Data.Colour.RGB:hslsv from colour-2.3.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 661.0ms

Alternatives: 3

Speedup: 1.1×

Specification

Math

\[\frac{x + y}{2} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (+ x y) 2.0))

C

double code(double x, double y) {
	return (x + y) / 2.0;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / 2.0d0
end function

Java

public static double code(double x, double y) {
	return (x + y) / 2.0;
}

Python

def code(x, y):
	return (x + y) / 2.0

Julia

function code(x, y)
	return Float64(Float64(x + y) / 2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / 2.0;
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / 2.0), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(x + y) / (2)
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\frac{x + y}{2} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (+ x y) 2.0))

C

double code(double x, double y) {
	return (x + y) / 2.0;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / 2.0d0
end function

Java

public static double code(double x, double y) {
	return (x + y) / 2.0;
}

Python

def code(x, y):
	return (x + y) / 2.0

Julia

function code(x, y)
	return Float64(Float64(x + y) / 2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / 2.0;
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / 2.0), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(x + y) / (2)
END code

Alternative 1: 100.0% accurate, 1.1× speedup

Math

\[0.5 \cdot \left(x + y\right) \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* 0.5 (+ x y)))

C

double code(double x, double y) {
	return 0.5 * (x + y);
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * (x + y)
end function

Java

public static double code(double x, double y) {
	return 0.5 * (x + y);
}

Python

def code(x, y):
	return 0.5 * (x + y)

Julia

function code(x, y)
	return Float64(0.5 * Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * (x + y);
end

Wolfram

code[x_, y_] := N[(0.5 * N[(x + y), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(5e-1) * (x + y)
END code

Derivation

1. Initial program 100.0%

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

3. Applied rewrites 100.0%

   \[\leadsto 0.5 \cdot \left(x + y\right) \]
4. Add Preprocessing

Alternative 2: 97.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\mathsf{min}\left(x, y\right) + \mathsf{max}\left(x, y\right) \leq -5 \cdot 10^{-243}:\\ \;\;\;\;0.5 \cdot \mathsf{min}\left(x, y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \mathsf{max}\left(x, y\right)\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (+ (fmin x y) (fmax x y)) -5e-243)
  (* 0.5 (fmin x y))
  (* 0.5 (fmax x y))))

C

double code(double x, double y) {
	double tmp;
	if ((fmin(x, y) + fmax(x, y)) <= -5e-243) {
		tmp = 0.5 * fmin(x, y);
	} else {
		tmp = 0.5 * fmax(x, 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 ((fmin(x, y) + fmax(x, y)) <= (-5d-243)) then
        tmp = 0.5d0 * fmin(x, y)
    else
        tmp = 0.5d0 * fmax(x, y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((fmin(x, y) + fmax(x, y)) <= -5e-243) {
		tmp = 0.5 * fmin(x, y);
	} else {
		tmp = 0.5 * fmax(x, y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (fmin(x, y) + fmax(x, y)) <= -5e-243:
		tmp = 0.5 * fmin(x, y)
	else:
		tmp = 0.5 * fmax(x, y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(fmin(x, y) + fmax(x, y)) <= -5e-243)
		tmp = Float64(0.5 * fmin(x, y));
	else
		tmp = Float64(0.5 * fmax(x, y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((min(x, y) + max(x, y)) <= -5e-243)
		tmp = 0.5 * min(x, y);
	else
		tmp = 0.5 * max(x, y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[Min[x, y], $MachinePrecision] + N[Max[x, y], $MachinePrecision]), $MachinePrecision], -5e-243], N[(0.5 * N[Min[x, y], $MachinePrecision]), $MachinePrecision], N[(0.5 * N[Max[x, y], $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_3 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_4 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_5 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF ((tmp_2 + tmp_3) <= (-499999999999999984683939913850061721489496590952589773390827798773737713095969188633192627621462316498790691672632378270778722894714282591665081646676534330402059887310135947479208884369292311377477501378209357934919133739094273166755544593266130898595976796117582471603708263244462299937705026182313773996576649739412955028089862877309315791663836061563811213000894375067941494972219497381288478141027142373996815747302928733577169901360013239235730522260790452621052053289221103216668717982290806856659157137617117372787702476621585898098080977451099317342653072129658731181933717380161397159099578857421875e-851)) THEN ((5e-1) * tmp_4) ELSE ((5e-1) * tmp_5) ENDIF IN
	tmp_1
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.9999999999999998e-243

   1. Initial program 100.0%

      \[\frac{x + y}{2} \]

   2. Taylor expanded in x around inf

      \[\leadsto \frac{1}{2} \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 51.3%

      \[\leadsto 0.5 \cdot x \]

   if -4.9999999999999998e-243 < (+.f64 x y)

   1. Initial program 100.0%

      \[\frac{x + y}{2} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot y \]
   3. Step-by-step derivation

   4. Applied rewrites 50.2%

      \[\leadsto 0.5 \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 50.3% accurate, 1.1× speedup

Math

\[0.5 \cdot \mathsf{min}\left(x, y\right) \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* 0.5 (fmin x y)))

C

double code(double x, double y) {
	return 0.5 * fmin(x, y);
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * fmin(x, y)
end function

Java

public static double code(double x, double y) {
	return 0.5 * fmin(x, y);
}

Python

def code(x, y):
	return 0.5 * fmin(x, y)

Julia

function code(x, y)
	return Float64(0.5 * fmin(x, y))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * min(x, y);
end

Wolfram

code[x_, y_] := N[(0.5 * N[Min[x, y], $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (x < y) THEN x ELSE y ENDIF IN
	(5e-1) * tmp
END code

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{2} \]

2. Taylor expanded in x around inf

   \[\leadsto \frac{1}{2} \cdot x \]
3. Step-by-step derivation

4. Applied rewrites 51.3%

   \[\leadsto 0.5 \cdot x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, A"
  :precision binary64
  (/ (+ x y) 2.0))