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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 7

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 75.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-23}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e-53)
   (/ x (+ x y))
   (if (<= x 2.75e-23) (/ (- x y) y) (+ 1.0 (* -2.0 (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e-53) {
		tmp = x / (x + y);
	} else if (x <= 2.75e-23) {
		tmp = (x - y) / y;
	} 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 (x <= (-9d-53)) then
        tmp = x / (x + y)
    else if (x <= 2.75d-23) then
        tmp = (x - y) / y
    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 (x <= -9e-53) {
		tmp = x / (x + y);
	} else if (x <= 2.75e-23) {
		tmp = (x - y) / y;
	} else {
		tmp = 1.0 + (-2.0 * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9e-53:
		tmp = x / (x + y)
	elif x <= 2.75e-23:
		tmp = (x - y) / y
	else:
		tmp = 1.0 + (-2.0 * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e-53)
		tmp = Float64(x / Float64(x + y));
	elseif (x <= 2.75e-23)
		tmp = Float64(Float64(x - y) / y);
	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 (x <= -9e-53)
		tmp = x / (x + y);
	elseif (x <= 2.75e-23)
		tmp = (x - y) / y;
	else
		tmp = 1.0 + (-2.0 * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e-53], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.75e-23], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.9999999999999997e-53

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.5%

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

   if -8.9999999999999997e-53 < x < 2.7500000000000001e-23

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.0%

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

   if 2.7500000000000001e-23 < x

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.9%

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

Alternative 3: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-52} \lor \neg \left(x \leq 7.5 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.15e-52) (not (<= x 7.5e-51))) (/ x (+ x y)) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.15e-52) || !(x <= 7.5e-51)) {
		tmp = x / (x + 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 <= (-1.15d-52)) .or. (.not. (x <= 7.5d-51))) then
        tmp = x / (x + y)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.15e-52) || !(x <= 7.5e-51)) {
		tmp = x / (x + y);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.15e-52) or not (x <= 7.5e-51):
		tmp = x / (x + y)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.15e-52) || !(x <= 7.5e-51))
		tmp = Float64(x / Float64(x + y));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.15e-52) || ~((x <= 7.5e-51)))
		tmp = x / (x + y);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.15e-52], N[Not[LessEqual[x, 7.5e-51]], $MachinePrecision]], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -1.14999999999999997e-52 or 7.49999999999999976e-51 < x

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 79.3%

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

   if -1.14999999999999997e-52 < x < 7.49999999999999976e-51

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-52} \lor \neg \left(x \leq 7.5 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-20}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.1e-57)
   (/ x (+ x y))
   (if (<= x 2.9e-20) (/ (- x y) y) (/ (- x y) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.1e-57) {
		tmp = x / (x + y);
	} else if (x <= 2.9e-20) {
		tmp = (x - y) / y;
	} else {
		tmp = (x - 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 (x <= (-4.1d-57)) then
        tmp = x / (x + y)
    else if (x <= 2.9d-20) then
        tmp = (x - y) / y
    else
        tmp = (x - y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.1e-57) {
		tmp = x / (x + y);
	} else if (x <= 2.9e-20) {
		tmp = (x - y) / y;
	} else {
		tmp = (x - y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.1e-57:
		tmp = x / (x + y)
	elif x <= 2.9e-20:
		tmp = (x - y) / y
	else:
		tmp = (x - y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.1e-57)
		tmp = Float64(x / Float64(x + y));
	elseif (x <= 2.9e-20)
		tmp = Float64(Float64(x - y) / y);
	else
		tmp = Float64(Float64(x - y) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.1e-57)
		tmp = x / (x + y);
	elseif (x <= 2.9e-20)
		tmp = (x - y) / y;
	else
		tmp = (x - y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.1e-57], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-20], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1000000000000001e-57

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.5%

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

   if -4.1000000000000001e-57 < x < 2.9e-20

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.0%

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

   if 2.9e-20 < x

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in x around inf 79.3%

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

Alternative 5: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-33}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.5e-56) (/ x (+ x y)) (if (<= x 1.15e-33) -1.0 (/ (- x y) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.5e-56) {
		tmp = x / (x + y);
	} else if (x <= 1.15e-33) {
		tmp = -1.0;
	} else {
		tmp = (x - 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 (x <= (-3.5d-56)) then
        tmp = x / (x + y)
    else if (x <= 1.15d-33) then
        tmp = -1.0d0
    else
        tmp = (x - y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.5e-56) {
		tmp = x / (x + y);
	} else if (x <= 1.15e-33) {
		tmp = -1.0;
	} else {
		tmp = (x - y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.5e-56:
		tmp = x / (x + y)
	elif x <= 1.15e-33:
		tmp = -1.0
	else:
		tmp = (x - y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.5e-56)
		tmp = Float64(x / Float64(x + y));
	elseif (x <= 1.15e-33)
		tmp = -1.0;
	else
		tmp = Float64(Float64(x - y) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.5e-56)
		tmp = x / (x + y);
	elseif (x <= 1.15e-33)
		tmp = -1.0;
	else
		tmp = (x - y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.5e-56], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-33], -1.0, N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4999999999999998e-56

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.5%

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

   if -3.4999999999999998e-56 < x < 1.14999999999999993e-33

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.6%

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

   if 1.14999999999999993e-33 < x

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in x around inf 77.7%

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

Alternative 6: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-56}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-50}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2e-56) 1.0 (if (<= x 2e-50) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2e-56) {
		tmp = 1.0;
	} else if (x <= 2e-50) {
		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 <= (-2d-56)) then
        tmp = 1.0d0
    else if (x <= 2d-50) 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 <= -2e-56) {
		tmp = 1.0;
	} else if (x <= 2e-50) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2e-56:
		tmp = 1.0
	elif x <= 2e-50:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2e-56)
		tmp = 1.0;
	elseif (x <= 2e-50)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2e-56)
		tmp = 1.0;
	elseif (x <= 2e-50)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2e-56], 1.0, If[LessEqual[x, 2e-50], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0000000000000001e-56 or 2.00000000000000002e-50 < x

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.8%

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

   if -2.0000000000000001e-56 < x < 2.00000000000000002e-50

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.7%

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

Alternative 7: 49.0% 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. Add Preprocessing

3. Taylor expanded in x around 0 49.8%

   \[\leadsto \color{blue}{-1} \]
4. Add Preprocessing

Developer Target 1: 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 2024160 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (+ x y)) (/ y (+ x y))))

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