Linear.Projection:perspective from linear-1.19.1.3, A

Percentage Accurate: 100.0% → 99.9%

Time: 8.2s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{x + y}\right)\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 (log1p (expm1 (/ (- x y) (+ x y))))))

C

double code(double x, double y) {
	return 1.0 / log1p(expm1(((x - y) / (x + y))));
}

Java

public static double code(double x, double y) {
	return 1.0 / Math.log1p(Math.expm1(((x - y) / (x + y))));
}

Python

def code(x, y):
	return 1.0 / math.log1p(math.expm1(((x - y) / (x + y))))

Julia

function code(x, y)
	return Float64(1.0 / log1p(expm1(Float64(Float64(x - y) / Float64(x + y)))))
end

Wolfram

code[x_, y_] := N[(1.0 / N[Log[1 + N[(Exp[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. add-log-exp 99.9%

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

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\log \left(e^{\frac{x + y}{x - y}}\right)} \]
5. Step-by-step derivation

   1. rem-log-exp 99.9%

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

   2. clear-num 99.9%

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

6. Applied egg-rr 99.9%

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

   1. log1p-expm1-u 99.9%

      \[\leadsto \frac{1}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{x + y}\right)\right)}} \]

8. Applied egg-rr 99.9%

   \[\leadsto \frac{1}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{x + y}\right)\right)}} \]

9. Final simplification 99.9%

   \[\leadsto \frac{1}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x - y}{x + y}\right)\right)} \]
10. Add Preprocessing

Alternative 2: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-100} \lor \neg \left(x \leq 3 \cdot 10^{-80}\right) \land \left(x \leq 2050000000000 \lor \neg \left(x \leq 1.7 \cdot 10^{+44}\right)\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.1e-100)
         (and (not (<= x 3e-80))
              (or (<= x 2050000000000.0) (not (<= x 1.7e+44)))))
   (+ 1.0 (* 2.0 (/ y x)))
   -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.1e-100) || (!(x <= 3e-80) && ((x <= 2050000000000.0) || !(x <= 1.7e+44)))) {
		tmp = 1.0 + (2.0 * (y / x));
	} 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 <= (-3.1d-100)) .or. (.not. (x <= 3d-80)) .and. (x <= 2050000000000.0d0) .or. (.not. (x <= 1.7d+44))) then
        tmp = 1.0d0 + (2.0d0 * (y / x))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -3.1e-100) || (!(x <= 3e-80) && ((x <= 2050000000000.0) || !(x <= 1.7e+44)))) {
		tmp = 1.0 + (2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.1e-100) or (not (x <= 3e-80) and ((x <= 2050000000000.0) or not (x <= 1.7e+44))):
		tmp = 1.0 + (2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.1e-100) || (!(x <= 3e-80) && ((x <= 2050000000000.0) || !(x <= 1.7e+44))))
		tmp = Float64(1.0 + Float64(2.0 * Float64(y / x)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.1e-100) || (~((x <= 3e-80)) && ((x <= 2050000000000.0) || ~((x <= 1.7e+44)))))
		tmp = 1.0 + (2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.1e-100], And[N[Not[LessEqual[x, 3e-80]], $MachinePrecision], Or[LessEqual[x, 2050000000000.0], N[Not[LessEqual[x, 1.7e+44]], $MachinePrecision]]]], N[(1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -3.0999999999999999e-100 or 3.00000000000000007e-80 < x < 2.05e12 or 1.7e44 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.5%

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

   if -3.0999999999999999e-100 < x < 3.00000000000000007e-80 or 2.05e12 < x < 1.7e44

