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

Percentage Accurate: 100.0% → 100.0%

Time: 2.9s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

3. Final simplification 100.0%

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

Alternative 2: 73.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{x}\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-25}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y x))))
   (if (<= x -5.4e-8)
     t_0
     (if (<= x 4.5e-68)
       (/ x y)
       (if (<= x 5e-25) 1.0 (if (<= x 3e+69) (/ x y) t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (y / x);
	double tmp;
	if (x <= -5.4e-8) {
		tmp = t_0;
	} else if (x <= 4.5e-68) {
		tmp = x / y;
	} else if (x <= 5e-25) {
		tmp = 1.0;
	} else if (x <= 3e+69) {
		tmp = x / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y / x)
    if (x <= (-5.4d-8)) then
        tmp = t_0
    else if (x <= 4.5d-68) then
        tmp = x / y
    else if (x <= 5d-25) then
        tmp = 1.0d0
    else if (x <= 3d+69) then
        tmp = x / y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (y / x);
	double tmp;
	if (x <= -5.4e-8) {
		tmp = t_0;
	} else if (x <= 4.5e-68) {
		tmp = x / y;
	} else if (x <= 5e-25) {
		tmp = 1.0;
	} else if (x <= 3e+69) {
		tmp = x / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (y / x)
	tmp = 0
	if x <= -5.4e-8:
		tmp = t_0
	elif x <= 4.5e-68:
		tmp = x / y
	elif x <= 5e-25:
		tmp = 1.0
	elif x <= 3e+69:
		tmp = x / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(y / x))
	tmp = 0.0
	if (x <= -5.4e-8)
		tmp = t_0;
	elseif (x <= 4.5e-68)
		tmp = Float64(x / y);
	elseif (x <= 5e-25)
		tmp = 1.0;
	elseif (x <= 3e+69)
		tmp = Float64(x / y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (y / x);
	tmp = 0.0;
	if (x <= -5.4e-8)
		tmp = t_0;
	elseif (x <= 4.5e-68)
		tmp = x / y;
	elseif (x <= 5e-25)
		tmp = 1.0;
	elseif (x <= 3e+69)
		tmp = x / y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e-8], t$95$0, If[LessEqual[x, 4.5e-68], N[(x / y), $MachinePrecision], If[LessEqual[x, 5e-25], 1.0, If[LessEqual[x, 3e+69], N[(x / y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.40000000000000005e-8 or 2.99999999999999983e69 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.9%

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

      1. mul-1-neg 87.9%

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

      2. unsub-neg 87.9%

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

   5. Simplified 87.9%

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

   if -5.40000000000000005e-8 < x < 4.49999999999999999e-68 or 4.99999999999999962e-25 < x < 2.99999999999999983e69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.6%

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

   if 4.49999999999999999e-68 < x < 4.99999999999999962e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-8}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-25}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0065:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-68} \lor \neg \left(x \leq 3.6 \cdot 10^{-25}\right) \land x \leq 8 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.0065)
   1.0
   (if (or (<= x 6e-68) (and (not (<= x 3.6e-25)) (<= x 8e+70))) (/ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.0065) {
		tmp = 1.0;
	} else if ((x <= 6e-68) || (!(x <= 3.6e-25) && (x <= 8e+70))) {
		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 <= (-0.0065d0)) then
        tmp = 1.0d0
    else if ((x <= 6d-68) .or. (.not. (x <= 3.6d-25)) .and. (x <= 8d+70)) 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 <= -0.0065) {
		tmp = 1.0;
	} else if ((x <= 6e-68) || (!(x <= 3.6e-25) && (x <= 8e+70))) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.0065:
		tmp = 1.0
	elif (x <= 6e-68) or (not (x <= 3.6e-25) and (x <= 8e+70)):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.0065)
		tmp = 1.0;
	elseif ((x <= 6e-68) || (!(x <= 3.6e-25) && (x <= 8e+70)))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.0065)
		tmp = 1.0;
	elseif ((x <= 6e-68) || (~((x <= 3.6e-25)) && (x <= 8e+70)))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.0065], 1.0, If[Or[LessEqual[x, 6e-68], And[N[Not[LessEqual[x, 3.6e-25]], $MachinePrecision], LessEqual[x, 8e+70]]], N[(x / y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0064999999999999997 or 6e-68 < x < 3.5999999999999999e-25 or 8.00000000000000058e70 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.6%

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

   if -0.0064999999999999997 < x < 6e-68 or 3.5999999999999999e-25 < x < 8.00000000000000058e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.6%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0065:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-68} \lor \neg \left(x \leq 3.6 \cdot 10^{-25}\right) \land x \leq 8 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.1% 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%

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

3. Taylor expanded in x around inf 53.7%

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

4. Final simplification 53.7%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024040 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))