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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 8

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: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-6}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-55}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.15e-6)
   (+ 1.0 (/ 2.0 y))
   (if (<= y -4.1e-55)
     (* y -0.5)
     (if (<= y 6.6e+53) (/ x (- 2.0 x)) (- 1.0 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.15e-6) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= -4.1e-55) {
		tmp = y * -0.5;
	} else if (y <= 6.6e+53) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.15d-6)) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (y <= (-4.1d-55)) then
        tmp = y * (-0.5d0)
    else if (y <= 6.6d+53) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.15e-6) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= -4.1e-55) {
		tmp = y * -0.5;
	} else if (y <= 6.6e+53) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.15e-6:
		tmp = 1.0 + (2.0 / y)
	elif y <= -4.1e-55:
		tmp = y * -0.5
	elif y <= 6.6e+53:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.15e-6)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (y <= -4.1e-55)
		tmp = Float64(y * -0.5);
	elseif (y <= 6.6e+53)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.15e-6)
		tmp = 1.0 + (2.0 / y);
	elseif (y <= -4.1e-55)
		tmp = y * -0.5;
	elseif (y <= 6.6e+53)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.15e-6], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.1e-55], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 6.6e+53], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.14999999999999991e-6

   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 74.8%

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

      1. mul-1-neg 74.8%

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

      2. distribute-neg-frac 74.8%

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

   6. Simplified 74.8%

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

   7. Taylor expanded in y around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. associate-*r/ 74.6%

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

      3. metadata-eval 74.6%

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

   9. Simplified 74.6%

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

   if -3.14999999999999991e-6 < y < -4.0999999999999998e-55

   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 74.6%

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

      1. mul-1-neg 74.6%

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

      2. distribute-neg-frac 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in y around 0 71.6%

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

      1. *-commutative 71.6%

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

   9. Simplified 71.6%

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

   if -4.0999999999999998e-55 < y < 6.6000000000000004e53

   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 76.9%

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

   if 6.6000000000000004e53 < 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 77.9%

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

   7. Taylor expanded in y around 0 78.2%

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

      1. mul-1-neg 78.2%

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

      2. unsub-neg 78.2%

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

   9. Simplified 78.2%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-6}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-55}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 3: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+25} \lor \neg \left(x \leq 40000000000000\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -7.5e+25) (not (<= x 40000000000000.0))) (+ (/ y x) -1.0) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -7.5e+25) || !(x <= 40000000000000.0)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-7.5d+25)) .or. (.not. (x <= 40000000000000.0d0))) then
        tmp = (y / x) + (-1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -7.5e+25) || !(x <= 40000000000000.0)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -7.5e+25) or not (x <= 40000000000000.0):
		tmp = (y / x) + -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -7.5e+25) || !(x <= 40000000000000.0))
		tmp = Float64(Float64(y / x) + -1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -7.5e+25) || ~((x <= 40000000000000.0)))
		tmp = (y / x) + -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -7.5e+25], N[Not[LessEqual[x, 40000000000000.0]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -7.49999999999999993e25 or 4e13 < x

   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/ 99.7%

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

      3. associate--l- 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 80.5%

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

   7. Taylor expanded in x around 0 80.7%

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

   if -7.49999999999999993e25 < x < 4e13

   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 56.3%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+25} \lor \neg \left(x \leq 40000000000000\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+33} \lor \neg \left(x \leq 6600000000000\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.8e+33) (not (<= x 6600000000000.0)))
   (+ (/ y x) -1.0)
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.8e+33) || !(x <= 6600000000000.0)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.8d+33)) .or. (.not. (x <= 6600000000000.0d0))) then
        tmp = (y / x) + (-1.0d0)
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.8e+33) || !(x <= 6600000000000.0)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.8e+33) or not (x <= 6600000000000.0):
		tmp = (y / x) + -1.0
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.8e+33) || !(x <= 6600000000000.0))
		tmp = Float64(Float64(y / x) + -1.0);
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.8e+33) || ~((x <= 6600000000000.0)))
		tmp = (y / x) + -1.0;
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.8e+33], N[Not[LessEqual[x, 6600000000000.0]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8000000000000001e33 or 6.6e12 < x

   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/ 99.7%

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

      3. associate--l- 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 80.5%

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

   7. Taylor expanded in x around 0 80.7%

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

   if -1.8000000000000001e33 < x < 6.6e12

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. distribute-neg-frac 80.8%

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

   6. Simplified 80.8%

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

      1. frac-2neg 80.8%

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

      2. div-inv 80.7%

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

      3. remove-double-neg 80.7%

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

      4. sub-neg 80.7%

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

      5. add-sqr-sqrt 46.3%

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

      6. sqrt-unprod 45.1%

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

      7. sqr-neg 45.1%

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

      8. sqrt-unprod 10.2%

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

      9. add-sqr-sqrt 24.9%

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

   8. Applied egg-rr 24.9%

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

      1. distribute-neg-in 24.9%

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

      2. metadata-eval 24.9%

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

   10. Simplified 24.9%

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

       1. expm1-log1p-u 24.9%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \frac{1}{-2 + \left(-y\right)}\right)\right)} \]

       2. expm1-udef 4.6%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \frac{1}{-2 + \left(-y\right)}\right)} - 1} \]

       3. un-div-inv 4.6%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{-2 + \left(-y\right)}}\right)} - 1 \]

       4. +-commutative 4.6%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\left(-y\right) + -2}}\right)} - 1 \]

       5. add-sqr-sqrt 2.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}} + -2}\right)} - 1 \]

       6. sqrt-unprod 20.0%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} + -2}\right)} - 1 \]

