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

Percentage Accurate: 99.9% → 99.9%

Time: 8.8s

Alternatives: 4

Speedup: 1.8×

Specification

Math

\[\begin{array}{l} \\ \frac{841}{108} \cdot x + \frac{4}{29} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))

C

double code(double x) {
	return ((841.0 / 108.0) * x) + (4.0 / 29.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((841.0d0 / 108.0d0) * x) + (4.0d0 / 29.0d0)
end function

Java

public static double code(double x) {
	return ((841.0 / 108.0) * x) + (4.0 / 29.0);
}

Python

def code(x):
	return ((841.0 / 108.0) * x) + (4.0 / 29.0)

Julia

function code(x)
	return Float64(Float64(Float64(841.0 / 108.0) * x) + Float64(4.0 / 29.0))
end

MATLAB

function tmp = code(x)
	tmp = ((841.0 / 108.0) * x) + (4.0 / 29.0);
end

Wolfram

code[x_] := N[(N[(N[(841.0 / 108.0), $MachinePrecision] * x), $MachinePrecision] + N[(4.0 / 29.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{841}{108} \cdot x + \frac{4}{29} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))

C

double code(double x) {
	return ((841.0 / 108.0) * x) + (4.0 / 29.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((841.0d0 / 108.0d0) * x) + (4.0d0 / 29.0d0)
end function

Java

public static double code(double x) {
	return ((841.0 / 108.0) * x) + (4.0 / 29.0);
}

Python

def code(x):
	return ((841.0 / 108.0) * x) + (4.0 / 29.0)

Julia

function code(x)
	return Float64(Float64(Float64(841.0 / 108.0) * x) + Float64(4.0 / 29.0))
end

MATLAB

function tmp = code(x)
	tmp = ((841.0 / 108.0) * x) + (4.0 / 29.0);
end

Wolfram

code[x_] := N[(N[(N[(841.0 / 108.0), $MachinePrecision] * x), $MachinePrecision] + N[(4.0 / 29.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(7.787037037037037 + \frac{0.13793103448275862}{x}\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (* x (+ 7.787037037037037 (/ 0.13793103448275862 x))))

C

double code(double x) {
	return x * (7.787037037037037 + (0.13793103448275862 / x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (7.787037037037037d0 + (0.13793103448275862d0 / x))
end function

Java

public static double code(double x) {
	return x * (7.787037037037037 + (0.13793103448275862 / x));
}

Python

def code(x):
	return x * (7.787037037037037 + (0.13793103448275862 / x))

Julia

function code(x)
	return Float64(x * Float64(7.787037037037037 + Float64(0.13793103448275862 / x)))
end

MATLAB

function tmp = code(x)
	tmp = x * (7.787037037037037 + (0.13793103448275862 / x));
end

Wolfram

code[x_] := N[(x * N[(7.787037037037037 + N[(0.13793103448275862 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{841}{108} \cdot x + \frac{4}{29} \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{841}{108} \cdot x\right), \color{blue}{\left(\frac{4}{29}\right)}\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{841}{108}\right), x\right), \left(\frac{\color{blue}{4}}{29}\right)\right) \]

   3. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \left(\frac{4}{29}\right)\right) \]

   4. metadata-eval 99.9%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \frac{4}{29}\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{7.787037037037037 \cdot x + 0.13793103448275862} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. flip-+ N/A

      \[\leadsto \frac{\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right) - \frac{4}{29} \cdot \frac{4}{29}}{\color{blue}{\frac{841}{108} \cdot x - \frac{4}{29}}} \]

   2. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{841}{108} \cdot x - \frac{4}{29}}{\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right) - \frac{4}{29} \cdot \frac{4}{29}}}} \]

   3. associate-/r/ N/A

      \[\leadsto \frac{1}{\frac{841}{108} \cdot x - \frac{4}{29}} \cdot \color{blue}{\left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right) - \frac{4}{29} \cdot \frac{4}{29}\right)} \]

   4. flip3-- N/A

      \[\leadsto \frac{1}{\frac{841}{108} \cdot x - \frac{4}{29}} \cdot \frac{{\left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right)}^{3} - {\left(\frac{4}{29} \cdot \frac{4}{29}\right)}^{3}}{\color{blue}{\left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) \cdot \left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) + \left(\left(\frac{4}{29} \cdot \frac{4}{29}\right) \cdot \left(\frac{4}{29} \cdot \frac{4}{29}\right) + \left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) \cdot \left(\frac{4}{29} \cdot \frac{4}{29}\right)\right)}} \]

