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

Percentage Accurate: 96.0% → 97.9%

Time: 5.8s

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: 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - y \cdot z\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))))
   (if (<= t_0 (- INFINITY)) (* (- y) (* x z)) t_0)))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = -y * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = -y * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - (y * z))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = -y * (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(Float64(-y) * Float64(x * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - (y * z));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = -y * (x * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[((-y) * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < -inf.0

   1. Initial program 76.9%

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

   2. Taylor expanded in y around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*r* 99.9%

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

      4. distribute-rgt-neg-out 99.9%

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

      5. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   if -inf.0 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 98.6%

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

4. Final simplification 98.8%

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

Alternative 2: 69.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-59} \lor \neg \left(z \leq 2.7 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.4e-59) (not (<= z 2.7e+70))) (* x (* y (- z))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e-59) || !(z <= 2.7e+70)) {
		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 <= (-1.4d-59)) .or. (.not. (z <= 2.7d+70))) 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 <= -1.4e-59) || !(z <= 2.7e+70)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.4e-59) or not (z <= 2.7e+70):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e-59) || !(z <= 2.7e+70))
		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 <= -1.4e-59) || ~((z <= 2.7e+70)))
		tmp = x * (y * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.4e-59], N[Not[LessEqual[z, 2.7e+70]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3999999999999999e-59 or 2.7e70 < z

   1. Initial program 93.1%

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

   2. Taylor expanded in y around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. distribute-rgt-neg-out 66.9%

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

      3. distribute-rgt-neg-in 66.9%

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

   4. Simplified 66.9%

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

   if -1.3999999999999999e-59 < z < 2.7e70

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 72.5%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-59} \lor \neg \left(z \leq 2.7 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-49}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.28e-49)
   (* (- y) (* x z))
   (if (<= z 2.9e+72) x (* x (* y (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.28e-49) {
		tmp = -y * (x * z);
	} else if (z <= 2.9e+72) {
		tmp = x;
	} else {
		tmp = x * (y * -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 <= (-1.28d-49)) then
        tmp = -y * (x * z)
    else if (z <= 2.9d+72) then
        tmp = x
    else
        tmp = x * (y * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.28e-49) {
		tmp = -y * (x * z);
	} else if (z <= 2.9e+72) {
		tmp = x;
	} else {
		tmp = x * (y * -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.28e-49:
		tmp = -y * (x * z)
	elif z <= 2.9e+72:
		tmp = x
	else:
		tmp = x * (y * -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.28e-49)
		tmp = Float64(Float64(-y) * Float64(x * z));
	elseif (z <= 2.9e+72)
		tmp = x;
	else
		tmp = Float64(x * Float64(y * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.28e-49)
		tmp = -y * (x * z);
	elseif (z <= 2.9e+72)
		tmp = x;
	else
		tmp = x * (y * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.28e-49], N[((-y) * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+72], x, N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.28e-49

   1. Initial program 92.5%

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

   2. Taylor expanded in y around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-*r* 67.8%

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

      4. distribute-rgt-neg-out 67.8%

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

      5. *-commutative 67.8%

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

   4. Simplified 67.8%

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

   if -1.28e-49 < z < 2.90000000000000017e72

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 72.5%

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

   if 2.90000000000000017e72 < z

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. distribute-rgt-neg-out 75.4%

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

      3. distribute-rgt-neg-in 75.4%

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

   4. Simplified 75.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-49}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 4: 70.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(-x \cdot y\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e-58) (* z (- (* x y))) (if (<= z 3.5e+67) x (* x (* y (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e-58) {
		tmp = z * -(x * y);
	} else if (z <= 3.5e+67) {
		tmp = x;
	} else {
		tmp = x * (y * -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 <= (-3d-58)) then
        tmp = z * -(x * y)
    else if (z <= 3.5d+67) then
        tmp = x
    else
        tmp = x * (y * -z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e-58) {
		tmp = z * -(x * y);
	} else if (z <= 3.5e+67) {
		tmp = x;
	} else {
		tmp = x * (y * -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3e-58:
		tmp = z * -(x * y)
	elif z <= 3.5e+67:
		tmp = x
	else:
		tmp = x * (y * -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e-58)
		tmp = Float64(z * Float64(-Float64(x * y)));
	elseif (z <= 3.5e+67)
		tmp = x;
	else
		tmp = Float64(x * Float64(y * Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e-58)
		tmp = z * -(x * y);
	elseif (z <= 3.5e+67)
		tmp = x;
	else
		tmp = x * (y * -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e-58], N[(z * (-N[(x * y), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3.5e+67], x, N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.00000000000000008e-58

   1. Initial program 92.5%

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

      1. flip-- 54.0%

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

      2. clear-num 53.9%

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

      3. un-div-inv 54.0%

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

      4. clear-num 53.9%

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

      5. flip-- 92.4%

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

   3. Applied egg-rr 92.4%

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

   4. Taylor expanded in y around inf 61.6%

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

      1. div-inv 61.6%

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

      2. frac-2neg 61.6%

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

      3. metadata-eval 61.6%

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

      4. remove-double-div 61.6%

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

      5. distribute-lft-neg-in 61.6%

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

      6. associate-*r* 67.7%

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

   6. Applied egg-rr 67.7%

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

   if -3.00000000000000008e-58 < z < 3.5e67

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 73.0%

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

   if 3.5e67 < z

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 75.9%

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

      1. mul-1-neg 75.9%

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

      2. distribute-rgt-neg-out 75.9%

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

      3. distribute-rgt-neg-in 75.9%

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

   4. Simplified 75.9%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(-x \cdot y\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 5: 49.6% 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 96.6%

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

2. Taylor expanded in y around 0 50.7%

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

3. Final simplification 50.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))