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

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -5.5 \cdot 10^{-17} \lor \neg \left(\frac{y}{500} \leq 10^{-40}\right):\\ \;\;\;\;\frac{y}{500}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (/ y 500.0) -5.5e-17) (not (<= (/ y 500.0) 1e-40)))
   (/ y 500.0)
   x))

C

double code(double x, double y) {
	double tmp;
	if (((y / 500.0) <= -5.5e-17) || !((y / 500.0) <= 1e-40)) {
		tmp = y / 500.0;
	} 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 (((y / 500.0d0) <= (-5.5d-17)) .or. (.not. ((y / 500.0d0) <= 1d-40))) then
        tmp = y / 500.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((y / 500.0) <= -5.5e-17) || !((y / 500.0) <= 1e-40)) {
		tmp = y / 500.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((y / 500.0) <= -5.5e-17) or not ((y / 500.0) <= 1e-40):
		tmp = y / 500.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(y / 500.0) <= -5.5e-17) || !(Float64(y / 500.0) <= 1e-40))
		tmp = Float64(y / 500.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((y / 500.0) <= -5.5e-17) || ~(((y / 500.0) <= 1e-40)))
		tmp = y / 500.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(y / 500.0), $MachinePrecision], -5.5e-17], N[Not[LessEqual[N[(y / 500.0), $MachinePrecision], 1e-40]], $MachinePrecision]], N[(y / 500.0), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y #s(literal 500 binary64)) < -5.50000000000000001e-17 or 9.9999999999999993e-41 < (/.f64 y #s(literal 500 binary64))

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. *-rgt-identity 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

      4. associate-/l* 99.8%

         \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

      5. metadata-eval 99.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

      6. metadata-eval 99.8%

         \[\leadsto x + y \cdot \color{blue}{0.002} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot 0.002} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.1%

      \[\leadsto \color{blue}{y \cdot \left(0.002 + \frac{x}{y}\right)} \]

   6. Taylor expanded in x around 0 79.3%

      \[\leadsto y \cdot \color{blue}{0.002} \]
   7. Step-by-step derivation

      1. metadata-eval 79.3%

         \[\leadsto y \cdot \color{blue}{\frac{1}{500}} \]

      2. div-inv 79.5%

         \[\leadsto \color{blue}{\frac{y}{500}} \]

   8. Applied egg-rr 79.5%

      \[\leadsto \color{blue}{\frac{y}{500}} \]

   if -5.50000000000000001e-17 < (/.f64 y #s(literal 500 binary64)) < 9.9999999999999993e-41

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. *-rgt-identity 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

      4. associate-/l* 99.9%

         \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

      5. metadata-eval 99.9%

         \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

      6. metadata-eval 99.9%

         \[\leadsto x + y \cdot \color{blue}{0.002} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + y \cdot 0.002} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 83.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{500} \leq -5.5 \cdot 10^{-17} \lor \neg \left(\frac{y}{500} \leq 10^{-40}\right):\\ \;\;\;\;\frac{y}{500}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-14} \lor \neg \left(y \leq 3.05 \cdot 10^{-37}\right):\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.7e-14) (not (<= y 3.05e-37))) (* y 0.002) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.7e-14) || !(y <= 3.05e-37)) {
		tmp = y * 0.002;
	} 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 ((y <= (-2.7d-14)) .or. (.not. (y <= 3.05d-37))) then
        tmp = y * 0.002d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.7e-14) || !(y <= 3.05e-37)) {
		tmp = y * 0.002;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.7e-14) or not (y <= 3.05e-37):
		tmp = y * 0.002
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.7e-14) || !(y <= 3.05e-37))
		tmp = Float64(y * 0.002);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.7e-14) || ~((y <= 3.05e-37)))
		tmp = y * 0.002;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.7e-14], N[Not[LessEqual[y, 3.05e-37]], $MachinePrecision]], N[(y * 0.002), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.6999999999999999e-14 or 3.0500000000000002e-37 < y

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. *-rgt-identity 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

      4. associate-/l* 99.8%

         \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

      5. metadata-eval 99.8%

         \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

      6. metadata-eval 99.8%

         \[\leadsto x + y \cdot \color{blue}{0.002} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot 0.002} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.1%

      \[\leadsto \color{blue}{y \cdot \left(0.002 + \frac{x}{y}\right)} \]

   6. Taylor expanded in x around 0 79.3%

      \[\leadsto y \cdot \color{blue}{0.002} \]

   if -2.6999999999999999e-14 < y < 3.0500000000000002e-37

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. *-rgt-identity 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

      2. metadata-eval 100.0%

         \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

      3. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

      4. associate-/l* 99.9%

         \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

      5. metadata-eval 99.9%

         \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

      6. metadata-eval 99.9%

         \[\leadsto x + y \cdot \color{blue}{0.002} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + y \cdot 0.002} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 83.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-14} \lor \neg \left(y \leq 3.05 \cdot 10^{-37}\right):\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot 0.002 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (* y 0.002)))

C

double code(double x, double y) {
	return x + (y * 0.002);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y * 0.002d0)
end function

Java

public static double code(double x, double y) {
	return x + (y * 0.002);
}

Python

def code(x, y):
	return x + (y * 0.002)

Julia

function code(x, y)
	return Float64(x + Float64(y * 0.002))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y * 0.002);
end

Wolfram

code[x_, y_] := N[(x + N[(y * 0.002), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]
2. Step-by-step derivation

   1. *-rgt-identity 100.0%

      \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

   2. metadata-eval 100.0%

      \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

   3. associate-*l/ 100.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

   4. associate-/l* 99.9%

      \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

   5. metadata-eval 99.9%

      \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

   6. metadata-eval 99.9%

      \[\leadsto x + y \cdot \color{blue}{0.002} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + y \cdot 0.002} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 5: 51.6% 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%

   \[x + \frac{y}{500} \]
2. Step-by-step derivation

   1. *-rgt-identity 100.0%

      \[\leadsto x + \color{blue}{\frac{y}{500} \cdot 1} \]

   2. metadata-eval 100.0%

      \[\leadsto x + \frac{y}{500} \cdot \color{blue}{\left(--1\right)} \]

   3. associate-*l/ 100.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(--1\right)}{500}} \]

   4. associate-/l* 99.9%

      \[\leadsto x + \color{blue}{y \cdot \frac{--1}{500}} \]

   5. metadata-eval 99.9%

      \[\leadsto x + y \cdot \frac{\color{blue}{1}}{500} \]

   6. metadata-eval 99.9%

      \[\leadsto x + y \cdot \color{blue}{0.002} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + y \cdot 0.002} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 49.1%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024132 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, C"
  :precision binary64
  (+ x (/ y 500.0)))