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

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

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: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-130}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -2.3e+46)
     1.0
     (if (<= y -1.7e-94)
       t_0
       (if (<= y -1.9e-130) (* y -0.5) (if (<= y 3.5e+63) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -2.3e+46) {
		tmp = 1.0;
	} else if (y <= -1.7e-94) {
		tmp = t_0;
	} else if (y <= -1.9e-130) {
		tmp = y * -0.5;
	} else if (y <= 3.5e+63) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-2.3d+46)) then
        tmp = 1.0d0
    else if (y <= (-1.7d-94)) then
        tmp = t_0
    else if (y <= (-1.9d-130)) then
        tmp = y * (-0.5d0)
    else if (y <= 3.5d+63) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -2.3e+46) {
		tmp = 1.0;
	} else if (y <= -1.7e-94) {
		tmp = t_0;
	} else if (y <= -1.9e-130) {
		tmp = y * -0.5;
	} else if (y <= 3.5e+63) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -2.3e+46:
		tmp = 1.0
	elif y <= -1.7e-94:
		tmp = t_0
	elif y <= -1.9e-130:
		tmp = y * -0.5
	elif y <= 3.5e+63:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -2.3e+46)
		tmp = 1.0;
	elseif (y <= -1.7e-94)
		tmp = t_0;
	elseif (y <= -1.9e-130)
		tmp = Float64(y * -0.5);
	elseif (y <= 3.5e+63)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -2.3e+46)
		tmp = 1.0;
	elseif (y <= -1.7e-94)
		tmp = t_0;
	elseif (y <= -1.9e-130)
		tmp = y * -0.5;
	elseif (y <= 3.5e+63)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+46], 1.0, If[LessEqual[y, -1.7e-94], t$95$0, If[LessEqual[y, -1.9e-130], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 3.5e+63], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3000000000000001e46 or 3.50000000000000029e63 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 82.8%

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

   if -2.3000000000000001e46 < y < -1.6999999999999999e-94 or -1.8999999999999999e-130 < y < 3.50000000000000029e63

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 73.1%

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

   if -1.6999999999999999e-94 < y < -1.8999999999999999e-130

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 84.5%

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

      1. associate-*r/ 84.5%

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

      2. mul-1-neg 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in y around 0 84.5%

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

      1. *-commutative 84.5%

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

   9. Simplified 84.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-130}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-130}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -2.4e+46)
     t_0
     (if (<= y -5.5e-89)
       t_1
       (if (<= y -1.9e-130) (* y -0.5) (if (<= y 3.5e+63) 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 <= -2.4e+46) {
		tmp = t_0;
	} else if (y <= -5.5e-89) {
		tmp = t_1;
	} else if (y <= -1.9e-130) {
		tmp = y * -0.5;
	} else if (y <= 3.5e+63) {
		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 <= (-2.4d+46)) then
        tmp = t_0
    else if (y <= (-5.5d-89)) then
        tmp = t_1
    else if (y <= (-1.9d-130)) then
        tmp = y * (-0.5d0)
    else if (y <= 3.5d+63) 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 <= -2.4e+46) {
		tmp = t_0;
	} else if (y <= -5.5e-89) {
		tmp = t_1;
	} else if (y <= -1.9e-130) {
		tmp = y * -0.5;
	} else if (y <= 3.5e+63) {
		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 <= -2.4e+46:
		tmp = t_0
	elif y <= -5.5e-89:
		tmp = t_1
	elif y <= -1.9e-130:
		tmp = y * -0.5
	elif y <= 3.5e+63:
		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 <= -2.4e+46)
		tmp = t_0;
	elseif (y <= -5.5e-89)
		tmp = t_1;
	elseif (y <= -1.9e-130)
		tmp = Float64(y * -0.5);
	elseif (y <= 3.5e+63)
		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 <= -2.4e+46)
		tmp = t_0;
	elseif (y <= -5.5e-89)
		tmp = t_1;
	elseif (y <= -1.9e-130)
		tmp = y * -0.5;
	elseif (y <= 3.5e+63)
		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, -2.4e+46], t$95$0, If[LessEqual[y, -5.5e-89], t$95$1, If[LessEqual[y, -1.9e-130], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 3.5e+63], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000008e46 or 3.50000000000000029e63 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 83.2%

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

      1. mul-1-neg 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in x around 0 83.2%

