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

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 13

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

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

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]]

Derivation

1. Initial program 99.9%

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

   1. associate--r+ 99.9%

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

3. Simplified 99.9%

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

   1. div-sub 100.0%

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

   2. associate--l- 100.0%

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

   3. associate--l- 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 68.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -7.9 \cdot 10^{+139}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+55}:\\ \;\;\;\;-1 + \frac{y}{x}\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-79}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-206}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-151}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -7.9e+139)
     1.0
     (if (<= y -2.05e+55)
       (+ -1.0 (/ y x))
       (if (<= y -4.9e+30)
         1.0
         (if (<= y -9.5e-35)
           t_0
           (if (<= y -5.4e-79)
             (* y -0.5)
             (if (<= y 6e-206)
               t_0
               (if (<= y 1.55e-151)
                 (* y -0.5)
                 (if (<= y 2.6e+30) t_0 1.0))))))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -7.9e+139) {
		tmp = 1.0;
	} else if (y <= -2.05e+55) {
		tmp = -1.0 + (y / x);
	} else if (y <= -4.9e+30) {
		tmp = 1.0;
	} else if (y <= -9.5e-35) {
		tmp = t_0;
	} else if (y <= -5.4e-79) {
		tmp = y * -0.5;
	} else if (y <= 6e-206) {
		tmp = t_0;
	} else if (y <= 1.55e-151) {
		tmp = y * -0.5;
	} else if (y <= 2.6e+30) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-7.9d+139)) then
        tmp = 1.0d0
    else if (y <= (-2.05d+55)) then
        tmp = (-1.0d0) + (y / x)
    else if (y <= (-4.9d+30)) then
        tmp = 1.0d0
    else if (y <= (-9.5d-35)) then
        tmp = t_0
    else if (y <= (-5.4d-79)) then
        tmp = y * (-0.5d0)
    else if (y <= 6d-206) then
        tmp = t_0
    else if (y <= 1.55d-151) then
        tmp = y * (-0.5d0)
    else if (y <= 2.6d+30) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -7.9e+139) {
		tmp = 1.0;
	} else if (y <= -2.05e+55) {
		tmp = -1.0 + (y / x);
	} else if (y <= -4.9e+30) {
		tmp = 1.0;
	} else if (y <= -9.5e-35) {
		tmp = t_0;
	} else if (y <= -5.4e-79) {
		tmp = y * -0.5;
	} else if (y <= 6e-206) {
		tmp = t_0;
	} else if (y <= 1.55e-151) {
		tmp = y * -0.5;
	} else if (y <= 2.6e+30) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -7.9e+139:
		tmp = 1.0
	elif y <= -2.05e+55:
		tmp = -1.0 + (y / x)
	elif y <= -4.9e+30:
		tmp = 1.0
	elif y <= -9.5e-35:
		tmp = t_0
	elif y <= -5.4e-79:
		tmp = y * -0.5
	elif y <= 6e-206:
		tmp = t_0
	elif y <= 1.55e-151:
		tmp = y * -0.5
	elif y <= 2.6e+30:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -7.9e+139)
		tmp = 1.0;
	elseif (y <= -2.05e+55)
		tmp = Float64(-1.0 + Float64(y / x));
	elseif (y <= -4.9e+30)
		tmp = 1.0;
	elseif (y <= -9.5e-35)
		tmp = t_0;
	elseif (y <= -5.4e-79)
		tmp = Float64(y * -0.5);
	elseif (y <= 6e-206)
		tmp = t_0;
	elseif (y <= 1.55e-151)
		tmp = Float64(y * -0.5);
	elseif (y <= 2.6e+30)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -7.9e+139)
		tmp = 1.0;
	elseif (y <= -2.05e+55)
		tmp = -1.0 + (y / x);
	elseif (y <= -4.9e+30)
		tmp = 1.0;
	elseif (y <= -9.5e-35)
		tmp = t_0;
	elseif (y <= -5.4e-79)
		tmp = y * -0.5;
	elseif (y <= 6e-206)
		tmp = t_0;
	elseif (y <= 1.55e-151)
		tmp = y * -0.5;
	elseif (y <= 2.6e+30)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.9e+139], 1.0, If[LessEqual[y, -2.05e+55], N[(-1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.9e+30], 1.0, If[LessEqual[y, -9.5e-35], t$95$0, If[LessEqual[y, -5.4e-79], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 6e-206], t$95$0, If[LessEqual[y, 1.55e-151], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 2.6e+30], t$95$0, 1.0]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.90000000000000019e139 or -2.04999999999999991e55 < y < -4.89999999999999984e30 or 2.59999999999999988e30 < y

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 81.5%

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

   if -7.90000000000000019e139 < y < -2.04999999999999991e55

   1. Initial program 99.7%

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

      1. associate--r+ 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.2%

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

      3. associate--l- 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in x around inf 62.0%

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

   7. Taylor expanded in x around 0 62.5%

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

   if -4.89999999999999984e30 < y < -9.5000000000000003e-35 or -5.4000000000000004e-79 < y < 6.0000000000000004e-206 or 1.54999999999999992e-151 < y < 2.59999999999999988e30

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 71.1%

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

   if -9.5000000000000003e-35 < y < -5.4000000000000004e-79 or 6.0000000000000004e-206 < y < 1.54999999999999992e-151

