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

Percentage Accurate: 99.9% → 99.8%

Time: 7.0s

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: 99.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, -60.63794581618656 \cdot \frac{x}{x \cdot -7.787037037037037}, 0.13793103448275862\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (fma
  x
  (* -60.63794581618656 (/ x (* x -7.787037037037037)))
  0.13793103448275862))

C

double code(double x) {
	return fma(x, (-60.63794581618656 * (x / (x * -7.787037037037037))), 0.13793103448275862);
}

Julia

function code(x)
	return fma(x, Float64(-60.63794581618656 * Float64(x / Float64(x * -7.787037037037037))), 0.13793103448275862)
end

Wolfram

code[x_] := N[(x * N[(-60.63794581618656 * N[(x / N[(x * -7.787037037037037), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 0.13793103448275862), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

4. Applied egg-rr 99.9%

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

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{fma}\left(x, \frac{-707281}{11664} \cdot \frac{x}{\mathsf{fma}\left(x, \frac{-841}{108}, \frac{4}{29}\right)}, \color{blue}{\frac{4}{29}}\right) \]
6. Step-by-step derivation

7. Simplified 98.6%

   \[\leadsto \mathsf{fma}\left(x, -60.63794581618656 \cdot \frac{x}{\mathsf{fma}\left(x, -7.787037037037037, 0.13793103448275862\right)}, \color{blue}{0.13793103448275862}\right) \]

8. Taylor expanded in x around inf

   \[\leadsto \mathsf{fma}\left(x, \frac{-707281}{11664} \cdot \frac{x}{\color{blue}{\frac{-841}{108} \cdot x}}, \frac{4}{29}\right) \]
9. Step-by-step derivation

   1. *-commutative N/A

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

   2. *-lowering-*.f64 99.9

      \[\leadsto \mathsf{fma}\left(x, -60.63794581618656 \cdot \frac{x}{\color{blue}{x \cdot -7.787037037037037}}, 0.13793103448275862\right) \]

10. Simplified 99.9%

    \[\leadsto \mathsf{fma}\left(x, -60.63794581618656 \cdot \frac{x}{\color{blue}{x \cdot -7.787037037037037}}, 0.13793103448275862\right) \]
11. Add Preprocessing

Alternative 2: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{841}{108}\\ \mathbf{if}\;t\_0 \leq -2000:\\ \;\;\;\;x \cdot 7.787037037037037\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-5}:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;x \cdot 7.787037037037037\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* x (/ 841.0 108.0))))
   (if (<= t_0 -2000.0)
     (* x 7.787037037037037)
     (if (<= t_0 5e-5) 0.13793103448275862 (* x 7.787037037037037)))))

C

double code(double x) {
	double t_0 = x * (841.0 / 108.0);
	double tmp;
	if (t_0 <= -2000.0) {
		tmp = x * 7.787037037037037;
	} else if (t_0 <= 5e-5) {
		tmp = 0.13793103448275862;
	} else {
		tmp = x * 7.787037037037037;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (841.0d0 / 108.0d0)
    if (t_0 <= (-2000.0d0)) then
        tmp = x * 7.787037037037037d0
    else if (t_0 <= 5d-5) then
        tmp = 0.13793103448275862d0
    else
        tmp = x * 7.787037037037037d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x * (841.0 / 108.0);
	double tmp;
	if (t_0 <= -2000.0) {
		tmp = x * 7.787037037037037;
	} else if (t_0 <= 5e-5) {
		tmp = 0.13793103448275862;
	} else {
		tmp = x * 7.787037037037037;
	}
	return tmp;
}

Python

def code(x):
	t_0 = x * (841.0 / 108.0)
	tmp = 0
	if t_0 <= -2000.0:
		tmp = x * 7.787037037037037
	elif t_0 <= 5e-5:
		tmp = 0.13793103448275862
	else:
		tmp = x * 7.787037037037037
	return tmp

Julia

function code(x)
	t_0 = Float64(x * Float64(841.0 / 108.0))
	tmp = 0.0
	if (t_0 <= -2000.0)
		tmp = Float64(x * 7.787037037037037);
	elseif (t_0 <= 5e-5)
		tmp = 0.13793103448275862;
	else
		tmp = Float64(x * 7.787037037037037);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x * (841.0 / 108.0);
	tmp = 0.0;
	if (t_0 <= -2000.0)
		tmp = x * 7.787037037037037;
	elseif (t_0 <= 5e-5)
		tmp = 0.13793103448275862;
	else
		tmp = x * 7.787037037037037;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x * N[(841.0 / 108.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2000.0], N[(x * 7.787037037037037), $MachinePrecision], If[LessEqual[t$95$0, 5e-5], 0.13793103448275862, N[(x * 7.787037037037037), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x) < -2e3 or 5.00000000000000024e-5 < (*.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. *-lowering-*.f64 98.8

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

   5. Simplified 98.8%

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

   if -2e3 < (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x) < 5.00000000000000024e-5

   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 98.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{841}{108} \leq -2000:\\ \;\;\;\;x \cdot 7.787037037037037\\ \mathbf{elif}\;x \cdot \frac{841}{108} \leq 5 \cdot 10^{-5}:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;x \cdot 7.787037037037037\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 4: 50.8% 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 46.1%

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

Reproduce

herbie shell --seed 2024198 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))