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

Percentage Accurate: 100.0% → 100.0%

Time: 8.8s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

   1. div-sub 100.0%

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

   2. +-commutative 100.0%

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

   3. associate-+l+ 100.0%

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

   4. +-commutative 100.0%

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

   5. +-commutative 100.0%

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

   6. associate-+l+ 100.0%

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

   7. +-commutative 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-286}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-283}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 12500000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+68}:\\ \;\;\;\;-1 + \frac{2}{x}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+76}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.4e+15)
   -1.0
   (if (<= x -2.4e-286)
     1.0
     (if (<= x 7.6e-283)
       (* y -0.5)
       (if (<= x 12500000000.0)
         1.0
         (if (<= x 3.9e+68)
           (+ -1.0 (/ 2.0 x))
           (if (<= x 2.4e+76) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.4e+15) {
		tmp = -1.0;
	} else if (x <= -2.4e-286) {
		tmp = 1.0;
	} else if (x <= 7.6e-283) {
		tmp = y * -0.5;
	} else if (x <= 12500000000.0) {
		tmp = 1.0;
	} else if (x <= 3.9e+68) {
		tmp = -1.0 + (2.0 / x);
	} else if (x <= 2.4e+76) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.4d+15)) then
        tmp = -1.0d0
    else if (x <= (-2.4d-286)) then
        tmp = 1.0d0
    else if (x <= 7.6d-283) then
        tmp = y * (-0.5d0)
    else if (x <= 12500000000.0d0) then
        tmp = 1.0d0
    else if (x <= 3.9d+68) then
        tmp = (-1.0d0) + (2.0d0 / x)
    else if (x <= 2.4d+76) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.4e+15) {
		tmp = -1.0;
	} else if (x <= -2.4e-286) {
		tmp = 1.0;
	} else if (x <= 7.6e-283) {
		tmp = y * -0.5;
	} else if (x <= 12500000000.0) {
		tmp = 1.0;
	} else if (x <= 3.9e+68) {
		tmp = -1.0 + (2.0 / x);
	} else if (x <= 2.4e+76) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.4e+15:
		tmp = -1.0
	elif x <= -2.4e-286:
		tmp = 1.0
	elif x <= 7.6e-283:
		tmp = y * -0.5
	elif x <= 12500000000.0:
		tmp = 1.0
	elif x <= 3.9e+68:
		tmp = -1.0 + (2.0 / x)
	elif x <= 2.4e+76:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.4e+15)
		tmp = -1.0;
	elseif (x <= -2.4e-286)
		tmp = 1.0;
	elseif (x <= 7.6e-283)
		tmp = Float64(y * -0.5);
	elseif (x <= 12500000000.0)
		tmp = 1.0;
	elseif (x <= 3.9e+68)
		tmp = Float64(-1.0 + Float64(2.0 / x));
	elseif (x <= 2.4e+76)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.4e+15)
		tmp = -1.0;
	elseif (x <= -2.4e-286)
		tmp = 1.0;
	elseif (x <= 7.6e-283)
		tmp = y * -0.5;
	elseif (x <= 12500000000.0)
		tmp = 1.0;
	elseif (x <= 3.9e+68)
		tmp = -1.0 + (2.0 / x);
	elseif (x <= 2.4e+76)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.4e+15], -1.0, If[LessEqual[x, -2.4e-286], 1.0, If[LessEqual[x, 7.6e-283], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 12500000000.0], 1.0, If[LessEqual[x, 3.9e+68], N[(-1.0 + N[(2.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+76], 1.0, -1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.4e15 or 2.4e76 < x

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 85.2%

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

   if -1.4e15 < x < -2.39999999999999993e-286 or 7.6000000000000002e-283 < x < 1.25e10 or 3.90000000000000019e68 < x < 2.4e76

