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

Percentage Accurate: 100.0% → 100.0%

Time: 1.3s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[x - \frac{y}{200} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    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]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	x - (y / (200))
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[x - \frac{y}{200} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    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]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	x - (y / (200))
END code

Alternative 1: 99.9% accurate, 1.2× speedup

Math

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

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (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]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((-5000000000000000104083408558608425664715468883514404296875e-60) * y) + x
END code

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Step-by-step derivation

3. Applied rewrites 99.9%

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

Alternative 2: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{y}{200} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{-200}\\ \mathbf{elif}\;\frac{y}{200} \leq 2 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-200}\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ y 200.0) -2e+44)
  (/ y -200.0)
  (if (<= (/ y 200.0) 2e+38) x (/ y -200.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y / 200.0) <= -2e+44) {
		tmp = y / -200.0;
	} else if ((y / 200.0) <= 2e+38) {
		tmp = x;
	} else {
		tmp = y / -200.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y / 200.0d0) <= (-2d+44)) then
        tmp = y / (-200.0d0)
    else if ((y / 200.0d0) <= 2d+38) then
        tmp = x
    else
        tmp = y / (-200.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y / 200.0) <= -2e+44) {
		tmp = y / -200.0;
	} else if ((y / 200.0) <= 2e+38) {
		tmp = x;
	} else {
		tmp = y / -200.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y / 200.0) <= -2e+44:
		tmp = y / -200.0
	elif (y / 200.0) <= 2e+38:
		tmp = x
	else:
		tmp = y / -200.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y / 200.0) <= -2e+44)
		tmp = Float64(y / -200.0);
	elseif (Float64(y / 200.0) <= 2e+38)
		tmp = x;
	else
		tmp = Float64(y / -200.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y / 200.0) <= -2e+44)
		tmp = y / -200.0;
	elseif ((y / 200.0) <= 2e+38)
		tmp = x;
	else
		tmp = y / -200.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y / 200.0), $MachinePrecision], -2e+44], N[(y / -200.0), $MachinePrecision], If[LessEqual[N[(y / 200.0), $MachinePrecision], 2e+38], x, N[(y / -200.0), $MachinePrecision]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_1 = IF ((y / (200)) <= (199999999999999995497619646912068059136)) THEN x ELSE (y / (-200)) ENDIF IN
	LET tmp = IF ((y / (200)) <= (-200000000000000017642722810612845281403731968)) THEN (y / (-200)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 y #s(literal 200 binary64)) < -2.0000000000000002e44 or 2e38 < (/.f64 y #s(literal 200 binary64))

   1. Initial program 100.0%

      \[x - \frac{y}{200} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 49.8%

      \[\leadsto -0.005 \cdot y \]
   5. Step-by-step derivation

   6. Applied rewrites 49.9%

      \[\leadsto \frac{y}{-200} \]

   if -2.0000000000000002e44 < (/.f64 y #s(literal 200 binary64)) < 2e38

   1. Initial program 100.0%

      \[x - \frac{y}{200} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 49.8%

      \[\leadsto -0.005 \cdot y \]
   5. Step-by-step derivation

   6. Applied rewrites 49.9%

      \[\leadsto \frac{y}{-200} \]

   7. Taylor expanded in x around inf

      \[\leadsto x \]
   8. Step-by-step derivation

   9. Applied rewrites 51.5%

      \[\leadsto x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{y}{200} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;-0.005 \cdot y\\ \mathbf{elif}\;\frac{y}{200} \leq 2 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.005 \cdot y\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (/ y 200.0) -2e+44)
  (* -0.005 y)
  (if (<= (/ y 200.0) 2e+38) x (* -0.005 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y / 200.0) <= -2e+44) {
		tmp = -0.005 * y;
	} else if ((y / 200.0) <= 2e+38) {
		tmp = x;
	} else {
		tmp = -0.005 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y / 200.0d0) <= (-2d+44)) then
        tmp = (-0.005d0) * y
    else if ((y / 200.0d0) <= 2d+38) then
        tmp = x
    else
        tmp = (-0.005d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y / 200.0) <= -2e+44) {
		tmp = -0.005 * y;
	} else if ((y / 200.0) <= 2e+38) {
		tmp = x;
	} else {
		tmp = -0.005 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y / 200.0) <= -2e+44:
		tmp = -0.005 * y
	elif (y / 200.0) <= 2e+38:
		tmp = x
	else:
		tmp = -0.005 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y / 200.0) <= -2e+44)
		tmp = Float64(-0.005 * y);
	elseif (Float64(y / 200.0) <= 2e+38)
		tmp = x;
	else
		tmp = Float64(-0.005 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y / 200.0) <= -2e+44)
		tmp = -0.005 * y;
	elseif ((y / 200.0) <= 2e+38)
		tmp = x;
	else
		tmp = -0.005 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y / 200.0), $MachinePrecision], -2e+44], N[(-0.005 * y), $MachinePrecision], If[LessEqual[N[(y / 200.0), $MachinePrecision], 2e+38], x, N[(-0.005 * y), $MachinePrecision]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_1 = IF ((y / (200)) <= (199999999999999995497619646912068059136)) THEN x ELSE ((-5000000000000000104083408558608425664715468883514404296875e-60) * y) ENDIF IN
	LET tmp = IF ((y / (200)) <= (-200000000000000017642722810612845281403731968)) THEN ((-5000000000000000104083408558608425664715468883514404296875e-60) * y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 y #s(literal 200 binary64)) < -2.0000000000000002e44 or 2e38 < (/.f64 y #s(literal 200 binary64))

   1. Initial program 100.0%

      \[x - \frac{y}{200} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 49.8%

      \[\leadsto -0.005 \cdot y \]

   if -2.0000000000000002e44 < (/.f64 y #s(literal 200 binary64)) < 2e38

   1. Initial program 100.0%

      \[x - \frac{y}{200} \]

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 49.8%

      \[\leadsto -0.005 \cdot y \]
   5. Step-by-step derivation

   6. Applied rewrites 49.9%

      \[\leadsto \frac{y}{-200} \]

   7. Taylor expanded in x around inf

      \[\leadsto x \]
   8. Step-by-step derivation

   9. Applied rewrites 51.5%

      \[\leadsto x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 51.5% accurate, 7.4× speedup

Math

\[x \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  x)

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	x
END code

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]

2. Taylor expanded in x around 0

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

4. Applied rewrites 49.8%

   \[\leadsto -0.005 \cdot y \]
5. Step-by-step derivation

6. Applied rewrites 49.9%

   \[\leadsto \frac{y}{-200} \]

7. Taylor expanded in x around inf

   \[\leadsto x \]
8. Step-by-step derivation

9. Applied rewrites 51.5%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))