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

Percentage Accurate: 100.0% → 100.0%

Time: 9.3s

Alternatives: 11

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 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. 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: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+40}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \mathbf{elif}\;x \leq -20000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{elif}\;x \leq 65000:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1 + \frac{y + \left(y - 2\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.8e+40)
   (- -1.0 (/ (* y -2.0) x))
   (if (<= x -20000000000000.0)
     1.0
     (if (<= x -5.6e-45)
       (/ (- x) (+ -2.0 x))
       (if (<= x 65000.0) (/ y (- y 2.0)) (+ -1.0 (/ (+ y (- y 2.0)) x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.8e+40) {
		tmp = -1.0 - ((y * -2.0) / x);
	} else if (x <= -20000000000000.0) {
		tmp = 1.0;
	} else if (x <= -5.6e-45) {
		tmp = -x / (-2.0 + x);
	} else if (x <= 65000.0) {
		tmp = y / (y - 2.0);
	} else {
		tmp = -1.0 + ((y + (y - 2.0)) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.8d+40)) then
        tmp = (-1.0d0) - ((y * (-2.0d0)) / x)
    else if (x <= (-20000000000000.0d0)) then
        tmp = 1.0d0
    else if (x <= (-5.6d-45)) then
        tmp = -x / ((-2.0d0) + x)
    else if (x <= 65000.0d0) then
        tmp = y / (y - 2.0d0)
    else
        tmp = (-1.0d0) + ((y + (y - 2.0d0)) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.8e+40) {
		tmp = -1.0 - ((y * -2.0) / x);
	} else if (x <= -20000000000000.0) {
		tmp = 1.0;
	} else if (x <= -5.6e-45) {
		tmp = -x / (-2.0 + x);
	} else if (x <= 65000.0) {
		tmp = y / (y - 2.0);
	} else {
		tmp = -1.0 + ((y + (y - 2.0)) / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.8e+40:
		tmp = -1.0 - ((y * -2.0) / x)
	elif x <= -20000000000000.0:
		tmp = 1.0
	elif x <= -5.6e-45:
		tmp = -x / (-2.0 + x)
	elif x <= 65000.0:
		tmp = y / (y - 2.0)
	else:
		tmp = -1.0 + ((y + (y - 2.0)) / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.8e+40)
		tmp = Float64(-1.0 - Float64(Float64(y * -2.0) / x));
	elseif (x <= -20000000000000.0)
		tmp = 1.0;
	elseif (x <= -5.6e-45)
		tmp = Float64(Float64(-x) / Float64(-2.0 + x));
	elseif (x <= 65000.0)
		tmp = Float64(y / Float64(y - 2.0));
	else
		tmp = Float64(-1.0 + Float64(Float64(y + Float64(y - 2.0)) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.8e+40)
		tmp = -1.0 - ((y * -2.0) / x);
	elseif (x <= -20000000000000.0)
		tmp = 1.0;
	elseif (x <= -5.6e-45)
		tmp = -x / (-2.0 + x);
	elseif (x <= 65000.0)
		tmp = y / (y - 2.0);
	else
		tmp = -1.0 + ((y + (y - 2.0)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.8e+40], N[(-1.0 - N[(N[(y * -2.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -20000000000000.0], 1.0, If[LessEqual[x, -5.6e-45], N[((-x) / N[(-2.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 65000.0], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], N[(-1.0 + N[(N[(y + N[(y - 2.0), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.8000000000000001e40

   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 84.5%

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

      1. sub-neg 84.5%

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

      2. metadata-eval 84.5%

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

      3. +-commutative 84.5%

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

      4. mul-1-neg 84.5%

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

      5. unsub-neg 84.5%

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

      6. mul-1-neg 84.5%

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

      7. unsub-neg 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in y around inf 84.5%

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

      1. *-commutative 84.5%

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

   9. Simplified 84.5%

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

   if -2.8000000000000001e40 < x < -2e13

   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%

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

   if -2e13 < x < -5.6000000000000003e-45

   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 0 72.9%

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

      1. associate-*r/ 72.9%

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

      2. mul-1-neg 72.9%

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

      3. sub-neg 72.9%

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

      4. metadata-eval 72.9%

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

   6. Simplified 72.9%

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

   if -5.6000000000000003e-45 < x < 65000

   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 82.1%

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

   if 65000 < 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 78.3%

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

      1. sub-neg 78.3%

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

      2. metadata-eval 78.3%

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

      3. +-commutative 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. mul-1-neg 78.3%

