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

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

Alternatives: 4

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: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+129}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-65} \lor \neg \left(x \leq -3.6 \cdot 10^{-145}\right) \land x \leq 2.65 \cdot 10^{-14}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.6e+129)
   1.0
   (if (or (<= x -4.8e-65) (and (not (<= x -3.6e-145)) (<= x 2.65e-14)))
     (+ (* 2.0 (/ x y)) -1.0)
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.6e+129) {
		tmp = 1.0;
	} else if ((x <= -4.8e-65) || (!(x <= -3.6e-145) && (x <= 2.65e-14))) {
		tmp = (2.0 * (x / y)) + -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 <= (-3.6d+129)) then
        tmp = 1.0d0
    else if ((x <= (-4.8d-65)) .or. (.not. (x <= (-3.6d-145))) .and. (x <= 2.65d-14)) then
        tmp = (2.0d0 * (x / y)) + (-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 <= -3.6e+129) {
		tmp = 1.0;
	} else if ((x <= -4.8e-65) || (!(x <= -3.6e-145) && (x <= 2.65e-14))) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.6e+129:
		tmp = 1.0
	elif (x <= -4.8e-65) or (not (x <= -3.6e-145) and (x <= 2.65e-14)):
		tmp = (2.0 * (x / y)) + -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.6e+129)
		tmp = 1.0;
	elseif ((x <= -4.8e-65) || (!(x <= -3.6e-145) && (x <= 2.65e-14)))
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.6e+129)
		tmp = 1.0;
	elseif ((x <= -4.8e-65) || (~((x <= -3.6e-145)) && (x <= 2.65e-14)))
		tmp = (2.0 * (x / y)) + -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.6e+129], 1.0, If[Or[LessEqual[x, -4.8e-65], And[N[Not[LessEqual[x, -3.6e-145]], $MachinePrecision], LessEqual[x, 2.65e-14]]], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6000000000000001e129 or -4.8000000000000003e-65 < x < -3.6e-145 or 2.6500000000000001e-14 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.5%

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

   if -3.6000000000000001e129 < x < -4.8000000000000003e-65 or -3.6e-145 < x < 2.6500000000000001e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 81.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+129}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-65} \lor \neg \left(x \leq -3.6 \cdot 10^{-145}\right) \land x \leq 2.65 \cdot 10^{-14}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 71.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+84}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-67}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-127}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-17}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e+84)
   1.0
   (if (<= x -3.5e-67)
     -1.0
     (if (<= x -1.65e-127) 1.0 (if (<= x 2.35e-17) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e+84) {
		tmp = 1.0;
	} else if (x <= -3.5e-67) {
		tmp = -1.0;
	} else if (x <= -1.65e-127) {
		tmp = 1.0;
	} else if (x <= 2.35e-17) {
		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 <= (-1d+84)) then
        tmp = 1.0d0
    else if (x <= (-3.5d-67)) then
        tmp = -1.0d0
    else if (x <= (-1.65d-127)) then
        tmp = 1.0d0
    else if (x <= 2.35d-17) 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 <= -1e+84) {
		tmp = 1.0;
	} else if (x <= -3.5e-67) {
		tmp = -1.0;
	} else if (x <= -1.65e-127) {
		tmp = 1.0;
	} else if (x <= 2.35e-17) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e+84:
		tmp = 1.0
	elif x <= -3.5e-67:
		tmp = -1.0
	elif x <= -1.65e-127:
		tmp = 1.0
	elif x <= 2.35e-17:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e+84)
		tmp = 1.0;
	elseif (x <= -3.5e-67)
		tmp = -1.0;
	elseif (x <= -1.65e-127)
		tmp = 1.0;
	elseif (x <= 2.35e-17)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e+84)
		tmp = 1.0;
	elseif (x <= -3.5e-67)
		tmp = -1.0;
	elseif (x <= -1.65e-127)
		tmp = 1.0;
	elseif (x <= 2.35e-17)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e+84], 1.0, If[LessEqual[x, -3.5e-67], -1.0, If[LessEqual[x, -1.65e-127], 1.0, If[LessEqual[x, 2.35e-17], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.00000000000000006e84 or -3.5e-67 < x < -1.6499999999999999e-127 or 2.35e-17 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.1%

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

   if -1.00000000000000006e84 < x < -3.5e-67 or -1.6499999999999999e-127 < x < 2.35e-17

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 81.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+84}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-67}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-127}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-17}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 49.7% 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 51.2%

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

3. Final simplification 51.2%

   \[\leadsto -1 \]

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 2023240 
(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)))