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

Percentage Accurate: 95.7% → 97.7%

Time: 5.9s

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: 95.7% 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: 97.7% accurate, 0.5× speedup

Math

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

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))))
   (if (<= t_0 (- INFINITY)) (* z (* y (- x))) t_0)))

C

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

Java

assert y < z;
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 = z * (y * -x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

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

Julia

y, z = sort([y, z])
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(z * Float64(y * Float64(-x)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - (y * z));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = z * (y * -x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
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[(z * N[(y * (-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 71.0%

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

      1. *-commutative 71.0%

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

      2. flip-- 42.3%

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

      3. associate-*l/ 42.3%

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

      4. metadata-eval 42.3%

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

      5. pow2 42.3%

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

   3. Applied egg-rr 42.3%

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

      1. unpow2 42.3%

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

      2. *-commutative 42.3%

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

      3. *-commutative 42.3%

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

      4. swap-sqr 42.3%

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

   5. Applied egg-rr 42.3%

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

   6. Taylor expanded in z around inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. unpow2 42.3%

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

      3. *-commutative 42.3%

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

      4. unpow2 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in y around inf 99.9%

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

       1. mul-1-neg 99.9%

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

       2. *-commutative 99.9%

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

       3. associate-*r* 99.8%

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

       4. *-commutative 99.8%

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

       5. distribute-rgt-neg-in 99.8%

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

   11. Simplified 99.8%

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

   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 98.7%

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

Alternative 2: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-110} \lor \neg \left(z \leq 1.8 \cdot 10^{-6} \lor \neg \left(z \leq 3.2 \cdot 10^{+15}\right) \land z \leq 3.7 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.8e-110)
         (not (or (<= z 1.8e-6) (and (not (<= z 3.2e+15)) (<= z 3.7e+34)))))
   (* x (* y (- z)))
   x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.8e-110) || !((z <= 1.8e-6) || (!(z <= 3.2e+15) && (z <= 3.7e+34)))) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 <= (-7.8d-110)) .or. (.not. (z <= 1.8d-6) .or. (.not. (z <= 3.2d+15)) .and. (z <= 3.7d+34))) then
        tmp = x * (y * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.8e-110) || !((z <= 1.8e-6) || (!(z <= 3.2e+15) && (z <= 3.7e+34)))) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -7.8e-110) or not ((z <= 1.8e-6) or (not (z <= 3.2e+15) and (z <= 3.7e+34))):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.8e-110) || !((z <= 1.8e-6) || (!(z <= 3.2e+15) && (z <= 3.7e+34))))
		tmp = Float64(x * Float64(y * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.8e-110) || ~(((z <= 1.8e-6) || (~((z <= 3.2e+15)) && (z <= 3.7e+34)))))
		tmp = x * (y * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -7.8e-110], N[Not[Or[LessEqual[z, 1.8e-6], And[N[Not[LessEqual[z, 3.2e+15]], $MachinePrecision], LessEqual[z, 3.7e+34]]]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.8e-110 or 1.79999999999999992e-6 < z < 3.2e15 or 3.70000000000000009e34 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 72.6%

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

      1. mul-1-neg 72.6%

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

      2. associate-*r* 68.8%

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

      3. distribute-lft-neg-in 68.8%

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

      4. distribute-rgt-neg-out 68.8%

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

      5. *-commutative 68.8%

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

   4. Simplified 68.8%

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

   if -7.8e-110 < z < 1.79999999999999992e-6 or 3.2e15 < z < 3.70000000000000009e34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.9%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-110} \lor \neg \left(z \leq 1.8 \cdot 10^{-6} \lor \neg \left(z \leq 3.2 \cdot 10^{+15}\right) \land z \leq 3.7 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-109} \lor \neg \left(z \leq 1.82 \cdot 10^{-6} \lor \neg \left(z \leq 5.5 \cdot 10^{+15}\right) \land z \leq 7 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.1e-109)
         (not (or (<= z 1.82e-6) (and (not (<= z 5.5e+15)) (<= z 7e+34)))))
   (* y (* x (- z)))
   x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.1e-109) || !((z <= 1.82e-6) || (!(z <= 5.5e+15) && (z <= 7e+34)))) {
		tmp = y * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 <= (-2.1d-109)) .or. (.not. (z <= 1.82d-6) .or. (.not. (z <= 5.5d+15)) .and. (z <= 7d+34))) then
        tmp = y * (x * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.1e-109) || !((z <= 1.82e-6) || (!(z <= 5.5e+15) && (z <= 7e+34)))) {
		tmp = y * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -2.1e-109) or not ((z <= 1.82e-6) or (not (z <= 5.5e+15) and (z <= 7e+34))):
		tmp = y * (x * -z)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.1e-109) || !((z <= 1.82e-6) || (!(z <= 5.5e+15) && (z <= 7e+34))))
		tmp = Float64(y * Float64(x * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.1e-109) || ~(((z <= 1.82e-6) || (~((z <= 5.5e+15)) && (z <= 7e+34)))))
		tmp = y * (x * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -2.1e-109], N[Not[Or[LessEqual[z, 1.82e-6], And[N[Not[LessEqual[z, 5.5e+15]], $MachinePrecision], LessEqual[z, 7e+34]]]], $MachinePrecision]], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999996e-109 or 1.8199999999999999e-6 < z < 5.5e15 or 6.99999999999999996e34 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 72.6%

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

      1. mul-1-neg 72.6%

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

      2. distribute-rgt-neg-in 72.6%

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

      3. distribute-lft-neg-out 72.6%

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

      4. *-commutative 72.6%

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

   4. Simplified 72.6%

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

   if -2.09999999999999996e-109 < z < 1.8199999999999999e-6 or 5.5e15 < z < 6.99999999999999996e34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-109} \lor \neg \left(z \leq 1.82 \cdot 10^{-6} \lor \neg \left(z \leq 5.5 \cdot 10^{+15}\right) \land z \leq 7 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 50.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ x \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

assert(y < z);
double code(double x, double y, double z) {
	return x;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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

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

Python

[y, z] = sort([y, z])
def code(x, y, z):
	return x

Julia

y, z = sort([y, z])
function code(x, y, z)
	return x
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 95.8%

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

2. Taylor expanded in y around 0 47.4%

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

3. Final simplification 47.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))