Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.7% → 99.4%

Time: 2.8s

Alternatives: 5

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \frac{x + x}{x - y}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-74}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e+50)
   (* y (/ (+ x x) (- x y)))
   (if (<= x 3.6e-74)
     (/ (* x 2.0) (/ (- x y) y))
     (* 2.0 (/ y (- 1.0 (/ y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e+50) {
		tmp = y * ((x + x) / (x - y));
	} else if (x <= 3.6e-74) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = 2.0 * (y / (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 <= (-1d+50)) then
        tmp = y * ((x + x) / (x - y))
    else if (x <= 3.6d-74) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    else
        tmp = 2.0d0 * (y / (1.0d0 - (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1e+50) {
		tmp = y * ((x + x) / (x - y));
	} else if (x <= 3.6e-74) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = 2.0 * (y / (1.0 - (y / x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e+50:
		tmp = y * ((x + x) / (x - y))
	elif x <= 3.6e-74:
		tmp = (x * 2.0) / ((x - y) / y)
	else:
		tmp = 2.0 * (y / (1.0 - (y / x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e+50)
		tmp = Float64(y * Float64(Float64(x + x) / Float64(x - y)));
	elseif (x <= 3.6e-74)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	else
		tmp = Float64(2.0 * Float64(y / Float64(1.0 - Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e+50)
		tmp = y * ((x + x) / (x - y));
	elseif (x <= 3.6e-74)
		tmp = (x * 2.0) / ((x - y) / y);
	else
		tmp = 2.0 * (y / (1.0 - (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e+50], N[(y * N[(N[(x + x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-74], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y / N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0000000000000001e50

   1. Initial program 82.3%

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

      1. associate-/l* 73.6%

         \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

   3. Simplified 73.6%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]
   4. Step-by-step derivation

      1. associate-/r/ 100.0%

         \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]

      2. add-log-exp 3.2%

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

      3. exp-lft-sqr 3.2%

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

      4. log-prod 3.2%

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

      5. add-log-exp 3.2%

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

      6. add-log-exp 100.0%

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

   5. Applied egg-rr 100.0%

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

   if -1.0000000000000001e50 < x < 3.6000000000000002e-74

   1. Initial program 79.6%

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

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

   if 3.6000000000000002e-74 < x

   1. Initial program 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-/l* 98.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{x - y}{x \cdot 2}}} \]

      3. associate-/r* 99.9%

         \[\leadsto \frac{y}{\color{blue}{\frac{\frac{x - y}{x}}{2}}} \]

      4. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{x - y}{x}} \cdot 2} \]

      5. div-sub 100.0%

         \[\leadsto \frac{y}{\color{blue}{\frac{x}{x} - \frac{y}{x}}} \cdot 2 \]

      6. *-inverses 100.0%

         \[\leadsto \frac{y}{\color{blue}{1} - \frac{y}{x}} \cdot 2 \]

   3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \frac{x + x}{x - y}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-74}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \end{array} \]

Alternative 2: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-146} \lor \neg \left(x \leq 7.2 \cdot 10^{-140}\right):\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.8e-146) (not (<= x 7.2e-140)))
   (* 2.0 (/ y (- 1.0 (/ y x))))
   (* x -2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.8e-146) || !(x <= 7.2e-140)) {
		tmp = 2.0 * (y / (1.0 - (y / x)));
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.8d-146)) .or. (.not. (x <= 7.2d-140))) then
        tmp = 2.0d0 * (y / (1.0d0 - (y / x)))
    else
        tmp = x * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.8e-146) || !(x <= 7.2e-140)) {
		tmp = 2.0 * (y / (1.0 - (y / x)));
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.8e-146) or not (x <= 7.2e-140):
		tmp = 2.0 * (y / (1.0 - (y / x)))
	else:
		tmp = x * -2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.8e-146) || !(x <= 7.2e-140))
		tmp = Float64(2.0 * Float64(y / Float64(1.0 - Float64(y / x))));
	else
		tmp = Float64(x * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.8e-146) || ~((x <= 7.2e-140)))
		tmp = 2.0 * (y / (1.0 - (y / x)));
	else
		tmp = x * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.8e-146], N[Not[LessEqual[x, 7.2e-140]], $MachinePrecision]], N[(2.0 * N[(y / N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.79999999999999989e-146 or 7.2000000000000001e-140 < x

