Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.4% → 99.6%

Time: 3.7s

Alternatives: 5

Speedup: 0.7×

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: 77.4% 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, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+72} \lor \neg \left(y \leq 500\right):\\ \;\;\;\;\frac{x \cdot -2}{1 - \frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{1 - \frac{y}{x}}{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.6e+72) (not (<= y 500.0)))
   (/ (* x -2.0) (- 1.0 (/ x y)))
   (/ y (/ (- 1.0 (/ y x)) 2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.6e+72) || !(y <= 500.0)) {
		tmp = (x * -2.0) / (1.0 - (x / y));
	} else {
		tmp = y / ((1.0 - (y / 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 ((y <= (-2.6d+72)) .or. (.not. (y <= 500.0d0))) then
        tmp = (x * (-2.0d0)) / (1.0d0 - (x / y))
    else
        tmp = y / ((1.0d0 - (y / x)) / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.6e+72) || !(y <= 500.0)) {
		tmp = (x * -2.0) / (1.0 - (x / y));
	} else {
		tmp = y / ((1.0 - (y / x)) / 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.6e+72) or not (y <= 500.0):
		tmp = (x * -2.0) / (1.0 - (x / y))
	else:
		tmp = y / ((1.0 - (y / x)) / 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.6e+72) || !(y <= 500.0))
		tmp = Float64(Float64(x * -2.0) / Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(y / Float64(Float64(1.0 - Float64(y / x)) / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.6e+72) || ~((y <= 500.0)))
		tmp = (x * -2.0) / (1.0 - (x / y));
	else
		tmp = y / ((1.0 - (y / x)) / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.6e+72], N[Not[LessEqual[y, 500.0]], $MachinePrecision]], N[(N[(x * -2.0), $MachinePrecision] / N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999981e72 or 500 < y

   1. Initial program 75.3%

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

      1. associate-*l* 75.3%

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

      2. *-commutative 75.3%

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

      3. *-commutative 75.3%

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

      4. associate-*l/ 99.9%

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

      5. *-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. distribute-lft-neg-out 99.9%

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

      8. distribute-rgt-neg-in 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-/l* 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{-2}{1 - \frac{x}{y}}} \]
   4. Step-by-step derivation

      1. associate-*r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   if -2.59999999999999981e72 < y < 500

   1. Initial program 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-/l* 99.9%

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

      3. associate-/r* 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+72} \lor \neg \left(y \leq 500\right):\\ \;\;\;\;\frac{x \cdot -2}{1 - \frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{1 - \frac{y}{x}}{2}}\\ \end{array} \]

Alternative 2: 93.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-176} \lor \neg \left(y \leq 1.2 \cdot 10^{-111}\right):\\ \;\;\;\;x \cdot \frac{-2}{1 - \frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.05e-176) (not (<= y 1.2e-111)))
   (* x (/ -2.0 (- 1.0 (/ x y))))
   (* y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.05e-176) || !(y <= 1.2e-111)) {
		tmp = x * (-2.0 / (1.0 - (x / y)));
	} 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 <= (-2.05d-176)) .or. (.not. (y <= 1.2d-111))) then
        tmp = x * ((-2.0d0) / (1.0d0 - (x / y)))
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.05e-176) || !(y <= 1.2e-111)) {
		tmp = x * (-2.0 / (1.0 - (x / y)));
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.05e-176) or not (y <= 1.2e-111):
		tmp = x * (-2.0 / (1.0 - (x / y)))
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.05e-176) || !(y <= 1.2e-111))
		tmp = Float64(x * Float64(-2.0 / Float64(1.0 - Float64(x / y))));
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.05e-176) || ~((y <= 1.2e-111)))
		tmp = x * (-2.0 / (1.0 - (x / y)));
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.05e-176], N[Not[LessEqual[y, 1.2e-111]], $MachinePrecision]], N[(x * N[(-2.0 / N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0500000000000001e-176 or 1.2e-111 < y

