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

Percentage Accurate: 100.0% → 100.0%

Time: 2.1s

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. Final simplification 100.0%

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

Alternative 2: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+131}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-53}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.7e+131)
   1.0
   (if (<= x -1.7e+120)
     (/ x y)
     (if (<= x -1.9e+90)
       1.0
       (if (<= x -8.6e-19)
         (/ x y)
         (if (<= x -1.7e-53)
           1.0
           (if (<= x 5e-79) (/ x y) (- 1.0 (/ y x)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.7e+131) {
		tmp = 1.0;
	} else if (x <= -1.7e+120) {
		tmp = x / y;
	} else if (x <= -1.9e+90) {
		tmp = 1.0;
	} else if (x <= -8.6e-19) {
		tmp = x / y;
	} else if (x <= -1.7e-53) {
		tmp = 1.0;
	} else if (x <= 5e-79) {
		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 <= (-1.7d+131)) then
        tmp = 1.0d0
    else if (x <= (-1.7d+120)) then
        tmp = x / y
    else if (x <= (-1.9d+90)) then
        tmp = 1.0d0
    else if (x <= (-8.6d-19)) then
        tmp = x / y
    else if (x <= (-1.7d-53)) then
        tmp = 1.0d0
    else if (x <= 5d-79) 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 <= -1.7e+131) {
		tmp = 1.0;
	} else if (x <= -1.7e+120) {
		tmp = x / y;
	} else if (x <= -1.9e+90) {
		tmp = 1.0;
	} else if (x <= -8.6e-19) {
		tmp = x / y;
	} else if (x <= -1.7e-53) {
		tmp = 1.0;
	} else if (x <= 5e-79) {
		tmp = x / y;
	} else {
		tmp = 1.0 - (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.7e+131:
		tmp = 1.0
	elif x <= -1.7e+120:
		tmp = x / y
	elif x <= -1.9e+90:
		tmp = 1.0
	elif x <= -8.6e-19:
		tmp = x / y
	elif x <= -1.7e-53:
		tmp = 1.0
	elif x <= 5e-79:
		tmp = x / y
	else:
		tmp = 1.0 - (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.7e+131)
		tmp = 1.0;
	elseif (x <= -1.7e+120)
		tmp = Float64(x / y);
	elseif (x <= -1.9e+90)
		tmp = 1.0;
	elseif (x <= -8.6e-19)
		tmp = Float64(x / y);
	elseif (x <= -1.7e-53)
		tmp = 1.0;
	elseif (x <= 5e-79)
		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 <= -1.7e+131)
		tmp = 1.0;
	elseif (x <= -1.7e+120)
		tmp = x / y;
	elseif (x <= -1.9e+90)
		tmp = 1.0;
	elseif (x <= -8.6e-19)
		tmp = x / y;
	elseif (x <= -1.7e-53)
		tmp = 1.0;
	elseif (x <= 5e-79)
		tmp = x / y;
	else
		tmp = 1.0 - (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.7e+131], 1.0, If[LessEqual[x, -1.7e+120], N[(x / y), $MachinePrecision], If[LessEqual[x, -1.9e+90], 1.0, If[LessEqual[x, -8.6e-19], N[(x / y), $MachinePrecision], If[LessEqual[x, -1.7e-53], 1.0, If[LessEqual[x, 5e-79], N[(x / y), $MachinePrecision], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.69999999999999993e131 or -1.69999999999999999e120 < x < -1.9000000000000001e90 or -8.6e-19 < x < -1.7e-53

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 85.6%

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

   if -1.69999999999999993e131 < x < -1.69999999999999999e120 or -1.9000000000000001e90 < x < -8.6e-19 or -1.7e-53 < x < 4.99999999999999999e-79

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.4%

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

   if 4.99999999999999999e-79 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

   4. Simplified 70.0%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+131}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-53}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x}\\ \end{array} \]

Alternative 3: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+131}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -1.58 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-59}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e+131)
   1.0
   (if (<= x -1.95e+120)
     (/ x y)
     (if (<= x -1.58e+90)
       1.0
       (if (<= x -2.05e-19)
         (/ x y)
         (if (<= x -3.55e-59) 1.0 (if (<= x 5e-79) (/ x y) 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+131) {
		tmp = 1.0;
	} else if (x <= -1.95e+120) {
		tmp = x / y;
	} else if (x <= -1.58e+90) {
		tmp = 1.0;
	} else if (x <= -2.05e-19) {
		tmp = x / y;
	} else if (x <= -3.55e-59) {
		tmp = 1.0;
	} else if (x <= 5e-79) {
		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 <= (-1.85d+131)) then
        tmp = 1.0d0
    else if (x <= (-1.95d+120)) then
        tmp = x / y
    else if (x <= (-1.58d+90)) then
        tmp = 1.0d0
    else if (x <= (-2.05d-19)) then
        tmp = x / y
    else if (x <= (-3.55d-59)) then
        tmp = 1.0d0
    else if (x <= 5d-79) 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 <= -1.85e+131) {
		tmp = 1.0;
	} else if (x <= -1.95e+120) {
		tmp = x / y;
	} else if (x <= -1.58e+90) {
		tmp = 1.0;
	} else if (x <= -2.05e-19) {
		tmp = x / y;
	} else if (x <= -3.55e-59) {
		tmp = 1.0;
	} else if (x <= 5e-79) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e+131:
		tmp = 1.0
	elif x <= -1.95e+120:
		tmp = x / y
	elif x <= -1.58e+90:
		tmp = 1.0
	elif x <= -2.05e-19:
		tmp = x / y
	elif x <= -3.55e-59:
		tmp = 1.0
	elif x <= 5e-79:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e+131)
		tmp = 1.0;
	elseif (x <= -1.95e+120)
		tmp = Float64(x / y);
	elseif (x <= -1.58e+90)
		tmp = 1.0;
	elseif (x <= -2.05e-19)
		tmp = Float64(x / y);
	elseif (x <= -3.55e-59)
		tmp = 1.0;
	elseif (x <= 5e-79)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.85e+131)
		tmp = 1.0;
	elseif (x <= -1.95e+120)
		tmp = x / y;
	elseif (x <= -1.58e+90)
		tmp = 1.0;
	elseif (x <= -2.05e-19)
		tmp = x / y;
	elseif (x <= -3.55e-59)
		tmp = 1.0;
	elseif (x <= 5e-79)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e+131], 1.0, If[LessEqual[x, -1.95e+120], N[(x / y), $MachinePrecision], If[LessEqual[x, -1.58e+90], 1.0, If[LessEqual[x, -2.05e-19], N[(x / y), $MachinePrecision], If[LessEqual[x, -3.55e-59], 1.0, If[LessEqual[x, 5e-79], N[(x / y), $MachinePrecision], 1.0]]]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.84999999999999998e131 or -1.9499999999999999e120 < x < -1.58e90 or -2.04999999999999993e-19 < x < -3.5499999999999998e-59 or 4.99999999999999999e-79 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.5%

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

   if -1.84999999999999998e131 < x < -1.9499999999999999e120 or -1.58e90 < x < -2.04999999999999993e-19 or -3.5499999999999998e-59 < x < 4.99999999999999999e-79

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+131}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -1.58 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-59}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

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%

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

2. Taylor expanded in x around inf 44.7%

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

3. Final simplification 44.7%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023276 
(FPCore (x y)
  :name "AI.Clustering.Hierarchical.Internal:average from clustering-0.2.1, B"
  :precision binary64
  (/ x (+ y x)))