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

      1. associate-*r/ 83.2%

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

      2. mul-1-neg 83.2%

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

   9. Simplified 83.2%

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

   if -2.40000000000000008e46 < y < -5.50000000000000012e-89 or -1.8999999999999999e-130 < y < 3.50000000000000029e63

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 73.1%

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

   if -5.50000000000000012e-89 < y < -1.8999999999999999e-130

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 84.5%

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

      1. associate-*r/ 84.5%

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

      2. mul-1-neg 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in y around 0 84.5%

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

      1. *-commutative 84.5%

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

   9. Simplified 84.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-130}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 4: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7800000000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+62}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7800000000.0)
   (/ x (- 2.0 x))
   (if (<= x 1.55e+62) (/ (- x y) (- 2.0 y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7800000000.0) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.55e+62) {
		tmp = (x - y) / (2.0 - y);
	} 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 <= (-7800000000.0d0)) then
        tmp = x / (2.0d0 - x)
    else if (x <= 1.55d+62) then
        tmp = (x - y) / (2.0d0 - y)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -7800000000.0) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.55e+62) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7800000000.0:
		tmp = x / (2.0 - x)
	elif x <= 1.55e+62:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7800000000.0)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 1.55e+62)
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7800000000.0)
		tmp = x / (2.0 - x);
	elseif (x <= 1.55e+62)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7800000000.0], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+62], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -7.8e9

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 72.7%

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

   if -7.8e9 < x < 1.55000000000000007e62

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 97.5%

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

   if 1.55000000000000007e62 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 78.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7800000000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+62}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8500000000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8500000000.0)
   (/ x (- 2.0 x))
   (if (<= x 3.1e+63) (/ (- y) (- 2.0 y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8500000000.0) {
		tmp = x / (2.0 - x);
	} else if (x <= 3.1e+63) {
		tmp = -y / (2.0 - y);
	} 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 <= (-8500000000.0d0)) then
        tmp = x / (2.0d0 - x)
    else if (x <= 3.1d+63) then
        tmp = -y / (2.0d0 - y)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -8500000000.0) {
		tmp = x / (2.0 - x);
	} else if (x <= 3.1e+63) {
		tmp = -y / (2.0 - y);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8500000000.0:
		tmp = x / (2.0 - x)
	elif x <= 3.1e+63:
		tmp = -y / (2.0 - y)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8500000000.0)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 3.1e+63)
		tmp = Float64(Float64(-y) / Float64(2.0 - y));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8500000000.0)
		tmp = x / (2.0 - x);
	elseif (x <= 3.1e+63)
		tmp = -y / (2.0 - y);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8500000000.0], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+63], N[((-y) / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5e9

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 72.7%

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

   if -8.5e9 < x < 3.1000000000000001e63

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. mul-1-neg 82.3%

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

   6. Simplified 82.3%

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

   if 3.1000000000000001e63 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 78.5%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8500000000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 60.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-94}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-199}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+63}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.25e+19)
   1.0
   (if (<= y -8.8e-94)
     -1.0
     (if (<= y -6e-199) (* y -0.5) (if (<= y 3.7e+63) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.25e+19) {
		tmp = 1.0;
	} else if (y <= -8.8e-94) {
		tmp = -1.0;
	} else if (y <= -6e-199) {
		tmp = y * -0.5;
	} else if (y <= 3.7e+63) {
		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 <= (-3.25d+19)) then
        tmp = 1.0d0
    else if (y <= (-8.8d-94)) then
        tmp = -1.0d0
    else if (y <= (-6d-199)) then
        tmp = y * (-0.5d0)
    else if (y <= 3.7d+63) 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 <= -3.25e+19) {
		tmp = 1.0;
	} else if (y <= -8.8e-94) {
		tmp = -1.0;
	} else if (y <= -6e-199) {
		tmp = y * -0.5;
	} else if (y <= 3.7e+63) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.25e+19:
		tmp = 1.0
	elif y <= -8.8e-94:
		tmp = -1.0
	elif y <= -6e-199:
		tmp = y * -0.5
	elif y <= 3.7e+63:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.25e+19)
		tmp = 1.0;
	elseif (y <= -8.8e-94)
		tmp = -1.0;
	elseif (y <= -6e-199)
		tmp = Float64(y * -0.5);
	elseif (y <= 3.7e+63)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.25e+19)
		tmp = 1.0;
	elseif (y <= -8.8e-94)
		tmp = -1.0;
	elseif (y <= -6e-199)
		tmp = y * -0.5;
	elseif (y <= 3.7e+63)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.25e+19], 1.0, If[LessEqual[y, -8.8e-94], -1.0, If[LessEqual[y, -6e-199], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 3.7e+63], -1.0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.25e19 or 3.69999999999999968e63 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 81.8%

