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

Percentage Accurate: 96.0% → 97.9%

Time: 7.1s

Alternatives: 4

Speedup: 0.6×

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: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = (-y * x) * z
	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(Float64(Float64(-y) * x) * z);
	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 = (-y * x) * z;
	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[(N[((-y) * x), $MachinePrecision] * z), $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 58.9%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 58.9

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

   5. Applied rewrites 58.9%

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

   7. Applied rewrites 58.9%

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

   9. Applied rewrites 58.9%

      \[\leadsto x \cdot \frac{z}{\color{blue}{\frac{-1}{y}}} \]

   10. Taylor expanded in y around inf

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

       1. associate-*r* N/A

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

       2. associate-*r* N/A

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

       3. lower-*.f64 N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. lower-*.f64 N/A

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

       7. mul-1-neg N/A

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

       8. lower-neg.f64 100.0

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

   12. Applied rewrites 100.0%

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

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

   1. Initial program 98.2%

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

Alternative 2: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;\left(\left(-y\right) \cdot x\right) \cdot z\\ \mathbf{elif}\;y \cdot z \leq -5 \lor \neg \left(y \cdot z \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(\left(-y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) (- INFINITY))
   (* (* (- y) x) z)
   (if (or (<= (* y z) -5.0) (not (<= (* y z) 5e-6)))
     (* x (* (- y) z))
     (* x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		tmp = (-y * x) * z;
	} else if (((y * z) <= -5.0) || !((y * z) <= 5e-6)) {
		tmp = x * (-y * z);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = (-y * x) * z;
	} else if (((y * z) <= -5.0) || !((y * z) <= 5e-6)) {
		tmp = x * (-y * z);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = (-y * x) * z
	elif ((y * z) <= -5.0) or not ((y * z) <= 5e-6):
		tmp = x * (-y * z)
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = Float64(Float64(Float64(-y) * x) * z);
	elseif ((Float64(y * z) <= -5.0) || !(Float64(y * z) <= 5e-6))
		tmp = Float64(x * Float64(Float64(-y) * z));
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -Inf)
		tmp = (-y * x) * z;
	elseif (((y * z) <= -5.0) || ~(((y * z) <= 5e-6)))
		tmp = x * (-y * z);
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], N[(N[((-y) * x), $MachinePrecision] * z), $MachinePrecision], If[Or[LessEqual[N[(y * z), $MachinePrecision], -5.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 5e-6]], $MachinePrecision]], N[(x * N[((-y) * z), $MachinePrecision]), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 58.9%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 58.9

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

   5. Applied rewrites 58.9%

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

   7. Applied rewrites 58.9%

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

   9. Applied rewrites 58.9%

      \[\leadsto x \cdot \frac{z}{\color{blue}{\frac{-1}{y}}} \]

   10. Taylor expanded in y around inf

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

       1. associate-*r* N/A

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

       2. associate-*r* N/A

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

       3. lower-*.f64 N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. lower-*.f64 N/A

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

       7. mul-1-neg N/A

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

       8. lower-neg.f64 100.0

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

   12. Applied rewrites 100.0%

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

   if -inf.0 < (*.f64 y z) < -5 or 5.00000000000000041e-6 < (*.f64 y z)

   1. Initial program 96.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 94.2

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

   5. Applied rewrites 94.2%

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

   if -5 < (*.f64 y z) < 5.00000000000000041e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 99.3%

      \[\leadsto x \cdot \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;\left(\left(-y\right) \cdot x\right) \cdot z\\ \mathbf{elif}\;y \cdot z \leq -5 \lor \neg \left(y \cdot z \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(\left(-y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+33} \lor \neg \left(y \cdot z \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;\left(\left(-y\right) \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2e+33) (not (<= (* y z) 5e-6)))
   (* (* (- y) x) z)
   (* x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2e+33) || !((y * z) <= 5e-6)) {
		tmp = (-y * x) * z;
	} else {
		tmp = x * 1.0;
	}
	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) <= (-2d+33)) .or. (.not. ((y * z) <= 5d-6))) then
        tmp = (-y * x) * z
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2e+33) || !((y * z) <= 5e-6)) {
		tmp = (-y * x) * z;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -2e+33) or not ((y * z) <= 5e-6):
		tmp = (-y * x) * z
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -2e+33) || !(Float64(y * z) <= 5e-6))
		tmp = Float64(Float64(Float64(-y) * x) * z);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((y * z) <= -2e+33) || ~(((y * z) <= 5e-6)))
		tmp = (-y * x) * z;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -2e+33], N[Not[LessEqual[N[(y * z), $MachinePrecision], 5e-6]], $MachinePrecision]], N[(N[((-y) * x), $MachinePrecision] * z), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.9999999999999999e33 or 5.00000000000000041e-6 < (*.f64 y z)

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 90.0

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

   5. Applied rewrites 90.0%

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

   7. Applied rewrites 62.5%

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

   9. Applied rewrites 89.9%

      \[\leadsto x \cdot \frac{z}{\color{blue}{\frac{-1}{y}}} \]

   10. Taylor expanded in y around inf

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

       1. associate-*r* N/A

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

       2. associate-*r* N/A

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

       3. lower-*.f64 N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. lower-*.f64 N/A

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

       7. mul-1-neg N/A

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

       8. lower-neg.f64 95.2

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

   12. Applied rewrites 95.2%

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

   if -1.9999999999999999e33 < (*.f64 y z) < 5.00000000000000041e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.3%

      \[\leadsto x \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+33} \lor \neg \left(y \cdot z \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;\left(\left(-y\right) \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x \cdot 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 1.0))

C

double code(double x, double y, double z) {
	return x * 1.0;
}

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
end function

Java

public static double code(double x, double y, double z) {
	return x * 1.0;
}

Python

def code(x, y, z):
	return x * 1.0

Julia

function code(x, y, z)
	return Float64(x * 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x * 1.0), $MachinePrecision]

Derivation

1. Initial program 95.5%

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

3. Taylor expanded in y around 0

   \[\leadsto x \cdot \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 51.8%

   \[\leadsto x \cdot \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024318 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))