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

Percentage Accurate: 96.0% → 98.0%

Time: 4.5s

Alternatives: 4

Speedup: 0.5×

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: 96.0% 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: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	t_0 = x * (1.0 - (y * z))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = y * (z * -x)
	else:
		tmp = t_0
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < -inf.0

   1. Initial program 78.3%

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

      1. flip-- 42.3%

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

      2. associate-*r/ 42.3%

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

      3. metadata-eval 42.3%

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

      4. pow2 42.3%

         \[\leadsto \frac{x \cdot \left(1 - \color{blue}{{\left(y \cdot z\right)}^{2}}\right)}{1 + y \cdot z} \]

   3. Applied egg-rr 42.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{1 + y \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l* 42.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{1 + y \cdot z}{1 - {\left(y \cdot z\right)}^{2}}}} \]

      2. +-commutative 42.3%

         \[\leadsto \frac{x}{\frac{\color{blue}{y \cdot z + 1}}{1 - {\left(y \cdot z\right)}^{2}}} \]

   5. Simplified 42.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{y \cdot z + 1}{1 - {\left(y \cdot z\right)}^{2}}}} \]

   6. Taylor expanded in y around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. *-commutative 78.3%

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

      3. associate-*l* 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

   8. Simplified 99.9%

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

   if -inf.0 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 98.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq -\infty:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 2: 71.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-65} \lor \neg \left(z \leq 1.9 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.2e-65) (not (<= z 1.9e+80))) (* x (* z (- y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e-65) || !(z <= 1.9e+80)) {
		tmp = x * (z * -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 ((z <= (-5.2d-65)) .or. (.not. (z <= 1.9d+80))) then
        tmp = x * (z * -y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e-65) || !(z <= 1.9e+80)) {
		tmp = x * (z * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.2e-65) or not (z <= 1.9e+80):
		tmp = x * (z * -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.2e-65) || !(z <= 1.9e+80))
		tmp = Float64(x * Float64(z * Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.2e-65) || ~((z <= 1.9e+80)))
		tmp = x * (z * -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.2e-65], N[Not[LessEqual[z, 1.9e+80]], $MachinePrecision]], N[(x * N[(z * (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000019e-65 or 1.89999999999999999e80 < z

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. distribute-rgt-neg-in 72.7%

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

      3. distribute-rgt-neg-out 72.7%

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

   4. Simplified 72.7%

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

   if -5.20000000000000019e-65 < z < 1.89999999999999999e80

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.1%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-65} \lor \neg \left(z \leq 1.9 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.9e-69)
   (* y (* z (- x)))
   (if (<= z 1.7e+80) x (* x (* z (- y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.9e-69) {
		tmp = y * (z * -x);
	} else if (z <= 1.7e+80) {
		tmp = x;
	} else {
		tmp = x * (z * -y);
	}
	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 (z <= (-2.9d-69)) then
        tmp = y * (z * -x)
    else if (z <= 1.7d+80) then
        tmp = x
    else
        tmp = x * (z * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.9e-69) {
		tmp = y * (z * -x);
	} else if (z <= 1.7e+80) {
		tmp = x;
	} else {
		tmp = x * (z * -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.9e-69:
		tmp = y * (z * -x)
	elif z <= 1.7e+80:
		tmp = x
	else:
		tmp = x * (z * -y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.9e-69)
		tmp = Float64(y * Float64(z * Float64(-x)));
	elseif (z <= 1.7e+80)
		tmp = x;
	else
		tmp = Float64(x * Float64(z * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.9e-69)
		tmp = y * (z * -x);
	elseif (z <= 1.7e+80)
		tmp = x;
	else
		tmp = x * (z * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.9e-69], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+80], x, N[(x * N[(z * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999998e-69

   1. Initial program 95.3%

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

      1. flip-- 59.7%

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

      2. associate-*r/ 55.5%

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

      3. metadata-eval 55.5%

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

      4. pow2 55.5%

         \[\leadsto \frac{x \cdot \left(1 - \color{blue}{{\left(y \cdot z\right)}^{2}}\right)}{1 + y \cdot z} \]

   3. Applied egg-rr 55.5%

      \[\leadsto \color{blue}{\frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{1 + y \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l* 59.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{1 + y \cdot z}{1 - {\left(y \cdot z\right)}^{2}}}} \]

      2. +-commutative 59.6%

         \[\leadsto \frac{x}{\frac{\color{blue}{y \cdot z + 1}}{1 - {\left(y \cdot z\right)}^{2}}} \]

   5. Simplified 59.6%

      \[\leadsto \color{blue}{\frac{x}{\frac{y \cdot z + 1}{1 - {\left(y \cdot z\right)}^{2}}}} \]

   6. Taylor expanded in y around inf 70.6%

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

      1. mul-1-neg 70.6%

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

      2. *-commutative 70.6%

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

      3. associate-*l* 68.8%

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

      4. distribute-rgt-neg-in 68.8%

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

   8. Simplified 68.8%

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

   if -2.8999999999999998e-69 < z < 1.69999999999999996e80

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.1%

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

   if 1.69999999999999996e80 < z

   1. Initial program 87.8%

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

   2. Taylor expanded in y around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-rgt-neg-in 75.7%

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

      3. distribute-rgt-neg-out 75.7%

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

   4. Simplified 75.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 4: 50.6% 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 96.6%

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

2. Taylor expanded in y around 0 54.1%

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

3. Final simplification 54.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))