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

Percentage Accurate: 100.0% → 100.0%

Time: 1.0s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\frac{x + 16}{116} \]

FPCore

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

C

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

Fortran

real(8) function code(x)
use fmin_fmax_functions
    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]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	(x + (16)) / (116)
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\frac{x + 16}{116} \]

FPCore

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

C

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

Fortran

real(8) function code(x)
use fmin_fmax_functions
    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]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	(x + (16)) / (116)
END code

Alternative 1: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	((86206896551724136734673464843581314198672771453857421875e-58) * x) + (137931034482758618775477543749730102717876434326171875e-54)
END code

Derivation

1. Initial program 100.0%

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

3. Applied rewrites 99.9%

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

Alternative 2: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x + 16 \leq -0.5:\\ \;\;\;\;\frac{x}{116}\\ \mathbf{elif}\;x + 16 \leq 20:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{116}\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (if (<= (+ x 16.0) -0.5)
  (/ x 116.0)
  (if (<= (+ x 16.0) 20.0) 0.13793103448275862 (/ x 116.0))))

C

double code(double x) {
	double tmp;
	if ((x + 16.0) <= -0.5) {
		tmp = x / 116.0;
	} else if ((x + 16.0) <= 20.0) {
		tmp = 0.13793103448275862;
	} else {
		tmp = x / 116.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x + 16.0d0) <= (-0.5d0)) then
        tmp = x / 116.0d0
    else if ((x + 16.0d0) <= 20.0d0) then
        tmp = 0.13793103448275862d0
    else
        tmp = x / 116.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x + 16.0) <= -0.5) {
		tmp = x / 116.0;
	} else if ((x + 16.0) <= 20.0) {
		tmp = 0.13793103448275862;
	} else {
		tmp = x / 116.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x + 16.0) <= -0.5:
		tmp = x / 116.0
	elif (x + 16.0) <= 20.0:
		tmp = 0.13793103448275862
	else:
		tmp = x / 116.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(x + 16.0) <= -0.5)
		tmp = Float64(x / 116.0);
	elseif (Float64(x + 16.0) <= 20.0)
		tmp = 0.13793103448275862;
	else
		tmp = Float64(x / 116.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x + 16.0) <= -0.5)
		tmp = x / 116.0;
	elseif ((x + 16.0) <= 20.0)
		tmp = 0.13793103448275862;
	else
		tmp = x / 116.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(x + 16.0), $MachinePrecision], -0.5], N[(x / 116.0), $MachinePrecision], If[LessEqual[N[(x + 16.0), $MachinePrecision], 20.0], 0.13793103448275862, N[(x / 116.0), $MachinePrecision]]]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	LET tmp_1 = IF ((x + (16)) <= (20)) THEN (137931034482758618775477543749730102717876434326171875e-54) ELSE (x / (116)) ENDIF IN
	LET tmp = IF ((x + (16)) <= (-5e-1)) THEN (x / (116)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 x #s(literal 16 binary64)) < -0.5 or 20 < (+.f64 x #s(literal 16 binary64))

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.4%

      \[\leadsto 0.008620689655172414 \cdot x \]
   5. Step-by-step derivation

   6. Applied rewrites 50.4%

      \[\leadsto \frac{x}{116} \]

   if -0.5 < (+.f64 x #s(literal 16 binary64)) < 20

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 51.2%

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

Alternative 3: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x + 16 \leq -0.5:\\ \;\;\;\;0.008620689655172414 \cdot x\\ \mathbf{elif}\;x + 16 \leq 20:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;0.008620689655172414 \cdot x\\ \end{array} \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  (if (<= (+ x 16.0) -0.5)
  (* 0.008620689655172414 x)
  (if (<= (+ x 16.0) 20.0)
    0.13793103448275862
    (* 0.008620689655172414 x))))

C

double code(double x) {
	double tmp;
	if ((x + 16.0) <= -0.5) {
		tmp = 0.008620689655172414 * x;
	} else if ((x + 16.0) <= 20.0) {
		tmp = 0.13793103448275862;
	} else {
		tmp = 0.008620689655172414 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x + 16.0d0) <= (-0.5d0)) then
        tmp = 0.008620689655172414d0 * x
    else if ((x + 16.0d0) <= 20.0d0) then
        tmp = 0.13793103448275862d0
    else
        tmp = 0.008620689655172414d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x + 16.0) <= -0.5) {
		tmp = 0.008620689655172414 * x;
	} else if ((x + 16.0) <= 20.0) {
		tmp = 0.13793103448275862;
	} else {
		tmp = 0.008620689655172414 * x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x + 16.0) <= -0.5:
		tmp = 0.008620689655172414 * x
	elif (x + 16.0) <= 20.0:
		tmp = 0.13793103448275862
	else:
		tmp = 0.008620689655172414 * x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(x + 16.0) <= -0.5)
		tmp = Float64(0.008620689655172414 * x);
	elseif (Float64(x + 16.0) <= 20.0)
		tmp = 0.13793103448275862;
	else
		tmp = Float64(0.008620689655172414 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x + 16.0) <= -0.5)
		tmp = 0.008620689655172414 * x;
	elseif ((x + 16.0) <= 20.0)
		tmp = 0.13793103448275862;
	else
		tmp = 0.008620689655172414 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(x + 16.0), $MachinePrecision], -0.5], N[(0.008620689655172414 * x), $MachinePrecision], If[LessEqual[N[(x + 16.0), $MachinePrecision], 20.0], 0.13793103448275862, N[(0.008620689655172414 * x), $MachinePrecision]]]

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	LET tmp_1 = IF ((x + (16)) <= (20)) THEN (137931034482758618775477543749730102717876434326171875e-54) ELSE ((86206896551724136734673464843581314198672771453857421875e-58) * x) ENDIF IN
	LET tmp = IF ((x + (16)) <= (-5e-1)) THEN ((86206896551724136734673464843581314198672771453857421875e-58) * x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 x #s(literal 16 binary64)) < -0.5 or 20 < (+.f64 x #s(literal 16 binary64))

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.4%

      \[\leadsto 0.008620689655172414 \cdot x \]

   if -0.5 < (+.f64 x #s(literal 16 binary64)) < 20

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 51.2%

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

Alternative 4: 51.2% accurate, 7.4× speedup

Math

\[0.13793103448275862 \]

FPCore

(FPCore (x)
  :precision binary64
  :pre TRUE
  0.13793103448275862)

C

double code(double x) {
	return 0.13793103448275862;
}

Fortran

real(8) function code(x)
use fmin_fmax_functions
    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

ReFlow

f(x):
	x in [-inf, +inf]
code: THEORY
BEGIN
f(x: real): real =
	137931034482758618775477543749730102717876434326171875e-54
END code

Derivation

1. Initial program 100.0%

   \[\frac{x + 16}{116} \]

2. Taylor expanded in x around 0

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

4. Applied rewrites 51.2%

   \[\leadsto 0.13793103448275862 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, B"
  :precision binary64
  (/ (+ x 16.0) 116.0))