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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x - y}{2 - \left(x + y\right)} \]

Alternative 2: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+163}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+146}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{+43}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.3e+163)
   1.0
   (if (<= y -1.5e+146)
     -1.0
     (if (<= y -1.08e+43) 1.0 (if (<= y 1.9e+65) (/ x (- 2.0 x)) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.3e+163) {
		tmp = 1.0;
	} else if (y <= -1.5e+146) {
		tmp = -1.0;
	} else if (y <= -1.08e+43) {
		tmp = 1.0;
	} else if (y <= 1.9e+65) {
		tmp = x / (2.0 - 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 <= (-2.3d+163)) then
        tmp = 1.0d0
    else if (y <= (-1.5d+146)) then
        tmp = -1.0d0
    else if (y <= (-1.08d+43)) then
        tmp = 1.0d0
    else if (y <= 1.9d+65) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.3e+163) {
		tmp = 1.0;
	} else if (y <= -1.5e+146) {
		tmp = -1.0;
	} else if (y <= -1.08e+43) {
		tmp = 1.0;
	} else if (y <= 1.9e+65) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.3e+163:
		tmp = 1.0
	elif y <= -1.5e+146:
		tmp = -1.0
	elif y <= -1.08e+43:
		tmp = 1.0
	elif y <= 1.9e+65:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.3e+163)
		tmp = 1.0;
	elseif (y <= -1.5e+146)
		tmp = -1.0;
	elseif (y <= -1.08e+43)
		tmp = 1.0;
	elseif (y <= 1.9e+65)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.3e+163)
		tmp = 1.0;
	elseif (y <= -1.5e+146)
		tmp = -1.0;
	elseif (y <= -1.08e+43)
		tmp = 1.0;
	elseif (y <= 1.9e+65)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.3e+163], 1.0, If[LessEqual[y, -1.5e+146], -1.0, If[LessEqual[y, -1.08e+43], 1.0, If[LessEqual[y, 1.9e+65], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000002e163 or -1.50000000000000001e146 < y < -1.08e43 or 1.90000000000000006e65 < y

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around inf 89.6%

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

   if -2.30000000000000002e163 < y < -1.50000000000000001e146

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in x around inf 100.0%

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

   if -1.08e43 < y < 1.90000000000000006e65

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around 0 72.6%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+163}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+146}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{+43}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+163}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+146}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+57}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.3e+163)
   1.0
   (if (<= y -1.5e+146)
     -1.0
     (if (<= y -2e+44) 1.0 (if (<= y 8.5e+57) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.3e+163) {
		tmp = 1.0;
	} else if (y <= -1.5e+146) {
		tmp = -1.0;
	} else if (y <= -2e+44) {
		tmp = 1.0;
	} else if (y <= 8.5e+57) {
		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 <= (-2.3d+163)) then
        tmp = 1.0d0
    else if (y <= (-1.5d+146)) then
        tmp = -1.0d0
    else if (y <= (-2d+44)) then
        tmp = 1.0d0
    else if (y <= 8.5d+57) 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 <= -2.3e+163) {
		tmp = 1.0;
	} else if (y <= -1.5e+146) {
		tmp = -1.0;
	} else if (y <= -2e+44) {
		tmp = 1.0;
	} else if (y <= 8.5e+57) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.3e+163:
		tmp = 1.0
	elif y <= -1.5e+146:
		tmp = -1.0
	elif y <= -2e+44:
		tmp = 1.0
	elif y <= 8.5e+57:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.3e+163)
		tmp = 1.0;
	elseif (y <= -1.5e+146)
		tmp = -1.0;
	elseif (y <= -2e+44)
		tmp = 1.0;
	elseif (y <= 8.5e+57)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.3e+163)
		tmp = 1.0;
	elseif (y <= -1.5e+146)
		tmp = -1.0;
	elseif (y <= -2e+44)
		tmp = 1.0;
	elseif (y <= 8.5e+57)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.3e+163], 1.0, If[LessEqual[y, -1.5e+146], -1.0, If[LessEqual[y, -2e+44], 1.0, If[LessEqual[y, 8.5e+57], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.30000000000000002e163 or -1.50000000000000001e146 < y < -2.0000000000000002e44 or 8.5000000000000001e57 < y

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in y around inf 88.9%

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

   if -2.30000000000000002e163 < y < -1.50000000000000001e146 or -2.0000000000000002e44 < y < 8.5000000000000001e57

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

         \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

   4. Taylor expanded in x around inf 55.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+163}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+146}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+57}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 38.3% accurate, 9.0× 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%

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

   1. associate--r+ 100.0%

      \[\leadsto \frac{x - y}{\color{blue}{\left(2 - x\right) - y}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{x - y}{\left(2 - x\right) - y}} \]

4. Taylor expanded in x around inf 37.6%

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

5. Final simplification 37.6%

   \[\leadsto -1 \]

Developer target: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t_0} - \frac{y}{t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))