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

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 11

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 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. 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: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x \cdot -2}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -7200000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-23}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-67}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-205}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* x -2.0) y))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -7200000000.0)
     t_0
     (if (<= y -1.3e-23)
       (+ (/ y x) -1.0)
       (if (<= y -2.25e-67)
         (* y -0.5)
         (if (<= y -1.4e-160)
           t_1
           (if (<= y -4e-205)
             (/ y (+ y -2.0))
             (if (<= y 5.5e+59) t_1 t_0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((x * -2.0) / y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -7200000000.0) {
		tmp = t_0;
	} else if (y <= -1.3e-23) {
		tmp = (y / x) + -1.0;
	} else if (y <= -2.25e-67) {
		tmp = y * -0.5;
	} else if (y <= -1.4e-160) {
		tmp = t_1;
	} else if (y <= -4e-205) {
		tmp = y / (y + -2.0);
	} else if (y <= 5.5e+59) {
		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 * (-2.0d0)) / y)
    t_1 = x / (2.0d0 - x)
    if (y <= (-7200000000.0d0)) then
        tmp = t_0
    else if (y <= (-1.3d-23)) then
        tmp = (y / x) + (-1.0d0)
    else if (y <= (-2.25d-67)) then
        tmp = y * (-0.5d0)
    else if (y <= (-1.4d-160)) then
        tmp = t_1
    else if (y <= (-4d-205)) then
        tmp = y / (y + (-2.0d0))
    else if (y <= 5.5d+59) 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 * -2.0) / y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -7200000000.0) {
		tmp = t_0;
	} else if (y <= -1.3e-23) {
		tmp = (y / x) + -1.0;
	} else if (y <= -2.25e-67) {
		tmp = y * -0.5;
	} else if (y <= -1.4e-160) {
		tmp = t_1;
	} else if (y <= -4e-205) {
		tmp = y / (y + -2.0);
	} else if (y <= 5.5e+59) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((x * -2.0) / y)
	t_1 = x / (2.0 - x)
	tmp = 0
	if y <= -7200000000.0:
		tmp = t_0
	elif y <= -1.3e-23:
		tmp = (y / x) + -1.0
	elif y <= -2.25e-67:
		tmp = y * -0.5
	elif y <= -1.4e-160:
		tmp = t_1
	elif y <= -4e-205:
		tmp = y / (y + -2.0)
	elif y <= 5.5e+59:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(x * -2.0) / y))
	t_1 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -7200000000.0)
		tmp = t_0;
	elseif (y <= -1.3e-23)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (y <= -2.25e-67)
		tmp = Float64(y * -0.5);
	elseif (y <= -1.4e-160)
		tmp = t_1;
	elseif (y <= -4e-205)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (y <= 5.5e+59)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((x * -2.0) / y);
	t_1 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -7200000000.0)
		tmp = t_0;
	elseif (y <= -1.3e-23)
		tmp = (y / x) + -1.0;
	elseif (y <= -2.25e-67)
		tmp = y * -0.5;
	elseif (y <= -1.4e-160)
		tmp = t_1;
	elseif (y <= -4e-205)
		tmp = y / (y + -2.0);
	elseif (y <= 5.5e+59)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(N[(x * -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7200000000.0], t$95$0, If[LessEqual[y, -1.3e-23], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[y, -2.25e-67], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -1.4e-160], t$95$1, If[LessEqual[y, -4e-205], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+59], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.2e9 or 5.4999999999999999e59 < 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 86.9%

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

      1. associate--l+ 86.9%

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

      2. associate-*r/ 86.9%

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

      3. associate-*r/ 86.9%

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

      4. div-sub 86.9%

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

      5. cancel-sign-sub-inv 86.9%

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

      6. metadata-eval 86.9%

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

      7. *-lft-identity 86.9%

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

      8. +-commutative 86.9%

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

      9. mul-1-neg 86.9%

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

      10. unsub-neg 86.9%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in x around inf 86.4%

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

      1. *-commutative 86.4%

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

   9. Simplified 86.4%

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

   if -7.2e9 < y < -1.3e-23

   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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. associate-/r/ 99.5%

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

      3. associate--l- 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around inf 88.8%

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

   7. Taylor expanded in x around 0 89.3%

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

   if -1.3e-23 < y < -2.25000000000000008e-67

   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 86.4%

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

      1. mul-1-neg 86.4%

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

      2. distribute-neg-frac 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in y around 0 86.4%

