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

Percentage Accurate: 100.0% → 100.0%

Time: 8.2s

Alternatives: 7

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: 73.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-44}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-120}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-83}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-59}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -2.1e+49)
     1.0
     (if (<= y -6.8e-6)
       t_0
       (if (<= y -7e-44)
         (* y -0.5)
         (if (<= y 1.3e-120)
           t_0
           (if (<= y 2e-83)
             (* y -0.5)
             (if (<= y 9.2e-59)
               t_0
               (if (<= y 3.5e-16)
                 (* y -0.5)
                 (if (<= y 1.1e+14) -1.0 1.0))))))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -2.1e+49) {
		tmp = 1.0;
	} else if (y <= -6.8e-6) {
		tmp = t_0;
	} else if (y <= -7e-44) {
		tmp = y * -0.5;
	} else if (y <= 1.3e-120) {
		tmp = t_0;
	} else if (y <= 2e-83) {
		tmp = y * -0.5;
	} else if (y <= 9.2e-59) {
		tmp = t_0;
	} else if (y <= 3.5e-16) {
		tmp = y * -0.5;
	} else if (y <= 1.1e+14) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-2.1d+49)) then
        tmp = 1.0d0
    else if (y <= (-6.8d-6)) then
        tmp = t_0
    else if (y <= (-7d-44)) then
        tmp = y * (-0.5d0)
    else if (y <= 1.3d-120) then
        tmp = t_0
    else if (y <= 2d-83) then
        tmp = y * (-0.5d0)
    else if (y <= 9.2d-59) then
        tmp = t_0
    else if (y <= 3.5d-16) then
        tmp = y * (-0.5d0)
    else if (y <= 1.1d+14) then
        tmp = -1.0d0
    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 <= -2.1e+49) {
		tmp = 1.0;
	} else if (y <= -6.8e-6) {
		tmp = t_0;
	} else if (y <= -7e-44) {
		tmp = y * -0.5;
	} else if (y <= 1.3e-120) {
		tmp = t_0;
	} else if (y <= 2e-83) {
		tmp = y * -0.5;
	} else if (y <= 9.2e-59) {
		tmp = t_0;
	} else if (y <= 3.5e-16) {
		tmp = y * -0.5;
	} else if (y <= 1.1e+14) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -2.1e+49:
		tmp = 1.0
	elif y <= -6.8e-6:
		tmp = t_0
	elif y <= -7e-44:
		tmp = y * -0.5
	elif y <= 1.3e-120:
		tmp = t_0
	elif y <= 2e-83:
		tmp = y * -0.5
	elif y <= 9.2e-59:
		tmp = t_0
	elif y <= 3.5e-16:
		tmp = y * -0.5
	elif y <= 1.1e+14:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -2.1e+49)
		tmp = 1.0;
	elseif (y <= -6.8e-6)
		tmp = t_0;
	elseif (y <= -7e-44)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.3e-120)
		tmp = t_0;
	elseif (y <= 2e-83)
		tmp = Float64(y * -0.5);
	elseif (y <= 9.2e-59)
		tmp = t_0;
	elseif (y <= 3.5e-16)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.1e+14)
		tmp = -1.0;
	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 <= -2.1e+49)
		tmp = 1.0;
	elseif (y <= -6.8e-6)
		tmp = t_0;
	elseif (y <= -7e-44)
		tmp = y * -0.5;
	elseif (y <= 1.3e-120)
		tmp = t_0;
	elseif (y <= 2e-83)
		tmp = y * -0.5;
	elseif (y <= 9.2e-59)
		tmp = t_0;
	elseif (y <= 3.5e-16)
		tmp = y * -0.5;
	elseif (y <= 1.1e+14)
		tmp = -1.0;
	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, -2.1e+49], 1.0, If[LessEqual[y, -6.8e-6], t$95$0, If[LessEqual[y, -7e-44], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.3e-120], t$95$0, If[LessEqual[y, 2e-83], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 9.2e-59], t$95$0, If[LessEqual[y, 3.5e-16], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.1e+14], -1.0, 1.0]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.10000000000000011e49 or 1.1e14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 76.8%

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

   if -2.10000000000000011e49 < y < -6.80000000000000012e-6 or -6.9999999999999995e-44 < y < 1.3000000000000001e-120 or 2.0000000000000001e-83 < y < 9.19999999999999918e-59

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.3%

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

   if -6.80000000000000012e-6 < y < -6.9999999999999995e-44 or 1.3000000000000001e-120 < y < 2.0000000000000001e-83 or 9.19999999999999918e-59 < y < 3.50000000000000017e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. distribute-neg-frac 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around 0 77.1%

