Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.5% → 99.2%

Time: 4.1s

Alternatives: 4

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: 77.5% 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: 99.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ t_1 := x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -2 \cdot 10^{-305}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-22}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (* x 2.0) y) (- x y))) (t_1 (* x (* 2.0 (/ y (- x y))))))
   (if (<= t_0 -2e-6)
     t_1
     (if (<= t_0 -2e-305)
       t_0
       (if (<= t_0 0.0)
         t_1
         (if (<= t_0 2e-22) t_0 (/ (* x 2.0) (+ (/ x y) -1.0))))))))

C

double code(double x, double y) {
	double t_0 = ((x * 2.0) * y) / (x - y);
	double t_1 = x * (2.0 * (y / (x - y)));
	double tmp;
	if (t_0 <= -2e-6) {
		tmp = t_1;
	} else if (t_0 <= -2e-305) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e-22) {
		tmp = t_0;
	} else {
		tmp = (x * 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((x * 2.0d0) * y) / (x - y)
    t_1 = x * (2.0d0 * (y / (x - y)))
    if (t_0 <= (-2d-6)) then
        tmp = t_1
    else if (t_0 <= (-2d-305)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 2d-22) then
        tmp = t_0
    else
        tmp = (x * 2.0d0) / ((x / y) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((x * 2.0) * y) / (x - y);
	double t_1 = x * (2.0 * (y / (x - y)));
	double tmp;
	if (t_0 <= -2e-6) {
		tmp = t_1;
	} else if (t_0 <= -2e-305) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e-22) {
		tmp = t_0;
	} else {
		tmp = (x * 2.0) / ((x / y) + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((x * 2.0) * y) / (x - y)
	t_1 = x * (2.0 * (y / (x - y)))
	tmp = 0
	if t_0 <= -2e-6:
		tmp = t_1
	elif t_0 <= -2e-305:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 2e-22:
		tmp = t_0
	else:
		tmp = (x * 2.0) / ((x / y) + -1.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
	t_1 = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))))
	tmp = 0.0
	if (t_0 <= -2e-6)
		tmp = t_1;
	elseif (t_0 <= -2e-305)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e-22)
		tmp = t_0;
	else
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x / y) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((x * 2.0) * y) / (x - y);
	t_1 = x * (2.0 * (y / (x - y)));
	tmp = 0.0;
	if (t_0 <= -2e-6)
		tmp = t_1;
	elseif (t_0 <= -2e-305)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e-22)
		tmp = t_0;
	else
		tmp = (x * 2.0) / ((x / y) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e-6], t$95$1, If[LessEqual[t$95$0, -2e-305], t$95$0, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 2e-22], t$95$0, N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y)) < -1.99999999999999991e-6 or -1.99999999999999999e-305 < (/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y)) < 0.0

   1. Initial program 29.1%

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

      1. associate-/l* 99.9%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   if -1.99999999999999991e-6 < (/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y)) < -1.99999999999999999e-305 or 0.0 < (/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y)) < 2.0000000000000001e-22

   1. Initial program 98.6%

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

   if 2.0000000000000001e-22 < (/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y))

   1. Initial program 52.4%

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

      1. associate-/l* 99.8%

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

      2. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-*r* 99.8%

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

      2. associate-/l* 52.4%

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

      3. add-log-exp 13.5%

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

      4. *-un-lft-identity 13.5%

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

      5. log-prod 13.5%

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

      6. metadata-eval 13.5%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\left(x \cdot 2\right) \cdot y}{x - y}}\right) \]

      7. add-log-exp 52.4%

         \[\leadsto 0 + \color{blue}{\frac{\left(x \cdot 2\right) \cdot y}{x - y}} \]

      8. associate-/l* 99.8%

         \[\leadsto 0 + \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      9. associate-*r* 99.8%

         \[\leadsto 0 + \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{0 + x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   7. Step-by-step derivation

      1. +-lft-identity 99.8%

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

      2. associate-*r* 99.8%

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

      3. associate-*r/ 52.4%

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

      4. associate-*l/ 99.6%

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

      5. associate-/r/ 99.7%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   8. Simplified 99.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq -2 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq -2 \cdot 10^{-305}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq 0:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq 2 \cdot 10^{-22}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+142} \lor \neg \left(x \leq 3.5 \cdot 10^{+218}\right):\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.2e+142) (not (<= x 3.5e+218)))
   (* 2.0 y)
   (* x (* 2.0 (/ y (- x y))))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.2e+142) || !(x <= 3.5e+218)) {
		tmp = 2.0 * y;
	} 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 <= (-5.2d+142)) .or. (.not. (x <= 3.5d+218))) then
        tmp = 2.0d0 * y
    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 <= -5.2e+142) || !(x <= 3.5e+218)) {
		tmp = 2.0 * y;
	} else {
		tmp = x * (2.0 * (y / (x - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.2e+142) or not (x <= 3.5e+218):
		tmp = 2.0 * y
	else:
		tmp = x * (2.0 * (y / (x - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.2e+142) || !(x <= 3.5e+218))
		tmp = Float64(2.0 * y);
	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 <= -5.2e+142) || ~((x <= 3.5e+218)))
		tmp = 2.0 * y;
	else
		tmp = x * (2.0 * (y / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.2e+142], N[Not[LessEqual[x, 3.5e+218]], $MachinePrecision]], N[(2.0 * y), $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 < -5.20000000000000043e142 or 3.50000000000000019e218 < x

   1. Initial program 71.6%

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

      1. associate-/l* 54.2%

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

      2. associate-*l* 54.2%

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

   3. Simplified 54.2%

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

   5. Taylor expanded in x around inf 92.1%

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

      1. *-commutative 92.1%

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

   7. Simplified 92.1%

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

   if -5.20000000000000043e142 < x < 3.50000000000000019e218

   1. Initial program 75.0%

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

      1. associate-/l* 97.0%

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

      2. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+142} \lor \neg \left(x \leq 3.5 \cdot 10^{+218}\right):\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-32} \lor \neg \left(y \leq 26000\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.5e-32) (not (<= y 26000.0))) (* x -2.0) (* 2.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e-32) || !(y <= 26000.0)) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * 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 <= (-4.5d-32)) .or. (.not. (y <= 26000.0d0))) then
        tmp = x * (-2.0d0)
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e-32) || !(y <= 26000.0)) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.5e-32) or not (y <= 26000.0):
		tmp = x * -2.0
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.5e-32) || !(y <= 26000.0))
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.5e-32) || ~((y <= 26000.0)))
		tmp = x * -2.0;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.5e-32], N[Not[LessEqual[y, 26000.0]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.50000000000000005e-32 or 26000 < y

   1. Initial program 75.7%

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

      1. associate-/l* 99.9%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 76.6%

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

   if -4.50000000000000005e-32 < y < 26000

   1. Initial program 72.6%

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

      1. associate-/l* 73.1%

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

      2. associate-*l* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in x around inf 78.5%

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

      1. *-commutative 78.5%

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

   7. Simplified 78.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-32} \lor \neg \left(y \leq 26000\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.6% 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 74.3%

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

   1. associate-/l* 87.5%

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

   2. associate-*l* 87.5%

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

3. Simplified 87.5%

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

5. Taylor expanded in y around inf 51.9%

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

6. Final simplification 51.9%

   \[\leadsto x \cdot -2 \]
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 2024054 
(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)))