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

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

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]

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{x + -2}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-83}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-96}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 - \frac{2}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x) (+ x -2.0))))
   (if (<= y -5.8e-22)
     (/ y (- y 2.0))
     (if (<= y -1.9e-83)
       t_0
       (if (<= y -1.05e-96)
         (* y -0.5)
         (if (<= y 2.3e-17) t_0 (/ 1.0 (- 1.0 (/ 2.0 y)))))))))

C

double code(double x, double y) {
	double t_0 = -x / (x + -2.0);
	double tmp;
	if (y <= -5.8e-22) {
		tmp = y / (y - 2.0);
	} else if (y <= -1.9e-83) {
		tmp = t_0;
	} else if (y <= -1.05e-96) {
		tmp = y * -0.5;
	} else if (y <= 2.3e-17) {
		tmp = t_0;
	} else {
		tmp = 1.0 / (1.0 - (2.0 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -x / (x + (-2.0d0))
    if (y <= (-5.8d-22)) then
        tmp = y / (y - 2.0d0)
    else if (y <= (-1.9d-83)) then
        tmp = t_0
    else if (y <= (-1.05d-96)) then
        tmp = y * (-0.5d0)
    else if (y <= 2.3d-17) then
        tmp = t_0
    else
        tmp = 1.0d0 / (1.0d0 - (2.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -x / (x + -2.0);
	double tmp;
	if (y <= -5.8e-22) {
		tmp = y / (y - 2.0);
	} else if (y <= -1.9e-83) {
		tmp = t_0;
	} else if (y <= -1.05e-96) {
		tmp = y * -0.5;
	} else if (y <= 2.3e-17) {
		tmp = t_0;
	} else {
		tmp = 1.0 / (1.0 - (2.0 / y));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -x / (x + -2.0)
	tmp = 0
	if y <= -5.8e-22:
		tmp = y / (y - 2.0)
	elif y <= -1.9e-83:
		tmp = t_0
	elif y <= -1.05e-96:
		tmp = y * -0.5
	elif y <= 2.3e-17:
		tmp = t_0
	else:
		tmp = 1.0 / (1.0 - (2.0 / y))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(-x) / Float64(x + -2.0))
	tmp = 0.0
	if (y <= -5.8e-22)
		tmp = Float64(y / Float64(y - 2.0));
	elseif (y <= -1.9e-83)
		tmp = t_0;
	elseif (y <= -1.05e-96)
		tmp = Float64(y * -0.5);
	elseif (y <= 2.3e-17)
		tmp = t_0;
	else
		tmp = Float64(1.0 / Float64(1.0 - Float64(2.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -x / (x + -2.0);
	tmp = 0.0;
	if (y <= -5.8e-22)
		tmp = y / (y - 2.0);
	elseif (y <= -1.9e-83)
		tmp = t_0;
	elseif (y <= -1.05e-96)
		tmp = y * -0.5;
	elseif (y <= 2.3e-17)
		tmp = t_0;
	else
		tmp = 1.0 / (1.0 - (2.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[((-x) / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e-22], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-83], t$95$0, If[LessEqual[y, -1.05e-96], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 2.3e-17], t$95$0, N[(1.0 / N[(1.0 - N[(2.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.8000000000000003e-22

   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 84.0%

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

   if -5.8000000000000003e-22 < y < -1.89999999999999988e-83 or -1.05000000000000001e-96 < y < 2.30000000000000009e-17

   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 85.6%

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

      1. associate-*r/ 85.6%

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

      2. mul-1-neg 85.6%

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

      3. sub-neg 85.6%

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

      4. metadata-eval 85.6%

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

   6. Simplified 85.6%

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

   if -1.89999999999999988e-83 < y < -1.05000000000000001e-96

   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 0 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 2.30000000000000009e-17 < y

   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 81.7%

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

      1. clear-num 81.7%

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

      2. inv-pow 81.7%

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

      3. sub-neg 81.7%

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

      4. metadata-eval 81.7%

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

   6. Applied egg-rr 81.7%

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

      1. unpow-1 81.7%

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

      2. metadata-eval 81.7%

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

      3. sub-neg 81.7%

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

      4. div-sub 81.7%

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

      5. *-inverses 81.7%

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

   8. Simplified 81.7%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-83}:\\ \;\;\;\;\frac{-x}{x + -2}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-96}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;\frac{-x}{x + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 - \frac{2}{y}}\\ \end{array} \]

