Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.8% → 99.3%

Time: 5.0s

Alternatives: 5

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 77.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-35} \lor \neg \left(y \leq 2.8 \cdot 10^{-99}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x \cdot 2\right) \cdot \frac{1}{x - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4e-35) (not (<= y 2.8e-99)))
   (* x (* 2.0 (/ y (- x y))))
   (* y (* (* x 2.0) (/ 1.0 (- x y))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4e-35) || !(y <= 2.8e-99)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y * ((x * 2.0) * (1.0 / (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 <= (-4d-35)) .or. (.not. (y <= 2.8d-99))) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else
        tmp = y * ((x * 2.0d0) * (1.0d0 / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4e-35) || !(y <= 2.8e-99)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y * ((x * 2.0) * (1.0 / (x - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4e-35) or not (y <= 2.8e-99):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = y * ((x * 2.0) * (1.0 / (x - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4e-35) || !(y <= 2.8e-99))
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	else
		tmp = Float64(y * Float64(Float64(x * 2.0) * Float64(1.0 / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4e-35) || ~((y <= 2.8e-99)))
		tmp = x * (2.0 * (y / (x - y)));
	else
		tmp = y * ((x * 2.0) * (1.0 / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4e-35], N[Not[LessEqual[y, 2.8e-99]], $MachinePrecision]], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * 2.0), $MachinePrecision] * N[(1.0 / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000003e-35 or 2.8000000000000001e-99 < y

   1. Initial program 74.6%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 100.0%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   if -4.00000000000000003e-35 < y < 2.8000000000000001e-99

   1. Initial program 73.1%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. div-inv 72.8%

         \[\leadsto \color{blue}{\left(\left(x \cdot 2\right) \cdot y\right) \cdot \frac{1}{x - y}} \]

      2. *-commutative 72.8%

         \[\leadsto \color{blue}{\left(y \cdot \left(x \cdot 2\right)\right)} \cdot \frac{1}{x - y} \]

      3. associate-*l* 99.8%

         \[\leadsto \color{blue}{y \cdot \left(\left(x \cdot 2\right) \cdot \frac{1}{x - y}\right)} \]

   4. Applied egg-rr 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-35} \lor \neg \left(y \leq 2.8 \cdot 10^{-99}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x \cdot 2\right) \cdot \frac{1}{x - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(x \cdot 2\right)}{x - y}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-71} \lor \neg \left(t\_0 \leq -5 \cdot 10^{-300}\right) \land \left(t\_0 \leq 0 \lor \neg \left(t\_0 \leq 5 \cdot 10^{-117}\right)\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (* x 2.0)) (- x y))))
   (if (or (<= t_0 -5e-71)
           (and (not (<= t_0 -5e-300))
                (or (<= t_0 0.0) (not (<= t_0 5e-117)))))
     (* x (* 2.0 (/ y (- x y))))
     t_0)))

C

double code(double x, double y) {
	double t_0 = (y * (x * 2.0)) / (x - y);
	double tmp;
	if ((t_0 <= -5e-71) || (!(t_0 <= -5e-300) && ((t_0 <= 0.0) || !(t_0 <= 5e-117)))) {
		tmp = x * (2.0 * (y / (x - y)));
	} 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 = (y * (x * 2.0d0)) / (x - y)
    if ((t_0 <= (-5d-71)) .or. (.not. (t_0 <= (-5d-300))) .and. (t_0 <= 0.0d0) .or. (.not. (t_0 <= 5d-117))) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (x * 2.0)) / (x - y);
	double tmp;
	if ((t_0 <= -5e-71) || (!(t_0 <= -5e-300) && ((t_0 <= 0.0) || !(t_0 <= 5e-117)))) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (x * 2.0)) / (x - y)
	tmp = 0
	if (t_0 <= -5e-71) or (not (t_0 <= -5e-300) and ((t_0 <= 0.0) or not (t_0 <= 5e-117))):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(x * 2.0)) / Float64(x - y))
	tmp = 0.0
	if ((t_0 <= -5e-71) || (!(t_0 <= -5e-300) && ((t_0 <= 0.0) || !(t_0 <= 5e-117))))
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (x * 2.0)) / (x - y);
	tmp = 0.0;
	if ((t_0 <= -5e-71) || (~((t_0 <= -5e-300)) && ((t_0 <= 0.0) || ~((t_0 <= 5e-117)))))
		tmp = x * (2.0 * (y / (x - y)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e-71], And[N[Not[LessEqual[t$95$0, -5e-300]], $MachinePrecision], Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 5e-117]], $MachinePrecision]]]], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -4.99999999999999998e-71 or -4.99999999999999996e-300 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < 0.0 or 5e-117 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y))

   1. Initial program 53.1%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 100.0%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   if -4.99999999999999998e-71 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -4.99999999999999996e-300 or 0.0 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < 5e-117

