Linear.Projection:perspective from linear-1.19.1.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 8.1s

Alternatives: 8

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: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision] + N[(x / N[(x - y), $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. *-un-lft-identity 99.9%

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

   3. associate-*l/ 99.7%

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

   4. +-commutative 99.7%

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

   5. distribute-rgt-in 99.7%

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

   6. div-inv 99.8%

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

   7. un-div-inv 100.0%

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

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{y}{x - y} + \frac{x}{x - y}} \]
7. Add Preprocessing

Alternative 2: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-21} \lor \neg \left(x \leq 1.4 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -9.2e-21) (not (<= x 1.4e-25))) (/ x (- x y)) (/ y (- x y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -9.2e-21) || !(x <= 1.4e-25)) {
		tmp = x / (x - y);
	} else {
		tmp = y / (x - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-9.2d-21)) .or. (.not. (x <= 1.4d-25))) then
        tmp = x / (x - y)
    else
        tmp = y / (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -9.2e-21) || !(x <= 1.4e-25)) {
		tmp = x / (x - y);
	} else {
		tmp = y / (x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -9.2e-21) or not (x <= 1.4e-25):
		tmp = x / (x - y)
	else:
		tmp = y / (x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -9.2e-21) || !(x <= 1.4e-25))
		tmp = Float64(x / Float64(x - y));
	else
		tmp = Float64(y / Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -9.2e-21) || ~((x <= 1.4e-25)))
		tmp = x / (x - y);
	else
		tmp = y / (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -9.2e-21], N[Not[LessEqual[x, 1.4e-25]], $MachinePrecision]], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.19999999999999998e-21 or 1.39999999999999994e-25 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.8%

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

   if -9.19999999999999998e-21 < x < 1.39999999999999994e-25

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-21} \lor \neg \left(x \leq 1.4 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-22} \lor \neg \left(x \leq 1.9 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.2e-22) (not (<= x 1.9e-25))) (/ x (- x y)) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.2e-22) || !(x <= 1.9e-25)) {
		tmp = x / (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 <= (-4.2d-22)) .or. (.not. (x <= 1.9d-25))) then
        tmp = x / (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 <= -4.2e-22) || !(x <= 1.9e-25)) {
		tmp = x / (x - y);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.2e-22) or not (x <= 1.9e-25):
		tmp = x / (x - y)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.2e-22) || !(x <= 1.9e-25))
		tmp = Float64(x / Float64(x - y));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.2e-22) || ~((x <= 1.9e-25)))
		tmp = x / (x - y);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.2e-22], N[Not[LessEqual[x, 1.9e-25]], $MachinePrecision]], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -4.20000000000000016e-22 or 1.8999999999999999e-25 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.8%

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

   if -4.20000000000000016e-22 < x < 1.8999999999999999e-25

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.6%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-22} \lor \neg \left(x \leq 1.9 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-24} \lor \neg \left(x \leq 3.9 \cdot 10^{-26}\right):\\ \;\;\;\;1 + \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.3e-24) (not (<= x 3.9e-26))) (+ 1.0 (/ y x)) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.3e-24) || !(x <= 3.9e-26)) {
		tmp = 1.0 + (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 <= (-3.3d-24)) .or. (.not. (x <= 3.9d-26))) then
        tmp = 1.0d0 + (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 <= -3.3e-24) || !(x <= 3.9e-26)) {
		tmp = 1.0 + (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.3e-24) or not (x <= 3.9e-26):
		tmp = 1.0 + (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.3e-24) || !(x <= 3.9e-26))
		tmp = Float64(1.0 + Float64(y / x));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.3e-24) || ~((x <= 3.9e-26)))
		tmp = 1.0 + (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.3e-24], N[Not[LessEqual[x, 3.9e-26]], $MachinePrecision]], N[(1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -3.29999999999999984e-24 or 3.89999999999999986e-26 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.8%

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

   4. Taylor expanded in x around inf 76.5%

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

   if -3.29999999999999984e-24 < x < 3.89999999999999986e-26

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-24} \lor \neg \left(x \leq 3.9 \cdot 10^{-26}\right):\\ \;\;\;\;1 + \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-16}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.8e-16)
   (+ 1.0 (* 2.0 (/ y x)))
   (if (<= x 1.6e-25) (/ y (- x y)) (/ x (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.8e-16) {
		tmp = 1.0 + (2.0 * (y / x));
	} else if (x <= 1.6e-25) {
		tmp = y / (x - y);
	} else {
		tmp = x / (x - y);
	}
	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-16)) then
        tmp = 1.0d0 + (2.0d0 * (y / x))
    else if (x <= 1.6d-25) then
        tmp = y / (x - y)
    else
        tmp = x / (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.8e-16) {
		tmp = 1.0 + (2.0 * (y / x));
	} else if (x <= 1.6e-25) {
		tmp = y / (x - y);
	} else {
		tmp = x / (x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.8e-16:
		tmp = 1.0 + (2.0 * (y / x))
	elif x <= 1.6e-25:
		tmp = y / (x - y)
	else:
		tmp = x / (x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.8e-16)
		tmp = Float64(1.0 + Float64(2.0 * Float64(y / x)));
	elseif (x <= 1.6e-25)
		tmp = Float64(y / Float64(x - y));
	else
		tmp = Float64(x / Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.8e-16)
		tmp = 1.0 + (2.0 * (y / x));
	elseif (x <= 1.6e-25)
		tmp = y / (x - y);
	else
		tmp = x / (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.8e-16], N[(1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e-25], N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999991e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.7%

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

   if -1.79999999999999991e-16 < x < 1.6000000000000001e-25

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.5%

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

   if 1.6000000000000001e-25 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.8%

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

Alternative 6: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-26}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2e-18) 1.0 (if (<= x 5e-26) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2e-18) {
		tmp = 1.0;
	} else if (x <= 5e-26) {
		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 <= (-2d-18)) then
        tmp = 1.0d0
    else if (x <= 5d-26) 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 <= -2e-18) {
		tmp = 1.0;
	} else if (x <= 5e-26) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2e-18:
		tmp = 1.0
	elif x <= 5e-26:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2e-18)
		tmp = 1.0;
	elseif (x <= 5e-26)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2e-18)
		tmp = 1.0;
	elseif (x <= 5e-26)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2e-18], 1.0, If[LessEqual[x, 5e-26], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0000000000000001e-18 or 5.00000000000000019e-26 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.0%

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

   if -2.0000000000000001e-18 < x < 5.00000000000000019e-26

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.6%

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

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 8: 49.0% 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 48.2%

   \[\leadsto \color{blue}{-1} \]
4. Add Preprocessing

Developer Target 1: 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 2024114 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ 1 (- (/ x (+ x y)) (/ y (+ x y)))))

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