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

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 6

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, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y + x}{x - y}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 (/ (+ y x) (- x y))))

C

double code(double x, double y) {
	return 1.0 / ((y + x) / (x - y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 / ((y + x) / (x - y))
end function

Java

public static double code(double x, double y) {
	return 1.0 / ((y + x) / (x - y));
}

Python

def code(x, y):
	return 1.0 / ((y + x) / (x - y))

Julia

function code(x, y)
	return Float64(1.0 / Float64(Float64(y + x) / Float64(x - y)))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 / ((y + x) / (x - y));
end

Wolfram

code[x_, y_] := N[(1.0 / N[(N[(y + x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{x + y} \]
2. Step-by-step derivation

   1. clear-num 100.0%

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

   2. inv-pow 100.0%

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

3. Applied egg-rr 100.0%

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

   1. unpow-1 100.0%

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

   2. +-commutative 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

   \[\leadsto \frac{1}{\frac{y + x}{x - y}} \]

Alternative 2: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+35} \lor \neg \left(x \leq 3.1 \cdot 10^{-79} \lor \neg \left(x \leq 4.1 \cdot 10^{+18}\right) \land x \leq 1.3 \cdot 10^{+97}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.8e+35)
         (not (or (<= x 3.1e-79) (and (not (<= x 4.1e+18)) (<= x 1.3e+97)))))
   (+ 1.0 (* -2.0 (/ y x)))
   -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8e+35) || !((x <= 3.1e-79) || (!(x <= 4.1e+18) && (x <= 1.3e+97)))) {
		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 ((x <= (-3.8d+35)) .or. (.not. (x <= 3.1d-79) .or. (.not. (x <= 4.1d+18)) .and. (x <= 1.3d+97))) 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 ((x <= -3.8e+35) || !((x <= 3.1e-79) || (!(x <= 4.1e+18) && (x <= 1.3e+97)))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.8e+35) or not ((x <= 3.1e-79) or (not (x <= 4.1e+18) and (x <= 1.3e+97))):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.8e+35) || !((x <= 3.1e-79) || (!(x <= 4.1e+18) && (x <= 1.3e+97))))
		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 ((x <= -3.8e+35) || ~(((x <= 3.1e-79) || (~((x <= 4.1e+18)) && (x <= 1.3e+97)))))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.8e+35], N[Not[Or[LessEqual[x, 3.1e-79], And[N[Not[LessEqual[x, 4.1e+18]], $MachinePrecision], LessEqual[x, 1.3e+97]]]], $MachinePrecision]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -3.8e35 or 3.0999999999999999e-79 < x < 4.1e18 or 1.3e97 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.0%

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

   if -3.8e35 < x < 3.0999999999999999e-79 or 4.1e18 < x < 1.3e97

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 78.9%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+35} \lor \neg \left(x \leq 3.1 \cdot 10^{-79} \lor \neg \left(x \leq 4.1 \cdot 10^{+18}\right) \land x \leq 1.3 \cdot 10^{+97}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+35} \lor \neg \left(x \leq 3.1 \cdot 10^{-79}\right) \land \left(x \leq 3.7 \cdot 10^{+18} \lor \neg \left(x \leq 1.3 \cdot 10^{+97}\right)\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.2e+35)
         (and (not (<= x 3.1e-79)) (or (<= x 3.7e+18) (not (<= x 1.3e+97)))))
   (+ 1.0 (* -2.0 (/ y x)))
   (+ (* 2.0 (/ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e+35) || (!(x <= 3.1e-79) && ((x <= 3.7e+18) || !(x <= 1.3e+97)))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (2.0 * (x / y)) + -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 <= (-1.2d+35)) .or. (.not. (x <= 3.1d-79)) .and. (x <= 3.7d+18) .or. (.not. (x <= 1.3d+97))) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e+35) || (!(x <= 3.1e-79) && ((x <= 3.7e+18) || !(x <= 1.3e+97)))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (2.0 * (x / y)) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.2e+35) or (not (x <= 3.1e-79) and ((x <= 3.7e+18) or not (x <= 1.3e+97))):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = (2.0 * (x / y)) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.2e+35) || (!(x <= 3.1e-79) && ((x <= 3.7e+18) || !(x <= 1.3e+97))))
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.2e+35) || (~((x <= 3.1e-79)) && ((x <= 3.7e+18) || ~((x <= 1.3e+97)))))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = (2.0 * (x / y)) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.2e+35], And[N[Not[LessEqual[x, 3.1e-79]], $MachinePrecision], Or[LessEqual[x, 3.7e+18], N[Not[LessEqual[x, 1.3e+97]], $MachinePrecision]]]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000007e35 or 3.0999999999999999e-79 < x < 3.7e18 or 1.3e97 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.0%

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

   if -1.20000000000000007e35 < x < 3.0999999999999999e-79 or 3.7e18 < x < 1.3e97

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 80.4%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+35} \lor \neg \left(x \leq 3.1 \cdot 10^{-79}\right) \land \left(x \leq 3.7 \cdot 10^{+18} \lor \neg \left(x \leq 1.3 \cdot 10^{+97}\right)\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]

Alternative 4: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+55}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-79}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.25e+55)
   1.0
   (if (<= x 2.8e-79)
     -1.0
     (if (<= x 1e+18) 1.0 (if (<= x 1.3e+97) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.25e+55) {
		tmp = 1.0;
	} else if (x <= 2.8e-79) {
		tmp = -1.0;
	} else if (x <= 1e+18) {
		tmp = 1.0;
	} else if (x <= 1.3e+97) {
		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 <= (-1.25d+55)) then
        tmp = 1.0d0
    else if (x <= 2.8d-79) then
        tmp = -1.0d0
    else if (x <= 1d+18) then
        tmp = 1.0d0
    else if (x <= 1.3d+97) 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 <= -1.25e+55) {
		tmp = 1.0;
	} else if (x <= 2.8e-79) {
		tmp = -1.0;
	} else if (x <= 1e+18) {
		tmp = 1.0;
	} else if (x <= 1.3e+97) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.25e+55:
		tmp = 1.0
	elif x <= 2.8e-79:
		tmp = -1.0
	elif x <= 1e+18:
		tmp = 1.0
	elif x <= 1.3e+97:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.25e+55)
		tmp = 1.0;
	elseif (x <= 2.8e-79)
		tmp = -1.0;
	elseif (x <= 1e+18)
		tmp = 1.0;
	elseif (x <= 1.3e+97)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.25e+55)
		tmp = 1.0;
	elseif (x <= 2.8e-79)
		tmp = -1.0;
	elseif (x <= 1e+18)
		tmp = 1.0;
	elseif (x <= 1.3e+97)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.25e+55], 1.0, If[LessEqual[x, 2.8e-79], -1.0, If[LessEqual[x, 1e+18], 1.0, If[LessEqual[x, 1.3e+97], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25000000000000011e55 or 2.80000000000000012e-79 < x < 1e18 or 1.3e97 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.5%

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

   if -1.25000000000000011e55 < x < 2.80000000000000012e-79 or 1e18 < x < 1.3e97

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 78.5%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+55}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-79}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 6: 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 49.9%

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

3. Final simplification 49.9%

   \[\leadsto -1 \]

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 2023334 
(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)))