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

Percentage Accurate: 100.0% → 100.0%

Time: 12.0s

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, 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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 61.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1300000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-113}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-148}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -3.75 \cdot 10^{-237}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-301}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-151}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-16}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+28}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1300000.0)
   1.0
   (if (<= y -1.95e-113)
     -1.0
     (if (<= y -3.5e-148)
       (* y -0.5)
       (if (<= y -3.75e-237)
         -1.0
         (if (<= y 1.6e-301)
           (* x 0.5)
           (if (<= y 3.6e-151)
             -1.0
             (if (<= y 1.5e-16)
               (* y -0.5)
               (if (<= y 2.65e+28) -1.0 1.0)))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1300000.0) {
		tmp = 1.0;
	} else if (y <= -1.95e-113) {
		tmp = -1.0;
	} else if (y <= -3.5e-148) {
		tmp = y * -0.5;
	} else if (y <= -3.75e-237) {
		tmp = -1.0;
	} else if (y <= 1.6e-301) {
		tmp = x * 0.5;
	} else if (y <= 3.6e-151) {
		tmp = -1.0;
	} else if (y <= 1.5e-16) {
		tmp = y * -0.5;
	} else if (y <= 2.65e+28) {
		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 <= (-1300000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-1.95d-113)) then
        tmp = -1.0d0
    else if (y <= (-3.5d-148)) then
        tmp = y * (-0.5d0)
    else if (y <= (-3.75d-237)) then
        tmp = -1.0d0
    else if (y <= 1.6d-301) then
        tmp = x * 0.5d0
    else if (y <= 3.6d-151) then
        tmp = -1.0d0
    else if (y <= 1.5d-16) then
        tmp = y * (-0.5d0)
    else if (y <= 2.65d+28) 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 <= -1300000.0) {
		tmp = 1.0;
	} else if (y <= -1.95e-113) {
		tmp = -1.0;
	} else if (y <= -3.5e-148) {
		tmp = y * -0.5;
	} else if (y <= -3.75e-237) {
		tmp = -1.0;
	} else if (y <= 1.6e-301) {
		tmp = x * 0.5;
	} else if (y <= 3.6e-151) {
		tmp = -1.0;
	} else if (y <= 1.5e-16) {
		tmp = y * -0.5;
	} else if (y <= 2.65e+28) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1300000.0:
		tmp = 1.0
	elif y <= -1.95e-113:
		tmp = -1.0
	elif y <= -3.5e-148:
		tmp = y * -0.5
	elif y <= -3.75e-237:
		tmp = -1.0
	elif y <= 1.6e-301:
		tmp = x * 0.5
	elif y <= 3.6e-151:
		tmp = -1.0
	elif y <= 1.5e-16:
		tmp = y * -0.5
	elif y <= 2.65e+28:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1300000.0)
		tmp = 1.0;
	elseif (y <= -1.95e-113)
		tmp = -1.0;
	elseif (y <= -3.5e-148)
		tmp = Float64(y * -0.5);
	elseif (y <= -3.75e-237)
		tmp = -1.0;
	elseif (y <= 1.6e-301)
		tmp = Float64(x * 0.5);
	elseif (y <= 3.6e-151)
		tmp = -1.0;
	elseif (y <= 1.5e-16)
		tmp = Float64(y * -0.5);
	elseif (y <= 2.65e+28)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1300000.0)
		tmp = 1.0;
	elseif (y <= -1.95e-113)
		tmp = -1.0;
	elseif (y <= -3.5e-148)
		tmp = y * -0.5;
	elseif (y <= -3.75e-237)
		tmp = -1.0;
	elseif (y <= 1.6e-301)
		tmp = x * 0.5;
	elseif (y <= 3.6e-151)
		tmp = -1.0;
	elseif (y <= 1.5e-16)
		tmp = y * -0.5;
	elseif (y <= 2.65e+28)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1300000.0], 1.0, If[LessEqual[y, -1.95e-113], -1.0, If[LessEqual[y, -3.5e-148], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, -3.75e-237], -1.0, If[LessEqual[y, 1.6e-301], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 3.6e-151], -1.0, If[LessEqual[y, 1.5e-16], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 2.65e+28], -1.0, 1.0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e6 or 2.6500000000000002e28 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.3%