   1. Initial program 98.4%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(x \cdot 2\right)}{x - y} \leq -5 \cdot 10^{-71} \lor \neg \left(\frac{y \cdot \left(x \cdot 2\right)}{x - y} \leq -5 \cdot 10^{-300}\right) \land \left(\frac{y \cdot \left(x \cdot 2\right)}{x - y} \leq 0 \lor \neg \left(\frac{y \cdot \left(x \cdot 2\right)}{x - y} \leq 5 \cdot 10^{-117}\right)\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 2\right)}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+17} \lor \neg \left(x \leq -1.25 \cdot 10^{-52} \lor \neg \left(x \leq -2.5 \cdot 10^{-90}\right) \land x \leq 3.5 \cdot 10^{-69}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -6.8e+17)
         (not
          (or (<= x -1.25e-52) (and (not (<= x -2.5e-90)) (<= x 3.5e-69)))))
   (* y 2.0)
   (* x -2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -6.8e+17) || !((x <= -1.25e-52) || (!(x <= -2.5e-90) && (x <= 3.5e-69)))) {
		tmp = y * 2.0;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-6.8d+17)) .or. (.not. (x <= (-1.25d-52)) .or. (.not. (x <= (-2.5d-90))) .and. (x <= 3.5d-69))) then
        tmp = y * 2.0d0
    else
        tmp = x * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -6.8e+17) || !((x <= -1.25e-52) || (!(x <= -2.5e-90) && (x <= 3.5e-69)))) {
		tmp = y * 2.0;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -6.8e+17) or not ((x <= -1.25e-52) or (not (x <= -2.5e-90) and (x <= 3.5e-69))):
		tmp = y * 2.0
	else:
		tmp = x * -2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -6.8e+17) || !((x <= -1.25e-52) || (!(x <= -2.5e-90) && (x <= 3.5e-69))))
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(x * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -6.8e+17) || ~(((x <= -1.25e-52) || (~((x <= -2.5e-90)) && (x <= 3.5e-69)))))
		tmp = y * 2.0;
	else
		tmp = x * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -6.8e+17], N[Not[Or[LessEqual[x, -1.25e-52], And[N[Not[LessEqual[x, -2.5e-90]], $MachinePrecision], LessEqual[x, 3.5e-69]]]], $MachinePrecision]], N[(y * 2.0), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.8e17 or -1.25e-52 < x < -2.5000000000000001e-90 or 3.5000000000000001e-69 < x

   1. Initial program 72.3%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 80.0%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 80.0%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 77.8%

      \[\leadsto \color{blue}{2 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto \color{blue}{y \cdot 2} \]

   7. Simplified 77.8%

      \[\leadsto \color{blue}{y \cdot 2} \]

   if -6.8e17 < x < -1.25e-52 or -2.5000000000000001e-90 < x < 3.5000000000000001e-69

   1. Initial program 76.3%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 100.0%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.3%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+17} \lor \neg \left(x \leq -1.25 \cdot 10^{-52} \lor \neg \left(x \leq -2.5 \cdot 10^{-90}\right) \land x \leq 3.5 \cdot 10^{-69}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+150} \lor \neg \left(x \leq 9 \cdot 10^{+87}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.65e+150) (not (<= x 9e+87)))
   (* y 2.0)
   (* x (* 2.0 (/ y (- x y))))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.65e+150) || !(x <= 9e+87)) {
		tmp = y * 2.0;
	} else {
		tmp = x * (2.0 * (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 <= (-2.65d+150)) .or. (.not. (x <= 9d+87))) then
        tmp = y * 2.0d0
    else
        tmp = x * (2.0d0 * (y / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.65e+150) || !(x <= 9e+87)) {
		tmp = y * 2.0;
	} else {
		tmp = x * (2.0 * (y / (x - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.65e+150) or not (x <= 9e+87):
		tmp = y * 2.0
	else:
		tmp = x * (2.0 * (y / (x - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.65e+150) || !(x <= 9e+87))
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.65e+150) || ~((x <= 9e+87)))
		tmp = y * 2.0;
	else
		tmp = x * (2.0 * (y / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.65e+150], N[Not[LessEqual[x, 9e+87]], $MachinePrecision]], N[(y * 2.0), $MachinePrecision], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.65000000000000007e150 or 9.0000000000000005e87 < x

   1. Initial program 60.8%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 65.7%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 65.7%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 65.7%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 89.6%

      \[\leadsto \color{blue}{2 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 89.6%

         \[\leadsto \color{blue}{y \cdot 2} \]

   7. Simplified 89.6%

      \[\leadsto \color{blue}{y \cdot 2} \]

   if -2.65000000000000007e150 < x < 9.0000000000000005e87

   1. Initial program 80.0%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.4%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 98.4%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 98.4%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+150} \lor \neg \left(x \leq 9 \cdot 10^{+87}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x \cdot -2 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x -2.0))

C

double code(double x, double y) {
	return x * -2.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (-2.0d0)
end function

Java

public static double code(double x, double y) {
	return x * -2.0;
}

Python

def code(x, y):
	return x * -2.0

Julia

function code(x, y)
	return Float64(x * -2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = x * -2.0;
end

Wolfram

code[x_, y_] := N[(x * -2.0), $MachinePrecision]

Derivation

1. Initial program 74.0%

   \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
2. Step-by-step derivation

   1. associate-/l* 88.2%

      \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

   2. associate-*l* 88.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

3. Simplified 88.2%

   \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 49.5%

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

6. Final simplification 49.5%

   \[\leadsto x \cdot -2 \]
7. Add Preprocessing

Developer target: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ (* 2.0 x) (- x y)) y)))
   (if (< x -1.7210442634149447e+81)
     t_0
     (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} 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 = ((2.0d0 * x) / (x - y)) * y
    if (x < (-1.7210442634149447d+81)) then
        tmp = t_0
    else if (x < 83645045635564430.0d0) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    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) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((2.0 * x) / (x - y)) * y
	tmp = 0
	if x < -1.7210442634149447e+81:
		tmp = t_0
	elif x < 83645045635564430.0:
		tmp = (x * 2.0) / ((x - y) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(2.0 * x) / Float64(x - y)) * y)
	tmp = 0.0
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((2.0 * x) / (x - y)) * y;
	tmp = 0.0;
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = (x * 2.0) / ((x - y) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[Less[x, -1.7210442634149447e+81], t$95$0, If[Less[x, 83645045635564430.0], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024059 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :alt
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))