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

Percentage Accurate: 99.7% → 99.5%

Time: 6.0s

Alternatives: 6

Speedup: N/A×

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: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-*r* 99.6%

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

   2. *-commutative 99.6%

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

   3. sub-neg 99.6%

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

   4. metadata-eval 99.6%

      \[\leadsto \left(3 \cdot y\right) \cdot \left(x + \left(-\color{blue}{0.13793103448275862}\right)\right) \]

   5. metadata-eval 99.6%

      \[\leadsto \left(3 \cdot y\right) \cdot \left(x + \color{blue}{-0.13793103448275862}\right) \]

   6. +-commutative 99.6%

      \[\leadsto \left(3 \cdot y\right) \cdot \color{blue}{\left(-0.13793103448275862 + x\right)} \]

   7. distribute-lft-in 99.6%

      \[\leadsto \color{blue}{\left(3 \cdot y\right) \cdot -0.13793103448275862 + \left(3 \cdot y\right) \cdot x} \]

   8. fma-define 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3 \cdot y, -0.13793103448275862, \left(3 \cdot y\right) \cdot x\right)} \]

4. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(3 \cdot y, -0.13793103448275862, \left(3 \cdot y\right) \cdot x\right)} \]
5. Add Preprocessing

Alternative 2: 97.7% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.135) (not (<= x 0.14)))
   (* (* 3.0 y) x)
   (* y -0.41379310344827586)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.135) || !(x <= 0.14)) {
		tmp = (3.0 * y) * x;
	} else {
		tmp = y * -0.41379310344827586;
	}
	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)) .or. (.not. (x <= 0.14d0))) then
        tmp = (3.0d0 * y) * x
    else
        tmp = y * (-0.41379310344827586d0)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if (x <= -0.135) or not (x <= 0.14):
		tmp = (3.0 * y) * x
	else:
		tmp = y * -0.41379310344827586
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.135], N[Not[LessEqual[x, 0.14]], $MachinePrecision]], N[(N[(3.0 * y), $MachinePrecision] * x), $MachinePrecision], N[(y * -0.41379310344827586), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.13500000000000001 or 0.14000000000000001 < x

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf 98.2%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 3} \]

      2. associate-*r* 98.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot 3\right)} \]

   5. Simplified 98.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot 3\right)} \]

   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 97.9%

      \[\leadsto \color{blue}{-0.41379310344827586 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.135 \lor \neg \left(x \leq 0.14\right):\\ \;\;\;\;\left(3 \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.41379310344827586\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.6% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.135) (not (<= x 0.14)))
   (* 3.0 (* y x))
   (* y -0.41379310344827586)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.135) || !(x <= 0.14)) {
		tmp = 3.0 * (y * x);
	} else {
		tmp = y * -0.41379310344827586;
	}
	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)) .or. (.not. (x <= 0.14d0))) then
        tmp = 3.0d0 * (y * x)
    else
        tmp = y * (-0.41379310344827586d0)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if (x <= -0.135) or not (x <= 0.14):
		tmp = 3.0 * (y * x)
	else:
		tmp = y * -0.41379310344827586
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.135], N[Not[LessEqual[x, 0.14]], $MachinePrecision]], N[(3.0 * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(y * -0.41379310344827586), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.13500000000000001 or 0.14000000000000001 < x

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf 98.2%

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]

   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 97.9%

      \[\leadsto \color{blue}{-0.41379310344827586 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.135 \lor \neg \left(x \leq 0.14\right):\\ \;\;\;\;3 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.41379310344827586\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-*l* 99.6%

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

   2. sub-neg 99.6%

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

   3. metadata-eval 99.6%

      \[\leadsto \left(x + \left(-\color{blue}{0.13793103448275862}\right)\right) \cdot \left(3 \cdot y\right) \]

   4. metadata-eval 99.6%

      \[\leadsto \left(x + \color{blue}{-0.13793103448275862}\right) \cdot \left(3 \cdot y\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\left(x + -0.13793103448275862\right) \cdot \left(3 \cdot y\right)} \]
4. Add Preprocessing

5. Final simplification 99.6%

   \[\leadsto \left(3 \cdot y\right) \cdot \left(-0.13793103448275862 + x\right) \]
6. Add Preprocessing

Alternative 5: 99.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

3. Taylor expanded in y around 0 99.6%

   \[\leadsto \color{blue}{3 \cdot \left(y \cdot \left(x - 0.13793103448275862\right)\right)} \]
4. Add Preprocessing

Alternative 6: 50.2% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

3. Taylor expanded in x around 0 51.2%

   \[\leadsto \color{blue}{-0.41379310344827586 \cdot y} \]

4. Final simplification 51.2%

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

Developer Target 1: 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 2024139 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (* y (- (* x 3) 20689655172413793/50000000000000000)))

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