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

      1. *-commutative 86.4%

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

   9. Simplified 86.4%

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

   if -2.25000000000000008e-67 < y < -1.40000000000000008e-160 or -4e-205 < y < 5.4999999999999999e59

   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 74.6%

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

   if -1.40000000000000008e-160 < y < -4e-205

   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 89.2%

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

      1. mul-1-neg 89.2%

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

      2. distribute-neg-frac 89.2%

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

   6. Simplified 89.2%

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

      1. frac-2neg 89.2%

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

      2. div-inv 89.2%

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

      3. remove-double-neg 89.2%

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

      4. sub-neg 89.2%

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

      5. distribute-neg-in 89.2%

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

      6. metadata-eval 89.2%

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

      7. remove-double-neg 89.2%

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

   8. Applied egg-rr 89.2%

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

      1. associate-*r/ 89.2%

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

      2. *-rgt-identity 89.2%

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

      3. +-commutative 89.2%

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

   10. Simplified 89.2%

       \[\leadsto \color{blue}{\frac{y}{y + -2}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7200000000:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-23}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-67}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-205}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \end{array} \]

Alternative 3: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -15500000000:\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-73}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-205}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+59}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -15500000000.0)
     (+ 1.0 (/ (- (- 2.0 x) x) y))
     (if (<= y -8.5e-24)
       (+ (/ y x) -1.0)
       (if (<= y -2.2e-73)
         (* y -0.5)
         (if (<= y -1.4e-160)
           t_0
           (if (<= y -4e-205)
             (/ y (+ y -2.0))
             (if (<= y 5.4e+59) t_0 (+ 1.0 (/ (* x -2.0) y))))))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -15500000000.0) {
		tmp = 1.0 + (((2.0 - x) - x) / y);
	} else if (y <= -8.5e-24) {
		tmp = (y / x) + -1.0;
	} else if (y <= -2.2e-73) {
		tmp = y * -0.5;
	} else if (y <= -1.4e-160) {
		tmp = t_0;
	} else if (y <= -4e-205) {
		tmp = y / (y + -2.0);
	} else if (y <= 5.4e+59) {
		tmp = t_0;
	} else {
		tmp = 1.0 + ((x * -2.0) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-15500000000.0d0)) then
        tmp = 1.0d0 + (((2.0d0 - x) - x) / y)
    else if (y <= (-8.5d-24)) then
        tmp = (y / x) + (-1.0d0)
    else if (y <= (-2.2d-73)) then
        tmp = y * (-0.5d0)
    else if (y <= (-1.4d-160)) then
        tmp = t_0
    else if (y <= (-4d-205)) then
        tmp = y / (y + (-2.0d0))
    else if (y <= 5.4d+59) then
        tmp = t_0
    else
        tmp = 1.0d0 + ((x * (-2.0d0)) / y)
    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 <= -15500000000.0) {
		tmp = 1.0 + (((2.0 - x) - x) / y);
	} else if (y <= -8.5e-24) {
		tmp = (y / x) + -1.0;
	} else if (y <= -2.2e-73) {
		tmp = y * -0.5;
	} else if (y <= -1.4e-160) {
		tmp = t_0;
	} else if (y <= -4e-205) {
		tmp = y / (y + -2.0);
	} else if (y <= 5.4e+59) {
		tmp = t_0;
	} else {
		tmp = 1.0 + ((x * -2.0) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -15500000000.0:
		tmp = 1.0 + (((2.0 - x) - x) / y)
	elif y <= -8.5e-24:
		tmp = (y / x) + -1.0
	elif y <= -2.2e-73:
		tmp = y * -0.5
	elif y <= -1.4e-160:
		tmp = t_0
	elif y <= -4e-205:
		tmp = y / (y + -2.0)
	elif y <= 5.4e+59:
		tmp = t_0
	else:
		tmp = 1.0 + ((x * -2.0) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -15500000000.0)
		tmp = Float64(1.0 + Float64(Float64(Float64(2.0 - x) - x) / y));
	elseif (y <= -8.5e-24)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (y <= -2.2e-73)
		tmp = Float64(y * -0.5);
	elseif (y <= -1.4e-160)
		tmp = t_0;
	elseif (y <= -4e-205)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (y <= 5.4e+59)
		tmp = t_0;
	else
		tmp = Float64(1.0 + Float64(Float64(x * -2.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -15500000000.0)
		tmp = 1.0 + (((2.0 - x) - x) / y);
	elseif (y <= -8.5e-24)
		tmp = (y / x) + -1.0;
	elseif (y <= -2.2e-73)
		tmp = y * -0.5;
	elseif (y <= -1.4e-160)
		tmp = t_0;
	elseif (y <= -4e-205)
		tmp = y / (y + -2.0);
	elseif (y <= 5.4e+59)
		tmp = t_0;
	else
		tmp = 1.0 + ((x * -2.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -15500000000.0], N[(1.0 + N[(N[(N[(2.0 - x), $MachinePrecision] - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-24], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[y, -2.2e-73], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -1.4e-160], t$95$0, If[LessEqual[y, -4e-205], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+59], t$95$0, N[(1.0 + N[(N[(x * -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.55e10

