Linear.Projection:perspective from linear-1.19.1.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

Alternatives: 9

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. Add Preprocessing

Alternative 2: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -59:\\ \;\;\;\;\frac{x + y}{-y}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-11}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -59.0)
   (/ (+ x y) (- y))
   (if (<= y 1.08e-11) (+ 1.0 (* 2.0 (/ y x))) (+ (* -2.0 (/ x y)) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -59.0) {
		tmp = (x + y) / -y;
	} else if (y <= 1.08e-11) {
		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 (y <= (-59.0d0)) then
        tmp = (x + y) / -y
    else if (y <= 1.08d-11) 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 (y <= -59.0) {
		tmp = (x + y) / -y;
	} else if (y <= 1.08e-11) {
		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 y <= -59.0:
		tmp = (x + y) / -y
	elif y <= 1.08e-11:
		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 (y <= -59.0)
		tmp = Float64(Float64(x + y) / Float64(-y));
	elseif (y <= 1.08e-11)
		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 (y <= -59.0)
		tmp = (x + y) / -y;
	elseif (y <= 1.08e-11)
		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[LessEqual[y, -59.0], N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, 1.08e-11], 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 3 regimes

2. if y < -59

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.1%

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

      1. neg-mul-1 75.1%

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

   5. Simplified 75.1%

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

   if -59 < y < 1.07999999999999992e-11

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 83.4%

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

   if 1.07999999999999992e-11 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -59:\\ \;\;\;\;\frac{x + y}{-y}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-11}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -59:\\ \;\;\;\;\frac{x + y}{-y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-12}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -59.0)
   (/ (+ x y) (- y))
   (if (<= y 7e-12) (+ 1.0 (* 2.0 (/ y x))) (/ y (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -59.0) {
		tmp = (x + y) / -y;
	} else if (y <= 7e-12) {
		tmp = 1.0 + (2.0 * (y / x));
	} 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 (y <= (-59.0d0)) then
        tmp = (x + y) / -y
    else if (y <= 7d-12) then
        tmp = 1.0d0 + (2.0d0 * (y / x))
    else
        tmp = y / (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -59.0) {
		tmp = (x + y) / -y;
	} else if (y <= 7e-12) {
		tmp = 1.0 + (2.0 * (y / x));
	} else {
		tmp = y / (x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -59.0:
		tmp = (x + y) / -y
	elif y <= 7e-12:
		tmp = 1.0 + (2.0 * (y / x))
	else:
		tmp = y / (x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -59.0)
		tmp = Float64(Float64(x + y) / Float64(-y));
	elseif (y <= 7e-12)
		tmp = Float64(1.0 + Float64(2.0 * Float64(y / x)));
	else
		tmp = Float64(y / Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -59.0)
		tmp = (x + y) / -y;
	elseif (y <= 7e-12)
		tmp = 1.0 + (2.0 * (y / x));
	else
		tmp = y / (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -59.0], N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, 7e-12], N[(1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -59

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.1%

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

      1. neg-mul-1 75.1%

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

   5. Simplified 75.1%

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

   if -59 < y < 7.0000000000000001e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 83.4%

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

   if 7.0000000000000001e-12 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.8%

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

Alternative 4: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -34 \lor \neg \left(y \leq 6 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -34.0) (not (<= y 6e-12))) (/ y (- x y)) (/ x (- x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -34.0) || !(y <= 6e-12)) {
		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 ((y <= (-34.0d0)) .or. (.not. (y <= 6d-12))) 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 ((y <= -34.0) || !(y <= 6e-12)) {
		tmp = y / (x - y);
	} else {
		tmp = x / (x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -34.0) or not (y <= 6e-12):
		tmp = y / (x - y)
	else:
		tmp = x / (x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -34.0) || !(y <= 6e-12))
		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 ((y <= -34.0) || ~((y <= 6e-12)))
		tmp = y / (x - y);
	else
		tmp = x / (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -34.0], N[Not[LessEqual[y, 6e-12]], $MachinePrecision]], N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -34 or 6.0000000000000003e-12 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.0%

