+108))) then
        tmp = (y / a) * t
    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 <= -7.2e+133) || !(t <= 5.5e+108)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.2e+133) or not (t <= 5.5e+108):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.2e+133) || !(t <= 5.5e+108))
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.2e+133) || ~((t <= 5.5e+108)))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.2e+133], N[Not[LessEqual[t, 5.5e+108]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -7.19999999999999956e133 or 5.4999999999999998e108 < t

   1. Initial program 84.9%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-*r/ 76.0%

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

   6. Simplified 76.0%

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

   if -7.19999999999999956e133 < t < 5.4999999999999998e108

   1. Initial program 91.8%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in x around inf 53.3%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+133} \lor \neg \left(t \leq 5.5 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 40.0% 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 89.2%

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

   1. associate-*l/ 97.1%

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

3. Simplified 97.1%

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

4. Taylor expanded in x around inf 40.5%

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

5. Final simplification 40.5%

   \[\leadsto x \]

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 2023268 
(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)))