Data.Colour.RGB:hslsv from colour-2.3.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 8.2s

Alternatives: 10

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{y - x}{y + \left(x + -2\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- y x) (+ y (+ x -2.0))))

C

double code(double x, double y) {
	return (y - x) / (y + (x + -2.0));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (y - x) / (y + (x + -2.0));
}

Python

def code(x, y):
	return (y - x) / (y + (x + -2.0))

Julia

function code(x, y)
	return Float64(Float64(y - x) / Float64(y + Float64(x + -2.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = (y - x) / (y + (x + -2.0));
end

Wolfram

code[x_, y_] := N[(N[(y - x), $MachinePrecision] / N[(y + N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. remove-double-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. distribute-neg-frac2 100.0%

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

   4. distribute-frac-neg 100.0%

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

   5. sub-neg 100.0%

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

   6. distribute-neg-in 100.0%

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

   7. remove-double-neg 100.0%

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

   8. +-commutative 100.0%

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

   9. sub-neg 100.0%

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

   10. neg-sub0 100.0%

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

   11. associate--r- 100.0%

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

   12. metadata-eval 100.0%

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

   13. metadata-eval 100.0%

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

   14. +-commutative 100.0%

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

   15. +-commutative 100.0%

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

   16. associate-+r+ 100.0%

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

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around 0 100.0%

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

   1. associate--l+ 100.0%

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

   2. sub-neg 100.0%

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

   3. metadata-eval 100.0%

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

   4. +-commutative 100.0%

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

   5. associate-+r+ 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 2: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 + 2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -1.14 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-56}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+104}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ -1.0 (* 2.0 (/ y x)))))
   (if (<= x -1.14e+33)
     t_0
     (if (<= x 3e-56)
       (/ y (- y 2.0))
       (if (<= x 4.9e+101) (/ x (- 2.0 x)) (if (<= x 5.3e+104) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = -1.0 + (2.0 * (y / x));
	double tmp;
	if (x <= -1.14e+33) {
		tmp = t_0;
	} else if (x <= 3e-56) {
		tmp = y / (y - 2.0);
	} else if (x <= 4.9e+101) {
		tmp = x / (2.0 - x);
	} else if (x <= 5.3e+104) {
		tmp = 1.0;
	} 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 = (-1.0d0) + (2.0d0 * (y / x))
    if (x <= (-1.14d+33)) then
        tmp = t_0
    else if (x <= 3d-56) then
        tmp = y / (y - 2.0d0)
    else if (x <= 4.9d+101) then
        tmp = x / (2.0d0 - x)
    else if (x <= 5.3d+104) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -1.0 + (2.0 * (y / x));
	double tmp;
	if (x <= -1.14e+33) {
		tmp = t_0;
	} else if (x <= 3e-56) {
		tmp = y / (y - 2.0);
	} else if (x <= 4.9e+101) {
		tmp = x / (2.0 - x);
	} else if (x <= 5.3e+104) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -1.0 + (2.0 * (y / x))
	tmp = 0
	if x <= -1.14e+33:
		tmp = t_0
	elif x <= 3e-56:
		tmp = y / (y - 2.0)
	elif x <= 4.9e+101:
		tmp = x / (2.0 - x)
	elif x <= 5.3e+104:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-1.0 + Float64(2.0 * Float64(y / x)))
	tmp = 0.0
	if (x <= -1.14e+33)
		tmp = t_0;
	elseif (x <= 3e-56)
		tmp = Float64(y / Float64(y - 2.0));
	elseif (x <= 4.9e+101)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 5.3e+104)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -1.0 + (2.0 * (y / x));
	tmp = 0.0;
	if (x <= -1.14e+33)
		tmp = t_0;
	elseif (x <= 3e-56)
		tmp = y / (y - 2.0);
	elseif (x <= 4.9e+101)
		tmp = x / (2.0 - x);
	elseif (x <= 5.3e+104)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.14e+33], t$95$0, If[LessEqual[x, 3e-56], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.9e+101], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.3e+104], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.14e33 or 5.2999999999999999e104 < x

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in y around inf 87.0%

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

   if -1.14e33 < x < 2.99999999999999989e-56

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 78.8%

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

   if 2.99999999999999989e-56 < x < 4.89999999999999983e101

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. distribute-neg-frac2 63.4%

