Data.Colour.CIE:cieLABView from colour-2.3.3, C

Percentage Accurate: 99.9% → 100.0%

Time: 3.0s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 200, -200 \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x 200.0 (* -200.0 y)))

C

double code(double x, double y) {
	return fma(x, 200.0, (-200.0 * y));
}

Julia

function code(x, y)
	return fma(x, 200.0, Float64(-200.0 * y))
end

Wolfram

code[x_, y_] := N[(x * 200.0 + N[(-200.0 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{200 \cdot \left(x - y\right)} \]

   2. lift--.f64 N/A

      \[\leadsto 200 \cdot \color{blue}{\left(x - y\right)} \]

   3. sub-neg N/A

      \[\leadsto 200 \cdot \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   4. distribute-rgt-in N/A

      \[\leadsto \color{blue}{x \cdot 200 + \left(\mathsf{neg}\left(y\right)\right) \cdot 200} \]

   5. *-commutative N/A

      \[\leadsto x \cdot 200 + \color{blue}{200 \cdot \left(\mathsf{neg}\left(y\right)\right)} \]

   6. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 200, 200 \cdot \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   7. neg-mul-1 N/A

      \[\leadsto \mathsf{fma}\left(x, 200, 200 \cdot \color{blue}{\left(-1 \cdot y\right)}\right) \]

   8. associate-*r* N/A

      \[\leadsto \mathsf{fma}\left(x, 200, \color{blue}{\left(200 \cdot -1\right) \cdot y}\right) \]

   9. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, 200, \color{blue}{\left(200 \cdot -1\right) \cdot y}\right) \]

   10. metadata-eval 100.0

       \[\leadsto \mathsf{fma}\left(x, 200, \color{blue}{-200} \cdot y\right) \]

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 200, -200 \cdot y\right)} \]
5. Add Preprocessing

Alternative 2: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-9} \lor \neg \left(x \leq 0.051\right):\\ \;\;\;\;200 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.32e-9) (not (<= x 0.051))) (* 200.0 x) (* -200.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.32e-9) || !(x <= 0.051)) {
		tmp = 200.0 * x;
	} else {
		tmp = -200.0 * 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 <= (-1.32d-9)) .or. (.not. (x <= 0.051d0))) then
        tmp = 200.0d0 * x
    else
        tmp = (-200.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.32e-9) || !(x <= 0.051)) {
		tmp = 200.0 * x;
	} else {
		tmp = -200.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.32e-9) or not (x <= 0.051):
		tmp = 200.0 * x
	else:
		tmp = -200.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.32e-9) || !(x <= 0.051))
		tmp = Float64(200.0 * x);
	else
		tmp = Float64(-200.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.32e-9) || ~((x <= 0.051)))
		tmp = 200.0 * x;
	else
		tmp = -200.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.32e-9], N[Not[LessEqual[x, 0.051]], $MachinePrecision]], N[(200.0 * x), $MachinePrecision], N[(-200.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.32e-9 or 0.0509999999999999967 < x

   1. Initial program 99.9%

      \[200 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{200 \cdot x} \]
   4. Step-by-step derivation

      1. lower-*.f64 76.5

         \[\leadsto \color{blue}{200 \cdot x} \]

   5. Applied rewrites 76.5%

      \[\leadsto \color{blue}{200 \cdot x} \]

   if -1.32e-9 < x < 0.0509999999999999967

   1. Initial program 100.0%

      \[200 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-200 \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 79.8

         \[\leadsto \color{blue}{-200 \cdot y} \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{-200 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-9} \lor \neg \left(x \leq 0.051\right):\\ \;\;\;\;200 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 4: 50.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ -200 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -200.0 y))

C

double code(double x, double y) {
	return -200.0 * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-200.0d0) * y
end function

Java

public static double code(double x, double y) {
	return -200.0 * y;
}

Python

def code(x, y):
	return -200.0 * y

Julia

function code(x, y)
	return Float64(-200.0 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = -200.0 * y;
end

Wolfram

code[x_, y_] := N[(-200.0 * y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-200 \cdot y} \]
4. Step-by-step derivation

   1. lower-*.f64 53.1

      \[\leadsto \color{blue}{-200 \cdot y} \]

5. Applied rewrites 53.1%

   \[\leadsto \color{blue}{-200 \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024318 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))