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

Percentage Accurate: 95.7% → 97.7%

Time: 5.7s

Alternatives: 7

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: 95.7% 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: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+179}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 1e+179) (- 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+179) {
		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+179) 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+179) {
		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+179:
		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+179)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(Float64(-y) * Float64(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) <= 1e+179)
		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+179], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[((-y) * N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 9.9999999999999998e178

   1. Initial program 98.6%

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

      1. sub-neg 98.6%

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

      2. distribute-rgt-in 98.6%

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

      3. *-un-lft-identity 98.6%

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

      4. distribute-rgt-neg-in 98.6%

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

   4. Applied egg-rr 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*r* 92.9%

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

      3. distribute-rgt-neg-out 92.9%

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

      4. distribute-lft-neg-out 92.9%

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

      5. add-sqr-sqrt 49.5%

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

      6. sqrt-unprod 63.3%

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

      7. sqr-neg 63.3%

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

      8. sqrt-unprod 22.6%

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

      9. add-sqr-sqrt 53.8%

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

      10. cancel-sign-sub-inv 53.8%

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

      11. associate-*r* 55.0%

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

      12. *-commutative 55.0%

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

      13. associate-*l* 53.3%

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

      14. add-sqr-sqrt 21.7%

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

      15. sqrt-unprod 63.5%

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

      16. sqr-neg 63.5%

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

      17. sqrt-unprod 49.2%

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

      18. add-sqr-sqrt 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in y around 0 98.6%

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

   if 9.9999999999999998e178 < (*.f64 y z)

   1. Initial program 73.2%

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

   3. Taylor expanded in y around inf 96.3%

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

   4. Taylor expanded in z around inf 96.3%

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

      1. mul-1-neg 96.3%

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

      2. *-commutative 96.3%

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

      3. distribute-rgt-neg-in 96.3%

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

   6. Simplified 96.3%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+179}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -20000000 \lor \neg \left(y \cdot z \leq 0.5\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -20000000.0) (not (<= (* y z) 0.5))) (* (* y z) (- x)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -20000000.0) || !((y * z) <= 0.5)) {
		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 (((y * z) <= (-20000000.0d0)) .or. (.not. ((y * z) <= 0.5d0))) 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 (((y * z) <= -20000000.0) || !((y * z) <= 0.5)) {
		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 ((y * z) <= -20000000.0) or not ((y * z) <= 0.5):
		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 ((Float64(y * z) <= -20000000.0) || !(Float64(y * z) <= 0.5))
		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 (((y * z) <= -20000000.0) || ~(((y * z) <= 0.5)))
		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[N[(y * z), $MachinePrecision], -20000000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.5]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2e7 or 0.5 < (*.f64 y z)

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 89.5%

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

      1. mul-1-neg 89.5%

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

      2. distribute-rgt-neg-in 89.5%

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

      3. distribute-rgt-neg-out 89.5%

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

   5. Simplified 89.5%

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

   if -2e7 < (*.f64 y z) < 0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -20000000 \lor \neg \left(y \cdot z \leq 0.5\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -20000000:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -20000000.0)
   (* z (* y (- x)))
   (if (<= (* 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) <= -20000000.0) {
		tmp = z * (y * -x);
	} else if ((y * z) <= 0.5) {
		tmp = 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) <= (-20000000.0d0)) then
        tmp = z * (y * -x)
    else if ((y * z) <= 0.5d0) then
        tmp = 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) <= -20000000.0) {
		tmp = z * (y * -x);
	} else if ((y * z) <= 0.5) {
		tmp = 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) <= -20000000.0:
		tmp = z * (y * -x)
	elif (y * z) <= 0.5:
		tmp = 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) <= -20000000.0)
		tmp = Float64(z * Float64(y * Float64(-x)));
	elseif (Float64(y * z) <= 0.5)
		tmp = x;
	else
		tmp = Float64(Float64(-y) * Float64(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) <= -20000000.0)
		tmp = z * (y * -x);
	elseif ((y * z) <= 0.5)
		tmp = 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], -20000000.0], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.5], x, N[((-y) * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2e7