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. distribute-neg-frac 75.9%

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

   6. Simplified 75.9%

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

   7. Taylor expanded in y around 0 75.9%

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

      1. *-commutative 75.9%

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

   9. Simplified 75.9%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.9 \cdot 10^{+139}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+55}:\\ \;\;\;\;-1 + \frac{y}{x}\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-79}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-151}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 + \frac{y}{x}\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-189}:\\ \;\;\;\;1 - \frac{2}{y}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-269}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-304}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-207}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ -1.0 (/ y x))))
   (if (<= x -2.9e+17)
     t_0
     (if (<= x -2.5e-189)
       (- 1.0 (/ 2.0 y))
       (if (<= x -6.2e-269)
         (* y -0.5)
         (if (<= x -5.5e-304)
           1.0
           (if (<= x 1.4e-207) (* y -0.5) (if (<= x 5.2e+14) 1.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = -1.0 + (y / x);
	double tmp;
	if (x <= -2.9e+17) {
		tmp = t_0;
	} else if (x <= -2.5e-189) {
		tmp = 1.0 - (2.0 / y);
	} else if (x <= -6.2e-269) {
		tmp = y * -0.5;
	} else if (x <= -5.5e-304) {
		tmp = 1.0;
	} else if (x <= 1.4e-207) {
		tmp = y * -0.5;
	} else if (x <= 5.2e+14) {
		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 / x)
    if (x <= (-2.9d+17)) then
        tmp = t_0
    else if (x <= (-2.5d-189)) then
        tmp = 1.0d0 - (2.0d0 / y)
    else if (x <= (-6.2d-269)) then
        tmp = y * (-0.5d0)
    else if (x <= (-5.5d-304)) then
        tmp = 1.0d0
    else if (x <= 1.4d-207) then
        tmp = y * (-0.5d0)
    else if (x <= 5.2d+14) 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 / x);
	double tmp;
	if (x <= -2.9e+17) {
		tmp = t_0;
	} else if (x <= -2.5e-189) {
		tmp = 1.0 - (2.0 / y);
	} else if (x <= -6.2e-269) {
		tmp = y * -0.5;
	} else if (x <= -5.5e-304) {
		tmp = 1.0;
	} else if (x <= 1.4e-207) {
		tmp = y * -0.5;
	} else if (x <= 5.2e+14) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -1.0 + (y / x)
	tmp = 0
	if x <= -2.9e+17:
		tmp = t_0
	elif x <= -2.5e-189:
		tmp = 1.0 - (2.0 / y)
	elif x <= -6.2e-269:
		tmp = y * -0.5
	elif x <= -5.5e-304:
		tmp = 1.0
	elif x <= 1.4e-207:
		tmp = y * -0.5
	elif x <= 5.2e+14:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-1.0 + Float64(y / x))
	tmp = 0.0
	if (x <= -2.9e+17)
		tmp = t_0;
	elseif (x <= -2.5e-189)
		tmp = Float64(1.0 - Float64(2.0 / y));
	elseif (x <= -6.2e-269)
		tmp = Float64(y * -0.5);
	elseif (x <= -5.5e-304)
		tmp = 1.0;
	elseif (x <= 1.4e-207)
		tmp = Float64(y * -0.5);
	elseif (x <= 5.2e+14)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -1.0 + (y / x);
	tmp = 0.0;
	if (x <= -2.9e+17)
		tmp = t_0;
	elseif (x <= -2.5e-189)
		tmp = 1.0 - (2.0 / y);
	elseif (x <= -6.2e-269)
		tmp = y * -0.5;
	elseif (x <= -5.5e-304)
		tmp = 1.0;
	elseif (x <= 1.4e-207)
		tmp = y * -0.5;
	elseif (x <= 5.2e+14)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e+17], t$95$0, If[LessEqual[x, -2.5e-189], N[(1.0 - N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e-269], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, -5.5e-304], 1.0, If[LessEqual[x, 1.4e-207], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 5.2e+14], 1.0, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.9e17 or 5.2e14 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.7%

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

      3. associate--l- 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 80.1%

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

   7. Taylor expanded in x around 0 80.4%

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

   if -2.9e17 < x < -2.4999999999999999e-189

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. distribute-neg-frac 71.3%

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

   6. Simplified 71.3%

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

      1. frac-2neg 71.3%

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

      2. div-inv 71.2%

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

      3. remove-double-neg 71.2%

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

      4. sub-neg 71.2%

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

      5. distribute-neg-in 71.2%

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

      6. metadata-eval 71.2%

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

      7. remove-double-neg 71.2%

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

   8. Applied egg-rr 71.2%

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

      1. associate-*r/ 71.3%

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

      2. *-rgt-identity 71.3%

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

      3. +-commutative 71.3%

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

   10. Simplified 71.3%

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

       1. frac-2neg 71.3%

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

       2. +-commutative 71.3%

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

       3. distribute-neg-in 71.3%

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

       4. metadata-eval 71.3%

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

       5. add-sqr-sqrt 29.7%

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

       6. sqrt-unprod 27.3%

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

       7. sqr-neg 27.3%

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

       8. sqrt-unprod 12.3%

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

       9. add-sqr-sqrt 17.2%

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

       10. *-un-lft-identity 17.2%

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

       11. add-cube-cbrt 16.8%

           \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{-y} \cdot \sqrt[3]{-y}\right) \cdot \sqrt[3]{-y}}}{1 \cdot \left(2 + y\right)} \]

       12. times-frac 16.8%

           \[\leadsto \color{blue}{\frac{\sqrt[3]{-y} \cdot \sqrt[3]{-y}}{1} \cdot \frac{\sqrt[3]{-y}}{2 + y}} \]

