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

Percentage Accurate: 99.9% → 99.9%

Time: 6.1s

Alternatives: 4

Speedup: 4.4×

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, 3.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. metadata-eval N/A

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

   4. metadata-eval N/A

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

   5. metadata-eval N/A

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

   6. metadata-eval N/A

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

   7. lift-/.f64 N/A

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

   8. sub-neg N/A

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

   9. lower--.f64 N/A

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

   10. lift-*.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 N/A

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

   13. lift-/.f64 N/A

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

   14. metadata-eval N/A

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

   15. lift-/.f64 N/A

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

   16. metadata-eval N/A

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

   17. metadata-eval 99.9

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

4. Applied rewrites 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{841}{108} \cdot x\\ \mathbf{if}\;t\_0 \leq -50:\\ \;\;\;\;7.787037037037037 \cdot x\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-8}:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;7.787037037037037 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* (/ 841.0 108.0) x)))
   (if (<= t_0 -50.0)
     (* 7.787037037037037 x)
     (if (<= t_0 2e-8) 0.13793103448275862 (* 7.787037037037037 x)))))

C

double code(double x) {
	double t_0 = (841.0 / 108.0) * x;
	double tmp;
	if (t_0 <= -50.0) {
		tmp = 7.787037037037037 * x;
	} else if (t_0 <= 2e-8) {
		tmp = 0.13793103448275862;
	} else {
		tmp = 7.787037037037037 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (841.0d0 / 108.0d0) * x
    if (t_0 <= (-50.0d0)) then
        tmp = 7.787037037037037d0 * x
    else if (t_0 <= 2d-8) then
        tmp = 0.13793103448275862d0
    else
        tmp = 7.787037037037037d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = (841.0 / 108.0) * x;
	double tmp;
	if (t_0 <= -50.0) {
		tmp = 7.787037037037037 * x;
	} else if (t_0 <= 2e-8) {
		tmp = 0.13793103448275862;
	} else {
		tmp = 7.787037037037037 * x;
	}
	return tmp;
}

Python

def code(x):
	t_0 = (841.0 / 108.0) * x
	tmp = 0
	if t_0 <= -50.0:
		tmp = 7.787037037037037 * x
	elif t_0 <= 2e-8:
		tmp = 0.13793103448275862
	else:
		tmp = 7.787037037037037 * x
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(841.0 / 108.0) * x)
	tmp = 0.0
	if (t_0 <= -50.0)
		tmp = Float64(7.787037037037037 * x);
	elseif (t_0 <= 2e-8)
		tmp = 0.13793103448275862;
	else
		tmp = Float64(7.787037037037037 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = (841.0 / 108.0) * x;
	tmp = 0.0;
	if (t_0 <= -50.0)
		tmp = 7.787037037037037 * x;
	elseif (t_0 <= 2e-8)
		tmp = 0.13793103448275862;
	else
		tmp = 7.787037037037037 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(841.0 / 108.0), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$0, -50.0], N[(7.787037037037037 * x), $MachinePrecision], If[LessEqual[t$95$0, 2e-8], 0.13793103448275862, N[(7.787037037037037 * x), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x) < -50 or 2e-8 < (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x)

   1. Initial program 99.8%

      \[\frac{841}{108} \cdot x + \frac{4}{29} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot \frac{841}{108}} \]

      2. lower-*.f64 97.2

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

   5. Applied rewrites 97.2%

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

   if -50 < (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x) < 2e-8

   1. Initial program 100.0%

      \[\frac{841}{108} \cdot x + \frac{4}{29} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.2%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{841}{108} \cdot x \leq -50:\\ \;\;\;\;7.787037037037037 \cdot x\\ \mathbf{elif}\;\frac{841}{108} \cdot x \leq 2 \cdot 10^{-8}:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;7.787037037037037 \cdot x\\ \end{array} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024230 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))