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

Percentage Accurate: 99.9% → 99.9%

Time: 5.9s

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf 99.8%

   \[\leadsto \color{blue}{x \cdot \left(7.787037037037037 + 0.13793103448275862 \cdot \frac{1}{x}\right)} \]
4. Step-by-step derivation

   1. expm1-log1p-u 72.5%

      \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(7.787037037037037 + 0.13793103448275862 \cdot \frac{1}{x}\right)\right)} \]

   2. expm1-undefine 71.9%

      \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(7.787037037037037 + 0.13793103448275862 \cdot \frac{1}{x}\right)} - 1\right)} \]

   3. un-div-inv 71.9%

      \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left(7.787037037037037 + \color{blue}{\frac{0.13793103448275862}{x}}\right)} - 1\right) \]

5. Applied egg-rr 71.9%

   \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(7.787037037037037 + \frac{0.13793103448275862}{x}\right)} - 1\right)} \]
6. Step-by-step derivation

   1. sub-neg 71.9%

      \[\leadsto x \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(7.787037037037037 + \frac{0.13793103448275862}{x}\right)} + \left(-1\right)\right)} \]

   2. metadata-eval 71.9%

      \[\leadsto x \cdot \left(e^{\mathsf{log1p}\left(7.787037037037037 + \frac{0.13793103448275862}{x}\right)} + \color{blue}{-1}\right) \]

   3. +-commutative 71.9%

      \[\leadsto x \cdot \color{blue}{\left(-1 + e^{\mathsf{log1p}\left(7.787037037037037 + \frac{0.13793103448275862}{x}\right)}\right)} \]

   4. log1p-undefine 71.9%

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

   5. rem-exp-log 99.2%

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

   6. associate-+r+ 99.2%

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

   7. metadata-eval 99.5%

      \[\leadsto x \cdot \left(-1 + \left(\color{blue}{8.787037037037036} + \frac{0.13793103448275862}{x}\right)\right) \]

7. Simplified 99.5%

   \[\leadsto x \cdot \color{blue}{\left(-1 + \left(8.787037037037036 + \frac{0.13793103448275862}{x}\right)\right)} \]
8. Step-by-step derivation

   1. associate-+r+ 99.5%

      \[\leadsto x \cdot \color{blue}{\left(\left(-1 + 8.787037037037036\right) + \frac{0.13793103448275862}{x}\right)} \]

   2. metadata-eval 99.8%

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

   3. +-commutative 99.8%

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

   4. distribute-rgt-in 99.9%

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

   5. fma-define 99.9%

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

   6. *-commutative 99.9%

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

9. Applied egg-rr 99.9%

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

Alternative 2: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 7.787037037037037 \leq -20 \lor \neg \left(x \cdot 7.787037037037037 \leq 10^{-7}\right):\\ \;\;\;\;x \cdot 7.787037037037037\\ \mathbf{else}:\\ \;\;\;\;0.13793103448275862\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= (* x 7.787037037037037) -20.0)
         (not (<= (* x 7.787037037037037) 1e-7)))
   (* x 7.787037037037037)
   0.13793103448275862))

C

double code(double x) {
	double tmp;
	if (((x * 7.787037037037037) <= -20.0) || !((x * 7.787037037037037) <= 1e-7)) {
		tmp = x * 7.787037037037037;
	} else {
		tmp = 0.13793103448275862;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x * 7.787037037037037d0) <= (-20.0d0)) .or. (.not. ((x * 7.787037037037037d0) <= 1d-7))) then
        tmp = x * 7.787037037037037d0
    else
        tmp = 0.13793103448275862d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((x * 7.787037037037037) <= -20.0) || !((x * 7.787037037037037) <= 1e-7)) {
		tmp = x * 7.787037037037037;
	} else {
		tmp = 0.13793103448275862;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((x * 7.787037037037037) <= -20.0) or not ((x * 7.787037037037037) <= 1e-7):
		tmp = x * 7.787037037037037
	else:
		tmp = 0.13793103448275862
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((Float64(x * 7.787037037037037) <= -20.0) || !(Float64(x * 7.787037037037037) <= 1e-7))
		tmp = Float64(x * 7.787037037037037);
	else
		tmp = 0.13793103448275862;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x * 7.787037037037037) <= -20.0) || ~(((x * 7.787037037037037) <= 1e-7)))
		tmp = x * 7.787037037037037;
	else
		tmp = 0.13793103448275862;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[N[(x * 7.787037037037037), $MachinePrecision], -20.0], N[Not[LessEqual[N[(x * 7.787037037037037), $MachinePrecision], 1e-7]], $MachinePrecision]], N[(x * 7.787037037037037), $MachinePrecision], 0.13793103448275862]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 841 binary64) #s(literal 108 binary64)) x) < -20 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. Step-by-step derivation

      1. fma-define 99.8%

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

      2. metadata-eval 99.8%

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

      3. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(7.787037037037037, x, 0.13793103448275862\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{841}{108}}, x, 0.13793103448275862\right) \]

      2. metadata-eval 99.8%

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

      3. fma-define 99.8%

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

      4. metadata-eval 99.8%

         \[\leadsto \color{blue}{7.787037037037037} \cdot x + \frac{4}{29} \]

      5. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 97.2%

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

   if -20 < (*.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 98.0%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 7.787037037037037 \leq -20 \lor \neg \left(x \cdot 7.787037037037037 \leq 10^{-7}\right):\\ \;\;\;\;x \cdot 7.787037037037037\\ \mathbf{else}:\\ \;\;\;\;0.13793103448275862\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-define 99.9%

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

   2. metadata-eval 99.9%

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

   3. metadata-eval 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(7.787037037037037, x, 0.13793103448275862\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. metadata-eval 99.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{841}{108}}, x, 0.13793103448275862\right) \]

   2. metadata-eval 99.9%

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

   3. fma-define 99.9%

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

   4. metadata-eval 99.9%

      \[\leadsto \color{blue}{7.787037037037037} \cdot x + \frac{4}{29} \]

   5. metadata-eval 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

3. Taylor expanded in x around 0 48.1%

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

Reproduce

herbie shell --seed 2024191 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))