       13. cbrt-unprod 16.8%

           \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(-y\right) \cdot \left(-y\right)}}}{1} \cdot \frac{\sqrt[3]{-y}}{2 + y} \]

       14. sqr-neg 16.8%

           \[\leadsto \frac{\sqrt[3]{\color{blue}{y \cdot y}}}{1} \cdot \frac{\sqrt[3]{-y}}{2 + y} \]

       15. cbrt-unprod 16.8%

           \[\leadsto \frac{\color{blue}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{1} \cdot \frac{\sqrt[3]{-y}}{2 + y} \]

       16. pow2 16.8%

           \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{-y}}{2 + y} \]

   12. Applied egg-rr 54.6%

       \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{y + 2}} \]
   13. Step-by-step derivation

       1. /-rgt-identity 54.6%

          \[\leadsto \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{y + 2} \]

       2. associate-*r/ 54.7%

          \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{y + 2}} \]

       3. unpow2 54.7%

          \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{y + 2} \]

       4. rem-3cbrt-lft 55.6%

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

   14. Simplified 55.6%

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

   15. Taylor expanded in y around inf 55.2%

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

       1. associate-*r/ 55.2%

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

       2. metadata-eval 55.2%

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

   17. Simplified 55.2%

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

   if -2.4999999999999999e-189 < x < -6.19999999999999933e-269 or -5.50000000000000035e-304 < x < 1.39999999999999996e-207

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 95.0%

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

      1. mul-1-neg 95.0%

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

      2. distribute-neg-frac 95.0%

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

   6. Simplified 95.0%

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

   7. Taylor expanded in y around 0 63.9%

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

      1. *-commutative 63.9%

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

   9. Simplified 63.9%

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

   if -6.19999999999999933e-269 < x < -5.50000000000000035e-304 or 1.39999999999999996e-207 < x < 5.2e14

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 60.7%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+17}:\\ \;\;\;\;-1 + \frac{y}{x}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-189}:\\ \;\;\;\;1 - \frac{2}{y}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-269}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-304}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-207}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1 + \frac{y}{x}\\ \end{array} \]

Alternative 4: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+18}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-25}:\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4100000000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{y}{2 - \left(x + y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7e+18)
   (/ (- y x) x)
   (if (<= x -3.1e-25)
     (+ 1.0 (/ (- (- 2.0 x) x) y))
     (if (<= x -7.2e-38)
       (* x 0.5)
       (if (<= x 4100000000000.0)
         (/ y (+ y -2.0))
         (- -1.0 (/ y (- 2.0 (+ x y)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7e+18) {
		tmp = (y - x) / x;
	} else if (x <= -3.1e-25) {
		tmp = 1.0 + (((2.0 - x) - x) / y);
	} else if (x <= -7.2e-38) {
		tmp = x * 0.5;
	} else if (x <= 4100000000000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = -1.0 - (y / (2.0 - (x + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-7d+18)) then
        tmp = (y - x) / x
    else if (x <= (-3.1d-25)) then
        tmp = 1.0d0 + (((2.0d0 - x) - x) / y)
    else if (x <= (-7.2d-38)) then
        tmp = x * 0.5d0
    else if (x <= 4100000000000.0d0) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = (-1.0d0) - (y / (2.0d0 - (x + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -7e+18) {
		tmp = (y - x) / x;
	} else if (x <= -3.1e-25) {
		tmp = 1.0 + (((2.0 - x) - x) / y);
	} else if (x <= -7.2e-38) {
		tmp = x * 0.5;
	} else if (x <= 4100000000000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = -1.0 - (y / (2.0 - (x + y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7e+18:
		tmp = (y - x) / x
	elif x <= -3.1e-25:
		tmp = 1.0 + (((2.0 - x) - x) / y)
	elif x <= -7.2e-38:
		tmp = x * 0.5
	elif x <= 4100000000000.0:
		tmp = y / (y + -2.0)
	else:
		tmp = -1.0 - (y / (2.0 - (x + y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7e+18)
		tmp = Float64(Float64(y - x) / x);
	elseif (x <= -3.1e-25)
		tmp = Float64(1.0 + Float64(Float64(Float64(2.0 - x) - x) / y));
	elseif (x <= -7.2e-38)
		tmp = Float64(x * 0.5);
	elseif (x <= 4100000000000.0)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(-1.0 - Float64(y / Float64(2.0 - Float64(x + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7e+18)
		tmp = (y - x) / x;
	elseif (x <= -3.1e-25)
		tmp = 1.0 + (((2.0 - x) - x) / y);
	elseif (x <= -7.2e-38)
		tmp = x * 0.5;
	elseif (x <= 4100000000000.0)
		tmp = y / (y + -2.0);
	else
		tmp = -1.0 - (y / (2.0 - (x + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7e+18], N[(N[(y - x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, -3.1e-25], N[(1.0 + N[(N[(N[(2.0 - x), $MachinePrecision] - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.2e-38], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 4100000000000.0], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(-1.0 - N[(y / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -7e18