Alternative 3: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y - 2}\\ t_1 := \frac{-x}{x + -2}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-96}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (- y 2.0))) (t_1 (/ (- x) (+ x -2.0))))
   (if (<= y -1.1e-20)
     t_0
     (if (<= y -2.4e-83)
       t_1
       (if (<= y -2.7e-96) (* y -0.5) (if (<= y 1.55e-17) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = y / (y - 2.0);
	double t_1 = -x / (x + -2.0);
	double tmp;
	if (y <= -1.1e-20) {
		tmp = t_0;
	} else if (y <= -2.4e-83) {
		tmp = t_1;
	} else if (y <= -2.7e-96) {
		tmp = y * -0.5;
	} else if (y <= 1.55e-17) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = y / (y - 2.0d0)
    t_1 = -x / (x + (-2.0d0))
    if (y <= (-1.1d-20)) then
        tmp = t_0
    else if (y <= (-2.4d-83)) then
        tmp = t_1
    else if (y <= (-2.7d-96)) then
        tmp = y * (-0.5d0)
    else if (y <= 1.55d-17) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y - 2.0);
	double t_1 = -x / (x + -2.0);
	double tmp;
	if (y <= -1.1e-20) {
		tmp = t_0;
	} else if (y <= -2.4e-83) {
		tmp = t_1;
	} else if (y <= -2.7e-96) {
		tmp = y * -0.5;
	} else if (y <= 1.55e-17) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y - 2.0)
	t_1 = -x / (x + -2.0)
	tmp = 0
	if y <= -1.1e-20:
		tmp = t_0
	elif y <= -2.4e-83:
		tmp = t_1
	elif y <= -2.7e-96:
		tmp = y * -0.5
	elif y <= 1.55e-17:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y - 2.0))
	t_1 = Float64(Float64(-x) / Float64(x + -2.0))
	tmp = 0.0
	if (y <= -1.1e-20)
		tmp = t_0;
	elseif (y <= -2.4e-83)
		tmp = t_1;
	elseif (y <= -2.7e-96)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.55e-17)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y - 2.0);
	t_1 = -x / (x + -2.0);
	tmp = 0.0;
	if (y <= -1.1e-20)
		tmp = t_0;
	elseif (y <= -2.4e-83)
		tmp = t_1;
	elseif (y <= -2.7e-96)
		tmp = y * -0.5;
	elseif (y <= 1.55e-17)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-x) / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e-20], t$95$0, If[LessEqual[y, -2.4e-83], t$95$1, If[LessEqual[y, -2.7e-96], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.55e-17], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.09999999999999995e-20 or 1.5499999999999999e-17 < y

   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 83.0%

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

   if -1.09999999999999995e-20 < y < -2.4000000000000001e-83 or -2.7e-96 < y < 1.5499999999999999e-17

   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 85.6%

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

      1. associate-*r/ 85.6%

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

      2. mul-1-neg 85.6%

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

      3. sub-neg 85.6%

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

      4. metadata-eval 85.6%

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

   6. Simplified 85.6%

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

   if -2.4000000000000001e-83 < y < -2.7e-96

   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 0 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-83}:\\ \;\;\;\;\frac{-x}{x + -2}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-96}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-17}:\\ \;\;\;\;\frac{-x}{x + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \]

Alternative 4: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+29} \lor \neg \left(x \leq 8.5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.5e+29) (not (<= x 8.5e+30))) (/ (- y x) x) (/ y (- y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.5e+29) || !(x <= 8.5e+30)) {
		tmp = (y - x) / 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 <= (-5.5d+29)) .or. (.not. (x <= 8.5d+30))) then
        tmp = (y - x) / 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 <= -5.5e+29) || !(x <= 8.5e+30)) {
		tmp = (y - x) / x;
	} else {
		tmp = y / (y - 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.5e+29) or not (x <= 8.5e+30):
		tmp = (y - x) / x
	else:
		tmp = y / (y - 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.5e+29) || !(x <= 8.5e+30))
		tmp = Float64(Float64(y - x) / 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 <= -5.5e+29) || ~((x <= 8.5e+30)))
		tmp = (y - x) / x;
	else
		tmp = y / (y - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.5e+29], N[Not[LessEqual[x, 8.5e+30]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / x), $MachinePrecision], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e29 or 8.4999999999999995e30 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. associate-/r/ 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 81.6%

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

      1. associate-*l/ 81.8%

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

      2. *-un-lft-identity 81.8%

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

   8. Applied egg-rr 81.8%

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

   if -5.5e29 < x < 8.4999999999999995e30

   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 80.2%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+29} \lor \neg \left(x \leq 8.5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \]

