Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, G

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

Alternatives: 3

Speedup: 1.7×

Specification

Math

\[\begin{array}{l} \\ x - \frac{1}{3} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- x (/ 1.0 3.0)))

C

double code(double x) {
	return x - (1.0 / 3.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x - (1.0d0 / 3.0d0)
end function

Java

public static double code(double x) {
	return x - (1.0 / 3.0);
}

Python

def code(x):
	return x - (1.0 / 3.0)

Julia

function code(x)
	return Float64(x - Float64(1.0 / 3.0))
end

MATLAB

function tmp = code(x)
	tmp = x - (1.0 / 3.0);
end

Wolfram

code[x_] := N[(x - N[(1.0 / 3.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{1}{3} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- x (/ 1.0 3.0)))

C

double code(double x) {
	return x - (1.0 / 3.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x - (1.0d0 / 3.0d0)
end function

Java

public static double code(double x) {
	return x - (1.0 / 3.0);
}

Python

def code(x):
	return x - (1.0 / 3.0)

Julia

function code(x)
	return Float64(x - Float64(1.0 / 3.0))
end

MATLAB

function tmp = code(x)
	tmp = x - (1.0 / 3.0);
end

Wolfram

code[x_] := N[(x - N[(1.0 / 3.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ x + -0.3333333333333333 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ x -0.3333333333333333))

C

double code(double x) {
	return x + -0.3333333333333333;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x + (-0.3333333333333333d0)
end function

Java

public static double code(double x) {
	return x + -0.3333333333333333;
}

Python

def code(x):
	return x + -0.3333333333333333

Julia

function code(x)
	return Float64(x + -0.3333333333333333)
end

MATLAB

function tmp = code(x)
	tmp = x + -0.3333333333333333;
end

Wolfram

code[x_] := N[(x + -0.3333333333333333), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{1}{3} \]
2. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)} \]

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}\right) \]

   3. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)\right) \]

   4. metadata-eval 100.0%

      \[\leadsto \mathsf{+.f64}\left(x, \frac{-1}{3}\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{x + -0.3333333333333333} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.33:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.33:\\ \;\;\;\;-0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.33) x (if (<= x 0.33) -0.3333333333333333 x)))

C

double code(double x) {
	double tmp;
	if (x <= -0.33) {
		tmp = x;
	} else if (x <= 0.33) {
		tmp = -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-0.33d0)) then
        tmp = x
    else if (x <= 0.33d0) then
        tmp = -0.3333333333333333d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.33) {
		tmp = x;
	} else if (x <= 0.33) {
		tmp = -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.33:
		tmp = x
	elif x <= 0.33:
		tmp = -0.3333333333333333
	else:
		tmp = x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.33)
		tmp = x;
	elseif (x <= 0.33)
		tmp = -0.3333333333333333;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.33)
		tmp = x;
	elseif (x <= 0.33)
		tmp = -0.3333333333333333;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.33], x, If[LessEqual[x, 0.33], -0.3333333333333333, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.330000000000000016 or 0.330000000000000016 < x

   1. Initial program 100.0%

      \[x - \frac{1}{3} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)\right) \]

      4. metadata-eval 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \frac{-1}{3}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + -0.3333333333333333} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 98.6%

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

   if -0.330000000000000016 < x < 0.330000000000000016

   1. Initial program 100.0%

      \[x - \frac{1}{3} \]
   2. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)\right) \]

      4. metadata-eval 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \frac{-1}{3}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + -0.3333333333333333} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1}{3}} \]
   6. Step-by-step derivation

   7. Simplified 98.0%

      \[\leadsto \color{blue}{-0.3333333333333333} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 50.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ -0.3333333333333333 \end{array} \]

FPCore

(FPCore (x) :precision binary64 -0.3333333333333333)

C

double code(double x) {
	return -0.3333333333333333;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = -0.3333333333333333d0
end function

Java

public static double code(double x) {
	return -0.3333333333333333;
}

Python

def code(x):
	return -0.3333333333333333

Julia

function code(x)
	return -0.3333333333333333
end

MATLAB

function tmp = code(x)
	tmp = -0.3333333333333333;
end

Wolfram

code[x_] := -0.3333333333333333

Derivation

1. Initial program 100.0%

   \[x - \frac{1}{3} \]
2. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)} \]

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}\right) \]

   3. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)\right) \]

   4. metadata-eval 100.0%

      \[\leadsto \mathsf{+.f64}\left(x, \frac{-1}{3}\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{x + -0.3333333333333333} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1}{3}} \]
6. Step-by-step derivation

7. Simplified 53.1%

   \[\leadsto \color{blue}{-0.3333333333333333} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024149 
(FPCore (x)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, G"
  :precision binary64
  (- x (/ 1.0 3.0)))