AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A

Percentage Accurate: 100.0% → 100.0%

Time: 2.9s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (+ x y)))

C

double code(double x, double y) {
	return x / (x + y);
}

Fortran

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

Java

public static double code(double x, double y) {
	return x / (x + y);
}

Python

def code(x, y):
	return x / (x + y)

Julia

function code(x, y)
	return Float64(x / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (x + y);
end

Wolfram

code[x_, y_] := N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (+ x y)))

C

double code(double x, double y) {
	return x / (x + y);
}

Fortran

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

Java

public static double code(double x, double y) {
	return x / (x + y);
}

Python

def code(x, y):
	return x / (x + y)

Julia

function code(x, y)
	return Float64(x / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (x + y);
end

Wolfram

code[x_, y_] := N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ x (+ x y)))

C

double code(double x, double y) {
	return x / (x + y);
}

Fortran

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

Java

public static double code(double x, double y) {
	return x / (x + y);
}

Python

def code(x, y):
	return x / (x + y)

Julia

function code(x, y)
	return Float64(x / Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = x / (x + y);
end

Wolfram

code[x_, y_] := N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x}{x + y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-48}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.65e-48) 1.0 (if (<= x 3.4e-44) (/ x y) (- 1.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.65e-48) {
		tmp = 1.0;
	} else if (x <= 3.4e-44) {
		tmp = x / y;
	} else {
		tmp = 1.0 - (y / 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 <= (-2.65d-48)) then
        tmp = 1.0d0
    else if (x <= 3.4d-44) then
        tmp = x / y
    else
        tmp = 1.0d0 - (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.65e-48) {
		tmp = 1.0;
	} else if (x <= 3.4e-44) {
		tmp = x / y;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.65e-48:
		tmp = 1.0
	elif x <= 3.4e-44:
		tmp = x / y
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.65e-48)
		tmp = 1.0;
	elseif (x <= 3.4e-44)
		tmp = Float64(x / y);
	else
		tmp = Float64(1.0 - Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.65e-48)
		tmp = 1.0;
	elseif (x <= 3.4e-44)
		tmp = x / y;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.65e-48], 1.0, If[LessEqual[x, 3.4e-44], N[(x / y), $MachinePrecision], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.65e-48

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 73.4%

      \[\leadsto \color{blue}{1} \]

   if -2.65e-48 < x < 3.40000000000000016e-44

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 85.4%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 85.4%

      \[\leadsto \color{blue}{\frac{x}{y}} \]

   if 3.40000000000000016e-44 < x

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{y}{x}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\frac{y}{x}\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto 1 - \color{blue}{\frac{y}{x}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{x}\right)}\right) \]

      4. /-lowering-/.f64 79.5%

         \[\leadsto \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{1 - \frac{y}{x}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-48}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.1e-48) 1.0 (if (<= x 3.2e-44) (/ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.1e-48) {
		tmp = 1.0;
	} else if (x <= 3.2e-44) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.1d-48)) then
        tmp = 1.0d0
    else if (x <= 3.2d-44) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.1e-48) {
		tmp = 1.0;
	} else if (x <= 3.2e-44) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.1e-48:
		tmp = 1.0
	elif x <= 3.2e-44:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.1e-48)
		tmp = 1.0;
	elseif (x <= 3.2e-44)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.1e-48)
		tmp = 1.0;
	elseif (x <= 3.2e-44)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.1e-48], 1.0, If[LessEqual[x, 3.2e-44], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.10000000000000016e-48 or 3.19999999999999995e-44 < x

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 76.1%

      \[\leadsto \color{blue}{1} \]

   if -3.10000000000000016e-48 < x < 3.19999999999999995e-44

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 85.4%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 85.4%

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

Alternative 4: 51.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

   \[\frac{x}{x + y} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Simplified 51.3%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024163 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))