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

Percentage Accurate: 99.7% → 99.7%

Time: 5.4s

Alternatives: 5

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, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Final simplification 99.7%

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

Alternative 2: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.135 \lor \neg \left(x \leq 0.135\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.41379310344827586\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.135) (not (<= x 0.135)))
   (* 3.0 (* x y))
   (* y -0.41379310344827586)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.135) || !(x <= 0.135)) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = y * -0.41379310344827586;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-0.135d0)) .or. (.not. (x <= 0.135d0))) then
        tmp = 3.0d0 * (x * y)
    else
        tmp = y * (-0.41379310344827586d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.135) || !(x <= 0.135)) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = y * -0.41379310344827586;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.135) or not (x <= 0.135):
		tmp = 3.0 * (x * y)
	else:
		tmp = y * -0.41379310344827586
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.135) || !(x <= 0.135))
		tmp = Float64(3.0 * Float64(x * y));
	else
		tmp = Float64(y * -0.41379310344827586);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.135) || ~((x <= 0.135)))
		tmp = 3.0 * (x * y);
	else
		tmp = y * -0.41379310344827586;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.135], N[Not[LessEqual[x, 0.135]], $MachinePrecision]], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(y * -0.41379310344827586), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.13500000000000001 or 0.13500000000000001 < 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 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -0.13500000000000001 < x < 0.13500000000000001

   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 98.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.135 \lor \neg \left(x \leq 0.135\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.41379310344827586\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Taylor expanded in y around 0 99.7%

   \[\leadsto \color{blue}{3 \cdot \left(y \cdot \left(x - 0.13793103448275862\right)\right)} \]
4. Step-by-step derivation

   1. sub-neg 99.7%

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

   2. distribute-lft-in 99.7%

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

   3. metadata-eval 99.7%

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

5. Applied egg-rr 99.7%

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

6. Final simplification 99.7%

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

Alternative 4: 99.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 99.7%

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

Alternative 5: 51.8% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 0 51.4%

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

4. Final simplification 51.4%

   \[\leadsto y \cdot -0.41379310344827586 \]
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 2024080 
(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))