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

      7. unsub-neg 78.3%

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

   6. Simplified 78.3%

      \[\leadsto \color{blue}{-1 - \frac{\left(2 - y\right) - y}{x}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+40}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \mathbf{elif}\;x \leq -20000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{elif}\;x \leq 65000:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1 + \frac{y + \left(y - 2\right)}{x}\\ \end{array} \]

Alternative 3: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - \frac{y \cdot -2}{x}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{elif}\;x \leq 85000:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- -1.0 (/ (* y -2.0) x))))
   (if (<= x -2.5e+39)
     t_0
     (if (<= x -1e+15)
       1.0
       (if (<= x -9e-45)
         (/ (- x) (+ -2.0 x))
         (if (<= x 85000.0) (/ y (- y 2.0)) t_0))))))

C

double code(double x, double y) {
	double t_0 = -1.0 - ((y * -2.0) / x);
	double tmp;
	if (x <= -2.5e+39) {
		tmp = t_0;
	} else if (x <= -1e+15) {
		tmp = 1.0;
	} else if (x <= -9e-45) {
		tmp = -x / (-2.0 + x);
	} else if (x <= 85000.0) {
		tmp = y / (y - 2.0);
	} 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 <= (-2.5d+39)) then
        tmp = t_0
    else if (x <= (-1d+15)) then
        tmp = 1.0d0
    else if (x <= (-9d-45)) then
        tmp = -x / ((-2.0d0) + x)
    else if (x <= 85000.0d0) then
        tmp = y / (y - 2.0d0)
    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 <= -2.5e+39) {
		tmp = t_0;
	} else if (x <= -1e+15) {
		tmp = 1.0;
	} else if (x <= -9e-45) {
		tmp = -x / (-2.0 + x);
	} else if (x <= 85000.0) {
		tmp = y / (y - 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -1.0 - ((y * -2.0) / x)
	tmp = 0
	if x <= -2.5e+39:
		tmp = t_0
	elif x <= -1e+15:
		tmp = 1.0
	elif x <= -9e-45:
		tmp = -x / (-2.0 + x)
	elif x <= 85000.0:
		tmp = y / (y - 2.0)
	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 <= -2.5e+39)
		tmp = t_0;
	elseif (x <= -1e+15)
		tmp = 1.0;
	elseif (x <= -9e-45)
		tmp = Float64(Float64(-x) / Float64(-2.0 + x));
	elseif (x <= 85000.0)
		tmp = Float64(y / Float64(y - 2.0));
	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 <= -2.5e+39)
		tmp = t_0;
	elseif (x <= -1e+15)
		tmp = 1.0;
	elseif (x <= -9e-45)
		tmp = -x / (-2.0 + x);
	elseif (x <= 85000.0)
		tmp = y / (y - 2.0);
	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, -2.5e+39], t$95$0, If[LessEqual[x, -1e+15], 1.0, If[LessEqual[x, -9e-45], N[((-x) / N[(-2.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 85000.0], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.50000000000000008e39 or 85000 < 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 80.8%

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

      1. sub-neg 80.8%

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

      2. metadata-eval 80.8%

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

      3. +-commutative 80.8%

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

      4. mul-1-neg 80.8%

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

      5. unsub-neg 80.8%

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

      6. mul-1-neg 80.8%

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

      7. unsub-neg 80.8%

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

   6. Simplified 80.8%

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

   7. Taylor expanded in y around inf 80.6%

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

      1. *-commutative 80.6%

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

   9. Simplified 80.6%

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

   if -2.50000000000000008e39 < x < -1e15

   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%

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

   if -1e15 < x < -8.9999999999999997e-45

   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 0 72.9%

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

      1. associate-*r/ 72.9%

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

      2. mul-1-neg 72.9%

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

      3. sub-neg 72.9%

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

      4. metadata-eval 72.9%

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

   6. Simplified 72.9%

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

   if -8.9999999999999997e-45 < x < 85000

   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 82.1%

      \[\leadsto \color{blue}{\frac{y}{y - 2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{elif}\;x \leq 85000:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \end{array} \]

