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

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

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: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-45}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.8e-45) (- 1.0 (/ y x)) (if (<= x 5e-70) (/ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.8e-45) {
		tmp = 1.0 - (y / x);
	} else if (x <= 5e-70) {
		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 <= (-5.8d-45)) then
        tmp = 1.0d0 - (y / x)
    else if (x <= 5d-70) 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 <= -5.8e-45) {
		tmp = 1.0 - (y / x);
	} else if (x <= 5e-70) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.8e-45:
		tmp = 1.0 - (y / x)
	elif x <= 5e-70:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.8e-45)
		tmp = Float64(1.0 - Float64(y / x));
	elseif (x <= 5e-70)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.8e-45)
		tmp = 1.0 - (y / x);
	elseif (x <= 5e-70)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.8e-45], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-70], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -5.8e-45

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. unsub-neg 72.7%

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

   5. Simplified 72.7%

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

   if -5.8e-45 < x < 4.9999999999999998e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.0%

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

   if 4.9999999999999998e-70 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.3%

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

Alternative 3: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-44}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.1e-44) 1.0 (if (<= x 5.1e-70) (/ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.1e-44) {
		tmp = 1.0;
	} else if (x <= 5.1e-70) {
		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 <= (-2.1d-44)) then
        tmp = 1.0d0
    else if (x <= 5.1d-70) 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 <= -2.1e-44) {
		tmp = 1.0;
	} else if (x <= 5.1e-70) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.1e-44:
		tmp = 1.0
	elif x <= 5.1e-70:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.1e-44)
		tmp = 1.0;
	elseif (x <= 5.1e-70)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.1e-44)
		tmp = 1.0;
	elseif (x <= 5.1e-70)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.1e-44], 1.0, If[LessEqual[x, 5.1e-70], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.10000000000000001e-44 or 5.10000000000000025e-70 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 77.1%

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

   if -2.10000000000000001e-44 < x < 5.10000000000000025e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.0%

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

Alternative 4: 51.3% 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 54.5%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))