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.6%

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

      3. associate--l- 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 79.7%

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

      1. associate-*l/ 80.0%

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

      2. sub-neg 80.0%

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

      3. distribute-lft-in 80.0%

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

      4. neg-mul-1 80.0%

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

      5. neg-mul-1 80.0%

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

      6. remove-double-neg 80.0%

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

   8. Applied egg-rr 80.0%

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

   if -7e18 < x < -3.09999999999999995e-25

   1. Initial program 99.8%

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

      1. associate--r+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 71.0%

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

      1. associate--l+ 71.0%

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

      2. associate-*r/ 71.0%

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

      3. associate-*r/ 71.0%

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

      4. div-sub 71.0%

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

      5. cancel-sign-sub-inv 71.0%

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

      6. metadata-eval 71.0%

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

      7. *-lft-identity 71.0%

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

      8. +-commutative 71.0%

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

      9. mul-1-neg 71.0%

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

      10. unsub-neg 71.0%

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

   6. Simplified 71.0%

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

   if -3.09999999999999995e-25 < x < -7.2000000000000001e-38

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -7.2000000000000001e-38 < x < 4.1e12

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. distribute-neg-frac 84.8%

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

   6. Simplified 84.8%

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

      1. frac-2neg 84.8%

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

      2. div-inv 84.7%

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

      3. remove-double-neg 84.7%

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

      4. sub-neg 84.7%

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

      5. distribute-neg-in 84.7%

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

      6. metadata-eval 84.7%

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

      7. remove-double-neg 84.7%

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

   8. Applied egg-rr 84.7%

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

      1. associate-*r/ 84.8%

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

      2. *-rgt-identity 84.8%

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

      3. +-commutative 84.8%

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

   10. Simplified 84.8%

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

   if 4.1e12 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. div-sub 100.0%

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

      2. associate--l- 100.0%

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

      3. associate--l- 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 80.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+18}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-25}:\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-38}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4100000000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1 - \frac{y}{2 - \left(x + y\right)}\\ \end{array} \]

Alternative 5: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-190}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-268}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-304}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-207}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 18000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.1e+19)
   -1.0
   (if (<= x -6.5e-190)
     1.0
     (if (<= x -2.3e-268)
       (* y -0.5)
       (if (<= x -4.5e-304)
         1.0
         (if (<= x 1.05e-207)
           (* y -0.5)
           (if (<= x 18000000000000.0) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.1e+19) {
		tmp = -1.0;
	} else if (x <= -6.5e-190) {
		tmp = 1.0;
	} else if (x <= -2.3e-268) {
		tmp = y * -0.5;
	} else if (x <= -4.5e-304) {
		tmp = 1.0;
	} else if (x <= 1.05e-207) {
		tmp = y * -0.5;
	} else if (x <= 18000000000000.0) {
		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 <= (-1.1d+19)) then
        tmp = -1.0d0
    else if (x <= (-6.5d-190)) then
        tmp = 1.0d0
    else if (x <= (-2.3d-268)) then
        tmp = y * (-0.5d0)
    else if (x <= (-4.5d-304)) then
        tmp = 1.0d0
    else if (x <= 1.05d-207) then
        tmp = y * (-0.5d0)
    else if (x <= 18000000000000.0d0) 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 <= -1.1e+19) {
		tmp = -1.0;
	} else if (x <= -6.5e-190) {
		tmp = 1.0;
	} else if (x <= -2.3e-268) {
		tmp = y * -0.5;
	} else if (x <= -4.5e-304) {
		tmp = 1.0;
	} else if (x <= 1.05e-207) {
		tmp = y * -0.5;
	} else if (x <= 18000000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.1e+19:
		tmp = -1.0
	elif x <= -6.5e-190:
		tmp = 1.0
	elif x <= -2.3e-268:
		tmp = y * -0.5
	elif x <= -4.5e-304:
		tmp = 1.0
	elif x <= 1.05e-207:
		tmp = y * -0.5
	elif x <= 18000000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.1e+19)
		tmp = -1.0;
	elseif (x <= -6.5e-190)
		tmp = 1.0;
	elseif (x <= -2.3e-268)
		tmp = Float64(y * -0.5);
	elseif (x <= -4.5e-304)
		tmp = 1.0;
	elseif (x <= 1.05e-207)
		tmp = Float64(y * -0.5);
	elseif (x <= 18000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.1e+19)
		tmp = -1.0;
	elseif (x <= -6.5e-190)
		tmp = 1.0;
	elseif (x <= -2.3e-268)
		tmp = y * -0.5;
	elseif (x <= -4.5e-304)
		tmp = 1.0;
	elseif (x <= 1.05e-207)
		tmp = y * -0.5;
	elseif (x <= 18000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.1e+19], -1.0, If[LessEqual[x, -6.5e-190], 1.0, If[LessEqual[x, -2.3e-268], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, -4.5e-304], 1.0, If[LessEqual[x, 1.05e-207], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 18000000000000.0], 1.0, -1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e19 or 1.8e13 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 79.8%

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

   if -1.1e19 < x < -6.4999999999999997e-190 or -2.3000000000000001e-268 < x < -4.4999999999999998e-304 or 1.05000000000000002e-207 < x < 1.8e13

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 57.7%

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

   if -6.4999999999999997e-190 < x < -2.3000000000000001e-268 or -4.4999999999999998e-304 < x < 1.05000000000000002e-207