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 53.2%

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

   if -2.39999999999999993e-286 < x < 7.6000000000000002e-283

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 92.8%

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

   5. Taylor expanded in y around 0 68.9%

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

      1. *-commutative 68.9%

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

   7. Simplified 68.9%

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

   if 1.25e10 < x < 3.90000000000000019e68

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 90.7%

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

      1. associate-*r/ 90.7%

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

      2. mul-1-neg 90.7%

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

      3. sub-neg 90.7%

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

      4. metadata-eval 90.7%

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

   6. Simplified 90.7%

      \[\leadsto \color{blue}{\frac{-x}{x + -2}} \]
   7. Step-by-step derivation

      1. div-inv 90.5%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 7.0%

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

      4. sqr-neg 7.0%

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

      5. sqrt-unprod 6.9%

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

      6. add-sqr-sqrt 7.0%

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

      7. frac-2neg 7.0%

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

      8. metadata-eval 7.0%

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

      9. distribute-neg-in 7.0%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 90.5%

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

      12. sqr-neg 90.5%

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

      13. sqrt-unprod 90.1%

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

      14. add-sqr-sqrt 90.5%

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

      15. metadata-eval 90.5%

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

   8. Applied egg-rr 90.5%

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

      1. associate-*r/ 90.7%

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

      2. *-commutative 90.7%

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

      3. mul-1-neg 90.7%

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

   10. Simplified 90.7%

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

   11. Taylor expanded in x around inf 90.7%

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

       1. sub-neg 90.7%

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

       2. associate-*r/ 90.7%

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

       3. metadata-eval 90.7%

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

       4. metadata-eval 90.7%

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

   13. Simplified 90.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-286}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-283}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 12500000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+68}:\\ \;\;\;\;-1 + \frac{2}{x}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+76}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3: 74.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-1.0d0) - ((y * (-2.0d0)) / x)
    if (x <= (-7.5d+14)) then
        tmp = t_0
    else if (x <= 6.8d-34) then
        tmp = y / (y - 2.0d0)
    else if (x <= 2.5d+68) then
        tmp = -x / (x + (-2.0d0))
    else if (x <= 9.5d+72) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 4 regimes

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

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around -inf 86.3%

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

      1. sub-neg 86.3%

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

      2. metadata-eval 86.3%

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

      3. +-commutative 86.3%

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

      4. mul-1-neg 86.3%

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

      5. neg-sub0 86.3%

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

      6. associate-+r- 86.3%

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

      7. metadata-eval 86.3%

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

      8. mul-1-neg 86.3%

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

      9. sub-neg 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in y around inf 86.3%

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

      1. *-commutative 86.3%

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

   9. Simplified 86.3%

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

   if -7.5e14 < x < 6.8000000000000001e-34

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 73.8%

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

   if 6.8000000000000001e-34 < x < 2.5000000000000002e68

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

      3. sub-neg 83.8%

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

      4. metadata-eval 83.8%

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

   6. Simplified 83.8%

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

   if 2.5000000000000002e68 < x < 9.50000000000000054e72

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

4. Final simplification 80.4%

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

Alternative 4: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+17}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.86 \cdot 10^{-286}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 430000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+68}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.5e+17)
   -1.0
   (if (<= x -1.86e-286)
     1.0
     (if (<= x 4e-288)
       (* y -0.5)
       (if (<= x 430000.0)
         1.0
         (if (<= x 4e+68) -1.0 (if (<= x 9.5e+72) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+17) {
		tmp = -1.0;
	} else if (x <= -1.86e-286) {
		tmp = 1.0;
	} else if (x <= 4e-288) {
		tmp = y * -0.5;
	} else if (x <= 430000.0) {
		tmp = 1.0;
	} else if (x <= 4e+68) {
		tmp = -1.0;
	} else if (x <= 9.5e+72) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.5d+17)) then
        tmp = -1.0d0
    else if (x <= (-1.86d-286)) then
        tmp = 1.0d0
    else if (x <= 4d-288) then
        tmp = y * (-0.5d0)
    else if (x <= 430000.0d0) then
        tmp = 1.0d0
    else if (x <= 4d+68) then
        tmp = -1.0d0
    else if (x <= 9.5d+72) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+17) {
		tmp = -1.0;
	} else if (x <= -1.86e-286) {
		tmp = 1.0;
	} else if (x <= 4e-288) {
		tmp = y * -0.5;
	} else if (x <= 430000.0) {
		tmp = 1.0;
	} else if (x <= 4e+68) {
		tmp = -1.0;
	} else if (x <= 9.5e+72) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.5e+17:
		tmp = -1.0
	elif x <= -1.86e-286:
		tmp = 1.0
	elif x <= 4e-288:
		tmp = y * -0.5
	elif x <= 430000.0:
		tmp = 1.0
	elif x <= 4e+68:
		tmp = -1.0
	elif x <= 9.5e+72:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.5e+17)
		tmp = -1.0;
	elseif (x <= -1.86e-286)
		tmp = 1.0;
	elseif (x <= 4e-288)
		tmp = Float64(y * -0.5);
	elseif (x <= 430000.0)
		tmp = 1.0;
	elseif (x <= 4e+68)
		tmp = -1.0;
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.5e+17)
		tmp = -1.0;
	elseif (x <= -1.86e-286)
		tmp = 1.0;
	elseif (x <= 4e-288)
		tmp = y * -0.5;
	elseif (x <= 430000.0)
		tmp = 1.0;
	elseif (x <= 4e+68)
		tmp = -1.0;
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.5e+17], -1.0, If[LessEqual[x, -1.86e-286], 1.0, If[LessEqual[x, 4e-288], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 430000.0], 1.0, If[LessEqual[x, 4e+68], -1.0, If[LessEqual[x, 9.5e+72], 1.0, -1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5e17 or 4.3e5 < x < 3.99999999999999981e68 or 9.50000000000000054e72 < x

