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

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

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: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot \frac{x}{y} + -1\\ \mathbf{if}\;y \leq -40000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-97} \lor \neg \left(y \leq 4.8 \cdot 10^{-21}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (* 2.0 (/ x y)) -1.0)))
   (if (<= y -40000000000.0)
     t_0
     (if (<= y -1.18e-17)
       1.0
       (if (or (<= y -3.7e-97) (not (<= y 4.8e-21)))
         t_0
         (+ 1.0 (* -2.0 (/ y x))))))))

C

double code(double x, double y) {
	double t_0 = (2.0 * (x / y)) + -1.0;
	double tmp;
	if (y <= -40000000000.0) {
		tmp = t_0;
	} else if (y <= -1.18e-17) {
		tmp = 1.0;
	} else if ((y <= -3.7e-97) || !(y <= 4.8e-21)) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = (2.0d0 * (x / y)) + (-1.0d0)
    if (y <= (-40000000000.0d0)) then
        tmp = t_0
    else if (y <= (-1.18d-17)) then
        tmp = 1.0d0
    else if ((y <= (-3.7d-97)) .or. (.not. (y <= 4.8d-21))) then
        tmp = t_0
    else
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (2.0 * (x / y)) + -1.0;
	double tmp;
	if (y <= -40000000000.0) {
		tmp = t_0;
	} else if (y <= -1.18e-17) {
		tmp = 1.0;
	} else if ((y <= -3.7e-97) || !(y <= 4.8e-21)) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (-2.0 * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (2.0 * (x / y)) + -1.0
	tmp = 0
	if y <= -40000000000.0:
		tmp = t_0
	elif y <= -1.18e-17:
		tmp = 1.0
	elif (y <= -3.7e-97) or not (y <= 4.8e-21):
		tmp = t_0
	else:
		tmp = 1.0 + (-2.0 * (y / x))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(2.0 * Float64(x / y)) + -1.0)
	tmp = 0.0
	if (y <= -40000000000.0)
		tmp = t_0;
	elseif (y <= -1.18e-17)
		tmp = 1.0;
	elseif ((y <= -3.7e-97) || !(y <= 4.8e-21))
		tmp = t_0;
	else
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (2.0 * (x / y)) + -1.0;
	tmp = 0.0;
	if (y <= -40000000000.0)
		tmp = t_0;
	elseif (y <= -1.18e-17)
		tmp = 1.0;
	elseif ((y <= -3.7e-97) || ~((y <= 4.8e-21)))
		tmp = t_0;
	else
		tmp = 1.0 + (-2.0 * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[y, -40000000000.0], t$95$0, If[LessEqual[y, -1.18e-17], 1.0, If[Or[LessEqual[y, -3.7e-97], N[Not[LessEqual[y, 4.8e-21]], $MachinePrecision]], t$95$0, N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4e10 or -1.18000000000000004e-17 < y < -3.69999999999999976e-97 or 4.7999999999999999e-21 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.0%

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

   if -4e10 < y < -1.18000000000000004e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   if -3.69999999999999976e-97 < y < 4.7999999999999999e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -40000000000:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-97} \lor \neg \left(y \leq 4.8 \cdot 10^{-21}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2000000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-96}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-21}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2000000000000.0)
   -1.0
   (if (<= y -1.12e-17)
     1.0
     (if (<= y -2e-96)
       -1.0
       (if (<= y 5.2e-21) (+ 1.0 (* -2.0 (/ y x))) -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2000000000000.0) {
		tmp = -1.0;
	} else if (y <= -1.12e-17) {
		tmp = 1.0;
	} else if (y <= -2e-96) {
		tmp = -1.0;
	} else if (y <= 5.2e-21) {
		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 <= (-2000000000000.0d0)) then
        tmp = -1.0d0
    else if (y <= (-1.12d-17)) then
        tmp = 1.0d0
    else if (y <= (-2d-96)) then
        tmp = -1.0d0
    else if (y <= 5.2d-21) 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 <= -2000000000000.0) {
		tmp = -1.0;
	} else if (y <= -1.12e-17) {
		tmp = 1.0;
	} else if (y <= -2e-96) {
		tmp = -1.0;
	} else if (y <= 5.2e-21) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2000000000000.0:
		tmp = -1.0
	elif y <= -1.12e-17:
		tmp = 1.0
	elif y <= -2e-96:
		tmp = -1.0
	elif y <= 5.2e-21:
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2000000000000.0)
		tmp = -1.0;
	elseif (y <= -1.12e-17)
		tmp = 1.0;
	elseif (y <= -2e-96)
		tmp = -1.0;
	elseif (y <= 5.2e-21)
		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 <= -2000000000000.0)
		tmp = -1.0;
	elseif (y <= -1.12e-17)
		tmp = 1.0;
	elseif (y <= -2e-96)
		tmp = -1.0;
	elseif (y <= 5.2e-21)
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2000000000000.0], -1.0, If[LessEqual[y, -1.12e-17], 1.0, If[LessEqual[y, -2e-96], -1.0, If[LessEqual[y, 5.2e-21], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2e12 or -1.12000000000000005e-17 < y < -1.9999999999999998e-96 or 5.20000000000000035e-21 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.3%

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

   if -2e12 < y < -1.12000000000000005e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   if -1.9999999999999998e-96 < y < 5.20000000000000035e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2000000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-96}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-21}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -31000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-97}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -31000000000.0)
   -1.0
   (if (<= y -9.2e-17)
     1.0
     (if (<= y -9.5e-97) -1.0 (if (<= y 1.8e-20) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -31000000000.0) {
		tmp = -1.0;
	} else if (y <= -9.2e-17) {
		tmp = 1.0;
	} else if (y <= -9.5e-97) {
		tmp = -1.0;
	} else if (y <= 1.8e-20) {
		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 <= (-31000000000.0d0)) then
        tmp = -1.0d0
    else if (y <= (-9.2d-17)) then
        tmp = 1.0d0
    else if (y <= (-9.5d-97)) then
        tmp = -1.0d0
    else if (y <= 1.8d-20) 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 <= -31000000000.0) {
		tmp = -1.0;
	} else if (y <= -9.2e-17) {
		tmp = 1.0;
	} else if (y <= -9.5e-97) {
		tmp = -1.0;
	} else if (y <= 1.8e-20) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -31000000000.0:
		tmp = -1.0
	elif y <= -9.2e-17:
		tmp = 1.0
	elif y <= -9.5e-97:
		tmp = -1.0
	elif y <= 1.8e-20:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -31000000000.0)
		tmp = -1.0;
	elseif (y <= -9.2e-17)
		tmp = 1.0;
	elseif (y <= -9.5e-97)
		tmp = -1.0;
	elseif (y <= 1.8e-20)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -31000000000.0)
		tmp = -1.0;
	elseif (y <= -9.2e-17)
		tmp = 1.0;
	elseif (y <= -9.5e-97)
		tmp = -1.0;
	elseif (y <= 1.8e-20)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -31000000000.0], -1.0, If[LessEqual[y, -9.2e-17], 1.0, If[LessEqual[y, -9.5e-97], -1.0, If[LessEqual[y, 1.8e-20], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1e10 or -9.20000000000000035e-17 < y < -9.5000000000000001e-97 or 1.79999999999999987e-20 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.3%

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

   if -3.1e10 < y < -9.20000000000000035e-17 or -9.5000000000000001e-97 < y < 1.79999999999999987e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-97}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.8% 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 55.5%

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

4. Final simplification 55.5%

   \[\leadsto -1 \]
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 2024067 
(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)))