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

Percentage Accurate: 96.0% → 99.3%

Time: 6.6s

Alternatives: 7

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: 96.0% 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: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5.2 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \cdot y \leq 10^{+105}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* z y) -5.2e+174)
   (* y (* x (- z)))
   (if (<= (* z y) 1e+105) (* x (- 1.0 (* z y))) (* z (* x (- y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z * y) <= -5.2e+174) {
		tmp = y * (x * -z);
	} else if ((z * y) <= 1e+105) {
		tmp = x * (1.0 - (z * y));
	} else {
		tmp = z * (x * -y);
	}
	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 * y) <= (-5.2d+174)) then
        tmp = y * (x * -z)
    else if ((z * y) <= 1d+105) then
        tmp = x * (1.0d0 - (z * y))
    else
        tmp = z * (x * -y)
    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 * y) <= -5.2e+174) {
		tmp = y * (x * -z);
	} else if ((z * y) <= 1e+105) {
		tmp = x * (1.0 - (z * y));
	} else {
		tmp = z * (x * -y);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z * y) <= -5.2e+174:
		tmp = y * (x * -z)
	elif (z * y) <= 1e+105:
		tmp = x * (1.0 - (z * y))
	else:
		tmp = z * (x * -y)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(z * y) <= -5.2e+174)
		tmp = Float64(y * Float64(x * Float64(-z)));
	elseif (Float64(z * y) <= 1e+105)
		tmp = Float64(x * Float64(1.0 - Float64(z * y)));
	else
		tmp = Float64(z * Float64(x * Float64(-y)));
	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 * y) <= -5.2e+174)
		tmp = y * (x * -z);
	elseif ((z * y) <= 1e+105)
		tmp = x * (1.0 - (z * y));
	else
		tmp = z * (x * -y);
	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[(z * y), $MachinePrecision], -5.2e+174], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * y), $MachinePrecision], 1e+105], N[(x * N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5.1999999999999997e174

   1. Initial program 87.0%

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

   3. Taylor expanded in y around inf 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*r* 87.0%

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

      3. neg-mul-1 87.0%

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

      4. distribute-rgt-neg-in 87.0%

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

      5. associate-*l* 99.8%

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

      6. distribute-lft-neg-in 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

   5. Simplified 99.8%

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

   if -5.1999999999999997e174 < (*.f64 y z) < 9.9999999999999994e104

   1. Initial program 99.9%

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

   if 9.9999999999999994e104 < (*.f64 y z)

   1. Initial program 80.3%

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

   3. Taylor expanded in z around inf 80.3%

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

   4. Taylor expanded in z around inf 80.3%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. neg-mul-1 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -5.2 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \cdot y \leq 10^{+105}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 3.3 \cdot 10^{-101}:\\ \;\;\;\;x - z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(z, -y, 1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 3.3e-101) (- x (* z (* x y))) (* x (fma z (- y) 1.0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.3e-101) {
		tmp = x - (z * (x * y));
	} else {
		tmp = x * fma(z, -y, 1.0);
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= 3.3e-101)
		tmp = Float64(x - Float64(z * Float64(x * y)));
	else
		tmp = Float64(x * fma(z, Float64(-y), 1.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[x, 3.3e-101], N[(x - N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-y) + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.29999999999999984e-101

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 92.5%

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

      1. mul-1-neg 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-*l* 92.9%

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

      4. *-commutative 92.9%

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

   5. Simplified 92.9%

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

      1. unsub-neg 92.9%

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

      2. associate-*r* 96.7%

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

      3. *-commutative 96.7%

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

   7. Applied egg-rr 96.7%

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

   if 3.29999999999999984e-101 < x

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. fma-define 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.3 \cdot 10^{-101}:\\ \;\;\;\;x - z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(z, -y, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-102} \lor \neg \left(z \leq 1.05 \cdot 10^{+78}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 -1.4e-102) (not (<= z 1.05e+78))) (* z (* x (- y))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e-102) || !(z <= 1.05e+78)) {
		tmp = z * (x * -y);
	} 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 <= (-1.4d-102)) .or. (.not. (z <= 1.05d+78))) then
        tmp = z * (x * -y)
    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 <= -1.4e-102) || !(z <= 1.05e+78)) {
		tmp = z * (x * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.4e-102) or not (z <= 1.05e+78):
		tmp = z * (x * -y)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e-102) || !(z <= 1.05e+78))
		tmp = Float64(z * Float64(x * Float64(-y)));
	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 <= -1.4e-102) || ~((z <= 1.05e+78)))
		tmp = z * (x * -y);
	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, -1.4e-102], N[Not[LessEqual[z, 1.05e+78]], $MachinePrecision]], N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000006e-102 or 1.05e78 < z

