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

Percentage Accurate: 95.7% → 99.8%

Time: 7.1s

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: 95.7% 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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+271}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+270}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -4e+271)
   (* y (* z (- x)))
   (if (<= (* y z) 5e+270) (* x (- 1.0 (* y z))) (* z (* x (- y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -4e+271) {
		tmp = y * (z * -x);
	} else if ((y * z) <= 5e+270) {
		tmp = x * (1.0 - (y * z));
	} 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 ((y * z) <= (-4d+271)) then
        tmp = y * (z * -x)
    else if ((y * z) <= 5d+270) then
        tmp = x * (1.0d0 - (y * z))
    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 ((y * z) <= -4e+271) {
		tmp = y * (z * -x);
	} else if ((y * z) <= 5e+270) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = z * (x * -y);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -4e+271:
		tmp = y * (z * -x)
	elif (y * z) <= 5e+270:
		tmp = x * (1.0 - (y * z))
	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(y * z) <= -4e+271)
		tmp = Float64(y * Float64(z * Float64(-x)));
	elseif (Float64(y * z) <= 5e+270)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	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 ((y * z) <= -4e+271)
		tmp = y * (z * -x);
	elseif ((y * z) <= 5e+270)
		tmp = x * (1.0 - (y * z));
	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[(y * z), $MachinePrecision], -4e+271], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 5e+270], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -3.99999999999999981e271

   1. Initial program 67.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. mul-1-neg 67.0%

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

      2. *-commutative 67.0%

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

      3. associate-*r* 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

   5. Simplified 99.8%

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

   if -3.99999999999999981e271 < (*.f64 y z) < 4.99999999999999976e270

   1. Initial program 99.9%

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

   if 4.99999999999999976e270 < (*.f64 y z)

   1. Initial program 71.0%

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

   3. Taylor expanded in z around inf 99.8%

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

   4. Taylor expanded in y around inf 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+271}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+270}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+271}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq -2000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x (- y)))))
   (if (<= (* y z) -4e+271)
     t_0
     (if (<= (* y z) -2000000.0)
       (* x (* y (- z)))
       (if (<= (* y z) 0.5) x t_0)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = z * (x * -y);
	double tmp;
	if ((y * z) <= -4e+271) {
		tmp = t_0;
	} else if ((y * z) <= -2000000.0) {
		tmp = x * (y * -z);
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = z * (x * -y)
    if ((y * z) <= (-4d+271)) then
        tmp = t_0
    else if ((y * z) <= (-2000000.0d0)) then
        tmp = x * (y * -z)
    else if ((y * z) <= 0.5d0) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = z * (x * -y);
	double tmp;
	if ((y * z) <= -4e+271) {
		tmp = t_0;
	} else if ((y * z) <= -2000000.0) {
		tmp = x * (y * -z);
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = z * (x * -y)
	tmp = 0
	if (y * z) <= -4e+271:
		tmp = t_0
	elif (y * z) <= -2000000.0:
		tmp = x * (y * -z)
	elif (y * z) <= 0.5:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(z * Float64(x * Float64(-y)))
	tmp = 0.0
	if (Float64(y * z) <= -4e+271)
		tmp = t_0;
	elseif (Float64(y * z) <= -2000000.0)
		tmp = Float64(x * Float64(y * Float64(-z)));
	elseif (Float64(y * z) <= 0.5)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = z * (x * -y);
	tmp = 0.0;
	if ((y * z) <= -4e+271)
		tmp = t_0;
	elseif ((y * z) <= -2000000.0)
		tmp = x * (y * -z);
	elseif ((y * z) <= 0.5)
		tmp = x;
	else
		tmp = t_0;
	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_] := Block[{t$95$0 = N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -4e+271], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], -2000000.0], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.5], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -3.99999999999999981e271 or 0.5 < (*.f64 y z)

   1. Initial program 85.0%

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

   3. Taylor expanded in z around inf 92.4%

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

   4. Taylor expanded in y around inf 92.4%

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

      1. neg-mul-1 92.4%

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

      2. distribute-rgt-neg-in 92.4%

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

   6. Simplified 92.4%

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

   if -3.99999999999999981e271 < (*.f64 y z) < -2e6

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 95.3%

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

      1. mul-1-neg 95.3%

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

      2. distribute-rgt-neg-out 95.3%

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

   5. Simplified 95.3%

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

   if -2e6 < (*.f64 y z) < 0.5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 98.1%

