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

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.6× speedup

Math

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

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: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -7.3 \cdot 10^{+56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-20}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-116}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -7.3e+56)
     t_0
     (if (<= y -5e-20)
       -1.0
       (if (<= y -3.8e-42)
         (* y -0.5)
         (if (<= y 3.4e-116)
           -1.0
           (if (<= y 2e-85) (* x 0.5) (if (<= y 2.5e+21) -1.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -7.3e+56) {
		tmp = t_0;
	} else if (y <= -5e-20) {
		tmp = -1.0;
	} else if (y <= -3.8e-42) {
		tmp = y * -0.5;
	} else if (y <= 3.4e-116) {
		tmp = -1.0;
	} else if (y <= 2e-85) {
		tmp = x * 0.5;
	} else if (y <= 2.5e+21) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-7.3d+56)) then
        tmp = t_0
    else if (y <= (-5d-20)) then
        tmp = -1.0d0
    else if (y <= (-3.8d-42)) then
        tmp = y * (-0.5d0)
    else if (y <= 3.4d-116) then
        tmp = -1.0d0
    else if (y <= 2d-85) then
        tmp = x * 0.5d0
    else if (y <= 2.5d+21) then
        tmp = -1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -7.3e+56) {
		tmp = t_0;
	} else if (y <= -5e-20) {
		tmp = -1.0;
	} else if (y <= -3.8e-42) {
		tmp = y * -0.5;
	} else if (y <= 3.4e-116) {
		tmp = -1.0;
	} else if (y <= 2e-85) {
		tmp = x * 0.5;
	} else if (y <= 2.5e+21) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -7.3e+56:
		tmp = t_0
	elif y <= -5e-20:
		tmp = -1.0
	elif y <= -3.8e-42:
		tmp = y * -0.5
	elif y <= 3.4e-116:
		tmp = -1.0
	elif y <= 2e-85:
		tmp = x * 0.5
	elif y <= 2.5e+21:
		tmp = -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -7.3e+56)
		tmp = t_0;
	elseif (y <= -5e-20)
		tmp = -1.0;
	elseif (y <= -3.8e-42)
		tmp = Float64(y * -0.5);
	elseif (y <= 3.4e-116)
		tmp = -1.0;
	elseif (y <= 2e-85)
		tmp = Float64(x * 0.5);
	elseif (y <= 2.5e+21)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -7.3e+56)
		tmp = t_0;
	elseif (y <= -5e-20)
		tmp = -1.0;
	elseif (y <= -3.8e-42)
		tmp = y * -0.5;
	elseif (y <= 3.4e-116)
		tmp = -1.0;
	elseif (y <= 2e-85)
		tmp = x * 0.5;
	elseif (y <= 2.5e+21)
		tmp = -1.0;
	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]}, If[LessEqual[y, -7.3e+56], t$95$0, If[LessEqual[y, -5e-20], -1.0, If[LessEqual[y, -3.8e-42], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 3.4e-116], -1.0, If[LessEqual[y, 2e-85], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 2.5e+21], -1.0, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.3e56 or 2.5e21 < 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/ 99.6%

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

      3. associate--l- 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 75.3%

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

   7. Taylor expanded in y around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   9. Simplified 75.5%

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

   if -7.3e56 < y < -4.9999999999999999e-20 or -3.80000000000000017e-42 < y < 3.39999999999999992e-116 or 2e-85 < y < 2.5e21

   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 65.9%

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

   if -4.9999999999999999e-20 < y < -3.80000000000000017e-42

   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. mul-1-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if 3.39999999999999992e-116 < y < 2e-85