Alternative 5: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+30}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 500000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{2}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e+30) -1.0 (if (<= x 500000000.0) 1.0 (- -1.0 (/ 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e+30) {
		tmp = -1.0;
	} else if (x <= 500000000.0) {
		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+30)) then
        tmp = -1.0d0
    else if (x <= 500000000.0d0) 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+30) {
		tmp = -1.0;
	} else if (x <= 500000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0 - (2.0 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e+30:
		tmp = -1.0
	elif x <= 500000000.0:
		tmp = 1.0
	else:
		tmp = -1.0 - (2.0 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e+30)
		tmp = -1.0;
	elseif (x <= 500000000.0)
		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+30)
		tmp = -1.0;
	elseif (x <= 500000000.0)
		tmp = 1.0;
	else
		tmp = -1.0 - (2.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e+30], -1.0, If[LessEqual[x, 500000000.0], 1.0, N[(-1.0 - N[(2.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.9999999999999998e30

   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 75.2%

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

   if -4.9999999999999998e30 < x < 5e8

   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 63.3%

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

   if 5e8 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 82.8%

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

      1. associate-*r/ 82.8%

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

      2. mul-1-neg 82.8%

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

      3. sub-neg 82.8%

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

      4. metadata-eval 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in x around inf 82.8%

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

      1. distribute-neg-in 82.8%

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

      2. metadata-eval 82.8%

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

      3. unsub-neg 82.8%

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

      4. associate-*r/ 82.8%

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

      5. metadata-eval 82.8%

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

   9. Simplified 82.8%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+30}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 500000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{2}{x}\\ \end{array} \]

Alternative 6: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+30}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3e+30) -1.0 (if (<= x 6.2e+38) (/ y (- y 2.0)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3e+30) {
		tmp = -1.0;
	} else if (x <= 6.2e+38) {
		tmp = y / (y - 2.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d+30)) then
        tmp = -1.0d0
    else if (x <= 6.2d+38) then
        tmp = y / (y - 2.0d0)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3e+30) {
		tmp = -1.0;
	} else if (x <= 6.2e+38) {
		tmp = y / (y - 2.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3e+30:
		tmp = -1.0
	elif x <= 6.2e+38:
		tmp = y / (y - 2.0)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3e+30)
		tmp = -1.0;
	elseif (x <= 6.2e+38)
		tmp = Float64(y / Float64(y - 2.0));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3e+30)
		tmp = -1.0;
	elseif (x <= 6.2e+38)
		tmp = y / (y - 2.0);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3e+30], -1.0, If[LessEqual[x, 6.2e+38], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e30 or 6.20000000000000035e38 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 81.2%

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

   if -2.3e30 < x < 6.20000000000000035e38

   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 80.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+30}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7: 63.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+30}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.1e+30) -1.0 (if (<= x 5.8e+16) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.1e+30) {
		tmp = -1.0;
	} else if (x <= 5.8e+16) {
		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 <= (-4.1d+30)) then
        tmp = -1.0d0
    else if (x <= 5.8d+16) 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 <= -4.1e+30) {
		tmp = -1.0;
	} else if (x <= 5.8e+16) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.1e+30:
		tmp = -1.0
	elif x <= 5.8e+16:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.1e+30)
		tmp = -1.0;
	elseif (x <= 5.8e+16)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.1e+30)
		tmp = -1.0;
	elseif (x <= 5.8e+16)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.1e+30], -1.0, If[LessEqual[x, 5.8e+16], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.10000000000000005e30 or 5.8e16 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 80.0%

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

   if -4.10000000000000005e30 < x < 5.8e16

   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 63.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+30}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8: 38.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. unsub-neg 100.0%

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

   4. distribute-neg-in 100.0%

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

   5. neg-mul-1 100.0%

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

   6. *-commutative 100.0%

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

   7. associate-/l* 100.0%

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

   8. +-commutative 100.0%

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

   9. sub-neg 100.0%

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

   10. div-sub 100.0%

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

   11. metadata-eval 100.0%

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

   12. metadata-eval 100.0%

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

   13. sub-neg 100.0%

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

   14. distribute-frac-neg 100.0%

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

   15. neg-mul-1 100.0%

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

   16. *-commutative 100.0%

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

   17. associate-/l* 100.0%

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

   18. metadata-eval 100.0%

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

   19. /-rgt-identity 100.0%

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

   20. +-commutative 100.0%

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

   21. +-commutative 100.0%

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

   22. associate-+r+ 100.0%

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

   23. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 36.5%

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

5. Final simplification 36.5%

   \[\leadsto -1 \]

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 2023306 
(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))))