Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.9% → 99.6%

Time: 8.4s

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: 76.9% 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: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+77} \lor \neg \left(y \leq 3 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - x} \cdot \frac{y}{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2e+77) (not (<= y 3e-36)))
   (* x (* 2.0 (/ y (- x y))))
   (* (/ x (- y x)) (/ y -0.5))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2e+77) || !(y <= 3e-36)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = (x / (y - x)) * (y / -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2d+77)) .or. (.not. (y <= 3d-36))) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else
        tmp = (x / (y - x)) * (y / (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2e+77) || !(y <= 3e-36)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = (x / (y - x)) * (y / -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2e+77) or not (y <= 3e-36):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = (x / (y - x)) * (y / -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2e+77) || !(y <= 3e-36))
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	else
		tmp = Float64(Float64(x / Float64(y - x)) * Float64(y / -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2e+77) || ~((y <= 3e-36)))
		tmp = x * (2.0 * (y / (x - y)));
	else
		tmp = (x / (y - x)) * (y / -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2e+77], N[Not[LessEqual[y, 3e-36]], $MachinePrecision]], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - x), $MachinePrecision]), $MachinePrecision] * N[(y / -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999997e77 or 3.0000000000000002e-36 < y

   1. Initial program 74.7%

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

   if -1.99999999999999997e77 < y < 3.0000000000000002e-36

   1. Initial program 81.1%

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

      1. sub-neg 81.1%

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

      2. +-commutative 81.1%

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

      3. neg-sub0 81.1%

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

      4. associate-+l- 81.1%

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

      5. sub0-neg 81.1%

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

      6. distribute-frac-neg2 81.1%

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

      7. distribute-frac-neg 81.1%

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

      8. *-commutative 81.1%

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

      9. associate-*r* 81.1%

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

      10. distribute-rgt-neg-in 81.1%

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

      11. associate-/l* 80.9%

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

      12. *-commutative 80.9%

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

      13. metadata-eval 80.9%

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

   3. Simplified 80.9%

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

      1. clear-num 80.9%

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

      2. un-div-inv 81.1%

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

      3. div-inv 81.1%

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

      4. metadata-eval 81.1%

         \[\leadsto \frac{x \cdot y}{\left(y - x\right) \cdot \color{blue}{-0.5}} \]

   6. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{\left(y - x\right) \cdot -0.5}} \]
   7. Step-by-step derivation

      1. times-frac 100.0%

         \[\leadsto \color{blue}{\frac{x}{y - x} \cdot \frac{y}{-0.5}} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{y - x} \cdot \frac{y}{-0.5}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+77} \lor \neg \left(y \leq 3 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - x} \cdot \frac{y}{-0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-125} \lor \neg \left(y \leq 8.2 \cdot 10^{-89}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y + y \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9.5e-125) (not (<= y 8.2e-89)))
   (* x (* 2.0 (/ y (- x y))))
   (* 2.0 (+ y (* y (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9.5e-125) || !(y <= 8.2e-89)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = 2.0 * (y + (y * (y / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-9.5d-125)) .or. (.not. (y <= 8.2d-89))) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else
        tmp = 2.0d0 * (y + (y * (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -9.5e-125) || !(y <= 8.2e-89)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = 2.0 * (y + (y * (y / x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9.5e-125) or not (y <= 8.2e-89):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = 2.0 * (y + (y * (y / x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9.5e-125) || !(y <= 8.2e-89))
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	else
		tmp = Float64(2.0 * Float64(y + Float64(y * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -9.5e-125) || ~((y <= 8.2e-89)))
		tmp = x * (2.0 * (y / (x - y)));
	else
		tmp = 2.0 * (y + (y * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9.5e-125], N[Not[LessEqual[y, 8.2e-89]], $MachinePrecision]], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y + N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000031e-125 or 8.1999999999999997e-89 < y

   1. Initial program 79.0%

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

      1. associate-/l* 97.2%

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

      2. associate-*l* 97.2%

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

   3. Simplified 97.2%

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

   if -9.50000000000000031e-125 < y < 8.1999999999999997e-89

   1. Initial program 75.8%

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

      1. associate-/l* 65.5%

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

      2. associate-*l* 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in x around inf 89.9%

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

      1. distribute-lft-out 89.9%

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

   7. Simplified 89.9%

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

      1. unpow2 89.9%

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

      2. associate-/l* 90.9%

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

   9. Applied egg-rr 90.9%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-125} \lor \neg \left(y \leq 8.2 \cdot 10^{-89}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y + y \cdot \frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+51} \lor \neg \left(y \leq 4.4 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y + y \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.5e+51) (not (<= y 4.4e-36)))
   (* x -2.0)
   (* 2.0 (+ y (* y (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e+51) || !(y <= 4.4e-36)) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * (y + (y * (y / x)));
	}
	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+51)) .or. (.not. (y <= 4.4d-36))) then
        tmp = x * (-2.0d0)
    else
        tmp = 2.0d0 * (y + (y * (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e+51) || !(y <= 4.4e-36)) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * (y + (y * (y / x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.5e+51) or not (y <= 4.4e-36):
		tmp = x * -2.0
	else:
		tmp = 2.0 * (y + (y * (y / x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.5e+51) || !(y <= 4.4e-36))
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(2.0 * Float64(y + Float64(y * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.5e+51) || ~((y <= 4.4e-36)))
		tmp = x * -2.0;
	else
		tmp = 2.0 * (y + (y * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.5e+51], N[Not[LessEqual[y, 4.4e-36]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(2.0 * N[(y + N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e51 or 4.3999999999999999e-36 < y

   1. Initial program 75.3%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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 76.8%

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

   if -4.5e51 < y < 4.3999999999999999e-36

   1. Initial program 80.7%

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

      1. associate-/l* 74.9%

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

      2. associate-*l* 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in x around inf 81.4%

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

      1. distribute-lft-out 81.4%

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

   7. Simplified 81.4%

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

      1. unpow2 81.4%

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

      2. associate-/l* 82.0%

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

   9. Applied egg-rr 82.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+51} \lor \neg \left(y \leq 4.4 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y + y \cdot \frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+52} \lor \neg \left(y \leq 4.2 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.15e+52) (not (<= y 4.2e-36))) (* x -2.0) (* y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.15e+52) || !(y <= 4.2e-36)) {
		tmp = x * -2.0;
	} else {
		tmp = y * 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 ((y <= (-2.15d+52)) .or. (.not. (y <= 4.2d-36))) then
        tmp = x * (-2.0d0)
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.15e+52) || !(y <= 4.2e-36)) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.15e+52) or not (y <= 4.2e-36):
		tmp = x * -2.0
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.15e+52) || !(y <= 4.2e-36))
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.15e+52) || ~((y <= 4.2e-36)))
		tmp = x * -2.0;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.15e+52], N[Not[LessEqual[y, 4.2e-36]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15e52 or 4.19999999999999982e-36 < y

   1. Initial program 75.3%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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 76.8%

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

   if -2.15e52 < y < 4.19999999999999982e-36

   1. Initial program 80.7%

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

      1. associate-/l* 74.9%

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

      2. associate-*l* 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in x around inf 80.8%

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

      1. *-commutative 80.8%

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

   7. Simplified 80.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+52} \lor \neg \left(y \leq 4.2 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
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 78.0%

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

   1. associate-/l* 87.4%

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

   2. associate-*l* 87.4%

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

3. Simplified 87.4%

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

5. Taylor expanded in y around inf 48.4%

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

Developer Target 1: 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 2024181 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1721044263414944700000000000000000000000000000000000000000000000000000000000000000) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564430) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y))))

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