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

Percentage Accurate: 95.6% → 95.6%

Time: 7.0s

Alternatives: 6

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: 95.6% 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: 95.6% 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 97.3%

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

3. Taylor expanded in y around 0 97.3%

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

   1. mul-1-neg 97.3%

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

   2. *-commutative 97.3%

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

   3. associate-*l* 93.0%

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

   4. *-commutative 93.0%

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

5. Simplified 93.0%

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

6. Taylor expanded in y around 0 97.3%

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

7. Final simplification 97.3%

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

Alternative 2: 65.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-201} \lor \neg \left(z \leq 1.4 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.45e-201) (not (<= z 1.4e+43))) (* x (* y (- z))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.45e-201) || !(z <= 1.4e+43)) {
		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 ((z <= (-2.45d-201)) .or. (.not. (z <= 1.4d+43))) 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 ((z <= -2.45e-201) || !(z <= 1.4e+43)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.45e-201) or not (z <= 1.4e+43):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.45e-201) || !(z <= 1.4e+43))
		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 ((z <= -2.45e-201) || ~((z <= 1.4e+43)))
		tmp = x * (y * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.45e-201], N[Not[LessEqual[z, 1.4e+43]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.4499999999999998e-201 or 1.40000000000000009e43 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in y around inf 66.1%

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

      1. associate-*r* 66.1%

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

      2. mul-1-neg 66.1%

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

   5. Simplified 66.1%

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

   if -2.4499999999999998e-201 < z < 1.40000000000000009e43

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-201} \lor \neg \left(z \leq 1.4 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.45e-201)
   (* x (* y (- z)))
   (if (<= z 1.35e+43) x (* y (* x (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.45e-201) {
		tmp = x * (y * -z);
	} else if (z <= 1.35e+43) {
		tmp = x;
	} else {
		tmp = y * (x * -z);
	}
	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 <= (-2.45d-201)) then
        tmp = x * (y * -z)
    else if (z <= 1.35d+43) then
        tmp = x
    else
        tmp = y * (x * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.45e-201) {
		tmp = x * (y * -z);
	} else if (z <= 1.35e+43) {
		tmp = x;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.45e-201:
		tmp = x * (y * -z)
	elif z <= 1.35e+43:
		tmp = x
	else:
		tmp = y * (x * -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.45e-201)
		tmp = Float64(x * Float64(y * Float64(-z)));
	elseif (z <= 1.35e+43)
		tmp = x;
	else
		tmp = Float64(y * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.45e-201)
		tmp = x * (y * -z);
	elseif (z <= 1.35e+43)
		tmp = x;
	else
		tmp = y * (x * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.45e-201], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+43], x, N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4499999999999998e-201

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 60.8%

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

      1. associate-*r* 60.8%

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

      2. mul-1-neg 60.8%

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

   5. Simplified 60.8%

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

   if -2.4499999999999998e-201 < z < 1.3500000000000001e43

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.1%

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

   if 1.3500000000000001e43 < z

   1. Initial program 95.9%

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

   3. Taylor expanded in y around inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-*l* 80.3%

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

      4. *-commutative 80.3%

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

      5. distribute-rgt-neg-in 80.3%

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

      6. distribute-rgt-neg-in 80.3%

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

   5. Simplified 80.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 7.5e+104) x (/ (* x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 7.5e+104) {
		tmp = x;
	} else {
		tmp = (x * z) / z;
	}
	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 <= 7.5d+104) then
        tmp = x
    else
        tmp = (x * z) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 7.5e+104) {
		tmp = x;
	} else {
		tmp = (x * z) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 7.5e+104:
		tmp = x
	else:
		tmp = (x * z) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 7.5e+104)
		tmp = x;
	else
		tmp = Float64(Float64(x * z) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 7.5e+104)
		tmp = x;
	else
		tmp = (x * z) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 7.5e+104], x, N[(N[(x * z), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.5000000000000002e104

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 51.2%

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

   if 7.5000000000000002e104 < z

   1. Initial program 95.0%

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

   3. Taylor expanded in y around 0 95.0%

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

   4. Taylor expanded in z around inf 97.5%

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

      1. +-commutative 97.5%

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

      2. mul-1-neg 97.5%

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

      3. sub-neg 97.5%

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

   6. Simplified 97.5%

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

   7. Taylor expanded in z around 0 18.8%

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

      1. associate-*r/ 30.6%

         \[\leadsto \color{blue}{\frac{z \cdot x}{z}} \]

      2. *-commutative 30.6%

         \[\leadsto \frac{\color{blue}{x \cdot z}}{z} \]

   9. Applied egg-rr 30.6%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.6% 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 97.3%

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

3. Final simplification 97.3%

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

Alternative 6: 51.2% 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 97.3%

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

3. Taylor expanded in y around 0 46.2%

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

4. Final simplification 46.2%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))