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

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

Alternatives: 7

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+118}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+55}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-26} \lor \neg \left(x \leq 1.25 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.12e+118)
   (- -1.0 (/ (* y -2.0) x))
   (if (<= x -4e+55)
     (+ 1.0 (/ (* x -2.0) y))
     (if (or (<= x -9.8e-26) (not (<= x 1.25e-29)))
       (/ x (- 2.0 x))
       (/ y (- y 2.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.12e+118) {
		tmp = -1.0 - ((y * -2.0) / x);
	} else if (x <= -4e+55) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else if ((x <= -9.8e-26) || !(x <= 1.25e-29)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.12d+118)) then
        tmp = (-1.0d0) - ((y * (-2.0d0)) / x)
    else if (x <= (-4d+55)) then
        tmp = 1.0d0 + ((x * (-2.0d0)) / y)
    else if ((x <= (-9.8d-26)) .or. (.not. (x <= 1.25d-29))) then
        tmp = x / (2.0d0 - x)
    else
        tmp = y / (y - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.12e+118) {
		tmp = -1.0 - ((y * -2.0) / x);
	} else if (x <= -4e+55) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else if ((x <= -9.8e-26) || !(x <= 1.25e-29)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y - 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.12e+118:
		tmp = -1.0 - ((y * -2.0) / x)
	elif x <= -4e+55:
		tmp = 1.0 + ((x * -2.0) / y)
	elif (x <= -9.8e-26) or not (x <= 1.25e-29):
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y - 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.12e+118)
		tmp = Float64(-1.0 - Float64(Float64(y * -2.0) / x));
	elseif (x <= -4e+55)
		tmp = Float64(1.0 + Float64(Float64(x * -2.0) / y));
	elseif ((x <= -9.8e-26) || !(x <= 1.25e-29))
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(y / Float64(y - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.12e+118)
		tmp = -1.0 - ((y * -2.0) / x);
	elseif (x <= -4e+55)
		tmp = 1.0 + ((x * -2.0) / y);
	elseif ((x <= -9.8e-26) || ~((x <= 1.25e-29)))
		tmp = x / (2.0 - x);
	else
		tmp = y / (y - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.12e+118], N[(-1.0 - N[(N[(y * -2.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e+55], N[(1.0 + N[(N[(x * -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -9.8e-26], N[Not[LessEqual[x, 1.25e-29]], $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 < -1.11999999999999999e118

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 90.1%

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

      1. sub-neg 90.1%

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

      2. +-commutative 90.1%

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

      3. distribute-neg-in 90.1%

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

      4. metadata-eval 90.1%

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

      5. mul-1-neg 90.1%

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

      6. remove-double-neg 90.1%

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

      7. associate-+l+ 90.1%

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

      8. remove-double-neg 90.1%

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

      9. mul-1-neg 90.1%

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

      10. neg-sub0 90.1%

          \[\leadsto -1 + \left(\color{blue}{\left(0 - -1 \cdot \frac{y - 2}{x}\right)} + \frac{y}{x}\right) \]

      11. associate--r- 90.1%

          \[\leadsto -1 + \color{blue}{\left(0 - \left(-1 \cdot \frac{y - 2}{x} - \frac{y}{x}\right)\right)} \]

      12. associate-*r/ 90.1%

          \[\leadsto -1 + \left(0 - \left(\color{blue}{\frac{-1 \cdot \left(y - 2\right)}{x}} - \frac{y}{x}\right)\right) \]

      13. sub-neg 90.1%

          \[\leadsto -1 + \left(0 - \left(\frac{-1 \cdot \color{blue}{\left(y + \left(-2\right)\right)}}{x} - \frac{y}{x}\right)\right) \]

      14. metadata-eval 90.1%

          \[\leadsto -1 + \left(0 - \left(\frac{-1 \cdot \left(y + \color{blue}{-2}\right)}{x} - \frac{y}{x}\right)\right) \]

      15. +-commutative 90.1%

          \[\leadsto -1 + \left(0 - \left(\frac{-1 \cdot \color{blue}{\left(-2 + y\right)}}{x} - \frac{y}{x}\right)\right) \]

      16. distribute-lft-in 90.1%

          \[\leadsto -1 + \left(0 - \left(\frac{\color{blue}{-1 \cdot -2 + -1 \cdot y}}{x} - \frac{y}{x}\right)\right) \]

      17. metadata-eval 90.1%

          \[\leadsto -1 + \left(0 - \left(\frac{\color{blue}{2} + -1 \cdot y}{x} - \frac{y}{x}\right)\right) \]

      18. div-sub 90.1%

          \[\leadsto -1 + \left(0 - \color{blue}{\frac{\left(2 + -1 \cdot y\right) - y}{x}}\right) \]

