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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

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. Final simplification 100.0%

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

Alternative 2: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8000000.0) 1.0 (if (<= x 1.2e+42) (/ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8000000.0) {
		tmp = 1.0;
	} else if (x <= 1.2e+42) {
		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 <= (-8000000.0d0)) then
        tmp = 1.0d0
    else if (x <= 1.2d+42) 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 <= -8000000.0) {
		tmp = 1.0;
	} else if (x <= 1.2e+42) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8000000.0:
		tmp = 1.0
	elif x <= 1.2e+42:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8000000.0)
		tmp = 1.0;
	elseif (x <= 1.2e+42)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8000000.0)
		tmp = 1.0;
	elseif (x <= 1.2e+42)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8000000.0], 1.0, If[LessEqual[x, 1.2e+42], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -8e6 or 1.1999999999999999e42 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.2%

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

   if -8e6 < x < 1.1999999999999999e42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 83.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 2.6% 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. Add Preprocessing
3. Step-by-step derivation

   1. clear-num 99.3%

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

   2. associate-/r/ 99.7%

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

4. Applied egg-rr 99.7%

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

   1. associate-/r/ 99.3%

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

   2. unpow-1 99.3%

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

   3. sqr-pow 80.2%

      \[\leadsto \color{blue}{{\left(\frac{x + y}{x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{x + y}{x}\right)}^{\left(\frac{-1}{2}\right)}} \]

   4. pow-prod-down 74.1%

      \[\leadsto \color{blue}{{\left(\frac{x + y}{x} \cdot \frac{x + y}{x}\right)}^{\left(\frac{-1}{2}\right)}} \]

   5. pow2 74.1%

      \[\leadsto {\color{blue}{\left({\left(\frac{x + y}{x}\right)}^{2}\right)}}^{\left(\frac{-1}{2}\right)} \]

   6. metadata-eval 74.1%

      \[\leadsto {\left({\left(\frac{x + y}{x}\right)}^{2}\right)}^{\color{blue}{-0.5}} \]

6. Applied egg-rr 74.1%

   \[\leadsto \color{blue}{{\left({\left(\frac{x + y}{x}\right)}^{2}\right)}^{-0.5}} \]

7. Taylor expanded in x around -inf 2.7%

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

8. Final simplification 2.7%

   \[\leadsto -1 \]
9. Add Preprocessing

Alternative 4: 51.4% 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. Add Preprocessing

3. Taylor expanded in x around inf 51.1%

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

4. Final simplification 51.1%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))