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

Percentage Accurate: 99.7% → 99.7%

Time: 1.5s

Alternatives: 5

Speedup: 1.5×

Specification

Math

\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* (* (- x (/ 16.0 116.0)) 3.0) y))

C

double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function

Java

public static double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Python

def code(x, y):
	return ((x - (16.0 / 116.0)) * 3.0) * y

Julia

function code(x, y)
	return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x - (16.0 / 116.0)) * 3.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((x - ((16) / (116))) * (3)) * y
END code

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* (* (- x (/ 16.0 116.0)) 3.0) y))

C

double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function

Java

public static double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Python

def code(x, y):
	return ((x - (16.0 / 116.0)) * 3.0) * y

Julia

function code(x, y)
	return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x - (16.0 / 116.0)) * 3.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((x - ((16) / (116))) * (3)) * y
END code

Alternative 1: 99.7% accurate, 1.5× speedup

Math

\[\mathsf{fma}\left(3, x, -0.41379310344827586\right) \cdot y \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* (fma 3.0 x -0.41379310344827586) y))

C

double code(double x, double y) {
	return fma(3.0, x, -0.41379310344827586) * y;
}

Julia

function code(x, y)
	return Float64(fma(3.0, x, -0.41379310344827586) * y)
end

Wolfram

code[x_, y_] := N[(N[(3.0 * x + -0.41379310344827586), $MachinePrecision] * y), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(((3) * x) + (-413793103448275856326432631249190308153629302978515625e-54)) * y
END code

Derivation

1. Initial program 99.7%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Step-by-step derivation

3. Applied rewrites 99.7%

   \[\leadsto \mathsf{fma}\left(3, x, -0.41379310344827586\right) \cdot y \]
4. Add Preprocessing

Alternative 2: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := x - \frac{16}{116}\\ \mathbf{if}\;t\_0 \leq -500:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t\_0 \leq -0.1:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(3 \cdot x\right) \cdot y\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- x (/ 16.0 116.0))))
  (if (<= t_0 -500.0)
    (* 3.0 (* x y))
    (if (<= t_0 -0.1) (* -0.41379310344827586 y) (* (* 3.0 x) y)))))

C

double code(double x, double y) {
	double t_0 = x - (16.0 / 116.0);
	double tmp;
	if (t_0 <= -500.0) {
		tmp = 3.0 * (x * y);
	} else if (t_0 <= -0.1) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = (3.0 * x) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x - (16.0d0 / 116.0d0)
    if (t_0 <= (-500.0d0)) then
        tmp = 3.0d0 * (x * y)
    else if (t_0 <= (-0.1d0)) then
        tmp = (-0.41379310344827586d0) * y
    else
        tmp = (3.0d0 * x) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (16.0 / 116.0);
	double tmp;
	if (t_0 <= -500.0) {
		tmp = 3.0 * (x * y);
	} else if (t_0 <= -0.1) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = (3.0 * x) * y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (16.0 / 116.0)
	tmp = 0
	if t_0 <= -500.0:
		tmp = 3.0 * (x * y)
	elif t_0 <= -0.1:
		tmp = -0.41379310344827586 * y
	else:
		tmp = (3.0 * x) * y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(16.0 / 116.0))
	tmp = 0.0
	if (t_0 <= -500.0)
		tmp = Float64(3.0 * Float64(x * y));
	elseif (t_0 <= -0.1)
		tmp = Float64(-0.41379310344827586 * y);
	else
		tmp = Float64(Float64(3.0 * x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (16.0 / 116.0);
	tmp = 0.0;
	if (t_0 <= -500.0)
		tmp = 3.0 * (x * y);
	elseif (t_0 <= -0.1)
		tmp = -0.41379310344827586 * y;
	else
		tmp = (3.0 * x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -500.0], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -0.1], N[(-0.41379310344827586 * y), $MachinePrecision], N[(N[(3.0 * x), $MachinePrecision] * y), $MachinePrecision]]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET t_0 = (x - ((16) / (116))) IN
		LET tmp_1 = IF (t_0 <= (-1000000000000000055511151231257827021181583404541015625e-55)) THEN ((-413793103448275856326432631249190308153629302978515625e-54) * y) ELSE (((3) * x) * y) ENDIF IN
		LET tmp = IF (t_0 <= (-500)) THEN ((3) * (x * y)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) < -500

