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

Percentage Accurate: 100.0% → 100.0%

Time: 8.6s

Alternatives: 9

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, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double t_0 = y + (-2.0 + x);
	return (y / t_0) - (x / 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 = y + ((-2.0d0) + x)
    code = (y / t_0) - (x / t_0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. unsub-neg 100.0%

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

   4. distribute-neg-in 100.0%

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

   5. neg-mul-1 100.0%

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

   6. *-commutative 100.0%

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

   7. associate-/l* 100.0%

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

   8. +-commutative 100.0%

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

   9. sub-neg 100.0%

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

   10. div-sub 100.0%

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

   11. metadata-eval 100.0%

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

   12. metadata-eval 100.0%

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

   13. sub-neg 100.0%

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

   14. distribute-frac-neg 100.0%

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

   15. neg-mul-1 100.0%

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

   16. *-commutative 100.0%

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

   17. associate-/l* 100.0%

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

   18. metadata-eval 100.0%

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

   19. /-rgt-identity 100.0%

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

   20. +-commutative 100.0%

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

   21. +-commutative 100.0%

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

   22. associate-+r+ 100.0%

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

   23. 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. Step-by-step derivation

   1. div-sub 100.0%

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

   2. +-commutative 100.0%

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

   3. associate-+l+ 100.0%

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

   4. +-commutative 100.0%

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

   5. associate-+l+ 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - \frac{y \cdot -2}{x}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+68}:\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- -1.0 (/ (* y -2.0) x))))
   (if (<= x -1.6e+15)
     t_0
     (if (<= x 2.1e-32)
       (/ y (- y 2.0))
       (if (<= x 4e+68) (/ (- x) (+ -2.0 x)) (if (<= x 9.5e+72) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = -1.0 - ((y * -2.0) / x);
	double tmp;
	if (x <= -1.6e+15) {
		tmp = t_0;
	} else if (x <= 2.1e-32) {
		tmp = y / (y - 2.0);
	} else if (x <= 4e+68) {
		tmp = -x / (-2.0 + x);
	} else if (x <= 9.5e+72) {
		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) - ((y * (-2.0d0)) / x)
    if (x <= (-1.6d+15)) then
        tmp = t_0
    else if (x <= 2.1d-32) then
        tmp = y / (y - 2.0d0)
    else if (x <= 4d+68) then
        tmp = -x / ((-2.0d0) + x)
    else if (x <= 9.5d+72) 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 - ((y * -2.0) / x);
	double tmp;
	if (x <= -1.6e+15) {
		tmp = t_0;
	} else if (x <= 2.1e-32) {
		tmp = y / (y - 2.0);
	} else if (x <= 4e+68) {
		tmp = -x / (-2.0 + x);
	} else if (x <= 9.5e+72) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -1.0 - ((y * -2.0) / x)
	tmp = 0
	if x <= -1.6e+15:
		tmp = t_0
	elif x <= 2.1e-32:
		tmp = y / (y - 2.0)
	elif x <= 4e+68:
		tmp = -x / (-2.0 + x)
	elif x <= 9.5e+72:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-1.0 - Float64(Float64(y * -2.0) / x))
	tmp = 0.0
	if (x <= -1.6e+15)
		tmp = t_0;
	elseif (x <= 2.1e-32)
		tmp = Float64(y / Float64(y - 2.0));
	elseif (x <= 4e+68)
		tmp = Float64(Float64(-x) / Float64(-2.0 + x));
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -1.0 - ((y * -2.0) / x);
	tmp = 0.0;
	if (x <= -1.6e+15)
		tmp = t_0;
	elseif (x <= 2.1e-32)
		tmp = y / (y - 2.0);
	elseif (x <= 4e+68)
		tmp = -x / (-2.0 + x);
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-1.0 - N[(N[(y * -2.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+15], t$95$0, If[LessEqual[x, 2.1e-32], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+68], N[((-x) / N[(-2.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+72], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6e15 or 9.50000000000000054e72 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in x around -inf 86.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(2 + -1 \cdot y\right) - y}{x} - 1} \]
   5. Step-by-step derivation

