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

Percentage Accurate: 100.0% → 100.0%

Time: 2.2s

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

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

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]

Derivation

1. Initial program 100.0%

   \[\sqrt{\left|x - y\right|} \]

2. Final simplification 100.0%

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

Alternative 2: 49.7% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\sqrt{\left|x - y\right|} \]
2. Step-by-step derivation

   1. fabs-sub 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around -inf 100.0%

   \[\leadsto \color{blue}{\sqrt{\left|-\left(x + -1 \cdot y\right)\right|}} \]
5. Step-by-step derivation

   1. fabs-neg 100.0%

      \[\leadsto \sqrt{\color{blue}{\left|x + -1 \cdot y\right|}} \]

   2. mul-1-neg 100.0%

      \[\leadsto \sqrt{\left|x + \color{blue}{\left(-y\right)}\right|} \]

   3. unsub-neg 100.0%

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

   4. fabs-sub 100.0%

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

   5. rem-square-sqrt 50.4%

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

   6. fabs-sqr 50.4%

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

   7. rem-sqrt-square 50.4%

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

   8. unpow1 50.4%

      \[\leadsto \left|\color{blue}{{\left(\sqrt{y - x}\right)}^{1}}\right| \]

   9. sqr-pow 50.0%

      \[\leadsto \left|\color{blue}{{\left(\sqrt{y - x}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\sqrt{y - x}\right)}^{\left(\frac{1}{2}\right)}}\right| \]

   10. fabs-sqr 50.0%

       \[\leadsto \color{blue}{{\left(\sqrt{y - x}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\sqrt{y - x}\right)}^{\left(\frac{1}{2}\right)}} \]

   11. sqr-pow 50.4%

       \[\leadsto \color{blue}{{\left(\sqrt{y - x}\right)}^{1}} \]

   12. unpow1 50.4%

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

6. Simplified 50.4%

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

7. Final simplification 50.4%

   \[\leadsto \sqrt{y - x} \]

Alternative 3: 26.2% accurate, 2.0× 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. Step-by-step derivation

   1. fabs-sub 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around -inf 100.0%

   \[\leadsto \color{blue}{\sqrt{\left|-\left(x + -1 \cdot y\right)\right|}} \]
5. Step-by-step derivation

   1. fabs-neg 100.0%

      \[\leadsto \sqrt{\color{blue}{\left|x + -1 \cdot y\right|}} \]

   2. mul-1-neg 100.0%

      \[\leadsto \sqrt{\left|x + \color{blue}{\left(-y\right)}\right|} \]

   3. unsub-neg 100.0%

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

   4. fabs-sub 100.0%

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

   5. rem-square-sqrt 50.4%

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

   6. fabs-sqr 50.4%

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

   7. rem-sqrt-square 50.4%

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

   8. unpow1 50.4%

      \[\leadsto \left|\color{blue}{{\left(\sqrt{y - x}\right)}^{1}}\right| \]

   9. sqr-pow 50.0%

      \[\leadsto \left|\color{blue}{{\left(\sqrt{y - x}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\sqrt{y - x}\right)}^{\left(\frac{1}{2}\right)}}\right| \]

   10. fabs-sqr 50.0%

       \[\leadsto \color{blue}{{\left(\sqrt{y - x}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\sqrt{y - x}\right)}^{\left(\frac{1}{2}\right)}} \]

   11. sqr-pow 50.4%

       \[\leadsto \color{blue}{{\left(\sqrt{y - x}\right)}^{1}} \]

   12. unpow1 50.4%

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

6. Simplified 50.4%

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

7. Taylor expanded in x around 0 25.2%

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

8. Final simplification 25.2%

   \[\leadsto \sqrt{y} \]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, C"
  :precision binary64
  (sqrt (fabs (- x y))))