Linear.Projection:perspective from linear-1.19.1.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

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, 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 100.0%

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

Alternative 2: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+111}:\\ \;\;\;\;-1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-122}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.02e+111)
   (- -1.0 (/ x y))
   (if (<= y 9e-122) (+ 1.0 (* 2.0 (/ y x))) (/ y (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.02e+111) {
		tmp = -1.0 - (x / y);
	} else if (y <= 9e-122) {
		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 <= (-1.02d+111)) then
        tmp = (-1.0d0) - (x / y)
    else if (y <= 9d-122) 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 <= -1.02e+111) {
		tmp = -1.0 - (x / y);
	} else if (y <= 9e-122) {
		tmp = 1.0 + (2.0 * (y / x));
	} else {
		tmp = y / (x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.02e+111:
		tmp = -1.0 - (x / y)
	elif y <= 9e-122:
		tmp = 1.0 + (2.0 * (y / x))
	else:
		tmp = y / (x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.02e+111)
		tmp = Float64(-1.0 - Float64(x / y));
	elseif (y <= 9e-122)
		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 <= -1.02e+111)
		tmp = -1.0 - (x / y);
	elseif (y <= 9e-122)
		tmp = 1.0 + (2.0 * (y / x));
	else
		tmp = y / (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.02e+111], N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-122], 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 < -1.02e111

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.3%

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

   4. Taylor expanded in y around inf 82.4%

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

      1. sub-neg 82.4%

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

      2. metadata-eval 82.4%

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

      3. +-commutative 82.4%

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

      4. mul-1-neg 82.4%

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

      5. unsub-neg 82.4%

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

   6. Simplified 82.4%

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

   if -1.02e111 < y < 8.99999999999999959e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.0%

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

   if 8.99999999999999959e-122 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.6%

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

Alternative 3: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+110} \lor \neg \left(y \leq 2.4 \cdot 10^{-114}\right):\\ \;\;\;\;-1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9.8e+110) (not (<= y 2.4e-114)))
   (- -1.0 (/ x y))
   (/ x (- x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9.8e+110) || !(y <= 2.4e-114)) {
		tmp = -1.0 - (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 <= (-9.8d+110)) .or. (.not. (y <= 2.4d-114))) then
        tmp = (-1.0d0) - (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 <= -9.8e+110) || !(y <= 2.4e-114)) {
		tmp = -1.0 - (x / y);
	} else {
		tmp = x / (x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9.8e+110) or not (y <= 2.4e-114):
		tmp = -1.0 - (x / y)
	else:
		tmp = x / (x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9.8e+110) || !(y <= 2.4e-114))
		tmp = Float64(-1.0 - 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 <= -9.8e+110) || ~((y <= 2.4e-114)))
		tmp = -1.0 - (x / y);
	else
		tmp = x / (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9.8e+110], N[Not[LessEqual[y, 2.4e-114]], $MachinePrecision]], N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.80000000000000003e110 or 2.4000000000000001e-114 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.2%

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

   4. Taylor expanded in y around inf 76.2%

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

      1. sub-neg 76.2%

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

      2. metadata-eval 76.2%

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

      3. +-commutative 76.2%

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

      4. mul-1-neg 76.2%

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

      5. unsub-neg 76.2%

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

   6. Simplified 76.2%

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

   if -9.80000000000000003e110 < y < 2.4000000000000001e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+110} \lor \neg \left(y \leq 2.4 \cdot 10^{-114}\right):\\ \;\;\;\;-1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+110} \lor \neg \left(y \leq 2.4 \cdot 10^{-114}\right):\\ \;\;\;\;-1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8e+110) (not (<= y 2.4e-114)))
   (- -1.0 (/ x y))
   (+ 1.0 (/ y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8e+110) || !(y <= 2.4e-114)) {
		tmp = -1.0 - (x / y);
	} else {
		tmp = 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 ((y <= (-8d+110)) .or. (.not. (y <= 2.4d-114))) then
        tmp = (-1.0d0) - (x / y)
    else
        tmp = 1.0d0 + (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8e+110) || !(y <= 2.4e-114)) {
		tmp = -1.0 - (x / y);
	} else {
		tmp = 1.0 + (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8e+110) or not (y <= 2.4e-114):
		tmp = -1.0 - (x / y)
	else:
		tmp = 1.0 + (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8e+110) || !(y <= 2.4e-114))
		tmp = Float64(-1.0 - Float64(x / y));
	else
		tmp = Float64(1.0 + Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8e+110) || ~((y <= 2.4e-114)))
		tmp = -1.0 - (x / y);
	else
		tmp = 1.0 + (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8e+110], N[Not[LessEqual[y, 2.4e-114]], $MachinePrecision]], N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.0000000000000002e110 or 2.4000000000000001e-114 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.2%

