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

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

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. Final simplification 100.0%

   \[\leadsto \frac{x}{x + y} \]

Alternative 2: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-18}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.9e+14) (/ x y) (if (<= y 1.5e-18) (- 1.0 (/ y x)) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.9e+14) {
		tmp = x / y;
	} else if (y <= 1.5e-18) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = x / 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 <= (-1.9d+14)) then
        tmp = x / y
    else if (y <= 1.5d-18) then
        tmp = 1.0d0 - (y / x)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.9e+14) {
		tmp = x / y;
	} else if (y <= 1.5e-18) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.9e+14:
		tmp = x / y
	elif y <= 1.5e-18:
		tmp = 1.0 - (y / x)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.9e+14)
		tmp = Float64(x / y);
	elseif (y <= 1.5e-18)
		tmp = Float64(1.0 - Float64(y / x));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.9e+14)
		tmp = x / y;
	elseif (y <= 1.5e-18)
		tmp = 1.0 - (y / x);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.9e+14], N[(x / y), $MachinePrecision], If[LessEqual[y, 1.5e-18], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e14 or 1.49999999999999991e-18 < y

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]

   2. Taylor expanded in x around 0 79.2%

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

   if -1.9e14 < y < 1.49999999999999991e-18

   1. Initial program 99.9%

      \[\frac{x}{x + y} \]

   2. Taylor expanded in x around inf 80.6%

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

      1. mul-1-neg 80.6%

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

      2. unsub-neg 80.6%

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

   4. Simplified 80.6%

      \[\leadsto \color{blue}{1 - \frac{y}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-18}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.85e+14) (/ x y) (if (<= y 1.3e-17) 1.0 (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.85e+14) {
		tmp = x / y;
	} else if (y <= 1.3e-17) {
		tmp = 1.0;
	} else {
		tmp = x / 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 <= (-1.85d+14)) then
        tmp = x / y
    else if (y <= 1.3d-17) then
        tmp = 1.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.85e+14) {
		tmp = x / y;
	} else if (y <= 1.3e-17) {
		tmp = 1.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.85e+14:
		tmp = x / y
	elif y <= 1.3e-17:
		tmp = 1.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.85e+14)
		tmp = Float64(x / y);
	elseif (y <= 1.3e-17)
		tmp = 1.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.85e+14)
		tmp = x / y;
	elseif (y <= 1.3e-17)
		tmp = 1.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.85e+14], N[(x / y), $MachinePrecision], If[LessEqual[y, 1.3e-17], 1.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e14 or 1.30000000000000002e-17 < y

   1. Initial program 100.0%

      \[\frac{x}{x + y} \]

   2. Taylor expanded in x around 0 79.2%

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

   if -1.85e14 < y < 1.30000000000000002e-17

   1. Initial program 99.9%

      \[\frac{x}{x + y} \]

   2. Taylor expanded in x around inf 80.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 52.0% 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. Taylor expanded in x around inf 50.8%

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

3. Final simplification 50.8%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023228 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))