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

Percentage Accurate: 100.0% → 100.0%

Time: 9.6s

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: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-245}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-277}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-302}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-232}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= x -3.3e+37)
     t_0
     (if (<= x -4.6e-245)
       (- 1.0 (/ x y))
       (if (<= x -1.9e-277)
         (* y -0.5)
         (if (<= x 1.4e-302)
           (+ 1.0 (/ 2.0 y))
           (if (<= x 1.25e-232)
             (* y -0.5)
             (if (<= x 1.3e-112)
               1.0
               (if (<= x 5e-20) (* x 0.5) (if (<= x 5.5e+19) 1.0 t_0))))))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -3.3e+37) {
		tmp = t_0;
	} else if (x <= -4.6e-245) {
		tmp = 1.0 - (x / y);
	} else if (x <= -1.9e-277) {
		tmp = y * -0.5;
	} else if (x <= 1.4e-302) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= 1.25e-232) {
		tmp = y * -0.5;
	} else if (x <= 1.3e-112) {
		tmp = 1.0;
	} else if (x <= 5e-20) {
		tmp = x * 0.5;
	} else if (x <= 5.5e+19) {
		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 = (y / x) + (-1.0d0)
    if (x <= (-3.3d+37)) then
        tmp = t_0
    else if (x <= (-4.6d-245)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= (-1.9d-277)) then
        tmp = y * (-0.5d0)
    else if (x <= 1.4d-302) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (x <= 1.25d-232) then
        tmp = y * (-0.5d0)
    else if (x <= 1.3d-112) then
        tmp = 1.0d0
    else if (x <= 5d-20) then
        tmp = x * 0.5d0
    else if (x <= 5.5d+19) 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 = (y / x) + -1.0;
	double tmp;
	if (x <= -3.3e+37) {
		tmp = t_0;
	} else if (x <= -4.6e-245) {
		tmp = 1.0 - (x / y);
	} else if (x <= -1.9e-277) {
		tmp = y * -0.5;
	} else if (x <= 1.4e-302) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= 1.25e-232) {
		tmp = y * -0.5;
	} else if (x <= 1.3e-112) {
		tmp = 1.0;
	} else if (x <= 5e-20) {
		tmp = x * 0.5;
	} else if (x <= 5.5e+19) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if x <= -3.3e+37:
		tmp = t_0
	elif x <= -4.6e-245:
		tmp = 1.0 - (x / y)
	elif x <= -1.9e-277:
		tmp = y * -0.5
	elif x <= 1.4e-302:
		tmp = 1.0 + (2.0 / y)
	elif x <= 1.25e-232:
		tmp = y * -0.5
	elif x <= 1.3e-112:
		tmp = 1.0
	elif x <= 5e-20:
		tmp = x * 0.5
	elif x <= 5.5e+19:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	tmp = 0.0
	if (x <= -3.3e+37)
		tmp = t_0;
	elseif (x <= -4.6e-245)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= -1.9e-277)
		tmp = Float64(y * -0.5);
	elseif (x <= 1.4e-302)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (x <= 1.25e-232)
		tmp = Float64(y * -0.5);
	elseif (x <= 1.3e-112)
		tmp = 1.0;
	elseif (x <= 5e-20)
		tmp = Float64(x * 0.5);
	elseif (x <= 5.5e+19)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) + -1.0;
	tmp = 0.0;
	if (x <= -3.3e+37)
		tmp = t_0;
	elseif (x <= -4.6e-245)
		tmp = 1.0 - (x / y);
	elseif (x <= -1.9e-277)
		tmp = y * -0.5;
	elseif (x <= 1.4e-302)
		tmp = 1.0 + (2.0 / y);
	elseif (x <= 1.25e-232)
		tmp = y * -0.5;
	elseif (x <= 1.3e-112)
		tmp = 1.0;
	elseif (x <= 5e-20)
		tmp = x * 0.5;
	elseif (x <= 5.5e+19)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[x, -3.3e+37], t$95$0, If[LessEqual[x, -4.6e-245], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e-277], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1.4e-302], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-232], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1.3e-112], 1.0, If[LessEqual[x, 5e-20], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 5.5e+19], 1.0, t$95$0]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.3000000000000001e37 or 5.5e19 < 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/ 99.8%

