Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 1.1s

Alternatives: 5

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.1× speedup

Math

\[\mathsf{fma}\left(y, 1 - x, x\right) \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (fma y (- 1.0 x) x))

C

double code(double x, double y) {
	return fma(y, (1.0 - x), x);
}

Julia

function code(x, y)
	return fma(y, Float64(1.0 - x), x)
end

Wolfram

code[x_, y_] := N[(y * N[(1.0 - x), $MachinePrecision] + x), $MachinePrecision]

ReFlow

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(y, 1 - x, x\right) \]
4. Add Preprocessing

Alternative 2: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\mathsf{min}\left(x, y\right) + \mathsf{max}\left(x, y\right)\right) - \mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right) \leq -5 \cdot 10^{-243}:\\ \;\;\;\;\mathsf{min}\left(x, y\right) \cdot \left(1 - \mathsf{max}\left(x, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{max}\left(x, y\right) \cdot \left(1 - \mathsf{min}\left(x, y\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<=
     (- (+ (fmin x y) (fmax x y)) (* (fmin x y) (fmax x y)))
     -5e-243)
  (* (fmin x y) (- 1.0 (fmax x y)))
  (* (fmax x y) (- 1.0 (fmin x y)))))

C

double code(double x, double y) {
	double tmp;
	if (((fmin(x, y) + fmax(x, y)) - (fmin(x, y) * fmax(x, y))) <= -5e-243) {
		tmp = fmin(x, y) * (1.0 - fmax(x, y));
	} else {
		tmp = fmax(x, y) * (1.0 - fmin(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)) - (fmin(x, y) * fmax(x, y))) <= (-5d-243)) then
        tmp = fmin(x, y) * (1.0d0 - fmax(x, y))
    else
        tmp = fmax(x, y) * (1.0d0 - fmin(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)) - (fmin(x, y) * fmax(x, y))) <= -5e-243) {
		tmp = fmin(x, y) * (1.0 - fmax(x, y));
	} else {
		tmp = fmax(x, y) * (1.0 - fmin(x, y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((fmin(x, y) + fmax(x, y)) - (fmin(x, y) * fmax(x, y))) <= -5e-243:
		tmp = fmin(x, y) * (1.0 - fmax(x, y))
	else:
		tmp = fmax(x, y) * (1.0 - fmin(x, y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(fmin(x, y) + fmax(x, y)) - Float64(fmin(x, y) * fmax(x, y))) <= -5e-243)
		tmp = Float64(fmin(x, y) * Float64(1.0 - fmax(x, y)));
	else
		tmp = Float64(fmax(x, y) * Float64(1.0 - fmin(x, y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((min(x, y) + max(x, y)) - (min(x, y) * max(x, y))) <= -5e-243)
		tmp = min(x, y) * (1.0 - max(x, y));
	else
		tmp = max(x, y) * (1.0 - min(x, y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(N[Min[x, y], $MachinePrecision] + N[Max[x, y], $MachinePrecision]), $MachinePrecision] - N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e-243], N[(N[Min[x, y], $MachinePrecision] * N[(1.0 - N[Max[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Max[x, y], $MachinePrecision] * N[(1.0 - N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	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_6 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_7 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_8 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_9 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_10 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_2 = IF (((tmp_3 + tmp_4) - (tmp_5 * tmp_6)) <= (-499999999999999984683939913850061721489496590952589773390827798773737713095969188633192627621462316498790691672632378270778722894714282591665081646676534330402059887310135947479208884369292311377477501378209357934919133739094273166755544593266130898595976796117582471603708263244462299937705026182313773996576649739412955028089862877309315791663836061563811213000894375067941494972219497381288478141027142373996815747302928733577169901360013239235730522260790452621052053289221103216668717982290806856659157137617117372787702476621585898098080977451099317342653072129658731181933717380161397159099578857421875e-851)) THEN (tmp_7 * ((1) - tmp_8)) ELSE (tmp_9 * ((1) - tmp_10)) ENDIF IN
	tmp_2
END code

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 - y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 63.6%

      \[\leadsto x \cdot \left(1 - y\right) \]

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

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto y \cdot \left(1 - x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 62.5%

      \[\leadsto y \cdot \left(1 - x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -764.2516277385:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 497724760173.6331:\\ \;\;\;\;\mathsf{fma}\left(y, 1, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (- 1.0 y))))
  (if (<= x -764.2516277385)
    t_0
    (if (<= x 497724760173.6331) (fma y 1.0 x) t_0))))

C

double code(double x, double y) {
	double t_0 = x * (1.0 - y);
	double tmp;
	if (x <= -764.2516277385) {
		tmp = t_0;
	} else if (x <= 497724760173.6331) {
		tmp = fma(y, 1.0, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (x <= -764.2516277385)
		tmp = t_0;
	elseif (x <= 497724760173.6331)
		tmp = fma(y, 1.0, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -764.2516277385], t$95$0, If[LessEqual[x, 497724760173.6331], N[(y * 1.0 + x), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET t_0 = (x * ((1) - y)) IN
		LET tmp_1 = IF (x <= (49772476017363311767578125e-14)) THEN ((y * (1)) + x) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-764251627738500019404455088078975677490234375e-42)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -764.25162773850002 or 497724760173.63312 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto x \cdot \left(1 - y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 63.6%

      \[\leadsto x \cdot \left(1 - y\right) \]

   if -764.25162773850002 < x < 497724760173.63312

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

   3. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(y, 1 - x, x\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 74.7%

      \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.7% accurate, 1.5× speedup

Math

\[\mathsf{fma}\left(y, 1, x\right) \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (fma y 1.0 x))

C

double code(double x, double y) {
	return fma(y, 1.0, x);
}

Julia

function code(x, y)
	return fma(y, 1.0, x)
end

Wolfram

code[x_, y_] := N[(y * 1.0 + x), $MachinePrecision]

ReFlow

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(y, 1 - x, x\right) \]

4. Taylor expanded in x around 0

   \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]
5. Step-by-step derivation

6. Applied rewrites 74.7%

   \[\leadsto \mathsf{fma}\left(y, 1, x\right) \]
7. Add Preprocessing

Alternative 5: 39.3% accurate, 2.3× speedup

Math

\[\mathsf{max}\left(x, y\right) \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return fmax(x, y)

Julia

function code(x, y)
	return fmax(x, y)
end

MATLAB

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

Wolfram

code[x_, y_] := N[Max[x, y], $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
	tmp
END code

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around inf

   \[\leadsto x \cdot \left(1 - y\right) \]
3. Step-by-step derivation

4. Applied rewrites 63.6%

   \[\leadsto x \cdot \left(1 - y\right) \]

5. Taylor expanded in x around 0

   \[\leadsto y \]
6. Step-by-step derivation

7. Applied rewrites 37.9%

   \[\leadsto y \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))