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

Alternative 3: 93.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2000000 \lor \neg \left(y \cdot z \leq 0.5\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2000000.0) (not (<= (* y z) 0.5))) (* x (* y (- z))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2000000.0) || !((y * z) <= 0.5)) {
		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 (((y * z) <= (-2000000.0d0)) .or. (.not. ((y * z) <= 0.5d0))) 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 (((y * z) <= -2000000.0) || !((y * z) <= 0.5)) {
		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 ((y * z) <= -2000000.0) or not ((y * z) <= 0.5):
		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 ((Float64(y * z) <= -2000000.0) || !(Float64(y * z) <= 0.5))
		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 (((y * z) <= -2000000.0) || ~(((y * z) <= 0.5)))
		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[N[(y * z), $MachinePrecision], -2000000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.5]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2e6 or 0.5 < (*.f64 y z)

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. distribute-rgt-neg-out 87.3%

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

   5. Simplified 87.3%

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

   if -2e6 < (*.f64 y z) < 0.5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 98.1%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2000000 \lor \neg \left(y \cdot z \leq 0.5\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -2000000.0)
   (* y (* z (- x)))
   (if (<= (* y z) 0.5) x (* z (* x (- y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -2000000.0) {
		tmp = y * (z * -x);
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} 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 ((y * z) <= (-2000000.0d0)) then
        tmp = y * (z * -x)
    else if ((y * z) <= 0.5d0) then
        tmp = x
    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 ((y * z) <= -2000000.0) {
		tmp = y * (z * -x);
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else {
		tmp = z * (x * -y);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -2000000.0:
		tmp = y * (z * -x)
	elif (y * z) <= 0.5:
		tmp = x
	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(y * z) <= -2000000.0)
		tmp = Float64(y * Float64(z * Float64(-x)));
	elseif (Float64(y * z) <= 0.5)
		tmp = x;
	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 ((y * z) <= -2000000.0)
		tmp = y * (z * -x);
	elseif ((y * z) <= 0.5)
		tmp = x;
	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[(y * z), $MachinePrecision], -2000000.0], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.5], x, N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2e6

   1. Initial program 88.0%

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

   3. Taylor expanded in y around inf 85.1%

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

      1. mul-1-neg 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-*r* 95.3%

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

      4. distribute-rgt-neg-in 95.3%

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

   5. Simplified 95.3%

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

   if -2e6 < (*.f64 y z) < 0.5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 98.1%

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

   if 0.5 < (*.f64 y z)

   1. Initial program 90.8%

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

   3. Taylor expanded in z around inf 90.0%

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

   4. Taylor expanded in y around inf 90.1%

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

      1. neg-mul-1 90.1%

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

      2. distribute-rgt-neg-in 90.1%

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

   6. Simplified 90.1%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2000000000:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -2000000000.0) (/ (* z x) z) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -2000000000.0) {
		tmp = (z * 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 ((y * z) <= (-2000000000.0d0)) then
        tmp = (z * 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 ((y * z) <= -2000000000.0) {
		tmp = (z * x) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -2000000000.0:
		tmp = (z * x) / z
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -2000000000.0)
		tmp = Float64(Float64(z * x) / 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 ((y * z) <= -2000000000.0)
		tmp = (z * 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[LessEqual[N[(y * z), $MachinePrecision], -2000000000.0], N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2e9

   1. Initial program 87.4%

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

   3. Taylor expanded in z around inf 92.3%

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

   4. Taylor expanded in y around 0 11.1%

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

      1. *-commutative 11.1%

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

      2. associate-*l/ 14.5%

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

   6. Applied egg-rr 14.5%

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

   if -2e9 < (*.f64 y z)

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0 61.7%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2000000000:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.5% 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 94.4%

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

3. Taylor expanded in y around 0 48.2%

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

Reproduce

herbie shell --seed 2024130 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))