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

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{x + y} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x - y}{x + y} \]

Alternative 2: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+50}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+29} \lor \neg \left(y \leq -3.9 \cdot 10^{-70}\right) \land \left(y \leq 1200 \lor \neg \left(y \leq 2.45 \cdot 10^{+29}\right) \land y \leq 5.5 \cdot 10^{+75}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.9e+50)
   -1.0
   (if (or (<= y -7.2e+29)
           (and (not (<= y -3.9e-70))
                (or (<= y 1200.0) (and (not (<= y 2.45e+29)) (<= y 5.5e+75)))))
     (+ 1.0 (* -2.0 (/ y x)))
     -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.9e+50) {
		tmp = -1.0;
	} else if ((y <= -7.2e+29) || (!(y <= -3.9e-70) && ((y <= 1200.0) || (!(y <= 2.45e+29) && (y <= 5.5e+75))))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} 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 <= (-4.9d+50)) then
        tmp = -1.0d0
    else if ((y <= (-7.2d+29)) .or. (.not. (y <= (-3.9d-70))) .and. (y <= 1200.0d0) .or. (.not. (y <= 2.45d+29)) .and. (y <= 5.5d+75)) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.9e+50) {
		tmp = -1.0;
	} else if ((y <= -7.2e+29) || (!(y <= -3.9e-70) && ((y <= 1200.0) || (!(y <= 2.45e+29) && (y <= 5.5e+75))))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.9e+50:
		tmp = -1.0
	elif (y <= -7.2e+29) or (not (y <= -3.9e-70) and ((y <= 1200.0) or (not (y <= 2.45e+29) and (y <= 5.5e+75)))):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.9e+50)
		tmp = -1.0;
	elseif ((y <= -7.2e+29) || (!(y <= -3.9e-70) && ((y <= 1200.0) || (!(y <= 2.45e+29) && (y <= 5.5e+75)))))
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.9e+50)
		tmp = -1.0;
	elseif ((y <= -7.2e+29) || (~((y <= -3.9e-70)) && ((y <= 1200.0) || (~((y <= 2.45e+29)) && (y <= 5.5e+75)))))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.9e+50], -1.0, If[Or[LessEqual[y, -7.2e+29], And[N[Not[LessEqual[y, -3.9e-70]], $MachinePrecision], Or[LessEqual[y, 1200.0], And[N[Not[LessEqual[y, 2.45e+29]], $MachinePrecision], LessEqual[y, 5.5e+75]]]]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9000000000000002e50 or -7.19999999999999952e29 < y < -3.90000000000000019e-70 or 1200 < y < 2.4500000000000001e29 or 5.5000000000000001e75 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 85.3%

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

   if -4.9000000000000002e50 < y < -7.19999999999999952e29 or -3.90000000000000019e-70 < y < 1200 or 2.4500000000000001e29 < y < 5.5000000000000001e75

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in y around 0 80.8%

      \[\leadsto \color{blue}{1 + -2 \cdot \frac{y}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+50}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+29} \lor \neg \left(y \leq -3.9 \cdot 10^{-70}\right) \land \left(y \leq 1200 \lor \neg \left(y \leq 2.45 \cdot 10^{+29}\right) \land y \leq 5.5 \cdot 10^{+75}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+46} \lor \neg \left(y \leq -6 \cdot 10^{+31}\right) \land \left(y \leq -3.9 \cdot 10^{-70} \lor \neg \left(y \leq 500\right)\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.3e+46)
         (and (not (<= y -6e+31)) (or (<= y -3.9e-70) (not (<= y 500.0)))))
   (+ (* 2.0 (/ x y)) -1.0)
   (+ 1.0 (* -2.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.3e+46) || (!(y <= -6e+31) && ((y <= -3.9e-70) || !(y <= 500.0)))) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0 + (-2.0 * (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-6.3d+46)) .or. (.not. (y <= (-6d+31))) .and. (y <= (-3.9d-70)) .or. (.not. (y <= 500.0d0))) then
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    else
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.3e+46) || (!(y <= -6e+31) && ((y <= -3.9e-70) || !(y <= 500.0)))) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0 + (-2.0 * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.3e+46) or (not (y <= -6e+31) and ((y <= -3.9e-70) or not (y <= 500.0))):
		tmp = (2.0 * (x / y)) + -1.0
	else:
		tmp = 1.0 + (-2.0 * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.3e+46) || (!(y <= -6e+31) && ((y <= -3.9e-70) || !(y <= 500.0))))
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	else
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.3e+46) || (~((y <= -6e+31)) && ((y <= -3.9e-70) || ~((y <= 500.0)))))
		tmp = (2.0 * (x / y)) + -1.0;
	else
		tmp = 1.0 + (-2.0 * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.3e+46], And[N[Not[LessEqual[y, -6e+31]], $MachinePrecision], Or[LessEqual[y, -3.9e-70], N[Not[LessEqual[y, 500.0]], $MachinePrecision]]]], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.3e46 or -5.99999999999999978e31 < y < -3.90000000000000019e-70 or 500 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 81.2%

