Data.Colour.CIE:cieLAB from colour-2.3.3, A

Percentage Accurate: 99.7% → 99.7%

Time: 5.5s

Alternatives: 6

Speedup: 1.3×

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))

C

double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function

Java

public static double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Python

def code(x, y):
	return ((x - (16.0 / 116.0)) * 3.0) * y

Julia

function code(x, y)
	return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x - (16.0 / 116.0)) * 3.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))

C

double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function

Java

public static double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Python

def code(x, y):
	return ((x - (16.0 / 116.0)) * 3.0) * y

Julia

function code(x, y)
	return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x - (16.0 / 116.0)) * 3.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 3, -0.41379310344827586\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (fma x 3.0 -0.41379310344827586) y))

C

double code(double x, double y) {
	return fma(x, 3.0, -0.41379310344827586) * y;
}

Julia

function code(x, y)
	return Float64(fma(x, 3.0, -0.41379310344827586) * y)
end

Wolfram

code[x_, y_] := N[(N[(x * 3.0 + -0.41379310344827586), $MachinePrecision] * y), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Step-by-step derivation

   1. *-commutative 99.8%

      \[\leadsto \color{blue}{\left(3 \cdot \left(x - \frac{16}{116}\right)\right)} \cdot y \]

   2. sub-neg 99.8%

      \[\leadsto \left(3 \cdot \color{blue}{\left(x + \left(-\frac{16}{116}\right)\right)}\right) \cdot y \]

   3. distribute-lft-in 99.8%

      \[\leadsto \color{blue}{\left(3 \cdot x + 3 \cdot \left(-\frac{16}{116}\right)\right)} \cdot y \]

   4. *-commutative 99.8%

      \[\leadsto \left(\color{blue}{x \cdot 3} + 3 \cdot \left(-\frac{16}{116}\right)\right) \cdot y \]

   5. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3, 3 \cdot \left(-\frac{16}{116}\right)\right)} \cdot y \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(x, 3, 3 \cdot \left(-\color{blue}{0.13793103448275862}\right)\right) \cdot y \]

   7. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(x, 3, 3 \cdot \color{blue}{-0.13793103448275862}\right) \cdot y \]

   8. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(x, 3, \color{blue}{-0.41379310344827586}\right) \cdot y \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3, -0.41379310344827586\right) \cdot y} \]
4. Add Preprocessing

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(x, 3, -0.41379310344827586\right) \cdot y \]
6. Add Preprocessing

Alternative 2: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.14 \lor \neg \left(x \leq 0.136\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.14) (not (<= x 0.136)))
   (* 3.0 (* x y))
   (* -0.41379310344827586 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.14) || !(x <= 0.136)) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -0.41379310344827586 * 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 <= (-0.14d0)) .or. (.not. (x <= 0.136d0))) then
        tmp = 3.0d0 * (x * y)
    else
        tmp = (-0.41379310344827586d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.14) || !(x <= 0.136)) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -0.41379310344827586 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.14) or not (x <= 0.136):
		tmp = 3.0 * (x * y)
	else:
		tmp = -0.41379310344827586 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.14) || !(x <= 0.136))
		tmp = Float64(3.0 * Float64(x * y));
	else
		tmp = Float64(-0.41379310344827586 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.14) || ~((x <= 0.136)))
		tmp = 3.0 * (x * y);
	else
		tmp = -0.41379310344827586 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.14], N[Not[LessEqual[x, 0.136]], $MachinePrecision]], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(-0.41379310344827586 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.14000000000000001 or 0.13600000000000001 < x

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.8%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto 3 \cdot \color{blue}{\left(y \cdot x\right)} \]

   5. Simplified 97.8%

      \[\leadsto \color{blue}{3 \cdot \left(y \cdot x\right)} \]

   if -0.14000000000000001 < x < 0.13600000000000001

   1. Initial program 99.9%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.6%

      \[\leadsto \color{blue}{-0.41379310344827586 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.14 \lor \neg \left(x \leq 0.136\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.14 \lor \neg \left(x \leq 0.136\right):\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.14) (not (<= x 0.136)))
   (* y (* x 3.0))
   (* -0.41379310344827586 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.14) || !(x <= 0.136)) {
		tmp = y * (x * 3.0);
	} else {
		tmp = -0.41379310344827586 * 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 <= (-0.14d0)) .or. (.not. (x <= 0.136d0))) then
        tmp = y * (x * 3.0d0)
    else
        tmp = (-0.41379310344827586d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.14) || !(x <= 0.136)) {
		tmp = y * (x * 3.0);
	} else {
		tmp = -0.41379310344827586 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.14) or not (x <= 0.136):
		tmp = y * (x * 3.0)
	else:
		tmp = -0.41379310344827586 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.14) || !(x <= 0.136))
		tmp = Float64(y * Float64(x * 3.0));
	else
		tmp = Float64(-0.41379310344827586 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.14) || ~((x <= 0.136)))
		tmp = y * (x * 3.0);
	else
		tmp = -0.41379310344827586 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.14], N[Not[LessEqual[x, 0.136]], $MachinePrecision]], N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(-0.41379310344827586 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.14000000000000001 or 0.13600000000000001 < x

