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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+67} \lor \neg \left(x \leq -1.05 \cdot 10^{-47} \lor \neg \left(x \leq -9.6 \cdot 10^{-94}\right) \land x \leq 36000000\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5e+67)
         (not
          (or (<= x -1.05e-47) (and (not (<= x -9.6e-94)) (<= x 36000000.0)))))
   (+ 1.0 (* -2.0 (/ y x)))
   -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5e+67) || !((x <= -1.05e-47) || (!(x <= -9.6e-94) && (x <= 36000000.0)))) {
		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 <= (-5d+67)) .or. (.not. (x <= (-1.05d-47)) .or. (.not. (x <= (-9.6d-94))) .and. (x <= 36000000.0d0))) 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 <= -5e+67) || !((x <= -1.05e-47) || (!(x <= -9.6e-94) && (x <= 36000000.0)))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5e+67) or not ((x <= -1.05e-47) or (not (x <= -9.6e-94) and (x <= 36000000.0))):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5e+67) || !((x <= -1.05e-47) || (!(x <= -9.6e-94) && (x <= 36000000.0))))
		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 <= -5e+67) || ~(((x <= -1.05e-47) || (~((x <= -9.6e-94)) && (x <= 36000000.0)))))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5e+67], N[Not[Or[LessEqual[x, -1.05e-47], And[N[Not[LessEqual[x, -9.6e-94]], $MachinePrecision], LessEqual[x, 36000000.0]]]], $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 < -4.99999999999999976e67 or -1.05e-47 < x < -9.6e-94 or 3.6e7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.5%

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

   if -4.99999999999999976e67 < x < -1.05e-47 or -9.6e-94 < x < 3.6e7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.2%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+67} \lor \neg \left(x \leq -1.05 \cdot 10^{-47} \lor \neg \left(x \leq -9.6 \cdot 10^{-94}\right) \land x \leq 36000000\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+67} \lor \neg \left(x \leq -3.45 \cdot 10^{-46} \lor \neg \left(x \leq -6.8 \cdot 10^{-114}\right) \land x \leq 36000000\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.6e+67)
         (not
          (or (<= x -3.45e-46)
              (and (not (<= x -6.8e-114)) (<= x 36000000.0)))))
   (+ 1.0 (* -2.0 (/ y x)))
   (+ (* 2.0 (/ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.6e+67) || !((x <= -3.45e-46) || (!(x <= -6.8e-114) && (x <= 36000000.0)))) {
		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 <= (-3.6d+67)) .or. (.not. (x <= (-3.45d-46)) .or. (.not. (x <= (-6.8d-114))) .and. (x <= 36000000.0d0))) 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 <= -3.6e+67) || !((x <= -3.45e-46) || (!(x <= -6.8e-114) && (x <= 36000000.0)))) {
		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 <= -3.6e+67) or not ((x <= -3.45e-46) or (not (x <= -6.8e-114) and (x <= 36000000.0))):
		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 <= -3.6e+67) || !((x <= -3.45e-46) || (!(x <= -6.8e-114) && (x <= 36000000.0))))
		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 <= -3.6e+67) || ~(((x <= -3.45e-46) || (~((x <= -6.8e-114)) && (x <= 36000000.0)))))
		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, -3.6e+67], N[Not[Or[LessEqual[x, -3.45e-46], And[N[Not[LessEqual[x, -6.8e-114]], $MachinePrecision], LessEqual[x, 36000000.0]]]], $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 < -3.5999999999999999e67 or -3.4499999999999999e-46 < x < -6.79999999999999962e-114 or 3.6e7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.0%

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

   if -3.5999999999999999e67 < x < -3.4499999999999999e-46 or -6.79999999999999962e-114 < x < 3.6e7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+67} \lor \neg \left(x \leq -3.45 \cdot 10^{-46} \lor \neg \left(x \leq -6.8 \cdot 10^{-114}\right) \land x \leq 36000000\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-47}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-94}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 34000000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.5e+58)
   1.0
   (if (<= x -5e-47)
     -1.0
     (if (<= x -9.5e-94) 1.0 (if (<= x 34000000.0) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.5e+58) {
		tmp = 1.0;
	} else if (x <= -5e-47) {
		tmp = -1.0;
	} else if (x <= -9.5e-94) {
		tmp = 1.0;
	} else if (x <= 34000000.0) {
		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 <= (-6.5d+58)) then
        tmp = 1.0d0
    else if (x <= (-5d-47)) then
        tmp = -1.0d0
    else if (x <= (-9.5d-94)) then
        tmp = 1.0d0
    else if (x <= 34000000.0d0) 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 <= -6.5e+58) {
		tmp = 1.0;
	} else if (x <= -5e-47) {
		tmp = -1.0;
	} else if (x <= -9.5e-94) {
		tmp = 1.0;
	} else if (x <= 34000000.0) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.5e+58:
		tmp = 1.0
	elif x <= -5e-47:
		tmp = -1.0
	elif x <= -9.5e-94:
		tmp = 1.0
	elif x <= 34000000.0:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.5e+58)
		tmp = 1.0;
	elseif (x <= -5e-47)
		tmp = -1.0;
	elseif (x <= -9.5e-94)
		tmp = 1.0;
	elseif (x <= 34000000.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.5e+58)
		tmp = 1.0;
	elseif (x <= -5e-47)
		tmp = -1.0;
	elseif (x <= -9.5e-94)
		tmp = 1.0;
	elseif (x <= 34000000.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.5e+58], 1.0, If[LessEqual[x, -5e-47], -1.0, If[LessEqual[x, -9.5e-94], 1.0, If[LessEqual[x, 34000000.0], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.49999999999999998e58 or -5.00000000000000011e-47 < x < -9.4999999999999997e-94 or 3.4e7 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.8%

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

   if -6.49999999999999998e58 < x < -5.00000000000000011e-47 or -9.4999999999999997e-94 < x < 3.4e7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.7%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-47}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-94}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 34000000:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.9% 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 50.2%

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

4. Final simplification 50.2%

   \[\leadsto -1 \]
5. Add Preprocessing

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 2024059 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :alt
  (- (/ x (+ x y)) (/ y (+ x y)))

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