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 91.0%

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

   4. Taylor expanded in y around inf 89.8%

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

      1. mul-1-neg 89.8%

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

      2. distribute-rgt-neg-in 89.8%

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

   6. Simplified 89.8%

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

   if -2e7 < (*.f64 y z) < 0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

   if 0.5 < (*.f64 y z)

   1. Initial program 85.3%

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

   3. Taylor expanded in y around inf 88.2%

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

   4. Taylor expanded in z around inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. *-commutative 91.3%

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

      3. distribute-rgt-neg-in 91.3%

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

   6. Simplified 91.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -20000000:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -20000000:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -20000000.0)
   (* (* y z) (- x))
   (if (<= (* 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) <= -20000000.0) {
		tmp = (y * z) * -x;
	} else if ((y * z) <= 0.5) {
		tmp = 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) <= (-20000000.0d0)) then
        tmp = (y * z) * -x
    else if ((y * z) <= 0.5d0) then
        tmp = 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) <= -20000000.0) {
		tmp = (y * z) * -x;
	} else if ((y * z) <= 0.5) {
		tmp = 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) <= -20000000.0:
		tmp = (y * z) * -x
	elif (y * z) <= 0.5:
		tmp = 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) <= -20000000.0)
		tmp = Float64(Float64(y * z) * Float64(-x));
	elseif (Float64(y * z) <= 0.5)
		tmp = x;
	else
		tmp = Float64(Float64(-y) * Float64(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) <= -20000000.0)
		tmp = (y * z) * -x;
	elseif ((y * z) <= 0.5)
		tmp = 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], -20000000.0], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.5], x, N[((-y) * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2e7

   1. Initial program 96.0%

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

   3. Taylor expanded in y around inf 94.8%

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

      1. mul-1-neg 94.8%

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

      2. distribute-rgt-neg-in 94.8%

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

      3. distribute-rgt-neg-out 94.8%

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

   5. Simplified 94.8%

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

   if -2e7 < (*.f64 y z) < 0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

   if 0.5 < (*.f64 y z)

   1. Initial program 85.3%

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

   3. Taylor expanded in y around inf 88.2%

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

   4. Taylor expanded in z around inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. *-commutative 91.3%

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

      3. distribute-rgt-neg-in 91.3%

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

   6. Simplified 91.3%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -20000000:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+179}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 1e+179) (* 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+179) {
		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+179) 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+179) {
		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+179:
		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+179)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(Float64(-y) * Float64(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) <= 1e+179)
		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+179], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-y) * N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 9.9999999999999998e178

   1. Initial program 98.6%

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

   if 9.9999999999999998e178 < (*.f64 y z)

   1. Initial program 73.2%

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

   3. Taylor expanded in y around inf 96.3%

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

   4. Taylor expanded in z around inf 96.3%

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

      1. mul-1-neg 96.3%

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

      2. *-commutative 96.3%

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

      3. distribute-rgt-neg-in 96.3%

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

   6. Simplified 96.3%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+179}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+63}:\\ \;\;\;\;\frac{y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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) -5e+63) (/ (* y x) y) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+63) {
		tmp = (y * 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 ((y * z) <= (-5d+63)) then
        tmp = (y * 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 ((y * z) <= -5e+63) {
		tmp = (y * x) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -5e+63:
		tmp = (y * x) / y
	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) <= -5e+63)
		tmp = Float64(Float64(y * x) / 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 ((y * z) <= -5e+63)
		tmp = (y * 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[LessEqual[N[(y * z), $MachinePrecision], -5e+63], N[(N[(y * x), $MachinePrecision] / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5.00000000000000011e63

   1. Initial program 95.3%

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

   3. Taylor expanded in y around inf 92.8%

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

   4. Taylor expanded in z around 0 8.1%

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

      1. *-commutative 8.1%

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

      2. associate-*l/ 26.7%

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

   6. Applied egg-rr 26.7%

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

   if -5.00000000000000011e63 < (*.f64 y z)

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0 66.0%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+63}:\\ \;\;\;\;\frac{y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.5% 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 95.8%

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

3. Taylor expanded in y around 0 50.5%

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))