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

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 5

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: 100.0% 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, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. sub-neg N/A

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

   2. distribute-rgt-in N/A

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

   3. +-commutative N/A

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

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

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

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

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

   6. metadata-eval N/A

      \[\leadsto y \cdot -200 + x \cdot 200 \]

   7. metadata-eval N/A

      \[\leadsto y \cdot \left(200 \cdot -1\right) + x \cdot 200 \]

   8. accelerator-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, \color{blue}{\left(200 \cdot -1\right)}, \left(x \cdot 200\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{fma.f64}\left(y, -200, \left(x \cdot 200\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{fma.f64}\left(y, -200, \left(200 \cdot x\right)\right) \]

   11. *-lowering-*.f64 100.0%

       \[\leadsto \mathsf{fma.f64}\left(y, -200, \mathsf{*.f64}\left(200, x\right)\right) \]

4. Applied egg-rr 100.0%

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

Alternative 2: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+71} \lor \neg \left(y \leq 1.02 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8.2e+71) (not (<= y 1.02e-13))) (* y -200.0) (* 200.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8.2e+71) || !(y <= 1.02e-13)) {
		tmp = y * -200.0;
	} 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 <= (-8.2d+71)) .or. (.not. (y <= 1.02d-13))) then
        tmp = y * (-200.0d0)
    else
        tmp = 200.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8.2e+71) || !(y <= 1.02e-13)) {
		tmp = y * -200.0;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8.2e+71) or not (y <= 1.02e-13):
		tmp = y * -200.0
	else:
		tmp = 200.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8.2e+71) || !(y <= 1.02e-13))
		tmp = Float64(y * -200.0);
	else
		tmp = Float64(200.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8.2e+71) || ~((y <= 1.02e-13)))
		tmp = y * -200.0;
	else
		tmp = 200.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8.2e+71], N[Not[LessEqual[y, 1.02e-13]], $MachinePrecision]], N[(y * -200.0), $MachinePrecision], N[(200.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000004e71 or 1.0199999999999999e-13 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 82.4%

         \[\leadsto \mathsf{*.f64}\left(-200, \color{blue}{y}\right) \]

   5. Simplified 82.4%

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

   if -8.2000000000000004e71 < y < 1.0199999999999999e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 79.7%

         \[\leadsto \mathsf{*.f64}\left(200, \color{blue}{x}\right) \]

   5. Simplified 79.7%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+71} \lor \neg \left(y \leq 1.02 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot -200\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. sub-neg N/A

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

   2. distribute-rgt-in N/A

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

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

      \[\leadsto x \cdot 200 + \left(\mathsf{neg}\left(y \cdot 200\right)\right) \]

   4. unsub-neg N/A

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

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot 200\right), \color{blue}{\left(y \cdot 200\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(200 \cdot x\right), \left(\color{blue}{y} \cdot 200\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(200, x\right), \left(\color{blue}{y} \cdot 200\right)\right) \]

   8. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(200, x\right), \mathsf{*.f64}\left(y, \color{blue}{200}\right)\right) \]

4. Applied egg-rr 100.0%

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

Alternative 4: 100.0% 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 99.9%

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

Alternative 5: 50.7% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0

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

   1. *-lowering-*.f64 48.9%

      \[\leadsto \mathsf{*.f64}\left(-200, \color{blue}{y}\right) \]

5. Simplified 48.9%

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

6. Final simplification 48.9%

   \[\leadsto y \cdot -200 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))