Alternative 4: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+48}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -13500000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-45} \lor \neg \left(x \leq 2.8 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2e+48)
   -1.0
   (if (<= x -13500000000.0)
     1.0
     (if (or (<= x -3.2e-45) (not (<= x 2.8e-12)))
       (/ (- x) (+ -2.0 x))
       (/ y (- y 2.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2e+48) {
		tmp = -1.0;
	} else if (x <= -13500000000.0) {
		tmp = 1.0;
	} else if ((x <= -3.2e-45) || !(x <= 2.8e-12)) {
		tmp = -x / (-2.0 + x);
	} else {
		tmp = y / (y - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2d+48)) then
        tmp = -1.0d0
    else if (x <= (-13500000000.0d0)) then
        tmp = 1.0d0
    else if ((x <= (-3.2d-45)) .or. (.not. (x <= 2.8d-12))) then
        tmp = -x / ((-2.0d0) + x)
    else
        tmp = y / (y - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2e+48) {
		tmp = -1.0;
	} else if (x <= -13500000000.0) {
		tmp = 1.0;
	} else if ((x <= -3.2e-45) || !(x <= 2.8e-12)) {
		tmp = -x / (-2.0 + x);
	} else {
		tmp = y / (y - 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2e+48:
		tmp = -1.0
	elif x <= -13500000000.0:
		tmp = 1.0
	elif (x <= -3.2e-45) or not (x <= 2.8e-12):
		tmp = -x / (-2.0 + x)
	else:
		tmp = y / (y - 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2e+48)
		tmp = -1.0;
	elseif (x <= -13500000000.0)
		tmp = 1.0;
	elseif ((x <= -3.2e-45) || !(x <= 2.8e-12))
		tmp = Float64(Float64(-x) / Float64(-2.0 + x));
	else
		tmp = Float64(y / Float64(y - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2e+48)
		tmp = -1.0;
	elseif (x <= -13500000000.0)
		tmp = 1.0;
	elseif ((x <= -3.2e-45) || ~((x <= 2.8e-12)))
		tmp = -x / (-2.0 + x);
	else
		tmp = y / (y - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2e+48], -1.0, If[LessEqual[x, -13500000000.0], 1.0, If[Or[LessEqual[x, -3.2e-45], N[Not[LessEqual[x, 2.8e-12]], $MachinePrecision]], N[((-x) / N[(-2.0 + x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.00000000000000009e48

   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 83.9%

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

   if -2.00000000000000009e48 < x < -1.35e10

   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%

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

   if -1.35e10 < x < -3.20000000000000007e-45 or 2.8000000000000002e-12 < 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 y around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. mul-1-neg 75.7%

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

      3. sub-neg 75.7%

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

      4. metadata-eval 75.7%

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

   6. Simplified 75.7%

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

   if -3.20000000000000007e-45 < x < 2.8000000000000002e-12

   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 83.1%

      \[\leadsto \color{blue}{\frac{y}{y - 2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+48}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -13500000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-45} \lor \neg \left(x \leq 2.8 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{-x}{-2 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \]

