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

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

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, 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 2: 60.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+114}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-210}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-306}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-123}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-105}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2900000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -2.2e+114)
     t_0
     (if (<= y -2.65e-210)
       -1.0
       (if (<= y -6e-306)
         (* x 0.5)
         (if (<= y 2.8e-123)
           -1.0
           (if (<= y 2.3e-105) (* x 0.5) (if (<= y 2900000.0) -1.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -2.2e+114) {
		tmp = t_0;
	} else if (y <= -2.65e-210) {
		tmp = -1.0;
	} else if (y <= -6e-306) {
		tmp = x * 0.5;
	} else if (y <= 2.8e-123) {
		tmp = -1.0;
	} else if (y <= 2.3e-105) {
		tmp = x * 0.5;
	} else if (y <= 2900000.0) {
		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 <= (-2.2d+114)) then
        tmp = t_0
    else if (y <= (-2.65d-210)) then
        tmp = -1.0d0
    else if (y <= (-6d-306)) then
        tmp = x * 0.5d0
    else if (y <= 2.8d-123) then
        tmp = -1.0d0
    else if (y <= 2.3d-105) then
        tmp = x * 0.5d0
    else if (y <= 2900000.0d0) 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 <= -2.2e+114) {
		tmp = t_0;
	} else if (y <= -2.65e-210) {
		tmp = -1.0;
	} else if (y <= -6e-306) {
		tmp = x * 0.5;
	} else if (y <= 2.8e-123) {
		tmp = -1.0;
	} else if (y <= 2.3e-105) {
		tmp = x * 0.5;
	} else if (y <= 2900000.0) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -2.2e+114:
		tmp = t_0
	elif y <= -2.65e-210:
		tmp = -1.0
	elif y <= -6e-306:
		tmp = x * 0.5
	elif y <= 2.8e-123:
		tmp = -1.0
	elif y <= 2.3e-105:
		tmp = x * 0.5
	elif y <= 2900000.0:
		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 <= -2.2e+114)
		tmp = t_0;
	elseif (y <= -2.65e-210)
		tmp = -1.0;
	elseif (y <= -6e-306)
		tmp = Float64(x * 0.5);
	elseif (y <= 2.8e-123)
		tmp = -1.0;
	elseif (y <= 2.3e-105)
		tmp = Float64(x * 0.5);
	elseif (y <= 2900000.0)
		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 <= -2.2e+114)
		tmp = t_0;
	elseif (y <= -2.65e-210)
		tmp = -1.0;
	elseif (y <= -6e-306)
		tmp = x * 0.5;
	elseif (y <= 2.8e-123)
		tmp = -1.0;
	elseif (y <= 2.3e-105)
		tmp = x * 0.5;
	elseif (y <= 2900000.0)
		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, -2.2e+114], t$95$0, If[LessEqual[y, -2.65e-210], -1.0, If[LessEqual[y, -6e-306], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 2.8e-123], -1.0, If[LessEqual[y, 2.3e-105], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 2900000.0], -1.0, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2e114 or 2.9e6 < 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 89.6%

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

      1. neg-mul-1 89.6%

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

   6. Simplified 89.6%

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

   7. Taylor expanded in x around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

   9. Simplified 89.6%

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

   if -2.2e114 < y < -2.65e-210 or -6.00000000000000048e-306 < y < 2.7999999999999999e-123 or 2.3000000000000001e-105 < y < 2.9e6

   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 55.4%

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

   if -2.65e-210 < y < -6.00000000000000048e-306 or 2.7999999999999999e-123 < y < 2.3000000000000001e-105

