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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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

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

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: 67.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{-72}:\\ \;\;\;\;\sqrt{y - x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 6e-72) (sqrt (- y x)) (sqrt x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6e-72) {
		tmp = sqrt((y - x));
	} else {
		tmp = sqrt(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 6d-72) then
        tmp = sqrt((y - x))
    else
        tmp = sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6e-72) {
		tmp = Math.sqrt((y - x));
	} else {
		tmp = Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6e-72:
		tmp = math.sqrt((y - x))
	else:
		tmp = math.sqrt(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6e-72)
		tmp = sqrt(Float64(y - x));
	else
		tmp = sqrt(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6e-72)
		tmp = sqrt((y - x));
	else
		tmp = sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6e-72], N[Sqrt[N[(y - x), $MachinePrecision]], $MachinePrecision], N[Sqrt[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6e-72

   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. Step-by-step derivation

      1. expm1-log1p-u 94.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{\left|y - x\right|}\right)\right)} \]

      2. expm1-udef 71.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{\left|y - x\right|}\right)} - 1} \]

      3. log1p-udef 71.0%

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

      4. add-exp-log 76.9%

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

      5. add-sqr-sqrt 54.9%

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

      6. fabs-sqr 54.9%

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

      7. add-sqr-sqrt 54.9%

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

   5. Applied egg-rr 54.9%

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

      1. +-commutative 54.9%

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

      2. associate--l+ 68.1%

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

      3. metadata-eval 68.1%

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

      4. +-rgt-identity 68.1%

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

   7. Simplified 68.1%

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

   if 6e-72 < x

   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. Step-by-step derivation

      1. expm1-log1p-u 93.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{\left|y - x\right|}\right)\right)} \]

      2. expm1-udef 80.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{\left|y - x\right|}\right)} - 1} \]

      3. log1p-udef 80.1%

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

      4. add-exp-log 86.6%

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

      5. add-sqr-sqrt 10.3%

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

      6. fabs-sqr 10.3%

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

      7. add-sqr-sqrt 10.3%

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

   5. Applied egg-rr 10.3%

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

      1. +-commutative 10.3%

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

      2. associate--l+ 10.3%

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

      3. metadata-eval 10.3%

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

      4. +-rgt-identity 10.3%

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

   7. Simplified 10.3%

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

      1. pow1/2 10.3%

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

      2. metadata-eval 10.3%

         \[\leadsto {\left(y - x\right)}^{\color{blue}{\left(2 \cdot 0.25\right)}} \]

      3. pow-pow 54.9%

         \[\leadsto \color{blue}{{\left({\left(y - x\right)}^{2}\right)}^{0.25}} \]

   9. Applied egg-rr 54.9%

      \[\leadsto \color{blue}{{\left({\left(y - x\right)}^{2}\right)}^{0.25}} \]

   10. Taylor expanded in y around 0 80.0%

       \[\leadsto \color{blue}{{1}^{0.25} \cdot \sqrt{x}} \]
   11. Step-by-step derivation

       1. pow-base-1 80.0%

          \[\leadsto \color{blue}{1} \cdot \sqrt{x} \]

       2. *-lft-identity 80.0%

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

   12. Simplified 80.0%

       \[\leadsto \color{blue}{\sqrt{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{-72}:\\ \;\;\;\;\sqrt{y - x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x}\\ \end{array} \]

Alternative 3: 42.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-154}:\\ \;\;\;\;\sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 2.5e-154) (sqrt x) (sqrt y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.5e-154) {
		tmp = sqrt(x);
	} 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 <= 2.5d-154) then
        tmp = sqrt(x)
    else
        tmp = sqrt(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.5e-154) {
		tmp = Math.sqrt(x);
	} else {
		tmp = Math.sqrt(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.5e-154:
		tmp = math.sqrt(x)
	else:
		tmp = math.sqrt(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.5e-154)
		tmp = sqrt(x);
	else
		tmp = sqrt(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.5e-154)
		tmp = sqrt(x);
	else
		tmp = sqrt(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.5e-154], N[Sqrt[x], $MachinePrecision], N[Sqrt[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5000000000000001e-154

   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. Step-by-step derivation

      1. expm1-log1p-u 94.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{\left|y - x\right|}\right)\right)} \]