   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 81.9%

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

      1. associate--l+ 81.9%

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

      2. associate-*r/ 81.9%

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

      3. associate-*r/ 81.9%

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

      4. div-sub 81.9%

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

      5. cancel-sign-sub-inv 81.9%

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

      6. metadata-eval 81.9%

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

      7. *-lft-identity 81.9%

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

      8. +-commutative 81.9%

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

      9. mul-1-neg 81.9%

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

      10. unsub-neg 81.9%

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

   6. Simplified 81.9%

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

   if -1.55e10 < y < -8.5000000000000002e-24

   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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. associate-/r/ 99.5%

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

      3. associate--l- 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around inf 88.8%

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

   7. Taylor expanded in x around 0 89.3%

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

   if -8.5000000000000002e-24 < y < -2.2e-73

   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 86.4%

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

      1. mul-1-neg 86.4%

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

      2. distribute-neg-frac 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in y around 0 86.4%

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

      1. *-commutative 86.4%

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

   9. Simplified 86.4%

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

   if -2.2e-73 < y < -1.40000000000000008e-160 or -4e-205 < y < 5.4000000000000002e59

   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 74.6%

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

   if -1.40000000000000008e-160 < y < -4e-205

   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 89.2%

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

      1. mul-1-neg 89.2%

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

      2. distribute-neg-frac 89.2%

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

   6. Simplified 89.2%

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

      1. frac-2neg 89.2%

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

      2. div-inv 89.2%

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

      3. remove-double-neg 89.2%

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

      4. sub-neg 89.2%

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

      5. distribute-neg-in 89.2%

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

      6. metadata-eval 89.2%

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

      7. remove-double-neg 89.2%

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

   8. Applied egg-rr 89.2%

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

      1. associate-*r/ 89.2%

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

      2. *-rgt-identity 89.2%

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

      3. +-commutative 89.2%

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

   10. Simplified 89.2%

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

   if 5.4000000000000002e59 < y

   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 94.4%

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

      1. associate--l+ 94.4%

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

      2. associate-*r/ 94.4%

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

      3. associate-*r/ 94.4%

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

      4. div-sub 94.4%

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

      5. cancel-sign-sub-inv 94.4%

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

      6. metadata-eval 94.4%

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

      7. *-lft-identity 94.4%

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

      8. +-commutative 94.4%

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

      9. mul-1-neg 94.4%

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

      10. unsub-neg 94.4%

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

   6. Simplified 94.4%

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

   7. Taylor expanded in x around inf 94.4%

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

      1. *-commutative 94.4%

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

   9. Simplified 94.4%

      \[\leadsto 1 + \frac{\color{blue}{x \cdot -2}}{y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15500000000:\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-73}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-205}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \end{array} \]