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 86.0%

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

   if -2.5e17 < x < -1.86000000000000003e-286 or 4.00000000000000023e-288 < x < 4.3e5 or 3.99999999999999981e68 < x < 9.50000000000000054e72

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 53.2%

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

   if -1.86000000000000003e-286 < x < 4.00000000000000023e-288

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 92.8%

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

   5. Taylor expanded in y around 0 68.9%

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

      1. *-commutative 68.9%

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

   7. Simplified 68.9%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+17}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.86 \cdot 10^{-286}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 430000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+68}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 74.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.6d+15)) then
        tmp = -1.0d0
    else if (x <= 2.1d-32) then
        tmp = y / (y - 2.0d0)
    else if (x <= 4d+68) then
        tmp = -x / (x + (-2.0d0))
    else if (x <= 9.5d+72) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 4 regimes

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

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 85.2%

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

   if -1.6e15 < x < 2.0999999999999999e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 73.8%

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

   if 2.0999999999999999e-32 < x < 3.99999999999999981e68

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 83.8%

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

      1. associate-*r/ 83.8%

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

      2. mul-1-neg 83.8%

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

      3. sub-neg 83.8%

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

      4. metadata-eval 83.8%

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

   6. Simplified 83.8%

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

   if 3.99999999999999981e68 < x < 9.50000000000000054e72

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

4. Final simplification 79.9%

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

Alternative 6: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+68}:\\ \;\;\;\;-1 + \frac{2}{x}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8e+15)
   -1.0
   (if (<= x 5.9e-5)
     (/ y (- y 2.0))
     (if (<= x 2.3e+68) (+ -1.0 (/ 2.0 x)) (if (<= x 9.5e+72) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8e+15) {
		tmp = -1.0;
	} else if (x <= 5.9e-5) {
		tmp = y / (y - 2.0);
	} else if (x <= 2.3e+68) {
		tmp = -1.0 + (2.0 / x);
	} else if (x <= 9.5e+72) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d+15)) then
        tmp = -1.0d0
    else if (x <= 5.9d-5) then
        tmp = y / (y - 2.0d0)
    else if (x <= 2.3d+68) then
        tmp = (-1.0d0) + (2.0d0 / x)
    else if (x <= 9.5d+72) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8e+15) {
		tmp = -1.0;
	} else if (x <= 5.9e-5) {
		tmp = y / (y - 2.0);
	} else if (x <= 2.3e+68) {
		tmp = -1.0 + (2.0 / x);
	} else if (x <= 9.5e+72) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8e+15:
		tmp = -1.0
	elif x <= 5.9e-5:
		tmp = y / (y - 2.0)
	elif x <= 2.3e+68:
		tmp = -1.0 + (2.0 / x)
	elif x <= 9.5e+72:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8e+15)
		tmp = -1.0;
	elseif (x <= 5.9e-5)
		tmp = Float64(y / Float64(y - 2.0));
	elseif (x <= 2.3e+68)
		tmp = Float64(-1.0 + Float64(2.0 / x));
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8e+15)
		tmp = -1.0;
	elseif (x <= 5.9e-5)
		tmp = y / (y - 2.0);
	elseif (x <= 2.3e+68)
		tmp = -1.0 + (2.0 / x);
	elseif (x <= 9.5e+72)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8e+15], -1.0, If[LessEqual[x, 5.9e-5], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+68], N[(-1.0 + N[(2.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+72], 1.0, -1.0]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 85.2%