   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 57.7%

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

   5. Taylor expanded in x around 0 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{+56}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-20}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-116}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 3: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x \cdot -2}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-41}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* x -2.0) y))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -1.05e+57)
     t_0
     (if (<= y -2.5e-18)
       t_1
       (if (<= y -1.8e-41) (* y -0.5) (if (<= y 4.1e+22) 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 <= -1.05e+57) {
		tmp = t_0;
	} else if (y <= -2.5e-18) {
		tmp = t_1;
	} else if (y <= -1.8e-41) {
		tmp = y * -0.5;
	} else if (y <= 4.1e+22) {
		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 <= (-1.05d+57)) then
        tmp = t_0
    else if (y <= (-2.5d-18)) then
        tmp = t_1
    else if (y <= (-1.8d-41)) then
        tmp = y * (-0.5d0)
    else if (y <= 4.1d+22) 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 <= -1.05e+57) {
		tmp = t_0;
	} else if (y <= -2.5e-18) {
		tmp = t_1;
	} else if (y <= -1.8e-41) {
		tmp = y * -0.5;
	} else if (y <= 4.1e+22) {
		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 <= -1.05e+57:
		tmp = t_0
	elif y <= -2.5e-18:
		tmp = t_1
	elif y <= -1.8e-41:
		tmp = y * -0.5
	elif y <= 4.1e+22:
		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 <= -1.05e+57)
		tmp = t_0;
	elseif (y <= -2.5e-18)
		tmp = t_1;
	elseif (y <= -1.8e-41)
		tmp = Float64(y * -0.5);
	elseif (y <= 4.1e+22)
		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 <= -1.05e+57)
		tmp = t_0;
	elseif (y <= -2.5e-18)
		tmp = t_1;
	elseif (y <= -1.8e-41)
		tmp = y * -0.5;
	elseif (y <= 4.1e+22)
		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, -1.05e+57], t$95$0, If[LessEqual[y, -2.5e-18], t$95$1, If[LessEqual[y, -1.8e-41], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 4.1e+22], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999995e57 or 4.09999999999999979e22 < 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 76.1%

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

      1. associate--l+ 76.2%

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

      2. associate-*r/ 76.2%

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

      3. associate-*r/ 76.2%

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

      4. div-sub 76.2%

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

      5. cancel-sign-sub-inv 76.2%

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

      6. metadata-eval 76.2%

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

      7. *-lft-identity 76.2%

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

      8. +-commutative 76.2%

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

      9. mul-1-neg 76.2%

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

      10. unsub-neg 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in x around inf 76.2%

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

      1. *-commutative 76.2%

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

   9. Simplified 76.2%

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

   if -1.04999999999999995e57 < y < -2.50000000000000018e-18 or -1.8e-41 < y < 4.09999999999999979e22

   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 82.8%

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

   if -2.50000000000000018e-18 < y < -1.8e-41

   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. mul-1-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+57}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-41}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \end{array} \]

