Data.Colour.CIE:cieLAB from colour-2.3.3, B

Percentage Accurate: 100.0% → 100.0%

Time: 1.9s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x + 16}{116} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (+ x 16.0) 116.0))

C

double code(double x) {
	return (x + 16.0) / 116.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x + 16.0d0) / 116.0d0
end function

Java

public static double code(double x) {
	return (x + 16.0) / 116.0;
}

Python

def code(x):
	return (x + 16.0) / 116.0

Julia

function code(x)
	return Float64(Float64(x + 16.0) / 116.0)
end

MATLAB

function tmp = code(x)
	tmp = (x + 16.0) / 116.0;
end

Wolfram

code[x_] := N[(N[(x + 16.0), $MachinePrecision] / 116.0), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + 16}{116} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (+ x 16.0) 116.0))

C

double code(double x) {
	return (x + 16.0) / 116.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x + 16.0d0) / 116.0d0
end function

Java

public static double code(double x) {
	return (x + 16.0) / 116.0;
}

Python

def code(x):
	return (x + 16.0) / 116.0

Julia

function code(x)
	return Float64(Float64(x + 16.0) / 116.0)
end

MATLAB

function tmp = code(x)
	tmp = (x + 16.0) / 116.0;
end

Wolfram

code[x_] := N[(N[(x + 16.0), $MachinePrecision] / 116.0), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + 16}{116} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (+ x 16.0) 116.0))

C

double code(double x) {
	return (x + 16.0) / 116.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x + 16.0d0) / 116.0d0
end function

Java

public static double code(double x) {
	return (x + 16.0) / 116.0;
}

Python

def code(x):
	return (x + 16.0) / 116.0

Julia

function code(x)
	return Float64(Float64(x + 16.0) / 116.0)
end

MATLAB

function tmp = code(x)
	tmp = (x + 16.0) / 116.0;
end

Wolfram

code[x_] := N[(N[(x + 16.0), $MachinePrecision] / 116.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x + 16}{116} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + 16 \leq -20000 \lor \neg \left(x + 16 \leq 40\right):\\ \;\;\;\;0.008620689655172414 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.13793103448275862\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= (+ x 16.0) -20000.0) (not (<= (+ x 16.0) 40.0)))
   (* 0.008620689655172414 x)
   0.13793103448275862))

C

double code(double x) {
	double tmp;
	if (((x + 16.0) <= -20000.0) || !((x + 16.0) <= 40.0)) {
		tmp = 0.008620689655172414 * x;
	} else {
		tmp = 0.13793103448275862;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x + 16.0d0) <= (-20000.0d0)) .or. (.not. ((x + 16.0d0) <= 40.0d0))) then
        tmp = 0.008620689655172414d0 * x
    else
        tmp = 0.13793103448275862d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((x + 16.0) <= -20000.0) || !((x + 16.0) <= 40.0)) {
		tmp = 0.008620689655172414 * x;
	} else {
		tmp = 0.13793103448275862;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((x + 16.0) <= -20000.0) or not ((x + 16.0) <= 40.0):
		tmp = 0.008620689655172414 * x
	else:
		tmp = 0.13793103448275862
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((Float64(x + 16.0) <= -20000.0) || !(Float64(x + 16.0) <= 40.0))
		tmp = Float64(0.008620689655172414 * x);
	else
		tmp = 0.13793103448275862;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x + 16.0) <= -20000.0) || ~(((x + 16.0) <= 40.0)))
		tmp = 0.008620689655172414 * x;
	else
		tmp = 0.13793103448275862;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[N[(x + 16.0), $MachinePrecision], -20000.0], N[Not[LessEqual[N[(x + 16.0), $MachinePrecision], 40.0]], $MachinePrecision]], N[(0.008620689655172414 * x), $MachinePrecision], 0.13793103448275862]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x #s(literal 16 binary64)) < -2e4 or 40 < (+.f64 x #s(literal 16 binary64))

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{116} \cdot x} \]
   4. Step-by-step derivation

      1. lower-*.f64 98.5

         \[\leadsto \color{blue}{0.008620689655172414 \cdot x} \]

   5. Applied rewrites 98.5%

      \[\leadsto \color{blue}{0.008620689655172414 \cdot x} \]

   if -2e4 < (+.f64 x #s(literal 16 binary64)) < 40

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 96.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + 16 \leq -20000 \lor \neg \left(x + 16 \leq 40\right):\\ \;\;\;\;0.008620689655172414 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.13793103448275862\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 0.008620689655172414, 0.13793103448275862\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (fma x 0.008620689655172414 0.13793103448275862))

C

double code(double x) {
	return fma(x, 0.008620689655172414, 0.13793103448275862);
}

Julia

function code(x)
	return fma(x, 0.008620689655172414, 0.13793103448275862)
end

Wolfram

code[x_] := N[(x * 0.008620689655172414 + 0.13793103448275862), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x + 16}{116} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{x + 16}{116}} \]

   2. clear-num N/A

      \[\leadsto \color{blue}{\frac{1}{\frac{116}{x + 16}}} \]

   3. associate-/r/ N/A

      \[\leadsto \color{blue}{\frac{1}{116} \cdot \left(x + 16\right)} \]

   4. lift-+.f64 N/A

      \[\leadsto \frac{1}{116} \cdot \color{blue}{\left(x + 16\right)} \]

   5. distribute-rgt-in N/A

      \[\leadsto \color{blue}{x \cdot \frac{1}{116} + 16 \cdot \frac{1}{116}} \]

   6. metadata-eval N/A

      \[\leadsto x \cdot \frac{1}{116} + 16 \cdot \color{blue}{\frac{1}{116}} \]

   7. metadata-eval N/A

      \[\leadsto x \cdot \frac{1}{116} + \color{blue}{\frac{4}{29}} \]

   8. metadata-eval N/A

      \[\leadsto x \cdot \frac{1}{116} + \color{blue}{\frac{1}{116} \cdot 16} \]

   9. metadata-eval N/A

      \[\leadsto x \cdot \frac{1}{116} + \color{blue}{\frac{1}{116}} \cdot 16 \]

   10. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{1}{116}, \frac{1}{116} \cdot 16\right)} \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{1}{116}}, \frac{1}{116} \cdot 16\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{1}{116}, \color{blue}{\frac{1}{116}} \cdot 16\right) \]

   13. metadata-eval 99.9

       \[\leadsto \mathsf{fma}\left(x, 0.008620689655172414, \color{blue}{0.13793103448275862}\right) \]

4. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.008620689655172414, 0.13793103448275862\right)} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 15.0× 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 100.0%

   \[\frac{x + 16}{116} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 50.4%

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

Reproduce

herbie shell --seed 2024313 
(FPCore (x)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, B"
  :precision binary64
  (/ (+ x 16.0) 116.0))