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

Percentage Accurate: 100.0% → 100.0%

Time: 2.3s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

3. Final simplification 100.0%

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

Alternative 2: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+30}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7.2e+30) (- 1.0 (/ y x)) (if (<= x 3.4e-29) (/ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7.2e+30) {
		tmp = 1.0 - (y / x);
	} else if (x <= 3.4e-29) {
		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 <= (-7.2d+30)) then
        tmp = 1.0d0 - (y / x)
    else if (x <= 3.4d-29) 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 <= -7.2e+30) {
		tmp = 1.0 - (y / x);
	} else if (x <= 3.4e-29) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7.2e+30:
		tmp = 1.0 - (y / x)
	elif x <= 3.4e-29:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7.2e+30)
		tmp = Float64(1.0 - Float64(y / x));
	elseif (x <= 3.4e-29)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7.2e+30)
		tmp = 1.0 - (y / x);
	elseif (x <= 3.4e-29)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7.2e+30], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e-29], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -7.2000000000000004e30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

   5. Simplified 80.5%

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

   if -7.2000000000000004e30 < x < 3.39999999999999972e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.2%

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

   if 3.39999999999999972e-29 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.8%

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

Alternative 3: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.8e+25) 1.0 (if (<= x 5.8e-31) (/ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.8e+25) {
		tmp = 1.0;
	} else if (x <= 5.8e-31) {
		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 <= (-4.8d+25)) then
        tmp = 1.0d0
    else if (x <= 5.8d-31) 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 <= -4.8e+25) {
		tmp = 1.0;
	} else if (x <= 5.8e-31) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.8e+25:
		tmp = 1.0
	elif x <= 5.8e-31:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.8e+25)
		tmp = 1.0;
	elseif (x <= 5.8e-31)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.8e+25)
		tmp = 1.0;
	elseif (x <= 5.8e-31)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.8e+25], 1.0, If[LessEqual[x, 5.8e-31], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999992e25 or 5.8000000000000001e-31 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.0%

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

   if -4.79999999999999992e25 < x < 5.8000000000000001e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.2%

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

Alternative 4: 51.7% 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%

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

3. Taylor expanded in x around inf 48.8%

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

Reproduce

herbie shell --seed 2024116 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))