Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2

Percentage Accurate: 99.9% → 99.9%

Time: 11.6s

Alternatives: 6

Speedup: 0.6×

• 24.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot y\right) \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x y) (- 1.0 y)))

C

double code(double x, double y) {
	return (x * y) * (1.0 - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) * (1.0d0 - y)
end function

Java

public static double code(double x, double y) {
	return (x * y) * (1.0 - y);
}

Python

def code(x, y):
	return (x * y) * (1.0 - y)

Julia

function code(x, y)
	return Float64(Float64(x * y) * Float64(1.0 - y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * y) * (1.0 - y);
end

Wolfram

code[x_, y_] := N[(N[(x * y), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot y\right) \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* x y) (- 1.0 y)))

C

double code(double x, double y) {
	return (x * y) * (1.0 - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * y) * (1.0d0 - y)
end function

Java

public static double code(double x, double y) {
	return (x * y) * (1.0 - y);
}

Python

def code(x, y):
	return (x * y) * (1.0 - y)

Julia

function code(x, y)
	return Float64(Float64(x * y) * Float64(1.0 - y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * y) * (1.0 - y);
end

Wolfram

code[x_, y_] := N[(N[(x * y), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+102} \lor \neg \left(y \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5e+102) (not (<= y 5e+114)))
   (* y (* y (- x)))
   (* x (- y (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5e+102) || !(y <= 5e+114)) {
		tmp = y * (y * -x);
	} else {
		tmp = x * (y - (y * 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 <= (-5d+102)) .or. (.not. (y <= 5d+114))) then
        tmp = y * (y * -x)
    else
        tmp = x * (y - (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5e+102) || !(y <= 5e+114)) {
		tmp = y * (y * -x);
	} else {
		tmp = x * (y - (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5e+102) or not (y <= 5e+114):
		tmp = y * (y * -x)
	else:
		tmp = x * (y - (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5e+102) || !(y <= 5e+114))
		tmp = Float64(y * Float64(y * Float64(-x)));
	else
		tmp = Float64(x * Float64(y - Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5e+102) || ~((y <= 5e+114)))
		tmp = y * (y * -x);
	else
		tmp = x * (y - (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5e+102], N[Not[LessEqual[y, 5e+114]], $MachinePrecision]], N[(y * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e102 or 5.0000000000000001e114 < y

   1. Initial program 99.9%

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
   2. Step-by-step derivation

      1. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in y around inf 83.4%

      \[\leadsto \color{blue}{-1 \cdot \left({y}^{2} \cdot x\right)} \]
   5. Step-by-step derivation

      1. unpow2 83.4%

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

      2. associate-*r* 83.4%

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

      3. mul-1-neg 83.4%

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

      4. distribute-rgt-neg-out 83.4%

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

      5. associate-*l* 99.9%

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

   6. Simplified 99.9%

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

   if -5e102 < y < 5.0000000000000001e114

   1. Initial program 99.8%

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 98.1%

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

      2. *-lft-identity 98.1%

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

      3. *-commutative 98.1%

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

      4. associate-*r* 98.1%

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

      5. *-commutative 98.1%

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

      6. distribute-rgt-out-- 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(y - y \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+102} \lor \neg \left(y \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - y \cdot y\right)\\ \end{array} \]

Alternative 2: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+102} \lor \neg \left(y \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5e+102) (not (<= y 5e+114)))
   (* y (* y (- x)))
   (* x (* y (- 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5e+102) || !(y <= 5e+114)) {
		tmp = y * (y * -x);
	} else {
		tmp = x * (y * (1.0 - 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 <= (-5d+102)) .or. (.not. (y <= 5d+114))) then
        tmp = y * (y * -x)
    else
        tmp = x * (y * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5e+102) || !(y <= 5e+114)) {
		tmp = y * (y * -x);
	} else {
		tmp = x * (y * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5e+102) or not (y <= 5e+114):
		tmp = y * (y * -x)
	else:
		tmp = x * (y * (1.0 - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5e+102) || !(y <= 5e+114))
		tmp = Float64(y * Float64(y * Float64(-x)));
	else
		tmp = Float64(x * Float64(y * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5e+102) || ~((y <= 5e+114)))
		tmp = y * (y * -x);
	else
		tmp = x * (y * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5e+102], N[Not[LessEqual[y, 5e+114]], $MachinePrecision]], N[(y * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e102 or 5.0000000000000001e114 < y