Alternative 5: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+41}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 85000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{2}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e+41)
   -1.0
   (if (<= x -7.2e-10)
     1.0
     (if (<= x -9e-45) (* x 0.5) (if (<= x 85000.0) 1.0 (- -1.0 (/ 2.0 x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e+41) {
		tmp = -1.0;
	} else if (x <= -7.2e-10) {
		tmp = 1.0;
	} else if (x <= -9e-45) {
		tmp = x * 0.5;
	} else if (x <= 85000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0 - (2.0 / x);
	}
	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+41)) then
        tmp = -1.0d0
    else if (x <= (-7.2d-10)) then
        tmp = 1.0d0
    else if (x <= (-9d-45)) then
        tmp = x * 0.5d0
    else if (x <= 85000.0d0) then
        tmp = 1.0d0
    else
        tmp = (-1.0d0) - (2.0d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5e+41) {
		tmp = -1.0;
	} else if (x <= -7.2e-10) {
		tmp = 1.0;
	} else if (x <= -9e-45) {
		tmp = x * 0.5;
	} else if (x <= 85000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0 - (2.0 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e+41:
		tmp = -1.0
	elif x <= -7.2e-10:
		tmp = 1.0
	elif x <= -9e-45:
		tmp = x * 0.5
	elif x <= 85000.0:
		tmp = 1.0
	else:
		tmp = -1.0 - (2.0 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e+41)
		tmp = -1.0;
	elseif (x <= -7.2e-10)
		tmp = 1.0;
	elseif (x <= -9e-45)
		tmp = Float64(x * 0.5);
	elseif (x <= 85000.0)
		tmp = 1.0;
	else
		tmp = Float64(-1.0 - Float64(2.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e+41)
		tmp = -1.0;
	elseif (x <= -7.2e-10)
		tmp = 1.0;
	elseif (x <= -9e-45)
		tmp = x * 0.5;
	elseif (x <= 85000.0)
		tmp = 1.0;
	else
		tmp = -1.0 - (2.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e+41], -1.0, If[LessEqual[x, -7.2e-10], 1.0, If[LessEqual[x, -9e-45], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 85000.0], 1.0, N[(-1.0 - N[(2.0 / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.00000000000000022e41

   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 83.9%

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

   if -5.00000000000000022e41 < x < -7.2e-10 or -8.9999999999999997e-45 < x < 85000

   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 60.6%

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

   if -7.2e-10 < x < -8.9999999999999997e-45

   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 0 71.9%

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

      1. associate-*r/ 71.9%

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

      2. mul-1-neg 71.9%

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

      3. sub-neg 71.9%

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

      4. metadata-eval 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in x around 0 67.7%

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

      1. *-commutative 67.7%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   9. Simplified 67.7%

      \[\leadsto \color{blue}{x \cdot 0.5} \]

   if 85000 < 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 78.3%

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

      1. sub-neg 78.3%

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

      2. metadata-eval 78.3%

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

      3. +-commutative 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. mul-1-neg 78.3%

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

      7. unsub-neg 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in y around 0 76.5%

      \[\leadsto -1 - \frac{\color{blue}{2}}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+41}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 85000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{2}{x}\\ \end{array} \]

Alternative 6: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 15000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{2}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.4e+45)
   -1.0
   (if (<= x -2.4e-9)
     (- 1.0 (/ x y))
     (if (<= x -1e-44) (* x 0.5) (if (<= x 15000.0) 1.0 (- -1.0 (/ 2.0 x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.4e+45) {
		tmp = -1.0;
	} else if (x <= -2.4e-9) {
		tmp = 1.0 - (x / y);
	} else if (x <= -1e-44) {
		tmp = x * 0.5;
	} else if (x <= 15000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0 - (2.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.4d+45)) then
        tmp = -1.0d0
    else if (x <= (-2.4d-9)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= (-1d-44)) then
        tmp = x * 0.5d0
    else if (x <= 15000.0d0) then
        tmp = 1.0d0
    else
        tmp = (-1.0d0) - (2.0d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.4e+45) {
		tmp = -1.0;
	} else if (x <= -2.4e-9) {
		tmp = 1.0 - (x / y);
	} else if (x <= -1e-44) {
		tmp = x * 0.5;
	} else if (x <= 15000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0 - (2.0 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.4e+45:
		tmp = -1.0
	elif x <= -2.4e-9:
		tmp = 1.0 - (x / y)
	elif x <= -1e-44:
		tmp = x * 0.5
	elif x <= 15000.0:
		tmp = 1.0
	else:
		tmp = -1.0 - (2.0 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.4e+45)
		tmp = -1.0;
	elseif (x <= -2.4e-9)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= -1e-44)
		tmp = Float64(x * 0.5);
	elseif (x <= 15000.0)
		tmp = 1.0;
	else
		tmp = Float64(-1.0 - Float64(2.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.4e+45)
		tmp = -1.0;
	elseif (x <= -2.4e-9)
		tmp = 1.0 - (x / y);
	elseif (x <= -1e-44)
		tmp = x * 0.5;
	elseif (x <= 15000.0)
		tmp = 1.0;
	else
		tmp = -1.0 - (2.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.4e+45], -1.0, If[LessEqual[x, -2.4e-9], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1e-44], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 15000.0], 1.0, N[(-1.0 - N[(2.0 / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.39999999999999989e45

