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

Percentage Accurate: 99.9% → 99.9%

Time: 8.6s

Alternatives: 12

Speedup: 1.0×

• 27.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(y + x\right) - z}{2 \cdot t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ y x) z) (* 2.0 t)))

C

double code(double x, double y, double z, double t) {
	return ((y + x) - z) / (2.0 * t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((y + x) - z) / (2.0d0 * t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((y + x) - z) / (2.0 * t);
}

Python

def code(x, y, z, t):
	return ((y + x) - z) / (2.0 * t)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(y + x) - z) / Float64(2.0 * t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((y + x) - z) / (2.0 * t);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(y + x), $MachinePrecision] - z), $MachinePrecision] / N[(2.0 * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 50.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -2 \cdot 10^{+40}:\\ \;\;\;\;\frac{0.5 \cdot x}{t}\\ \mathbf{elif}\;y + x \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ y x) -2e+40)
   (/ (* 0.5 x) t)
   (if (<= (+ y x) 2e-7) (/ (* -0.5 z) t) (/ (* 0.5 y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y + x) <= -2e+40) {
		tmp = (0.5 * x) / t;
	} else if ((y + x) <= 2e-7) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = (0.5 * y) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y + x) <= (-2d+40)) then
        tmp = (0.5d0 * x) / t
    else if ((y + x) <= 2d-7) then
        tmp = ((-0.5d0) * z) / t
    else
        tmp = (0.5d0 * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y + x) <= -2e+40) {
		tmp = (0.5 * x) / t;
	} else if ((y + x) <= 2e-7) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = (0.5 * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y + x) <= -2e+40:
		tmp = (0.5 * x) / t
	elif (y + x) <= 2e-7:
		tmp = (-0.5 * z) / t
	else:
		tmp = (0.5 * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y + x) <= -2e+40)
		tmp = Float64(Float64(0.5 * x) / t);
	elseif (Float64(y + x) <= 2e-7)
		tmp = Float64(Float64(-0.5 * z) / t);
	else
		tmp = Float64(Float64(0.5 * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y + x) <= -2e+40)
		tmp = (0.5 * x) / t;
	elseif ((y + x) <= 2e-7)
		tmp = (-0.5 * z) / t;
	else
		tmp = (0.5 * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y + x), $MachinePrecision], -2e+40], N[(N[(0.5 * x), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(y + x), $MachinePrecision], 2e-7], N[(N[(-0.5 * z), $MachinePrecision] / t), $MachinePrecision], N[(N[(0.5 * y), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -2.00000000000000006e40

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-lft-identity N/A

         \[\leadsto \frac{1}{2} \cdot \frac{\color{blue}{1 \cdot x}}{t} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\frac{1}{t} \cdot x\right)} \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{1}{t}\right) \cdot x} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{1}{t}\right) \cdot x} \]

      5. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot 1}{t}} \cdot x \]

      6. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2}}}{t} \cdot x \]

      7. lower-/.f64 44.5

         \[\leadsto \color{blue}{\frac{0.5}{t}} \cdot x \]

   5. Applied rewrites 44.5%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot x} \]
   6. Step-by-step derivation

   7. Applied rewrites 44.6%

      \[\leadsto \frac{0.5 \cdot x}{\color{blue}{t}} \]

   if -2.00000000000000006e40 < (+.f64 x y) < 1.9999999999999999e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. *-lft-identity N/A

         \[\leadsto \frac{-1}{2} \cdot \frac{\color{blue}{1 \cdot z}}{t} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{-1}{2} \cdot \color{blue}{\left(\frac{1}{t} \cdot z\right)} \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\frac{-1}{2} \cdot \frac{1}{t}\right) \cdot z} \]

      4. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)} \cdot \frac{1}{t}\right) \cdot z \]

      5. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{t}\right)\right)} \cdot z \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2} \cdot \frac{1}{t}\right)\right) \cdot z} \]

      7. associate-*r/ N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{1}{2} \cdot 1}{t}}\right)\right) \cdot z \]

      8. metadata-eval N/A

         \[\leadsto \left(\mathsf{neg}\left(\frac{\color{blue}{\frac{1}{2}}}{t}\right)\right) \cdot z \]

      9. distribute-neg-frac N/A

         \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\frac{1}{2}\right)}{t}} \cdot z \]

      10. metadata-eval N/A

          \[\leadsto \frac{\color{blue}{\frac{-1}{2}}}{t} \cdot z \]

      11. lower-/.f64 68.7

          \[\leadsto \color{blue}{\frac{-0.5}{t}} \cdot z \]

   5. Applied rewrites 68.7%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 68.9%

      \[\leadsto \frac{-0.5 \cdot z}{\color{blue}{t}} \]

   if 1.9999999999999999e-7 < (+.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. *-lft-identity N/A

         \[\leadsto \frac{1}{2} \cdot \frac{\color{blue}{1 \cdot y}}{t} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\frac{1}{t} \cdot y\right)} \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{1}{t}\right) \cdot y} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{1}{t}\right) \cdot y} \]

      5. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot 1}{t}} \cdot y \]

      6. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2}}}{t} \cdot y \]

      7. lower-/.f64 41.7

         \[\leadsto \color{blue}{\frac{0.5}{t}} \cdot y \]

   5. Applied rewrites 41.7%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot y} \]
   6. Step-by-step derivation

   7. Applied rewrites 41.8%

      \[\leadsto \frac{y \cdot 0.5}{\color{blue}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -2 \cdot 10^{+40}:\\ \;\;\;\;\frac{0.5 \cdot x}{t}\\ \mathbf{elif}\;y + x \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024230 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))