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

Percentage Accurate: 100.0% → 100.0%

Time: 6.4s

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, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} + \frac{-1}{\frac{x + y}{y}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (/ x (+ x y)) (/ -1.0 (/ (+ x y) y))))

C

double code(double x, double y) {
	return (x / (x + y)) + (-1.0 / ((x + y) / y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / (x + y)) + ((-1.0d0) / ((x + y) / y))
end function

Java

public static double code(double x, double y) {
	return (x / (x + y)) + (-1.0 / ((x + y) / y));
}

Python

def code(x, y):
	return (x / (x + y)) + (-1.0 / ((x + y) / y))

Julia

function code(x, y)
	return Float64(Float64(x / Float64(x + y)) + Float64(-1.0 / Float64(Float64(x + y) / y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x / (x + y)) + (-1.0 / ((x + y) / y));
end

Wolfram

code[x_, y_] := N[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. *-un-lft-identity 100.0%

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

   2. add-sqr-sqrt 50.8%

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

   3. times-frac 50.8%

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

4. Applied egg-rr 50.8%

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

   1. frac-times 50.8%

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

   2. add-sqr-sqrt 100.0%

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

   3. associate-*l/ 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-lft-in 99.8%

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

6. Applied egg-rr 99.8%

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

   1. add-log-exp 99.9%

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

   2. *-un-lft-identity 99.9%

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

   3. log-prod 99.9%

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

   4. metadata-eval 99.9%

      \[\leadsto \left(\color{blue}{0} + \log \left(e^{\frac{1}{x + y} \cdot x}\right)\right) + \frac{1}{x + y} \cdot \left(-y\right) \]

   5. add-log-exp 99.8%

      \[\leadsto \left(0 + \color{blue}{\frac{1}{x + y} \cdot x}\right) + \frac{1}{x + y} \cdot \left(-y\right) \]

   6. associate-*l/ 99.9%

      \[\leadsto \left(0 + \color{blue}{\frac{1 \cdot x}{x + y}}\right) + \frac{1}{x + y} \cdot \left(-y\right) \]

   7. *-un-lft-identity 99.9%

      \[\leadsto \left(0 + \frac{\color{blue}{x}}{x + y}\right) + \frac{1}{x + y} \cdot \left(-y\right) \]

8. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\left(0 + \frac{x}{x + y}\right)} + \frac{1}{x + y} \cdot \left(-y\right) \]
9. Step-by-step derivation

   1. +-lft-identity 99.9%

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

10. Simplified 99.9%

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

    1. associate-*l/ 100.0%

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

    2. *-un-lft-identity 100.0%

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

    3. neg-mul-1 100.0%

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

    4. associate-/l* 100.0%

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

12. Applied egg-rr 100.0%

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

13. Final simplification 100.0%

    \[\leadsto \frac{x}{x + y} + \frac{-1}{\frac{x + y}{y}} \]
14. Add Preprocessing

Alternative 2: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+114}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+45}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.32e+114) -1.0 (if (<= y 7.2e+45) (+ 1.0 (* -2.0 (/ y x))) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.32e+114) {
		tmp = -1.0;
	} else if (y <= 7.2e+45) {
		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 <= (-1.32d+114)) then
        tmp = -1.0d0
    else if (y <= 7.2d+45) 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 <= -1.32e+114) {
		tmp = -1.0;
	} else if (y <= 7.2e+45) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.32e+114:
		tmp = -1.0
	elif y <= 7.2e+45:
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.32e+114)
		tmp = -1.0;
	elseif (y <= 7.2e+45)
		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 <= -1.32e+114)
		tmp = -1.0;
	elseif (y <= 7.2e+45)
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.32e+114], -1.0, If[LessEqual[y, 7.2e+45], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3200000000000001e114 or 7.2e45 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.9%

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

   if -1.3200000000000001e114 < y < 7.2e45

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+114}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+45}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+48}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+34}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.5e+48) -1.0 (if (<= y 7.8e+34) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.5e+48) {
		tmp = -1.0;
	} else if (y <= 7.8e+34) {
		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 <= (-3.5d+48)) then
        tmp = -1.0d0
    else if (y <= 7.8d+34) 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 <= -3.5e+48) {
		tmp = -1.0;
	} else if (y <= 7.8e+34) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.5e+48:
		tmp = -1.0
	elif y <= 7.8e+34:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.5e+48)
		tmp = -1.0;
	elseif (y <= 7.8e+34)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.5e+48)
		tmp = -1.0;
	elseif (y <= 7.8e+34)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.5e+48], -1.0, If[LessEqual[y, 7.8e+34], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999997e48 or 7.80000000000000038e34 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.9%

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

   if -3.4999999999999997e48 < y < 7.80000000000000038e34

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+48}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+34}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Final simplification 100.0%

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

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. Add Preprocessing

3. Taylor expanded in x around 0 44.5%

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

4. Final simplification 44.5%

   \[\leadsto -1 \]
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 2024011 
(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)))