   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 83.9%

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

   if -2.39999999999999989e45 < x < -2.4e-9

   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. Taylor expanded in y around inf 71.1%

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

   7. Taylor expanded in y around inf 71.1%

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

   if -2.4e-9 < x < -9.99999999999999953e-45

   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 0 71.9%

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

      1. associate-*r/ 71.9%

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

      2. mul-1-neg 71.9%

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

      3. sub-neg 71.9%

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

      4. metadata-eval 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in x around 0 67.7%

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

      1. *-commutative 67.7%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   9. Simplified 67.7%

      \[\leadsto \color{blue}{x \cdot 0.5} \]

   if -9.99999999999999953e-45 < x < 15000

   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 59.7%

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

   if 15000 < 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 78.3%

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

      1. sub-neg 78.3%

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

      2. metadata-eval 78.3%

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

      3. +-commutative 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. mul-1-neg 78.3%

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

      7. unsub-neg 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in y around 0 76.5%

      \[\leadsto -1 - \frac{\color{blue}{2}}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 15000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{2}{x}\\ \end{array} \]

Alternative 7: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-10}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 85000:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{2}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.2e+46)
   -1.0
   (if (<= x -7.2e-10)
     (- 1.0 (/ x y))
     (if (<= x -9e-45)
       (* x 0.5)
       (if (<= x 85000.0) (/ y (- y 2.0)) (- -1.0 (/ 2.0 x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.2e+46) {
		tmp = -1.0;
	} else if (x <= -7.2e-10) {
		tmp = 1.0 - (x / y);
	} else if (x <= -9e-45) {
		tmp = x * 0.5;
	} else if (x <= 85000.0) {
		tmp = y / (y - 2.0);
	} else {
		tmp = -1.0 - (2.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.2d+46)) then
        tmp = -1.0d0
    else if (x <= (-7.2d-10)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= (-9d-45)) then
        tmp = x * 0.5d0
    else if (x <= 85000.0d0) then
        tmp = y / (y - 2.0d0)
    else
        tmp = (-1.0d0) - (2.0d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.2e+46) {
		tmp = -1.0;
	} else if (x <= -7.2e-10) {
		tmp = 1.0 - (x / y);
	} else if (x <= -9e-45) {
		tmp = x * 0.5;
	} else if (x <= 85000.0) {
		tmp = y / (y - 2.0);
	} else {
		tmp = -1.0 - (2.0 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.2e+46:
		tmp = -1.0
	elif x <= -7.2e-10:
		tmp = 1.0 - (x / y)
	elif x <= -9e-45:
		tmp = x * 0.5
	elif x <= 85000.0:
		tmp = y / (y - 2.0)
	else:
		tmp = -1.0 - (2.0 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.2e+46)
		tmp = -1.0;
	elseif (x <= -7.2e-10)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= -9e-45)
		tmp = Float64(x * 0.5);
	elseif (x <= 85000.0)
		tmp = Float64(y / Float64(y - 2.0));
	else
		tmp = Float64(-1.0 - Float64(2.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.2e+46)
		tmp = -1.0;
	elseif (x <= -7.2e-10)
		tmp = 1.0 - (x / y);
	elseif (x <= -9e-45)
		tmp = x * 0.5;
	elseif (x <= 85000.0)
		tmp = y / (y - 2.0);
	else
		tmp = -1.0 - (2.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.2e+46], -1.0, If[LessEqual[x, -7.2e-10], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9e-45], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 85000.0], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], N[(-1.0 - N[(2.0 / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.1999999999999998e46

   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 83.9%

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

   if -3.1999999999999998e46 < x < -7.2e-10

   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. Taylor expanded in y around inf 71.1%

