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

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.14 \cdot 10^{-39}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+17}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* -2.0 (/ y x)))))
   (if (<= x -4.3e-131)
     t_0
     (if (<= x 1.14e-39)
       -1.0
       (if (<= x 4e-20) 1.0 (if (<= x 1.5e+17) -1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (x <= -4.3e-131) {
		tmp = t_0;
	} else if (x <= 1.14e-39) {
		tmp = -1.0;
	} else if (x <= 4e-20) {
		tmp = 1.0;
	} else if (x <= 1.5e+17) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	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 = 1.0d0 + ((-2.0d0) * (y / x))
    if (x <= (-4.3d-131)) then
        tmp = t_0
    else if (x <= 1.14d-39) then
        tmp = -1.0d0
    else if (x <= 4d-20) then
        tmp = 1.0d0
    else if (x <= 1.5d+17) then
        tmp = -1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (x <= -4.3e-131) {
		tmp = t_0;
	} else if (x <= 1.14e-39) {
		tmp = -1.0;
	} else if (x <= 4e-20) {
		tmp = 1.0;
	} else if (x <= 1.5e+17) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (-2.0 * (y / x))
	tmp = 0
	if x <= -4.3e-131:
		tmp = t_0
	elif x <= 1.14e-39:
		tmp = -1.0
	elif x <= 4e-20:
		tmp = 1.0
	elif x <= 1.5e+17:
		tmp = -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(-2.0 * Float64(y / x)))
	tmp = 0.0
	if (x <= -4.3e-131)
		tmp = t_0;
	elseif (x <= 1.14e-39)
		tmp = -1.0;
	elseif (x <= 4e-20)
		tmp = 1.0;
	elseif (x <= 1.5e+17)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (-2.0 * (y / x));
	tmp = 0.0;
	if (x <= -4.3e-131)
		tmp = t_0;
	elseif (x <= 1.14e-39)
		tmp = -1.0;
	elseif (x <= 4e-20)
		tmp = 1.0;
	elseif (x <= 1.5e+17)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e-131], t$95$0, If[LessEqual[x, 1.14e-39], -1.0, If[LessEqual[x, 4e-20], 1.0, If[LessEqual[x, 1.5e+17], -1.0, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.30000000000000019e-131 or 1.5e17 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.7%

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

   if -4.30000000000000019e-131 < x < 1.13999999999999997e-39 or 3.99999999999999978e-20 < x < 1.5e17

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 81.0%

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

   if 1.13999999999999997e-39 < x < 3.99999999999999978e-20

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-131}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 1.14 \cdot 10^{-39}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+17}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]

Alternative 3: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-40}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+16}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* -2.0 (/ y x)))))
   (if (<= x -4.3e-131)
     t_0
     (if (<= x 7e-40)
       (+ (* 2.0 (/ x y)) -1.0)
       (if (<= x 9.2e-19) 1.0 (if (<= x 1.8e+16) -1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (x <= -4.3e-131) {
		tmp = t_0;
	} else if (x <= 7e-40) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else if (x <= 9.2e-19) {
		tmp = 1.0;
	} else if (x <= 1.8e+16) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	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 = 1.0d0 + ((-2.0d0) * (y / x))
    if (x <= (-4.3d-131)) then
        tmp = t_0
    else if (x <= 7d-40) then
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    else if (x <= 9.2d-19) then
        tmp = 1.0d0
    else if (x <= 1.8d+16) then
        tmp = -1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (x <= -4.3e-131) {
		tmp = t_0;
	} else if (x <= 7e-40) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else if (x <= 9.2e-19) {
		tmp = 1.0;
	} else if (x <= 1.8e+16) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (-2.0 * (y / x))
	tmp = 0
	if x <= -4.3e-131:
		tmp = t_0
	elif x <= 7e-40:
		tmp = (2.0 * (x / y)) + -1.0
	elif x <= 9.2e-19:
		tmp = 1.0
	elif x <= 1.8e+16:
		tmp = -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(-2.0 * Float64(y / x)))
	tmp = 0.0
	if (x <= -4.3e-131)
		tmp = t_0;
	elseif (x <= 7e-40)
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	elseif (x <= 9.2e-19)
		tmp = 1.0;
	elseif (x <= 1.8e+16)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (-2.0 * (y / x));
	tmp = 0.0;
	if (x <= -4.3e-131)
		tmp = t_0;
	elseif (x <= 7e-40)
		tmp = (2.0 * (x / y)) + -1.0;
	elseif (x <= 9.2e-19)
		tmp = 1.0;
	elseif (x <= 1.8e+16)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e-131], t$95$0, If[LessEqual[x, 7e-40], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, 9.2e-19], 1.0, If[LessEqual[x, 1.8e+16], -1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.30000000000000019e-131 or 1.8e16 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.7%

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

   if -4.30000000000000019e-131 < x < 7.0000000000000003e-40

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 83.6%

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

   if 7.0000000000000003e-40 < x < 9.19999999999999919e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   if 9.19999999999999919e-19 < x < 1.8e16

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.4%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-131}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-40}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+16}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]

Alternative 4: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-131}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+16}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.3e-131)
   1.0
   (if (<= x 2e-38) -1.0 (if (<= x 5e-18) 1.0 (if (<= x 3.2e+16) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.3e-131) {
		tmp = 1.0;
	} else if (x <= 2e-38) {
		tmp = -1.0;
	} else if (x <= 5e-18) {
		tmp = 1.0;
	} else if (x <= 3.2e+16) {
		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 <= (-4.3d-131)) then
        tmp = 1.0d0
    else if (x <= 2d-38) then
        tmp = -1.0d0
    else if (x <= 5d-18) then
        tmp = 1.0d0
    else if (x <= 3.2d+16) 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 <= -4.3e-131) {
		tmp = 1.0;
	} else if (x <= 2e-38) {
		tmp = -1.0;
	} else if (x <= 5e-18) {
		tmp = 1.0;
	} else if (x <= 3.2e+16) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.3e-131:
		tmp = 1.0
	elif x <= 2e-38:
		tmp = -1.0
	elif x <= 5e-18:
		tmp = 1.0
	elif x <= 3.2e+16:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.3e-131)
		tmp = 1.0;
	elseif (x <= 2e-38)
		tmp = -1.0;
	elseif (x <= 5e-18)
		tmp = 1.0;
	elseif (x <= 3.2e+16)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.3e-131)
		tmp = 1.0;
	elseif (x <= 2e-38)
		tmp = -1.0;
	elseif (x <= 5e-18)
		tmp = 1.0;
	elseif (x <= 3.2e+16)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.3e-131], 1.0, If[LessEqual[x, 2e-38], -1.0, If[LessEqual[x, 5e-18], 1.0, If[LessEqual[x, 3.2e+16], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.30000000000000019e-131 or 1.9999999999999999e-38 < x < 5.00000000000000036e-18 or 3.2e16 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 77.7%

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

   if -4.30000000000000019e-131 < x < 1.9999999999999999e-38 or 5.00000000000000036e-18 < x < 3.2e16

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 81.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-131}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+16}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 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 99.9%

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

2. Taylor expanded in x around 0 45.4%

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

3. Final simplification 45.4%

   \[\leadsto -1 \]

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 2023213 
(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)))