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

Percentage Accurate: 96.2% → 98.8%

Time: 6.1s

Alternatives: 6

Speedup: 0.3×

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: 96.2% 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: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+259} \lor \neg \left(y \cdot z \leq 5 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2e+259) (not (<= (* y z) 5e+53)))
   (* y (* z (- x)))
   (- x (* (* y z) x))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2e+259) || !((y * z) <= 5e+53)) {
		tmp = y * (z * -x);
	} else {
		tmp = x - ((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) <= (-2d+259)) .or. (.not. ((y * z) <= 5d+53))) then
        tmp = y * (z * -x)
    else
        tmp = x - ((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) <= -2e+259) || !((y * z) <= 5e+53)) {
		tmp = y * (z * -x);
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -2e+259) or not ((y * z) <= 5e+53):
		tmp = y * (z * -x)
	else:
		tmp = x - ((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) <= -2e+259) || !(Float64(y * z) <= 5e+53))
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = Float64(x - Float64(Float64(y * z) * 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) <= -2e+259) || ~(((y * z) <= 5e+53)))
		tmp = y * (z * -x);
	else
		tmp = x - ((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[Or[LessEqual[N[(y * z), $MachinePrecision], -2e+259], N[Not[LessEqual[N[(y * z), $MachinePrecision], 5e+53]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2e259 or 5.0000000000000004e53 < (*.f64 y z)

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 86.1%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. associate-*r* 86.1%

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

      2. mul-1-neg 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in x around 0 86.1%

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

      1. associate-*r* 98.5%

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

      2. associate-*r* 98.5%

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

      3. mul-1-neg 98.5%

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

      4. *-commutative 98.5%

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

      5. distribute-rgt-neg-in 98.5%

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

      6. associate-*r* 98.6%

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

   9. Simplified 98.6%

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

   if -2e259 < (*.f64 y z) < 5.0000000000000004e53

   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%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+259} \lor \neg \left(y \cdot z \leq 5 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+259} \lor \neg \left(y \cdot z \leq 5 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2e+259) (not (<= (* y z) 5e+53)))
   (* y (* z (- x)))
   (* x (- 1.0 (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2e+259) || !((y * z) <= 5e+53)) {
		tmp = y * (z * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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) <= (-2d+259)) .or. (.not. ((y * z) <= 5d+53))) then
        tmp = y * (z * -x)
    else
        tmp = x * (1.0d0 - (y * z))
    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) <= -2e+259) || !((y * z) <= 5e+53)) {
		tmp = y * (z * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -2e+259) or not ((y * z) <= 5e+53):
		tmp = y * (z * -x)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -2e+259) || !(Float64(y * z) <= 5e+53))
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	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) <= -2e+259) || ~(((y * z) <= 5e+53)))
		tmp = y * (z * -x);
	else
		tmp = x * (1.0 - (y * z));
	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[N[(y * z), $MachinePrecision], -2e+259], N[Not[LessEqual[N[(y * z), $MachinePrecision], 5e+53]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2e259 or 5.0000000000000004e53 < (*.f64 y z)

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 86.1%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. associate-*r* 86.1%

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

      2. mul-1-neg 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in x around 0 86.1%

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

      1. associate-*r* 98.5%

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

      2. associate-*r* 98.5%

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

      3. mul-1-neg 98.5%

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

      4. *-commutative 98.5%

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

      5. distribute-rgt-neg-in 98.5%

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

      6. associate-*r* 98.6%

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

   9. Simplified 98.6%

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

   if -2e259 < (*.f64 y z) < 5.0000000000000004e53

   1. Initial program 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+259} \lor \neg \left(y \cdot z \leq 5 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-104} \lor \neg \left(z \leq 1.42 \cdot 10^{+104}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 -1.6e-104) (not (<= z 1.42e+104))) (* (* y z) (- x)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.6e-104) || !(z <= 1.42e+104)) {
		tmp = (y * z) * -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 <= (-1.6d-104)) .or. (.not. (z <= 1.42d+104))) then
        tmp = (y * z) * -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 <= -1.6e-104) || !(z <= 1.42e+104)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.6e-104) or not (z <= 1.42e+104):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.6e-104) || !(z <= 1.42e+104))
		tmp = Float64(Float64(y * z) * Float64(-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 <= -1.6e-104) || ~((z <= 1.42e+104)))
		tmp = (y * z) * -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, -1.6e-104], N[Not[LessEqual[z, 1.42e+104]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999994e-104 or 1.42e104 < z

   1. Initial program 92.1%

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

   3. Taylor expanded in y around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. distribute-rgt-neg-in 69.6%

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

      3. distribute-rgt-neg-out 69.6%

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

   5. Simplified 69.6%

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

   if -1.59999999999999994e-104 < z < 1.42e104

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.7%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-104} \lor \neg \left(z \leq 1.42 \cdot 10^{+104}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-104} \lor \neg \left(z \leq 6.5 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 -1.6e-104) (not (<= z 6.5e+84))) (* y (* z (- x))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.6e-104) || !(z <= 6.5e+84)) {
		tmp = y * (z * -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 <= (-1.6d-104)) .or. (.not. (z <= 6.5d+84))) then
        tmp = y * (z * -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 <= -1.6e-104) || !(z <= 6.5e+84)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.6e-104) or not (z <= 6.5e+84):
		tmp = y * (z * -x)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.6e-104) || !(z <= 6.5e+84))
		tmp = Float64(y * Float64(z * Float64(-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 <= -1.6e-104) || ~((z <= 6.5e+84)))
		tmp = y * (z * -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, -1.6e-104], N[Not[LessEqual[z, 6.5e+84]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999994e-104 or 6.50000000000000027e84 < z

   1. Initial program 92.2%

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

   3. Taylor expanded in y around inf 92.1%

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

   4. Taylor expanded in y around inf 68.7%

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

      1. associate-*r* 68.7%

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

      2. mul-1-neg 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in x around 0 68.7%

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

      1. associate-*r* 71.5%

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

      2. associate-*r* 71.5%

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

      3. mul-1-neg 71.5%

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

      4. *-commutative 71.5%

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

      5. distribute-rgt-neg-in 71.5%

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

      6. associate-*r* 73.2%

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

   9. Simplified 73.2%

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

   if -1.59999999999999994e-104 < z < 6.50000000000000027e84

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-104} \lor \neg \left(z \leq 6.5 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 6.3 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= z 6.3e+137) x (/ (* z x) z)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= 6.3e+137) {
		tmp = x;
	} else {
		tmp = (z * x) / z;
	}
	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 <= 6.3d+137) then
        tmp = x
    else
        tmp = (z * x) / z
    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 <= 6.3e+137) {
		tmp = x;
	} else {
		tmp = (z * x) / z;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if z <= 6.3e+137:
		tmp = x
	else:
		tmp = (z * x) / z
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= 6.3e+137)
		tmp = x;
	else
		tmp = Float64(Float64(z * x) / z);
	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 <= 6.3e+137)
		tmp = x;
	else
		tmp = (z * x) / z;
	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, 6.3e+137], x, N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.29999999999999971e137

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 57.5%

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

   if 6.29999999999999971e137 < z

   1. Initial program 85.8%

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

   3. Taylor expanded in z around inf 90.6%

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

   4. Taylor expanded in y around 0 4.8%

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

      1. *-commutative 4.8%

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

      2. associate-*l/ 11.8%

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

   6. Applied egg-rr 11.8%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.3 \cdot 10^{+137}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 95.8%

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

3. Taylor expanded in y around 0 49.4%

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

4. Final simplification 49.4%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))