Alternative 4: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+55}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-20}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-41}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-116}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.9e+55)
   1.0
   (if (<= y -7e-20)
     -1.0
     (if (<= y -1.85e-41)
       (* y -0.5)
       (if (<= y 3.4e-116)
         -1.0
         (if (<= y 2e-85) (* x 0.5) (if (<= y 9.6e+22) -1.0 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.9e+55) {
		tmp = 1.0;
	} else if (y <= -7e-20) {
		tmp = -1.0;
	} else if (y <= -1.85e-41) {
		tmp = y * -0.5;
	} else if (y <= 3.4e-116) {
		tmp = -1.0;
	} else if (y <= 2e-85) {
		tmp = x * 0.5;
	} else if (y <= 9.6e+22) {
		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 <= (-3.9d+55)) then
        tmp = 1.0d0
    else if (y <= (-7d-20)) then
        tmp = -1.0d0
    else if (y <= (-1.85d-41)) then
        tmp = y * (-0.5d0)
    else if (y <= 3.4d-116) then
        tmp = -1.0d0
    else if (y <= 2d-85) then
        tmp = x * 0.5d0
    else if (y <= 9.6d+22) 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 <= -3.9e+55) {
		tmp = 1.0;
	} else if (y <= -7e-20) {
		tmp = -1.0;
	} else if (y <= -1.85e-41) {
		tmp = y * -0.5;
	} else if (y <= 3.4e-116) {
		tmp = -1.0;
	} else if (y <= 2e-85) {
		tmp = x * 0.5;
	} else if (y <= 9.6e+22) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.9e+55:
		tmp = 1.0
	elif y <= -7e-20:
		tmp = -1.0
	elif y <= -1.85e-41:
		tmp = y * -0.5
	elif y <= 3.4e-116:
		tmp = -1.0
	elif y <= 2e-85:
		tmp = x * 0.5
	elif y <= 9.6e+22:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.9e+55)
		tmp = 1.0;
	elseif (y <= -7e-20)
		tmp = -1.0;
	elseif (y <= -1.85e-41)
		tmp = Float64(y * -0.5);
	elseif (y <= 3.4e-116)
		tmp = -1.0;
	elseif (y <= 2e-85)
		tmp = Float64(x * 0.5);
	elseif (y <= 9.6e+22)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.9e+55)
		tmp = 1.0;
	elseif (y <= -7e-20)
		tmp = -1.0;
	elseif (y <= -1.85e-41)
		tmp = y * -0.5;
	elseif (y <= 3.4e-116)
		tmp = -1.0;
	elseif (y <= 2e-85)
		tmp = x * 0.5;
	elseif (y <= 9.6e+22)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.9e+55], 1.0, If[LessEqual[y, -7e-20], -1.0, If[LessEqual[y, -1.85e-41], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 3.4e-116], -1.0, If[LessEqual[y, 2e-85], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 9.6e+22], -1.0, 1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.90000000000000027e55 or 9.6e22 < 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 74.9%

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

   if -3.90000000000000027e55 < y < -7.00000000000000007e-20 or -1.8500000000000001e-41 < y < 3.39999999999999992e-116 or 2e-85 < y < 9.6e22

   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 65.9%

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

   if -7.00000000000000007e-20 < y < -1.8500000000000001e-41

   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. mul-1-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if 3.39999999999999992e-116 < y < 2e-85

   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 57.7%

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

   5. Taylor expanded in x around 0 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+55}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-20}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-41}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-116}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-41}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -8.2e+56)
     t_0
     (if (<= y -1.65e-19)
       t_1
       (if (<= y -1.85e-41) (* y -0.5) (if (<= y 6.2e+24) 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 <= -8.2e+56) {
		tmp = t_0;
	} else if (y <= -1.65e-19) {
		tmp = t_1;
	} else if (y <= -1.85e-41) {
		tmp = y * -0.5;
	} else if (y <= 6.2e+24) {
		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 <= (-8.2d+56)) then
        tmp = t_0
    else if (y <= (-1.65d-19)) then
        tmp = t_1
    else if (y <= (-1.85d-41)) then
        tmp = y * (-0.5d0)
    else if (y <= 6.2d+24) 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 <= -8.2e+56) {
		tmp = t_0;
	} else if (y <= -1.65e-19) {
		tmp = t_1;
	} else if (y <= -1.85e-41) {
		tmp = y * -0.5;
	} else if (y <= 6.2e+24) {
		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 <= -8.2e+56:
		tmp = t_0
	elif y <= -1.65e-19:
		tmp = t_1
	elif y <= -1.85e-41:
		tmp = y * -0.5
	elif y <= 6.2e+24:
		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 <= -8.2e+56)
		tmp = t_0;
	elseif (y <= -1.65e-19)
		tmp = t_1;
	elseif (y <= -1.85e-41)
		tmp = Float64(y * -0.5);
	elseif (y <= 6.2e+24)
		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 <= -8.2e+56)
		tmp = t_0;
	elseif (y <= -1.65e-19)
		tmp = t_1;
	elseif (y <= -1.85e-41)
		tmp = y * -0.5;
	elseif (y <= 6.2e+24)
		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, -8.2e+56], t$95$0, If[LessEqual[y, -1.65e-19], t$95$1, If[LessEqual[y, -1.85e-41], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 6.2e+24], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.2000000000000007e56 or 6.20000000000000022e24 < 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/ 99.6%

