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

Percentage Accurate: 100.0% → 100.0%

Time: 2.0s

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: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;1\\ \mathbf{elif}\;\neg \left(y \leq 4.4 \cdot 10^{+207}\right) \land y \leq 2.55 \cdot 10^{+222}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.1e+58)
   (/ x y)
   (if (<= y 0.00165)
     1.0
     (if (and (not (<= y 4.4e+207)) (<= y 2.55e+222))
       (- 1.0 (/ y x))
       (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.1e+58) {
		tmp = x / y;
	} else if (y <= 0.00165) {
		tmp = 1.0;
	} else if (!(y <= 4.4e+207) && (y <= 2.55e+222)) {
		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 <= (-3.1d+58)) then
        tmp = x / y
    else if (y <= 0.00165d0) then
        tmp = 1.0d0
    else if ((.not. (y <= 4.4d+207)) .and. (y <= 2.55d+222)) 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 <= -3.1e+58) {
		tmp = x / y;
	} else if (y <= 0.00165) {
		tmp = 1.0;
	} else if (!(y <= 4.4e+207) && (y <= 2.55e+222)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.1e+58:
		tmp = x / y
	elif y <= 0.00165:
		tmp = 1.0
	elif not (y <= 4.4e+207) and (y <= 2.55e+222):
		tmp = 1.0 - (y / x)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.1e+58)
		tmp = Float64(x / y);
	elseif (y <= 0.00165)
		tmp = 1.0;
	elseif (!(y <= 4.4e+207) && (y <= 2.55e+222))
		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 <= -3.1e+58)
		tmp = x / y;
	elseif (y <= 0.00165)
		tmp = 1.0;
	elseif (~((y <= 4.4e+207)) && (y <= 2.55e+222))
		tmp = 1.0 - (y / x);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.1e+58], N[(x / y), $MachinePrecision], If[LessEqual[y, 0.00165], 1.0, If[And[N[Not[LessEqual[y, 4.4e+207]], $MachinePrecision], LessEqual[y, 2.55e+222]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0999999999999999e58 or 0.00165 < y < 4.40000000000000017e207 or 2.55e222 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.0%

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

   if -3.0999999999999999e58 < y < 0.00165

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.1%

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

   if 4.40000000000000017e207 < y < 2.55e222

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 0.00165:\\ \;\;\;\;1\\ \mathbf{elif}\;\neg \left(y \leq 4.4 \cdot 10^{+207}\right) \land y \leq 2.55 \cdot 10^{+222}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3: 72.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 0.017:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+222}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.5e+58)
   (/ x y)
   (if (<= y 0.017)
     1.0
     (if (<= y 4.4e+207) (/ x y) (if (<= y 2.55e+222) 1.0 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.5e+58) {
		tmp = x / y;
	} else if (y <= 0.017) {
		tmp = 1.0;
	} else if (y <= 4.4e+207) {
		tmp = x / y;
	} else if (y <= 2.55e+222) {
		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 <= (-3.5d+58)) then
        tmp = x / y
    else if (y <= 0.017d0) then
        tmp = 1.0d0
    else if (y <= 4.4d+207) then
        tmp = x / y
    else if (y <= 2.55d+222) 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 <= -3.5e+58) {
		tmp = x / y;
	} else if (y <= 0.017) {
		tmp = 1.0;
	} else if (y <= 4.4e+207) {
		tmp = x / y;
	} else if (y <= 2.55e+222) {
		tmp = 1.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.5e+58:
		tmp = x / y
	elif y <= 0.017:
		tmp = 1.0
	elif y <= 4.4e+207:
		tmp = x / y
	elif y <= 2.55e+222:
		tmp = 1.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.5e+58)
		tmp = Float64(x / y);
	elseif (y <= 0.017)
		tmp = 1.0;
	elseif (y <= 4.4e+207)
		tmp = Float64(x / y);
	elseif (y <= 2.55e+222)
		tmp = 1.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.5e+58)
		tmp = x / y;
	elseif (y <= 0.017)
		tmp = 1.0;
	elseif (y <= 4.4e+207)
		tmp = x / y;
	elseif (y <= 2.55e+222)
		tmp = 1.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.5e+58], N[(x / y), $MachinePrecision], If[LessEqual[y, 0.017], 1.0, If[LessEqual[y, 4.4e+207], N[(x / y), $MachinePrecision], If[LessEqual[y, 2.55e+222], 1.0, N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999997e58 or 0.017000000000000001 < y < 4.40000000000000017e207 or 2.55e222 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.0%

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

   if -3.4999999999999997e58 < y < 0.017000000000000001 or 4.40000000000000017e207 < y < 2.55e222

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.8%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 0.017:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+222}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 50.8% 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. Taylor expanded in x around inf 53.2%

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

3. Final simplification 53.2%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))