Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H

Percentage Accurate: 100.0% → 100.0%

Time: 4.2s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (fma (- y) x x))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. +-commutative N/A

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

   5. distribute-rgt-in N/A

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

   6. *-lft-identity N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-neg.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -40000 \lor \neg \left(1 - y \leq 2\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (- 1.0 y) -40000.0) (not (<= (- 1.0 y) 2.0)))
   (* x (- y))
   (* x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - y) <= -40000.0) || !((1.0 - y) <= 2.0)) {
		tmp = x * -y;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((1.0d0 - y) <= (-40000.0d0)) .or. (.not. ((1.0d0 - y) <= 2.0d0))) then
        tmp = x * -y
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((1.0 - y) <= -40000.0) || !((1.0 - y) <= 2.0)) {
		tmp = x * -y;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - y) <= -40000.0) or not ((1.0 - y) <= 2.0):
		tmp = x * -y
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(1.0 - y) <= -40000.0) || !(Float64(1.0 - y) <= 2.0))
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - y) <= -40000.0) || ~(((1.0 - y) <= 2.0)))
		tmp = x * -y;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(1.0 - y), $MachinePrecision], -40000.0], N[Not[LessEqual[N[(1.0 - y), $MachinePrecision], 2.0]], $MachinePrecision]], N[(x * (-y)), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -4e4 or 2 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \]

      2. lower-neg.f64 96.9

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

   5. Applied rewrites 96.9%

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

   if -4e4 < (-.f64 #s(literal 1 binary64) y) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 98.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -40000 \lor \neg \left(1 - y \leq 2\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 4: 50.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ x \cdot 1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 53.7%

   \[\leadsto x \cdot \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024342 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, H"
  :precision binary64
  (* x (- 1.0 y)))