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-/l* 97.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{x - y}{x \cdot 2}}} \]

      3. associate-/r* 97.5%

         \[\leadsto \frac{y}{\color{blue}{\frac{\frac{x - y}{x}}{2}}} \]

      4. associate-/r/ 97.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{x - y}{x}} \cdot 2} \]

      5. div-sub 97.5%

         \[\leadsto \frac{y}{\color{blue}{\frac{x}{x} - \frac{y}{x}}} \cdot 2 \]

      6. *-inverses 97.5%

         \[\leadsto \frac{y}{\color{blue}{1} - \frac{y}{x}} \cdot 2 \]

   3. Simplified 97.5%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{x}} \cdot 2} \]

   if -1.79999999999999989e-146 < x < 7.2000000000000001e-140

   1. Initial program 70.9%

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

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

   4. Taylor expanded in x around 0 90.7%

      \[\leadsto \color{blue}{-2 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 90.7%

         \[\leadsto \color{blue}{x \cdot -2} \]

   6. Simplified 90.7%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-146} \lor \neg \left(x \leq 7.2 \cdot 10^{-140}\right):\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]

Alternative 3: 93.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{x + x}{x - y}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-139}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e-147)
   (* y (/ (+ x x) (- x y)))
   (if (<= x 2.5e-139) (* x -2.0) (* 2.0 (/ y (- 1.0 (/ y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e-147) {
		tmp = y * ((x + x) / (x - y));
	} else if (x <= 2.5e-139) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * (y / (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 <= (-5d-147)) then
        tmp = y * ((x + x) / (x - y))
    else if (x <= 2.5d-139) then
        tmp = x * (-2.0d0)
    else
        tmp = 2.0d0 * (y / (1.0d0 - (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5e-147) {
		tmp = y * ((x + x) / (x - y));
	} else if (x <= 2.5e-139) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * (y / (1.0 - (y / x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e-147:
		tmp = y * ((x + x) / (x - y))
	elif x <= 2.5e-139:
		tmp = x * -2.0
	else:
		tmp = 2.0 * (y / (1.0 - (y / x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e-147)
		tmp = Float64(y * Float64(Float64(x + x) / Float64(x - y)));
	elseif (x <= 2.5e-139)
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(2.0 * Float64(y / Float64(1.0 - Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e-147)
		tmp = y * ((x + x) / (x - y));
	elseif (x <= 2.5e-139)
		tmp = x * -2.0;
	else
		tmp = 2.0 * (y / (1.0 - (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e-147], N[(y * N[(N[(x + x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-139], N[(x * -2.0), $MachinePrecision], N[(2.0 * N[(y / N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.00000000000000013e-147

   1. Initial program 85.1%

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

      1. associate-/l* 86.0%

         \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]
   4. Step-by-step derivation

      1. associate-/r/ 98.1%

         \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]

      2. add-log-exp 5.6%

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

      3. exp-lft-sqr 5.6%

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

      4. log-prod 5.7%

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

      5. add-log-exp 9.8%

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

      6. add-log-exp 98.1%

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

   5. Applied egg-rr 98.1%

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

   if -5.00000000000000013e-147 < x < 2.50000000000000017e-139

   1. Initial program 70.9%

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

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

   4. Taylor expanded in x around 0 90.7%

      \[\leadsto \color{blue}{-2 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 90.7%

         \[\leadsto \color{blue}{x \cdot -2} \]

   6. Simplified 90.7%

      \[\leadsto \color{blue}{x \cdot -2} \]

   if 2.50000000000000017e-139 < x

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 96.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{x - y}{x \cdot 2}}} \]

      3. associate-/r* 97.8%

         \[\leadsto \frac{y}{\color{blue}{\frac{\frac{x - y}{x}}{2}}} \]

      4. associate-/r/ 97.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{x - y}{x}} \cdot 2} \]

      5. div-sub 97.9%

         \[\leadsto \frac{y}{\color{blue}{\frac{x}{x} - \frac{y}{x}}} \cdot 2 \]

      6. *-inverses 97.9%

         \[\leadsto \frac{y}{\color{blue}{1} - \frac{y}{x}} \cdot 2 \]

   3. Simplified 97.9%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \frac{x + x}{x - y}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-139}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{y}{1 - \frac{y}{x}}\\ \end{array} \]

