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

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 3

Speedup: 1.3×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(y + 1\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(y + 1\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (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]

Derivation

1. Initial program 100.0%

   \[x \cdot \left(y + 1\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. distribute-lft-in N/A

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

   3. *-rgt-identity N/A

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

   4. lower-fma.f64 100.0

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

5. Simplified 100.0%

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

Alternative 2: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + 1 \leq -100000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y + 1 \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (+ y 1.0) -100000.0) (* x y) (if (<= (+ y 1.0) 2.0) x (* x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y + 1.0) <= -100000.0) {
		tmp = x * y;
	} else if ((y + 1.0) <= 2.0) {
		tmp = x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y + 1.0d0) <= (-100000.0d0)) then
        tmp = x * y
    else if ((y + 1.0d0) <= 2.0d0) then
        tmp = x
    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) <= -100000.0) {
		tmp = x * y;
	} else if ((y + 1.0) <= 2.0) {
		tmp = x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y + 1.0) <= -100000.0:
		tmp = x * y
	elif (y + 1.0) <= 2.0:
		tmp = x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y + 1.0) <= -100000.0)
		tmp = Float64(x * y);
	elseif (Float64(y + 1.0) <= 2.0)
		tmp = x;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y + 1.0) <= -100000.0)
		tmp = x * y;
	elseif ((y + 1.0) <= 2.0)
		tmp = x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y + 1.0), $MachinePrecision], -100000.0], N[(x * y), $MachinePrecision], If[LessEqual[N[(y + 1.0), $MachinePrecision], 2.0], x, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y #s(literal 1 binary64)) < -1e5 or 2 < (+.f64 y #s(literal 1 binary64))

   1. Initial program 100.0%

      \[x \cdot \left(y + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 96.8

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

   5. Simplified 96.8%

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

   if -1e5 < (+.f64 y #s(literal 1 binary64)) < 2

   1. Initial program 100.0%

      \[x \cdot \left(y + 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 97.7%

      \[\leadsto x \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + 1 \leq -100000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y + 1 \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.8% accurate, 9.0× 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%

   \[x \cdot \left(y + 1\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto x \cdot \color{blue}{1} \]
4. Step-by-step derivation

5. Simplified 50.9%

   \[\leadsto x \cdot \color{blue}{1} \]

6. Final simplification 50.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + x \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (* x y)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024215 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (* x y)))

  (* x (+ y 1.0)))