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

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

Alternatives: 4

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. Final simplification 100.0%

   \[\leadsto x + \frac{y}{500} \]
4. Add Preprocessing

Alternative 2: 72.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-75} \lor \neg \left(x \leq 1.4 \cdot 10^{+42}\right) \land x \leq 7.8 \cdot 10^{+74}:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.15e+71)
   x
   (if (or (<= x 1.7e-75) (and (not (<= x 1.4e+42)) (<= x 7.8e+74)))
     (* y 0.002)
     x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.15e+71) {
		tmp = x;
	} else if ((x <= 1.7e-75) || (!(x <= 1.4e+42) && (x <= 7.8e+74))) {
		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 (x <= (-2.15d+71)) then
        tmp = x
    else if ((x <= 1.7d-75) .or. (.not. (x <= 1.4d+42)) .and. (x <= 7.8d+74)) 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 (x <= -2.15e+71) {
		tmp = x;
	} else if ((x <= 1.7e-75) || (!(x <= 1.4e+42) && (x <= 7.8e+74))) {
		tmp = y * 0.002;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.15e+71:
		tmp = x
	elif (x <= 1.7e-75) or (not (x <= 1.4e+42) and (x <= 7.8e+74)):
		tmp = y * 0.002
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.15e+71)
		tmp = x;
	elseif ((x <= 1.7e-75) || (!(x <= 1.4e+42) && (x <= 7.8e+74)))
		tmp = Float64(y * 0.002);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.15e+71)
		tmp = x;
	elseif ((x <= 1.7e-75) || (~((x <= 1.4e+42)) && (x <= 7.8e+74)))
		tmp = y * 0.002;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.15e+71], x, If[Or[LessEqual[x, 1.7e-75], And[N[Not[LessEqual[x, 1.4e+42]], $MachinePrecision], LessEqual[x, 7.8e+74]]], N[(y * 0.002), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.14999999999999992e71 or 1.70000000000000008e-75 < x < 1.4e42 or 7.80000000000000015e74 < x

   1. Initial program 99.9%

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

      1. *-rgt-identity 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-*l/ 99.9%

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

      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 79.1%

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

   if -2.14999999999999992e71 < x < 1.70000000000000008e-75 or 1.4e42 < x < 7.80000000000000015e74

   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 x around inf 80.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + 0.002 \cdot \frac{y}{x}\right)} \]

   6. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{0.002 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-75} \lor \neg \left(x \leq 1.4 \cdot 10^{+42}\right) \land x \leq 7.8 \cdot 10^{+74}:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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* 99.8%

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

   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. Final simplification 99.8%

   \[\leadsto x + y \cdot 0.002 \]
6. Add Preprocessing

Alternative 4: 51.5% 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* 99.8%

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

   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 x around inf 48.5%

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

6. Final simplification 48.5%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, C"
  :precision binary64
  (+ x (/ y 500.0)))