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

   2. Taylor expanded in x around inf

      \[\leadsto 3 \cdot \left(x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 51.2%

      \[\leadsto 3 \cdot \left(x \cdot y\right) \]

   if -500 < (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) < -0.10000000000000001

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{-12}{29} \cdot y \]
   3. Step-by-step derivation

   4. Applied rewrites 50.6%

      \[\leadsto -0.41379310344827586 \cdot y \]

   if -0.10000000000000001 < (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64)))

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

   2. Taylor expanded in x around inf

      \[\leadsto \left(3 \cdot x\right) \cdot y \]
   3. Step-by-step derivation

   4. Applied rewrites 51.2%

      \[\leadsto \left(3 \cdot x\right) \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := x - \frac{16}{116}\\ \mathbf{if}\;t\_0 \leq -500:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t\_0 \leq -0.1:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 3\right)\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- x (/ 16.0 116.0))))
  (if (<= t_0 -500.0)
    (* 3.0 (* x y))
    (if (<= t_0 -0.1) (* -0.41379310344827586 y) (* x (* y 3.0))))))

C

double code(double x, double y) {
	double t_0 = x - (16.0 / 116.0);
	double tmp;
	if (t_0 <= -500.0) {
		tmp = 3.0 * (x * y);
	} else if (t_0 <= -0.1) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = x * (y * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x - (16.0d0 / 116.0d0)
    if (t_0 <= (-500.0d0)) then
        tmp = 3.0d0 * (x * y)
    else if (t_0 <= (-0.1d0)) then
        tmp = (-0.41379310344827586d0) * y
    else
        tmp = x * (y * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (16.0 / 116.0);
	double tmp;
	if (t_0 <= -500.0) {
		tmp = 3.0 * (x * y);
	} else if (t_0 <= -0.1) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = x * (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (16.0 / 116.0)
	tmp = 0
	if t_0 <= -500.0:
		tmp = 3.0 * (x * y)
	elif t_0 <= -0.1:
		tmp = -0.41379310344827586 * y
	else:
		tmp = x * (y * 3.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(16.0 / 116.0))
	tmp = 0.0
	if (t_0 <= -500.0)
		tmp = Float64(3.0 * Float64(x * y));
	elseif (t_0 <= -0.1)
		tmp = Float64(-0.41379310344827586 * y);
	else
		tmp = Float64(x * Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (16.0 / 116.0);
	tmp = 0.0;
	if (t_0 <= -500.0)
		tmp = 3.0 * (x * y);
	elseif (t_0 <= -0.1)
		tmp = -0.41379310344827586 * y;
	else
		tmp = x * (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -500.0], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -0.1], N[(-0.41379310344827586 * y), $MachinePrecision], N[(x * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET t_0 = (x - ((16) / (116))) IN
		LET tmp_1 = IF (t_0 <= (-1000000000000000055511151231257827021181583404541015625e-55)) THEN ((-413793103448275856326432631249190308153629302978515625e-54) * y) ELSE (x * (y * (3))) ENDIF IN
		LET tmp = IF (t_0 <= (-500)) THEN ((3) * (x * y)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) < -500

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

   2. Taylor expanded in x around inf

      \[\leadsto 3 \cdot \left(x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 51.2%

      \[\leadsto 3 \cdot \left(x \cdot y\right) \]

   if -500 < (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) < -0.10000000000000001

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{-12}{29} \cdot y \]
   3. Step-by-step derivation

   4. Applied rewrites 50.6%

      \[\leadsto -0.41379310344827586 \cdot y \]

   if -0.10000000000000001 < (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64)))

