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

Percentage Accurate: 96.0% → 96.0%

Time: 4.3s

Alternatives: 4

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: 96.0% 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: 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]

Derivation

1. Initial program 97.6%

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

2. Final simplification 97.6%

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

Alternative 2: 94.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -200 \lor \neg \left(y \cdot z \leq 0.05\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -200.0) (not (<= (* y z) 0.05))) (* z (* y (- x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -200.0) || !((y * z) <= 0.05)) {
		tmp = z * (y * -x);
	} 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 * z) <= (-200.0d0)) .or. (.not. ((y * z) <= 0.05d0))) then
        tmp = z * (y * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -200.0) || !((y * z) <= 0.05)) {
		tmp = z * (y * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -200.0) or not ((y * z) <= 0.05):
		tmp = z * (y * -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -200.0) || !(Float64(y * z) <= 0.05))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((y * z) <= -200.0) || ~(((y * z) <= 0.05)))
		tmp = z * (y * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -200.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.05]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -200 or 0.050000000000000003 < (*.f64 y z)

   1. Initial program 95.6%

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

      1. flip3-- 39.9%

         \[\leadsto x \cdot \color{blue}{\frac{{1}^{3} - {\left(y \cdot z\right)}^{3}}{1 \cdot 1 + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)}} \]

      2. associate-*r/ 35.8%

         \[\leadsto \color{blue}{\frac{x \cdot \left({1}^{3} - {\left(y \cdot z\right)}^{3}\right)}{1 \cdot 1 + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)}} \]

      3. metadata-eval 35.8%

         \[\leadsto \frac{x \cdot \left(\color{blue}{1} - {\left(y \cdot z\right)}^{3}\right)}{1 \cdot 1 + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)} \]

      4. metadata-eval 35.8%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{3}\right)}{\color{blue}{1} + \left(\left(y \cdot z\right) \cdot \left(y \cdot z\right) + 1 \cdot \left(y \cdot z\right)\right)} \]

      5. distribute-rgt-out 35.8%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{3}\right)}{1 + \color{blue}{\left(y \cdot z\right) \cdot \left(y \cdot z + 1\right)}} \]

      6. +-commutative 35.8%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{3}\right)}{1 + \left(y \cdot z\right) \cdot \color{blue}{\left(1 + y \cdot z\right)}} \]

   3. Applied egg-rr 35.8%

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

      1. associate-/l* 39.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{1 + \left(y \cdot z\right) \cdot \left(1 + y \cdot z\right)}{1 - {\left(y \cdot z\right)}^{3}}}} \]

   5. Simplified 39.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{1 + \left(y \cdot z\right) \cdot \left(1 + y \cdot z\right)}{1 - {\left(y \cdot z\right)}^{3}}}} \]

   6. Taylor expanded in y around inf 94.3%

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

      1. associate-/r/ 94.4%

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

      2. associate-*r* 88.0%

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

      3. div-inv 88.0%

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

      4. metadata-eval 88.0%

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

   8. Applied egg-rr 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-*r* 88.0%

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

      3. associate-*r* 88.0%

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

      4. neg-mul-1 88.0%

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

      5. associate-*r* 93.9%

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

      6. distribute-rgt-neg-out 93.9%

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

      7. distribute-rgt-neg-out 93.9%

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

      8. add-sqr-sqrt 49.0%

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

      9. sqrt-unprod 39.1%

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

      10. sqr-neg 39.1%

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

      11. sqrt-unprod 0.5%

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

      12. add-sqr-sqrt 0.9%

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

      13. distribute-rgt-neg-out 0.9%

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

      14. distribute-rgt-neg-out 0.9%

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

      15. associate-*r* 1.0%

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

      16. *-commutative 1.0%

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

      17. add-sqr-sqrt 0.5%

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

      18. sqrt-unprod 36.6%

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

      19. sqr-neg 36.6%

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

      20. sqrt-unprod 45.3%

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

      21. add-sqr-sqrt 88.0%

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

   10. Applied egg-rr 88.0%

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

   if -200 < (*.f64 y z) < 0.050000000000000003

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -200 \lor \neg \left(y \cdot z \leq 0.05\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \lor \neg \left(y \cdot z \leq 0.05\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -1.0) (not (<= (* y z) 0.05))) (* x (* y (- z))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -1.0) || !((y * z) <= 0.05)) {
		tmp = x * (y * -z);
	} 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 * z) <= (-1.0d0)) .or. (.not. ((y * z) <= 0.05d0))) then
        tmp = x * (y * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -1.0) || !((y * z) <= 0.05)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -1.0) or not ((y * z) <= 0.05):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -1.0) || !(Float64(y * z) <= 0.05))
		tmp = Float64(x * Float64(y * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((y * z) <= -1.0) || ~(((y * z) <= 0.05)))
		tmp = x * (y * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -1.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.05]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1 or 0.050000000000000003 < (*.f64 y z)

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 93.3%

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

      1. mul-1-neg 93.3%

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

      2. associate-*r* 93.9%

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

      3. distribute-lft-neg-in 93.9%

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

      4. distribute-rgt-neg-out 93.9%

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

      5. *-commutative 93.9%

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

   4. Simplified 93.9%

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

   if -1 < (*.f64 y z) < 0.050000000000000003

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.4%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \lor \neg \left(y \cdot z \leq 0.05\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 50.0% 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 97.6%

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

2. Taylor expanded in y around 0 46.6%

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

3. Final simplification 46.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023182 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))