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

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 98.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ x (+ x y)) 2e-5) (/ x y) (- 1.0 (/ y x))))

C

double code(double x, double y) {
	double tmp;
	if ((x / (x + y)) <= 2e-5) {
		tmp = x / y;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x / (x + y)) <= 2d-5) then
        tmp = x / y
    else
        tmp = 1.0d0 - (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x / (x + y)) <= 2e-5) {
		tmp = x / y;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x / (x + y)) <= 2e-5:
		tmp = x / y
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x / Float64(x + y)) <= 2e-5)
		tmp = Float64(x / y);
	else
		tmp = Float64(1.0 - Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x / (x + y)) <= 2e-5)
		tmp = x / y;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], 2e-5], N[(x / y), $MachinePrecision], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x y)) < 2.00000000000000016e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 98.3

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

   5. Simplified 98.3%

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

   if 2.00000000000000016e-5 < (/.f64 x (+.f64 x y))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 98.9

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

   5. Simplified 98.9%

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

Alternative 3: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= (/ x (+ x y)) 2e-5) (/ x y) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x / (x + y)) <= 2e-5) {
		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 / (x + y)) <= 2d-5) 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 / (x + y)) <= 2e-5) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x / (x + y)) <= 2e-5:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x / Float64(x + y)) <= 2e-5)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x / (x + y)) <= 2e-5)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], 2e-5], N[(x / y), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x y)) < 2.00000000000000016e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 98.3

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

   5. Simplified 98.3%

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

   if 2.00000000000000016e-5 < (/.f64 x (+.f64 x y))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 97.4%

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

Alternative 4: 51.3% accurate, 15.0× 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. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Simplified 52.4%

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

Reproduce

herbie shell --seed 2024208 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))