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

Percentage Accurate: 96.0% → 98.1%

Time: 5.1s

Alternatives: 6

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: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 4 \cdot 10^{+278}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 4e+278) (- x (* (* y z) x)) (* z (* y (- x)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 4e+278) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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) <= 4d+278) then
        tmp = x - ((y * z) * x)
    else
        tmp = z * (y * -x)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 4e+278) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 4e+278:
		tmp = x - ((y * z) * x)
	else:
		tmp = z * (y * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 4e+278)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(z * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 4e+278)
		tmp = x - ((y * z) * x);
	else
		tmp = z * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 4e+278], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 3.99999999999999985e278

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-rgt-in 98.3%

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

      3. *-un-lft-identity 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

   3. Applied egg-rr 98.3%

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

   if 3.99999999999999985e278 < (*.f64 y z)

   1. Initial program 75.8%

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

      1. add-sqr-sqrt 40.5%

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

      2. pow2 40.5%

         \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \left(1 - y \cdot z\right)}\right)}^{2}} \]

   3. Applied egg-rr 40.5%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \left(1 - y \cdot z\right)}\right)}^{2}} \]

   4. Taylor expanded in y around inf 54.8%

      \[\leadsto {\left(\sqrt{\color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)}}\right)}^{2} \]
   5. Step-by-step derivation

      1. mul-1-neg 54.8%

         \[\leadsto {\left(\sqrt{\color{blue}{-y \cdot \left(z \cdot x\right)}}\right)}^{2} \]

      2. distribute-rgt-neg-in 54.8%

         \[\leadsto {\left(\sqrt{\color{blue}{y \cdot \left(-z \cdot x\right)}}\right)}^{2} \]

      3. distribute-rgt-neg-in 54.8%

         \[\leadsto {\left(\sqrt{y \cdot \color{blue}{\left(z \cdot \left(-x\right)\right)}}\right)}^{2} \]

   6. Simplified 54.8%

      \[\leadsto {\left(\sqrt{\color{blue}{y \cdot \left(z \cdot \left(-x\right)\right)}}\right)}^{2} \]
   7. Step-by-step derivation

      1. unpow2 54.8%

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

      2. add-sqr-sqrt 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.6%

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

      5. distribute-lft-neg-in 99.6%

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

      6. neg-mul-1 99.6%

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

      7. associate-*r* 99.6%

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

   8. Applied egg-rr 99.6%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 4 \cdot 10^{+278}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 2: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 4 \cdot 10^{+239}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 4e+239) (* x (- 1.0 (* y z))) (* y (* z (- x)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 4e+239) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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) <= 4d+239) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 4e+239) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 4e+239:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (z * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 4e+239)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 4e+239)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 4e+239], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 3.99999999999999996e239

   1. Initial program 98.2%

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

   if 3.99999999999999996e239 < (*.f64 y z)

   1. Initial program 83.3%

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

   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 44.6%

         \[\leadsto {\left(\sqrt{\color{blue}{-y \cdot \left(z \cdot x\right)}}\right)}^{2} \]

      2. distribute-rgt-neg-in 44.6%

         \[\leadsto {\left(\sqrt{\color{blue}{y \cdot \left(-z \cdot x\right)}}\right)}^{2} \]

      3. distribute-rgt-neg-in 44.6%

         \[\leadsto {\left(\sqrt{y \cdot \color{blue}{\left(z \cdot \left(-x\right)\right)}}\right)}^{2} \]

   4. Simplified 99.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 4 \cdot 10^{+239}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 3: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 4 \cdot 10^{+278}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 4e+278) (* x (- 1.0 (* y z))) (* z (* y (- x)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 4e+278) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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) <= 4d+278) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = z * (y * -x)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 4e+278) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 4e+278:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = z * (y * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 4e+278)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(z * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 4e+278)
		tmp = x * (1.0 - (y * z));
	else
		tmp = z * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 4e+278], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 3.99999999999999985e278

   1. Initial program 98.3%

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

   if 3.99999999999999985e278 < (*.f64 y z)

   1. Initial program 75.8%

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

      1. add-sqr-sqrt 40.5%

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

      2. pow2 40.5%

         \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \left(1 - y \cdot z\right)}\right)}^{2}} \]

   3. Applied egg-rr 40.5%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \left(1 - y \cdot z\right)}\right)}^{2}} \]

   4. Taylor expanded in y around inf 54.8%

      \[\leadsto {\left(\sqrt{\color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)}}\right)}^{2} \]
   5. Step-by-step derivation