      1. sub-neg 86.3%

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

      2. metadata-eval 86.3%

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

      3. +-commutative 86.3%

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

      4. mul-1-neg 86.3%

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

      5. unsub-neg 86.3%

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

      6. mul-1-neg 86.3%

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

      7. unsub-neg 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in y around inf 86.3%

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

      1. *-commutative 86.3%

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

   9. Simplified 86.3%

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

   if -1.6e15 < x < 2.0999999999999999e-32

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in x around 0 73.8%

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

   if 2.0999999999999999e-32 < x < 3.99999999999999981e68

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-neg-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-/l* 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. div-sub 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. sub-neg 99.9%

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

      14. distribute-frac-neg 99.9%

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

      15. neg-mul-1 99.9%

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

      16. *-commutative 99.9%

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

      17. associate-/l* 99.9%

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

      18. metadata-eval 99.9%

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

      19. /-rgt-identity 99.9%

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

      20. +-commutative 99.9%

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

      21. +-commutative 99.9%

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

      22. associate-+r+ 99.9%

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

      23. 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. Taylor expanded in y around 0 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

      3. sub-neg 83.8%

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

      4. metadata-eval 83.8%

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

   6. Simplified 83.8%

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

   if 3.99999999999999981e68 < x < 9.50000000000000054e72

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around inf 100.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+68}:\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \end{array} \]

Alternative 3: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - \frac{y \cdot -2}{x}\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{x + \left(y + -2\right)}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- -1.0 (/ (* y -2.0) x))))
   (if (<= x -7.5e+14)
     t_0
     (if (<= x 6.8e-34)
       (/ y (+ x (+ y -2.0)))
       (if (<= x 2.5e+68) (/ (- x) (+ -2.0 x)) (if (<= x 9.5e+72) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = -1.0 - ((y * -2.0) / x);
	double tmp;
	if (x <= -7.5e+14) {
		tmp = t_0;
	} else if (x <= 6.8e-34) {
		tmp = y / (x + (y + -2.0));
	} else if (x <= 2.5e+68) {
		tmp = -x / (-2.0 + x);
	} else if (x <= 9.5e+72) {
		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) - ((y * (-2.0d0)) / x)
    if (x <= (-7.5d+14)) then
        tmp = t_0
    else if (x <= 6.8d-34) then
        tmp = y / (x + (y + (-2.0d0)))
    else if (x <= 2.5d+68) then
        tmp = -x / ((-2.0d0) + x)
    else if (x <= 9.5d+72) 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 - ((y * -2.0) / x);
	double tmp;
	if (x <= -7.5e+14) {
		tmp = t_0;
	} else if (x <= 6.8e-34) {
		tmp = y / (x + (y + -2.0));
	} else if (x <= 2.5e+68) {
		tmp = -x / (-2.0 + x);
	} else if (x <= 9.5e+72) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -1.0 - ((y * -2.0) / x)
	tmp = 0
	if x <= -7.5e+14:
		tmp = t_0
	elif x <= 6.8e-34:
		tmp = y / (x + (y + -2.0))
	elif x <= 2.5e+68:
		tmp = -x / (-2.0 + x)
	elif x <= 9.5e+72:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-1.0 - Float64(Float64(y * -2.0) / x))
	tmp = 0.0
	if (x <= -7.5e+14)
		tmp = t_0;
	elseif (x <= 6.8e-34)
		tmp = Float64(y / Float64(x + Float64(y + -2.0)));
	elseif (x <= 2.5e+68)
		tmp = Float64(Float64(-x) / Float64(-2.0 + x));
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -1.0 - ((y * -2.0) / x);
	tmp = 0.0;
	if (x <= -7.5e+14)
		tmp = t_0;
	elseif (x <= 6.8e-34)
		tmp = y / (x + (y + -2.0));
	elseif (x <= 2.5e+68)
		tmp = -x / (-2.0 + x);
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-1.0 - N[(N[(y * -2.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e+14], t$95$0, If[LessEqual[x, 6.8e-34], N[(y / N[(x + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+68], N[((-x) / N[(-2.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+72], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.5e14 or 9.50000000000000054e72 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in x around -inf 86.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{\left(2 + -1 \cdot y\right) - y}{x} - 1} \]
   5. Step-by-step derivation