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.9%

      \[\leadsto \color{blue}{\left(3 \cdot x\right)} \cdot y \]

   if -0.14000000000000001 < x < 0.13600000000000001

   1. Initial program 99.9%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.6%

      \[\leadsto \color{blue}{-0.41379310344827586 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.14 \lor \neg \left(x \leq 0.136\right):\\ \;\;\;\;y \cdot \left(x \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(y \cdot \left(x - 0.13793103448275862\right)\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 3.0 (* y (- x 0.13793103448275862))))

C

double code(double x, double y) {
	return 3.0 * (y * (x - 0.13793103448275862));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 3.0d0 * (y * (x - 0.13793103448275862d0))
end function

Java

public static double code(double x, double y) {
	return 3.0 * (y * (x - 0.13793103448275862));
}

Python

def code(x, y):
	return 3.0 * (y * (x - 0.13793103448275862))

Julia

function code(x, y)
	return Float64(3.0 * Float64(y * Float64(x - 0.13793103448275862)))
end

MATLAB

function tmp = code(x, y)
	tmp = 3.0 * (y * (x - 0.13793103448275862));
end

Wolfram

code[x_, y_] := N[(3.0 * N[(y * N[(x - 0.13793103448275862), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.6%

   \[\leadsto \color{blue}{3 \cdot \left(y \cdot \left(x - 0.13793103448275862\right)\right)} \]

4. Final simplification 99.6%

   \[\leadsto 3 \cdot \left(y \cdot \left(x - 0.13793103448275862\right)\right) \]
5. Add Preprocessing

Alternative 5: 99.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(3 \cdot \left(x - 0.13793103448275862\right)\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* y (* 3.0 (- x 0.13793103448275862))))

C

double code(double x, double y) {
	return y * (3.0 * (x - 0.13793103448275862));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * (3.0d0 * (x - 0.13793103448275862d0))
end function

Java

public static double code(double x, double y) {
	return y * (3.0 * (x - 0.13793103448275862));
}

Python

def code(x, y):
	return y * (3.0 * (x - 0.13793103448275862))

Julia

function code(x, y)
	return Float64(y * Float64(3.0 * Float64(x - 0.13793103448275862)))
end

MATLAB

function tmp = code(x, y)
	tmp = y * (3.0 * (x - 0.13793103448275862));
end

Wolfram

code[x_, y_] := N[(y * N[(3.0 * N[(x - 0.13793103448275862), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto y \cdot \left(3 \cdot \left(x - 0.13793103448275862\right)\right) \]
4. Add Preprocessing

Alternative 6: 50.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ -0.41379310344827586 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -0.41379310344827586 y))

C

double code(double x, double y) {
	return -0.41379310344827586 * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-0.41379310344827586d0) * y
end function

Java

public static double code(double x, double y) {
	return -0.41379310344827586 * y;
}

Python

def code(x, y):
	return -0.41379310344827586 * y

Julia

function code(x, y)
	return Float64(-0.41379310344827586 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = -0.41379310344827586 * y;
end

Wolfram

code[x_, y_] := N[(-0.41379310344827586 * y), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Add Preprocessing

3. Taylor expanded in x around 0 51.8%

   \[\leadsto \color{blue}{-0.41379310344827586 \cdot y} \]

4. Final simplification 51.8%

   \[\leadsto -0.41379310344827586 \cdot y \]
5. Add Preprocessing

Developer target: 99.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(x \cdot 3 - 0.41379310344827586\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* y (- (* x 3.0) 0.41379310344827586)))

C

double code(double x, double y) {
	return y * ((x * 3.0) - 0.41379310344827586);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * ((x * 3.0d0) - 0.41379310344827586d0)
end function

Java

public static double code(double x, double y) {
	return y * ((x * 3.0) - 0.41379310344827586);
}

Python

def code(x, y):
	return y * ((x * 3.0) - 0.41379310344827586)

Julia

function code(x, y)
	return Float64(y * Float64(Float64(x * 3.0) - 0.41379310344827586))
end

MATLAB

function tmp = code(x, y)
	tmp = y * ((x * 3.0) - 0.41379310344827586);
end

Wolfram

code[x_, y_] := N[(y * N[(N[(x * 3.0), $MachinePrecision] - 0.41379310344827586), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024043 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :alt
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))