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

Percentage Accurate: 99.7% → 99.7%

Time: 3.7s

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, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(N[(x * 3.0), $MachinePrecision] + -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-rgt-in 99.8%

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

   4. metadata-eval 99.8%

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

   5. metadata-eval 99.8%

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

   6. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \left(x \cdot 3 + -0.41379310344827586\right) \cdot y \]

Alternative 2: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.135 \lor \neg \left(x \leq 0.14\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.135) (not (<= x 0.14)))
   (* 3.0 (* x y))
   (* -0.41379310344827586 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.135) || !(x <= 0.14)) {
		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 <= (-0.135d0)) .or. (.not. (x <= 0.14d0))) 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 <= -0.135) || !(x <= 0.14)) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -0.41379310344827586 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.135) or not (x <= 0.14):
		tmp = 3.0 * (x * y)
	else:
		tmp = -0.41379310344827586 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.135) || !(x <= 0.14))
		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 <= -0.135) || ~((x <= 0.14)))
		tmp = 3.0 * (x * y);
	else
		tmp = -0.41379310344827586 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.135], N[Not[LessEqual[x, 0.14]], $MachinePrecision]], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(-0.41379310344827586 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.13500000000000001 or 0.14000000000000001 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 97.0%

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

   if -0.13500000000000001 < x < 0.14000000000000001

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 98.8%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.135 \lor \neg \left(x \leq 0.14\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \end{array} \]

Alternative 3: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.135 \lor \neg \left(x \leq 0.14\right):\\ \;\;\;\;\left(x \cdot 3\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.135) (not (<= x 0.14)))
   (* (* x 3.0) y)
   (* -0.41379310344827586 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.135) || !(x <= 0.14)) {
		tmp = (x * 3.0) * 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 <= (-0.135d0)) .or. (.not. (x <= 0.14d0))) then
        tmp = (x * 3.0d0) * 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 <= -0.135) || !(x <= 0.14)) {
		tmp = (x * 3.0) * y;
	} else {
		tmp = -0.41379310344827586 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.135) or not (x <= 0.14):
		tmp = (x * 3.0) * y
	else:
		tmp = -0.41379310344827586 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.135) || !(x <= 0.14))
		tmp = Float64(Float64(x * 3.0) * y);
	else
		tmp = Float64(-0.41379310344827586 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.135) || ~((x <= 0.14)))
		tmp = (x * 3.0) * y;
	else
		tmp = -0.41379310344827586 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.135], N[Not[LessEqual[x, 0.14]], $MachinePrecision]], N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision], N[(-0.41379310344827586 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.13500000000000001 or 0.14000000000000001 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 97.1%

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

   if -0.13500000000000001 < x < 0.14000000000000001

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 98.8%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.135 \lor \neg \left(x \leq 0.14\right):\\ \;\;\;\;\left(x \cdot 3\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \end{array} \]

Alternative 4: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.135:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 3\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.135)
   (* x (* 3.0 y))
   (if (<= x 0.14) (* -0.41379310344827586 y) (* (* x 3.0) y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.135) {
		tmp = x * (3.0 * y);
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = (x * 3.0) * 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 <= (-0.135d0)) then
        tmp = x * (3.0d0 * y)
    else if (x <= 0.14d0) then
        tmp = (-0.41379310344827586d0) * y
    else
        tmp = (x * 3.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.135) {
		tmp = x * (3.0 * y);
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = (x * 3.0) * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.135:
		tmp = x * (3.0 * y)
	elif x <= 0.14:
		tmp = -0.41379310344827586 * y
	else:
		tmp = (x * 3.0) * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.135)
		tmp = Float64(x * Float64(3.0 * y));
	elseif (x <= 0.14)
		tmp = Float64(-0.41379310344827586 * y);
	else
		tmp = Float64(Float64(x * 3.0) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.135)
		tmp = x * (3.0 * y);
	elseif (x <= 0.14)
		tmp = -0.41379310344827586 * y;
	else
		tmp = (x * 3.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.135], N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.14], N[(-0.41379310344827586 * y), $MachinePrecision], N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.13500000000000001

   1. Initial program 99.7%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. metadata-eval 99.8%

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

      6. flip-+ 70.1%

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

      7. associate-*r/ 65.5%

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

      8. metadata-eval 65.5%

         \[\leadsto \frac{\left(3 \cdot y\right) \cdot \left(x \cdot x - \color{blue}{0.019024970273483946}\right)}{x - -0.13793103448275862} \]

      9. metadata-eval 65.5%

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

      10. metadata-eval 65.5%

          \[\leadsto \frac{\left(3 \cdot y\right) \cdot \left(x \cdot x - \color{blue}{\frac{16}{116}} \cdot 0.13793103448275862\right)}{x - -0.13793103448275862} \]

      11. metadata-eval 65.5%

          \[\leadsto \frac{\left(3 \cdot y\right) \cdot \left(x \cdot x - \frac{16}{116} \cdot \color{blue}{\frac{16}{116}}\right)}{x - -0.13793103448275862} \]

      12. fma-neg 65.5%

          \[\leadsto \frac{\left(3 \cdot y\right) \cdot \color{blue}{\mathsf{fma}\left(x, x, -\frac{16}{116} \cdot \frac{16}{116}\right)}}{x - -0.13793103448275862} \]