   5. clear-num N/A

      \[\leadsto \frac{1}{\frac{841}{108} \cdot x - \frac{4}{29}} \cdot \frac{1}{\color{blue}{\frac{\left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) \cdot \left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) + \left(\left(\frac{4}{29} \cdot \frac{4}{29}\right) \cdot \left(\frac{4}{29} \cdot \frac{4}{29}\right) + \left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) \cdot \left(\frac{4}{29} \cdot \frac{4}{29}\right)\right)}{{\left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right)}^{3} - {\left(\frac{4}{29} \cdot \frac{4}{29}\right)}^{3}}}} \]

   6. un-div-inv N/A

      \[\leadsto \frac{\frac{1}{\frac{841}{108} \cdot x - \frac{4}{29}}}{\color{blue}{\frac{\left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) \cdot \left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) + \left(\left(\frac{4}{29} \cdot \frac{4}{29}\right) \cdot \left(\frac{4}{29} \cdot \frac{4}{29}\right) + \left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) \cdot \left(\frac{4}{29} \cdot \frac{4}{29}\right)\right)}{{\left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right)}^{3} - {\left(\frac{4}{29} \cdot \frac{4}{29}\right)}^{3}}}} \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{841}{108} \cdot x - \frac{4}{29}}\right), \color{blue}{\left(\frac{\left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) \cdot \left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) + \left(\left(\frac{4}{29} \cdot \frac{4}{29}\right) \cdot \left(\frac{4}{29} \cdot \frac{4}{29}\right) + \left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right) \cdot \left(\frac{4}{29} \cdot \frac{4}{29}\right)\right)}{{\left(\left(\frac{841}{108} \cdot x\right) \cdot \left(\frac{841}{108} \cdot x\right)\right)}^{3} - {\left(\frac{4}{29} \cdot \frac{4}{29}\right)}^{3}}\right)}\right) \]

6. Applied egg-rr 74.2%

   \[\leadsto \color{blue}{\frac{\frac{1}{7.787037037037037 \cdot x + -0.13793103448275862}}{\frac{1}{x \cdot \left(x \cdot 60.63794581618656\right) + -0.019024970273483946}}} \]

7. Taylor expanded in x around inf

   \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \frac{-4}{29}\right)\right), \color{blue}{\left(\frac{\frac{11664}{707281}}{{x}^{2}}\right)}\right) \]
8. Step-by-step derivation

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \frac{-4}{29}\right)\right), \mathsf{/.f64}\left(\frac{11664}{707281}, \color{blue}{\left({x}^{2}\right)}\right)\right) \]

   2. unpow2 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \frac{-4}{29}\right)\right), \mathsf{/.f64}\left(\frac{11664}{707281}, \left(x \cdot \color{blue}{x}\right)\right)\right) \]

   3. *-lowering-*.f64 26.4%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \frac{-4}{29}\right)\right), \mathsf{/.f64}\left(\frac{11664}{707281}, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right)\right) \]

9. Simplified 26.4%

   \[\leadsto \frac{\frac{1}{7.787037037037037 \cdot x + -0.13793103448275862}}{\color{blue}{\frac{0.016491323816135314}{x \cdot x}}} \]
10. Step-by-step derivation

    1. clear-num N/A

       \[\leadsto \frac{1}{\color{blue}{\frac{\frac{\frac{11664}{707281}}{x \cdot x}}{\frac{1}{\frac{841}{108} \cdot x + \frac{-4}{29}}}}} \]

    2. associate-/r/ N/A

       \[\leadsto \frac{1}{\frac{\frac{11664}{707281}}{x \cdot x}} \cdot \color{blue}{\frac{1}{\frac{841}{108} \cdot x + \frac{-4}{29}}} \]

    3. associate-/r/ N/A

       \[\leadsto \left(\frac{1}{\frac{11664}{707281}} \cdot \left(x \cdot x\right)\right) \cdot \frac{\color{blue}{1}}{\frac{841}{108} \cdot x + \frac{-4}{29}} \]

    4. metadata-eval N/A

       \[\leadsto \left(\frac{707281}{11664} \cdot \left(x \cdot x\right)\right) \cdot \frac{1}{\frac{841}{108} \cdot x + \frac{-4}{29}} \]

    5. associate-*l* N/A

       \[\leadsto \left(\left(\frac{707281}{11664} \cdot x\right) \cdot x\right) \cdot \frac{\color{blue}{1}}{\frac{841}{108} \cdot x + \frac{-4}{29}} \]