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

   if -1.3e6 < y < -1.9499999999999999e-113 or -3.5e-148 < y < -3.75000000000000017e-237 or 1.5999999999999999e-301 < y < 3.60000000000000032e-151 or 1.49999999999999997e-16 < y < 2.6500000000000002e28

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.9%

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

   if -1.9499999999999999e-113 < y < -3.5e-148 or 3.60000000000000032e-151 < y < 1.49999999999999997e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. distribute-neg-frac 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in y around 0 70.4%

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

      1. *-commutative 70.4%

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

   8. Simplified 70.4%

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

   if -3.75000000000000017e-237 < y < 1.5999999999999999e-301

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.4%

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

   4. Taylor expanded in x around 0 70.9%

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

      1. *-commutative 70.9%

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

   6. Simplified 70.9%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1300000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-113}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-148}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq -3.75 \cdot 10^{-237}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-301}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-151}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-16}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+28}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -320000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-149}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-16}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+78}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -320000.0)
     1.0
     (if (<= y 4.4e-149)
       t_0
       (if (<= y 3.6e-16) (* y -0.5) (if (<= y 6.6e+78) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -320000.0) {
		tmp = 1.0;
	} else if (y <= 4.4e-149) {
		tmp = t_0;
	} else if (y <= 3.6e-16) {
		tmp = y * -0.5;
	} else if (y <= 6.6e+78) {
		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 <= (-320000.0d0)) then
        tmp = 1.0d0
    else if (y <= 4.4d-149) then
        tmp = t_0
    else if (y <= 3.6d-16) then
        tmp = y * (-0.5d0)
    else if (y <= 6.6d+78) 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 <= -320000.0) {
		tmp = 1.0;
	} else if (y <= 4.4e-149) {
		tmp = t_0;
	} else if (y <= 3.6e-16) {
		tmp = y * -0.5;
	} else if (y <= 6.6e+78) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -320000.0:
		tmp = 1.0
	elif y <= 4.4e-149:
		tmp = t_0
	elif y <= 3.6e-16:
		tmp = y * -0.5
	elif y <= 6.6e+78:
		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 <= -320000.0)
		tmp = 1.0;
	elseif (y <= 4.4e-149)
		tmp = t_0;
	elseif (y <= 3.6e-16)
		tmp = Float64(y * -0.5);
	elseif (y <= 6.6e+78)
		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 <= -320000.0)
		tmp = 1.0;
	elseif (y <= 4.4e-149)
		tmp = t_0;
	elseif (y <= 3.6e-16)
		tmp = y * -0.5;
	elseif (y <= 6.6e+78)
		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, -320000.0], 1.0, If[LessEqual[y, 4.4e-149], t$95$0, If[LessEqual[y, 3.6e-16], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 6.6e+78], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e5 or 6.6e78 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 80.8%

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

   if -3.2e5 < y < 4.3999999999999996e-149 or 3.59999999999999983e-16 < y < 6.6e78

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.3%

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

   if 4.3999999999999996e-149 < y < 3.59999999999999983e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. distribute-neg-frac 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in y around 0 73.9%