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

      3. neg-sub0 63.4%

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

      4. associate-+l- 63.4%

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

      5. neg-sub0 63.4%

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

      6. +-commutative 63.4%

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

      7. unsub-neg 63.4%

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

   7. Simplified 63.4%

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

   if 4.89999999999999983e101 < x < 5.2999999999999999e104

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.14 \cdot 10^{+33}:\\ \;\;\;\;-1 + 2 \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-56}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+104}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 + 2 \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;x \leq -1 \cdot 10^{-20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+104}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= x -1e-20)
     t_0
     (if (<= x 3.8e-57)
       (/ y (- y 2.0))
       (if (<= x 2.5e+101) t_0 (if (<= x 9e+104) 1.0 (/ (- y x) x)))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (x <= -1e-20) {
		tmp = t_0;
	} else if (x <= 3.8e-57) {
		tmp = y / (y - 2.0);
	} else if (x <= 2.5e+101) {
		tmp = t_0;
	} else if (x <= 9e+104) {
		tmp = 1.0;
	} else {
		tmp = (y - x) / x;
	}
	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 - x)
    if (x <= (-1d-20)) then
        tmp = t_0
    else if (x <= 3.8d-57) then
        tmp = y / (y - 2.0d0)
    else if (x <= 2.5d+101) then
        tmp = t_0
    else if (x <= 9d+104) then
        tmp = 1.0d0
    else
        tmp = (y - x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (x <= -1e-20) {
		tmp = t_0;
	} else if (x <= 3.8e-57) {
		tmp = y / (y - 2.0);
	} else if (x <= 2.5e+101) {
		tmp = t_0;
	} else if (x <= 9e+104) {
		tmp = 1.0;
	} else {
		tmp = (y - x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if x <= -1e-20:
		tmp = t_0
	elif x <= 3.8e-57:
		tmp = y / (y - 2.0)
	elif x <= 2.5e+101:
		tmp = t_0
	elif x <= 9e+104:
		tmp = 1.0
	else:
		tmp = (y - x) / x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (x <= -1e-20)
		tmp = t_0;
	elseif (x <= 3.8e-57)
		tmp = Float64(y / Float64(y - 2.0));
	elseif (x <= 2.5e+101)
		tmp = t_0;
	elseif (x <= 9e+104)
		tmp = 1.0;
	else
		tmp = Float64(Float64(y - x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (x <= -1e-20)
		tmp = t_0;
	elseif (x <= 3.8e-57)
		tmp = y / (y - 2.0);
	elseif (x <= 2.5e+101)
		tmp = t_0;
	elseif (x <= 9e+104)
		tmp = 1.0;
	else
		tmp = (y - x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e-20], t$95$0, If[LessEqual[x, 3.8e-57], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+101], t$95$0, If[LessEqual[x, 9e+104], 1.0, N[(N[(y - x), $MachinePrecision] / x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.99999999999999945e-21 or 3.7999999999999997e-57 < x < 2.49999999999999994e101

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. distribute-neg-frac2 73.9%

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

      3. neg-sub0 73.9%

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

      4. associate-+l- 73.9%

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

      5. neg-sub0 73.9%

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

      6. +-commutative 73.9%

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

      7. unsub-neg 73.9%

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

   7. Simplified 73.9%

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

   if -9.99999999999999945e-21 < x < 3.7999999999999997e-57

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 81.1%

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

   if 2.49999999999999994e101 < x < 8.9999999999999997e104

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{1} \]

   if 8.9999999999999997e104 < x

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 91.8%

      \[\leadsto \frac{y - x}{\color{blue}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+104}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+33}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-124}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-305}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.35e+33)
   -1.0
   (if (<= x -1.7e-124)
     1.0
     (if (<= x 3.1e-305) (* y -0.5) (if (<= x 1.65e+17) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.35e+33) {
		tmp = -1.0;
	} else if (x <= -1.7e-124) {
		tmp = 1.0;
	} else if (x <= 3.1e-305) {
		tmp = y * -0.5;
	} else if (x <= 1.65e+17) {
		tmp = 1.0;
	} else {
		tmp = -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 <= (-1.35d+33)) then
        tmp = -1.0d0
    else if (x <= (-1.7d-124)) then
        tmp = 1.0d0
    else if (x <= 3.1d-305) then
        tmp = y * (-0.5d0)
    else if (x <= 1.65d+17) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.35e+33) {
		tmp = -1.0;
	} else if (x <= -1.7e-124) {
		tmp = 1.0;
	} else if (x <= 3.1e-305) {
		tmp = y * -0.5;
	} else if (x <= 1.65e+17) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.35e+33:
		tmp = -1.0
	elif x <= -1.7e-124:
		tmp = 1.0
	elif x <= 3.1e-305:
		tmp = y * -0.5
	elif x <= 1.65e+17:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.35e+33)
		tmp = -1.0;
	elseif (x <= -1.7e-124)
		tmp = 1.0;
	elseif (x <= 3.1e-305)
		tmp = Float64(y * -0.5);
	elseif (x <= 1.65e+17)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.35e+33)
		tmp = -1.0;
	elseif (x <= -1.7e-124)
		tmp = 1.0;
	elseif (x <= 3.1e-305)
		tmp = y * -0.5;
	elseif (x <= 1.65e+17)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.35e+33], -1.0, If[LessEqual[x, -1.7e-124], 1.0, If[LessEqual[x, 3.1e-305], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1.65e+17], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.34999999999999996e33 or 1.65e17 < x