      1. mul-1-neg 54.8%

         \[\leadsto {\left(\sqrt{\color{blue}{-y \cdot \left(z \cdot x\right)}}\right)}^{2} \]

      2. distribute-rgt-neg-in 54.8%

         \[\leadsto {\left(\sqrt{\color{blue}{y \cdot \left(-z \cdot x\right)}}\right)}^{2} \]

      3. distribute-rgt-neg-in 54.8%

         \[\leadsto {\left(\sqrt{y \cdot \color{blue}{\left(z \cdot \left(-x\right)\right)}}\right)}^{2} \]

   6. Simplified 54.8%

      \[\leadsto {\left(\sqrt{\color{blue}{y \cdot \left(z \cdot \left(-x\right)\right)}}\right)}^{2} \]
   7. Step-by-step derivation

      1. unpow2 54.8%

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

      2. add-sqr-sqrt 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*r* 99.6%

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

      5. distribute-lft-neg-in 99.6%

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

      6. neg-mul-1 99.6%

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

      7. associate-*r* 99.6%

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

   8. Applied egg-rr 99.6%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 4 \cdot 10^{+278}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 4: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-95} \lor \neg \left(z \leq 3.2 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e-95) (not (<= z 3.2e-19))) (* x (* z (- y))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-95) || !(z <= 3.2e-19)) {
		tmp = x * (z * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 <= (-1.35d-95)) .or. (.not. (z <= 3.2d-19))) then
        tmp = x * (z * -y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-95) || !(z <= 3.2e-19)) {
		tmp = x * (z * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.35e-95) or not (z <= 3.2e-19):
		tmp = x * (z * -y)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e-95) || !(z <= 3.2e-19))
		tmp = Float64(x * Float64(z * Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e-95) || ~((z <= 3.2e-19)))
		tmp = x * (z * -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e-95], N[Not[LessEqual[z, 3.2e-19]], $MachinePrecision]], N[(x * N[(z * (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e-95 or 3.19999999999999982e-19 < z

   1. Initial program 94.3%

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

   2. Taylor expanded in y around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-rgt-neg-out 72.3%

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

   4. Simplified 72.3%

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

   if -1.35e-95 < z < 3.19999999999999982e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.3%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-95} \lor \neg \left(z \leq 3.2 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-96} \lor \neg \left(z \leq 4.3 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e-96) (not (<= z 4.3e-18))) (* y (* z (- x))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-96) || !(z <= 4.3e-18)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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 <= (-1.1d-96)) .or. (.not. (z <= 4.3d-18))) then
        tmp = y * (z * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-96) || !(z <= 4.3e-18)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.1e-96) or not (z <= 4.3e-18):
		tmp = y * (z * -x)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1e-96) || !(z <= 4.3e-18))
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.1e-96) || ~((z <= 4.3e-18)))
		tmp = y * (z * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e-96], N[Not[LessEqual[z, 4.3e-18]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.0999999999999999e-96 or 4.3000000000000002e-18 < z

   1. Initial program 94.3%

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

   2. Taylor expanded in y around inf 73.0%

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

      1. mul-1-neg 30.1%

         \[\leadsto {\left(\sqrt{\color{blue}{-y \cdot \left(z \cdot x\right)}}\right)}^{2} \]

      2. distribute-rgt-neg-in 30.1%

         \[\leadsto {\left(\sqrt{\color{blue}{y \cdot \left(-z \cdot x\right)}}\right)}^{2} \]

      3. distribute-rgt-neg-in 30.1%

         \[\leadsto {\left(\sqrt{y \cdot \color{blue}{\left(z \cdot \left(-x\right)\right)}}\right)}^{2} \]

   4. Simplified 73.0%

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

   if -1.0999999999999999e-96 < z < 4.3000000000000002e-18

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.3%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-96} \lor \neg \left(z \leq 4.3 \cdot 10^{-18}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 50.5% accurate, 7.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ x \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

assert(y < z);
double code(double x, double y, double z) {
	return x;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
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

assert y < z;
public static double code(double x, double y, double z) {
	return x;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	return x

Julia

y, z = sort([y, z])
function code(x, y, z)
	return x
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 96.5%

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

2. Taylor expanded in y around 0 46.7%

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

3. Final simplification 46.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))