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

Percentage Accurate: 99.7% → 99.7%

Time: 9.3s

Alternatives: 6

Speedup: 1.3×

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (* (* (- 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)
    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]

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (* (* (- 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)
    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]

Alternative 1: 99.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(-0.41379310344827586 - x \cdot -3\right) \cdot y \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((-0.41379310344827586d0) - (x * (-3.0d0))) * y
end function

Java

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

Python

def code(x, y):
	return (-0.41379310344827586 - (x * -3.0)) * y

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = (-0.41379310344827586 - (x * -3.0)) * y;
end

Wolfram

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

Derivation

1. Initial program 99.7%

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

3. Taylor expanded in x around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 2: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.135:\\ \;\;\;\;\left(x \cdot 3\right) \cdot y\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.135)
   (* (* x 3.0) y)
   (if (<= x 0.14) (* -0.41379310344827586 y) (* (* y x) 3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.135) {
		tmp = (x * 3.0) * y;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = (y * x) * 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.135d0)) then
        tmp = (x * 3.0d0) * y
    else if (x <= 0.14d0) then
        tmp = (-0.41379310344827586d0) * y
    else
        tmp = (y * x) * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.135) {
		tmp = (x * 3.0) * y;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = (y * x) * 3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.135:
		tmp = (x * 3.0) * y
	elif x <= 0.14:
		tmp = -0.41379310344827586 * y
	else:
		tmp = (y * x) * 3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.135)
		tmp = Float64(Float64(x * 3.0) * y);
	elseif (x <= 0.14)
		tmp = Float64(-0.41379310344827586 * y);
	else
		tmp = Float64(Float64(y * x) * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.135)
		tmp = (x * 3.0) * y;
	elseif (x <= 0.14)
		tmp = -0.41379310344827586 * y;
	else
		tmp = (y * x) * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.135], N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[x, 0.14], N[(-0.41379310344827586 * y), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.13500000000000001

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -0.13500000000000001 < x < 0.14000000000000001

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 0.14000000000000001 < x

   1. Initial program 99.6%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 3: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot 3\right) \cdot y\\ \mathbf{if}\;x \leq -0.135:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* x 3.0) y)))
   (if (<= x -0.135) t_0 (if (<= x 0.14) (* -0.41379310344827586 y) t_0))))

C

double code(double x, double y) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (x <= -0.135) {
		tmp = t_0;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * 3.0d0) * y
    if (x <= (-0.135d0)) then
        tmp = t_0
    else if (x <= 0.14d0) then
        tmp = (-0.41379310344827586d0) * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (x <= -0.135) {
		tmp = t_0;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x * 3.0) * y
	tmp = 0
	if x <= -0.135:
		tmp = t_0
	elif x <= 0.14:
		tmp = -0.41379310344827586 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x * 3.0) * y)
	tmp = 0.0
	if (x <= -0.135)
		tmp = t_0;
	elseif (x <= 0.14)
		tmp = Float64(-0.41379310344827586 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x * 3.0) * y;
	tmp = 0.0;
	if (x <= -0.135)
		tmp = t_0;
	elseif (x <= 0.14)
		tmp = -0.41379310344827586 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[x, -0.135], t$95$0, If[LessEqual[x, 0.14], N[(-0.41379310344827586 * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.13500000000000001 or 0.14000000000000001 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -0.13500000000000001 < x < 0.14000000000000001

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 4: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot 3\right)\\ \mathbf{if}\;x \leq -0.135:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;-0.41379310344827586 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (* y 3.0))))
   (if (<= x -0.135) t_0 (if (<= x 0.14) (* -0.41379310344827586 y) t_0))))

C

double code(double x, double y) {
	double t_0 = x * (y * 3.0);
	double tmp;
	if (x <= -0.135) {
		tmp = t_0;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y * 3.0d0)
    if (x <= (-0.135d0)) then
        tmp = t_0
    else if (x <= 0.14d0) then
        tmp = (-0.41379310344827586d0) * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (y * 3.0);
	double tmp;
	if (x <= -0.135) {
		tmp = t_0;
	} else if (x <= 0.14) {
		tmp = -0.41379310344827586 * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y * 3.0)
	tmp = 0
	if x <= -0.135:
		tmp = t_0
	elif x <= 0.14:
		tmp = -0.41379310344827586 * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y * 3.0))
	tmp = 0.0
	if (x <= -0.135)
		tmp = t_0;
	elseif (x <= 0.14)
		tmp = Float64(-0.41379310344827586 * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (y * 3.0);
	tmp = 0.0;
	if (x <= -0.135)
		tmp = t_0;
	elseif (x <= 0.14)
		tmp = -0.41379310344827586 * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.135], t$95$0, If[LessEqual[x, 0.14], N[(-0.41379310344827586 * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.13500000000000001 or 0.14000000000000001 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -0.13500000000000001 < x < 0.14000000000000001

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 5: 99.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + -0.13793103448275862\right) \cdot y\right) \cdot 3 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* (+ x -0.13793103448275862) y) 3.0))

C

double code(double x, double y) {
	return ((x + -0.13793103448275862) * y) * 3.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + (-0.13793103448275862d0)) * y) * 3.0d0
end function

Java

public static double code(double x, double y) {
	return ((x + -0.13793103448275862) * y) * 3.0;
}

Python

def code(x, y):
	return ((x + -0.13793103448275862) * y) * 3.0

Julia

function code(x, y)
	return Float64(Float64(Float64(x + -0.13793103448275862) * y) * 3.0)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + -0.13793103448275862) * y) * 3.0;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + -0.13793103448275862), $MachinePrecision] * y), $MachinePrecision] * 3.0), $MachinePrecision]

Derivation

1. Initial program 99.7%

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

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ -0.41379310344827586 \cdot y \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    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]

Derivation

1. Initial program 99.7%

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

3. Taylor expanded in x around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Developer target: 99.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(x \cdot 3 - 0.41379310344827586\right) \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * ((x * 3.0d0) - 0.41379310344827586d0)
end function

Java

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

Python

def code(x, y):
	return y * ((x * 3.0) - 0.41379310344827586)

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = y * ((x * 3.0) - 0.41379310344827586);
end

Wolfram

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :alt
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))