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

      1. *-commutative 77.1%

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

   8. Simplified 77.1%

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

   if 3.50000000000000017e-16 < y < 1.1e14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 42.7%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-44}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-83}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-16}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-65}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-171}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-204}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-306}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4e+35)
   -1.0
   (if (<= x -4.6e-65)
     1.0
     (if (<= x -2e-171)
       (* x 0.5)
       (if (<= x -4.9e-204)
         1.0
         (if (<= x 8e-306) (* y -0.5) (if (<= x 2.5e+35) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4e+35) {
		tmp = -1.0;
	} else if (x <= -4.6e-65) {
		tmp = 1.0;
	} else if (x <= -2e-171) {
		tmp = x * 0.5;
	} else if (x <= -4.9e-204) {
		tmp = 1.0;
	} else if (x <= 8e-306) {
		tmp = y * -0.5;
	} else if (x <= 2.5e+35) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4d+35)) then
        tmp = -1.0d0
    else if (x <= (-4.6d-65)) then
        tmp = 1.0d0
    else if (x <= (-2d-171)) then
        tmp = x * 0.5d0
    else if (x <= (-4.9d-204)) then
        tmp = 1.0d0
    else if (x <= 8d-306) then
        tmp = y * (-0.5d0)
    else if (x <= 2.5d+35) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4e+35) {
		tmp = -1.0;
	} else if (x <= -4.6e-65) {
		tmp = 1.0;
	} else if (x <= -2e-171) {
		tmp = x * 0.5;
	} else if (x <= -4.9e-204) {
		tmp = 1.0;
	} else if (x <= 8e-306) {
		tmp = y * -0.5;
	} else if (x <= 2.5e+35) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4e+35:
		tmp = -1.0
	elif x <= -4.6e-65:
		tmp = 1.0
	elif x <= -2e-171:
		tmp = x * 0.5
	elif x <= -4.9e-204:
		tmp = 1.0
	elif x <= 8e-306:
		tmp = y * -0.5
	elif x <= 2.5e+35:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4e+35)
		tmp = -1.0;
	elseif (x <= -4.6e-65)
		tmp = 1.0;
	elseif (x <= -2e-171)
		tmp = Float64(x * 0.5);
	elseif (x <= -4.9e-204)
		tmp = 1.0;
	elseif (x <= 8e-306)
		tmp = Float64(y * -0.5);
	elseif (x <= 2.5e+35)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4e+35)
		tmp = -1.0;
	elseif (x <= -4.6e-65)
		tmp = 1.0;
	elseif (x <= -2e-171)
		tmp = x * 0.5;
	elseif (x <= -4.9e-204)
		tmp = 1.0;
	elseif (x <= 8e-306)
		tmp = y * -0.5;
	elseif (x <= 2.5e+35)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4e+35], -1.0, If[LessEqual[x, -4.6e-65], 1.0, If[LessEqual[x, -2e-171], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -4.9e-204], 1.0, If[LessEqual[x, 8e-306], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 2.5e+35], 1.0, -1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.9999999999999999e35 or 2.50000000000000011e35 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.0%

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

   if -3.9999999999999999e35 < x < -4.5999999999999999e-65 or -2e-171 < x < -4.90000000000000009e-204 or 8.00000000000000022e-306 < x < 2.50000000000000011e35

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 57.4%

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

   if -4.5999999999999999e-65 < x < -2e-171

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 60.4%

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

   4. Taylor expanded in x around 0 60.4%

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

      1. *-commutative 60.4%

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

   6. Simplified 60.4%

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

   if -4.90000000000000009e-204 < x < 8.00000000000000022e-306

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.7%

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

      1. mul-1-neg 95.7%

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

      2. distribute-neg-frac 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in y around 0 67.6%

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

      1. *-commutative 67.6%

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

   8. Simplified 67.6%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+35}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-65}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-171}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-204}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-306}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-142}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))))
   (if (<= x -1.2e+32)
     -1.0
     (if (<= x -1.8e-68)
       t_0
       (if (<= x -3.5e-142) (* x 0.5) (if (<= x 6.5e+52) t_0 -1.0))))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (x <= -1.2e+32) {
		tmp = -1.0;
	} else if (x <= -1.8e-68) {
		tmp = t_0;
	} else if (x <= -3.5e-142) {
		tmp = x * 0.5;
	} else if (x <= 6.5e+52) {
		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 = y / (y + (-2.0d0))
    if (x <= (-1.2d+32)) then
        tmp = -1.0d0
    else if (x <= (-1.8d-68)) then
        tmp = t_0
    else if (x <= (-3.5d-142)) then
        tmp = x * 0.5d0
    else if (x <= 6.5d+52) 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 = y / (y + -2.0);
	double tmp;
	if (x <= -1.2e+32) {
		tmp = -1.0;
	} else if (x <= -1.8e-68) {
		tmp = t_0;
	} else if (x <= -3.5e-142) {
		tmp = x * 0.5;
	} else if (x <= 6.5e+52) {
		tmp = t_0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	tmp = 0
	if x <= -1.2e+32:
		tmp = -1.0
	elif x <= -1.8e-68:
		tmp = t_0
	elif x <= -3.5e-142:
		tmp = x * 0.5
	elif x <= 6.5e+52:
		tmp = t_0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	tmp = 0.0
	if (x <= -1.2e+32)
		tmp = -1.0;
	elseif (x <= -1.8e-68)
		tmp = t_0;
	elseif (x <= -3.5e-142)
		tmp = Float64(x * 0.5);
	elseif (x <= 6.5e+52)
		tmp = t_0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	tmp = 0.0;
	if (x <= -1.2e+32)
		tmp = -1.0;
	elseif (x <= -1.8e-68)
		tmp = t_0;
	elseif (x <= -3.5e-142)
		tmp = x * 0.5;
	elseif (x <= 6.5e+52)
		tmp = t_0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+32], -1.0, If[LessEqual[x, -1.8e-68], t$95$0, If[LessEqual[x, -3.5e-142], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 6.5e+52], t$95$0, -1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.19999999999999996e32 or 6.49999999999999996e52 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.5%