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

      3. associate--l- 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 82.2%

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

   7. Taylor expanded in x around 0 82.3%

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

   if -3.3000000000000001e37 < x < -4.6000000000000003e-245

   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 99.8%

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

      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 y around inf 54.5%

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

   7. Taylor expanded in y around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

   9. Simplified 54.6%

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

   if -4.6000000000000003e-245 < x < -1.89999999999999993e-277 or 1.4e-302 < x < 1.25e-232

   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 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in y around 0 62.8%

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

      1. *-commutative 62.8%

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

   9. Simplified 62.8%

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

   if -1.89999999999999993e-277 < x < 1.4e-302

   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 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 80.3%

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

      1. associate-*r/ 80.3%

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

      2. metadata-eval 80.3%

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

   9. Simplified 80.3%

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

   if 1.25e-232 < x < 1.29999999999999996e-112 or 4.9999999999999999e-20 < x < 5.5e19

   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 61.8%

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

   if 1.29999999999999996e-112 < x < 4.9999999999999999e-20

   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 57.9%

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

   5. Taylor expanded in x around 0 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-245}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-277}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-302}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-232}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 3: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-240}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-277}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-301}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-232}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-110}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.7e+37)
   -1.0
   (if (<= x -1.35e-240)
     1.0
     (if (<= x -3.6e-277)
       (* y -0.5)
       (if (<= x 6.1e-301)
         (+ 1.0 (/ 2.0 y))
         (if (<= x 4e-232)
           (* y -0.5)
           (if (<= x 2.05e-110)
             1.0
             (if (<= x 2.4e-20) (* x 0.5) (if (<= x 1e+20) 1.0 -1.0)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.7e+37) {
		tmp = -1.0;
	} else if (x <= -1.35e-240) {
		tmp = 1.0;
	} else if (x <= -3.6e-277) {
		tmp = y * -0.5;
	} else if (x <= 6.1e-301) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= 4e-232) {
		tmp = y * -0.5;
	} else if (x <= 2.05e-110) {
		tmp = 1.0;
	} else if (x <= 2.4e-20) {
		tmp = x * 0.5;
	} else if (x <= 1e+20) {
		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 <= (-2.7d+37)) then
        tmp = -1.0d0
    else if (x <= (-1.35d-240)) then
        tmp = 1.0d0
    else if (x <= (-3.6d-277)) then
        tmp = y * (-0.5d0)
    else if (x <= 6.1d-301) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (x <= 4d-232) then
        tmp = y * (-0.5d0)
    else if (x <= 2.05d-110) then
        tmp = 1.0d0
    else if (x <= 2.4d-20) then
        tmp = x * 0.5d0
    else if (x <= 1d+20) 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 <= -2.7e+37) {
		tmp = -1.0;
	} else if (x <= -1.35e-240) {
		tmp = 1.0;
	} else if (x <= -3.6e-277) {
		tmp = y * -0.5;
	} else if (x <= 6.1e-301) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= 4e-232) {
		tmp = y * -0.5;
	} else if (x <= 2.05e-110) {
		tmp = 1.0;
	} else if (x <= 2.4e-20) {
		tmp = x * 0.5;
	} else if (x <= 1e+20) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.7e+37:
		tmp = -1.0
	elif x <= -1.35e-240:
		tmp = 1.0
	elif x <= -3.6e-277:
		tmp = y * -0.5
	elif x <= 6.1e-301:
		tmp = 1.0 + (2.0 / y)
	elif x <= 4e-232:
		tmp = y * -0.5
	elif x <= 2.05e-110:
		tmp = 1.0
	elif x <= 2.4e-20:
		tmp = x * 0.5
	elif x <= 1e+20:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.7e+37)
		tmp = -1.0;
	elseif (x <= -1.35e-240)
		tmp = 1.0;
	elseif (x <= -3.6e-277)
		tmp = Float64(y * -0.5);
	elseif (x <= 6.1e-301)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (x <= 4e-232)
		tmp = Float64(y * -0.5);
	elseif (x <= 2.05e-110)
		tmp = 1.0;
	elseif (x <= 2.4e-20)
		tmp = Float64(x * 0.5);
	elseif (x <= 1e+20)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.7e+37)
		tmp = -1.0;
	elseif (x <= -1.35e-240)
		tmp = 1.0;
	elseif (x <= -3.6e-277)
		tmp = y * -0.5;
	elseif (x <= 6.1e-301)
		tmp = 1.0 + (2.0 / y);
	elseif (x <= 4e-232)
		tmp = y * -0.5;
	elseif (x <= 2.05e-110)
		tmp = 1.0;
	elseif (x <= 2.4e-20)
		tmp = x * 0.5;
	elseif (x <= 1e+20)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.7e+37], -1.0, If[LessEqual[x, -1.35e-240], 1.0, If[LessEqual[x, -3.6e-277], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 6.1e-301], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e-232], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 2.05e-110], 1.0, If[LessEqual[x, 2.4e-20], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1e+20], 1.0, -1.0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.69999999999999986e37 or 1e20 < 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 81.8%

