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

Percentage Accurate: 100.0% → 100.0%

Time: 2.1s

Alternatives: 3

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. Final simplification 100.0%

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

Alternative 2: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;\neg \left(y \leq 7.8 \cdot 10^{+28}\right) \land y \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.6e+108)
   (/ x y)
   (if (<= y -4.6e+38)
     1.0
     (if (<= y -4.8e-64)
       (/ x y)
       (if (<= y 4e-14)
         1.0
         (if (and (not (<= y 7.8e+28)) (<= y 4.2e+55)) 1.0 (/ x y)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.6e+108) {
		tmp = x / y;
	} else if (y <= -4.6e+38) {
		tmp = 1.0;
	} else if (y <= -4.8e-64) {
		tmp = x / y;
	} else if (y <= 4e-14) {
		tmp = 1.0;
	} else if (!(y <= 7.8e+28) && (y <= 4.2e+55)) {
		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 <= (-4.6d+108)) then
        tmp = x / y
    else if (y <= (-4.6d+38)) then
        tmp = 1.0d0
    else if (y <= (-4.8d-64)) then
        tmp = x / y
    else if (y <= 4d-14) then
        tmp = 1.0d0
    else if ((.not. (y <= 7.8d+28)) .and. (y <= 4.2d+55)) 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 <= -4.6e+108) {
		tmp = x / y;
	} else if (y <= -4.6e+38) {
		tmp = 1.0;
	} else if (y <= -4.8e-64) {
		tmp = x / y;
	} else if (y <= 4e-14) {
		tmp = 1.0;
	} else if (!(y <= 7.8e+28) && (y <= 4.2e+55)) {
		tmp = 1.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.6e+108:
		tmp = x / y
	elif y <= -4.6e+38:
		tmp = 1.0
	elif y <= -4.8e-64:
		tmp = x / y
	elif y <= 4e-14:
		tmp = 1.0
	elif not (y <= 7.8e+28) and (y <= 4.2e+55):
		tmp = 1.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.6e+108)
		tmp = Float64(x / y);
	elseif (y <= -4.6e+38)
		tmp = 1.0;
	elseif (y <= -4.8e-64)
		tmp = Float64(x / y);
	elseif (y <= 4e-14)
		tmp = 1.0;
	elseif (!(y <= 7.8e+28) && (y <= 4.2e+55))
		tmp = 1.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.6e+108)
		tmp = x / y;
	elseif (y <= -4.6e+38)
		tmp = 1.0;
	elseif (y <= -4.8e-64)
		tmp = x / y;
	elseif (y <= 4e-14)
		tmp = 1.0;
	elseif (~((y <= 7.8e+28)) && (y <= 4.2e+55))
		tmp = 1.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.6e+108], N[(x / y), $MachinePrecision], If[LessEqual[y, -4.6e+38], 1.0, If[LessEqual[y, -4.8e-64], N[(x / y), $MachinePrecision], If[LessEqual[y, 4e-14], 1.0, If[And[N[Not[LessEqual[y, 7.8e+28]], $MachinePrecision], LessEqual[y, 4.2e+55]], 1.0, N[(x / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999998e108 or -4.6000000000000002e38 < y < -4.79999999999999997e-64 or 4e-14 < y < 7.7999999999999997e28 or 4.2000000000000001e55 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.3%

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

   if -4.5999999999999998e108 < y < -4.6000000000000002e38 or -4.79999999999999997e-64 < y < 4e-14 or 7.7999999999999997e28 < y < 4.2000000000000001e55

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.5%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+108}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;\neg \left(y \leq 7.8 \cdot 10^{+28}\right) \land y \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3: 51.0% 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%

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

2. Taylor expanded in x around inf 51.6%

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

3. Final simplification 51.6%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))