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

Percentage Accurate: 99.9% → 99.9%

Time: 6.5s

Alternatives: 3

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, 4.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 7.787037037037037, 0.13793103448275862\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (fma x 7.787037037037037 0.13793103448275862))

C

double code(double x) {
	return fma(x, 7.787037037037037, 0.13793103448275862);
}

Julia

function code(x)
	return fma(x, 7.787037037037037, 0.13793103448275862)
end

Wolfram

code[x_] := N[(x * 7.787037037037037 + 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. *-commutative N/A

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

   2. accelerator-lowering-fma.f64 N/A

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

   3. metadata-eval N/A

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

   4. metadata-eval 99.9

      \[\leadsto \mathsf{fma}\left(x, 7.787037037037037, \color{blue}{0.13793103448275862}\right) \]

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 7.787037037037037, 0.13793103448275862\right)} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.017500000000000002 or 0.0179999999999999986 < 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. *-lowering-*.f64 98.2

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

   5. Simplified 98.2%

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

   if -0.017500000000000002 < x < 0.0179999999999999986

   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. Simplified 96.8%

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

4. Final simplification 97.5%

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

Alternative 3: 51.5% accurate, 31.0× 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. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Simplified 50.1%

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

Reproduce

herbie shell --seed 2024197 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))