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

Percentage Accurate: 95.5% → 95.5%

Time: 4.5s

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: 95.5% 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: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

   1. sub-neg 97.0%

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

   2. distribute-rgt-in 97.0%

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

   3. *-un-lft-identity 97.0%

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

   4. distribute-rgt-neg-in 97.0%

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

3. Applied egg-rr 97.0%

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

   1. *-commutative 97.0%

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

   2. associate-*r* 92.6%

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

   3. distribute-rgt-neg-in 92.6%

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

   4. unsub-neg 92.6%

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

   5. *-commutative 92.6%

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

   6. associate-*r* 92.9%

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

   7. *-commutative 92.9%

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

5. Applied egg-rr 92.9%

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

6. Taylor expanded in y around 0 97.0%

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

7. Final simplification 97.0%

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

Alternative 2: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+139} \lor \neg \left(y \leq -1.25 \cdot 10^{+132} \lor \neg \left(y \leq -1.4 \cdot 10^{+75}\right) \land y \leq 1.3 \cdot 10^{-98}\right):\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.85e+139)
         (not
          (or (<= y -1.25e+132) (and (not (<= y -1.4e+75)) (<= y 1.3e-98)))))
   (- (* z (* x y)))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.85e+139) || !((y <= -1.25e+132) || (!(y <= -1.4e+75) && (y <= 1.3e-98)))) {
		tmp = -(z * (x * y));
	} else {
		tmp = x;
	}
	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) :: tmp
    if ((y <= (-1.85d+139)) .or. (.not. (y <= (-1.25d+132)) .or. (.not. (y <= (-1.4d+75))) .and. (y <= 1.3d-98))) then
        tmp = -(z * (x * y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.85e+139) || !((y <= -1.25e+132) || (!(y <= -1.4e+75) && (y <= 1.3e-98)))) {
		tmp = -(z * (x * y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.85e+139) or not ((y <= -1.25e+132) or (not (y <= -1.4e+75) and (y <= 1.3e-98))):
		tmp = -(z * (x * y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.85e+139) || !((y <= -1.25e+132) || (!(y <= -1.4e+75) && (y <= 1.3e-98))))
		tmp = Float64(-Float64(z * Float64(x * y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.85e+139) || ~(((y <= -1.25e+132) || (~((y <= -1.4e+75)) && (y <= 1.3e-98)))))
		tmp = -(z * (x * y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.85e+139], N[Not[Or[LessEqual[y, -1.25e+132], And[N[Not[LessEqual[y, -1.4e+75]], $MachinePrecision], LessEqual[y, 1.3e-98]]]], $MachinePrecision]], (-N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if y < -1.84999999999999996e139 or -1.25e132 < y < -1.40000000000000006e75 or 1.30000000000000007e-98 < y

   1. Initial program 94.9%

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

   2. Taylor expanded in y around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-*r* 67.8%

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

   4. Simplified 67.8%

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

   if -1.84999999999999996e139 < y < -1.25e132 or -1.40000000000000006e75 < y < 1.30000000000000007e-98

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 75.5%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+139} \lor \neg \left(y \leq -1.25 \cdot 10^{+132} \lor \neg \left(y \leq -1.4 \cdot 10^{+75}\right) \land y \leq 1.3 \cdot 10^{-98}\right):\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 70.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+139}:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+132} \lor \neg \left(y \leq -6.2 \cdot 10^{+75}\right) \land y \leq 1.8 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.5e+139)
   (- (* z (* x y)))
   (if (or (<= y -1.25e+132) (and (not (<= y -6.2e+75)) (<= y 1.8e-100)))
     x
     (* y (* z (- x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e+139) {
		tmp = -(z * (x * y));
	} else if ((y <= -1.25e+132) || (!(y <= -6.2e+75) && (y <= 1.8e-100))) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	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) :: tmp
    if (y <= (-2.5d+139)) then
        tmp = -(z * (x * y))
    else if ((y <= (-1.25d+132)) .or. (.not. (y <= (-6.2d+75))) .and. (y <= 1.8d-100)) then
        tmp = x
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e+139) {
		tmp = -(z * (x * y));
	} else if ((y <= -1.25e+132) || (!(y <= -6.2e+75) && (y <= 1.8e-100))) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.5e+139:
		tmp = -(z * (x * y))
	elif (y <= -1.25e+132) or (not (y <= -6.2e+75) and (y <= 1.8e-100)):
		tmp = x
	else:
		tmp = y * (z * -x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.5e+139)
		tmp = Float64(-Float64(z * Float64(x * y)));
	elseif ((y <= -1.25e+132) || (!(y <= -6.2e+75) && (y <= 1.8e-100)))
		tmp = x;
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.5e+139)
		tmp = -(z * (x * y));
	elseif ((y <= -1.25e+132) || (~((y <= -6.2e+75)) && (y <= 1.8e-100)))
		tmp = x;
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.5e+139], (-N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), If[Or[LessEqual[y, -1.25e+132], And[N[Not[LessEqual[y, -6.2e+75]], $MachinePrecision], LessEqual[y, 1.8e-100]]], x, N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000015e139

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. associate-*r* 91.7%

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

   4. Simplified 91.7%

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

   if -2.50000000000000015e139 < y < -1.25e132 or -6.2000000000000002e75 < y < 1.7999999999999999e-100

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 75.5%

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

   if -1.25e132 < y < -6.2000000000000002e75 or 1.7999999999999999e-100 < y

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf 63.1%

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

      1. mul-1-neg 63.1%

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

      2. associate-*r* 61.4%

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

      3. distribute-rgt-neg-in 61.4%

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

      4. *-commutative 61.4%

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

      5. associate-*r* 65.7%

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

      6. distribute-rgt-neg-out 65.7%

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

   4. Simplified 65.7%

      \[\leadsto \color{blue}{y \cdot \left(-x \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+139}:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+132} \lor \neg \left(y \leq -6.2 \cdot 10^{+75}\right) \land y \leq 1.8 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 4: 95.5% 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]

Derivation

1. Initial program 97.0%

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

2. Final simplification 97.0%

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

Alternative 5: 49.8% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 97.0%

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

2. Taylor expanded in y around 0 50.9%

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

3. Final simplification 50.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))