      2. expm1-udef 70.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{\left|y - x\right|}\right)} - 1} \]

      3. log1p-udef 70.5%

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

      4. add-exp-log 76.1%

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

      5. add-sqr-sqrt 24.7%

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

      6. fabs-sqr 24.7%

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

      7. add-sqr-sqrt 24.7%

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

   5. Applied egg-rr 24.7%

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

      1. +-commutative 24.7%

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

      2. associate--l+ 32.1%

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

      3. metadata-eval 32.1%

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

      4. +-rgt-identity 32.1%

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

   7. Simplified 32.1%

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

      1. pow1/2 32.1%

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

      2. metadata-eval 32.1%

         \[\leadsto {\left(y - x\right)}^{\color{blue}{\left(2 \cdot 0.25\right)}} \]

      3. pow-pow 59.0%

         \[\leadsto \color{blue}{{\left({\left(y - x\right)}^{2}\right)}^{0.25}} \]

   9. Applied egg-rr 59.0%

      \[\leadsto \color{blue}{{\left({\left(y - x\right)}^{2}\right)}^{0.25}} \]

   10. Taylor expanded in y around 0 32.0%

       \[\leadsto \color{blue}{{1}^{0.25} \cdot \sqrt{x}} \]
   11. Step-by-step derivation

       1. pow-base-1 32.0%

          \[\leadsto \color{blue}{1} \cdot \sqrt{x} \]

       2. *-lft-identity 32.0%

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

   12. Simplified 32.0%

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

   if 2.5000000000000001e-154 < y

   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. Step-by-step derivation

      1. expm1-log1p-u 93.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{\left|y - x\right|}\right)\right)} \]

      2. expm1-udef 79.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{\left|y - x\right|}\right)} - 1} \]

      3. log1p-udef 79.0%

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

      4. add-exp-log 86.0%

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

      5. add-sqr-sqrt 78.1%

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

      6. fabs-sqr 78.1%

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

      7. add-sqr-sqrt 78.1%

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

   5. Applied egg-rr 78.1%

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

      1. +-commutative 78.1%

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

      2. associate--l+ 92.0%

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

      3. metadata-eval 92.0%

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

      4. +-rgt-identity 92.0%

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

   7. Simplified 92.0%

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

   8. Taylor expanded in x around 0 75.8%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-154}:\\ \;\;\;\;\sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y}\\ \end{array} \]

Alternative 4: 26.5% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[Sqrt[x], $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. Step-by-step derivation

   1. expm1-log1p-u 93.9%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{\left|y - x\right|}\right)\right)} \]

   2. expm1-udef 73.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{\left|y - x\right|}\right)} - 1} \]

   3. log1p-udef 73.4%

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

   4. add-exp-log 79.5%

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

   5. add-sqr-sqrt 43.0%

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

   6. fabs-sqr 43.0%

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

   7. add-sqr-sqrt 43.0%

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

5. Applied egg-rr 43.0%

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

   1. +-commutative 43.0%

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

   2. associate--l+ 52.7%

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

   3. metadata-eval 52.7%

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

   4. +-rgt-identity 52.7%

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

7. Simplified 52.7%

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

   1. pow1/2 52.7%

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

   2. metadata-eval 52.7%

      \[\leadsto {\left(y - x\right)}^{\color{blue}{\left(2 \cdot 0.25\right)}} \]

   3. pow-pow 54.4%

      \[\leadsto \color{blue}{{\left({\left(y - x\right)}^{2}\right)}^{0.25}} \]

9. Applied egg-rr 54.4%

   \[\leadsto \color{blue}{{\left({\left(y - x\right)}^{2}\right)}^{0.25}} \]

10. Taylor expanded in y around 0 24.5%

    \[\leadsto \color{blue}{{1}^{0.25} \cdot \sqrt{x}} \]
11. Step-by-step derivation

    1. pow-base-1 24.5%

       \[\leadsto \color{blue}{1} \cdot \sqrt{x} \]

    2. *-lft-identity 24.5%

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

12. Simplified 24.5%

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

13. Final simplification 24.5%

    \[\leadsto \sqrt{x} \]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, C"
  :precision binary64
  (sqrt (fabs (- x y))))