Linear.Projection:perspective from linear-1.19.1.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

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: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+29} \lor \neg \left(x \leq 4.1 \cdot 10^{-88}\right) \land \left(x \leq 7.8 \cdot 10^{-46} \lor \neg \left(x \leq 70000\right)\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.5e+29)
         (and (not (<= x 4.1e-88)) (or (<= x 7.8e-46) (not (<= x 70000.0)))))
   (+ 1.0 (* 2.0 (/ y x)))
   (+ (* -2.0 (/ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.5e+29) || (!(x <= 4.1e-88) && ((x <= 7.8e-46) || !(x <= 70000.0)))) {
		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 <= (-5.5d+29)) .or. (.not. (x <= 4.1d-88)) .and. (x <= 7.8d-46) .or. (.not. (x <= 70000.0d0))) 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 <= -5.5e+29) || (!(x <= 4.1e-88) && ((x <= 7.8e-46) || !(x <= 70000.0)))) {
		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 <= -5.5e+29) or (not (x <= 4.1e-88) and ((x <= 7.8e-46) or not (x <= 70000.0))):
		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 <= -5.5e+29) || (!(x <= 4.1e-88) && ((x <= 7.8e-46) || !(x <= 70000.0))))
		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 <= -5.5e+29) || (~((x <= 4.1e-88)) && ((x <= 7.8e-46) || ~((x <= 70000.0)))))
		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, -5.5e+29], And[N[Not[LessEqual[x, 4.1e-88]], $MachinePrecision], Or[LessEqual[x, 7.8e-46], N[Not[LessEqual[x, 70000.0]], $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 < -5.5e29 or 4.1000000000000001e-88 < x < 7.8000000000000005e-46 or 7e4 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.0%

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

   if -5.5e29 < x < 4.1000000000000001e-88 or 7.8000000000000005e-46 < x < 7e4

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+29} \lor \neg \left(x \leq 4.1 \cdot 10^{-88}\right) \land \left(x \leq 7.8 \cdot 10^{-46} \lor \neg \left(x \leq 70000\right)\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + 2 \cdot \frac{y}{x}\\ t_1 := \frac{y}{x - y}\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{x - y}\\ \mathbf{elif}\;x \leq 24000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* 2.0 (/ y x)))) (t_1 (/ y (- x y))))
   (if (<= x -6.8e+23)
     t_0
     (if (<= x 8e-77)
       t_1
       (if (<= x 7e-46) (/ x (- x y)) (if (<= x 24000.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (2.0 * (y / x));
	double t_1 = y / (x - y);
	double tmp;
	if (x <= -6.8e+23) {
		tmp = t_0;
	} else if (x <= 8e-77) {
		tmp = t_1;
	} else if (x <= 7e-46) {
		tmp = x / (x - y);
	} else if (x <= 24000.0) {
		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 = 1.0d0 + (2.0d0 * (y / x))
    t_1 = y / (x - y)
    if (x <= (-6.8d+23)) then
        tmp = t_0
    else if (x <= 8d-77) then
        tmp = t_1
    else if (x <= 7d-46) then
        tmp = x / (x - y)
    else if (x <= 24000.0d0) 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 = 1.0 + (2.0 * (y / x));
	double t_1 = y / (x - y);
	double tmp;
	if (x <= -6.8e+23) {
		tmp = t_0;
	} else if (x <= 8e-77) {
		tmp = t_1;
	} else if (x <= 7e-46) {
		tmp = x / (x - y);
	} else if (x <= 24000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (2.0 * (y / x))
	t_1 = y / (x - y)
	tmp = 0
	if x <= -6.8e+23:
		tmp = t_0
	elif x <= 8e-77:
		tmp = t_1
	elif x <= 7e-46:
		tmp = x / (x - y)
	elif x <= 24000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(2.0 * Float64(y / x)))
	t_1 = Float64(y / Float64(x - y))
	tmp = 0.0
	if (x <= -6.8e+23)
		tmp = t_0;
	elseif (x <= 8e-77)
		tmp = t_1;
	elseif (x <= 7e-46)
		tmp = Float64(x / Float64(x - y));
	elseif (x <= 24000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (2.0 * (y / x));
	t_1 = y / (x - y);
	tmp = 0.0;
	if (x <= -6.8e+23)
		tmp = t_0;
	elseif (x <= 8e-77)
		tmp = t_1;
	elseif (x <= 7e-46)
		tmp = x / (x - y);
	elseif (x <= 24000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e+23], t$95$0, If[LessEqual[x, 8e-77], t$95$1, If[LessEqual[x, 7e-46], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 24000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.79999999999999983e23 or 24000 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.3%

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

   if -6.79999999999999983e23 < x < 7.9999999999999994e-77 or 7.0000000000000004e-46 < x < 24000