      1. sub-neg 86.3%

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

      2. metadata-eval 86.3%

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

      3. +-commutative 86.3%

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

      4. mul-1-neg 86.3%

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

      5. unsub-neg 86.3%

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

      6. mul-1-neg 86.3%

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

      7. unsub-neg 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in y around inf 86.3%

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

      1. *-commutative 86.3%

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

   9. Simplified 86.3%

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

   if -7.5e14 < x < 6.8000000000000001e-34

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Step-by-step derivation

      1. div-sub 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. frac-sub 78.4%

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

      2. associate-/r* 79.1%

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

      3. +-commutative 79.1%

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

      4. +-commutative 79.1%

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

      5. associate-+l+ 79.1%

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

      6. +-commutative 79.1%

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

      7. *-commutative 79.1%

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

      8. +-commutative 79.1%

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

      9. +-commutative 79.1%

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

      10. associate-+l+ 79.1%

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

      11. +-commutative 79.1%

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

      12. +-commutative 79.1%

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

      13. +-commutative 79.1%

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

      14. associate-+l+ 79.1%

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

      15. +-commutative 79.1%

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

      16. +-commutative 79.1%

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

   7. Applied egg-rr 79.1%

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

   8. Taylor expanded in y around inf 73.8%

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

   if 6.8000000000000001e-34 < x < 2.5000000000000002e68

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-neg-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-/l* 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. div-sub 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. sub-neg 99.9%

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

      14. distribute-frac-neg 99.9%

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

      15. neg-mul-1 99.9%

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

      16. *-commutative 99.9%

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

      17. associate-/l* 99.9%

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

      18. metadata-eval 99.9%

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

      19. /-rgt-identity 99.9%

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

      20. +-commutative 99.9%

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

      21. +-commutative 99.9%

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

      22. associate-+r+ 99.9%

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

      23. 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. Taylor expanded in y around 0 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

      3. sub-neg 83.8%

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

      4. metadata-eval 83.8%

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

   6. Simplified 83.8%

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

   if 2.5000000000000002e68 < x < 9.50000000000000054e72

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around inf 100.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{x + \left(y + -2\right)}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \end{array} \]