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

   if -34 < y < 6.0000000000000003e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -34 \lor \neg \left(y \leq 6 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -21:\\ \;\;\;\;\frac{x + y}{-y}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -21.0)
   (/ (+ x y) (- y))
   (if (<= y 5.9e-12) (/ x (- x y)) (/ y (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -21.0) {
		tmp = (x + y) / -y;
	} else if (y <= 5.9e-12) {
		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 (y <= (-21.0d0)) then
        tmp = (x + y) / -y
    else if (y <= 5.9d-12) 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 (y <= -21.0) {
		tmp = (x + y) / -y;
	} else if (y <= 5.9e-12) {
		tmp = x / (x - y);
	} else {
		tmp = y / (x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -21.0:
		tmp = (x + y) / -y
	elif y <= 5.9e-12:
		tmp = x / (x - y)
	else:
		tmp = y / (x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -21.0)
		tmp = Float64(Float64(x + y) / Float64(-y));
	elseif (y <= 5.9e-12)
		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 (y <= -21.0)
		tmp = (x + y) / -y;
	elseif (y <= 5.9e-12)
		tmp = x / (x - y);
	else
		tmp = y / (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -21.0], N[(N[(x + y), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, 5.9e-12], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -21

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.1%

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

      1. neg-mul-1 75.1%

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

   5. Simplified 75.1%

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

   if -21 < y < 5.9e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.8%

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

   if 5.9e-12 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.8%

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

Alternative 6: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -28:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -28.0) -1.0 (if (<= y 1.95e-7) (/ x (- x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -28.0) {
		tmp = -1.0;
	} else if (y <= 1.95e-7) {
		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 (y <= (-28.0d0)) then
        tmp = -1.0d0
    else if (y <= 1.95d-7) 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 (y <= -28.0) {
		tmp = -1.0;
	} else if (y <= 1.95e-7) {
		tmp = x / (x - y);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -28.0:
		tmp = -1.0
	elif y <= 1.95e-7:
		tmp = x / (x - y)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -28.0)
		tmp = -1.0;
	elseif (y <= 1.95e-7)
		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 (y <= -28.0)
		tmp = -1.0;
	elseif (y <= 1.95e-7)
		tmp = x / (x - y);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -28.0], -1.0, If[LessEqual[y, 1.95e-7], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -28 or 1.95000000000000012e-7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.6%

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

   if -28 < y < 1.95000000000000012e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.4%

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

Alternative 7: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13.6:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-11}:\\ \;\;\;\;1 + \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -13.6) -1.0 (if (<= y 1.7e-11) (+ 1.0 (/ y x)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -13.6) {
		tmp = -1.0;
	} else if (y <= 1.7e-11) {
		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 (y <= (-13.6d0)) then
        tmp = -1.0d0
    else if (y <= 1.7d-11) 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 (y <= -13.6) {
		tmp = -1.0;
	} else if (y <= 1.7e-11) {
		tmp = 1.0 + (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -13.6:
		tmp = -1.0
	elif y <= 1.7e-11:
		tmp = 1.0 + (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -13.6)
		tmp = -1.0;
	elseif (y <= 1.7e-11)
		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 (y <= -13.6)
		tmp = -1.0;
	elseif (y <= 1.7e-11)
		tmp = 1.0 + (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -13.6], -1.0, If[LessEqual[y, 1.7e-11], N[(1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -13.5999999999999996 or 1.6999999999999999e-11 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.2%

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

   if -13.5999999999999996 < y < 1.6999999999999999e-11

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.8%

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

   4. Taylor expanded in x around inf 82.8%

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

Alternative 8: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -110:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -110.0) -1.0 (if (<= y 9.6e-12) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -110.0) {
		tmp = -1.0;
	} else if (y <= 9.6e-12) {
		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 <= (-110.0d0)) then
        tmp = -1.0d0
    else if (y <= 9.6d-12) 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 <= -110.0) {
		tmp = -1.0;
	} else if (y <= 9.6e-12) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -110.0:
		tmp = -1.0
	elif y <= 9.6e-12:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -110.0)
		tmp = -1.0;
	elseif (y <= 9.6e-12)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -110.0)
		tmp = -1.0;
	elseif (y <= 9.6e-12)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -110.0], -1.0, If[LessEqual[y, 9.6e-12], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -110 or 9.59999999999999948e-12 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.2%

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

   if -110 < y < 9.59999999999999948e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.3%

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

Alternative 9: 51.0% 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 47.3%

   \[\leadsto \color{blue}{-1} \]
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 2024172 
(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)))