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 81.1%

      \[\leadsto \color{blue}{-1} \]

   if -1.34999999999999996e33 < x < -1.7e-124 or 3.0999999999999998e-305 < x < 1.65e17

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 58.2%

      \[\leadsto \color{blue}{1} \]

   if -1.7e-124 < x < 3.0999999999999998e-305

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 77.6%

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

   6. Taylor expanded in y around 0 47.4%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 47.4%

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

   8. Simplified 47.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+33}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-124}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-305}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+75}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4e+75)
   1.0
   (if (<= y 5e-44)
     (/ x (- 2.0 x))
     (if (<= y 9.5e-12) (* y -0.5) (if (<= y 1.45e+59) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4e+75) {
		tmp = 1.0;
	} else if (y <= 5e-44) {
		tmp = x / (2.0 - x);
	} else if (y <= 9.5e-12) {
		tmp = y * -0.5;
	} else if (y <= 1.45e+59) {
		tmp = -1.0;
	} else {
		tmp = 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 (y <= (-4d+75)) then
        tmp = 1.0d0
    else if (y <= 5d-44) then
        tmp = x / (2.0d0 - x)
    else if (y <= 9.5d-12) then
        tmp = y * (-0.5d0)
    else if (y <= 1.45d+59) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4e+75) {
		tmp = 1.0;
	} else if (y <= 5e-44) {
		tmp = x / (2.0 - x);
	} else if (y <= 9.5e-12) {
		tmp = y * -0.5;
	} else if (y <= 1.45e+59) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4e+75:
		tmp = 1.0
	elif y <= 5e-44:
		tmp = x / (2.0 - x)
	elif y <= 9.5e-12:
		tmp = y * -0.5
	elif y <= 1.45e+59:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4e+75)
		tmp = 1.0;
	elseif (y <= 5e-44)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (y <= 9.5e-12)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.45e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4e+75)
		tmp = 1.0;
	elseif (y <= 5e-44)
		tmp = x / (2.0 - x);
	elseif (y <= 9.5e-12)
		tmp = y * -0.5;
	elseif (y <= 1.45e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4e+75], 1.0, If[LessEqual[y, 5e-44], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-12], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.45e+59], -1.0, 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.99999999999999971e75 or 1.44999999999999995e59 < y

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 81.8%

      \[\leadsto \color{blue}{1} \]

   if -3.99999999999999971e75 < y < 5.00000000000000039e-44

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. distribute-neg-frac2 79.8%

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

      3. neg-sub0 79.8%

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

      4. associate-+l- 79.8%

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

      5. neg-sub0 79.8%

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

      6. +-commutative 79.8%

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

      7. unsub-neg 79.8%

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

   7. Simplified 79.8%

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

   if 5.00000000000000039e-44 < y < 9.4999999999999995e-12

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 86.9%

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

   6. Taylor expanded in y around 0 83.8%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 83.8%

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

   8. Simplified 83.8%

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

   if 9.4999999999999995e-12 < y < 1.44999999999999995e59

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. neg-sub0 99.9%

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

      11. associate--r- 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. +-commutative 99.9%

