Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.0% → 99.3%

Time: 5.1s

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: 77.0% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-9} \lor \neg \left(y \leq 5.8 \cdot 10^{-80}\right):\\ \;\;\;\;2 \cdot \frac{x}{\frac{x}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{2}{x - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8e-9) (not (<= y 5.8e-80)))
   (* 2.0 (/ x (+ (/ x y) -1.0)))
   (* y (* x (/ 2.0 (- x y))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8e-9) || !(y <= 5.8e-80)) {
		tmp = 2.0 * (x / ((x / y) + -1.0));
	} else {
		tmp = y * (x * (2.0 / (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 <= (-8d-9)) .or. (.not. (y <= 5.8d-80))) then
        tmp = 2.0d0 * (x / ((x / y) + (-1.0d0)))
    else
        tmp = y * (x * (2.0d0 / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8e-9) || !(y <= 5.8e-80)) {
		tmp = 2.0 * (x / ((x / y) + -1.0));
	} else {
		tmp = y * (x * (2.0 / (x - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8e-9) or not (y <= 5.8e-80):
		tmp = 2.0 * (x / ((x / y) + -1.0))
	else:
		tmp = y * (x * (2.0 / (x - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8e-9) || !(y <= 5.8e-80))
		tmp = Float64(2.0 * Float64(x / Float64(Float64(x / y) + -1.0)));
	else
		tmp = Float64(y * Float64(x * Float64(2.0 / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8e-9) || ~((y <= 5.8e-80)))
		tmp = 2.0 * (x / ((x / y) + -1.0));
	else
		tmp = y * (x * (2.0 / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8e-9], N[Not[LessEqual[y, 5.8e-80]], $MachinePrecision]], N[(2.0 * N[(x / N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * N[(2.0 / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.0000000000000005e-9 or 5.79999999999999996e-80 < y

   1. Initial program 79.1%

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

      1. associate-*r* 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. div-sub 100.0%

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

      4. sub-neg 100.0%

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

      5. *-inverses 100.0%

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

      6. metadata-eval 100.0%

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

   8. Simplified 100.0%

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

   if -8.0000000000000005e-9 < y < 5.79999999999999996e-80

   1. Initial program 69.5%

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

      1. associate-*l* 69.5%

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

      2. associate-*r/ 72.2%

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

      3. associate-*l/ 72.0%

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

      4. associate-*r* 99.8%

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

   4. Applied egg-rr 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-9} \lor \neg \left(y \leq 5.8 \cdot 10^{-80}\right):\\ \;\;\;\;2 \cdot \frac{x}{\frac{x}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{2}{x - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+171} \lor \neg \left(x \leq -8.6 \cdot 10^{+122}\right) \land \left(x \leq -5.8 \cdot 10^{-28} \lor \neg \left(x \leq 2.3 \cdot 10^{+64}\right)\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.85e+171)
         (and (not (<= x -8.6e+122))
              (or (<= x -5.8e-28) (not (<= x 2.3e+64)))))
   (* y 2.0)
   (* x -2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.85e+171) || (!(x <= -8.6e+122) && ((x <= -5.8e-28) || !(x <= 2.3e+64)))) {
		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 <= (-2.85d+171)) .or. (.not. (x <= (-8.6d+122))) .and. (x <= (-5.8d-28)) .or. (.not. (x <= 2.3d+64))) 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 <= -2.85e+171) || (!(x <= -8.6e+122) && ((x <= -5.8e-28) || !(x <= 2.3e+64)))) {
		tmp = y * 2.0;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.85e+171) or (not (x <= -8.6e+122) and ((x <= -5.8e-28) or not (x <= 2.3e+64))):
		tmp = y * 2.0
	else:
		tmp = x * -2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.85e+171) || (!(x <= -8.6e+122) && ((x <= -5.8e-28) || !(x <= 2.3e+64))))
		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 <= -2.85e+171) || (~((x <= -8.6e+122)) && ((x <= -5.8e-28) || ~((x <= 2.3e+64)))))
		tmp = y * 2.0;
	else
		tmp = x * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.85e+171], And[N[Not[LessEqual[x, -8.6e+122]], $MachinePrecision], Or[LessEqual[x, -5.8e-28], N[Not[LessEqual[x, 2.3e+64]], $MachinePrecision]]]], N[(y * 2.0), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.85e171 or -8.59999999999999943e122 < x < -5.80000000000000026e-28 or 2.3e64 < x