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

   if -6.3e46 < y < -5.99999999999999978e31 or -3.90000000000000019e-70 < y < 500

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in y around 0 82.6%

      \[\leadsto \color{blue}{1 + -2 \cdot \frac{y}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+46} \lor \neg \left(y \leq -6 \cdot 10^{+31}\right) \land \left(y \leq -3.9 \cdot 10^{-70} \lor \neg \left(y \leq 500\right)\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]

Alternative 4: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+46}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-70}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 0.6:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+28}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+73}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8e+46)
   -1.0
   (if (<= y -1e+29)
     1.0
     (if (<= y -3.9e-70)
       -1.0
       (if (<= y 0.6)
         1.0
         (if (<= y 5e+28) -1.0 (if (<= y 3e+73) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8e+46) {
		tmp = -1.0;
	} else if (y <= -1e+29) {
		tmp = 1.0;
	} else if (y <= -3.9e-70) {
		tmp = -1.0;
	} else if (y <= 0.6) {
		tmp = 1.0;
	} else if (y <= 5e+28) {
		tmp = -1.0;
	} else if (y <= 3e+73) {
		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 <= (-8d+46)) then
        tmp = -1.0d0
    else if (y <= (-1d+29)) then
        tmp = 1.0d0
    else if (y <= (-3.9d-70)) then
        tmp = -1.0d0
    else if (y <= 0.6d0) then
        tmp = 1.0d0
    else if (y <= 5d+28) then
        tmp = -1.0d0
    else if (y <= 3d+73) 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 <= -8e+46) {
		tmp = -1.0;
	} else if (y <= -1e+29) {
		tmp = 1.0;
	} else if (y <= -3.9e-70) {
		tmp = -1.0;
	} else if (y <= 0.6) {
		tmp = 1.0;
	} else if (y <= 5e+28) {
		tmp = -1.0;
	} else if (y <= 3e+73) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8e+46:
		tmp = -1.0
	elif y <= -1e+29:
		tmp = 1.0
	elif y <= -3.9e-70:
		tmp = -1.0
	elif y <= 0.6:
		tmp = 1.0
	elif y <= 5e+28:
		tmp = -1.0
	elif y <= 3e+73:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8e+46)
		tmp = -1.0;
	elseif (y <= -1e+29)
		tmp = 1.0;
	elseif (y <= -3.9e-70)
		tmp = -1.0;
	elseif (y <= 0.6)
		tmp = 1.0;
	elseif (y <= 5e+28)
		tmp = -1.0;
	elseif (y <= 3e+73)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8e+46)
		tmp = -1.0;
	elseif (y <= -1e+29)
		tmp = 1.0;
	elseif (y <= -3.9e-70)
		tmp = -1.0;
	elseif (y <= 0.6)
		tmp = 1.0;
	elseif (y <= 5e+28)
		tmp = -1.0;
	elseif (y <= 3e+73)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8e+46], -1.0, If[LessEqual[y, -1e+29], 1.0, If[LessEqual[y, -3.9e-70], -1.0, If[LessEqual[y, 0.6], 1.0, If[LessEqual[y, 5e+28], -1.0, If[LessEqual[y, 3e+73], 1.0, -1.0]]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999999e46 or -9.99999999999999914e28 < y < -3.90000000000000019e-70 or 0.599999999999999978 < y < 4.99999999999999957e28 or 3.00000000000000011e73 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 85.3%

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

   if -7.9999999999999999e46 < y < -9.99999999999999914e28 or -3.90000000000000019e-70 < y < 0.599999999999999978 or 4.99999999999999957e28 < y < 3.00000000000000011e73

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around inf 79.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+46}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-70}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 0.6:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+28}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+73}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 49.4% accurate, 7.0× 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%

   \[\frac{x - y}{x + y} \]

2. Taylor expanded in x around 0 51.9%

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

3. Final simplification 51.9%

   \[\leadsto -1 \]

Developer target: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} - \frac{y}{x + y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ x (+ x y)) (/ y (+ x y))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))