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 81.6%

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

   5. Taylor expanded in y around 0 55.1%

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

      1. *-commutative 55.1%

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

   7. Simplified 55.1%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+114}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-210}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-306}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-123}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-105}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2900000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 3: 60.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-213}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-305}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-123}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-105}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2900000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -2.2e+112)
     t_0
     (if (<= y -2.45e-213)
       (+ (/ y x) -1.0)
       (if (<= y -1.35e-305)
         (* x 0.5)
         (if (<= y 5.4e-123)
           -1.0
           (if (<= y 2.3e-105) (* x 0.5) (if (<= y 2900000.0) -1.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -2.2e+112) {
		tmp = t_0;
	} else if (y <= -2.45e-213) {
		tmp = (y / x) + -1.0;
	} else if (y <= -1.35e-305) {
		tmp = x * 0.5;
	} else if (y <= 5.4e-123) {
		tmp = -1.0;
	} else if (y <= 2.3e-105) {
		tmp = x * 0.5;
	} else if (y <= 2900000.0) {
		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 <= (-2.2d+112)) then
        tmp = t_0
    else if (y <= (-2.45d-213)) then
        tmp = (y / x) + (-1.0d0)
    else if (y <= (-1.35d-305)) then
        tmp = x * 0.5d0
    else if (y <= 5.4d-123) then
        tmp = -1.0d0
    else if (y <= 2.3d-105) then
        tmp = x * 0.5d0
    else if (y <= 2900000.0d0) 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 <= -2.2e+112) {
		tmp = t_0;
	} else if (y <= -2.45e-213) {
		tmp = (y / x) + -1.0;
	} else if (y <= -1.35e-305) {
		tmp = x * 0.5;
	} else if (y <= 5.4e-123) {
		tmp = -1.0;
	} else if (y <= 2.3e-105) {
		tmp = x * 0.5;
	} else if (y <= 2900000.0) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -2.2e+112:
		tmp = t_0
	elif y <= -2.45e-213:
		tmp = (y / x) + -1.0
	elif y <= -1.35e-305:
		tmp = x * 0.5
	elif y <= 5.4e-123:
		tmp = -1.0
	elif y <= 2.3e-105:
		tmp = x * 0.5
	elif y <= 2900000.0:
		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 <= -2.2e+112)
		tmp = t_0;
	elseif (y <= -2.45e-213)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (y <= -1.35e-305)
		tmp = Float64(x * 0.5);
	elseif (y <= 5.4e-123)
		tmp = -1.0;
	elseif (y <= 2.3e-105)
		tmp = Float64(x * 0.5);
	elseif (y <= 2900000.0)
		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 <= -2.2e+112)
		tmp = t_0;
	elseif (y <= -2.45e-213)
		tmp = (y / x) + -1.0;
	elseif (y <= -1.35e-305)
		tmp = x * 0.5;
	elseif (y <= 5.4e-123)
		tmp = -1.0;
	elseif (y <= 2.3e-105)
		tmp = x * 0.5;
	elseif (y <= 2900000.0)
		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, -2.2e+112], t$95$0, If[LessEqual[y, -2.45e-213], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[y, -1.35e-305], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 5.4e-123], -1.0, If[LessEqual[y, 2.3e-105], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 2900000.0], -1.0, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.1999999999999999e112 or 2.9e6 < 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 89.6%

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

      1. neg-mul-1 89.6%

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

   6. Simplified 89.6%

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

   7. Taylor expanded in x around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

   9. Simplified 89.6%

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

   if -2.1999999999999999e112 < y < -2.4499999999999999e-213

   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 55.0%

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

      1. neg-mul-1 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in x around 0 55.0%

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

   if -2.4499999999999999e-213 < y < -1.35e-305 or 5.4000000000000002e-123 < y < 2.3000000000000001e-105

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 81.6%

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

   5. Taylor expanded in y around 0 55.1%

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

      1. *-commutative 55.1%

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

   7. Simplified 55.1%

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

   if -1.35e-305 < y < 5.4000000000000002e-123 or 2.3000000000000001e-105 < y < 2.9e6

   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 56.5%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-213}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-305}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-123}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-105}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2900000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 4: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{2 - y}\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+73}:\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -0.215:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+137}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- 2.0 y))))
   (if (<= x -6.4e+73)
     (/ (- x y) (- x))
     (if (<= x -6.6e+37)
       t_0
       (if (<= x -0.215)
         (/ x (- 2.0 x))
         (if (<= x 1.15e+137) t_0 (+ (/ y x) -1.0)))))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - y);
	double tmp;
	if (x <= -6.4e+73) {
		tmp = (x - y) / -x;
	} else if (x <= -6.6e+37) {
		tmp = t_0;
	} else if (x <= -0.215) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.15e+137) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / (2.0d0 - y)
    if (x <= (-6.4d+73)) then
        tmp = (x - y) / -x
    else if (x <= (-6.6d+37)) then
        tmp = t_0
    else if (x <= (-0.215d0)) then
        tmp = x / (2.0d0 - x)
    else if (x <= 1.15d+137) then
        tmp = t_0
    else
        tmp = (y / x) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - y);
	double tmp;
	if (x <= -6.4e+73) {
		tmp = (x - y) / -x;
	} else if (x <= -6.6e+37) {
		tmp = t_0;
	} else if (x <= -0.215) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.15e+137) {
		tmp = t_0;
	} else {
		tmp = (y / x) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / (2.0 - y)
	tmp = 0
	if x <= -6.4e+73:
		tmp = (x - y) / -x
	elif x <= -6.6e+37:
		tmp = t_0
	elif x <= -0.215:
		tmp = x / (2.0 - x)
	elif x <= 1.15e+137:
		tmp = t_0
	else:
		tmp = (y / x) + -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(2.0 - y))
	tmp = 0.0
	if (x <= -6.4e+73)
		tmp = Float64(Float64(x - y) / Float64(-x));
	elseif (x <= -6.6e+37)
		tmp = t_0;
	elseif (x <= -0.215)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 1.15e+137)
		tmp = t_0;
	else
		tmp = Float64(Float64(y / x) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / (2.0 - y);
	tmp = 0.0;
	if (x <= -6.4e+73)
		tmp = (x - y) / -x;
	elseif (x <= -6.6e+37)
		tmp = t_0;
	elseif (x <= -0.215)
		tmp = x / (2.0 - x);
	elseif (x <= 1.15e+137)
		tmp = t_0;
	else
		tmp = (y / x) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+73], N[(N[(x - y), $MachinePrecision] / (-x)), $MachinePrecision], If[LessEqual[x, -6.6e+37], t$95$0, If[LessEqual[x, -0.215], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+137], t$95$0, N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.39999999999999964e73

