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

Percentage Accurate: 96.3% → 96.3%

Time: 9.2s

Alternatives: 5

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. distribute-rgt-in N/A

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

   5. *-lft-identity N/A

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

   6. distribute-lft-neg-out N/A

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

   7. unsub-neg N/A

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

   8. lower--.f64 N/A

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

   9. lower-*.f64 98.0

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

   10. lift-*.f64 N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 98.0

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

4. Applied rewrites 98.0%

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

5. Final simplification 98.0%

   \[\leadsto x - \left(y \cdot z\right) \cdot x \]
6. Add Preprocessing

Alternative 2: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ t_1 := \left(\left(-z\right) \cdot y\right) \cdot x\\ \mathbf{if}\;t\_0 \leq -500000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))) (t_1 (* (* (- z) y) x)))
   (if (<= t_0 -500000.0) t_1 (if (<= t_0 2.0) (* 1.0 x) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double t_1 = (-z * y) * x;
	double tmp;
	if (t_0 <= -500000.0) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    t_1 = (-z * y) * x
    if (t_0 <= (-500000.0d0)) then
        tmp = t_1
    else if (t_0 <= 2.0d0) then
        tmp = 1.0d0 * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double t_1 = (-z * y) * x;
	double tmp;
	if (t_0 <= -500000.0) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 1.0 * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y * z)
	t_1 = (-z * y) * x
	tmp = 0
	if t_0 <= -500000.0:
		tmp = t_1
	elif t_0 <= 2.0:
		tmp = 1.0 * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	t_1 = Float64(Float64(Float64(-z) * y) * x)
	tmp = 0.0
	if (t_0 <= -500000.0)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = Float64(1.0 * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	t_1 = (-z * y) * x;
	tmp = 0.0;
	if (t_0 <= -500000.0)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = 1.0 * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[((-z) * y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$0, -500000.0], t$95$1, If[LessEqual[t$95$0, 2.0], N[(1.0 * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -5e5 or 2 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 94.4

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

   5. Applied rewrites 94.4%

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

   if -5e5 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.2%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -500000:\\ \;\;\;\;\left(\left(-z\right) \cdot y\right) \cdot x\\ \mathbf{elif}\;1 - y \cdot z \leq 2:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(-x\right) \cdot y\right) \cdot z\\ \mathbf{if}\;y \cdot z \leq -50000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 0.0005:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* (- x) y) z)))
   (if (<= (* y z) -50000.0) t_0 (if (<= (* y z) 0.0005) (* 1.0 x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (-x * y) * z;
	double tmp;
	if ((y * z) <= -50000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.0005) {
		tmp = 1.0 * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-x * y) * z
    if ((y * z) <= (-50000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 0.0005d0) then
        tmp = 1.0d0 * x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (-x * y) * z;
	double tmp;
	if ((y * z) <= -50000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.0005) {
		tmp = 1.0 * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (-x * y) * z
	tmp = 0
	if (y * z) <= -50000.0:
		tmp = t_0
	elif (y * z) <= 0.0005:
		tmp = 1.0 * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(-x) * y) * z)
	tmp = 0.0
	if (Float64(y * z) <= -50000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 0.0005)
		tmp = Float64(1.0 * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (-x * y) * z;
	tmp = 0.0;
	if ((y * z) <= -50000.0)
		tmp = t_0;
	elseif ((y * z) <= 0.0005)
		tmp = 1.0 * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[((-x) * y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -50000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 0.0005], N[(1.0 * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5e4 or 5.0000000000000001e-4 < (*.f64 y z)

   1. Initial program 96.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. distribute-rgt-in N/A

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

      5. *-lft-identity N/A

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

      6. distribute-lft-neg-out N/A

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

      9. lower-*.f64 96.1

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 96.1

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

   4. Applied rewrites 96.1%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. +-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r* N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot y, x, \frac{x}{z}\right)} \cdot z \]

      9. mul-1-neg N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-/.f64 90.2

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

   7. Applied rewrites 90.2%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 90.7%

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

   if -5e4 < (*.f64 y z) < 5.0000000000000001e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.2%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -50000:\\ \;\;\;\;\left(\left(-x\right) \cdot y\right) \cdot z\\ \mathbf{elif}\;y \cdot z \leq 0.0005:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-x\right) \cdot y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Final simplification 98.0%

   \[\leadsto \left(1 - y \cdot z\right) \cdot x \]
4. Add Preprocessing

Alternative 5: 50.1% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in z around 0

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

5. Applied rewrites 50.0%

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

6. Final simplification 50.0%

   \[\leadsto 1 \cdot x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024235 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))