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.9%

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

   if 7.9999999999999994e-77 < x < 7.0000000000000004e-46

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.8%

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

Alternative 4: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+25} \lor \neg \left(x \leq 4.1 \cdot 10^{-88}\right) \land \left(x \leq 7 \cdot 10^{-46} \lor \neg \left(x \leq 37000\right)\right):\\ \;\;\;\;1 + \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.6e+25)
         (and (not (<= x 4.1e-88)) (or (<= x 7e-46) (not (<= x 37000.0)))))
   (+ 1.0 (/ y x))
   -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.6e+25) || (!(x <= 4.1e-88) && ((x <= 7e-46) || !(x <= 37000.0)))) {
		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 <= (-5.6d+25)) .or. (.not. (x <= 4.1d-88)) .and. (x <= 7d-46) .or. (.not. (x <= 37000.0d0))) 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 <= -5.6e+25) || (!(x <= 4.1e-88) && ((x <= 7e-46) || !(x <= 37000.0)))) {
		tmp = 1.0 + (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.6e+25) or (not (x <= 4.1e-88) and ((x <= 7e-46) or not (x <= 37000.0))):
		tmp = 1.0 + (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.6e+25) || (!(x <= 4.1e-88) && ((x <= 7e-46) || !(x <= 37000.0))))
		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 <= -5.6e+25) || (~((x <= 4.1e-88)) && ((x <= 7e-46) || ~((x <= 37000.0)))))
		tmp = 1.0 + (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.6e+25], And[N[Not[LessEqual[x, 4.1e-88]], $MachinePrecision], Or[LessEqual[x, 7e-46], N[Not[LessEqual[x, 37000.0]], $MachinePrecision]]]], N[(1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -5.6000000000000003e25 or 4.1000000000000001e-88 < x < 7.0000000000000004e-46 or 37000 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.1%

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

   4. Taylor expanded in x around inf 79.3%

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

   if -5.6000000000000003e25 < x < 4.1000000000000001e-88 or 7.0000000000000004e-46 < x < 37000

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+25} \lor \neg \left(x \leq 4.1 \cdot 10^{-88}\right) \land \left(x \leq 7 \cdot 10^{-46} \lor \neg \left(x \leq 37000\right)\right):\\ \;\;\;\;1 + \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{y}{x}\\ t_1 := \frac{y}{x - y}\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{x - y}\\ \mathbf{elif}\;x \leq 180000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ y x))) (t_1 (/ y (- x y))))
   (if (<= x -2.3e+31)
     t_0
     (if (<= x 7.2e-77)
       t_1
       (if (<= x 6.8e-46) (/ x (- x y)) (if (<= x 180000.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (y / x);
	double t_1 = y / (x - y);
	double tmp;
	if (x <= -2.3e+31) {
		tmp = t_0;
	} else if (x <= 7.2e-77) {
		tmp = t_1;
	} else if (x <= 6.8e-46) {
		tmp = x / (x - y);
	} else if (x <= 180000.0) {
		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 = 1.0d0 + (y / x)
    t_1 = y / (x - y)
    if (x <= (-2.3d+31)) then
        tmp = t_0
    else if (x <= 7.2d-77) then
        tmp = t_1
    else if (x <= 6.8d-46) then
        tmp = x / (x - y)
    else if (x <= 180000.0d0) 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 = 1.0 + (y / x);
	double t_1 = y / (x - y);
	double tmp;
	if (x <= -2.3e+31) {
		tmp = t_0;
	} else if (x <= 7.2e-77) {
		tmp = t_1;
	} else if (x <= 6.8e-46) {
		tmp = x / (x - y);
	} else if (x <= 180000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (y / x)
	t_1 = y / (x - y)
	tmp = 0
	if x <= -2.3e+31:
		tmp = t_0
	elif x <= 7.2e-77:
		tmp = t_1
	elif x <= 6.8e-46:
		tmp = x / (x - y)
	elif x <= 180000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(y / x))
	t_1 = Float64(y / Float64(x - y))
	tmp = 0.0
	if (x <= -2.3e+31)
		tmp = t_0;
	elseif (x <= 7.2e-77)
		tmp = t_1;
	elseif (x <= 6.8e-46)
		tmp = Float64(x / Float64(x - y));
	elseif (x <= 180000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (y / x);
	t_1 = y / (x - y);
	tmp = 0.0;
	if (x <= -2.3e+31)
		tmp = t_0;
	elseif (x <= 7.2e-77)
		tmp = t_1;
	elseif (x <= 6.8e-46)
		tmp = x / (x - y);
	elseif (x <= 180000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+31], t$95$0, If[LessEqual[x, 7.2e-77], t$95$1, If[LessEqual[x, 6.8e-46], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 180000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3e31 or 1.8e5 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.3%

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

   4. Taylor expanded in x around inf 80.6%

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

   if -2.3e31 < x < 7.2e-77 or 6.79999999999999992e-46 < x < 1.8e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.9%