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

      3. associate--l- 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 75.3%

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

   7. Taylor expanded in y around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   9. Simplified 75.5%

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

   if -8.2000000000000007e56 < y < -1.6499999999999999e-19 or -1.8500000000000001e-41 < y < 6.20000000000000022e24

   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 82.8%

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

   if -1.6499999999999999e-19 < y < -1.8500000000000001e-41

   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. mul-1-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+56}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-41}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 6: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-116}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2e+61)
   1.0
   (if (<= y 3.3e-116)
     -1.0
     (if (<= y 2e-85) (* x 0.5) (if (<= y 4e+19) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2e+61) {
		tmp = 1.0;
	} else if (y <= 3.3e-116) {
		tmp = -1.0;
	} else if (y <= 2e-85) {
		tmp = x * 0.5;
	} else if (y <= 4e+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 (y <= (-2d+61)) then
        tmp = 1.0d0
    else if (y <= 3.3d-116) then
        tmp = -1.0d0
    else if (y <= 2d-85) then
        tmp = x * 0.5d0
    else if (y <= 4d+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 (y <= -2e+61) {
		tmp = 1.0;
	} else if (y <= 3.3e-116) {
		tmp = -1.0;
	} else if (y <= 2e-85) {
		tmp = x * 0.5;
	} else if (y <= 4e+19) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2e+61:
		tmp = 1.0
	elif y <= 3.3e-116:
		tmp = -1.0
	elif y <= 2e-85:
		tmp = x * 0.5
	elif y <= 4e+19:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2e+61)
		tmp = 1.0;
	elseif (y <= 3.3e-116)
		tmp = -1.0;
	elseif (y <= 2e-85)
		tmp = Float64(x * 0.5);
	elseif (y <= 4e+19)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2e+61)
		tmp = 1.0;
	elseif (y <= 3.3e-116)
		tmp = -1.0;
	elseif (y <= 2e-85)
		tmp = x * 0.5;
	elseif (y <= 4e+19)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2e+61], 1.0, If[LessEqual[y, 3.3e-116], -1.0, If[LessEqual[y, 2e-85], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 4e+19], -1.0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e61 or 4e19 < 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 74.9%

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

   if -1.9999999999999999e61 < y < 3.30000000000000001e-116 or 2e-85 < y < 4e19

   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 61.9%

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

   if 3.30000000000000001e-116 < y < 2e-85

   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 57.7%

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

   5. Taylor expanded in x around 0 55.6%

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

      1. *-commutative 55.6%

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

   7. Simplified 55.6%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-116}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 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 8: 62.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{+24}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.85e+59) 1.0 (if (<= y 1e+24) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.85e+59) {
		tmp = 1.0;
	} else if (y <= 1e+24) {
		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 <= (-1.85d+59)) then
        tmp = 1.0d0
    else if (y <= 1d+24) 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 <= -1.85e+59) {
		tmp = 1.0;
	} else if (y <= 1e+24) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.85e+59:
		tmp = 1.0
	elif y <= 1e+24:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.85e+59)
		tmp = 1.0;
	elseif (y <= 1e+24)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.85e+59)
		tmp = 1.0;
	elseif (y <= 1e+24)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.85e+59], 1.0, If[LessEqual[y, 1e+24], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.84999999999999999e59 or 9.9999999999999998e23 < 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 74.9%

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

   if -1.84999999999999999e59 < y < 9.9999999999999998e23

   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 57.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{+24}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 38.9% 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 41.9%

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

5. Final simplification 41.9%

   \[\leadsto -1 \]

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 2023173 
(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))))