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 95.0%

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

      1. mul-1-neg 95.0%

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

      2. distribute-neg-frac 95.0%

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

   6. Simplified 95.0%

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

   7. Taylor expanded in y around 0 63.9%

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

      1. *-commutative 63.9%

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

   9. Simplified 63.9%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-190}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-268}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-304}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-207}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 18000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1500000000:\\ \;\;\;\;-1 + \frac{-2}{x}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-190}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-266}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-304}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-206}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 55000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1500000000.0)
   (+ -1.0 (/ -2.0 x))
   (if (<= x -7e-190)
     1.0
     (if (<= x -2.35e-266)
       (* y -0.5)
       (if (<= x -6e-304)
         1.0
         (if (<= x 6.2e-206)
           (* y -0.5)
           (if (<= x 55000000000000.0) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1500000000.0) {
		tmp = -1.0 + (-2.0 / x);
	} else if (x <= -7e-190) {
		tmp = 1.0;
	} else if (x <= -2.35e-266) {
		tmp = y * -0.5;
	} else if (x <= -6e-304) {
		tmp = 1.0;
	} else if (x <= 6.2e-206) {
		tmp = y * -0.5;
	} else if (x <= 55000000000000.0) {
		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 <= (-1500000000.0d0)) then
        tmp = (-1.0d0) + ((-2.0d0) / x)
    else if (x <= (-7d-190)) then
        tmp = 1.0d0
    else if (x <= (-2.35d-266)) then
        tmp = y * (-0.5d0)
    else if (x <= (-6d-304)) then
        tmp = 1.0d0
    else if (x <= 6.2d-206) then
        tmp = y * (-0.5d0)
    else if (x <= 55000000000000.0d0) 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 <= -1500000000.0) {
		tmp = -1.0 + (-2.0 / x);
	} else if (x <= -7e-190) {
		tmp = 1.0;
	} else if (x <= -2.35e-266) {
		tmp = y * -0.5;
	} else if (x <= -6e-304) {
		tmp = 1.0;
	} else if (x <= 6.2e-206) {
		tmp = y * -0.5;
	} else if (x <= 55000000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1500000000.0:
		tmp = -1.0 + (-2.0 / x)
	elif x <= -7e-190:
		tmp = 1.0
	elif x <= -2.35e-266:
		tmp = y * -0.5
	elif x <= -6e-304:
		tmp = 1.0
	elif x <= 6.2e-206:
		tmp = y * -0.5
	elif x <= 55000000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1500000000.0)
		tmp = Float64(-1.0 + Float64(-2.0 / x));
	elseif (x <= -7e-190)
		tmp = 1.0;
	elseif (x <= -2.35e-266)
		tmp = Float64(y * -0.5);
	elseif (x <= -6e-304)
		tmp = 1.0;
	elseif (x <= 6.2e-206)
		tmp = Float64(y * -0.5);
	elseif (x <= 55000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1500000000.0)
		tmp = -1.0 + (-2.0 / x);
	elseif (x <= -7e-190)
		tmp = 1.0;
	elseif (x <= -2.35e-266)
		tmp = y * -0.5;
	elseif (x <= -6e-304)
		tmp = 1.0;
	elseif (x <= 6.2e-206)
		tmp = y * -0.5;
	elseif (x <= 55000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1500000000.0], N[(-1.0 + N[(-2.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-190], 1.0, If[LessEqual[x, -2.35e-266], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, -6e-304], 1.0, If[LessEqual[x, 6.2e-206], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 55000000000000.0], 1.0, -1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.5e9

   1. Initial program 99.8%

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

      1. associate--r+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 77.3%

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

   5. Taylor expanded in x around inf 77.3%

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

      1. distribute-neg-in 77.3%

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

      2. metadata-eval 77.3%

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

      3. associate-*r/ 77.3%

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

      4. metadata-eval 77.3%

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

      5. distribute-neg-frac 77.3%

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

      6. metadata-eval 77.3%

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

   7. Simplified 77.3%

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

   if -1.5e9 < x < -6.9999999999999999e-190 or -2.35000000000000014e-266 < x < -6.0000000000000002e-304 or 6.2000000000000005e-206 < x < 5.5e13

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 58.0%

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

   if -6.9999999999999999e-190 < x < -2.35000000000000014e-266 or -6.0000000000000002e-304 < x < 6.2000000000000005e-206

