Linear.Projection:perspective from linear-1.19.1.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 4.2s

Alternatives: 5

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, 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 2: 73.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+125}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+113} \lor \neg \left(y \leq -2.6 \cdot 10^{+18}\right) \land \left(y \leq 1.45 \cdot 10^{+43} \lor \neg \left(y \leq 3.7 \cdot 10^{+70}\right) \land y \leq 6.6 \cdot 10^{+131}\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.9e+125)
   -1.0
   (if (or (<= y -6.4e+113)
           (and (not (<= y -2.6e+18))
                (or (<= y 1.45e+43)
                    (and (not (<= y 3.7e+70)) (<= y 6.6e+131)))))
     (+ 1.0 (* 2.0 (/ y x)))
     -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.9e+125) {
		tmp = -1.0;
	} else if ((y <= -6.4e+113) || (!(y <= -2.6e+18) && ((y <= 1.45e+43) || (!(y <= 3.7e+70) && (y <= 6.6e+131))))) {
		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 (y <= (-2.9d+125)) then
        tmp = -1.0d0
    else if ((y <= (-6.4d+113)) .or. (.not. (y <= (-2.6d+18))) .and. (y <= 1.45d+43) .or. (.not. (y <= 3.7d+70)) .and. (y <= 6.6d+131)) 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 (y <= -2.9e+125) {
		tmp = -1.0;
	} else if ((y <= -6.4e+113) || (!(y <= -2.6e+18) && ((y <= 1.45e+43) || (!(y <= 3.7e+70) && (y <= 6.6e+131))))) {
		tmp = 1.0 + (2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.9e+125:
		tmp = -1.0
	elif (y <= -6.4e+113) or (not (y <= -2.6e+18) and ((y <= 1.45e+43) or (not (y <= 3.7e+70) and (y <= 6.6e+131)))):
		tmp = 1.0 + (2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.9e+125)
		tmp = -1.0;
	elseif ((y <= -6.4e+113) || (!(y <= -2.6e+18) && ((y <= 1.45e+43) || (!(y <= 3.7e+70) && (y <= 6.6e+131)))))
		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 (y <= -2.9e+125)
		tmp = -1.0;
	elseif ((y <= -6.4e+113) || (~((y <= -2.6e+18)) && ((y <= 1.45e+43) || (~((y <= 3.7e+70)) && (y <= 6.6e+131)))))
		tmp = 1.0 + (2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.9e+125], -1.0, If[Or[LessEqual[y, -6.4e+113], And[N[Not[LessEqual[y, -2.6e+18]], $MachinePrecision], Or[LessEqual[y, 1.45e+43], And[N[Not[LessEqual[y, 3.7e+70]], $MachinePrecision], LessEqual[y, 6.6e+131]]]]], N[(1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.89999999999999993e125 or -6.3999999999999996e113 < y < -2.6e18 or 1.4500000000000001e43 < y < 3.69999999999999989e70 or 6.5999999999999997e131 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 89.3%

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

   if -2.89999999999999993e125 < y < -6.3999999999999996e113 or -2.6e18 < y < 1.4500000000000001e43 or 3.69999999999999989e70 < y < 6.5999999999999997e131

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+125}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+113} \lor \neg \left(y \leq -2.6 \cdot 10^{+18}\right) \land \left(y \leq 1.45 \cdot 10^{+43} \lor \neg \left(y \leq 3.7 \cdot 10^{+70}\right) \land y \leq 6.6 \cdot 10^{+131}\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -2 \cdot \frac{x}{y} + -1\\ t_1 := 1 + 2 \cdot \frac{y}{x}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+124}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -28000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+70}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (* -2.0 (/ x y)) -1.0)) (t_1 (+ 1.0 (* 2.0 (/ y x)))))
   (if (<= y -1.25e+124)
     t_0
     (if (<= y -6.4e+113)
       t_1
       (if (<= y -28000000000000.0)
         t_0
         (if (<= y 1.95e+42)
           t_1
           (if (<= y 1.45e+70) -1.0 (if (<= y 1.65e+131) t_1 t_0))))))))

