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

Percentage Accurate: 93.5% → 97.4%

Time: 8.9s

Alternatives: 7

Speedup: 1.0×

• 24.7% 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: 93.5% 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: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (a / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

   1. associate-/l* 94.0%

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

3. Simplified 94.0%

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

   1. associate-*r/ 92.0%

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

   2. *-commutative 92.0%

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

   3. associate-*r/ 98.1%

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

   4. clear-num 98.0%

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

   5. un-div-inv 98.2%

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

6. Applied egg-rr 98.2%

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

7. Final simplification 98.2%

   \[\leadsto x + \frac{z - t}{\frac{a}{y}} \]
8. Add Preprocessing

Alternative 2: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{-8} \lor \neg \left(t \leq 5.2 \cdot 10^{+39}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.7e-8) (not (<= t 5.2e+39)))
   (- x (* t (/ y a)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.7e-8) || !(t <= 5.2e+39)) {
		tmp = x - (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 <= (-5.7d-8)) .or. (.not. (t <= 5.2d+39))) then
        tmp = x - (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 <= -5.7e-8) || !(t <= 5.2e+39)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.7e-8) or not (t <= 5.2e+39):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.7e-8) || !(t <= 5.2e+39))
		tmp = Float64(x - Float64(t * Float64(y / 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 <= -5.7e-8) || ~((t <= 5.2e+39)))
		tmp = x - (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, -5.7e-8], N[Not[LessEqual[t, 5.2e+39]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.70000000000000009e-8 or 5.2e39 < t

   1. Initial program 87.7%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

      1. associate-*r/ 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*r/ 99.0%

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

      4. clear-num 98.9%

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

      5. un-div-inv 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in z around 0 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-*r/ 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. unsub-neg 83.8%

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

      5. associate-*r/ 79.5%

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

      6. associate-*l/ 86.9%

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

      7. *-commutative 86.9%

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

   9. Simplified 86.9%

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

   if -5.70000000000000009e-8 < t < 5.2e39

   1. Initial program 95.6%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

      1. associate-*r/ 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*r/ 97.3%

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

      4. clear-num 97.3%

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

      5. un-div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in z around inf 87.7%

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

      1. associate-*l/ 90.8%

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

      2. *-commutative 90.8%

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

   9. Simplified 90.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{-8} \lor \neg \left(t \leq 5.2 \cdot 10^{+39}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.00039 \lor \neg \left(t \leq 4.5 \cdot 10^{+39}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.00039) (not (<= t 4.5e+39)))
   (- x (/ t (/ a y)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.00039) || !(t <= 4.5e+39)) {
		tmp = x - (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 <= (-0.00039d0)) .or. (.not. (t <= 4.5d+39))) then
        tmp = x - (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 <= -0.00039) || !(t <= 4.5e+39)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.00039) or not (t <= 4.5e+39):
		tmp = x - (t / (a / y))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.00039) || !(t <= 4.5e+39))
		tmp = Float64(x - Float64(t / Float64(a / 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 <= -0.00039) || ~((t <= 4.5e+39)))
		tmp = x - (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, -0.00039], N[Not[LessEqual[t, 4.5e+39]], $MachinePrecision]], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.89999999999999993e-4 or 4.49999999999999996e39 < t

   1. Initial program 87.7%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

      1. associate-*r/ 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*r/ 99.0%

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

      4. clear-num 98.9%

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

      5. un-div-inv 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in z around 0 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-*r/ 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. unsub-neg 83.8%

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

      5. associate-*r/ 79.5%

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

      6. associate-*l/ 86.9%

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

      7. *-commutative 86.9%

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

   9. Simplified 86.9%

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

       1. clear-num 86.9%

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

       2. un-div-inv 87.0%

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

   11. Applied egg-rr 87.0%

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

   if -3.89999999999999993e-4 < t < 4.49999999999999996e39

   1. Initial program 95.6%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

      1. associate-*r/ 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*r/ 97.3%

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

      4. clear-num 97.3%

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

      5. un-div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in z around inf 87.7%

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

      1. associate-*l/ 90.8%

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

      2. *-commutative 90.8%

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

   9. Simplified 90.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00039 \lor \neg \left(t \leq 4.5 \cdot 10^{+39}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.1% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.0%

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

   1. associate-/l* 94.0%

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

3. Simplified 94.0%

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

5. Final simplification 94.0%

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

Alternative 5: 97.4% 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 92.0%

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

   1. *-commutative 92.0%

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

   2. associate-/l* 98.1%

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

3. Simplified 98.1%

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

5. Final simplification 98.1%

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

Alternative 6: 71.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

   1. associate-/l* 94.0%

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

3. Simplified 94.0%

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

   1. associate-*r/ 92.0%

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

   2. *-commutative 92.0%

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

   3. associate-*r/ 98.1%

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

   4. clear-num 98.0%

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

   5. un-div-inv 98.2%

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

6. Applied egg-rr 98.2%

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

7. Taylor expanded in z around inf 67.9%

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

   1. associate-*l/ 72.2%

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

   2. *-commutative 72.2%

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

9. Simplified 72.2%

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

10. Final simplification 72.2%

    \[\leadsto x + z \cdot \frac{y}{a} \]
11. Add Preprocessing

Alternative 7: 39.9% 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 92.0%

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

   1. associate-/l* 94.0%

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

3. Simplified 94.0%

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

5. Taylor expanded in x around inf 38.5%

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

6. Final simplification 38.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024048 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :alt
  (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)))