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

      1. *-commutative 73.9%

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

   8. Simplified 73.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -320000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-16}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1300000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{-236}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-301}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1300000.0)
   1.0
   (if (<= y -3.65e-236)
     -1.0
     (if (<= y 1.46e-301) (* x 0.5) (if (<= y 4.9e+27) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1300000.0) {
		tmp = 1.0;
	} else if (y <= -3.65e-236) {
		tmp = -1.0;
	} else if (y <= 1.46e-301) {
		tmp = x * 0.5;
	} else if (y <= 4.9e+27) {
		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 <= (-1300000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-3.65d-236)) then
        tmp = -1.0d0
    else if (y <= 1.46d-301) then
        tmp = x * 0.5d0
    else if (y <= 4.9d+27) 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 <= -1300000.0) {
		tmp = 1.0;
	} else if (y <= -3.65e-236) {
		tmp = -1.0;
	} else if (y <= 1.46e-301) {
		tmp = x * 0.5;
	} else if (y <= 4.9e+27) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1300000.0:
		tmp = 1.0
	elif y <= -3.65e-236:
		tmp = -1.0
	elif y <= 1.46e-301:
		tmp = x * 0.5
	elif y <= 4.9e+27:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1300000.0)
		tmp = 1.0;
	elseif (y <= -3.65e-236)
		tmp = -1.0;
	elseif (y <= 1.46e-301)
		tmp = Float64(x * 0.5);
	elseif (y <= 4.9e+27)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1300000.0)
		tmp = 1.0;
	elseif (y <= -3.65e-236)
		tmp = -1.0;
	elseif (y <= 1.46e-301)
		tmp = x * 0.5;
	elseif (y <= 4.9e+27)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1300000.0], 1.0, If[LessEqual[y, -3.65e-236], -1.0, If[LessEqual[y, 1.46e-301], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 4.9e+27], -1.0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e6 or 4.90000000000000015e27 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.3%

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

   if -1.3e6 < y < -3.65000000000000014e-236 or 1.46000000000000002e-301 < y < 4.90000000000000015e27

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 55.6%

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

   if -3.65000000000000014e-236 < y < 1.46000000000000002e-301

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.4%

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

   4. Taylor expanded in x around 0 70.9%

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

      1. *-commutative 70.9%

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

   6. Simplified 70.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1300000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{-236}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-301}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+30} \lor \neg \left(x \leq 3800000000000\right):\\ \;\;\;\;2 \cdot \frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.8e+30) (not (<= x 3800000000000.0)))
   (+ (* 2.0 (/ y x)) -1.0)
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.8e+30) || !(x <= 3800000000000.0)) {
		tmp = (2.0 * (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 <= (-4.8d+30)) .or. (.not. (x <= 3800000000000.0d0))) then
        tmp = (2.0d0 * (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 <= -4.8e+30) || !(x <= 3800000000000.0)) {
		tmp = (2.0 * (y / x)) + -1.0;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.8e+30) or not (x <= 3800000000000.0):
		tmp = (2.0 * (y / x)) + -1.0
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.8e+30) || !(x <= 3800000000000.0))
		tmp = Float64(Float64(2.0 * 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 <= -4.8e+30) || ~((x <= 3800000000000.0)))
		tmp = (2.0 * (y / x)) + -1.0;
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.8e+30], N[Not[LessEqual[x, 3800000000000.0]], $MachinePrecision]], N[(N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7999999999999999e30 or 3.8e12 < x

   1. Initial program 99.9%

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

      1. expm1-log1p-u 97.3%

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

      2. expm1-udef 97.3%

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

   4. Applied egg-rr 97.3%

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

      1. log1p-udef 97.3%

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

      2. rem-exp-log 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around -inf 78.8%

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

   8. Taylor expanded in y around inf 78.8%

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

   if -4.7999999999999999e30 < x < 3.8e12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. distribute-neg-frac 78.3%