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

      16. associate-+r+ 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 57.7%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+75}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-12}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+76}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{y - x}{x - 2}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.8e+76) 1.0 (if (<= y 1.5e+47) (/ (- y x) (- x 2.0)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.8e+76) {
		tmp = 1.0;
	} else if (y <= 1.5e+47) {
		tmp = (y - x) / (x - 2.0);
	} else {
		tmp = 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 (y <= (-3.8d+76)) then
        tmp = 1.0d0
    else if (y <= 1.5d+47) then
        tmp = (y - x) / (x - 2.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.8e+76) {
		tmp = 1.0;
	} else if (y <= 1.5e+47) {
		tmp = (y - x) / (x - 2.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.8e+76:
		tmp = 1.0
	elif y <= 1.5e+47:
		tmp = (y - x) / (x - 2.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.8e+76)
		tmp = 1.0;
	elseif (y <= 1.5e+47)
		tmp = Float64(Float64(y - x) / Float64(x - 2.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.8e+76)
		tmp = 1.0;
	elseif (y <= 1.5e+47)
		tmp = (y - x) / (x - 2.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.8e+76], 1.0, If[LessEqual[y, 1.5e+47], N[(N[(y - x), $MachinePrecision] / N[(x - 2.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000024e76 or 1.5000000000000001e47 < y

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 81.2%

      \[\leadsto \color{blue}{1} \]

   if -3.80000000000000024e76 < y < 1.5000000000000001e47

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 91.3%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+76}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{y - x}{x - 2}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-18} \lor \neg \left(x \leq 4.2 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.45e-18) (not (<= x 4.2e-60)))
   (/ x (- 2.0 x))
   (/ y (- y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.45e-18) || !(x <= 4.2e-60)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (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 ((x <= (-1.45d-18)) .or. (.not. (x <= 4.2d-60))) then
        tmp = x / (2.0d0 - x)
    else
        tmp = y / (y - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.45e-18) || !(x <= 4.2e-60)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y - 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.45e-18) or not (x <= 4.2e-60):
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y - 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.45e-18) || !(x <= 4.2e-60))
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(y / Float64(y - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.45e-18) || ~((x <= 4.2e-60)))
		tmp = x / (2.0 - x);
	else
		tmp = y / (y - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.45e-18], N[Not[LessEqual[x, 4.2e-60]], $MachinePrecision]], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e-18 or 4.19999999999999982e-60 < x

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. distribute-neg-frac2 77.0%

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

      3. neg-sub0 77.0%

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

      4. associate-+l- 77.0%

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

      5. neg-sub0 77.0%

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

      6. +-commutative 77.0%

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

      7. unsub-neg 77.0%

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

   7. Simplified 77.0%

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

   if -1.45e-18 < x < 4.19999999999999982e-60

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 81.1%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-18} \lor \neg \left(x \leq 4.2 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.14 \cdot 10^{+33}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.14e+33) -1.0 (if (<= x 1.85e+15) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.14e+33) {
		tmp = -1.0;
	} else if (x <= 1.85e+15) {
		tmp = 1.0;
	} else {
		tmp = -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 <= (-1.14d+33)) then
        tmp = -1.0d0
    else if (x <= 1.85d+15) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.14e+33) {
		tmp = -1.0;
	} else if (x <= 1.85e+15) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.14e+33:
		tmp = -1.0
	elif x <= 1.85e+15:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.14e+33)
		tmp = -1.0;
	elseif (x <= 1.85e+15)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.14e+33)
		tmp = -1.0;
	elseif (x <= 1.85e+15)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.14e+33], -1.0, If[LessEqual[x, 1.85e+15], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.14e33 or 1.85e15 < x

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 81.1%

      \[\leadsto \color{blue}{-1} \]

   if -1.14e33 < x < 1.85e15

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 52.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.14 \cdot 10^{+33}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(y + x\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ y x))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (y + x));
}

Fortran

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

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (y + x));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (y + x))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(y + x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (y + x));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 10: 37.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

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

   1. remove-double-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. distribute-neg-frac2 100.0%

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

   4. distribute-frac-neg 100.0%

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

   5. sub-neg 100.0%

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

   6. distribute-neg-in 100.0%

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

   7. remove-double-neg 100.0%

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

   8. +-commutative 100.0%

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

   9. sub-neg 100.0%

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

   10. neg-sub0 100.0%

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

   11. associate--r- 100.0%

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

   12. metadata-eval 100.0%

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

   13. metadata-eval 100.0%

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

   14. +-commutative 100.0%

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

   15. +-commutative 100.0%

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

   16. associate-+r+ 100.0%

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

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around inf 43.6%

   \[\leadsto \color{blue}{-1} \]

6. Final simplification 43.6%

   \[\leadsto -1 \]
7. Add Preprocessing

Developer target: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t\_0} - \frac{y}{t\_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024078 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :alt
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))