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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 5

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: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+48} \lor \neg \left(y \leq 1.9 \cdot 10^{+27}\right):\\ \;\;\;\;1 + \frac{x}{\frac{y}{-2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.06e+48) (not (<= y 1.9e+27)))
   (+ 1.0 (/ x (/ y -2.0)))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.06e+48) || !(y <= 1.9e+27)) {
		tmp = 1.0 + (x / (y / -2.0));
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.06d+48)) .or. (.not. (y <= 1.9d+27))) then
        tmp = 1.0d0 + (x / (y / (-2.0d0)))
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.06e+48) || !(y <= 1.9e+27)) {
		tmp = 1.0 + (x / (y / -2.0));
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.06e+48) or not (y <= 1.9e+27):
		tmp = 1.0 + (x / (y / -2.0))
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.06e+48) || !(y <= 1.9e+27))
		tmp = Float64(1.0 + Float64(x / Float64(y / -2.0)));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.06e+48) || ~((y <= 1.9e+27)))
		tmp = 1.0 + (x / (y / -2.0));
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.06e+48], N[Not[LessEqual[y, 1.9e+27]], $MachinePrecision]], N[(1.0 + N[(x / N[(y / -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e48 or 1.90000000000000011e27 < 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 69.4%

      \[\leadsto \color{blue}{\left(1 + \left(\frac{\left(-1 \cdot x - -1 \cdot \left(2 - x\right)\right) \cdot \left(2 - x\right)}{{y}^{2}} + -1 \cdot \frac{x}{y}\right)\right) - -1 \cdot \frac{2 - x}{y}} \]
   5. Step-by-step derivation

      1. associate--l+ 69.4%

         \[\leadsto \color{blue}{1 + \left(\left(\frac{\left(-1 \cdot x - -1 \cdot \left(2 - x\right)\right) \cdot \left(2 - x\right)}{{y}^{2}} + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{2 - x}{y}\right)} \]

      2. *-commutative 69.4%

         \[\leadsto 1 + \left(\left(\frac{\color{blue}{\left(2 - x\right) \cdot \left(-1 \cdot x - -1 \cdot \left(2 - x\right)\right)}}{{y}^{2}} + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{2 - x}{y}\right) \]

      3. associate--l+ 69.4%

         \[\leadsto 1 + \color{blue}{\left(\frac{\left(2 - x\right) \cdot \left(-1 \cdot x - -1 \cdot \left(2 - x\right)\right)}{{y}^{2}} + \left(-1 \cdot \frac{x}{y} - -1 \cdot \frac{2 - x}{y}\right)\right)} \]

      4. unpow2 69.4%

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

      5. times-frac 77.5%

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

      6. fma-def 77.5%

         \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(\frac{2 - x}{y}, \frac{-1 \cdot x - -1 \cdot \left(2 - x\right)}{y}, -1 \cdot \frac{x}{y} - -1 \cdot \frac{2 - x}{y}\right)} \]

   6. Simplified 77.5%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(\frac{2 - x}{y}, \frac{\left(2 - x\right) - x}{y}, \frac{\left(2 - x\right) - x}{y}\right)} \]
   7. Step-by-step derivation

      1. fma-udef 77.5%

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

      2. *-un-lft-identity 77.5%

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

      3. distribute-rgt-out 77.5%

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

      4. associate--l- 77.5%

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

   8. Applied egg-rr 77.5%

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

   9. Taylor expanded in x around inf 77.5%

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

   10. Taylor expanded in y around inf 78.0%

       \[\leadsto 1 + \color{blue}{-2 \cdot \frac{x}{y}} \]
   11. Step-by-step derivation

       1. associate-*r/ 78.0%

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

       2. *-commutative 78.0%

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

       3. associate-/l* 78.0%

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

   12. Simplified 78.0%

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

   if -1.06e48 < y < 1.90000000000000011e27

   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 74.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+48} \lor \neg \left(y \leq 1.9 \cdot 10^{+27}\right):\\ \;\;\;\;1 + \frac{x}{\frac{y}{-2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 3: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+48}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.85e+48) 1.0 (if (<= y 4e+26) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.85e+48) {
		tmp = 1.0;
	} else if (y <= 4e+26) {
		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 <= (-1.85d+48)) then
        tmp = 1.0d0
    else if (y <= 4d+26) 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 <= -1.85e+48) {
		tmp = 1.0;
	} else if (y <= 4e+26) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.85e+48:
		tmp = 1.0
	elif y <= 4e+26:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.85e+48)
		tmp = 1.0;
	elseif (y <= 4e+26)
		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 <= -1.85e+48)
		tmp = 1.0;
	elseif (y <= 4e+26)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.85e+48], 1.0, If[LessEqual[y, 4e+26], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e48 or 4.00000000000000019e26 < 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 77.1%

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

   if -1.85e48 < y < 4.00000000000000019e26

   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 74.5%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+48}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 62.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+48}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.22e+48) 1.0 (if (<= y 1.15e+27) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.22e+48) {
		tmp = 1.0;
	} else if (y <= 1.15e+27) {
		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 <= (-1.22d+48)) then
        tmp = 1.0d0
    else if (y <= 1.15d+27) 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 <= -1.22e+48) {
		tmp = 1.0;
	} else if (y <= 1.15e+27) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.22e+48:
		tmp = 1.0
	elif y <= 1.15e+27:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.22e+48)
		tmp = 1.0;
	elseif (y <= 1.15e+27)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.22e+48)
		tmp = 1.0;
	elseif (y <= 1.15e+27)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.22e+48], 1.0, If[LessEqual[y, 1.15e+27], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22000000000000004e48 or 1.15e27 < 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 77.1%

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

   if -1.22000000000000004e48 < y < 1.15e27

   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 51.6%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+48}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 37.8% 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 40.5%

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

5. Final simplification 40.5%

   \[\leadsto -1 \]

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 2023258 
(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))))