Alternative 4: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -136000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-23}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-67}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-205}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+59}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -136000000000.0)
     1.0
     (if (<= y -1e-23)
       (+ (/ y x) -1.0)
       (if (<= y -1.4e-67)
         (* y -0.5)
         (if (<= y -1.4e-160)
           t_0
           (if (<= y -4e-205) (* y -0.5) (if (<= y 8e+59) t_0 1.0))))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -136000000000.0) {
		tmp = 1.0;
	} else if (y <= -1e-23) {
		tmp = (y / x) + -1.0;
	} else if (y <= -1.4e-67) {
		tmp = y * -0.5;
	} else if (y <= -1.4e-160) {
		tmp = t_0;
	} else if (y <= -4e-205) {
		tmp = y * -0.5;
	} else if (y <= 8e+59) {
		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 <= (-136000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-1d-23)) then
        tmp = (y / x) + (-1.0d0)
    else if (y <= (-1.4d-67)) then
        tmp = y * (-0.5d0)
    else if (y <= (-1.4d-160)) then
        tmp = t_0
    else if (y <= (-4d-205)) then
        tmp = y * (-0.5d0)
    else if (y <= 8d+59) 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 <= -136000000000.0) {
		tmp = 1.0;
	} else if (y <= -1e-23) {
		tmp = (y / x) + -1.0;
	} else if (y <= -1.4e-67) {
		tmp = y * -0.5;
	} else if (y <= -1.4e-160) {
		tmp = t_0;
	} else if (y <= -4e-205) {
		tmp = y * -0.5;
	} else if (y <= 8e+59) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -136000000000.0:
		tmp = 1.0
	elif y <= -1e-23:
		tmp = (y / x) + -1.0
	elif y <= -1.4e-67:
		tmp = y * -0.5
	elif y <= -1.4e-160:
		tmp = t_0
	elif y <= -4e-205:
		tmp = y * -0.5
	elif y <= 8e+59:
		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 <= -136000000000.0)
		tmp = 1.0;
	elseif (y <= -1e-23)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (y <= -1.4e-67)
		tmp = Float64(y * -0.5);
	elseif (y <= -1.4e-160)
		tmp = t_0;
	elseif (y <= -4e-205)
		tmp = Float64(y * -0.5);
	elseif (y <= 8e+59)
		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 <= -136000000000.0)
		tmp = 1.0;
	elseif (y <= -1e-23)
		tmp = (y / x) + -1.0;
	elseif (y <= -1.4e-67)
		tmp = y * -0.5;
	elseif (y <= -1.4e-160)
		tmp = t_0;
	elseif (y <= -4e-205)
		tmp = y * -0.5;
	elseif (y <= 8e+59)
		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, -136000000000.0], 1.0, If[LessEqual[y, -1e-23], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[y, -1.4e-67], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -1.4e-160], t$95$0, If[LessEqual[y, -4e-205], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 8e+59], t$95$0, 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.36e11 or 7.99999999999999977e59 < 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 85.5%

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

   if -1.36e11 < y < -9.9999999999999996e-24

   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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. associate-/r/ 99.5%

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

      3. associate--l- 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around inf 88.8%

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

   7. Taylor expanded in x around 0 89.3%

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

   if -9.9999999999999996e-24 < y < -1.40000000000000005e-67 or -1.40000000000000008e-160 < y < -4e-205

   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 87.7%

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

      1. mul-1-neg 87.7%

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

      2. distribute-neg-frac 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in y around 0 87.7%

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

      1. *-commutative 87.7%

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

   9. Simplified 87.7%

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

   if -1.40000000000000005e-67 < y < -1.40000000000000008e-160 or -4e-205 < y < 7.99999999999999977e59

