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

Percentage Accurate: 95.9% → 95.9%

Time: 3.9s

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: 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: 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]

Derivation

1. Initial program 97.3%

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

2. Final simplification 97.3%

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

Alternative 2: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+48} \lor \neg \left(y \leq -56000000\right) \land \left(y \leq -1.7 \cdot 10^{-29} \lor \neg \left(y \leq 4.4 \cdot 10^{-104}\right)\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.2e+48)
         (and (not (<= y -56000000.0))
              (or (<= y -1.7e-29) (not (<= y 4.4e-104)))))
   (* x (* y (- z)))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.2e+48) || (!(y <= -56000000.0) && ((y <= -1.7e-29) || !(y <= 4.4e-104)))) {
		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 <= (-9.2d+48)) .or. (.not. (y <= (-56000000.0d0))) .and. (y <= (-1.7d-29)) .or. (.not. (y <= 4.4d-104))) 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 <= -9.2e+48) || (!(y <= -56000000.0) && ((y <= -1.7e-29) || !(y <= 4.4e-104)))) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.2e+48) or (not (y <= -56000000.0) and ((y <= -1.7e-29) or not (y <= 4.4e-104))):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.2e+48) || (!(y <= -56000000.0) && ((y <= -1.7e-29) || !(y <= 4.4e-104))))
		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 <= -9.2e+48) || (~((y <= -56000000.0)) && ((y <= -1.7e-29) || ~((y <= 4.4e-104)))))
		tmp = x * (y * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.2e+48], And[N[Not[LessEqual[y, -56000000.0]], $MachinePrecision], Or[LessEqual[y, -1.7e-29], N[Not[LessEqual[y, 4.4e-104]], $MachinePrecision]]]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.2000000000000001e48 or -5.6e7 < y < -1.69999999999999986e-29 or 4.40000000000000023e-104 < y

   1. Initial program 96.1%

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

   2. Taylor expanded in y around inf 69.1%

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

      1. mul-1-neg 69.1%

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

      2. associate-*r* 69.2%

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

      3. distribute-lft-neg-in 69.2%

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

      4. distribute-rgt-neg-out 69.2%

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

      5. *-commutative 69.2%

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

   4. Simplified 69.2%

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

   if -9.2000000000000001e48 < y < -5.6e7 or -1.69999999999999986e-29 < y < 4.40000000000000023e-104

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 80.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+48} \lor \neg \left(y \leq -56000000\right) \land \left(y \leq -1.7 \cdot 10^{-29} \lor \neg \left(y \leq 4.4 \cdot 10^{-104}\right)\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -235000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x (- z)))))
   (if (<= y -1.22e+48)
     t_0
     (if (<= y -235000000.0)
       x
       (if (<= y -1.06e-29) (* x (* y (- z))) (if (<= y 1.12e-102) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * -z);
	double tmp;
	if (y <= -1.22e+48) {
		tmp = t_0;
	} else if (y <= -235000000.0) {
		tmp = x;
	} else if (y <= -1.06e-29) {
		tmp = x * (y * -z);
	} else if (y <= 1.12e-102) {
		tmp = x;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y * (x * -z)
    if (y <= (-1.22d+48)) then
        tmp = t_0
    else if (y <= (-235000000.0d0)) then
        tmp = x
    else if (y <= (-1.06d-29)) then
        tmp = x * (y * -z)
    else if (y <= 1.12d-102) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * -z);
	double tmp;
	if (y <= -1.22e+48) {
		tmp = t_0;
	} else if (y <= -235000000.0) {
		tmp = x;
	} else if (y <= -1.06e-29) {
		tmp = x * (y * -z);
	} else if (y <= 1.12e-102) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * -z)
	tmp = 0
	if y <= -1.22e+48:
		tmp = t_0
	elif y <= -235000000.0:
		tmp = x
	elif y <= -1.06e-29:
		tmp = x * (y * -z)
	elif y <= 1.12e-102:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * Float64(-z)))
	tmp = 0.0
	if (y <= -1.22e+48)
		tmp = t_0;
	elseif (y <= -235000000.0)
		tmp = x;
	elseif (y <= -1.06e-29)
		tmp = Float64(x * Float64(y * Float64(-z)));
	elseif (y <= 1.12e-102)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * -z);
	tmp = 0.0;
	if (y <= -1.22e+48)
		tmp = t_0;
	elseif (y <= -235000000.0)
		tmp = x;
	elseif (y <= -1.06e-29)
		tmp = x * (y * -z);
	elseif (y <= 1.12e-102)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.22e+48], t$95$0, If[LessEqual[y, -235000000.0], x, If[LessEqual[y, -1.06e-29], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e-102], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.22000000000000004e48 or 1.12000000000000009e-102 < y

   1. Initial program 95.9%

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

   2. Taylor expanded in y around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. distribute-rgt-neg-in 67.6%

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

      3. distribute-lft-neg-out 67.6%

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

      4. *-commutative 67.6%

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

   4. Simplified 67.6%

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

   if -1.22000000000000004e48 < y < -2.35e8 or -1.05999999999999995e-29 < y < 1.12000000000000009e-102

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 80.4%

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

   if -2.35e8 < y < -1.05999999999999995e-29

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. associate-*r* 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. distribute-rgt-neg-out 100.0%

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

      5. *-commutative 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq -235000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 4: 50.2% 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. Taylor expanded in y around 0 50.5%

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

3. Final simplification 50.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))