C

double code(double x, double y) {
	double t_0 = (-2.0 * (x / y)) + -1.0;
	double t_1 = 1.0 + (2.0 * (y / x));
	double tmp;
	if (y <= -1.25e+124) {
		tmp = t_0;
	} else if (y <= -6.4e+113) {
		tmp = t_1;
	} else if (y <= -28000000000000.0) {
		tmp = t_0;
	} else if (y <= 1.95e+42) {
		tmp = t_1;
	} else if (y <= 1.45e+70) {
		tmp = -1.0;
	} else if (y <= 1.65e+131) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = ((-2.0d0) * (x / y)) + (-1.0d0)
    t_1 = 1.0d0 + (2.0d0 * (y / x))
    if (y <= (-1.25d+124)) then
        tmp = t_0
    else if (y <= (-6.4d+113)) then
        tmp = t_1
    else if (y <= (-28000000000000.0d0)) then
        tmp = t_0
    else if (y <= 1.95d+42) then
        tmp = t_1
    else if (y <= 1.45d+70) then
        tmp = -1.0d0
    else if (y <= 1.65d+131) then
        tmp = t_1
    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 / y)) + -1.0;
	double t_1 = 1.0 + (2.0 * (y / x));
	double tmp;
	if (y <= -1.25e+124) {
		tmp = t_0;
	} else if (y <= -6.4e+113) {
		tmp = t_1;
	} else if (y <= -28000000000000.0) {
		tmp = t_0;
	} else if (y <= 1.95e+42) {
		tmp = t_1;
	} else if (y <= 1.45e+70) {
		tmp = -1.0;
	} else if (y <= 1.65e+131) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (-2.0 * (x / y)) + -1.0
	t_1 = 1.0 + (2.0 * (y / x))
	tmp = 0
	if y <= -1.25e+124:
		tmp = t_0
	elif y <= -6.4e+113:
		tmp = t_1
	elif y <= -28000000000000.0:
		tmp = t_0
	elif y <= 1.95e+42:
		tmp = t_1
	elif y <= 1.45e+70:
		tmp = -1.0
	elif y <= 1.65e+131:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(-2.0 * Float64(x / y)) + -1.0)
	t_1 = Float64(1.0 + Float64(2.0 * Float64(y / x)))
	tmp = 0.0
	if (y <= -1.25e+124)
		tmp = t_0;
	elseif (y <= -6.4e+113)
		tmp = t_1;
	elseif (y <= -28000000000000.0)
		tmp = t_0;
	elseif (y <= 1.95e+42)
		tmp = t_1;
	elseif (y <= 1.45e+70)
		tmp = -1.0;
	elseif (y <= 1.65e+131)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (-2.0 * (x / y)) + -1.0;
	t_1 = 1.0 + (2.0 * (y / x));
	tmp = 0.0;
	if (y <= -1.25e+124)
		tmp = t_0;
	elseif (y <= -6.4e+113)
		tmp = t_1;
	elseif (y <= -28000000000000.0)
		tmp = t_0;
	elseif (y <= 1.95e+42)
		tmp = t_1;
	elseif (y <= 1.45e+70)
		tmp = -1.0;
	elseif (y <= 1.65e+131)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(-2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+124], t$95$0, If[LessEqual[y, -6.4e+113], t$95$1, If[LessEqual[y, -28000000000000.0], t$95$0, If[LessEqual[y, 1.95e+42], t$95$1, If[LessEqual[y, 1.45e+70], -1.0, If[LessEqual[y, 1.65e+131], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2499999999999999e124 or -6.3999999999999996e113 < y < -2.8e13 or 1.6499999999999999e131 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 89.4%

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

   if -1.2499999999999999e124 < y < -6.3999999999999996e113 or -2.8e13 < y < 1.94999999999999985e42 or 1.4499999999999999e70 < y < 1.6499999999999999e131

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.2%

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

   if 1.94999999999999985e42 < y < 1.4499999999999999e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+124}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+113}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq -28000000000000:\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+42}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+70}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+131}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+124}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{+108}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+66}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+131}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.25e+124)
   -1.0
   (if (<= y -1.62e+108)
     1.0
     (if (<= y -3.8e-37)
       -1.0
       (if (<= y 5e+42)
         1.0
         (if (<= y 5e+66) -1.0 (if (<= y 1.65e+131) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.25e+124) {
		tmp = -1.0;
	} else if (y <= -1.62e+108) {
		tmp = 1.0;
	} else if (y <= -3.8e-37) {
		tmp = -1.0;
	} else if (y <= 5e+42) {
		tmp = 1.0;
	} else if (y <= 5e+66) {
		tmp = -1.0;
	} else if (y <= 1.65e+131) {
		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 (y <= (-1.25d+124)) then
        tmp = -1.0d0
    else if (y <= (-1.62d+108)) then
        tmp = 1.0d0
    else if (y <= (-3.8d-37)) then
        tmp = -1.0d0
    else if (y <= 5d+42) then
        tmp = 1.0d0
    else if (y <= 5d+66) then
        tmp = -1.0d0
    else if (y <= 1.65d+131) 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 (y <= -1.25e+124) {
		tmp = -1.0;
	} else if (y <= -1.62e+108) {
		tmp = 1.0;
	} else if (y <= -3.8e-37) {
		tmp = -1.0;
	} else if (y <= 5e+42) {
		tmp = 1.0;
	} else if (y <= 5e+66) {
		tmp = -1.0;
	} else if (y <= 1.65e+131) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.25e+124:
		tmp = -1.0
	elif y <= -1.62e+108:
		tmp = 1.0
	elif y <= -3.8e-37:
		tmp = -1.0
	elif y <= 5e+42:
		tmp = 1.0
	elif y <= 5e+66:
		tmp = -1.0
	elif y <= 1.65e+131:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.25e+124)
		tmp = -1.0;
	elseif (y <= -1.62e+108)
		tmp = 1.0;
	elseif (y <= -3.8e-37)
		tmp = -1.0;
	elseif (y <= 5e+42)
		tmp = 1.0;
	elseif (y <= 5e+66)
		tmp = -1.0;
	elseif (y <= 1.65e+131)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.25e+124)
		tmp = -1.0;
	elseif (y <= -1.62e+108)
		tmp = 1.0;
	elseif (y <= -3.8e-37)
		tmp = -1.0;
	elseif (y <= 5e+42)
		tmp = 1.0;
	elseif (y <= 5e+66)
		tmp = -1.0;
	elseif (y <= 1.65e+131)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.25e+124], -1.0, If[LessEqual[y, -1.62e+108], 1.0, If[LessEqual[y, -3.8e-37], -1.0, If[LessEqual[y, 5e+42], 1.0, If[LessEqual[y, 5e+66], -1.0, If[LessEqual[y, 1.65e+131], 1.0, -1.0]]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2499999999999999e124 or -1.61999999999999996e108 < y < -3.8000000000000004e-37 or 5.00000000000000007e42 < y < 4.99999999999999991e66 or 1.6499999999999999e131 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.7%

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

   if -1.2499999999999999e124 < y < -1.61999999999999996e108 or -3.8000000000000004e-37 < y < 5.00000000000000007e42 or 4.99999999999999991e66 < y < 1.6499999999999999e131

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+124}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{+108}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+66}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+131}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.6% 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 48.7%

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

4. Final simplification 48.7%

   \[\leadsto -1 \]
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 2024027 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

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