   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 71.0%

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

      1. neg-mul-1 71.0%

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

   6. Simplified 71.0%

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

   if -6.39999999999999964e73 < x < -6.6000000000000002e37 or -0.214999999999999997 < x < 1.15e137

   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 92.7%

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

   if -6.6000000000000002e37 < x < -0.214999999999999997

   1. Initial program 99.8%

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

      1. associate--r+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 76.7%

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

   if 1.15e137 < 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 86.3%

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

      1. neg-mul-1 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in x around 0 86.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+73}:\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{elif}\;x \leq -0.215:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+137}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 5: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-211}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-307}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-121}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-100}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1700000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.2e+112)
   1.0
   (if (<= y -1.22e-211)
     -1.0
     (if (<= y -8.5e-307)
       (* x 0.5)
       (if (<= y 2.15e-121)
         -1.0
         (if (<= y 1.1e-100) (* x 0.5) (if (<= y 1700000.0) -1.0 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.2e+112) {
		tmp = 1.0;
	} else if (y <= -1.22e-211) {
		tmp = -1.0;
	} else if (y <= -8.5e-307) {
		tmp = x * 0.5;
	} else if (y <= 2.15e-121) {
		tmp = -1.0;
	} else if (y <= 1.1e-100) {
		tmp = x * 0.5;
	} else if (y <= 1700000.0) {
		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 (y <= (-2.2d+112)) then
        tmp = 1.0d0
    else if (y <= (-1.22d-211)) then
        tmp = -1.0d0
    else if (y <= (-8.5d-307)) then
        tmp = x * 0.5d0
    else if (y <= 2.15d-121) then
        tmp = -1.0d0
    else if (y <= 1.1d-100) then
        tmp = x * 0.5d0
    else if (y <= 1700000.0d0) 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 (y <= -2.2e+112) {
		tmp = 1.0;
	} else if (y <= -1.22e-211) {
		tmp = -1.0;
	} else if (y <= -8.5e-307) {
		tmp = x * 0.5;
	} else if (y <= 2.15e-121) {
		tmp = -1.0;
	} else if (y <= 1.1e-100) {
		tmp = x * 0.5;
	} else if (y <= 1700000.0) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.2e+112:
		tmp = 1.0
	elif y <= -1.22e-211:
		tmp = -1.0
	elif y <= -8.5e-307:
		tmp = x * 0.5
	elif y <= 2.15e-121:
		tmp = -1.0
	elif y <= 1.1e-100:
		tmp = x * 0.5
	elif y <= 1700000.0:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.2e+112)
		tmp = 1.0;
	elseif (y <= -1.22e-211)
		tmp = -1.0;
	elseif (y <= -8.5e-307)
		tmp = Float64(x * 0.5);
	elseif (y <= 2.15e-121)
		tmp = -1.0;
	elseif (y <= 1.1e-100)
		tmp = Float64(x * 0.5);
	elseif (y <= 1700000.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.2e+112)
		tmp = 1.0;
	elseif (y <= -1.22e-211)
		tmp = -1.0;
	elseif (y <= -8.5e-307)
		tmp = x * 0.5;
	elseif (y <= 2.15e-121)
		tmp = -1.0;
	elseif (y <= 1.1e-100)
		tmp = x * 0.5;
	elseif (y <= 1700000.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.2e+112], 1.0, If[LessEqual[y, -1.22e-211], -1.0, If[LessEqual[y, -8.5e-307], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 2.15e-121], -1.0, If[LessEqual[y, 1.1e-100], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 1700000.0], -1.0, 1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1999999999999999e112 or 1.7e6 < 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 89.4%