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

   if -3.8e15 < x < 5.8999999999999998e-5

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 72.2%

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

   if 5.8999999999999998e-5 < x < 2.3e68

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 91.6%

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

      1. associate-*r/ 91.6%

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

      2. mul-1-neg 91.6%

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

      3. sub-neg 91.6%

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

      4. metadata-eval 91.6%

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

   6. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{-x}{x + -2}} \]
   7. Step-by-step derivation

      1. div-inv 91.4%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 6.5%

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

      4. sqr-neg 6.5%

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

      5. sqrt-unprod 6.4%

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

      6. add-sqr-sqrt 6.5%

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

      7. frac-2neg 6.5%

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

      8. metadata-eval 6.5%

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

      9. distribute-neg-in 6.5%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 81.6%

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

      12. sqr-neg 81.6%

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

      13. sqrt-unprod 81.2%

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

      14. add-sqr-sqrt 81.6%

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

      15. metadata-eval 81.6%

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

   8. Applied egg-rr 81.6%

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

      1. associate-*r/ 81.8%

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

      2. *-commutative 81.8%

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

      3. mul-1-neg 81.8%

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

   10. Simplified 81.8%

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

   11. Taylor expanded in x around inf 83.3%

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

       1. sub-neg 83.3%

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

       2. associate-*r/ 83.3%

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

       3. metadata-eval 83.3%

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

       4. metadata-eval 83.3%

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

   13. Simplified 83.3%

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

   if 2.3e68 < x < 9.50000000000000054e72

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{y - 2}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+68}:\\ \;\;\;\;-1 + \frac{2}{x}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 165000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+68}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+73}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.9e+21)
   -1.0
   (if (<= x 165000000000.0)
     1.0
     (if (<= x 4e+68) -1.0 (if (<= x 1.55e+73) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.9e+21) {
		tmp = -1.0;
	} else if (x <= 165000000000.0) {
		tmp = 1.0;
	} else if (x <= 4e+68) {
		tmp = -1.0;
	} else if (x <= 1.55e+73) {
		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 <= (-1.9d+21)) then
        tmp = -1.0d0
    else if (x <= 165000000000.0d0) then
        tmp = 1.0d0
    else if (x <= 4d+68) then
        tmp = -1.0d0
    else if (x <= 1.55d+73) 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 <= -1.9e+21) {
		tmp = -1.0;
	} else if (x <= 165000000000.0) {
		tmp = 1.0;
	} else if (x <= 4e+68) {
		tmp = -1.0;
	} else if (x <= 1.55e+73) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.9e+21:
		tmp = -1.0
	elif x <= 165000000000.0:
		tmp = 1.0
	elif x <= 4e+68:
		tmp = -1.0
	elif x <= 1.55e+73:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.9e+21)
		tmp = -1.0;
	elseif (x <= 165000000000.0)
		tmp = 1.0;
	elseif (x <= 4e+68)
		tmp = -1.0;
	elseif (x <= 1.55e+73)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.9e+21)
		tmp = -1.0;
	elseif (x <= 165000000000.0)
		tmp = 1.0;
	elseif (x <= 4e+68)
		tmp = -1.0;
	elseif (x <= 1.55e+73)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.9e+21], -1.0, If[LessEqual[x, 165000000000.0], 1.0, If[LessEqual[x, 4e+68], -1.0, If[LessEqual[x, 1.55e+73], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e21 or 1.65e11 < x < 3.99999999999999981e68 or 1.55e73 < x

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 86.0%

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

   if -1.9e21 < x < 1.65e11 or 3.99999999999999981e68 < x < 1.55e73

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 50.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 165000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+68}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+73}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 9: 38.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 42.4%

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

5. Final simplification 42.4%

   \[\leadsto -1 \]

Developer target: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

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

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

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