   1. Initial program 80.6%

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

      1. associate-*l* 80.6%

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

      2. *-commutative 80.6%

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

      3. *-commutative 80.6%

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

      4. associate-*l/ 98.3%

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

      5. *-commutative 98.3%

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

      6. remove-double-neg 98.3%

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

      7. distribute-lft-neg-out 98.3%

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

      8. distribute-rgt-neg-in 98.3%

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

      9. *-commutative 98.3%

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

      10. associate-/l* 97.5%

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

      11. metadata-eval 97.5%

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

   3. Simplified 97.6%

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

   if -2.0500000000000001e-176 < y < 1.2e-111

   1. Initial program 74.2%

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

      1. associate-*l* 74.2%

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

      2. *-commutative 74.2%

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

      3. *-commutative 74.2%

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

      4. associate-*l/ 59.5%

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

      5. *-commutative 59.5%

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

      6. remove-double-neg 59.5%

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

      7. distribute-lft-neg-out 59.5%

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

      8. distribute-rgt-neg-in 59.5%

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

      9. *-commutative 59.5%

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

      10. associate-/l* 57.5%

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

      11. metadata-eval 57.5%

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

   3. Simplified 57.5%

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

   4. Taylor expanded in x around inf 89.8%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-176} \lor \neg \left(y \leq 1.2 \cdot 10^{-111}\right):\\ \;\;\;\;x \cdot \frac{-2}{1 - \frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]

Alternative 3: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+72} \lor \neg \left(y \leq 4.5 \cdot 10^{+85}\right):\\ \;\;\;\;x \cdot \frac{-2}{1 - \frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{1 - \frac{y}{x}}{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.6e+72) (not (<= y 4.5e+85)))
   (* x (/ -2.0 (- 1.0 (/ x y))))
   (/ y (/ (- 1.0 (/ y x)) 2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.6e+72) || !(y <= 4.5e+85)) {
		tmp = x * (-2.0 / (1.0 - (x / y)));
	} else {
		tmp = y / ((1.0 - (y / 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 ((y <= (-2.6d+72)) .or. (.not. (y <= 4.5d+85))) then
        tmp = x * ((-2.0d0) / (1.0d0 - (x / y)))
    else
        tmp = y / ((1.0d0 - (y / x)) / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.6e+72) || !(y <= 4.5e+85)) {
		tmp = x * (-2.0 / (1.0 - (x / y)));
	} else {
		tmp = y / ((1.0 - (y / x)) / 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.6e+72) or not (y <= 4.5e+85):
		tmp = x * (-2.0 / (1.0 - (x / y)))
	else:
		tmp = y / ((1.0 - (y / x)) / 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.6e+72) || !(y <= 4.5e+85))
		tmp = Float64(x * Float64(-2.0 / Float64(1.0 - Float64(x / y))));
	else
		tmp = Float64(y / Float64(Float64(1.0 - Float64(y / x)) / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.6e+72) || ~((y <= 4.5e+85)))
		tmp = x * (-2.0 / (1.0 - (x / y)));
	else
		tmp = y / ((1.0 - (y / x)) / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.6e+72], N[Not[LessEqual[y, 4.5e+85]], $MachinePrecision]], N[(x * N[(-2.0 / N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999981e72 or 4.50000000000000007e85 < y

   1. Initial program 73.1%

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

      1. associate-*l* 73.1%

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

      2. *-commutative 73.1%

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

      3. *-commutative 73.1%

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

      4. associate-*l/ 99.9%

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

      5. *-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. distribute-lft-neg-out 99.9%

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

      8. distribute-rgt-neg-in 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-/l* 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.9%

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

   if -2.59999999999999981e72 < y < 4.50000000000000007e85

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-/l* 99.9%

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

      3. associate-/r* 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+72} \lor \neg \left(y \leq 4.5 \cdot 10^{+85}\right):\\ \;\;\;\;x \cdot \frac{-2}{1 - \frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{1 - \frac{y}{x}}{2}}\\ \end{array} \]