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 95.0%

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

      1. mul-1-neg 95.0%

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

      2. distribute-neg-frac 95.0%

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

   6. Simplified 95.0%

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

   7. Taylor expanded in y around 0 63.9%

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

      1. *-commutative 63.9%

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

   9. Simplified 63.9%

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

   if 5.5e13 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 80.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1500000000:\\ \;\;\;\;-1 + \frac{-2}{x}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-190}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-266}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-304}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-206}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 55000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7: 61.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -245000000000:\\ \;\;\;\;-1 + \frac{-2}{x}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-189}:\\ \;\;\;\;1 - \frac{2}{y}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-264}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-304}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-207}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 64000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -245000000000.0)
   (+ -1.0 (/ -2.0 x))
   (if (<= x -4.8e-189)
     (- 1.0 (/ 2.0 y))
     (if (<= x -7.5e-264)
       (* y -0.5)
       (if (<= x -2.5e-304)
         1.0
         (if (<= x 2.8e-207)
           (* y -0.5)
           (if (<= x 64000000000000.0) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -245000000000.0) {
		tmp = -1.0 + (-2.0 / x);
	} else if (x <= -4.8e-189) {
		tmp = 1.0 - (2.0 / y);
	} else if (x <= -7.5e-264) {
		tmp = y * -0.5;
	} else if (x <= -2.5e-304) {
		tmp = 1.0;
	} else if (x <= 2.8e-207) {
		tmp = y * -0.5;
	} else if (x <= 64000000000000.0) {
		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 <= (-245000000000.0d0)) then
        tmp = (-1.0d0) + ((-2.0d0) / x)
    else if (x <= (-4.8d-189)) then
        tmp = 1.0d0 - (2.0d0 / y)
    else if (x <= (-7.5d-264)) then
        tmp = y * (-0.5d0)
    else if (x <= (-2.5d-304)) then
        tmp = 1.0d0
    else if (x <= 2.8d-207) then
        tmp = y * (-0.5d0)
    else if (x <= 64000000000000.0d0) 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 <= -245000000000.0) {
		tmp = -1.0 + (-2.0 / x);
	} else if (x <= -4.8e-189) {
		tmp = 1.0 - (2.0 / y);
	} else if (x <= -7.5e-264) {
		tmp = y * -0.5;
	} else if (x <= -2.5e-304) {
		tmp = 1.0;
	} else if (x <= 2.8e-207) {
		tmp = y * -0.5;
	} else if (x <= 64000000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -245000000000.0:
		tmp = -1.0 + (-2.0 / x)
	elif x <= -4.8e-189:
		tmp = 1.0 - (2.0 / y)
	elif x <= -7.5e-264:
		tmp = y * -0.5
	elif x <= -2.5e-304:
		tmp = 1.0
	elif x <= 2.8e-207:
		tmp = y * -0.5
	elif x <= 64000000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -245000000000.0)
		tmp = Float64(-1.0 + Float64(-2.0 / x));
	elseif (x <= -4.8e-189)
		tmp = Float64(1.0 - Float64(2.0 / y));
	elseif (x <= -7.5e-264)
		tmp = Float64(y * -0.5);
	elseif (x <= -2.5e-304)
		tmp = 1.0;
	elseif (x <= 2.8e-207)
		tmp = Float64(y * -0.5);
	elseif (x <= 64000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -245000000000.0)
		tmp = -1.0 + (-2.0 / x);
	elseif (x <= -4.8e-189)
		tmp = 1.0 - (2.0 / y);
	elseif (x <= -7.5e-264)
		tmp = y * -0.5;
	elseif (x <= -2.5e-304)
		tmp = 1.0;
	elseif (x <= 2.8e-207)
		tmp = y * -0.5;
	elseif (x <= 64000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -245000000000.0], N[(-1.0 + N[(-2.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.8e-189], N[(1.0 - N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e-264], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, -2.5e-304], 1.0, If[LessEqual[x, 2.8e-207], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 64000000000000.0], 1.0, -1.0]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.45e11

   1. Initial program 99.8%

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

      1. associate--r+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 77.3%

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

   5. Taylor expanded in x around inf 77.3%

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

      1. distribute-neg-in 77.3%

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

      2. metadata-eval 77.3%

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

      3. associate-*r/ 77.3%

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

      4. metadata-eval 77.3%

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

      5. distribute-neg-frac 77.3%

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

      6. metadata-eval 77.3%

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

   7. Simplified 77.3%

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

   if -2.45e11 < x < -4.7999999999999997e-189

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. distribute-neg-frac 73.0%

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

   6. Simplified 73.0%

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

      1. frac-2neg 73.0%

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

      2. div-inv 72.9%

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

      3. remove-double-neg 72.9%

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

      4. sub-neg 72.9%

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

      5. distribute-neg-in 72.9%

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

      6. metadata-eval 72.9%

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

      7. remove-double-neg 72.9%

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

   8. Applied egg-rr 72.9%

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

      1. associate-*r/ 73.0%

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

      2. *-rgt-identity 73.0%

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

      3. +-commutative 73.0%

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

   10. Simplified 73.0%

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

       1. frac-2neg 73.0%

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

       2. +-commutative 73.0%

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

       3. distribute-neg-in 73.0%

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

       4. metadata-eval 73.0%

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

       5. add-sqr-sqrt 30.1%

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

       6. sqrt-unprod 29.4%

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

       7. sqr-neg 29.4%

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

       8. sqrt-unprod 13.3%

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

       9. add-sqr-sqrt 18.5%

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

       10. *-un-lft-identity 18.5%

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

       11. add-cube-cbrt 18.1%

           \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{-y} \cdot \sqrt[3]{-y}\right) \cdot \sqrt[3]{-y}}}{1 \cdot \left(2 + y\right)} \]

       12. times-frac 18.1%

           \[\leadsto \color{blue}{\frac{\sqrt[3]{-y} \cdot \sqrt[3]{-y}}{1} \cdot \frac{\sqrt[3]{-y}}{2 + y}} \]

       13. cbrt-unprod 18.1%

           \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(-y\right) \cdot \left(-y\right)}}}{1} \cdot \frac{\sqrt[3]{-y}}{2 + y} \]

       14. sqr-neg 18.1%

           \[\leadsto \frac{\sqrt[3]{\color{blue}{y \cdot y}}}{1} \cdot \frac{\sqrt[3]{-y}}{2 + y} \]

       15. cbrt-unprod 18.1%

           \[\leadsto \frac{\color{blue}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{1} \cdot \frac{\sqrt[3]{-y}}{2 + y} \]

       16. pow2 18.1%

           \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{-y}}{2 + y} \]

   12. Applied egg-rr 54.8%

       \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{y + 2}} \]
   13. Step-by-step derivation

       1. /-rgt-identity 54.8%

          \[\leadsto \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{y + 2} \]

       2. associate-*r/ 55.0%

          \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{y + 2}} \]

       3. unpow2 55.0%

          \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{y + 2} \]

