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

Percentage Accurate: 95.9% → 97.9%

Time: 6.0s

Alternatives: 5

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: 95.9% 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: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 36.9%

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

   3. Taylor expanded in y around inf 36.9%

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

      1. mul-1-neg 36.9%

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

      2. associate-*r* 99.9%

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

   5. Simplified 99.9%

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

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

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. distribute-rgt-in 98.7%

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

      3. *-un-lft-identity 98.7%

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

      4. distribute-rgt-neg-in 98.7%

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

   4. Applied egg-rr 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-*l* 89.0%

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

      3. add-sqr-sqrt 43.4%

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

      4. sqrt-unprod 61.9%

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

      5. sqr-neg 61.9%

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

      6. sqrt-unprod 24.1%

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

      7. add-sqr-sqrt 49.0%

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

      8. associate-*r* 52.2%

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

      9. *-commutative 52.2%

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

      10. cancel-sign-sub 52.2%

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

      11. distribute-rgt-neg-out 52.2%

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

      12. add-sqr-sqrt 37.1%

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

      13. add-sqr-sqrt 52.2%

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

      14. associate-*l* 50.6%

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

      15. add-sqr-sqrt 26.1%

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

      16. sqrt-unprod 65.8%

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

      17. sqr-neg 65.8%

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

      18. sqrt-unprod 48.5%

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

      19. add-sqr-sqrt 95.1%

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

   6. Applied egg-rr 95.1%

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

   7. Taylor expanded in y around 0 98.7%

      \[\leadsto x - \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

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

Alternative 2: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \cdot z \leq -5 \lor \neg \left(y \cdot z \leq 4 \cdot 10^{-15}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) (- INFINITY))
   (* z (* x (- y)))
   (if (or (<= (* y z) -5.0) (not (<= (* y z) 4e-15))) (* (* y z) (- x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		tmp = z * (x * -y);
	} else if (((y * z) <= -5.0) || !((y * z) <= 4e-15)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = z * (x * -y);
	} else if (((y * z) <= -5.0) || !((y * z) <= 4e-15)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = z * (x * -y)
	elif ((y * z) <= -5.0) or not ((y * z) <= 4e-15):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = Float64(z * Float64(x * Float64(-y)));
	elseif ((Float64(y * z) <= -5.0) || !(Float64(y * z) <= 4e-15))
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -Inf)
		tmp = z * (x * -y);
	elseif (((y * z) <= -5.0) || ~(((y * z) <= 4e-15)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(y * z), $MachinePrecision], -5.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 4e-15]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 36.9%

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

   3. Taylor expanded in y around inf 36.9%

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

      1. mul-1-neg 36.9%

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

      2. associate-*r* 99.9%

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

   5. Simplified 99.9%

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

   if -inf.0 < (*.f64 y z) < -5 or 4.0000000000000003e-15 < (*.f64 y z)

   1. Initial program 97.3%

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

   3. Taylor expanded in y around inf 94.7%

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

      1. mul-1-neg 94.7%

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

      2. associate-*r* 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in x around 0 94.7%

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

   if -5 < (*.f64 y z) < 4.0000000000000003e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.9%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \cdot z \leq -5 \lor \neg \left(y \cdot z \leq 4 \cdot 10^{-15}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.7% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -1.0) || !(Float64(y * z) <= 1.0))
		tmp = Float64(Float64(y * z) * Float64(-x));
	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) <= 1.0)))
		tmp = (y * z) * -x;
	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], 1.0]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.4%

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

   3. Taylor expanded in y around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. associate-*r* 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in x around 0 88.0%

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

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

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.9%

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

4. Final simplification 93.4%

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

Alternative 4: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 36.9%

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

   3. Taylor expanded in y around inf 36.9%

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

      1. mul-1-neg 36.9%

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

      2. associate-*r* 99.9%

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

   5. Simplified 99.9%

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

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

   1. Initial program 98.7%

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

4. Final simplification 98.8%

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

Alternative 5: 52.1% 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 95.1%

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

3. Taylor expanded in y around 0 50.7%

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

4. Final simplification 50.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))