Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.6% → 98.8%

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: 76.6% 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: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{if}\;t\_0 \leq -0.05:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{elif}\;t\_0 \leq -1 \cdot 10^{-305} \lor \neg \left(t\_0 \leq 5 \cdot 10^{-297}\right) \land t\_0 \leq 5 \cdot 10^{+75}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (* x 2.0) y) (- x y))))
   (if (<= t_0 -0.05)
     (* x (* 2.0 (/ y (- x y))))
     (if (or (<= t_0 -1e-305) (and (not (<= t_0 5e-297)) (<= t_0 5e+75)))
       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 tmp;
	if (t_0 <= -0.05) {
		tmp = x * (2.0 * (y / (x - y)));
	} else if ((t_0 <= -1e-305) || (!(t_0 <= 5e-297) && (t_0 <= 5e+75))) {
		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) :: tmp
    t_0 = ((x * 2.0d0) * y) / (x - y)
    if (t_0 <= (-0.05d0)) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else if ((t_0 <= (-1d-305)) .or. (.not. (t_0 <= 5d-297)) .and. (t_0 <= 5d+75)) 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 tmp;
	if (t_0 <= -0.05) {
		tmp = x * (2.0 * (y / (x - y)));
	} else if ((t_0 <= -1e-305) || (!(t_0 <= 5e-297) && (t_0 <= 5e+75))) {
		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)
	tmp = 0
	if t_0 <= -0.05:
		tmp = x * (2.0 * (y / (x - y)))
	elif (t_0 <= -1e-305) or (not (t_0 <= 5e-297) and (t_0 <= 5e+75)):
		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))
	tmp = 0.0
	if (t_0 <= -0.05)
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	elseif ((t_0 <= -1e-305) || (!(t_0 <= 5e-297) && (t_0 <= 5e+75)))
		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);
	tmp = 0.0;
	if (t_0 <= -0.05)
		tmp = x * (2.0 * (y / (x - y)));
	elseif ((t_0 <= -1e-305) || (~((t_0 <= 5e-297)) && (t_0 <= 5e+75)))
		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]}, If[LessEqual[t$95$0, -0.05], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$0, -1e-305], And[N[Not[LessEqual[t$95$0, 5e-297]], $MachinePrecision], LessEqual[t$95$0, 5e+75]]], 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 #s(literal 2 binary64)) y) (-.f64 x y)) < -0.050000000000000003

   1. Initial program 45.4%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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 -0.050000000000000003 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -9.99999999999999996e-306 or 5e-297 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < 5.0000000000000002e75

   1. Initial program 99.2%

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

   if -9.99999999999999996e-306 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < 5e-297 or 5.0000000000000002e75 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y))

   1. Initial program 15.4%

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

      1. associate-*r* 99.9%

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

      2. associate-/l* 15.4%

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

      3. add-log-exp 6.5%

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

      4. *-un-lft-identity 6.5%

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

      5. log-prod 6.5%

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

      6. metadata-eval 6.5%

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

      7. add-log-exp 15.4%

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

      8. associate-/l* 99.9%

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

      9. associate-*r* 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. +-lft-identity 99.9%

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

      2. associate-*r* 99.9%

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

      3. associate-*r/ 15.4%

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

      4. associate-*l/ 98.2%

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

      5. associate-/r/ 99.9%

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

      6. div-sub 100.0%

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

      7. sub-neg 100.0%

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

      8. *-inverses 100.0%

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

      9. metadata-eval 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq -0.05:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{elif}\;\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq -1 \cdot 10^{-305} \lor \neg \left(\frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq 5 \cdot 10^{-297}\right) \land \frac{\left(x \cdot 2\right) \cdot y}{x - y} \leq 5 \cdot 10^{+75}:\\ \;\;\;\;\frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x}{y} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-161} \lor \neg \left(y \leq 1.14 \cdot 10^{-89}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.5e-161) (not (<= y 1.14e-89)))
   (* x (* 2.0 (/ y (- x y))))
   (* 2.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.5e-161) || !(y <= 1.14e-89)) {
		tmp = x * (2.0 * (y / (x - y)));
	} 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 <= (-1.5d-161)) .or. (.not. (y <= 1.14d-89))) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.5e-161) || !(y <= 1.14e-89)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.5e-161) or not (y <= 1.14e-89):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.5e-161) || !(y <= 1.14e-89))
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.5e-161) || ~((y <= 1.14e-89)))
		tmp = x * (2.0 * (y / (x - y)));
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.5e-161], N[Not[LessEqual[y, 1.14e-89]], $MachinePrecision]], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.49999999999999994e-161 or 1.14e-89 < y

   1. Initial program 76.6%

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

      1. associate-/l* 97.5%

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

      2. associate-*l* 97.5%

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

   3. Simplified 97.5%

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

   if -1.49999999999999994e-161 < y < 1.14e-89

   1. Initial program 74.6%

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

      1. associate-/l* 67.2%

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

      2. associate-*l* 67.2%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in x around inf 90.3%

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

      1. *-commutative 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-161} \lor \neg \left(y \leq 1.14 \cdot 10^{-89}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-23} \lor \neg \left(y \leq 2.8 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.65e-23) (not (<= y 2.8e-56))) (* x -2.0) (* 2.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.65e-23) || !(y <= 2.8e-56)) {
		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 <= (-1.65d-23)) .or. (.not. (y <= 2.8d-56))) 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 <= -1.65e-23) || !(y <= 2.8e-56)) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.65e-23) or not (y <= 2.8e-56):
		tmp = x * -2.0
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.65e-23) || !(y <= 2.8e-56))
		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 <= -1.65e-23) || ~((y <= 2.8e-56)))
		tmp = x * -2.0;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.65e-23], N[Not[LessEqual[y, 2.8e-56]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6500000000000001e-23 or 2.79999999999999993e-56 < y

   1. Initial program 74.0%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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 77.2%

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

   if -1.6500000000000001e-23 < y < 2.79999999999999993e-56

   1. Initial program 78.1%

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

      1. associate-/l* 73.3%

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

      2. associate-*l* 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in x around inf 83.4%

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

      1. *-commutative 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-23} \lor \neg \left(y \leq 2.8 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.4% 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 75.9%

   \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
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 50.0%

   \[\leadsto x \cdot \color{blue}{-2} \]
6. Add Preprocessing

Developer target: 99.6% 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 2024085 
(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)))