Alternative 4: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-286}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-286}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4400000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+68}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.6e+22)
   -1.0
   (if (<= x -2.7e-286)
     1.0
     (if (<= x 2.7e-286)
       (* y -0.5)
       (if (<= x 4400000000.0)
         1.0
         (if (<= x 3.2e+68) -1.0 (if (<= x 9.5e+72) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.6e+22) {
		tmp = -1.0;
	} else if (x <= -2.7e-286) {
		tmp = 1.0;
	} else if (x <= 2.7e-286) {
		tmp = y * -0.5;
	} else if (x <= 4400000000.0) {
		tmp = 1.0;
	} else if (x <= 3.2e+68) {
		tmp = -1.0;
	} else if (x <= 9.5e+72) {
		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 <= (-2.6d+22)) then
        tmp = -1.0d0
    else if (x <= (-2.7d-286)) then
        tmp = 1.0d0
    else if (x <= 2.7d-286) then
        tmp = y * (-0.5d0)
    else if (x <= 4400000000.0d0) then
        tmp = 1.0d0
    else if (x <= 3.2d+68) then
        tmp = -1.0d0
    else if (x <= 9.5d+72) 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 <= -2.6e+22) {
		tmp = -1.0;
	} else if (x <= -2.7e-286) {
		tmp = 1.0;
	} else if (x <= 2.7e-286) {
		tmp = y * -0.5;
	} else if (x <= 4400000000.0) {
		tmp = 1.0;
	} else if (x <= 3.2e+68) {
		tmp = -1.0;
	} else if (x <= 9.5e+72) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.6e+22:
		tmp = -1.0
	elif x <= -2.7e-286:
		tmp = 1.0
	elif x <= 2.7e-286:
		tmp = y * -0.5
	elif x <= 4400000000.0:
		tmp = 1.0
	elif x <= 3.2e+68:
		tmp = -1.0
	elif x <= 9.5e+72:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.6e+22)
		tmp = -1.0;
	elseif (x <= -2.7e-286)
		tmp = 1.0;
	elseif (x <= 2.7e-286)
		tmp = Float64(y * -0.5);
	elseif (x <= 4400000000.0)
		tmp = 1.0;
	elseif (x <= 3.2e+68)
		tmp = -1.0;
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.6e+22)
		tmp = -1.0;
	elseif (x <= -2.7e-286)
		tmp = 1.0;
	elseif (x <= 2.7e-286)
		tmp = y * -0.5;
	elseif (x <= 4400000000.0)
		tmp = 1.0;
	elseif (x <= 3.2e+68)
		tmp = -1.0;
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.6e+22], -1.0, If[LessEqual[x, -2.7e-286], 1.0, If[LessEqual[x, 2.7e-286], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 4400000000.0], 1.0, If[LessEqual[x, 3.2e+68], -1.0, If[LessEqual[x, 9.5e+72], 1.0, -1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6e22 or 4.4e9 < x < 3.19999999999999994e68 or 9.50000000000000054e72 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-neg-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-/l* 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. div-sub 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. sub-neg 99.9%

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

      14. distribute-frac-neg 99.9%

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

      15. neg-mul-1 99.9%

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

      16. *-commutative 99.9%

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

      17. associate-/l* 99.9%

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

      18. metadata-eval 99.9%

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

      19. /-rgt-identity 99.9%

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

      20. +-commutative 99.9%

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

      21. +-commutative 99.9%

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

      22. associate-+r+ 99.9%

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

      23. 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. Taylor expanded in x around inf 86.0%

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

   if -2.6e22 < x < -2.7000000000000002e-286 or 2.7000000000000002e-286 < x < 4.4e9 or 3.19999999999999994e68 < x < 9.50000000000000054e72

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around inf 53.2%

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

   if -2.7000000000000002e-286 < x < 2.7000000000000002e-286

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in x around 0 92.8%

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

   5. Taylor expanded in y around 0 68.9%

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

      1. *-commutative 68.9%

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

   7. Simplified 68.9%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-286}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-286}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4400000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+68}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+68}:\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8e+15)
   -1.0
   (if (<= x 1.3e-33)
     (/ y (- y 2.0))
     (if (<= x 2.3e+68) (/ (- x) (+ -2.0 x)) (if (<= x 9.5e+72) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8e+15) {
		tmp = -1.0;
	} else if (x <= 1.3e-33) {
		tmp = y / (y - 2.0);
	} else if (x <= 2.3e+68) {
		tmp = -x / (-2.0 + x);
	} else if (x <= 9.5e+72) {
		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 <= (-3.8d+15)) then
        tmp = -1.0d0
    else if (x <= 1.3d-33) then
        tmp = y / (y - 2.0d0)
    else if (x <= 2.3d+68) then
        tmp = -x / ((-2.0d0) + x)
    else if (x <= 9.5d+72) 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 <= -3.8e+15) {
		tmp = -1.0;
	} else if (x <= 1.3e-33) {
		tmp = y / (y - 2.0);
	} else if (x <= 2.3e+68) {
		tmp = -x / (-2.0 + x);
	} else if (x <= 9.5e+72) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8e+15:
		tmp = -1.0
	elif x <= 1.3e-33:
		tmp = y / (y - 2.0)
	elif x <= 2.3e+68:
		tmp = -x / (-2.0 + x)
	elif x <= 9.5e+72:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8e+15)
		tmp = -1.0;
	elseif (x <= 1.3e-33)
		tmp = Float64(y / Float64(y - 2.0));
	elseif (x <= 2.3e+68)
		tmp = Float64(Float64(-x) / Float64(-2.0 + x));
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8e+15)
		tmp = -1.0;
	elseif (x <= 1.3e-33)
		tmp = y / (y - 2.0);
	elseif (x <= 2.3e+68)
		tmp = -x / (-2.0 + x);
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8e+15], -1.0, If[LessEqual[x, 1.3e-33], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+68], N[((-x) / N[(-2.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+72], 1.0, -1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.8e15 or 9.50000000000000054e72 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in x around inf 85.2%