   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 74.6%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -136000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-23}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-67}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-205}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1860000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{-68}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -1860000000.0)
     t_0
     (if (<= y -1.06e-24)
       (+ (/ y x) -1.0)
       (if (<= y -5.9e-68)
         (* y -0.5)
         (if (<= y -1.4e-160)
           t_1
           (if (<= y -4e-205) t_0 (if (<= y 1.25e+63) t_1 1.0))))))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -1860000000.0) {
		tmp = t_0;
	} else if (y <= -1.06e-24) {
		tmp = (y / x) + -1.0;
	} else if (y <= -5.9e-68) {
		tmp = y * -0.5;
	} else if (y <= -1.4e-160) {
		tmp = t_1;
	} else if (y <= -4e-205) {
		tmp = t_0;
	} else if (y <= 1.25e+63) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = y / (y + (-2.0d0))
    t_1 = x / (2.0d0 - x)
    if (y <= (-1860000000.0d0)) then
        tmp = t_0
    else if (y <= (-1.06d-24)) then
        tmp = (y / x) + (-1.0d0)
    else if (y <= (-5.9d-68)) then
        tmp = y * (-0.5d0)
    else if (y <= (-1.4d-160)) then
        tmp = t_1
    else if (y <= (-4d-205)) then
        tmp = t_0
    else if (y <= 1.25d+63) then
        tmp = t_1
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -1860000000.0) {
		tmp = t_0;
	} else if (y <= -1.06e-24) {
		tmp = (y / x) + -1.0;
	} else if (y <= -5.9e-68) {
		tmp = y * -0.5;
	} else if (y <= -1.4e-160) {
		tmp = t_1;
	} else if (y <= -4e-205) {
		tmp = t_0;
	} else if (y <= 1.25e+63) {
		tmp = t_1;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	t_1 = x / (2.0 - x)
	tmp = 0
	if y <= -1860000000.0:
		tmp = t_0
	elif y <= -1.06e-24:
		tmp = (y / x) + -1.0
	elif y <= -5.9e-68:
		tmp = y * -0.5
	elif y <= -1.4e-160:
		tmp = t_1
	elif y <= -4e-205:
		tmp = t_0
	elif y <= 1.25e+63:
		tmp = t_1
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	t_1 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -1860000000.0)
		tmp = t_0;
	elseif (y <= -1.06e-24)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (y <= -5.9e-68)
		tmp = Float64(y * -0.5);
	elseif (y <= -1.4e-160)
		tmp = t_1;
	elseif (y <= -4e-205)
		tmp = t_0;
	elseif (y <= 1.25e+63)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	t_1 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -1860000000.0)
		tmp = t_0;
	elseif (y <= -1.06e-24)
		tmp = (y / x) + -1.0;
	elseif (y <= -5.9e-68)
		tmp = y * -0.5;
	elseif (y <= -1.4e-160)
		tmp = t_1;
	elseif (y <= -4e-205)
		tmp = t_0;
	elseif (y <= 1.25e+63)
		tmp = t_1;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1860000000.0], t$95$0, If[LessEqual[y, -1.06e-24], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[y, -5.9e-68], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -1.4e-160], t$95$1, If[LessEqual[y, -4e-205], t$95$0, If[LessEqual[y, 1.25e+63], t$95$1, 1.0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.86e9 or -1.40000000000000008e-160 < y < -4e-205

   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 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-neg-frac 82.0%

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

   6. Simplified 82.0%

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

      1. frac-2neg 82.0%

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

      2. div-inv 81.8%

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

      3. remove-double-neg 81.8%

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

      4. sub-neg 81.8%

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

      5. distribute-neg-in 81.8%

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

      6. metadata-eval 81.8%

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

      7. remove-double-neg 81.8%

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

   8. Applied egg-rr 81.8%

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

      1. associate-*r/ 82.0%

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

      2. *-rgt-identity 82.0%

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

      3. +-commutative 82.0%

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

   10. Simplified 82.0%

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

   if -1.86e9 < y < -1.0599999999999999e-24

   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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. associate-/r/ 99.5%

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

      3. associate--l- 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around inf 88.8%

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

   7. Taylor expanded in x around 0 89.3%

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

   if -1.0599999999999999e-24 < y < -5.9e-68

   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 86.4%

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

      1. mul-1-neg 86.4%

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

      2. distribute-neg-frac 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in y around 0 86.4%

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

      1. *-commutative 86.4%

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

   9. Simplified 86.4%

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

   if -5.9e-68 < y < -1.40000000000000008e-160 or -4e-205 < y < 1.25000000000000003e63

