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

Percentage Accurate: 99.9% → 99.9%

Time: 4.4s

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. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 99.9

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

   5. lift-/.f64 N/A

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

   6. metadata-eval 99.9

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{7.787037037037037}, \frac{4}{29}\right) \]

   7. lift-/.f64 N/A

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

   8. metadata-eval 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{841}{108} \cdot x\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+16}:\\ \;\;\;\;7.787037037037037 \cdot x\\ \mathbf{elif}\;t\_0 \leq 10^{-7}:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;7.787037037037037 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* (/ 841.0 108.0) x)))
   (if (<= t_0 -5e+16)
     (* 7.787037037037037 x)
     (if (<= t_0 1e-7) 0.13793103448275862 (* 7.787037037037037 x)))))

C

double code(double x) {
	double t_0 = (841.0 / 108.0) * x;
	double tmp;
	if (t_0 <= -5e+16) {
		tmp = 7.787037037037037 * x;
	} else if (t_0 <= 1e-7) {
		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 <= (-5d+16)) then
        tmp = 7.787037037037037d0 * x
    else if (t_0 <= 1d-7) 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 <= -5e+16) {
		tmp = 7.787037037037037 * x;
	} else if (t_0 <= 1e-7) {
		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 <= -5e+16:
		tmp = 7.787037037037037 * x
	elif t_0 <= 1e-7:
		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 <= -5e+16)
		tmp = Float64(7.787037037037037 * x);
	elseif (t_0 <= 1e-7)
		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 <= -5e+16)
		tmp = 7.787037037037037 * x;
	elseif (t_0 <= 1e-7)
		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, -5e+16], N[(7.787037037037037 * x), $MachinePrecision], If[LessEqual[t$95$0, 1e-7], 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) < -5e16 or 9.9999999999999995e-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. 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

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

      3. *-commutative N/A

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

      4. lower-fma.f64 99.8

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

      5. lift-/.f64 N/A

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

      6. metadata-eval 99.8

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{7.787037037037037}, \frac{4}{29}\right) \]

      7. lift-/.f64 N/A

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

      8. metadata-eval 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 99.5

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

   7. Applied rewrites 99.5%

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

   if -5e16 < (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x) < 9.9999999999999995e-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 98.8%

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

Alternative 3: 50.5% 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. Applied rewrites 51.5%

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

Reproduce

herbie shell --seed 2024295 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))