       4. rem-3cbrt-lft 55.8%

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

   14. Simplified 55.8%

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

   15. Taylor expanded in y around inf 55.6%

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

       1. associate-*r/ 55.6%

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

       2. metadata-eval 55.6%

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

   17. Simplified 55.6%

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

   if -4.7999999999999997e-189 < x < -7.5000000000000001e-264 or -2.49999999999999983e-304 < x < 2.79999999999999993e-207

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 95.0%

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

      1. mul-1-neg 95.0%

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

      2. distribute-neg-frac 95.0%

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

   6. Simplified 95.0%

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

   7. Taylor expanded in y around 0 63.9%

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

      1. *-commutative 63.9%

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

   9. Simplified 63.9%

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

   if -7.5000000000000001e-264 < x < -2.49999999999999983e-304 or 2.79999999999999993e-207 < x < 6.4e13

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 60.7%

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

   if 6.4e13 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 80.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -245000000000:\\ \;\;\;\;-1 + \frac{-2}{x}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-189}:\\ \;\;\;\;1 - \frac{2}{y}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-264}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-304}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-207}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 64000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-25}:\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-38}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 65000000000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1 + \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.1e+18)
   (/ (- y x) x)
   (if (<= x -2.7e-25)
     (+ 1.0 (/ (- (- 2.0 x) x) y))
     (if (<= x -6.5e-38)
       (* x 0.5)
       (if (<= x 65000000000000.0) (/ y (+ y -2.0)) (+ -1.0 (/ y x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.1e+18) {
		tmp = (y - x) / x;
	} else if (x <= -2.7e-25) {
		tmp = 1.0 + (((2.0 - x) - x) / y);
	} else if (x <= -6.5e-38) {
		tmp = x * 0.5;
	} else if (x <= 65000000000000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = -1.0 + (y / 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 <= (-4.1d+18)) then
        tmp = (y - x) / x
    else if (x <= (-2.7d-25)) then
        tmp = 1.0d0 + (((2.0d0 - x) - x) / y)
    else if (x <= (-6.5d-38)) then
        tmp = x * 0.5d0
    else if (x <= 65000000000000.0d0) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = (-1.0d0) + (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.1e+18) {
		tmp = (y - x) / x;
	} else if (x <= -2.7e-25) {
		tmp = 1.0 + (((2.0 - x) - x) / y);
	} else if (x <= -6.5e-38) {
		tmp = x * 0.5;
	} else if (x <= 65000000000000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = -1.0 + (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.1e+18:
		tmp = (y - x) / x
	elif x <= -2.7e-25:
		tmp = 1.0 + (((2.0 - x) - x) / y)
	elif x <= -6.5e-38:
		tmp = x * 0.5
	elif x <= 65000000000000.0:
		tmp = y / (y + -2.0)
	else:
		tmp = -1.0 + (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.1e+18)
		tmp = Float64(Float64(y - x) / x);
	elseif (x <= -2.7e-25)
		tmp = Float64(1.0 + Float64(Float64(Float64(2.0 - x) - x) / y));
	elseif (x <= -6.5e-38)
		tmp = Float64(x * 0.5);
	elseif (x <= 65000000000000.0)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(-1.0 + Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.1e+18)
		tmp = (y - x) / x;
	elseif (x <= -2.7e-25)
		tmp = 1.0 + (((2.0 - x) - x) / y);
	elseif (x <= -6.5e-38)
		tmp = x * 0.5;
	elseif (x <= 65000000000000.0)
		tmp = y / (y + -2.0);
	else
		tmp = -1.0 + (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.1e+18], N[(N[(y - x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, -2.7e-25], N[(1.0 + N[(N[(N[(2.0 - x), $MachinePrecision] - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-38], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 65000000000000.0], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(-1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.1e18

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.6%

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

      3. associate--l- 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 79.7%

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

      1. associate-*l/ 80.0%

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

      2. sub-neg 80.0%

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

      3. distribute-lft-in 80.0%

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

      4. neg-mul-1 80.0%

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

      5. neg-mul-1 80.0%

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

      6. remove-double-neg 80.0%

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

   8. Applied egg-rr 80.0%

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

   if -4.1e18 < x < -2.70000000000000016e-25

   1. Initial program 99.8%

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

      1. associate--r+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 71.0%

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

      1. associate--l+ 71.0%

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

      2. associate-*r/ 71.0%

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

      3. associate-*r/ 71.0%

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

      4. div-sub 71.0%

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

      5. cancel-sign-sub-inv 71.0%

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

      6. metadata-eval 71.0%

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

      7. *-lft-identity 71.0%

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

      8. +-commutative 71.0%

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

      9. mul-1-neg 71.0%

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

      10. unsub-neg 71.0%

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

   6. Simplified 71.0%

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

   if -2.70000000000000016e-25 < x < -6.49999999999999949e-38

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -6.49999999999999949e-38 < x < 6.5e13

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. distribute-neg-frac 84.8%

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

   6. Simplified 84.8%

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

      1. frac-2neg 84.8%

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

      2. div-inv 84.7%

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

      3. remove-double-neg 84.7%

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

      4. sub-neg 84.7%

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

      5. distribute-neg-in 84.7%

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

      6. metadata-eval 84.7%

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

      7. remove-double-neg 84.7%

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

   8. Applied egg-rr 84.7%

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

      1. associate-*r/ 84.8%

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

      2. *-rgt-identity 84.8%

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

      3. +-commutative 84.8%

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

   10. Simplified 84.8%

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

   if 6.5e13 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.7%

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

      3. associate--l- 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 80.6%

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

   7. Taylor expanded in x around 0 80.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-25}:\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-38}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 65000000000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1 + \frac{y}{x}\\ \end{array} \]

