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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \sqrt{\left|x - y\right|} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (sqrt (fabs (- x y))))

C

double code(double x, double y) {
	return sqrt(fabs((x - y)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt(abs((x - y)))
end function

Java

public static double code(double x, double y) {
	return Math.sqrt(Math.abs((x - y)));
}

Python

def code(x, y):
	return math.sqrt(math.fabs((x - y)))

Julia

function code(x, y)
	return sqrt(abs(Float64(x - y)))
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt(abs((x - y)));
end

Wolfram

code[x_, y_] := N[Sqrt[N[Abs[N[(x - y), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{\left|x - y\right|} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (sqrt (fabs (- x y))))

C

double code(double x, double y) {
	return sqrt(fabs((x - y)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt(abs((x - y)))
end function

Java

public static double code(double x, double y) {
	return Math.sqrt(Math.abs((x - y)));
}

Python

def code(x, y):
	return math.sqrt(math.fabs((x - y)))

Julia

function code(x, y)
	return sqrt(abs(Float64(x - y)))
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt(abs((x - y)));
end

Wolfram

code[x_, y_] := N[Sqrt[N[Abs[N[(x - y), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{\left|y - x\right|} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (sqrt (fabs (- y x))))

C

double code(double x, double y) {
	return sqrt(fabs((y - x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt(abs((y - x)))
end function

Java

public static double code(double x, double y) {
	return Math.sqrt(Math.abs((y - x)));
}

Python

def code(x, y):
	return math.sqrt(math.fabs((y - x)))

Julia

function code(x, y)
	return sqrt(abs(Float64(y - x)))
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt(abs((y - x)));
end

Wolfram

code[x_, y_] := N[Sqrt[N[Abs[N[(y - x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\sqrt{\left|x - y\right|} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \sqrt{\left|y - x\right|} \]
4. Add Preprocessing

Alternative 2: 52.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \sqrt{\left|y\right|} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (sqrt (fabs y)))

C

double code(double x, double y) {
	return sqrt(fabs(y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt(abs(y))
end function

Java

public static double code(double x, double y) {
	return Math.sqrt(Math.abs(y));
}

Python

def code(x, y):
	return math.sqrt(math.fabs(y))

Julia

function code(x, y)
	return sqrt(abs(y))
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt(abs(y));
end

Wolfram

code[x_, y_] := N[Sqrt[N[Abs[y], $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\sqrt{\left|x - y\right|} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \sqrt{\left|\color{blue}{-1 \cdot y}\right|} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \sqrt{\left|\color{blue}{\mathsf{neg}\left(y\right)}\right|} \]

   2. lower-neg.f64 50.9

      \[\leadsto \sqrt{\left|\color{blue}{-y}\right|} \]

5. Applied rewrites 50.9%

   \[\leadsto \sqrt{\left|\color{blue}{-y}\right|} \]

6. Final simplification 50.9%

   \[\leadsto \sqrt{\left|y\right|} \]
7. Add Preprocessing

Alternative 3: 25.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \sqrt{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (sqrt y))

C

double code(double x, double y) {
	return sqrt(y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt(y)
end function

Java

public static double code(double x, double y) {
	return Math.sqrt(y);
}

Python

def code(x, y):
	return math.sqrt(y)

Julia

function code(x, y)
	return sqrt(y)
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt(y);
end

Wolfram

code[x_, y_] := N[Sqrt[y], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\sqrt{\left|x - y\right|} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \sqrt{\left|\color{blue}{-1 \cdot y}\right|} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \sqrt{\left|\color{blue}{\mathsf{neg}\left(y\right)}\right|} \]

   2. lower-neg.f64 50.9

      \[\leadsto \sqrt{\left|\color{blue}{-y}\right|} \]

5. Applied rewrites 50.9%

   \[\leadsto \sqrt{\left|\color{blue}{-y}\right|} \]
6. Step-by-step derivation

   1. lift-neg.f64 N/A

      \[\leadsto \sqrt{\left|\color{blue}{\mathsf{neg}\left(y\right)}\right|} \]