       7. sqr-neg 20.0%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\sqrt{\color{blue}{y \cdot y}} + -2}\right)} - 1 \]

       8. sqrt-unprod 25.6%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\sqrt{y} \cdot \sqrt{y}} + -2}\right)} - 1 \]

       9. add-sqr-sqrt 59.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{y} + -2}\right)} - 1 \]

   12. Applied egg-rr 59.5%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{y + -2}\right)} - 1} \]
   13. Step-by-step derivation

       1. expm1-def 80.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{y + -2}\right)\right)} \]

       2. expm1-log1p 80.8%

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

   14. Simplified 80.8%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+33} \lor \neg \left(x \leq 6600000000000\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 5: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+29}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;x \leq 1250000000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.35e+29)
   (/ (- y x) x)
   (if (<= x 1250000000000.0) (/ y (+ y -2.0)) (+ (/ y x) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.35e+29) {
		tmp = (y - x) / x;
	} else if (x <= 1250000000000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = (y / x) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.35d+29)) then
        tmp = (y - x) / x
    else if (x <= 1250000000000.0d0) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = (y / x) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.35e+29) {
		tmp = (y - x) / x;
	} else if (x <= 1250000000000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = (y / x) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.35e+29:
		tmp = (y - x) / x
	elif x <= 1250000000000.0:
		tmp = y / (y + -2.0)
	else:
		tmp = (y / x) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.35e+29)
		tmp = Float64(Float64(y - x) / x);
	elseif (x <= 1250000000000.0)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(Float64(y / x) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.35e+29)
		tmp = (y - x) / x;
	elseif (x <= 1250000000000.0)
		tmp = y / (y + -2.0);
	else
		tmp = (y / x) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.35e+29], N[(N[(y - x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 1250000000000.0], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e29

   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 100.0%

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

      2. associate-/r/ 99.8%

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

      3. associate--l- 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 85.9%

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

      1. associate-*l/ 86.0%

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

      2. sub-neg 86.0%

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

      3. distribute-lft-in 86.0%

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

      4. neg-mul-1 86.0%

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

      5. add-sqr-sqrt 42.9%

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

      6. sqrt-unprod 79.0%

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

      7. sqr-neg 79.0%

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

      8. sqrt-unprod 43.3%

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

      9. add-sqr-sqrt 85.6%

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

      10. neg-mul-1 85.6%

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

      11. add-sqr-sqrt 42.3%

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

      12. sqrt-unprod 78.8%

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

      13. sqr-neg 78.8%

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

      14. sqrt-unprod 43.2%

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

      15. add-sqr-sqrt 86.0%

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

   8. Applied egg-rr 86.0%

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

   if -1.35e29 < x < 1.25e12

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. distribute-neg-frac 80.8%

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

   6. Simplified 80.8%

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

      1. frac-2neg 80.8%

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

      2. div-inv 80.7%

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

      3. remove-double-neg 80.7%

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

      4. sub-neg 80.7%

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

      5. add-sqr-sqrt 46.3%

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

      6. sqrt-unprod 45.1%

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

      7. sqr-neg 45.1%

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

      8. sqrt-unprod 10.2%

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

      9. add-sqr-sqrt 24.9%

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

   8. Applied egg-rr 24.9%

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

      1. distribute-neg-in 24.9%

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

      2. metadata-eval 24.9%

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

   10. Simplified 24.9%

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

       1. expm1-log1p-u 24.9%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \frac{1}{-2 + \left(-y\right)}\right)\right)} \]

       2. expm1-udef 4.6%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \frac{1}{-2 + \left(-y\right)}\right)} - 1} \]

       3. un-div-inv 4.6%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{-2 + \left(-y\right)}}\right)} - 1 \]

       4. +-commutative 4.6%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\left(-y\right) + -2}}\right)} - 1 \]

       5. add-sqr-sqrt 2.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}} + -2}\right)} - 1 \]

       6. sqrt-unprod 20.0%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} + -2}\right)} - 1 \]

       7. sqr-neg 20.0%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\sqrt{\color{blue}{y \cdot y}} + -2}\right)} - 1 \]

       8. sqrt-unprod 25.6%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{\sqrt{y} \cdot \sqrt{y}} + -2}\right)} - 1 \]

       9. add-sqr-sqrt 59.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{y}{\color{blue}{y} + -2}\right)} - 1 \]

   12. Applied egg-rr 59.5%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{y + -2}\right)} - 1} \]
   13. Step-by-step derivation

       1. expm1-def 80.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{y + -2}\right)\right)} \]

       2. expm1-log1p 80.8%

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

   14. Simplified 80.8%

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

   if 1.25e12 < x

   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/ 99.6%

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

      3. associate--l- 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 76.8%

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

   7. Taylor expanded in x around 0 77.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+29}:\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{elif}\;x \leq 1250000000000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 6: 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 7: 61.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+74}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e+74) -1.0 (if (<= x 7000000000000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e+74) {
		tmp = -1.0;
	} else if (x <= 7000000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-9d+74)) then
        tmp = -1.0d0
    else if (x <= 7000000000000.0d0) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9e+74) {
		tmp = -1.0;
	} else if (x <= 7000000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9e+74:
		tmp = -1.0
	elif x <= 7000000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e+74)
		tmp = -1.0;
	elseif (x <= 7000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9e+74)
		tmp = -1.0;
	elseif (x <= 7000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e+74], -1.0, If[LessEqual[x, 7000000000000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -8.9999999999999999e74 or 7e12 < x

   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 80.7%

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

   if -8.9999999999999999e74 < x < 7e12

   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 56.2%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+74}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8: 38.3% 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 40.5%

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

5. Final simplification 40.5%

   \[\leadsto -1 \]

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 2023238 
(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))))