Alternative 4: 74.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+18}:\\ \;\;\;\;x \cdot -2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.08e+18) (* x -2.0) (if (<= y 8.2e-20) (* y 2.0) (* x -2.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.08e+18) {
		tmp = x * -2.0;
	} else if (y <= 8.2e-20) {
		tmp = y * 2.0;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.08d+18)) then
        tmp = x * (-2.0d0)
    else if (y <= 8.2d-20) then
        tmp = y * 2.0d0
    else
        tmp = x * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.08e+18) {
		tmp = x * -2.0;
	} else if (y <= 8.2e-20) {
		tmp = y * 2.0;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.08e+18:
		tmp = x * -2.0
	elif y <= 8.2e-20:
		tmp = y * 2.0
	else:
		tmp = x * -2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.08e+18)
		tmp = Float64(x * -2.0);
	elseif (y <= 8.2e-20)
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(x * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.08e+18)
		tmp = x * -2.0;
	elseif (y <= 8.2e-20)
		tmp = y * 2.0;
	else
		tmp = x * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.08e+18], N[(x * -2.0), $MachinePrecision], If[LessEqual[y, 8.2e-20], N[(y * 2.0), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.08e18 or 8.2000000000000002e-20 < y

   1. Initial program 77.1%

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

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

   4. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{-2 \cdot x} \]
   5. Step-by-step derivation

      1. *-commutative 79.0%

         \[\leadsto \color{blue}{x \cdot -2} \]

   6. Simplified 79.0%

      \[\leadsto \color{blue}{x \cdot -2} \]

   if -1.08e18 < y < 8.2000000000000002e-20

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-/l* 99.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{x - y}{x \cdot 2}}} \]

      3. associate-/r* 99.9%

         \[\leadsto \frac{y}{\color{blue}{\frac{\frac{x - y}{x}}{2}}} \]

      4. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{y}{\frac{x - y}{x}} \cdot 2} \]

      5. div-sub 100.0%

         \[\leadsto \frac{y}{\color{blue}{\frac{x}{x} - \frac{y}{x}}} \cdot 2 \]

      6. *-inverses 100.0%

         \[\leadsto \frac{y}{\color{blue}{1} - \frac{y}{x}} \cdot 2 \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{y}{1 - \frac{y}{x}} \cdot 2} \]

   4. Taylor expanded in y around 0 80.8%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+18}:\\ \;\;\;\;x \cdot -2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-20}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]

Alternative 5: 50.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x \cdot -2 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x -2.0))

C

double code(double x, double y) {
	return x * -2.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (-2.0d0)
end function

Java

public static double code(double x, double y) {
	return x * -2.0;
}

Python

def code(x, y):
	return x * -2.0

Julia

function code(x, y)
	return Float64(x * -2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = x * -2.0;
end

Wolfram

code[x_, y_] := N[(x * -2.0), $MachinePrecision]

Derivation

1. Initial program 79.6%

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

   1. associate-/l* 87.8%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

3. Simplified 87.8%

   \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]

4. Taylor expanded in x around 0 48.5%

   \[\leadsto \color{blue}{-2 \cdot x} \]
5. Step-by-step derivation

   1. *-commutative 48.5%

      \[\leadsto \color{blue}{x \cdot -2} \]

6. Simplified 48.5%

   \[\leadsto \color{blue}{x \cdot -2} \]

7. Final simplification 48.5%

   \[\leadsto x \cdot -2 \]

Developer target: 99.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ (* 2.0 x) (- x y)) y)))
   (if (< x -1.7210442634149447e+81)
     t_0
     (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / 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 = ((2.0d0 * x) / (x - y)) * y
    if (x < (-1.7210442634149447d+81)) then
        tmp = t_0
    else if (x < 83645045635564430.0d0) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((2.0 * x) / (x - y)) * y
	tmp = 0
	if x < -1.7210442634149447e+81:
		tmp = t_0
	elif x < 83645045635564430.0:
		tmp = (x * 2.0) / ((x - y) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(2.0 * x) / Float64(x - y)) * y)
	tmp = 0.0
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((2.0 * x) / (x - y)) * y;
	tmp = 0.0;
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = (x * 2.0) / ((x - y) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[Less[x, -1.7210442634149447e+81], t$95$0, If[Less[x, 83645045635564430.0], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))