   2. neg-fabs N/A

      \[\leadsto \sqrt{\color{blue}{\left|\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right|}} \]

   3. lift-neg.f64 N/A

      \[\leadsto \sqrt{\left|\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right|} \]

   4. remove-double-neg N/A

      \[\leadsto \sqrt{\left|\color{blue}{y}\right|} \]

   5. unpow1 N/A

      \[\leadsto \sqrt{\left|\color{blue}{{y}^{1}}\right|} \]

   6. metadata-eval N/A

      \[\leadsto \sqrt{\left|{y}^{\color{blue}{\left(3 - 2\right)}}\right|} \]

   7. pow-div N/A

      \[\leadsto \sqrt{\left|\color{blue}{\frac{{y}^{3}}{{y}^{2}}}\right|} \]

   8. pow2 N/A

      \[\leadsto \sqrt{\left|\frac{{y}^{3}}{\color{blue}{y \cdot y}}\right|} \]

   9. div-fabs N/A

      \[\leadsto \sqrt{\color{blue}{\frac{\left|{y}^{3}\right|}{\left|y \cdot y\right|}}} \]

   10. neg-fabs N/A

       \[\leadsto \sqrt{\frac{\color{blue}{\left|\mathsf{neg}\left({y}^{3}\right)\right|}}{\left|y \cdot y\right|}} \]

   11. cube-neg N/A

       \[\leadsto \sqrt{\frac{\left|\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{3}}\right|}{\left|y \cdot y\right|}} \]

   12. lift-neg.f64 N/A

       \[\leadsto \sqrt{\frac{\left|{\color{blue}{\left(\mathsf{neg}\left(y\right)\right)}}^{3}\right|}{\left|y \cdot y\right|}} \]

   13. sqr-pow N/A

       \[\leadsto \sqrt{\frac{\left|\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)}}\right|}{\left|y \cdot y\right|}} \]

   14. fabs-sqr N/A

       \[\leadsto \sqrt{\frac{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)}}}{\left|y \cdot y\right|}} \]

   15. pow-prod-down N/A

       \[\leadsto \sqrt{\frac{\color{blue}{{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}^{\left(\frac{3}{2}\right)}}}{\left|y \cdot y\right|}} \]

   16. lift-neg.f64 N/A

       \[\leadsto \sqrt{\frac{{\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{\left|y \cdot y\right|}} \]

   17. lift-neg.f64 N/A

       \[\leadsto \sqrt{\frac{{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)}^{\left(\frac{3}{2}\right)}}{\left|y \cdot y\right|}} \]

   18. sqr-neg N/A

       \[\leadsto \sqrt{\frac{{\color{blue}{\left(y \cdot y\right)}}^{\left(\frac{3}{2}\right)}}{\left|y \cdot y\right|}} \]

   19. pow-prod-down N/A

       \[\leadsto \sqrt{\frac{\color{blue}{{y}^{\left(\frac{3}{2}\right)} \cdot {y}^{\left(\frac{3}{2}\right)}}}{\left|y \cdot y\right|}} \]

   20. sqr-pow N/A

       \[\leadsto \sqrt{\frac{\color{blue}{{y}^{3}}}{\left|y \cdot y\right|}} \]

   21. fabs-sqr N/A

       \[\leadsto \sqrt{\frac{{y}^{3}}{\color{blue}{y \cdot y}}} \]

   22. pow2 N/A

       \[\leadsto \sqrt{\frac{{y}^{3}}{\color{blue}{{y}^{2}}}} \]

   23. pow-div N/A

       \[\leadsto \sqrt{\color{blue}{{y}^{\left(3 - 2\right)}}} \]

   24. metadata-eval N/A

       \[\leadsto \sqrt{{y}^{\color{blue}{1}}} \]

   25. unpow1 31.1

       \[\leadsto \sqrt{\color{blue}{y}} \]

7. Applied rewrites 31.1%

   \[\leadsto \sqrt{\color{blue}{y}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024219 
(FPCore (x y)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, C"
  :precision binary64
  (sqrt (fabs (- x y))))