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

   if -2.69999999999999986e37 < x < -1.35000000000000009e-240 or 4.0000000000000001e-232 < x < 2.04999999999999991e-110 or 2.39999999999999993e-20 < x < 1e20

   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 56.7%

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

   if -1.35000000000000009e-240 < x < -3.59999999999999984e-277 or 6.1000000000000001e-301 < x < 4.0000000000000001e-232

   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 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in y around 0 62.8%

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

      1. *-commutative 62.8%

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

   9. Simplified 62.8%

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

   if -3.59999999999999984e-277 < x < 6.1000000000000001e-301

   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 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 80.3%

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

      1. associate-*r/ 80.3%

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

      2. metadata-eval 80.3%

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

   9. Simplified 80.3%

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

   if 2.04999999999999991e-110 < x < 2.39999999999999993e-20

   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 57.9%

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

   5. Taylor expanded in x around 0 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-240}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-277}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-301}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-232}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-110}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 60.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-242}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-273}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-303}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-232}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-110}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.2e+36)
   -1.0
   (if (<= x -1.05e-242)
     (- 1.0 (/ x y))
     (if (<= x -1.45e-273)
       (* y -0.5)
       (if (<= x 4.1e-303)
         (+ 1.0 (/ 2.0 y))
         (if (<= x 1.9e-232)
           (* y -0.5)
           (if (<= x 1.5e-110)
             1.0
             (if (<= x 1.95e-20) (* x 0.5) (if (<= x 1.7e+19) 1.0 -1.0)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.2e+36) {
		tmp = -1.0;
	} else if (x <= -1.05e-242) {
		tmp = 1.0 - (x / y);
	} else if (x <= -1.45e-273) {
		tmp = y * -0.5;
	} else if (x <= 4.1e-303) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= 1.9e-232) {
		tmp = y * -0.5;
	} else if (x <= 1.5e-110) {
		tmp = 1.0;
	} else if (x <= 1.95e-20) {
		tmp = x * 0.5;
	} else if (x <= 1.7e+19) {
		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 <= (-9.2d+36)) then
        tmp = -1.0d0
    else if (x <= (-1.05d-242)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= (-1.45d-273)) then
        tmp = y * (-0.5d0)
    else if (x <= 4.1d-303) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (x <= 1.9d-232) then
        tmp = y * (-0.5d0)
    else if (x <= 1.5d-110) then
        tmp = 1.0d0
    else if (x <= 1.95d-20) then
        tmp = x * 0.5d0
    else if (x <= 1.7d+19) 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 <= -9.2e+36) {
		tmp = -1.0;
	} else if (x <= -1.05e-242) {
		tmp = 1.0 - (x / y);
	} else if (x <= -1.45e-273) {
		tmp = y * -0.5;
	} else if (x <= 4.1e-303) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= 1.9e-232) {
		tmp = y * -0.5;
	} else if (x <= 1.5e-110) {
		tmp = 1.0;
	} else if (x <= 1.95e-20) {
		tmp = x * 0.5;
	} else if (x <= 1.7e+19) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.2e+36:
		tmp = -1.0
	elif x <= -1.05e-242:
		tmp = 1.0 - (x / y)
	elif x <= -1.45e-273:
		tmp = y * -0.5
	elif x <= 4.1e-303:
		tmp = 1.0 + (2.0 / y)
	elif x <= 1.9e-232:
		tmp = y * -0.5
	elif x <= 1.5e-110:
		tmp = 1.0
	elif x <= 1.95e-20:
		tmp = x * 0.5
	elif x <= 1.7e+19:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.2e+36)
		tmp = -1.0;
	elseif (x <= -1.05e-242)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= -1.45e-273)
		tmp = Float64(y * -0.5);
	elseif (x <= 4.1e-303)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (x <= 1.9e-232)
		tmp = Float64(y * -0.5);
	elseif (x <= 1.5e-110)
		tmp = 1.0;
	elseif (x <= 1.95e-20)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.7e+19)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.2e+36)
		tmp = -1.0;
	elseif (x <= -1.05e-242)
		tmp = 1.0 - (x / y);
	elseif (x <= -1.45e-273)
		tmp = y * -0.5;
	elseif (x <= 4.1e-303)
		tmp = 1.0 + (2.0 / y);
	elseif (x <= 1.9e-232)
		tmp = y * -0.5;
	elseif (x <= 1.5e-110)
		tmp = 1.0;
	elseif (x <= 1.95e-20)
		tmp = x * 0.5;
	elseif (x <= 1.7e+19)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.2e+36], -1.0, If[LessEqual[x, -1.05e-242], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.45e-273], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 4.1e-303], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-232], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1.5e-110], 1.0, If[LessEqual[x, 1.95e-20], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.7e+19], 1.0, -1.0]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -9.19999999999999986e36 or 1.7e19 < 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 81.8%