Alternative 9: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+17} \lor \neg \left(x \leq 1.1 \cdot 10^{+16}\right):\\ \;\;\;\;-1 + \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.55e+17) (not (<= x 1.1e+16)))
   (+ -1.0 (/ y x))
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.55e+17) || !(x <= 1.1e+16)) {
		tmp = -1.0 + (y / 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 <= (-2.55d+17)) .or. (.not. (x <= 1.1d+16))) then
        tmp = (-1.0d0) + (y / 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 <= -2.55e+17) || !(x <= 1.1e+16)) {
		tmp = -1.0 + (y / x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.55e+17) or not (x <= 1.1e+16):
		tmp = -1.0 + (y / x)
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.55e+17) || !(x <= 1.1e+16))
		tmp = Float64(-1.0 + Float64(y / 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 <= -2.55e+17) || ~((x <= 1.1e+16)))
		tmp = -1.0 + (y / x);
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.55e+17], N[Not[LessEqual[x, 1.1e+16]], $MachinePrecision]], N[(-1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.55e17 or 1.1e16 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.7%

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

      3. associate--l- 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 80.1%

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

   7. Taylor expanded in x around 0 80.4%

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

   if -2.55e17 < x < 1.1e16

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. distribute-neg-frac 81.0%

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

   6. Simplified 81.0%

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

      1. frac-2neg 81.0%

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

      2. div-inv 80.9%

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

      3. remove-double-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. distribute-neg-in 80.9%

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

      6. metadata-eval 80.9%

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

      7. remove-double-neg 80.9%

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

   8. Applied egg-rr 80.9%

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

      1. associate-*r/ 81.0%

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

      2. *-rgt-identity 81.0%

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

      3. +-commutative 81.0%

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

   10. Simplified 81.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+17} \lor \neg \left(x \leq 1.1 \cdot 10^{+16}\right):\\ \;\;\;\;-1 + \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 10: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+18}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;x \leq 8500000000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1 + \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3e+18)
   (/ (- y x) x)
   (if (<= x 8500000000000.0) (/ y (+ y -2.0)) (+ -1.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3e+18) {
		tmp = (y - x) / x;
	} else if (x <= 8500000000000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = -1.0 + (y / 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 <= (-3d+18)) then
        tmp = (y - x) / x
    else if (x <= 8500000000000.0d0) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = (-1.0d0) + (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3e+18) {
		tmp = (y - x) / x;
	} else if (x <= 8500000000000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = -1.0 + (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3e+18:
		tmp = (y - x) / x
	elif x <= 8500000000000.0:
		tmp = y / (y + -2.0)
	else:
		tmp = -1.0 + (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3e+18)
		tmp = Float64(Float64(y - x) / x);
	elseif (x <= 8500000000000.0)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(-1.0 + Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3e+18)
		tmp = (y - x) / x;
	elseif (x <= 8500000000000.0)
		tmp = y / (y + -2.0);
	else
		tmp = -1.0 + (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3e+18], N[(N[(y - x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 8500000000000.0], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(-1.0 + N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3e18

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.6%

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

      3. associate--l- 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 79.7%

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

      1. associate-*l/ 80.0%

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

      2. sub-neg 80.0%

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

      3. distribute-lft-in 80.0%

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

      4. neg-mul-1 80.0%

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

      5. neg-mul-1 80.0%

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

      6. remove-double-neg 80.0%

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

   8. Applied egg-rr 80.0%

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

   if -3e18 < x < 8.5e12

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. distribute-neg-frac 81.0%

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

   6. Simplified 81.0%

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

      1. frac-2neg 81.0%

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

      2. div-inv 80.9%

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

      3. remove-double-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. distribute-neg-in 80.9%

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

      6. metadata-eval 80.9%

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

      7. remove-double-neg 80.9%

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

   8. Applied egg-rr 80.9%

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

      1. associate-*r/ 81.0%

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

      2. *-rgt-identity 81.0%

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

      3. +-commutative 81.0%

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

   10. Simplified 81.0%

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

   if 8.5e12 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.7%

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

      3. associate--l- 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 80.6%

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

   7. Taylor expanded in x around 0 80.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+18}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;x \leq 8500000000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1 + \frac{y}{x}\\ \end{array} \]

Alternative 11: 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 99.9%

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

2. Final simplification 99.9%

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

Alternative 12: 63.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 980000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.6e+18) -1.0 (if (<= x 980000000000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.6e+18) {
		tmp = -1.0;
	} else if (x <= 980000000000.0) {
		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 <= (-1.6d+18)) then
        tmp = -1.0d0
    else if (x <= 980000000000.0d0) 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 <= -1.6e+18) {
		tmp = -1.0;
	} else if (x <= 980000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.6e+18:
		tmp = -1.0
	elif x <= 980000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.6e+18)
		tmp = -1.0;
	elseif (x <= 980000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.6e+18)
		tmp = -1.0;
	elseif (x <= 980000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.6e+18], -1.0, If[LessEqual[x, 980000000000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e18 or 9.8e11 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 79.8%

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

   if -1.6e18 < x < 9.8e11

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 50.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 980000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 13: 38.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 99.9%

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

   1. associate--r+ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 39.1%

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

5. Final simplification 39.1%

   \[\leadsto -1 \]

Developer target: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023266 
(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))))