    6. *-commutative N/A

       \[\leadsto \left(\left(x \cdot \frac{707281}{11664}\right) \cdot x\right) \cdot \frac{1}{\frac{841}{108} \cdot x + \frac{-4}{29}} \]

    7. associate-*r* N/A

       \[\leadsto \left(x \cdot \frac{707281}{11664}\right) \cdot \color{blue}{\left(x \cdot \frac{1}{\frac{841}{108} \cdot x + \frac{-4}{29}}\right)} \]

    8. div-inv N/A

       \[\leadsto \left(x \cdot \frac{707281}{11664}\right) \cdot \frac{x}{\color{blue}{\frac{841}{108} \cdot x + \frac{-4}{29}}} \]

    9. associate-*l* N/A

       \[\leadsto x \cdot \color{blue}{\left(\frac{707281}{11664} \cdot \frac{x}{\frac{841}{108} \cdot x + \frac{-4}{29}}\right)} \]

    10. *-commutative N/A

        \[\leadsto x \cdot \left(\frac{707281}{11664} \cdot \frac{x}{x \cdot \frac{841}{108} + \frac{-4}{29}}\right) \]

    11. associate-*r/ N/A

        \[\leadsto x \cdot \frac{\frac{707281}{11664} \cdot x}{\color{blue}{x \cdot \frac{841}{108} + \frac{-4}{29}}} \]

    12. *-commutative N/A

        \[\leadsto x \cdot \frac{x \cdot \frac{707281}{11664}}{\color{blue}{x \cdot \frac{841}{108}} + \frac{-4}{29}} \]

    13. *-commutative N/A

        \[\leadsto \frac{x \cdot \frac{707281}{11664}}{x \cdot \frac{841}{108} + \frac{-4}{29}} \cdot \color{blue}{x} \]

    14. *-lowering-*.f64 N/A

        \[\leadsto \mathsf{*.f64}\left(\left(\frac{x \cdot \frac{707281}{11664}}{x \cdot \frac{841}{108} + \frac{-4}{29}}\right), \color{blue}{x}\right) \]

11. Applied egg-rr 51.2%

    \[\leadsto \color{blue}{\frac{60.63794581618656}{\frac{x \cdot 7.787037037037037 + -0.13793103448275862}{x}} \cdot x} \]

12. Taylor expanded in x around inf

    \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{841}{108} + \frac{4}{29} \cdot \frac{1}{x}\right)}, x\right) \]
13. Step-by-step derivation

    1. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{841}{108}, \left(\frac{4}{29} \cdot \frac{1}{x}\right)\right), x\right) \]

    2. associate-*r/ N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{841}{108}, \left(\frac{\frac{4}{29} \cdot 1}{x}\right)\right), x\right) \]

    3. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{841}{108}, \left(\frac{\frac{4}{29}}{x}\right)\right), x\right) \]

    4. /-lowering-/.f64 99.9%

       \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{841}{108}, \mathsf{/.f64}\left(\frac{4}{29}, x\right)\right), x\right) \]

14. Simplified 99.9%

    \[\leadsto \color{blue}{\left(7.787037037037037 + \frac{0.13793103448275862}{x}\right)} \cdot x \]

15. Final simplification 99.9%

    \[\leadsto x \cdot \left(7.787037037037037 + \frac{0.13793103448275862}{x}\right) \]
16. Add Preprocessing

Alternative 2: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.018:\\ \;\;\;\;7.787037037037037 \cdot x\\ \mathbf{elif}\;x \leq 0.0175:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;7.787037037037037 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -0.018)
   (* 7.787037037037037 x)
   (if (<= x 0.0175) 0.13793103448275862 (* 7.787037037037037 x))))

C

double code(double x) {
	double tmp;
	if (x <= -0.018) {
		tmp = 7.787037037037037 * x;
	} else if (x <= 0.0175) {
		tmp = 0.13793103448275862;
	} else {
		tmp = 7.787037037037037 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-0.018d0)) then
        tmp = 7.787037037037037d0 * x
    else if (x <= 0.0175d0) then
        tmp = 0.13793103448275862d0
    else
        tmp = 7.787037037037037d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -0.018) {
		tmp = 7.787037037037037 * x;
	} else if (x <= 0.0175) {
		tmp = 0.13793103448275862;
	} else {
		tmp = 7.787037037037037 * x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -0.018:
		tmp = 7.787037037037037 * x
	elif x <= 0.0175:
		tmp = 0.13793103448275862
	else:
		tmp = 7.787037037037037 * x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -0.018)
		tmp = Float64(7.787037037037037 * x);
	elseif (x <= 0.0175)
		tmp = 0.13793103448275862;
	else
		tmp = Float64(7.787037037037037 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -0.018)
		tmp = 7.787037037037037 * x;
	elseif (x <= 0.0175)
		tmp = 0.13793103448275862;
	else
		tmp = 7.787037037037037 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -0.018], N[(7.787037037037037 * x), $MachinePrecision], If[LessEqual[x, 0.0175], 0.13793103448275862, N[(7.787037037037037 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0179999999999999986 or 0.017500000000000002 < x