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

   if -9.19999999999999986e36 < x < -1.05000000000000009e-242

   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 99.8%

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

      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 y around inf 54.5%

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

   7. Taylor expanded in y around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

   9. Simplified 54.6%

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

   if -1.05000000000000009e-242 < x < -1.44999999999999993e-273 or 4.10000000000000018e-303 < x < 1.9000000000000001e-232

   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 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in y around 0 62.8%

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

      1. *-commutative 62.8%

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

   9. Simplified 62.8%

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

   if -1.44999999999999993e-273 < x < 4.10000000000000018e-303

   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 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 80.3%

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

      1. associate-*r/ 80.3%

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

      2. metadata-eval 80.3%

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

   9. Simplified 80.3%

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

   if 1.9000000000000001e-232 < x < 1.49999999999999993e-110 or 1.95000000000000004e-20 < x < 1.7e19

   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 61.8%

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

   if 1.49999999999999993e-110 < x < 1.95000000000000004e-20

   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 57.9%

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

   5. Taylor expanded in x around 0 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-242}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-273}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-303}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-232}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-110}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-244}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-272}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-111}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-20}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e+37)
   -1.0
   (if (<= x -1.95e-244)
     1.0
     (if (<= x -1.2e-272)
       (* y -0.5)
       (if (<= x 3.8e-111)
         1.0
         (if (<= x 1e-20) (* x 0.5) (if (<= x 2.3e+19) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e+37) {
		tmp = -1.0;
	} else if (x <= -1.95e-244) {
		tmp = 1.0;
	} else if (x <= -1.2e-272) {
		tmp = y * -0.5;
	} else if (x <= 3.8e-111) {
		tmp = 1.0;
	} else if (x <= 1e-20) {
		tmp = x * 0.5;
	} else if (x <= 2.3e+19) {
		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 <= (-1d+37)) then
        tmp = -1.0d0
    else if (x <= (-1.95d-244)) then
        tmp = 1.0d0
    else if (x <= (-1.2d-272)) then
        tmp = y * (-0.5d0)
    else if (x <= 3.8d-111) then
        tmp = 1.0d0
    else if (x <= 1d-20) then
        tmp = x * 0.5d0
    else if (x <= 2.3d+19) 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 <= -1e+37) {
		tmp = -1.0;
	} else if (x <= -1.95e-244) {
		tmp = 1.0;
	} else if (x <= -1.2e-272) {
		tmp = y * -0.5;
	} else if (x <= 3.8e-111) {
		tmp = 1.0;
	} else if (x <= 1e-20) {
		tmp = x * 0.5;
	} else if (x <= 2.3e+19) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e+37:
		tmp = -1.0
	elif x <= -1.95e-244:
		tmp = 1.0
	elif x <= -1.2e-272:
		tmp = y * -0.5
	elif x <= 3.8e-111:
		tmp = 1.0
	elif x <= 1e-20:
		tmp = x * 0.5
	elif x <= 2.3e+19:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e+37)
		tmp = -1.0;
	elseif (x <= -1.95e-244)
		tmp = 1.0;
	elseif (x <= -1.2e-272)
		tmp = Float64(y * -0.5);
	elseif (x <= 3.8e-111)
		tmp = 1.0;
	elseif (x <= 1e-20)
		tmp = Float64(x * 0.5);
	elseif (x <= 2.3e+19)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e+37)
		tmp = -1.0;
	elseif (x <= -1.95e-244)
		tmp = 1.0;
	elseif (x <= -1.2e-272)
		tmp = y * -0.5;
	elseif (x <= 3.8e-111)
		tmp = 1.0;
	elseif (x <= 1e-20)
		tmp = x * 0.5;
	elseif (x <= 2.3e+19)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e+37], -1.0, If[LessEqual[x, -1.95e-244], 1.0, If[LessEqual[x, -1.2e-272], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 3.8e-111], 1.0, If[LessEqual[x, 1e-20], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 2.3e+19], 1.0, -1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.99999999999999954e36 or 2.3e19 < 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 81.8%