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

   4. Taylor expanded in y around inf 76.2%

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

      1. sub-neg 76.2%

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

      2. metadata-eval 76.2%

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

      3. +-commutative 76.2%

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

      4. mul-1-neg 76.2%

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

      5. unsub-neg 76.2%

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

   6. Simplified 76.2%

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

   if -8.0000000000000002e110 < y < 2.4000000000000001e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.3%

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

   4. Taylor expanded in x around inf 82.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+110} \lor \neg \left(y \leq 2.4 \cdot 10^{-114}\right):\\ \;\;\;\;-1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+111}:\\ \;\;\;\;-1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.8e+111)
   (- -1.0 (/ x y))
   (if (<= y 2.4e-114) (/ x (- x y)) (/ y (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.8e+111) {
		tmp = -1.0 - (x / y);
	} else if (y <= 2.4e-114) {
		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 <= (-1.8d+111)) then
        tmp = (-1.0d0) - (x / y)
    else if (y <= 2.4d-114) 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 <= -1.8e+111) {
		tmp = -1.0 - (x / y);
	} else if (y <= 2.4e-114) {
		tmp = x / (x - y);
	} else {
		tmp = y / (x - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.8e+111:
		tmp = -1.0 - (x / y)
	elif y <= 2.4e-114:
		tmp = x / (x - y)
	else:
		tmp = y / (x - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.8e+111)
		tmp = Float64(-1.0 - Float64(x / y));
	elseif (y <= 2.4e-114)
		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 <= -1.8e+111)
		tmp = -1.0 - (x / y);
	elseif (y <= 2.4e-114)
		tmp = x / (x - y);
	else
		tmp = y / (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.8e+111], N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-114], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8000000000000001e111

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.3%

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

   4. Taylor expanded in y around inf 82.4%

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

      1. sub-neg 82.4%

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

      2. metadata-eval 82.4%

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

      3. +-commutative 82.4%

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

      4. mul-1-neg 82.4%

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

      5. unsub-neg 82.4%

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

   6. Simplified 82.4%

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

   if -1.8000000000000001e111 < y < 2.4000000000000001e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.3%

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

   if 2.4000000000000001e-114 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.0%

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

Alternative 6: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+112}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-122}:\\ \;\;\;\;1 + \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.5e+112) -1.0 (if (<= y 9e-122) (+ 1.0 (/ y x)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.5e+112) {
		tmp = -1.0;
	} else if (y <= 9e-122) {
		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 <= (-4.5d+112)) then
        tmp = -1.0d0
    else if (y <= 9d-122) 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 <= -4.5e+112) {
		tmp = -1.0;
	} else if (y <= 9e-122) {
		tmp = 1.0 + (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.5e+112:
		tmp = -1.0
	elif y <= 9e-122:
		tmp = 1.0 + (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.5e+112)
		tmp = -1.0;
	elseif (y <= 9e-122)
		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 <= -4.5e+112)
		tmp = -1.0;
	elseif (y <= 9e-122)
		tmp = 1.0 + (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.5e+112], -1.0, If[LessEqual[y, 9e-122], N[(1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999999e112 or 8.99999999999999959e-122 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.2%

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

   if -4.4999999999999999e112 < y < 8.99999999999999959e-122

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]
   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 82.7%

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

Alternative 7: 71.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+111}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-122}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.8e+111) -1.0 (if (<= y 9e-122) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.8e+111) {
		tmp = -1.0;
	} else if (y <= 9e-122) {
		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 <= (-1.8d+111)) then
        tmp = -1.0d0
    else if (y <= 9d-122) 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 <= -1.8e+111) {
		tmp = -1.0;
	} else if (y <= 9e-122) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.8e+111:
		tmp = -1.0
	elif y <= 9e-122:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.8e+111)
		tmp = -1.0;
	elseif (y <= 9e-122)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.8e+111)
		tmp = -1.0;
	elseif (y <= 9e-122)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.8e+111], -1.0, If[LessEqual[y, 9e-122], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8000000000000001e111 or 8.99999999999999959e-122 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.2%

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

   if -1.8000000000000001e111 < y < 8.99999999999999959e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.4%

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

Alternative 8: 50.5% 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 100.0%

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

3. Taylor expanded in x around 0 48.5%

   \[\leadsto \color{blue}{-1} \]
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 2024185 
(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)))