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

   if -1.19999999999999996e32 < x < -1.80000000000000004e-68 or -3.50000000000000015e-142 < x < 6.49999999999999996e52

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-neg-frac 82.0%

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

   5. Simplified 82.0%

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

      1. frac-2neg 82.0%

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

      2. div-inv 81.9%

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

      3. remove-double-neg 81.9%

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

      4. sub-neg 81.9%

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

      5. distribute-neg-in 81.9%

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

      6. metadata-eval 81.9%

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

      7. remove-double-neg 81.9%

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

   7. Applied egg-rr 81.9%

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

      1. associate-*r/ 82.0%

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

      2. *-rgt-identity 82.0%

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

      3. +-commutative 82.0%

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

   9. Simplified 82.0%

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

   if -1.80000000000000004e-68 < x < -3.50000000000000015e-142

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.3%

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

   4. Taylor expanded in x around 0 67.3%

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

      1. *-commutative 67.3%

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

   6. Simplified 67.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-68}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-142}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-67}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-171}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e+27)
   -1.0
   (if (<= x -1.8e-67)
     1.0
     (if (<= x -2.2e-171) (* x 0.5) (if (<= x 2.35e+35) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e+27) {
		tmp = -1.0;
	} else if (x <= -1.8e-67) {
		tmp = 1.0;
	} else if (x <= -2.2e-171) {
		tmp = x * 0.5;
	} else if (x <= 2.35e+35) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-5d+27)) then
        tmp = -1.0d0
    else if (x <= (-1.8d-67)) then
        tmp = 1.0d0
    else if (x <= (-2.2d-171)) then
        tmp = x * 0.5d0
    else if (x <= 2.35d+35) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5e+27) {
		tmp = -1.0;
	} else if (x <= -1.8e-67) {
		tmp = 1.0;
	} else if (x <= -2.2e-171) {
		tmp = x * 0.5;
	} else if (x <= 2.35e+35) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e+27:
		tmp = -1.0
	elif x <= -1.8e-67:
		tmp = 1.0
	elif x <= -2.2e-171:
		tmp = x * 0.5
	elif x <= 2.35e+35:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e+27)
		tmp = -1.0;
	elseif (x <= -1.8e-67)
		tmp = 1.0;
	elseif (x <= -2.2e-171)
		tmp = Float64(x * 0.5);
	elseif (x <= 2.35e+35)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e+27)
		tmp = -1.0;
	elseif (x <= -1.8e-67)
		tmp = 1.0;
	elseif (x <= -2.2e-171)
		tmp = x * 0.5;
	elseif (x <= 2.35e+35)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e+27], -1.0, If[LessEqual[x, -1.8e-67], 1.0, If[LessEqual[x, -2.2e-171], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 2.35e+35], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.99999999999999979e27 or 2.35000000000000017e35 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.0%

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

   if -4.99999999999999979e27 < x < -1.8e-67 or -2.2000000000000001e-171 < x < 2.35000000000000017e35

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 51.4%

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

   if -1.8e-67 < x < -2.2000000000000001e-171

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 60.4%

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

   4. Taylor expanded in x around 0 60.4%

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

      1. *-commutative 60.4%

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

   6. Simplified 60.4%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-67}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-171}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.4e+27) -1.0 (if (<= x 2.9e+35) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.4e+27) {
		tmp = -1.0;
	} else if (x <= 2.9e+35) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.4d+27)) then
        tmp = -1.0d0
    else if (x <= 2.9d+35) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.4e+27) {
		tmp = -1.0;
	} else if (x <= 2.9e+35) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.4e+27:
		tmp = -1.0
	elif x <= 2.9e+35:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.4e+27)
		tmp = -1.0;
	elseif (x <= 2.9e+35)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.4e+27)
		tmp = -1.0;
	elseif (x <= 2.9e+35)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.4e+27], -1.0, If[LessEqual[x, 2.9e+35], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4000000000000003e27 or 2.89999999999999995e35 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.0%

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

   if -6.4000000000000003e27 < x < 2.89999999999999995e35

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 48.4%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.7% 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 36.1%

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

4. Final simplification 36.1%

   \[\leadsto -1 \]
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 2024017 
(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))))