   7. Simplified 90.1%

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

   8. Taylor expanded in y around inf 90.1%

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

      1. associate-*r/ 90.1%

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

      2. *-commutative 90.1%

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

   10. Simplified 90.1%

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

   if -1.11999999999999999e118 < x < -4.00000000000000004e55

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 83.7%

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

      1. associate--l+ 83.7%

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

      2. +-commutative 83.7%

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

      3. mul-1-neg 83.7%

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

      4. unsub-neg 83.7%

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

      5. associate-*r/ 83.7%

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

      6. metadata-eval 83.7%

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

      7. div-sub 83.7%

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

      8. unsub-neg 83.7%

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

      9. mul-1-neg 83.7%

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

      10. div-sub 83.7%

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

      11. mul-1-neg 83.7%

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

      12. associate--l+ 83.7%

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

      13. sub-neg 83.7%

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

      14. mul-1-neg 83.7%

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

      15. mul-1-neg 83.7%

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

      16. distribute-rgt-out 83.7%

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

      17. metadata-eval 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in x around inf 83.7%

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

      1. associate-*r/ 83.7%

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

      2. *-commutative 83.7%

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

   10. Simplified 83.7%

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

   if -4.00000000000000004e55 < x < -9.7999999999999998e-26 or 1.24999999999999996e-29 < x

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. distribute-neg-frac2 81.0%

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

      3. neg-sub0 81.0%

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

      4. associate-+l- 81.0%

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

      5. neg-sub0 81.0%

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

      6. +-commutative 81.0%

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

      7. unsub-neg 81.0%

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

   7. Simplified 81.0%

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

   if -9.7999999999999998e-26 < x < 1.24999999999999996e-29

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 81.7%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+118}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+55}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-26} \lor \neg \left(x \leq 1.25 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+118}:\\ \;\;\;\;-1 - \frac{y \cdot -2}{x}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{1}{y - 2} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.12e+118)
   (- -1.0 (/ (* y -2.0) x))
   (if (<= x 2.6e-9) (* (/ 1.0 (- y 2.0)) (- y x)) (/ x (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.12e+118) {
		tmp = -1.0 - ((y * -2.0) / x);
	} else if (x <= 2.6e-9) {
		tmp = (1.0 / (y - 2.0)) * (y - x);
	} else {
		tmp = x / (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 <= (-1.12d+118)) then
        tmp = (-1.0d0) - ((y * (-2.0d0)) / x)
    else if (x <= 2.6d-9) then
        tmp = (1.0d0 / (y - 2.0d0)) * (y - x)
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.12e+118) {
		tmp = -1.0 - ((y * -2.0) / x);
	} else if (x <= 2.6e-9) {
		tmp = (1.0 / (y - 2.0)) * (y - x);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.12e+118:
		tmp = -1.0 - ((y * -2.0) / x)
	elif x <= 2.6e-9:
		tmp = (1.0 / (y - 2.0)) * (y - x)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.12e+118)
		tmp = Float64(-1.0 - Float64(Float64(y * -2.0) / x));
	elseif (x <= 2.6e-9)
		tmp = Float64(Float64(1.0 / Float64(y - 2.0)) * Float64(y - x));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.12e+118)
		tmp = -1.0 - ((y * -2.0) / x);
	elseif (x <= 2.6e-9)
		tmp = (1.0 / (y - 2.0)) * (y - x);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.12e+118], N[(-1.0 - N[(N[(y * -2.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e-9], N[(N[(1.0 / N[(y - 2.0), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.11999999999999999e118

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 90.1%

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

      1. sub-neg 90.1%

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

      2. +-commutative 90.1%

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

      3. distribute-neg-in 90.1%

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

      4. metadata-eval 90.1%

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

      5. mul-1-neg 90.1%

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

      6. remove-double-neg 90.1%

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

      7. associate-+l+ 90.1%

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

      8. remove-double-neg 90.1%

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

      9. mul-1-neg 90.1%

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

      10. neg-sub0 90.1%

          \[\leadsto -1 + \left(\color{blue}{\left(0 - -1 \cdot \frac{y - 2}{x}\right)} + \frac{y}{x}\right) \]

      11. associate--r- 90.1%

          \[\leadsto -1 + \color{blue}{\left(0 - \left(-1 \cdot \frac{y - 2}{x} - \frac{y}{x}\right)\right)} \]

      12. associate-*r/ 90.1%

          \[\leadsto -1 + \left(0 - \left(\color{blue}{\frac{-1 \cdot \left(y - 2\right)}{x}} - \frac{y}{x}\right)\right) \]

      13. sub-neg 90.1%

          \[\leadsto -1 + \left(0 - \left(\frac{-1 \cdot \color{blue}{\left(y + \left(-2\right)\right)}}{x} - \frac{y}{x}\right)\right) \]

      14. metadata-eval 90.1%

          \[\leadsto -1 + \left(0 - \left(\frac{-1 \cdot \left(y + \color{blue}{-2}\right)}{x} - \frac{y}{x}\right)\right) \]

      15. +-commutative 90.1%

          \[\leadsto -1 + \left(0 - \left(\frac{-1 \cdot \color{blue}{\left(-2 + y\right)}}{x} - \frac{y}{x}\right)\right) \]

      16. distribute-lft-in 90.1%

          \[\leadsto -1 + \left(0 - \left(\frac{\color{blue}{-1 \cdot -2 + -1 \cdot y}}{x} - \frac{y}{x}\right)\right) \]