   1. Initial program 99.8%

      \[\frac{841}{108} \cdot x + \frac{4}{29} \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{841}{108} \cdot x\right), \color{blue}{\left(\frac{4}{29}\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{841}{108}\right), x\right), \left(\frac{\color{blue}{4}}{29}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \left(\frac{4}{29}\right)\right) \]

      4. metadata-eval 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \frac{4}{29}\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{7.787037037037037 \cdot x + 0.13793103448275862} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{841}{108} \cdot x} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{*.f64}\left(\frac{841}{108}, \color{blue}{x}\right) \]

   7. Simplified 98.3%

      \[\leadsto \color{blue}{7.787037037037037 \cdot x} \]

   if -0.0179999999999999986 < x < 0.017500000000000002

   1. Initial program 100.0%

      \[\frac{841}{108} \cdot x + \frac{4}{29} \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{841}{108} \cdot x\right), \color{blue}{\left(\frac{4}{29}\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{841}{108}\right), x\right), \left(\frac{\color{blue}{4}}{29}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \left(\frac{4}{29}\right)\right) \]

      4. metadata-eval 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \frac{4}{29}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{7.787037037037037 \cdot x + 0.13793103448275862} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{4}{29}} \]
   6. Step-by-step derivation

   7. Simplified 99.0%

      \[\leadsto \color{blue}{0.13793103448275862} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ 0.13793103448275862 + 7.787037037037037 \cdot x \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (+ 0.13793103448275862 (* 7.787037037037037 x)))

C

double code(double x) {
	return 0.13793103448275862 + (7.787037037037037 * x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.13793103448275862d0 + (7.787037037037037d0 * x)
end function

Java

public static double code(double x) {
	return 0.13793103448275862 + (7.787037037037037 * x);
}

Python

def code(x):
	return 0.13793103448275862 + (7.787037037037037 * x)

Julia

function code(x)
	return Float64(0.13793103448275862 + Float64(7.787037037037037 * x))
end

MATLAB

function tmp = code(x)
	tmp = 0.13793103448275862 + (7.787037037037037 * x);
end

Wolfram

code[x_] := N[(0.13793103448275862 + N[(7.787037037037037 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\frac{841}{108} \cdot x + \frac{4}{29} \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{841}{108} \cdot x\right), \color{blue}{\left(\frac{4}{29}\right)}\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{841}{108}\right), x\right), \left(\frac{\color{blue}{4}}{29}\right)\right) \]

   3. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \left(\frac{4}{29}\right)\right) \]

   4. metadata-eval 99.9%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \frac{4}{29}\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{7.787037037037037 \cdot x + 0.13793103448275862} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto 0.13793103448275862 + 7.787037037037037 \cdot x \]
6. Add Preprocessing

Alternative 4: 50.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 0.13793103448275862 \end{array} \]

FPCore

(FPCore (x) :precision binary64 0.13793103448275862)

C

double code(double x) {
	return 0.13793103448275862;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.13793103448275862d0
end function

Java

public static double code(double x) {
	return 0.13793103448275862;
}

Python

def code(x):
	return 0.13793103448275862

Julia

function code(x)
	return 0.13793103448275862
end

MATLAB

function tmp = code(x)
	tmp = 0.13793103448275862;
end

Wolfram

code[x_] := 0.13793103448275862

Derivation

1. Initial program 99.9%

   \[\frac{841}{108} \cdot x + \frac{4}{29} \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{841}{108} \cdot x\right), \color{blue}{\left(\frac{4}{29}\right)}\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{841}{108}\right), x\right), \left(\frac{\color{blue}{4}}{29}\right)\right) \]

   3. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \left(\frac{4}{29}\right)\right) \]

   4. metadata-eval 99.9%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{841}{108}, x\right), \frac{4}{29}\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{7.787037037037037 \cdot x + 0.13793103448275862} \]
4. Add Preprocessing

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{4}{29}} \]
6. Step-by-step derivation

7. Simplified 50.7%

   \[\leadsto \color{blue}{0.13793103448275862} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024161 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))