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

   if -3.25e19 < y < -8.80000000000000004e-94 or -5.99999999999999966e-199 < y < 3.69999999999999968e63

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 60.1%

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

   if -8.80000000000000004e-94 < y < -5.99999999999999966e-199

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 54.3%

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

      1. associate-*r/ 54.3%

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

      2. mul-1-neg 54.3%

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

   6. Simplified 54.3%

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

   7. Taylor expanded in y around 0 54.3%

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

      1. *-commutative 54.3%

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

   9. Simplified 54.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-94}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-199}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+63}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 59.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -10000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-92}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-199}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -10000000000.0)
   (+ 1.0 (/ 2.0 y))
   (if (<= y -9.5e-92)
     -1.0
     (if (<= y -6.4e-199) (* y -0.5) (if (<= y 3.5e+63) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -10000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= -9.5e-92) {
		tmp = -1.0;
	} else if (y <= -6.4e-199) {
		tmp = y * -0.5;
	} else if (y <= 3.5e+63) {
		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 <= (-10000000000.0d0)) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (y <= (-9.5d-92)) then
        tmp = -1.0d0
    else if (y <= (-6.4d-199)) then
        tmp = y * (-0.5d0)
    else if (y <= 3.5d+63) 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 <= -10000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= -9.5e-92) {
		tmp = -1.0;
	} else if (y <= -6.4e-199) {
		tmp = y * -0.5;
	} else if (y <= 3.5e+63) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -10000000000.0:
		tmp = 1.0 + (2.0 / y)
	elif y <= -9.5e-92:
		tmp = -1.0
	elif y <= -6.4e-199:
		tmp = y * -0.5
	elif y <= 3.5e+63:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -10000000000.0)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (y <= -9.5e-92)
		tmp = -1.0;
	elseif (y <= -6.4e-199)
		tmp = Float64(y * -0.5);
	elseif (y <= 3.5e+63)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -10000000000.0)
		tmp = 1.0 + (2.0 / y);
	elseif (y <= -9.5e-92)
		tmp = -1.0;
	elseif (y <= -6.4e-199)
		tmp = y * -0.5;
	elseif (y <= 3.5e+63)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -10000000000.0], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-92], -1.0, If[LessEqual[y, -6.4e-199], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 3.5e+63], -1.0, 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1e10

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 74.9%

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

      1. associate-*r/ 74.9%

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

      2. mul-1-neg 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in y around inf 74.9%

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

      1. associate-*r/ 74.9%

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

      2. metadata-eval 74.9%

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

   9. Simplified 74.9%

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

   if -1e10 < y < -9.49999999999999946e-92 or -6.3999999999999999e-199 < y < 3.50000000000000029e63

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 60.2%

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

   if -9.49999999999999946e-92 < y < -6.3999999999999999e-199

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 54.3%

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

      1. associate-*r/ 54.3%

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

      2. mul-1-neg 54.3%

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

   6. Simplified 54.3%

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

   7. Taylor expanded in y around 0 54.3%

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

      1. *-commutative 54.3%

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

   9. Simplified 54.3%

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

   if 3.50000000000000029e63 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 89.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -10000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-92}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-199}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 61.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.5e+46) 1.0 (if (<= y 3.5e+63) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.5e+46) {
		tmp = 1.0;
	} else if (y <= 3.5e+63) {
		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 <= (-2.5d+46)) then
        tmp = 1.0d0
    else if (y <= 3.5d+63) 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 <= -2.5e+46) {
		tmp = 1.0;
	} else if (y <= 3.5e+63) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.5e+46:
		tmp = 1.0
	elif y <= 3.5e+63:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.5e+46)
		tmp = 1.0;
	elseif (y <= 3.5e+63)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.5e+46)
		tmp = 1.0;
	elseif (y <= 3.5e+63)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.5e+46], 1.0, If[LessEqual[y, 3.5e+63], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5000000000000001e46 or 3.50000000000000029e63 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 82.8%

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

   if -2.5000000000000001e46 < y < 3.50000000000000029e63

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 55.2%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+63}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 39.3% 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. +-commutative 100.0%

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

   2. associate--r+ 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 37.3%

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

5. Final simplification 37.3%

   \[\leadsto -1 \]

Developer target: 100.0% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023301 
(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))))