      17. metadata-eval 90.1%

          \[\leadsto -1 + \left(0 - \left(\frac{\color{blue}{2} + -1 \cdot y}{x} - \frac{y}{x}\right)\right) \]

      18. div-sub 90.1%

          \[\leadsto -1 + \left(0 - \color{blue}{\frac{\left(2 + -1 \cdot y\right) - y}{x}}\right) \]

   7. Simplified 90.1%

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

   8. Taylor expanded in y around inf 90.1%

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

      1. associate-*r/ 90.1%

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

      2. *-commutative 90.1%

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

   10. Simplified 90.1%

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

   if -1.11999999999999999e118 < x < 2.6000000000000001e-9

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 91.2%

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

   if 2.6000000000000001e-9 < x

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. distribute-neg-frac2 83.7%

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

      3. neg-sub0 83.7%

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

      4. associate-+l- 83.7%

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

      5. neg-sub0 83.7%

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

      6. +-commutative 83.7%

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

      7. unsub-neg 83.7%

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

   7. Simplified 83.7%

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

Alternative 4: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-24} \lor \neg \left(x \leq 1.1 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.2e-24) (not (<= x 1.1e-29)))
   (/ x (- 2.0 x))
   (/ y (- y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e-24) || !(x <= 1.1e-29)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.2d-24)) .or. (.not. (x <= 1.1d-29))) then
        tmp = x / (2.0d0 - x)
    else
        tmp = y / (y - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e-24) || !(x <= 1.1e-29)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y - 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.2e-24) or not (x <= 1.1e-29):
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y - 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.2e-24) || !(x <= 1.1e-29))
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(y / Float64(y - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.2e-24) || ~((x <= 1.1e-29)))
		tmp = x / (2.0 - x);
	else
		tmp = y / (y - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.2e-24], N[Not[LessEqual[x, 1.1e-29]], $MachinePrecision]], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1999999999999999e-24 or 1.09999999999999995e-29 < x

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. distribute-neg-frac2 78.7%

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

      3. neg-sub0 78.7%

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

      4. associate-+l- 78.7%

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

      5. neg-sub0 78.7%

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

      6. +-commutative 78.7%

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

      7. unsub-neg 78.7%

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

   7. Simplified 78.7%

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

   if -1.1999999999999999e-24 < x < 1.09999999999999995e-29

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 81.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-24} \lor \neg \left(x \leq 1.1 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+15) 1.0 (if (<= y 6.2e+56) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+15) {
		tmp = 1.0;
	} else if (y <= 6.2e+56) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5d+15)) then
        tmp = 1.0d0
    else if (y <= 6.2d+56) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5e+15) {
		tmp = 1.0;
	} else if (y <= 6.2e+56) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+15:
		tmp = 1.0
	elif y <= 6.2e+56:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+15)
		tmp = 1.0;
	elseif (y <= 6.2e+56)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+15)
		tmp = 1.0;
	elseif (y <= 6.2e+56)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+15], 1.0, If[LessEqual[y, 6.2e+56], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5e15 or 6.20000000000000009e56 < y

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 74.3%

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

   if -5e15 < y < 6.20000000000000009e56

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. distribute-neg-frac2 74.3%

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

      3. neg-sub0 74.3%

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

      4. associate-+l- 74.3%

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

      5. neg-sub0 74.3%

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

      6. +-commutative 74.3%

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

      7. unsub-neg 74.3%

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

   7. Simplified 74.3%

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

Alternative 6: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+118}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 9500000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.12e+118) -1.0 (if (<= x 9500000000000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.12e+118) {
		tmp = -1.0;
	} else if (x <= 9500000000000.0) {
		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 <= (-1.12d+118)) then
        tmp = -1.0d0
    else if (x <= 9500000000000.0d0) 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 <= -1.12e+118) {
		tmp = -1.0;
	} else if (x <= 9500000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.12e+118:
		tmp = -1.0
	elif x <= 9500000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.12e+118)
		tmp = -1.0;
	elseif (x <= 9500000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.12e+118)
		tmp = -1.0;
	elseif (x <= 9500000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.12e+118], -1.0, If[LessEqual[x, 9500000000000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.11999999999999999e118 or 9.5e12 < x

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 87.3%

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

   if -1.11999999999999999e118 < x < 9.5e12

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 48.6%

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

Alternative 7: 37.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

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

   1. remove-double-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. distribute-neg-frac2 100.0%

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

   4. distribute-frac-neg 100.0%

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

   5. sub-neg 100.0%

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

   6. distribute-neg-in 100.0%

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

   7. remove-double-neg 100.0%

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

   8. +-commutative 100.0%

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

   9. sub-neg 100.0%

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

   10. neg-sub0 100.0%

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

   11. associate--r- 100.0%

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

   12. metadata-eval 100.0%

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

   13. metadata-eval 100.0%

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

   14. +-commutative 100.0%

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

   15. +-commutative 100.0%

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

   16. associate-+r+ 100.0%

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

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around inf 44.4%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Developer target: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024106 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

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

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