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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -0.0095:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.1e+63)
   (/ x y)
   (if (<= y -0.0095)
     1.0
     (if (<= y -5.2e-84)
       (/ x y)
       (if (<= y 8.5e+34) (- 1.0 (/ y x)) (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.1e+63) {
		tmp = x / y;
	} else if (y <= -0.0095) {
		tmp = 1.0;
	} else if (y <= -5.2e-84) {
		tmp = x / y;
	} else if (y <= 8.5e+34) {
		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 <= (-5.1d+63)) then
        tmp = x / y
    else if (y <= (-0.0095d0)) then
        tmp = 1.0d0
    else if (y <= (-5.2d-84)) then
        tmp = x / y
    else if (y <= 8.5d+34) 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 <= -5.1e+63) {
		tmp = x / y;
	} else if (y <= -0.0095) {
		tmp = 1.0;
	} else if (y <= -5.2e-84) {
		tmp = x / y;
	} else if (y <= 8.5e+34) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.1e+63:
		tmp = x / y
	elif y <= -0.0095:
		tmp = 1.0
	elif y <= -5.2e-84:
		tmp = x / y
	elif y <= 8.5e+34:
		tmp = 1.0 - (y / x)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.1e+63)
		tmp = Float64(x / y);
	elseif (y <= -0.0095)
		tmp = 1.0;
	elseif (y <= -5.2e-84)
		tmp = Float64(x / y);
	elseif (y <= 8.5e+34)
		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 <= -5.1e+63)
		tmp = x / y;
	elseif (y <= -0.0095)
		tmp = 1.0;
	elseif (y <= -5.2e-84)
		tmp = x / y;
	elseif (y <= 8.5e+34)
		tmp = 1.0 - (y / x);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.1e+63], N[(x / y), $MachinePrecision], If[LessEqual[y, -0.0095], 1.0, If[LessEqual[y, -5.2e-84], N[(x / y), $MachinePrecision], If[LessEqual[y, 8.5e+34], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0999999999999998e63 or -0.00949999999999999976 < y < -5.2e-84 or 8.5000000000000003e34 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.2%

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

   if -5.0999999999999998e63 < y < -0.00949999999999999976

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.8%

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

   if -5.2e-84 < y < 8.5000000000000003e34

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

   4. Simplified 79.9%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -0.0095:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+34}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -0.018:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.1e+63)
   (/ x y)
   (if (<= y -0.018)
     1.0
     (if (<= y -5e-85) (/ x y) (if (<= y 8.4e+33) 1.0 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.1e+63) {
		tmp = x / y;
	} else if (y <= -0.018) {
		tmp = 1.0;
	} else if (y <= -5e-85) {
		tmp = x / y;
	} else if (y <= 8.4e+33) {
		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 <= (-2.1d+63)) then
        tmp = x / y
    else if (y <= (-0.018d0)) then
        tmp = 1.0d0
    else if (y <= (-5d-85)) then
        tmp = x / y
    else if (y <= 8.4d+33) 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 <= -2.1e+63) {
		tmp = x / y;
	} else if (y <= -0.018) {
		tmp = 1.0;
	} else if (y <= -5e-85) {
		tmp = x / y;
	} else if (y <= 8.4e+33) {
		tmp = 1.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.1e+63:
		tmp = x / y
	elif y <= -0.018:
		tmp = 1.0
	elif y <= -5e-85:
		tmp = x / y
	elif y <= 8.4e+33:
		tmp = 1.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.1e+63)
		tmp = Float64(x / y);
	elseif (y <= -0.018)
		tmp = 1.0;
	elseif (y <= -5e-85)
		tmp = Float64(x / y);
	elseif (y <= 8.4e+33)
		tmp = 1.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.1e+63)
		tmp = x / y;
	elseif (y <= -0.018)
		tmp = 1.0;
	elseif (y <= -5e-85)
		tmp = x / y;
	elseif (y <= 8.4e+33)
		tmp = 1.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.1e+63], N[(x / y), $MachinePrecision], If[LessEqual[y, -0.018], 1.0, If[LessEqual[y, -5e-85], N[(x / y), $MachinePrecision], If[LessEqual[y, 8.4e+33], 1.0, N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000002e63 or -0.0179999999999999986 < y < -5.0000000000000002e-85 or 8.4000000000000002e33 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.2%

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

   if -2.1000000000000002e63 < y < -0.0179999999999999986 or -5.0000000000000002e-85 < y < 8.4000000000000002e33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.8%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -0.018:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 50.9% 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 47.3%

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

3. Final simplification 47.3%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023207 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))