   1. Initial program 99.9%

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
   2. Step-by-step derivation

      1. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in y around inf 83.4%

      \[\leadsto \color{blue}{-1 \cdot \left({y}^{2} \cdot x\right)} \]
   5. Step-by-step derivation

      1. unpow2 83.4%

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

      2. associate-*r* 83.4%

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

      3. mul-1-neg 83.4%

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

      4. distribute-rgt-neg-out 83.4%

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

      5. associate-*l* 99.9%

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

   6. Simplified 99.9%

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

   if -5e102 < y < 5.0000000000000001e114

   1. Initial program 99.8%

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(1 - y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+102} \lor \neg \left(y \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 3: 92.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (* x (* y (- y))) (* y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x * (y * -y);
	} else {
		tmp = 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 ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * (y * -y)
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x * (y * -y);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = x * (y * -y)
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(x * Float64(y * Float64(-y)));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = x * (y * -y);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * N[(y * (-y)), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 99.8%

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
   2. Step-by-step derivation

      1. associate-*l* 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in y around inf 86.3%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot {y}^{2}\right)} \]
   5. Step-by-step derivation

      1. unpow2 86.3%

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

      2. mul-1-neg 86.3%

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

      3. distribute-rgt-neg-out 86.3%

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

   6. Simplified 86.3%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 96.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (* y (* y (- x))) (* y x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = y * (y * -x);
	} else {
		tmp = 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 ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (y * -x)
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = y * (y * -x);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = y * (y * -x)
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(y * Float64(y * Float64(-x)));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = y * (y * -x);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 99.8%

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
   2. Step-by-step derivation

      1. associate-*l* 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in y around inf 86.3%

      \[\leadsto \color{blue}{-1 \cdot \left({y}^{2} \cdot x\right)} \]
   5. Step-by-step derivation

      1. unpow2 86.3%

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

      2. associate-*r* 86.3%

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

      3. mul-1-neg 86.3%

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

      4. distribute-rgt-neg-out 86.3%

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

      5. associate-*l* 97.1%

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

   6. Simplified 97.1%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 96.5%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(x - y \cdot x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
2. Step-by-step derivation

   1. associate-*l* 94.4%

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

3. Simplified 94.4%

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

   1. distribute-rgt-out-- 94.4%

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

   2. *-un-lft-identity 94.4%

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

   3. sub-neg 94.4%

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

   4. distribute-rgt-in 87.0%

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

   5. *-commutative 87.0%

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

   6. distribute-rgt-neg-in 87.0%

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

5. Applied egg-rr 87.0%

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

6. Taylor expanded in x around 0 94.4%

   \[\leadsto \color{blue}{\left(-1 \cdot {y}^{2} + y\right) \cdot x} \]
7. Step-by-step derivation

   1. *-commutative 94.4%

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

   2. +-commutative 94.4%

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

   3. unpow2 94.4%

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

   4. mul-1-neg 94.4%

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

   5. sub-neg 94.4%

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

   6. distribute-rgt-out-- 87.0%

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

   7. associate-*r* 92.4%

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

   8. distribute-lft-out-- 99.9%

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

8. Simplified 99.9%

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

9. Final simplification 99.9%

   \[\leadsto y \cdot \left(x - y \cdot x\right) \]

Alternative 6: 56.6% accurate, 2.3× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (* y x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y * x

Julia

function code(x, y)
	return Float64(y * x)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y\right) \cdot \left(1 - y\right) \]
2. Step-by-step derivation

   1. associate-*l* 94.4%

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

3. Simplified 94.4%

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

4. Taylor expanded in y around 0 56.1%

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

5. Final simplification 56.1%

   \[\leadsto y \cdot x \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1.0 y)))