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

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

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. Final simplification 100.0%

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

Alternative 2: 74.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{+18} \lor \neg \left(x \leq -2.3 \cdot 10^{-30}\right) \land x \leq 7.4 \cdot 10^{-9}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7e+54)
   x
   (if (or (<= x -1.56e+18) (and (not (<= x -2.3e-30)) (<= x 7.4e-9)))
     (* y -0.005)
     x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7e+54) {
		tmp = x;
	} else if ((x <= -1.56e+18) || (!(x <= -2.3e-30) && (x <= 7.4e-9))) {
		tmp = y * -0.005;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-7d+54)) then
        tmp = x
    else if ((x <= (-1.56d+18)) .or. (.not. (x <= (-2.3d-30))) .and. (x <= 7.4d-9)) then
        tmp = y * (-0.005d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -7e+54) {
		tmp = x;
	} else if ((x <= -1.56e+18) || (!(x <= -2.3e-30) && (x <= 7.4e-9))) {
		tmp = y * -0.005;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7e+54:
		tmp = x
	elif (x <= -1.56e+18) or (not (x <= -2.3e-30) and (x <= 7.4e-9)):
		tmp = y * -0.005
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7e+54)
		tmp = x;
	elseif ((x <= -1.56e+18) || (!(x <= -2.3e-30) && (x <= 7.4e-9)))
		tmp = Float64(y * -0.005);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7e+54)
		tmp = x;
	elseif ((x <= -1.56e+18) || (~((x <= -2.3e-30)) && (x <= 7.4e-9)))
		tmp = y * -0.005;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7e+54], x, If[Or[LessEqual[x, -1.56e+18], And[N[Not[LessEqual[x, -2.3e-30]], $MachinePrecision], LessEqual[x, 7.4e-9]]], N[(y * -0.005), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.0000000000000002e54 or -1.56e18 < x < -2.29999999999999984e-30 or 7.4e-9 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.8%

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

   if -7.0000000000000002e54 < x < -1.56e18 or -2.29999999999999984e-30 < x < 7.4e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.6%

      \[\leadsto \color{blue}{-0.005 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{+18} \lor \neg \left(x \leq -2.3 \cdot 10^{-30}\right) \land x \leq 7.4 \cdot 10^{-9}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 2.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.0)

C

double code(double x, double y) {
	return 0.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0
end function

Java

public static double code(double x, double y) {
	return 0.0;
}

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0;
end

Wolfram

code[x_, y_] := 0.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 51.3%

   \[\leadsto \color{blue}{-0.005 \cdot y} \]
4. Step-by-step derivation

   1. expm1-log1p-u 31.7%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-0.005 \cdot y\right)\right)} \]

   2. expm1-udef 21.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-0.005 \cdot y\right)} - 1} \]

   3. sub-neg 21.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-0.005 \cdot y\right)} + \left(-1\right)} \]

   4. log1p-udef 21.4%

      \[\leadsto e^{\color{blue}{\log \left(1 + -0.005 \cdot y\right)}} + \left(-1\right) \]

   5. rem-exp-log 41.0%

      \[\leadsto \color{blue}{\left(1 + -0.005 \cdot y\right)} + \left(-1\right) \]

   6. +-commutative 41.0%

      \[\leadsto \color{blue}{\left(-0.005 \cdot y + 1\right)} + \left(-1\right) \]

   7. metadata-eval 41.0%

      \[\leadsto \left(-0.005 \cdot y + 1\right) + \color{blue}{-1} \]

5. Applied egg-rr 41.0%

   \[\leadsto \color{blue}{\left(-0.005 \cdot y + 1\right) + -1} \]

7. Simplified 2.6%

   \[\leadsto \color{blue}{0} \]

8. Final simplification 2.6%

   \[\leadsto 0 \]
9. Add Preprocessing

Alternative 4: 51.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 49.6%

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

4. Final simplification 49.6%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))