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

   if -9.99999999999999954e36 < x < -1.9499999999999999e-244 or -1.19999999999999995e-272 < x < 3.80000000000000022e-111 or 9.99999999999999945e-21 < x < 2.3e19

   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 55.1%

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

   if -1.9499999999999999e-244 < x < -1.19999999999999995e-272

   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 78.5%

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

      1. associate-*r/ 78.5%

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

      2. neg-mul-1 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in y around 0 78.5%

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

      1. *-commutative 78.5%

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

   9. Simplified 78.5%

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

   if 3.80000000000000022e-111 < x < 9.99999999999999945e-21

   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 57.9%

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

   5. Taylor expanded in x around 0 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-244}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-272}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-111}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-20}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-79}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 32000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -1.3e+25)
     t_0
     (if (<= y -5.9e-62)
       t_1
       (if (<= y -1.35e-79) (* y -0.5) (if (<= y 32000.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -1.3e+25) {
		tmp = t_0;
	} else if (y <= -5.9e-62) {
		tmp = t_1;
	} else if (y <= -1.35e-79) {
		tmp = y * -0.5;
	} else if (y <= 32000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    t_1 = x / (2.0d0 - x)
    if (y <= (-1.3d+25)) then
        tmp = t_0
    else if (y <= (-5.9d-62)) then
        tmp = t_1
    else if (y <= (-1.35d-79)) then
        tmp = y * (-0.5d0)
    else if (y <= 32000.0d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -1.3e+25) {
		tmp = t_0;
	} else if (y <= -5.9e-62) {
		tmp = t_1;
	} else if (y <= -1.35e-79) {
		tmp = y * -0.5;
	} else if (y <= 32000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	t_1 = x / (2.0 - x)
	tmp = 0
	if y <= -1.3e+25:
		tmp = t_0
	elif y <= -5.9e-62:
		tmp = t_1
	elif y <= -1.35e-79:
		tmp = y * -0.5
	elif y <= 32000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	t_1 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -1.3e+25)
		tmp = t_0;
	elseif (y <= -5.9e-62)
		tmp = t_1;
	elseif (y <= -1.35e-79)
		tmp = Float64(y * -0.5);
	elseif (y <= 32000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	t_1 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -1.3e+25)
		tmp = t_0;
	elseif (y <= -5.9e-62)
		tmp = t_1;
	elseif (y <= -1.35e-79)
		tmp = y * -0.5;
	elseif (y <= 32000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+25], t$95$0, If[LessEqual[y, -5.9e-62], t$95$1, If[LessEqual[y, -1.35e-79], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 32000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e25 or 32000 < 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. 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/ 99.8%

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

      3. associate--l- 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 72.5%

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

   7. Taylor expanded in y around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. unsub-neg 72.6%

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

   9. Simplified 72.6%

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

   if -1.2999999999999999e25 < y < -5.9000000000000004e-62 or -1.3500000000000001e-79 < y < 32000