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

   5. Simplified 78.3%

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

      1. expm1-log1p-u 78.2%

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

      2. expm1-udef 54.4%

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

      3. add-sqr-sqrt 30.8%

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

      4. sqrt-unprod 18.3%

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

      5. sqr-neg 18.3%

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

      6. sqrt-unprod 1.0%

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

      7. add-sqr-sqrt 2.7%

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

      8. frac-2neg 2.7%

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

      9. add-sqr-sqrt 1.6%

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

      10. sqrt-unprod 14.8%

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

      11. sqr-neg 14.8%

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

      12. sqrt-unprod 23.5%

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

      13. add-sqr-sqrt 54.4%

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

      14. sub-neg 54.4%

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

      15. distribute-neg-in 54.4%

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

      16. metadata-eval 54.4%

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

      17. remove-double-neg 54.4%

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

   7. Applied egg-rr 54.4%

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

      1. expm1-def 78.2%

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

      2. expm1-log1p 78.3%

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

      3. +-commutative 78.3%

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

   9. Simplified 78.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+30} \lor \neg \left(x \leq 3800000000000\right):\\ \;\;\;\;2 \cdot \frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-42}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.35e+32)
   -1.0
   (if (<= x 1.02e-42) (/ y (+ y -2.0)) (/ x (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.35e+32) {
		tmp = -1.0;
	} else if (x <= 1.02e-42) {
		tmp = y / (y + -2.0);
	} 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 (x <= (-2.35d+32)) then
        tmp = -1.0d0
    else if (x <= 1.02d-42) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.35e+32) {
		tmp = -1.0;
	} else if (x <= 1.02e-42) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.35e+32:
		tmp = -1.0
	elif x <= 1.02e-42:
		tmp = y / (y + -2.0)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.35e+32)
		tmp = -1.0;
	elseif (x <= 1.02e-42)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.35e+32)
		tmp = -1.0;
	elseif (x <= 1.02e-42)
		tmp = y / (y + -2.0);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.35e+32], -1.0, If[LessEqual[x, 1.02e-42], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.35000000000000012e32

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.9%

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

   if -2.35000000000000012e32 < x < 1.0199999999999999e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. distribute-neg-frac 80.4%

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

   5. Simplified 80.4%

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

      1. expm1-log1p-u 80.4%

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

      2. expm1-udef 55.0%

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

      3. add-sqr-sqrt 31.3%

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

      4. sqrt-unprod 18.6%

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

      5. sqr-neg 18.6%

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

      6. sqrt-unprod 1.0%

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

      7. add-sqr-sqrt 2.8%

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

      8. frac-2neg 2.8%

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

      9. add-sqr-sqrt 1.6%

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

      10. sqrt-unprod 14.2%

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

      11. sqr-neg 14.2%

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

      12. sqrt-unprod 23.5%

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

      13. add-sqr-sqrt 55.0%

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

      14. sub-neg 55.0%

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

      15. distribute-neg-in 55.0%

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

      16. metadata-eval 55.0%

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

      17. remove-double-neg 55.0%

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

   7. Applied egg-rr 55.0%

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

      1. expm1-def 80.4%

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

      2. expm1-log1p 80.4%

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

      3. +-commutative 80.4%

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

   9. Simplified 80.4%

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

   if 1.0199999999999999e-42 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-42}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -82000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+34}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -82000.0) 1.0 (if (<= y 2e+34) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -82000.0) {
		tmp = 1.0;
	} else if (y <= 2e+34) {
		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 <= (-82000.0d0)) then
        tmp = 1.0d0
    else if (y <= 2d+34) 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 <= -82000.0) {
		tmp = 1.0;
	} else if (y <= 2e+34) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -82000.0:
		tmp = 1.0
	elif y <= 2e+34:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -82000.0)
		tmp = 1.0;
	elseif (y <= 2e+34)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -82000.0)
		tmp = 1.0;
	elseif (y <= 2e+34)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -82000.0], 1.0, If[LessEqual[y, 2e+34], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -82000 or 1.99999999999999989e34 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.3%

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

   if -82000 < y < 1.99999999999999989e34

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 51.5%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -82000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+34}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.8% 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. Add Preprocessing

3. Taylor expanded in x around inf 36.2%

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

4. Final simplification 36.2%

   \[\leadsto -1 \]
5. Add Preprocessing

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 2024026 
(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))))