   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 74.6%

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

   if 1.25000000000000003e63 < y

   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 93.7%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1860000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{-68}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-205}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 59.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -95000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-24}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-205}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-303}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -95000000000.0)
   1.0
   (if (<= y -8e-24)
     -1.0
     (if (<= y -3.9e-205)
       (* y -0.5)
       (if (<= y -4.8e-303) (* x 0.5) (if (<= y 5.4e+59) -1.0 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -95000000000.0) {
		tmp = 1.0;
	} else if (y <= -8e-24) {
		tmp = -1.0;
	} else if (y <= -3.9e-205) {
		tmp = y * -0.5;
	} else if (y <= -4.8e-303) {
		tmp = x * 0.5;
	} else if (y <= 5.4e+59) {
		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 (y <= (-95000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-8d-24)) then
        tmp = -1.0d0
    else if (y <= (-3.9d-205)) then
        tmp = y * (-0.5d0)
    else if (y <= (-4.8d-303)) then
        tmp = x * 0.5d0
    else if (y <= 5.4d+59) 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 (y <= -95000000000.0) {
		tmp = 1.0;
	} else if (y <= -8e-24) {
		tmp = -1.0;
	} else if (y <= -3.9e-205) {
		tmp = y * -0.5;
	} else if (y <= -4.8e-303) {
		tmp = x * 0.5;
	} else if (y <= 5.4e+59) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -95000000000.0:
		tmp = 1.0
	elif y <= -8e-24:
		tmp = -1.0
	elif y <= -3.9e-205:
		tmp = y * -0.5
	elif y <= -4.8e-303:
		tmp = x * 0.5
	elif y <= 5.4e+59:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -95000000000.0)
		tmp = 1.0;
	elseif (y <= -8e-24)
		tmp = -1.0;
	elseif (y <= -3.9e-205)
		tmp = Float64(y * -0.5);
	elseif (y <= -4.8e-303)
		tmp = Float64(x * 0.5);
	elseif (y <= 5.4e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -95000000000.0)
		tmp = 1.0;
	elseif (y <= -8e-24)
		tmp = -1.0;
	elseif (y <= -3.9e-205)
		tmp = y * -0.5;
	elseif (y <= -4.8e-303)
		tmp = x * 0.5;
	elseif (y <= 5.4e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -95000000000.0], 1.0, If[LessEqual[y, -8e-24], -1.0, If[LessEqual[y, -3.9e-205], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -4.8e-303], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 5.4e+59], -1.0, 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.5e10 or 5.4000000000000002e59 < 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 85.5%

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

   if -9.5e10 < y < -7.99999999999999939e-24 or -4.8000000000000002e-303 < y < 5.4000000000000002e59

   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 inf 56.9%

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

   if -7.99999999999999939e-24 < y < -3.90000000000000018e-205

   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 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-neg-frac 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in y around 0 61.1%

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

      1. *-commutative 61.1%

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

   9. Simplified 61.1%

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

   if -3.90000000000000018e-205 < y < -4.8000000000000002e-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 y around 0 85.2%

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

   5. Taylor expanded in x around 0 64.4%

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

      1. *-commutative 64.4%

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

   7. Simplified 64.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -95000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-24}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-205}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-303}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 59.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -240000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-205}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-302}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -240000000000.0)
   1.0
   (if (<= y -2.7e-24)
     (+ (/ y x) -1.0)
     (if (<= y -3.3e-205)
       (* y -0.5)
       (if (<= y -4.6e-302) (* x 0.5) (if (<= y 5.5e+59) -1.0 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -240000000000.0) {
		tmp = 1.0;
	} else if (y <= -2.7e-24) {
		tmp = (y / x) + -1.0;
	} else if (y <= -3.3e-205) {
		tmp = y * -0.5;
	} else if (y <= -4.6e-302) {
		tmp = x * 0.5;
	} else if (y <= 5.5e+59) {
		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 (y <= (-240000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-2.7d-24)) then
        tmp = (y / x) + (-1.0d0)
    else if (y <= (-3.3d-205)) then
        tmp = y * (-0.5d0)
    else if (y <= (-4.6d-302)) then
        tmp = x * 0.5d0
    else if (y <= 5.5d+59) 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 (y <= -240000000000.0) {
		tmp = 1.0;
	} else if (y <= -2.7e-24) {
		tmp = (y / x) + -1.0;
	} else if (y <= -3.3e-205) {
		tmp = y * -0.5;
	} else if (y <= -4.6e-302) {
		tmp = x * 0.5;
	} else if (y <= 5.5e+59) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -240000000000.0:
		tmp = 1.0
	elif y <= -2.7e-24:
		tmp = (y / x) + -1.0
	elif y <= -3.3e-205:
		tmp = y * -0.5
	elif y <= -4.6e-302:
		tmp = x * 0.5
	elif y <= 5.5e+59:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -240000000000.0)
		tmp = 1.0;
	elseif (y <= -2.7e-24)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (y <= -3.3e-205)
		tmp = Float64(y * -0.5);
	elseif (y <= -4.6e-302)
		tmp = Float64(x * 0.5);
	elseif (y <= 5.5e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -240000000000.0)
		tmp = 1.0;
	elseif (y <= -2.7e-24)
		tmp = (y / x) + -1.0;
	elseif (y <= -3.3e-205)
		tmp = y * -0.5;
	elseif (y <= -4.6e-302)
		tmp = x * 0.5;
	elseif (y <= 5.5e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -240000000000.0], 1.0, If[LessEqual[y, -2.7e-24], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[y, -3.3e-205], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -4.6e-302], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 5.5e+59], -1.0, 1.0]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.4e11 or 5.4999999999999999e59 < 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 85.5%