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

   7. Taylor expanded in y around inf 71.1%

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

   if -7.2e-10 < x < -8.9999999999999997e-45

   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 0 71.9%

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

      1. associate-*r/ 71.9%

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

      2. mul-1-neg 71.9%

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

      3. sub-neg 71.9%

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

      4. metadata-eval 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in x around 0 67.7%

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

      1. *-commutative 67.7%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   9. Simplified 67.7%

      \[\leadsto \color{blue}{x \cdot 0.5} \]

   if -8.9999999999999997e-45 < x < 85000

   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 82.1%

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

   if 85000 < 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 78.3%

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

      1. sub-neg 78.3%

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

      2. metadata-eval 78.3%

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

      3. +-commutative 78.3%

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

      4. mul-1-neg 78.3%

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

      5. unsub-neg 78.3%

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

      6. mul-1-neg 78.3%

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

      7. unsub-neg 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in y around 0 76.5%

      \[\leadsto -1 - \frac{\color{blue}{2}}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-10}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-45}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 85000:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{2}{x}\\ \end{array} \]

Alternative 8: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+39}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 65000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.8e+39)
   -1.0
   (if (<= x -7.2e-10)
     1.0
     (if (<= x -1.2e-44) (* x 0.5) (if (<= x 65000.0) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.8e+39) {
		tmp = -1.0;
	} else if (x <= -7.2e-10) {
		tmp = 1.0;
	} else if (x <= -1.2e-44) {
		tmp = x * 0.5;
	} else if (x <= 65000.0) {
		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 <= (-1.8d+39)) then
        tmp = -1.0d0
    else if (x <= (-7.2d-10)) then
        tmp = 1.0d0
    else if (x <= (-1.2d-44)) then
        tmp = x * 0.5d0
    else if (x <= 65000.0d0) 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 <= -1.8e+39) {
		tmp = -1.0;
	} else if (x <= -7.2e-10) {
		tmp = 1.0;
	} else if (x <= -1.2e-44) {
		tmp = x * 0.5;
	} else if (x <= 65000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.8e+39:
		tmp = -1.0
	elif x <= -7.2e-10:
		tmp = 1.0
	elif x <= -1.2e-44:
		tmp = x * 0.5
	elif x <= 65000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.8e+39)
		tmp = -1.0;
	elseif (x <= -7.2e-10)
		tmp = 1.0;
	elseif (x <= -1.2e-44)
		tmp = Float64(x * 0.5);
	elseif (x <= 65000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.8e+39)
		tmp = -1.0;
	elseif (x <= -7.2e-10)
		tmp = 1.0;
	elseif (x <= -1.2e-44)
		tmp = x * 0.5;
	elseif (x <= 65000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.8e+39], -1.0, If[LessEqual[x, -7.2e-10], 1.0, If[LessEqual[x, -1.2e-44], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 65000.0], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999992e39 or 65000 < 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 79.3%

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

   if -1.79999999999999992e39 < x < -7.2e-10 or -1.20000000000000004e-44 < x < 65000

   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 60.6%

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

   if -7.2e-10 < x < -1.20000000000000004e-44

   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 0 71.9%

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

      1. associate-*r/ 71.9%

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

      2. mul-1-neg 71.9%

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

      3. sub-neg 71.9%

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

      4. metadata-eval 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in x around 0 67.7%

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

      1. *-commutative 67.7%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   9. Simplified 67.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+39}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-44}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 65000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 10: 62.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 75000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e+43) -1.0 (if (<= x 75000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e+43) {
		tmp = -1.0;
	} else if (x <= 75000.0) {
		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+43)) then
        tmp = -1.0d0
    else if (x <= 75000.0d0) 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+43) {
		tmp = -1.0;
	} else if (x <= 75000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e+43:
		tmp = -1.0
	elif x <= 75000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e+43)
		tmp = -1.0;
	elseif (x <= 75000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e+43)
		tmp = -1.0;
	elseif (x <= 75000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e+43], -1.0, If[LessEqual[x, 75000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000004e43 or 75000 < 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 79.3%

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

   if -5.0000000000000004e43 < x < 75000

   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 58.0%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 75000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 11: 37.8% 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 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 39.1%

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

5. Final simplification 39.1%

   \[\leadsto -1 \]

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 2023309 
(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))))