   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 0 75.7%

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

   if -5.9000000000000004e-62 < y < -1.3500000000000001e-79

   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 95.3%

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

      1. associate-*r/ 95.3%

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

      2. neg-mul-1 95.3%

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

   6. Simplified 95.3%

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

   7. Taylor expanded in y around 0 95.3%

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

      1. *-commutative 95.3%

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

   9. Simplified 95.3%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-79}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 32000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 7: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+37} \lor \neg \left(x \leq 6.8 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{1}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.2e+37) (not (<= x 6.8e+18)))
   (/ (- x y) (- x))
   (* (- x y) (/ 1.0 (- 2.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e+37) || !(x <= 6.8e+18)) {
		tmp = (x - y) / -x;
	} else {
		tmp = (x - y) * (1.0 / (2.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.2d+37)) .or. (.not. (x <= 6.8d+18))) then
        tmp = (x - y) / -x
    else
        tmp = (x - y) * (1.0d0 / (2.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e+37) || !(x <= 6.8e+18)) {
		tmp = (x - y) / -x;
	} else {
		tmp = (x - y) * (1.0 / (2.0 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.2e+37) or not (x <= 6.8e+18):
		tmp = (x - y) / -x
	else:
		tmp = (x - y) * (1.0 / (2.0 - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.2e+37) || !(x <= 6.8e+18))
		tmp = Float64(Float64(x - y) / Float64(-x));
	else
		tmp = Float64(Float64(x - y) * Float64(1.0 / Float64(2.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.2e+37) || ~((x <= 6.8e+18)))
		tmp = (x - y) / -x;
	else
		tmp = (x - y) * (1.0 / (2.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.2e+37], N[Not[LessEqual[x, 6.8e+18]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] / (-x)), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(1.0 / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e37 or 6.8e18 < 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/ 99.8%

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

      3. associate--l- 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 82.2%

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

      1. *-commutative 82.2%

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

      2. frac-2neg 82.2%

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

      3. metadata-eval 82.2%

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

      4. un-div-inv 82.3%

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

   8. Applied egg-rr 82.3%

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

   if -1.2e37 < x < 6.8e18

   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 99.8%

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

      2. associate-/r/ 99.8%

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

      3. associate--l- 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 94.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+37} \lor \neg \left(x \leq 6.8 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{1}{2 - y}\\ \end{array} \]

Alternative 8: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-79}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.5e+36)
   (+ (/ y x) -1.0)
   (if (<= x 8.2e-79) (/ (- y) (- 2.0 y)) (/ x (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+36) {
		tmp = (y / x) + -1.0;
	} else if (x <= 8.2e-79) {
		tmp = -y / (2.0 - y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.5d+36)) then
        tmp = (y / x) + (-1.0d0)
    else if (x <= 8.2d-79) then
        tmp = -y / (2.0d0 - y)
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+36) {
		tmp = (y / x) + -1.0;
	} else if (x <= 8.2e-79) {
		tmp = -y / (2.0 - y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.5e+36:
		tmp = (y / x) + -1.0
	elif x <= 8.2e-79:
		tmp = -y / (2.0 - y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.5e+36)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (x <= 8.2e-79)
		tmp = Float64(Float64(-y) / Float64(2.0 - y));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.5e+36)
		tmp = (y / x) + -1.0;
	elseif (x <= 8.2e-79)
		tmp = -y / (2.0 - y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.5e+36], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, 8.2e-79], N[((-y) / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.49999999999999988e36

   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/ 99.8%

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

      3. associate--l- 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 83.9%

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

   7. Taylor expanded in x around 0 84.0%

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

   if -2.49999999999999988e36 < x < 8.19999999999999987e-79

   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 80.1%

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

      1. associate-*r/ 80.1%

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

      2. neg-mul-1 80.1%

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

   6. Simplified 80.1%

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

   if 8.19999999999999987e-79 < 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 y around 0 73.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-79}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 9: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+37}:\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.8e+37)
   (/ (- x y) (- x))
   (if (<= x 5.6e-79) (/ (- y) (- 2.0 y)) (/ x (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.8e+37) {
		tmp = (x - y) / -x;
	} else if (x <= 5.6e-79) {
		tmp = -y / (2.0 - y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.8d+37)) then
        tmp = (x - y) / -x
    else if (x <= 5.6d-79) then
        tmp = -y / (2.0d0 - y)
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.8e+37) {
		tmp = (x - y) / -x;
	} else if (x <= 5.6e-79) {
		tmp = -y / (2.0 - y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.8e+37:
		tmp = (x - y) / -x
	elif x <= 5.6e-79:
		tmp = -y / (2.0 - y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.8e+37)
		tmp = Float64(Float64(x - y) / Float64(-x));
	elseif (x <= 5.6e-79)
		tmp = Float64(Float64(-y) / Float64(2.0 - y));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.8e+37)
		tmp = (x - y) / -x;
	elseif (x <= 5.6e-79)
		tmp = -y / (2.0 - y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.8e+37], N[(N[(x - y), $MachinePrecision] / (-x)), $MachinePrecision], If[LessEqual[x, 5.6e-79], N[((-y) / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e37

