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

Percentage Accurate: 100.0% → 100.0%

Time: 4.2s

Alternatives: 4

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: 52.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{-y}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -5e-310) (sqrt (- y)) (sqrt y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e-310) {
		tmp = sqrt(-y);
	} else {
		tmp = sqrt(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5d-310)) then
        tmp = sqrt(-y)
    else
        tmp = sqrt(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5e-310) {
		tmp = Math.sqrt(-y);
	} else {
		tmp = Math.sqrt(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e-310:
		tmp = math.sqrt(-y)
	else:
		tmp = math.sqrt(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e-310)
		tmp = sqrt(Float64(-y));
	else
		tmp = sqrt(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e-310)
		tmp = sqrt(-y);
	else
		tmp = sqrt(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e-310], N[Sqrt[(-y)], $MachinePrecision], N[Sqrt[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.999999999999985e-310

   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 48.8

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

   5. Applied rewrites 48.8%

      \[\leadsto \sqrt{\left|\color{blue}{-y}\right|} \]
   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. sqr-pow N/A

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

      16. lift-neg.f64 N/A

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

      17. cube-neg N/A

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

      18. neg-sub0 N/A

          \[\leadsto \sqrt{\frac{\color{blue}{0 - {y}^{3}}}{\left|y \cdot y\right|}} \]

      19. metadata-eval N/A

          \[\leadsto \sqrt{\frac{\color{blue}{{0}^{3}} - {y}^{3}}{\left|y \cdot y\right|}} \]

      20. fabs-sqr N/A

          \[\leadsto \sqrt{\frac{{0}^{3} - {y}^{3}}{\color{blue}{y \cdot y}}} \]

      21. +-lft-identity N/A

          \[\leadsto \sqrt{\frac{{0}^{3} - {y}^{3}}{y \cdot \color{blue}{\left(0 + y\right)}}} \]

      22. +-commutative N/A

          \[\leadsto \sqrt{\frac{{0}^{3} - {y}^{3}}{y \cdot \color{blue}{\left(y + 0\right)}}} \]

      23. distribute-rgt-out N/A

          \[\leadsto \sqrt{\frac{{0}^{3} - {y}^{3}}{\color{blue}{y \cdot y + 0 \cdot y}}} \]

      24. +-lft-identity N/A

          \[\leadsto \sqrt{\frac{{0}^{3} - {y}^{3}}{\color{blue}{0 + \left(y \cdot y + 0 \cdot y\right)}}} \]

      25. metadata-eval N/A

          \[\leadsto \sqrt{\frac{{0}^{3} - {y}^{3}}{\color{blue}{0 \cdot 0} + \left(y \cdot y + 0 \cdot y\right)}} \]

      26. flip3-- N/A

          \[\leadsto \sqrt{\color{blue}{0 - y}} \]

      27. neg-sub0 N/A

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

      28. lift-neg.f64 48.8

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

   7. Applied rewrites 48.8%

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

   if -4.999999999999985e-310 < y

   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 46.7

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

   5. Applied rewrites 46.7%

      \[\leadsto \sqrt{\left|\color{blue}{-y}\right|} \]
   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. unpow-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 46.7

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

   7. Applied rewrites 46.7%

      \[\leadsto \sqrt{\color{blue}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 52.9% 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 47.7

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

5. Applied rewrites 47.7%

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

6. Final simplification 47.7%

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

Alternative 4: 26.7% 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 47.7

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

5. Applied rewrites 47.7%

   \[\leadsto \sqrt{\left|\color{blue}{-y}\right|} \]
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. unpow-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 22.4

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

7. Applied rewrites 22.4%

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

Reproduce

herbie shell --seed 2024216 
(FPCore (x y)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, C"
  :precision binary64
  (sqrt (fabs (- x y))))