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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 2

Speedup: 2.0×

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, 2.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \sqrt{y - x} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (sqrt (- y x)))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt((y - x))
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return math.sqrt((y - x))

Julia

x, y = sort([x, y])
function code(x, y)
	return sqrt(Float64(y - x))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = sqrt((y - x));
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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. Add Preprocessing
5. Step-by-step derivation

   1. add-log-exp 9.3%

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

   2. *-un-lft-identity 9.3%

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

   3. log-prod 9.3%

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

   4. metadata-eval 9.3%

      \[\leadsto \color{blue}{0} + \log \left(e^{\sqrt{\left|y - x\right|}}\right) \]

   5. add-log-exp 100.0%

      \[\leadsto 0 + \color{blue}{\sqrt{\left|y - x\right|}} \]

   6. add-sqr-sqrt 50.8%

      \[\leadsto 0 + \sqrt{\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|} \]

   7. fabs-sqr 50.8%

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

   8. add-sqr-sqrt 50.8%

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

6. Applied egg-rr 50.8%

   \[\leadsto \color{blue}{0 + \sqrt{y - x}} \]
7. Step-by-step derivation

   1. +-lft-identity 50.8%

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

8. Simplified 50.8%

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

9. Final simplification 50.8%

   \[\leadsto \sqrt{y - x} \]
10. Add Preprocessing

Alternative 2: 49.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \sqrt{y} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (sqrt y))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt(y)
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return math.sqrt(y)

Julia

x, y = sort([x, y])
function code(x, y)
	return sqrt(y)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = sqrt(y);
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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. Add Preprocessing
5. Step-by-step derivation

   1. add-cbrt-cube 71.0%

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

   2. pow1/3 66.2%

      \[\leadsto \color{blue}{{\left(\left(\sqrt{\left|y - x\right|} \cdot \sqrt{\left|y - x\right|}\right) \cdot \sqrt{\left|y - x\right|}\right)}^{0.3333333333333333}} \]

   3. add-sqr-sqrt 66.2%

      \[\leadsto {\left(\color{blue}{\left|y - x\right|} \cdot \sqrt{\left|y - x\right|}\right)}^{0.3333333333333333} \]

   4. pow1 66.2%

      \[\leadsto {\left(\color{blue}{{\left(\left|y - x\right|\right)}^{1}} \cdot \sqrt{\left|y - x\right|}\right)}^{0.3333333333333333} \]

   5. pow1/2 66.2%

      \[\leadsto {\left({\left(\left|y - x\right|\right)}^{1} \cdot \color{blue}{{\left(\left|y - x\right|\right)}^{0.5}}\right)}^{0.3333333333333333} \]

   6. pow-prod-up 66.2%

      \[\leadsto {\color{blue}{\left({\left(\left|y - x\right|\right)}^{\left(1 + 0.5\right)}\right)}}^{0.3333333333333333} \]

   7. add-sqr-sqrt 34.5%

      \[\leadsto {\left({\left(\left|\color{blue}{\sqrt{y - x} \cdot \sqrt{y - x}}\right|\right)}^{\left(1 + 0.5\right)}\right)}^{0.3333333333333333} \]

   8. fabs-sqr 34.5%

      \[\leadsto {\left({\color{blue}{\left(\sqrt{y - x} \cdot \sqrt{y - x}\right)}}^{\left(1 + 0.5\right)}\right)}^{0.3333333333333333} \]

   9. add-sqr-sqrt 34.5%

      \[\leadsto {\left({\color{blue}{\left(y - x\right)}}^{\left(1 + 0.5\right)}\right)}^{0.3333333333333333} \]

   10. metadata-eval 34.5%

       \[\leadsto {\left({\left(y - x\right)}^{\color{blue}{1.5}}\right)}^{0.3333333333333333} \]

6. Applied egg-rr 34.5%

   \[\leadsto \color{blue}{{\left({\left(y - x\right)}^{1.5}\right)}^{0.3333333333333333}} \]
7. Step-by-step derivation

   1. unpow1/3 37.0%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(y - x\right)}^{1.5}}} \]

8. Simplified 37.0%

   \[\leadsto \color{blue}{\sqrt[3]{{\left(y - x\right)}^{1.5}}} \]

9. Taylor expanded in y around inf 24.0%

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

10. Final simplification 24.0%

    \[\leadsto \sqrt{y} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024057 
(FPCore (x y)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, C"
  :precision binary64
  (sqrt (fabs (- x y))))