   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/ 99.8%

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

      3. associate--l- 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 83.9%

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

      1. *-commutative 83.9%

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

      2. frac-2neg 83.9%

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

      3. metadata-eval 83.9%

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

      4. un-div-inv 84.0%

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

   8. Applied egg-rr 84.0%

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

   if -4.8e37 < x < 5.60000000000000023e-79

   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 80.1%

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

      1. associate-*r/ 80.1%

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

      2. neg-mul-1 80.1%

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

   6. Simplified 80.1%

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

   if 5.60000000000000023e-79 < 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 y around 0 73.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+37}:\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 10: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-111}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6e+36)
   -1.0
   (if (<= x 2.6e-111)
     1.0
     (if (<= x 8.5e-20) (* x 0.5) (if (<= x 8.5e+18) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6e+36) {
		tmp = -1.0;
	} else if (x <= 2.6e-111) {
		tmp = 1.0;
	} else if (x <= 8.5e-20) {
		tmp = x * 0.5;
	} else if (x <= 8.5e+18) {
		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 <= (-6d+36)) then
        tmp = -1.0d0
    else if (x <= 2.6d-111) then
        tmp = 1.0d0
    else if (x <= 8.5d-20) then
        tmp = x * 0.5d0
    else if (x <= 8.5d+18) 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 <= -6e+36) {
		tmp = -1.0;
	} else if (x <= 2.6e-111) {
		tmp = 1.0;
	} else if (x <= 8.5e-20) {
		tmp = x * 0.5;
	} else if (x <= 8.5e+18) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6e+36:
		tmp = -1.0
	elif x <= 2.6e-111:
		tmp = 1.0
	elif x <= 8.5e-20:
		tmp = x * 0.5
	elif x <= 8.5e+18:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6e+36)
		tmp = -1.0;
	elseif (x <= 2.6e-111)
		tmp = 1.0;
	elseif (x <= 8.5e-20)
		tmp = Float64(x * 0.5);
	elseif (x <= 8.5e+18)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6e+36)
		tmp = -1.0;
	elseif (x <= 2.6e-111)
		tmp = 1.0;
	elseif (x <= 8.5e-20)
		tmp = x * 0.5;
	elseif (x <= 8.5e+18)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6e+36], -1.0, If[LessEqual[x, 2.6e-111], 1.0, If[LessEqual[x, 8.5e-20], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 8.5e+18], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6e36 or 8.5e18 < 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 81.8%

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

   if -6e36 < x < 2.59999999999999982e-111 or 8.5000000000000005e-20 < x < 8.5e18

   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 52.5%

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

   if 2.59999999999999982e-111 < x < 8.5000000000000005e-20

   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 57.9%

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

   5. Taylor expanded in x around 0 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-111}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

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: 62.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.5e+36) -1.0 (if (<= x 2.6e+19) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.5e+36) {
		tmp = -1.0;
	} else if (x <= 2.6e+19) {
		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+36)) then
        tmp = -1.0d0
    else if (x <= 2.6d+19) 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+36) {
		tmp = -1.0;
	} else if (x <= 2.6e+19) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.5e+36:
		tmp = -1.0
	elif x <= 2.6e+19:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.5e+36)
		tmp = -1.0;
	elseif (x <= 2.6e+19)
		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+36)
		tmp = -1.0;
	elseif (x <= 2.6e+19)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.5e+36], -1.0, If[LessEqual[x, 2.6e+19], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.49999999999999988e36 or 2.6e19 < 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 81.8%

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

   if -2.49999999999999988e36 < x < 2.6e19

   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 49.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+36}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 13: 37.5% 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 39.3%

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

5. Final simplification 39.3%

   \[\leadsto -1 \]

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 2023287 
(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))))