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

   if -3.8e15 < x < 1.29999999999999997e-33

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in x around 0 73.8%

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

   if 1.29999999999999997e-33 < x < 2.3e68

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-neg-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-/l* 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. div-sub 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. sub-neg 99.9%

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

      14. distribute-frac-neg 99.9%

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

      15. neg-mul-1 99.9%

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

      16. *-commutative 99.9%

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

      17. associate-/l* 99.9%

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

      18. metadata-eval 99.9%

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

      19. /-rgt-identity 99.9%

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

      20. +-commutative 99.9%

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

      21. +-commutative 99.9%

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

      22. associate-+r+ 99.9%

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

      23. 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. Taylor expanded in y around 0 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

      3. sub-neg 83.8%

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

      4. metadata-eval 83.8%

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

   6. Simplified 83.8%

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

   if 2.3e68 < x < 9.50000000000000054e72

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around inf 100.0%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+68}:\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+16}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2050000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+67}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e+16)
   -1.0
   (if (<= x 2050000.0)
     1.0
     (if (<= x 5.3e+67) -1.0 (if (<= x 6.2e+77) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e+16) {
		tmp = -1.0;
	} else if (x <= 2050000.0) {
		tmp = 1.0;
	} else if (x <= 5.3e+67) {
		tmp = -1.0;
	} else if (x <= 6.2e+77) {
		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 <= (-5d+16)) then
        tmp = -1.0d0
    else if (x <= 2050000.0d0) then
        tmp = 1.0d0
    else if (x <= 5.3d+67) then
        tmp = -1.0d0
    else if (x <= 6.2d+77) 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 <= -5e+16) {
		tmp = -1.0;
	} else if (x <= 2050000.0) {
		tmp = 1.0;
	} else if (x <= 5.3e+67) {
		tmp = -1.0;
	} else if (x <= 6.2e+77) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e+16:
		tmp = -1.0
	elif x <= 2050000.0:
		tmp = 1.0
	elif x <= 5.3e+67:
		tmp = -1.0
	elif x <= 6.2e+77:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e+16)
		tmp = -1.0;
	elseif (x <= 2050000.0)
		tmp = 1.0;
	elseif (x <= 5.3e+67)
		tmp = -1.0;
	elseif (x <= 6.2e+77)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e+16)
		tmp = -1.0;
	elseif (x <= 2050000.0)
		tmp = 1.0;
	elseif (x <= 5.3e+67)
		tmp = -1.0;
	elseif (x <= 6.2e+77)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e+16], -1.0, If[LessEqual[x, 2050000.0], 1.0, If[LessEqual[x, 5.3e+67], -1.0, If[LessEqual[x, 6.2e+77], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -5e16 or 2.05e6 < x < 5.3e67 or 6.19999999999999997e77 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-neg-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-/l* 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. div-sub 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. sub-neg 99.9%

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

      14. distribute-frac-neg 99.9%

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

      15. neg-mul-1 99.9%

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

      16. *-commutative 99.9%

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

      17. associate-/l* 99.9%

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

      18. metadata-eval 99.9%

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

      19. /-rgt-identity 99.9%

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

      20. +-commutative 99.9%

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

      21. +-commutative 99.9%

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

      22. associate-+r+ 99.9%

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

      23. 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. Taylor expanded in x around inf 86.0%

