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

Percentage Accurate: 99.7% → 99.7%

Time: 5.7s

Alternatives: 4

Speedup: 2.1×

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, 2.1× speedup

Math

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

FPCore

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

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

   \[\leadsto \color{blue}{\left(3 \cdot x - \frac{12}{29}\right)} \cdot y \]
4. Step-by-step derivation

   1. metadata-eval N/A

      \[\leadsto \left(3 \cdot x - \color{blue}{\frac{12}{29} \cdot 1}\right) \cdot y \]

   2. metadata-eval N/A

      \[\leadsto \left(3 \cdot x - \color{blue}{\left(\mathsf{neg}\left(\frac{-12}{29}\right)\right)} \cdot 1\right) \cdot y \]

   3. lft-mult-inverse N/A

      \[\leadsto \left(3 \cdot x - \left(\mathsf{neg}\left(\frac{-12}{29}\right)\right) \cdot \color{blue}{\left(\frac{1}{x} \cdot x\right)}\right) \cdot y \]

   4. fp-cancel-sign-sub-inv N/A

      \[\leadsto \color{blue}{\left(3 \cdot x + \frac{-12}{29} \cdot \left(\frac{1}{x} \cdot x\right)\right)} \cdot y \]

   5. associate-*l* N/A

      \[\leadsto \left(3 \cdot x + \color{blue}{\left(\frac{-12}{29} \cdot \frac{1}{x}\right) \cdot x}\right) \cdot y \]

   6. metadata-eval N/A

      \[\leadsto \left(3 \cdot x + \left(\color{blue}{\left(\mathsf{neg}\left(\frac{12}{29}\right)\right)} \cdot \frac{1}{x}\right) \cdot x\right) \cdot y \]

   7. metadata-eval N/A

      \[\leadsto \left(3 \cdot x + \left(\color{blue}{\frac{-12}{29}} \cdot \frac{1}{x}\right) \cdot x\right) \cdot y \]

   8. associate-*l* N/A

      \[\leadsto \left(3 \cdot x + \color{blue}{\frac{-12}{29} \cdot \left(\frac{1}{x} \cdot x\right)}\right) \cdot y \]

   9. lft-mult-inverse N/A

      \[\leadsto \left(3 \cdot x + \frac{-12}{29} \cdot \color{blue}{1}\right) \cdot y \]

   10. metadata-eval N/A

       \[\leadsto \left(3 \cdot x + \color{blue}{\frac{-12}{29}}\right) \cdot y \]

   11. lower-fma.f64 99.8

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

5. Applied rewrites 99.8%

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

Alternative 2: 97.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-0.14d0)) .or. (.not. (x <= 0.14d0))) then
        tmp = (y * x) * 3.0d0
    else
        tmp = (-0.41379310344827586d0) * y
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.14000000000000001 or 0.14000000000000001 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 97.0

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

   5. Applied rewrites 97.0%

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

   if -0.14000000000000001 < x < 0.14000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 97.4%

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

4. Final simplification 97.2%

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

Alternative 3: 97.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-0.14d0)) .or. (.not. (x <= 0.14d0))) then
        tmp = (y * 3.0d0) * x
    else
        tmp = (-0.41379310344827586d0) * y
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.14000000000000001 or 0.14000000000000001 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(3 \cdot x - \frac{12}{29}\right)} \cdot y \]
   4. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto \left(3 \cdot x - \color{blue}{\frac{12}{29} \cdot 1}\right) \cdot y \]

      2. metadata-eval N/A

         \[\leadsto \left(3 \cdot x - \color{blue}{\left(\mathsf{neg}\left(\frac{-12}{29}\right)\right)} \cdot 1\right) \cdot y \]

      3. lft-mult-inverse N/A

         \[\leadsto \left(3 \cdot x - \left(\mathsf{neg}\left(\frac{-12}{29}\right)\right) \cdot \color{blue}{\left(\frac{1}{x} \cdot x\right)}\right) \cdot y \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\left(3 \cdot x + \frac{-12}{29} \cdot \left(\frac{1}{x} \cdot x\right)\right)} \cdot y \]

      5. associate-*l* N/A

         \[\leadsto \left(3 \cdot x + \color{blue}{\left(\frac{-12}{29} \cdot \frac{1}{x}\right) \cdot x}\right) \cdot y \]

      6. metadata-eval N/A

         \[\leadsto \left(3 \cdot x + \left(\color{blue}{\left(\mathsf{neg}\left(\frac{12}{29}\right)\right)} \cdot \frac{1}{x}\right) \cdot x\right) \cdot y \]

      7. metadata-eval N/A

         \[\leadsto \left(3 \cdot x + \left(\color{blue}{\frac{-12}{29}} \cdot \frac{1}{x}\right) \cdot x\right) \cdot y \]

      8. associate-*l* N/A

         \[\leadsto \left(3 \cdot x + \color{blue}{\frac{-12}{29} \cdot \left(\frac{1}{x} \cdot x\right)}\right) \cdot y \]

      9. lft-mult-inverse N/A

         \[\leadsto \left(3 \cdot x + \frac{-12}{29} \cdot \color{blue}{1}\right) \cdot y \]

      10. metadata-eval N/A

          \[\leadsto \left(3 \cdot x + \color{blue}{\frac{-12}{29}}\right) \cdot y \]

      11. lower-fma.f64 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 96.8

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

   8. Applied rewrites 96.8%

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

   if -0.14000000000000001 < x < 0.14000000000000001

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 97.4%

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

4. Final simplification 97.1%

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

Alternative 4: 50.4% accurate, 4.2× 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

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

5. Applied rewrites 48.7%

   \[\leadsto \color{blue}{-0.41379310344827586} \cdot y \]
6. Add Preprocessing

Developer Target 1: 99.7% accurate, 1.8× 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 2024337 
(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))