      13. metadata-eval 65.5%

          \[\leadsto \frac{\left(3 \cdot y\right) \cdot \mathsf{fma}\left(x, x, -\color{blue}{0.13793103448275862} \cdot \frac{16}{116}\right)}{x - -0.13793103448275862} \]

      14. metadata-eval 65.5%

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

      15. metadata-eval 65.5%

          \[\leadsto \frac{\left(3 \cdot y\right) \cdot \mathsf{fma}\left(x, x, -\color{blue}{0.019024970273483946}\right)}{x - -0.13793103448275862} \]

      16. metadata-eval 65.5%

          \[\leadsto \frac{\left(3 \cdot y\right) \cdot \mathsf{fma}\left(x, x, \color{blue}{-0.019024970273483946}\right)}{x - -0.13793103448275862} \]

      17. sub-neg 65.5%

          \[\leadsto \frac{\left(3 \cdot y\right) \cdot \mathsf{fma}\left(x, x, -0.019024970273483946\right)}{\color{blue}{x + \left(--0.13793103448275862\right)}} \]

      18. metadata-eval 65.5%

          \[\leadsto \frac{\left(3 \cdot y\right) \cdot \mathsf{fma}\left(x, x, -0.019024970273483946\right)}{x + \color{blue}{0.13793103448275862}} \]

   3. Applied egg-rr 65.5%

      \[\leadsto \color{blue}{\frac{\left(3 \cdot y\right) \cdot \mathsf{fma}\left(x, x, -0.019024970273483946\right)}{x + 0.13793103448275862}} \]
   4. Step-by-step derivation

      1. *-commutative 65.5%

         \[\leadsto \frac{\color{blue}{\left(y \cdot 3\right)} \cdot \mathsf{fma}\left(x, x, -0.019024970273483946\right)}{x + 0.13793103448275862} \]

      2. associate-*l* 65.5%

         \[\leadsto \frac{\color{blue}{y \cdot \left(3 \cdot \mathsf{fma}\left(x, x, -0.019024970273483946\right)\right)}}{x + 0.13793103448275862} \]

      3. *-commutative 65.5%

         \[\leadsto \frac{y \cdot \color{blue}{\left(\mathsf{fma}\left(x, x, -0.019024970273483946\right) \cdot 3\right)}}{x + 0.13793103448275862} \]

      4. associate-/l* 70.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{x + 0.13793103448275862}{\mathsf{fma}\left(x, x, -0.019024970273483946\right) \cdot 3}}} \]

      5. *-commutative 70.0%

         \[\leadsto \frac{y}{\frac{x + 0.13793103448275862}{\color{blue}{3 \cdot \mathsf{fma}\left(x, x, -0.019024970273483946\right)}}} \]

      6. fma-udef 69.9%

         \[\leadsto \frac{y}{\frac{x + 0.13793103448275862}{3 \cdot \color{blue}{\left(x \cdot x + -0.019024970273483946\right)}}} \]

      7. distribute-lft-in 70.0%

         \[\leadsto \frac{y}{\frac{x + 0.13793103448275862}{\color{blue}{3 \cdot \left(x \cdot x\right) + 3 \cdot -0.019024970273483946}}} \]

      8. fma-def 69.9%

         \[\leadsto \frac{y}{\frac{x + 0.13793103448275862}{\color{blue}{\mathsf{fma}\left(3, x \cdot x, 3 \cdot -0.019024970273483946\right)}}} \]

      9. metadata-eval 69.9%

         \[\leadsto \frac{y}{\frac{x + 0.13793103448275862}{\mathsf{fma}\left(3, x \cdot x, \color{blue}{-0.057074910820451845}\right)}} \]

   5. Simplified 69.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{x + 0.13793103448275862}{\mathsf{fma}\left(3, x \cdot x, -0.057074910820451845\right)}}} \]

   6. Taylor expanded in x around inf 94.9%

      \[\leadsto \frac{y}{\color{blue}{\frac{0.3333333333333333}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 95.1%

         \[\leadsto \color{blue}{\frac{y}{0.3333333333333333} \cdot x} \]

      2. div-inv 95.3%

         \[\leadsto \color{blue}{\left(y \cdot \frac{1}{0.3333333333333333}\right)} \cdot x \]

      3. metadata-eval 95.3%

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

   8. Applied egg-rr 95.3%

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

   if -0.13500000000000001 < x < 0.14000000000000001

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 98.8%

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

   if 0.14000000000000001 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 99.1%

      \[\leadsto \color{blue}{\left(3 \cdot x\right)} \cdot y \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.135:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 3\right) \cdot y\\ \end{array} \]

Alternative 5: 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. Taylor expanded in y around 0 99.6%

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

3. Final simplification 99.6%

   \[\leadsto 3 \cdot \left(y \cdot \left(x - 0.13793103448275862\right)\right) \]

Alternative 6: 50.5% 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. Taylor expanded in x around 0 55.5%

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

3. Final simplification 55.5%

   \[\leadsto -0.41379310344827586 \cdot y \]

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 2023221 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

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