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

   if -2.1999999999999999e112 < y < -1.21999999999999996e-211 or -8.4999999999999995e-307 < y < 2.14999999999999983e-121 or 1.09999999999999995e-100 < y < 1.7e6

   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 55.4%

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

   if -1.21999999999999996e-211 < y < -8.4999999999999995e-307 or 2.14999999999999983e-121 < y < 1.09999999999999995e-100

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 81.6%

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

   5. Taylor expanded in y around 0 55.1%

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

      1. *-commutative 55.1%

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

   7. Simplified 55.1%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-211}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-307}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-121}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-100}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1700000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.2e+112)
   (- 1.0 (/ x y))
   (if (<= y 3.6e-97) (/ x (- 2.0 x)) (/ (- y) (- 2.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.2e+112) {
		tmp = 1.0 - (x / y);
	} else if (y <= 3.6e-97) {
		tmp = x / (2.0 - x);
	} else {
		tmp = -y / (2.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.2d+112)) then
        tmp = 1.0d0 - (x / y)
    else if (y <= 3.6d-97) then
        tmp = x / (2.0d0 - x)
    else
        tmp = -y / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.2e+112) {
		tmp = 1.0 - (x / y);
	} else if (y <= 3.6e-97) {
		tmp = x / (2.0 - x);
	} else {
		tmp = -y / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.2e+112:
		tmp = 1.0 - (x / y)
	elif y <= 3.6e-97:
		tmp = x / (2.0 - x)
	else:
		tmp = -y / (2.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.2e+112)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (y <= 3.6e-97)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(Float64(-y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.2e+112)
		tmp = 1.0 - (x / y);
	elseif (y <= 3.6e-97)
		tmp = x / (2.0 - x);
	else
		tmp = -y / (2.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.2e+112], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-97], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[((-y) / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1999999999999999e112

   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 99.9%

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

      1. neg-mul-1 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in x around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

   9. Simplified 99.9%

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

   if -2.1999999999999999e112 < y < 3.59999999999999997e-97

   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 75.4%

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

   if 3.59999999999999997e-97 < 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 x around 0 79.4%

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

      1. associate-*r/ 79.4%

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

      2. neg-mul-1 79.4%

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

   6. Simplified 79.4%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+112}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \end{array} \]

Alternative 7: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+112} \lor \neg \left(y \leq 1900000000\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.2e+112) (not (<= y 1900000000.0)))
   (- 1.0 (/ x y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.2e+112) || !(y <= 1900000000.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.2d+112)) .or. (.not. (y <= 1900000000.0d0))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.2e+112) || !(y <= 1900000000.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.2e+112) or not (y <= 1900000000.0):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.2e+112) || !(y <= 1900000000.0))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.2e+112) || ~((y <= 1900000000.0)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.2e+112], N[Not[LessEqual[y, 1900000000.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1999999999999999e112 or 1.9e9 < 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 89.6%

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

      1. neg-mul-1 89.6%

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

   6. Simplified 89.6%

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

   7. Taylor expanded in x around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

   9. Simplified 89.6%

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

   if -2.1999999999999999e112 < y < 1.9e9

   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 72.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+112} \lor \neg \left(y \leq 1900000000\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 8: 61.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 78000000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.35e+116) 1.0 (if (<= y 78000000.0) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.35e+116) {
		tmp = 1.0;
	} else if (y <= 78000000.0) {
		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 (y <= (-2.35d+116)) then
        tmp = 1.0d0
    else if (y <= 78000000.0d0) 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 (y <= -2.35e+116) {
		tmp = 1.0;
	} else if (y <= 78000000.0) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.35e+116:
		tmp = 1.0
	elif y <= 78000000.0:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.35e+116)
		tmp = 1.0;
	elseif (y <= 78000000.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.35e+116)
		tmp = 1.0;
	elseif (y <= 78000000.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.35e+116], 1.0, If[LessEqual[y, 78000000.0], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3500000000000002e116 or 7.8e7 < 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 89.4%

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

   if -2.3500000000000002e116 < y < 7.8e7

   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 48.9%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 78000000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 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 33.4%

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

5. Final simplification 33.4%

   \[\leadsto -1 \]

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 2023196 
(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))))