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

Percentage Accurate: 100.0% → 100.0%

Time: 2.9s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 99.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ x - 0.005 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (* 0.005 y)))

C

double code(double x, double y) {
	return x - (0.005 * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (0.005d0 * y)
end function

Java

public static double code(double x, double y) {
	return x - (0.005 * y);
}

Python

def code(x, y):
	return x - (0.005 * y)

Julia

function code(x, y)
	return Float64(x - Float64(0.005 * y))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (0.005 * y);
end

Wolfram

code[x_, y_] := N[(x - N[(0.005 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto x - \color{blue}{\frac{1}{200} \cdot y} \]
4. Step-by-step derivation

   1. lower-*.f64 99.9

      \[\leadsto x - \color{blue}{0.005 \cdot y} \]

5. Applied rewrites 99.9%

   \[\leadsto x - \color{blue}{0.005 \cdot y} \]
6. Add Preprocessing

Alternative 3: 99.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-0.005, y, x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma -0.005 y x))

C

double code(double x, double y) {
	return fma(-0.005, y, x);
}

Julia

function code(x, y)
	return fma(-0.005, y, x)
end

Wolfram

code[x_, y_] := N[(-0.005 * y + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x - \frac{1}{200} \cdot y} \]
4. Step-by-step derivation

   1. metadata-eval N/A

      \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{200}\right)\right)} \cdot y \]

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

      \[\leadsto \color{blue}{x + \frac{-1}{200} \cdot y} \]

   3. +-commutative N/A

      \[\leadsto \color{blue}{\frac{-1}{200} \cdot y + x} \]

   4. lower-fma.f64 99.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.005, y, x\right)} \]

5. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-0.005, y, x\right)} \]
6. Add Preprocessing

Alternative 4: 51.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ -0.005 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -0.005 y))

C

double code(double x, double y) {
	return -0.005 * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-0.005d0) * y
end function

Java

public static double code(double x, double y) {
	return -0.005 * y;
}

Python

def code(x, y):
	return -0.005 * y

Julia

function code(x, y)
	return Float64(-0.005 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = -0.005 * y;
end

Wolfram

code[x_, y_] := N[(-0.005 * y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1}{200} \cdot y} \]
4. Step-by-step derivation

   1. lower-*.f64 56.0

      \[\leadsto \color{blue}{-0.005 \cdot y} \]

5. Applied rewrites 56.0%

   \[\leadsto \color{blue}{-0.005 \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024339 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))