   1. Initial program 89.4%

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

   3. Taylor expanded in z around inf 89.4%

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

   4. Taylor expanded in z around inf 67.0%

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

      1. associate-*r* 74.2%

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

      2. *-commutative 74.2%

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

      3. *-commutative 74.2%

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

      4. neg-mul-1 74.2%

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

      5. distribute-lft-neg-in 74.2%

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

   6. Simplified 74.2%

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

   if -1.40000000000000006e-102 < z < 1.05e78

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.4%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-102} \lor \neg \left(z \leq 1.05 \cdot 10^{+78}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-102} \lor \neg \left(z \leq 2.3 \cdot 10^{+78}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 -1.4e-102) (not (<= z 2.3e+78))) (* y (* x (- z))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e-102) || !(z <= 2.3e+78)) {
		tmp = y * (x * -z);
	} 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 <= (-1.4d-102)) .or. (.not. (z <= 2.3d+78))) then
        tmp = y * (x * -z)
    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 <= -1.4e-102) || !(z <= 2.3e+78)) {
		tmp = y * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.4e-102) or not (z <= 2.3e+78):
		tmp = y * (x * -z)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e-102) || !(z <= 2.3e+78))
		tmp = Float64(y * Float64(x * Float64(-z)));
	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 <= -1.4e-102) || ~((z <= 2.3e+78)))
		tmp = y * (x * -z);
	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, -1.4e-102], N[Not[LessEqual[z, 2.3e+78]], $MachinePrecision]], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000006e-102 or 2.3000000000000002e78 < z

   1. Initial program 89.4%

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

   3. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. associate-*r* 67.0%

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

      3. neg-mul-1 67.0%

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

      4. distribute-rgt-neg-in 67.0%

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

      5. associate-*l* 70.7%

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

      6. distribute-lft-neg-in 70.7%

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

      7. distribute-rgt-neg-in 70.7%

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

   5. Simplified 70.7%

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

   if -1.40000000000000006e-102 < z < 2.3000000000000002e78

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-102} \lor \neg \left(z \leq 2.3 \cdot 10^{+78}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-102} \lor \neg \left(z \leq 1.1 \cdot 10^{+78}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 -1.4e-102) (not (<= z 1.1e+78))) (* x (* y (- z))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e-102) || !(z <= 1.1e+78)) {
		tmp = x * (y * -z);
	} 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 <= (-1.4d-102)) .or. (.not. (z <= 1.1d+78))) then
        tmp = x * (y * -z)
    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 <= -1.4e-102) || !(z <= 1.1e+78)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.4e-102) or not (z <= 1.1e+78):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e-102) || !(z <= 1.1e+78))
		tmp = Float64(x * Float64(y * Float64(-z)));
	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 <= -1.4e-102) || ~((z <= 1.1e+78)))
		tmp = x * (y * -z);
	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, -1.4e-102], N[Not[LessEqual[z, 1.1e+78]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000006e-102 or 1.10000000000000007e78 < z

   1. Initial program 89.4%

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

   3. Taylor expanded in y around inf 67.0%

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

      1. neg-mul-1 67.0%

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

      2. distribute-rgt-neg-in 67.0%

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

   5. Simplified 67.0%

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

   if -1.40000000000000006e-102 < z < 1.10000000000000007e78

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-102} \lor \neg \left(z \leq 1.1 \cdot 10^{+78}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 3.2 \cdot 10^{-101}:\\ \;\;\;\;x - z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 3.2e-101) (- x (* z (* x y))) (* x (- 1.0 (* z y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.2e-101) {
		tmp = x - (z * (x * y));
	} else {
		tmp = x * (1.0 - (z * y));
	}
	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 (x <= 3.2d-101) then
        tmp = x - (z * (x * y))
    else
        tmp = x * (1.0d0 - (z * y))
    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 (x <= 3.2e-101) {
		tmp = x - (z * (x * y));
	} else {
		tmp = x * (1.0 - (z * y));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if x <= 3.2e-101:
		tmp = x - (z * (x * y))
	else:
		tmp = x * (1.0 - (z * y))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= 3.2e-101)
		tmp = Float64(x - Float64(z * Float64(x * y)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z * y)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 3.2e-101)
		tmp = x - (z * (x * y));
	else
		tmp = x * (1.0 - (z * y));
	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[x, 3.2e-101], N[(x - N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.19999999999999978e-101

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 92.5%

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

      1. mul-1-neg 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-*l* 92.9%

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

      4. *-commutative 92.9%

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

   5. Simplified 92.9%

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

      1. unsub-neg 92.9%

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

      2. associate-*r* 96.7%

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

      3. *-commutative 96.7%

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

   7. Applied egg-rr 96.7%

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

   if 3.19999999999999978e-101 < x

   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 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.2 \cdot 10^{-101}:\\ \;\;\;\;x - z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% 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 94.7%

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

3. Taylor expanded in y around 0 50.5%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024163 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))