   1. Initial program 80.4%

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

      1. associate-/l* 70.7%

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

      2. associate-*l* 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in x around inf 85.2%

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

      1. *-commutative 85.2%

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

   7. Simplified 85.2%

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

   if -2.85e171 < x < -8.59999999999999943e122 or -5.80000000000000026e-28 < x < 2.3e64

   1. Initial program 70.9%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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 74.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+171} \lor \neg \left(x \leq -8.6 \cdot 10^{+122}\right) \land \left(x \leq -5.8 \cdot 10^{-28} \lor \neg \left(x \leq 2.3 \cdot 10^{+64}\right)\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+172} \lor \neg \left(x \leq 3.1 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -8.8e+172) (not (<= x 3.1e+124)))
   (* y 2.0)
   (* x (* 2.0 (/ y (- x y))))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -8.8e+172) || !(x <= 3.1e+124)) {
		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 <= (-8.8d+172)) .or. (.not. (x <= 3.1d+124))) 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 <= -8.8e+172) || !(x <= 3.1e+124)) {
		tmp = y * 2.0;
	} else {
		tmp = x * (2.0 * (y / (x - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -8.8e+172) or not (x <= 3.1e+124):
		tmp = y * 2.0
	else:
		tmp = x * (2.0 * (y / (x - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -8.8e+172) || !(x <= 3.1e+124))
		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 <= -8.8e+172) || ~((x <= 3.1e+124)))
		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, -8.8e+172], N[Not[LessEqual[x, 3.1e+124]], $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 < -8.8000000000000005e172 or 3.1000000000000002e124 < x

   1. Initial program 69.2%

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

      1. associate-/l* 56.3%

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

      2. associate-*l* 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in x around inf 89.4%

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

      1. *-commutative 89.4%

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

   7. Simplified 89.4%

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

   if -8.8000000000000005e172 < x < 3.1000000000000002e124

   1. Initial program 76.8%

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

      1. associate-/l* 98.3%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+172} \lor \neg \left(x \leq 3.1 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+175} \lor \neg \left(x \leq 1.7 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{\frac{x}{y} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.5e+175) (not (<= x 1.7e+124)))
   (* y 2.0)
   (* 2.0 (/ x (+ (/ x y) -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e+175) || !(x <= 1.7e+124)) {
		tmp = y * 2.0;
	} else {
		tmp = 2.0 * (x / ((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 <= (-1.5d+175)) .or. (.not. (x <= 1.7d+124))) then
        tmp = y * 2.0d0
    else
        tmp = 2.0d0 * (x / ((x / y) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e+175) || !(x <= 1.7e+124)) {
		tmp = y * 2.0;
	} else {
		tmp = 2.0 * (x / ((x / y) + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.5e+175) or not (x <= 1.7e+124):
		tmp = y * 2.0
	else:
		tmp = 2.0 * (x / ((x / y) + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.5e+175) || !(x <= 1.7e+124))
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(2.0 * Float64(x / Float64(Float64(x / y) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.5e+175) || ~((x <= 1.7e+124)))
		tmp = y * 2.0;
	else
		tmp = 2.0 * (x / ((x / y) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.5e+175], N[Not[LessEqual[x, 1.7e+124]], $MachinePrecision]], N[(y * 2.0), $MachinePrecision], N[(2.0 * N[(x / N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5000000000000001e175 or 1.7e124 < x

   1. Initial program 69.2%

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

      1. associate-/l* 56.3%

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

      2. associate-*l* 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in x around inf 89.4%

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

      1. *-commutative 89.4%

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

   7. Simplified 89.4%

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

   if -1.5000000000000001e175 < x < 1.7e124

   1. Initial program 76.8%

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

      1. associate-/l* 98.3%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

      1. associate-*r* 98.3%

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

      2. clear-num 97.9%

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

      3. un-div-inv 98.0%

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

   6. Applied egg-rr 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-/l* 98.0%

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

      3. div-sub 98.0%

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

      4. sub-neg 98.0%

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

      5. *-inverses 98.0%

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

      6. metadata-eval 98.0%

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

   8. Simplified 98.0%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+175} \lor \neg \left(x \leq 1.7 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{\frac{x}{y} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.2% 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 74.9%

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

   1. associate-/l* 87.7%

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

   2. associate-*l* 87.7%

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

3. Simplified 87.7%

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

5. Taylor expanded in y around inf 49.7%

   \[\leadsto x \cdot \color{blue}{-2} \]
6. 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 2024103 
(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)))