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

Percentage Accurate: 95.9% → 99.7%

Time: 5.1s

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: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+247}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+192}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+247)
   (- (* z (* y x)))
   (if (<= (* y z) 5e+192) (- x (* (* y z) x)) (* y (* z (- x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+247) {
		tmp = -(z * (y * x));
	} else if ((y * z) <= 5e+192) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

NOTE: x, 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) <= (-1d+247)) then
        tmp = -(z * (y * x))
    else if ((y * z) <= 5d+192) then
        tmp = x - ((y * z) * x)
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+247) {
		tmp = -(z * (y * x));
	} else if ((y * z) <= 5e+192) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -1e+247:
		tmp = -(z * (y * x))
	elif (y * z) <= 5e+192:
		tmp = x - ((y * z) * x)
	else:
		tmp = y * (z * -x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+247)
		tmp = Float64(-Float64(z * Float64(y * x)));
	elseif (Float64(y * z) <= 5e+192)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -1e+247)
		tmp = -(z * (y * x));
	elseif ((y * z) <= 5e+192)
		tmp = x - ((y * z) * x);
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -1e+247], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(y * z), $MachinePrecision], 5e+192], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -9.99999999999999952e246

   1. Initial program 57.3%

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

   3. Taylor expanded in y around inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. associate-*r* 99.6%

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

   5. Simplified 99.6%

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

   if -9.99999999999999952e246 < (*.f64 y z) < 5.00000000000000033e192

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   if 5.00000000000000033e192 < (*.f64 y z)

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. associate-*r* 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r* 97.1%

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

      6. distribute-rgt-neg-out 97.1%

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

   5. Simplified 97.1%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+247}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+192}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+247}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+247)
   (- (* z (* y x)))
   (if (<= (* y z) 5e+192) (* x (- 1.0 (* y z))) (* y (* z (- x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+247) {
		tmp = -(z * (y * x));
	} else if ((y * z) <= 5e+192) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

NOTE: x, 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) <= (-1d+247)) then
        tmp = -(z * (y * x))
    else if ((y * z) <= 5d+192) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+247) {
		tmp = -(z * (y * x));
	} else if ((y * z) <= 5e+192) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -1e+247:
		tmp = -(z * (y * x))
	elif (y * z) <= 5e+192:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (z * -x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+247)
		tmp = Float64(-Float64(z * Float64(y * x)));
	elseif (Float64(y * z) <= 5e+192)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -1e+247)
		tmp = -(z * (y * x));
	elseif ((y * z) <= 5e+192)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -1e+247], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(y * z), $MachinePrecision], 5e+192], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -9.99999999999999952e246

   1. Initial program 57.3%

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

   3. Taylor expanded in y around inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. associate-*r* 99.6%

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

   5. Simplified 99.6%

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

   if -9.99999999999999952e246 < (*.f64 y z) < 5.00000000000000033e192

   1. Initial program 99.9%

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

   if 5.00000000000000033e192 < (*.f64 y z)

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. associate-*r* 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r* 97.1%

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

      6. distribute-rgt-neg-out 97.1%

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

   5. Simplified 97.1%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+247}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-90} \lor \neg \left(z \leq 9 \cdot 10^{+110}\right):\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.3e-90) (not (<= z 9e+110))) (- (* z (* y x))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e-90) || !(z <= 9e+110)) {
		tmp = -(z * (y * x));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, 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 <= (-3.3d-90)) .or. (.not. (z <= 9d+110))) then
        tmp = -(z * (y * x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e-90) || !(z <= 9e+110)) {
		tmp = -(z * (y * x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -3.3e-90) or not (z <= 9e+110):
		tmp = -(z * (y * x))
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.3e-90) || !(z <= 9e+110))
		tmp = Float64(-Float64(z * Float64(y * x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.3e-90) || ~((z <= 9e+110)))
		tmp = -(z * (y * x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -3.3e-90], N[Not[LessEqual[z, 9e+110]], $MachinePrecision]], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e-90 or 9.0000000000000005e110 < z

   1. Initial program 89.9%

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

   3. Taylor expanded in y around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. associate-*r* 68.6%

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

   5. Simplified 68.6%

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

   if -3.3e-90 < z < 9.0000000000000005e110

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 80.3%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-90} \lor \neg \left(z \leq 9 \cdot 10^{+110}\right):\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -1.75e-90)
   (* y (* z (- x)))
   (if (<= z 9.8e+112) x (- (* z (* y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.75e-90) {
		tmp = y * (z * -x);
	} else if (z <= 9.8e+112) {
		tmp = x;
	} else {
		tmp = -(z * (y * x));
	}
	return tmp;
}

Fortran

NOTE: x, 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 <= (-1.75d-90)) then
        tmp = y * (z * -x)
    else if (z <= 9.8d+112) then
        tmp = x
    else
        tmp = -(z * (y * x))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.75e-90) {
		tmp = y * (z * -x);
	} else if (z <= 9.8e+112) {
		tmp = x;
	} else {
		tmp = -(z * (y * x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if z <= -1.75e-90:
		tmp = y * (z * -x)
	elif z <= 9.8e+112:
		tmp = x
	else:
		tmp = -(z * (y * x))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= -1.75e-90)
		tmp = Float64(y * Float64(z * Float64(-x)));
	elseif (z <= 9.8e+112)
		tmp = x;
	else
		tmp = Float64(-Float64(z * Float64(y * x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.75e-90)
		tmp = y * (z * -x);
	elseif (z <= 9.8e+112)
		tmp = x;
	else
		tmp = -(z * (y * x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -1.75e-90], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+112], x, (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7499999999999999e-90

   1. Initial program 91.2%

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

   3. Taylor expanded in y around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-*r* 65.1%

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

      3. distribute-rgt-neg-in 65.1%

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

      4. *-commutative 65.1%

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

      5. associate-*r* 64.1%

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

      6. distribute-rgt-neg-out 64.1%

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

   5. Simplified 64.1%

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

   if -1.7499999999999999e-90 < z < 9.80000000000000008e112

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 80.3%

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

   if 9.80000000000000008e112 < z

   1. Initial program 86.2%

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

   3. Taylor expanded in y around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-*r* 78.4%

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

   5. Simplified 78.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.1% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, 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 x < y && y < z;
public static double code(double x, double y, double z) {
	return x;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

3. Taylor expanded in y around 0 52.8%

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

4. Final simplification 52.8%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024011 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))