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

   if -2.4e11 < y < -2.70000000000000007e-24

   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. Step-by-step derivation

      1. clear-num 100.0%

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

      2. associate-/r/ 99.5%

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

      3. associate--l- 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around inf 88.8%

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

   7. Taylor expanded in x around 0 89.3%

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

   if -2.70000000000000007e-24 < y < -3.2999999999999999e-205

   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 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-neg-frac 61.1%

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

   6. Simplified 61.1%

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

   7. Taylor expanded in y around 0 61.1%

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

      1. *-commutative 61.1%

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

   9. Simplified 61.1%

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

   if -3.2999999999999999e-205 < y < -4.60000000000000004e-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 y around 0 85.2%

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

   5. Taylor expanded in x around 0 64.4%

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

      1. *-commutative 64.4%

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

   7. Simplified 64.4%

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

   if -4.60000000000000004e-302 < y < 5.4999999999999999e59

   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 inf 53.7%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -240000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-205}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-302}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -230000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-155}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-304}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -230000000000.0)
   1.0
   (if (<= y -1.75e-155)
     -1.0
     (if (<= y -7.2e-304) (* x 0.5) (if (<= y 5.4e+59) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -230000000000.0) {
		tmp = 1.0;
	} else if (y <= -1.75e-155) {
		tmp = -1.0;
	} else if (y <= -7.2e-304) {
		tmp = x * 0.5;
	} else if (y <= 5.4e+59) {
		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 (y <= (-230000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-1.75d-155)) then
        tmp = -1.0d0
    else if (y <= (-7.2d-304)) then
        tmp = x * 0.5d0
    else if (y <= 5.4d+59) 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 (y <= -230000000000.0) {
		tmp = 1.0;
	} else if (y <= -1.75e-155) {
		tmp = -1.0;
	} else if (y <= -7.2e-304) {
		tmp = x * 0.5;
	} else if (y <= 5.4e+59) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -230000000000.0:
		tmp = 1.0
	elif y <= -1.75e-155:
		tmp = -1.0
	elif y <= -7.2e-304:
		tmp = x * 0.5
	elif y <= 5.4e+59:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -230000000000.0)
		tmp = 1.0;
	elseif (y <= -1.75e-155)
		tmp = -1.0;
	elseif (y <= -7.2e-304)
		tmp = Float64(x * 0.5);
	elseif (y <= 5.4e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -230000000000.0)
		tmp = 1.0;
	elseif (y <= -1.75e-155)
		tmp = -1.0;
	elseif (y <= -7.2e-304)
		tmp = x * 0.5;
	elseif (y <= 5.4e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -230000000000.0], 1.0, If[LessEqual[y, -1.75e-155], -1.0, If[LessEqual[y, -7.2e-304], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 5.4e+59], -1.0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3e11 or 5.4000000000000002e59 < 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 85.5%

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

   if -2.3e11 < y < -1.75000000000000008e-155 or -7.2000000000000003e-304 < y < 5.4000000000000002e59

   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 inf 52.0%

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

   if -1.75000000000000008e-155 < y < -7.2000000000000003e-304

   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 64.0%

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

   5. Taylor expanded in x around 0 50.5%

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

      1. *-commutative 50.5%

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

   7. Simplified 50.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -230000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-155}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-304}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 10: 62.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8800000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8800000000.0) 1.0 (if (<= y 6e+59) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8800000000.0) {
		tmp = 1.0;
	} else if (y <= 6e+59) {
		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 (y <= (-8800000000.0d0)) then
        tmp = 1.0d0
    else if (y <= 6d+59) 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 (y <= -8800000000.0) {
		tmp = 1.0;
	} else if (y <= 6e+59) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8800000000.0:
		tmp = 1.0
	elif y <= 6e+59:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8800000000.0)
		tmp = 1.0;
	elseif (y <= 6e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8800000000.0)
		tmp = 1.0;
	elseif (y <= 6e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8800000000.0], 1.0, If[LessEqual[y, 6e+59], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8e9 or 6.0000000000000001e59 < 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 85.5%

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

   if -8.8e9 < y < 6.0000000000000001e59

   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 inf 45.5%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8800000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 38.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]
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 inf 32.1%

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

5. Final simplification 32.1%

   \[\leadsto -1 \]

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 2023218 
(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))))