Data.Colour.CIE:cieLABView from colour-2.3.3, C

Percentage Accurate: 99.9% → 100.0%

Time: 3.4s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 200, y \cdot -200\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x 200.0 (* y -200.0)))

C

double code(double x, double y) {
	return fma(x, 200.0, (y * -200.0));
}

Julia

function code(x, y)
	return fma(x, 200.0, Float64(y * -200.0))
end

Wolfram

code[x_, y_] := N[(x * 200.0 + N[(y * -200.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

4. Applied rewrites 52.5%

   \[\leadsto 200 \cdot \color{blue}{\mathsf{fma}\left(\sqrt{-y}, \sqrt{-y}, x\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{200 \cdot \mathsf{fma}\left(\sqrt{-y}, \sqrt{-y}, x\right)} \]

   2. lift-fma.f64 N/A

      \[\leadsto 200 \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y} + x\right)} \]

   3. lift-sqrt.f64 N/A

      \[\leadsto 200 \cdot \left(\color{blue}{\sqrt{-y}} \cdot \sqrt{-y} + x\right) \]

   4. lift-sqrt.f64 N/A

      \[\leadsto 200 \cdot \left(\sqrt{-y} \cdot \color{blue}{\sqrt{-y}} + x\right) \]

   5. rem-square-sqrt N/A

      \[\leadsto 200 \cdot \left(\color{blue}{\left(-y\right)} + x\right) \]

   6. +-commutative N/A

      \[\leadsto 200 \cdot \color{blue}{\left(x + \left(-y\right)\right)} \]

   7. distribute-rgt-in N/A

      \[\leadsto \color{blue}{x \cdot 200 + \left(-y\right) \cdot 200} \]

   8. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 200, \left(-y\right) \cdot 200\right)} \]

   9. lift-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(x, 200, \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot 200\right) \]

   10. distribute-lft-neg-out N/A

       \[\leadsto \mathsf{fma}\left(x, 200, \color{blue}{\mathsf{neg}\left(y \cdot 200\right)}\right) \]

   11. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{fma}\left(x, 200, \color{blue}{y \cdot \left(\mathsf{neg}\left(200\right)\right)}\right) \]

   12. remove-double-neg N/A

       \[\leadsto \mathsf{fma}\left(x, 200, \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)} \cdot \left(\mathsf{neg}\left(200\right)\right)\right) \]

   13. lift-neg.f64 N/A

       \[\leadsto \mathsf{fma}\left(x, 200, \left(\mathsf{neg}\left(\color{blue}{\left(-y\right)}\right)\right) \cdot \left(\mathsf{neg}\left(200\right)\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(x, 200, \left(\mathsf{neg}\left(\left(-y\right)\right)\right) \cdot \color{blue}{-200}\right) \]

   15. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(x, 200, \color{blue}{\left(\mathsf{neg}\left(\left(-y\right)\right)\right) \cdot -200}\right) \]

   16. lift-neg.f64 N/A

       \[\leadsto \mathsf{fma}\left(x, 200, \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \cdot -200\right) \]

   17. remove-double-neg 100.0

       \[\leadsto \mathsf{fma}\left(x, 200, \color{blue}{y} \cdot -200\right) \]

6. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 200, y \cdot -200\right)} \]
7. Add Preprocessing

Alternative 2: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-43} \lor \neg \left(y \leq 8 \cdot 10^{-38}\right):\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.75e-43) (not (<= y 8e-38))) (* -200.0 y) (* 200.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.75e-43) || !(y <= 8e-38)) {
		tmp = -200.0 * y;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.75d-43)) .or. (.not. (y <= 8d-38))) then
        tmp = (-200.0d0) * y
    else
        tmp = 200.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.75e-43) || !(y <= 8e-38)) {
		tmp = -200.0 * y;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.75e-43) or not (y <= 8e-38):
		tmp = -200.0 * y
	else:
		tmp = 200.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.75e-43) || !(y <= 8e-38))
		tmp = Float64(-200.0 * y);
	else
		tmp = Float64(200.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.75e-43) || ~((y <= 8e-38)))
		tmp = -200.0 * y;
	else
		tmp = 200.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.75e-43], N[Not[LessEqual[y, 8e-38]], $MachinePrecision]], N[(-200.0 * y), $MachinePrecision], N[(200.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.74999999999999999e-43 or 7.9999999999999997e-38 < y

   1. Initial program 100.0%

      \[200 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-200 \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 75.9

         \[\leadsto \color{blue}{-200 \cdot y} \]

   5. Applied rewrites 75.9%

      \[\leadsto \color{blue}{-200 \cdot y} \]

   if -1.74999999999999999e-43 < y < 7.9999999999999997e-38

   1. Initial program 99.9%

      \[200 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{200 \cdot x} \]
   4. Step-by-step derivation

      1. lower-*.f64 81.6

         \[\leadsto \color{blue}{200 \cdot x} \]

   5. Applied rewrites 81.6%

      \[\leadsto \color{blue}{200 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-43} \lor \neg \left(y \leq 8 \cdot 10^{-38}\right):\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 4: 52.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ -200 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -200.0 y))

C

double code(double x, double y) {
	return -200.0 * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-200.0d0) * y
end function

Java

public static double code(double x, double y) {
	return -200.0 * y;
}

Python

def code(x, y):
	return -200.0 * y

Julia

function code(x, y)
	return Float64(-200.0 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = -200.0 * y;
end

Wolfram

code[x_, y_] := N[(-200.0 * y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-200 \cdot y} \]
4. Step-by-step derivation

   1. lower-*.f64 51.9

      \[\leadsto \color{blue}{-200 \cdot y} \]

5. Applied rewrites 51.9%

   \[\leadsto \color{blue}{-200 \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024326 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))