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

   if -5e16 < x < 2.05e6 or 5.3e67 < x < 6.19999999999999997e77

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around inf 50.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+16}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2050000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+67}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 52000000000:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+68}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.4e+15)
   -1.0
   (if (<= x 52000000000.0)
     (/ y (- y 2.0))
     (if (<= x 4e+68) -1.0 (if (<= x 3.8e+74) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.4e+15) {
		tmp = -1.0;
	} else if (x <= 52000000000.0) {
		tmp = y / (y - 2.0);
	} else if (x <= 4e+68) {
		tmp = -1.0;
	} else if (x <= 3.8e+74) {
		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 <= (-1.4d+15)) then
        tmp = -1.0d0
    else if (x <= 52000000000.0d0) then
        tmp = y / (y - 2.0d0)
    else if (x <= 4d+68) then
        tmp = -1.0d0
    else if (x <= 3.8d+74) 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 <= -1.4e+15) {
		tmp = -1.0;
	} else if (x <= 52000000000.0) {
		tmp = y / (y - 2.0);
	} else if (x <= 4e+68) {
		tmp = -1.0;
	} else if (x <= 3.8e+74) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.4e+15:
		tmp = -1.0
	elif x <= 52000000000.0:
		tmp = y / (y - 2.0)
	elif x <= 4e+68:
		tmp = -1.0
	elif x <= 3.8e+74:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.4e+15)
		tmp = -1.0;
	elseif (x <= 52000000000.0)
		tmp = Float64(y / Float64(y - 2.0));
	elseif (x <= 4e+68)
		tmp = -1.0;
	elseif (x <= 3.8e+74)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.4e+15)
		tmp = -1.0;
	elseif (x <= 52000000000.0)
		tmp = y / (y - 2.0);
	elseif (x <= 4e+68)
		tmp = -1.0;
	elseif (x <= 3.8e+74)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.4e+15], -1.0, If[LessEqual[x, 52000000000.0], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+68], -1.0, If[LessEqual[x, 3.8e+74], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4e15 or 5.2e10 < x < 3.99999999999999981e68 or 3.7999999999999998e74 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. distribute-neg-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-/l* 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. div-sub 99.9%

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

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. sub-neg 99.9%

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

      14. distribute-frac-neg 99.9%

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

      15. neg-mul-1 99.9%

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

      16. *-commutative 99.9%

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

      17. associate-/l* 99.9%

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

      18. metadata-eval 99.9%

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

      19. /-rgt-identity 99.9%

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

      20. +-commutative 99.9%

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

      21. +-commutative 99.9%

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

      22. associate-+r+ 99.9%

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

      23. 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. Taylor expanded in x around inf 86.0%

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

   if -1.4e15 < x < 5.2e10

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in x around 0 71.1%

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

   if 3.99999999999999981e68 < x < 3.7999999999999998e74

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around inf 100.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 52000000000:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+68}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8: 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. Final simplification 100.0%

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

Alternative 9: 38.1% 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. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. unsub-neg 100.0%

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

   4. distribute-neg-in 100.0%

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

   5. neg-mul-1 100.0%

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

   6. *-commutative 100.0%

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

   7. associate-/l* 100.0%

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

   8. +-commutative 100.0%

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

   9. sub-neg 100.0%

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

   10. div-sub 100.0%

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

   11. metadata-eval 100.0%

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

   12. metadata-eval 100.0%

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

   13. sub-neg 100.0%

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

   14. distribute-frac-neg 100.0%

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

   15. neg-mul-1 100.0%

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

   16. *-commutative 100.0%

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

   17. associate-/l* 100.0%

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

   18. metadata-eval 100.0%

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

   19. /-rgt-identity 100.0%

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

   20. +-commutative 100.0%

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

   21. +-commutative 100.0%

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

   22. associate-+r+ 100.0%

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

   23. 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. Taylor expanded in x around inf 42.4%

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

5. Final simplification 42.4%

   \[\leadsto -1 \]

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 2023336 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

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