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

   if 7.2e-77 < x < 6.79999999999999992e-46

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.8%

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

Alternative 6: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{y}{x}\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-88}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{x - y}\\ \mathbf{elif}\;x \leq 800000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ y x))))
   (if (<= x -3.4e+24)
     t_0
     (if (<= x 4.2e-88)
       -1.0
       (if (<= x 7e-46) (/ x (- x y)) (if (<= x 800000.0) -1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (y / x);
	double tmp;
	if (x <= -3.4e+24) {
		tmp = t_0;
	} else if (x <= 4.2e-88) {
		tmp = -1.0;
	} else if (x <= 7e-46) {
		tmp = x / (x - y);
	} else if (x <= 800000.0) {
		tmp = -1.0;
	} 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) :: tmp
    t_0 = 1.0d0 + (y / x)
    if (x <= (-3.4d+24)) then
        tmp = t_0
    else if (x <= 4.2d-88) then
        tmp = -1.0d0
    else if (x <= 7d-46) then
        tmp = x / (x - y)
    else if (x <= 800000.0d0) then
        tmp = -1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (y / x);
	double tmp;
	if (x <= -3.4e+24) {
		tmp = t_0;
	} else if (x <= 4.2e-88) {
		tmp = -1.0;
	} else if (x <= 7e-46) {
		tmp = x / (x - y);
	} else if (x <= 800000.0) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (y / x)
	tmp = 0
	if x <= -3.4e+24:
		tmp = t_0
	elif x <= 4.2e-88:
		tmp = -1.0
	elif x <= 7e-46:
		tmp = x / (x - y)
	elif x <= 800000.0:
		tmp = -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(y / x))
	tmp = 0.0
	if (x <= -3.4e+24)
		tmp = t_0;
	elseif (x <= 4.2e-88)
		tmp = -1.0;
	elseif (x <= 7e-46)
		tmp = Float64(x / Float64(x - y));
	elseif (x <= 800000.0)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (y / x);
	tmp = 0.0;
	if (x <= -3.4e+24)
		tmp = t_0;
	elseif (x <= 4.2e-88)
		tmp = -1.0;
	elseif (x <= 7e-46)
		tmp = x / (x - y);
	elseif (x <= 800000.0)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+24], t$95$0, If[LessEqual[x, 4.2e-88], -1.0, If[LessEqual[x, 7e-46], N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 800000.0], -1.0, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4000000000000001e24 or 8e5 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.3%

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

   4. Taylor expanded in x around inf 80.6%

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

   if -3.4000000000000001e24 < x < 4.1999999999999999e-88 or 7.0000000000000004e-46 < x < 8e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.8%

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

   if 4.1999999999999999e-88 < x < 7.0000000000000004e-46

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.2%

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

Alternative 7: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+27}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-88}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-46}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 115000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4e+27)
   1.0
   (if (<= x 4.1e-88)
     -1.0
     (if (<= x 7.8e-46) 1.0 (if (<= x 115000.0) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4e+27) {
		tmp = 1.0;
	} else if (x <= 4.1e-88) {
		tmp = -1.0;
	} else if (x <= 7.8e-46) {
		tmp = 1.0;
	} else if (x <= 115000.0) {
		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 <= (-4d+27)) then
        tmp = 1.0d0
    else if (x <= 4.1d-88) then
        tmp = -1.0d0
    else if (x <= 7.8d-46) then
        tmp = 1.0d0
    else if (x <= 115000.0d0) 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 <= -4e+27) {
		tmp = 1.0;
	} else if (x <= 4.1e-88) {
		tmp = -1.0;
	} else if (x <= 7.8e-46) {
		tmp = 1.0;
	} else if (x <= 115000.0) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4e+27:
		tmp = 1.0
	elif x <= 4.1e-88:
		tmp = -1.0
	elif x <= 7.8e-46:
		tmp = 1.0
	elif x <= 115000.0:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4e+27)
		tmp = 1.0;
	elseif (x <= 4.1e-88)
		tmp = -1.0;
	elseif (x <= 7.8e-46)
		tmp = 1.0;
	elseif (x <= 115000.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4e+27)
		tmp = 1.0;
	elseif (x <= 4.1e-88)
		tmp = -1.0;
	elseif (x <= 7.8e-46)
		tmp = 1.0;
	elseif (x <= 115000.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4e+27], 1.0, If[LessEqual[x, 4.1e-88], -1.0, If[LessEqual[x, 7.8e-46], 1.0, If[LessEqual[x, 115000.0], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0000000000000001e27 or 4.1000000000000001e-88 < x < 7.8000000000000005e-46 or 115000 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.6%

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

   if -4.0000000000000001e27 < x < 4.1000000000000001e-88 or 7.8000000000000005e-46 < x < 115000

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.8%

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

Alternative 8: 49.2% 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 50.7%

   \[\leadsto \color{blue}{-1} \]
4. 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 2024111 
(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)))