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

Percentage Accurate: 100.0% → 100.0%

Time: 1.3s

Alternatives: 3

Speedup: 1.1×

Specification

Math

\[x \cdot \left(y + 1\right) \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* x (+ y 1.0)))

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (y + 1.0d0)
end function

Java

public static double code(double x, double y) {
	return x * (y + 1.0);
}

Python

def code(x, y):
	return x * (y + 1.0)

Julia

function code(x, y)
	return Float64(x * Float64(y + 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (y + 1.0);
end

Wolfram

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

ReFlow

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[x \cdot \left(y + 1\right) \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* x (+ y 1.0)))

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (y + 1.0d0)
end function

Java

public static double code(double x, double y) {
	return x * (y + 1.0);
}

Python

def code(x, y):
	return x * (y + 1.0)

Julia

function code(x, y)
	return Float64(x * Float64(y + 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (y + 1.0);
end

Wolfram

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

ReFlow

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

Alternative 1: 100.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

ReFlow

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

Derivation

1. Initial program 100.0%

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

3. Applied rewrites 100.0%

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

Alternative 2: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y + 1 \leq -5:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y + 1 \leq 2:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (+ y 1.0) -5.0)
  (* x y)
  (if (<= (+ y 1.0) 2.0) (* x 1.0) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y + 1.0) <= -5.0) {
		tmp = x * y;
	} else if ((y + 1.0) <= 2.0) {
		tmp = x * 1.0;
	} else {
		tmp = 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 ((y + 1.0d0) <= (-5.0d0)) then
        tmp = x * y
    else if ((y + 1.0d0) <= 2.0d0) then
        tmp = x * 1.0d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y + 1.0) <= -5.0) {
		tmp = x * y;
	} else if ((y + 1.0) <= 2.0) {
		tmp = x * 1.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y + 1.0) <= -5.0:
		tmp = x * y
	elif (y + 1.0) <= 2.0:
		tmp = x * 1.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y + 1.0) <= -5.0)
		tmp = Float64(x * y);
	elseif (Float64(y + 1.0) <= 2.0)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y + 1.0) <= -5.0)
		tmp = x * y;
	elseif ((y + 1.0) <= 2.0)
		tmp = x * 1.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y + 1.0), $MachinePrecision], -5.0], N[(x * y), $MachinePrecision], If[LessEqual[N[(y + 1.0), $MachinePrecision], 2.0], N[(x * 1.0), $MachinePrecision], N[(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_1 = IF ((y + (1)) <= (2)) THEN (x * (1)) ELSE (x * y) ENDIF IN
	LET tmp = IF ((y + (1)) <= (-5)) THEN (x * y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 y #s(literal 1 binary64)) < -5 or 2 < (+.f64 y #s(literal 1 binary64))

   1. Initial program 100.0%

      \[x \cdot \left(y + 1\right) \]

   2. Taylor expanded in y around inf

      \[\leadsto x \cdot y \]
   3. Step-by-step derivation

   4. Applied rewrites 51.3%

      \[\leadsto x \cdot y \]

   if -5 < (+.f64 y #s(literal 1 binary64)) < 2

   1. Initial program 100.0%

      \[x \cdot \left(y + 1\right) \]

   2. Taylor expanded in y around 0

      \[\leadsto x \cdot 1 \]
   3. Step-by-step derivation

   4. Applied rewrites 50.7%

      \[\leadsto x \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 51.3% accurate, 1.6× speedup

Math

\[x \cdot y \]

FPCore

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

C

double code(double x, double y) {
	return 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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Derivation

1. Initial program 100.0%

   \[x \cdot \left(y + 1\right) \]

2. Taylor expanded in y around inf

   \[\leadsto x \cdot y \]
3. Step-by-step derivation

4. Applied rewrites 51.3%

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

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B"
  :precision binary64
  (* x (+ y 1.0)))