Alternative 4: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+45} \lor \neg \left(x \leq -6.2 \cdot 10^{-36}\right) \land \left(x \leq -2.4 \cdot 10^{-74} \lor \neg \left(x \leq 7 \cdot 10^{-13}\right)\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.35e+45)
         (and (not (<= x -6.2e-36)) (or (<= x -2.4e-74) (not (<= x 7e-13)))))
   (* y 2.0)
   (* x -2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.35e+45) || (!(x <= -6.2e-36) && ((x <= -2.4e-74) || !(x <= 7e-13)))) {
		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 <= (-1.35d+45)) .or. (.not. (x <= (-6.2d-36))) .and. (x <= (-2.4d-74)) .or. (.not. (x <= 7d-13))) 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 <= -1.35e+45) || (!(x <= -6.2e-36) && ((x <= -2.4e-74) || !(x <= 7e-13)))) {
		tmp = y * 2.0;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.35e+45) or (not (x <= -6.2e-36) and ((x <= -2.4e-74) or not (x <= 7e-13))):
		tmp = y * 2.0
	else:
		tmp = x * -2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.35e+45) || (!(x <= -6.2e-36) && ((x <= -2.4e-74) || !(x <= 7e-13))))
		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 <= -1.35e+45) || (~((x <= -6.2e-36)) && ((x <= -2.4e-74) || ~((x <= 7e-13)))))
		tmp = y * 2.0;
	else
		tmp = x * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.35e+45], And[N[Not[LessEqual[x, -6.2e-36]], $MachinePrecision], Or[LessEqual[x, -2.4e-74], N[Not[LessEqual[x, 7e-13]], $MachinePrecision]]]], N[(y * 2.0), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.34999999999999992e45 or -6.1999999999999997e-36 < x < -2.3999999999999999e-74 or 7.0000000000000005e-13 < x

   1. Initial program 82.1%

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

      1. associate-*l* 82.1%

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

      2. *-commutative 82.1%

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

      3. *-commutative 82.1%

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

      4. associate-*l/ 71.2%

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

      5. *-commutative 71.2%

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

      6. remove-double-neg 71.2%

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

      7. distribute-lft-neg-out 71.2%

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

      8. distribute-rgt-neg-in 71.2%

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

      9. *-commutative 71.2%

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

      10. associate-/l* 69.0%

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

      11. metadata-eval 69.0%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in x around inf 85.6%

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

   if -1.34999999999999992e45 < x < -6.1999999999999997e-36 or -2.3999999999999999e-74 < x < 7.0000000000000005e-13

   1. Initial program 74.9%

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

      1. associate-*l* 74.9%

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

      2. *-commutative 74.9%

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

      3. *-commutative 74.9%

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

      4. associate-*l/ 99.9%

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

      5. *-commutative 99.9%

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

      6. remove-double-neg 99.9%

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

      7. distribute-lft-neg-out 99.9%

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

      8. distribute-rgt-neg-in 99.9%

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

      9. *-commutative 99.9%

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

      10. associate-/l* 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 77.2%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+45} \lor \neg \left(x \leq -6.2 \cdot 10^{-36}\right) \land \left(x \leq -2.4 \cdot 10^{-74} \lor \neg \left(x \leq 7 \cdot 10^{-13}\right)\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]

Alternative 5: 51.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ y \cdot 2 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.5%

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

   1. associate-*l* 78.5%

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

   2. *-commutative 78.5%

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

   3. *-commutative 78.5%

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

   4. associate-*l/ 85.6%

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

   5. *-commutative 85.6%

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

   6. remove-double-neg 85.6%

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

   7. distribute-lft-neg-out 85.6%

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

   8. distribute-rgt-neg-in 85.6%

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

   9. *-commutative 85.6%

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

   10. associate-/l* 84.4%

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

   11. metadata-eval 84.4%

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

3. Simplified 84.4%

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

4. Taylor expanded in x around inf 54.7%

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

5. Final simplification 54.7%

   \[\leadsto y \cdot 2 \]

Developer target: 99.5% accurate, 0.7× 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 2023298 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (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)))