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

   2. Taylor expanded in x around inf

      \[\leadsto 3 \cdot \left(x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 51.2%

      \[\leadsto 3 \cdot \left(x \cdot y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 51.2%

      \[\leadsto x \cdot \left(y \cdot 3\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := x - \frac{16}{116}\\ t_1 := 3 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;t\_0 \leq -500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -0.1:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- x (/ 16.0 116.0))) (t_1 (* 3.0 (* x y))))
  (if (<= t_0 -500.0)
    t_1
    (if (<= t_0 -0.1) (* -0.41379310344827586 y) t_1))))

C

double code(double x, double y) {
	double t_0 = x - (16.0 / 116.0);
	double t_1 = 3.0 * (x * y);
	double tmp;
	if (t_0 <= -500.0) {
		tmp = t_1;
	} else if (t_0 <= -0.1) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x - (16.0d0 / 116.0d0)
    t_1 = 3.0d0 * (x * y)
    if (t_0 <= (-500.0d0)) then
        tmp = t_1
    else if (t_0 <= (-0.1d0)) then
        tmp = (-0.41379310344827586d0) * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (16.0 / 116.0);
	double t_1 = 3.0 * (x * y);
	double tmp;
	if (t_0 <= -500.0) {
		tmp = t_1;
	} else if (t_0 <= -0.1) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (16.0 / 116.0)
	t_1 = 3.0 * (x * y)
	tmp = 0
	if t_0 <= -500.0:
		tmp = t_1
	elif t_0 <= -0.1:
		tmp = -0.41379310344827586 * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(16.0 / 116.0))
	t_1 = Float64(3.0 * Float64(x * y))
	tmp = 0.0
	if (t_0 <= -500.0)
		tmp = t_1;
	elseif (t_0 <= -0.1)
		tmp = Float64(-0.41379310344827586 * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (16.0 / 116.0);
	t_1 = 3.0 * (x * y);
	tmp = 0.0;
	if (t_0 <= -500.0)
		tmp = t_1;
	elseif (t_0 <= -0.1)
		tmp = -0.41379310344827586 * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -500.0], t$95$1, If[LessEqual[t$95$0, -0.1], N[(-0.41379310344827586 * y), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET t_0 = (x - ((16) / (116))) IN
		LET t_1 = ((3) * (x * y)) IN
			LET tmp_1 = IF (t_0 <= (-1000000000000000055511151231257827021181583404541015625e-55)) THEN ((-413793103448275856326432631249190308153629302978515625e-54) * y) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (-500)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) < -500 or -0.10000000000000001 < (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64)))

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

   2. Taylor expanded in x around inf

      \[\leadsto 3 \cdot \left(x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 51.2%

      \[\leadsto 3 \cdot \left(x \cdot y\right) \]

   if -500 < (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) < -0.10000000000000001

   1. Initial program 99.7%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{-12}{29} \cdot y \]
   3. Step-by-step derivation

   4. Applied rewrites 50.6%

      \[\leadsto -0.41379310344827586 \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 50.6% accurate, 3.4× speedup

Math

\[-0.41379310344827586 \cdot y \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* -0.41379310344827586 y))

C

double code(double x, double y) {
	return -0.41379310344827586 * y;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-0.41379310344827586d0) * y
end function

Java

public static double code(double x, double y) {
	return -0.41379310344827586 * y;
}

Python

def code(x, y):
	return -0.41379310344827586 * y

Julia

function code(x, y)
	return Float64(-0.41379310344827586 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = -0.41379310344827586 * y;
end

Wolfram

code[x_, y_] := N[(-0.41379310344827586 * y), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(-413793103448275856326432631249190308153629302978515625e-54) * y
END code

Derivation

1. Initial program 99.7%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

2. Taylor expanded in x around 0

   \[\leadsto \frac{-12}{29} \cdot y \]
3. Step-by-step derivation

4. Applied rewrites 50.6%

   \[\leadsto -0.41379310344827586 \cdot y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64
  (* (* (- x (/ 16.0 116.0)) 3.0) y))