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

Percentage Accurate: 100.0% → 100.0%

Time: 1.9s

Alternatives: 4

Speedup: N/A×

Specification

Math

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

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

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

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, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(1 - x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

   2. *-lft-identity 100.0%

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

   3. metadata-eval 100.0%

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

   4. distribute-rgt-out-- 100.0%

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

   5. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{x + y \cdot \left(1 - x\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(1 - x\right) \]
6. Add Preprocessing

Alternative 2: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0))) (* x (- 1.0 y)) (+ x y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = x * (1.0 - y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = x * (1.0 - y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.4%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. *-lft-identity 100.0%

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

      3. metadata-eval 100.0%

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

      4. distribute-rgt-out-- 100.0%

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

      5. metadata-eval 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + y \cdot \left(1 - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 97.9%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 2.3× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ x y))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + y
end function

Java

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

Python

def code(x, y):
	return x + y

Julia

function code(x, y)
	return Float64(x + y)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

   2. *-lft-identity 100.0%

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

   3. metadata-eval 100.0%

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

   4. distribute-rgt-out-- 100.0%

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

   5. metadata-eval 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{x + y \cdot \left(1 - x\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 73.9%

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

6. Final simplification 73.9%

   \[\leadsto x + y \]
7. Add Preprocessing

Alternative 4: 38.4% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

public static double code(double x, double y) {
	return x;
}

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Add Preprocessing

3. Taylor expanded in y around 0 41.1%

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

4. Final simplification 41.1%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024048 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))