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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

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, 0.4× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \frac{x - y}{x + y}}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x (/ (- x y) (+ x y))) (- x y)))

C

double code(double x, double y) {
	return (x * ((x - y) / (x + y))) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * ((x - y) / (x + y))) / (x - y)
end function

Java

public static double code(double x, double y) {
	return (x * ((x - y) / (x + y))) / (x - y);
}

Python

def code(x, y):
	return (x * ((x - y) / (x + y))) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(x * Float64(Float64(x - y) / Float64(x + y))) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * ((x - y) / (x + y))) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(x * N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x}{x + y} \]
2. Step-by-step derivation

   1. clear-num 99.1%

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

   2. associate-/r/ 99.8%

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

3. Applied egg-rr 99.8%

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

   1. flip-+ 59.7%

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

   2. associate-/r/ 59.2%

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

   3. difference-of-squares 59.4%

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

5. Applied egg-rr 59.4%

   \[\leadsto \color{blue}{\left(\frac{1}{\left(x + y\right) \cdot \left(x - y\right)} \cdot \left(x - y\right)\right)} \cdot x \]
6. Step-by-step derivation

   1. associate-*l/ 59.9%

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

   2. *-lft-identity 59.9%

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

   3. +-commutative 59.9%

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

7. Simplified 59.9%

   \[\leadsto \color{blue}{\frac{x - y}{\left(y + x\right) \cdot \left(x - y\right)}} \cdot x \]
8. Step-by-step derivation

   1. associate-/r* 99.8%

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

   2. associate-*l/ 100.0%

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

   3. +-commutative 100.0%

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

9. Applied egg-rr 100.0%

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

10. Final simplification 100.0%

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

Alternative 2: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.5e+81) (/ x y) (if (<= y 3.1e-21) 1.0 (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.5e+81) {
		tmp = x / y;
	} else if (y <= 3.1e-21) {
		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 <= (-7.5d+81)) then
        tmp = x / y
    else if (y <= 3.1d-21) 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 <= -7.5e+81) {
		tmp = x / y;
	} else if (y <= 3.1e-21) {
		tmp = 1.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.5e+81:
		tmp = x / y
	elif y <= 3.1e-21:
		tmp = 1.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.5e+81)
		tmp = Float64(x / y);
	elseif (y <= 3.1e-21)
		tmp = 1.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.5e+81)
		tmp = x / y;
	elseif (y <= 3.1e-21)
		tmp = 1.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.5e+81], N[(x / y), $MachinePrecision], If[LessEqual[y, 3.1e-21], 1.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999973e81 or 3.0999999999999998e-21 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 81.9%

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

   if -7.49999999999999973e81 < y < 3.0999999999999998e-21

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.4%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3: 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 4: 51.1% 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 52.2%

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

3. Final simplification 52.2%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023217 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, A"
  :precision binary64
  (/ x (+ x y)))