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

Percentage Accurate: 100.0% → 100.0%

Time: 3.7s

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, 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]

Derivation

1. Initial program 100.0%

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

   1. div-sub 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+53}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-51}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-11}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+53)
   -1.0
   (if (<= y -8.5e-18)
     1.0
     (if (<= y -1.65e-51)
       -1.0
       (if (<= y 3.9e-11) (+ 1.0 (* -2.0 (/ y x))) -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+53) {
		tmp = -1.0;
	} else if (y <= -8.5e-18) {
		tmp = 1.0;
	} else if (y <= -1.65e-51) {
		tmp = -1.0;
	} else if (y <= 3.9e-11) {
		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 <= (-5d+53)) then
        tmp = -1.0d0
    else if (y <= (-8.5d-18)) then
        tmp = 1.0d0
    else if (y <= (-1.65d-51)) then
        tmp = -1.0d0
    else if (y <= 3.9d-11) 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 <= -5e+53) {
		tmp = -1.0;
	} else if (y <= -8.5e-18) {
		tmp = 1.0;
	} else if (y <= -1.65e-51) {
		tmp = -1.0;
	} else if (y <= 3.9e-11) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+53:
		tmp = -1.0
	elif y <= -8.5e-18:
		tmp = 1.0
	elif y <= -1.65e-51:
		tmp = -1.0
	elif y <= 3.9e-11:
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+53)
		tmp = -1.0;
	elseif (y <= -8.5e-18)
		tmp = 1.0;
	elseif (y <= -1.65e-51)
		tmp = -1.0;
	elseif (y <= 3.9e-11)
		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 <= -5e+53)
		tmp = -1.0;
	elseif (y <= -8.5e-18)
		tmp = 1.0;
	elseif (y <= -1.65e-51)
		tmp = -1.0;
	elseif (y <= 3.9e-11)
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+53], -1.0, If[LessEqual[y, -8.5e-18], 1.0, If[LessEqual[y, -1.65e-51], -1.0, If[LessEqual[y, 3.9e-11], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000004e53 or -8.4999999999999995e-18 < y < -1.64999999999999986e-51 or 3.9000000000000001e-11 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 85.6%

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

   if -5.0000000000000004e53 < y < -8.4999999999999995e-18

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 89.1%

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

   if -1.64999999999999986e-51 < y < 3.9000000000000001e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.3%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+53}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-51}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-11}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+54}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-62}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-11}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+54)
   -1.0
   (if (<= y -6e-17)
     1.0
     (if (<= y -4.2e-62) -1.0 (if (<= y 4e-11) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+54) {
		tmp = -1.0;
	} else if (y <= -6e-17) {
		tmp = 1.0;
	} else if (y <= -4.2e-62) {
		tmp = -1.0;
	} else if (y <= 4e-11) {
		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 <= (-5d+54)) then
        tmp = -1.0d0
    else if (y <= (-6d-17)) then
        tmp = 1.0d0
    else if (y <= (-4.2d-62)) then
        tmp = -1.0d0
    else if (y <= 4d-11) 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 <= -5e+54) {
		tmp = -1.0;
	} else if (y <= -6e-17) {
		tmp = 1.0;
	} else if (y <= -4.2e-62) {
		tmp = -1.0;
	} else if (y <= 4e-11) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+54:
		tmp = -1.0
	elif y <= -6e-17:
		tmp = 1.0
	elif y <= -4.2e-62:
		tmp = -1.0
	elif y <= 4e-11:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+54)
		tmp = -1.0;
	elseif (y <= -6e-17)
		tmp = 1.0;
	elseif (y <= -4.2e-62)
		tmp = -1.0;
	elseif (y <= 4e-11)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+54)
		tmp = -1.0;
	elseif (y <= -6e-17)
		tmp = 1.0;
	elseif (y <= -4.2e-62)
		tmp = -1.0;
	elseif (y <= 4e-11)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+54], -1.0, If[LessEqual[y, -6e-17], 1.0, If[LessEqual[y, -4.2e-62], -1.0, If[LessEqual[y, 4e-11], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000005e54 or -6.00000000000000012e-17 < y < -4.1999999999999998e-62 or 3.99999999999999976e-11 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 85.1%

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

   if -5.00000000000000005e54 < y < -6.00000000000000012e-17 or -4.1999999999999998e-62 < y < 3.99999999999999976e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.0%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+54}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-62}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-11}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 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 5: 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 49.7%

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

3. Final simplification 49.7%

   \[\leadsto -1 \]

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 2023195 
(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)))