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.0%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-100} \lor \neg \left(x \leq 3 \cdot 10^{-80}\right) \land \left(x \leq 2050000000000 \lor \neg \left(x \leq 1.7 \cdot 10^{+44}\right)\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-99} \lor \neg \left(x \leq 3 \cdot 10^{-80} \lor \neg \left(x \leq 1.35 \cdot 10^{+17}\right) \land x \leq 6.4 \cdot 10^{+45}\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.6e-99)
         (not (or (<= x 3e-80) (and (not (<= x 1.35e+17)) (<= x 6.4e+45)))))
   (+ 1.0 (* 2.0 (/ y x)))
   (+ (* -2.0 (/ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.6e-99) || !((x <= 3e-80) || (!(x <= 1.35e+17) && (x <= 6.4e+45)))) {
		tmp = 1.0 + (2.0 * (y / x));
	} else {
		tmp = (-2.0 * (x / y)) + -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 <= (-1.6d-99)) .or. (.not. (x <= 3d-80) .or. (.not. (x <= 1.35d+17)) .and. (x <= 6.4d+45))) then
        tmp = 1.0d0 + (2.0d0 * (y / x))
    else
        tmp = ((-2.0d0) * (x / y)) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.6e-99) || !((x <= 3e-80) || (!(x <= 1.35e+17) && (x <= 6.4e+45)))) {
		tmp = 1.0 + (2.0 * (y / x));
	} else {
		tmp = (-2.0 * (x / y)) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.6e-99) or not ((x <= 3e-80) or (not (x <= 1.35e+17) and (x <= 6.4e+45))):
		tmp = 1.0 + (2.0 * (y / x))
	else:
		tmp = (-2.0 * (x / y)) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.6e-99) || !((x <= 3e-80) || (!(x <= 1.35e+17) && (x <= 6.4e+45))))
		tmp = Float64(1.0 + Float64(2.0 * Float64(y / x)));
	else
		tmp = Float64(Float64(-2.0 * Float64(x / y)) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.6e-99) || ~(((x <= 3e-80) || (~((x <= 1.35e+17)) && (x <= 6.4e+45)))))
		tmp = 1.0 + (2.0 * (y / x));
	else
		tmp = (-2.0 * (x / y)) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.6e-99], N[Not[Or[LessEqual[x, 3e-80], And[N[Not[LessEqual[x, 1.35e+17]], $MachinePrecision], LessEqual[x, 6.4e+45]]]], $MachinePrecision]], N[(1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e-99 or 3.00000000000000007e-80 < x < 1.35e17 or 6.4000000000000006e45 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.5%

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

   if -1.6e-99 < x < 3.00000000000000007e-80 or 1.35e17 < x < 6.4000000000000006e45

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-99} \lor \neg \left(x \leq 3 \cdot 10^{-80} \lor \neg \left(x \leq 1.35 \cdot 10^{+17}\right) \land x \leq 6.4 \cdot 10^{+45}\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-84}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 20000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.6e-99)
   1.0
   (if (<= x 1e-84)
     -1.0
     (if (<= x 20000000000.0) 1.0 (if (<= x 2.3e+44) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.6e-99) {
		tmp = 1.0;
	} else if (x <= 1e-84) {
		tmp = -1.0;
	} else if (x <= 20000000000.0) {
		tmp = 1.0;
	} else if (x <= 2.3e+44) {
		tmp = -1.0;
	} 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 <= (-1.6d-99)) then
        tmp = 1.0d0
    else if (x <= 1d-84) then
        tmp = -1.0d0
    else if (x <= 20000000000.0d0) then
        tmp = 1.0d0
    else if (x <= 2.3d+44) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.6e-99) {
		tmp = 1.0;
	} else if (x <= 1e-84) {
		tmp = -1.0;
	} else if (x <= 20000000000.0) {
		tmp = 1.0;
	} else if (x <= 2.3e+44) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.6e-99:
		tmp = 1.0
	elif x <= 1e-84:
		tmp = -1.0
	elif x <= 20000000000.0:
		tmp = 1.0
	elif x <= 2.3e+44:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.6e-99)
		tmp = 1.0;
	elseif (x <= 1e-84)
		tmp = -1.0;
	elseif (x <= 20000000000.0)
		tmp = 1.0;
	elseif (x <= 2.3e+44)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.6e-99)
		tmp = 1.0;
	elseif (x <= 1e-84)
		tmp = -1.0;
	elseif (x <= 20000000000.0)
		tmp = 1.0;
	elseif (x <= 2.3e+44)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.6e-99], 1.0, If[LessEqual[x, 1e-84], -1.0, If[LessEqual[x, 20000000000.0], 1.0, If[LessEqual[x, 2.3e+44], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e-99 or 1e-84 < x < 2e10 or 2.30000000000000004e44 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.1%

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

   if -1.6e-99 < x < 1e-84 or 2e10 < x < 2.30000000000000004e44

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-84}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 20000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 100.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{x}{x + y} - \frac{y}{x + y}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y)))))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0 / ((x / (x + y)) - (y / (x + y)))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. add-log-exp 99.9%

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

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\log \left(e^{\frac{x + y}{x - y}}\right)} \]
5. Step-by-step derivation

   1. rem-log-exp 99.9%

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

   2. clear-num 99.9%

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

6. Applied egg-rr 99.9%

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

   1. div-sub 99.9%

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

8. Applied egg-rr 99.9%

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

9. Final simplification 99.9%

   \[\leadsto \frac{1}{\frac{x}{x + y} - \frac{y}{x + y}} \]
10. Add Preprocessing

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 7: 50.7% accurate, 7.0× 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 99.9%

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

3. Taylor expanded in x around 0 50.0%

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

4. Final simplification 50.0%

   \[\leadsto -1 \]
5. Add Preprocessing

Developer target: 100.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{x}{x + y} - \frac{y}{x + y}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y)))))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0 / ((x / (x + y)) - (y / (x + y)))

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024115 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

  (/ (+ x y) (- x y)))